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
[ 6, 50, 10, 53 ]
36
[ "53-50=3", "10*3=30", "6+30=36" ]
Current State: 36:[6, 50, 10, 53], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [6, 10, 3] Generated Node #2: [6, 10, 3] from Operation: 53-50=3 Current State: 36:[6, 10, 3], Operations: ['53-50=3'] Exploring Operation: 10*3=30, Resulting Numbers: [6, 30] Generated Node #3: [6, 30] from Operation: 10*3=30 Current State: 36:[6, 30], Operations: ['53-50=3', '10*3=30'] Exploring Operation: 6+30=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[6, 50, 10, 53], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [6, 10, 3] Generated Node #0,0: 36:[6, 10, 3] Operation: 53-50=3 Exploring Operation: 53-10=43, Resulting Numbers: [6, 50, 43] Generated Node #0,1: 36:[6, 50, 43] Operation: 53-10=43 Exploring Operation: 50-10=40, Resulting Numbers: [6, 53, 40] Generated Node #0,2: 36:[6, 53, 40] Operation: 50-10=40 Exploring Operation: 50/10=5, Resulting Numbers: [6, 53, 5] Generated Node #0,3: 36:[6, 53, 5] Operation: 50/10=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[6, 10, 3], Operations: ['53-50=3'] Exploring Operation: 6*3=18, Resulting Numbers: [10, 18] Generated Node #0,0,0: 36:[10, 18] Operation: 6*3=18 Exploring Operation: 6-3=3, Resulting Numbers: [10, 3] Generated Node #0,0,1: 36:[10, 3] Operation: 6-3=3 Exploring Operation: 10-6=4, Resulting Numbers: [3, 4] Generated Node #0,0,2: 36:[3, 4] Operation: 10-6=4 Exploring Operation: 6+3=9, Resulting Numbers: [10, 9] Generated Node #0,0,3: 36:[10, 9] Operation: 6+3=9 Moving to Node #0,0,2 Current State: 36:[3, 4], Operations: ['53-50=3', '10-6=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,36 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,36 unequal: No Solution Moving to Node #0,0,1 Current State: 36:[10, 3], Operations: ['53-50=3', '6-3=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,36 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,36 unequal: No Solution Moving to Node #0,0,0 Current State: 36:[10, 18], Operations: ['53-50=3', '6*3=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,36 unequal: No Solution Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,36 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,36 unequal: No Solution Moving to Node #0,0,3 Current State: 36:[10, 9], Operations: ['53-50=3', '6+3=9'] Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,36 unequal: No Solution Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,36 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,36 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: 36:[6, 53, 5], Operations: ['50/10=5'] Exploring Operation: 53-6=47, Resulting Numbers: [5, 47] Generated Node #0,3,0: 36:[5, 47] Operation: 53-6=47 Exploring Operation: 6+5=11, Resulting Numbers: [53, 11] Generated Node #0,3,1: 36:[53, 11] Operation: 6+5=11 Exploring Operation: 6-5=1, Resulting Numbers: [53, 1] Generated Node #0,3,2: 36:[53, 1] Operation: 6-5=1 Exploring Operation: 53-5=48, Resulting Numbers: [6, 48] Generated Node #0,3,3: 36:[6, 48] Operation: 53-5=48 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 36:[5, 47], Operations: ['50/10=5', '53-6=47'] Exploring Operation: 5*47=235, Resulting Numbers: [235] 235,36 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,36 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: 36:[6, 48], Operations: ['50/10=5', '53-5=48'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,36 unequal: No Solution Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,36 unequal: No Solution Exploring Operation: 6*48=288, Resulting Numbers: [288] 288,36 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: 36:[53, 11], Operations: ['50/10=5', '6+5=11'] Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 53*11=583, Resulting Numbers: [583] 583,36 unequal: No Solution Exploring Operation: 53+11=64, Resulting Numbers: [64] 64,36 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: 36:[53, 1], Operations: ['50/10=5', '6-5=1'] Exploring Operation: 53+1=54, Resulting Numbers: [54] 54,36 unequal: No Solution Exploring Operation: 53*1=53, Resulting Numbers: [53] 53,36 unequal: No Solution Exploring Operation: 53/1=53, Resulting Numbers: [53] 53,36 unequal: No Solution Exploring Operation: 53-1=52, Resulting Numbers: [52] 52,36 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: 36:[6, 50, 43], Operations: ['53-10=43'] Exploring Operation: 50-6=44, Resulting Numbers: [43, 44] Generated Node #0,1,0: 36:[43, 44] Operation: 50-6=44 Exploring Operation: 50-43=7, Resulting Numbers: [6, 7] Generated Node #0,1,1: 36:[6, 7] Operation: 50-43=7 Exploring Operation: 43-6=37, Resulting Numbers: [50, 37] Generated Node #0,1,2: 36:[50, 37] Operation: 43-6=37 Exploring Operation: 6+50=56, Resulting Numbers: [43, 56] Generated Node #0,1,3: 36:[43, 56] Operation: 6+50=56 Moving to Node #0,1,1 Current State: 36:[6, 7], Operations: ['53-10=43', '50-43=7'] Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,36 unequal: No Solution Moving to Node #0,1,2 Current State: 36:[50, 37], Operations: ['53-10=43', '43-6=37'] Exploring Operation: 50*37=1850, Resulting Numbers: [1850] 1850,36 unequal: No Solution Exploring Operation: 50-37=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 50+37=87, Resulting Numbers: [87] 87,36 unequal: No Solution Moving to Node #0,1,0 Current State: 36:[43, 44], Operations: ['53-10=43', '50-6=44'] Exploring Operation: 43+44=87, Resulting Numbers: [87] 87,36 unequal: No Solution Exploring Operation: 44-43=1, Resulting Numbers: [1] 1,36 unequal: No Solution Exploring Operation: 43*44=1892, Resulting Numbers: [1892] 1892,36 unequal: No Solution Moving to Node #0,1,3 Current State: 36:[43, 56], Operations: ['53-10=43', '6+50=56'] Exploring Operation: 43*56=2408, Resulting Numbers: [2408] 2408,36 unequal: No Solution Exploring Operation: 43+56=99, Resulting Numbers: [99] 99,36 unequal: No Solution Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,36 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: 36:[6, 53, 40], Operations: ['50-10=40'] Exploring Operation: 40-6=34, Resulting Numbers: [53, 34] Generated Node #0,2,0: 36:[53, 34] Operation: 40-6=34 Exploring Operation: 53-40=13, Resulting Numbers: [6, 13] Generated Node #0,2,1: 36:[6, 13] Operation: 53-40=13 Exploring Operation: 6+53=59, Resulting Numbers: [40, 59] Generated Node #0,2,2: 36:[40, 59] Operation: 6+53=59 Exploring Operation: 53-6=47, Resulting Numbers: [40, 47] Generated Node #0,2,3: 36:[40, 47] Operation: 53-6=47 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 36:[6, 13], Operations: ['50-10=40', '53-40=13'] Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,36 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,36 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: 36:[40, 47], Operations: ['50-10=40', '53-6=47'] Exploring Operation: 40*47=1880, Resulting Numbers: [1880] 1880,36 unequal: No Solution Exploring Operation: 40+47=87, Resulting Numbers: [87] 87,36 unequal: No Solution Exploring Operation: 47-40=7, Resulting Numbers: [7] 7,36 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: 36:[53, 34], Operations: ['50-10=40', '40-6=34'] Exploring Operation: 53*34=1802, Resulting Numbers: [1802] 1802,36 unequal: No Solution Exploring Operation: 53-34=19, Resulting Numbers: [19] 19,36 unequal: No Solution Exploring Operation: 53+34=87, Resulting Numbers: [87] 87,36 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: 36:[40, 59], Operations: ['50-10=40', '6+53=59'] Exploring Operation: 40+59=99, Resulting Numbers: [99] 99,36 unequal: No Solution Exploring Operation: 40*59=2360, Resulting Numbers: [2360] 2360,36 unequal: No Solution Exploring Operation: 59-40=19, Resulting Numbers: [19] 19,36 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, 70, 74, 12 ]
17
[ "80-12=68", "74-70=4", "68/4=17" ]
Current State: 17:[80, 70, 74, 12], Operations: [] Exploring Operation: 80-12=68, Resulting Numbers: [70, 74, 68] Generated Node #2: [70, 74, 68] from Operation: 80-12=68 Current State: 17:[70, 74, 68], Operations: ['80-12=68'] Exploring Operation: 74-70=4, Resulting Numbers: [68, 4] Generated Node #3: [68, 4] from Operation: 74-70=4 Current State: 17:[68, 4], Operations: ['80-12=68', '74-70=4'] Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[80, 70, 74, 12], Operations: [] Exploring Operation: 80-74=6, Resulting Numbers: [70, 12, 6] Generated Node #0,0: 17:[70, 12, 6] Operation: 80-74=6 Exploring Operation: 80-70=10, Resulting Numbers: [74, 12, 10] Generated Node #0,1: 17:[74, 12, 10] Operation: 80-70=10 Exploring Operation: 74-70=4, Resulting Numbers: [80, 12, 4] Generated Node #0,2: 17:[80, 12, 4] Operation: 74-70=4 Moving to Node #0,0 Current State: 17:[70, 12, 6], Operations: ['80-74=6'] Exploring Operation: 70-12=58, Resulting Numbers: [6, 58] Generated Node #0,0,0: 17:[6, 58] Operation: 70-12=58 Exploring Operation: 12+6=18, Resulting Numbers: [70, 18] Generated Node #0,0,1: 17:[70, 18] Operation: 12+6=18 Exploring Operation: 70-6=64, Resulting Numbers: [12, 64] Generated Node #0,0,2: 17:[12, 64] Operation: 70-6=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 17:[6, 58], Operations: ['80-74=6', '70-12=58'] Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 6*58=348, Resulting Numbers: [348] 348,17 unequal: No Solution Exploring Operation: 6+58=64, Resulting Numbers: [64] 64,17 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: 17:[12, 64], Operations: ['80-74=6', '70-6=64'] Exploring Operation: 12+64=76, Resulting Numbers: [76] 76,17 unequal: No Solution Exploring Operation: 64-12=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 12*64=768, Resulting Numbers: [768] 768,17 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: 17:[70, 18], Operations: ['80-74=6', '12+6=18'] Exploring Operation: 70+18=88, Resulting Numbers: [88] 88,17 unequal: No Solution Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 70*18=1260, Resulting Numbers: [1260] 1260,17 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: 17:[74, 12, 10], Operations: ['80-70=10'] Exploring Operation: 74-10=64, Resulting Numbers: [12, 64] Generated Node #0,1,0: 17:[12, 64] Operation: 74-10=64 Exploring Operation: 74-12=62, Resulting Numbers: [10, 62] Generated Node #0,1,1: 17:[10, 62] Operation: 74-12=62 Exploring Operation: 12+10=22, Resulting Numbers: [74, 22] Generated Node #0,1,2: 17:[74, 22] Operation: 12+10=22 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 17:[12, 64], Operations: ['80-70=10', '74-10=64'] Exploring Operation: 64-12=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 12*64=768, Resulting Numbers: [768] 768,17 unequal: No Solution Exploring Operation: 12+64=76, Resulting Numbers: [76] 76,17 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: 17:[10, 62], Operations: ['80-70=10', '74-12=62'] Exploring Operation: 10*62=620, Resulting Numbers: [620] 620,17 unequal: No Solution Exploring Operation: 10+62=72, Resulting Numbers: [72] 72,17 unequal: No Solution Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,17 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: 17:[74, 22], Operations: ['80-70=10', '12+10=22'] Exploring Operation: 74*22=1628, Resulting Numbers: [1628] 1628,17 unequal: No Solution Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 74+22=96, Resulting Numbers: [96] 96,17 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: 17:[80, 12, 4], Operations: ['74-70=4'] Exploring Operation: 80-12=68, Resulting Numbers: [4, 68] Generated Node #0,2,0: 17:[4, 68] Operation: 80-12=68 Exploring Operation: 80/4=20, Resulting Numbers: [12, 20] Generated Node #0,2,1: 17:[12, 20] Operation: 80/4=20 Exploring Operation: 80-4=76, Resulting Numbers: [12, 76] Generated Node #0,2,2: 17:[12, 76] Operation: 80-4=76 Moving to Node #0,2,1 Current State: 17:[12, 20], Operations: ['74-70=4', '80/4=20'] Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 12+20=32, Resulting Numbers: [32] 32,17 unequal: No Solution Exploring Operation: 12*20=240, Resulting Numbers: [240] 240,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[4, 68], Operations: ['74-70=4', '80-12=68'] Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,17 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[80, 70, 74, 12], Operations: [] Exploring Operation: 74-70=4, Resulting Numbers: [80, 12, 4] Generated Node #0,2: 17:[80, 12, 4] Operation: 74-70=4 Moving to Node #0,2 Current State: 17:[80, 12, 4], Operations: ['74-70=4'] Exploring Operation: 80-12=68, Resulting Numbers: [4, 68] Generated Node #0,2,0: 17:[4, 68] Operation: 80-12=68 Moving to Node #0,2,0 Current State: 17:[4, 68], Operations: ['74-70=4', '80-12=68'] Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
0.966146
hs_3
sum_heuristic
[ 59, 90, 21, 7 ]
70
[ "90-59=31", "31-21=10", "7*10=70" ]
Current State: 70:[59, 90, 21, 7], Operations: [] Exploring Operation: 90-59=31, Resulting Numbers: [21, 7, 31] Generated Node #2: [21, 7, 31] from Operation: 90-59=31 Current State: 70:[21, 7, 31], Operations: ['90-59=31'] Exploring Operation: 31-21=10, Resulting Numbers: [7, 10] Generated Node #3: [7, 10] from Operation: 31-21=10 Current State: 70:[7, 10], Operations: ['90-59=31', '31-21=10'] Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[59, 90, 21, 7], Operations: [] Exploring Operation: 90-59=31, Resulting Numbers: [21, 7, 31] Generated Node #0,0: 70:[21, 7, 31] Operation: 90-59=31 Exploring Operation: 90-21=69, Resulting Numbers: [59, 7, 69] Generated Node #0,1: 70:[59, 7, 69] Operation: 90-21=69 Exploring Operation: 59+21=80, Resulting Numbers: [90, 7, 80] Generated Node #0,2: 70:[90, 7, 80] Operation: 59+21=80 Exploring Operation: 59+7=66, Resulting Numbers: [90, 21, 66] Generated Node #0,3: 70:[90, 21, 66] Operation: 59+7=66 Exploring Operation: 59-21=38, Resulting Numbers: [90, 7, 38] Generated Node #0,4: 70:[90, 7, 38] Operation: 59-21=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[21, 7, 31], Operations: ['90-59=31'] Exploring Operation: 21+7=28, Resulting Numbers: [31, 28] Generated Node #0,0,0: 70:[31, 28] Operation: 21+7=28 Exploring Operation: 21/7=3, Resulting Numbers: [31, 3] Generated Node #0,0,1: 70:[31, 3] Operation: 21/7=3 Exploring Operation: 31-21=10, Resulting Numbers: [7, 10] Generated Node #0,0,2: 70:[7, 10] Operation: 31-21=10 Exploring Operation: 21-7=14, Resulting Numbers: [31, 14] Generated Node #0,0,3: 70:[31, 14] Operation: 21-7=14 Exploring Operation: 7+31=38, Resulting Numbers: [21, 38] Generated Node #0,0,4: 70:[21, 38] Operation: 7+31=38 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 70:[7, 10], Operations: ['90-59=31', '31-21=10'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,70 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,70 unequal: No Solution Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[59, 90, 21, 7], Operations: [] Exploring Operation: 90-59=31, Resulting Numbers: [21, 7, 31] Generated Node #0,0: 70:[21, 7, 31] Operation: 90-59=31 Moving to Node #0,0 Current State: 70:[21, 7, 31], Operations: ['90-59=31'] Exploring Operation: 31-21=10, Resulting Numbers: [7, 10] Generated Node #0,0,2: 70:[7, 10] Operation: 31-21=10 Moving to Node #0,0,2 Current State: 70:[7, 10], Operations: ['90-59=31', '31-21=10'] Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 57, 37, 64, 68 ]
