Datasets:
Parallel-Reasoning
/
sosp_sft_data

Dataset card Data Studio Files
xet
Community
nums
listlengths
4
4
target
int64
10
100
solution
listlengths
3
3
optimal_path
stringlengths
282
529
start_size
int64
4
4
search_path
stringlengths
505
16.8k
rating
float64
0
0.99
search_type
stringclasses
5 values
heuristic
stringclasses
2 values
[ 2, 46, 31, 13 ]
67
[ "46/2=23", "31+13=44", "23+44=67" ]
Current State: 67:[2, 46, 31, 13], Operations: [] Exploring Operation: 46/2=23, Resulting Numbers: [31, 13, 23] Generated Node #2: [31, 13, 23] from Operation: 46/2=23 Current State: 67:[31, 13, 23], Operations: ['46/2=23'] Exploring Operation: 31+13=44, Resulting Numbers: [23, 44] Generated Node #3: [23, 44] from Operation: 31+13=44 Current State: 67:[23, 44], Operations: ['46/2=23', '31+13=44'] Exploring Operation: 23+44=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[2, 46, 31, 13], Operations: [] Exploring Operation: 2*31=62, Resulting Numbers: [46, 13, 62] Generated Node #0,0: 67:[46, 13, 62] Operation: 2*31=62 Exploring Operation: 2+46=48, Resulting Numbers: [31, 13, 48] Generated Node #0,1: 67:[31, 13, 48] Operation: 2+46=48 Exploring Operation: 2*13=26, Resulting Numbers: [46, 31, 26] Generated Node #0,2: 67:[46, 31, 26] Operation: 2*13=26 Moving to Node #0,0 Current State: 67:[46, 13, 62], Operations: ['2*31=62'] Exploring Operation: 46-13=33, Resulting Numbers: [62, 33] Generated Node #0,0,0: 67:[62, 33] Operation: 46-13=33 Exploring Operation: 13+62=75, Resulting Numbers: [46, 75] Generated Node #0,0,1: 67:[46, 75] Operation: 13+62=75 Exploring Operation: 46+13=59, Resulting Numbers: [62, 59] Generated Node #0,0,2: 67:[62, 59] Operation: 46+13=59 Moving to Node #0,2 Current State: 67:[46, 31, 26], Operations: ['2*13=26'] Exploring Operation: 31+26=57, Resulting Numbers: [46, 57] Generated Node #0,2,0: 67:[46, 57] Operation: 31+26=57 Exploring Operation: 46+26=72, Resulting Numbers: [31, 72] Generated Node #0,2,1: 67:[31, 72] Operation: 46+26=72 Exploring Operation: 46+31=77, Resulting Numbers: [26, 77] Generated Node #0,2,2: 67:[26, 77] Operation: 46+31=77 Moving to Node #0,1 Current State: 67:[31, 13, 48], Operations: ['2+46=48'] Exploring Operation: 31+48=79, Resulting Numbers: [13, 79] Generated Node #0,1,0: 67:[13, 79] Operation: 31+48=79 Exploring Operation: 13+48=61, Resulting Numbers: [31, 61] Generated Node #0,1,1: 67:[31, 61] Operation: 13+48=61 Exploring Operation: 31+13=44, Resulting Numbers: [48, 44] Generated Node #0,1,2: 67:[48, 44] Operation: 31+13=44 Moving to Node #0,0,2 Current State: 67:[62, 59], Operations: ['2*31=62', '46+13=59'] Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 62+59=121, Resulting Numbers: [121] 121,67 unequal: No Solution Exploring Operation: 62*59=3658, Resulting Numbers: [3658] 3658,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[46, 75], Operations: ['2*31=62', '13+62=75'] Exploring Operation: 75-46=29, Resulting Numbers: [29] 29,67 unequal: No Solution Exploring Operation: 46*75=3450, Resulting Numbers: [3450] 3450,67 unequal: No Solution Exploring Operation: 46+75=121, Resulting Numbers: [121] 121,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[46, 57], Operations: ['2*13=26', '31+26=57'] Exploring Operation: 57-46=11, Resulting Numbers: [11] 11,67 unequal: No Solution Exploring Operation: 46*57=2622, Resulting Numbers: [2622] 2622,67 unequal: No Solution Exploring Operation: 46+57=103, Resulting Numbers: [103] 103,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[62, 33], Operations: ['2*31=62', '46-13=33'] Exploring Operation: 62-33=29, Resulting Numbers: [29] 29,67 unequal: No Solution Exploring Operation: 62+33=95, Resulting Numbers: [95] 95,67 unequal: No Solution Exploring Operation: 62*33=2046, Resulting Numbers: [2046] 2046,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[31, 72], Operations: ['2*13=26', '46+26=72'] Exploring Operation: 31*72=2232, Resulting Numbers: [2232] 2232,67 unequal: No Solution Exploring Operation: 31+72=103, Resulting Numbers: [103] 103,67 unequal: No Solution Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[31, 61], Operations: ['2+46=48', '13+48=61'] Exploring Operation: 31*61=1891, Resulting Numbers: [1891] 1891,67 unequal: No Solution Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,67 unequal: No Solution Exploring Operation: 31+61=92, Resulting Numbers: [92] 92,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[48, 44], Operations: ['2+46=48', '31+13=44'] Exploring Operation: 48*44=2112, Resulting Numbers: [2112] 2112,67 unequal: No Solution Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,67 unequal: No Solution Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,67 unequal: No Solution Moving to Node #0,2,2 Current State: 67:[26, 77], Operations: ['2*13=26', '46+31=77'] Exploring Operation: 26+77=103, Resulting Numbers: [103] 103,67 unequal: No Solution Exploring Operation: 26*77=2002, Resulting Numbers: [2002] 2002,67 unequal: No Solution Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[13, 79], Operations: ['2+46=48', '31+48=79'] Exploring Operation: 79-13=66, Resulting Numbers: [66] 66,67 unequal: No Solution Exploring Operation: 13+79=92, Resulting Numbers: [92] 92,67 unequal: No Solution Exploring Operation: 13*79=1027, Resulting Numbers: [1027] 1027,67 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 32, 24, 66, 80 ]
76
[ "32-24=8", "80/8=10", "66+10=76" ]
Current State: 76:[32, 24, 66, 80], Operations: [] Exploring Operation: 32-24=8, Resulting Numbers: [66, 80, 8] Generated Node #2: [66, 80, 8] from Operation: 32-24=8 Current State: 76:[66, 80, 8], Operations: ['32-24=8'] Exploring Operation: 80/8=10, Resulting Numbers: [66, 10] Generated Node #3: [66, 10] from Operation: 80/8=10 Current State: 76:[66, 10], Operations: ['32-24=8', '80/8=10'] Exploring Operation: 66+10=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[32, 24, 66, 80], Operations: [] Exploring Operation: 80-66=14, Resulting Numbers: [32, 24, 14] Generated Node #0,0: 76:[32, 24, 14] Operation: 80-66=14 Exploring Operation: 32-24=8, Resulting Numbers: [66, 80, 8] Generated Node #0,1: 76:[66, 80, 8] Operation: 32-24=8 Exploring Operation: 24+66=90, Resulting Numbers: [32, 80, 90] Generated Node #0,2: 76:[32, 80, 90] Operation: 24+66=90 Exploring Operation: 66-32=34, Resulting Numbers: [24, 80, 34] Generated Node #0,3: 76:[24, 80, 34] Operation: 66-32=34 Exploring Operation: 66-24=42, Resulting Numbers: [32, 80, 42] Generated Node #0,4: 76:[32, 80, 42] Operation: 66-24=42 Moving to Node #0,3 Current State: 76:[24, 80, 34], Operations: ['66-32=34'] Exploring Operation: 24+80=104, Resulting Numbers: [34, 104] Generated Node #0,3,0: 76:[34, 104] Operation: 24+80=104 Exploring Operation: 80-24=56, Resulting Numbers: [34, 56] Generated Node #0,3,1: 76:[34, 56] Operation: 80-24=56 Exploring Operation: 80-34=46, Resulting Numbers: [24, 46] Generated Node #0,3,2: 76:[24, 46] Operation: 80-34=46 Exploring Operation: 24+34=58, Resulting Numbers: [80, 58] Generated Node #0,3,3: 76:[80, 58] Operation: 24+34=58 Exploring Operation: 34-24=10, Resulting Numbers: [80, 10] Generated Node #0,3,4: 76:[80, 10] Operation: 34-24=10 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 76:[80, 10], Operations: ['66-32=34', '34-24=10'] Exploring Operation: 80*10=800, Resulting Numbers: [800] 800,76 unequal: No Solution Exploring Operation: 80/10=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 80+10=90, Resulting Numbers: [90] 90,76 unequal: No Solution Exploring Operation: 80-10=70, Resulting Numbers: [70] 70,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 76:[24, 46], Operations: ['66-32=34', '80-34=46'] Exploring Operation: 24+46=70, Resulting Numbers: [70] 70,76 unequal: No Solution Exploring Operation: 46-24=22, Resulting Numbers: [22] 22,76 unequal: No Solution Exploring Operation: 24*46=1104, Resulting Numbers: [1104] 1104,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 76:[34, 56], Operations: ['66-32=34', '80-24=56'] Exploring Operation: 34+56=90, Resulting Numbers: [90] 90,76 unequal: No Solution Exploring Operation: 34*56=1904, Resulting Numbers: [1904] 1904,76 unequal: No Solution Exploring Operation: 56-34=22, Resulting Numbers: [22] 22,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 76:[80, 58], Operations: ['66-32=34', '24+34=58'] Exploring Operation: 80+58=138, Resulting Numbers: [138] 138,76 unequal: No Solution Exploring Operation: 80*58=4640, Resulting Numbers: [4640] 4640,76 unequal: No Solution Exploring Operation: 80-58=22, Resulting Numbers: [22] 22,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 76:[34, 104], Operations: ['66-32=34', '24+80=104'] Exploring Operation: 34*104=3536, Resulting Numbers: [3536] 3536,76 unequal: No Solution Exploring Operation: 34+104=138, Resulting Numbers: [138] 138,76 unequal: No Solution Exploring Operation: 104-34=70, Resulting Numbers: [70] 70,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 76:[32, 80, 42], Operations: ['66-24=42'] Exploring Operation: 80-42=38, Resulting Numbers: [32, 38] Generated Node #0,4,0: 76:[32, 38] Operation: 80-42=38 Exploring Operation: 32+80=112, Resulting Numbers: [42, 112] Generated Node #0,4,1: 76:[42, 112] Operation: 32+80=112 Exploring Operation: 80-32=48, Resulting Numbers: [42, 48] Generated Node #0,4,2: 76:[42, 48] Operation: 80-32=48 Exploring Operation: 32+42=74, Resulting Numbers: [80, 74] Generated Node #0,4,3: 76:[80, 74] Operation: 32+42=74 Exploring Operation: 42-32=10, Resulting Numbers: [80, 10] Generated Node #0,4,4: 76:[80, 10] Operation: 42-32=10 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 76:[32, 38], Operations: ['66-24=42', '80-42=38'] Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 32*38=1216, Resulting Numbers: [1216] 1216,76 unequal: No Solution Exploring Operation: 32+38=70, Resulting Numbers: [70] 70,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 76:[80, 74], Operations: ['66-24=42', '32+42=74'] Exploring Operation: 80+74=154, Resulting Numbers: [154] 154,76 unequal: No Solution Exploring Operation: 80-74=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 80*74=5920, Resulting Numbers: [5920] 5920,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 76:[80, 10], Operations: ['66-24=42', '42-32=10'] Exploring Operation: 80+10=90, Resulting Numbers: [90] 90,76 unequal: No Solution Exploring Operation: 80/10=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 80-10=70, Resulting Numbers: [70] 70,76 unequal: No Solution Exploring Operation: 80*10=800, Resulting Numbers: [800] 800,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 76:[42, 48], Operations: ['66-24=42', '80-32=48'] Exploring Operation: 42*48=2016, Resulting Numbers: [2016] 2016,76 unequal: No Solution Exploring Operation: 42+48=90, Resulting Numbers: [90] 90,76 unequal: No Solution Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 76:[42, 112], Operations: ['66-24=42', '32+80=112'] Exploring Operation: 42+112=154, Resulting Numbers: [154] 154,76 unequal: No Solution Exploring Operation: 112-42=70, Resulting Numbers: [70] 70,76 unequal: No Solution Exploring Operation: 42*112=4704, Resulting Numbers: [4704] 4704,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 76:[32, 24, 14], Operations: ['80-66=14'] Exploring Operation: 32-24=8, Resulting Numbers: [14, 8] Generated Node #0,0,0: 76:[14, 8] Operation: 32-24=8 Exploring Operation: 32-14=18, Resulting Numbers: [24, 18] Generated Node #0,0,1: 76:[24, 18] Operation: 32-14=18 Exploring Operation: 24+14=38, Resulting Numbers: [32, 38] Generated Node #0,0,2: 76:[32, 38] Operation: 24+14=38 Exploring Operation: 32+14=46, Resulting Numbers: [24, 46] Generated Node #0,0,3: 76:[24, 46] Operation: 32+14=46 Exploring Operation: 24-14=10, Resulting Numbers: [32, 10] Generated Node #0,0,4: 76:[32, 10] Operation: 24-14=10 Moving to Node #0,1 Current State: 76:[66, 80, 8], Operations: ['32-24=8'] Exploring Operation: 80-8=72, Resulting Numbers: [66, 72] Generated Node #0,1,0: 76:[66, 72] Operation: 80-8=72 Exploring Operation: 66-8=58, Resulting Numbers: [80, 58] Generated Node #0,1,1: 76:[80, 58] Operation: 66-8=58 Exploring Operation: 66+8=74, Resulting Numbers: [80, 74] Generated Node #0,1,2: 76:[80, 74] Operation: 66+8=74 Exploring Operation: 80/8=10, Resulting Numbers: [66, 10] Generated Node #0,1,3: 76:[66, 10] Operation: 80/8=10 Exploring Operation: 80-66=14, Resulting Numbers: [8, 14] Generated Node #0,1,4: 76:[8, 14] Operation: 80-66=14 Moving to Node #0,2 Current State: 76:[32, 80, 90], Operations: ['24+66=90'] Exploring Operation: 90-80=10, Resulting Numbers: [32, 10] Generated Node #0,2,0: 76:[32, 10] Operation: 90-80=10 Exploring Operation: 90-32=58, Resulting Numbers: [80, 58] Generated Node #0,2,1: 76:[80, 58] Operation: 90-32=58 Exploring Operation: 80-32=48, Resulting Numbers: [90, 48] Generated Node #0,2,2: 76:[90, 48] Operation: 80-32=48 Exploring Operation: 32+80=112, Resulting Numbers: [90, 112] Generated Node #0,2,3: 76:[90, 112] Operation: 32+80=112 Exploring Operation: 32+90=122, Resulting Numbers: [80, 122] Generated Node #0,2,4: 76:[80, 122] Operation: 32+90=122 Moving to Node #0,0,1 Current State: 76:[24, 18], Operations: ['80-66=14', '32-14=18'] Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,76 unequal: No Solution Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[80, 74], Operations: ['32-24=8', '66+8=74'] Exploring Operation: 80*74=5920, Resulting Numbers: [5920] 5920,76 unequal: No Solution Exploring Operation: 80-74=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 80+74=154, Resulting Numbers: [154] 154,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[32, 38], Operations: ['80-66=14', '24+14=38'] Exploring Operation: 32+38=70, Resulting Numbers: [70] 70,76 unequal: No Solution Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 32*38=1216, Resulting Numbers: [1216] 1216,76 unequal: No Solution Moving to Node #0,1,4 Current State: 76:[8, 14], Operations: ['32-24=8', '80-66=14'] Exploring Operation: 8+14=22, Resulting Numbers: [22] 22,76 unequal: No Solution Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 8*14=112, Resulting Numbers: [112] 112,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[14, 8], Operations: ['80-66=14', '32-24=8'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,76 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[32, 10], Operations: ['24+66=90', '90-80=10'] Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,76 unequal: No Solution Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,76 unequal: No Solution Moving to Node #0,0,4 Current State: 76:[32, 10], Operations: ['80-66=14', '24-14=10'] Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,76 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,76 unequal: No Solution Moving to Node #0,0,3 Current State: 76:[24, 46], Operations: ['80-66=14', '32+14=46'] Exploring Operation: 24*46=1104, Resulting Numbers: [1104] 1104,76 unequal: No Solution Exploring Operation: 46-24=22, Resulting Numbers: [22] 22,76 unequal: No Solution Exploring Operation: 24+46=70, Resulting Numbers: [70] 70,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[66, 72], Operations: ['32-24=8', '80-8=72'] Exploring Operation: 66+72=138, Resulting Numbers: [138] 138,76 unequal: No Solution Exploring Operation: 72-66=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 66*72=4752, Resulting Numbers: [4752] 4752,76 unequal: No Solution Moving to Node #0,1,3 Current State: 76:[66, 10], Operations: ['32-24=8', '80/8=10'] Exploring Operation: 66+10=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[32, 24, 66, 80], Operations: [] Exploring Operation: 32-24=8, Resulting Numbers: [66, 80, 8] Generated Node #0,1: 76:[66, 80, 8] Operation: 32-24=8 Moving to Node #0,1 Current State: 76:[66, 80, 8], Operations: ['32-24=8'] Exploring Operation: 80/8=10, Resulting Numbers: [66, 10] Generated Node #0,1,3: 76:[66, 10] Operation: 80/8=10 Moving to Node #0,1,3 Current State: 76:[66, 10], Operations: ['32-24=8', '80/8=10'] Exploring Operation: 66+10=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
0.918403
hs_5
sum_heuristic
[ 92, 3, 99, 13 ]
60
[ "99-92=7", "13+7=20", "3*20=60" ]
Current State: 60:[92, 3, 99, 13], Operations: [] Exploring Operation: 99-92=7, Resulting Numbers: [3, 13, 7] Generated Node #2: [3, 13, 7] from Operation: 99-92=7 Current State: 60:[3, 13, 7], Operations: ['99-92=7'] Exploring Operation: 13+7=20, Resulting Numbers: [3, 20] Generated Node #3: [3, 20] from Operation: 13+7=20 Current State: 60:[3, 20], Operations: ['99-92=7', '13+7=20'] Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[92, 3, 99, 13], Operations: [] Exploring Operation: 99-92=7, Resulting Numbers: [3, 13, 7] Generated Node #0,0: 60:[3, 13, 7] Operation: 99-92=7 Exploring Operation: 99/3=33, Resulting Numbers: [92, 13, 33] Generated Node #0,1: 60:[92, 13, 33] Operation: 99/3=33 Exploring Operation: 92-13=79, Resulting Numbers: [3, 99, 79] Generated Node #0,2: 60:[3, 99, 79] Operation: 92-13=79 Moving to Node #0,0 Current State: 60:[3, 13, 7], Operations: ['99-92=7'] Exploring Operation: 13-3=10, Resulting Numbers: [7, 10] Generated Node #0,0,0: 60:[7, 10] Operation: 13-3=10 Exploring Operation: 13-7=6, Resulting Numbers: [3, 6] Generated Node #0,0,1: 60:[3, 6] Operation: 13-7=6 Exploring Operation: 13+7=20, Resulting Numbers: [3, 20] Generated Node #0,0,2: 60:[3, 20] Operation: 13+7=20 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[3, 6], Operations: ['99-92=7', '13-7=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,60 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[3, 20], Operations: ['99-92=7', '13+7=20'] Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[92, 3, 99, 13], Operations: [] Exploring Operation: 99-92=7, Resulting Numbers: [3, 13, 7] Generated Node #0,0: 60:[3, 13, 7] Operation: 99-92=7 Moving to Node #0,0 Current State: 60:[3, 13, 7], Operations: ['99-92=7'] Exploring Operation: 13+7=20, Resulting Numbers: [3, 20] Generated Node #0,0,2: 60:[3, 20] Operation: 13+7=20 Moving to Node #0,0,2 Current State: 60:[3, 20], Operations: ['99-92=7', '13+7=20'] Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 21, 98, 21, 86 ]
30
[ "98-21=77", "21+86=107", "107-77=30" ]
Current State: 30:[21, 98, 21, 86], Operations: [] Exploring Operation: 98-21=77, Resulting Numbers: [86, 77] Generated Node #2: [86, 77] from Operation: 98-21=77 Current State: 30:[86, 77], Operations: ['98-21=77'] Exploring Operation: 21+86=107, Resulting Numbers: [77, 107] Generated Node #3: [77, 107] from Operation: 21+86=107 Current State: 30:[77, 107], Operations: ['98-21=77', '21+86=107'] Exploring Operation: 107-77=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[21, 98, 21, 86], Operations: [] Exploring Operation: 98-86=12, Resulting Numbers: [21, 21, 12] Generated Node #0,0: 30:[21, 21, 12] Operation: 98-86=12 Exploring Operation: 98-21=77, Resulting Numbers: [21, 86, 77] Generated Node #0,1: 30:[21, 86, 77] Operation: 98-21=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[21, 21, 12], Operations: ['98-86=12'] Exploring Operation: 21-21=0, Resulting Numbers: [12, 0] Generated Node #0,0,0: 30:[12, 0] Operation: 21-21=0 Exploring Operation: 21/21=1, Resulting Numbers: [12, 1] Generated Node #0,0,1: 30:[12, 1] Operation: 21/21=1 Moving to Node #0,0,1 Current State: 30:[12, 1], Operations: ['98-86=12', '21/21=1'] Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,30 unequal: No Solution Exploring Operation: 12+1=13, Resulting Numbers: [13] 13,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[12, 0], Operations: ['98-86=12', '21-21=0'] Exploring Operation: 12+0=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 12*0=0, Resulting Numbers: [0] 0,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[21, 86, 77], Operations: ['98-21=77'] Exploring Operation: 86-77=9, Resulting Numbers: [21, 9] Generated Node #0,1,0: 30:[21, 9] Operation: 86-77=9 Exploring Operation: 86-21=65, Resulting Numbers: [77, 65] Generated Node #0,1,1: 30:[77, 65] Operation: 86-21=65 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[21, 9], Operations: ['98-21=77', '86-77=9'] Exploring Operation: 21+9=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[21, 98, 21, 86], Operations: [] Exploring Operation: 98-21=77, Resulting Numbers: [21, 86, 77] Generated Node #0,1: 30:[21, 86, 77] Operation: 98-21=77 Moving to Node #0,1 Current State: 30:[21, 86, 77], Operations: ['98-21=77'] Exploring Operation: 86-77=9, Resulting Numbers: [21, 9] Generated Node #0,1,0: 30:[21, 9] Operation: 86-77=9 Moving to Node #0,1,0 Current State: 30:[21, 9], Operations: ['98-21=77', '86-77=9'] Exploring Operation: 21+9=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 31, 16, 87, 84 ]
24
[ "87-31=56", "16*84=1344", "1344/56=24" ]
Current State: 24:[31, 16, 87, 84], Operations: [] Exploring Operation: 87-31=56, Resulting Numbers: [16, 84, 56] Generated Node #2: [16, 84, 56] from Operation: 87-31=56 Current State: 24:[16, 84, 56], Operations: ['87-31=56'] Exploring Operation: 16*84=1344, Resulting Numbers: [56, 1344] Generated Node #3: [56, 1344] from Operation: 16*84=1344 Current State: 24:[56, 1344], Operations: ['87-31=56', '16*84=1344'] Exploring Operation: 1344/56=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[31, 16, 87, 84], Operations: [] Exploring Operation: 87-84=3, Resulting Numbers: [31, 16, 3] Generated Node #0,0: 24:[31, 16, 3] Operation: 87-84=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[31, 16, 3], Operations: ['87-84=3'] Exploring Operation: 31-16=15, Resulting Numbers: [3, 15] Generated Node #0,0,0: 24:[3, 15] Operation: 31-16=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[3, 15], Operations: ['87-84=3', '31-16=15'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 77, 20, 36, 9 ]
82
[ "20*9=180", "180/36=5", "77+5=82" ]
Current State: 82:[77, 20, 36, 9], Operations: [] Exploring Operation: 20*9=180, Resulting Numbers: [77, 36, 180] Generated Node #2: [77, 36, 180] from Operation: 20*9=180 Current State: 82:[77, 36, 180], Operations: ['20*9=180'] Exploring Operation: 180/36=5, Resulting Numbers: [77, 5] Generated Node #3: [77, 5] from Operation: 180/36=5 Current State: 82:[77, 5], Operations: ['20*9=180', '180/36=5'] Exploring Operation: 77+5=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[77, 20, 36, 9], Operations: [] Exploring Operation: 77-36=41, Resulting Numbers: [20, 9, 41] Generated Node #0,0: 82:[20, 9, 41] Operation: 77-36=41 Exploring Operation: 20+9=29, Resulting Numbers: [77, 36, 29] Generated Node #0,1: 82:[77, 36, 29] Operation: 20+9=29 Exploring Operation: 20-9=11, Resulting Numbers: [77, 36, 11] Generated Node #0,2: 82:[77, 36, 11] Operation: 20-9=11 Moving to Node #0,2 Current State: 82:[77, 36, 11], Operations: ['20-9=11'] Exploring Operation: 77-36=41, Resulting Numbers: [11, 41] Generated Node #0,2,0: 82:[11, 41] Operation: 77-36=41 Exploring Operation: 77+11=88, Resulting Numbers: [36, 88] Generated Node #0,2,1: 82:[36, 88] Operation: 77+11=88 Exploring Operation: 77/11=7, Resulting Numbers: [36, 7] Generated Node #0,2,2: 82:[36, 7] Operation: 77/11=7 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 82:[11, 41], Operations: ['20-9=11', '77-36=41'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 11+41=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 11*41=451, Resulting Numbers: [451] 451,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 82:[36, 7], Operations: ['20-9=11', '77/11=7'] Exploring Operation: 36+7=43, Resulting Numbers: [43] 43,82 unequal: No Solution Exploring Operation: 36-7=29, Resulting Numbers: [29] 29,82 unequal: No Solution Exploring Operation: 36*7=252, Resulting Numbers: [252] 252,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 82:[36, 88], Operations: ['20-9=11', '77+11=88'] Exploring Operation: 88-36=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 36*88=3168, Resulting Numbers: [3168] 3168,82 unequal: No Solution Exploring Operation: 36+88=124, Resulting Numbers: [124] 124,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 82:[77, 36, 29], Operations: ['20+9=29'] Exploring Operation: 77-29=48, Resulting Numbers: [36, 48] Generated Node #0,1,0: 82:[36, 48] Operation: 77-29=48 Exploring Operation: 36-29=7, Resulting Numbers: [77, 7] Generated Node #0,1,1: 82:[77, 7] Operation: 36-29=7 Exploring Operation: 77-36=41, Resulting Numbers: [29, 41] Generated Node #0,1,2: 82:[29, 41] Operation: 77-36=41 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 82:[77, 7], Operations: ['20+9=29', '36-29=7'] Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 77-7=70, Resulting Numbers: [70] 70,82 unequal: No Solution Exploring Operation: 77+7=84, Resulting Numbers: [84] 84,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 82:[36, 48], Operations: ['20+9=29', '77-29=48'] Exploring Operation: 36+48=84, Resulting Numbers: [84] 84,82 unequal: No Solution Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,82 unequal: No Solution Exploring Operation: 36*48=1728, Resulting Numbers: [1728] 1728,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 82:[29, 41], Operations: ['20+9=29', '77-36=41'] Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,82 unequal: No Solution Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,82 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 82:[20, 9, 41], Operations: ['77-36=41'] Exploring Operation: 20+9=29, Resulting Numbers: [41, 29] Generated Node #0,0,0: 82:[41, 29] Operation: 20+9=29 Exploring Operation: 41-20=21, Resulting Numbers: [9, 21] Generated Node #0,0,1: 82:[9, 21] Operation: 41-20=21 Exploring Operation: 20-9=11, Resulting Numbers: [41, 11] Generated Node #0,0,2: 82:[41, 11] Operation: 20-9=11 Moving to Node #0,0,2 Current State: 82:[41, 11], Operations: ['77-36=41', '20-9=11'] Exploring Operation: 41+11=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 41*11=451, Resulting Numbers: [451] 451,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[41, 29], Operations: ['77-36=41', '20+9=29'] Exploring Operation: 41+29=70, Resulting Numbers: [70] 70,82 unequal: No Solution Exploring Operation: 41*29=1189, Resulting Numbers: [1189] 1189,82 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[9, 21], Operations: ['77-36=41', '41-20=21'] Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,82 unequal: No Solution Exploring Operation: 9*21=189, Resulting Numbers: [189] 189,82 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 5, 90, 26, 53 ]
13
[ "5*26=130", "90+53=143", "143-130=13" ]
Current State: 13:[5, 90, 26, 53], Operations: [] Exploring Operation: 5*26=130, Resulting Numbers: [90, 53, 130] Generated Node #2: [90, 53, 130] from Operation: 5*26=130 Current State: 13:[90, 53, 130], Operations: ['5*26=130'] Exploring Operation: 90+53=143, Resulting Numbers: [130, 143] Generated Node #3: [130, 143] from Operation: 90+53=143 Current State: 13:[130, 143], Operations: ['5*26=130', '90+53=143'] Exploring Operation: 143-130=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[5, 90, 26, 53], Operations: [] Exploring Operation: 90-26=64, Resulting Numbers: [5, 53, 64] Generated Node #0,0: 13:[5, 53, 64] Operation: 90-26=64 Exploring Operation: 53-26=27, Resulting Numbers: [5, 90, 27] Generated Node #0,1: 13:[5, 90, 27] Operation: 53-26=27 Exploring Operation: 90-53=37, Resulting Numbers: [5, 26, 37] Generated Node #0,2: 13:[5, 26, 37] Operation: 90-53=37 Exploring Operation: 90/5=18, Resulting Numbers: [26, 53, 18] Generated Node #0,3: 13:[26, 53, 18] Operation: 90/5=18 Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[5, 26, 37], Operations: ['90-53=37'] Exploring Operation: 5+26=31, Resulting Numbers: [37, 31] Generated Node #0,2,0: 13:[37, 31] Operation: 5+26=31 Exploring Operation: 37-5=32, Resulting Numbers: [26, 32] Generated Node #0,2,1: 13:[26, 32] Operation: 37-5=32 Exploring Operation: 26-5=21, Resulting Numbers: [37, 21] Generated Node #0,2,2: 13:[37, 21] Operation: 26-5=21 Exploring Operation: 37-26=11, Resulting Numbers: [5, 11] Generated Node #0,2,3: 13:[5, 11] Operation: 37-26=11 Moving to Node #0,2,3 Current State: 13:[5, 11], Operations: ['90-53=37', '37-26=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,13 unequal: No Solution Moving to Node #0,2,2 Current State: 13:[37, 21], Operations: ['90-53=37', '26-5=21'] Exploring Operation: 37-21=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 37*21=777, Resulting Numbers: [777] 777,13 unequal: No Solution Exploring Operation: 37+21=58, Resulting Numbers: [58] 58,13 unequal: No Solution Moving to Node #0,2,1 Current State: 13:[26, 32], Operations: ['90-53=37', '37-5=32'] Exploring Operation: 26+32=58, Resulting Numbers: [58] 58,13 unequal: No Solution Exploring Operation: 26*32=832, Resulting Numbers: [832] 832,13 unequal: No Solution Exploring Operation: 32-26=6, Resulting Numbers: [6] 6,13 unequal: No Solution Moving to Node #0,2,0 Current State: 13:[37, 31], Operations: ['90-53=37', '5+26=31'] Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 37*31=1147, Resulting Numbers: [1147] 1147,13 unequal: No Solution Exploring Operation: 37+31=68, Resulting Numbers: [68] 68,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 13:[26, 53, 18], Operations: ['90/5=18'] Exploring Operation: 26+53=79, Resulting Numbers: [18, 79] Generated Node #0,3,0: 13:[18, 79] Operation: 26+53=79 Exploring Operation: 53-26=27, Resulting Numbers: [18, 27] Generated Node #0,3,1: 13:[18, 27] Operation: 53-26=27 Exploring Operation: 53-18=35, Resulting Numbers: [26, 35] Generated Node #0,3,2: 13:[26, 35] Operation: 53-18=35 Exploring Operation: 26-18=8, Resulting Numbers: [53, 8] Generated Node #0,3,3: 13:[53, 8] Operation: 26-18=8 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 13:[18, 27], Operations: ['90/5=18', '53-26=27'] Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,13 unequal: No Solution Exploring Operation: 18*27=486, Resulting Numbers: [486] 486,13 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 13:[26, 35], Operations: ['90/5=18', '53-18=35'] Exploring Operation: 26*35=910, Resulting Numbers: [910] 910,13 unequal: No Solution Exploring Operation: 26+35=61, Resulting Numbers: [61] 61,13 unequal: No Solution Exploring Operation: 35-26=9, Resulting Numbers: [9] 9,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 13:[53, 8], Operations: ['90/5=18', '26-18=8'] Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,13 unequal: No Solution Exploring Operation: 53+8=61, Resulting Numbers: [61] 61,13 unequal: No Solution Exploring Operation: 53*8=424, Resulting Numbers: [424] 424,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 13:[18, 79], Operations: ['90/5=18', '26+53=79'] Exploring Operation: 18+79=97, Resulting Numbers: [97] 97,13 unequal: No Solution Exploring Operation: 79-18=61, Resulting Numbers: [61] 61,13 unequal: No Solution Exploring Operation: 18*79=1422, Resulting Numbers: [1422] 1422,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[5, 53, 64], Operations: ['90-26=64'] Exploring Operation: 53-5=48, Resulting Numbers: [64, 48] Generated Node #0,0,0: 13:[64, 48] Operation: 53-5=48 Exploring Operation: 64-53=11, Resulting Numbers: [5, 11] Generated Node #0,0,1: 13:[5, 11] Operation: 64-53=11 Exploring Operation: 64-5=59, Resulting Numbers: [53, 59] Generated Node #0,0,2: 13:[53, 59] Operation: 64-5=59 Exploring Operation: 5+53=58, Resulting Numbers: [64, 58] Generated Node #0,0,3: 13:[64, 58] Operation: 5+53=58 Moving to Node #0,0,1 Current State: 13:[5, 11], Operations: ['90-26=64', '64-53=11'] Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,13 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,13 unequal: No Solution Moving to Node #0,0,2 Current State: 13:[53, 59], Operations: ['90-26=64', '64-5=59'] Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 53*59=3127, Resulting Numbers: [3127] 3127,13 unequal: No Solution Exploring Operation: 53+59=112, Resulting Numbers: [112] 112,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[64, 48], Operations: ['90-26=64', '53-5=48'] Exploring Operation: 64+48=112, Resulting Numbers: [112] 112,13 unequal: No Solution Exploring Operation: 64-48=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 64*48=3072, Resulting Numbers: [3072] 3072,13 unequal: No Solution Moving to Node #0,0,3 Current State: 13:[64, 58], Operations: ['90-26=64', '5+53=58'] Exploring Operation: 64-58=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 64*58=3712, Resulting Numbers: [3712] 3712,13 unequal: No Solution Exploring Operation: 64+58=122, Resulting Numbers: [122] 122,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[5, 90, 27], Operations: ['53-26=27'] Exploring Operation: 27-5=22, Resulting Numbers: [90, 22] Generated Node #0,1,0: 13:[90, 22] Operation: 27-5=22 Exploring Operation: 90/5=18, Resulting Numbers: [27, 18] Generated Node #0,1,1: 13:[27, 18] Operation: 90/5=18 Exploring Operation: 90-27=63, Resulting Numbers: [5, 63] Generated Node #0,1,2: 13:[5, 63] Operation: 90-27=63 Exploring Operation: 90-5=85, Resulting Numbers: [27, 85] Generated Node #0,1,3: 13:[27, 85] Operation: 90-5=85 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[27, 18], Operations: ['53-26=27', '90/5=18'] Exploring Operation: 27+18=45, Resulting Numbers: [45] 45,13 unequal: No Solution Exploring Operation: 27*18=486, Resulting Numbers: [486] 486,13 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 13:[5, 63], Operations: ['53-26=27', '90-27=63'] Exploring Operation: 5*63=315, Resulting Numbers: [315] 315,13 unequal: No Solution Exploring Operation: 63-5=58, Resulting Numbers: [58] 58,13 unequal: No Solution Exploring Operation: 5+63=68, Resulting Numbers: [68] 68,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 13:[90, 22], Operations: ['53-26=27', '27-5=22'] Exploring Operation: 90-22=68, Resulting Numbers: [68] 68,13 unequal: No Solution Exploring Operation: 90+22=112, Resulting Numbers: [112] 112,13 unequal: No Solution Exploring Operation: 90*22=1980, Resulting Numbers: [1980] 1980,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 13:[27, 85], Operations: ['53-26=27', '90-5=85'] Exploring Operation: 27*85=2295, Resulting Numbers: [2295] 2295,13 unequal: No Solution Exploring Operation: 85-27=58, Resulting Numbers: [58] 58,13 unequal: No Solution Exploring Operation: 27+85=112, Resulting Numbers: [112] 112,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 29, 95, 1, 99 ]
32
[ "95-29=66", "99-1=98", "98-66=32" ]
Current State: 32:[29, 95, 1, 99], Operations: [] Exploring Operation: 95-29=66, Resulting Numbers: [1, 99, 66] Generated Node #2: [1, 99, 66] from Operation: 95-29=66 Current State: 32:[1, 99, 66], Operations: ['95-29=66'] Exploring Operation: 99-1=98, Resulting Numbers: [66, 98] Generated Node #3: [66, 98] from Operation: 99-1=98 Current State: 32:[66, 98], Operations: ['95-29=66', '99-1=98'] Exploring Operation: 98-66=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[29, 95, 1, 99], Operations: [] Exploring Operation: 95-1=94, Resulting Numbers: [29, 99, 94] Generated Node #0,0: 32:[29, 99, 94] Operation: 95-1=94 Exploring Operation: 99-95=4, Resulting Numbers: [29, 1, 4] Generated Node #0,1: 32:[29, 1, 4] Operation: 99-95=4 Exploring Operation: 29+1=30, Resulting Numbers: [95, 99, 30] Generated Node #0,2: 32:[95, 99, 30] Operation: 29+1=30 Exploring Operation: 99-29=70, Resulting Numbers: [95, 1, 70] Generated Node #0,3: 32:[95, 1, 70] Operation: 99-29=70 Exploring Operation: 95-29=66, Resulting Numbers: [1, 99, 66] Generated Node #0,4: 32:[1, 99, 66] Operation: 95-29=66 Moving to Node #0,1 Current State: 32:[29, 1, 4], Operations: ['99-95=4'] Exploring Operation: 29*1=29, Resulting Numbers: [4, 29] Generated Node #0,1,0: 32:[4, 29] Operation: 29*1=29 Exploring Operation: 29+4=33, Resulting Numbers: [1, 33] Generated Node #0,1,1: 32:[1, 33] Operation: 29+4=33 Exploring Operation: 1*4=4, Resulting Numbers: [29, 4] Generated Node #0,1,2: 32:[29, 4] Operation: 1*4=4 Exploring Operation: 29+1=30, Resulting Numbers: [4, 30] Generated Node #0,1,3: 32:[4, 30] Operation: 29+1=30 Exploring Operation: 29/1=29, Resulting Numbers: [4, 29] Generated Node #0,1,4: 32:[4, 29] Operation: 29/1=29 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[1, 33], Operations: ['99-95=4', '29+4=33'] Exploring Operation: 1+33=34, Resulting Numbers: [34] 34,32 unequal: No Solution Exploring Operation: 1*33=33, Resulting Numbers: [33] 33,32 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,32 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[29, 95, 1, 99], Operations: [] Exploring Operation: 99-95=4, Resulting Numbers: [29, 1, 4] Generated Node #0,1: 32:[29, 1, 4] Operation: 99-95=4 Moving to Node #0,1 Current State: 32:[29, 1, 4], Operations: ['99-95=4'] Exploring Operation: 29+4=33, Resulting Numbers: [1, 33] Generated Node #0,1,1: 32:[1, 33] Operation: 29+4=33 Moving to Node #0,1,1 Current State: 32:[1, 33], Operations: ['99-95=4', '29+4=33'] Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 88, 94, 2, 39 ]
52
[ "88+94=182", "182/2=91", "91-39=52" ]
Current State: 52:[88, 94, 2, 39], Operations: [] Exploring Operation: 88+94=182, Resulting Numbers: [2, 39, 182] Generated Node #2: [2, 39, 182] from Operation: 88+94=182 Current State: 52:[2, 39, 182], Operations: ['88+94=182'] Exploring Operation: 182/2=91, Resulting Numbers: [39, 91] Generated Node #3: [39, 91] from Operation: 182/2=91 Current State: 52:[39, 91], Operations: ['88+94=182', '182/2=91'] Exploring Operation: 91-39=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[88, 94, 2, 39], Operations: [] Exploring Operation: 94/2=47, Resulting Numbers: [88, 39, 47] Generated Node #0,0: 52:[88, 39, 47] Operation: 94/2=47 Exploring Operation: 94-39=55, Resulting Numbers: [88, 2, 55] Generated Node #0,1: 52:[88, 2, 55] Operation: 94-39=55 Exploring Operation: 94-88=6, Resulting Numbers: [2, 39, 6] Generated Node #0,2: 52:[2, 39, 6] Operation: 94-88=6 Exploring Operation: 88-39=49, Resulting Numbers: [94, 2, 49] Generated Node #0,3: 52:[94, 2, 49] Operation: 88-39=49 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[2, 39, 6], Operations: ['94-88=6'] Exploring Operation: 39-2=37, Resulting Numbers: [6, 37] Generated Node #0,2,0: 52:[6, 37] Operation: 39-2=37 Exploring Operation: 39-6=33, Resulting Numbers: [2, 33] Generated Node #0,2,1: 52:[2, 33] Operation: 39-6=33 Exploring Operation: 39+6=45, Resulting Numbers: [2, 45] Generated Node #0,2,2: 52:[2, 45] Operation: 39+6=45 Exploring Operation: 2+39=41, Resulting Numbers: [6, 41] Generated Node #0,2,3: 52:[6, 41] Operation: 2+39=41 Moving to Node #0,2,1 Current State: 52:[2, 33], Operations: ['94-88=6', '39-6=33'] Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,52 unequal: No Solution Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,52 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,52 unequal: No Solution Moving to Node #0,2,2 Current State: 52:[2, 45], Operations: ['94-88=6', '39+6=45'] Exploring Operation: 2+45=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,52 unequal: No Solution Moving to Node #0,2,3 Current State: 52:[6, 41], Operations: ['94-88=6', '2+39=41'] Exploring Operation: 6+41=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 6*41=246, Resulting Numbers: [246] 246,52 unequal: No Solution Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,52 unequal: No Solution Moving to Node #0,2,0 Current State: 52:[6, 37], Operations: ['94-88=6', '39-2=37'] Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 6*37=222, Resulting Numbers: [222] 222,52 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[88, 2, 55], Operations: ['94-39=55'] Exploring Operation: 55-2=53, Resulting Numbers: [88, 53] Generated Node #0,1,0: 52:[88, 53] Operation: 55-2=53 Exploring Operation: 88-2=86, Resulting Numbers: [55, 86] Generated Node #0,1,1: 52:[55, 86] Operation: 88-2=86 Exploring Operation: 88/2=44, Resulting Numbers: [55, 44] Generated Node #0,1,2: 52:[55, 44] Operation: 88/2=44 Exploring Operation: 88-55=33, Resulting Numbers: [2, 33] Generated Node #0,1,3: 52:[2, 33] Operation: 88-55=33 Moving to Node #0,1,3 Current State: 52:[2, 33], Operations: ['94-39=55', '88-55=33'] Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,52 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,52 unequal: No Solution Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,52 unequal: No Solution Moving to Node #0,1,2 Current State: 52:[55, 44], Operations: ['94-39=55', '88/2=44'] Exploring Operation: 55*44=2420, Resulting Numbers: [2420] 2420,52 unequal: No Solution Exploring Operation: 55-44=11, Resulting Numbers: [11] 11,52 unequal: No Solution Exploring Operation: 55+44=99, Resulting Numbers: [99] 99,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[55, 86], Operations: ['94-39=55', '88-2=86'] Exploring Operation: 55*86=4730, Resulting Numbers: [4730] 4730,52 unequal: No Solution Exploring Operation: 55+86=141, Resulting Numbers: [141] 141,52 unequal: No Solution Exploring Operation: 86-55=31, Resulting Numbers: [31] 31,52 unequal: No Solution Moving to Node #0,1,0 Current State: 52:[88, 53], Operations: ['94-39=55', '55-2=53'] Exploring Operation: 88+53=141, Resulting Numbers: [141] 141,52 unequal: No Solution Exploring Operation: 88-53=35, Resulting Numbers: [35] 35,52 unequal: No Solution Exploring Operation: 88*53=4664, Resulting Numbers: [4664] 4664,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[94, 2, 49], Operations: ['88-39=49'] Exploring Operation: 94-49=45, Resulting Numbers: [2, 45] Generated Node #0,3,0: 52:[2, 45] Operation: 94-49=45 Exploring Operation: 2+49=51, Resulting Numbers: [94, 51] Generated Node #0,3,1: 52:[94, 51] Operation: 2+49=51 Exploring Operation: 94-2=92, Resulting Numbers: [49, 92] Generated Node #0,3,2: 52:[49, 92] Operation: 94-2=92 Exploring Operation: 94/2=47, Resulting Numbers: [49, 47] Generated Node #0,3,3: 52:[49, 47] Operation: 94/2=47 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 52:[2, 45], Operations: ['88-39=49', '94-49=45'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,52 unequal: No Solution Exploring Operation: 2+45=47, Resulting Numbers: [47] 47,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 52:[49, 47], Operations: ['88-39=49', '94/2=47'] Exploring Operation: 49*47=2303, Resulting Numbers: [2303] 2303,52 unequal: No Solution Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,52 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 52:[94, 51], Operations: ['88-39=49', '2+49=51'] Exploring Operation: 94*51=4794, Resulting Numbers: [4794] 4794,52 unequal: No Solution Exploring Operation: 94+51=145, Resulting Numbers: [145] 145,52 unequal: No Solution Exploring Operation: 94-51=43, Resulting Numbers: [43] 43,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 52:[49, 92], Operations: ['88-39=49', '94-2=92'] Exploring Operation: 49+92=141, Resulting Numbers: [141] 141,52 unequal: No Solution Exploring Operation: 49*92=4508, Resulting Numbers: [4508] 4508,52 unequal: No Solution Exploring Operation: 92-49=43, Resulting Numbers: [43] 43,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[88, 39, 47], Operations: ['94/2=47'] Exploring Operation: 88-39=49, Resulting Numbers: [47, 49] Generated Node #0,0,0: 52:[47, 49] Operation: 88-39=49 Exploring Operation: 47-39=8, Resulting Numbers: [88, 8] Generated Node #0,0,1: 52:[88, 8] Operation: 47-39=8 Exploring Operation: 39+47=86, Resulting Numbers: [88, 86] Generated Node #0,0,2: 52:[88, 86] Operation: 39+47=86 Exploring Operation: 88-47=41, Resulting Numbers: [39, 41] Generated Node #0,0,3: 52:[39, 41] Operation: 88-47=41 Moving to Node #0,0,0 Current State: 52:[47, 49], Operations: ['94/2=47', '88-39=49'] Exploring Operation: 47*49=2303, Resulting Numbers: [2303] 2303,52 unequal: No Solution Exploring Operation: 47+49=96, Resulting Numbers: [96] 96,52 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,52 unequal: No Solution Moving to Node #0,0,3 Current State: 52:[39, 41], Operations: ['94/2=47', '88-47=41'] Exploring Operation: 39+41=80, Resulting Numbers: [80] 80,52 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 39*41=1599, Resulting Numbers: [1599] 1599,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[88, 8], Operations: ['94/2=47', '47-39=8'] Exploring Operation: 88/8=11, Resulting Numbers: [11] 11,52 unequal: No Solution Exploring Operation: 88+8=96, Resulting Numbers: [96] 96,52 unequal: No Solution Exploring Operation: 88-8=80, Resulting Numbers: [80] 80,52 unequal: No Solution Exploring Operation: 88*8=704, Resulting Numbers: [704] 704,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[88, 86], Operations: ['94/2=47', '39+47=86'] Exploring Operation: 88+86=174, Resulting Numbers: [174] 174,52 unequal: No Solution Exploring Operation: 88*86=7568, Resulting Numbers: [7568] 7568,52 unequal: No Solution Exploring Operation: 88-86=2, Resulting Numbers: [2] 2,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 7, 12, 52, 55 ]
28
[ "7*12=84", "55-52=3", "84/3=28" ]
Current State: 28:[7, 12, 52, 55], Operations: [] Exploring Operation: 7*12=84, Resulting Numbers: [52, 55, 84] Generated Node #2: [52, 55, 84] from Operation: 7*12=84 Current State: 28:[52, 55, 84], Operations: ['7*12=84'] Exploring Operation: 55-52=3, Resulting Numbers: [84, 3] Generated Node #3: [84, 3] from Operation: 55-52=3 Current State: 28:[84, 3], Operations: ['7*12=84', '55-52=3'] Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[7, 12, 52, 55], Operations: [] Exploring Operation: 55-52=3, Resulting Numbers: [7, 12, 3] Generated Node #0,0: 28:[7, 12, 3] Operation: 55-52=3 Exploring Operation: 55-12=43, Resulting Numbers: [7, 52, 43] Generated Node #0,1: 28:[7, 52, 43] Operation: 55-12=43 Exploring Operation: 52-12=40, Resulting Numbers: [7, 55, 40] Generated Node #0,2: 28:[7, 55, 40] Operation: 52-12=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[7, 12, 3], Operations: ['55-52=3'] Exploring Operation: 12+3=15, Resulting Numbers: [7, 15] Generated Node #0,0,0: 28:[7, 15] Operation: 12+3=15 Exploring Operation: 12-7=5, Resulting Numbers: [3, 5] Generated Node #0,0,1: 28:[3, 5] Operation: 12-7=5 Exploring Operation: 12/3=4, Resulting Numbers: [7, 4] Generated Node #0,0,2: 28:[7, 4] Operation: 12/3=4 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 28:[7, 4], Operations: ['55-52=3', '12/3=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[7, 12, 52, 55], Operations: [] Exploring Operation: 55-52=3, Resulting Numbers: [7, 12, 3] Generated Node #0,0: 28:[7, 12, 3] Operation: 55-52=3 Moving to Node #0,0 Current State: 28:[7, 12, 3], Operations: ['55-52=3'] Exploring Operation: 12/3=4, Resulting Numbers: [7, 4] Generated Node #0,0,2: 28:[7, 4] Operation: 12/3=4 Moving to Node #0,0,2 Current State: 28:[7, 4], Operations: ['55-52=3', '12/3=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 89, 5, 45, 4 ]
94
[ "89-4=85", "45/5=9", "85+9=94" ]
Current State: 94:[89, 5, 45, 4], Operations: [] Exploring Operation: 89-4=85, Resulting Numbers: [5, 45, 85] Generated Node #2: [5, 45, 85] from Operation: 89-4=85 Current State: 94:[5, 45, 85], Operations: ['89-4=85'] Exploring Operation: 45/5=9, Resulting Numbers: [85, 9] Generated Node #3: [85, 9] from Operation: 45/5=9 Current State: 94:[85, 9], Operations: ['89-4=85', '45/5=9'] Exploring Operation: 85+9=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[89, 5, 45, 4], Operations: [] Exploring Operation: 5-4=1, Resulting Numbers: [89, 45, 1] Generated Node #0,0: 94:[89, 45, 1] Operation: 5-4=1 Exploring Operation: 5+45=50, Resulting Numbers: [89, 4, 50] Generated Node #0,1: 94:[89, 4, 50] Operation: 5+45=50 Exploring Operation: 89+5=94, Resulting Numbers: [45, 4, 94] Generated Node #0,2: 94:[45, 4, 94] Operation: 89+5=94 Exploring Operation: 89-45=44, Resulting Numbers: [5, 4, 44] Generated Node #0,3: 94:[5, 4, 44] Operation: 89-45=44 Exploring Operation: 89+4=93, Resulting Numbers: [5, 45, 93] Generated Node #0,4: 94:[5, 45, 93] Operation: 89+4=93 Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[45, 4, 94], Operations: ['89+5=94'] Exploring Operation: 94-4=90, Resulting Numbers: [45, 90] Generated Node #0,2,0: 94:[45, 90] Operation: 94-4=90 Exploring Operation: 45+4=49, Resulting Numbers: [94, 49] Generated Node #0,2,1: 94:[94, 49] Operation: 45+4=49 Exploring Operation: 45-4=41, Resulting Numbers: [94, 41] Generated Node #0,2,2: 94:[94, 41] Operation: 45-4=41 Exploring Operation: 4+94=98, Resulting Numbers: [45, 98] Generated Node #0,2,3: 94:[45, 98] Operation: 4+94=98 Exploring Operation: 94-45=49, Resulting Numbers: [4, 49] Generated Node #0,2,4: 94:[4, 49] Operation: 94-45=49 Moving to Node #0,2,1 Current State: 94:[94, 49], Operations: ['89+5=94', '45+4=49'] Exploring Operation: 94-49=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 94+49=143, Resulting Numbers: [143] 143,94 unequal: No Solution Exploring Operation: 94*49=4606, Resulting Numbers: [4606] 4606,94 unequal: No Solution Moving to Node #0,2,4 Current State: 94:[4, 49], Operations: ['89+5=94', '94-45=49'] Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,94 unequal: No Solution Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,94 unequal: No Solution Moving to Node #0,2,0 Current State: 94:[45, 90], Operations: ['89+5=94', '94-4=90'] Exploring Operation: 45*90=4050, Resulting Numbers: [4050] 4050,94 unequal: No Solution Exploring Operation: 90-45=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 45+90=135, Resulting Numbers: [135] 135,94 unequal: No Solution Exploring Operation: 90/45=2, Resulting Numbers: [2] 2,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[94, 41], Operations: ['89+5=94', '45-4=41'] Exploring Operation: 94-41=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 94*41=3854, Resulting Numbers: [3854] 3854,94 unequal: No Solution Exploring Operation: 94+41=135, Resulting Numbers: [135] 135,94 unequal: No Solution Moving to Node #0,2,3 Current State: 94:[45, 98], Operations: ['89+5=94', '4+94=98'] Exploring Operation: 45*98=4410, Resulting Numbers: [4410] 4410,94 unequal: No Solution Exploring Operation: 45+98=143, Resulting Numbers: [143] 143,94 unequal: No Solution Exploring Operation: 98-45=53, Resulting Numbers: [53] 53,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 94:[5, 45, 93], Operations: ['89+4=93'] Exploring Operation: 5+93=98, Resulting Numbers: [45, 98] Generated Node #0,4,0: 94:[45, 98] Operation: 5+93=98 Exploring Operation: 45/5=9, Resulting Numbers: [93, 9] Generated Node #0,4,1: 94:[93, 9] Operation: 45/5=9 Exploring Operation: 5+45=50, Resulting Numbers: [93, 50] Generated Node #0,4,2: 94:[93, 50] Operation: 5+45=50 Exploring Operation: 93-45=48, Resulting Numbers: [5, 48] Generated Node #0,4,3: 94:[5, 48] Operation: 93-45=48 Exploring Operation: 45-5=40, Resulting Numbers: [93, 40] Generated Node #0,4,4: 94:[93, 40] Operation: 45-5=40 Moving to Node #0,4,2 Current State: 94:[93, 50], Operations: ['89+4=93', '5+45=50'] Exploring Operation: 93+50=143, Resulting Numbers: [143] 143,94 unequal: No Solution Exploring Operation: 93*50=4650, Resulting Numbers: [4650] 4650,94 unequal: No Solution Exploring Operation: 93-50=43, Resulting Numbers: [43] 43,94 unequal: No Solution Moving to Node #0,4,3 Current State: 94:[5, 48], Operations: ['89+4=93', '93-45=48'] Exploring Operation: 5+48=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,94 unequal: No Solution Exploring Operation: 5*48=240, Resulting Numbers: [240] 240,94 unequal: No Solution Moving to Node #0,4,0 Current State: 94:[45, 98], Operations: ['89+4=93', '5+93=98'] Exploring Operation: 98-45=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 45*98=4410, Resulting Numbers: [4410] 4410,94 unequal: No Solution Exploring Operation: 45+98=143, Resulting Numbers: [143] 143,94 unequal: No Solution Moving to Node #0,4,1 Current State: 94:[93, 9], Operations: ['89+4=93', '45/5=9'] Exploring Operation: 93*9=837, Resulting Numbers: [837] 837,94 unequal: No Solution Exploring Operation: 93-9=84, Resulting Numbers: [84] 84,94 unequal: No Solution Exploring Operation: 93+9=102, Resulting Numbers: [102] 102,94 unequal: No Solution Moving to Node #0,4,4 Current State: 94:[93, 40], Operations: ['89+4=93', '45-5=40'] Exploring Operation: 93*40=3720, Resulting Numbers: [3720] 3720,94 unequal: No Solution Exploring Operation: 93-40=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 93+40=133, Resulting Numbers: [133] 133,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[89, 45, 1], Operations: ['5-4=1'] Exploring Operation: 89+1=90, Resulting Numbers: [45, 90] Generated Node #0,0,0: 94:[45, 90] Operation: 89+1=90 Exploring Operation: 45+1=46, Resulting Numbers: [89, 46] Generated Node #0,0,1: 94:[89, 46] Operation: 45+1=46 Exploring Operation: 89-45=44, Resulting Numbers: [1, 44] Generated Node #0,0,2: 94:[1, 44] Operation: 89-45=44 Exploring Operation: 89*1=89, Resulting Numbers: [45, 89] Generated Node #0,0,3: 94:[45, 89] Operation: 89*1=89 Exploring Operation: 89/1=89, Resulting Numbers: [45, 89] Generated Node #0,0,4: 94:[45, 89] Operation: 89/1=89 Moving to Node #0,0,2 Current State: 94:[1, 44], Operations: ['5-4=1', '89-45=44'] Exploring Operation: 1*44=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 1+44=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,94 unequal: No Solution Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[89, 46], Operations: ['5-4=1', '45+1=46'] Exploring Operation: 89-46=43, Resulting Numbers: [43] 43,94 unequal: No Solution Exploring Operation: 89*46=4094, Resulting Numbers: [4094] 4094,94 unequal: No Solution Exploring Operation: 89+46=135, Resulting Numbers: [135] 135,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[45, 90], Operations: ['5-4=1', '89+1=90'] Exploring Operation: 90-45=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 45+90=135, Resulting Numbers: [135] 135,94 unequal: No Solution Exploring Operation: 45*90=4050, Resulting Numbers: [4050] 4050,94 unequal: No Solution Exploring Operation: 90/45=2, Resulting Numbers: [2] 2,94 unequal: No Solution Moving to Node #0,0,3 Current State: 94:[45, 89], Operations: ['5-4=1', '89*1=89'] Exploring Operation: 45*89=4005, Resulting Numbers: [4005] 4005,94 unequal: No Solution Exploring Operation: 89-45=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 45+89=134, Resulting Numbers: [134] 134,94 unequal: No Solution Moving to Node #0,0,4 Current State: 94:[45, 89], Operations: ['5-4=1', '89/1=89'] Exploring Operation: 45+89=134, Resulting Numbers: [134] 134,94 unequal: No Solution Exploring Operation: 89-45=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 45*89=4005, Resulting Numbers: [4005] 4005,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[5, 4, 44], Operations: ['89-45=44'] Exploring Operation: 5+4=9, Resulting Numbers: [44, 9] Generated Node #0,3,0: 94:[44, 9] Operation: 5+4=9 Exploring Operation: 4+44=48, Resulting Numbers: [5, 48] Generated Node #0,3,1: 94:[5, 48] Operation: 4+44=48 Exploring Operation: 5+44=49, Resulting Numbers: [4, 49] Generated Node #0,3,2: 94:[4, 49] Operation: 5+44=49 Exploring Operation: 5-4=1, Resulting Numbers: [44, 1] Generated Node #0,3,3: 94:[44, 1] Operation: 5-4=1 Exploring Operation: 44-5=39, Resulting Numbers: [4, 39] Generated Node #0,3,4: 94:[4, 39] Operation: 44-5=39 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 94:[5, 48], Operations: ['89-45=44', '4+44=48'] Exploring Operation: 5+48=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 5*48=240, Resulting Numbers: [240] 240,94 unequal: No Solution Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 94:[4, 49], Operations: ['89-45=44', '5+44=49'] Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,94 unequal: No Solution Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 94:[44, 1], Operations: ['89-45=44', '5-4=1'] Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,94 unequal: No Solution Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 94:[44, 9], Operations: ['89-45=44', '5+4=9'] Exploring Operation: 44+9=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 44*9=396, Resulting Numbers: [396] 396,94 unequal: No Solution Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 94:[4, 39], Operations: ['89-45=44', '44-5=39'] Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,94 unequal: No Solution Exploring Operation: 4+39=43, Resulting Numbers: [43] 43,94 unequal: No Solution Exploring Operation: 4*39=156, Resulting Numbers: [156] 156,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[89, 4, 50], Operations: ['5+45=50'] Exploring Operation: 50-4=46, Resulting Numbers: [89, 46] Generated Node #0,1,0: 94:[89, 46] Operation: 50-4=46 Exploring Operation: 4+50=54, Resulting Numbers: [89, 54] Generated Node #0,1,1: 94:[89, 54] Operation: 4+50=54 Exploring Operation: 89-50=39, Resulting Numbers: [4, 39] Generated Node #0,1,2: 94:[4, 39] Operation: 89-50=39 Exploring Operation: 89+4=93, Resulting Numbers: [50, 93] Generated Node #0,1,3: 94:[50, 93] Operation: 89+4=93 Exploring Operation: 89-4=85, Resulting Numbers: [50, 85] Generated Node #0,1,4: 94:[50, 85] Operation: 89-4=85 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 94:[50, 93], Operations: ['5+45=50', '89+4=93'] Exploring Operation: 50+93=143, Resulting Numbers: [143] 143,94 unequal: No Solution Exploring Operation: 93-50=43, Resulting Numbers: [43] 43,94 unequal: No Solution Exploring Operation: 50*93=4650, Resulting Numbers: [4650] 4650,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[89, 46], Operations: ['5+45=50', '50-4=46'] Exploring Operation: 89+46=135, Resulting Numbers: [135] 135,94 unequal: No Solution Exploring Operation: 89-46=43, Resulting Numbers: [43] 43,94 unequal: No Solution Exploring Operation: 89*46=4094, Resulting Numbers: [4094] 4094,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 94:[4, 39], Operations: ['5+45=50', '89-50=39'] Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,94 unequal: No Solution Exploring Operation: 4+39=43, Resulting Numbers: [43] 43,94 unequal: No Solution Exploring Operation: 4*39=156, Resulting Numbers: [156] 156,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[89, 54], Operations: ['5+45=50', '4+50=54'] Exploring Operation: 89*54=4806, Resulting Numbers: [4806] 4806,94 unequal: No Solution Exploring Operation: 89-54=35, Resulting Numbers: [35] 35,94 unequal: No Solution Exploring Operation: 89+54=143, Resulting Numbers: [143] 143,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 94:[50, 85], Operations: ['5+45=50', '89-4=85'] Exploring Operation: 85-50=35, Resulting Numbers: [35] 35,94 unequal: No Solution Exploring Operation: 50+85=135, Resulting Numbers: [135] 135,94 unequal: No Solution Exploring Operation: 50*85=4250, Resulting Numbers: [4250] 4250,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 7, 10, 53, 8 ]
20
[ "7+53=60", "10*8=80", "80-60=20" ]
Current State: 20:[7, 10, 53, 8], Operations: [] Exploring Operation: 7+53=60, Resulting Numbers: [10, 8, 60] Generated Node #2: [10, 8, 60] from Operation: 7+53=60 Current State: 20:[10, 8, 60], Operations: ['7+53=60'] Exploring Operation: 10*8=80, Resulting Numbers: [60, 80] Generated Node #3: [60, 80] from Operation: 10*8=80 Current State: 20:[60, 80], Operations: ['7+53=60', '10*8=80'] Exploring Operation: 80-60=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[7, 10, 53, 8], Operations: [] Exploring Operation: 53-10=43, Resulting Numbers: [7, 8, 43] Generated Node #0,0: 20:[7, 8, 43] Operation: 53-10=43 Exploring Operation: 53-8=45, Resulting Numbers: [7, 10, 45] Generated Node #0,1: 20:[7, 10, 45] Operation: 53-8=45 Exploring Operation: 53-7=46, Resulting Numbers: [10, 8, 46] Generated Node #0,2: 20:[10, 8, 46] Operation: 53-7=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[7, 8, 43], Operations: ['53-10=43'] Exploring Operation: 43-8=35, Resulting Numbers: [7, 35] Generated Node #0,0,0: 20:[7, 35] Operation: 43-8=35 Exploring Operation: 43-7=36, Resulting Numbers: [8, 36] Generated Node #0,0,1: 20:[8, 36] Operation: 43-7=36 Exploring Operation: 8-7=1, Resulting Numbers: [43, 1] Generated Node #0,0,2: 20:[43, 1] Operation: 8-7=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 20:[7, 35], Operations: ['53-10=43', '43-8=35'] Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,20 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 20:[8, 36], Operations: ['53-10=43', '43-7=36'] Exploring Operation: 8+36=44, Resulting Numbers: [44] 44,20 unequal: No Solution Exploring Operation: 8*36=288, Resulting Numbers: [288] 288,20 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 20:[43, 1], Operations: ['53-10=43', '8-7=1'] Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,20 unequal: No Solution Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[7, 10, 45], Operations: ['53-8=45'] Exploring Operation: 45-7=38, Resulting Numbers: [10, 38] Generated Node #0,1,0: 20:[10, 38] Operation: 45-7=38 Exploring Operation: 10-7=3, Resulting Numbers: [45, 3] Generated Node #0,1,1: 20:[45, 3] Operation: 10-7=3 Exploring Operation: 45-10=35, Resulting Numbers: [7, 35] Generated Node #0,1,2: 20:[7, 35] Operation: 45-10=35 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 20:[7, 35], Operations: ['53-8=45', '45-10=35'] Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,20 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,20 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 20:[10, 38], Operations: ['53-8=45', '45-7=38'] Exploring Operation: 10+38=48, Resulting Numbers: [48] 48,20 unequal: No Solution Exploring Operation: 10*38=380, Resulting Numbers: [380] 380,20 unequal: No Solution Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 20:[45, 3], Operations: ['53-8=45', '10-7=3'] Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,20 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,20 unequal: No Solution Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 20:[10, 8, 46], Operations: ['53-7=46'] Exploring Operation: 46-10=36, Resulting Numbers: [8, 36] Generated Node #0,2,0: 20:[8, 36] Operation: 46-10=36 Exploring Operation: 10-8=2, Resulting Numbers: [46, 2] Generated Node #0,2,1: 20:[46, 2] Operation: 10-8=2 Exploring Operation: 46-8=38, Resulting Numbers: [10, 38] Generated Node #0,2,2: 20:[10, 38] Operation: 46-8=38 Moving to Node #0,2,0 Current State: 20:[8, 36], Operations: ['53-7=46', '46-10=36'] Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,20 unequal: No Solution Exploring Operation: 8*36=288, Resulting Numbers: [288] 288,20 unequal: No Solution Exploring Operation: 8+36=44, Resulting Numbers: [44] 44,20 unequal: No Solution Moving to Node #0,2,2 Current State: 20:[10, 38], Operations: ['53-7=46', '46-8=38'] Exploring Operation: 10*38=380, Resulting Numbers: [380] 380,20 unequal: No Solution Exploring Operation: 10+38=48, Resulting Numbers: [48] 48,20 unequal: No Solution Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,20 unequal: No Solution Moving to Node #0,2,1 Current State: 20:[46, 2], Operations: ['53-7=46', '10-8=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,20 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,20 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 22, 18, 2, 30 ]
92
[ "22*2=44", "18+30=48", "44+48=92" ]
Current State: 92:[22, 18, 2, 30], Operations: [] Exploring Operation: 22*2=44, Resulting Numbers: [18, 30, 44] Generated Node #2: [18, 30, 44] from Operation: 22*2=44 Current State: 92:[18, 30, 44], Operations: ['22*2=44'] Exploring Operation: 18+30=48, Resulting Numbers: [44, 48] Generated Node #3: [44, 48] from Operation: 18+30=48 Current State: 92:[44, 48], Operations: ['22*2=44', '18+30=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[22, 18, 2, 30], Operations: [] Exploring Operation: 22-18=4, Resulting Numbers: [2, 30, 4] Generated Node #0,0: 92:[2, 30, 4] Operation: 22-18=4 Exploring Operation: 18+30=48, Resulting Numbers: [22, 2, 48] Generated Node #0,1: 92:[22, 2, 48] Operation: 18+30=48 Moving to Node #0,1 Current State: 92:[22, 2, 48], Operations: ['18+30=48'] Exploring Operation: 48/2=24, Resulting Numbers: [22, 24] Generated Node #0,1,0: 92:[22, 24] Operation: 48/2=24 Exploring Operation: 48-2=46, Resulting Numbers: [22, 46] Generated Node #0,1,1: 92:[22, 46] Operation: 48-2=46 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[22, 46], Operations: ['18+30=48', '48-2=46'] Exploring Operation: 22+46=68, Resulting Numbers: [68] 68,92 unequal: No Solution Exploring Operation: 46-22=24, Resulting Numbers: [24] 24,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[22, 24], Operations: ['18+30=48', '48/2=24'] Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 92:[2, 30, 4], Operations: ['22-18=4'] Exploring Operation: 30-4=26, Resulting Numbers: [2, 26] Generated Node #0,0,0: 92:[2, 26] Operation: 30-4=26 Exploring Operation: 30-2=28, Resulting Numbers: [4, 28] Generated Node #0,0,1: 92:[4, 28] Operation: 30-2=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[2, 26], Operations: ['22-18=4', '30-4=26'] Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[4, 28], Operations: ['22-18=4', '30-2=28'] Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 48, 96, 99, 31 ]
20
[ "96-48=48", "99-31=68", "68-48=20" ]
Current State: 20:[48, 96, 99, 31], Operations: [] Exploring Operation: 96-48=48, Resulting Numbers: [99, 31, 48] Generated Node #2: [99, 31, 48] from Operation: 96-48=48 Current State: 20:[99, 31, 48], Operations: ['96-48=48'] Exploring Operation: 99-31=68, Resulting Numbers: [48, 68] Generated Node #3: [48, 68] from Operation: 99-31=68 Current State: 20:[48, 68], Operations: ['96-48=48', '99-31=68'] Exploring Operation: 68-48=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[48, 96, 99, 31], Operations: [] Exploring Operation: 99-96=3, Resulting Numbers: [48, 31, 3] Generated Node #0,0: 20:[48, 31, 3] Operation: 99-96=3 Moving to Node #0,0 Current State: 20:[48, 31, 3], Operations: ['99-96=3'] Exploring Operation: 48-31=17, Resulting Numbers: [3, 17] Generated Node #0,0,0: 20:[3, 17] Operation: 48-31=17 Moving to Node #0,0,0 Current State: 20:[3, 17], Operations: ['99-96=3', '48-31=17'] Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[48, 96, 99, 31], Operations: [] Exploring Operation: 99-96=3, Resulting Numbers: [48, 31, 3] Generated Node #0,0: 20:[48, 31, 3] Operation: 99-96=3 Moving to Node #0,0 Current State: 20:[48, 31, 3], Operations: ['99-96=3'] Exploring Operation: 48-31=17, Resulting Numbers: [3, 17] Generated Node #0,0,0: 20:[3, 17] Operation: 48-31=17 Moving to Node #0,0,0 Current State: 20:[3, 17], Operations: ['99-96=3', '48-31=17'] Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 89, 64, 72, 85 ]
12
[ "89-64=25", "85-72=13", "25-13=12" ]
Current State: 12:[89, 64, 72, 85], Operations: [] Exploring Operation: 89-64=25, Resulting Numbers: [72, 85, 25] Generated Node #2: [72, 85, 25] from Operation: 89-64=25 Current State: 12:[72, 85, 25], Operations: ['89-64=25'] Exploring Operation: 85-72=13, Resulting Numbers: [25, 13] Generated Node #3: [25, 13] from Operation: 85-72=13 Current State: 12:[25, 13], Operations: ['89-64=25', '85-72=13'] Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[89, 64, 72, 85], Operations: [] Exploring Operation: 85-72=13, Resulting Numbers: [89, 64, 13] Generated Node #0,0: 12:[89, 64, 13] Operation: 85-72=13 Exploring Operation: 89-85=4, Resulting Numbers: [64, 72, 4] Generated Node #0,1: 12:[64, 72, 4] Operation: 89-85=4 Exploring Operation: 89-72=17, Resulting Numbers: [64, 85, 17] Generated Node #0,2: 12:[64, 85, 17] Operation: 89-72=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[64, 72, 4], Operations: ['89-85=4'] Exploring Operation: 72/4=18, Resulting Numbers: [64, 18] Generated Node #0,1,0: 12:[64, 18] Operation: 72/4=18 Exploring Operation: 64/4=16, Resulting Numbers: [72, 16] Generated Node #0,1,1: 12:[72, 16] Operation: 64/4=16 Exploring Operation: 72-64=8, Resulting Numbers: [4, 8] Generated Node #0,1,2: 12:[4, 8] Operation: 72-64=8 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 12:[4, 8], Operations: ['89-85=4', '72-64=8'] Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[89, 64, 72, 85], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [64, 72, 4] Generated Node #0,1: 12:[64, 72, 4] Operation: 89-85=4 Moving to Node #0,1 Current State: 12:[64, 72, 4], Operations: ['89-85=4'] Exploring Operation: 72-64=8, Resulting Numbers: [4, 8] Generated Node #0,1,2: 12:[4, 8] Operation: 72-64=8 Moving to Node #0,1,2 Current State: 12:[4, 8], Operations: ['89-85=4', '72-64=8'] Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 2, 68, 47, 52 ]
94
[ "68-47=21", "2*21=42", "52+42=94" ]
Current State: 94:[2, 68, 47, 52], Operations: [] Exploring Operation: 68-47=21, Resulting Numbers: [2, 52, 21] Generated Node #2: [2, 52, 21] from Operation: 68-47=21 Current State: 94:[2, 52, 21], Operations: ['68-47=21'] Exploring Operation: 2*21=42, Resulting Numbers: [52, 42] Generated Node #3: [52, 42] from Operation: 2*21=42 Current State: 94:[52, 42], Operations: ['68-47=21', '2*21=42'] Exploring Operation: 52+42=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[2, 68, 47, 52], Operations: [] Exploring Operation: 68/2=34, Resulting Numbers: [47, 52, 34] Generated Node #0,0: 94:[47, 52, 34] Operation: 68/2=34 Exploring Operation: 68-2=66, Resulting Numbers: [47, 52, 66] Generated Node #0,1: 94:[47, 52, 66] Operation: 68-2=66 Exploring Operation: 68-52=16, Resulting Numbers: [2, 47, 16] Generated Node #0,2: 94:[2, 47, 16] Operation: 68-52=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[2, 47, 16], Operations: ['68-52=16'] Exploring Operation: 16-2=14, Resulting Numbers: [47, 14] Generated Node #0,2,0: 94:[47, 14] Operation: 16-2=14 Exploring Operation: 2*47=94, Resulting Numbers: [16, 94] Generated Node #0,2,1: 94:[16, 94] Operation: 2*47=94 Exploring Operation: 16/2=8, Resulting Numbers: [47, 8] Generated Node #0,2,2: 94:[47, 8] Operation: 16/2=8 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 94:[47, 8], Operations: ['68-52=16', '16/2=8'] Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,94 unequal: No Solution Exploring Operation: 47+8=55, Resulting Numbers: [55] 55,94 unequal: No Solution Exploring Operation: 47*8=376, Resulting Numbers: [376] 376,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 94:[47, 14], Operations: ['68-52=16', '16-2=14'] Exploring Operation: 47+14=61, Resulting Numbers: [61] 61,94 unequal: No Solution Exploring Operation: 47*14=658, Resulting Numbers: [658] 658,94 unequal: No Solution Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 94:[16, 94], Operations: ['68-52=16', '2*47=94'] Exploring Operation: 94-16=78, Resulting Numbers: [78] 78,94 unequal: No Solution Exploring Operation: 16+94=110, Resulting Numbers: [110] 110,94 unequal: No Solution Exploring Operation: 16*94=1504, Resulting Numbers: [1504] 1504,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[47, 52, 34], Operations: ['68/2=34'] Exploring Operation: 52+34=86, Resulting Numbers: [47, 86] Generated Node #0,0,0: 94:[47, 86] Operation: 52+34=86 Exploring Operation: 47-34=13, Resulting Numbers: [52, 13] Generated Node #0,0,1: 94:[52, 13] Operation: 47-34=13 Exploring Operation: 52-47=5, Resulting Numbers: [34, 5] Generated Node #0,0,2: 94:[34, 5] Operation: 52-47=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[47, 86], Operations: ['68/2=34', '52+34=86'] Exploring Operation: 47*86=4042, Resulting Numbers: [4042] 4042,94 unequal: No Solution Exploring Operation: 47+86=133, Resulting Numbers: [133] 133,94 unequal: No Solution Exploring Operation: 86-47=39, Resulting Numbers: [39] 39,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[52, 13], Operations: ['68/2=34', '47-34=13'] Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,94 unequal: No Solution Exploring Operation: 52+13=65, Resulting Numbers: [65] 65,94 unequal: No Solution Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 94:[34, 5], Operations: ['68/2=34', '52-47=5'] Exploring Operation: 34+5=39, Resulting Numbers: [39] 39,94 unequal: No Solution Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,94 unequal: No Solution Exploring Operation: 34*5=170, Resulting Numbers: [170] 170,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[47, 52, 66], Operations: ['68-2=66'] Exploring Operation: 52-47=5, Resulting Numbers: [66, 5] Generated Node #0,1,0: 94:[66, 5] Operation: 52-47=5 Exploring Operation: 66-52=14, Resulting Numbers: [47, 14] Generated Node #0,1,1: 94:[47, 14] Operation: 66-52=14 Exploring Operation: 66-47=19, Resulting Numbers: [52, 19] Generated Node #0,1,2: 94:[52, 19] Operation: 66-47=19 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[47, 14], Operations: ['68-2=66', '66-52=14'] Exploring Operation: 47+14=61, Resulting Numbers: [61] 61,94 unequal: No Solution Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,94 unequal: No Solution Exploring Operation: 47*14=658, Resulting Numbers: [658] 658,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[66, 5], Operations: ['68-2=66', '52-47=5'] Exploring Operation: 66*5=330, Resulting Numbers: [330] 330,94 unequal: No Solution Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,94 unequal: No Solution Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 94:[52, 19], Operations: ['68-2=66', '66-47=19'] Exploring Operation: 52*19=988, Resulting Numbers: [988] 988,94 unequal: No Solution Exploring Operation: 52+19=71, Resulting Numbers: [71] 71,94 unequal: No Solution Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 24, 35, 87, 49 ]
97
[ "24+35=59", "87-49=38", "59+38=97" ]
Current State: 97:[24, 35, 87, 49], Operations: [] Exploring Operation: 24+35=59, Resulting Numbers: [87, 49, 59] Generated Node #2: [87, 49, 59] from Operation: 24+35=59 Current State: 97:[87, 49, 59], Operations: ['24+35=59'] Exploring Operation: 87-49=38, Resulting Numbers: [59, 38] Generated Node #3: [59, 38] from Operation: 87-49=38 Current State: 97:[59, 38], Operations: ['24+35=59', '87-49=38'] Exploring Operation: 59+38=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[24, 35, 87, 49], Operations: [] Exploring Operation: 24+35=59, Resulting Numbers: [87, 49, 59] Generated Node #0,0: 97:[87, 49, 59] Operation: 24+35=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[87, 49, 59], Operations: ['24+35=59'] Exploring Operation: 49+59=108, Resulting Numbers: [87, 108] Generated Node #0,0,0: 97:[87, 108] Operation: 49+59=108 Moving to Node #0,0,0 Current State: 97:[87, 108], Operations: ['24+35=59', '49+59=108'] Exploring Operation: 108-87=21, Resulting Numbers: [21] 21,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 10, 89, 74, 68 ]
43
[ "10+89=99", "74+68=142", "142-99=43" ]
Current State: 43:[10, 89, 74, 68], Operations: [] Exploring Operation: 10+89=99, Resulting Numbers: [74, 68, 99] Generated Node #2: [74, 68, 99] from Operation: 10+89=99 Current State: 43:[74, 68, 99], Operations: ['10+89=99'] Exploring Operation: 74+68=142, Resulting Numbers: [99, 142] Generated Node #3: [99, 142] from Operation: 74+68=142 Current State: 43:[99, 142], Operations: ['10+89=99', '74+68=142'] Exploring Operation: 142-99=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[10, 89, 74, 68], Operations: [] Exploring Operation: 89-74=15, Resulting Numbers: [10, 68, 15] Generated Node #0,0: 43:[10, 68, 15] Operation: 89-74=15 Exploring Operation: 89-68=21, Resulting Numbers: [10, 74, 21] Generated Node #0,1: 43:[10, 74, 21] Operation: 89-68=21 Exploring Operation: 89-10=79, Resulting Numbers: [74, 68, 79] Generated Node #0,2: 43:[74, 68, 79] Operation: 89-10=79 Exploring Operation: 74-10=64, Resulting Numbers: [89, 68, 64] Generated Node #0,3: 43:[89, 68, 64] Operation: 74-10=64 Moving to Node #0,0 Current State: 43:[10, 68, 15], Operations: ['89-74=15'] Exploring Operation: 68-10=58, Resulting Numbers: [15, 58] Generated Node #0,0,0: 43:[15, 58] Operation: 68-10=58 Exploring Operation: 68-15=53, Resulting Numbers: [10, 53] Generated Node #0,0,1: 43:[10, 53] Operation: 68-15=53 Exploring Operation: 10+15=25, Resulting Numbers: [68, 25] Generated Node #0,0,2: 43:[68, 25] Operation: 10+15=25 Exploring Operation: 10+68=78, Resulting Numbers: [15, 78] Generated Node #0,0,3: 43:[15, 78] Operation: 10+68=78 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[15, 58], Operations: ['89-74=15', '68-10=58'] Exploring Operation: 58-15=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[10, 89, 74, 68], Operations: [] Exploring Operation: 89-74=15, Resulting Numbers: [10, 68, 15] Generated Node #0,0: 43:[10, 68, 15] Operation: 89-74=15 Moving to Node #0,0 Current State: 43:[10, 68, 15], Operations: ['89-74=15'] Exploring Operation: 68-10=58, Resulting Numbers: [15, 58] Generated Node #0,0,0: 43:[15, 58] Operation: 68-10=58 Moving to Node #0,0,0 Current State: 43:[15, 58], Operations: ['89-74=15', '68-10=58'] Exploring Operation: 58-15=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 69, 35, 19, 42 ]
95
[ "69-35=34", "19+42=61", "34+61=95" ]
Current State: 95:[69, 35, 19, 42], Operations: [] Exploring Operation: 69-35=34, Resulting Numbers: [19, 42, 34] Generated Node #2: [19, 42, 34] from Operation: 69-35=34 Current State: 95:[19, 42, 34], Operations: ['69-35=34'] Exploring Operation: 19+42=61, Resulting Numbers: [34, 61] Generated Node #3: [34, 61] from Operation: 19+42=61 Current State: 95:[34, 61], Operations: ['69-35=34', '19+42=61'] Exploring Operation: 34+61=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[69, 35, 19, 42], Operations: [] Exploring Operation: 69-42=27, Resulting Numbers: [35, 19, 27] Generated Node #0,0: 95:[35, 19, 27] Operation: 69-42=27 Moving to Node #0,0 Current State: 95:[35, 19, 27], Operations: ['69-42=27'] Exploring Operation: 35-27=8, Resulting Numbers: [19, 8] Generated Node #0,0,0: 95:[19, 8] Operation: 35-27=8 Moving to Node #0,0,0 Current State: 95:[19, 8], Operations: ['69-42=27', '35-27=8'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,95 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 48, 53, 52, 50 ]
55
[ "48+52=100", "100/50=2", "53+2=55" ]
Current State: 55:[48, 53, 52, 50], Operations: [] Exploring Operation: 48+52=100, Resulting Numbers: [53, 50, 100] Generated Node #2: [53, 50, 100] from Operation: 48+52=100 Current State: 55:[53, 50, 100], Operations: ['48+52=100'] Exploring Operation: 100/50=2, Resulting Numbers: [53, 2] Generated Node #3: [53, 2] from Operation: 100/50=2 Current State: 55:[53, 2], Operations: ['48+52=100', '100/50=2'] Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[48, 53, 52, 50], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [48, 52, 3] Generated Node #0,0: 55:[48, 52, 3] Operation: 53-50=3 Exploring Operation: 52-50=2, Resulting Numbers: [48, 53, 2] Generated Node #0,1: 55:[48, 53, 2] Operation: 52-50=2 Exploring Operation: 53-48=5, Resulting Numbers: [52, 50, 5] Generated Node #0,2: 55:[52, 50, 5] Operation: 53-48=5 Exploring Operation: 52-48=4, Resulting Numbers: [53, 50, 4] Generated Node #0,3: 55:[53, 50, 4] Operation: 52-48=4 Exploring Operation: 50-48=2, Resulting Numbers: [53, 52, 2] Generated Node #0,4: 55:[53, 52, 2] Operation: 50-48=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[52, 50, 5], Operations: ['53-48=5'] Exploring Operation: 52-50=2, Resulting Numbers: [5, 2] Generated Node #0,2,0: 55:[5, 2] Operation: 52-50=2 Exploring Operation: 52+5=57, Resulting Numbers: [50, 57] Generated Node #0,2,1: 55:[50, 57] Operation: 52+5=57 Exploring Operation: 52-5=47, Resulting Numbers: [50, 47] Generated Node #0,2,2: 55:[50, 47] Operation: 52-5=47 Exploring Operation: 50+5=55, Resulting Numbers: [52, 55] Generated Node #0,2,3: 55:[52, 55] Operation: 50+5=55 Exploring Operation: 50/5=10, Resulting Numbers: [52, 10] Generated Node #0,2,4: 55:[52, 10] Operation: 50/5=10 Moving to Node #0,2,0 Current State: 55:[5, 2], Operations: ['53-48=5', '52-50=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,55 unequal: No Solution Moving to Node #0,2,3 Current State: 55:[52, 55], Operations: ['53-48=5', '50+5=55'] Exploring Operation: 52+55=107, Resulting Numbers: [107] 107,55 unequal: No Solution Exploring Operation: 52*55=2860, Resulting Numbers: [2860] 2860,55 unequal: No Solution Exploring Operation: 55-52=3, Resulting Numbers: [3] 3,55 unequal: No Solution Moving to Node #0,2,4 Current State: 55:[52, 10], Operations: ['53-48=5', '50/5=10'] Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 52*10=520, Resulting Numbers: [520] 520,55 unequal: No Solution Exploring Operation: 52+10=62, Resulting Numbers: [62] 62,55 unequal: No Solution Moving to Node #0,2,1 Current State: 55:[50, 57], Operations: ['53-48=5', '52+5=57'] Exploring Operation: 50*57=2850, Resulting Numbers: [2850] 2850,55 unequal: No Solution Exploring Operation: 57-50=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 50+57=107, Resulting Numbers: [107] 107,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[50, 47], Operations: ['53-48=5', '52-5=47'] Exploring Operation: 50+47=97, Resulting Numbers: [97] 97,55 unequal: No Solution Exploring Operation: 50*47=2350, Resulting Numbers: [2350] 2350,55 unequal: No Solution Exploring Operation: 50-47=3, Resulting Numbers: [3] 3,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 55:[53, 50, 4], Operations: ['52-48=4'] Exploring Operation: 50+4=54, Resulting Numbers: [53, 54] Generated Node #0,3,0: 55:[53, 54] Operation: 50+4=54 Exploring Operation: 53-50=3, Resulting Numbers: [4, 3] Generated Node #0,3,1: 55:[4, 3] Operation: 53-50=3 Exploring Operation: 53+4=57, Resulting Numbers: [50, 57] Generated Node #0,3,2: 55:[50, 57] Operation: 53+4=57 Exploring Operation: 53-4=49, Resulting Numbers: [50, 49] Generated Node #0,3,3: 55:[50, 49] Operation: 53-4=49 Exploring Operation: 50-4=46, Resulting Numbers: [53, 46] Generated Node #0,3,4: 55:[53, 46] Operation: 50-4=46 Moving to Node #0,3,0 Current State: 55:[53, 54], Operations: ['52-48=4', '50+4=54'] Exploring Operation: 54-53=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 53+54=107, Resulting Numbers: [107] 107,55 unequal: No Solution Exploring Operation: 53*54=2862, Resulting Numbers: [2862] 2862,55 unequal: No Solution Moving to Node #0,3,1 Current State: 55:[4, 3], Operations: ['52-48=4', '53-50=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,55 unequal: No Solution Moving to Node #0,3,2 Current State: 55:[50, 57], Operations: ['52-48=4', '53+4=57'] Exploring Operation: 57-50=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 50*57=2850, Resulting Numbers: [2850] 2850,55 unequal: No Solution Exploring Operation: 50+57=107, Resulting Numbers: [107] 107,55 unequal: No Solution Moving to Node #0,3,3 Current State: 55:[50, 49], Operations: ['52-48=4', '53-4=49'] Exploring Operation: 50-49=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 50+49=99, Resulting Numbers: [99] 99,55 unequal: No Solution Exploring Operation: 50*49=2450, Resulting Numbers: [2450] 2450,55 unequal: No Solution Moving to Node #0,3,4 Current State: 55:[53, 46], Operations: ['52-48=4', '50-4=46'] Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 53*46=2438, Resulting Numbers: [2438] 2438,55 unequal: No Solution Exploring Operation: 53+46=99, Resulting Numbers: [99] 99,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 55:[53, 52, 2], Operations: ['50-48=2'] Exploring Operation: 52+2=54, Resulting Numbers: [53, 54] Generated Node #0,4,0: 55:[53, 54] Operation: 52+2=54 Exploring Operation: 52-2=50, Resulting Numbers: [53, 50] Generated Node #0,4,1: 55:[53, 50] Operation: 52-2=50 Exploring Operation: 53+2=55, Resulting Numbers: [52, 55] Generated Node #0,4,2: 55:[52, 55] Operation: 53+2=55 Exploring Operation: 53-52=1, Resulting Numbers: [2, 1] Generated Node #0,4,3: 55:[2, 1] Operation: 53-52=1 Exploring Operation: 53-2=51, Resulting Numbers: [52, 51] Generated Node #0,4,4: 55:[52, 51] Operation: 53-2=51 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 55:[53, 54], Operations: ['50-48=2', '52+2=54'] Exploring Operation: 53*54=2862, Resulting Numbers: [2862] 2862,55 unequal: No Solution Exploring Operation: 53+54=107, Resulting Numbers: [107] 107,55 unequal: No Solution Exploring Operation: 54-53=1, Resulting Numbers: [1] 1,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 55:[52, 55], Operations: ['50-48=2', '53+2=55'] Exploring Operation: 55-52=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 52*55=2860, Resulting Numbers: [2860] 2860,55 unequal: No Solution Exploring Operation: 52+55=107, Resulting Numbers: [107] 107,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 55:[53, 50], Operations: ['50-48=2', '52-2=50'] Exploring Operation: 53+50=103, Resulting Numbers: [103] 103,55 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 53*50=2650, Resulting Numbers: [2650] 2650,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 55:[2, 1], Operations: ['50-48=2', '53-52=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 55:[52, 51], Operations: ['50-48=2', '53-2=51'] Exploring Operation: 52*51=2652, Resulting Numbers: [2652] 2652,55 unequal: No Solution Exploring Operation: 52+51=103, Resulting Numbers: [103] 103,55 unequal: No Solution Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[48, 52, 3], Operations: ['53-50=3'] Exploring Operation: 52-48=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 55:[3, 4] Operation: 52-48=4 Exploring Operation: 52+3=55, Resulting Numbers: [48, 55] Generated Node #0,0,1: 55:[48, 55] Operation: 52+3=55 Exploring Operation: 48-3=45, Resulting Numbers: [52, 45] Generated Node #0,0,2: 55:[52, 45] Operation: 48-3=45 Exploring Operation: 48+3=51, Resulting Numbers: [52, 51] Generated Node #0,0,3: 55:[52, 51] Operation: 48+3=51 Exploring Operation: 48/3=16, Resulting Numbers: [52, 16] Generated Node #0,0,4: 55:[52, 16] Operation: 48/3=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[3, 4], Operations: ['53-50=3', '52-48=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 55:[48, 55], Operations: ['53-50=3', '52+3=55'] Exploring Operation: 48+55=103, Resulting Numbers: [103] 103,55 unequal: No Solution Exploring Operation: 48*55=2640, Resulting Numbers: [2640] 2640,55 unequal: No Solution Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 55:[52, 51], Operations: ['53-50=3', '48+3=51'] Exploring Operation: 52*51=2652, Resulting Numbers: [2652] 2652,55 unequal: No Solution Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 52+51=103, Resulting Numbers: [103] 103,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 55:[52, 16], Operations: ['53-50=3', '48/3=16'] Exploring Operation: 52*16=832, Resulting Numbers: [832] 832,55 unequal: No Solution Exploring Operation: 52+16=68, Resulting Numbers: [68] 68,55 unequal: No Solution Exploring Operation: 52-16=36, Resulting Numbers: [36] 36,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 55:[52, 45], Operations: ['53-50=3', '48-3=45'] Exploring Operation: 52*45=2340, Resulting Numbers: [2340] 2340,55 unequal: No Solution Exploring Operation: 52+45=97, Resulting Numbers: [97] 97,55 unequal: No Solution Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[48, 53, 2], Operations: ['52-50=2'] Exploring Operation: 53-48=5, Resulting Numbers: [2, 5] Generated Node #0,1,0: 55:[2, 5] Operation: 53-48=5 Exploring Operation: 48+2=50, Resulting Numbers: [53, 50] Generated Node #0,1,1: 55:[53, 50] Operation: 48+2=50 Exploring Operation: 53-2=51, Resulting Numbers: [48, 51] Generated Node #0,1,2: 55:[48, 51] Operation: 53-2=51 Exploring Operation: 48-2=46, Resulting Numbers: [53, 46] Generated Node #0,1,3: 55:[53, 46] Operation: 48-2=46 Exploring Operation: 53+2=55, Resulting Numbers: [48, 55] Generated Node #0,1,4: 55:[48, 55] Operation: 53+2=55 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[2, 5], Operations: ['52-50=2', '53-48=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 55:[53, 50], Operations: ['52-50=2', '48+2=50'] Exploring Operation: 53*50=2650, Resulting Numbers: [2650] 2650,55 unequal: No Solution Exploring Operation: 53+50=103, Resulting Numbers: [103] 103,55 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 55:[48, 55], Operations: ['52-50=2', '53+2=55'] Exploring Operation: 48+55=103, Resulting Numbers: [103] 103,55 unequal: No Solution Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 48*55=2640, Resulting Numbers: [2640] 2640,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 55:[48, 51], Operations: ['52-50=2', '53-2=51'] Exploring Operation: 48+51=99, Resulting Numbers: [99] 99,55 unequal: No Solution Exploring Operation: 48*51=2448, Resulting Numbers: [2448] 2448,55 unequal: No Solution Exploring Operation: 51-48=3, Resulting Numbers: [3] 3,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 55:[53, 46], Operations: ['52-50=2', '48-2=46'] Exploring Operation: 53+46=99, Resulting Numbers: [99] 99,55 unequal: No Solution Exploring Operation: 53*46=2438, Resulting Numbers: [2438] 2438,55 unequal: No Solution Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 69, 26, 73, 5 ]
27
[ "69+26=95", "73-5=68", "95-68=27" ]
Current State: 27:[69, 26, 73, 5], Operations: [] Exploring Operation: 69+26=95, Resulting Numbers: [73, 5, 95] Generated Node #2: [73, 5, 95] from Operation: 69+26=95 Current State: 27:[73, 5, 95], Operations: ['69+26=95'] Exploring Operation: 73-5=68, Resulting Numbers: [95, 68] Generated Node #3: [95, 68] from Operation: 73-5=68 Current State: 27:[95, 68], Operations: ['69+26=95', '73-5=68'] Exploring Operation: 95-68=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[69, 26, 73, 5], Operations: [] Exploring Operation: 69-5=64, Resulting Numbers: [26, 73, 64] Generated Node #0,0: 27:[26, 73, 64] Operation: 69-5=64 Exploring Operation: 73-26=47, Resulting Numbers: [69, 5, 47] Generated Node #0,1: 27:[69, 5, 47] Operation: 73-26=47 Exploring Operation: 73-5=68, Resulting Numbers: [69, 26, 68] Generated Node #0,2: 27:[69, 26, 68] Operation: 73-5=68 Exploring Operation: 73-69=4, Resulting Numbers: [26, 5, 4] Generated Node #0,3: 27:[26, 5, 4] Operation: 73-69=4 Exploring Operation: 69-26=43, Resulting Numbers: [73, 5, 43] Generated Node #0,4: 27:[73, 5, 43] Operation: 69-26=43 Start Sub Search at level 1: Moving to Node #0,3 Current State: 27:[26, 5, 4], Operations: ['73-69=4'] Exploring Operation: 26+5=31, Resulting Numbers: [4, 31] Generated Node #0,3,0: 27:[4, 31] Operation: 26+5=31 Exploring Operation: 26-5=21, Resulting Numbers: [4, 21] Generated Node #0,3,1: 27:[4, 21] Operation: 26-5=21 Exploring Operation: 5-4=1, Resulting Numbers: [26, 1] Generated Node #0,3,2: 27:[26, 1] Operation: 5-4=1 Exploring Operation: 26+4=30, Resulting Numbers: [5, 30] Generated Node #0,3,3: 27:[5, 30] Operation: 26+4=30 Exploring Operation: 5+4=9, Resulting Numbers: [26, 9] Generated Node #0,3,4: 27:[26, 9] Operation: 5+4=9 Moving to Node #0,3,4 Current State: 27:[26, 9], Operations: ['73-69=4', '5+4=9'] Exploring Operation: 26+9=35, Resulting Numbers: [35] 35,27 unequal: No Solution Exploring Operation: 26*9=234, Resulting Numbers: [234] 234,27 unequal: No Solution Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,27 unequal: No Solution Moving to Node #0,3,2 Current State: 27:[26, 1], Operations: ['73-69=4', '5-4=1'] Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,27 unequal: No Solution Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 26+1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[69, 26, 73, 5], Operations: [] Exploring Operation: 73-69=4, Resulting Numbers: [26, 5, 4] Generated Node #0,3: 27:[26, 5, 4] Operation: 73-69=4 Moving to Node #0,3 Current State: 27:[26, 5, 4], Operations: ['73-69=4'] Exploring Operation: 5-4=1, Resulting Numbers: [26, 1] Generated Node #0,3,2: 27:[26, 1] Operation: 5-4=1 Moving to Node #0,3,2 Current State: 27:[26, 1], Operations: ['73-69=4', '5-4=1'] Exploring Operation: 26+1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 2, 23, 65, 45 ]
64
[ "2*23=46", "65+45=110", "110-46=64" ]
Current State: 64:[2, 23, 65, 45], Operations: [] Exploring Operation: 2*23=46, Resulting Numbers: [65, 45, 46] Generated Node #2: [65, 45, 46] from Operation: 2*23=46 Current State: 64:[65, 45, 46], Operations: ['2*23=46'] Exploring Operation: 65+45=110, Resulting Numbers: [46, 110] Generated Node #3: [46, 110] from Operation: 65+45=110 Current State: 64:[46, 110], Operations: ['2*23=46', '65+45=110'] Exploring Operation: 110-46=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[2, 23, 65, 45], Operations: [] Exploring Operation: 65-45=20, Resulting Numbers: [2, 23, 20] Generated Node #0,0: 64:[2, 23, 20] Operation: 65-45=20 Exploring Operation: 23+45=68, Resulting Numbers: [2, 65, 68] Generated Node #0,1: 64:[2, 65, 68] Operation: 23+45=68 Exploring Operation: 23-2=21, Resulting Numbers: [65, 45, 21] Generated Node #0,2: 64:[65, 45, 21] Operation: 23-2=21 Exploring Operation: 45-23=22, Resulting Numbers: [2, 65, 22] Generated Node #0,3: 64:[2, 65, 22] Operation: 45-23=22 Moving to Node #0,1 Current State: 64:[2, 65, 68], Operations: ['23+45=68'] Exploring Operation: 68/2=34, Resulting Numbers: [65, 34] Generated Node #0,1,0: 64:[65, 34] Operation: 68/2=34 Exploring Operation: 65-2=63, Resulting Numbers: [68, 63] Generated Node #0,1,1: 64:[68, 63] Operation: 65-2=63 Exploring Operation: 68-65=3, Resulting Numbers: [2, 3] Generated Node #0,1,2: 64:[2, 3] Operation: 68-65=3 Exploring Operation: 68-2=66, Resulting Numbers: [65, 66] Generated Node #0,1,3: 64:[65, 66] Operation: 68-2=66 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 64:[2, 3], Operations: ['23+45=68', '68-65=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,64 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 64:[65, 34], Operations: ['23+45=68', '68/2=34'] Exploring Operation: 65+34=99, Resulting Numbers: [99] 99,64 unequal: No Solution Exploring Operation: 65-34=31, Resulting Numbers: [31] 31,64 unequal: No Solution Exploring Operation: 65*34=2210, Resulting Numbers: [2210] 2210,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 64:[65, 66], Operations: ['23+45=68', '68-2=66'] Exploring Operation: 66-65=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 65+66=131, Resulting Numbers: [131] 131,64 unequal: No Solution Exploring Operation: 65*66=4290, Resulting Numbers: [4290] 4290,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 64:[68, 63], Operations: ['23+45=68', '65-2=63'] Exploring Operation: 68+63=131, Resulting Numbers: [131] 131,64 unequal: No Solution Exploring Operation: 68-63=5, Resulting Numbers: [5] 5,64 unequal: No Solution Exploring Operation: 68*63=4284, Resulting Numbers: [4284] 4284,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 64:[2, 65, 22], Operations: ['45-23=22'] Exploring Operation: 22/2=11, Resulting Numbers: [65, 11] Generated Node #0,3,0: 64:[65, 11] Operation: 22/2=11 Exploring Operation: 22-2=20, Resulting Numbers: [65, 20] Generated Node #0,3,1: 64:[65, 20] Operation: 22-2=20 Exploring Operation: 65-2=63, Resulting Numbers: [22, 63] Generated Node #0,3,2: 64:[22, 63] Operation: 65-2=63 Exploring Operation: 2+65=67, Resulting Numbers: [22, 67] Generated Node #0,3,3: 64:[22, 67] Operation: 2+65=67 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 64:[65, 11], Operations: ['45-23=22', '22/2=11'] Exploring Operation: 65+11=76, Resulting Numbers: [76] 76,64 unequal: No Solution Exploring Operation: 65*11=715, Resulting Numbers: [715] 715,64 unequal: No Solution Exploring Operation: 65-11=54, Resulting Numbers: [54] 54,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 64:[65, 20], Operations: ['45-23=22', '22-2=20'] Exploring Operation: 65+20=85, Resulting Numbers: [85] 85,64 unequal: No Solution Exploring Operation: 65-20=45, Resulting Numbers: [45] 45,64 unequal: No Solution Exploring Operation: 65*20=1300, Resulting Numbers: [1300] 1300,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 64:[22, 63], Operations: ['45-23=22', '65-2=63'] Exploring Operation: 22+63=85, Resulting Numbers: [85] 85,64 unequal: No Solution Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,64 unequal: No Solution Exploring Operation: 22*63=1386, Resulting Numbers: [1386] 1386,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 64:[22, 67], Operations: ['45-23=22', '2+65=67'] Exploring Operation: 67-22=45, Resulting Numbers: [45] 45,64 unequal: No Solution Exploring Operation: 22*67=1474, Resulting Numbers: [1474] 1474,64 unequal: No Solution Exploring Operation: 22+67=89, Resulting Numbers: [89] 89,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 64:[2, 23, 20], Operations: ['65-45=20'] Exploring Operation: 20/2=10, Resulting Numbers: [23, 10] Generated Node #0,0,0: 64:[23, 10] Operation: 20/2=10 Exploring Operation: 20-2=18, Resulting Numbers: [23, 18] Generated Node #0,0,1: 64:[23, 18] Operation: 20-2=18 Exploring Operation: 23-2=21, Resulting Numbers: [20, 21] Generated Node #0,0,2: 64:[20, 21] Operation: 23-2=21 Exploring Operation: 23-20=3, Resulting Numbers: [2, 3] Generated Node #0,0,3: 64:[2, 3] Operation: 23-20=3 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 64:[2, 3], Operations: ['65-45=20', '23-20=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,64 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[23, 10], Operations: ['65-45=20', '20/2=10'] Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,64 unequal: No Solution Exploring Operation: 23*10=230, Resulting Numbers: [230] 230,64 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 64:[23, 18], Operations: ['65-45=20', '20-2=18'] Exploring Operation: 23*18=414, Resulting Numbers: [414] 414,64 unequal: No Solution Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,64 unequal: No Solution Exploring Operation: 23+18=41, Resulting Numbers: [41] 41,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 64:[20, 21], Operations: ['65-45=20', '23-2=21'] Exploring Operation: 20*21=420, Resulting Numbers: [420] 420,64 unequal: No Solution Exploring Operation: 20+21=41, Resulting Numbers: [41] 41,64 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 64:[65, 45, 21], Operations: ['23-2=21'] Exploring Operation: 45-21=24, Resulting Numbers: [65, 24] Generated Node #0,2,0: 64:[65, 24] Operation: 45-21=24 Exploring Operation: 45+21=66, Resulting Numbers: [65, 66] Generated Node #0,2,1: 64:[65, 66] Operation: 45+21=66 Exploring Operation: 65-21=44, Resulting Numbers: [45, 44] Generated Node #0,2,2: 64:[45, 44] Operation: 65-21=44 Exploring Operation: 65-45=20, Resulting Numbers: [21, 20] Generated Node #0,2,3: 64:[21, 20] Operation: 65-45=20 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 64:[65, 66], Operations: ['23-2=21', '45+21=66'] Exploring Operation: 65*66=4290, Resulting Numbers: [4290] 4290,64 unequal: No Solution Exploring Operation: 66-65=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 65+66=131, Resulting Numbers: [131] 131,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 64:[65, 24], Operations: ['23-2=21', '45-21=24'] Exploring Operation: 65+24=89, Resulting Numbers: [89] 89,64 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,64 unequal: No Solution Exploring Operation: 65*24=1560, Resulting Numbers: [1560] 1560,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 64:[21, 20], Operations: ['23-2=21', '65-45=20'] Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 21*20=420, Resulting Numbers: [420] 420,64 unequal: No Solution Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 64:[45, 44], Operations: ['23-2=21', '65-21=44'] Exploring Operation: 45+44=89, Resulting Numbers: [89] 89,64 unequal: No Solution Exploring Operation: 45*44=1980, Resulting Numbers: [1980] 1980,64 unequal: No Solution Exploring Operation: 45-44=1, Resulting Numbers: [1] 1,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 6, 59, 54, 42 ]
72
[ "59-54=5", "6*5=30", "42+30=72" ]
Current State: 72:[6, 59, 54, 42], Operations: [] Exploring Operation: 59-54=5, Resulting Numbers: [6, 42, 5] Generated Node #2: [6, 42, 5] from Operation: 59-54=5 Current State: 72:[6, 42, 5], Operations: ['59-54=5'] Exploring Operation: 6*5=30, Resulting Numbers: [42, 30] Generated Node #3: [42, 30] from Operation: 6*5=30 Current State: 72:[42, 30], Operations: ['59-54=5', '6*5=30'] Exploring Operation: 42+30=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[6, 59, 54, 42], Operations: [] Exploring Operation: 54-42=12, Resulting Numbers: [6, 59, 12] Generated Node #0,0: 72:[6, 59, 12] Operation: 54-42=12 Exploring Operation: 59-54=5, Resulting Numbers: [6, 42, 5] Generated Node #0,1: 72:[6, 42, 5] Operation: 59-54=5 Exploring Operation: 54/6=9, Resulting Numbers: [59, 42, 9] Generated Node #0,2: 72:[59, 42, 9] Operation: 54/6=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[6, 42, 5], Operations: ['59-54=5'] Exploring Operation: 42/6=7, Resulting Numbers: [5, 7] Generated Node #0,1,0: 72:[5, 7] Operation: 42/6=7 Exploring Operation: 42-5=37, Resulting Numbers: [6, 37] Generated Node #0,1,1: 72:[6, 37] Operation: 42-5=37 Exploring Operation: 42-6=36, Resulting Numbers: [5, 36] Generated Node #0,1,2: 72:[5, 36] Operation: 42-6=36 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 72:[6, 37], Operations: ['59-54=5', '42-5=37'] Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,72 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,72 unequal: No Solution Exploring Operation: 6*37=222, Resulting Numbers: [222] 222,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 72:[5, 36], Operations: ['59-54=5', '42-6=36'] Exploring Operation: 5*36=180, Resulting Numbers: [180] 180,72 unequal: No Solution Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,72 unequal: No Solution Exploring Operation: 5+36=41, Resulting Numbers: [41] 41,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 72:[5, 7], Operations: ['59-54=5', '42/6=7'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,72 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[6, 59, 12], Operations: ['54-42=12'] Exploring Operation: 59-12=47, Resulting Numbers: [6, 47] Generated Node #0,0,0: 72:[6, 47] Operation: 59-12=47 Exploring Operation: 6+59=65, Resulting Numbers: [12, 65] Generated Node #0,0,1: 72:[12, 65] Operation: 6+59=65 Exploring Operation: 59+12=71, Resulting Numbers: [6, 71] Generated Node #0,0,2: 72:[6, 71] Operation: 59+12=71 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 72:[6, 71], Operations: ['54-42=12', '59+12=71'] Exploring Operation: 6*71=426, Resulting Numbers: [426] 426,72 unequal: No Solution Exploring Operation: 6+71=77, Resulting Numbers: [77] 77,72 unequal: No Solution Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 72:[12, 65], Operations: ['54-42=12', '6+59=65'] Exploring Operation: 12+65=77, Resulting Numbers: [77] 77,72 unequal: No Solution Exploring Operation: 65-12=53, Resulting Numbers: [53] 53,72 unequal: No Solution Exploring Operation: 12*65=780, Resulting Numbers: [780] 780,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[6, 47], Operations: ['54-42=12', '59-12=47'] Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,72 unequal: No Solution Exploring Operation: 6*47=282, Resulting Numbers: [282] 282,72 unequal: No Solution Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[59, 42, 9], Operations: ['54/6=9'] Exploring Operation: 42-9=33, Resulting Numbers: [59, 33] Generated Node #0,2,0: 72:[59, 33] Operation: 42-9=33 Exploring Operation: 59-42=17, Resulting Numbers: [9, 17] Generated Node #0,2,1: 72:[9, 17] Operation: 59-42=17 Exploring Operation: 59+9=68, Resulting Numbers: [42, 68] Generated Node #0,2,2: 72:[42, 68] Operation: 59+9=68 Moving to Node #0,2,1 Current State: 72:[9, 17], Operations: ['54/6=9', '59-42=17'] Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,72 unequal: No Solution Exploring Operation: 9*17=153, Resulting Numbers: [153] 153,72 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[42, 68], Operations: ['54/6=9', '59+9=68'] Exploring Operation: 42*68=2856, Resulting Numbers: [2856] 2856,72 unequal: No Solution Exploring Operation: 42+68=110, Resulting Numbers: [110] 110,72 unequal: No Solution Exploring Operation: 68-42=26, Resulting Numbers: [26] 26,72 unequal: No Solution Moving to Node #0,2,0 Current State: 72:[59, 33], Operations: ['54/6=9', '42-9=33'] Exploring Operation: 59+33=92, Resulting Numbers: [92] 92,72 unequal: No Solution Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,72 unequal: No Solution Exploring Operation: 59*33=1947, Resulting Numbers: [1947] 1947,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 80, 41, 33, 72 ]
16
[ "80+41=121", "33+72=105", "121-105=16" ]
Current State: 16:[80, 41, 33, 72], Operations: [] Exploring Operation: 80+41=121, Resulting Numbers: [33, 72, 121] Generated Node #2: [33, 72, 121] from Operation: 80+41=121 Current State: 16:[33, 72, 121], Operations: ['80+41=121'] Exploring Operation: 33+72=105, Resulting Numbers: [121, 105] Generated Node #3: [121, 105] from Operation: 33+72=105 Current State: 16:[121, 105], Operations: ['80+41=121', '33+72=105'] Exploring Operation: 121-105=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[80, 41, 33, 72], Operations: [] Exploring Operation: 80-72=8, Resulting Numbers: [41, 33, 8] Generated Node #0,0: 16:[41, 33, 8] Operation: 80-72=8 Moving to Node #0,0 Current State: 16:[41, 33, 8], Operations: ['80-72=8'] Exploring Operation: 41-33=8, Resulting Numbers: [8, 8] Generated Node #0,0,0: 16:[8, 8] Operation: 41-33=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[8, 8], Operations: ['80-72=8', '41-33=8'] Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[80, 41, 33, 72], Operations: [] Exploring Operation: 80-72=8, Resulting Numbers: [41, 33, 8] Generated Node #0,0: 16:[41, 33, 8] Operation: 80-72=8 Moving to Node #0,0 Current State: 16:[41, 33, 8], Operations: ['80-72=8'] Exploring Operation: 41-33=8, Resulting Numbers: [8, 8] Generated Node #0,0,0: 16:[8, 8] Operation: 41-33=8 Moving to Node #0,0,0 Current State: 16:[8, 8], Operations: ['80-72=8', '41-33=8'] Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 77, 76, 86, 75 ]
48
[ "77-75=2", "76/2=38", "86-38=48" ]
Current State: 48:[77, 76, 86, 75], Operations: [] Exploring Operation: 77-75=2, Resulting Numbers: [76, 86, 2] Generated Node #2: [76, 86, 2] from Operation: 77-75=2 Current State: 48:[76, 86, 2], Operations: ['77-75=2'] Exploring Operation: 76/2=38, Resulting Numbers: [86, 38] Generated Node #3: [86, 38] from Operation: 76/2=38 Current State: 48:[86, 38], Operations: ['77-75=2', '76/2=38'] Exploring Operation: 86-38=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[77, 76, 86, 75], Operations: [] Exploring Operation: 86-76=10, Resulting Numbers: [77, 75, 10] Generated Node #0,0: 48:[77, 75, 10] Operation: 86-76=10 Exploring Operation: 86-77=9, Resulting Numbers: [76, 75, 9] Generated Node #0,1: 48:[76, 75, 9] Operation: 86-77=9 Moving to Node #0,1 Current State: 48:[76, 75, 9], Operations: ['86-77=9'] Exploring Operation: 76-75=1, Resulting Numbers: [9, 1] Generated Node #0,1,0: 48:[9, 1] Operation: 76-75=1 Exploring Operation: 76-9=67, Resulting Numbers: [75, 67] Generated Node #0,1,1: 48:[75, 67] Operation: 76-9=67 Moving to Node #0,0 Current State: 48:[77, 75, 10], Operations: ['86-76=10'] Exploring Operation: 77-10=67, Resulting Numbers: [75, 67] Generated Node #0,0,0: 48:[75, 67] Operation: 77-10=67 Exploring Operation: 77-75=2, Resulting Numbers: [10, 2] Generated Node #0,0,1: 48:[10, 2] Operation: 77-75=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 48:[10, 2], Operations: ['86-76=10', '77-75=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,48 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[75, 67], Operations: ['86-76=10', '77-10=67'] Exploring Operation: 75+67=142, Resulting Numbers: [142] 142,48 unequal: No Solution Exploring Operation: 75-67=8, Resulting Numbers: [8] 8,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 48:[9, 1], Operations: ['86-77=9', '76-75=1'] Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 9*1=9, Resulting Numbers: [9] 9,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[75, 67], Operations: ['86-77=9', '76-9=67'] Exploring Operation: 75-67=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 75+67=142, Resulting Numbers: [142] 142,48 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 33, 20, 33, 18 ]
37
[ "33/33=1", "20+18=38", "38-1=37" ]
Current State: 37:[33, 20, 33, 18], Operations: [] Exploring Operation: 33/33=1, Resulting Numbers: [20, 18, 1] Generated Node #2: [20, 18, 1] from Operation: 33/33=1 Current State: 37:[20, 18, 1], Operations: ['33/33=1'] Exploring Operation: 20+18=38, Resulting Numbers: [1, 38] Generated Node #3: [1, 38] from Operation: 20+18=38 Current State: 37:[1, 38], Operations: ['33/33=1', '20+18=38'] Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[33, 20, 33, 18], Operations: [] Exploring Operation: 20+18=38, Resulting Numbers: [33, 33, 38] Generated Node #0,0: 37:[33, 33, 38] Operation: 20+18=38 Exploring Operation: 33+18=51, Resulting Numbers: [33, 20, 51] Generated Node #0,1: 37:[33, 20, 51] Operation: 33+18=51 Exploring Operation: 33+18=51, Resulting Numbers: [20, 33, 51] Generated Node #0,2: 37:[20, 33, 51] Operation: 33+18=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[33, 33, 38], Operations: ['20+18=38'] Exploring Operation: 38-33=5, Resulting Numbers: [33, 5] Generated Node #0,0,0: 37:[33, 5] Operation: 38-33=5 Exploring Operation: 38-33=5, Resulting Numbers: [33, 5] Generated Node #0,0,1: 37:[33, 5] Operation: 38-33=5 Exploring Operation: 33+33=66, Resulting Numbers: [38, 66] Generated Node #0,0,2: 37:[38, 66] Operation: 33+33=66 Moving to Node #0,0,2 Current State: 37:[38, 66], Operations: ['20+18=38', '33+33=66'] Exploring Operation: 66-38=28, Resulting Numbers: [28] 28,37 unequal: No Solution Exploring Operation: 38+66=104, Resulting Numbers: [104] 104,37 unequal: No Solution Exploring Operation: 38*66=2508, Resulting Numbers: [2508] 2508,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[33, 5], Operations: ['20+18=38', '38-33=5'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,37 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,37 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[33, 5], Operations: ['20+18=38', '38-33=5'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,37 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[33, 20, 51], Operations: ['33+18=51'] Exploring Operation: 51-20=31, Resulting Numbers: [33, 31] Generated Node #0,1,0: 37:[33, 31] Operation: 51-20=31 Exploring Operation: 51-33=18, Resulting Numbers: [20, 18] Generated Node #0,1,1: 37:[20, 18] Operation: 51-33=18 Exploring Operation: 33+20=53, Resulting Numbers: [51, 53] Generated Node #0,1,2: 37:[51, 53] Operation: 33+20=53 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 37:[33, 31], Operations: ['33+18=51', '51-20=31'] Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,37 unequal: No Solution Exploring Operation: 33-31=2, Resulting Numbers: [2] 2,37 unequal: No Solution Exploring Operation: 33*31=1023, Resulting Numbers: [1023] 1023,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 37:[51, 53], Operations: ['33+18=51', '33+20=53'] Exploring Operation: 51+53=104, Resulting Numbers: [104] 104,37 unequal: No Solution Exploring Operation: 51*53=2703, Resulting Numbers: [2703] 2703,37 unequal: No Solution Exploring Operation: 53-51=2, Resulting Numbers: [2] 2,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 37:[20, 18], Operations: ['33+18=51', '51-33=18'] Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,37 unequal: No Solution Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 37:[20, 33, 51], Operations: ['33+18=51'] Exploring Operation: 51-33=18, Resulting Numbers: [20, 18] Generated Node #0,2,0: 37:[20, 18] Operation: 51-33=18 Exploring Operation: 51-20=31, Resulting Numbers: [33, 31] Generated Node #0,2,1: 37:[33, 31] Operation: 51-20=31 Exploring Operation: 20+33=53, Resulting Numbers: [51, 53] Generated Node #0,2,2: 37:[51, 53] Operation: 20+33=53 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 37:[33, 31], Operations: ['33+18=51', '51-20=31'] Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,37 unequal: No Solution Exploring Operation: 33*31=1023, Resulting Numbers: [1023] 1023,37 unequal: No Solution Exploring Operation: 33-31=2, Resulting Numbers: [2] 2,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 37:[51, 53], Operations: ['33+18=51', '20+33=53'] Exploring Operation: 51*53=2703, Resulting Numbers: [2703] 2703,37 unequal: No Solution Exploring Operation: 53-51=2, Resulting Numbers: [2] 2,37 unequal: No Solution Exploring Operation: 51+53=104, Resulting Numbers: [104] 104,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 37:[20, 18], Operations: ['33+18=51', '51-33=18'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,37 unequal: No Solution Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 12, 18, 34, 54 ]
37
[ "54-18=36", "36/12=3", "34+3=37" ]