16
[ "57-37=20", "68-64=4", "20-4=16" ]
Current State: 16:[57, 37, 64, 68], Operations: [] Exploring Operation: 57-37=20, Resulting Numbers: [64, 68, 20] Generated Node #2: [64, 68, 20] from Operation: 57-37=20 Current State: 16:[64, 68, 20], Operations: ['57-37=20'] Exploring Operation: 68-64=4, Resulting Numbers: [20, 4] Generated Node #3: [20, 4] from Operation: 68-64=4 Current State: 16:[20, 4], Operations: ['57-37=20', '68-64=4'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[57, 37, 64, 68], Operations: [] Exploring Operation: 68-64=4, Resulting Numbers: [57, 37, 4] Generated Node #0,0: 16:[57, 37, 4] Operation: 68-64=4 Exploring Operation: 64-57=7, Resulting Numbers: [37, 68, 7] Generated Node #0,1: 16:[37, 68, 7] Operation: 64-57=7 Exploring Operation: 68-57=11, Resulting Numbers: [37, 64, 11] Generated Node #0,2: 16:[37, 64, 11] Operation: 68-57=11 Exploring Operation: 57-37=20, Resulting Numbers: [64, 68, 20] Generated Node #0,3: 16:[64, 68, 20] Operation: 57-37=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[57, 37, 4], Operations: ['68-64=4'] Exploring Operation: 57+4=61, Resulting Numbers: [37, 61] Generated Node #0,0,0: 16:[37, 61] Operation: 57+4=61 Exploring Operation: 57-4=53, Resulting Numbers: [37, 53] Generated Node #0,0,1: 16:[37, 53] Operation: 57-4=53 Exploring Operation: 37-4=33, Resulting Numbers: [57, 33] Generated Node #0,0,2: 16:[57, 33] Operation: 37-4=33 Exploring Operation: 57-37=20, Resulting Numbers: [4, 20] Generated Node #0,0,3: 16:[4, 20] Operation: 57-37=20 Moving to Node #0,0,3 Current State: 16:[4, 20], Operations: ['68-64=4', '57-37=20'] Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,16 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[57, 37, 64, 68], Operations: [] Exploring Operation: 68-64=4, Resulting Numbers: [57, 37, 4] Generated Node #0,0: 16:[57, 37, 4] Operation: 68-64=4 Moving to Node #0,0 Current State: 16:[57, 37, 4], Operations: ['68-64=4'] Exploring Operation: 57-37=20, Resulting Numbers: [4, 20] Generated Node #0,0,3: 16:[4, 20] Operation: 57-37=20 Moving to Node #0,0,3 Current State: 16:[4, 20], Operations: ['68-64=4', '57-37=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 32, 99, 12, 98 ]
19
[ "99-32=67", "98-12=86", "86-67=19" ]
Current State: 19:[32, 99, 12, 98], Operations: [] Exploring Operation: 99-32=67, Resulting Numbers: [12, 98, 67] Generated Node #2: [12, 98, 67] from Operation: 99-32=67 Current State: 19:[12, 98, 67], Operations: ['99-32=67'] Exploring Operation: 98-12=86, Resulting Numbers: [67, 86] Generated Node #3: [67, 86] from Operation: 98-12=86 Current State: 19:[67, 86], Operations: ['99-32=67', '98-12=86'] Exploring Operation: 86-67=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[32, 99, 12, 98], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [32, 12, 1] Generated Node #0,0: 19:[32, 12, 1] Operation: 99-98=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[32, 12, 1], Operations: ['99-98=1'] Exploring Operation: 32-12=20, Resulting Numbers: [1, 20] Generated Node #0,0,0: 19:[1, 20] Operation: 32-12=20 Moving to Node #0,0,0 Current State: 19:[1, 20], Operations: ['99-98=1', '32-12=20'] Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[32, 99, 12, 98], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [32, 12, 1] Generated Node #0,0: 19:[32, 12, 1] Operation: 99-98=1 Moving to Node #0,0 Current State: 19:[32, 12, 1], Operations: ['99-98=1'] Exploring Operation: 32-12=20, Resulting Numbers: [1, 20] Generated Node #0,0,0: 19:[1, 20] Operation: 32-12=20 Moving to Node #0,0,0 Current State: 19:[1, 20], Operations: ['99-98=1', '32-12=20'] Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 58, 12, 47, 60 ]
33
[ "58-12=46", "60-47=13", "46-13=33" ]
Current State: 33:[58, 12, 47, 60], Operations: [] Exploring Operation: 58-12=46, Resulting Numbers: [47, 60, 46] Generated Node #2: [47, 60, 46] from Operation: 58-12=46 Current State: 33:[47, 60, 46], Operations: ['58-12=46'] Exploring Operation: 60-47=13, Resulting Numbers: [46, 13] Generated Node #3: [46, 13] from Operation: 60-47=13 Current State: 33:[46, 13], Operations: ['58-12=46', '60-47=13'] Exploring Operation: 46-13=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[58, 12, 47, 60], Operations: [] Exploring Operation: 60/12=5, Resulting Numbers: [58, 47, 5] Generated Node #0,0: 33:[58, 47, 5] Operation: 60/12=5 Exploring Operation: 58-47=11, Resulting Numbers: [12, 60, 11] Generated Node #0,1: 33:[12, 60, 11] Operation: 58-47=11 Exploring Operation: 60-47=13, Resulting Numbers: [58, 12, 13] Generated Node #0,2: 33:[58, 12, 13] Operation: 60-47=13 Exploring Operation: 60-58=2, Resulting Numbers: [12, 47, 2] Generated Node #0,3: 33:[12, 47, 2] Operation: 60-58=2 Exploring Operation: 58-12=46, Resulting Numbers: [47, 60, 46] Generated Node #0,4: 33:[47, 60, 46] Operation: 58-12=46 Moving to Node #0,3 Current State: 33:[12, 47, 2], Operations: ['60-58=2'] Exploring Operation: 12+2=14, Resulting Numbers: [47, 14] Generated Node #0,3,0: 33:[47, 14] Operation: 12+2=14 Exploring Operation: 47-12=35, Resulting Numbers: [2, 35] Generated Node #0,3,1: 33:[2, 35] Operation: 47-12=35 Exploring Operation: 12/2=6, Resulting Numbers: [47, 6] Generated Node #0,3,2: 33:[47, 6] Operation: 12/2=6 Exploring Operation: 47-2=45, Resulting Numbers: [12, 45] Generated Node #0,3,3: 33:[12, 45] Operation: 47-2=45 Exploring Operation: 12-2=10, Resulting Numbers: [47, 10] Generated Node #0,3,4: 33:[47, 10] Operation: 12-2=10 Moving to Node #0,2 Current State: 33:[58, 12, 13], Operations: ['60-47=13'] Exploring Operation: 12+13=25, Resulting Numbers: [58, 25] Generated Node #0,2,0: 33:[58, 25] Operation: 12+13=25 Exploring Operation: 58+12=70, Resulting Numbers: [13, 70] Generated Node #0,2,1: 33:[13, 70] Operation: 58+12=70 Exploring Operation: 58-12=46, Resulting Numbers: [13, 46] Generated Node #0,2,2: 33:[13, 46] Operation: 58-12=46 Exploring Operation: 13-12=1, Resulting Numbers: [58, 1] Generated Node #0,2,3: 33:[58, 1] Operation: 13-12=1 Exploring Operation: 58-13=45, Resulting Numbers: [12, 45] Generated Node #0,2,4: 33:[12, 45] Operation: 58-13=45 Moving to Node #0,1 Current State: 33:[12, 60, 11], Operations: ['58-47=11'] Exploring Operation: 12+11=23, Resulting Numbers: [60, 23] Generated Node #0,1,0: 33:[60, 23] Operation: 12+11=23 Exploring Operation: 60-11=49, Resulting Numbers: [12, 49] Generated Node #0,1,1: 33:[12, 49] Operation: 60-11=49 Exploring Operation: 60/12=5, Resulting Numbers: [11, 5] Generated Node #0,1,2: 33:[11, 5] Operation: 60/12=5 Exploring Operation: 12-11=1, Resulting Numbers: [60, 1] Generated Node #0,1,3: 33:[60, 1] Operation: 12-11=1 Exploring Operation: 60-12=48, Resulting Numbers: [11, 48] Generated Node #0,1,4: 33:[11, 48] Operation: 60-12=48 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 33:[11, 5], Operations: ['58-47=11', '60/12=5'] Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,33 unequal: No Solution Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,33 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: 33:[11, 48], Operations: ['58-47=11', '60-12=48'] Exploring Operation: 48-11=37, Resulting Numbers: [37] 37,33 unequal: No Solution Exploring Operation: 11+48=59, Resulting Numbers: [59] 59,33 unequal: No Solution Exploring Operation: 11*48=528, Resulting Numbers: [528] 528,33 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: 33:[12, 49], Operations: ['58-47=11', '60-11=49'] Exploring Operation: 49-12=37, Resulting Numbers: [37] 37,33 unequal: No Solution Exploring Operation: 12+49=61, Resulting Numbers: [61] 61,33 unequal: No Solution Exploring Operation: 12*49=588, Resulting Numbers: [588] 588,33 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: 33:[60, 1], Operations: ['58-47=11', '12-11=1'] Exploring Operation: 60+1=61, Resulting Numbers: [61] 61,33 unequal: No Solution Exploring Operation: 60-1=59, Resulting Numbers: [59] 59,33 unequal: No Solution Exploring Operation: 60*1=60, Resulting Numbers: [60] 60,33 unequal: No Solution Exploring Operation: 60/1=60, Resulting Numbers: [60] 60,33 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: 33:[60, 23], Operations: ['58-47=11', '12+11=23'] Exploring Operation: 60+23=83, Resulting Numbers: [83] 83,33 unequal: No Solution Exploring Operation: 60*23=1380, Resulting Numbers: [1380] 1380,33 unequal: No Solution Exploring Operation: 60-23=37, Resulting Numbers: [37] 37,33 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: 33:[58, 47, 5], Operations: ['60/12=5'] Exploring Operation: 47+5=52, Resulting Numbers: [58, 52] Generated Node #0,0,0: 33:[58, 52] Operation: 47+5=52 Exploring Operation: 58-47=11, Resulting Numbers: [5, 11] Generated Node #0,0,1: 33:[5, 11] Operation: 58-47=11 Exploring Operation: 58-5=53, Resulting Numbers: [47, 53] Generated Node #0,0,2: 33:[47, 53] Operation: 58-5=53 Exploring Operation: 47-5=42, Resulting Numbers: [58, 42] Generated Node #0,0,3: 33:[58, 42] Operation: 47-5=42 Exploring Operation: 58+5=63, Resulting Numbers: [47, 63] Generated Node #0,0,4: 33:[47, 63] Operation: 58+5=63 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 33:[5, 11], Operations: ['60/12=5', '58-47=11'] Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,33 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,33 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: 33:[47, 53], Operations: ['60/12=5', '58-5=53'] Exploring Operation: 47+53=100, Resulting Numbers: [100] 100,33 unequal: No Solution Exploring Operation: 47*53=2491, Resulting Numbers: [2491] 2491,33 unequal: No Solution Exploring Operation: 53-47=6, Resulting Numbers: [6] 6,33 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: 33:[58, 42], Operations: ['60/12=5', '47-5=42'] Exploring Operation: 58+42=100, Resulting Numbers: [100] 100,33 unequal: No Solution Exploring Operation: 58*42=2436, Resulting Numbers: [2436] 2436,33 unequal: No Solution Exploring Operation: 58-42=16, Resulting Numbers: [16] 16,33 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: 33:[58, 52], Operations: ['60/12=5', '47+5=52'] Exploring Operation: 58+52=110, Resulting Numbers: [110] 110,33 unequal: No Solution Exploring Operation: 58-52=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 58*52=3016, Resulting Numbers: [3016] 3016,33 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: 33:[47, 63], Operations: ['60/12=5', '58+5=63'] Exploring Operation: 47+63=110, Resulting Numbers: [110] 110,33 unequal: No Solution Exploring Operation: 47*63=2961, Resulting Numbers: [2961] 2961,33 unequal: No Solution Exploring Operation: 63-47=16, Resulting Numbers: [16] 16,33 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: 33:[47, 60, 46], Operations: ['58-12=46'] Exploring Operation: 47+46=93, Resulting Numbers: [60, 93] Generated Node #0,4,0: 33:[60, 93] Operation: 47+46=93 Exploring Operation: 60-46=14, Resulting Numbers: [47, 14] Generated Node #0,4,1: 33:[47, 14] Operation: 60-46=14 Exploring Operation: 47+60=107, Resulting Numbers: [46, 107] Generated Node #0,4,2: 33:[46, 107] Operation: 47+60=107 Exploring Operation: 47-46=1, Resulting Numbers: [60, 1] Generated Node #0,4,3: 33:[60, 1] Operation: 47-46=1 Exploring Operation: 60-47=13, Resulting Numbers: [46, 13] Generated Node #0,4,4: 33:[46, 13] Operation: 60-47=13 Moving to Node #0,3,1 Current State: 33:[2, 35], Operations: ['60-58=2', '47-12=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,33 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,33 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[58, 12, 47, 60], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [12, 47, 2] Generated Node #0,3: 33:[12, 47, 2] Operation: 60-58=2 Moving to Node #0,3 Current State: 33:[12, 47, 2], Operations: ['60-58=2'] Exploring Operation: 47-12=35, Resulting Numbers: [2, 35] Generated Node #0,3,1: 33:[2, 35] Operation: 47-12=35 Moving to Node #0,3,1 Current State: 33:[2, 35], Operations: ['60-58=2', '47-12=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
0.940972
hs_5
sum_heuristic
[ 83, 83, 26, 90 ]
99
[ "90-83=7", "26*7=182", "182-83=99" ]
Current State: 99:[83, 83, 26, 90], Operations: [] Exploring Operation: 90-83=7, Resulting Numbers: [26, 7] Generated Node #2: [26, 7] from Operation: 90-83=7 Current State: 99:[26, 7], Operations: ['90-83=7'] Exploring Operation: 26*7=182, Resulting Numbers: [182] 182,99 equal: Goal Reached Exploring Operation: 182-83=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[83, 83, 26, 90], Operations: [] Exploring Operation: 83/83=1, Resulting Numbers: [26, 90, 1] Generated Node #0,0: 99:[26, 90, 1] Operation: 83/83=1 Moving to Node #0,0 Current State: 99:[26, 90, 1], Operations: ['83/83=1'] Exploring Operation: 26+1=27, Resulting Numbers: [90, 27] Generated Node #0,0,0: 99:[90, 27] Operation: 26+1=27 Moving to Node #0,0,0 Current State: 99:[90, 27], Operations: ['83/83=1', '26+1=27'] Exploring Operation: 90+27=117, Resulting Numbers: [117] 117,99 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 21, 38, 83, 45 ]
55
[ "38-21=17", "83-45=38", "17+38=55" ]
Current State: 55:[21, 38, 83, 45], Operations: [] Exploring Operation: 38-21=17, Resulting Numbers: [83, 45, 17] Generated Node #2: [83, 45, 17] from Operation: 38-21=17 Current State: 55:[83, 45, 17], Operations: ['38-21=17'] Exploring Operation: 83-45=38, Resulting Numbers: [17, 38] Generated Node #3: [17, 38] from Operation: 83-45=38 Current State: 55:[17, 38], Operations: ['38-21=17', '83-45=38'] Exploring Operation: 17+38=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[21, 38, 83, 45], Operations: [] Exploring Operation: 83-38=45, Resulting Numbers: [21, 45, 45] Generated Node #0,0: 55:[21, 45, 45] Operation: 83-38=45 Exploring Operation: 83-21=62, Resulting Numbers: [38, 45, 62] Generated Node #0,1: 55:[38, 45, 62] Operation: 83-21=62 Moving to Node #0,0 Current State: 55:[21, 45, 45], Operations: ['83-38=45'] Exploring Operation: 45/45=1, Resulting Numbers: [21, 1] Generated Node #0,0,0: 55:[21, 1] Operation: 45/45=1 Exploring Operation: 45-45=0, Resulting Numbers: [21, 0] Generated Node #0,0,1: 55:[21, 0] Operation: 45-45=0 Moving to Node #0,1 Current State: 55:[38, 45, 62], Operations: ['83-21=62'] Exploring Operation: 62-38=24, Resulting Numbers: [45, 24] Generated Node #0,1,0: 55:[45, 24] Operation: 62-38=24 Exploring Operation: 45-38=7, Resulting Numbers: [62, 7] Generated Node #0,1,1: 55:[62, 7] Operation: 45-38=7 Moving to Node #0,1,1 Current State: 55:[62, 7], Operations: ['83-21=62', '45-38=7'] Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[21, 38, 83, 45], Operations: [] Exploring Operation: 83-21=62, Resulting Numbers: [38, 45, 62] Generated Node #0,1: 55:[38, 45, 62] Operation: 83-21=62 Moving to Node #0,1 Current State: 55:[38, 45, 62], Operations: ['83-21=62'] Exploring Operation: 45-38=7, Resulting Numbers: [62, 7] Generated Node #0,1,1: 55:[62, 7] Operation: 45-38=7 Moving to Node #0,1,1 Current State: 55:[62, 7], Operations: ['83-21=62', '45-38=7'] Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 59, 90, 77, 70 ]
97
[ "70-59=11", "77/11=7", "90+7=97" ]
Current State: 97:[59, 90, 77, 70], Operations: [] Exploring Operation: 70-59=11, Resulting Numbers: [90, 77, 11] Generated Node #2: [90, 77, 11] from Operation: 70-59=11 Current State: 97:[90, 77, 11], Operations: ['70-59=11'] Exploring Operation: 77/11=7, Resulting Numbers: [90, 7] Generated Node #3: [90, 7] from Operation: 77/11=7 Current State: 97:[90, 7], Operations: ['70-59=11', '77/11=7'] Exploring Operation: 90+7=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[59, 90, 77, 70], Operations: [] Exploring Operation: 59+70=129, Resulting Numbers: [90, 77, 129] Generated Node #0,0: 97:[90, 77, 129] Operation: 59+70=129 Exploring Operation: 77+70=147, Resulting Numbers: [59, 90, 147] Generated Node #0,1: 97:[59, 90, 147] Operation: 77+70=147 Exploring Operation: 59+77=136, Resulting Numbers: [90, 70, 136] Generated Node #0,2: 97:[90, 70, 136] Operation: 59+77=136 Moving to Node #0,0 Current State: 97:[90, 77, 129], Operations: ['59+70=129'] Exploring Operation: 129-90=39, Resulting Numbers: [77, 39] Generated Node #0,0,0: 97:[77, 39] Operation: 129-90=39 Exploring Operation: 90+77=167, Resulting Numbers: [129, 167] Generated Node #0,0,1: 97:[129, 167] Operation: 90+77=167 Exploring Operation: 129-77=52, Resulting Numbers: [90, 52] Generated Node #0,0,2: 97:[90, 52] Operation: 129-77=52 Moving to Node #0,2 Current State: 97:[90, 70, 136], Operations: ['59+77=136'] Exploring Operation: 136-70=66, Resulting Numbers: [90, 66] Generated Node #0,2,0: 97:[90, 66] Operation: 136-70=66 Exploring Operation: 90+70=160, Resulting Numbers: [136, 160] Generated Node #0,2,1: 97:[136, 160] Operation: 90+70=160 Exploring Operation: 136-90=46, Resulting Numbers: [70, 46] Generated Node #0,2,2: 97:[70, 46] Operation: 136-90=46 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[90, 66], Operations: ['59+77=136', '136-70=66'] Exploring Operation: 90-66=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 90+66=156, Resulting Numbers: [156] 156,97 unequal: No Solution Exploring Operation: 90*66=5940, Resulting Numbers: [5940] 5940,97 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: 97:[70, 46], Operations: ['59+77=136', '136-90=46'] Exploring Operation: 70-46=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 70+46=116, Resulting Numbers: [116] 116,97 unequal: No Solution Exploring Operation: 70*46=3220, Resulting Numbers: [3220] 3220,97 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: 97:[136, 160], Operations: ['59+77=136', '90+70=160'] Exploring Operation: 136+160=296, Resulting Numbers: [296] 296,97 unequal: No Solution Exploring Operation: 160-136=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 136*160=21760, Resulting Numbers: [21760] 21760,97 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: 97:[59, 90, 147], Operations: ['77+70=147'] Exploring Operation: 147-90=57, Resulting Numbers: [59, 57] Generated Node #0,1,0: 97:[59, 57] Operation: 147-90=57 Exploring Operation: 59+90=149, Resulting Numbers: [147, 149] Generated Node #0,1,1: 97:[147, 149] Operation: 59+90=149 Exploring Operation: 147-59=88, Resulting Numbers: [90, 88] Generated Node #0,1,2: 97:[90, 88] Operation: 147-59=88 Moving to Node #0,1,2 Current State: 97:[90, 88], Operations: ['77+70=147', '147-59=88'] Exploring Operation: 90*88=7920, Resulting Numbers: [7920] 7920,97 unequal: No Solution Exploring Operation: 90-88=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 90+88=178, Resulting Numbers: [178] 178,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[90, 52], Operations: ['59+70=129', '129-77=52'] Exploring Operation: 90-52=38, Resulting Numbers: [38] 38,97 unequal: No Solution Exploring Operation: 90+52=142, Resulting Numbers: [142] 142,97 unequal: No Solution Exploring Operation: 90*52=4680, Resulting Numbers: [4680] 4680,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[59, 57], Operations: ['77+70=147', '147-90=57'] Exploring Operation: 59-57=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 59*57=3363, Resulting Numbers: [3363] 3363,97 unequal: No Solution Exploring Operation: 59+57=116, Resulting Numbers: [116] 116,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[77, 39], Operations: ['59+70=129', '129-90=39'] Exploring Operation: 77*39=3003, Resulting Numbers: [3003] 3003,97 unequal: No Solution Exploring Operation: 77+39=116, Resulting Numbers: [116] 116,97 unequal: No Solution Exploring Operation: 77-39=38, Resulting Numbers: [38] 38,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[147, 149], Operations: ['77+70=147', '59+90=149'] Exploring Operation: 147*149=21903, Resulting Numbers: [21903] 21903,97 unequal: No Solution Exploring Operation: 149-147=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 147+149=296, Resulting Numbers: [296] 296,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[129, 167], Operations: ['59+70=129', '90+77=167'] Exploring Operation: 129+167=296, Resulting Numbers: [296] 296,97 unequal: No Solution Exploring Operation: 129*167=21543, Resulting Numbers: [21543] 21543,97 unequal: No Solution Exploring Operation: 167-129=38, Resulting Numbers: [38] 38,97 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 4, 47, 97, 16 ]
80
[ "4*16=64", "47+97=144", "144-64=80" ]
Current State: 80:[4, 47, 97, 16], Operations: [] Exploring Operation: 4*16=64, Resulting Numbers: [47, 97, 64] Generated Node #2: [47, 97, 64] from Operation: 4*16=64 Current State: 80:[47, 97, 64], Operations: ['4*16=64'] Exploring Operation: 47+97=144, Resulting Numbers: [64, 144] Generated Node #3: [64, 144] from Operation: 47+97=144 Current State: 80:[64, 144], Operations: ['4*16=64', '47+97=144'] Exploring Operation: 144-64=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[4, 47, 97, 16], Operations: [] Exploring Operation: 47-4=43, Resulting Numbers: [97, 16, 43] Generated Node #0,0: 80:[97, 16, 43] Operation: 47-4=43 Exploring Operation: 97-16=81, Resulting Numbers: [4, 47, 81] Generated Node #0,1: 80:[4, 47, 81] Operation: 97-16=81 Exploring Operation: 97-4=93, Resulting Numbers: [47, 16, 93] Generated Node #0,2: 80:[47, 16, 93] Operation: 97-4=93 Exploring Operation: 97-47=50, Resulting Numbers: [4, 16, 50] Generated Node #0,3: 80:[4, 16, 50] Operation: 97-47=50 Moving to Node #0,1 Current State: 80:[4, 47, 81], Operations: ['97-16=81'] Exploring Operation: 81-47=34, Resulting Numbers: [4, 34] Generated Node #0,1,0: 80:[4, 34] Operation: 81-47=34 Exploring Operation: 47-4=43, Resulting Numbers: [81, 43] Generated Node #0,1,1: 80:[81, 43] Operation: 47-4=43 Exploring Operation: 81-4=77, Resulting Numbers: [47, 77] Generated Node #0,1,2: 80:[47, 77] Operation: 81-4=77 Exploring Operation: 4+47=51, Resulting Numbers: [81, 51] Generated Node #0,1,3: 80:[81, 51] Operation: 4+47=51 Moving to Node #0,3 Current State: 80:[4, 16, 50], Operations: ['97-47=50'] Exploring Operation: 4+16=20, Resulting Numbers: [50, 20] Generated Node #0,3,0: 80:[50, 20] Operation: 4+16=20 Exploring Operation: 50-16=34, Resulting Numbers: [4, 34] Generated Node #0,3,1: 80:[4, 34] Operation: 50-16=34 Exploring Operation: 50-4=46, Resulting Numbers: [16, 46] Generated Node #0,3,2: 80:[16, 46] Operation: 50-4=46 Exploring Operation: 16/4=4, Resulting Numbers: [50, 4] Generated Node #0,3,3: 80:[50, 4] Operation: 16/4=4 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 80:[4, 34], Operations: ['97-47=50', '50-16=34'] Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,80 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,80 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,80 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: 80:[16, 46], Operations: ['97-47=50', '50-4=46'] Exploring Operation: 16*46=736, Resulting Numbers: [736] 736,80 unequal: No Solution Exploring Operation: 16+46=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,80 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: 80:[50, 20], Operations: ['97-47=50', '4+16=20'] Exploring Operation: 50-20=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 50*20=1000, Resulting Numbers: [1000] 1000,80 unequal: No Solution Exploring Operation: 50+20=70, Resulting Numbers: [70] 70,80 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: 80:[50, 4], Operations: ['97-47=50', '16/4=4'] Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,80 unequal: No Solution Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,80 unequal: No Solution Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,80 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: 80:[47, 16, 93], Operations: ['97-4=93'] Exploring Operation: 93-16=77, Resulting Numbers: [47, 77] Generated Node #0,2,0: 80:[47, 77] Operation: 93-16=77 Exploring Operation: 47+16=63, Resulting Numbers: [93, 63] Generated Node #0,2,1: 80:[93, 63] Operation: 47+16=63 Exploring Operation: 93-47=46, Resulting Numbers: [16, 46] Generated Node #0,2,2: 80:[16, 46] Operation: 93-47=46 Exploring Operation: 47-16=31, Resulting Numbers: [93, 31] Generated Node #0,2,3: 80:[93, 31] Operation: 47-16=31 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 80:[16, 46], Operations: ['97-4=93', '93-47=46'] Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 16*46=736, Resulting Numbers: [736] 736,80 unequal: No Solution Exploring Operation: 16+46=62, Resulting Numbers: [62] 62,80 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: 80:[47, 77], Operations: ['97-4=93', '93-16=77'] Exploring Operation: 47*77=3619, Resulting Numbers: [3619] 3619,80 unequal: No Solution Exploring Operation: 77-47=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 47+77=124, Resulting Numbers: [124] 124,80 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: 80:[93, 31], Operations: ['97-4=93', '47-16=31'] Exploring Operation: 93+31=124, Resulting Numbers: [124] 124,80 unequal: No Solution Exploring Operation: 93*31=2883, Resulting Numbers: [2883] 2883,80 unequal: No Solution Exploring Operation: 93-31=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 93/31=3, Resulting Numbers: [3] 3,80 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: 80:[93, 63], Operations: ['97-4=93', '47+16=63'] Exploring Operation: 93-63=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 93*63=5859, Resulting Numbers: [5859] 5859,80 unequal: No Solution Exploring Operation: 93+63=156, Resulting Numbers: [156] 156,80 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: 80:[97, 16, 43], Operations: ['47-4=43'] Exploring Operation: 97-43=54, Resulting Numbers: [16, 54] Generated Node #0,0,0: 80:[16, 54] Operation: 97-43=54 Exploring Operation: 43-16=27, Resulting Numbers: [97, 27] Generated Node #0,0,1: 80:[97, 27] Operation: 43-16=27 Exploring Operation: 97+16=113, Resulting Numbers: [43, 113] Generated Node #0,0,2: 80:[43, 113] Operation: 97+16=113 Exploring Operation: 97-16=81, Resulting Numbers: [43, 81] Generated Node #0,0,3: 80:[43, 81] Operation: 97-16=81 Moving to Node #0,1,1 Current State: 80:[81, 43], Operations: ['97-16=81', '47-4=43'] Exploring Operation: 81*43=3483, Resulting Numbers: [3483] 3483,80 unequal: No Solution Exploring Operation: 81-43=38, Resulting Numbers: [38] 38,80 unequal: No Solution Exploring Operation: 81+43=124, Resulting Numbers: [124] 124,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[43, 81], Operations: ['47-4=43', '97-16=81'] Exploring Operation: 43*81=3483, Resulting Numbers: [3483] 3483,80 unequal: No Solution Exploring Operation: 81-43=38, Resulting Numbers: [38] 38,80 unequal: No Solution Exploring Operation: 43+81=124, Resulting Numbers: [124] 124,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[4, 34], Operations: ['97-16=81', '81-47=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,80 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[47, 77], Operations: ['97-16=81', '81-4=77'] Exploring Operation: 47*77=3619, Resulting Numbers: [3619] 3619,80 unequal: No Solution Exploring Operation: 47+77=124, Resulting Numbers: [124] 124,80 unequal: No Solution Exploring Operation: 77-47=30, Resulting Numbers: [30] 30,80 unequal: No Solution Moving to Node #0,1,3 Current State: 80:[81, 51], Operations: ['97-16=81', '4+47=51'] Exploring Operation: 81-51=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 81*51=4131, Resulting Numbers: [4131] 4131,80 unequal: No Solution Exploring Operation: 81+51=132, Resulting Numbers: [132] 132,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[16, 54], Operations: ['47-4=43', '97-43=54'] Exploring Operation: 16+54=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 54-16=38, Resulting Numbers: [38] 38,80 unequal: No Solution Exploring Operation: 16*54=864, Resulting Numbers: [864] 864,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[97, 27], Operations: ['47-4=43', '43-16=27'] Exploring Operation: 97-27=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 97+27=124, Resulting Numbers: [124] 124,80 unequal: No Solution Exploring Operation: 97*27=2619, Resulting Numbers: [2619] 2619,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[43, 113], Operations: ['47-4=43', '97+16=113'] Exploring Operation: 43*113=4859, Resulting Numbers: [4859] 4859,80 unequal: No Solution Exploring Operation: 113-43=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 43+113=156, Resulting Numbers: [156] 156,80 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 86, 24, 80, 64 ]
92
[ "80+64=144", "144/24=6", "86+6=92" ]