Current State: 37:[12, 18, 34, 54], Operations: [] Exploring Operation: 54-18=36, Resulting Numbers: [12, 34, 36] Generated Node #2: [12, 34, 36] from Operation: 54-18=36 Current State: 37:[12, 34, 36], Operations: ['54-18=36'] Exploring Operation: 36/12=3, Resulting Numbers: [34, 3] Generated Node #3: [34, 3] from Operation: 36/12=3 Current State: 37:[34, 3], Operations: ['54-18=36', '36/12=3'] Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[12, 18, 34, 54], Operations: [] Exploring Operation: 12+34=46, Resulting Numbers: [18, 54, 46] Generated Node #0,0: 37:[18, 54, 46] Operation: 12+34=46 Exploring Operation: 12+18=30, Resulting Numbers: [34, 54, 30] Generated Node #0,1: 37:[34, 54, 30] Operation: 12+18=30 Exploring Operation: 54-12=42, Resulting Numbers: [18, 34, 42] Generated Node #0,2: 37:[18, 34, 42] Operation: 54-12=42 Exploring Operation: 54-18=36, Resulting Numbers: [12, 34, 36] Generated Node #0,3: 37:[12, 34, 36] Operation: 54-18=36 Moving to Node #0,1 Current State: 37:[34, 54, 30], Operations: ['12+18=30'] Exploring Operation: 34+30=64, Resulting Numbers: [54, 64] Generated Node #0,1,0: 37:[54, 64] Operation: 34+30=64 Exploring Operation: 54-34=20, Resulting Numbers: [30, 20] Generated Node #0,1,1: 37:[30, 20] Operation: 54-34=20 Exploring Operation: 54-30=24, Resulting Numbers: [34, 24] Generated Node #0,1,2: 37:[34, 24] Operation: 54-30=24 Exploring Operation: 34-30=4, Resulting Numbers: [54, 4] Generated Node #0,1,3: 37:[54, 4] Operation: 34-30=4 Moving to Node #0,2 Current State: 37:[18, 34, 42], Operations: ['54-12=42'] Exploring Operation: 18+42=60, Resulting Numbers: [34, 60] Generated Node #0,2,0: 37:[34, 60] Operation: 18+42=60 Exploring Operation: 34-18=16, Resulting Numbers: [42, 16] Generated Node #0,2,1: 37:[42, 16] Operation: 34-18=16 Exploring Operation: 42-18=24, Resulting Numbers: [34, 24] Generated Node #0,2,2: 37:[34, 24] Operation: 42-18=24 Exploring Operation: 18+34=52, Resulting Numbers: [42, 52] Generated Node #0,2,3: 37:[42, 52] Operation: 18+34=52 Moving to Node #0,3 Current State: 37:[12, 34, 36], Operations: ['54-18=36'] Exploring Operation: 12+36=48, Resulting Numbers: [34, 48] Generated Node #0,3,0: 37:[34, 48] Operation: 12+36=48 Exploring Operation: 36-12=24, Resulting Numbers: [34, 24] Generated Node #0,3,1: 37:[34, 24] Operation: 36-12=24 Exploring Operation: 12+34=46, Resulting Numbers: [36, 46] Generated Node #0,3,2: 37:[36, 46] Operation: 12+34=46 Exploring Operation: 34-12=22, Resulting Numbers: [36, 22] Generated Node #0,3,3: 37:[36, 22] Operation: 34-12=22 Moving to Node #0,0 Current State: 37:[18, 54, 46], Operations: ['12+34=46'] Exploring Operation: 54-18=36, Resulting Numbers: [46, 36] Generated Node #0,0,0: 37:[46, 36] Operation: 54-18=36 Exploring Operation: 54/18=3, Resulting Numbers: [46, 3] Generated Node #0,0,1: 37:[46, 3] Operation: 54/18=3 Exploring Operation: 46-18=28, Resulting Numbers: [54, 28] Generated Node #0,0,2: 37:[54, 28] Operation: 46-18=28 Exploring Operation: 18+54=72, Resulting Numbers: [46, 72] Generated Node #0,0,3: 37:[46, 72] Operation: 18+54=72 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[46, 36], Operations: ['12+34=46', '54-18=36'] Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 46+36=82, Resulting Numbers: [82] 82,37 unequal: No Solution Exploring Operation: 46*36=1656, Resulting Numbers: [1656] 1656,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 37:[54, 28], Operations: ['12+34=46', '46-18=28'] Exploring Operation: 54-28=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 54+28=82, Resulting Numbers: [82] 82,37 unequal: No Solution Exploring Operation: 54*28=1512, Resulting Numbers: [1512] 1512,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[46, 3], Operations: ['12+34=46', '54/18=3'] Exploring Operation: 46+3=49, Resulting Numbers: [49] 49,37 unequal: No Solution Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,37 unequal: No Solution Exploring Operation: 46*3=138, Resulting Numbers: [138] 138,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 37:[46, 72], Operations: ['12+34=46', '18+54=72'] Exploring Operation: 46*72=3312, Resulting Numbers: [3312] 3312,37 unequal: No Solution Exploring Operation: 72-46=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 46+72=118, Resulting Numbers: [118] 118,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 37:[36, 46], Operations: ['54-18=36', '12+34=46'] Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 36*46=1656, Resulting Numbers: [1656] 1656,37 unequal: No Solution Exploring Operation: 36+46=82, Resulting Numbers: [82] 82,37 unequal: No Solution Moving to Node #0,3,0 Current State: 37:[34, 48], Operations: ['54-18=36', '12+36=48'] Exploring Operation: 34*48=1632, Resulting Numbers: [1632] 1632,37 unequal: No Solution Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,37 unequal: No Solution Exploring Operation: 34+48=82, Resulting Numbers: [82] 82,37 unequal: No Solution Moving to Node #0,3,3 Current State: 37:[36, 22], Operations: ['54-18=36', '34-12=22'] Exploring Operation: 36*22=792, Resulting Numbers: [792] 792,37 unequal: No Solution Exploring Operation: 36+22=58, Resulting Numbers: [58] 58,37 unequal: No Solution Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[34, 24], Operations: ['12+18=30', '54-30=24'] Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,37 unequal: No Solution Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,37 unequal: No Solution Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,37 unequal: No Solution Moving to Node #0,3,1 Current State: 37:[34, 24], Operations: ['54-18=36', '36-12=24'] Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,37 unequal: No Solution Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[34, 24], Operations: ['54-12=42', '42-18=24'] Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,37 unequal: No Solution Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[42, 52], Operations: ['54-12=42', '18+34=52'] Exploring Operation: 42*52=2184, Resulting Numbers: [2184] 2184,37 unequal: No Solution Exploring Operation: 42+52=94, Resulting Numbers: [94] 94,37 unequal: No Solution Exploring Operation: 52-42=10, Resulting Numbers: [10] 10,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[30, 20], Operations: ['12+18=30', '54-34=20'] Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 30*20=600, Resulting Numbers: [600] 600,37 unequal: No Solution Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[34, 60], Operations: ['54-12=42', '18+42=60'] Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 34+60=94, Resulting Numbers: [94] 94,37 unequal: No Solution Exploring Operation: 34*60=2040, Resulting Numbers: [2040] 2040,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[42, 16], Operations: ['54-12=42', '34-18=16'] Exploring Operation: 42*16=672, Resulting Numbers: [672] 672,37 unequal: No Solution Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[54, 64], Operations: ['12+18=30', '34+30=64'] Exploring Operation: 54*64=3456, Resulting Numbers: [3456] 3456,37 unequal: No Solution Exploring Operation: 54+64=118, Resulting Numbers: [118] 118,37 unequal: No Solution Exploring Operation: 64-54=10, Resulting Numbers: [10] 10,37 unequal: No Solution Moving to Node #0,1,3 Current State: 37:[54, 4], Operations: ['12+18=30', '34-30=4'] Exploring Operation: 54*4=216, Resulting Numbers: [216] 216,37 unequal: No Solution Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,37 unequal: No Solution Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,37 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 36, 18, 39, 31 ]
16
[ "36+18=54", "39+31=70", "70-54=16" ]
Current State: 16:[36, 18, 39, 31], Operations: [] Exploring Operation: 36+18=54, Resulting Numbers: [39, 31, 54] Generated Node #2: [39, 31, 54] from Operation: 36+18=54 Current State: 16:[39, 31, 54], Operations: ['36+18=54'] Exploring Operation: 39+31=70, Resulting Numbers: [54, 70] Generated Node #3: [54, 70] from Operation: 39+31=70 Current State: 16:[54, 70], Operations: ['36+18=54', '39+31=70'] Exploring Operation: 70-54=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[36, 18, 39, 31], Operations: [] Exploring Operation: 39-31=8, Resulting Numbers: [36, 18, 8] Generated Node #0,0: 16:[36, 18, 8] Operation: 39-31=8 Exploring Operation: 39-36=3, Resulting Numbers: [18, 31, 3] Generated Node #0,1: 16:[18, 31, 3] Operation: 39-36=3 Exploring Operation: 36/18=2, Resulting Numbers: [39, 31, 2] Generated Node #0,2: 16:[39, 31, 2] Operation: 36/18=2 Exploring Operation: 36-31=5, Resulting Numbers: [18, 39, 5] Generated Node #0,3: 16:[18, 39, 5] Operation: 36-31=5 Exploring Operation: 36-18=18, Resulting Numbers: [39, 31, 18] Generated Node #0,4: 16:[39, 31, 18] Operation: 36-18=18 Moving to Node #0,1 Current State: 16:[18, 31, 3], Operations: ['39-36=3'] Exploring Operation: 31-18=13, Resulting Numbers: [3, 13] Generated Node #0,1,0: 16:[3, 13] Operation: 31-18=13 Exploring Operation: 31-3=28, Resulting Numbers: [18, 28] Generated Node #0,1,1: 16:[18, 28] Operation: 31-3=28 Exploring Operation: 18-3=15, Resulting Numbers: [31, 15] Generated Node #0,1,2: 16:[31, 15] Operation: 18-3=15 Exploring Operation: 18+3=21, Resulting Numbers: [31, 21] Generated Node #0,1,3: 16:[31, 21] Operation: 18+3=21 Exploring Operation: 18/3=6, Resulting Numbers: [31, 6] Generated Node #0,1,4: 16:[31, 6] Operation: 18/3=6 Moving to Node #0,0 Current State: 16:[36, 18, 8], Operations: ['39-31=8'] Exploring Operation: 36-18=18, Resulting Numbers: [8, 18] Generated Node #0,0,0: 16:[8, 18] Operation: 36-18=18 Exploring Operation: 36+8=44, Resulting Numbers: [18, 44] Generated Node #0,0,1: 16:[18, 44] Operation: 36+8=44 Exploring Operation: 36/18=2, Resulting Numbers: [8, 2] Generated Node #0,0,2: 16:[8, 2] Operation: 36/18=2 Exploring Operation: 36-8=28, Resulting Numbers: [18, 28] Generated Node #0,0,3: 16:[18, 28] Operation: 36-8=28 Exploring Operation: 18-8=10, Resulting Numbers: [36, 10] Generated Node #0,0,4: 16:[36, 10] Operation: 18-8=10 Moving to Node #0,3 Current State: 16:[18, 39, 5], Operations: ['36-31=5'] Exploring Operation: 39-5=34, Resulting Numbers: [18, 34] Generated Node #0,3,0: 16:[18, 34] Operation: 39-5=34 Exploring Operation: 18-5=13, Resulting Numbers: [39, 13] Generated Node #0,3,1: 16:[39, 13] Operation: 18-5=13 Exploring Operation: 39+5=44, Resulting Numbers: [18, 44] Generated Node #0,3,2: 16:[18, 44] Operation: 39+5=44 Exploring Operation: 18+5=23, Resulting Numbers: [39, 23] Generated Node #0,3,3: 16:[39, 23] Operation: 18+5=23 Exploring Operation: 39-18=21, Resulting Numbers: [5, 21] Generated Node #0,3,4: 16:[5, 21] Operation: 39-18=21 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 16:[5, 21], Operations: ['36-31=5', '39-18=21'] Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,16 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,16 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[36, 18, 39, 31], Operations: [] Exploring Operation: 36-31=5, Resulting Numbers: [18, 39, 5] Generated Node #0,3: 16:[18, 39, 5] Operation: 36-31=5 Moving to Node #0,3 Current State: 16:[18, 39, 5], Operations: ['36-31=5'] Exploring Operation: 39-18=21, Resulting Numbers: [5, 21] Generated Node #0,3,4: 16:[5, 21] Operation: 39-18=21 Moving to Node #0,3,4 Current State: 16:[5, 21], Operations: ['36-31=5', '39-18=21'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_5
sum_heuristic
[ 74, 79, 72, 51 ]
65
[ "74-72=2", "79+51=130", "130/2=65" ]
Current State: 65:[74, 79, 72, 51], Operations: [] Exploring Operation: 74-72=2, Resulting Numbers: [79, 51, 2] Generated Node #2: [79, 51, 2] from Operation: 74-72=2 Current State: 65:[79, 51, 2], Operations: ['74-72=2'] Exploring Operation: 79+51=130, Resulting Numbers: [2, 130] Generated Node #3: [2, 130] from Operation: 79+51=130 Current State: 65:[2, 130], Operations: ['74-72=2', '79+51=130'] Exploring Operation: 130/2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[74, 79, 72, 51], Operations: [] Exploring Operation: 74-51=23, Resulting Numbers: [79, 72, 23] Generated Node #0,0: 65:[79, 72, 23] Operation: 74-51=23 Exploring Operation: 79-72=7, Resulting Numbers: [74, 51, 7] Generated Node #0,1: 65:[74, 51, 7] Operation: 79-72=7 Exploring Operation: 79-74=5, Resulting Numbers: [72, 51, 5] Generated Node #0,2: 65:[72, 51, 5] Operation: 79-74=5 Exploring Operation: 74-72=2, Resulting Numbers: [79, 51, 2] Generated Node #0,3: 65:[79, 51, 2] Operation: 74-72=2 Moving to Node #0,2 Current State: 65:[72, 51, 5], Operations: ['79-74=5'] Exploring Operation: 72+5=77, Resulting Numbers: [51, 77] Generated Node #0,2,0: 65:[51, 77] Operation: 72+5=77 Exploring Operation: 72-51=21, Resulting Numbers: [5, 21] Generated Node #0,2,1: 65:[5, 21] Operation: 72-51=21 Exploring Operation: 51+5=56, Resulting Numbers: [72, 56] Generated Node #0,2,2: 65:[72, 56] Operation: 51+5=56 Exploring Operation: 72-5=67, Resulting Numbers: [51, 67] Generated Node #0,2,3: 65:[51, 67] Operation: 72-5=67 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 65:[5, 21], Operations: ['79-74=5', '72-51=21'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 65:[72, 56], Operations: ['79-74=5', '51+5=56'] Exploring Operation: 72*56=4032, Resulting Numbers: [4032] 4032,65 unequal: No Solution Exploring Operation: 72-56=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 72+56=128, Resulting Numbers: [128] 128,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 65:[51, 67], Operations: ['79-74=5', '72-5=67'] Exploring Operation: 51*67=3417, Resulting Numbers: [3417] 3417,65 unequal: No Solution Exploring Operation: 67-51=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 51+67=118, Resulting Numbers: [118] 118,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 65:[51, 77], Operations: ['79-74=5', '72+5=77'] Exploring Operation: 51+77=128, Resulting Numbers: [128] 128,65 unequal: No Solution Exploring Operation: 51*77=3927, Resulting Numbers: [3927] 3927,65 unequal: No Solution Exploring Operation: 77-51=26, Resulting Numbers: [26] 26,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 65:[74, 51, 7], Operations: ['79-72=7'] Exploring Operation: 74-7=67, Resulting Numbers: [51, 67] Generated Node #0,1,0: 65:[51, 67] Operation: 74-7=67 Exploring Operation: 51+7=58, Resulting Numbers: [74, 58] Generated Node #0,1,1: 65:[74, 58] Operation: 51+7=58 Exploring Operation: 74-51=23, Resulting Numbers: [7, 23] Generated Node #0,1,2: 65:[7, 23] Operation: 74-51=23 Exploring Operation: 74+7=81, Resulting Numbers: [51, 81] Generated Node #0,1,3: 65:[51, 81] Operation: 74+7=81 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[7, 23], Operations: ['79-72=7', '74-51=23'] Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 7*23=161, Resulting Numbers: [161] 161,65 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[51, 67], Operations: ['79-72=7', '74-7=67'] Exploring Operation: 51+67=118, Resulting Numbers: [118] 118,65 unequal: No Solution Exploring Operation: 67-51=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 51*67=3417, Resulting Numbers: [3417] 3417,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[74, 58], Operations: ['79-72=7', '51+7=58'] Exploring Operation: 74-58=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 74+58=132, Resulting Numbers: [132] 132,65 unequal: No Solution Exploring Operation: 74*58=4292, Resulting Numbers: [4292] 4292,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 65:[51, 81], Operations: ['79-72=7', '74+7=81'] Exploring Operation: 51*81=4131, Resulting Numbers: [4131] 4131,65 unequal: No Solution Exploring Operation: 51+81=132, Resulting Numbers: [132] 132,65 unequal: No Solution Exploring Operation: 81-51=30, Resulting Numbers: [30] 30,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 65:[79, 51, 2], Operations: ['74-72=2'] Exploring Operation: 79-2=77, Resulting Numbers: [51, 77] Generated Node #0,3,0: 65:[51, 77] Operation: 79-2=77 Exploring Operation: 51+2=53, Resulting Numbers: [79, 53] Generated Node #0,3,1: 65:[79, 53] Operation: 51+2=53 Exploring Operation: 79+2=81, Resulting Numbers: [51, 81] Generated Node #0,3,2: 65:[51, 81] Operation: 79+2=81 Exploring Operation: 79-51=28, Resulting Numbers: [2, 28] Generated Node #0,3,3: 65:[2, 28] Operation: 79-51=28 Moving to Node #0,0 Current State: 65:[79, 72, 23], Operations: ['74-51=23'] Exploring Operation: 79+23=102, Resulting Numbers: [72, 102] Generated Node #0,0,0: 65:[72, 102] Operation: 79+23=102 Exploring Operation: 79-72=7, Resulting Numbers: [23, 7] Generated Node #0,0,1: 65:[23, 7] Operation: 79-72=7 Exploring Operation: 79-23=56, Resulting Numbers: [72, 56] Generated Node #0,0,2: 65:[72, 56] Operation: 79-23=56 Exploring Operation: 72-23=49, Resulting Numbers: [79, 49] Generated Node #0,0,3: 65:[79, 49] Operation: 72-23=49 Moving to Node #0,0,1 Current State: 65:[23, 7], Operations: ['74-51=23', '79-72=7'] Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 23*7=161, Resulting Numbers: [161] 161,65 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,65 unequal: No Solution Moving to Node #0,0,2 Current State: 65:[72, 56], Operations: ['74-51=23', '79-23=56'] Exploring Operation: 72-56=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 72+56=128, Resulting Numbers: [128] 128,65 unequal: No Solution Exploring Operation: 72*56=4032, Resulting Numbers: [4032] 4032,65 unequal: No Solution Moving to Node #0,3,3 Current State: 65:[2, 28], Operations: ['74-72=2', '79-51=28'] Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,65 unequal: No Solution Moving to Node #0,3,1 Current State: 65:[79, 53], Operations: ['74-72=2', '51+2=53'] Exploring Operation: 79-53=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 79+53=132, Resulting Numbers: [132] 132,65 unequal: No Solution Exploring Operation: 79*53=4187, Resulting Numbers: [4187] 4187,65 unequal: No Solution Moving to Node #0,3,0 Current State: 65:[51, 77], Operations: ['74-72=2', '79-2=77'] Exploring Operation: 51+77=128, Resulting Numbers: [128] 128,65 unequal: No Solution Exploring Operation: 77-51=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 51*77=3927, Resulting Numbers: [3927] 3927,65 unequal: No Solution Moving to Node #0,3,2 Current State: 65:[51, 81], Operations: ['74-72=2', '79+2=81'] Exploring Operation: 51+81=132, Resulting Numbers: [132] 132,65 unequal: No Solution Exploring Operation: 51*81=4131, Resulting Numbers: [4131] 4131,65 unequal: No Solution Exploring Operation: 81-51=30, Resulting Numbers: [30] 30,65 unequal: No Solution Moving to Node #0,0,3 Current State: 65:[79, 49], Operations: ['74-51=23', '72-23=49'] Exploring Operation: 79*49=3871, Resulting Numbers: [3871] 3871,65 unequal: No Solution Exploring Operation: 79+49=128, Resulting Numbers: [128] 128,65 unequal: No Solution Exploring Operation: 79-49=30, Resulting Numbers: [30] 30,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[72, 102], Operations: ['74-51=23', '79+23=102'] Exploring Operation: 72*102=7344, Resulting Numbers: [7344] 7344,65 unequal: No Solution Exploring Operation: 102-72=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 72+102=174, Resulting Numbers: [174] 174,65 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 10, 27, 53, 86 ]
50
[ "27-10=17", "86-53=33", "17+33=50" ]
Current State: 50:[10, 27, 53, 86], Operations: [] Exploring Operation: 27-10=17, Resulting Numbers: [53, 86, 17] Generated Node #2: [53, 86, 17] from Operation: 27-10=17 Current State: 50:[53, 86, 17], Operations: ['27-10=17'] Exploring Operation: 86-53=33, Resulting Numbers: [17, 33] Generated Node #3: [17, 33] from Operation: 86-53=33 Current State: 50:[17, 33], Operations: ['27-10=17', '86-53=33'] Exploring Operation: 17+33=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[10, 27, 53, 86], Operations: [] Exploring Operation: 86-10=76, Resulting Numbers: [27, 53, 76] Generated Node #0,0: 50:[27, 53, 76] Operation: 86-10=76 Exploring Operation: 86-53=33, Resulting Numbers: [10, 27, 33] Generated Node #0,1: 50:[10, 27, 33] Operation: 86-53=33 Exploring Operation: 86-27=59, Resulting Numbers: [10, 53, 59] Generated Node #0,2: 50:[10, 53, 59] Operation: 86-27=59 Moving to Node #0,1 Current State: 50:[10, 27, 33], Operations: ['86-53=33'] Exploring Operation: 33-10=23, Resulting Numbers: [27, 23] Generated Node #0,1,0: 50:[27, 23] Operation: 33-10=23 Exploring Operation: 10+33=43, Resulting Numbers: [27, 43] Generated Node #0,1,1: 50:[27, 43] Operation: 10+33=43 Exploring Operation: 33-27=6, Resulting Numbers: [10, 6] Generated Node #0,1,2: 50:[10, 6] Operation: 33-27=6 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 50:[10, 6], Operations: ['86-53=33', '33-27=6'] Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 10*6=60, Resulting Numbers: [60] 60,50 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[27, 23], Operations: ['86-53=33', '33-10=23'] Exploring Operation: 27*23=621, Resulting Numbers: [621] 621,50 unequal: No Solution Exploring Operation: 27+23=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[10, 27, 53, 86], Operations: [] Exploring Operation: 86-53=33, Resulting Numbers: [10, 27, 33] Generated Node #0,1: 50:[10, 27, 33] Operation: 86-53=33 Moving to Node #0,1 Current State: 50:[10, 27, 33], Operations: ['86-53=33'] Exploring Operation: 33-10=23, Resulting Numbers: [27, 23] Generated Node #0,1,0: 50:[27, 23] Operation: 33-10=23 Moving to Node #0,1,0 Current State: 50:[27, 23], Operations: ['86-53=33', '33-10=23'] Exploring Operation: 27+23=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 91, 5, 98, 44 ]
93
[ "5+44=49", "98/49=2", "91+2=93" ]
Current State: 93:[91, 5, 98, 44], Operations: [] Exploring Operation: 5+44=49, Resulting Numbers: [91, 98, 49] Generated Node #2: [91, 98, 49] from Operation: 5+44=49 Current State: 93:[91, 98, 49], Operations: ['5+44=49'] Exploring Operation: 98/49=2, Resulting Numbers: [91, 2] Generated Node #3: [91, 2] from Operation: 98/49=2 Current State: 93:[91, 2], Operations: ['5+44=49', '98/49=2'] Exploring Operation: 91+2=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[91, 5, 98, 44], Operations: [] Exploring Operation: 98-5=93, Resulting Numbers: [91, 44, 93] Generated Node #0,0: 93:[91, 44, 93] Operation: 98-5=93 Moving to Node #0,0 Current State: 93:[91, 44, 93], Operations: ['98-5=93'] Exploring Operation: 93-91=2, Resulting Numbers: [44, 2] Generated Node #0,0,0: 93:[44, 2] Operation: 93-91=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[44, 2], Operations: ['98-5=93', '93-91=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 17, 88, 75, 97 ]
83
[ "17+88=105", "97-75=22", "105-22=83" ]
Current State: 83:[17, 88, 75, 97], Operations: [] Exploring Operation: 17+88=105, Resulting Numbers: [75, 97, 105] Generated Node #2: [75, 97, 105] from Operation: 17+88=105 Current State: 83:[75, 97, 105], Operations: ['17+88=105'] Exploring Operation: 97-75=22, Resulting Numbers: [105, 22] Generated Node #3: [105, 22] from Operation: 97-75=22 Current State: 83:[105, 22], Operations: ['17+88=105', '97-75=22'] Exploring Operation: 105-22=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[17, 88, 75, 97], Operations: [] Exploring Operation: 97-17=80, Resulting Numbers: [88, 75, 80] Generated Node #0,0: 83:[88, 75, 80] Operation: 97-17=80 Exploring Operation: 17+75=92, Resulting Numbers: [88, 97, 92] Generated Node #0,1: 83:[88, 97, 92] Operation: 17+75=92 Exploring Operation: 88-17=71, Resulting Numbers: [75, 97, 71] Generated Node #0,2: 83:[75, 97, 71] Operation: 88-17=71 Exploring Operation: 75-17=58, Resulting Numbers: [88, 97, 58] Generated Node #0,3: 83:[88, 97, 58] Operation: 75-17=58 Exploring Operation: 17+88=105, Resulting Numbers: [75, 97, 105] Generated Node #0,4: 83:[75, 97, 105] Operation: 17+88=105 Moving to Node #0,0 Current State: 83:[88, 75, 80], Operations: ['97-17=80'] Exploring Operation: 88-80=8, Resulting Numbers: [75, 8] Generated Node #0,0,0: 83:[75, 8] Operation: 88-80=8 Exploring Operation: 80-75=5, Resulting Numbers: [88, 5] Generated Node #0,0,1: 83:[88, 5] Operation: 80-75=5 Exploring Operation: 88-75=13, Resulting Numbers: [80, 13] Generated Node #0,0,2: 83:[80, 13] Operation: 88-75=13 Exploring Operation: 75+80=155, Resulting Numbers: [88, 155] Generated Node #0,0,3: 83:[88, 155] Operation: 75+80=155 Exploring Operation: 88+75=163, Resulting Numbers: [80, 163] Generated Node #0,0,4: 83:[80, 163] Operation: 88+75=163 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[80, 13], Operations: ['97-17=80', '88-75=13'] Exploring Operation: 80*13=1040, Resulting Numbers: [1040] 1040,83 unequal: No Solution Exploring Operation: 80+13=93, Resulting Numbers: [93] 93,83 unequal: No Solution Exploring Operation: 80-13=67, Resulting Numbers: [67] 67,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 83:[88, 155], Operations: ['97-17=80', '75+80=155'] Exploring Operation: 88+155=243, Resulting Numbers: [243] 243,83 unequal: No Solution Exploring Operation: 88*155=13640, Resulting Numbers: [13640] 13640,83 unequal: No Solution Exploring Operation: 155-88=67, Resulting Numbers: [67] 67,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[75, 8], Operations: ['97-17=80', '88-80=8'] Exploring Operation: 75-8=67, Resulting Numbers: [67] 67,83 unequal: No Solution Exploring Operation: 75*8=600, Resulting Numbers: [600] 600,83 unequal: No Solution Exploring Operation: 75+8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[17, 88, 75, 97], Operations: [] Exploring Operation: 97-17=80, Resulting Numbers: [88, 75, 80] Generated Node #0,0: 83:[88, 75, 80] Operation: 97-17=80 Moving to Node #0,0 Current State: 83:[88, 75, 80], Operations: ['97-17=80'] Exploring Operation: 88-80=8, Resulting Numbers: [75, 8] Generated Node #0,0,0: 83:[75, 8] Operation: 88-80=8 Moving to Node #0,0,0 Current State: 83:[75, 8], Operations: ['97-17=80', '88-80=8'] Exploring Operation: 75+8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 57, 22, 11, 69 ]
24
[ "69-57=12", "22/11=2", "12*2=24" ]
Current State: 24:[57, 22, 11, 69], Operations: [] Exploring Operation: 69-57=12, Resulting Numbers: [22, 11, 12] Generated Node #2: [22, 11, 12] from Operation: 69-57=12 Current State: 24:[22, 11, 12], Operations: ['69-57=12'] Exploring Operation: 22/11=2, Resulting Numbers: [12, 2] Generated Node #3: [12, 2] from Operation: 22/11=2 Current State: 24:[12, 2], Operations: ['69-57=12', '22/11=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[57, 22, 11, 69], Operations: [] Exploring Operation: 69-57=12, Resulting Numbers: [22, 11, 12] Generated Node #0,0: 24:[22, 11, 12] Operation: 69-57=12 Exploring Operation: 57-22=35, Resulting Numbers: [11, 69, 35] Generated Node #0,1: 24:[11, 69, 35] Operation: 57-22=35 Exploring Operation: 57-11=46, Resulting Numbers: [22, 69, 46] Generated Node #0,2: 24:[22, 69, 46] Operation: 57-11=46 Exploring Operation: 69-22=47, Resulting Numbers: [57, 11, 47] Generated Node #0,3: 24:[57, 11, 47] Operation: 69-22=47 Moving to Node #0,0 Current State: 24:[22, 11, 12], Operations: ['69-57=12'] Exploring Operation: 22-11=11, Resulting Numbers: [12, 11] Generated Node #0,0,0: 24:[12, 11] Operation: 22-11=11 Exploring Operation: 22-12=10, Resulting Numbers: [11, 10] Generated Node #0,0,1: 24:[11, 10] Operation: 22-12=10 Exploring Operation: 22/11=2, Resulting Numbers: [12, 2] Generated Node #0,0,2: 24:[12, 2] Operation: 22/11=2 Exploring Operation: 11+12=23, Resulting Numbers: [22, 23] Generated Node #0,0,3: 24:[22, 23] Operation: 11+12=23 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 24:[12, 2], Operations: ['69-57=12', '22/11=2'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,24 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,24 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[57, 22, 11, 69], Operations: [] Exploring Operation: 69-57=12, Resulting Numbers: [22, 11, 12] Generated Node #0,0: 24:[22, 11, 12] Operation: 69-57=12 Moving to Node #0,0 Current State: 24:[22, 11, 12], Operations: ['69-57=12'] Exploring Operation: 22/11=2, Resulting Numbers: [12, 2] Generated Node #0,0,2: 24:[12, 2] Operation: 22/11=2 Moving to Node #0,0,2 Current State: 24:[12, 2], Operations: ['69-57=12', '22/11=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 72, 75, 21, 24 ]
12
[ "72*21=1512", "1512/24=63", "75-63=12" ]
Current State: 12:[72, 75, 21, 24], Operations: [] Exploring Operation: 72*21=1512, Resulting Numbers: [75, 24, 1512] Generated Node #2: [75, 24, 1512] from Operation: 72*21=1512 Current State: 12:[75, 24, 1512], Operations: ['72*21=1512'] Exploring Operation: 1512/24=63, Resulting Numbers: [75, 63] Generated Node #3: [75, 63] from Operation: 1512/24=63 Current State: 12:[75, 63], Operations: ['72*21=1512', '1512/24=63'] Exploring Operation: 75-63=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[72, 75, 21, 24], Operations: [] Exploring Operation: 75-72=3, Resulting Numbers: [21, 24, 3] Generated Node #0,0: 12:[21, 24, 3] Operation: 75-72=3 Exploring Operation: 72/24=3, Resulting Numbers: [75, 21, 3] Generated Node #0,1: 12:[75, 21, 3] Operation: 72/24=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[21, 24, 3], Operations: ['75-72=3'] Exploring Operation: 24-21=3, Resulting Numbers: [3, 3] Generated Node #0,0,0: 12:[3, 3] Operation: 24-21=3 Exploring Operation: 24/3=8, Resulting Numbers: [21, 8] Generated Node #0,0,1: 12:[21, 8] Operation: 24/3=8 Moving to Node #0,0,0 Current State: 12:[3, 3], Operations: ['75-72=3', '24-21=3'] Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[21, 8], Operations: ['75-72=3', '24/3=8'] Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,12 unequal: No Solution Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[75, 21, 3], Operations: ['72/24=3'] Exploring Operation: 75-21=54, Resulting Numbers: [3, 54] Generated Node #0,1,0: 12:[3, 54] Operation: 75-21=54 Exploring Operation: 75/3=25, Resulting Numbers: [21, 25] Generated Node #0,1,1: 12:[21, 25] Operation: 75/3=25 Moving to Node #0,1,1 Current State: 12:[21, 25], Operations: ['72/24=3', '75/3=25'] Exploring Operation: 21+25=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[3, 54], Operations: ['72/24=3', '75-21=54'] Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 45, 1, 74, 91 ]
37
[ "45*74=3330", "91-1=90", "3330/90=37" ]
Current State: 37:[45, 1, 74, 91], Operations: [] Exploring Operation: 45*74=3330, Resulting Numbers: [1, 91, 3330] Generated Node #2: [1, 91, 3330] from Operation: 45*74=3330 Current State: 37:[1, 91, 3330], Operations: ['45*74=3330'] Exploring Operation: 91-1=90, Resulting Numbers: [3330, 90] Generated Node #3: [3330, 90] from Operation: 91-1=90 Current State: 37:[3330, 90], Operations: ['45*74=3330', '91-1=90'] Exploring Operation: 3330/90=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[45, 1, 74, 91], Operations: [] Exploring Operation: 74-45=29, Resulting Numbers: [1, 91, 29] Generated Node #0,0: 37:[1, 91, 29] Operation: 74-45=29 Exploring Operation: 91-45=46, Resulting Numbers: [1, 74, 46] Generated Node #0,1: 37:[1, 74, 46] Operation: 91-45=46 Exploring Operation: 91-74=17, Resulting Numbers: [45, 1, 17] Generated Node #0,2: 37:[45, 1, 17] Operation: 91-74=17 Exploring Operation: 45-1=44, Resulting Numbers: [74, 91, 44] Generated Node #0,3: 37:[74, 91, 44] Operation: 45-1=44 Moving to Node #0,2 Current State: 37:[45, 1, 17], Operations: ['91-74=17'] Exploring Operation: 45/1=45, Resulting Numbers: [17, 45] Generated Node #0,2,0: 37:[17, 45] Operation: 45/1=45 Exploring Operation: 1+17=18, Resulting Numbers: [45, 18] Generated Node #0,2,1: 37:[45, 18] Operation: 1+17=18 Exploring Operation: 45-1=44, Resulting Numbers: [17, 44] Generated Node #0,2,2: 37:[17, 44] Operation: 45-1=44 Exploring Operation: 45*1=45, Resulting Numbers: [17, 45] Generated Node #0,2,3: 37:[17, 45] Operation: 45*1=45 Moving to Node #0,1 Current State: 37:[1, 74, 46], Operations: ['91-45=46'] Exploring Operation: 46-1=45, Resulting Numbers: [74, 45] Generated Node #0,1,0: 37:[74, 45] Operation: 46-1=45 Exploring Operation: 74-1=73, Resulting Numbers: [46, 73] Generated Node #0,1,1: 37:[46, 73] Operation: 74-1=73 Exploring Operation: 74-46=28, Resulting Numbers: [1, 28] Generated Node #0,1,2: 37:[1, 28] Operation: 74-46=28 Exploring Operation: 1*74=74, Resulting Numbers: [46, 74] Generated Node #0,1,3: 37:[46, 74] Operation: 1*74=74 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[74, 45], Operations: ['91-45=46', '46-1=45'] Exploring Operation: 74+45=119, Resulting Numbers: [119] 119,37 unequal: No Solution Exploring Operation: 74-45=29, Resulting Numbers: [29] 29,37 unequal: No Solution Exploring Operation: 74*45=3330, Resulting Numbers: [3330] 3330,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 37:[46, 73], Operations: ['91-45=46', '74-1=73'] Exploring Operation: 46*73=3358, Resulting Numbers: [3358] 3358,37 unequal: No Solution Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 46+73=119, Resulting Numbers: [119] 119,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 37:[1, 28], Operations: ['91-45=46', '74-46=28'] Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,37 unequal: No Solution Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,37 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 1+28=29, Resulting Numbers: [29] 29,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 37:[46, 74], Operations: ['91-45=46', '1*74=74'] Exploring Operation: 46+74=120, Resulting Numbers: [120] 120,37 unequal: No Solution Exploring Operation: 74-46=28, Resulting Numbers: [28] 28,37 unequal: No Solution Exploring Operation: 46*74=3404, Resulting Numbers: [3404] 3404,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 37:[74, 91, 44], Operations: ['45-1=44'] Exploring Operation: 91-74=17, Resulting Numbers: [44, 17] Generated Node #0,3,0: 37:[44, 17] Operation: 91-74=17 Exploring Operation: 74+91=165, Resulting Numbers: [44, 165] Generated Node #0,3,1: 37:[44, 165] Operation: 74+91=165 Exploring Operation: 74-44=30, Resulting Numbers: [91, 30] Generated Node #0,3,2: 37:[91, 30] Operation: 74-44=30 Exploring Operation: 91-44=47, Resulting Numbers: [74, 47] Generated Node #0,3,3: 37:[74, 47] Operation: 91-44=47 Moving to Node #0,0 Current State: 37:[1, 91, 29], Operations: ['74-45=29'] Exploring Operation: 91-29=62, Resulting Numbers: [1, 62] Generated Node #0,0,0: 37:[1, 62] Operation: 91-29=62 Exploring Operation: 1+29=30, Resulting Numbers: [91, 30] Generated Node #0,0,1: 37:[91, 30] Operation: 1+29=30 Exploring Operation: 1*91=91, Resulting Numbers: [29, 91] Generated Node #0,0,2: 37:[29, 91] Operation: 1*91=91 Exploring Operation: 91-1=90, Resulting Numbers: [29, 90] Generated Node #0,0,3: 37:[29, 90] Operation: 91-1=90 Moving to Node #0,2,1 Current State: 37:[45, 18], Operations: ['91-74=17', '1+17=18'] Exploring Operation: 45+18=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 45-18=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 45*18=810, Resulting Numbers: [810] 810,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[17, 44], Operations: ['91-74=17', '45-1=44'] Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 17*44=748, Resulting Numbers: [748] 748,37 unequal: No Solution Exploring Operation: 17+44=61, Resulting Numbers: [61] 61,37 unequal: No Solution Moving to Node #0,3,0 Current State: 37:[44, 17], Operations: ['45-1=44', '91-74=17'] Exploring Operation: 44*17=748, Resulting Numbers: [748] 748,37 unequal: No Solution Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 44+17=61, Resulting Numbers: [61] 61,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[17, 45], Operations: ['91-74=17', '45/1=45'] Exploring Operation: 17+45=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,37 unequal: No Solution Exploring Operation: 17*45=765, Resulting Numbers: [765] 765,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[17, 45], Operations: ['91-74=17', '45*1=45'] Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,37 unequal: No Solution Exploring Operation: 17*45=765, Resulting Numbers: [765] 765,37 unequal: No Solution Exploring Operation: 17+45=62, Resulting Numbers: [62] 62,37 unequal: No Solution Moving to Node #0,3,3 Current State: 37:[74, 47], Operations: ['45-1=44', '91-44=47'] Exploring Operation: 74-47=27, Resulting Numbers: [27] 27,37 unequal: No Solution Exploring Operation: 74*47=3478, Resulting Numbers: [3478] 3478,37 unequal: No Solution Exploring Operation: 74+47=121, Resulting Numbers: [121] 121,37 unequal: No Solution Moving to Node #0,3,2 Current State: 37:[91, 30], Operations: ['45-1=44', '74-44=30'] Exploring Operation: 91*30=2730, Resulting Numbers: [2730] 2730,37 unequal: No Solution Exploring Operation: 91+30=121, Resulting Numbers: [121] 121,37 unequal: No Solution Exploring Operation: 91-30=61, Resulting Numbers: [61] 61,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[91, 30], Operations: ['74-45=29', '1+29=30'] Exploring Operation: 91+30=121, Resulting Numbers: [121] 121,37 unequal: No Solution Exploring Operation: 91*30=2730, Resulting Numbers: [2730] 2730,37 unequal: No Solution Exploring Operation: 91-30=61, Resulting Numbers: [61] 61,37 unequal: No Solution Moving to Node #0,0,3 Current State: 37:[29, 90], Operations: ['74-45=29', '91-1=90'] Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,37 unequal: No Solution Exploring Operation: 29+90=119, Resulting Numbers: [119] 119,37 unequal: No Solution Exploring Operation: 29*90=2610, Resulting Numbers: [2610] 2610,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[1, 62], Operations: ['74-45=29', '91-29=62'] Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 1+62=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,37 unequal: No Solution Exploring Operation: 1*62=62, Resulting Numbers: [62] 62,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[29, 91], Operations: ['74-45=29', '1*91=91'] Exploring Operation: 29+91=120, Resulting Numbers: [120] 120,37 unequal: No Solution Exploring Operation: 29*91=2639, Resulting Numbers: [2639] 2639,37 unequal: No Solution Exploring Operation: 91-29=62, Resulting Numbers: [62] 62,37 unequal: No Solution Moving to Node #0,3,1 Current State: 37:[44, 165], Operations: ['45-1=44', '74+91=165'] Exploring Operation: 44+165=209, Resulting Numbers: [209] 209,37 unequal: No Solution Exploring Operation: 165-44=121, Resulting Numbers: [121] 121,37 unequal: No Solution Exploring Operation: 44*165=7260, Resulting Numbers: [7260] 7260,37 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 71, 95, 7, 56 ]
25
[ "95-71=24", "56-7=49", "49-24=25" ]
Current State: 25:[71, 95, 7, 56], Operations: [] Exploring Operation: 95-71=24, Resulting Numbers: [7, 56, 24] Generated Node #2: [7, 56, 24] from Operation: 95-71=24 Current State: 25:[7, 56, 24], Operations: ['95-71=24'] Exploring Operation: 56-7=49, Resulting Numbers: [24, 49] Generated Node #3: [24, 49] from Operation: 56-7=49 Current State: 25:[24, 49], Operations: ['95-71=24', '56-7=49'] Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[71, 95, 7, 56], Operations: [] Exploring Operation: 95-56=39, Resulting Numbers: [71, 7, 39] Generated Node #0,0: 25:[71, 7, 39] Operation: 95-56=39 Exploring Operation: 95-71=24, Resulting Numbers: [7, 56, 24] Generated Node #0,1: 25:[7, 56, 24] Operation: 95-71=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[7, 56, 24], Operations: ['95-71=24'] Exploring Operation: 56-24=32, Resulting Numbers: [7, 32] Generated Node #0,1,0: 25:[7, 32] Operation: 56-24=32 Exploring Operation: 56/7=8, Resulting Numbers: [24, 8] Generated Node #0,1,1: 25:[24, 8] Operation: 56/7=8 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 25:[24, 8], Operations: ['95-71=24', '56/7=8'] Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,25 unequal: No Solution Exploring Operation: 24+8=32, Resulting Numbers: [32] 32,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[7, 32], Operations: ['95-71=24', '56-24=32'] Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,25 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[71, 95, 7, 56], Operations: [] Exploring Operation: 95-71=24, Resulting Numbers: [7, 56, 24] Generated Node #0,1: 25:[7, 56, 24] Operation: 95-71=24 Moving to Node #0,1 Current State: 25:[7, 56, 24], Operations: ['95-71=24'] Exploring Operation: 56-24=32, Resulting Numbers: [7, 32] Generated Node #0,1,0: 25:[7, 32] Operation: 56-24=32 Moving to Node #0,1,0 Current State: 25:[7, 32], Operations: ['95-71=24', '56-24=32'] Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 36, 11, 39, 48 ]
63
[ "39*48=1872", "1872/36=52", "11+52=63" ]
Current State: 63:[36, 11, 39, 48], Operations: [] Exploring Operation: 39*48=1872, Resulting Numbers: [36, 11, 1872] Generated Node #2: [36, 11, 1872] from Operation: 39*48=1872 Current State: 63:[36, 11, 1872], Operations: ['39*48=1872'] Exploring Operation: 1872/36=52, Resulting Numbers: [11, 52] Generated Node #3: [11, 52] from Operation: 1872/36=52 Current State: 63:[11, 52], Operations: ['39*48=1872', '1872/36=52'] Exploring Operation: 11+52=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[36, 11, 39, 48], Operations: [] Exploring Operation: 48-39=9, Resulting Numbers: [36, 11, 9] Generated Node #0,0: 63:[36, 11, 9] Operation: 48-39=9 Exploring Operation: 48-36=12, Resulting Numbers: [11, 39, 12] Generated Node #0,1: 63:[11, 39, 12] Operation: 48-36=12 Exploring Operation: 39-36=3, Resulting Numbers: [11, 48, 3] Generated Node #0,2: 63:[11, 48, 3] Operation: 39-36=3 Moving to Node #0,0 Current State: 63:[36, 11, 9], Operations: ['48-39=9'] Exploring Operation: 36-11=25, Resulting Numbers: [9, 25] Generated Node #0,0,0: 63:[9, 25] Operation: 36-11=25 Exploring Operation: 36-9=27, Resulting Numbers: [11, 27] Generated Node #0,0,1: 63:[11, 27] Operation: 36-9=27 Exploring Operation: 36/9=4, Resulting Numbers: [11, 4] Generated Node #0,0,2: 63:[11, 4] Operation: 36/9=4 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 63:[11, 4], Operations: ['48-39=9', '36/9=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,63 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[9, 25], Operations: ['48-39=9', '36-11=25'] Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,63 unequal: No Solution Exploring Operation: 9+25=34, Resulting Numbers: [34] 34,63 unequal: No Solution Exploring Operation: 9*25=225, Resulting Numbers: [225] 225,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[11, 27], Operations: ['48-39=9', '36-9=27'] Exploring Operation: 11*27=297, Resulting Numbers: [297] 297,63 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,63 unequal: No Solution Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 63:[11, 48, 3], Operations: ['39-36=3'] Exploring Operation: 48/3=16, Resulting Numbers: [11, 16] Generated Node #0,2,0: 63:[11, 16] Operation: 48/3=16 Exploring Operation: 11+48=59, Resulting Numbers: [3, 59] Generated Node #0,2,1: 63:[3, 59] Operation: 11+48=59 Exploring Operation: 48+3=51, Resulting Numbers: [11, 51] Generated Node #0,2,2: 63:[11, 51] Operation: 48+3=51 Moving to Node #0,1 Current State: 63:[11, 39, 12], Operations: ['48-36=12'] Exploring Operation: 39-11=28, Resulting Numbers: [12, 28] Generated Node #0,1,0: 63:[12, 28] Operation: 39-11=28 Exploring Operation: 39+12=51, Resulting Numbers: [11, 51] Generated Node #0,1,1: 63:[11, 51] Operation: 39+12=51 Exploring Operation: 39-12=27, Resulting Numbers: [11, 27] Generated Node #0,1,2: 63:[11, 27] Operation: 39-12=27 Moving to Node #0,2,1 Current State: 63:[3, 59], Operations: ['39-36=3', '11+48=59'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 3+59=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 3*59=177, Resulting Numbers: [177] 177,63 unequal: No Solution Moving to Node #0,2,0 Current State: 63:[11, 16], Operations: ['39-36=3', '48/3=16'] Exploring Operation: 11*16=176, Resulting Numbers: [176] 176,63 unequal: No Solution Exploring Operation: 11+16=27, Resulting Numbers: [27] 27,63 unequal: No Solution Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[11, 27], Operations: ['48-36=12', '39-12=27'] Exploring Operation: 11*27=297, Resulting Numbers: [297] 297,63 unequal: No Solution Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,63 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[12, 28], Operations: ['48-36=12', '39-11=28'] Exploring Operation: 12+28=40, Resulting Numbers: [40] 40,63 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,63 unequal: No Solution Exploring Operation: 12*28=336, Resulting Numbers: [336] 336,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[11, 51], Operations: ['48-36=12', '39+12=51'] Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,63 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,63 unequal: No Solution Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[11, 51], Operations: ['39-36=3', '48+3=51'] Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,63 unequal: No Solution Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,63 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 15, 32, 80, 47 ]
81
[ "15+32=47", "47/47=1", "80+1=81" ]
Current State: 81:[15, 32, 80, 47], Operations: [] Exploring Operation: 15+32=47, Resulting Numbers: [80, 47, 47] Generated Node #2: [80, 47, 47] from Operation: 15+32=47 Current State: 81:[80, 47, 47], Operations: ['15+32=47'] Exploring Operation: 47/47=1, Resulting Numbers: [80, 1] Generated Node #3: [80, 1] from Operation: 47/47=1 Current State: 81:[80, 1], Operations: ['15+32=47', '47/47=1'] Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[15, 32, 80, 47], Operations: [] Exploring Operation: 47-15=32, Resulting Numbers: [32, 80, 32] Generated Node #0,0: 81:[32, 80, 32] Operation: 47-15=32 Exploring Operation: 32+47=79, Resulting Numbers: [15, 80, 79] Generated Node #0,1: 81:[15, 80, 79] Operation: 32+47=79 Exploring Operation: 47-32=15, Resulting Numbers: [15, 80, 15] Generated Node #0,2: 81:[15, 80, 15] Operation: 47-32=15 Exploring Operation: 80-47=33, Resulting Numbers: [15, 32, 33] Generated Node #0,3: 81:[15, 32, 33] Operation: 80-47=33 Moving to Node #0,1 Current State: 81:[15, 80, 79], Operations: ['32+47=79'] Exploring Operation: 15+80=95, Resulting Numbers: [79, 95] Generated Node #0,1,0: 81:[79, 95] Operation: 15+80=95 Exploring Operation: 80-15=65, Resulting Numbers: [79, 65] Generated Node #0,1,1: 81:[79, 65] Operation: 80-15=65 Exploring Operation: 15+79=94, Resulting Numbers: [80, 94] Generated Node #0,1,2: 81:[80, 94] Operation: 15+79=94 Exploring Operation: 80-79=1, Resulting Numbers: [15, 1] Generated Node #0,1,3: 81:[15, 1] Operation: 80-79=1 Moving to Node #0,0 Current State: 81:[32, 80, 32], Operations: ['47-15=32'] Exploring Operation: 32+32=64, Resulting Numbers: [80, 64] Generated Node #0,0,0: 81:[80, 64] Operation: 32+32=64 Exploring Operation: 80-32=48, Resulting Numbers: [32, 48] Generated Node #0,0,1: 81:[32, 48] Operation: 80-32=48 Exploring Operation: 32/32=1, Resulting Numbers: [80, 1] Generated Node #0,0,2: 81:[80, 1] Operation: 32/32=1 Exploring Operation: 32-32=0, Resulting Numbers: [80, 0] Generated Node #0,0,3: 81:[80, 0] Operation: 32-32=0 Moving to Node #0,2 Current State: 81:[15, 80, 15], Operations: ['47-32=15'] Exploring Operation: 15/15=1, Resulting Numbers: [80, 1] Generated Node #0,2,0: 81:[80, 1] Operation: 15/15=1 Exploring Operation: 15+15=30, Resulting Numbers: [80, 30] Generated Node #0,2,1: 81:[80, 30] Operation: 15+15=30 Exploring Operation: 15+80=95, Resulting Numbers: [15, 95] Generated Node #0,2,2: 81:[15, 95] Operation: 15+80=95 Exploring Operation: 15-15=0, Resulting Numbers: [80, 0] Generated Node #0,2,3: 81:[80, 0] Operation: 15-15=0 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 81:[80, 1], Operations: ['47-32=15', '15/15=1'] Exploring Operation: 80*1=80, Resulting Numbers: [80] 80,81 unequal: No Solution Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[15, 32, 80, 47], Operations: [] Exploring Operation: 47-32=15, Resulting Numbers: [15, 80, 15] Generated Node #0,2: 81:[15, 80, 15] Operation: 47-32=15 Moving to Node #0,2 Current State: 81:[15, 80, 15], Operations: ['47-32=15'] Exploring Operation: 15/15=1, Resulting Numbers: [80, 1] Generated Node #0,2,0: 81:[80, 1] Operation: 15/15=1 Moving to Node #0,2,0 Current State: 81:[80, 1], Operations: ['47-32=15', '15/15=1'] Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
mult_heuristic
[ 77, 64, 52, 79 ]
90
[ "79-77=2", "52/2=26", "64+26=90" ]
Current State: 90:[77, 64, 52, 79], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [64, 52, 2] Generated Node #2: [64, 52, 2] from Operation: 79-77=2 Current State: 90:[64, 52, 2], Operations: ['79-77=2'] Exploring Operation: 52/2=26, Resulting Numbers: [64, 26] Generated Node #3: [64, 26] from Operation: 52/2=26 Current State: 90:[64, 26], Operations: ['79-77=2', '52/2=26'] Exploring Operation: 64+26=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[77, 64, 52, 79], Operations: [] Exploring Operation: 77-64=13, Resulting Numbers: [52, 79, 13] Generated Node #0,0: 90:[52, 79, 13] Operation: 77-64=13 Exploring Operation: 77-52=25, Resulting Numbers: [64, 79, 25] Generated Node #0,1: 90:[64, 79, 25] Operation: 77-52=25 Exploring Operation: 79-64=15, Resulting Numbers: [77, 52, 15] Generated Node #0,2: 90:[77, 52, 15] Operation: 79-64=15 Exploring Operation: 64-52=12, Resulting Numbers: [77, 79, 12] Generated Node #0,3: 90:[77, 79, 12] Operation: 64-52=12 Exploring Operation: 79-77=2, Resulting Numbers: [64, 52, 2] Generated Node #0,4: 90:[64, 52, 2] Operation: 79-77=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[52, 79, 13], Operations: ['77-64=13'] Exploring Operation: 79-13=66, Resulting Numbers: [52, 66] Generated Node #0,0,0: 90:[52, 66] Operation: 79-13=66 Exploring Operation: 52-13=39, Resulting Numbers: [79, 39] Generated Node #0,0,1: 90:[79, 39] Operation: 52-13=39 Exploring Operation: 79-52=27, Resulting Numbers: [13, 27] Generated Node #0,0,2: 90:[13, 27] Operation: 79-52=27 Exploring Operation: 79+13=92, Resulting Numbers: [52, 92] Generated Node #0,0,3: 90:[52, 92] Operation: 79+13=92 Exploring Operation: 52/13=4, Resulting Numbers: [79, 4] Generated Node #0,0,4: 90:[79, 4] Operation: 52/13=4 Moving to Node #0,0,2 Current State: 90:[13, 27], Operations: ['77-64=13', '79-52=27'] Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 13+27=40, Resulting Numbers: [40] 40,90 unequal: No Solution Exploring Operation: 13*27=351, Resulting Numbers: [351] 351,90 unequal: No Solution Moving to Node #0,0,3 Current State: 90:[52, 92], Operations: ['77-64=13', '79+13=92'] Exploring Operation: 52+92=144, Resulting Numbers: [144] 144,90 unequal: No Solution Exploring Operation: 92-52=40, Resulting Numbers: [40] 40,90 unequal: No Solution Exploring Operation: 52*92=4784, Resulting Numbers: [4784] 4784,90 unequal: No Solution Moving to Node #0,0,4 Current State: 90:[79, 4], Operations: ['77-64=13', '52/13=4'] Exploring Operation: 79*4=316, Resulting Numbers: [316] 316,90 unequal: No Solution Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[79, 39], Operations: ['77-64=13', '52-13=39'] Exploring Operation: 79-39=40, Resulting Numbers: [40] 40,90 unequal: No Solution Exploring Operation: 79*39=3081, Resulting Numbers: [3081] 3081,90 unequal: No Solution Exploring Operation: 79+39=118, Resulting Numbers: [118] 118,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[52, 66], Operations: ['77-64=13', '79-13=66'] Exploring Operation: 52*66=3432, Resulting Numbers: [3432] 3432,90 unequal: No Solution Exploring Operation: 66-52=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 52+66=118, Resulting Numbers: [118] 118,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[77, 52, 15], Operations: ['79-64=15'] Exploring Operation: 52+15=67, Resulting Numbers: [77, 67] Generated Node #0,2,0: 90:[77, 67] Operation: 52+15=67 Exploring Operation: 77-15=62, Resulting Numbers: [52, 62] Generated Node #0,2,1: 90:[52, 62] Operation: 77-15=62 Exploring Operation: 77+15=92, Resulting Numbers: [52, 92] Generated Node #0,2,2: 90:[52, 92] Operation: 77+15=92 Exploring Operation: 52-15=37, Resulting Numbers: [77, 37] Generated Node #0,2,3: 90:[77, 37] Operation: 52-15=37 Exploring Operation: 77-52=25, Resulting Numbers: [15, 25] Generated Node #0,2,4: 90:[15, 25] Operation: 77-52=25 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 90:[15, 25], Operations: ['79-64=15', '77-52=25'] Exploring Operation: 15*25=375, Resulting Numbers: [375] 375,90 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 90:[52, 92], Operations: ['79-64=15', '77+15=92'] Exploring Operation: 52+92=144, Resulting Numbers: [144] 144,90 unequal: No Solution Exploring Operation: 52*92=4784, Resulting Numbers: [4784] 4784,90 unequal: No Solution Exploring Operation: 92-52=40, Resulting Numbers: [40] 40,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 90:[77, 37], Operations: ['79-64=15', '52-15=37'] Exploring Operation: 77*37=2849, Resulting Numbers: [2849] 2849,90 unequal: No Solution Exploring Operation: 77+37=114, Resulting Numbers: [114] 114,90 unequal: No Solution Exploring Operation: 77-37=40, Resulting Numbers: [40] 40,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 90:[52, 62], Operations: ['79-64=15', '77-15=62'] Exploring Operation: 52*62=3224, Resulting Numbers: [3224] 3224,90 unequal: No Solution Exploring Operation: 62-52=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 52+62=114, Resulting Numbers: [114] 114,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 90:[77, 67], Operations: ['79-64=15', '52+15=67'] Exploring Operation: 77+67=144, Resulting Numbers: [144] 144,90 unequal: No Solution Exploring Operation: 77-67=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 77*67=5159, Resulting Numbers: [5159] 5159,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[77, 79, 12], Operations: ['64-52=12'] Exploring Operation: 79+12=91, Resulting Numbers: [77, 91] Generated Node #0,3,0: 90:[77, 91] Operation: 79+12=91 Exploring Operation: 79-12=67, Resulting Numbers: [77, 67] Generated Node #0,3,1: 90:[77, 67] Operation: 79-12=67 Exploring Operation: 79-77=2, Resulting Numbers: [12, 2] Generated Node #0,3,2: 90:[12, 2] Operation: 79-77=2 Exploring Operation: 77+12=89, Resulting Numbers: [79, 89] Generated Node #0,3,3: 90:[79, 89] Operation: 77+12=89 Exploring Operation: 77-12=65, Resulting Numbers: [79, 65] Generated Node #0,3,4: 90:[79, 65] Operation: 77-12=65 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 90:[12, 2], Operations: ['64-52=12', '79-77=2'] Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,90 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 90:[79, 89], Operations: ['64-52=12', '77+12=89'] Exploring Operation: 89-79=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 79*89=7031, Resulting Numbers: [7031] 7031,90 unequal: No Solution Exploring Operation: 79+89=168, Resulting Numbers: [168] 168,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 90:[77, 91], Operations: ['64-52=12', '79+12=91'] Exploring Operation: 77*91=7007, Resulting Numbers: [7007] 7007,90 unequal: No Solution Exploring Operation: 77+91=168, Resulting Numbers: [168] 168,90 unequal: No Solution Exploring Operation: 91-77=14, Resulting Numbers: [14] 14,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 90:[79, 65], Operations: ['64-52=12', '77-12=65'] Exploring Operation: 79+65=144, Resulting Numbers: [144] 144,90 unequal: No Solution Exploring Operation: 79*65=5135, Resulting Numbers: [5135] 5135,90 unequal: No Solution Exploring Operation: 79-65=14, Resulting Numbers: [14] 14,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 90:[77, 67], Operations: ['64-52=12', '79-12=67'] Exploring Operation: 77-67=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 77*67=5159, Resulting Numbers: [5159] 5159,90 unequal: No Solution Exploring Operation: 77+67=144, Resulting Numbers: [144] 144,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 90:[64, 52, 2], Operations: ['79-77=2'] Exploring Operation: 64-2=62, Resulting Numbers: [52, 62] Generated Node #0,4,0: 90:[52, 62] Operation: 64-2=62 Exploring Operation: 64-52=12, Resulting Numbers: [2, 12] Generated Node #0,4,1: 90:[2, 12] Operation: 64-52=12 Exploring Operation: 64/2=32, Resulting Numbers: [52, 32] Generated Node #0,4,2: 90:[52, 32] Operation: 64/2=32 Exploring Operation: 52-2=50, Resulting Numbers: [64, 50] Generated Node #0,4,3: 90:[64, 50] Operation: 52-2=50 Exploring Operation: 52/2=26, Resulting Numbers: [64, 26] Generated Node #0,4,4: 90:[64, 26] Operation: 52/2=26 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 90:[2, 12], Operations: ['79-77=2', '64-52=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,90 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 90:[52, 32], Operations: ['79-77=2', '64/2=32'] Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,90 unequal: No Solution Exploring Operation: 52*32=1664, Resulting Numbers: [1664] 1664,90 unequal: No Solution Exploring Operation: 52+32=84, Resulting Numbers: [84] 84,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 90:[64, 26], Operations: ['79-77=2', '52/2=26'] Exploring Operation: 64*26=1664, Resulting Numbers: [1664] 1664,90 unequal: No Solution Exploring Operation: 64-26=38, Resulting Numbers: [38] 38,90 unequal: No Solution Exploring Operation: 64+26=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[77, 64, 52, 79], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [64, 52, 2] Generated Node #0,4: 90:[64, 52, 2] Operation: 79-77=2 Moving to Node #0,4 Current State: 90:[64, 52, 2], Operations: ['79-77=2'] Exploring Operation: 52/2=26, Resulting Numbers: [64, 26] Generated Node #0,4,4: 90:[64, 26] Operation: 52/2=26 Moving to Node #0,4,4 Current State: 90:[64, 26], Operations: ['79-77=2', '52/2=26'] Exploring Operation: 64+26=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.926215
hs_5
sum_heuristic
[ 35, 23, 9, 87 ]
22
[ "35*23=805", "9*87=783", "805-783=22" ]
Current State: 22:[35, 23, 9, 87], Operations: [] Exploring Operation: 35*23=805, Resulting Numbers: [9, 87, 805] Generated Node #2: [9, 87, 805] from Operation: 35*23=805 Current State: 22:[9, 87, 805], Operations: ['35*23=805'] Exploring Operation: 9*87=783, Resulting Numbers: [805, 783] Generated Node #3: [805, 783] from Operation: 9*87=783 Current State: 22:[805, 783], Operations: ['35*23=805', '9*87=783'] Exploring Operation: 805-783=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[35, 23, 9, 87], Operations: [] Exploring Operation: 87-23=64, Resulting Numbers: [35, 9, 64] Generated Node #0,0: 22:[35, 9, 64] Operation: 87-23=64 Exploring Operation: 35-23=12, Resulting Numbers: [9, 87, 12] Generated Node #0,1: 22:[9, 87, 12] Operation: 35-23=12 Exploring Operation: 87-35=52, Resulting Numbers: [23, 9, 52] Generated Node #0,2: 22:[23, 9, 52] Operation: 87-35=52 Moving to Node #0,2 Current State: 22:[23, 9, 52], Operations: ['87-35=52'] Exploring Operation: 23-9=14, Resulting Numbers: [52, 14] Generated Node #0,2,0: 22:[52, 14] Operation: 23-9=14 Exploring Operation: 52-23=29, Resulting Numbers: [9, 29] Generated Node #0,2,1: 22:[9, 29] Operation: 52-23=29 Exploring Operation: 52-9=43, Resulting Numbers: [23, 43] Generated Node #0,2,2: 22:[23, 43] Operation: 52-9=43 Moving to Node #0,0 Current State: 22:[35, 9, 64], Operations: ['87-23=64'] Exploring Operation: 64-9=55, Resulting Numbers: [35, 55] Generated Node #0,0,0: 22:[35, 55] Operation: 64-9=55 Exploring Operation: 35-9=26, Resulting Numbers: [64, 26] Generated Node #0,0,1: 22:[64, 26] Operation: 35-9=26 Exploring Operation: 64-35=29, Resulting Numbers: [9, 29] Generated Node #0,0,2: 22:[9, 29] Operation: 64-35=29 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 22:[9, 29], Operations: ['87-23=64', '64-35=29'] Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,22 unequal: No Solution Exploring Operation: 9*29=261, Resulting Numbers: [261] 261,22 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[35, 55], Operations: ['87-23=64', '64-9=55'] Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,22 unequal: No Solution Exploring Operation: 35+55=90, Resulting Numbers: [90] 90,22 unequal: No Solution Exploring Operation: 35*55=1925, Resulting Numbers: [1925] 1925,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 22:[64, 26], Operations: ['87-23=64', '35-9=26'] Exploring Operation: 64+26=90, Resulting Numbers: [90] 90,22 unequal: No Solution Exploring Operation: 64*26=1664, Resulting Numbers: [1664] 1664,22 unequal: No Solution Exploring Operation: 64-26=38, Resulting Numbers: [38] 38,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 22:[9, 87, 12], Operations: ['35-23=12'] Exploring Operation: 87-12=75, Resulting Numbers: [9, 75] Generated Node #0,1,0: 22:[9, 75] Operation: 87-12=75 Exploring Operation: 87-9=78, Resulting Numbers: [12, 78] Generated Node #0,1,1: 22:[12, 78] Operation: 87-9=78 Exploring Operation: 9+12=21, Resulting Numbers: [87, 21] Generated Node #0,1,2: 22:[87, 21] Operation: 9+12=21 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[9, 75], Operations: ['35-23=12', '87-12=75'] Exploring Operation: 9+75=84, Resulting Numbers: [84] 84,22 unequal: No Solution Exploring Operation: 75-9=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 9*75=675, Resulting Numbers: [675] 675,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[12, 78], Operations: ['35-23=12', '87-9=78'] Exploring Operation: 78-12=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 12*78=936, Resulting Numbers: [936] 936,22 unequal: No Solution Exploring Operation: 12+78=90, Resulting Numbers: [90] 90,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 22:[87, 21], Operations: ['35-23=12', '9+12=21'] Exploring Operation: 87-21=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 87+21=108, Resulting Numbers: [108] 108,22 unequal: No Solution Exploring Operation: 87*21=1827, Resulting Numbers: [1827] 1827,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 22:[9, 29], Operations: ['87-35=52', '52-23=29'] Exploring Operation: 9*29=261, Resulting Numbers: [261] 261,22 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,22 unequal: No Solution Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[23, 43], Operations: ['87-35=52', '52-9=43'] Exploring Operation: 23*43=989, Resulting Numbers: [989] 989,22 unequal: No Solution Exploring Operation: 23+43=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,22 unequal: No Solution Moving to Node #0,2,0 Current State: 22:[52, 14], Operations: ['87-35=52', '23-9=14'] Exploring Operation: 52+14=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,22 unequal: No Solution Exploring Operation: 52*14=728, Resulting Numbers: [728] 728,22 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 89, 28, 5, 26 ]