Current State: 92:[86, 24, 80, 64], Operations: [] Exploring Operation: 80+64=144, Resulting Numbers: [86, 24, 144] Generated Node #2: [86, 24, 144] from Operation: 80+64=144 Current State: 92:[86, 24, 144], Operations: ['80+64=144'] Exploring Operation: 144/24=6, Resulting Numbers: [86, 6] Generated Node #3: [86, 6] from Operation: 144/24=6 Current State: 92:[86, 6], Operations: ['80+64=144', '144/24=6'] Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[86, 24, 80, 64], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [24, 64, 6] Generated Node #0,0: 92:[24, 64, 6] Operation: 86-80=6 Exploring Operation: 24+64=88, Resulting Numbers: [86, 80, 88] Generated Node #0,1: 92:[86, 80, 88] Operation: 24+64=88 Exploring Operation: 80-64=16, Resulting Numbers: [86, 24, 16] Generated Node #0,2: 92:[86, 24, 16] Operation: 80-64=16 Exploring Operation: 86-64=22, Resulting Numbers: [24, 80, 22] Generated Node #0,3: 92:[24, 80, 22] Operation: 86-64=22 Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[86, 24, 16], Operations: ['80-64=16'] Exploring Operation: 86-24=62, Resulting Numbers: [16, 62] Generated Node #0,2,0: 92:[16, 62] Operation: 86-24=62 Exploring Operation: 24+16=40, Resulting Numbers: [86, 40] Generated Node #0,2,1: 92:[86, 40] Operation: 24+16=40 Exploring Operation: 24-16=8, Resulting Numbers: [86, 8] Generated Node #0,2,2: 92:[86, 8] Operation: 24-16=8 Exploring Operation: 86+16=102, Resulting Numbers: [24, 102] Generated Node #0,2,3: 92:[24, 102] Operation: 86+16=102 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 92:[86, 8], Operations: ['80-64=16', '24-16=8'] Exploring Operation: 86*8=688, Resulting Numbers: [688] 688,92 unequal: No Solution Exploring Operation: 86+8=94, Resulting Numbers: [94] 94,92 unequal: No Solution Exploring Operation: 86-8=78, Resulting Numbers: [78] 78,92 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: 92:[24, 102], Operations: ['80-64=16', '86+16=102'] Exploring Operation: 24+102=126, Resulting Numbers: [126] 126,92 unequal: No Solution Exploring Operation: 24*102=2448, Resulting Numbers: [2448] 2448,92 unequal: No Solution Exploring Operation: 102-24=78, Resulting Numbers: [78] 78,92 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: 92:[86, 40], Operations: ['80-64=16', '24+16=40'] Exploring Operation: 86+40=126, Resulting Numbers: [126] 126,92 unequal: No Solution Exploring Operation: 86*40=3440, Resulting Numbers: [3440] 3440,92 unequal: No Solution Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,92 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: 92:[16, 62], Operations: ['80-64=16', '86-24=62'] Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 16+62=78, Resulting Numbers: [78] 78,92 unequal: No Solution Exploring Operation: 16*62=992, Resulting Numbers: [992] 992,92 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: 92:[24, 80, 22], Operations: ['86-64=22'] Exploring Operation: 80+22=102, Resulting Numbers: [24, 102] Generated Node #0,3,0: 92:[24, 102] Operation: 80+22=102 Exploring Operation: 24+22=46, Resulting Numbers: [80, 46] Generated Node #0,3,1: 92:[80, 46] Operation: 24+22=46 Exploring Operation: 24-22=2, Resulting Numbers: [80, 2] Generated Node #0,3,2: 92:[80, 2] Operation: 24-22=2 Exploring Operation: 80-24=56, Resulting Numbers: [22, 56] Generated Node #0,3,3: 92:[22, 56] Operation: 80-24=56 Moving to Node #0,3,0 Current State: 92:[24, 102], Operations: ['86-64=22', '80+22=102'] Exploring Operation: 24*102=2448, Resulting Numbers: [2448] 2448,92 unequal: No Solution Exploring Operation: 102-24=78, Resulting Numbers: [78] 78,92 unequal: No Solution Exploring Operation: 24+102=126, Resulting Numbers: [126] 126,92 unequal: No Solution Moving to Node #0,3,3 Current State: 92:[22, 56], Operations: ['86-64=22', '80-24=56'] Exploring Operation: 22*56=1232, Resulting Numbers: [1232] 1232,92 unequal: No Solution Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,92 unequal: No Solution Exploring Operation: 22+56=78, Resulting Numbers: [78] 78,92 unequal: No Solution Moving to Node #0,3,2 Current State: 92:[80, 2], Operations: ['86-64=22', '24-22=2'] Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,92 unequal: No Solution Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,92 unequal: No Solution Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,92 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,92 unequal: No Solution Moving to Node #0,3,1 Current State: 92:[80, 46], Operations: ['86-64=22', '24+22=46'] Exploring Operation: 80+46=126, Resulting Numbers: [126] 126,92 unequal: No Solution Exploring Operation: 80*46=3680, Resulting Numbers: [3680] 3680,92 unequal: No Solution Exploring Operation: 80-46=34, Resulting Numbers: [34] 34,92 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 Current State: 92:[24, 64, 6], Operations: ['86-80=6'] Exploring Operation: 24+64=88, Resulting Numbers: [6, 88] Generated Node #0,0,0: 92:[6, 88] Operation: 24+64=88 Exploring Operation: 64-24=40, Resulting Numbers: [6, 40] Generated Node #0,0,1: 92:[6, 40] Operation: 64-24=40 Exploring Operation: 64-6=58, Resulting Numbers: [24, 58] Generated Node #0,0,2: 92:[24, 58] Operation: 64-6=58 Exploring Operation: 24/6=4, Resulting Numbers: [64, 4] Generated Node #0,0,3: 92:[64, 4] Operation: 24/6=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[6, 88], Operations: ['86-80=6', '24+64=88'] Exploring Operation: 88-6=82, Resulting Numbers: [82] 82,92 unequal: No Solution Exploring Operation: 6+88=94, Resulting Numbers: [94] 94,92 unequal: No Solution Exploring Operation: 6*88=528, Resulting Numbers: [528] 528,92 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: 92:[6, 40], Operations: ['86-80=6', '64-24=40'] Exploring Operation: 6+40=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 6*40=240, Resulting Numbers: [240] 240,92 unequal: No Solution Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,92 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: 92:[24, 58], Operations: ['86-80=6', '64-6=58'] Exploring Operation: 24+58=82, Resulting Numbers: [82] 82,92 unequal: No Solution Exploring Operation: 58-24=34, Resulting Numbers: [34] 34,92 unequal: No Solution Exploring Operation: 24*58=1392, Resulting Numbers: [1392] 1392,92 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: 92:[64, 4], Operations: ['86-80=6', '24/6=4'] Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,92 unequal: No Solution Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,92 unequal: No Solution Exploring Operation: 64*4=256, Resulting Numbers: [256] 256,92 unequal: No Solution Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,92 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: 92:[86, 80, 88], Operations: ['24+64=88'] Exploring Operation: 86+80=166, Resulting Numbers: [88, 166] Generated Node #0,1,0: 92:[88, 166] Operation: 86+80=166 Exploring Operation: 88-86=2, Resulting Numbers: [80, 2] Generated Node #0,1,1: 92:[80, 2] Operation: 88-86=2 Exploring Operation: 86-80=6, Resulting Numbers: [88, 6] Generated Node #0,1,2: 92:[88, 6] Operation: 86-80=6 Exploring Operation: 88-80=8, Resulting Numbers: [86, 8] Generated Node #0,1,3: 92:[86, 8] Operation: 88-80=8 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 92:[88, 6], Operations: ['24+64=88', '86-80=6'] Exploring Operation: 88-6=82, Resulting Numbers: [82] 82,92 unequal: No Solution Exploring Operation: 88*6=528, Resulting Numbers: [528] 528,92 unequal: No Solution Exploring Operation: 88+6=94, Resulting Numbers: [94] 94,92 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: 92:[86, 8], Operations: ['24+64=88', '88-80=8'] Exploring Operation: 86+8=94, Resulting Numbers: [94] 94,92 unequal: No Solution Exploring Operation: 86-8=78, Resulting Numbers: [78] 78,92 unequal: No Solution Exploring Operation: 86*8=688, Resulting Numbers: [688] 688,92 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: 92:[80, 2], Operations: ['24+64=88', '88-86=2'] Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,92 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,92 unequal: No Solution Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,92 unequal: No Solution Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,92 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: 92:[88, 166], Operations: ['24+64=88', '86+80=166'] Exploring Operation: 166-88=78, Resulting Numbers: [78] 78,92 unequal: No Solution Exploring Operation: 88+166=254, Resulting Numbers: [254] 254,92 unequal: No Solution Exploring Operation: 88*166=14608, Resulting Numbers: [14608] 14608,92 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
[ 90, 50, 40, 99 ]
10
[ "99-90=9", "50+40=90", "90/9=10" ]
Current State: 10:[90, 50, 40, 99], Operations: [] Exploring Operation: 99-90=9, Resulting Numbers: [50, 40, 9] Generated Node #2: [50, 40, 9] from Operation: 99-90=9 Current State: 10:[50, 40, 9], Operations: ['99-90=9'] Exploring Operation: 50+40=90, Resulting Numbers: [9, 90] Generated Node #3: [9, 90] from Operation: 50+40=90 Current State: 10:[9, 90], Operations: ['99-90=9', '50+40=90'] Exploring Operation: 90/9=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[90, 50, 40, 99], Operations: [] Exploring Operation: 99-90=9, Resulting Numbers: [50, 40, 9] Generated Node #0,0: 10:[50, 40, 9] Operation: 99-90=9 Exploring Operation: 99-50=49, Resulting Numbers: [90, 40, 49] Generated Node #0,1: 10:[90, 40, 49] Operation: 99-50=49 Exploring Operation: 90-50=40, Resulting Numbers: [40, 99, 40] Generated Node #0,2: 10:[40, 99, 40] Operation: 90-50=40 Moving to Node #0,0 Current State: 10:[50, 40, 9], Operations: ['99-90=9'] Exploring Operation: 50-9=41, Resulting Numbers: [40, 41] Generated Node #0,0,0: 10:[40, 41] Operation: 50-9=41 Exploring Operation: 50-40=10, Resulting Numbers: [9, 10] Generated Node #0,0,1: 10:[9, 10] Operation: 50-40=10 Exploring Operation: 40-9=31, Resulting Numbers: [50, 31] Generated Node #0,0,2: 10:[50, 31] Operation: 40-9=31 Moving to Node #0,1 Current State: 10:[90, 40, 49], Operations: ['99-50=49'] Exploring Operation: 49-40=9, Resulting Numbers: [90, 9] Generated Node #0,1,0: 10:[90, 9] Operation: 49-40=9 Exploring Operation: 90-49=41, Resulting Numbers: [40, 41] Generated Node #0,1,1: 10:[40, 41] Operation: 90-49=41 Exploring Operation: 90-40=50, Resulting Numbers: [49, 50] Generated Node #0,1,2: 10:[49, 50] Operation: 90-40=50 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 10:[40, 41], Operations: ['99-50=49', '90-49=41'] Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,10 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,10 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: 10:[49, 50], Operations: ['99-50=49', '90-40=50'] Exploring Operation: 49+50=99, Resulting Numbers: [99] 99,10 unequal: No Solution Exploring Operation: 49*50=2450, Resulting Numbers: [2450] 2450,10 unequal: No Solution Exploring Operation: 50-49=1, Resulting Numbers: [1] 1,10 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: 10:[90, 9], Operations: ['99-50=49', '49-40=9'] Exploring Operation: 90/9=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[90, 50, 40, 99], Operations: [] Exploring Operation: 99-50=49, Resulting Numbers: [90, 40, 49] Generated Node #0,1: 10:[90, 40, 49] Operation: 99-50=49 Moving to Node #0,1 Current State: 10:[90, 40, 49], Operations: ['99-50=49'] Exploring Operation: 49-40=9, Resulting Numbers: [90, 9] Generated Node #0,1,0: 10:[90, 9] Operation: 49-40=9 Moving to Node #0,1,0 Current State: 10:[90, 9], Operations: ['99-50=49', '49-40=9'] Exploring Operation: 90/9=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_3
sum_heuristic
[ 36, 31, 34, 8 ]
93
[ "36+31=67", "34-8=26", "67+26=93" ]
Current State: 93:[36, 31, 34, 8], Operations: [] Exploring Operation: 36+31=67, Resulting Numbers: [34, 8, 67] Generated Node #2: [34, 8, 67] from Operation: 36+31=67 Current State: 93:[34, 8, 67], Operations: ['36+31=67'] Exploring Operation: 34-8=26, Resulting Numbers: [67, 26] Generated Node #3: [67, 26] from Operation: 34-8=26 Current State: 93:[67, 26], Operations: ['36+31=67', '34-8=26'] Exploring Operation: 67+26=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[36, 31, 34, 8], Operations: [] Exploring Operation: 36-8=28, Resulting Numbers: [31, 34, 28] Generated Node #0,0: 93:[31, 34, 28] Operation: 36-8=28 Exploring Operation: 36-34=2, Resulting Numbers: [31, 8, 2] Generated Node #0,1: 93:[31, 8, 2] Operation: 36-34=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[31, 34, 28], Operations: ['36-8=28'] Exploring Operation: 34-31=3, Resulting Numbers: [28, 3] Generated Node #0,0,0: 93:[28, 3] Operation: 34-31=3 Exploring Operation: 31-28=3, Resulting Numbers: [34, 3] Generated Node #0,0,1: 93:[34, 3] Operation: 31-28=3 Moving to Node #0,0,0 Current State: 93:[28, 3], Operations: ['36-8=28', '34-31=3'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,93 unequal: No Solution Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[34, 3], Operations: ['36-8=28', '31-28=3'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,93 unequal: No Solution Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,93 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:[31, 8, 2], Operations: ['36-34=2'] Exploring Operation: 8-2=6, Resulting Numbers: [31, 6] Generated Node #0,1,0: 93:[31, 6] Operation: 8-2=6 Exploring Operation: 8/2=4, Resulting Numbers: [31, 4] Generated Node #0,1,1: 93:[31, 4] Operation: 8/2=4 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 93:[31, 4], Operations: ['36-34=2', '8/2=4'] Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,93 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,93 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: 93:[31, 6], Operations: ['36-34=2', '8-2=6'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,93 unequal: No Solution Exploring Operation: 31+6=37, Resulting Numbers: [37] 37,93 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
[ 56, 25, 51, 18 ]
64
[ "56-25=31", "51-18=33", "31+33=64" ]
Current State: 64:[56, 25, 51, 18], Operations: [] Exploring Operation: 56-25=31, Resulting Numbers: [51, 18, 31] Generated Node #2: [51, 18, 31] from Operation: 56-25=31 Current State: 64:[51, 18, 31], Operations: ['56-25=31'] Exploring Operation: 51-18=33, Resulting Numbers: [31, 33] Generated Node #3: [31, 33] from Operation: 51-18=33 Current State: 64:[31, 33], Operations: ['56-25=31', '51-18=33'] Exploring Operation: 31+33=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[56, 25, 51, 18], Operations: [] Exploring Operation: 56-25=31, Resulting Numbers: [51, 18, 31] Generated Node #0,0: 64:[51, 18, 31] Operation: 56-25=31 Exploring Operation: 51-25=26, Resulting Numbers: [56, 18, 26] Generated Node #0,1: 64:[56, 18, 26] Operation: 51-25=26 Exploring Operation: 51-18=33, Resulting Numbers: [56, 25, 33] Generated Node #0,2: 64:[56, 25, 33] Operation: 51-18=33 Exploring Operation: 56-51=5, Resulting Numbers: [25, 18, 5] Generated Node #0,3: 64:[25, 18, 5] Operation: 56-51=5 Start Sub Search at level 1: Moving to Node #0,3 Current State: 64:[25, 18, 5], Operations: ['56-51=5'] Exploring Operation: 25-18=7, Resulting Numbers: [5, 7] Generated Node #0,3,0: 64:[5, 7] Operation: 25-18=7 Exploring Operation: 25-5=20, Resulting Numbers: [18, 20] Generated Node #0,3,1: 64:[18, 20] Operation: 25-5=20 Exploring Operation: 25+5=30, Resulting Numbers: [18, 30] Generated Node #0,3,2: 64:[18, 30] Operation: 25+5=30 Exploring Operation: 25/5=5, Resulting Numbers: [18, 5] Generated Node #0,3,3: 64:[18, 5] Operation: 25/5=5 Moving to Node #0,3,0 Current State: 64:[5, 7], Operations: ['56-51=5', '25-18=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,64 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,64 unequal: No Solution Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,64 unequal: No Solution Moving to Node #0,3,3 Current State: 64:[18, 5], Operations: ['56-51=5', '25/5=5'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,64 unequal: No Solution Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,64 unequal: No Solution Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,64 unequal: No Solution Moving to Node #0,3,2 Current State: 64:[18, 30], Operations: ['56-51=5', '25+5=30'] Exploring Operation: 18+30=48, Resulting Numbers: [48] 48,64 unequal: No Solution Exploring Operation: 18*30=540, Resulting Numbers: [540] 540,64 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,64 unequal: No Solution Moving to Node #0,3,1 Current State: 64:[18, 20], Operations: ['56-51=5', '25-5=20'] Exploring Operation: 18*20=360, Resulting Numbers: [360] 360,64 unequal: No Solution Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,64 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,64 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 Current State: 64:[51, 18, 31], Operations: ['56-25=31'] Exploring Operation: 31-18=13, Resulting Numbers: [51, 13] Generated Node #0,0,0: 64:[51, 13] Operation: 31-18=13 Exploring Operation: 51-31=20, Resulting Numbers: [18, 20] Generated Node #0,0,1: 64:[18, 20] Operation: 51-31=20 Exploring Operation: 51-18=33, Resulting Numbers: [31, 33] Generated Node #0,0,2: 64:[31, 33] Operation: 51-18=33 Exploring Operation: 51+18=69, Resulting Numbers: [31, 69] Generated Node #0,0,3: 64:[31, 69] Operation: 51+18=69 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 64:[31, 33], Operations: ['56-25=31', '51-18=33'] Exploring Operation: 31+33=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[56, 25, 51, 18], Operations: [] Exploring Operation: 56-25=31, Resulting Numbers: [51, 18, 31] Generated Node #0,0: 64:[51, 18, 31] Operation: 56-25=31 Moving to Node #0,0 Current State: 64:[51, 18, 31], Operations: ['56-25=31'] Exploring Operation: 51-18=33, Resulting Numbers: [31, 33] Generated Node #0,0,2: 64:[31, 33] Operation: 51-18=33 Moving to Node #0,0,2 Current State: 64:[31, 33], Operations: ['56-25=31', '51-18=33'] Exploring Operation: 31+33=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic
[ 27, 12, 3, 51 ]
96
[ "27-12=15", "3*15=45", "51+45=96" ]
Current State: 96:[27, 12, 3, 51], Operations: [] Exploring Operation: 27-12=15, Resulting Numbers: [3, 51, 15] Generated Node #2: [3, 51, 15] from Operation: 27-12=15 Current State: 96:[3, 51, 15], Operations: ['27-12=15'] Exploring Operation: 3*15=45, Resulting Numbers: [51, 45] Generated Node #3: [51, 45] from Operation: 3*15=45 Current State: 96:[51, 45], Operations: ['27-12=15', '3*15=45'] Exploring Operation: 51+45=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[27, 12, 3, 51], Operations: [] Exploring Operation: 27-3=24, Resulting Numbers: [12, 51, 24] Generated Node #0,0: 96:[12, 51, 24] Operation: 27-3=24 Exploring Operation: 51-3=48, Resulting Numbers: [27, 12, 48] Generated Node #0,1: 96:[27, 12, 48] Operation: 51-3=48 Exploring Operation: 51-27=24, Resulting Numbers: [12, 3, 24] Generated Node #0,2: 96:[12, 3, 24] Operation: 51-27=24 Moving to Node #0,2 Current State: 96:[12, 3, 24], Operations: ['51-27=24'] Exploring Operation: 12/3=4, Resulting Numbers: [24, 4] Generated Node #0,2,0: 96:[24, 4] Operation: 12/3=4 Exploring Operation: 24-12=12, Resulting Numbers: [3, 12] Generated Node #0,2,1: 96:[3, 12] Operation: 24-12=12 Exploring Operation: 24/12=2, Resulting Numbers: [3, 2] Generated Node #0,2,2: 96:[3, 2] Operation: 24/12=2 Moving to Node #0,0 Current State: 96:[12, 51, 24], Operations: ['27-3=24'] Exploring Operation: 24-12=12, Resulting Numbers: [51, 12] Generated Node #0,0,0: 96:[51, 12] Operation: 24-12=12 Exploring Operation: 24/12=2, Resulting Numbers: [51, 2] Generated Node #0,0,1: 96:[51, 2] Operation: 24/12=2 Exploring Operation: 51-24=27, Resulting Numbers: [12, 27] Generated Node #0,0,2: 96:[12, 27] Operation: 51-24=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[51, 12], Operations: ['27-3=24', '24-12=12'] Exploring Operation: 51*12=612, Resulting Numbers: [612] 612,96 unequal: No Solution Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,96 unequal: No Solution Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,96 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 #0,0,1 Current State: 96:[51, 2], Operations: ['27-3=24', '24/12=2'] Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,96 unequal: No Solution Exploring Operation: 51*2=102, Resulting Numbers: [102] 102,96 unequal: No Solution Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,96 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 #0,0,2 Current State: 96:[12, 27], Operations: ['27-3=24', '51-24=27'] Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,96 unequal: No Solution Exploring Operation: 12+27=39, Resulting Numbers: [39] 39,96 unequal: No Solution Exploring Operation: 12*27=324, Resulting Numbers: [324] 324,96 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: 96:[27, 12, 48], Operations: ['51-3=48'] Exploring Operation: 27-12=15, Resulting Numbers: [48, 15] Generated Node #0,1,0: 96:[48, 15] Operation: 27-12=15 Exploring Operation: 48-27=21, Resulting Numbers: [12, 21] Generated Node #0,1,1: 96:[12, 21] Operation: 48-27=21 Exploring Operation: 48/12=4, Resulting Numbers: [27, 4] Generated Node #0,1,2: 96:[27, 4] Operation: 48/12=4 Moving to Node #0,2,0 Current State: 96:[24, 4], Operations: ['51-27=24', '12/3=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[27, 12, 3, 51], Operations: [] Exploring Operation: 51-27=24, Resulting Numbers: [12, 3, 24] Generated Node #0,2: 96:[12, 3, 24] Operation: 51-27=24 Moving to Node #0,2 Current State: 96:[12, 3, 24], Operations: ['51-27=24'] Exploring Operation: 12/3=4, Resulting Numbers: [24, 4] Generated Node #0,2,0: 96:[24, 4] Operation: 12/3=4 Moving to Node #0,2,0 Current State: 96:[24, 4], Operations: ['51-27=24', '12/3=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
0.977431
hs_3
sum_heuristic
[ 2, 16, 39, 30 ]
72
[ "16/2=8", "39-30=9", "8*9=72" ]
Current State: 72:[2, 16, 39, 30], Operations: [] Exploring Operation: 16/2=8, Resulting Numbers: [39, 30, 8] Generated Node #2: [39, 30, 8] from Operation: 16/2=8 Current State: 72:[39, 30, 8], Operations: ['16/2=8'] Exploring Operation: 39-30=9, Resulting Numbers: [8, 9] Generated Node #3: [8, 9] from Operation: 39-30=9 Current State: 72:[8, 9], Operations: ['16/2=8', '39-30=9'] Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[2, 16, 39, 30], Operations: [] Exploring Operation: 39+30=69, Resulting Numbers: [2, 16, 69] Generated Node #0,0: 72:[2, 16, 69] Operation: 39+30=69 Exploring Operation: 30-16=14, Resulting Numbers: [2, 39, 14] Generated Node #0,1: 72:[2, 39, 14] Operation: 30-16=14 Exploring Operation: 39-30=9, Resulting Numbers: [2, 16, 9] Generated Node #0,2: 72:[2, 16, 9] Operation: 39-30=9 Exploring Operation: 39-16=23, Resulting Numbers: [2, 30, 23] Generated Node #0,3: 72:[2, 30, 23] Operation: 39-16=23 Moving to Node #0,2 Current State: 72:[2, 16, 9], Operations: ['39-30=9'] Exploring Operation: 2+16=18, Resulting Numbers: [9, 18] Generated Node #0,2,0: 72:[9, 18] Operation: 2+16=18 Exploring Operation: 16-9=7, Resulting Numbers: [2, 7] Generated Node #0,2,1: 72:[2, 7] Operation: 16-9=7 Exploring Operation: 16/2=8, Resulting Numbers: [9, 8] Generated Node #0,2,2: 72:[9, 8] Operation: 16/2=8 Exploring Operation: 16+9=25, Resulting Numbers: [2, 25] Generated Node #0,2,3: 72:[2, 25] Operation: 16+9=25 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 72:[9, 18], Operations: ['39-30=9', '2+16=18'] Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,72 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 9*18=162, Resulting Numbers: [162] 162,72 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: 72:[9, 8], Operations: ['39-30=9', '16/2=8'] Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,72 unequal: No Solution Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[2, 16, 39, 30], Operations: [] Exploring Operation: 39-30=9, Resulting Numbers: [2, 16, 9] Generated Node #0,2: 72:[2, 16, 9] Operation: 39-30=9 Moving to Node #0,2 Current State: 72:[2, 16, 9], Operations: ['39-30=9'] Exploring Operation: 16/2=8, Resulting Numbers: [9, 8] Generated Node #0,2,2: 72:[9, 8] Operation: 16/2=8 Moving to Node #0,2,2 Current State: 72:[9, 8], Operations: ['39-30=9', '16/2=8'] Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 24, 64, 21, 39 ]
21
[ "64-24=40", "40-39=1", "21*1=21" ]
Current State: 21:[24, 64, 21, 39], Operations: [] Exploring Operation: 64-24=40, Resulting Numbers: [21, 39, 40] Generated Node #2: [21, 39, 40] from Operation: 64-24=40 Current State: 21:[21, 39, 40], Operations: ['64-24=40'] Exploring Operation: 40-39=1, Resulting Numbers: [21, 1] Generated Node #3: [21, 1] from Operation: 40-39=1 Current State: 21:[21, 1], Operations: ['64-24=40', '40-39=1'] Exploring Operation: 21*1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[24, 64, 21, 39], Operations: [] Exploring Operation: 64-39=25, Resulting Numbers: [24, 21, 25] Generated Node #0,0: 21:[24, 21, 25] Operation: 64-39=25 Exploring Operation: 64-24=40, Resulting Numbers: [21, 39, 40] Generated Node #0,1: 21:[21, 39, 40] Operation: 64-24=40 Exploring Operation: 39-24=15, Resulting Numbers: [64, 21, 15] Generated Node #0,2: 21:[64, 21, 15] Operation: 39-24=15 Exploring Operation: 39-21=18, Resulting Numbers: [24, 64, 18] Generated Node #0,3: 21:[24, 64, 18] Operation: 39-21=18 Exploring Operation: 64-21=43, Resulting Numbers: [24, 39, 43] Generated Node #0,4: 21:[24, 39, 43] Operation: 64-21=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[24, 21, 25], Operations: ['64-39=25'] Exploring Operation: 24+21=45, Resulting Numbers: [25, 45] Generated Node #0,0,0: 21:[25, 45] Operation: 24+21=45 Exploring Operation: 25-21=4, Resulting Numbers: [24, 4] Generated Node #0,0,1: 21:[24, 4] Operation: 25-21=4 Exploring Operation: 24-21=3, Resulting Numbers: [25, 3] Generated Node #0,0,2: 21:[25, 3] Operation: 24-21=3 Exploring Operation: 25-24=1, Resulting Numbers: [21, 1] Generated Node #0,0,3: 21:[21, 1] Operation: 25-24=1 Exploring Operation: 24+25=49, Resulting Numbers: [21, 49] Generated Node #0,0,4: 21:[21, 49] Operation: 24+25=49 Moving to Node #0,0,3 Current State: 21:[21, 1], Operations: ['64-39=25', '25-24=1'] Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[24, 64, 21, 39], Operations: [] Exploring Operation: 64-39=25, Resulting Numbers: [24, 21, 25] Generated Node #0,0: 21:[24, 21, 25] Operation: 64-39=25 Moving to Node #0,0 Current State: 21:[24, 21, 25], Operations: ['64-39=25'] Exploring Operation: 25-24=1, Resulting Numbers: [21, 1] Generated Node #0,0,3: 21:[21, 1] Operation: 25-24=1 Moving to Node #0,0,3 Current State: 21:[21, 1], Operations: ['64-39=25', '25-24=1'] Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 84, 98, 44, 51 ]
87
[ "84+98=182", "44+51=95", "182-95=87" ]
Current State: 87:[84, 98, 44, 51], Operations: [] Exploring Operation: 84+98=182, Resulting Numbers: [44, 51, 182] Generated Node #2: [44, 51, 182] from Operation: 84+98=182 Current State: 87:[44, 51, 182], Operations: ['84+98=182'] Exploring Operation: 44+51=95, Resulting Numbers: [182, 95] Generated Node #3: [182, 95] from Operation: 44+51=95 Current State: 87:[182, 95], Operations: ['84+98=182', '44+51=95'] Exploring Operation: 182-95=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[84, 98, 44, 51], Operations: [] Exploring Operation: 51-44=7, Resulting Numbers: [84, 98, 7] Generated Node #0,0: 87:[84, 98, 7] Operation: 51-44=7 Exploring Operation: 44+51=95, Resulting Numbers: [84, 98, 95] Generated Node #0,1: 87:[84, 98, 95] Operation: 44+51=95 Moving to Node #0,0 Current State: 87:[84, 98, 7], Operations: ['51-44=7'] Exploring Operation: 98-7=91, Resulting Numbers: [84, 91] Generated Node #0,0,0: 87:[84, 91] Operation: 98-7=91 Exploring Operation: 98/7=14, Resulting Numbers: [84, 14] Generated Node #0,0,1: 87:[84, 14] Operation: 98/7=14 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[84, 91], Operations: ['51-44=7', '98-7=91'] Exploring Operation: 84+91=175, Resulting Numbers: [175] 175,87 unequal: No Solution Exploring Operation: 91-84=7, Resulting Numbers: [7] 7,87 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: 87:[84, 14], Operations: ['51-44=7', '98/7=14'] Exploring Operation: 84/14=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 84+14=98, Resulting Numbers: [98] 98,87 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: 87:[84, 98, 95], Operations: ['44+51=95'] Exploring Operation: 98-95=3, Resulting Numbers: [84, 3] Generated Node #0,1,0: 87:[84, 3] Operation: 98-95=3 Exploring Operation: 98-84=14, Resulting Numbers: [95, 14] Generated Node #0,1,1: 87:[95, 14] Operation: 98-84=14 Moving to Node #0,1,0 Current State: 87:[84, 3], Operations: ['44+51=95', '98-95=3'] Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[84, 98, 44, 51], Operations: [] Exploring Operation: 44+51=95, Resulting Numbers: [84, 98, 95] Generated Node #0,1: 87:[84, 98, 95] Operation: 44+51=95 Moving to Node #0,1 Current State: 87:[84, 98, 95], Operations: ['44+51=95'] Exploring Operation: 98-95=3, Resulting Numbers: [84, 3] Generated Node #0,1,0: 87:[84, 3] Operation: 98-95=3 Moving to Node #0,1,0 Current State: 87:[84, 3], Operations: ['44+51=95', '98-95=3'] Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 79, 5, 17, 11 ]
79
[ "17-5=12", "12-11=1", "79*1=79" ]
Current State: 79:[79, 5, 17, 11], Operations: [] Exploring Operation: 17-5=12, Resulting Numbers: [79, 11, 12] Generated Node #2: [79, 11, 12] from Operation: 17-5=12 Current State: 79:[79, 11, 12], Operations: ['17-5=12'] Exploring Operation: 12-11=1, Resulting Numbers: [79, 1] Generated Node #3: [79, 1] from Operation: 12-11=1 Current State: 79:[79, 1], Operations: ['17-5=12', '12-11=1'] Exploring Operation: 79*1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[79, 5, 17, 11], Operations: [] Exploring Operation: 5*17=85, Resulting Numbers: [79, 11, 85] Generated Node #0,0: 79:[79, 11, 85] Operation: 5*17=85 Exploring Operation: 5*11=55, Resulting Numbers: [79, 17, 55] Generated Node #0,1: 79:[79, 17, 55] Operation: 5*11=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[79, 11, 85], Operations: ['5*17=85'] Exploring Operation: 85-11=74, Resulting Numbers: [79, 74] Generated Node #0,0,0: 79:[79, 74] Operation: 85-11=74 Exploring Operation: 79+11=90, Resulting Numbers: [85, 90] Generated Node #0,0,1: 79:[85, 90] Operation: 79+11=90 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[79, 74], Operations: ['5*17=85', '85-11=74'] Exploring Operation: 79-74=5, Resulting Numbers: [5] 5,79 unequal: No Solution Exploring Operation: 79+74=153, Resulting Numbers: [153] 153,79 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: 79:[85, 90], Operations: ['5*17=85', '79+11=90'] Exploring Operation: 85+90=175, Resulting Numbers: [175] 175,79 unequal: No Solution Exploring Operation: 90-85=5, Resulting Numbers: [5] 5,79 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: 79:[79, 17, 55], Operations: ['5*11=55'] Exploring Operation: 17+55=72, Resulting Numbers: [79, 72] Generated Node #0,1,0: 79:[79, 72] Operation: 17+55=72 Exploring Operation: 79+17=96, Resulting Numbers: [55, 96] Generated Node #0,1,1: 79:[55, 96] Operation: 79+17=96 Moving to Node #0,1,0 Current State: 79:[79, 72], Operations: ['5*11=55', '17+55=72'] Exploring Operation: 79-72=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 79+72=151, Resulting Numbers: [151] 151,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[55, 96], Operations: ['5*11=55', '79+17=96'] Exploring Operation: 96-55=41, Resulting Numbers: [41] 41,79 unequal: No Solution Exploring Operation: 55+96=151, Resulting Numbers: [151] 151,79 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