13
[ "89+28=117", "5*26=130", "130-117=13" ]
Current State: 13:[89, 28, 5, 26], Operations: [] Exploring Operation: 89+28=117, Resulting Numbers: [5, 26, 117] Generated Node #2: [5, 26, 117] from Operation: 89+28=117 Current State: 13:[5, 26, 117], Operations: ['89+28=117'] Exploring Operation: 5*26=130, Resulting Numbers: [117, 130] Generated Node #3: [117, 130] from Operation: 5*26=130 Current State: 13:[117, 130], Operations: ['89+28=117', '5*26=130'] Exploring Operation: 130-117=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[89, 28, 5, 26], Operations: [] Exploring Operation: 89-26=63, Resulting Numbers: [28, 5, 63] Generated Node #0,0: 13:[28, 5, 63] Operation: 89-26=63 Exploring Operation: 28-26=2, Resulting Numbers: [89, 5, 2] Generated Node #0,1: 13:[89, 5, 2] Operation: 28-26=2 Exploring Operation: 89-5=84, Resulting Numbers: [28, 26, 84] Generated Node #0,2: 13:[28, 26, 84] Operation: 89-5=84 Exploring Operation: 89-28=61, Resulting Numbers: [5, 26, 61] Generated Node #0,3: 13:[5, 26, 61] Operation: 89-28=61 Exploring Operation: 28-5=23, Resulting Numbers: [89, 26, 23] Generated Node #0,4: 13:[89, 26, 23] Operation: 28-5=23 Moving to Node #0,3 Current State: 13:[5, 26, 61], Operations: ['89-28=61'] Exploring Operation: 5+61=66, Resulting Numbers: [26, 66] Generated Node #0,3,0: 13:[26, 66] Operation: 5+61=66 Exploring Operation: 26-5=21, Resulting Numbers: [61, 21] Generated Node #0,3,1: 13:[61, 21] Operation: 26-5=21 Exploring Operation: 61-26=35, Resulting Numbers: [5, 35] Generated Node #0,3,2: 13:[5, 35] Operation: 61-26=35 Exploring Operation: 61-5=56, Resulting Numbers: [26, 56] Generated Node #0,3,3: 13:[26, 56] Operation: 61-5=56 Exploring Operation: 5+26=31, Resulting Numbers: [61, 31] Generated Node #0,3,4: 13:[61, 31] Operation: 5+26=31 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 13:[5, 35], Operations: ['89-28=61', '61-26=35'] Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 5*35=175, Resulting Numbers: [175] 175,13 unequal: No Solution Exploring Operation: 5+35=40, Resulting Numbers: [40] 40,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 13:[61, 21], Operations: ['89-28=61', '26-5=21'] Exploring Operation: 61*21=1281, Resulting Numbers: [1281] 1281,13 unequal: No Solution Exploring Operation: 61-21=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 61+21=82, Resulting Numbers: [82] 82,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 13:[26, 56], Operations: ['89-28=61', '61-5=56'] Exploring Operation: 26*56=1456, Resulting Numbers: [1456] 1456,13 unequal: No Solution Exploring Operation: 56-26=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 26+56=82, Resulting Numbers: [82] 82,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 13:[26, 66], Operations: ['89-28=61', '5+61=66'] Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 26+66=92, Resulting Numbers: [92] 92,13 unequal: No Solution Exploring Operation: 26*66=1716, Resulting Numbers: [1716] 1716,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 13:[61, 31], Operations: ['89-28=61', '5+26=31'] Exploring Operation: 61+31=92, Resulting Numbers: [92] 92,13 unequal: No Solution Exploring Operation: 61*31=1891, Resulting Numbers: [1891] 1891,13 unequal: No Solution Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 13:[28, 5, 63], Operations: ['89-26=63'] Exploring Operation: 63-5=58, Resulting Numbers: [28, 58] Generated Node #0,0,0: 13:[28, 58] Operation: 63-5=58 Exploring Operation: 28-5=23, Resulting Numbers: [63, 23] Generated Node #0,0,1: 13:[63, 23] Operation: 28-5=23 Exploring Operation: 28+5=33, Resulting Numbers: [63, 33] Generated Node #0,0,2: 13:[63, 33] Operation: 28+5=33 Exploring Operation: 63-28=35, Resulting Numbers: [5, 35] Generated Node #0,0,3: 13:[5, 35] Operation: 63-28=35 Exploring Operation: 5+63=68, Resulting Numbers: [28, 68] Generated Node #0,0,4: 13:[28, 68] Operation: 5+63=68 Moving to Node #0,1 Current State: 13:[89, 5, 2], Operations: ['28-26=2'] Exploring Operation: 89-2=87, Resulting Numbers: [5, 87] Generated Node #0,1,0: 13:[5, 87] Operation: 89-2=87 Exploring Operation: 89+2=91, Resulting Numbers: [5, 91] Generated Node #0,1,1: 13:[5, 91] Operation: 89+2=91 Exploring Operation: 5+2=7, Resulting Numbers: [89, 7] Generated Node #0,1,2: 13:[89, 7] Operation: 5+2=7 Exploring Operation: 89-5=84, Resulting Numbers: [2, 84] Generated Node #0,1,3: 13:[2, 84] Operation: 89-5=84 Exploring Operation: 5*2=10, Resulting Numbers: [89, 10] Generated Node #0,1,4: 13:[89, 10] Operation: 5*2=10 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 13:[89, 10], Operations: ['28-26=2', '5*2=10'] Exploring Operation: 89-10=79, Resulting Numbers: [79] 79,13 unequal: No Solution Exploring Operation: 89*10=890, Resulting Numbers: [890] 890,13 unequal: No Solution Exploring Operation: 89+10=99, Resulting Numbers: [99] 99,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 13:[5, 87], Operations: ['28-26=2', '89-2=87'] Exploring Operation: 87-5=82, Resulting Numbers: [82] 82,13 unequal: No Solution Exploring Operation: 5*87=435, Resulting Numbers: [435] 435,13 unequal: No Solution Exploring Operation: 5+87=92, Resulting Numbers: [92] 92,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 13:[89, 7], Operations: ['28-26=2', '5+2=7'] Exploring Operation: 89*7=623, Resulting Numbers: [623] 623,13 unequal: No Solution Exploring Operation: 89+7=96, Resulting Numbers: [96] 96,13 unequal: No Solution Exploring Operation: 89-7=82, Resulting Numbers: [82] 82,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 13:[2, 84], Operations: ['28-26=2', '89-5=84'] Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,13 unequal: No Solution Exploring Operation: 2*84=168, Resulting Numbers: [168] 168,13 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,13 unequal: No Solution Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 13:[5, 91], Operations: ['28-26=2', '89+2=91'] Exploring Operation: 5+91=96, Resulting Numbers: [96] 96,13 unequal: No Solution Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,13 unequal: No Solution Exploring Operation: 5*91=455, Resulting Numbers: [455] 455,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 13:[28, 26, 84], Operations: ['89-5=84'] Exploring Operation: 84-28=56, Resulting Numbers: [26, 56] Generated Node #0,2,0: 13:[26, 56] Operation: 84-28=56 Exploring Operation: 28+26=54, Resulting Numbers: [84, 54] Generated Node #0,2,1: 13:[84, 54] Operation: 28+26=54 Exploring Operation: 84/28=3, Resulting Numbers: [26, 3] Generated Node #0,2,2: 13:[26, 3] Operation: 84/28=3 Exploring Operation: 84-26=58, Resulting Numbers: [28, 58] Generated Node #0,2,3: 13:[28, 58] Operation: 84-26=58 Exploring Operation: 28-26=2, Resulting Numbers: [84, 2] Generated Node #0,2,4: 13:[84, 2] Operation: 28-26=2 Moving to Node #0,4 Current State: 13:[89, 26, 23], Operations: ['28-5=23'] Exploring Operation: 89-23=66, Resulting Numbers: [26, 66] Generated Node #0,4,0: 13:[26, 66] Operation: 89-23=66 Exploring Operation: 26-23=3, Resulting Numbers: [89, 3] Generated Node #0,4,1: 13:[89, 3] Operation: 26-23=3 Exploring Operation: 89+26=115, Resulting Numbers: [23, 115] Generated Node #0,4,2: 13:[23, 115] Operation: 89+26=115 Exploring Operation: 89+23=112, Resulting Numbers: [26, 112] Generated Node #0,4,3: 13:[26, 112] Operation: 89+23=112 Exploring Operation: 89-26=63, Resulting Numbers: [23, 63] Generated Node #0,4,4: 13:[23, 63] Operation: 89-26=63 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 13:[23, 63], Operations: ['28-5=23', '89-26=63'] Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 23*63=1449, Resulting Numbers: [1449] 1449,13 unequal: No Solution Exploring Operation: 23+63=86, Resulting Numbers: [86] 86,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 13:[26, 66], Operations: ['28-5=23', '89-23=66'] Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 26*66=1716, Resulting Numbers: [1716] 1716,13 unequal: No Solution Exploring Operation: 26+66=92, Resulting Numbers: [92] 92,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 13:[89, 3], Operations: ['28-5=23', '26-23=3'] Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,13 unequal: No Solution Exploring Operation: 89*3=267, Resulting Numbers: [267] 267,13 unequal: No Solution Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 13:[23, 115], Operations: ['28-5=23', '89+26=115'] Exploring Operation: 115/23=5, Resulting Numbers: [5] 5,13 unequal: No Solution Exploring Operation: 23+115=138, Resulting Numbers: [138] 138,13 unequal: No Solution Exploring Operation: 23*115=2645, Resulting Numbers: [2645] 2645,13 unequal: No Solution Exploring Operation: 115-23=92, Resulting Numbers: [92] 92,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 13:[26, 112], Operations: ['28-5=23', '89+23=112'] Exploring Operation: 26*112=2912, Resulting Numbers: [2912] 2912,13 unequal: No Solution Exploring Operation: 112-26=86, Resulting Numbers: [86] 86,13 unequal: No Solution Exploring Operation: 26+112=138, Resulting Numbers: [138] 138,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 13:[26, 3], Operations: ['89-5=84', '84/28=3'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,13 unequal: No Solution Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,13 unequal: No Solution Exploring Operation: 26*3=78, Resulting Numbers: [78] 78,13 unequal: No Solution Moving to Node #0,0,3 Current State: 13:[5, 35], Operations: ['89-26=63', '63-28=35'] Exploring Operation: 5+35=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 5*35=175, Resulting Numbers: [175] 175,13 unequal: No Solution Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,13 unequal: No Solution Moving to Node #0,2,0 Current State: 13:[26, 56], Operations: ['89-5=84', '84-28=56'] Exploring Operation: 56-26=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 26*56=1456, Resulting Numbers: [1456] 1456,13 unequal: No Solution Exploring Operation: 26+56=82, Resulting Numbers: [82] 82,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[63, 23], Operations: ['89-26=63', '28-5=23'] Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 63+23=86, Resulting Numbers: [86] 86,13 unequal: No Solution Exploring Operation: 63*23=1449, Resulting Numbers: [1449] 1449,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[28, 58], Operations: ['89-26=63', '63-5=58'] Exploring Operation: 28+58=86, Resulting Numbers: [86] 86,13 unequal: No Solution Exploring Operation: 28*58=1624, Resulting Numbers: [1624] 1624,13 unequal: No Solution Exploring Operation: 58-28=30, Resulting Numbers: [30] 30,13 unequal: No Solution Moving to Node #0,2,3 Current State: 13:[28, 58], Operations: ['89-5=84', '84-26=58'] Exploring Operation: 28*58=1624, Resulting Numbers: [1624] 1624,13 unequal: No Solution Exploring Operation: 58-28=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 28+58=86, Resulting Numbers: [86] 86,13 unequal: No Solution Moving to Node #0,0,2 Current State: 13:[63, 33], Operations: ['89-26=63', '28+5=33'] Exploring Operation: 63*33=2079, Resulting Numbers: [2079] 2079,13 unequal: No Solution Exploring Operation: 63+33=96, Resulting Numbers: [96] 96,13 unequal: No Solution Exploring Operation: 63-33=30, Resulting Numbers: [30] 30,13 unequal: No Solution Moving to Node #0,0,4 Current State: 13:[28, 68], Operations: ['89-26=63', '5+63=68'] Exploring Operation: 68-28=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 28+68=96, Resulting Numbers: [96] 96,13 unequal: No Solution Exploring Operation: 28*68=1904, Resulting Numbers: [1904] 1904,13 unequal: No Solution Moving to Node #0,2,4 Current State: 13:[84, 2], Operations: ['89-5=84', '28-26=2'] Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,13 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,13 unequal: No Solution Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,13 unequal: No Solution Exploring Operation: 84*2=168, Resulting Numbers: [168] 168,13 unequal: No Solution Moving to Node #0,2,1 Current State: 13:[84, 54], Operations: ['89-5=84', '28+26=54'] Exploring Operation: 84*54=4536, Resulting Numbers: [4536] 4536,13 unequal: No Solution Exploring Operation: 84-54=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 84+54=138, Resulting Numbers: [138] 138,13 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 4, 41, 39, 11 ]
30
[ "4+11=15", "41-39=2", "15*2=30" ]
Current State: 30:[4, 41, 39, 11], Operations: [] Exploring Operation: 4+11=15, Resulting Numbers: [41, 39, 15] Generated Node #2: [41, 39, 15] from Operation: 4+11=15 Current State: 30:[41, 39, 15], Operations: ['4+11=15'] Exploring Operation: 41-39=2, Resulting Numbers: [15, 2] Generated Node #3: [15, 2] from Operation: 41-39=2 Current State: 30:[15, 2], Operations: ['4+11=15', '41-39=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[4, 41, 39, 11], Operations: [] Exploring Operation: 39-11=28, Resulting Numbers: [4, 41, 28] Generated Node #0,0: 30:[4, 41, 28] Operation: 39-11=28 Exploring Operation: 41-11=30, Resulting Numbers: [4, 39, 30] Generated Node #0,1: 30:[4, 39, 30] Operation: 41-11=30 Exploring Operation: 41-4=37, Resulting Numbers: [39, 11, 37] Generated Node #0,2: 30:[39, 11, 37] Operation: 41-4=37 Exploring Operation: 41-39=2, Resulting Numbers: [4, 11, 2] Generated Node #0,3: 30:[4, 11, 2] Operation: 41-39=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 30:[4, 11, 2], Operations: ['41-39=2'] Exploring Operation: 4+11=15, Resulting Numbers: [2, 15] Generated Node #0,3,0: 30:[2, 15] Operation: 4+11=15 Exploring Operation: 11-4=7, Resulting Numbers: [2, 7] Generated Node #0,3,1: 30:[2, 7] Operation: 11-4=7 Exploring Operation: 4+2=6, Resulting Numbers: [11, 6] Generated Node #0,3,2: 30:[11, 6] Operation: 4+2=6 Exploring Operation: 4-2=2, Resulting Numbers: [11, 2] Generated Node #0,3,3: 30:[11, 2] Operation: 4-2=2 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 30:[2, 15], Operations: ['41-39=2', '4+11=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[4, 41, 39, 11], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [4, 11, 2] Generated Node #0,3: 30:[4, 11, 2] Operation: 41-39=2 Moving to Node #0,3 Current State: 30:[4, 11, 2], Operations: ['41-39=2'] Exploring Operation: 4+11=15, Resulting Numbers: [2, 15] Generated Node #0,3,0: 30:[2, 15] Operation: 4+11=15 Moving to Node #0,3,0 Current State: 30:[2, 15], Operations: ['41-39=2', '4+11=15'] Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 34, 31, 13, 26 ]
73
[ "34-26=8", "13*8=104", "104-31=73" ]
Current State: 73:[34, 31, 13, 26], Operations: [] Exploring Operation: 34-26=8, Resulting Numbers: [31, 13, 8] Generated Node #2: [31, 13, 8] from Operation: 34-26=8 Current State: 73:[31, 13, 8], Operations: ['34-26=8'] Exploring Operation: 13*8=104, Resulting Numbers: [31, 104] Generated Node #3: [31, 104] from Operation: 13*8=104 Current State: 73:[31, 104], Operations: ['34-26=8', '13*8=104'] Exploring Operation: 104-31=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[34, 31, 13, 26], Operations: [] Exploring Operation: 34+13=47, Resulting Numbers: [31, 26, 47] Generated Node #0,0: 73:[31, 26, 47] Operation: 34+13=47 Exploring Operation: 34+26=60, Resulting Numbers: [31, 13, 60] Generated Node #0,1: 73:[31, 13, 60] Operation: 34+26=60 Exploring Operation: 34+31=65, Resulting Numbers: [13, 26, 65] Generated Node #0,2: 73:[13, 26, 65] Operation: 34+31=65 Exploring Operation: 31+13=44, Resulting Numbers: [34, 26, 44] Generated Node #0,3: 73:[34, 26, 44] Operation: 31+13=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[31, 26, 47], Operations: ['34+13=47'] Exploring Operation: 26+47=73, Resulting Numbers: [31, 73] Generated Node #0,0,0: 73:[31, 73] Operation: 26+47=73 Exploring Operation: 31+26=57, Resulting Numbers: [47, 57] Generated Node #0,0,1: 73:[47, 57] Operation: 31+26=57 Exploring Operation: 31-26=5, Resulting Numbers: [47, 5] Generated Node #0,0,2: 73:[47, 5] Operation: 31-26=5 Exploring Operation: 31+47=78, Resulting Numbers: [26, 78] Generated Node #0,0,3: 73:[26, 78] Operation: 31+47=78 Moving to Node #0,0,0 Current State: 73:[31, 73], Operations: ['34+13=47', '26+47=73'] Exploring Operation: 73-31=42, Resulting Numbers: [42] 42,73 unequal: No Solution Exploring Operation: 31+73=104, Resulting Numbers: [104] 104,73 unequal: No Solution Exploring Operation: 31*73=2263, Resulting Numbers: [2263] 2263,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[47, 57], Operations: ['34+13=47', '31+26=57'] Exploring Operation: 57-47=10, Resulting Numbers: [10] 10,73 unequal: No Solution Exploring Operation: 47*57=2679, Resulting Numbers: [2679] 2679,73 unequal: No Solution Exploring Operation: 47+57=104, Resulting Numbers: [104] 104,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[26, 78], Operations: ['34+13=47', '31+47=78'] Exploring Operation: 26*78=2028, Resulting Numbers: [2028] 2028,73 unequal: No Solution Exploring Operation: 78/26=3, Resulting Numbers: [3] 3,73 unequal: No Solution Exploring Operation: 26+78=104, Resulting Numbers: [104] 104,73 unequal: No Solution Exploring Operation: 78-26=52, Resulting Numbers: [52] 52,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[47, 5], Operations: ['34+13=47', '31-26=5'] Exploring Operation: 47*5=235, Resulting Numbers: [235] 235,73 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,73 unequal: No Solution Exploring Operation: 47+5=52, Resulting Numbers: [52] 52,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[31, 13, 60], Operations: ['34+26=60'] Exploring Operation: 13+60=73, Resulting Numbers: [31, 73] Generated Node #0,1,0: 73:[31, 73] Operation: 13+60=73 Exploring Operation: 60-13=47, Resulting Numbers: [31, 47] Generated Node #0,1,1: 73:[31, 47] Operation: 60-13=47 Exploring Operation: 31-13=18, Resulting Numbers: [60, 18] Generated Node #0,1,2: 73:[60, 18] Operation: 31-13=18 Exploring Operation: 31+13=44, Resulting Numbers: [60, 44] Generated Node #0,1,3: 73:[60, 44] Operation: 31+13=44 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[31, 73], Operations: ['34+26=60', '13+60=73'] Exploring Operation: 31*73=2263, Resulting Numbers: [2263] 2263,73 unequal: No Solution Exploring Operation: 31+73=104, Resulting Numbers: [104] 104,73 unequal: No Solution Exploring Operation: 73-31=42, Resulting Numbers: [42] 42,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 73:[60, 44], Operations: ['34+26=60', '31+13=44'] Exploring Operation: 60*44=2640, Resulting Numbers: [2640] 2640,73 unequal: No Solution Exploring Operation: 60-44=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 60+44=104, Resulting Numbers: [104] 104,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[31, 47], Operations: ['34+26=60', '60-13=47'] Exploring Operation: 31+47=78, Resulting Numbers: [78] 78,73 unequal: No Solution Exploring Operation: 31*47=1457, Resulting Numbers: [1457] 1457,73 unequal: No Solution Exploring Operation: 47-31=16, Resulting Numbers: [16] 16,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 73:[60, 18], Operations: ['34+26=60', '31-13=18'] Exploring Operation: 60-18=42, Resulting Numbers: [42] 42,73 unequal: No Solution Exploring Operation: 60*18=1080, Resulting Numbers: [1080] 1080,73 unequal: No Solution Exploring Operation: 60+18=78, Resulting Numbers: [78] 78,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[13, 26, 65], Operations: ['34+31=65'] Exploring Operation: 26-13=13, Resulting Numbers: [65, 13] Generated Node #0,2,0: 73:[65, 13] Operation: 26-13=13 Exploring Operation: 13+65=78, Resulting Numbers: [26, 78] Generated Node #0,2,1: 73:[26, 78] Operation: 13+65=78 Exploring Operation: 13+26=39, Resulting Numbers: [65, 39] Generated Node #0,2,2: 73:[65, 39] Operation: 13+26=39 Exploring Operation: 65-13=52, Resulting Numbers: [26, 52] Generated Node #0,2,3: 73:[26, 52] Operation: 65-13=52 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 73:[65, 39], Operations: ['34+31=65', '13+26=39'] Exploring Operation: 65+39=104, Resulting Numbers: [104] 104,73 unequal: No Solution Exploring Operation: 65-39=26, Resulting Numbers: [26] 26,73 unequal: No Solution Exploring Operation: 65*39=2535, Resulting Numbers: [2535] 2535,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 73:[26, 78], Operations: ['34+31=65', '13+65=78'] Exploring Operation: 26*78=2028, Resulting Numbers: [2028] 2028,73 unequal: No Solution Exploring Operation: 78-26=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 78/26=3, Resulting Numbers: [3] 3,73 unequal: No Solution Exploring Operation: 26+78=104, Resulting Numbers: [104] 104,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 73:[65, 13], Operations: ['34+31=65', '26-13=13'] Exploring Operation: 65*13=845, Resulting Numbers: [845] 845,73 unequal: No Solution Exploring Operation: 65-13=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 65+13=78, Resulting Numbers: [78] 78,73 unequal: No Solution Exploring Operation: 65/13=5, Resulting Numbers: [5] 5,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 73:[26, 52], Operations: ['34+31=65', '65-13=52'] Exploring Operation: 26+52=78, Resulting Numbers: [78] 78,73 unequal: No Solution Exploring Operation: 26*52=1352, Resulting Numbers: [1352] 1352,73 unequal: No Solution Exploring Operation: 52/26=2, Resulting Numbers: [2] 2,73 unequal: No Solution Exploring Operation: 52-26=26, Resulting Numbers: [26] 26,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 73:[34, 26, 44], Operations: ['31+13=44'] Exploring Operation: 26+44=70, Resulting Numbers: [34, 70] Generated Node #0,3,0: 73:[34, 70] Operation: 26+44=70 Exploring Operation: 34+26=60, Resulting Numbers: [44, 60] Generated Node #0,3,1: 73:[44, 60] Operation: 34+26=60 Exploring Operation: 34-26=8, Resulting Numbers: [44, 8] Generated Node #0,3,2: 73:[44, 8] Operation: 34-26=8 Exploring Operation: 34+44=78, Resulting Numbers: [26, 78] Generated Node #0,3,3: 73:[26, 78] Operation: 34+44=78 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 73:[34, 70], Operations: ['31+13=44', '26+44=70'] Exploring Operation: 34+70=104, Resulting Numbers: [104] 104,73 unequal: No Solution Exploring Operation: 34*70=2380, Resulting Numbers: [2380] 2380,73 unequal: No Solution Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 73:[44, 60], Operations: ['31+13=44', '34+26=60'] Exploring Operation: 44+60=104, Resulting Numbers: [104] 104,73 unequal: No Solution Exploring Operation: 44*60=2640, Resulting Numbers: [2640] 2640,73 unequal: No Solution Exploring Operation: 60-44=16, Resulting Numbers: [16] 16,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 73:[26, 78], Operations: ['31+13=44', '34+44=78'] Exploring Operation: 26*78=2028, Resulting Numbers: [2028] 2028,73 unequal: No Solution Exploring Operation: 78/26=3, Resulting Numbers: [3] 3,73 unequal: No Solution Exploring Operation: 78-26=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 26+78=104, Resulting Numbers: [104] 104,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 73:[44, 8], Operations: ['31+13=44', '34-26=8'] Exploring Operation: 44+8=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,73 unequal: No Solution Exploring Operation: 44*8=352, Resulting Numbers: [352] 352,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 42, 49, 7, 8 ]
57
[ "49-42=7", "7*7=49", "8+49=57" ]
Current State: 57:[42, 49, 7, 8], Operations: [] Exploring Operation: 49-42=7, Resulting Numbers: [7, 8, 7] Generated Node #2: [7, 8, 7] from Operation: 49-42=7 Current State: 57:[7, 8, 7], Operations: ['49-42=7'] Exploring Operation: 7*7=49, Resulting Numbers: [8, 49] Generated Node #3: [8, 49] from Operation: 7*7=49 Current State: 57:[8, 49], Operations: ['49-42=7', '7*7=49'] Exploring Operation: 8+49=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[42, 49, 7, 8], Operations: [] Exploring Operation: 49+8=57, Resulting Numbers: [42, 7, 57] Generated Node #0,0: 57:[42, 7, 57] Operation: 49+8=57 Exploring Operation: 49-42=7, Resulting Numbers: [7, 8, 7] Generated Node #0,1: 57:[7, 8, 7] Operation: 49-42=7 Exploring Operation: 42+7=49, Resulting Numbers: [49, 8, 49] Generated Node #0,2: 57:[49, 8, 49] Operation: 42+7=49 Exploring Operation: 42/7=6, Resulting Numbers: [49, 8, 6] Generated Node #0,3: 57:[49, 8, 6] Operation: 42/7=6 Exploring Operation: 42+8=50, Resulting Numbers: [49, 7, 50] Generated Node #0,4: 57:[49, 7, 50] Operation: 42+8=50 Moving to Node #0,1 Current State: 57:[7, 8, 7], Operations: ['49-42=7'] Exploring Operation: 8*7=56, Resulting Numbers: [7, 56] Generated Node #0,1,0: 57:[7, 56] Operation: 8*7=56 Exploring Operation: 8-7=1, Resulting Numbers: [7, 1] Generated Node #0,1,1: 57:[7, 1] Operation: 8-7=1 Exploring Operation: 7/7=1, Resulting Numbers: [8, 1] Generated Node #0,1,2: 57:[8, 1] Operation: 7/7=1 Exploring Operation: 7*8=56, Resulting Numbers: [7, 56] Generated Node #0,1,3: 57:[7, 56] Operation: 7*8=56 Exploring Operation: 8-7=1, Resulting Numbers: [7, 1] Generated Node #0,1,4: 57:[7, 1] Operation: 8-7=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[7, 56], Operations: ['49-42=7', '8*7=56'] Exploring Operation: 7*56=392, Resulting Numbers: [392] 392,57 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,57 unequal: No Solution Exploring Operation: 7+56=63, Resulting Numbers: [63] 63,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 57:[7, 56], Operations: ['49-42=7', '7*8=56'] Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 7*56=392, Resulting Numbers: [392] 392,57 unequal: No Solution Exploring Operation: 7+56=63, Resulting Numbers: [63] 63,57 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 57:[7, 1], Operations: ['49-42=7', '8-7=1'] Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,57 unequal: No Solution Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 57:[7, 1], Operations: ['49-42=7', '8-7=1'] Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,57 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,57 unequal: No Solution Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 57:[8, 1], Operations: ['49-42=7', '7/7=1'] Exploring Operation: 8+1=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,57 unequal: No Solution Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 57:[49, 8, 6], Operations: ['42/7=6'] Exploring Operation: 8*6=48, Resulting Numbers: [49, 48] Generated Node #0,3,0: 57:[49, 48] Operation: 8*6=48 Exploring Operation: 49+6=55, Resulting Numbers: [8, 55] Generated Node #0,3,1: 57:[8, 55] Operation: 49+6=55 Exploring Operation: 8+6=14, Resulting Numbers: [49, 14] Generated Node #0,3,2: 57:[49, 14] Operation: 8+6=14 Exploring Operation: 8-6=2, Resulting Numbers: [49, 2] Generated Node #0,3,3: 57:[49, 2] Operation: 8-6=2 Exploring Operation: 49+8=57, Resulting Numbers: [6, 57] Generated Node #0,3,4: 57:[6, 57] Operation: 49+8=57 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 57:[6, 57], Operations: ['42/7=6', '49+8=57'] Exploring Operation: 6*57=342, Resulting Numbers: [342] 342,57 unequal: No Solution Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,57 unequal: No Solution Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 57:[8, 55], Operations: ['42/7=6', '49+6=55'] Exploring Operation: 8+55=63, Resulting Numbers: [63] 63,57 unequal: No Solution Exploring Operation: 8*55=440, Resulting Numbers: [440] 440,57 unequal: No Solution Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 57:[49, 2], Operations: ['42/7=6', '8-6=2'] Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,57 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,57 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 57:[49, 14], Operations: ['42/7=6', '8+6=14'] Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 49*14=686, Resulting Numbers: [686] 686,57 unequal: No Solution Exploring Operation: 49+14=63, Resulting Numbers: [63] 63,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 57:[49, 48], Operations: ['42/7=6', '8*6=48'] Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,57 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 57:[42, 7, 57], Operations: ['49+8=57'] Exploring Operation: 7+57=64, Resulting Numbers: [42, 64] Generated Node #0,0,0: 57:[42, 64] Operation: 7+57=64 Exploring Operation: 42+7=49, Resulting Numbers: [57, 49] Generated Node #0,0,1: 57:[57, 49] Operation: 42+7=49 Exploring Operation: 42-7=35, Resulting Numbers: [57, 35] Generated Node #0,0,2: 57:[57, 35] Operation: 42-7=35 Exploring Operation: 57-42=15, Resulting Numbers: [7, 15] Generated Node #0,0,3: 57:[7, 15] Operation: 57-42=15 Exploring Operation: 42/7=6, Resulting Numbers: [57, 6] Generated Node #0,0,4: 57:[57, 6] Operation: 42/7=6 Moving to Node #0,4 Current State: 57:[49, 7, 50], Operations: ['42+8=50'] Exploring Operation: 50-49=1, Resulting Numbers: [7, 1] Generated Node #0,4,0: 57:[7, 1] Operation: 50-49=1 Exploring Operation: 49+7=56, Resulting Numbers: [50, 56] Generated Node #0,4,1: 57:[50, 56] Operation: 49+7=56 Exploring Operation: 49-7=42, Resulting Numbers: [50, 42] Generated Node #0,4,2: 57:[50, 42] Operation: 49-7=42 Exploring Operation: 7+50=57, Resulting Numbers: [49, 57] Generated Node #0,4,3: 57:[49, 57] Operation: 7+50=57 Exploring Operation: 49/7=7, Resulting Numbers: [50, 7] Generated Node #0,4,4: 57:[50, 7] Operation: 49/7=7 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 57:[7, 1], Operations: ['42+8=50', '50-49=1'] Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,57 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,57 unequal: No Solution Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 57:[50, 56], Operations: ['42+8=50', '49+7=56'] Exploring Operation: 50+56=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 56-50=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 50*56=2800, Resulting Numbers: [2800] 2800,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 57:[49, 57], Operations: ['42+8=50', '7+50=57'] Exploring Operation: 49*57=2793, Resulting Numbers: [2793] 2793,57 unequal: No Solution Exploring Operation: 57-49=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 49+57=106, Resulting Numbers: [106] 106,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 57:[50, 7], Operations: ['42+8=50', '49/7=7'] Exploring Operation: 50+7=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[42, 49, 7, 8], Operations: [] Exploring Operation: 42+8=50, Resulting Numbers: [49, 7, 50] Generated Node #0,4: 57:[49, 7, 50] Operation: 42+8=50 Moving to Node #0,4 Current State: 57:[49, 7, 50], Operations: ['42+8=50'] Exploring Operation: 49/7=7, Resulting Numbers: [50, 7] Generated Node #0,4,4: 57:[50, 7] Operation: 49/7=7 Moving to Node #0,4,4 Current State: 57:[50, 7], Operations: ['42+8=50', '49/7=7'] Exploring Operation: 50+7=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.934896
hs_5
mult_heuristic
[ 6, 3, 18, 84 ]
29
[ "18/6=3", "3+84=87", "87/3=29" ]
Current State: 29:[6, 3, 18, 84], Operations: [] Exploring Operation: 18/6=3, Resulting Numbers: [3, 84, 3] Generated Node #2: [3, 84, 3] from Operation: 18/6=3 Current State: 29:[3, 84, 3], Operations: ['18/6=3'] Exploring Operation: 3+84=87, Resulting Numbers: [87] 87,29 equal: Goal Reached Exploring Operation: 87/3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[6, 3, 18, 84], Operations: [] Exploring Operation: 84/3=28, Resulting Numbers: [6, 18, 28] Generated Node #0,0: 29:[6, 18, 28] Operation: 84/3=28 Exploring Operation: 84/6=14, Resulting Numbers: [3, 18, 14] Generated Node #0,1: 29:[3, 18, 14] Operation: 84/6=14 Exploring Operation: 6*3=18, Resulting Numbers: [18, 84, 18] Generated Node #0,2: 29:[18, 84, 18] Operation: 6*3=18 Exploring Operation: 6+3=9, Resulting Numbers: [18, 84, 9] Generated Node #0,3: 29:[18, 84, 9] Operation: 6+3=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[6, 18, 28], Operations: ['84/3=28'] Exploring Operation: 28-6=22, Resulting Numbers: [18, 22] Generated Node #0,0,0: 29:[18, 22] Operation: 28-6=22 Exploring Operation: 6+18=24, Resulting Numbers: [28, 24] Generated Node #0,0,1: 29:[28, 24] Operation: 6+18=24 Exploring Operation: 18-6=12, Resulting Numbers: [28, 12] Generated Node #0,0,2: 29:[28, 12] Operation: 18-6=12 Exploring Operation: 6+28=34, Resulting Numbers: [18, 34] Generated Node #0,0,3: 29:[18, 34] Operation: 6+28=34 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 29:[28, 24], Operations: ['84/3=28', '6+18=24'] Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,29 unequal: No Solution Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,29 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 29:[18, 34], Operations: ['84/3=28', '6+28=34'] Exploring Operation: 18+34=52, Resulting Numbers: [52] 52,29 unequal: No Solution Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,29 unequal: No Solution Exploring Operation: 18*34=612, Resulting Numbers: [612] 612,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[18, 22], Operations: ['84/3=28', '28-6=22'] Exploring Operation: 18*22=396, Resulting Numbers: [396] 396,29 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,29 unequal: No Solution Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 29:[28, 12], Operations: ['84/3=28', '18-6=12'] Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,29 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,29 unequal: No Solution Exploring Operation: 28*12=336, Resulting Numbers: [336] 336,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[3, 18, 14], Operations: ['84/6=14'] Exploring Operation: 18-3=15, Resulting Numbers: [14, 15] Generated Node #0,1,0: 29:[14, 15] Operation: 18-3=15 Exploring Operation: 3*14=42, Resulting Numbers: [18, 42] Generated Node #0,1,1: 29:[18, 42] Operation: 3*14=42 Exploring Operation: 3+18=21, Resulting Numbers: [14, 21] Generated Node #0,1,2: 29:[14, 21] Operation: 3+18=21 Exploring Operation: 3+14=17, Resulting Numbers: [18, 17] Generated Node #0,1,3: 29:[18, 17] Operation: 3+14=17 Moving to Node #0,1,2 Current State: 29:[14, 21], Operations: ['84/6=14', '3+18=21'] Exploring Operation: 14*21=294, Resulting Numbers: [294] 294,29 unequal: No Solution Exploring Operation: 14+21=35, Resulting Numbers: [35] 35,29 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,29 unequal: No Solution Moving to Node #0,1,3 Current State: 29:[18, 17], Operations: ['84/6=14', '3+14=17'] Exploring Operation: 18*17=306, Resulting Numbers: [306] 306,29 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[18, 42], Operations: ['84/6=14', '3*14=42'] Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,29 unequal: No Solution Exploring Operation: 18*42=756, Resulting Numbers: [756] 756,29 unequal: No Solution Exploring Operation: 18+42=60, Resulting Numbers: [60] 60,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[14, 15], Operations: ['84/6=14', '18-3=15'] Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[6, 3, 18, 84], Operations: [] Exploring Operation: 84/6=14, Resulting Numbers: [3, 18, 14] Generated Node #0,1: 29:[3, 18, 14] Operation: 84/6=14 Moving to Node #0,1 Current State: 29:[3, 18, 14], Operations: ['84/6=14'] Exploring Operation: 18-3=15, Resulting Numbers: [14, 15] Generated Node #0,1,0: 29:[14, 15] Operation: 18-3=15 Moving to Node #0,1,0 Current State: 29:[14, 15], Operations: ['84/6=14', '18-3=15'] Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_4
sum_heuristic
[ 10, 21, 77, 10 ]
98
[ "10+21=31", "77-10=67", "31+67=98" ]
Current State: 98:[10, 21, 77, 10], Operations: [] Exploring Operation: 10+21=31, Resulting Numbers: [77, 31] Generated Node #2: [77, 31] from Operation: 10+21=31 Current State: 98:[77, 31], Operations: ['10+21=31'] Exploring Operation: 77-10=67, Resulting Numbers: [31, 67] Generated Node #3: [31, 67] from Operation: 77-10=67 Current State: 98:[31, 67], Operations: ['10+21=31', '77-10=67'] Exploring Operation: 31+67=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[10, 21, 77, 10], Operations: [] Exploring Operation: 77-21=56, Resulting Numbers: [10, 10, 56] Generated Node #0,0: 98:[10, 10, 56] Operation: 77-21=56 Exploring Operation: 10+77=87, Resulting Numbers: [21, 10, 87] Generated Node #0,1: 98:[21, 10, 87] Operation: 10+77=87 Exploring Operation: 21+77=98, Resulting Numbers: [10, 10, 98] Generated Node #0,2: 98:[10, 10, 98] Operation: 21+77=98 Moving to Node #0,2 Current State: 98:[10, 10, 98], Operations: ['21+77=98'] Exploring Operation: 10/10=1, Resulting Numbers: [98, 1] Generated Node #0,2,0: 98:[98, 1] Operation: 10/10=1 Exploring Operation: 10-10=0, Resulting Numbers: [98, 0] Generated Node #0,2,1: 98:[98, 0] Operation: 10-10=0 Exploring Operation: 10*10=100, Resulting Numbers: [98, 100] Generated Node #0,2,2: 98:[98, 100] Operation: 10*10=100 Moving to Node #0,0 Current State: 98:[10, 10, 56], Operations: ['77-21=56'] Exploring Operation: 56-10=46, Resulting Numbers: [10, 46] Generated Node #0,0,0: 98:[10, 46] Operation: 56-10=46 Exploring Operation: 10/10=1, Resulting Numbers: [56, 1] Generated Node #0,0,1: 98:[56, 1] Operation: 10/10=1 Exploring Operation: 56-10=46, Resulting Numbers: [10, 46] Generated Node #0,0,2: 98:[10, 46] Operation: 56-10=46 Moving to Node #0,1 Current State: 98:[21, 10, 87], Operations: ['10+77=87'] Exploring Operation: 21-10=11, Resulting Numbers: [87, 11] Generated Node #0,1,0: 98:[87, 11] Operation: 21-10=11 Exploring Operation: 21+87=108, Resulting Numbers: [10, 108] Generated Node #0,1,1: 98:[10, 108] Operation: 21+87=108 Exploring Operation: 10+87=97, Resulting Numbers: [21, 97] Generated Node #0,1,2: 98:[21, 97] Operation: 10+87=97 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 98:[21, 97], Operations: ['10+77=87', '10+87=97'] Exploring Operation: 97-21=76, Resulting Numbers: [76] 76,98 unequal: No Solution Exploring Operation: 21+97=118, Resulting Numbers: [118] 118,98 unequal: No Solution Exploring Operation: 21*97=2037, Resulting Numbers: [2037] 2037,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 98:[10, 108], Operations: ['10+77=87', '21+87=108'] Exploring Operation: 10*108=1080, Resulting Numbers: [1080] 1080,98 unequal: No Solution Exploring Operation: 10+108=118, Resulting Numbers: [118] 118,98 unequal: No Solution Exploring Operation: 108-10=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[10, 21, 77, 10], Operations: [] Exploring Operation: 10+77=87, Resulting Numbers: [21, 10, 87] Generated Node #0,1: 98:[21, 10, 87] Operation: 10+77=87 Moving to Node #0,1 Current State: 98:[21, 10, 87], Operations: ['10+77=87'] Exploring Operation: 21+87=108, Resulting Numbers: [10, 108] Generated Node #0,1,1: 98:[10, 108] Operation: 21+87=108 Moving to Node #0,1,1 Current State: 98:[10, 108], Operations: ['10+77=87', '21+87=108'] Exploring Operation: 108-10=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_3
mult_heuristic
[ 13, 59, 61, 69 ]
28
[ "69-13=56", "61-59=2", "56/2=28" ]
Current State: 28:[13, 59, 61, 69], Operations: [] Exploring Operation: 69-13=56, Resulting Numbers: [59, 61, 56] Generated Node #2: [59, 61, 56] from Operation: 69-13=56 Current State: 28:[59, 61, 56], Operations: ['69-13=56'] Exploring Operation: 61-59=2, Resulting Numbers: [56, 2] Generated Node #3: [56, 2] from Operation: 61-59=2 Current State: 28:[56, 2], Operations: ['69-13=56', '61-59=2'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[13, 59, 61, 69], Operations: [] Exploring Operation: 69-61=8, Resulting Numbers: [13, 59, 8] Generated Node #0,0: 28:[13, 59, 8] Operation: 69-61=8 Exploring Operation: 69-59=10, Resulting Numbers: [13, 61, 10] Generated Node #0,1: 28:[13, 61, 10] Operation: 69-59=10 Moving to Node #0,0 Current State: 28:[13, 59, 8], Operations: ['69-61=8'] Exploring Operation: 59-13=46, Resulting Numbers: [8, 46] Generated Node #0,0,0: 28:[8, 46] Operation: 59-13=46 Exploring Operation: 59-8=51, Resulting Numbers: [13, 51] Generated Node #0,0,1: 28:[13, 51] Operation: 59-8=51 Moving to Node #0,1 Current State: 28:[13, 61, 10], Operations: ['69-59=10'] Exploring Operation: 61-13=48, Resulting Numbers: [10, 48] Generated Node #0,1,0: 28:[10, 48] Operation: 61-13=48 Exploring Operation: 61-10=51, Resulting Numbers: [13, 51] Generated Node #0,1,1: 28:[13, 51] Operation: 61-10=51 Moving to Node #0,0,0 Current State: 28:[8, 46], Operations: ['69-61=8', '59-13=46'] Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[10, 48], Operations: ['69-59=10', '61-13=48'] Exploring Operation: 10+48=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,28 unequal: No Solution Moving to Node #0,0,1 Current State: 28:[13, 51], Operations: ['69-61=8', '59-8=51'] Exploring Operation: 13+51=64, Resulting Numbers: [64] 64,28 unequal: No Solution Exploring Operation: 51-13=38, Resulting Numbers: [38] 38,28 unequal: No Solution Moving to Node #0,1,1 Current State: 28:[13, 51], Operations: ['69-59=10', '61-10=51'] Exploring Operation: 13+51=64, Resulting Numbers: [64] 64,28 unequal: No Solution Exploring Operation: 51-13=38, Resulting Numbers: [38] 38,28 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 21, 95, 12, 24 ]
37
[ "95-21=74", "24/12=2", "74/2=37" ]
Current State: 37:[21, 95, 12, 24], Operations: [] Exploring Operation: 95-21=74, Resulting Numbers: [12, 24, 74] Generated Node #2: [12, 24, 74] from Operation: 95-21=74 Current State: 37:[12, 24, 74], Operations: ['95-21=74'] Exploring Operation: 24/12=2, Resulting Numbers: [74, 2] Generated Node #3: [74, 2] from Operation: 24/12=2 Current State: 37:[74, 2], Operations: ['95-21=74', '24/12=2'] Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[21, 95, 12, 24], Operations: [] Exploring Operation: 95-21=74, Resulting Numbers: [12, 24, 74] Generated Node #0,0: 37:[12, 24, 74] Operation: 95-21=74 Exploring Operation: 95-12=83, Resulting Numbers: [21, 24, 83] Generated Node #0,1: 37:[21, 24, 83] Operation: 95-12=83 Exploring Operation: 21+12=33, Resulting Numbers: [95, 24, 33] Generated Node #0,2: 37:[95, 24, 33] Operation: 21+12=33 Exploring Operation: 95-24=71, Resulting Numbers: [21, 12, 71] Generated Node #0,3: 37:[21, 12, 71] Operation: 95-24=71 Exploring Operation: 12+24=36, Resulting Numbers: [21, 95, 36] Generated Node #0,4: 37:[21, 95, 36] Operation: 12+24=36 Moving to Node #0,0 Current State: 37:[12, 24, 74], Operations: ['95-21=74'] Exploring Operation: 74-12=62, Resulting Numbers: [24, 62] Generated Node #0,0,0: 37:[24, 62] Operation: 74-12=62 Exploring Operation: 74-24=50, Resulting Numbers: [12, 50] Generated Node #0,0,1: 37:[12, 50] Operation: 74-24=50 Exploring Operation: 24-12=12, Resulting Numbers: [74, 12] Generated Node #0,0,2: 37:[74, 12] Operation: 24-12=12 Exploring Operation: 12+24=36, Resulting Numbers: [74, 36] Generated Node #0,0,3: 37:[74, 36] Operation: 12+24=36 Exploring Operation: 12+74=86, Resulting Numbers: [24, 86] Generated Node #0,0,4: 37:[24, 86] Operation: 12+74=86 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[24, 62], Operations: ['95-21=74', '74-12=62'] Exploring Operation: 24*62=1488, Resulting Numbers: [1488] 1488,37 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[12, 50], Operations: ['95-21=74', '74-24=50'] Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 12+50=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 12*50=600, Resulting Numbers: [600] 600,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 37:[74, 36], Operations: ['95-21=74', '12+24=36'] Exploring Operation: 74*36=2664, Resulting Numbers: [2664] 2664,37 unequal: No Solution Exploring Operation: 74+36=110, Resulting Numbers: [110] 110,37 unequal: No Solution Exploring Operation: 74-36=38, Resulting Numbers: [38] 38,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 37:[74, 12], Operations: ['95-21=74', '24-12=12'] Exploring Operation: 74*12=888, Resulting Numbers: [888] 888,37 unequal: No Solution Exploring Operation: 74-12=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 74+12=86, Resulting Numbers: [86] 86,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 37:[24, 86], Operations: ['95-21=74', '12+74=86'] Exploring Operation: 24+86=110, Resulting Numbers: [110] 110,37 unequal: No Solution Exploring Operation: 86-24=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 24*86=2064, Resulting Numbers: [2064] 2064,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 37:[95, 24, 33], Operations: ['21+12=33'] Exploring Operation: 95+24=119, Resulting Numbers: [33, 119] Generated Node #0,2,0: 37:[33, 119] Operation: 95+24=119 Exploring Operation: 33-24=9, Resulting Numbers: [95, 9] Generated Node #0,2,1: 37:[95, 9] Operation: 33-24=9 Exploring Operation: 95-24=71, Resulting Numbers: [33, 71] Generated Node #0,2,2: 37:[33, 71] Operation: 95-24=71 Exploring Operation: 95-33=62, Resulting Numbers: [24, 62] Generated Node #0,2,3: 37:[24, 62] Operation: 95-33=62 Exploring Operation: 24+33=57, Resulting Numbers: [95, 57] Generated Node #0,2,4: 37:[95, 57] Operation: 24+33=57 Moving to Node #0,4 Current State: 37:[21, 95, 36], Operations: ['12+24=36'] Exploring Operation: 95-21=74, Resulting Numbers: [36, 74] Generated Node #0,4,0: 37:[36, 74] Operation: 95-21=74 Exploring Operation: 21+36=57, Resulting Numbers: [95, 57] Generated Node #0,4,1: 37:[95, 57] Operation: 21+36=57 Exploring Operation: 36-21=15, Resulting Numbers: [95, 15] Generated Node #0,4,2: 37:[95, 15] Operation: 36-21=15 Exploring Operation: 21+95=116, Resulting Numbers: [36, 116] Generated Node #0,4,3: 37:[36, 116] Operation: 21+95=116 Exploring Operation: 95-36=59, Resulting Numbers: [21, 59] Generated Node #0,4,4: 37:[21, 59] Operation: 95-36=59 Moving to Node #0,1 Current State: 37:[21, 24, 83], Operations: ['95-12=83'] Exploring Operation: 83-24=59, Resulting Numbers: [21, 59] Generated Node #0,1,0: 37:[21, 59] Operation: 83-24=59 Exploring Operation: 21+83=104, Resulting Numbers: [24, 104] Generated Node #0,1,1: 37:[24, 104] Operation: 21+83=104 Exploring Operation: 24-21=3, Resulting Numbers: [83, 3] Generated Node #0,1,2: 37:[83, 3] Operation: 24-21=3 Exploring Operation: 83-21=62, Resulting Numbers: [24, 62] Generated Node #0,1,3: 37:[24, 62] Operation: 83-21=62 Exploring Operation: 21+24=45, Resulting Numbers: [83, 45] Generated Node #0,1,4: 37:[83, 45] Operation: 21+24=45 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[21, 59], Operations: ['95-12=83', '83-24=59'] Exploring Operation: 21+59=80, Resulting Numbers: [80] 80,37 unequal: No Solution Exploring Operation: 21*59=1239, Resulting Numbers: [1239] 1239,37 unequal: No Solution Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 37:[24, 62], Operations: ['95-12=83', '83-21=62'] Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 24*62=1488, Resulting Numbers: [1488] 1488,37 unequal: No Solution Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 37:[83, 45], Operations: ['95-12=83', '21+24=45'] Exploring Operation: 83-45=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 83*45=3735, Resulting Numbers: [3735] 3735,37 unequal: No Solution Exploring Operation: 83+45=128, Resulting Numbers: [128] 128,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 37:[24, 104], Operations: ['95-12=83', '21+83=104'] Exploring Operation: 24*104=2496, Resulting Numbers: [2496] 2496,37 unequal: No Solution Exploring Operation: 104-24=80, Resulting Numbers: [80] 80,37 unequal: No Solution Exploring Operation: 24+104=128, Resulting Numbers: [128] 128,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 37:[83, 3], Operations: ['95-12=83', '24-21=3'] Exploring Operation: 83-3=80, Resulting Numbers: [80] 80,37 unequal: No Solution Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 83*3=249, Resulting Numbers: [249] 249,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 37:[21, 12, 71], Operations: ['95-24=71'] Exploring Operation: 71-12=59, Resulting Numbers: [21, 59] Generated Node #0,3,0: 37:[21, 59] Operation: 71-12=59 Exploring Operation: 21+12=33, Resulting Numbers: [71, 33] Generated Node #0,3,1: 37:[71, 33] Operation: 21+12=33 Exploring Operation: 71-21=50, Resulting Numbers: [12, 50] Generated Node #0,3,2: 37:[12, 50] Operation: 71-21=50 Exploring Operation: 21-12=9, Resulting Numbers: [71, 9] Generated Node #0,3,3: 37:[71, 9] Operation: 21-12=9 Exploring Operation: 12+71=83, Resulting Numbers: [21, 83] Generated Node #0,3,4: 37:[21, 83] Operation: 12+71=83 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 37:[21, 59], Operations: ['95-24=71', '71-12=59'] Exploring Operation: 21+59=80, Resulting Numbers: [80] 80,37 unequal: No Solution Exploring Operation: 21*59=1239, Resulting Numbers: [1239] 1239,37 unequal: No Solution Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 37:[71, 33], Operations: ['95-24=71', '21+12=33'] Exploring Operation: 71+33=104, Resulting Numbers: [104] 104,37 unequal: No Solution Exploring Operation: 71*33=2343, Resulting Numbers: [2343] 2343,37 unequal: No Solution Exploring Operation: 71-33=38, Resulting Numbers: [38] 38,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 37:[12, 50], Operations: ['95-24=71', '71-21=50'] Exploring Operation: 12+50=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 12*50=600, Resulting Numbers: [600] 600,37 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 37:[71, 9], Operations: ['95-24=71', '21-12=9'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 71+9=80, Resulting Numbers: [80] 80,37 unequal: No Solution Exploring Operation: 71*9=639, Resulting Numbers: [639] 639,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 37:[21, 83], Operations: ['95-24=71', '12+71=83'] Exploring Operation: 21+83=104, Resulting Numbers: [104] 104,37 unequal: No Solution Exploring Operation: 21*83=1743, Resulting Numbers: [1743] 1743,37 unequal: No Solution Exploring Operation: 83-21=62, Resulting Numbers: [62] 62,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 37:[33, 71], Operations: ['21+12=33', '95-24=71'] Exploring Operation: 33+71=104, Resulting Numbers: [104] 104,37 unequal: No Solution Exploring Operation: 33*71=2343, Resulting Numbers: [2343] 2343,37 unequal: No Solution Exploring Operation: 71-33=38, Resulting Numbers: [38] 38,37 unequal: No Solution Moving to Node #0,4,0 Current State: 37:[36, 74], Operations: ['12+24=36', '95-21=74'] Exploring Operation: 74-36=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 36*74=2664, Resulting Numbers: [2664] 2664,37 unequal: No Solution Exploring Operation: 36+74=110, Resulting Numbers: [110] 110,37 unequal: No Solution Moving to Node #0,4,4 Current State: 37:[21, 59], Operations: ['12+24=36', '95-36=59'] Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 21*59=1239, Resulting Numbers: [1239] 1239,37 unequal: No Solution Exploring Operation: 21+59=80, Resulting Numbers: [80] 80,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[24, 62], Operations: ['21+12=33', '95-33=62'] Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 24*62=1488, Resulting Numbers: [1488] 1488,37 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,37 unequal: No Solution Moving to Node #0,2,4 Current State: 37:[95, 57], Operations: ['21+12=33', '24+33=57'] Exploring Operation: 95*57=5415, Resulting Numbers: [5415] 5415,37 unequal: No Solution Exploring Operation: 95-57=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 95+57=152, Resulting Numbers: [152] 152,37 unequal: No Solution Moving to Node #0,4,1 Current State: 37:[95, 57], Operations: ['12+24=36', '21+36=57'] Exploring Operation: 95+57=152, Resulting Numbers: [152] 152,37 unequal: No Solution Exploring Operation: 95*57=5415, Resulting Numbers: [5415] 5415,37 unequal: No Solution Exploring Operation: 95-57=38, Resulting Numbers: [38] 38,37 unequal: No Solution Moving to Node #0,4,2 Current State: 37:[95, 15], Operations: ['12+24=36', '36-21=15'] Exploring Operation: 95-15=80, Resulting Numbers: [80] 80,37 unequal: No Solution Exploring Operation: 95+15=110, Resulting Numbers: [110] 110,37 unequal: No Solution Exploring Operation: 95*15=1425, Resulting Numbers: [1425] 1425,37 unequal: No Solution Moving to Node #0,4,3 Current State: 37:[36, 116], Operations: ['12+24=36', '21+95=116'] Exploring Operation: 36+116=152, Resulting Numbers: [152] 152,37 unequal: No Solution Exploring Operation: 116-36=80, Resulting Numbers: [80] 80,37 unequal: No Solution Exploring Operation: 36*116=4176, Resulting Numbers: [4176] 4176,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[33, 119], Operations: ['21+12=33', '95+24=119'] Exploring Operation: 33*119=3927, Resulting Numbers: [3927] 3927,37 unequal: No Solution Exploring Operation: 119-33=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 33+119=152, Resulting Numbers: [152] 152,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[95, 9], Operations: ['21+12=33', '33-24=9'] Exploring Operation: 95*9=855, Resulting Numbers: [855] 855,37 unequal: No Solution Exploring Operation: 95+9=104, Resulting Numbers: [104] 104,37 unequal: No Solution Exploring Operation: 95-9=86, Resulting Numbers: [86] 86,37 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 82, 4, 33, 11 ]
81
[ "82-4=78", "33/11=3", "78+3=81" ]
Current State: 81:[82, 4, 33, 11], Operations: [] Exploring Operation: 82-4=78, Resulting Numbers: [33, 11, 78] Generated Node #2: [33, 11, 78] from Operation: 82-4=78 Current State: 81:[33, 11, 78], Operations: ['82-4=78'] Exploring Operation: 33/11=3, Resulting Numbers: [78, 3] Generated Node #3: [78, 3] from Operation: 33/11=3 Current State: 81:[78, 3], Operations: ['82-4=78', '33/11=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[82, 4, 33, 11], Operations: [] Exploring Operation: 11-4=7, Resulting Numbers: [82, 33, 7] Generated Node #0,0: 81:[82, 33, 7] Operation: 11-4=7 Exploring Operation: 33-11=22, Resulting Numbers: [82, 4, 22] Generated Node #0,1: 81:[82, 4, 22] Operation: 33-11=22 Exploring Operation: 82-4=78, Resulting Numbers: [33, 11, 78] Generated Node #0,2: 81:[33, 11, 78] Operation: 82-4=78 Exploring Operation: 33-4=29, Resulting Numbers: [82, 11, 29] Generated Node #0,3: 81:[82, 11, 29] Operation: 33-4=29 Exploring Operation: 33/11=3, Resulting Numbers: [82, 4, 3] Generated Node #0,4: 81:[82, 4, 3] Operation: 33/11=3 Start Sub Search at level 1: Moving to Node #0,4 Current State: 81:[82, 4, 3], Operations: ['33/11=3'] Exploring Operation: 82-3=79, Resulting Numbers: [4, 79] Generated Node #0,4,0: 81:[4, 79] Operation: 82-3=79 Exploring Operation: 4-3=1, Resulting Numbers: [82, 1] Generated Node #0,4,1: 81:[82, 1] Operation: 4-3=1 Exploring Operation: 82-4=78, Resulting Numbers: [3, 78] Generated Node #0,4,2: 81:[3, 78] Operation: 82-4=78 Exploring Operation: 4+3=7, Resulting Numbers: [82, 7] Generated Node #0,4,3: 81:[82, 7] Operation: 4+3=7 Exploring Operation: 4*3=12, Resulting Numbers: [82, 12] Generated Node #0,4,4: 81:[82, 12] Operation: 4*3=12 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 81:[4, 79], Operations: ['33/11=3', '82-3=79'] Exploring Operation: 4+79=83, Resulting Numbers: [83] 83,81 unequal: No Solution Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,81 unequal: No Solution Exploring Operation: 4*79=316, Resulting Numbers: [316] 316,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 81:[82, 1], Operations: ['33/11=3', '4-3=1'] Exploring Operation: 82/1=82, Resulting Numbers: [82] 82,81 unequal: No Solution Exploring Operation: 82*1=82, Resulting Numbers: [82] 82,81 unequal: No Solution Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[82, 4, 33, 11], Operations: [] Exploring Operation: 33/11=3, Resulting Numbers: [82, 4, 3] Generated Node #0,4: 81:[82, 4, 3] Operation: 33/11=3 Moving to Node #0,4 Current State: 81:[82, 4, 3], Operations: ['33/11=3'] Exploring Operation: 4-3=1, Resulting Numbers: [82, 1] Generated Node #0,4,1: 81:[82, 1] Operation: 4-3=1 Moving to Node #0,4,1 Current State: 81:[82, 1], Operations: ['33/11=3', '4-3=1'] Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 7, 38, 11, 44 ]
59
[ "44-38=6", "11*6=66", "66-7=59" ]