[ 2, 8, 27, 77 ]
60
[ "2+8=10", "77-27=50", "10+50=60" ]
Current State: 60:[2, 8, 27, 77], Operations: [] Exploring Operation: 2+8=10, Resulting Numbers: [27, 77, 10] Generated Node #2: [27, 77, 10] from Operation: 2+8=10 Current State: 60:[27, 77, 10], Operations: ['2+8=10'] Exploring Operation: 77-27=50, Resulting Numbers: [10, 50] Generated Node #3: [10, 50] from Operation: 77-27=50 Current State: 60:[10, 50], Operations: ['2+8=10', '77-27=50'] Exploring Operation: 10+50=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[2, 8, 27, 77], Operations: [] Exploring Operation: 27-8=19, Resulting Numbers: [2, 77, 19] Generated Node #0,0: 60:[2, 77, 19] Operation: 27-8=19 Exploring Operation: 77-8=69, Resulting Numbers: [2, 27, 69] Generated Node #0,1: 60:[2, 27, 69] Operation: 77-8=69 Exploring Operation: 77-27=50, Resulting Numbers: [2, 8, 50] Generated Node #0,2: 60:[2, 8, 50] Operation: 77-27=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 60:[2, 27, 69], Operations: ['77-8=69'] Exploring Operation: 2+27=29, Resulting Numbers: [69, 29] Generated Node #0,1,0: 60:[69, 29] Operation: 2+27=29 Exploring Operation: 69-27=42, Resulting Numbers: [2, 42] Generated Node #0,1,1: 60:[2, 42] Operation: 69-27=42 Exploring Operation: 69-2=67, Resulting Numbers: [27, 67] Generated Node #0,1,2: 60:[27, 67] Operation: 69-2=67 Moving to Node #0,1,0 Current State: 60:[69, 29], Operations: ['77-8=69', '2+27=29'] Exploring Operation: 69*29=2001, Resulting Numbers: [2001] 2001,60 unequal: No Solution Exploring Operation: 69-29=40, Resulting Numbers: [40] 40,60 unequal: No Solution Exploring Operation: 69+29=98, Resulting Numbers: [98] 98,60 unequal: No Solution Moving to Node #0,1,2 Current State: 60:[27, 67], Operations: ['77-8=69', '69-2=67'] Exploring Operation: 27*67=1809, Resulting Numbers: [1809] 1809,60 unequal: No Solution Exploring Operation: 27+67=94, Resulting Numbers: [94] 94,60 unequal: No Solution Exploring Operation: 67-27=40, Resulting Numbers: [40] 40,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[2, 42], Operations: ['77-8=69', '69-27=42'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,60 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,60 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,60 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 #0,2 Current State: 60:[2, 8, 50], Operations: ['77-27=50'] Exploring Operation: 50/2=25, Resulting Numbers: [8, 25] Generated Node #0,2,0: 60:[8, 25] Operation: 50/2=25 Exploring Operation: 2+8=10, Resulting Numbers: [50, 10] Generated Node #0,2,1: 60:[50, 10] Operation: 2+8=10 Exploring Operation: 8+50=58, Resulting Numbers: [2, 58] Generated Node #0,2,2: 60:[2, 58] Operation: 8+50=58 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 60:[2, 58], Operations: ['77-27=50', '8+50=58'] Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[2, 8, 27, 77], Operations: [] Exploring Operation: 77-27=50, Resulting Numbers: [2, 8, 50] Generated Node #0,2: 60:[2, 8, 50] Operation: 77-27=50 Moving to Node #0,2 Current State: 60:[2, 8, 50], Operations: ['77-27=50'] Exploring Operation: 8+50=58, Resulting Numbers: [2, 58] Generated Node #0,2,2: 60:[2, 58] Operation: 8+50=58 Moving to Node #0,2,2 Current State: 60:[2, 58], Operations: ['77-27=50', '8+50=58'] Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 88, 55, 32, 69 ]
70
[ "88-55=33", "69-32=37", "33+37=70" ]
Current State: 70:[88, 55, 32, 69], Operations: [] Exploring Operation: 88-55=33, Resulting Numbers: [32, 69, 33] Generated Node #2: [32, 69, 33] from Operation: 88-55=33 Current State: 70:[32, 69, 33], Operations: ['88-55=33'] Exploring Operation: 69-32=37, Resulting Numbers: [33, 37] Generated Node #3: [33, 37] from Operation: 69-32=37 Current State: 70:[33, 37], Operations: ['88-55=33', '69-32=37'] Exploring Operation: 33+37=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[88, 55, 32, 69], Operations: [] Exploring Operation: 88-55=33, Resulting Numbers: [32, 69, 33] Generated Node #0,0: 70:[32, 69, 33] Operation: 88-55=33 Exploring Operation: 69-55=14, Resulting Numbers: [88, 32, 14] Generated Node #0,1: 70:[88, 32, 14] Operation: 69-55=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[32, 69, 33], Operations: ['88-55=33'] Exploring Operation: 33-32=1, Resulting Numbers: [69, 1] Generated Node #0,0,0: 70:[69, 1] Operation: 33-32=1 Exploring Operation: 69-32=37, Resulting Numbers: [33, 37] Generated Node #0,0,1: 70:[33, 37] Operation: 69-32=37 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 70:[69, 1], Operations: ['88-55=33', '33-32=1'] Exploring Operation: 69*1=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 69+1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[88, 55, 32, 69], Operations: [] Exploring Operation: 88-55=33, Resulting Numbers: [32, 69, 33] Generated Node #0,0: 70:[32, 69, 33] Operation: 88-55=33 Moving to Node #0,0 Current State: 70:[32, 69, 33], Operations: ['88-55=33'] Exploring Operation: 33-32=1, Resulting Numbers: [69, 1] Generated Node #0,0,0: 70:[69, 1] Operation: 33-32=1 Moving to Node #0,0,0 Current State: 70:[69, 1], Operations: ['88-55=33', '33-32=1'] Exploring Operation: 69+1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 77, 72, 5, 32 ]
22
[ "77-72=5", "32-5=27", "27-5=22" ]
Current State: 22:[77, 72, 5, 32], Operations: [] Exploring Operation: 77-72=5, Resulting Numbers: [5, 32, 5] Generated Node #2: [5, 32, 5] from Operation: 77-72=5 Current State: 22:[5, 32, 5], Operations: ['77-72=5'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,22 equal: Goal Reached Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[77, 72, 5, 32], Operations: [] Exploring Operation: 77-32=45, Resulting Numbers: [72, 5, 45] Generated Node #0,0: 22:[72, 5, 45] Operation: 77-32=45 Exploring Operation: 72-32=40, Resulting Numbers: [77, 5, 40] Generated Node #0,1: 22:[77, 5, 40] Operation: 72-32=40 Exploring Operation: 77-72=5, Resulting Numbers: [5, 32, 5] Generated Node #0,2: 22:[5, 32, 5] Operation: 77-72=5 Moving to Node #0,2 Current State: 22:[5, 32, 5], Operations: ['77-72=5'] Exploring Operation: 5+5=10, Resulting Numbers: [32, 10] Generated Node #0,2,0: 22:[32, 10] Operation: 5+5=10 Exploring Operation: 32-5=27, Resulting Numbers: [5, 27] Generated Node #0,2,1: 22:[5, 27] Operation: 32-5=27 Exploring Operation: 32-5=27, Resulting Numbers: [5, 27] Generated Node #0,2,2: 22:[5, 27] Operation: 32-5=27 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 22:[5, 27], Operations: ['77-72=5', '32-5=27'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[77, 72, 5, 32], Operations: [] Exploring Operation: 77-72=5, Resulting Numbers: [5, 32, 5] Generated Node #0,2: 22:[5, 32, 5] Operation: 77-72=5 Moving to Node #0,2 Current State: 22:[5, 32, 5], Operations: ['77-72=5'] Exploring Operation: 32-5=27, Resulting Numbers: [5, 27] Generated Node #0,2,1: 22:[5, 27] Operation: 32-5=27 Moving to Node #0,2,1 Current State: 22:[5, 27], Operations: ['77-72=5', '32-5=27'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 34, 39, 38, 44 ]
36
[ "34+44=78", "78/39=2", "38-2=36" ]
Current State: 36:[34, 39, 38, 44], Operations: [] Exploring Operation: 34+44=78, Resulting Numbers: [39, 38, 78] Generated Node #2: [39, 38, 78] from Operation: 34+44=78 Current State: 36:[39, 38, 78], Operations: ['34+44=78'] Exploring Operation: 78/39=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 78/39=2 Current State: 36:[38, 2], Operations: ['34+44=78', '78/39=2'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[34, 39, 38, 44], Operations: [] Exploring Operation: 44-39=5, Resulting Numbers: [34, 38, 5] Generated Node #0,0: 36:[34, 38, 5] Operation: 44-39=5 Moving to Node #0,0 Current State: 36:[34, 38, 5], Operations: ['44-39=5'] Exploring Operation: 38-34=4, Resulting Numbers: [5, 4] Generated Node #0,0,0: 36:[5, 4] Operation: 38-34=4 Moving to Node #0,0,0 Current State: 36:[5, 4], Operations: ['44-39=5', '38-34=4'] Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,36 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 59, 90, 66, 81 ]
36
[ "59*90=5310", "66*81=5346", "5346-5310=36" ]
Current State: 36:[59, 90, 66, 81], Operations: [] Exploring Operation: 59*90=5310, Resulting Numbers: [66, 81, 5310] Generated Node #2: [66, 81, 5310] from Operation: 59*90=5310 Current State: 36:[66, 81, 5310], Operations: ['59*90=5310'] Exploring Operation: 66*81=5346, Resulting Numbers: [5310, 5346] Generated Node #3: [5310, 5346] from Operation: 66*81=5346 Current State: 36:[5310, 5346], Operations: ['59*90=5310', '66*81=5346'] Exploring Operation: 5346-5310=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[59, 90, 66, 81], Operations: [] Exploring Operation: 81-66=15, Resulting Numbers: [59, 90, 15] Generated Node #0,0: 36:[59, 90, 15] Operation: 81-66=15 Exploring Operation: 90-81=9, Resulting Numbers: [59, 66, 9] Generated Node #0,1: 36:[59, 66, 9] Operation: 90-81=9 Exploring Operation: 90-66=24, Resulting Numbers: [59, 81, 24] Generated Node #0,2: 36:[59, 81, 24] Operation: 90-66=24 Exploring Operation: 90-59=31, Resulting Numbers: [66, 81, 31] Generated Node #0,3: 36:[66, 81, 31] Operation: 90-59=31 Moving to Node #0,1 Current State: 36:[59, 66, 9], Operations: ['90-81=9'] Exploring Operation: 59-9=50, Resulting Numbers: [66, 50] Generated Node #0,1,0: 36:[66, 50] Operation: 59-9=50 Exploring Operation: 59+9=68, Resulting Numbers: [66, 68] Generated Node #0,1,1: 36:[66, 68] Operation: 59+9=68 Exploring Operation: 66-9=57, Resulting Numbers: [59, 57] Generated Node #0,1,2: 36:[59, 57] Operation: 66-9=57 Exploring Operation: 66-59=7, Resulting Numbers: [9, 7] Generated Node #0,1,3: 36:[9, 7] Operation: 66-59=7 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 36:[9, 7], Operations: ['90-81=9', '66-59=7'] Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,36 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,36 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: 36:[66, 50], Operations: ['90-81=9', '59-9=50'] Exploring Operation: 66-50=16, Resulting Numbers: [16] 16,36 unequal: No Solution Exploring Operation: 66*50=3300, Resulting Numbers: [3300] 3300,36 unequal: No Solution Exploring Operation: 66+50=116, Resulting Numbers: [116] 116,36 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: 36:[59, 57], Operations: ['90-81=9', '66-9=57'] Exploring Operation: 59*57=3363, Resulting Numbers: [3363] 3363,36 unequal: No Solution Exploring Operation: 59-57=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 59+57=116, Resulting Numbers: [116] 116,36 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: 36:[66, 68], Operations: ['90-81=9', '59+9=68'] Exploring Operation: 66*68=4488, Resulting Numbers: [4488] 4488,36 unequal: No Solution Exploring Operation: 66+68=134, Resulting Numbers: [134] 134,36 unequal: No Solution Exploring Operation: 68-66=2, Resulting Numbers: [2] 2,36 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: 36:[59, 81, 24], Operations: ['90-66=24'] Exploring Operation: 81-24=57, Resulting Numbers: [59, 57] Generated Node #0,2,0: 36:[59, 57] Operation: 81-24=57 Exploring Operation: 59+24=83, Resulting Numbers: [81, 83] Generated Node #0,2,1: 36:[81, 83] Operation: 59+24=83 Exploring Operation: 59-24=35, Resulting Numbers: [81, 35] Generated Node #0,2,2: 36:[81, 35] Operation: 59-24=35 Exploring Operation: 81-59=22, Resulting Numbers: [24, 22] Generated Node #0,2,3: 36:[24, 22] Operation: 81-59=22 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 36:[24, 22], Operations: ['90-66=24', '81-59=22'] Exploring Operation: 24*22=528, Resulting Numbers: [528] 528,36 unequal: No Solution Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,36 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,36 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: 36:[59, 57], Operations: ['90-66=24', '81-24=57'] Exploring Operation: 59*57=3363, Resulting Numbers: [3363] 3363,36 unequal: No Solution Exploring Operation: 59+57=116, Resulting Numbers: [116] 116,36 unequal: No Solution Exploring Operation: 59-57=2, Resulting Numbers: [2] 2,36 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: 36:[81, 35], Operations: ['90-66=24', '59-24=35'] Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,36 unequal: No Solution Exploring Operation: 81*35=2835, Resulting Numbers: [2835] 2835,36 unequal: No Solution Exploring Operation: 81+35=116, Resulting Numbers: [116] 116,36 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: 36:[81, 83], Operations: ['90-66=24', '59+24=83'] Exploring Operation: 83-81=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 81*83=6723, Resulting Numbers: [6723] 6723,36 unequal: No Solution Exploring Operation: 81+83=164, Resulting Numbers: [164] 164,36 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: 36:[66, 81, 31], Operations: ['90-59=31'] Exploring Operation: 81-66=15, Resulting Numbers: [31, 15] Generated Node #0,3,0: 36:[31, 15] Operation: 81-66=15 Exploring Operation: 81-31=50, Resulting Numbers: [66, 50] Generated Node #0,3,1: 36:[66, 50] Operation: 81-31=50 Exploring Operation: 66-31=35, Resulting Numbers: [81, 35] Generated Node #0,3,2: 36:[81, 35] Operation: 66-31=35 Exploring Operation: 66+31=97, Resulting Numbers: [81, 97] Generated Node #0,3,3: 36:[81, 97] Operation: 66+31=97 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 36:[31, 15], Operations: ['90-59=31', '81-66=15'] Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,36 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,36 unequal: No Solution Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,36 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: 36:[66, 50], Operations: ['90-59=31', '81-31=50'] Exploring Operation: 66-50=16, Resulting Numbers: [16] 16,36 unequal: No Solution Exploring Operation: 66*50=3300, Resulting Numbers: [3300] 3300,36 unequal: No Solution Exploring Operation: 66+50=116, Resulting Numbers: [116] 116,36 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: 36:[81, 35], Operations: ['90-59=31', '66-31=35'] Exploring Operation: 81+35=116, Resulting Numbers: [116] 116,36 unequal: No Solution Exploring Operation: 81*35=2835, Resulting Numbers: [2835] 2835,36 unequal: No Solution Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,36 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: 36:[81, 97], Operations: ['90-59=31', '66+31=97'] Exploring Operation: 81*97=7857, Resulting Numbers: [7857] 7857,36 unequal: No Solution Exploring Operation: 81+97=178, Resulting Numbers: [178] 178,36 unequal: No Solution Exploring Operation: 97-81=16, Resulting Numbers: [16] 16,36 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: 36:[59, 90, 15], Operations: ['81-66=15'] Exploring Operation: 90-15=75, Resulting Numbers: [59, 75] Generated Node #0,0,0: 36:[59, 75] Operation: 90-15=75 Exploring Operation: 90/15=6, Resulting Numbers: [59, 6] Generated Node #0,0,1: 36:[59, 6] Operation: 90/15=6 Exploring Operation: 90-59=31, Resulting Numbers: [15, 31] Generated Node #0,0,2: 36:[15, 31] Operation: 90-59=31 Exploring Operation: 59-15=44, Resulting Numbers: [90, 44] Generated Node #0,0,3: 36:[90, 44] Operation: 59-15=44 Moving to Node #0,0,2 Current State: 36:[15, 31], Operations: ['81-66=15', '90-59=31'] Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,36 unequal: No Solution Exploring Operation: 15*31=465, Resulting Numbers: [465] 465,36 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,36 unequal: No Solution Moving to Node #0,0,1 Current State: 36:[59, 6], Operations: ['81-66=15', '90/15=6'] Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,36 unequal: No Solution Exploring Operation: 59*6=354, Resulting Numbers: [354] 354,36 unequal: No Solution Exploring Operation: 59+6=65, Resulting Numbers: [65] 65,36 unequal: No Solution Moving to Node #0,0,3 Current State: 36:[90, 44], Operations: ['81-66=15', '59-15=44'] Exploring Operation: 90-44=46, Resulting Numbers: [46] 46,36 unequal: No Solution Exploring Operation: 90+44=134, Resulting Numbers: [134] 134,36 unequal: No Solution Exploring Operation: 90*44=3960, Resulting Numbers: [3960] 3960,36 unequal: No Solution Moving to Node #0,0,0 Current State: 36:[59, 75], Operations: ['81-66=15', '90-15=75'] Exploring Operation: 75-59=16, Resulting Numbers: [16] 16,36 unequal: No Solution Exploring Operation: 59+75=134, Resulting Numbers: [134] 134,36 unequal: No Solution Exploring Operation: 59*75=4425, Resulting Numbers: [4425] 4425,36 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 5, 86, 68, 34 ]