Current State: 59:[7, 38, 11, 44], Operations: [] Exploring Operation: 44-38=6, Resulting Numbers: [7, 11, 6] Generated Node #2: [7, 11, 6] from Operation: 44-38=6 Current State: 59:[7, 11, 6], Operations: ['44-38=6'] Exploring Operation: 11*6=66, Resulting Numbers: [7, 66] Generated Node #3: [7, 66] from Operation: 11*6=66 Current State: 59:[7, 66], Operations: ['44-38=6', '11*6=66'] Exploring Operation: 66-7=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[7, 38, 11, 44], Operations: [] Exploring Operation: 7*11=77, Resulting Numbers: [38, 44, 77] Generated Node #0,0: 59:[38, 44, 77] Operation: 7*11=77 Exploring Operation: 7+11=18, Resulting Numbers: [38, 44, 18] Generated Node #0,1: 59:[38, 44, 18] Operation: 7+11=18 Exploring Operation: 7+38=45, Resulting Numbers: [11, 44, 45] Generated Node #0,2: 59:[11, 44, 45] Operation: 7+38=45 Moving to Node #0,0 Current State: 59:[38, 44, 77], Operations: ['7*11=77'] Exploring Operation: 38+44=82, Resulting Numbers: [77, 82] Generated Node #0,0,0: 59:[77, 82] Operation: 38+44=82 Exploring Operation: 77-44=33, Resulting Numbers: [38, 33] Generated Node #0,0,1: 59:[38, 33] Operation: 77-44=33 Exploring Operation: 77-38=39, Resulting Numbers: [44, 39] Generated Node #0,0,2: 59:[44, 39] Operation: 77-38=39 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 59:[44, 39], Operations: ['7*11=77', '77-38=39'] Exploring Operation: 44*39=1716, Resulting Numbers: [1716] 1716,59 unequal: No Solution Exploring Operation: 44+39=83, Resulting Numbers: [83] 83,59 unequal: No Solution Exploring Operation: 44-39=5, Resulting Numbers: [5] 5,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[77, 82], Operations: ['7*11=77', '38+44=82'] Exploring Operation: 77+82=159, Resulting Numbers: [159] 159,59 unequal: No Solution Exploring Operation: 82-77=5, Resulting Numbers: [5] 5,59 unequal: No Solution Exploring Operation: 77*82=6314, Resulting Numbers: [6314] 6314,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[38, 33], Operations: ['7*11=77', '77-44=33'] Exploring Operation: 38+33=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 38*33=1254, Resulting Numbers: [1254] 1254,59 unequal: No Solution Exploring Operation: 38-33=5, Resulting Numbers: [5] 5,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 59:[38, 44, 18], Operations: ['7+11=18'] Exploring Operation: 38-18=20, Resulting Numbers: [44, 20] Generated Node #0,1,0: 59:[44, 20] Operation: 38-18=20 Exploring Operation: 44+18=62, Resulting Numbers: [38, 62] Generated Node #0,1,1: 59:[38, 62] Operation: 44+18=62 Exploring Operation: 38+18=56, Resulting Numbers: [44, 56] Generated Node #0,1,2: 59:[44, 56] Operation: 38+18=56 Moving to Node #0,2 Current State: 59:[11, 44, 45], Operations: ['7+38=45'] Exploring Operation: 11+44=55, Resulting Numbers: [45, 55] Generated Node #0,2,0: 59:[45, 55] Operation: 11+44=55 Exploring Operation: 44-11=33, Resulting Numbers: [45, 33] Generated Node #0,2,1: 59:[45, 33] Operation: 44-11=33 Exploring Operation: 11+45=56, Resulting Numbers: [44, 56] Generated Node #0,2,2: 59:[44, 56] Operation: 11+45=56 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[45, 55], Operations: ['7+38=45', '11+44=55'] Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,59 unequal: No Solution Exploring Operation: 45+55=100, Resulting Numbers: [100] 100,59 unequal: No Solution Exploring Operation: 45*55=2475, Resulting Numbers: [2475] 2475,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[44, 56], Operations: ['7+38=45', '11+45=56'] Exploring Operation: 44*56=2464, Resulting Numbers: [2464] 2464,59 unequal: No Solution Exploring Operation: 44+56=100, Resulting Numbers: [100] 100,59 unequal: No Solution Exploring Operation: 56-44=12, Resulting Numbers: [12] 12,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[45, 33], Operations: ['7+38=45', '44-11=33'] Exploring Operation: 45*33=1485, Resulting Numbers: [1485] 1485,59 unequal: No Solution Exploring Operation: 45+33=78, Resulting Numbers: [78] 78,59 unequal: No Solution Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 59:[44, 56], Operations: ['7+11=18', '38+18=56'] Exploring Operation: 44*56=2464, Resulting Numbers: [2464] 2464,59 unequal: No Solution Exploring Operation: 56-44=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 44+56=100, Resulting Numbers: [100] 100,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[38, 62], Operations: ['7+11=18', '44+18=62'] Exploring Operation: 38*62=2356, Resulting Numbers: [2356] 2356,59 unequal: No Solution Exploring Operation: 38+62=100, Resulting Numbers: [100] 100,59 unequal: No Solution Exploring Operation: 62-38=24, Resulting Numbers: [24] 24,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[44, 20], Operations: ['7+11=18', '38-18=20'] Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,59 unequal: No Solution Exploring Operation: 44*20=880, Resulting Numbers: [880] 880,59 unequal: No Solution Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,59 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 41, 97, 25, 79 ]
11
[ "41-25=16", "97+79=176", "176/16=11" ]
Current State: 11:[41, 97, 25, 79], Operations: [] Exploring Operation: 41-25=16, Resulting Numbers: [97, 79, 16] Generated Node #2: [97, 79, 16] from Operation: 41-25=16 Current State: 11:[97, 79, 16], Operations: ['41-25=16'] Exploring Operation: 97+79=176, Resulting Numbers: [16, 176] Generated Node #3: [16, 176] from Operation: 97+79=176 Current State: 11:[16, 176], Operations: ['41-25=16', '97+79=176'] Exploring Operation: 176/16=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[41, 97, 25, 79], Operations: [] Exploring Operation: 97-79=18, Resulting Numbers: [41, 25, 18] Generated Node #0,0: 11:[41, 25, 18] Operation: 97-79=18 Exploring Operation: 97-41=56, Resulting Numbers: [25, 79, 56] Generated Node #0,1: 11:[25, 79, 56] Operation: 97-41=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[41, 25, 18], Operations: ['97-79=18'] Exploring Operation: 41-25=16, Resulting Numbers: [18, 16] Generated Node #0,0,0: 11:[18, 16] Operation: 41-25=16 Exploring Operation: 41-18=23, Resulting Numbers: [25, 23] Generated Node #0,0,1: 11:[25, 23] Operation: 41-18=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[18, 16], Operations: ['97-79=18', '41-25=16'] Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 11:[25, 23], Operations: ['97-79=18', '41-18=23'] Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 25+23=48, Resulting Numbers: [48] 48,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[25, 79, 56], Operations: ['97-41=56'] Exploring Operation: 79-25=54, Resulting Numbers: [56, 54] Generated Node #0,1,0: 11:[56, 54] Operation: 79-25=54 Exploring Operation: 79-56=23, Resulting Numbers: [25, 23] Generated Node #0,1,1: 11:[25, 23] Operation: 79-56=23 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 11:[25, 23], Operations: ['97-41=56', '79-56=23'] Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 25+23=48, Resulting Numbers: [48] 48,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 11:[56, 54], Operations: ['97-41=56', '79-25=54'] Exploring Operation: 56-54=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 56+54=110, Resulting Numbers: [110] 110,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 66, 59, 83, 50 ]
61
[ "83-50=33", "66/33=2", "59+2=61" ]
Current State: 61:[66, 59, 83, 50], Operations: [] Exploring Operation: 83-50=33, Resulting Numbers: [66, 59, 33] Generated Node #2: [66, 59, 33] from Operation: 83-50=33 Current State: 61:[66, 59, 33], Operations: ['83-50=33'] Exploring Operation: 66/33=2, Resulting Numbers: [59, 2] Generated Node #3: [59, 2] from Operation: 66/33=2 Current State: 61:[59, 2], Operations: ['83-50=33', '66/33=2'] Exploring Operation: 59+2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[66, 59, 83, 50], Operations: [] Exploring Operation: 66-50=16, Resulting Numbers: [59, 83, 16] Generated Node #0,0: 61:[59, 83, 16] Operation: 66-50=16 Exploring Operation: 59+50=109, Resulting Numbers: [66, 83, 109] Generated Node #0,1: 61:[66, 83, 109] Operation: 59+50=109 Exploring Operation: 83-59=24, Resulting Numbers: [66, 50, 24] Generated Node #0,2: 61:[66, 50, 24] Operation: 83-59=24 Exploring Operation: 83-50=33, Resulting Numbers: [66, 59, 33] Generated Node #0,3: 61:[66, 59, 33] Operation: 83-50=33 Exploring Operation: 83-66=17, Resulting Numbers: [59, 50, 17] Generated Node #0,4: 61:[59, 50, 17] Operation: 83-66=17 Moving to Node #0,3 Current State: 61:[66, 59, 33], Operations: ['83-50=33'] Exploring Operation: 59+33=92, Resulting Numbers: [66, 92] Generated Node #0,3,0: 61:[66, 92] Operation: 59+33=92 Exploring Operation: 66/33=2, Resulting Numbers: [59, 2] Generated Node #0,3,1: 61:[59, 2] Operation: 66/33=2 Exploring Operation: 66+33=99, Resulting Numbers: [59, 99] Generated Node #0,3,2: 61:[59, 99] Operation: 66+33=99 Exploring Operation: 59-33=26, Resulting Numbers: [66, 26] Generated Node #0,3,3: 61:[66, 26] Operation: 59-33=26 Exploring Operation: 66-33=33, Resulting Numbers: [59, 33] Generated Node #0,3,4: 61:[59, 33] Operation: 66-33=33 Moving to Node #0,2 Current State: 61:[66, 50, 24], Operations: ['83-59=24'] Exploring Operation: 66-50=16, Resulting Numbers: [24, 16] Generated Node #0,2,0: 61:[24, 16] Operation: 66-50=16 Exploring Operation: 50-24=26, Resulting Numbers: [66, 26] Generated Node #0,2,1: 61:[66, 26] Operation: 50-24=26 Exploring Operation: 66-24=42, Resulting Numbers: [50, 42] Generated Node #0,2,2: 61:[50, 42] Operation: 66-24=42 Exploring Operation: 50+24=74, Resulting Numbers: [66, 74] Generated Node #0,2,3: 61:[66, 74] Operation: 50+24=74 Exploring Operation: 66+24=90, Resulting Numbers: [50, 90] Generated Node #0,2,4: 61:[50, 90] Operation: 66+24=90 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 61:[66, 74], Operations: ['83-59=24', '50+24=74'] Exploring Operation: 74-66=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 66+74=140, Resulting Numbers: [140] 140,61 unequal: No Solution Exploring Operation: 66*74=4884, Resulting Numbers: [4884] 4884,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 61:[50, 42], Operations: ['83-59=24', '66-24=42'] Exploring Operation: 50+42=92, Resulting Numbers: [92] 92,61 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 50*42=2100, Resulting Numbers: [2100] 2100,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 61:[66, 26], Operations: ['83-59=24', '50-24=26'] Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,61 unequal: No Solution Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 61:[50, 90], Operations: ['83-59=24', '66+24=90'] Exploring Operation: 50*90=4500, Resulting Numbers: [4500] 4500,61 unequal: No Solution Exploring Operation: 50+90=140, Resulting Numbers: [140] 140,61 unequal: No Solution Exploring Operation: 90-50=40, Resulting Numbers: [40] 40,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[24, 16], Operations: ['83-59=24', '66-50=16'] Exploring Operation: 24+16=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 24*16=384, Resulting Numbers: [384] 384,61 unequal: No Solution Exploring Operation: 24-16=8, Resulting Numbers: [8] 8,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 61:[59, 50, 17], Operations: ['83-66=17'] Exploring Operation: 59+17=76, Resulting Numbers: [50, 76] Generated Node #0,4,0: 61:[50, 76] Operation: 59+17=76 Exploring Operation: 59-17=42, Resulting Numbers: [50, 42] Generated Node #0,4,1: 61:[50, 42] Operation: 59-17=42 Exploring Operation: 50+17=67, Resulting Numbers: [59, 67] Generated Node #0,4,2: 61:[59, 67] Operation: 50+17=67 Exploring Operation: 59+50=109, Resulting Numbers: [17, 109] Generated Node #0,4,3: 61:[17, 109] Operation: 59+50=109 Exploring Operation: 50-17=33, Resulting Numbers: [59, 33] Generated Node #0,4,4: 61:[59, 33] Operation: 50-17=33 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 61:[59, 67], Operations: ['83-66=17', '50+17=67'] Exploring Operation: 59+67=126, Resulting Numbers: [126] 126,61 unequal: No Solution Exploring Operation: 59*67=3953, Resulting Numbers: [3953] 3953,61 unequal: No Solution Exploring Operation: 67-59=8, Resulting Numbers: [8] 8,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 61:[50, 76], Operations: ['83-66=17', '59+17=76'] Exploring Operation: 50*76=3800, Resulting Numbers: [3800] 3800,61 unequal: No Solution Exploring Operation: 76-50=26, Resulting Numbers: [26] 26,61 unequal: No Solution Exploring Operation: 50+76=126, Resulting Numbers: [126] 126,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 61:[50, 42], Operations: ['83-66=17', '59-17=42'] Exploring Operation: 50+42=92, Resulting Numbers: [92] 92,61 unequal: No Solution Exploring Operation: 50*42=2100, Resulting Numbers: [2100] 2100,61 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 61:[59, 33], Operations: ['83-66=17', '50-17=33'] Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,61 unequal: No Solution Exploring Operation: 59*33=1947, Resulting Numbers: [1947] 1947,61 unequal: No Solution Exploring Operation: 59+33=92, Resulting Numbers: [92] 92,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 61:[17, 109], Operations: ['83-66=17', '59+50=109'] Exploring Operation: 17+109=126, Resulting Numbers: [126] 126,61 unequal: No Solution Exploring Operation: 17*109=1853, Resulting Numbers: [1853] 1853,61 unequal: No Solution Exploring Operation: 109-17=92, Resulting Numbers: [92] 92,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 61:[59, 83, 16], Operations: ['66-50=16'] Exploring Operation: 83+16=99, Resulting Numbers: [59, 99] Generated Node #0,0,0: 61:[59, 99] Operation: 83+16=99 Exploring Operation: 59+16=75, Resulting Numbers: [83, 75] Generated Node #0,0,1: 61:[83, 75] Operation: 59+16=75 Exploring Operation: 83-59=24, Resulting Numbers: [16, 24] Generated Node #0,0,2: 61:[16, 24] Operation: 83-59=24 Exploring Operation: 59-16=43, Resulting Numbers: [83, 43] Generated Node #0,0,3: 61:[83, 43] Operation: 59-16=43 Exploring Operation: 83-16=67, Resulting Numbers: [59, 67] Generated Node #0,0,4: 61:[59, 67] Operation: 83-16=67 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 61:[59, 67], Operations: ['66-50=16', '83-16=67'] Exploring Operation: 59*67=3953, Resulting Numbers: [3953] 3953,61 unequal: No Solution Exploring Operation: 67-59=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 59+67=126, Resulting Numbers: [126] 126,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[83, 75], Operations: ['66-50=16', '59+16=75'] Exploring Operation: 83-75=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 83*75=6225, Resulting Numbers: [6225] 6225,61 unequal: No Solution Exploring Operation: 83+75=158, Resulting Numbers: [158] 158,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[59, 99], Operations: ['66-50=16', '83+16=99'] Exploring Operation: 99-59=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 59+99=158, Resulting Numbers: [158] 158,61 unequal: No Solution Exploring Operation: 59*99=5841, Resulting Numbers: [5841] 5841,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 61:[83, 43], Operations: ['66-50=16', '59-16=43'] Exploring Operation: 83-43=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 83+43=126, Resulting Numbers: [126] 126,61 unequal: No Solution Exploring Operation: 83*43=3569, Resulting Numbers: [3569] 3569,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 61:[16, 24], Operations: ['66-50=16', '83-59=24'] Exploring Operation: 16+24=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 16*24=384, Resulting Numbers: [384] 384,61 unequal: No Solution Exploring Operation: 24-16=8, Resulting Numbers: [8] 8,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 61:[66, 83, 109], Operations: ['59+50=109'] Exploring Operation: 109-66=43, Resulting Numbers: [83, 43] Generated Node #0,1,0: 61:[83, 43] Operation: 109-66=43 Exploring Operation: 109-83=26, Resulting Numbers: [66, 26] Generated Node #0,1,1: 61:[66, 26] Operation: 109-83=26 Exploring Operation: 66+83=149, Resulting Numbers: [109, 149] Generated Node #0,1,2: 61:[109, 149] Operation: 66+83=149 Exploring Operation: 66+109=175, Resulting Numbers: [83, 175] Generated Node #0,1,3: 61:[83, 175] Operation: 66+109=175 Exploring Operation: 83-66=17, Resulting Numbers: [109, 17] Generated Node #0,1,4: 61:[109, 17] Operation: 83-66=17 Moving to Node #0,3,4 Current State: 61:[59, 33], Operations: ['83-50=33', '66-33=33'] Exploring Operation: 59*33=1947, Resulting Numbers: [1947] 1947,61 unequal: No Solution Exploring Operation: 59+33=92, Resulting Numbers: [92] 92,61 unequal: No Solution Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[66, 92], Operations: ['83-50=33', '59+33=92'] Exploring Operation: 66+92=158, Resulting Numbers: [158] 158,61 unequal: No Solution Exploring Operation: 92-66=26, Resulting Numbers: [26] 26,61 unequal: No Solution Exploring Operation: 66*92=6072, Resulting Numbers: [6072] 6072,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[59, 99], Operations: ['83-50=33', '66+33=99'] Exploring Operation: 59*99=5841, Resulting Numbers: [5841] 5841,61 unequal: No Solution Exploring Operation: 59+99=158, Resulting Numbers: [158] 158,61 unequal: No Solution Exploring Operation: 99-59=40, Resulting Numbers: [40] 40,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[66, 26], Operations: ['59+50=109', '109-83=26'] Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,61 unequal: No Solution Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[83, 43], Operations: ['59+50=109', '109-66=43'] Exploring Operation: 83*43=3569, Resulting Numbers: [3569] 3569,61 unequal: No Solution Exploring Operation: 83-43=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 83+43=126, Resulting Numbers: [126] 126,61 unequal: No Solution Moving to Node #0,3,3 Current State: 61:[66, 26], Operations: ['83-50=33', '59-33=26'] Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,61 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[59, 2], Operations: ['83-50=33', '66/33=2'] Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,61 unequal: No Solution Exploring Operation: 59+2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[66, 59, 83, 50], Operations: [] Exploring Operation: 83-50=33, Resulting Numbers: [66, 59, 33] Generated Node #0,3: 61:[66, 59, 33] Operation: 83-50=33 Moving to Node #0,3 Current State: 61:[66, 59, 33], Operations: ['83-50=33'] Exploring Operation: 66/33=2, Resulting Numbers: [59, 2] Generated Node #0,3,1: 61:[59, 2] Operation: 66/33=2 Moving to Node #0,3,1 Current State: 61:[59, 2], Operations: ['83-50=33', '66/33=2'] Exploring Operation: 59+2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
0.914063
hs_5
sum_heuristic
[ 94, 6, 89, 6 ]
94
[ "6-6=0", "89*0=0", "94+0=94" ]
Current State: 94:[94, 6, 89, 6], Operations: [] Exploring Operation: 6-6=0, Resulting Numbers: [94, 89, 0] Generated Node #2: [94, 89, 0] from Operation: 6-6=0 Current State: 94:[94, 89, 0], Operations: ['6-6=0'] Exploring Operation: 89*0=0, Resulting Numbers: [94, 0] Generated Node #3: [94, 0] from Operation: 89*0=0 Current State: 94:[94, 0], Operations: ['6-6=0', '89*0=0'] Exploring Operation: 94+0=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[94, 6, 89, 6], Operations: [] Exploring Operation: 6+89=95, Resulting Numbers: [94, 6, 95] Generated Node #0,0: 94:[94, 6, 95] Operation: 6+89=95 Exploring Operation: 6/6=1, Resulting Numbers: [94, 89, 1] Generated Node #0,1: 94:[94, 89, 1] Operation: 6/6=1 Exploring Operation: 89+6=95, Resulting Numbers: [94, 6, 95] Generated Node #0,2: 94:[94, 6, 95] Operation: 89+6=95 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[94, 6, 95], Operations: ['6+89=95'] Exploring Operation: 95-94=1, Resulting Numbers: [6, 1] Generated Node #0,0,0: 94:[6, 1] Operation: 95-94=1 Exploring Operation: 94+6=100, Resulting Numbers: [95, 100] Generated Node #0,0,1: 94:[95, 100] Operation: 94+6=100 Exploring Operation: 95-6=89, Resulting Numbers: [94, 89] Generated Node #0,0,2: 94:[94, 89] Operation: 95-6=89 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[6, 1], Operations: ['6+89=95', '95-94=1'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,94 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 94:[94, 89], Operations: ['6+89=95', '95-6=89'] Exploring Operation: 94*89=8366, Resulting Numbers: [8366] 8366,94 unequal: No Solution Exploring Operation: 94-89=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 94+89=183, Resulting Numbers: [183] 183,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[95, 100], Operations: ['6+89=95', '94+6=100'] Exploring Operation: 100-95=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 95*100=9500, Resulting Numbers: [9500] 9500,94 unequal: No Solution Exploring Operation: 95+100=195, Resulting Numbers: [195] 195,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[94, 6, 95], Operations: ['89+6=95'] Exploring Operation: 95-6=89, Resulting Numbers: [94, 89] Generated Node #0,2,0: 94:[94, 89] Operation: 95-6=89 Exploring Operation: 95-94=1, Resulting Numbers: [6, 1] Generated Node #0,2,1: 94:[6, 1] Operation: 95-94=1 Exploring Operation: 94+6=100, Resulting Numbers: [95, 100] Generated Node #0,2,2: 94:[95, 100] Operation: 94+6=100 Moving to Node #0,2,0 Current State: 94:[94, 89], Operations: ['89+6=95', '95-6=89'] Exploring Operation: 94*89=8366, Resulting Numbers: [8366] 8366,94 unequal: No Solution Exploring Operation: 94+89=183, Resulting Numbers: [183] 183,94 unequal: No Solution Exploring Operation: 94-89=5, Resulting Numbers: [5] 5,94 unequal: No Solution Moving to Node #0,2,1 Current State: 94:[6, 1], Operations: ['89+6=95', '95-94=1'] Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,94 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[95, 100], Operations: ['89+6=95', '94+6=100'] Exploring Operation: 100-95=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 95+100=195, Resulting Numbers: [195] 195,94 unequal: No Solution Exploring Operation: 95*100=9500, Resulting Numbers: [9500] 9500,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[94, 89, 1], Operations: ['6/6=1'] Exploring Operation: 94-89=5, Resulting Numbers: [1, 5] Generated Node #0,1,0: 94:[1, 5] Operation: 94-89=5 Exploring Operation: 94*1=94, Resulting Numbers: [89, 94] Generated Node #0,1,1: 94:[89, 94] Operation: 94*1=94 Exploring Operation: 89+1=90, Resulting Numbers: [94, 90] Generated Node #0,1,2: 94:[94, 90] Operation: 89+1=90 Moving to Node #0,1,0 Current State: 94:[1, 5], Operations: ['6/6=1', '94-89=5'] Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[94, 90], Operations: ['6/6=1', '89+1=90'] Exploring Operation: 94-90=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 94+90=184, Resulting Numbers: [184] 184,94 unequal: No Solution Exploring Operation: 94*90=8460, Resulting Numbers: [8460] 8460,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[89, 94], Operations: ['6/6=1', '94*1=94'] Exploring Operation: 89+94=183, Resulting Numbers: [183] 183,94 unequal: No Solution Exploring Operation: 94-89=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 89*94=8366, Resulting Numbers: [8366] 8366,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 83, 4, 76, 93 ]
65
[ "83-76=7", "4*7=28", "93-28=65" ]
Current State: 65:[83, 4, 76, 93], Operations: [] Exploring Operation: 83-76=7, Resulting Numbers: [4, 93, 7] Generated Node #2: [4, 93, 7] from Operation: 83-76=7 Current State: 65:[4, 93, 7], Operations: ['83-76=7'] Exploring Operation: 4*7=28, Resulting Numbers: [93, 28] Generated Node #3: [93, 28] from Operation: 4*7=28 Current State: 65:[93, 28], Operations: ['83-76=7', '4*7=28'] Exploring Operation: 93-28=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[83, 4, 76, 93], Operations: [] Exploring Operation: 93-76=17, Resulting Numbers: [83, 4, 17] Generated Node #0,0: 65:[83, 4, 17] Operation: 93-76=17 Exploring Operation: 76/4=19, Resulting Numbers: [83, 93, 19] Generated Node #0,1: 65:[83, 93, 19] Operation: 76/4=19 Exploring Operation: 93-83=10, Resulting Numbers: [4, 76, 10] Generated Node #0,2: 65:[4, 76, 10] Operation: 93-83=10 Exploring Operation: 83-76=7, Resulting Numbers: [4, 93, 7] Generated Node #0,3: 65:[4, 93, 7] Operation: 83-76=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[4, 76, 10], Operations: ['93-83=10'] Exploring Operation: 76-4=72, Resulting Numbers: [10, 72] Generated Node #0,2,0: 65:[10, 72] Operation: 76-4=72 Exploring Operation: 76/4=19, Resulting Numbers: [10, 19] Generated Node #0,2,1: 65:[10, 19] Operation: 76/4=19 Exploring Operation: 76-10=66, Resulting Numbers: [4, 66] Generated Node #0,2,2: 65:[4, 66] Operation: 76-10=66 Exploring Operation: 4+10=14, Resulting Numbers: [76, 14] Generated Node #0,2,3: 65:[76, 14] Operation: 4+10=14 Moving to Node #0,2,2 Current State: 65:[4, 66], Operations: ['93-83=10', '76-10=66'] Exploring Operation: 4*66=264, Resulting Numbers: [264] 264,65 unequal: No Solution Exploring Operation: 4+66=70, Resulting Numbers: [70] 70,65 unequal: No Solution Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[10, 19], Operations: ['93-83=10', '76/4=19'] Exploring Operation: 10+19=29, Resulting Numbers: [29] 29,65 unequal: No Solution Exploring Operation: 10*19=190, Resulting Numbers: [190] 190,65 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[10, 72], Operations: ['93-83=10', '76-4=72'] Exploring Operation: 10+72=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 72-10=62, Resulting Numbers: [62] 62,65 unequal: No Solution Exploring Operation: 10*72=720, Resulting Numbers: [720] 720,65 unequal: No Solution Moving to Node #0,2,3 Current State: 65:[76, 14], Operations: ['93-83=10', '4+10=14'] Exploring Operation: 76-14=62, Resulting Numbers: [62] 62,65 unequal: No Solution Exploring Operation: 76*14=1064, Resulting Numbers: [1064] 1064,65 unequal: No Solution Exploring Operation: 76+14=90, Resulting Numbers: [90] 90,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[83, 4, 17], Operations: ['93-76=17'] Exploring Operation: 83-17=66, Resulting Numbers: [4, 66] Generated Node #0,0,0: 65:[4, 66] Operation: 83-17=66 Exploring Operation: 4*17=68, Resulting Numbers: [83, 68] Generated Node #0,0,1: 65:[83, 68] Operation: 4*17=68 Exploring Operation: 83-4=79, Resulting Numbers: [17, 79] Generated Node #0,0,2: 65:[17, 79] Operation: 83-4=79 Exploring Operation: 17-4=13, Resulting Numbers: [83, 13] Generated Node #0,0,3: 65:[83, 13] Operation: 17-4=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 65:[4, 66], Operations: ['93-76=17', '83-17=66'] Exploring Operation: 4*66=264, Resulting Numbers: [264] 264,65 unequal: No Solution Exploring Operation: 4+66=70, Resulting Numbers: [70] 70,65 unequal: No Solution Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 65:[17, 79], Operations: ['93-76=17', '83-4=79'] Exploring Operation: 17+79=96, Resulting Numbers: [96] 96,65 unequal: No Solution Exploring Operation: 79-17=62, Resulting Numbers: [62] 62,65 unequal: No Solution Exploring Operation: 17*79=1343, Resulting Numbers: [1343] 1343,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 65:[83, 13], Operations: ['93-76=17', '17-4=13'] Exploring Operation: 83+13=96, Resulting Numbers: [96] 96,65 unequal: No Solution Exploring Operation: 83*13=1079, Resulting Numbers: [1079] 1079,65 unequal: No Solution Exploring Operation: 83-13=70, Resulting Numbers: [70] 70,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 65:[83, 68], Operations: ['93-76=17', '4*17=68'] Exploring Operation: 83*68=5644, Resulting Numbers: [5644] 5644,65 unequal: No Solution Exploring Operation: 83-68=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 83+68=151, Resulting Numbers: [151] 151,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 65:[4, 93, 7], Operations: ['83-76=7'] Exploring Operation: 93-4=89, Resulting Numbers: [7, 89] Generated Node #0,3,0: 65:[7, 89] Operation: 93-4=89 Exploring Operation: 7-4=3, Resulting Numbers: [93, 3] Generated Node #0,3,1: 65:[93, 3] Operation: 7-4=3 Exploring Operation: 4+7=11, Resulting Numbers: [93, 11] Generated Node #0,3,2: 65:[93, 11] Operation: 4+7=11 Exploring Operation: 93-7=86, Resulting Numbers: [4, 86] Generated Node #0,3,3: 65:[4, 86] Operation: 93-7=86 Moving to Node #0,3,3 Current State: 65:[4, 86], Operations: ['83-76=7', '93-7=86'] Exploring Operation: 4*86=344, Resulting Numbers: [344] 344,65 unequal: No Solution Exploring Operation: 4+86=90, Resulting Numbers: [90] 90,65 unequal: No Solution Exploring Operation: 86-4=82, Resulting Numbers: [82] 82,65 unequal: No Solution Moving to Node #0,3,0 Current State: 65:[7, 89], Operations: ['83-76=7', '93-4=89'] Exploring Operation: 7+89=96, Resulting Numbers: [96] 96,65 unequal: No Solution Exploring Operation: 89-7=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 7*89=623, Resulting Numbers: [623] 623,65 unequal: No Solution Moving to Node #0,3,2 Current State: 65:[93, 11], Operations: ['83-76=7', '4+7=11'] Exploring Operation: 93*11=1023, Resulting Numbers: [1023] 1023,65 unequal: No Solution Exploring Operation: 93-11=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 93+11=104, Resulting Numbers: [104] 104,65 unequal: No Solution Moving to Node #0,3,1 Current State: 65:[93, 3], Operations: ['83-76=7', '7-4=3'] Exploring Operation: 93*3=279, Resulting Numbers: [279] 279,65 unequal: No Solution Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,65 unequal: No Solution Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,65 unequal: No Solution Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[83, 93, 19], Operations: ['76/4=19'] Exploring Operation: 83+19=102, Resulting Numbers: [93, 102] Generated Node #0,1,0: 65:[93, 102] Operation: 83+19=102 Exploring Operation: 83-19=64, Resulting Numbers: [93, 64] Generated Node #0,1,1: 65:[93, 64] Operation: 83-19=64 Exploring Operation: 93-19=74, Resulting Numbers: [83, 74] Generated Node #0,1,2: 65:[83, 74] Operation: 93-19=74 Exploring Operation: 93-83=10, Resulting Numbers: [19, 10] Generated Node #0,1,3: 65:[19, 10] Operation: 93-83=10 Moving to Node #0,1,3 Current State: 65:[19, 10], Operations: ['76/4=19', '93-83=10'] Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,65 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,65 unequal: No Solution Moving to Node #0,1,2 Current State: 65:[83, 74], Operations: ['76/4=19', '93-19=74'] Exploring Operation: 83-74=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 83*74=6142, Resulting Numbers: [6142] 6142,65 unequal: No Solution Exploring Operation: 83+74=157, Resulting Numbers: [157] 157,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[93, 64], Operations: ['76/4=19', '83-19=64'] Exploring Operation: 93+64=157, Resulting Numbers: [157] 157,65 unequal: No Solution Exploring Operation: 93-64=29, Resulting Numbers: [29] 29,65 unequal: No Solution Exploring Operation: 93*64=5952, Resulting Numbers: [5952] 5952,65 unequal: No Solution Moving to Node #0,1,0 Current State: 65:[93, 102], Operations: ['76/4=19', '83+19=102'] Exploring Operation: 93*102=9486, Resulting Numbers: [9486] 9486,65 unequal: No Solution Exploring Operation: 102-93=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 93+102=195, Resulting Numbers: [195] 195,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 54, 23, 76, 52 ]
55
[ "54-23=31", "76-52=24", "31+24=55" ]
Current State: 55:[54, 23, 76, 52], Operations: [] Exploring Operation: 54-23=31, Resulting Numbers: [76, 52, 31] Generated Node #2: [76, 52, 31] from Operation: 54-23=31 Current State: 55:[76, 52, 31], Operations: ['54-23=31'] Exploring Operation: 76-52=24, Resulting Numbers: [31, 24] Generated Node #3: [31, 24] from Operation: 76-52=24 Current State: 55:[31, 24], Operations: ['54-23=31', '76-52=24'] Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[54, 23, 76, 52], Operations: [] Exploring Operation: 76-54=22, Resulting Numbers: [23, 52, 22] Generated Node #0,0: 55:[23, 52, 22] Operation: 76-54=22 Exploring Operation: 76-23=53, Resulting Numbers: [54, 52, 53] Generated Node #0,1: 55:[54, 52, 53] Operation: 76-23=53 Exploring Operation: 76-52=24, Resulting Numbers: [54, 23, 24] Generated Node #0,2: 55:[54, 23, 24] Operation: 76-52=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[54, 52, 53], Operations: ['76-23=53'] Exploring Operation: 53-52=1, Resulting Numbers: [54, 1] Generated Node #0,1,0: 55:[54, 1] Operation: 53-52=1 Exploring Operation: 54-52=2, Resulting Numbers: [53, 2] Generated Node #0,1,1: 55:[53, 2] Operation: 54-52=2 Exploring Operation: 54-53=1, Resulting Numbers: [52, 1] Generated Node #0,1,2: 55:[52, 1] Operation: 54-53=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[54, 1], Operations: ['76-23=53', '53-52=1'] Exploring Operation: 54*1=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 54/1=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 54+1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[54, 23, 76, 52], Operations: [] Exploring Operation: 76-23=53, Resulting Numbers: [54, 52, 53] Generated Node #0,1: 55:[54, 52, 53] Operation: 76-23=53 Moving to Node #0,1 Current State: 55:[54, 52, 53], Operations: ['76-23=53'] Exploring Operation: 53-52=1, Resulting Numbers: [54, 1] Generated Node #0,1,0: 55:[54, 1] Operation: 53-52=1 Moving to Node #0,1,0 Current State: 55:[54, 1], Operations: ['76-23=53', '53-52=1'] Exploring Operation: 54+1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 97, 86, 2, 71 ]
30
[ "97-86=11", "71-11=60", "60/2=30" ]
Current State: 30:[97, 86, 2, 71], Operations: [] Exploring Operation: 97-86=11, Resulting Numbers: [2, 71, 11] Generated Node #2: [2, 71, 11] from Operation: 97-86=11 Current State: 30:[2, 71, 11], Operations: ['97-86=11'] Exploring Operation: 71-11=60, Resulting Numbers: [2, 60] Generated Node #3: [2, 60] from Operation: 71-11=60 Current State: 30:[2, 60], Operations: ['97-86=11', '71-11=60'] Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[97, 86, 2, 71], Operations: [] Exploring Operation: 86/2=43, Resulting Numbers: [97, 71, 43] Generated Node #0,0: 30:[97, 71, 43] Operation: 86/2=43 Exploring Operation: 86-71=15, Resulting Numbers: [97, 2, 15] Generated Node #0,1: 30:[97, 2, 15] Operation: 86-71=15 Exploring Operation: 97-86=11, Resulting Numbers: [2, 71, 11] Generated Node #0,2: 30:[2, 71, 11] Operation: 97-86=11 Exploring Operation: 97-71=26, Resulting Numbers: [86, 2, 26] Generated Node #0,3: 30:[86, 2, 26] Operation: 97-71=26 Exploring Operation: 97-2=95, Resulting Numbers: [86, 71, 95] Generated Node #0,4: 30:[86, 71, 95] Operation: 97-2=95 Moving to Node #0,2 Current State: 30:[2, 71, 11], Operations: ['97-86=11'] Exploring Operation: 71-2=69, Resulting Numbers: [11, 69] Generated Node #0,2,0: 30:[11, 69] Operation: 71-2=69 Exploring Operation: 71-11=60, Resulting Numbers: [2, 60] Generated Node #0,2,1: 30:[2, 60] Operation: 71-11=60 Exploring Operation: 2+11=13, Resulting Numbers: [71, 13] Generated Node #0,2,2: 30:[71, 13] Operation: 2+11=13 Exploring Operation: 11-2=9, Resulting Numbers: [71, 9] Generated Node #0,2,3: 30:[71, 9] Operation: 11-2=9 Exploring Operation: 2+71=73, Resulting Numbers: [11, 73] Generated Node #0,2,4: 30:[11, 73] Operation: 2+71=73 Moving to Node #0,3 Current State: 30:[86, 2, 26], Operations: ['97-71=26'] Exploring Operation: 86-26=60, Resulting Numbers: [2, 60] Generated Node #0,3,0: 30:[2, 60] Operation: 86-26=60 Exploring Operation: 86/2=43, Resulting Numbers: [26, 43] Generated Node #0,3,1: 30:[26, 43] Operation: 86/2=43 Exploring Operation: 2+26=28, Resulting Numbers: [86, 28] Generated Node #0,3,2: 30:[86, 28] Operation: 2+26=28 Exploring Operation: 26/2=13, Resulting Numbers: [86, 13] Generated Node #0,3,3: 30:[86, 13] Operation: 26/2=13 Exploring Operation: 86-2=84, Resulting Numbers: [26, 84] Generated Node #0,3,4: 30:[26, 84] Operation: 86-2=84 Moving to Node #0,1 Current State: 30:[97, 2, 15], Operations: ['86-71=15'] Exploring Operation: 97-2=95, Resulting Numbers: [15, 95] Generated Node #0,1,0: 30:[15, 95] Operation: 97-2=95 Exploring Operation: 2+15=17, Resulting Numbers: [97, 17] Generated Node #0,1,1: 30:[97, 17] Operation: 2+15=17 Exploring Operation: 97-15=82, Resulting Numbers: [2, 82] Generated Node #0,1,2: 30:[2, 82] Operation: 97-15=82 Exploring Operation: 2*15=30, Resulting Numbers: [97, 30] Generated Node #0,1,3: 30:[97, 30] Operation: 2*15=30 Exploring Operation: 97+2=99, Resulting Numbers: [15, 99] Generated Node #0,1,4: 30:[15, 99] Operation: 97+2=99 Moving to Node #0,0 Current State: 30:[97, 71, 43], Operations: ['86/2=43'] Exploring Operation: 71-43=28, Resulting Numbers: [97, 28] Generated Node #0,0,0: 30:[97, 28] Operation: 71-43=28 Exploring Operation: 97+71=168, Resulting Numbers: [43, 168] Generated Node #0,0,1: 30:[43, 168] Operation: 97+71=168 Exploring Operation: 97-71=26, Resulting Numbers: [43, 26] Generated Node #0,0,2: 30:[43, 26] Operation: 97-71=26 Exploring Operation: 97+43=140, Resulting Numbers: [71, 140] Generated Node #0,0,3: 30:[71, 140] Operation: 97+43=140 Exploring Operation: 97-43=54, Resulting Numbers: [71, 54] Generated Node #0,0,4: 30:[71, 54] Operation: 97-43=54 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 30:[43, 26], Operations: ['86/2=43', '97-71=26'] Exploring Operation: 43+26=69, Resulting Numbers: [69] 69,30 unequal: No Solution Exploring Operation: 43-26=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 43*26=1118, Resulting Numbers: [1118] 1118,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 30:[71, 54], Operations: ['86/2=43', '97-43=54'] Exploring Operation: 71+54=125, Resulting Numbers: [125] 125,30 unequal: No Solution Exploring Operation: 71*54=3834, Resulting Numbers: [3834] 3834,30 unequal: No Solution Exploring Operation: 71-54=17, Resulting Numbers: [17] 17,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[97, 28], Operations: ['86/2=43', '71-43=28'] Exploring Operation: 97+28=125, Resulting Numbers: [125] 125,30 unequal: No Solution Exploring Operation: 97*28=2716, Resulting Numbers: [2716] 2716,30 unequal: No Solution Exploring Operation: 97-28=69, Resulting Numbers: [69] 69,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[43, 168], Operations: ['86/2=43', '97+71=168'] Exploring Operation: 43+168=211, Resulting Numbers: [211] 211,30 unequal: No Solution Exploring Operation: 43*168=7224, Resulting Numbers: [7224] 7224,30 unequal: No Solution Exploring Operation: 168-43=125, Resulting Numbers: [125] 125,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 30:[71, 140], Operations: ['86/2=43', '97+43=140'] Exploring Operation: 140-71=69, Resulting Numbers: [69] 69,30 unequal: No Solution Exploring Operation: 71*140=9940, Resulting Numbers: [9940] 9940,30 unequal: No Solution Exploring Operation: 71+140=211, Resulting Numbers: [211] 211,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 30:[86, 71, 95], Operations: ['97-2=95'] Exploring Operation: 86+95=181, Resulting Numbers: [71, 181] Generated Node #0,4,0: 30:[71, 181] Operation: 86+95=181 Exploring Operation: 95-86=9, Resulting Numbers: [71, 9] Generated Node #0,4,1: 30:[71, 9] Operation: 95-86=9 Exploring Operation: 95-71=24, Resulting Numbers: [86, 24] Generated Node #0,4,2: 30:[86, 24] Operation: 95-71=24 Exploring Operation: 86+71=157, Resulting Numbers: [95, 157] Generated Node #0,4,3: 30:[95, 157] Operation: 86+71=157 Exploring Operation: 86-71=15, Resulting Numbers: [95, 15] Generated Node #0,4,4: 30:[95, 15] Operation: 86-71=15 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 30:[71, 9], Operations: ['97-2=95', '95-86=9'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 71+9=80, Resulting Numbers: [80] 80,30 unequal: No Solution Exploring Operation: 71*9=639, Resulting Numbers: [639] 639,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 30:[86, 24], Operations: ['97-2=95', '95-71=24'] Exploring Operation: 86+24=110, Resulting Numbers: [110] 110,30 unequal: No Solution Exploring Operation: 86-24=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 86*24=2064, Resulting Numbers: [2064] 2064,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 30:[95, 15], Operations: ['97-2=95', '86-71=15'] Exploring Operation: 95+15=110, Resulting Numbers: [110] 110,30 unequal: No Solution Exploring Operation: 95*15=1425, Resulting Numbers: [1425] 1425,30 unequal: No Solution Exploring Operation: 95-15=80, Resulting Numbers: [80] 80,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 30:[71, 181], Operations: ['97-2=95', '86+95=181'] Exploring Operation: 71+181=252, Resulting Numbers: [252] 252,30 unequal: No Solution Exploring Operation: 71*181=12851, Resulting Numbers: [12851] 12851,30 unequal: No Solution Exploring Operation: 181-71=110, Resulting Numbers: [110] 110,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 30:[95, 157], Operations: ['97-2=95', '86+71=157'] Exploring Operation: 95+157=252, Resulting Numbers: [252] 252,30 unequal: No Solution Exploring Operation: 157-95=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 95*157=14915, Resulting Numbers: [14915] 14915,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 30:[26, 43], Operations: ['97-71=26', '86/2=43'] Exploring Operation: 26+43=69, Resulting Numbers: [69] 69,30 unequal: No Solution Exploring Operation: 43-26=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 26*43=1118, Resulting Numbers: [1118] 1118,30 unequal: No Solution Moving to Node #0,2,1 Current State: 30:[2, 60], Operations: ['97-86=11', '71-11=60'] Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[97, 86, 2, 71], Operations: [] Exploring Operation: 97-86=11, Resulting Numbers: [2, 71, 11] Generated Node #0,2: 30:[2, 71, 11] Operation: 97-86=11 Moving to Node #0,2 Current State: 30:[2, 71, 11], Operations: ['97-86=11'] Exploring Operation: 71-11=60, Resulting Numbers: [2, 60] Generated Node #0,2,1: 30:[2, 60] Operation: 71-11=60 Moving to Node #0,2,1 Current State: 30:[2, 60], Operations: ['97-86=11', '71-11=60'] Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
0.940104
hs_5
sum_heuristic
[ 39, 70, 2, 18 ]
93
[ "39+70=109", "18-2=16", "109-16=93" ]
Current State: 93:[39, 70, 2, 18], Operations: [] Exploring Operation: 39+70=109, Resulting Numbers: [2, 18, 109] Generated Node #2: [2, 18, 109] from Operation: 39+70=109 Current State: 93:[2, 18, 109], Operations: ['39+70=109'] Exploring Operation: 18-2=16, Resulting Numbers: [109, 16] Generated Node #3: [109, 16] from Operation: 18-2=16 Current State: 93:[109, 16], Operations: ['39+70=109', '18-2=16'] Exploring Operation: 109-16=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[39, 70, 2, 18], Operations: [] Exploring Operation: 70-39=31, Resulting Numbers: [2, 18, 31] Generated Node #0,0: 93:[2, 18, 31] Operation: 70-39=31 Exploring Operation: 39+70=109, Resulting Numbers: [2, 18, 109] Generated Node #0,1: 93:[2, 18, 109] Operation: 39+70=109 Exploring Operation: 70+18=88, Resulting Numbers: [39, 2, 88] Generated Node #0,2: 93:[39, 2, 88] Operation: 70+18=88 Exploring Operation: 70/2=35, Resulting Numbers: [39, 18, 35] Generated Node #0,3: 93:[39, 18, 35] Operation: 70/2=35 Exploring Operation: 70-18=52, Resulting Numbers: [39, 2, 52] Generated Node #0,4: 93:[39, 2, 52] Operation: 70-18=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[2, 18, 31], Operations: ['70-39=31'] Exploring Operation: 31-18=13, Resulting Numbers: [2, 13] Generated Node #0,0,0: 93:[2, 13] Operation: 31-18=13 Exploring Operation: 2*18=36, Resulting Numbers: [31, 36] Generated Node #0,0,1: 93:[31, 36] Operation: 2*18=36 Exploring Operation: 18/2=9, Resulting Numbers: [31, 9] Generated Node #0,0,2: 93:[31, 9] Operation: 18/2=9 Exploring Operation: 18-2=16, Resulting Numbers: [31, 16] Generated Node #0,0,3: 93:[31, 16] Operation: 18-2=16 Exploring Operation: 2+18=20, Resulting Numbers: [31, 20] Generated Node #0,0,4: 93:[31, 20] Operation: 2+18=20 Moving to Node #0,0,1 Current State: 93:[31, 36], Operations: ['70-39=31', '2*18=36'] Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,93 unequal: No Solution Exploring Operation: 31+36=67, Resulting Numbers: [67] 67,93 unequal: No Solution Exploring Operation: 31*36=1116, Resulting Numbers: [1116] 1116,93 unequal: No Solution Moving to Node #0,0,2 Current State: 93:[31, 9], Operations: ['70-39=31', '18/2=9'] Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,93 unequal: No Solution Exploring Operation: 31*9=279, Resulting Numbers: [279] 279,93 unequal: No Solution Exploring Operation: 31+9=40, Resulting Numbers: [40] 40,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[2, 13], Operations: ['70-39=31', '31-18=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,93 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,93 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,93 unequal: No Solution Moving to Node #0,0,4 Current State: 93:[31, 20], Operations: ['70-39=31', '2+18=20'] Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,93 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,93 unequal: No Solution Exploring Operation: 31*20=620, Resulting Numbers: [620] 620,93 unequal: No Solution Moving to Node #0,0,3 Current State: 93:[31, 16], Operations: ['70-39=31', '18-2=16'] Exploring Operation: 31*16=496, Resulting Numbers: [496] 496,93 unequal: No Solution Exploring Operation: 31-16=15, Resulting Numbers: [15] 15,93 unequal: No Solution Exploring Operation: 31+16=47, Resulting Numbers: [47] 47,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[39, 2, 88], Operations: ['70+18=88'] Exploring Operation: 2+88=90, Resulting Numbers: [39, 90] Generated Node #0,2,0: 93:[39, 90] Operation: 2+88=90 Exploring Operation: 88-2=86, Resulting Numbers: [39, 86] Generated Node #0,2,1: 93:[39, 86] Operation: 88-2=86 Exploring Operation: 39-2=37, Resulting Numbers: [88, 37] Generated Node #0,2,2: 93:[88, 37] Operation: 39-2=37 Exploring Operation: 88-39=49, Resulting Numbers: [2, 49] Generated Node #0,2,3: 93:[2, 49] Operation: 88-39=49 Exploring Operation: 39+2=41, Resulting Numbers: [88, 41] Generated Node #0,2,4: 93:[88, 41] Operation: 39+2=41 Moving to Node #0,2,0 Current State: 93:[39, 90], Operations: ['70+18=88', '2+88=90'] Exploring Operation: 39*90=3510, Resulting Numbers: [3510] 3510,93 unequal: No Solution Exploring Operation: 90-39=51, Resulting Numbers: [51] 51,93 unequal: No Solution Exploring Operation: 39+90=129, Resulting Numbers: [129] 129,93 unequal: No Solution Moving to Node #0,2,2 Current State: 93:[88, 37], Operations: ['70+18=88', '39-2=37'] Exploring Operation: 88-37=51, Resulting Numbers: [51] 51,93 unequal: No Solution Exploring Operation: 88*37=3256, Resulting Numbers: [3256] 3256,93 unequal: No Solution Exploring Operation: 88+37=125, Resulting Numbers: [125] 125,93 unequal: No Solution Moving to Node #0,2,1 Current State: 93:[39, 86], Operations: ['70+18=88', '88-2=86'] Exploring Operation: 39+86=125, Resulting Numbers: [125] 125,93 unequal: No Solution Exploring Operation: 39*86=3354, Resulting Numbers: [3354] 3354,93 unequal: No Solution Exploring Operation: 86-39=47, Resulting Numbers: [47] 47,93 unequal: No Solution Moving to Node #0,2,4 Current State: 93:[88, 41], Operations: ['70+18=88', '39+2=41'] Exploring Operation: 88+41=129, Resulting Numbers: [129] 129,93 unequal: No Solution Exploring Operation: 88*41=3608, Resulting Numbers: [3608] 3608,93 unequal: No Solution Exploring Operation: 88-41=47, Resulting Numbers: [47] 47,93 unequal: No Solution Moving to Node #0,2,3 Current State: 93:[2, 49], Operations: ['70+18=88', '88-39=49'] Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,93 unequal: No Solution Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,93 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 93:[39, 18, 35], Operations: ['70/2=35'] Exploring Operation: 39-18=21, Resulting Numbers: [35, 21] Generated Node #0,3,0: 93:[35, 21] Operation: 39-18=21 Exploring Operation: 39+18=57, Resulting Numbers: [35, 57] Generated Node #0,3,1: 93:[35, 57] Operation: 39+18=57 Exploring Operation: 39-35=4, Resulting Numbers: [18, 4] Generated Node #0,3,2: 93:[18, 4] Operation: 39-35=4 Exploring Operation: 35-18=17, Resulting Numbers: [39, 17] Generated Node #0,3,3: 93:[39, 17] Operation: 35-18=17 Exploring Operation: 18+35=53, Resulting Numbers: [39, 53] Generated Node #0,3,4: 93:[39, 53] Operation: 18+35=53 Moving to Node #0,3,0 Current State: 93:[35, 21], Operations: ['70/2=35', '39-18=21'] Exploring Operation: 35+21=56, Resulting Numbers: [56] 56,93 unequal: No Solution Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,93 unequal: No Solution Exploring Operation: 35*21=735, Resulting Numbers: [735] 735,93 unequal: No Solution Moving to Node #0,3,2 Current State: 93:[18, 4], Operations: ['70/2=35', '39-35=4'] Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,93 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,93 unequal: No Solution Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,93 unequal: No Solution Moving to Node #0,3,3 Current State: 93:[39, 17], Operations: ['70/2=35', '35-18=17'] Exploring Operation: 39-17=22, Resulting Numbers: [22] 22,93 unequal: No Solution Exploring Operation: 39+17=56, Resulting Numbers: [56] 56,93 unequal: No Solution Exploring Operation: 39*17=663, Resulting Numbers: [663] 663,93 unequal: No Solution Moving to Node #0,3,1 Current State: 93:[35, 57], Operations: ['70/2=35', '39+18=57'] Exploring Operation: 35*57=1995, Resulting Numbers: [1995] 1995,93 unequal: No Solution Exploring Operation: 35+57=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,93 unequal: No Solution Moving to Node #0,3,4 Current State: 93:[39, 53], Operations: ['70/2=35', '18+35=53'] Exploring Operation: 39*53=2067, Resulting Numbers: [2067] 2067,93 unequal: No Solution Exploring Operation: 39+53=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 53-39=14, Resulting Numbers: [14] 14,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[2, 18, 109], Operations: ['39+70=109'] Exploring Operation: 18/2=9, Resulting Numbers: [109, 9] Generated Node #0,1,0: 93:[109, 9] Operation: 18/2=9 Exploring Operation: 109-18=91, Resulting Numbers: [2, 91] Generated Node #0,1,1: 93:[2, 91] Operation: 109-18=91 Exploring Operation: 109-2=107, Resulting Numbers: [18, 107] Generated Node #0,1,2: 93:[18, 107] Operation: 109-2=107 Exploring Operation: 2*18=36, Resulting Numbers: [109, 36] Generated Node #0,1,3: 93:[109, 36] Operation: 2*18=36 Exploring Operation: 2+18=20, Resulting Numbers: [109, 20] Generated Node #0,1,4: 93:[109, 20] Operation: 2+18=20 Moving to Node #0,1,1 Current State: 93:[2, 91], Operations: ['39+70=109', '109-18=91'] Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,93 unequal: No Solution Exploring Operation: 2+91=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[39, 70, 2, 18], Operations: [] Exploring Operation: 39+70=109, Resulting Numbers: [2, 18, 109] Generated Node #0,1: 93:[2, 18, 109] Operation: 39+70=109 Moving to Node #0,1 Current State: 93:[2, 18, 109], Operations: ['39+70=109'] Exploring Operation: 109-18=91, Resulting Numbers: [2, 91] Generated Node #0,1,1: 93:[2, 91] Operation: 109-18=91 Moving to Node #0,1,1 Current State: 93:[2, 91], Operations: ['39+70=109', '109-18=91'] Exploring Operation: 2+91=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.934028
hs_5
mult_heuristic
[ 77, 67, 18, 41 ]
69
[ "77-67=10", "18+41=59", "10+59=69" ]
Current State: 69:[77, 67, 18, 41], Operations: [] Exploring Operation: 77-67=10, Resulting Numbers: [18, 41, 10] Generated Node #2: [18, 41, 10] from Operation: 77-67=10 Current State: 69:[18, 41, 10], Operations: ['77-67=10'] Exploring Operation: 18+41=59, Resulting Numbers: [10, 59] Generated Node #3: [10, 59] from Operation: 18+41=59 Current State: 69:[10, 59], Operations: ['77-67=10', '18+41=59'] Exploring Operation: 10+59=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[77, 67, 18, 41], Operations: [] Exploring Operation: 41-18=23, Resulting Numbers: [77, 67, 23] Generated Node #0,0: 69:[77, 67, 23] Operation: 41-18=23 Exploring Operation: 67-41=26, Resulting Numbers: [77, 18, 26] Generated Node #0,1: 69:[77, 18, 26] Operation: 67-41=26 Exploring Operation: 18+41=59, Resulting Numbers: [77, 67, 59] Generated Node #0,2: 69:[77, 67, 59] Operation: 18+41=59 Exploring Operation: 77-41=36, Resulting Numbers: [67, 18, 36] Generated Node #0,3: 69:[67, 18, 36] Operation: 77-41=36 Moving to Node #0,0 Current State: 69:[77, 67, 23], Operations: ['41-18=23'] Exploring Operation: 77-23=54, Resulting Numbers: [67, 54] Generated Node #0,0,0: 69:[67, 54] Operation: 77-23=54 Exploring Operation: 67-23=44, Resulting Numbers: [77, 44] Generated Node #0,0,1: 69:[77, 44] Operation: 67-23=44 Exploring Operation: 67+23=90, Resulting Numbers: [77, 90] Generated Node #0,0,2: 69:[77, 90] Operation: 67+23=90 Exploring Operation: 77-67=10, Resulting Numbers: [23, 10] Generated Node #0,0,3: 69:[23, 10] Operation: 77-67=10 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 69:[23, 10], Operations: ['41-18=23', '77-67=10'] Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 23*10=230, Resulting Numbers: [230] 230,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[67, 54], Operations: ['41-18=23', '77-23=54'] Exploring Operation: 67+54=121, Resulting Numbers: [121] 121,69 unequal: No Solution Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 67*54=3618, Resulting Numbers: [3618] 3618,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[77, 44], Operations: ['41-18=23', '67-23=44'] Exploring Operation: 77-44=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 77+44=121, Resulting Numbers: [121] 121,69 unequal: No Solution Exploring Operation: 77*44=3388, Resulting Numbers: [3388] 3388,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[77, 90], Operations: ['41-18=23', '67+23=90'] Exploring Operation: 90-77=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 77*90=6930, Resulting Numbers: [6930] 6930,69 unequal: No Solution Exploring Operation: 77+90=167, Resulting Numbers: [167] 167,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 69:[77, 18, 26], Operations: ['67-41=26'] Exploring Operation: 26-18=8, Resulting Numbers: [77, 8] Generated Node #0,1,0: 69:[77, 8] Operation: 26-18=8 Exploring Operation: 77-18=59, Resulting Numbers: [26, 59] Generated Node #0,1,1: 69:[26, 59] Operation: 77-18=59 Exploring Operation: 77+18=95, Resulting Numbers: [26, 95] Generated Node #0,1,2: 69:[26, 95] Operation: 77+18=95 Exploring Operation: 77-26=51, Resulting Numbers: [18, 51] Generated Node #0,1,3: 69:[18, 51] Operation: 77-26=51 Moving to Node #0,3 Current State: 69:[67, 18, 36], Operations: ['77-41=36'] Exploring Operation: 36/18=2, Resulting Numbers: [67, 2] Generated Node #0,3,0: 69:[67, 2] Operation: 36/18=2 Exploring Operation: 67-36=31, Resulting Numbers: [18, 31] Generated Node #0,3,1: 69:[18, 31] Operation: 67-36=31 Exploring Operation: 18+36=54, Resulting Numbers: [67, 54] Generated Node #0,3,2: 69:[67, 54] Operation: 18+36=54 Exploring Operation: 36-18=18, Resulting Numbers: [67, 18] Generated Node #0,3,3: 69:[67, 18] Operation: 36-18=18 Moving to Node #0,2 Current State: 69:[77, 67, 59], Operations: ['18+41=59'] Exploring Operation: 67+59=126, Resulting Numbers: [77, 126] Generated Node #0,2,0: 69:[77, 126] Operation: 67+59=126 Exploring Operation: 67-59=8, Resulting Numbers: [77, 8] Generated Node #0,2,1: 69:[77, 8] Operation: 67-59=8 Exploring Operation: 77-59=18, Resulting Numbers: [67, 18] Generated Node #0,2,2: 69:[67, 18] Operation: 77-59=18 Exploring Operation: 77-67=10, Resulting Numbers: [59, 10] Generated Node #0,2,3: 69:[59, 10] Operation: 77-67=10 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 69:[67, 18], Operations: ['18+41=59', '77-59=18'] Exploring Operation: 67-18=49, Resulting Numbers: [49] 49,69 unequal: No Solution Exploring Operation: 67+18=85, Resulting Numbers: [85] 85,69 unequal: No Solution Exploring Operation: 67*18=1206, Resulting Numbers: [1206] 1206,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 69:[77, 8], Operations: ['18+41=59', '67-59=8'] Exploring Operation: 77-8=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[77, 67, 18, 41], Operations: [] Exploring Operation: 18+41=59, Resulting Numbers: [77, 67, 59] Generated Node #0,2: 69:[77, 67, 59] Operation: 18+41=59 Moving to Node #0,2 Current State: 69:[77, 67, 59], Operations: ['18+41=59'] Exploring Operation: 67-59=8, Resulting Numbers: [77, 8] Generated Node #0,2,1: 69:[77, 8] Operation: 67-59=8 Moving to Node #0,2,1 Current State: 69:[77, 8], Operations: ['18+41=59', '67-59=8'] Exploring Operation: 77-8=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_4
mult_heuristic
[ 8, 23, 48, 69 ]
37
[ "48-8=40", "69/23=3", "40-3=37" ]
Current State: 37:[8, 23, 48, 69], Operations: [] Exploring Operation: 48-8=40, Resulting Numbers: [23, 69, 40] Generated Node #2: [23, 69, 40] from Operation: 48-8=40 Current State: 37:[23, 69, 40], Operations: ['48-8=40'] Exploring Operation: 69/23=3, Resulting Numbers: [40, 3] Generated Node #3: [40, 3] from Operation: 69/23=3 Current State: 37:[40, 3], Operations: ['48-8=40', '69/23=3'] Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[8, 23, 48, 69], Operations: [] Exploring Operation: 48-8=40, Resulting Numbers: [23, 69, 40] Generated Node #0,0: 37:[23, 69, 40] Operation: 48-8=40 Exploring Operation: 69-23=46, Resulting Numbers: [8, 48, 46] Generated Node #0,1: 37:[8, 48, 46] Operation: 69-23=46 Exploring Operation: 8+23=31, Resulting Numbers: [48, 69, 31] Generated Node #0,2: 37:[48, 69, 31] Operation: 8+23=31 Exploring Operation: 69-8=61, Resulting Numbers: [23, 48, 61] Generated Node #0,3: 37:[23, 48, 61] Operation: 69-8=61 Moving to Node #0,0 Current State: 37:[23, 69, 40], Operations: ['48-8=40'] Exploring Operation: 69-40=29, Resulting Numbers: [23, 29] Generated Node #0,0,0: 37:[23, 29] Operation: 69-40=29 Exploring Operation: 40-23=17, Resulting Numbers: [69, 17] Generated Node #0,0,1: 37:[69, 17] Operation: 40-23=17 Exploring Operation: 69/23=3, Resulting Numbers: [40, 3] Generated Node #0,0,2: 37:[40, 3] Operation: 69/23=3 Exploring Operation: 69-23=46, Resulting Numbers: [40, 46] Generated Node #0,0,3: 37:[40, 46] Operation: 69-23=46 Moving to Node #0,2 Current State: 37:[48, 69, 31], Operations: ['8+23=31'] Exploring Operation: 69-31=38, Resulting Numbers: [48, 38] Generated Node #0,2,0: 37:[48, 38] Operation: 69-31=38 Exploring Operation: 69-48=21, Resulting Numbers: [31, 21] Generated Node #0,2,1: 37:[31, 21] Operation: 69-48=21 Exploring Operation: 48-31=17, Resulting Numbers: [69, 17] Generated Node #0,2,2: 37:[69, 17] Operation: 48-31=17 Exploring Operation: 48+31=79, Resulting Numbers: [69, 79] Generated Node #0,2,3: 37:[69, 79] Operation: 48+31=79 Moving to Node #0,1 Current State: 37:[8, 48, 46], Operations: ['69-23=46'] Exploring Operation: 8+46=54, Resulting Numbers: [48, 54] Generated Node #0,1,0: 37:[48, 54] Operation: 8+46=54 Exploring Operation: 8+48=56, Resulting Numbers: [46, 56] Generated Node #0,1,1: 37:[46, 56] Operation: 8+48=56 Exploring Operation: 48-8=40, Resulting Numbers: [46, 40] Generated Node #0,1,2: 37:[46, 40] Operation: 48-8=40 Exploring Operation: 46-8=38, Resulting Numbers: [48, 38] Generated Node #0,1,3: 37:[48, 38] Operation: 46-8=38 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 37:[46, 40], Operations: ['69-23=46', '48-8=40'] Exploring Operation: 46-40=6, Resulting Numbers: [6] 6,37 unequal: No Solution Exploring Operation: 46+40=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 46*40=1840, Resulting Numbers: [1840] 1840,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 37:[48, 38], Operations: ['69-23=46', '46-8=38'] Exploring Operation: 48+38=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 48*38=1824, Resulting Numbers: [1824] 1824,37 unequal: No Solution Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[48, 54], Operations: ['69-23=46', '8+46=54'] Exploring Operation: 54-48=6, Resulting Numbers: [6] 6,37 unequal: No Solution Exploring Operation: 48*54=2592, Resulting Numbers: [2592] 2592,37 unequal: No Solution Exploring Operation: 48+54=102, Resulting Numbers: [102] 102,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 37:[46, 56], Operations: ['69-23=46', '8+48=56'] Exploring Operation: 46*56=2576, Resulting Numbers: [2576] 2576,37 unequal: No Solution Exploring Operation: 56-46=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 46+56=102, Resulting Numbers: [102] 102,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 37:[23, 48, 61], Operations: ['69-8=61'] Exploring Operation: 61-48=13, Resulting Numbers: [23, 13] Generated Node #0,3,0: 37:[23, 13] Operation: 61-48=13 Exploring Operation: 23+48=71, Resulting Numbers: [61, 71] Generated Node #0,3,1: 37:[61, 71] Operation: 23+48=71 Exploring Operation: 48-23=25, Resulting Numbers: [61, 25] Generated Node #0,3,2: 37:[61, 25] Operation: 48-23=25 Exploring Operation: 61-23=38, Resulting Numbers: [48, 38] Generated Node #0,3,3: 37:[48, 38] Operation: 61-23=38 Moving to Node #0,0,3 Current State: 37:[40, 46], Operations: ['48-8=40', '69-23=46'] Exploring Operation: 40*46=1840, Resulting Numbers: [1840] 1840,37 unequal: No Solution Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 46-40=6, Resulting Numbers: [6] 6,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[48, 38], Operations: ['8+23=31', '69-31=38'] Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 48+38=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 48*38=1824, Resulting Numbers: [1824] 1824,37 unequal: No Solution Moving to Node #0,3,3 Current State: 37:[48, 38], Operations: ['69-8=61', '61-23=38'] Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 48+38=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 48*38=1824, Resulting Numbers: [1824] 1824,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[31, 21], Operations: ['8+23=31', '69-48=21'] Exploring Operation: 31*21=651, Resulting Numbers: [651] 651,37 unequal: No Solution Exploring Operation: 31+21=52, Resulting Numbers: [52] 52,37 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[23, 29], Operations: ['48-8=40', '69-40=29'] Exploring Operation: 23*29=667, Resulting Numbers: [667] 667,37 unequal: No Solution Exploring Operation: 23+29=52, Resulting Numbers: [52] 52,37 unequal: No Solution Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,37 unequal: No Solution Moving to Node #0,3,2 Current State: 37:[61, 25], Operations: ['69-8=61', '48-23=25'] Exploring Operation: 61*25=1525, Resulting Numbers: [1525] 1525,37 unequal: No Solution Exploring Operation: 61-25=36, Resulting Numbers: [36] 36,37 unequal: No Solution Exploring Operation: 61+25=86, Resulting Numbers: [86] 86,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[40, 3], Operations: ['48-8=40', '69/23=3'] Exploring Operation: 40+3=43, Resulting Numbers: [43] 43,37 unequal: No Solution Exploring Operation: 40*3=120, Resulting Numbers: [120] 120,37 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[8, 23, 48, 69], Operations: [] Exploring Operation: 48-8=40, Resulting Numbers: [23, 69, 40] Generated Node #0,0: 37:[23, 69, 40] Operation: 48-8=40 Moving to Node #0,0 Current State: 37:[23, 69, 40], Operations: ['48-8=40'] Exploring Operation: 69/23=3, Resulting Numbers: [40, 3] Generated Node #0,0,2: 37:[40, 3] Operation: 69/23=3 Moving to Node #0,0,2 Current State: 37:[40, 3], Operations: ['48-8=40', '69/23=3'] Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
0.950521
hs_4
mult_heuristic
[ 82, 12, 10, 51 ]
62
[ "82-51=31", "12-10=2", "31*2=62" ]
Current State: 62:[82, 12, 10, 51], Operations: [] Exploring Operation: 82-51=31, Resulting Numbers: [12, 10, 31] Generated Node #2: [12, 10, 31] from Operation: 82-51=31 Current State: 62:[12, 10, 31], Operations: ['82-51=31'] Exploring Operation: 12-10=2, Resulting Numbers: [31, 2] Generated Node #3: [31, 2] from Operation: 12-10=2 Current State: 62:[31, 2], Operations: ['82-51=31', '12-10=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[82, 12, 10, 51], Operations: [] Exploring Operation: 82-51=31, Resulting Numbers: [12, 10, 31] Generated Node #0,0: 62:[12, 10, 31] Operation: 82-51=31 Exploring Operation: 12+51=63, Resulting Numbers: [82, 10, 63] Generated Node #0,1: 62:[82, 10, 63] Operation: 12+51=63 Exploring Operation: 82-12=70, Resulting Numbers: [10, 51, 70] Generated Node #0,2: 62:[10, 51, 70] Operation: 82-12=70 Moving to Node #0,0 Current State: 62:[12, 10, 31], Operations: ['82-51=31'] Exploring Operation: 12+10=22, Resulting Numbers: [31, 22] Generated Node #0,0,0: 62:[31, 22] Operation: 12+10=22 Exploring Operation: 12-10=2, Resulting Numbers: [31, 2] Generated Node #0,0,1: 62:[31, 2] Operation: 12-10=2 Exploring Operation: 12+31=43, Resulting Numbers: [10, 43] Generated Node #0,0,2: 62:[10, 43] Operation: 12+31=43 Moving to Node #0,2 Current State: 62:[10, 51, 70], Operations: ['82-12=70'] Exploring Operation: 10+51=61, Resulting Numbers: [70, 61] Generated Node #0,2,0: 62:[70, 61] Operation: 10+51=61 Exploring Operation: 70-10=60, Resulting Numbers: [51, 60] Generated Node #0,2,1: 62:[51, 60] Operation: 70-10=60 Exploring Operation: 70/10=7, Resulting Numbers: [51, 7] Generated Node #0,2,2: 62:[51, 7] Operation: 70/10=7 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 62:[70, 61], Operations: ['82-12=70', '10+51=61'] Exploring Operation: 70+61=131, Resulting Numbers: [131] 131,62 unequal: No Solution Exploring Operation: 70-61=9, Resulting Numbers: [9] 9,62 unequal: No Solution Exploring Operation: 70*61=4270, Resulting Numbers: [4270] 4270,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 62:[51, 60], Operations: ['82-12=70', '70-10=60'] Exploring Operation: 51*60=3060, Resulting Numbers: [3060] 3060,62 unequal: No Solution Exploring Operation: 51+60=111, Resulting Numbers: [111] 111,62 unequal: No Solution Exploring Operation: 60-51=9, Resulting Numbers: [9] 9,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 62:[51, 7], Operations: ['82-12=70', '70/10=7'] Exploring Operation: 51-7=44, Resulting Numbers: [44] 44,62 unequal: No Solution Exploring Operation: 51*7=357, Resulting Numbers: [357] 357,62 unequal: No Solution Exploring Operation: 51+7=58, Resulting Numbers: [58] 58,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 62:[82, 10, 63], Operations: ['12+51=63'] Exploring Operation: 82-63=19, Resulting Numbers: [10, 19] Generated Node #0,1,0: 62:[10, 19] Operation: 82-63=19 Exploring Operation: 82-10=72, Resulting Numbers: [63, 72] Generated Node #0,1,1: 62:[63, 72] Operation: 82-10=72 Exploring Operation: 63-10=53, Resulting Numbers: [82, 53] Generated Node #0,1,2: 62:[82, 53] Operation: 63-10=53 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 62:[63, 72], Operations: ['12+51=63', '82-10=72'] Exploring Operation: 63+72=135, Resulting Numbers: [135] 135,62 unequal: No Solution Exploring Operation: 72-63=9, Resulting Numbers: [9] 9,62 unequal: No Solution Exploring Operation: 63*72=4536, Resulting Numbers: [4536] 4536,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[10, 19], Operations: ['12+51=63', '82-63=19'] Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,62 unequal: No Solution Exploring Operation: 10+19=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 10*19=190, Resulting Numbers: [190] 190,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 62:[82, 53], Operations: ['12+51=63', '63-10=53'] Exploring Operation: 82-53=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 82+53=135, Resulting Numbers: [135] 135,62 unequal: No Solution Exploring Operation: 82*53=4346, Resulting Numbers: [4346] 4346,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 62:[31, 2], Operations: ['82-51=31', '12-10=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[82, 12, 10, 51], Operations: [] Exploring Operation: 82-51=31, Resulting Numbers: [12, 10, 31] Generated Node #0,0: 62:[12, 10, 31] Operation: 82-51=31 Moving to Node #0,0 Current State: 62:[12, 10, 31], Operations: ['82-51=31'] Exploring Operation: 12-10=2, Resulting Numbers: [31, 2] Generated Node #0,0,1: 62:[31, 2] Operation: 12-10=2 Moving to Node #0,0,1 Current State: 62:[31, 2], Operations: ['82-51=31', '12-10=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.969618
hs_3
mult_heuristic
[ 15, 88, 89, 28 ]
44
[ "88-15=73", "89+28=117", "117-73=44" ]
Current State: 44:[15, 88, 89, 28], Operations: [] Exploring Operation: 88-15=73, Resulting Numbers: [89, 28, 73] Generated Node #2: [89, 28, 73] from Operation: 88-15=73 Current State: 44:[89, 28, 73], Operations: ['88-15=73'] Exploring Operation: 89+28=117, Resulting Numbers: [73, 117] Generated Node #3: [73, 117] from Operation: 89+28=117 Current State: 44:[73, 117], Operations: ['88-15=73', '89+28=117'] Exploring Operation: 117-73=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[15, 88, 89, 28], Operations: [] Exploring Operation: 88-15=73, Resulting Numbers: [89, 28, 73] Generated Node #0,0: 44:[89, 28, 73] Operation: 88-15=73 Exploring Operation: 88-28=60, Resulting Numbers: [15, 89, 60] Generated Node #0,1: 44:[15, 89, 60] Operation: 88-28=60 Exploring Operation: 89-28=61, Resulting Numbers: [15, 88, 61] Generated Node #0,2: 44:[15, 88, 61] Operation: 89-28=61 Exploring Operation: 89-88=1, Resulting Numbers: [15, 28, 1] Generated Node #0,3: 44:[15, 28, 1] Operation: 89-88=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[15, 28, 1], Operations: ['89-88=1'] Exploring Operation: 15+28=43, Resulting Numbers: [1, 43] Generated Node #0,3,0: 44:[1, 43] Operation: 15+28=43 Exploring Operation: 28-1=27, Resulting Numbers: [15, 27] Generated Node #0,3,1: 44:[15, 27] Operation: 28-1=27 Exploring Operation: 15-1=14, Resulting Numbers: [28, 14] Generated Node #0,3,2: 44:[28, 14] Operation: 15-1=14 Exploring Operation: 28-15=13, Resulting Numbers: [1, 13] Generated Node #0,3,3: 44:[1, 13] Operation: 28-15=13 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 44:[1, 43], Operations: ['89-88=1', '15+28=43'] Exploring Operation: 1*43=43, Resulting Numbers: [43] 43,44 unequal: No Solution Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,44 unequal: No Solution Exploring Operation: 1+43=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[15, 88, 89, 28], Operations: [] Exploring Operation: 89-88=1, Resulting Numbers: [15, 28, 1] Generated Node #0,3: 44:[15, 28, 1] Operation: 89-88=1 Moving to Node #0,3 Current State: 44:[15, 28, 1], Operations: ['89-88=1'] Exploring Operation: 15+28=43, Resulting Numbers: [1, 43] Generated Node #0,3,0: 44:[1, 43] Operation: 15+28=43 Moving to Node #0,3,0 Current State: 44:[1, 43], Operations: ['89-88=1', '15+28=43'] Exploring Operation: 1+43=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 25, 80, 35, 71 ]
91
[ "80-25=55", "71-35=36", "55+36=91" ]
Current State: 91:[25, 80, 35, 71], Operations: [] Exploring Operation: 80-25=55, Resulting Numbers: [35, 71, 55] Generated Node #2: [35, 71, 55] from Operation: 80-25=55 Current State: 91:[35, 71, 55], Operations: ['80-25=55'] Exploring Operation: 71-35=36, Resulting Numbers: [55, 36] Generated Node #3: [55, 36] from Operation: 71-35=36 Current State: 91:[55, 36], Operations: ['80-25=55', '71-35=36'] Exploring Operation: 55+36=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[25, 80, 35, 71], Operations: [] Exploring Operation: 35-25=10, Resulting Numbers: [80, 71, 10] Generated Node #0,0: 91:[80, 71, 10] Operation: 35-25=10 Exploring Operation: 71-35=36, Resulting Numbers: [25, 80, 36] Generated Node #0,1: 91:[25, 80, 36] Operation: 71-35=36 Exploring Operation: 80-71=9, Resulting Numbers: [25, 35, 9] Generated Node #0,2: 91:[25, 35, 9] Operation: 80-71=9 Exploring Operation: 35+71=106, Resulting Numbers: [25, 80, 106] Generated Node #0,3: 91:[25, 80, 106] Operation: 35+71=106 Exploring Operation: 25+71=96, Resulting Numbers: [80, 35, 96] Generated Node #0,4: 91:[80, 35, 96] Operation: 25+71=96 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[80, 71, 10], Operations: ['35-25=10'] Exploring Operation: 80/10=8, Resulting Numbers: [71, 8] Generated Node #0,0,0: 91:[71, 8] Operation: 80/10=8 Exploring Operation: 80+10=90, Resulting Numbers: [71, 90] Generated Node #0,0,1: 91:[71, 90] Operation: 80+10=90 Exploring Operation: 71+10=81, Resulting Numbers: [80, 81] Generated Node #0,0,2: 91:[80, 81] Operation: 71+10=81 Exploring Operation: 80-10=70, Resulting Numbers: [71, 70] Generated Node #0,0,3: 91:[71, 70] Operation: 80-10=70 Exploring Operation: 80-71=9, Resulting Numbers: [10, 9] Generated Node #0,0,4: 91:[10, 9] Operation: 80-71=9 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 91:[10, 9], Operations: ['35-25=10', '80-71=9'] Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,91 unequal: No Solution Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,91 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[71, 8], Operations: ['35-25=10', '80/10=8'] Exploring Operation: 71-8=63, Resulting Numbers: [63] 63,91 unequal: No Solution Exploring Operation: 71*8=568, Resulting Numbers: [568] 568,91 unequal: No Solution Exploring Operation: 71+8=79, Resulting Numbers: [79] 79,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[71, 90], Operations: ['35-25=10', '80+10=90'] Exploring Operation: 71*90=6390, Resulting Numbers: [6390] 6390,91 unequal: No Solution Exploring Operation: 90-71=19, Resulting Numbers: [19] 19,91 unequal: No Solution Exploring Operation: 71+90=161, Resulting Numbers: [161] 161,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 91:[80, 81], Operations: ['35-25=10', '71+10=81'] Exploring Operation: 80+81=161, Resulting Numbers: [161] 161,91 unequal: No Solution Exploring Operation: 80*81=6480, Resulting Numbers: [6480] 6480,91 unequal: No Solution Exploring Operation: 81-80=1, Resulting Numbers: [1] 1,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 91:[71, 70], Operations: ['35-25=10', '80-10=70'] Exploring Operation: 71-70=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 71*70=4970, Resulting Numbers: [4970] 4970,91 unequal: No Solution Exploring Operation: 71+70=141, Resulting Numbers: [141] 141,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[25, 35, 9], Operations: ['80-71=9'] Exploring Operation: 25+35=60, Resulting Numbers: [9, 60] Generated Node #0,2,0: 91:[9, 60] Operation: 25+35=60 Exploring Operation: 25+9=34, Resulting Numbers: [35, 34] Generated Node #0,2,1: 91:[35, 34] Operation: 25+9=34 Exploring Operation: 35-9=26, Resulting Numbers: [25, 26] Generated Node #0,2,2: 91:[25, 26] Operation: 35-9=26 Exploring Operation: 35-25=10, Resulting Numbers: [9, 10] Generated Node #0,2,3: 91:[9, 10] Operation: 35-25=10 Exploring Operation: 25-9=16, Resulting Numbers: [35, 16] Generated Node #0,2,4: 91:[35, 16] Operation: 25-9=16 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 91:[9, 10], Operations: ['80-71=9', '35-25=10'] Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,91 unequal: No Solution Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,91 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 91:[25, 26], Operations: ['80-71=9', '35-9=26'] Exploring Operation: 25*26=650, Resulting Numbers: [650] 650,91 unequal: No Solution Exploring Operation: 25+26=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 26-25=1, Resulting Numbers: [1] 1,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 91:[35, 16], Operations: ['80-71=9', '25-9=16'] Exploring Operation: 35*16=560, Resulting Numbers: [560] 560,91 unequal: No Solution Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 91:[9, 60], Operations: ['80-71=9', '25+35=60'] Exploring Operation: 9+60=69, Resulting Numbers: [69] 69,91 unequal: No Solution Exploring Operation: 60-9=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 9*60=540, Resulting Numbers: [540] 540,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 91:[35, 34], Operations: ['80-71=9', '25+9=34'] Exploring Operation: 35-34=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 35+34=69, Resulting Numbers: [69] 69,91 unequal: No Solution Exploring Operation: 35*34=1190, Resulting Numbers: [1190] 1190,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 91:[25, 80, 106], Operations: ['35+71=106'] Exploring Operation: 106-25=81, Resulting Numbers: [80, 81] Generated Node #0,3,0: 91:[80, 81] Operation: 106-25=81 Exploring Operation: 25+106=131, Resulting Numbers: [80, 131] Generated Node #0,3,1: 91:[80, 131] Operation: 25+106=131 Exploring Operation: 106-80=26, Resulting Numbers: [25, 26] Generated Node #0,3,2: 91:[25, 26] Operation: 106-80=26 Exploring Operation: 80-25=55, Resulting Numbers: [106, 55] Generated Node #0,3,3: 91:[106, 55] Operation: 80-25=55 Exploring Operation: 25+80=105, Resulting Numbers: [106, 105] Generated Node #0,3,4: 91:[106, 105] Operation: 25+80=105 Moving to Node #0,3,0 Current State: 91:[80, 81], Operations: ['35+71=106', '106-25=81'] Exploring Operation: 80+81=161, Resulting Numbers: [161] 161,91 unequal: No Solution Exploring Operation: 81-80=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 80*81=6480, Resulting Numbers: [6480] 6480,91 unequal: No Solution Moving to Node #0,3,2 Current State: 91:[25, 26], Operations: ['35+71=106', '106-80=26'] Exploring Operation: 26-25=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 25*26=650, Resulting Numbers: [650] 650,91 unequal: No Solution Exploring Operation: 25+26=51, Resulting Numbers: [51] 51,91 unequal: No Solution Moving to Node #0,3,4 Current State: 91:[106, 105], Operations: ['35+71=106', '25+80=105'] Exploring Operation: 106-105=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 106*105=11130, Resulting Numbers: [11130] 11130,91 unequal: No Solution Exploring Operation: 106+105=211, Resulting Numbers: [211] 211,91 unequal: No Solution Moving to Node #0,3,1 Current State: 91:[80, 131], Operations: ['35+71=106', '25+106=131'] Exploring Operation: 131-80=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 80*131=10480, Resulting Numbers: [10480] 10480,91 unequal: No Solution Exploring Operation: 80+131=211, Resulting Numbers: [211] 211,91 unequal: No Solution Moving to Node #0,3,3 Current State: 91:[106, 55], Operations: ['35+71=106', '80-25=55'] Exploring Operation: 106*55=5830, Resulting Numbers: [5830] 5830,91 unequal: No Solution Exploring Operation: 106-55=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 106+55=161, Resulting Numbers: [161] 161,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 91:[80, 35, 96], Operations: ['25+71=96'] Exploring Operation: 80-35=45, Resulting Numbers: [96, 45] Generated Node #0,4,0: 91:[96, 45] Operation: 80-35=45 Exploring Operation: 96-35=61, Resulting Numbers: [80, 61] Generated Node #0,4,1: 91:[80, 61] Operation: 96-35=61 Exploring Operation: 96-80=16, Resulting Numbers: [35, 16] Generated Node #0,4,2: 91:[35, 16] Operation: 96-80=16 Exploring Operation: 35+96=131, Resulting Numbers: [80, 131] Generated Node #0,4,3: 91:[80, 131] Operation: 35+96=131 Exploring Operation: 80+35=115, Resulting Numbers: [96, 115] Generated Node #0,4,4: 91:[96, 115] Operation: 80+35=115 Moving to Node #0,4,2 Current State: 91:[35, 16], Operations: ['25+71=96', '96-80=16'] Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,91 unequal: No Solution Exploring Operation: 35*16=560, Resulting Numbers: [560] 560,91 unequal: No Solution Moving to Node #0,4,4 Current State: 91:[96, 115], Operations: ['25+71=96', '80+35=115'] Exploring Operation: 96*115=11040, Resulting Numbers: [11040] 11040,91 unequal: No Solution Exploring Operation: 115-96=19, Resulting Numbers: [19] 19,91 unequal: No Solution Exploring Operation: 96+115=211, Resulting Numbers: [211] 211,91 unequal: No Solution Moving to Node #0,4,0 Current State: 91:[96, 45], Operations: ['25+71=96', '80-35=45'] Exploring Operation: 96+45=141, Resulting Numbers: [141] 141,91 unequal: No Solution Exploring Operation: 96*45=4320, Resulting Numbers: [4320] 4320,91 unequal: No Solution Exploring Operation: 96-45=51, Resulting Numbers: [51] 51,91 unequal: No Solution Moving to Node #0,4,1 Current State: 91:[80, 61], Operations: ['25+71=96', '96-35=61'] Exploring Operation: 80*61=4880, Resulting Numbers: [4880] 4880,91 unequal: No Solution Exploring Operation: 80-61=19, Resulting Numbers: [19] 19,91 unequal: No Solution Exploring Operation: 80+61=141, Resulting Numbers: [141] 141,91 unequal: No Solution Moving to Node #0,4,3 Current State: 91:[80, 131], Operations: ['25+71=96', '35+96=131'] Exploring Operation: 131-80=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 80+131=211, Resulting Numbers: [211] 211,91 unequal: No Solution Exploring Operation: 80*131=10480, Resulting Numbers: [10480] 10480,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[25, 80, 36], Operations: ['71-35=36'] Exploring Operation: 25+36=61, Resulting Numbers: [80, 61] Generated Node #0,1,0: 91:[80, 61] Operation: 25+36=61 Exploring Operation: 80+36=116, Resulting Numbers: [25, 116] Generated Node #0,1,1: 91:[25, 116] Operation: 80+36=116 Exploring Operation: 25+80=105, Resulting Numbers: [36, 105] Generated Node #0,1,2: 91:[36, 105] Operation: 25+80=105 Exploring Operation: 36-25=11, Resulting Numbers: [80, 11] Generated Node #0,1,3: 91:[80, 11] Operation: 36-25=11 Exploring Operation: 80-36=44, Resulting Numbers: [25, 44] Generated Node #0,1,4: 91:[25, 44] Operation: 80-36=44 Moving to Node #0,1,3 Current State: 91:[80, 11], Operations: ['71-35=36', '36-25=11'] Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,91 unequal: No Solution Exploring Operation: 80+11=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[25, 80, 35, 71], Operations: [] Exploring Operation: 71-35=36, Resulting Numbers: [25, 80, 36] Generated Node #0,1: 91:[25, 80, 36] Operation: 71-35=36 Moving to Node #0,1 Current State: 91:[25, 80, 36], Operations: ['71-35=36'] Exploring Operation: 36-25=11, Resulting Numbers: [80, 11] Generated Node #0,1,3: 91:[80, 11] Operation: 36-25=11 Moving to Node #0,1,3 Current State: 91:[80, 11], Operations: ['71-35=36', '36-25=11'] Exploring Operation: 80+11=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.916667
hs_5
mult_heuristic
[ 96, 49, 25, 71 ]
20
[ "96*25=2400", "49+71=120", "2400/120=20" ]
Current State: 20:[96, 49, 25, 71], Operations: [] Exploring Operation: 96*25=2400, Resulting Numbers: [49, 71, 2400] Generated Node #2: [49, 71, 2400] from Operation: 96*25=2400 Current State: 20:[49, 71, 2400], Operations: ['96*25=2400'] Exploring Operation: 49+71=120, Resulting Numbers: [2400, 120] Generated Node #3: [2400, 120] from Operation: 49+71=120 Current State: 20:[2400, 120], Operations: ['96*25=2400', '49+71=120'] Exploring Operation: 2400/120=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[96, 49, 25, 71], Operations: [] Exploring Operation: 96-71=25, Resulting Numbers: [49, 25, 25] Generated Node #0,0: 20:[49, 25, 25] Operation: 96-71=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[49, 25, 25], Operations: ['96-71=25'] Exploring Operation: 49-25=24, Resulting Numbers: [25, 24] Generated Node #0,0,0: 20:[25, 24] Operation: 49-25=24 Moving to Node #0,0,0 Current State: 20:[25, 24], Operations: ['96-71=25', '49-25=24'] Exploring Operation: 25-24=1, Resulting Numbers: [1] 1,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 56, 39, 33, 54 ]
42
[ "56*54=3024", "39+33=72", "3024/72=42" ]
Current State: 42:[56, 39, 33, 54], Operations: [] Exploring Operation: 56*54=3024, Resulting Numbers: [39, 33, 3024] Generated Node #2: [39, 33, 3024] from Operation: 56*54=3024 Current State: 42:[39, 33, 3024], Operations: ['56*54=3024'] Exploring Operation: 39+33=72, Resulting Numbers: [3024, 72] Generated Node #3: [3024, 72] from Operation: 39+33=72 Current State: 42:[3024, 72], Operations: ['56*54=3024', '39+33=72'] Exploring Operation: 3024/72=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[56, 39, 33, 54], Operations: [] Exploring Operation: 56-54=2, Resulting Numbers: [39, 33, 2] Generated Node #0,0: 42:[39, 33, 2] Operation: 56-54=2 Exploring Operation: 56-33=23, Resulting Numbers: [39, 54, 23] Generated Node #0,1: 42:[39, 54, 23] Operation: 56-33=23 Exploring Operation: 56-39=17, Resulting Numbers: [33, 54, 17] Generated Node #0,2: 42:[33, 54, 17] Operation: 56-39=17 Exploring Operation: 54-33=21, Resulting Numbers: [56, 39, 21] Generated Node #0,3: 42:[56, 39, 21] Operation: 54-33=21 Moving to Node #0,0 Current State: 42:[39, 33, 2], Operations: ['56-54=2'] Exploring Operation: 39+2=41, Resulting Numbers: [33, 41] Generated Node #0,0,0: 42:[33, 41] Operation: 39+2=41 Exploring Operation: 39-33=6, Resulting Numbers: [2, 6] Generated Node #0,0,1: 42:[2, 6] Operation: 39-33=6 Exploring Operation: 33-2=31, Resulting Numbers: [39, 31] Generated Node #0,0,2: 42:[39, 31] Operation: 33-2=31 Exploring Operation: 33+2=35, Resulting Numbers: [39, 35] Generated Node #0,0,3: 42:[39, 35] Operation: 33+2=35 Moving to Node #0,3 Current State: 42:[56, 39, 21], Operations: ['54-33=21'] Exploring Operation: 56-21=35, Resulting Numbers: [39, 35] Generated Node #0,3,0: 42:[39, 35] Operation: 56-21=35 Exploring Operation: 56-39=17, Resulting Numbers: [21, 17] Generated Node #0,3,1: 42:[21, 17] Operation: 56-39=17 Exploring Operation: 39-21=18, Resulting Numbers: [56, 18] Generated Node #0,3,2: 42:[56, 18] Operation: 39-21=18 Exploring Operation: 39+21=60, Resulting Numbers: [56, 60] Generated Node #0,3,3: 42:[56, 60] Operation: 39+21=60 Moving to Node #0,1 Current State: 42:[39, 54, 23], Operations: ['56-33=23'] Exploring Operation: 54-23=31, Resulting Numbers: [39, 31] Generated Node #0,1,0: 42:[39, 31] Operation: 54-23=31 Exploring Operation: 54-39=15, Resulting Numbers: [23, 15] Generated Node #0,1,1: 42:[23, 15] Operation: 54-39=15 Exploring Operation: 39-23=16, Resulting Numbers: [54, 16] Generated Node #0,1,2: 42:[54, 16] Operation: 39-23=16 Exploring Operation: 39+23=62, Resulting Numbers: [54, 62] Generated Node #0,1,3: 42:[54, 62] Operation: 39+23=62 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 42:[23, 15], Operations: ['56-33=23', '54-39=15'] Exploring Operation: 23+15=38, Resulting Numbers: [38] 38,42 unequal: No Solution Exploring Operation: 23*15=345, Resulting Numbers: [345] 345,42 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 42:[39, 31], Operations: ['56-33=23', '54-23=31'] Exploring Operation: 39*31=1209, Resulting Numbers: [1209] 1209,42 unequal: No Solution Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 39+31=70, Resulting Numbers: [70] 70,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 42:[54, 16], Operations: ['56-33=23', '39-23=16'] Exploring Operation: 54*16=864, Resulting Numbers: [864] 864,42 unequal: No Solution Exploring Operation: 54-16=38, Resulting Numbers: [38] 38,42 unequal: No Solution Exploring Operation: 54+16=70, Resulting Numbers: [70] 70,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 42:[54, 62], Operations: ['56-33=23', '39+23=62'] Exploring Operation: 54+62=116, Resulting Numbers: [116] 116,42 unequal: No Solution Exploring Operation: 62-54=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 54*62=3348, Resulting Numbers: [3348] 3348,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 42:[33, 54, 17], Operations: ['56-39=17'] Exploring Operation: 54-33=21, Resulting Numbers: [17, 21] Generated Node #0,2,0: 42:[17, 21] Operation: 54-33=21 Exploring Operation: 33+17=50, Resulting Numbers: [54, 50] Generated Node #0,2,1: 42:[54, 50] Operation: 33+17=50 Exploring Operation: 33-17=16, Resulting Numbers: [54, 16] Generated Node #0,2,2: 42:[54, 16] Operation: 33-17=16 Exploring Operation: 54-17=37, Resulting Numbers: [33, 37] Generated Node #0,2,3: 42:[33, 37] Operation: 54-17=37 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 42:[17, 21], Operations: ['56-39=17', '54-33=21'] Exploring Operation: 17+21=38, Resulting Numbers: [38] 38,42 unequal: No Solution Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 17*21=357, Resulting Numbers: [357] 357,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 42:[54, 16], Operations: ['56-39=17', '33-17=16'] Exploring Operation: 54-16=38, Resulting Numbers: [38] 38,42 unequal: No Solution Exploring Operation: 54+16=70, Resulting Numbers: [70] 70,42 unequal: No Solution Exploring Operation: 54*16=864, Resulting Numbers: [864] 864,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 42:[33, 37], Operations: ['56-39=17', '54-17=37'] Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 33+37=70, Resulting Numbers: [70] 70,42 unequal: No Solution Exploring Operation: 33*37=1221, Resulting Numbers: [1221] 1221,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 42:[54, 50], Operations: ['56-39=17', '33+17=50'] Exploring Operation: 54*50=2700, Resulting Numbers: [2700] 2700,42 unequal: No Solution Exploring Operation: 54-50=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 54+50=104, Resulting Numbers: [104] 104,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 42:[2, 6], Operations: ['56-54=2', '39-33=6'] Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,42 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,42 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,42 unequal: No Solution Moving to Node #0,3,1 Current State: 42:[21, 17], Operations: ['54-33=21', '56-39=17'] Exploring Operation: 21+17=38, Resulting Numbers: [38] 38,42 unequal: No Solution Exploring Operation: 21*17=357, Resulting Numbers: [357] 357,42 unequal: No Solution Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,42 unequal: No Solution Moving to Node #0,0,3 Current State: 42:[39, 35], Operations: ['56-54=2', '33+2=35'] Exploring Operation: 39+35=74, Resulting Numbers: [74] 74,42 unequal: No Solution Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 39*35=1365, Resulting Numbers: [1365] 1365,42 unequal: No Solution Moving to Node #0,3,0 Current State: 42:[39, 35], Operations: ['54-33=21', '56-21=35'] Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 39+35=74, Resulting Numbers: [74] 74,42 unequal: No Solution Exploring Operation: 39*35=1365, Resulting Numbers: [1365] 1365,42 unequal: No Solution Moving to Node #0,0,0 Current State: 42:[33, 41], Operations: ['56-54=2', '39+2=41'] Exploring Operation: 41-33=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 33*41=1353, Resulting Numbers: [1353] 1353,42 unequal: No Solution Exploring Operation: 33+41=74, Resulting Numbers: [74] 74,42 unequal: No Solution Moving to Node #0,0,2 Current State: 42:[39, 31], Operations: ['56-54=2', '33-2=31'] Exploring Operation: 39*31=1209, Resulting Numbers: [1209] 1209,42 unequal: No Solution Exploring Operation: 39+31=70, Resulting Numbers: [70] 70,42 unequal: No Solution Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,42 unequal: No Solution Moving to Node #0,3,2 Current State: 42:[56, 18], Operations: ['54-33=21', '39-21=18'] Exploring Operation: 56+18=74, Resulting Numbers: [74] 74,42 unequal: No Solution Exploring Operation: 56*18=1008, Resulting Numbers: [1008] 1008,42 unequal: No Solution Exploring Operation: 56-18=38, Resulting Numbers: [38] 38,42 unequal: No Solution Moving to Node #0,3,3 Current State: 42:[56, 60], Operations: ['54-33=21', '39+21=60'] Exploring Operation: 56+60=116, Resulting Numbers: [116] 116,42 unequal: No Solution Exploring Operation: 56*60=3360, Resulting Numbers: [3360] 3360,42 unequal: No Solution Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,42 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 25, 2, 44, 24 ]
27
[ "25+24=49", "44/2=22", "49-22=27" ]
Current State: 27:[25, 2, 44, 24], Operations: [] Exploring Operation: 25+24=49, Resulting Numbers: [2, 44, 49] Generated Node #2: [2, 44, 49] from Operation: 25+24=49 Current State: 27:[2, 44, 49], Operations: ['25+24=49'] Exploring Operation: 44/2=22, Resulting Numbers: [49, 22] Generated Node #3: [49, 22] from Operation: 44/2=22 Current State: 27:[49, 22], Operations: ['25+24=49', '44/2=22'] Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[25, 2, 44, 24], Operations: [] Exploring Operation: 44/2=22, Resulting Numbers: [25, 24, 22] Generated Node #0,0: 27:[25, 24, 22] Operation: 44/2=22 Moving to Node #0,0 Current State: 27:[25, 24, 22], Operations: ['44/2=22'] Exploring Operation: 25-22=3, Resulting Numbers: [24, 3] Generated Node #0,0,0: 27:[24, 3] Operation: 25-22=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[24, 3], Operations: ['44/2=22', '25-22=3'] Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[25, 2, 44, 24], Operations: [] Exploring Operation: 44/2=22, Resulting Numbers: [25, 24, 22] Generated Node #0,0: 27:[25, 24, 22] Operation: 44/2=22 Moving to Node #0,0 Current State: 27:[25, 24, 22], Operations: ['44/2=22'] Exploring Operation: 25-22=3, Resulting Numbers: [24, 3] Generated Node #0,0,0: 27:[24, 3] Operation: 25-22=3 Moving to Node #0,0,0 Current State: 27:[24, 3], Operations: ['44/2=22', '25-22=3'] Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 17, 17, 11, 5 ]
85
[ "11-5=6", "17*6=102", "102-17=85" ]
Current State: 85:[17, 17, 11, 5], Operations: [] Exploring Operation: 11-5=6, Resulting Numbers: [17, 17, 6] Generated Node #2: [17, 17, 6] from Operation: 11-5=6 Current State: 85:[17, 17, 6], Operations: ['11-5=6'] Exploring Operation: 17*6=102, Resulting Numbers: [102] 102,85 equal: Goal Reached Exploring Operation: 102-17=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[17, 17, 11, 5], Operations: [] Exploring Operation: 11-5=6, Resulting Numbers: [17, 17, 6] Generated Node #0,0: 85:[17, 17, 6] Operation: 11-5=6 Exploring Operation: 17-11=6, Resulting Numbers: [17, 5, 6] Generated Node #0,1: 85:[17, 5, 6] Operation: 17-11=6 Exploring Operation: 17-11=6, Resulting Numbers: [17, 5, 6] Generated Node #0,2: 85:[17, 5, 6] Operation: 17-11=6 Exploring Operation: 11+5=16, Resulting Numbers: [17, 17, 16] Generated Node #0,3: 85:[17, 17, 16] Operation: 11+5=16 Moving to Node #0,0 Current State: 85:[17, 17, 6], Operations: ['11-5=6'] Exploring Operation: 17+6=23, Resulting Numbers: [17, 23] Generated Node #0,0,0: 85:[17, 23] Operation: 17+6=23 Exploring Operation: 17/17=1, Resulting Numbers: [6, 1] Generated Node #0,0,1: 85:[6, 1] Operation: 17/17=1 Exploring Operation: 17-17=0, Resulting Numbers: [6, 0] Generated Node #0,0,2: 85:[6, 0] Operation: 17-17=0 Exploring Operation: 17-6=11, Resulting Numbers: [17, 11] Generated Node #0,0,3: 85:[17, 11] Operation: 17-6=11 Moving to Node #0,2 Current State: 85:[17, 5, 6], Operations: ['17-11=6'] Exploring Operation: 6-5=1, Resulting Numbers: [17, 1] Generated Node #0,2,0: 85:[17, 1] Operation: 6-5=1 Exploring Operation: 17-5=12, Resulting Numbers: [6, 12] Generated Node #0,2,1: 85:[6, 12] Operation: 17-5=12 Exploring Operation: 17+5=22, Resulting Numbers: [6, 22] Generated Node #0,2,2: 85:[6, 22] Operation: 17+5=22 Exploring Operation: 17*5=85, Resulting Numbers: [6, 85] Generated Node #0,2,3: 85:[6, 85] Operation: 17*5=85 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 85:[6, 85], Operations: ['17-11=6', '17*5=85'] Exploring Operation: 85-6=79, Resulting Numbers: [79] 79,85 unequal: No Solution Exploring Operation: 6*85=510, Resulting Numbers: [510] 510,85 unequal: No Solution Exploring Operation: 6+85=91, Resulting Numbers: [91] 91,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 85:[17, 1], Operations: ['17-11=6', '6-5=1'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,85 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,85 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 85:[6, 12], Operations: ['17-11=6', '17-5=12'] Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 85:[6, 22], Operations: ['17-11=6', '17+5=22'] Exploring Operation: 6+22=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 6*22=132, Resulting Numbers: [132] 132,85 unequal: No Solution Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 85:[17, 5, 6], Operations: ['17-11=6'] Exploring Operation: 17*5=85, Resulting Numbers: [6, 85] Generated Node #0,1,0: 85:[6, 85] Operation: 17*5=85 Exploring Operation: 17-5=12, Resulting Numbers: [6, 12] Generated Node #0,1,1: 85:[6, 12] Operation: 17-5=12 Exploring Operation: 6-5=1, Resulting Numbers: [17, 1] Generated Node #0,1,2: 85:[17, 1] Operation: 6-5=1 Exploring Operation: 17+5=22, Resulting Numbers: [6, 22] Generated Node #0,1,3: 85:[6, 22] Operation: 17+5=22 Moving to Node #0,3 Current State: 85:[17, 17, 16], Operations: ['11+5=16'] Exploring Operation: 17-17=0, Resulting Numbers: [16, 0] Generated Node #0,3,0: 85:[16, 0] Operation: 17-17=0 Exploring Operation: 17-16=1, Resulting Numbers: [17, 1] Generated Node #0,3,1: 85:[17, 1] Operation: 17-16=1 Exploring Operation: 17-16=1, Resulting Numbers: [17, 1] Generated Node #0,3,2: 85:[17, 1] Operation: 17-16=1 Exploring Operation: 17/17=1, Resulting Numbers: [16, 1] Generated Node #0,3,3: 85:[16, 1] Operation: 17/17=1 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 85:[17, 1], Operations: ['11+5=16', '17-16=1'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,85 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,85 unequal: No Solution Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 85:[17, 1], Operations: ['11+5=16', '17-16=1'] Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,85 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,85 unequal: No Solution Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 85:[16, 1], Operations: ['11+5=16', '17/17=1'] Exploring Operation: 16+1=17, Resulting Numbers: [17] 17,85 unequal: No Solution Exploring Operation: 16*1=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 85:[16, 0], Operations: ['11+5=16', '17-17=0'] Exploring Operation: 16+0=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 16-0=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 16*0=0, Resulting Numbers: [0] 0,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 85:[6, 85], Operations: ['17-11=6', '17*5=85'] Exploring Operation: 6+85=91, Resulting Numbers: [91] 91,85 unequal: No Solution Exploring Operation: 85-6=79, Resulting Numbers: [79] 79,85 unequal: No Solution Exploring Operation: 6*85=510, Resulting Numbers: [510] 510,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[17, 1], Operations: ['17-11=6', '6-5=1'] Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,85 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[6, 1], Operations: ['11-5=6', '17/17=1'] Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,85 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[6, 12], Operations: ['17-11=6', '17-5=12'] Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,85 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,85 unequal: No Solution Moving to Node #0,0,2 Current State: 85:[6, 0], Operations: ['11-5=6', '17-17=0'] Exploring Operation: 6*0=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 6+0=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 6-0=6, Resulting Numbers: [6] 6,85 unequal: No Solution Moving to Node #0,1,3 Current State: 85:[6, 22], Operations: ['17-11=6', '17+5=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 6+22=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 6*22=132, Resulting Numbers: [132] 132,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[17, 23], Operations: ['11-5=6', '17+6=23'] Exploring Operation: 17*23=391, Resulting Numbers: [391] 391,85 unequal: No Solution Exploring Operation: 17+23=40, Resulting Numbers: [40] 40,85 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[17, 11], Operations: ['11-5=6', '17-6=11'] Exploring Operation: 17*11=187, Resulting Numbers: [187] 187,85 unequal: No Solution Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,85 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 72, 94, 18, 70 ]
21
[ "94-70=24", "72/24=3", "18+3=21" ]
Current State: 21:[72, 94, 18, 70], Operations: [] Exploring Operation: 94-70=24, Resulting Numbers: [72, 18, 24] Generated Node #2: [72, 18, 24] from Operation: 94-70=24 Current State: 21:[72, 18, 24], Operations: ['94-70=24'] Exploring Operation: 72/24=3, Resulting Numbers: [18, 3] Generated Node #3: [18, 3] from Operation: 72/24=3 Current State: 21:[18, 3], Operations: ['94-70=24', '72/24=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[72, 94, 18, 70], Operations: [] Exploring Operation: 72-70=2, Resulting Numbers: [94, 18, 2] Generated Node #0,0: 21:[94, 18, 2] Operation: 72-70=2 Exploring Operation: 72-18=54, Resulting Numbers: [94, 70, 54] Generated Node #0,1: 21:[94, 70, 54] Operation: 72-18=54 Exploring Operation: 94-72=22, Resulting Numbers: [18, 70, 22] Generated Node #0,2: 21:[18, 70, 22] Operation: 94-72=22 Exploring Operation: 72/18=4, Resulting Numbers: [94, 70, 4] Generated Node #0,3: 21:[94, 70, 4] Operation: 72/18=4 Exploring Operation: 94-70=24, Resulting Numbers: [72, 18, 24] Generated Node #0,4: 21:[72, 18, 24] Operation: 94-70=24 Moving to Node #0,2 Current State: 21:[18, 70, 22], Operations: ['94-72=22'] Exploring Operation: 70-22=48, Resulting Numbers: [18, 48] Generated Node #0,2,0: 21:[18, 48] Operation: 70-22=48 Exploring Operation: 22-18=4, Resulting Numbers: [70, 4] Generated Node #0,2,1: 21:[70, 4] Operation: 22-18=4 Exploring Operation: 18+70=88, Resulting Numbers: [22, 88] Generated Node #0,2,2: 21:[22, 88] Operation: 18+70=88 Exploring Operation: 18+22=40, Resulting Numbers: [70, 40] Generated Node #0,2,3: 21:[70, 40] Operation: 18+22=40 Exploring Operation: 70-18=52, Resulting Numbers: [22, 52] Generated Node #0,2,4: 21:[22, 52] Operation: 70-18=52 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 21:[18, 48], Operations: ['94-72=22', '70-22=48'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,21 unequal: No Solution Exploring Operation: 18+48=66, Resulting Numbers: [66] 66,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 21:[22, 52], Operations: ['94-72=22', '70-18=52'] Exploring Operation: 22+52=74, Resulting Numbers: [74] 74,21 unequal: No Solution Exploring Operation: 52-22=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 22*52=1144, Resulting Numbers: [1144] 1144,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 21:[70, 4], Operations: ['94-72=22', '22-18=4'] Exploring Operation: 70*4=280, Resulting Numbers: [280] 280,21 unequal: No Solution Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,21 unequal: No Solution Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 21:[22, 88], Operations: ['94-72=22', '18+70=88'] Exploring Operation: 22+88=110, Resulting Numbers: [110] 110,21 unequal: No Solution Exploring Operation: 88/22=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 22*88=1936, Resulting Numbers: [1936] 1936,21 unequal: No Solution Exploring Operation: 88-22=66, Resulting Numbers: [66] 66,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 21:[70, 40], Operations: ['94-72=22', '18+22=40'] Exploring Operation: 70+40=110, Resulting Numbers: [110] 110,21 unequal: No Solution Exploring Operation: 70*40=2800, Resulting Numbers: [2800] 2800,21 unequal: No Solution Exploring Operation: 70-40=30, Resulting Numbers: [30] 30,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 21:[72, 18, 24], Operations: ['94-70=24'] Exploring Operation: 72/24=3, Resulting Numbers: [18, 3] Generated Node #0,4,0: 21:[18, 3] Operation: 72/24=3 Exploring Operation: 72-24=48, Resulting Numbers: [18, 48] Generated Node #0,4,1: 21:[18, 48] Operation: 72-24=48 Exploring Operation: 72-18=54, Resulting Numbers: [24, 54] Generated Node #0,4,2: 21:[24, 54] Operation: 72-18=54 Exploring Operation: 24-18=6, Resulting Numbers: [72, 6] Generated Node #0,4,3: 21:[72, 6] Operation: 24-18=6 Exploring Operation: 72/18=4, Resulting Numbers: [24, 4] Generated Node #0,4,4: 21:[24, 4] Operation: 72/18=4 Moving to Node #0,0 Current State: 21:[94, 18, 2], Operations: ['72-70=2'] Exploring Operation: 94/2=47, Resulting Numbers: [18, 47] Generated Node #0,0,0: 21:[18, 47] Operation: 94/2=47 Exploring Operation: 18/2=9, Resulting Numbers: [94, 9] Generated Node #0,0,1: 21:[94, 9] Operation: 18/2=9 Exploring Operation: 18+2=20, Resulting Numbers: [94, 20] Generated Node #0,0,2: 21:[94, 20] Operation: 18+2=20 Exploring Operation: 94-18=76, Resulting Numbers: [2, 76] Generated Node #0,0,3: 21:[2, 76] Operation: 94-18=76 Exploring Operation: 94-2=92, Resulting Numbers: [18, 92] Generated Node #0,0,4: 21:[18, 92] Operation: 94-2=92 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[18, 47], Operations: ['72-70=2', '94/2=47'] Exploring Operation: 18+47=65, Resulting Numbers: [65] 65,21 unequal: No Solution Exploring Operation: 18*47=846, Resulting Numbers: [846] 846,21 unequal: No Solution Exploring Operation: 47-18=29, Resulting Numbers: [29] 29,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 21:[2, 76], Operations: ['72-70=2', '94-18=76'] Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,21 unequal: No Solution Exploring Operation: 2+76=78, Resulting Numbers: [78] 78,21 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,21 unequal: No Solution Exploring Operation: 2*76=152, Resulting Numbers: [152] 152,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 21:[94, 20], Operations: ['72-70=2', '18+2=20'] Exploring Operation: 94+20=114, Resulting Numbers: [114] 114,21 unequal: No Solution Exploring Operation: 94*20=1880, Resulting Numbers: [1880] 1880,21 unequal: No Solution Exploring Operation: 94-20=74, Resulting Numbers: [74] 74,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 21:[18, 92], Operations: ['72-70=2', '94-2=92'] Exploring Operation: 92-18=74, Resulting Numbers: [74] 74,21 unequal: No Solution Exploring Operation: 18*92=1656, Resulting Numbers: [1656] 1656,21 unequal: No Solution Exploring Operation: 18+92=110, Resulting Numbers: [110] 110,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[94, 9], Operations: ['72-70=2', '18/2=9'] Exploring Operation: 94+9=103, Resulting Numbers: [103] 103,21 unequal: No Solution Exploring Operation: 94*9=846, Resulting Numbers: [846] 846,21 unequal: No Solution Exploring Operation: 94-9=85, Resulting Numbers: [85] 85,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 21:[94, 70, 4], Operations: ['72/18=4'] Exploring Operation: 94+4=98, Resulting Numbers: [70, 98] Generated Node #0,3,0: 21:[70, 98] Operation: 94+4=98 Exploring Operation: 70-4=66, Resulting Numbers: [94, 66] Generated Node #0,3,1: 21:[94, 66] Operation: 70-4=66 Exploring Operation: 70+4=74, Resulting Numbers: [94, 74] Generated Node #0,3,2: 21:[94, 74] Operation: 70+4=74 Exploring Operation: 94-70=24, Resulting Numbers: [4, 24] Generated Node #0,3,3: 21:[4, 24] Operation: 94-70=24 Exploring Operation: 94-4=90, Resulting Numbers: [70, 90] Generated Node #0,3,4: 21:[70, 90] Operation: 94-4=90 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 21:[4, 24], Operations: ['72/18=4', '94-70=24'] Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,21 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 21:[94, 66], Operations: ['72/18=4', '70-4=66'] Exploring Operation: 94*66=6204, Resulting Numbers: [6204] 6204,21 unequal: No Solution Exploring Operation: 94+66=160, Resulting Numbers: [160] 160,21 unequal: No Solution Exploring Operation: 94-66=28, Resulting Numbers: [28] 28,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 21:[70, 90], Operations: ['72/18=4', '94-4=90'] Exploring Operation: 90-70=20, Resulting Numbers: [20] 20,21 unequal: No Solution Exploring Operation: 70*90=6300, Resulting Numbers: [6300] 6300,21 unequal: No Solution Exploring Operation: 70+90=160, Resulting Numbers: [160] 160,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 21:[70, 98], Operations: ['72/18=4', '94+4=98'] Exploring Operation: 70*98=6860, Resulting Numbers: [6860] 6860,21 unequal: No Solution Exploring Operation: 70+98=168, Resulting Numbers: [168] 168,21 unequal: No Solution Exploring Operation: 98-70=28, Resulting Numbers: [28] 28,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 21:[94, 74], Operations: ['72/18=4', '70+4=74'] Exploring Operation: 94+74=168, Resulting Numbers: [168] 168,21 unequal: No Solution Exploring Operation: 94*74=6956, Resulting Numbers: [6956] 6956,21 unequal: No Solution Exploring Operation: 94-74=20, Resulting Numbers: [20] 20,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 21:[94, 70, 54], Operations: ['72-18=54'] Exploring Operation: 94-70=24, Resulting Numbers: [54, 24] Generated Node #0,1,0: 21:[54, 24] Operation: 94-70=24 Exploring Operation: 94+54=148, Resulting Numbers: [70, 148] Generated Node #0,1,1: 21:[70, 148] Operation: 94+54=148 Exploring Operation: 94-54=40, Resulting Numbers: [70, 40] Generated Node #0,1,2: 21:[70, 40] Operation: 94-54=40 Exploring Operation: 94+70=164, Resulting Numbers: [54, 164] Generated Node #0,1,3: 21:[54, 164] Operation: 94+70=164 Exploring Operation: 70-54=16, Resulting Numbers: [94, 16] Generated Node #0,1,4: 21:[94, 16] Operation: 70-54=16 Moving to Node #0,4,0 Current State: 21:[18, 3], Operations: ['94-70=24', '72/24=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[72, 94, 18, 70], Operations: [] Exploring Operation: 94-70=24, Resulting Numbers: [72, 18, 24] Generated Node #0,4: 21:[72, 18, 24] Operation: 94-70=24 Moving to Node #0,4 Current State: 21:[72, 18, 24], Operations: ['94-70=24'] Exploring Operation: 72/24=3, Resulting Numbers: [18, 3] Generated Node #0,4,0: 21:[18, 3] Operation: 72/24=3 Moving to Node #0,4,0 Current State: 21:[18, 3], Operations: ['94-70=24', '72/24=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.927951
hs_5
mult_heuristic
[ 20, 96, 28, 35 ]
80
[ "20*28=560", "560/35=16", "96-16=80" ]
Current State: 80:[20, 96, 28, 35], Operations: [] Exploring Operation: 20*28=560, Resulting Numbers: [96, 35, 560] Generated Node #2: [96, 35, 560] from Operation: 20*28=560 Current State: 80:[96, 35, 560], Operations: ['20*28=560'] Exploring Operation: 560/35=16, Resulting Numbers: [96, 16] Generated Node #3: [96, 16] from Operation: 560/35=16 Current State: 80:[96, 16], Operations: ['20*28=560', '560/35=16'] Exploring Operation: 96-16=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[20, 96, 28, 35], Operations: [] Exploring Operation: 35-28=7, Resulting Numbers: [20, 96, 7] Generated Node #0,0: 80:[20, 96, 7] Operation: 35-28=7 Exploring Operation: 96-20=76, Resulting Numbers: [28, 35, 76] Generated Node #0,1: 80:[28, 35, 76] Operation: 96-20=76 Exploring Operation: 96-28=68, Resulting Numbers: [20, 35, 68] Generated Node #0,2: 80:[20, 35, 68] Operation: 96-28=68 Exploring Operation: 35-20=15, Resulting Numbers: [96, 28, 15] Generated Node #0,3: 80:[96, 28, 15] Operation: 35-20=15 Exploring Operation: 28-20=8, Resulting Numbers: [96, 35, 8] Generated Node #0,4: 80:[96, 35, 8] Operation: 28-20=8 Moving to Node #0,0 Current State: 80:[20, 96, 7], Operations: ['35-28=7'] Exploring Operation: 96-7=89, Resulting Numbers: [20, 89] Generated Node #0,0,0: 80:[20, 89] Operation: 96-7=89 Exploring Operation: 20-7=13, Resulting Numbers: [96, 13] Generated Node #0,0,1: 80:[96, 13] Operation: 20-7=13 Exploring Operation: 20+7=27, Resulting Numbers: [96, 27] Generated Node #0,0,2: 80:[96, 27] Operation: 20+7=27 Exploring Operation: 96-20=76, Resulting Numbers: [7, 76] Generated Node #0,0,3: 80:[7, 76] Operation: 96-20=76 Exploring Operation: 96+7=103, Resulting Numbers: [20, 103] Generated Node #0,0,4: 80:[20, 103] Operation: 96+7=103 Moving to Node #0,2 Current State: 80:[20, 35, 68], Operations: ['96-28=68'] Exploring Operation: 68-20=48, Resulting Numbers: [35, 48] Generated Node #0,2,0: 80:[35, 48] Operation: 68-20=48 Exploring Operation: 35+68=103, Resulting Numbers: [20, 103] Generated Node #0,2,1: 80:[20, 103] Operation: 35+68=103 Exploring Operation: 68-35=33, Resulting Numbers: [20, 33] Generated Node #0,2,2: 80:[20, 33] Operation: 68-35=33 Exploring Operation: 20+68=88, Resulting Numbers: [35, 88] Generated Node #0,2,3: 80:[35, 88] Operation: 20+68=88 Exploring Operation: 35-20=15, Resulting Numbers: [68, 15] Generated Node #0,2,4: 80:[68, 15] Operation: 35-20=15 Moving to Node #0,1 Current State: 80:[28, 35, 76], Operations: ['96-20=76'] Exploring Operation: 28+76=104, Resulting Numbers: [35, 104] Generated Node #0,1,0: 80:[35, 104] Operation: 28+76=104 Exploring Operation: 35-28=7, Resulting Numbers: [76, 7] Generated Node #0,1,1: 80:[76, 7] Operation: 35-28=7 Exploring Operation: 28+35=63, Resulting Numbers: [76, 63] Generated Node #0,1,2: 80:[76, 63] Operation: 28+35=63 Exploring Operation: 76-35=41, Resulting Numbers: [28, 41] Generated Node #0,1,3: 80:[28, 41] Operation: 76-35=41 Exploring Operation: 76-28=48, Resulting Numbers: [35, 48] Generated Node #0,1,4: 80:[35, 48] Operation: 76-28=48 Moving to Node #0,4 Current State: 80:[96, 35, 8], Operations: ['28-20=8'] Exploring Operation: 96-8=88, Resulting Numbers: [35, 88] Generated Node #0,4,0: 80:[35, 88] Operation: 96-8=88 Exploring Operation: 96/8=12, Resulting Numbers: [35, 12] Generated Node #0,4,1: 80:[35, 12] Operation: 96/8=12 Exploring Operation: 35+8=43, Resulting Numbers: [96, 43] Generated Node #0,4,2: 80:[96, 43] Operation: 35+8=43 Exploring Operation: 35-8=27, Resulting Numbers: [96, 27] Generated Node #0,4,3: 80:[96, 27] Operation: 35-8=27 Exploring Operation: 96-35=61, Resulting Numbers: [8, 61] Generated Node #0,4,4: 80:[8, 61] Operation: 96-35=61 Moving to Node #0,3 Current State: 80:[96, 28, 15], Operations: ['35-20=15'] Exploring Operation: 96+15=111, Resulting Numbers: [28, 111] Generated Node #0,3,0: 80:[28, 111] Operation: 96+15=111 Exploring Operation: 28+15=43, Resulting Numbers: [96, 43] Generated Node #0,3,1: 80:[96, 43] Operation: 28+15=43 Exploring Operation: 96-28=68, Resulting Numbers: [15, 68] Generated Node #0,3,2: 80:[15, 68] Operation: 96-28=68 Exploring Operation: 28-15=13, Resulting Numbers: [96, 13] Generated Node #0,3,3: 80:[96, 13] Operation: 28-15=13 Exploring Operation: 96-15=81, Resulting Numbers: [28, 81] Generated Node #0,3,4: 80:[28, 81] Operation: 96-15=81 Moving to Node #0,0,3 Current State: 80:[7, 76], Operations: ['35-28=7', '96-20=76'] Exploring Operation: 7*76=532, Resulting Numbers: [532] 532,80 unequal: No Solution Exploring Operation: 7+76=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[76, 7], Operations: ['96-20=76', '35-28=7'] Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,80 unequal: No Solution Exploring Operation: 76*7=532, Resulting Numbers: [532] 532,80 unequal: No Solution Exploring Operation: 76+7=83, Resulting Numbers: [83] 83,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[20, 33], Operations: ['96-28=68', '68-35=33'] Exploring Operation: 20+33=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 33-20=13, Resulting Numbers: [13] 13,80 unequal: No Solution Exploring Operation: 20*33=660, Resulting Numbers: [660] 660,80 unequal: No Solution Moving to Node #0,4,1 Current State: 80:[35, 12], Operations: ['28-20=8', '96/8=12'] Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,80 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,80 unequal: No Solution Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,80 unequal: No Solution Moving to Node #0,1,3 Current State: 80:[28, 41], Operations: ['96-20=76', '76-35=41'] Exploring Operation: 28*41=1148, Resulting Numbers: [1148] 1148,80 unequal: No Solution Exploring Operation: 28+41=69, Resulting Numbers: [69] 69,80 unequal: No Solution Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[20, 89], Operations: ['35-28=7', '96-7=89'] Exploring Operation: 20*89=1780, Resulting Numbers: [1780] 1780,80 unequal: No Solution Exploring Operation: 89-20=69, Resulting Numbers: [69] 69,80 unequal: No Solution Exploring Operation: 20+89=109, Resulting Numbers: [109] 109,80 unequal: No Solution Moving to Node #0,3,4 Current State: 80:[28, 81], Operations: ['35-20=15', '96-15=81'] Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 28+81=109, Resulting Numbers: [109] 109,80 unequal: No Solution Exploring Operation: 28*81=2268, Resulting Numbers: [2268] 2268,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[35, 48], Operations: ['96-28=68', '68-20=48'] Exploring Operation: 35*48=1680, Resulting Numbers: [1680] 1680,80 unequal: No Solution Exploring Operation: 48-35=13, Resulting Numbers: [13] 13,80 unequal: No Solution Exploring Operation: 35+48=83, Resulting Numbers: [83] 83,80 unequal: No Solution Moving to Node #0,1,4 Current State: 80:[35, 48], Operations: ['96-20=76', '76-28=48'] Exploring Operation: 35+48=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 48-35=13, Resulting Numbers: [13] 13,80 unequal: No Solution Exploring Operation: 35*48=1680, Resulting Numbers: [1680] 1680,80 unequal: No Solution Moving to Node #0,3,2 Current State: 80:[15, 68], Operations: ['35-20=15', '96-28=68'] Exploring Operation: 68-15=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 15*68=1020, Resulting Numbers: [1020] 1020,80 unequal: No Solution Exploring Operation: 15+68=83, Resulting Numbers: [83] 83,80 unequal: No Solution Moving to Node #0,2,4 Current State: 80:[68, 15], Operations: ['96-28=68', '35-20=15'] Exploring Operation: 68-15=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 68*15=1020, Resulting Numbers: [1020] 1020,80 unequal: No Solution Exploring Operation: 68+15=83, Resulting Numbers: [83] 83,80 unequal: No Solution Moving to Node #0,2,3 Current State: 80:[35, 88], Operations: ['96-28=68', '20+68=88'] Exploring Operation: 88-35=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 35*88=3080, Resulting Numbers: [3080] 3080,80 unequal: No Solution Exploring Operation: 35+88=123, Resulting Numbers: [123] 123,80 unequal: No Solution Moving to Node #0,4,0 Current State: 80:[35, 88], Operations: ['28-20=8', '96-8=88'] Exploring Operation: 35+88=123, Resulting Numbers: [123] 123,80 unequal: No Solution Exploring Operation: 35*88=3080, Resulting Numbers: [3080] 3080,80 unequal: No Solution Exploring Operation: 88-35=53, Resulting Numbers: [53] 53,80 unequal: No Solution Moving to Node #0,3,3 Current State: 80:[96, 13], Operations: ['35-20=15', '28-15=13'] Exploring Operation: 96*13=1248, Resulting Numbers: [1248] 1248,80 unequal: No Solution Exploring Operation: 96+13=109, Resulting Numbers: [109] 109,80 unequal: No Solution Exploring Operation: 96-13=83, Resulting Numbers: [83] 83,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[96, 13], Operations: ['35-28=7', '20-7=13'] Exploring Operation: 96*13=1248, Resulting Numbers: [1248] 1248,80 unequal: No Solution Exploring Operation: 96+13=109, Resulting Numbers: [109] 109,80 unequal: No Solution Exploring Operation: 96-13=83, Resulting Numbers: [83] 83,80 unequal: No Solution Moving to Node #0,4,2 Current State: 80:[96, 43], Operations: ['28-20=8', '35+8=43'] Exploring Operation: 96+43=139, Resulting Numbers: [139] 139,80 unequal: No Solution Exploring Operation: 96*43=4128, Resulting Numbers: [4128] 4128,80 unequal: No Solution Exploring Operation: 96-43=53, Resulting Numbers: [53] 53,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[96, 43], Operations: ['35-20=15', '28+15=43'] Exploring Operation: 96-43=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 96+43=139, Resulting Numbers: [139] 139,80 unequal: No Solution Exploring Operation: 96*43=4128, Resulting Numbers: [4128] 4128,80 unequal: No Solution Moving to Node #0,4,4 Current State: 80:[8, 61], Operations: ['28-20=8', '96-35=61'] Exploring Operation: 8+61=69, Resulting Numbers: [69] 69,80 unequal: No Solution Exploring Operation: 61-8=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 8*61=488, Resulting Numbers: [488] 488,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[76, 63], Operations: ['96-20=76', '28+35=63'] Exploring Operation: 76*63=4788, Resulting Numbers: [4788] 4788,80 unequal: No Solution Exploring Operation: 76+63=139, Resulting Numbers: [139] 139,80 unequal: No Solution Exploring Operation: 76-63=13, Resulting Numbers: [13] 13,80 unequal: No Solution Moving to Node #0,0,4 Current State: 80:[20, 103], Operations: ['35-28=7', '96+7=103'] Exploring Operation: 103-20=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 20+103=123, Resulting Numbers: [123] 123,80 unequal: No Solution Exploring Operation: 20*103=2060, Resulting Numbers: [2060] 2060,80 unequal: No Solution Moving to Node #0,4,3 Current State: 80:[96, 27], Operations: ['28-20=8', '35-8=27'] Exploring Operation: 96+27=123, Resulting Numbers: [123] 123,80 unequal: No Solution Exploring Operation: 96*27=2592, Resulting Numbers: [2592] 2592,80 unequal: No Solution Exploring Operation: 96-27=69, Resulting Numbers: [69] 69,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[20, 103], Operations: ['96-28=68', '35+68=103'] Exploring Operation: 20+103=123, Resulting Numbers: [123] 123,80 unequal: No Solution Exploring Operation: 20*103=2060, Resulting Numbers: [2060] 2060,80 unequal: No Solution Exploring Operation: 103-20=83, Resulting Numbers: [83] 83,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[96, 27], Operations: ['35-28=7', '20+7=27'] Exploring Operation: 96*27=2592, Resulting Numbers: [2592] 2592,80 unequal: No Solution Exploring Operation: 96-27=69, Resulting Numbers: [69] 69,80 unequal: No Solution Exploring Operation: 96+27=123, Resulting Numbers: [123] 123,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[35, 104], Operations: ['96-20=76', '28+76=104'] Exploring Operation: 104-35=69, Resulting Numbers: [69] 69,80 unequal: No Solution Exploring Operation: 35+104=139, Resulting Numbers: [139] 139,80 unequal: No Solution Exploring Operation: 35*104=3640, Resulting Numbers: [3640] 3640,80 unequal: No Solution Moving to Node #0,3,0 Current State: 80:[28, 111], Operations: ['35-20=15', '96+15=111'] Exploring Operation: 28+111=139, Resulting Numbers: [139] 139,80 unequal: No Solution Exploring Operation: 28*111=3108, Resulting Numbers: [3108] 3108,80 unequal: No Solution Exploring Operation: 111-28=83, Resulting Numbers: [83] 83,80 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 17, 34, 61, 68 ]