48
[ "86*34=2924", "2924/68=43", "5+43=48" ]
Current State: 48:[5, 86, 68, 34], Operations: [] Exploring Operation: 86*34=2924, Resulting Numbers: [5, 68, 2924] Generated Node #2: [5, 68, 2924] from Operation: 86*34=2924 Current State: 48:[5, 68, 2924], Operations: ['86*34=2924'] Exploring Operation: 2924/68=43, Resulting Numbers: [5, 43] Generated Node #3: [5, 43] from Operation: 2924/68=43 Current State: 48:[5, 43], Operations: ['86*34=2924', '2924/68=43'] Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[5, 86, 68, 34], Operations: [] Exploring Operation: 86-68=18, Resulting Numbers: [5, 34, 18] Generated Node #0,0: 48:[5, 34, 18] Operation: 86-68=18 Exploring Operation: 68/34=2, Resulting Numbers: [5, 86, 2] Generated Node #0,1: 48:[5, 86, 2] Operation: 68/34=2 Exploring Operation: 86-34=52, Resulting Numbers: [5, 68, 52] Generated Node #0,2: 48:[5, 68, 52] Operation: 86-34=52 Exploring Operation: 68-34=34, Resulting Numbers: [5, 86, 34] Generated Node #0,3: 48:[5, 86, 34] Operation: 68-34=34 Moving to Node #0,0 Current State: 48:[5, 34, 18], Operations: ['86-68=18'] Exploring Operation: 34-5=29, Resulting Numbers: [18, 29] Generated Node #0,0,0: 48:[18, 29] Operation: 34-5=29 Exploring Operation: 34+18=52, Resulting Numbers: [5, 52] Generated Node #0,0,1: 48:[5, 52] Operation: 34+18=52 Exploring Operation: 5+34=39, Resulting Numbers: [18, 39] Generated Node #0,0,2: 48:[18, 39] Operation: 5+34=39 Exploring Operation: 34-18=16, Resulting Numbers: [5, 16] Generated Node #0,0,3: 48:[5, 16] Operation: 34-18=16 Moving to Node #0,2 Current State: 48:[5, 68, 52], Operations: ['86-34=52'] Exploring Operation: 68-5=63, Resulting Numbers: [52, 63] Generated Node #0,2,0: 48:[52, 63] Operation: 68-5=63 Exploring Operation: 68-52=16, Resulting Numbers: [5, 16] Generated Node #0,2,1: 48:[5, 16] Operation: 68-52=16 Exploring Operation: 52-5=47, Resulting Numbers: [68, 47] Generated Node #0,2,2: 48:[68, 47] Operation: 52-5=47 Exploring Operation: 5+68=73, Resulting Numbers: [52, 73] Generated Node #0,2,3: 48:[52, 73] Operation: 5+68=73 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 48:[5, 16], Operations: ['86-34=52', '68-52=16'] Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,48 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,48 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 #0,2,0 Current State: 48:[52, 63], Operations: ['86-34=52', '68-5=63'] Exploring Operation: 52+63=115, Resulting Numbers: [115] 115,48 unequal: No Solution Exploring Operation: 52*63=3276, Resulting Numbers: [3276] 3276,48 unequal: No Solution Exploring Operation: 63-52=11, Resulting Numbers: [11] 11,48 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 #0,2,2 Current State: 48:[68, 47], Operations: ['86-34=52', '52-5=47'] Exploring Operation: 68+47=115, Resulting Numbers: [115] 115,48 unequal: No Solution Exploring Operation: 68-47=21, Resulting Numbers: [21] 21,48 unequal: No Solution Exploring Operation: 68*47=3196, Resulting Numbers: [3196] 3196,48 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 #0,2,3 Current State: 48:[52, 73], Operations: ['86-34=52', '5+68=73'] Exploring Operation: 52+73=125, Resulting Numbers: [125] 125,48 unequal: No Solution Exploring Operation: 52*73=3796, Resulting Numbers: [3796] 3796,48 unequal: No Solution Exploring Operation: 73-52=21, Resulting Numbers: [21] 21,48 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: 48:[5, 86, 2], Operations: ['68/34=2'] Exploring Operation: 86-5=81, Resulting Numbers: [2, 81] Generated Node #0,1,0: 48:[2, 81] Operation: 86-5=81 Exploring Operation: 86-2=84, Resulting Numbers: [5, 84] Generated Node #0,1,1: 48:[5, 84] Operation: 86-2=84 Exploring Operation: 86/2=43, Resulting Numbers: [5, 43] Generated Node #0,1,2: 48:[5, 43] Operation: 86/2=43 Exploring Operation: 5-2=3, Resulting Numbers: [86, 3] Generated Node #0,1,3: 48:[86, 3] Operation: 5-2=3 Moving to Node #0,3 Current State: 48:[5, 86, 34], Operations: ['68-34=34'] Exploring Operation: 86-34=52, Resulting Numbers: [5, 52] Generated Node #0,3,0: 48:[5, 52] Operation: 86-34=52 Exploring Operation: 86-5=81, Resulting Numbers: [34, 81] Generated Node #0,3,1: 48:[34, 81] Operation: 86-5=81 Exploring Operation: 34-5=29, Resulting Numbers: [86, 29] Generated Node #0,3,2: 48:[86, 29] Operation: 34-5=29 Exploring Operation: 5+34=39, Resulting Numbers: [86, 39] Generated Node #0,3,3: 48:[86, 39] Operation: 5+34=39 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 48:[5, 52], Operations: ['68-34=34', '86-34=52'] Exploring Operation: 5+52=57, Resulting Numbers: [57] 57,48 unequal: No Solution Exploring Operation: 5*52=260, Resulting Numbers: [260] 260,48 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,48 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 #0,3,1 Current State: 48:[34, 81], Operations: ['68-34=34', '86-5=81'] Exploring Operation: 81-34=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 34+81=115, Resulting Numbers: [115] 115,48 unequal: No Solution Exploring Operation: 34*81=2754, Resulting Numbers: [2754] 2754,48 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 #0,3,2 Current State: 48:[86, 29], Operations: ['68-34=34', '34-5=29'] Exploring Operation: 86*29=2494, Resulting Numbers: [2494] 2494,48 unequal: No Solution Exploring Operation: 86+29=115, Resulting Numbers: [115] 115,48 unequal: No Solution Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,48 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 #0,3,3 Current State: 48:[86, 39], Operations: ['68-34=34', '5+34=39'] Exploring Operation: 86+39=125, Resulting Numbers: [125] 125,48 unequal: No Solution Exploring Operation: 86-39=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 86*39=3354, Resulting Numbers: [3354] 3354,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 48:[5, 16], Operations: ['86-68=18', '34-18=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,48 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[5, 52], Operations: ['86-68=18', '34+18=52'] Exploring Operation: 5+52=57, Resulting Numbers: [57] 57,48 unequal: No Solution Exploring Operation: 5*52=260, Resulting Numbers: [260] 260,48 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,48 unequal: No Solution Moving to Node #0,1,2 Current State: 48:[5, 43], Operations: ['68/34=2', '86/2=43'] Exploring Operation: 5*43=215, Resulting Numbers: [215] 215,48 unequal: No Solution Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[5, 86, 68, 34], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [5, 86, 2] Generated Node #0,1: 48:[5, 86, 2] Operation: 68/34=2 Moving to Node #0,1 Current State: 48:[5, 86, 2], Operations: ['68/34=2'] Exploring Operation: 86/2=43, Resulting Numbers: [5, 43] Generated Node #0,1,2: 48:[5, 43] Operation: 86/2=43 Moving to Node #0,1,2 Current State: 48:[5, 43], Operations: ['68/34=2', '86/2=43'] Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.951389
hs_4
sum_heuristic
[ 35, 11, 10, 16 ]
91
[ "35-16=19", "11*10=110", "110-19=91" ]
Current State: 91:[35, 11, 10, 16], Operations: [] Exploring Operation: 35-16=19, Resulting Numbers: [11, 10, 19] Generated Node #2: [11, 10, 19] from Operation: 35-16=19 Current State: 91:[11, 10, 19], Operations: ['35-16=19'] Exploring Operation: 11*10=110, Resulting Numbers: [19, 110] Generated Node #3: [19, 110] from Operation: 11*10=110 Current State: 91:[19, 110], Operations: ['35-16=19', '11*10=110'] Exploring Operation: 110-19=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[35, 11, 10, 16], Operations: [] Exploring Operation: 35-16=19, Resulting Numbers: [11, 10, 19] Generated Node #0,0: 91:[11, 10, 19] Operation: 35-16=19 Moving to Node #0,0 Current State: 91:[11, 10, 19], Operations: ['35-16=19'] Exploring Operation: 19-11=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 91:[10, 8] Operation: 19-11=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 91:[10, 8], Operations: ['35-16=19', '19-11=8'] Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,91 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
[ 22, 61, 52, 31 ]
44
[ "61-22=39", "52+31=83", "83-39=44" ]
Current State: 44:[22, 61, 52, 31], Operations: [] Exploring Operation: 61-22=39, Resulting Numbers: [52, 31, 39] Generated Node #2: [52, 31, 39] from Operation: 61-22=39 Current State: 44:[52, 31, 39], Operations: ['61-22=39'] Exploring Operation: 52+31=83, Resulting Numbers: [39, 83] Generated Node #3: [39, 83] from Operation: 52+31=83 Current State: 44:[39, 83], Operations: ['61-22=39', '52+31=83'] Exploring Operation: 83-39=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[22, 61, 52, 31], Operations: [] Exploring Operation: 61-31=30, Resulting Numbers: [22, 52, 30] Generated Node #0,0: 44:[22, 52, 30] Operation: 61-31=30 Exploring Operation: 61-22=39, Resulting Numbers: [52, 31, 39] Generated Node #0,1: 44:[52, 31, 39] Operation: 61-22=39 Exploring Operation: 52-31=21, Resulting Numbers: [22, 61, 21] Generated Node #0,2: 44:[22, 61, 21] Operation: 52-31=21 Exploring Operation: 61-52=9, Resulting Numbers: [22, 31, 9] Generated Node #0,3: 44:[22, 31, 9] Operation: 61-52=9 Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[22, 31, 9], Operations: ['61-52=9'] Exploring Operation: 31-9=22, Resulting Numbers: [22, 22] Generated Node #0,3,0: 44:[22, 22] Operation: 31-9=22 Exploring Operation: 31+9=40, Resulting Numbers: [22, 40] Generated Node #0,3,1: 44:[22, 40] Operation: 31+9=40 Exploring Operation: 22+31=53, Resulting Numbers: [9, 53] Generated Node #0,3,2: 44:[9, 53] Operation: 22+31=53 Exploring Operation: 31-22=9, Resulting Numbers: [9, 9] Generated Node #0,3,3: 44:[9, 9] Operation: 31-22=9 Moving to Node #0,3,0 Current State: 44:[22, 22], Operations: ['61-52=9', '31-9=22'] Exploring Operation: 22*22=484, Resulting Numbers: [484] 484,44 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,44 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[22, 61, 52, 31], Operations: [] Exploring Operation: 61-52=9, Resulting Numbers: [22, 31, 9] Generated Node #0,3: 44:[22, 31, 9] Operation: 61-52=9 Moving to Node #0,3 Current State: 44:[22, 31, 9], Operations: ['61-52=9'] Exploring Operation: 31-9=22, Resulting Numbers: [22, 22] Generated Node #0,3,0: 44:[22, 22] Operation: 31-9=22 Moving to Node #0,3,0 Current State: 44:[22, 22], Operations: ['61-52=9', '31-9=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 42, 37, 90, 99 ]
81
[ "42-37=5", "90/5=18", "99-18=81" ]
Current State: 81:[42, 37, 90, 99], Operations: [] Exploring Operation: 42-37=5, Resulting Numbers: [90, 99, 5] Generated Node #2: [90, 99, 5] from Operation: 42-37=5 Current State: 81:[90, 99, 5], Operations: ['42-37=5'] Exploring Operation: 90/5=18, Resulting Numbers: [99, 18] Generated Node #3: [99, 18] from Operation: 90/5=18 Current State: 81:[99, 18], Operations: ['42-37=5', '90/5=18'] Exploring Operation: 99-18=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[42, 37, 90, 99], Operations: [] Exploring Operation: 99-90=9, Resulting Numbers: [42, 37, 9] Generated Node #0,0: 81:[42, 37, 9] Operation: 99-90=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[42, 37, 9], Operations: ['99-90=9'] Exploring Operation: 42+37=79, Resulting Numbers: [9, 79] Generated Node #0,0,0: 81:[9, 79] Operation: 42+37=79 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[9, 79], Operations: ['99-90=9', '42+37=79'] Exploring Operation: 9+79=88, Resulting Numbers: [88] 88,81 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
[ 95, 68, 10, 2 ]
31
[ "95+10=105", "68*2=136", "136-105=31" ]
Current State: 31:[95, 68, 10, 2], Operations: [] Exploring Operation: 95+10=105, Resulting Numbers: [68, 2, 105] Generated Node #2: [68, 2, 105] from Operation: 95+10=105 Current State: 31:[68, 2, 105], Operations: ['95+10=105'] Exploring Operation: 68*2=136, Resulting Numbers: [105, 136] Generated Node #3: [105, 136] from Operation: 68*2=136 Current State: 31:[105, 136], Operations: ['95+10=105', '68*2=136'] Exploring Operation: 136-105=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[95, 68, 10, 2], Operations: [] Exploring Operation: 95-68=27, Resulting Numbers: [10, 2, 27] Generated Node #0,0: 31:[10, 2, 27] Operation: 95-68=27 Moving to Node #0,0 Current State: 31:[10, 2, 27], Operations: ['95-68=27'] Exploring Operation: 10*2=20, Resulting Numbers: [27, 20] Generated Node #0,0,0: 31:[27, 20] Operation: 10*2=20 Moving to Node #0,0,0 Current State: 31:[27, 20], Operations: ['95-68=27', '10*2=20'] Exploring Operation: 27+20=47, Resulting Numbers: [47] 47,31 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 54, 33, 67, 65 ]
89
[ "54+33=87", "67-65=2", "87+2=89" ]