95
[ "34/17=2", "68/2=34", "61+34=95" ]
Current State: 95:[17, 34, 61, 68], Operations: [] Exploring Operation: 34/17=2, Resulting Numbers: [61, 68, 2] Generated Node #2: [61, 68, 2] from Operation: 34/17=2 Current State: 95:[61, 68, 2], Operations: ['34/17=2'] Exploring Operation: 68/2=34, Resulting Numbers: [61, 34] Generated Node #3: [61, 34] from Operation: 68/2=34 Current State: 95:[61, 34], Operations: ['34/17=2', '68/2=34'] Exploring Operation: 61+34=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[17, 34, 61, 68], Operations: [] Exploring Operation: 61-34=27, Resulting Numbers: [17, 68, 27] Generated Node #0,0: 95:[17, 68, 27] Operation: 61-34=27 Exploring Operation: 34+61=95, Resulting Numbers: [17, 68, 95] Generated Node #0,1: 95:[17, 68, 95] Operation: 34+61=95 Exploring Operation: 68-61=7, Resulting Numbers: [17, 34, 7] Generated Node #0,2: 95:[17, 34, 7] Operation: 68-61=7 Exploring Operation: 34+68=102, Resulting Numbers: [17, 61, 102] Generated Node #0,3: 95:[17, 61, 102] Operation: 34+68=102 Exploring Operation: 68/34=2, Resulting Numbers: [17, 61, 2] Generated Node #0,4: 95:[17, 61, 2] Operation: 68/34=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 95:[17, 34, 7], Operations: ['68-61=7'] Exploring Operation: 17+7=24, Resulting Numbers: [34, 24] Generated Node #0,2,0: 95:[34, 24] Operation: 17+7=24 Exploring Operation: 34-17=17, Resulting Numbers: [7, 17] Generated Node #0,2,1: 95:[7, 17] Operation: 34-17=17 Exploring Operation: 34/17=2, Resulting Numbers: [7, 2] Generated Node #0,2,2: 95:[7, 2] Operation: 34/17=2 Exploring Operation: 34-7=27, Resulting Numbers: [17, 27] Generated Node #0,2,3: 95:[17, 27] Operation: 34-7=27 Exploring Operation: 17-7=10, Resulting Numbers: [34, 10] Generated Node #0,2,4: 95:[34, 10] Operation: 17-7=10 Moving to Node #0,2,1 Current State: 95:[7, 17], Operations: ['68-61=7', '34-17=17'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,95 unequal: No Solution Moving to Node #0,2,2 Current State: 95:[7, 2], Operations: ['68-61=7', '34/17=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,95 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,95 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,95 unequal: No Solution Moving to Node #0,2,3 Current State: 95:[17, 27], Operations: ['68-61=7', '34-7=27'] Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 17+27=44, Resulting Numbers: [44] 44,95 unequal: No Solution Exploring Operation: 17*27=459, Resulting Numbers: [459] 459,95 unequal: No Solution Moving to Node #0,2,0 Current State: 95:[34, 24], Operations: ['68-61=7', '17+7=24'] Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,95 unequal: No Solution Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,95 unequal: No Solution Moving to Node #0,2,4 Current State: 95:[34, 10], Operations: ['68-61=7', '17-7=10'] Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 34*10=340, Resulting Numbers: [340] 340,95 unequal: No Solution Exploring Operation: 34+10=44, Resulting Numbers: [44] 44,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[17, 68, 95], Operations: ['34+61=95'] Exploring Operation: 95-68=27, Resulting Numbers: [17, 27] Generated Node #0,1,0: 95:[17, 27] Operation: 95-68=27 Exploring Operation: 68/17=4, Resulting Numbers: [95, 4] Generated Node #0,1,1: 95:[95, 4] Operation: 68/17=4 Exploring Operation: 17+68=85, Resulting Numbers: [95, 85] Generated Node #0,1,2: 95:[95, 85] Operation: 17+68=85 Exploring Operation: 17+95=112, Resulting Numbers: [68, 112] Generated Node #0,1,3: 95:[68, 112] Operation: 17+95=112 Exploring Operation: 68-17=51, Resulting Numbers: [95, 51] Generated Node #0,1,4: 95:[95, 51] Operation: 68-17=51 Moving to Node #0,1,1 Current State: 95:[95, 4], Operations: ['34+61=95', '68/17=4'] Exploring Operation: 95+4=99, Resulting Numbers: [99] 99,95 unequal: No Solution Exploring Operation: 95-4=91, Resulting Numbers: [91] 91,95 unequal: No Solution Exploring Operation: 95*4=380, Resulting Numbers: [380] 380,95 unequal: No Solution Moving to Node #0,1,2 Current State: 95:[95, 85], Operations: ['34+61=95', '17+68=85'] Exploring Operation: 95+85=180, Resulting Numbers: [180] 180,95 unequal: No Solution Exploring Operation: 95*85=8075, Resulting Numbers: [8075] 8075,95 unequal: No Solution Exploring Operation: 95-85=10, Resulting Numbers: [10] 10,95 unequal: No Solution Moving to Node #0,1,0 Current State: 95:[17, 27], Operations: ['34+61=95', '95-68=27'] Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 17*27=459, Resulting Numbers: [459] 459,95 unequal: No Solution Exploring Operation: 17+27=44, Resulting Numbers: [44] 44,95 unequal: No Solution Moving to Node #0,1,4 Current State: 95:[95, 51], Operations: ['34+61=95', '68-17=51'] Exploring Operation: 95+51=146, Resulting Numbers: [146] 146,95 unequal: No Solution Exploring Operation: 95-51=44, Resulting Numbers: [44] 44,95 unequal: No Solution Exploring Operation: 95*51=4845, Resulting Numbers: [4845] 4845,95 unequal: No Solution Moving to Node #0,1,3 Current State: 95:[68, 112], Operations: ['34+61=95', '17+95=112'] Exploring Operation: 68+112=180, Resulting Numbers: [180] 180,95 unequal: No Solution Exploring Operation: 112-68=44, Resulting Numbers: [44] 44,95 unequal: No Solution Exploring Operation: 68*112=7616, Resulting Numbers: [7616] 7616,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[17, 68, 27], Operations: ['61-34=27'] Exploring Operation: 68/17=4, Resulting Numbers: [27, 4] Generated Node #0,0,0: 95:[27, 4] Operation: 68/17=4 Exploring Operation: 27-17=10, Resulting Numbers: [68, 10] Generated Node #0,0,1: 95:[68, 10] Operation: 27-17=10 Exploring Operation: 17+68=85, Resulting Numbers: [27, 85] Generated Node #0,0,2: 95:[27, 85] Operation: 17+68=85 Exploring Operation: 68-27=41, Resulting Numbers: [17, 41] Generated Node #0,0,3: 95:[17, 41] Operation: 68-27=41 Exploring Operation: 68+27=95, Resulting Numbers: [17, 95] Generated Node #0,0,4: 95:[17, 95] Operation: 68+27=95 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 95:[17, 95], Operations: ['61-34=27', '68+27=95'] Exploring Operation: 95-17=78, Resulting Numbers: [78] 78,95 unequal: No Solution Exploring Operation: 17+95=112, Resulting Numbers: [112] 112,95 unequal: No Solution Exploring Operation: 17*95=1615, Resulting Numbers: [1615] 1615,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 95:[27, 4], Operations: ['61-34=27', '68/17=4'] Exploring Operation: 27*4=108, Resulting Numbers: [108] 108,95 unequal: No Solution Exploring Operation: 27+4=31, Resulting Numbers: [31] 31,95 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 95:[27, 85], Operations: ['61-34=27', '17+68=85'] Exploring Operation: 27+85=112, Resulting Numbers: [112] 112,95 unequal: No Solution Exploring Operation: 27*85=2295, Resulting Numbers: [2295] 2295,95 unequal: No Solution Exploring Operation: 85-27=58, Resulting Numbers: [58] 58,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 95:[17, 41], Operations: ['61-34=27', '68-27=41'] Exploring Operation: 17*41=697, Resulting Numbers: [697] 697,95 unequal: No Solution Exploring Operation: 17+41=58, Resulting Numbers: [58] 58,95 unequal: No Solution Exploring Operation: 41-17=24, Resulting Numbers: [24] 24,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 95:[68, 10], Operations: ['61-34=27', '27-17=10'] Exploring Operation: 68*10=680, Resulting Numbers: [680] 680,95 unequal: No Solution Exploring Operation: 68+10=78, Resulting Numbers: [78] 78,95 unequal: No Solution Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 95:[17, 61, 2], Operations: ['68/34=2'] Exploring Operation: 17+2=19, Resulting Numbers: [61, 19] Generated Node #0,4,0: 95:[61, 19] Operation: 17+2=19 Exploring Operation: 61*2=122, Resulting Numbers: [17, 122] Generated Node #0,4,1: 95:[17, 122] Operation: 61*2=122 Exploring Operation: 17+61=78, Resulting Numbers: [2, 78] Generated Node #0,4,2: 95:[2, 78] Operation: 17+61=78 Exploring Operation: 61-17=44, Resulting Numbers: [2, 44] Generated Node #0,4,3: 95:[2, 44] Operation: 61-17=44 Exploring Operation: 61+2=63, Resulting Numbers: [17, 63] Generated Node #0,4,4: 95:[17, 63] Operation: 61+2=63 Moving to Node #0,4,2 Current State: 95:[2, 78], Operations: ['68/34=2', '17+61=78'] Exploring Operation: 2+78=80, Resulting Numbers: [80] 80,95 unequal: No Solution Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,95 unequal: No Solution Exploring Operation: 2*78=156, Resulting Numbers: [156] 156,95 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,95 unequal: No Solution Moving to Node #0,4,3 Current State: 95:[2, 44], Operations: ['68/34=2', '61-17=44'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,95 unequal: No Solution Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,95 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,95 unequal: No Solution Moving to Node #0,4,1 Current State: 95:[17, 122], Operations: ['68/34=2', '61*2=122'] Exploring Operation: 122-17=105, Resulting Numbers: [105] 105,95 unequal: No Solution Exploring Operation: 17*122=2074, Resulting Numbers: [2074] 2074,95 unequal: No Solution Exploring Operation: 17+122=139, Resulting Numbers: [139] 139,95 unequal: No Solution Moving to Node #0,4,0 Current State: 95:[61, 19], Operations: ['68/34=2', '17+2=19'] Exploring Operation: 61+19=80, Resulting Numbers: [80] 80,95 unequal: No Solution Exploring Operation: 61*19=1159, Resulting Numbers: [1159] 1159,95 unequal: No Solution Exploring Operation: 61-19=42, Resulting Numbers: [42] 42,95 unequal: No Solution Moving to Node #0,4,4 Current State: 95:[17, 63], Operations: ['68/34=2', '61+2=63'] Exploring Operation: 17+63=80, Resulting Numbers: [80] 80,95 unequal: No Solution Exploring Operation: 63-17=46, Resulting Numbers: [46] 46,95 unequal: No Solution Exploring Operation: 17*63=1071, Resulting Numbers: [1071] 1071,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 95:[17, 61, 102], Operations: ['34+68=102'] Exploring Operation: 17+61=78, Resulting Numbers: [102, 78] Generated Node #0,3,0: 95:[102, 78] Operation: 17+61=78 Exploring Operation: 102/17=6, Resulting Numbers: [61, 6] Generated Node #0,3,1: 95:[61, 6] Operation: 102/17=6 Exploring Operation: 61-17=44, Resulting Numbers: [102, 44] Generated Node #0,3,2: 95:[102, 44] Operation: 61-17=44 Exploring Operation: 102-17=85, Resulting Numbers: [61, 85] Generated Node #0,3,3: 95:[61, 85] Operation: 102-17=85 Exploring Operation: 102-61=41, Resulting Numbers: [17, 41] Generated Node #0,3,4: 95:[17, 41] Operation: 102-61=41 Moving to Node #0,3,0 Current State: 95:[102, 78], Operations: ['34+68=102', '17+61=78'] Exploring Operation: 102+78=180, Resulting Numbers: [180] 180,95 unequal: No Solution Exploring Operation: 102*78=7956, Resulting Numbers: [7956] 7956,95 unequal: No Solution Exploring Operation: 102-78=24, Resulting Numbers: [24] 24,95 unequal: No Solution Moving to Node #0,3,4 Current State: 95:[17, 41], Operations: ['34+68=102', '102-61=41'] Exploring Operation: 41-17=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 17+41=58, Resulting Numbers: [58] 58,95 unequal: No Solution Exploring Operation: 17*41=697, Resulting Numbers: [697] 697,95 unequal: No Solution Moving to Node #0,3,2 Current State: 95:[102, 44], Operations: ['34+68=102', '61-17=44'] Exploring Operation: 102+44=146, Resulting Numbers: [146] 146,95 unequal: No Solution Exploring Operation: 102-44=58, Resulting Numbers: [58] 58,95 unequal: No Solution Exploring Operation: 102*44=4488, Resulting Numbers: [4488] 4488,95 unequal: No Solution Moving to Node #0,3,1 Current State: 95:[61, 6], Operations: ['34+68=102', '102/17=6'] Exploring Operation: 61+6=67, Resulting Numbers: [67] 67,95 unequal: No Solution Exploring Operation: 61*6=366, Resulting Numbers: [366] 366,95 unequal: No Solution Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,95 unequal: No Solution Moving to Node #0,3,3 Current State: 95:[61, 85], Operations: ['34+68=102', '102-17=85'] Exploring Operation: 61*85=5185, Resulting Numbers: [5185] 5185,95 unequal: No Solution Exploring Operation: 85-61=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 61+85=146, Resulting Numbers: [146] 146,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 43, 74, 66, 76 ]
21
[ "74-43=31", "76-66=10", "31-10=21" ]
Current State: 21:[43, 74, 66, 76], Operations: [] Exploring Operation: 74-43=31, Resulting Numbers: [66, 76, 31] Generated Node #2: [66, 76, 31] from Operation: 74-43=31 Current State: 21:[66, 76, 31], Operations: ['74-43=31'] Exploring Operation: 76-66=10, Resulting Numbers: [31, 10] Generated Node #3: [31, 10] from Operation: 76-66=10 Current State: 21:[31, 10], Operations: ['74-43=31', '76-66=10'] Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[43, 74, 66, 76], Operations: [] Exploring Operation: 76-66=10, Resulting Numbers: [43, 74, 10] Generated Node #0,0: 21:[43, 74, 10] Operation: 76-66=10 Exploring Operation: 76-74=2, Resulting Numbers: [43, 66, 2] Generated Node #0,1: 21:[43, 66, 2] Operation: 76-74=2 Exploring Operation: 74-66=8, Resulting Numbers: [43, 76, 8] Generated Node #0,2: 21:[43, 76, 8] Operation: 74-66=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[43, 66, 2], Operations: ['76-74=2'] Exploring Operation: 66-43=23, Resulting Numbers: [2, 23] Generated Node #0,1,0: 21:[2, 23] Operation: 66-43=23 Exploring Operation: 43-2=41, Resulting Numbers: [66, 41] Generated Node #0,1,1: 21:[66, 41] Operation: 43-2=41 Exploring Operation: 66/2=33, Resulting Numbers: [43, 33] Generated Node #0,1,2: 21:[43, 33] Operation: 66/2=33 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 21:[2, 23], Operations: ['76-74=2', '66-43=23'] Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,21 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[43, 74, 66, 76], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [43, 66, 2] Generated Node #0,1: 21:[43, 66, 2] Operation: 76-74=2 Moving to Node #0,1 Current State: 21:[43, 66, 2], Operations: ['76-74=2'] Exploring Operation: 66-43=23, Resulting Numbers: [2, 23] Generated Node #0,1,0: 21:[2, 23] Operation: 66-43=23 Moving to Node #0,1,0 Current State: 21:[2, 23], Operations: ['76-74=2', '66-43=23'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 2, 8, 9, 97 ]
96
[ "2+8=10", "9+97=106", "106-10=96" ]
Current State: 96:[2, 8, 9, 97], Operations: [] Exploring Operation: 2+8=10, Resulting Numbers: [9, 97, 10] Generated Node #2: [9, 97, 10] from Operation: 2+8=10 Current State: 96:[9, 97, 10], Operations: ['2+8=10'] Exploring Operation: 9+97=106, Resulting Numbers: [10, 106] Generated Node #3: [10, 106] from Operation: 9+97=106 Current State: 96:[10, 106], Operations: ['2+8=10', '9+97=106'] Exploring Operation: 106-10=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[2, 8, 9, 97], Operations: [] Exploring Operation: 8-2=6, Resulting Numbers: [9, 97, 6] Generated Node #0,0: 96:[9, 97, 6] Operation: 8-2=6 Exploring Operation: 8/2=4, Resulting Numbers: [9, 97, 4] Generated Node #0,1: 96:[9, 97, 4] Operation: 8/2=4 Exploring Operation: 2+9=11, Resulting Numbers: [8, 97, 11] Generated Node #0,2: 96:[8, 97, 11] Operation: 2+9=11 Exploring Operation: 2*8=16, Resulting Numbers: [9, 97, 16] Generated Node #0,3: 96:[9, 97, 16] Operation: 2*8=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[9, 97, 6], Operations: ['8-2=6'] Exploring Operation: 97-6=91, Resulting Numbers: [9, 91] Generated Node #0,0,0: 96:[9, 91] Operation: 97-6=91 Exploring Operation: 9*6=54, Resulting Numbers: [97, 54] Generated Node #0,0,1: 96:[97, 54] Operation: 9*6=54 Exploring Operation: 9-6=3, Resulting Numbers: [97, 3] Generated Node #0,0,2: 96:[97, 3] Operation: 9-6=3 Exploring Operation: 9+6=15, Resulting Numbers: [97, 15] Generated Node #0,0,3: 96:[97, 15] Operation: 9+6=15 Moving to Node #0,0,2 Current State: 96:[97, 3], Operations: ['8-2=6', '9-6=3'] Exploring Operation: 97*3=291, Resulting Numbers: [291] 291,96 unequal: No Solution Exploring Operation: 97+3=100, Resulting Numbers: [100] 100,96 unequal: No Solution Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[97, 15], Operations: ['8-2=6', '9+6=15'] Exploring Operation: 97*15=1455, Resulting Numbers: [1455] 1455,96 unequal: No Solution Exploring Operation: 97+15=112, Resulting Numbers: [112] 112,96 unequal: No Solution Exploring Operation: 97-15=82, Resulting Numbers: [82] 82,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[9, 91], Operations: ['8-2=6', '97-6=91'] Exploring Operation: 91-9=82, Resulting Numbers: [82] 82,96 unequal: No Solution Exploring Operation: 9*91=819, Resulting Numbers: [819] 819,96 unequal: No Solution Exploring Operation: 9+91=100, Resulting Numbers: [100] 100,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[97, 54], Operations: ['8-2=6', '9*6=54'] Exploring Operation: 97-54=43, Resulting Numbers: [43] 43,96 unequal: No Solution Exploring Operation: 97+54=151, Resulting Numbers: [151] 151,96 unequal: No Solution Exploring Operation: 97*54=5238, Resulting Numbers: [5238] 5238,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[9, 97, 4], Operations: ['8/2=4'] Exploring Operation: 9-4=5, Resulting Numbers: [97, 5] Generated Node #0,1,0: 96:[97, 5] Operation: 9-4=5 Exploring Operation: 9+4=13, Resulting Numbers: [97, 13] Generated Node #0,1,1: 96:[97, 13] Operation: 9+4=13 Exploring Operation: 9*4=36, Resulting Numbers: [97, 36] Generated Node #0,1,2: 96:[97, 36] Operation: 9*4=36 Exploring Operation: 97-4=93, Resulting Numbers: [9, 93] Generated Node #0,1,3: 96:[9, 93] Operation: 97-4=93 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[97, 5], Operations: ['8/2=4', '9-4=5'] Exploring Operation: 97*5=485, Resulting Numbers: [485] 485,96 unequal: No Solution Exploring Operation: 97+5=102, Resulting Numbers: [102] 102,96 unequal: No Solution Exploring Operation: 97-5=92, Resulting Numbers: [92] 92,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[97, 13], Operations: ['8/2=4', '9+4=13'] Exploring Operation: 97+13=110, Resulting Numbers: [110] 110,96 unequal: No Solution Exploring Operation: 97-13=84, Resulting Numbers: [84] 84,96 unequal: No Solution Exploring Operation: 97*13=1261, Resulting Numbers: [1261] 1261,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 96:[9, 93], Operations: ['8/2=4', '97-4=93'] Exploring Operation: 9*93=837, Resulting Numbers: [837] 837,96 unequal: No Solution Exploring Operation: 93-9=84, Resulting Numbers: [84] 84,96 unequal: No Solution Exploring Operation: 9+93=102, Resulting Numbers: [102] 102,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 96:[97, 36], Operations: ['8/2=4', '9*4=36'] Exploring Operation: 97*36=3492, Resulting Numbers: [3492] 3492,96 unequal: No Solution Exploring Operation: 97-36=61, Resulting Numbers: [61] 61,96 unequal: No Solution Exploring Operation: 97+36=133, Resulting Numbers: [133] 133,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[8, 97, 11], Operations: ['2+9=11'] Exploring Operation: 11-8=3, Resulting Numbers: [97, 3] Generated Node #0,2,0: 96:[97, 3] Operation: 11-8=3 Exploring Operation: 8+11=19, Resulting Numbers: [97, 19] Generated Node #0,2,1: 96:[97, 19] Operation: 8+11=19 Exploring Operation: 97-8=89, Resulting Numbers: [11, 89] Generated Node #0,2,2: 96:[11, 89] Operation: 97-8=89 Exploring Operation: 8*11=88, Resulting Numbers: [97, 88] Generated Node #0,2,3: 96:[97, 88] Operation: 8*11=88 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 96:[97, 3], Operations: ['2+9=11', '11-8=3'] Exploring Operation: 97*3=291, Resulting Numbers: [291] 291,96 unequal: No Solution Exploring Operation: 97+3=100, Resulting Numbers: [100] 100,96 unequal: No Solution Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 96:[97, 19], Operations: ['2+9=11', '8+11=19'] Exploring Operation: 97+19=116, Resulting Numbers: [116] 116,96 unequal: No Solution Exploring Operation: 97-19=78, Resulting Numbers: [78] 78,96 unequal: No Solution Exploring Operation: 97*19=1843, Resulting Numbers: [1843] 1843,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 96:[11, 89], Operations: ['2+9=11', '97-8=89'] Exploring Operation: 89-11=78, Resulting Numbers: [78] 78,96 unequal: No Solution Exploring Operation: 11*89=979, Resulting Numbers: [979] 979,96 unequal: No Solution Exploring Operation: 11+89=100, Resulting Numbers: [100] 100,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 96:[97, 88], Operations: ['2+9=11', '8*11=88'] Exploring Operation: 97+88=185, Resulting Numbers: [185] 185,96 unequal: No Solution Exploring Operation: 97*88=8536, Resulting Numbers: [8536] 8536,96 unequal: No Solution Exploring Operation: 97-88=9, Resulting Numbers: [9] 9,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 96:[9, 97, 16], Operations: ['2*8=16'] Exploring Operation: 16-9=7, Resulting Numbers: [97, 7] Generated Node #0,3,0: 96:[97, 7] Operation: 16-9=7 Exploring Operation: 9+97=106, Resulting Numbers: [16, 106] Generated Node #0,3,1: 96:[16, 106] Operation: 9+97=106 Exploring Operation: 97-9=88, Resulting Numbers: [16, 88] Generated Node #0,3,2: 96:[16, 88] Operation: 97-9=88 Exploring Operation: 9+16=25, Resulting Numbers: [97, 25] Generated Node #0,3,3: 96:[97, 25] Operation: 9+16=25 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 96:[97, 7], Operations: ['2*8=16', '16-9=7'] Exploring Operation: 97-7=90, Resulting Numbers: [90] 90,96 unequal: No Solution Exploring Operation: 97*7=679, Resulting Numbers: [679] 679,96 unequal: No Solution Exploring Operation: 97+7=104, Resulting Numbers: [104] 104,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 96:[97, 25], Operations: ['2*8=16', '9+16=25'] Exploring Operation: 97+25=122, Resulting Numbers: [122] 122,96 unequal: No Solution Exploring Operation: 97-25=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 97*25=2425, Resulting Numbers: [2425] 2425,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 96:[16, 88], Operations: ['2*8=16', '97-9=88'] Exploring Operation: 88-16=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 16*88=1408, Resulting Numbers: [1408] 1408,96 unequal: No Solution Exploring Operation: 16+88=104, Resulting Numbers: [104] 104,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 96:[16, 106], Operations: ['2*8=16', '9+97=106'] Exploring Operation: 106-16=90, Resulting Numbers: [90] 90,96 unequal: No Solution Exploring Operation: 16+106=122, Resulting Numbers: [122] 122,96 unequal: No Solution Exploring Operation: 16*106=1696, Resulting Numbers: [1696] 1696,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 80, 94, 22, 95 ]
59
[ "94-80=14", "95-22=73", "73-14=59" ]
Current State: 59:[80, 94, 22, 95], Operations: [] Exploring Operation: 94-80=14, Resulting Numbers: [22, 95, 14] Generated Node #2: [22, 95, 14] from Operation: 94-80=14 Current State: 59:[22, 95, 14], Operations: ['94-80=14'] Exploring Operation: 95-22=73, Resulting Numbers: [14, 73] Generated Node #3: [14, 73] from Operation: 95-22=73 Current State: 59:[14, 73], Operations: ['94-80=14', '95-22=73'] Exploring Operation: 73-14=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[80, 94, 22, 95], Operations: [] Exploring Operation: 94-22=72, Resulting Numbers: [80, 95, 72] Generated Node #0,0: 59:[80, 95, 72] Operation: 94-22=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[80, 95, 72], Operations: ['94-22=72'] Exploring Operation: 95-80=15, Resulting Numbers: [72, 15] Generated Node #0,0,0: 59:[72, 15] Operation: 95-80=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[72, 15], Operations: ['94-22=72', '95-80=15'] Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 57, 63, 43, 80 ]
43
[ "63-57=6", "80-43=37", "6+37=43" ]
Current State: 43:[57, 63, 43, 80], Operations: [] Exploring Operation: 63-57=6, Resulting Numbers: [43, 80, 6] Generated Node #2: [43, 80, 6] from Operation: 63-57=6 Current State: 43:[43, 80, 6], Operations: ['63-57=6'] Exploring Operation: 80-43=37, Resulting Numbers: [6, 37] Generated Node #3: [6, 37] from Operation: 80-43=37 Current State: 43:[6, 37], Operations: ['63-57=6', '80-43=37'] Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[57, 63, 43, 80], Operations: [] Exploring Operation: 80-57=23, Resulting Numbers: [63, 43, 23] Generated Node #0,0: 43:[63, 43, 23] Operation: 80-57=23 Exploring Operation: 80-63=17, Resulting Numbers: [57, 43, 17] Generated Node #0,1: 43:[57, 43, 17] Operation: 80-63=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[63, 43, 23], Operations: ['80-57=23'] Exploring Operation: 63-43=20, Resulting Numbers: [23, 20] Generated Node #0,0,0: 43:[23, 20] Operation: 63-43=20 Exploring Operation: 63-23=40, Resulting Numbers: [43, 40] Generated Node #0,0,1: 43:[43, 40] Operation: 63-23=40 Moving to Node #0,0,1 Current State: 43:[43, 40], Operations: ['80-57=23', '63-23=40'] Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 43+40=83, Resulting Numbers: [83] 83,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[23, 20], Operations: ['80-57=23', '63-43=20'] Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 23+20=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[57, 63, 43, 80], Operations: [] Exploring Operation: 80-57=23, Resulting Numbers: [63, 43, 23] Generated Node #0,0: 43:[63, 43, 23] Operation: 80-57=23 Moving to Node #0,0 Current State: 43:[63, 43, 23], Operations: ['80-57=23'] Exploring Operation: 63-43=20, Resulting Numbers: [23, 20] Generated Node #0,0,0: 43:[23, 20] Operation: 63-43=20 Moving to Node #0,0,0 Current State: 43:[23, 20], Operations: ['80-57=23', '63-43=20'] Exploring Operation: 23+20=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 31, 93, 19, 8 ]
89
[ "93-31=62", "19+8=27", "62+27=89" ]
Current State: 89:[31, 93, 19, 8], Operations: [] Exploring Operation: 93-31=62, Resulting Numbers: [19, 8, 62] Generated Node #2: [19, 8, 62] from Operation: 93-31=62 Current State: 89:[19, 8, 62], Operations: ['93-31=62'] Exploring Operation: 19+8=27, Resulting Numbers: [62, 27] Generated Node #3: [62, 27] from Operation: 19+8=27 Current State: 89:[62, 27], Operations: ['93-31=62', '19+8=27'] Exploring Operation: 62+27=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[31, 93, 19, 8], Operations: [] Exploring Operation: 31+19=50, Resulting Numbers: [93, 8, 50] Generated Node #0,0: 89:[93, 8, 50] Operation: 31+19=50 Exploring Operation: 31+8=39, Resulting Numbers: [93, 19, 39] Generated Node #0,1: 89:[93, 19, 39] Operation: 31+8=39 Moving to Node #0,0 Current State: 89:[93, 8, 50], Operations: ['31+19=50'] Exploring Operation: 93-8=85, Resulting Numbers: [50, 85] Generated Node #0,0,0: 89:[50, 85] Operation: 93-8=85 Exploring Operation: 8+50=58, Resulting Numbers: [93, 58] Generated Node #0,0,1: 89:[93, 58] Operation: 8+50=58 Moving to Node #0,1 Current State: 89:[93, 19, 39], Operations: ['31+8=39'] Exploring Operation: 93-19=74, Resulting Numbers: [39, 74] Generated Node #0,1,0: 89:[39, 74] Operation: 93-19=74 Exploring Operation: 19+39=58, Resulting Numbers: [93, 58] Generated Node #0,1,1: 89:[93, 58] Operation: 19+39=58 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[93, 58], Operations: ['31+8=39', '19+39=58'] Exploring Operation: 93-58=35, Resulting Numbers: [35] 35,89 unequal: No Solution Exploring Operation: 93+58=151, Resulting Numbers: [151] 151,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[39, 74], Operations: ['31+8=39', '93-19=74'] Exploring Operation: 39+74=113, Resulting Numbers: [113] 113,89 unequal: No Solution Exploring Operation: 74-39=35, Resulting Numbers: [35] 35,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 89:[93, 58], Operations: ['31+19=50', '8+50=58'] Exploring Operation: 93-58=35, Resulting Numbers: [35] 35,89 unequal: No Solution Exploring Operation: 93+58=151, Resulting Numbers: [151] 151,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[50, 85], Operations: ['31+19=50', '93-8=85'] Exploring Operation: 50+85=135, Resulting Numbers: [135] 135,89 unequal: No Solution Exploring Operation: 85-50=35, Resulting Numbers: [35] 35,89 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 35, 31, 1, 66 ]
63
[ "35-31=4", "1+66=67", "67-4=63" ]
Current State: 63:[35, 31, 1, 66], Operations: [] Exploring Operation: 35-31=4, Resulting Numbers: [1, 66, 4] Generated Node #2: [1, 66, 4] from Operation: 35-31=4 Current State: 63:[1, 66, 4], Operations: ['35-31=4'] Exploring Operation: 1+66=67, Resulting Numbers: [4, 67] Generated Node #3: [4, 67] from Operation: 1+66=67 Current State: 63:[4, 67], Operations: ['35-31=4', '1+66=67'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[35, 31, 1, 66], Operations: [] Exploring Operation: 35-1=34, Resulting Numbers: [31, 66, 34] Generated Node #0,0: 63:[31, 66, 34] Operation: 35-1=34 Exploring Operation: 31-1=30, Resulting Numbers: [35, 66, 30] Generated Node #0,1: 63:[35, 66, 30] Operation: 31-1=30 Exploring Operation: 35-31=4, Resulting Numbers: [1, 66, 4] Generated Node #0,2: 63:[1, 66, 4] Operation: 35-31=4 Exploring Operation: 66-35=31, Resulting Numbers: [31, 1, 31] Generated Node #0,3: 63:[31, 1, 31] Operation: 66-35=31 Exploring Operation: 35+31=66, Resulting Numbers: [1, 66, 66] Generated Node #0,4: 63:[1, 66, 66] Operation: 35+31=66 Moving to Node #0,2 Current State: 63:[1, 66, 4], Operations: ['35-31=4'] Exploring Operation: 66-4=62, Resulting Numbers: [1, 62] Generated Node #0,2,0: 63:[1, 62] Operation: 66-4=62 Exploring Operation: 1*66=66, Resulting Numbers: [4, 66] Generated Node #0,2,1: 63:[4, 66] Operation: 1*66=66 Exploring Operation: 66/1=66, Resulting Numbers: [4, 66] Generated Node #0,2,2: 63:[4, 66] Operation: 66/1=66 Exploring Operation: 66-1=65, Resulting Numbers: [4, 65] Generated Node #0,2,3: 63:[4, 65] Operation: 66-1=65 Exploring Operation: 4-1=3, Resulting Numbers: [66, 3] Generated Node #0,2,4: 63:[66, 3] Operation: 4-1=3 Moving to Node #0,4 Current State: 63:[1, 66, 66], Operations: ['35+31=66'] Exploring Operation: 66-66=0, Resulting Numbers: [1, 0] Generated Node #0,4,0: 63:[1, 0] Operation: 66-66=0 Exploring Operation: 1*66=66, Resulting Numbers: [66, 66] Generated Node #0,4,1: 63:[66, 66] Operation: 1*66=66 Exploring Operation: 66-1=65, Resulting Numbers: [66, 65] Generated Node #0,4,2: 63:[66, 65] Operation: 66-1=65 Exploring Operation: 66/66=1, Resulting Numbers: [1, 1] Generated Node #0,4,3: 63:[1, 1] Operation: 66/66=1 Exploring Operation: 66-1=65, Resulting Numbers: [66, 65] Generated Node #0,4,4: 63:[66, 65] Operation: 66-1=65 Moving to Node #0,3 Current State: 63:[31, 1, 31], Operations: ['66-35=31'] Exploring Operation: 31-31=0, Resulting Numbers: [1, 0] Generated Node #0,3,0: 63:[1, 0] Operation: 31-31=0 Exploring Operation: 31-1=30, Resulting Numbers: [31, 30] Generated Node #0,3,1: 63:[31, 30] Operation: 31-1=30 Exploring Operation: 31-1=30, Resulting Numbers: [31, 30] Generated Node #0,3,2: 63:[31, 30] Operation: 31-1=30 Exploring Operation: 31+31=62, Resulting Numbers: [1, 62] Generated Node #0,3,3: 63:[1, 62] Operation: 31+31=62 Exploring Operation: 31/31=1, Resulting Numbers: [1, 1] Generated Node #0,3,4: 63:[1, 1] Operation: 31/31=1 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 63:[1, 62], Operations: ['66-35=31', '31+31=62'] Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 1+62=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[35, 31, 1, 66], Operations: [] Exploring Operation: 66-35=31, Resulting Numbers: [31, 1, 31] Generated Node #0,3: 63:[31, 1, 31] Operation: 66-35=31 Moving to Node #0,3 Current State: 63:[31, 1, 31], Operations: ['66-35=31'] Exploring Operation: 31+31=62, Resulting Numbers: [1, 62] Generated Node #0,3,3: 63:[1, 62] Operation: 31+31=62 Moving to Node #0,3,3 Current State: 63:[1, 62], Operations: ['66-35=31', '31+31=62'] Exploring Operation: 1+62=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
mult_heuristic
[ 56, 86, 43, 70 ]
42
[ "56*86=4816", "4816/43=112", "112-70=42" ]
Current State: 42:[56, 86, 43, 70], Operations: [] Exploring Operation: 56*86=4816, Resulting Numbers: [43, 70, 4816] Generated Node #2: [43, 70, 4816] from Operation: 56*86=4816 Current State: 42:[43, 70, 4816], Operations: ['56*86=4816'] Exploring Operation: 4816/43=112, Resulting Numbers: [70, 112] Generated Node #3: [70, 112] from Operation: 4816/43=112 Current State: 42:[70, 112], Operations: ['56*86=4816', '4816/43=112'] Exploring Operation: 112-70=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[56, 86, 43, 70], Operations: [] Exploring Operation: 86-70=16, Resulting Numbers: [56, 43, 16] Generated Node #0,0: 42:[56, 43, 16] Operation: 86-70=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[56, 43, 16], Operations: ['86-70=16'] Exploring Operation: 56-43=13, Resulting Numbers: [16, 13] Generated Node #0,0,0: 42:[16, 13] Operation: 56-43=13 Moving to Node #0,0,0 Current State: 42:[16, 13], Operations: ['86-70=16', '56-43=13'] Exploring Operation: 16-13=3, Resulting Numbers: [3] 3,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 87, 13, 25, 53 ]
81
[ "25+53=78", "78/13=6", "87-6=81" ]
Current State: 81:[87, 13, 25, 53], Operations: [] Exploring Operation: 25+53=78, Resulting Numbers: [87, 13, 78] Generated Node #2: [87, 13, 78] from Operation: 25+53=78 Current State: 81:[87, 13, 78], Operations: ['25+53=78'] Exploring Operation: 78/13=6, Resulting Numbers: [87, 6] Generated Node #3: [87, 6] from Operation: 78/13=6 Current State: 81:[87, 6], Operations: ['25+53=78', '78/13=6'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[87, 13, 25, 53], Operations: [] Exploring Operation: 53-25=28, Resulting Numbers: [87, 13, 28] Generated Node #0,0: 81:[87, 13, 28] Operation: 53-25=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[87, 13, 28], Operations: ['53-25=28'] Exploring Operation: 87-13=74, Resulting Numbers: [28, 74] Generated Node #0,0,0: 81:[28, 74] Operation: 87-13=74 Moving to Node #0,0,0 Current State: 81:[28, 74], Operations: ['53-25=28', '87-13=74'] Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 67, 44, 52, 90 ]
61
[ "67-44=23", "90-52=38", "23+38=61" ]
Current State: 61:[67, 44, 52, 90], Operations: [] Exploring Operation: 67-44=23, Resulting Numbers: [52, 90, 23] Generated Node #2: [52, 90, 23] from Operation: 67-44=23 Current State: 61:[52, 90, 23], Operations: ['67-44=23'] Exploring Operation: 90-52=38, Resulting Numbers: [23, 38] Generated Node #3: [23, 38] from Operation: 90-52=38 Current State: 61:[23, 38], Operations: ['67-44=23', '90-52=38'] Exploring Operation: 23+38=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[67, 44, 52, 90], Operations: [] Exploring Operation: 90-52=38, Resulting Numbers: [67, 44, 38] Generated Node #0,0: 61:[67, 44, 38] Operation: 90-52=38 Exploring Operation: 44+52=96, Resulting Numbers: [67, 90, 96] Generated Node #0,1: 61:[67, 90, 96] Operation: 44+52=96 Exploring Operation: 90-44=46, Resulting Numbers: [67, 52, 46] Generated Node #0,2: 61:[67, 52, 46] Operation: 90-44=46 Exploring Operation: 90-67=23, Resulting Numbers: [44, 52, 23] Generated Node #0,3: 61:[44, 52, 23] Operation: 90-67=23 Moving to Node #0,2 Current State: 61:[67, 52, 46], Operations: ['90-44=46'] Exploring Operation: 52+46=98, Resulting Numbers: [67, 98] Generated Node #0,2,0: 61:[67, 98] Operation: 52+46=98 Exploring Operation: 67+46=113, Resulting Numbers: [52, 113] Generated Node #0,2,1: 61:[52, 113] Operation: 67+46=113 Exploring Operation: 67-46=21, Resulting Numbers: [52, 21] Generated Node #0,2,2: 61:[52, 21] Operation: 67-46=21 Exploring Operation: 67-52=15, Resulting Numbers: [46, 15] Generated Node #0,2,3: 61:[46, 15] Operation: 67-52=15 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[67, 98], Operations: ['90-44=46', '52+46=98'] Exploring Operation: 98-67=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 67+98=165, Resulting Numbers: [165] 165,61 unequal: No Solution Exploring Operation: 67*98=6566, Resulting Numbers: [6566] 6566,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 61:[52, 21], Operations: ['90-44=46', '67-46=21'] Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,61 unequal: No Solution Exploring Operation: 52*21=1092, Resulting Numbers: [1092] 1092,61 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 61:[52, 113], Operations: ['90-44=46', '67+46=113'] Exploring Operation: 52*113=5876, Resulting Numbers: [5876] 5876,61 unequal: No Solution Exploring Operation: 113-52=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[67, 44, 52, 90], Operations: [] Exploring Operation: 90-44=46, Resulting Numbers: [67, 52, 46] Generated Node #0,2: 61:[67, 52, 46] Operation: 90-44=46 Moving to Node #0,2 Current State: 61:[67, 52, 46], Operations: ['90-44=46'] Exploring Operation: 67+46=113, Resulting Numbers: [52, 113] Generated Node #0,2,1: 61:[52, 113] Operation: 67+46=113 Moving to Node #0,2,1 Current State: 61:[52, 113], Operations: ['90-44=46', '67+46=113'] Exploring Operation: 113-52=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 94, 42, 12, 18 ]
82
[ "94-42=52", "12+18=30", "52+30=82" ]
Current State: 82:[94, 42, 12, 18], Operations: [] Exploring Operation: 94-42=52, Resulting Numbers: [12, 18, 52] Generated Node #2: [12, 18, 52] from Operation: 94-42=52 Current State: 82:[12, 18, 52], Operations: ['94-42=52'] Exploring Operation: 12+18=30, Resulting Numbers: [52, 30] Generated Node #3: [52, 30] from Operation: 12+18=30 Current State: 82:[52, 30], Operations: ['94-42=52', '12+18=30'] Exploring Operation: 52+30=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[94, 42, 12, 18], Operations: [] Exploring Operation: 12+18=30, Resulting Numbers: [94, 42, 30] Generated Node #0,0: 82:[94, 42, 30] Operation: 12+18=30 Exploring Operation: 18-12=6, Resulting Numbers: [94, 42, 6] Generated Node #0,1: 82:[94, 42, 6] Operation: 18-12=6 Exploring Operation: 94-12=82, Resulting Numbers: [42, 18, 82] Generated Node #0,2: 82:[42, 18, 82] Operation: 94-12=82 Exploring Operation: 94-18=76, Resulting Numbers: [42, 12, 76] Generated Node #0,3: 82:[42, 12, 76] Operation: 94-18=76 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[94, 42, 6], Operations: ['18-12=6'] Exploring Operation: 94-42=52, Resulting Numbers: [6, 52] Generated Node #0,1,0: 82:[6, 52] Operation: 94-42=52 Exploring Operation: 42/6=7, Resulting Numbers: [94, 7] Generated Node #0,1,1: 82:[94, 7] Operation: 42/6=7 Exploring Operation: 42-6=36, Resulting Numbers: [94, 36] Generated Node #0,1,2: 82:[94, 36] Operation: 42-6=36 Exploring Operation: 94-6=88, Resulting Numbers: [42, 88] Generated Node #0,1,3: 82:[42, 88] Operation: 94-6=88 Moving to Node #0,1,3 Current State: 82:[42, 88], Operations: ['18-12=6', '94-6=88'] Exploring Operation: 42+88=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 88-42=46, Resulting Numbers: [46] 46,82 unequal: No Solution Exploring Operation: 42*88=3696, Resulting Numbers: [3696] 3696,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[6, 52], Operations: ['18-12=6', '94-42=52'] Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,82 unequal: No Solution Exploring Operation: 6*52=312, Resulting Numbers: [312] 312,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[94, 36], Operations: ['18-12=6', '42-6=36'] Exploring Operation: 94-36=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 94*36=3384, Resulting Numbers: [3384] 3384,82 unequal: No Solution Exploring Operation: 94+36=130, Resulting Numbers: [130] 130,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[94, 7], Operations: ['18-12=6', '42/6=7'] Exploring Operation: 94+7=101, Resulting Numbers: [101] 101,82 unequal: No Solution Exploring Operation: 94-7=87, Resulting Numbers: [87] 87,82 unequal: No Solution Exploring Operation: 94*7=658, Resulting Numbers: [658] 658,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[42, 18, 82], Operations: ['94-12=82'] Exploring Operation: 42+18=60, Resulting Numbers: [82, 60] Generated Node #0,2,0: 82:[82, 60] Operation: 42+18=60 Exploring Operation: 42-18=24, Resulting Numbers: [82, 24] Generated Node #0,2,1: 82:[82, 24] Operation: 42-18=24 Exploring Operation: 82-42=40, Resulting Numbers: [18, 40] Generated Node #0,2,2: 82:[18, 40] Operation: 82-42=40 Exploring Operation: 18+82=100, Resulting Numbers: [42, 100] Generated Node #0,2,3: 82:[42, 100] Operation: 18+82=100 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[82, 24], Operations: ['94-12=82', '42-18=24'] Exploring Operation: 82*24=1968, Resulting Numbers: [1968] 1968,82 unequal: No Solution Exploring Operation: 82-24=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 82+24=106, Resulting Numbers: [106] 106,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 82:[18, 40], Operations: ['94-12=82', '82-42=40'] Exploring Operation: 18*40=720, Resulting Numbers: [720] 720,82 unequal: No Solution Exploring Operation: 18+40=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 40-18=22, Resulting Numbers: [22] 22,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[82, 60], Operations: ['94-12=82', '42+18=60'] Exploring Operation: 82*60=4920, Resulting Numbers: [4920] 4920,82 unequal: No Solution Exploring Operation: 82-60=22, Resulting Numbers: [22] 22,82 unequal: No Solution Exploring Operation: 82+60=142, Resulting Numbers: [142] 142,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 82:[42, 100], Operations: ['94-12=82', '18+82=100'] Exploring Operation: 42*100=4200, Resulting Numbers: [4200] 4200,82 unequal: No Solution Exploring Operation: 100-42=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 42+100=142, Resulting Numbers: [142] 142,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[42, 12, 76], Operations: ['94-18=76'] Exploring Operation: 42+12=54, Resulting Numbers: [76, 54] Generated Node #0,3,0: 82:[76, 54] Operation: 42+12=54 Exploring Operation: 12+76=88, Resulting Numbers: [42, 88] Generated Node #0,3,1: 82:[42, 88] Operation: 12+76=88 Exploring Operation: 76-42=34, Resulting Numbers: [12, 34] Generated Node #0,3,2: 82:[12, 34] Operation: 76-42=34 Exploring Operation: 42-12=30, Resulting Numbers: [76, 30] Generated Node #0,3,3: 82:[76, 30] Operation: 42-12=30 Moving to Node #0,3,1 Current State: 82:[42, 88], Operations: ['94-18=76', '12+76=88'] Exploring Operation: 88-42=46, Resulting Numbers: [46] 46,82 unequal: No Solution Exploring Operation: 42*88=3696, Resulting Numbers: [3696] 3696,82 unequal: No Solution Exploring Operation: 42+88=130, Resulting Numbers: [130] 130,82 unequal: No Solution Moving to Node #0,3,3 Current State: 82:[76, 30], Operations: ['94-18=76', '42-12=30'] Exploring Operation: 76*30=2280, Resulting Numbers: [2280] 2280,82 unequal: No Solution Exploring Operation: 76+30=106, Resulting Numbers: [106] 106,82 unequal: No Solution Exploring Operation: 76-30=46, Resulting Numbers: [46] 46,82 unequal: No Solution Moving to Node #0,3,2 Current State: 82:[12, 34], Operations: ['94-18=76', '76-42=34'] Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,82 unequal: No Solution Exploring Operation: 12+34=46, Resulting Numbers: [46] 46,82 unequal: No Solution Exploring Operation: 12*34=408, Resulting Numbers: [408] 408,82 unequal: No Solution Moving to Node #0,3,0 Current State: 82:[76, 54], Operations: ['94-18=76', '42+12=54'] Exploring Operation: 76*54=4104, Resulting Numbers: [4104] 4104,82 unequal: No Solution Exploring Operation: 76-54=22, Resulting Numbers: [22] 22,82 unequal: No Solution Exploring Operation: 76+54=130, Resulting Numbers: [130] 130,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[94, 42, 30], Operations: ['12+18=30'] Exploring Operation: 94-30=64, Resulting Numbers: [42, 64] Generated Node #0,0,0: 82:[42, 64] Operation: 94-30=64 Exploring Operation: 42-30=12, Resulting Numbers: [94, 12] Generated Node #0,0,1: 82:[94, 12] Operation: 42-30=12 Exploring Operation: 94-42=52, Resulting Numbers: [30, 52] Generated Node #0,0,2: 82:[30, 52] Operation: 94-42=52 Exploring Operation: 42+30=72, Resulting Numbers: [94, 72] Generated Node #0,0,3: 82:[94, 72] Operation: 42+30=72 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[42, 64], Operations: ['12+18=30', '94-30=64'] Exploring Operation: 42+64=106, Resulting Numbers: [106] 106,82 unequal: No Solution Exploring Operation: 42*64=2688, Resulting Numbers: [2688] 2688,82 unequal: No Solution Exploring Operation: 64-42=22, Resulting Numbers: [22] 22,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[94, 12], Operations: ['12+18=30', '42-30=12'] Exploring Operation: 94*12=1128, Resulting Numbers: [1128] 1128,82 unequal: No Solution Exploring Operation: 94+12=106, Resulting Numbers: [106] 106,82 unequal: No Solution Exploring Operation: 94-12=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[94, 42, 12, 18], Operations: [] Exploring Operation: 12+18=30, Resulting Numbers: [94, 42, 30] Generated Node #0,0: 82:[94, 42, 30] Operation: 12+18=30 Moving to Node #0,0 Current State: 82:[94, 42, 30], Operations: ['12+18=30'] Exploring Operation: 42-30=12, Resulting Numbers: [94, 12] Generated Node #0,0,1: 82:[94, 12] Operation: 42-30=12 Moving to Node #0,0,1 Current State: 82:[94, 12], Operations: ['12+18=30', '42-30=12'] Exploring Operation: 94-12=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.942708
hs_4
mult_heuristic
[ 32, 84, 92, 96 ]
72
[ "32+84=116", "92+96=188", "188-116=72" ]
Current State: 72:[32, 84, 92, 96], Operations: [] Exploring Operation: 32+84=116, Resulting Numbers: [92, 96, 116] Generated Node #2: [92, 96, 116] from Operation: 32+84=116 Current State: 72:[92, 96, 116], Operations: ['32+84=116'] Exploring Operation: 92+96=188, Resulting Numbers: [116, 188] Generated Node #3: [116, 188] from Operation: 92+96=188 Current State: 72:[116, 188], Operations: ['32+84=116', '92+96=188'] Exploring Operation: 188-116=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[32, 84, 92, 96], Operations: [] Exploring Operation: 96-92=4, Resulting Numbers: [32, 84, 4] Generated Node #0,0: 72:[32, 84, 4] Operation: 96-92=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[32, 84, 4], Operations: ['96-92=4'] Exploring Operation: 84/4=21, Resulting Numbers: [32, 21] Generated Node #0,0,0: 72:[32, 21] Operation: 84/4=21 Moving to Node #0,0,0 Current State: 72:[32, 21], Operations: ['96-92=4', '84/4=21'] Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 37, 45, 37, 73 ]
44
[ "45-37=8", "73-37=36", "8+36=44" ]
Current State: 44:[37, 45, 37, 73], Operations: [] Exploring Operation: 45-37=8, Resulting Numbers: [73, 8] Generated Node #2: [73, 8] from Operation: 45-37=8 Current State: 44:[73, 8], Operations: ['45-37=8'] Exploring Operation: 73-37=36, Resulting Numbers: [8, 36] Generated Node #3: [8, 36] from Operation: 73-37=36 Current State: 44:[8, 36], Operations: ['45-37=8', '73-37=36'] Exploring Operation: 8+36=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[37, 45, 37, 73], Operations: [] Exploring Operation: 73-37=36, Resulting Numbers: [37, 45, 36] Generated Node #0,0: 44:[37, 45, 36] Operation: 73-37=36 Exploring Operation: 73-37=36, Resulting Numbers: [45, 37, 36] Generated Node #0,1: 44:[45, 37, 36] Operation: 73-37=36 Exploring Operation: 37-37=0, Resulting Numbers: [45, 73, 0] Generated Node #0,2: 44:[45, 73, 0] Operation: 37-37=0 Exploring Operation: 37/37=1, Resulting Numbers: [45, 73, 1] Generated Node #0,3: 44:[45, 73, 1] Operation: 37/37=1 Exploring Operation: 73-45=28, Resulting Numbers: [37, 37, 28] Generated Node #0,4: 44:[37, 37, 28] Operation: 73-45=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[37, 45, 36], Operations: ['73-37=36'] Exploring Operation: 37+36=73, Resulting Numbers: [45, 73] Generated Node #0,0,0: 44:[45, 73] Operation: 37+36=73 Exploring Operation: 45+36=81, Resulting Numbers: [37, 81] Generated Node #0,0,1: 44:[37, 81] Operation: 45+36=81 Exploring Operation: 37-36=1, Resulting Numbers: [45, 1] Generated Node #0,0,2: 44:[45, 1] Operation: 37-36=1 Exploring Operation: 45-37=8, Resulting Numbers: [36, 8] Generated Node #0,0,3: 44:[36, 8] Operation: 45-37=8 Exploring Operation: 45-36=9, Resulting Numbers: [37, 9] Generated Node #0,0,4: 44:[37, 9] Operation: 45-36=9 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 44:[45, 1], Operations: ['73-37=36', '37-36=1'] Exploring Operation: 45+1=46, Resulting Numbers: [46] 46,44 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[37, 45, 37, 73], Operations: [] Exploring Operation: 73-37=36, Resulting Numbers: [37, 45, 36] Generated Node #0,0: 44:[37, 45, 36] Operation: 73-37=36 Moving to Node #0,0 Current State: 44:[37, 45, 36], Operations: ['73-37=36'] Exploring Operation: 37-36=1, Resulting Numbers: [45, 1] Generated Node #0,0,2: 44:[45, 1] Operation: 37-36=1 Moving to Node #0,0,2 Current State: 44:[45, 1], Operations: ['73-37=36', '37-36=1'] Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 55, 5, 85, 54 ]
48
[ "85-55=30", "30/5=6", "54-6=48" ]
Current State: 48:[55, 5, 85, 54], Operations: [] Exploring Operation: 85-55=30, Resulting Numbers: [5, 54, 30] Generated Node #2: [5, 54, 30] from Operation: 85-55=30 Current State: 48:[5, 54, 30], Operations: ['85-55=30'] Exploring Operation: 30/5=6, Resulting Numbers: [54, 6] Generated Node #3: [54, 6] from Operation: 30/5=6 Current State: 48:[54, 6], Operations: ['85-55=30', '30/5=6'] Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[55, 5, 85, 54], Operations: [] Exploring Operation: 85-55=30, Resulting Numbers: [5, 54, 30] Generated Node #0,0: 48:[5, 54, 30] Operation: 85-55=30 Moving to Node #0,0 Current State: 48:[5, 54, 30], Operations: ['85-55=30'] Exploring Operation: 54-30=24, Resulting Numbers: [5, 24] Generated Node #0,0,0: 48:[5, 24] Operation: 54-30=24 Moving to Node #0,0,0 Current State: 48:[5, 24], Operations: ['85-55=30', '54-30=24'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,48 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 33, 85, 7, 77 ]
88
[ "33*7=231", "231/77=3", "85+3=88" ]
Current State: 88:[33, 85, 7, 77], Operations: [] Exploring Operation: 33*7=231, Resulting Numbers: [85, 77, 231] Generated Node #2: [85, 77, 231] from Operation: 33*7=231 Current State: 88:[85, 77, 231], Operations: ['33*7=231'] Exploring Operation: 231/77=3, Resulting Numbers: [85, 3] Generated Node #3: [85, 3] from Operation: 231/77=3 Current State: 88:[85, 3], Operations: ['33*7=231', '231/77=3'] Exploring Operation: 85+3=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[33, 85, 7, 77], Operations: [] Exploring Operation: 77-33=44, Resulting Numbers: [85, 7, 44] Generated Node #0,0: 88:[85, 7, 44] Operation: 77-33=44 Moving to Node #0,0 Current State: 88:[85, 7, 44], Operations: ['77-33=44'] Exploring Operation: 85+7=92, Resulting Numbers: [44, 92] Generated Node #0,0,0: 88:[44, 92] Operation: 85+7=92 Moving to Node #0,0,0 Current State: 88:[44, 92], Operations: ['77-33=44', '85+7=92'] Exploring Operation: 92-44=48, Resulting Numbers: [48] 48,88 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 93, 66, 44, 62 ]
82
[ "66-62=4", "44/4=11", "93-11=82" ]