Current State: 89:[54, 33, 67, 65], Operations: [] Exploring Operation: 54+33=87, Resulting Numbers: [67, 65, 87] Generated Node #2: [67, 65, 87] from Operation: 54+33=87 Current State: 89:[67, 65, 87], Operations: ['54+33=87'] Exploring Operation: 67-65=2, Resulting Numbers: [87, 2] Generated Node #3: [87, 2] from Operation: 67-65=2 Current State: 89:[87, 2], Operations: ['54+33=87', '67-65=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[54, 33, 67, 65], Operations: [] Exploring Operation: 54+67=121, Resulting Numbers: [33, 65, 121] Generated Node #0,0: 89:[33, 65, 121] Operation: 54+67=121 Exploring Operation: 54+65=119, Resulting Numbers: [33, 67, 119] Generated Node #0,1: 89:[33, 67, 119] Operation: 54+65=119 Exploring Operation: 54+33=87, Resulting Numbers: [67, 65, 87] Generated Node #0,2: 89:[67, 65, 87] Operation: 54+33=87 Exploring Operation: 33+67=100, Resulting Numbers: [54, 65, 100] Generated Node #0,3: 89:[54, 65, 100] Operation: 33+67=100 Exploring Operation: 33+65=98, Resulting Numbers: [54, 67, 98] Generated Node #0,4: 89:[54, 67, 98] Operation: 33+65=98 Moving to Node #0,2 Current State: 89:[67, 65, 87], Operations: ['54+33=87'] Exploring Operation: 65+87=152, Resulting Numbers: [67, 152] Generated Node #0,2,0: 89:[67, 152] Operation: 65+87=152 Exploring Operation: 67+87=154, Resulting Numbers: [65, 154] Generated Node #0,2,1: 89:[65, 154] Operation: 67+87=154 Exploring Operation: 87-65=22, Resulting Numbers: [67, 22] Generated Node #0,2,2: 89:[67, 22] Operation: 87-65=22 Exploring Operation: 67-65=2, Resulting Numbers: [87, 2] Generated Node #0,2,3: 89:[87, 2] Operation: 67-65=2 Exploring Operation: 67+65=132, Resulting Numbers: [87, 132] Generated Node #0,2,4: 89:[87, 132] Operation: 67+65=132 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 89:[87, 132], Operations: ['54+33=87', '67+65=132'] Exploring Operation: 87*132=11484, Resulting Numbers: [11484] 11484,89 unequal: No Solution Exploring Operation: 132-87=45, Resulting Numbers: [45] 45,89 unequal: No Solution Exploring Operation: 87+132=219, Resulting Numbers: [219] 219,89 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 #0,2,0 Current State: 89:[67, 152], Operations: ['54+33=87', '65+87=152'] Exploring Operation: 67+152=219, Resulting Numbers: [219] 219,89 unequal: No Solution Exploring Operation: 67*152=10184, Resulting Numbers: [10184] 10184,89 unequal: No Solution Exploring Operation: 152-67=85, Resulting Numbers: [85] 85,89 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 #0,2,1 Current State: 89:[65, 154], Operations: ['54+33=87', '67+87=154'] Exploring Operation: 65+154=219, Resulting Numbers: [219] 219,89 unequal: No Solution Exploring Operation: 154-65=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[54, 33, 67, 65], Operations: [] Exploring Operation: 54+33=87, Resulting Numbers: [67, 65, 87] Generated Node #0,2: 89:[67, 65, 87] Operation: 54+33=87 Moving to Node #0,2 Current State: 89:[67, 65, 87], Operations: ['54+33=87'] Exploring Operation: 67+87=154, Resulting Numbers: [65, 154] Generated Node #0,2,1: 89:[65, 154] Operation: 67+87=154 Moving to Node #0,2,1 Current State: 89:[65, 154], Operations: ['54+33=87', '67+87=154'] Exploring Operation: 154-65=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 7, 61, 97, 29 ]
14
[ "61-7=54", "97-29=68", "68-54=14" ]
Current State: 14:[7, 61, 97, 29], Operations: [] Exploring Operation: 61-7=54, Resulting Numbers: [97, 29, 54] Generated Node #2: [97, 29, 54] from Operation: 61-7=54 Current State: 14:[97, 29, 54], Operations: ['61-7=54'] Exploring Operation: 97-29=68, Resulting Numbers: [54, 68] Generated Node #3: [54, 68] from Operation: 97-29=68 Current State: 14:[54, 68], Operations: ['61-7=54', '97-29=68'] Exploring Operation: 68-54=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[7, 61, 97, 29], Operations: [] Exploring Operation: 61-29=32, Resulting Numbers: [7, 97, 32] Generated Node #0,0: 14:[7, 97, 32] Operation: 61-29=32 Exploring Operation: 97-61=36, Resulting Numbers: [7, 29, 36] Generated Node #0,1: 14:[7, 29, 36] Operation: 97-61=36 Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[7, 29, 36], Operations: ['97-61=36'] Exploring Operation: 29-7=22, Resulting Numbers: [36, 22] Generated Node #0,1,0: 14:[36, 22] Operation: 29-7=22 Exploring Operation: 36-29=7, Resulting Numbers: [7, 7] Generated Node #0,1,1: 14:[7, 7] Operation: 36-29=7 Moving to Node #0,1,1 Current State: 14:[7, 7], Operations: ['97-61=36', '36-29=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[7, 61, 97, 29], Operations: [] Exploring Operation: 97-61=36, Resulting Numbers: [7, 29, 36] Generated Node #0,1: 14:[7, 29, 36] Operation: 97-61=36 Moving to Node #0,1 Current State: 14:[7, 29, 36], Operations: ['97-61=36'] Exploring Operation: 36-29=7, Resulting Numbers: [7, 7] Generated Node #0,1,1: 14:[7, 7] Operation: 36-29=7 Moving to Node #0,1,1 Current State: 14:[7, 7], Operations: ['97-61=36', '36-29=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 69, 16, 27, 81 ]
39
[ "69*27=1863", "1863/81=23", "16+23=39" ]
Current State: 39:[69, 16, 27, 81], Operations: [] Exploring Operation: 69*27=1863, Resulting Numbers: [16, 81, 1863] Generated Node #2: [16, 81, 1863] from Operation: 69*27=1863 Current State: 39:[16, 81, 1863], Operations: ['69*27=1863'] Exploring Operation: 1863/81=23, Resulting Numbers: [16, 23] Generated Node #3: [16, 23] from Operation: 1863/81=23 Current State: 39:[16, 23], Operations: ['69*27=1863', '1863/81=23'] Exploring Operation: 16+23=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[69, 16, 27, 81], Operations: [] Exploring Operation: 81-69=12, Resulting Numbers: [16, 27, 12] Generated Node #0,0: 39:[16, 27, 12] Operation: 81-69=12 Exploring Operation: 81/27=3, Resulting Numbers: [69, 16, 3] Generated Node #0,1: 39:[69, 16, 3] Operation: 81/27=3 Exploring Operation: 69-27=42, Resulting Numbers: [16, 81, 42] Generated Node #0,2: 39:[16, 81, 42] Operation: 69-27=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[16, 27, 12], Operations: ['81-69=12'] Exploring Operation: 27+12=39, Resulting Numbers: [16, 39] Generated Node #0,0,0: 39:[16, 39] Operation: 27+12=39 Exploring Operation: 16+27=43, Resulting Numbers: [12, 43] Generated Node #0,0,1: 39:[12, 43] Operation: 16+27=43 Exploring Operation: 27-16=11, Resulting Numbers: [12, 11] Generated Node #0,0,2: 39:[12, 11] Operation: 27-16=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[16, 39], Operations: ['81-69=12', '27+12=39'] Exploring Operation: 39-16=23, Resulting Numbers: [23] 23,39 unequal: No Solution Exploring Operation: 16+39=55, Resulting Numbers: [55] 55,39 unequal: No Solution Exploring Operation: 16*39=624, Resulting Numbers: [624] 624,39 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: 39:[12, 11], Operations: ['81-69=12', '27-16=11'] Exploring Operation: 12*11=132, Resulting Numbers: [132] 132,39 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,39 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: 39:[12, 43], Operations: ['81-69=12', '16+27=43'] Exploring Operation: 12+43=55, Resulting Numbers: [55] 55,39 unequal: No Solution Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 12*43=516, Resulting Numbers: [516] 516,39 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: 39:[69, 16, 3], Operations: ['81/27=3'] Exploring Operation: 69-16=53, Resulting Numbers: [3, 53] Generated Node #0,1,0: 39:[3, 53] Operation: 69-16=53 Exploring Operation: 69/3=23, Resulting Numbers: [16, 23] Generated Node #0,1,1: 39:[16, 23] Operation: 69/3=23 Exploring Operation: 69-3=66, Resulting Numbers: [16, 66] Generated Node #0,1,2: 39:[16, 66] Operation: 69-3=66 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 39:[16, 23], Operations: ['81/27=3', '69/3=23'] Exploring Operation: 16+23=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[69, 16, 27, 81], Operations: [] Exploring Operation: 81/27=3, Resulting Numbers: [69, 16, 3] Generated Node #0,1: 39:[69, 16, 3] Operation: 81/27=3 Moving to Node #0,1 Current State: 39:[69, 16, 3], Operations: ['81/27=3'] Exploring Operation: 69/3=23, Resulting Numbers: [16, 23] Generated Node #0,1,1: 39:[16, 23] Operation: 69/3=23 Moving to Node #0,1,1 Current State: 39:[16, 23], Operations: ['81/27=3', '69/3=23'] Exploring Operation: 16+23=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 69, 23, 71, 23 ]
91
[ "69/23=3", "71+23=94", "94-3=91" ]
Current State: 91:[69, 23, 71, 23], Operations: [] Exploring Operation: 69/23=3, Resulting Numbers: [71, 3] Generated Node #2: [71, 3] from Operation: 69/23=3 Current State: 91:[71, 3], Operations: ['69/23=3'] Exploring Operation: 71+23=94, Resulting Numbers: [3, 94] Generated Node #3: [3, 94] from Operation: 71+23=94 Current State: 91:[3, 94], Operations: ['69/23=3', '71+23=94'] Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[69, 23, 71, 23], Operations: [] Exploring Operation: 69+23=92, Resulting Numbers: [71, 23, 92] Generated Node #0,0: 91:[71, 23, 92] Operation: 69+23=92 Exploring Operation: 71-69=2, Resulting Numbers: [23, 23, 2] Generated Node #0,1: 91:[23, 23, 2] Operation: 71-69=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[23, 23, 2], Operations: ['71-69=2'] Exploring Operation: 23/23=1, Resulting Numbers: [2, 1] Generated Node #0,1,0: 91:[2, 1] Operation: 23/23=1 Exploring Operation: 23-23=0, Resulting Numbers: [2, 0] Generated Node #0,1,1: 91:[2, 0] Operation: 23-23=0 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[2, 1], Operations: ['71-69=2', '23/23=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,91 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 #0,1,1 Current State: 91:[2, 0], Operations: ['71-69=2', '23-23=0'] Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,91 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 #0,0 Current State: 91:[71, 23, 92], Operations: ['69+23=92'] Exploring Operation: 92-71=21, Resulting Numbers: [23, 21] Generated Node #0,0,0: 91:[23, 21] Operation: 92-71=21 Exploring Operation: 71+23=94, Resulting Numbers: [92, 94] Generated Node #0,0,1: 91:[92, 94] Operation: 71+23=94 Moving to Node #0,0,1 Current State: 91:[92, 94], Operations: ['69+23=92', '71+23=94'] Exploring Operation: 92+94=186, Resulting Numbers: [186] 186,91 unequal: No Solution Exploring Operation: 94-92=2, Resulting Numbers: [2] 2,91 unequal: No Solution Moving to Node #0,0,0 Current State: 91:[23, 21], Operations: ['69+23=92', '92-71=21'] Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,91 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
[ 33, 12, 59, 9 ]
82
[ "59-33=26", "12*9=108", "108-26=82" ]
Current State: 82:[33, 12, 59, 9], Operations: [] Exploring Operation: 59-33=26, Resulting Numbers: [12, 9, 26] Generated Node #2: [12, 9, 26] from Operation: 59-33=26 Current State: 82:[12, 9, 26], Operations: ['59-33=26'] Exploring Operation: 12*9=108, Resulting Numbers: [26, 108] Generated Node #3: [26, 108] from Operation: 12*9=108 Current State: 82:[26, 108], Operations: ['59-33=26', '12*9=108'] Exploring Operation: 108-26=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[33, 12, 59, 9], Operations: [] Exploring Operation: 59-12=47, Resulting Numbers: [33, 9, 47] Generated Node #0,0: 82:[33, 9, 47] Operation: 59-12=47 Exploring Operation: 33+59=92, Resulting Numbers: [12, 9, 92] Generated Node #0,1: 82:[12, 9, 92] Operation: 33+59=92 Exploring Operation: 12+59=71, Resulting Numbers: [33, 9, 71] Generated Node #0,2: 82:[33, 9, 71] Operation: 12+59=71 Exploring Operation: 12-9=3, Resulting Numbers: [33, 59, 3] Generated Node #0,3: 82:[33, 59, 3] Operation: 12-9=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[33, 9, 47], Operations: ['59-12=47'] Exploring Operation: 47-33=14, Resulting Numbers: [9, 14] Generated Node #0,0,0: 82:[9, 14] Operation: 47-33=14 Exploring Operation: 47-9=38, Resulting Numbers: [33, 38] Generated Node #0,0,1: 82:[33, 38] Operation: 47-9=38 Exploring Operation: 33+47=80, Resulting Numbers: [9, 80] Generated Node #0,0,2: 82:[9, 80] Operation: 33+47=80 Exploring Operation: 33+9=42, Resulting Numbers: [47, 42] Generated Node #0,0,3: 82:[47, 42] Operation: 33+9=42 Moving to Node #0,0,3 Current State: 82:[47, 42], Operations: ['59-12=47', '33+9=42'] Exploring Operation: 47+42=89, Resulting Numbers: [89] 89,82 unequal: No Solution Exploring Operation: 47*42=1974, Resulting Numbers: [1974] 1974,82 unequal: No Solution Exploring Operation: 47-42=5, Resulting Numbers: [5] 5,82 unequal: No Solution Moving to Node #0,0,2 Current State: 82:[9, 80], Operations: ['59-12=47', '33+47=80'] Exploring Operation: 9+80=89, Resulting Numbers: [89] 89,82 unequal: No Solution Exploring Operation: 9*80=720, Resulting Numbers: [720] 720,82 unequal: No Solution Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[33, 38], Operations: ['59-12=47', '47-9=38'] Exploring Operation: 33+38=71, Resulting Numbers: [71] 71,82 unequal: No Solution Exploring Operation: 33*38=1254, Resulting Numbers: [1254] 1254,82 unequal: No Solution Exploring Operation: 38-33=5, Resulting Numbers: [5] 5,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[9, 14], Operations: ['59-12=47', '47-33=14'] Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,82 unequal: No Solution Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,82 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,82 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:[33, 9, 71], Operations: ['12+59=71'] Exploring Operation: 71-33=38, Resulting Numbers: [9, 38] Generated Node #0,2,0: 82:[9, 38] Operation: 71-33=38 Exploring Operation: 33-9=24, Resulting Numbers: [71, 24] Generated Node #0,2,1: 82:[71, 24] Operation: 33-9=24 Exploring Operation: 9+71=80, Resulting Numbers: [33, 80] Generated Node #0,2,2: 82:[33, 80] Operation: 9+71=80 Exploring Operation: 33+9=42, Resulting Numbers: [71, 42] Generated Node #0,2,3: 82:[71, 42] Operation: 33+9=42 Moving to Node #0,2,0 Current State: 82:[9, 38], Operations: ['12+59=71', '71-33=38'] Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,82 unequal: No Solution Exploring Operation: 9+38=47, Resulting Numbers: [47] 47,82 unequal: No Solution Exploring Operation: 9*38=342, Resulting Numbers: [342] 342,82 unequal: No Solution Moving to Node #0,2,2 Current State: 82:[33, 80], Operations: ['12+59=71', '9+71=80'] Exploring Operation: 33*80=2640, Resulting Numbers: [2640] 2640,82 unequal: No Solution Exploring Operation: 33+80=113, Resulting Numbers: [113] 113,82 unequal: No Solution Exploring Operation: 80-33=47, Resulting Numbers: [47] 47,82 unequal: No Solution Moving to Node #0,2,3 Current State: 82:[71, 42], Operations: ['12+59=71', '33+9=42'] Exploring Operation: 71-42=29, Resulting Numbers: [29] 29,82 unequal: No Solution Exploring Operation: 71*42=2982, Resulting Numbers: [2982] 2982,82 unequal: No Solution Exploring Operation: 71+42=113, Resulting Numbers: [113] 113,82 unequal: No Solution Moving to Node #0,2,1 Current State: 82:[71, 24], Operations: ['12+59=71', '33-9=24'] Exploring Operation: 71*24=1704, Resulting Numbers: [1704] 1704,82 unequal: No Solution Exploring Operation: 71+24=95, Resulting Numbers: [95] 95,82 unequal: No Solution Exploring Operation: 71-24=47, Resulting Numbers: [47] 47,82 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 Current State: 82:[12, 9, 92], Operations: ['33+59=92'] Exploring Operation: 12+9=21, Resulting Numbers: [92, 21] Generated Node #0,1,0: 82:[92, 21] Operation: 12+9=21 Exploring Operation: 92-12=80, Resulting Numbers: [9, 80] Generated Node #0,1,1: 82:[9, 80] Operation: 92-12=80 Exploring Operation: 92-9=83, Resulting Numbers: [12, 83] Generated Node #0,1,2: 82:[12, 83] Operation: 92-9=83 Exploring Operation: 12-9=3, Resulting Numbers: [92, 3] Generated Node #0,1,3: 82:[92, 3] Operation: 12-9=3 Moving to Node #0,1,1 Current State: 82:[9, 80], Operations: ['33+59=92', '92-12=80'] Exploring Operation: 