Current State: 82:[93, 66, 44, 62], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [93, 44, 4] Generated Node #2: [93, 44, 4] from Operation: 66-62=4 Current State: 82:[93, 44, 4], Operations: ['66-62=4'] Exploring Operation: 44/4=11, Resulting Numbers: [93, 11] Generated Node #3: [93, 11] from Operation: 44/4=11 Current State: 82:[93, 11], Operations: ['66-62=4', '44/4=11'] Exploring Operation: 93-11=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[93, 66, 44, 62], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [93, 44, 4] Generated Node #0,0: 82:[93, 44, 4] Operation: 66-62=4 Exploring Operation: 93-62=31, Resulting Numbers: [66, 44, 31] Generated Node #0,1: 82:[66, 44, 31] Operation: 93-62=31 Exploring Operation: 93-66=27, Resulting Numbers: [44, 62, 27] Generated Node #0,2: 82:[44, 62, 27] Operation: 93-66=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[93, 44, 4], Operations: ['66-62=4'] Exploring Operation: 93-4=89, Resulting Numbers: [44, 89] Generated Node #0,0,0: 82:[44, 89] Operation: 93-4=89 Exploring Operation: 44-4=40, Resulting Numbers: [93, 40] Generated Node #0,0,1: 82:[93, 40] Operation: 44-4=40 Exploring Operation: 93-44=49, Resulting Numbers: [4, 49] Generated Node #0,0,2: 82:[4, 49] Operation: 93-44=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[44, 89], Operations: ['66-62=4', '93-4=89'] Exploring Operation: 89-44=45, Resulting Numbers: [45] 45,82 unequal: No Solution Exploring Operation: 44*89=3916, Resulting Numbers: [3916] 3916,82 unequal: No Solution Exploring Operation: 44+89=133, Resulting Numbers: [133] 133,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[4, 49], Operations: ['66-62=4', '93-44=49'] Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,82 unequal: No Solution Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,82 unequal: No Solution Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[93, 40], Operations: ['66-62=4', '44-4=40'] Exploring Operation: 93+40=133, Resulting Numbers: [133] 133,82 unequal: No Solution Exploring Operation: 93-40=53, Resulting Numbers: [53] 53,82 unequal: No Solution Exploring Operation: 93*40=3720, Resulting Numbers: [3720] 3720,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[66, 44, 31], Operations: ['93-62=31'] Exploring Operation: 44+31=75, Resulting Numbers: [66, 75] Generated Node #0,1,0: 82:[66, 75] Operation: 44+31=75 Exploring Operation: 66-31=35, Resulting Numbers: [44, 35] Generated Node #0,1,1: 82:[44, 35] Operation: 66-31=35 Exploring Operation: 66+31=97, Resulting Numbers: [44, 97] Generated Node #0,1,2: 82:[44, 97] Operation: 66+31=97 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[44, 35], Operations: ['93-62=31', '66-31=35'] Exploring Operation: 44*35=1540, Resulting Numbers: [1540] 1540,82 unequal: No Solution Exploring Operation: 44-35=9, Resulting Numbers: [9] 9,82 unequal: No Solution Exploring Operation: 44+35=79, Resulting Numbers: [79] 79,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 82:[44, 97], Operations: ['93-62=31', '66+31=97'] Exploring Operation: 44*97=4268, Resulting Numbers: [4268] 4268,82 unequal: No Solution Exploring Operation: 44+97=141, Resulting Numbers: [141] 141,82 unequal: No Solution Exploring Operation: 97-44=53, Resulting Numbers: [53] 53,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[66, 75], Operations: ['93-62=31', '44+31=75'] Exploring Operation: 66*75=4950, Resulting Numbers: [4950] 4950,82 unequal: No Solution Exploring Operation: 75-66=9, Resulting Numbers: [9] 9,82 unequal: No Solution Exploring Operation: 66+75=141, Resulting Numbers: [141] 141,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[44, 62, 27], Operations: ['93-66=27'] Exploring Operation: 62-44=18, Resulting Numbers: [27, 18] Generated Node #0,2,0: 82:[27, 18] Operation: 62-44=18 Exploring Operation: 62+27=89, Resulting Numbers: [44, 89] Generated Node #0,2,1: 82:[44, 89] Operation: 62+27=89 Exploring Operation: 62-27=35, Resulting Numbers: [44, 35] Generated Node #0,2,2: 82:[44, 35] Operation: 62-27=35 Moving to Node #0,2,2 Current State: 82:[44, 35], Operations: ['93-66=27', '62-27=35'] Exploring Operation: 44*35=1540, Resulting Numbers: [1540] 1540,82 unequal: No Solution Exploring Operation: 44+35=79, Resulting Numbers: [79] 79,82 unequal: No Solution Exploring Operation: 44-35=9, Resulting Numbers: [9] 9,82 unequal: No Solution Moving to Node #0,2,1 Current State: 82:[44, 89], Operations: ['93-66=27', '62+27=89'] Exploring Operation: 44*89=3916, Resulting Numbers: [3916] 3916,82 unequal: No Solution Exploring Operation: 44+89=133, Resulting Numbers: [133] 133,82 unequal: No Solution Exploring Operation: 89-44=45, Resulting Numbers: [45] 45,82 unequal: No Solution Moving to Node #0,2,0 Current State: 82:[27, 18], Operations: ['93-66=27', '62-44=18'] Exploring Operation: 27+18=45, Resulting Numbers: [45] 45,82 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,82 unequal: No Solution Exploring Operation: 27*18=486, Resulting Numbers: [486] 486,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 40, 92, 59, 17 ]
24
[ "92-40=52", "59+17=76", "76-52=24" ]
Current State: 24:[40, 92, 59, 17], Operations: [] Exploring Operation: 92-40=52, Resulting Numbers: [59, 17, 52] Generated Node #2: [59, 17, 52] from Operation: 92-40=52 Current State: 24:[59, 17, 52], Operations: ['92-40=52'] Exploring Operation: 59+17=76, Resulting Numbers: [52, 76] Generated Node #3: [52, 76] from Operation: 59+17=76 Current State: 24:[52, 76], Operations: ['92-40=52', '59+17=76'] Exploring Operation: 76-52=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[40, 92, 59, 17], Operations: [] Exploring Operation: 92-59=33, Resulting Numbers: [40, 17, 33] Generated Node #0,0: 24:[40, 17, 33] Operation: 92-59=33 Exploring Operation: 92-40=52, Resulting Numbers: [59, 17, 52] Generated Node #0,1: 24:[59, 17, 52] Operation: 92-40=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[40, 17, 33], Operations: ['92-59=33'] Exploring Operation: 40-33=7, Resulting Numbers: [17, 7] Generated Node #0,0,0: 24:[17, 7] Operation: 40-33=7 Exploring Operation: 40-17=23, Resulting Numbers: [33, 23] Generated Node #0,0,1: 24:[33, 23] Operation: 40-17=23 Moving to Node #0,0,0 Current State: 24:[17, 7], Operations: ['92-59=33', '40-33=7'] Exploring Operation: 17+7=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[40, 92, 59, 17], Operations: [] Exploring Operation: 92-59=33, Resulting Numbers: [40, 17, 33] Generated Node #0,0: 24:[40, 17, 33] Operation: 92-59=33 Moving to Node #0,0 Current State: 24:[40, 17, 33], Operations: ['92-59=33'] Exploring Operation: 40-33=7, Resulting Numbers: [17, 7] Generated Node #0,0,0: 24:[17, 7] Operation: 40-33=7 Moving to Node #0,0,0 Current State: 24:[17, 7], Operations: ['92-59=33', '40-33=7'] Exploring Operation: 17+7=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 19, 35, 5, 41 ]
20
[ "35-19=16", "41-5=36", "36-16=20" ]
Current State: 20:[19, 35, 5, 41], Operations: [] Exploring Operation: 35-19=16, Resulting Numbers: [5, 41, 16] Generated Node #2: [5, 41, 16] from Operation: 35-19=16 Current State: 20:[5, 41, 16], Operations: ['35-19=16'] Exploring Operation: 41-5=36, Resulting Numbers: [16, 36] Generated Node #3: [16, 36] from Operation: 41-5=36 Current State: 20:[16, 36], Operations: ['35-19=16', '41-5=36'] Exploring Operation: 36-16=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[19, 35, 5, 41], Operations: [] Exploring Operation: 41-35=6, Resulting Numbers: [19, 5, 6] Generated Node #0,0: 20:[19, 5, 6] Operation: 41-35=6 Exploring Operation: 41-19=22, Resulting Numbers: [35, 5, 22] Generated Node #0,1: 20:[35, 5, 22] Operation: 41-19=22 Moving to Node #0,0 Current State: 20:[19, 5, 6], Operations: ['41-35=6'] Exploring Operation: 5+6=11, Resulting Numbers: [19, 11] Generated Node #0,0,0: 20:[19, 11] Operation: 5+6=11 Exploring Operation: 6-5=1, Resulting Numbers: [19, 1] Generated Node #0,0,1: 20:[19, 1] Operation: 6-5=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[19, 11], Operations: ['41-35=6', '5+6=11'] Exploring Operation: 19+11=30, Resulting Numbers: [30] 30,20 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 20:[19, 1], Operations: ['41-35=6', '6-5=1'] Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,20 unequal: No Solution Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[19, 35, 5, 41], Operations: [] Exploring Operation: 41-35=6, Resulting Numbers: [19, 5, 6] Generated Node #0,0: 20:[19, 5, 6] Operation: 41-35=6 Moving to Node #0,0 Current State: 20:[19, 5, 6], Operations: ['41-35=6'] Exploring Operation: 6-5=1, Resulting Numbers: [19, 1] Generated Node #0,0,1: 20:[19, 1] Operation: 6-5=1 Moving to Node #0,0,1 Current State: 20:[19, 1], Operations: ['41-35=6', '6-5=1'] Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 89, 80, 11, 4 ]
45
[ "89+80=169", "11+169=180", "180/4=45" ]
Current State: 45:[89, 80, 11, 4], Operations: [] Exploring Operation: 89+80=169, Resulting Numbers: [11, 4, 169] Generated Node #2: [11, 4, 169] from Operation: 89+80=169 Current State: 45:[11, 4, 169], Operations: ['89+80=169'] Exploring Operation: 11+169=180, Resulting Numbers: [4, 180] Generated Node #3: [4, 180] from Operation: 11+169=180 Current State: 45:[4, 180], Operations: ['89+80=169', '11+169=180'] Exploring Operation: 180/4=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[89, 80, 11, 4], Operations: [] Exploring Operation: 80-11=69, Resulting Numbers: [89, 4, 69] Generated Node #0,0: 45:[89, 4, 69] Operation: 80-11=69 Exploring Operation: 89-80=9, Resulting Numbers: [11, 4, 9] Generated Node #0,1: 45:[11, 4, 9] Operation: 89-80=9 Exploring Operation: 89-11=78, Resulting Numbers: [80, 4, 78] Generated Node #0,2: 45:[80, 4, 78] Operation: 89-11=78 Exploring Operation: 80/4=20, Resulting Numbers: [89, 11, 20] Generated Node #0,3: 45:[89, 11, 20] Operation: 80/4=20 Moving to Node #0,1 Current State: 45:[11, 4, 9], Operations: ['89-80=9'] Exploring Operation: 11-9=2, Resulting Numbers: [4, 2] Generated Node #0,1,0: 45:[4, 2] Operation: 11-9=2 Exploring Operation: 11-4=7, Resulting Numbers: [9, 7] Generated Node #0,1,1: 45:[9, 7] Operation: 11-4=7 Exploring Operation: 11*4=44, Resulting Numbers: [9, 44] Generated Node #0,1,2: 45:[9, 44] Operation: 11*4=44 Exploring Operation: 11+4=15, Resulting Numbers: [9, 15] Generated Node #0,1,3: 45:[9, 15] Operation: 11+4=15 Moving to Node #0,3 Current State: 45:[89, 11, 20], Operations: ['80/4=20'] Exploring Operation: 11+20=31, Resulting Numbers: [89, 31] Generated Node #0,3,0: 45:[89, 31] Operation: 11+20=31 Exploring Operation: 20-11=9, Resulting Numbers: [89, 9] Generated Node #0,3,1: 45:[89, 9] Operation: 20-11=9 Exploring Operation: 89-20=69, Resulting Numbers: [11, 69] Generated Node #0,3,2: 45:[11, 69] Operation: 89-20=69 Exploring Operation: 89-11=78, Resulting Numbers: [20, 78] Generated Node #0,3,3: 45:[20, 78] Operation: 89-11=78 Moving to Node #0,2 Current State: 45:[80, 4, 78], Operations: ['89-11=78'] Exploring Operation: 80/4=20, Resulting Numbers: [78, 20] Generated Node #0,2,0: 45:[78, 20] Operation: 80/4=20 Exploring Operation: 78-4=74, Resulting Numbers: [80, 74] Generated Node #0,2,1: 45:[80, 74] Operation: 78-4=74 Exploring Operation: 80-4=76, Resulting Numbers: [78, 76] Generated Node #0,2,2: 45:[78, 76] Operation: 80-4=76 Exploring Operation: 80-78=2, Resulting Numbers: [4, 2] Generated Node #0,2,3: 45:[4, 2] Operation: 80-78=2 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 45:[4, 2], Operations: ['89-11=78', '80-78=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 45:[78, 20], Operations: ['89-11=78', '80/4=20'] Exploring Operation: 78-20=58, Resulting Numbers: [58] 58,45 unequal: No Solution Exploring Operation: 78*20=1560, Resulting Numbers: [1560] 1560,45 unequal: No Solution Exploring Operation: 78+20=98, Resulting Numbers: [98] 98,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 45:[80, 74], Operations: ['89-11=78', '78-4=74'] Exploring Operation: 80*74=5920, Resulting Numbers: [5920] 5920,45 unequal: No Solution Exploring Operation: 80-74=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 80+74=154, Resulting Numbers: [154] 154,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 45:[78, 76], Operations: ['89-11=78', '80-4=76'] Exploring Operation: 78+76=154, Resulting Numbers: [154] 154,45 unequal: No Solution Exploring Operation: 78*76=5928, Resulting Numbers: [5928] 5928,45 unequal: No Solution Exploring Operation: 78-76=2, Resulting Numbers: [2] 2,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 45:[89, 4, 69], Operations: ['80-11=69'] Exploring Operation: 89-4=85, Resulting Numbers: [69, 85] Generated Node #0,0,0: 45:[69, 85] Operation: 89-4=85 Exploring Operation: 89+4=93, Resulting Numbers: [69, 93] Generated Node #0,0,1: 45:[69, 93] Operation: 89+4=93 Exploring Operation: 89-69=20, Resulting Numbers: [4, 20] Generated Node #0,0,2: 45:[4, 20] Operation: 89-69=20 Exploring Operation: 69-4=65, Resulting Numbers: [89, 65] Generated Node #0,0,3: 45:[89, 65] Operation: 69-4=65 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 45:[4, 20], Operations: ['80-11=69', '89-69=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,45 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,45 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[69, 85], Operations: ['80-11=69', '89-4=85'] Exploring Operation: 69*85=5865, Resulting Numbers: [5865] 5865,45 unequal: No Solution Exploring Operation: 85-69=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 69+85=154, Resulting Numbers: [154] 154,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 45:[89, 65], Operations: ['80-11=69', '69-4=65'] Exploring Operation: 89+65=154, Resulting Numbers: [154] 154,45 unequal: No Solution Exploring Operation: 89-65=24, Resulting Numbers: [24] 24,45 unequal: No Solution Exploring Operation: 89*65=5785, Resulting Numbers: [5785] 5785,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[69, 93], Operations: ['80-11=69', '89+4=93'] Exploring Operation: 69*93=6417, Resulting Numbers: [6417] 6417,45 unequal: No Solution Exploring Operation: 93-69=24, Resulting Numbers: [24] 24,45 unequal: No Solution Exploring Operation: 69+93=162, Resulting Numbers: [162] 162,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 45:[9, 15], Operations: ['89-80=9', '11+4=15'] Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,45 unequal: No Solution Exploring Operation: 9*15=135, Resulting Numbers: [135] 135,45 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,45 unequal: No Solution Moving to Node #0,1,2 Current State: 45:[9, 44], Operations: ['89-80=9', '11*4=44'] Exploring Operation: 9*44=396, Resulting Numbers: [396] 396,45 unequal: No Solution Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,45 unequal: No Solution Exploring Operation: 9+44=53, Resulting Numbers: [53] 53,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[4, 2], Operations: ['89-80=9', '11-9=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[9, 7], Operations: ['89-80=9', '11-4=7'] Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,45 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,45 unequal: No Solution Moving to Node #0,3,2 Current State: 45:[11, 69], Operations: ['80/4=20', '89-20=69'] Exploring Operation: 11*69=759, Resulting Numbers: [759] 759,45 unequal: No Solution Exploring Operation: 69-11=58, Resulting Numbers: [58] 58,45 unequal: No Solution Exploring Operation: 11+69=80, Resulting Numbers: [80] 80,45 unequal: No Solution Moving to Node #0,3,3 Current State: 45:[20, 78], Operations: ['80/4=20', '89-11=78'] Exploring Operation: 20+78=98, Resulting Numbers: [98] 98,45 unequal: No Solution Exploring Operation: 20*78=1560, Resulting Numbers: [1560] 1560,45 unequal: No Solution Exploring Operation: 78-20=58, Resulting Numbers: [58] 58,45 unequal: No Solution Moving to Node #0,3,1 Current State: 45:[89, 9], Operations: ['80/4=20', '20-11=9'] Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,45 unequal: No Solution Exploring Operation: 89+9=98, Resulting Numbers: [98] 98,45 unequal: No Solution Exploring Operation: 89*9=801, Resulting Numbers: [801] 801,45 unequal: No Solution Moving to Node #0,3,0 Current State: 45:[89, 31], Operations: ['80/4=20', '11+20=31'] Exploring Operation: 89-31=58, Resulting Numbers: [58] 58,45 unequal: No Solution Exploring Operation: 89*31=2759, Resulting Numbers: [2759] 2759,45 unequal: No Solution Exploring Operation: 89+31=120, Resulting Numbers: [120] 120,45 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 20, 32, 55, 85 ]
10
[ "32+55=87", "87-85=2", "20/2=10" ]
Current State: 10:[20, 32, 55, 85], Operations: [] Exploring Operation: 32+55=87, Resulting Numbers: [20, 85, 87] Generated Node #2: [20, 85, 87] from Operation: 32+55=87 Current State: 10:[20, 85, 87], Operations: ['32+55=87'] Exploring Operation: 87-85=2, Resulting Numbers: [20, 2] Generated Node #3: [20, 2] from Operation: 87-85=2 Current State: 10:[20, 2], Operations: ['32+55=87', '87-85=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[20, 32, 55, 85], Operations: [] Exploring Operation: 55-20=35, Resulting Numbers: [32, 85, 35] Generated Node #0,0: 10:[32, 85, 35] Operation: 55-20=35 Exploring Operation: 85-55=30, Resulting Numbers: [20, 32, 30] Generated Node #0,1: 10:[20, 32, 30] Operation: 85-55=30 Exploring Operation: 32-20=12, Resulting Numbers: [55, 85, 12] Generated Node #0,2: 10:[55, 85, 12] Operation: 32-20=12 Exploring Operation: 85-32=53, Resulting Numbers: [20, 55, 53] Generated Node #0,3: 10:[20, 55, 53] Operation: 85-32=53 Exploring Operation: 55-32=23, Resulting Numbers: [20, 85, 23] Generated Node #0,4: 10:[20, 85, 23] Operation: 55-32=23 Moving to Node #0,1 Current State: 10:[20, 32, 30], Operations: ['85-55=30'] Exploring Operation: 30-20=10, Resulting Numbers: [32, 10] Generated Node #0,1,0: 10:[32, 10] Operation: 30-20=10 Exploring Operation: 32-20=12, Resulting Numbers: [30, 12] Generated Node #0,1,1: 10:[30, 12] Operation: 32-20=12 Exploring Operation: 20+32=52, Resulting Numbers: [30, 52] Generated Node #0,1,2: 10:[30, 52] Operation: 20+32=52 Exploring Operation: 20+30=50, Resulting Numbers: [32, 50] Generated Node #0,1,3: 10:[32, 50] Operation: 20+30=50 Exploring Operation: 32-30=2, Resulting Numbers: [20, 2] Generated Node #0,1,4: 10:[20, 2] Operation: 32-30=2 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 10:[20, 2], Operations: ['85-55=30', '32-30=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,10 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[20, 32, 55, 85], Operations: [] Exploring Operation: 85-55=30, Resulting Numbers: [20, 32, 30] Generated Node #0,1: 10:[20, 32, 30] Operation: 85-55=30 Moving to Node #0,1 Current State: 10:[20, 32, 30], Operations: ['85-55=30'] Exploring Operation: 32-30=2, Resulting Numbers: [20, 2] Generated Node #0,1,4: 10:[20, 2] Operation: 32-30=2 Moving to Node #0,1,4 Current State: 10:[20, 2], Operations: ['85-55=30', '32-30=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 40, 87, 41, 6 ]
82
[ "87-40=47", "41-6=35", "47+35=82" ]
Current State: 82:[40, 87, 41, 6], Operations: [] Exploring Operation: 87-40=47, Resulting Numbers: [41, 6, 47] Generated Node #2: [41, 6, 47] from Operation: 87-40=47 Current State: 82:[41, 6, 47], Operations: ['87-40=47'] Exploring Operation: 41-6=35, Resulting Numbers: [47, 35] Generated Node #3: [47, 35] from Operation: 41-6=35 Current State: 82:[47, 35], Operations: ['87-40=47', '41-6=35'] Exploring Operation: 47+35=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[40, 87, 41, 6], Operations: [] Exploring Operation: 87-40=47, Resulting Numbers: [41, 6, 47] Generated Node #0,0: 82:[41, 6, 47] Operation: 87-40=47 Exploring Operation: 87-6=81, Resulting Numbers: [40, 41, 81] Generated Node #0,1: 82:[40, 41, 81] Operation: 87-6=81 Moving to Node #0,1 Current State: 82:[40, 41, 81], Operations: ['87-6=81'] Exploring Operation: 40+41=81, Resulting Numbers: [81, 81] Generated Node #0,1,0: 82:[81, 81] Operation: 40+41=81 Exploring Operation: 81-40=41, Resulting Numbers: [41, 41] Generated Node #0,1,1: 82:[41, 41] Operation: 81-40=41 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 82:[41, 41], Operations: ['87-6=81', '81-40=41'] Exploring Operation: 41/41=1, Resulting Numbers: [1] 1,82 unequal: No Solution Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[40, 87, 41, 6], Operations: [] Exploring Operation: 87-6=81, Resulting Numbers: [40, 41, 81] Generated Node #0,1: 82:[40, 41, 81] Operation: 87-6=81 Moving to Node #0,1 Current State: 82:[40, 41, 81], Operations: ['87-6=81'] Exploring Operation: 81-40=41, Resulting Numbers: [41, 41] Generated Node #0,1,1: 82:[41, 41] Operation: 81-40=41 Moving to Node #0,1,1 Current State: 82:[41, 41], Operations: ['87-6=81', '81-40=41'] Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 68, 97, 51, 49 ]
58
[ "97-68=29", "51-49=2", "29*2=58" ]
Current State: 58:[68, 97, 51, 49], Operations: [] Exploring Operation: 97-68=29, Resulting Numbers: [51, 49, 29] Generated Node #2: [51, 49, 29] from Operation: 97-68=29 Current State: 58:[51, 49, 29], Operations: ['97-68=29'] Exploring Operation: 51-49=2, Resulting Numbers: [29, 2] Generated Node #3: [29, 2] from Operation: 51-49=2 Current State: 58:[29, 2], Operations: ['97-68=29', '51-49=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[68, 97, 51, 49], Operations: [] Exploring Operation: 97-49=48, Resulting Numbers: [68, 51, 48] Generated Node #0,0: 58:[68, 51, 48] Operation: 97-49=48 Exploring Operation: 51-49=2, Resulting Numbers: [68, 97, 2] Generated Node #0,1: 58:[68, 97, 2] Operation: 51-49=2 Exploring Operation: 68-49=19, Resulting Numbers: [97, 51, 19] Generated Node #0,2: 58:[97, 51, 19] Operation: 68-49=19 Exploring Operation: 97-68=29, Resulting Numbers: [51, 49, 29] Generated Node #0,3: 58:[51, 49, 29] Operation: 97-68=29 Exploring Operation: 97-51=46, Resulting Numbers: [68, 49, 46] Generated Node #0,4: 58:[68, 49, 46] Operation: 97-51=46 Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[51, 49, 29], Operations: ['97-68=29'] Exploring Operation: 49-29=20, Resulting Numbers: [51, 20] Generated Node #0,3,0: 58:[51, 20] Operation: 49-29=20 Exploring Operation: 49+29=78, Resulting Numbers: [51, 78] Generated Node #0,3,1: 58:[51, 78] Operation: 49+29=78 Exploring Operation: 51+29=80, Resulting Numbers: [49, 80] Generated Node #0,3,2: 58:[49, 80] Operation: 51+29=80 Exploring Operation: 51-29=22, Resulting Numbers: [49, 22] Generated Node #0,3,3: 58:[49, 22] Operation: 51-29=22 Exploring Operation: 51-49=2, Resulting Numbers: [29, 2] Generated Node #0,3,4: 58:[29, 2] Operation: 51-49=2 Moving to Node #0,3,4 Current State: 58:[29, 2], Operations: ['97-68=29', '51-49=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[68, 97, 51, 49], Operations: [] Exploring Operation: 97-68=29, Resulting Numbers: [51, 49, 29] Generated Node #0,3: 58:[51, 49, 29] Operation: 97-68=29 Moving to Node #0,3 Current State: 58:[51, 49, 29], Operations: ['97-68=29'] Exploring Operation: 51-49=2, Resulting Numbers: [29, 2] Generated Node #0,3,4: 58:[29, 2] Operation: 51-49=2 Moving to Node #0,3,4 Current State: 58:[29, 2], Operations: ['97-68=29', '51-49=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 90, 12, 9, 2 ]
28
[ "12-9=3", "90/3=30", "30-2=28" ]
Current State: 28:[90, 12, 9, 2], Operations: [] Exploring Operation: 12-9=3, Resulting Numbers: [90, 2, 3] Generated Node #2: [90, 2, 3] from Operation: 12-9=3 Current State: 28:[90, 2, 3], Operations: ['12-9=3'] Exploring Operation: 90/3=30, Resulting Numbers: [2, 30] Generated Node #3: [2, 30] from Operation: 90/3=30 Current State: 28:[2, 30], Operations: ['12-9=3', '90/3=30'] Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[90, 12, 9, 2], Operations: [] Exploring Operation: 90/9=10, Resulting Numbers: [12, 2, 10] Generated Node #0,0: 28:[12, 2, 10] Operation: 90/9=10 Moving to Node #0,0 Current State: 28:[12, 2, 10], Operations: ['90/9=10'] Exploring Operation: 12-10=2, Resulting Numbers: [2, 2] Generated Node #0,0,0: 28:[2, 2] Operation: 12-10=2 Moving to Node #0,0,0 Current State: 28:[2, 2], Operations: ['90/9=10', '12-10=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,28 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 15, 33, 36, 68 ]
51
[ "15+33=48", "36*68=2448", "2448/48=51" ]
Current State: 51:[15, 33, 36, 68], Operations: [] Exploring Operation: 15+33=48, Resulting Numbers: [36, 68, 48] Generated Node #2: [36, 68, 48] from Operation: 15+33=48 Current State: 51:[36, 68, 48], Operations: ['15+33=48'] Exploring Operation: 36*68=2448, Resulting Numbers: [48, 2448] Generated Node #3: [48, 2448] from Operation: 36*68=2448 Current State: 51:[48, 2448], Operations: ['15+33=48', '36*68=2448'] Exploring Operation: 2448/48=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[15, 33, 36, 68], Operations: [] Exploring Operation: 68-15=53, Resulting Numbers: [33, 36, 53] Generated Node #0,0: 51:[33, 36, 53] Operation: 68-15=53 Exploring Operation: 68-33=35, Resulting Numbers: [15, 36, 35] Generated Node #0,1: 51:[15, 36, 35] Operation: 68-33=35 Exploring Operation: 36-33=3, Resulting Numbers: [15, 68, 3] Generated Node #0,2: 51:[15, 68, 3] Operation: 36-33=3 Exploring Operation: 33-15=18, Resulting Numbers: [36, 68, 18] Generated Node #0,3: 51:[36, 68, 18] Operation: 33-15=18 Exploring Operation: 15+36=51, Resulting Numbers: [33, 68, 51] Generated Node #0,4: 51:[33, 68, 51] Operation: 15+36=51 Moving to Node #0,2 Current State: 51:[15, 68, 3], Operations: ['36-33=3'] Exploring Operation: 15/3=5, Resulting Numbers: [68, 5] Generated Node #0,2,0: 51:[68, 5] Operation: 15/3=5 Exploring Operation: 68-15=53, Resulting Numbers: [3, 53] Generated Node #0,2,1: 51:[3, 53] Operation: 68-15=53 Exploring Operation: 15+3=18, Resulting Numbers: [68, 18] Generated Node #0,2,2: 51:[68, 18] Operation: 15+3=18 Exploring Operation: 15-3=12, Resulting Numbers: [68, 12] Generated Node #0,2,3: 51:[68, 12] Operation: 15-3=12 Exploring Operation: 68-3=65, Resulting Numbers: [15, 65] Generated Node #0,2,4: 51:[15, 65] Operation: 68-3=65 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 51:[3, 53], Operations: ['36-33=3', '68-15=53'] Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 3+53=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 3*53=159, Resulting Numbers: [159] 159,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 51:[15, 65], Operations: ['36-33=3', '68-3=65'] Exploring Operation: 15*65=975, Resulting Numbers: [975] 975,51 unequal: No Solution Exploring Operation: 15+65=80, Resulting Numbers: [80] 80,51 unequal: No Solution Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 51:[68, 18], Operations: ['36-33=3', '15+3=18'] Exploring Operation: 68+18=86, Resulting Numbers: [86] 86,51 unequal: No Solution Exploring Operation: 68*18=1224, Resulting Numbers: [1224] 1224,51 unequal: No Solution Exploring Operation: 68-18=50, Resulting Numbers: [50] 50,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 51:[68, 5], Operations: ['36-33=3', '15/3=5'] Exploring Operation: 68*5=340, Resulting Numbers: [340] 340,51 unequal: No Solution Exploring Operation: 68+5=73, Resulting Numbers: [73] 73,51 unequal: No Solution Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 51:[68, 12], Operations: ['36-33=3', '15-3=12'] Exploring Operation: 68-12=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 68+12=80, Resulting Numbers: [80] 80,51 unequal: No Solution Exploring Operation: 68*12=816, Resulting Numbers: [816] 816,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 51:[15, 36, 35], Operations: ['68-33=35'] Exploring Operation: 15+36=51, Resulting Numbers: [35, 51] Generated Node #0,1,0: 51:[35, 51] Operation: 15+36=51 Exploring Operation: 36-35=1, Resulting Numbers: [15, 1] Generated Node #0,1,1: 51:[15, 1] Operation: 36-35=1 Exploring Operation: 36-15=21, Resulting Numbers: [35, 21] Generated Node #0,1,2: 51:[35, 21] Operation: 36-15=21 Exploring Operation: 35-15=20, Resulting Numbers: [36, 20] Generated Node #0,1,3: 51:[36, 20] Operation: 35-15=20 Exploring Operation: 15+35=50, Resulting Numbers: [36, 50] Generated Node #0,1,4: 51:[36, 50] Operation: 15+35=50 Moving to Node #0,4 Current State: 51:[33, 68, 51], Operations: ['15+36=51'] Exploring Operation: 33+68=101, Resulting Numbers: [51, 101] Generated Node #0,4,0: 51:[51, 101] Operation: 33+68=101 Exploring Operation: 51-33=18, Resulting Numbers: [68, 18] Generated Node #0,4,1: 51:[68, 18] Operation: 51-33=18 Exploring Operation: 33+51=84, Resulting Numbers: [68, 84] Generated Node #0,4,2: 51:[68, 84] Operation: 33+51=84 Exploring Operation: 68-33=35, Resulting Numbers: [51, 35] Generated Node #0,4,3: 51:[51, 35] Operation: 68-33=35 Exploring Operation: 68-51=17, Resulting Numbers: [33, 17] Generated Node #0,4,4: 51:[33, 17] Operation: 68-51=17 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 51:[51, 35], Operations: ['15+36=51', '68-33=35'] Exploring Operation: 51+35=86, Resulting Numbers: [86] 86,51 unequal: No Solution Exploring Operation: 51-35=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 51*35=1785, Resulting Numbers: [1785] 1785,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 51:[33, 17], Operations: ['15+36=51', '68-51=17'] Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 33*17=561, Resulting Numbers: [561] 561,51 unequal: No Solution Exploring Operation: 33+17=50, Resulting Numbers: [50] 50,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 51:[68, 18], Operations: ['15+36=51', '51-33=18'] Exploring Operation: 68+18=86, Resulting Numbers: [86] 86,51 unequal: No Solution Exploring Operation: 68*18=1224, Resulting Numbers: [1224] 1224,51 unequal: No Solution Exploring Operation: 68-18=50, Resulting Numbers: [50] 50,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 51:[51, 101], Operations: ['15+36=51', '33+68=101'] Exploring Operation: 51+101=152, Resulting Numbers: [152] 152,51 unequal: No Solution Exploring Operation: 51*101=5151, Resulting Numbers: [5151] 5151,51 unequal: No Solution Exploring Operation: 101-51=50, Resulting Numbers: [50] 50,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 51:[68, 84], Operations: ['15+36=51', '33+51=84'] Exploring Operation: 68*84=5712, Resulting Numbers: [5712] 5712,51 unequal: No Solution Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 68+84=152, Resulting Numbers: [152] 152,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 51:[33, 36, 53], Operations: ['68-15=53'] Exploring Operation: 53-33=20, Resulting Numbers: [36, 20] Generated Node #0,0,0: 51:[36, 20] Operation: 53-33=20 Exploring Operation: 53-36=17, Resulting Numbers: [33, 17] Generated Node #0,0,1: 51:[33, 17] Operation: 53-36=17 Exploring Operation: 33+53=86, Resulting Numbers: [36, 86] Generated Node #0,0,2: 51:[36, 86] Operation: 33+53=86 Exploring Operation: 33+36=69, Resulting Numbers: [53, 69] Generated Node #0,0,3: 51:[53, 69] Operation: 33+36=69 Exploring Operation: 36-33=3, Resulting Numbers: [53, 3] Generated Node #0,0,4: 51:[53, 3] Operation: 36-33=3 Moving to Node #0,3 Current State: 51:[36, 68, 18], Operations: ['33-15=18'] Exploring Operation: 68-36=32, Resulting Numbers: [18, 32] Generated Node #0,3,0: 51:[18, 32] Operation: 68-36=32 Exploring Operation: 68-18=50, Resulting Numbers: [36, 50] Generated Node #0,3,1: 51:[36, 50] Operation: 68-18=50 Exploring Operation: 36+18=54, Resulting Numbers: [68, 54] Generated Node #0,3,2: 51:[68, 54] Operation: 36+18=54 Exploring Operation: 36/18=2, Resulting Numbers: [68, 2] Generated Node #0,3,3: 51:[68, 2] Operation: 36/18=2 Exploring Operation: 36-18=18, Resulting Numbers: [68, 18] Generated Node #0,3,4: 51:[68, 18] Operation: 36-18=18 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 51:[18, 32], Operations: ['33-15=18', '68-36=32'] Exploring Operation: 18*32=576, Resulting Numbers: [576] 576,51 unequal: No Solution Exploring Operation: 18+32=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 51:[36, 50], Operations: ['33-15=18', '68-18=50'] Exploring Operation: 36*50=1800, Resulting Numbers: [1800] 1800,51 unequal: No Solution Exploring Operation: 36+50=86, Resulting Numbers: [86] 86,51 unequal: No Solution Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 51:[68, 2], Operations: ['33-15=18', '36/18=2'] Exploring Operation: 68*2=136, Resulting Numbers: [136] 136,51 unequal: No Solution Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,51 unequal: No Solution Exploring Operation: 68+2=70, Resulting Numbers: [70] 70,51 unequal: No Solution Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 51:[68, 18], Operations: ['33-15=18', '36-18=18'] Exploring Operation: 68+18=86, Resulting Numbers: [86] 86,51 unequal: No Solution Exploring Operation: 68-18=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 68*18=1224, Resulting Numbers: [1224] 1224,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 51:[68, 54], Operations: ['33-15=18', '36+18=54'] Exploring Operation: 68-54=14, Resulting Numbers: [14] 14,51 unequal: No Solution Exploring Operation: 68*54=3672, Resulting Numbers: [3672] 3672,51 unequal: No Solution Exploring Operation: 68+54=122, Resulting Numbers: [122] 122,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,4 Current State: 51:[53, 3], Operations: ['68-15=53', '36-33=3'] Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 53+3=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 53*3=159, Resulting Numbers: [159] 159,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[15, 1], Operations: ['68-33=35', '36-35=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,51 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 15+1=16, Resulting Numbers: [16] 16,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[33, 17], Operations: ['68-15=53', '53-36=17'] Exploring Operation: 33*17=561, Resulting Numbers: [561] 561,51 unequal: No Solution Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 33+17=50, Resulting Numbers: [50] 50,51 unequal: No Solution Moving to Node #0,1,4 Current State: 51:[36, 50], Operations: ['68-33=35', '15+35=50'] Exploring Operation: 36+50=86, Resulting Numbers: [86] 86,51 unequal: No Solution Exploring Operation: 36*50=1800, Resulting Numbers: [1800] 1800,51 unequal: No Solution Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[35, 51], Operations: ['68-33=35', '15+36=51'] Exploring Operation: 51-35=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 35*51=1785, Resulting Numbers: [1785] 1785,51 unequal: No Solution Exploring Operation: 35+51=86, Resulting Numbers: [86] 86,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[36, 20], Operations: ['68-15=53', '53-33=20'] Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,51 unequal: No Solution Moving to Node #0,1,3 Current State: 51:[36, 20], Operations: ['68-33=35', '35-15=20'] Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,51 unequal: No Solution Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,51 unequal: No Solution Moving to Node #0,0,3 Current State: 51:[53, 69], Operations: ['68-15=53', '33+36=69'] Exploring Operation: 69-53=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 53+69=122, Resulting Numbers: [122] 122,51 unequal: No Solution Exploring Operation: 53*69=3657, Resulting Numbers: [3657] 3657,51 unequal: No Solution Moving to Node #0,1,2 Current State: 51:[35, 21], Operations: ['68-33=35', '36-15=21'] Exploring Operation: 35*21=735, Resulting Numbers: [735] 735,51 unequal: No Solution Exploring Operation: 35+21=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[36, 86], Operations: ['68-15=53', '33+53=86'] Exploring Operation: 36+86=122, Resulting Numbers: [122] 122,51 unequal: No Solution Exploring Operation: 36*86=3096, Resulting Numbers: [3096] 3096,51 unequal: No Solution Exploring Operation: 86-36=50, Resulting Numbers: [50] 50,51 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 85, 19, 74, 2 ]
22
[ "85+19=104", "104/2=52", "74-52=22" ]
Current State: 22:[85, 19, 74, 2], Operations: [] Exploring Operation: 85+19=104, Resulting Numbers: [74, 2, 104] Generated Node #2: [74, 2, 104] from Operation: 85+19=104 Current State: 22:[74, 2, 104], Operations: ['85+19=104'] Exploring Operation: 104/2=52, Resulting Numbers: [74, 52] Generated Node #3: [74, 52] from Operation: 104/2=52 Current State: 22:[74, 52], Operations: ['85+19=104', '104/2=52'] Exploring Operation: 74-52=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[85, 19, 74, 2], Operations: [] Exploring Operation: 85-74=11, Resulting Numbers: [19, 2, 11] Generated Node #0,0: 22:[19, 2, 11] Operation: 85-74=11 Exploring Operation: 74/2=37, Resulting Numbers: [85, 19, 37] Generated Node #0,1: 22:[85, 19, 37] Operation: 74/2=37 Moving to Node #0,0 Current State: 22:[19, 2, 11], Operations: ['85-74=11'] Exploring Operation: 19+2=21, Resulting Numbers: [11, 21] Generated Node #0,0,0: 22:[11, 21] Operation: 19+2=21 Exploring Operation: 19-11=8, Resulting Numbers: [2, 8] Generated Node #0,0,1: 22:[2, 8] Operation: 19-11=8 Moving to Node #0,1 Current State: 22:[85, 19, 37], Operations: ['74/2=37'] Exploring Operation: 85-37=48, Resulting Numbers: [19, 48] Generated Node #0,1,0: 22:[19, 48] Operation: 85-37=48 Exploring Operation: 85-19=66, Resulting Numbers: [37, 66] Generated Node #0,1,1: 22:[37, 66] Operation: 85-19=66 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[19, 48], Operations: ['74/2=37', '85-37=48'] Exploring Operation: 19+48=67, Resulting Numbers: [67] 67,22 unequal: No Solution Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[37, 66], Operations: ['74/2=37', '85-19=66'] Exploring Operation: 37+66=103, Resulting Numbers: [103] 103,22 unequal: No Solution Exploring Operation: 66-37=29, Resulting Numbers: [29] 29,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 22:[11, 21], Operations: ['85-74=11', '19+2=21'] Exploring Operation: 11+21=32, Resulting Numbers: [32] 32,22 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[2, 8], Operations: ['85-74=11', '19-11=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,22 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,22 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 26, 26, 3, 4 ]
75
[ "26+3=29", "26*4=104", "104-29=75" ]
Current State: 75:[26, 26, 3, 4], Operations: [] Exploring Operation: 26+3=29, Resulting Numbers: [4, 29] Generated Node #2: [4, 29] from Operation: 26+3=29 Current State: 75:[4, 29], Operations: ['26+3=29'] Exploring Operation: 26*4=104, Resulting Numbers: [29, 104] Generated Node #3: [29, 104] from Operation: 26*4=104 Current State: 75:[29, 104], Operations: ['26+3=29', '26*4=104'] Exploring Operation: 104-29=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[26, 26, 3, 4], Operations: [] Exploring Operation: 26/26=1, Resulting Numbers: [3, 4, 1] Generated Node #0,0: 75:[3, 4, 1] Operation: 26/26=1 Moving to Node #0,0 Current State: 75:[3, 4, 1], Operations: ['26/26=1'] Exploring Operation: 4+1=5, Resulting Numbers: [3, 5] Generated Node #0,0,0: 75:[3, 5] Operation: 4+1=5 Moving to Node #0,0,0 Current State: 75:[3, 5], Operations: ['26/26=1', '4+1=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,75 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 31, 50, 25, 32 ]
76
[ "50-31=19", "25+32=57", "19+57=76" ]
Current State: 76:[31, 50, 25, 32], Operations: [] Exploring Operation: 50-31=19, Resulting Numbers: [25, 32, 19] Generated Node #2: [25, 32, 19] from Operation: 50-31=19 Current State: 76:[25, 32, 19], Operations: ['50-31=19'] Exploring Operation: 25+32=57, Resulting Numbers: [19, 57] Generated Node #3: [19, 57] from Operation: 25+32=57 Current State: 76:[19, 57], Operations: ['50-31=19', '25+32=57'] Exploring Operation: 19+57=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[31, 50, 25, 32], Operations: [] Exploring Operation: 50/25=2, Resulting Numbers: [31, 32, 2] Generated Node #0,0: 76:[31, 32, 2] Operation: 50/25=2 Exploring Operation: 50-31=19, Resulting Numbers: [25, 32, 19] Generated Node #0,1: 76:[25, 32, 19] Operation: 50-31=19 Exploring Operation: 50+25=75, Resulting Numbers: [31, 32, 75] Generated Node #0,2: 76:[31, 32, 75] Operation: 50+25=75 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[25, 32, 19], Operations: ['50-31=19'] Exploring Operation: 25+19=44, Resulting Numbers: [32, 44] Generated Node #0,1,0: 76:[32, 44] Operation: 25+19=44 Exploring Operation: 25-19=6, Resulting Numbers: [32, 6] Generated Node #0,1,1: 76:[32, 6] Operation: 25-19=6 Exploring Operation: 32-25=7, Resulting Numbers: [19, 7] Generated Node #0,1,2: 76:[19, 7] Operation: 32-25=7 Moving to Node #0,1,2 Current State: 76:[19, 7], Operations: ['50-31=19', '32-25=7'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 19*7=133, Resulting Numbers: [133] 133,76 unequal: No Solution Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[32, 6], Operations: ['50-31=19', '25-19=6'] Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,76 unequal: No Solution Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,76 unequal: No Solution Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[32, 44], Operations: ['50-31=19', '25+19=44'] Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 32*44=1408, Resulting Numbers: [1408] 1408,76 unequal: No Solution Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[31, 50, 25, 32], Operations: [] Exploring Operation: 50-31=19, Resulting Numbers: [25, 32, 19] Generated Node #0,1: 76:[25, 32, 19] Operation: 50-31=19 Moving to Node #0,1 Current State: 76:[25, 32, 19], Operations: ['50-31=19'] Exploring Operation: 25+19=44, Resulting Numbers: [32, 44] Generated Node #0,1,0: 76:[32, 44] Operation: 25+19=44 Moving to Node #0,1,0 Current State: 76:[32, 44], Operations: ['50-31=19', '25+19=44'] Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
mult_heuristic
[ 8, 76, 83, 15 ]
35
[ "8*76=608", "608-83=525", "525/15=35" ]
Current State: 35:[8, 76, 83, 15], Operations: [] Exploring Operation: 8*76=608, Resulting Numbers: [83, 15, 608] Generated Node #2: [83, 15, 608] from Operation: 8*76=608 Current State: 35:[83, 15, 608], Operations: ['8*76=608'] Exploring Operation: 608-83=525, Resulting Numbers: [15, 525] Generated Node #3: [15, 525] from Operation: 608-83=525 Current State: 35:[15, 525], Operations: ['8*76=608', '608-83=525'] Exploring Operation: 525/15=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[8, 76, 83, 15], Operations: [] Exploring Operation: 76-8=68, Resulting Numbers: [83, 15, 68] Generated Node #0,0: 35:[83, 15, 68] Operation: 76-8=68 Exploring Operation: 83-76=7, Resulting Numbers: [8, 15, 7] Generated Node #0,1: 35:[8, 15, 7] Operation: 83-76=7 Exploring Operation: 83-15=68, Resulting Numbers: [8, 76, 68] Generated Node #0,2: 35:[8, 76, 68] Operation: 83-15=68 Exploring Operation: 76-15=61, Resulting Numbers: [8, 83, 61] Generated Node #0,3: 35:[8, 83, 61] Operation: 76-15=61 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[8, 15, 7], Operations: ['83-76=7'] Exploring Operation: 8-7=1, Resulting Numbers: [15, 1] Generated Node #0,1,0: 35:[15, 1] Operation: 8-7=1 Exploring Operation: 15-8=7, Resulting Numbers: [7, 7] Generated Node #0,1,1: 35:[7, 7] Operation: 15-8=7 Exploring Operation: 8+15=23, Resulting Numbers: [7, 23] Generated Node #0,1,2: 35:[7, 23] Operation: 8+15=23 Exploring Operation: 15-7=8, Resulting Numbers: [8, 8] Generated Node #0,1,3: 35:[8, 8] Operation: 15-7=8 Moving to Node #0,1,1 Current State: 35:[7, 7], Operations: ['83-76=7', '15-8=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,35 unequal: No Solution Moving to Node #0,1,3 Current State: 35:[8, 8], Operations: ['83-76=7', '15-7=8'] Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,35 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,35 unequal: No Solution Moving to Node #0,1,2 Current State: 35:[7, 23], Operations: ['83-76=7', '8+15=23'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 7*23=161, Resulting Numbers: [161] 161,35 unequal: No Solution Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[15, 1], Operations: ['83-76=7', '8-7=1'] Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,35 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,35 unequal: No Solution Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 15+1=16, Resulting Numbers: [16] 16,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[8, 76, 68], Operations: ['83-15=68'] Exploring Operation: 76-8=68, Resulting Numbers: [68, 68] Generated Node #0,2,0: 35:[68, 68] Operation: 76-8=68 Exploring Operation: 8+76=84, Resulting Numbers: [68, 84] Generated Node #0,2,1: 35:[68, 84] Operation: 8+76=84 Exploring Operation: 76-68=8, Resulting Numbers: [8, 8] Generated Node #0,2,2: 35:[8, 8] Operation: 76-68=8 Exploring Operation: 68-8=60, Resulting Numbers: [76, 60] Generated Node #0,2,3: 35:[76, 60] Operation: 68-8=60 Moving to Node #0,2,2 Current State: 35:[8, 8], Operations: ['83-15=68', '76-68=8'] Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,35 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,35 unequal: No Solution Moving to Node #0,2,3 Current State: 35:[76, 60], Operations: ['83-15=68', '68-8=60'] Exploring Operation: 76+60=136, Resulting Numbers: [136] 136,35 unequal: No Solution Exploring Operation: 76*60=4560, Resulting Numbers: [4560] 4560,35 unequal: No Solution Exploring Operation: 76-60=16, Resulting Numbers: [16] 16,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[68, 68], Operations: ['83-15=68', '76-8=68'] Exploring Operation: 68-68=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 68*68=4624, Resulting Numbers: [4624] 4624,35 unequal: No Solution Exploring Operation: 68+68=136, Resulting Numbers: [136] 136,35 unequal: No Solution Exploring Operation: 68/68=1, Resulting Numbers: [1] 1,35 unequal: No Solution Moving to Node #0,2,1 Current State: 35:[68, 84], Operations: ['83-15=68', '8+76=84'] Exploring Operation: 68+84=152, Resulting Numbers: [152] 152,35 unequal: No Solution Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,35 unequal: No Solution Exploring Operation: 68*84=5712, Resulting Numbers: [5712] 5712,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 35:[8, 83, 61], Operations: ['76-15=61'] Exploring Operation: 83-61=22, Resulting Numbers: [8, 22] Generated Node #0,3,0: 35:[8, 22] Operation: 83-61=22 Exploring Operation: 83-8=75, Resulting Numbers: [61, 75] Generated Node #0,3,1: 35:[61, 75] Operation: 83-8=75 Exploring Operation: 61-8=53, Resulting Numbers: [83, 53] Generated Node #0,3,2: 35:[83, 53] Operation: 61-8=53 Exploring Operation: 8+83=91, Resulting Numbers: [61, 91] Generated Node #0,3,3: 35:[61, 91] Operation: 8+83=91 Moving to Node #0,3,0 Current State: 35:[8, 22], Operations: ['76-15=61', '83-61=22'] Exploring Operation: 8*22=176, Resulting Numbers: [176] 176,35 unequal: No Solution Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 8+22=30, Resulting Numbers: [30] 30,35 unequal: No Solution Moving to Node #0,3,2 Current State: 35:[83, 53], Operations: ['76-15=61', '61-8=53'] Exploring Operation: 83*53=4399, Resulting Numbers: [4399] 4399,35 unequal: No Solution Exploring Operation: 83+53=136, Resulting Numbers: [136] 136,35 unequal: No Solution Exploring Operation: 83-53=30, Resulting Numbers: [30] 30,35 unequal: No Solution Moving to Node #0,3,1 Current State: 35:[61, 75], Operations: ['76-15=61', '83-8=75'] Exploring Operation: 61*75=4575, Resulting Numbers: [4575] 4575,35 unequal: No Solution Exploring Operation: 75-61=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 61+75=136, Resulting Numbers: [136] 136,35 unequal: No Solution Moving to Node #0,3,3 Current State: 35:[61, 91], Operations: ['76-15=61', '8+83=91'] Exploring Operation: 61+91=152, Resulting Numbers: [152] 152,35 unequal: No Solution Exploring Operation: 61*91=5551, Resulting Numbers: [5551] 5551,35 unequal: No Solution Exploring Operation: 91-61=30, Resulting Numbers: [30] 30,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[83, 15, 68], Operations: ['76-8=68'] Exploring Operation: 68-15=53, Resulting Numbers: [83, 53] Generated Node #0,0,0: 35:[83, 53] Operation: 68-15=53 Exploring Operation: 83-68=15, Resulting Numbers: [15, 15] Generated Node #0,0,1: 35:[15, 15] Operation: 83-68=15 Exploring Operation: 83+15=98, Resulting Numbers: [68, 98] Generated Node #0,0,2: 35:[68, 98] Operation: 83+15=98 Exploring Operation: 83-15=68, Resulting Numbers: [68, 68] Generated Node #0,0,3: 35:[68, 68] Operation: 83-15=68 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 35:[15, 15], Operations: ['76-8=68', '83-68=15'] Exploring Operation: 15/15=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 15*15=225, Resulting Numbers: [225] 225,35 unequal: No Solution Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,35 unequal: No Solution Exploring Operation: 15-15=0, Resulting Numbers: [0] 0,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[83, 53], Operations: ['76-8=68', '68-15=53'] Exploring Operation: 83*53=4399, Resulting Numbers: [4399] 4399,35 unequal: No Solution Exploring Operation: 83-53=30, Resulting Numbers: [30] 30,35 unequal: No Solution Exploring Operation: 83+53=136, Resulting Numbers: [136] 136,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 35:[68, 68], Operations: ['76-8=68', '83-15=68'] Exploring Operation: 68-68=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 68/68=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 68*68=4624, Resulting Numbers: [4624] 4624,35 unequal: No Solution Exploring Operation: 68+68=136, Resulting Numbers: [136] 136,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 35:[68, 98], Operations: ['76-8=68', '83+15=98'] Exploring Operation: 68*98=6664, Resulting Numbers: [6664] 6664,35 unequal: No Solution Exploring Operation: 98-68=30, Resulting Numbers: [30] 30,35 unequal: No Solution Exploring Operation: 68+98=166, Resulting Numbers: [166] 166,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 28, 32, 3, 16 ]
53
[ "28*32=896", "896/16=56", "56-3=53" ]
Current State: 53:[28, 32, 3, 16], Operations: [] Exploring Operation: 28*32=896, Resulting Numbers: [3, 16, 896] Generated Node #2: [3, 16, 896] from Operation: 28*32=896 Current State: 53:[3, 16, 896], Operations: ['28*32=896'] Exploring Operation: 896/16=56, Resulting Numbers: [3, 56] Generated Node #3: [3, 56] from Operation: 896/16=56 Current State: 53:[3, 56], Operations: ['28*32=896', '896/16=56'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[28, 32, 3, 16], Operations: [] Exploring Operation: 3*16=48, Resulting Numbers: [28, 32, 48] Generated Node #0,0: 53:[28, 32, 48] Operation: 3*16=48 Exploring Operation: 28+3=31, Resulting Numbers: [32, 16, 31] Generated Node #0,1: 53:[32, 16, 31] Operation: 28+3=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[28, 32, 48], Operations: ['3*16=48'] Exploring Operation: 28+48=76, Resulting Numbers: [32, 76] Generated Node #0,0,0: 53:[32, 76] Operation: 28+48=76 Exploring Operation: 28+32=60, Resulting Numbers: [48, 60] Generated Node #0,0,1: 53:[48, 60] Operation: 28+32=60 Moving to Node #0,0,1 Current State: 53:[48, 60], Operations: ['3*16=48', '28+32=60'] Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,53 unequal: No Solution Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[32, 76], Operations: ['3*16=48', '28+48=76'] Exploring Operation: 32+76=108, Resulting Numbers: [108] 108,53 unequal: No Solution Exploring Operation: 76-32=44, Resulting Numbers: [44] 44,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[32, 16, 31], Operations: ['28+3=31'] Exploring Operation: 32+16=48, Resulting Numbers: [31, 48] Generated Node #0,1,0: 53:[31, 48] Operation: 32+16=48 Exploring Operation: 16+31=47, Resulting Numbers: [32, 47] Generated Node #0,1,1: 53:[32, 47] Operation: 16+31=47 Moving to Node #0,1,0 Current State: 53:[31, 48], Operations: ['28+3=31', '32+16=48'] Exploring Operation: 31+48=79, Resulting Numbers: [79] 79,53 unequal: No Solution Exploring Operation: 48-31=17, Resulting Numbers: [17] 17,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[32, 47], Operations: ['28+3=31', '16+31=47'] Exploring Operation: 32+47=79, Resulting Numbers: [79] 79,53 unequal: No Solution Exploring Operation: 47-32=15, Resulting Numbers: [15] 15,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 77, 47, 82, 95 ]
66
[ "82-77=5", "95/5=19", "47+19=66" ]
Current State: 66:[77, 47, 82, 95], Operations: [] Exploring Operation: 82-77=5, Resulting Numbers: [47, 95, 5] Generated Node #2: [47, 95, 5] from Operation: 82-77=5 Current State: 66:[47, 95, 5], Operations: ['82-77=5'] Exploring Operation: 95/5=19, Resulting Numbers: [47, 19] Generated Node #3: [47, 19] from Operation: 95/5=19 Current State: 66:[47, 19], Operations: ['82-77=5', '95/5=19'] Exploring Operation: 47+19=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[77, 47, 82, 95], Operations: [] Exploring Operation: 95-82=13, Resulting Numbers: [77, 47, 13] Generated Node #0,0: 66:[77, 47, 13] Operation: 95-82=13 Exploring Operation: 95-77=18, Resulting Numbers: [47, 82, 18] Generated Node #0,1: 66:[47, 82, 18] Operation: 95-77=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[77, 47, 13], Operations: ['95-82=13'] Exploring Operation: 77-47=30, Resulting Numbers: [13, 30] Generated Node #0,0,0: 66:[13, 30] Operation: 77-47=30 Exploring Operation: 47-13=34, Resulting Numbers: [77, 34] Generated Node #0,0,1: 66:[77, 34] Operation: 47-13=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 66:[13, 30], Operations: ['95-82=13', '77-47=30'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,66 unequal: No Solution Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 66:[77, 34], Operations: ['95-82=13', '47-13=34'] Exploring Operation: 77-34=43, Resulting Numbers: [43] 43,66 unequal: No Solution Exploring Operation: 77+34=111, Resulting Numbers: [111] 111,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[47, 82, 18], Operations: ['95-77=18'] Exploring Operation: 82-18=64, Resulting Numbers: [47, 64] Generated Node #0,1,0: 66:[47, 64] Operation: 82-18=64 Exploring Operation: 82-47=35, Resulting Numbers: [18, 35] Generated Node #0,1,1: 66:[18, 35] Operation: 82-47=35 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 66:[18, 35], Operations: ['95-77=18', '82-47=35'] Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,66 unequal: No Solution Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 66:[47, 64], Operations: ['95-77=18', '82-18=64'] Exploring Operation: 64-47=17, Resulting Numbers: [17] 17,66 unequal: No Solution Exploring Operation: 47+64=111, Resulting Numbers: [111] 111,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 61, 54, 61, 91 ]
38
[ "61/61=1", "91-54=37", "1+37=38" ]
Current State: 38:[61, 54, 61, 91], Operations: [] Exploring Operation: 61/61=1, Resulting Numbers: [54, 91, 1] Generated Node #2: [54, 91, 1] from Operation: 61/61=1 Current State: 38:[54, 91, 1], Operations: ['61/61=1'] Exploring Operation: 91-54=37, Resulting Numbers: [1, 37] Generated Node #3: [1, 37] from Operation: 91-54=37 Current State: 38:[1, 37], Operations: ['61/61=1', '91-54=37'] Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[61, 54, 61, 91], Operations: [] Exploring Operation: 91-61=30, Resulting Numbers: [54, 61, 30] Generated Node #0,0: 38:[54, 61, 30] Operation: 91-61=30 Moving to Node #0,0 Current State: 38:[54, 61, 30], Operations: ['91-61=30'] Exploring Operation: 61-54=7, Resulting Numbers: [30, 7] Generated Node #0,0,0: 38:[30, 7] Operation: 61-54=7 Moving to Node #0,0,0 Current State: 38:[30, 7], Operations: ['91-61=30', '61-54=7'] Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,38 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 19, 71, 65, 61 ]
94
[ "19+71=90", "65-61=4", "90+4=94" ]
Current State: 94:[19, 71, 65, 61], Operations: [] Exploring Operation: 19+71=90, Resulting Numbers: [65, 61, 90] Generated Node #2: [65, 61, 90] from Operation: 19+71=90 Current State: 94:[65, 61, 90], Operations: ['19+71=90'] Exploring Operation: 65-61=4, Resulting Numbers: [90, 4] Generated Node #3: [90, 4] from Operation: 65-61=4 Current State: 94:[90, 4], Operations: ['19+71=90', '65-61=4'] Exploring Operation: 90+4=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[19, 71, 65, 61], Operations: [] Exploring Operation: 71-65=6, Resulting Numbers: [19, 61, 6] Generated Node #0,0: 94:[19, 61, 6] Operation: 71-65=6 Exploring Operation: 65-19=46, Resulting Numbers: [71, 61, 46] Generated Node #0,1: 94:[71, 61, 46] Operation: 65-19=46 Exploring Operation: 19+71=90, Resulting Numbers: [65, 61, 90] Generated Node #0,2: 94:[65, 61, 90] Operation: 19+71=90 Exploring Operation: 71-19=52, Resulting Numbers: [65, 61, 52] Generated Node #0,3: 94:[65, 61, 52] Operation: 71-19=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[19, 61, 6], Operations: ['71-65=6'] Exploring Operation: 61-19=42, Resulting Numbers: [6, 42] Generated Node #0,0,0: 94:[6, 42] Operation: 61-19=42 Exploring Operation: 61-6=55, Resulting Numbers: [19, 55] Generated Node #0,0,1: 94:[19, 55] Operation: 61-6=55 Exploring Operation: 19+61=80, Resulting Numbers: [6, 80] Generated Node #0,0,2: 94:[6, 80] Operation: 19+61=80 Exploring Operation: 19-6=13, Resulting Numbers: [61, 13] Generated Node #0,0,3: 94:[61, 13] Operation: 19-6=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[6, 42], Operations: ['71-65=6', '61-19=42'] Exploring Operation: 6+42=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 6*42=252, Resulting Numbers: [252] 252,94 unequal: No Solution Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,94 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 94:[6, 80], Operations: ['71-65=6', '19+61=80'] Exploring Operation: 6+80=86, Resulting Numbers: [86] 86,94 unequal: No Solution Exploring Operation: 6*80=480, Resulting Numbers: [480] 480,94 unequal: No Solution Exploring Operation: 80-6=74, Resulting Numbers: [74] 74,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[19, 55], Operations: ['71-65=6', '61-6=55'] Exploring Operation: 19*55=1045, Resulting Numbers: [1045] 1045,94 unequal: No Solution Exploring Operation: 55-19=36, Resulting Numbers: [36] 36,94 unequal: No Solution Exploring Operation: 19+55=74, Resulting Numbers: [74] 74,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 94:[61, 13], Operations: ['71-65=6', '19-6=13'] Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,94 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[65, 61, 90], Operations: ['19+71=90'] Exploring Operation: 90-65=25, Resulting Numbers: [61, 25] Generated Node #0,2,0: 94:[61, 25] Operation: 90-65=25 Exploring Operation: 65-61=4, Resulting Numbers: [90, 4] Generated Node #0,2,1: 94:[90, 4] Operation: 65-61=4 Exploring Operation: 65+61=126, Resulting Numbers: [90, 126] Generated Node #0,2,2: 94:[90, 126] Operation: 65+61=126 Exploring Operation: 90-61=29, Resulting Numbers: [65, 29] Generated Node #0,2,3: 94:[65, 29] Operation: 90-61=29 Moving to Node #0,2,1 Current State: 94:[90, 4], Operations: ['19+71=90', '65-61=4'] Exploring Operation: 90*4=360, Resulting Numbers: [360] 360,94 unequal: No Solution Exploring Operation: 90+4=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[19, 71, 65, 61], Operations: [] Exploring Operation: 19+71=90, Resulting Numbers: [65, 61, 90] Generated Node #0,2: 94:[65, 61, 90] Operation: 19+71=90 Moving to Node #0,2 Current State: 94:[65, 61, 90], Operations: ['19+71=90'] Exploring Operation: 65-61=4, Resulting Numbers: [90, 4] Generated Node #0,2,1: 94:[90, 4] Operation: 65-61=4 Moving to Node #0,2,1 Current State: 94:[90, 4], Operations: ['19+71=90', '65-61=4'] Exploring Operation: 90+4=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic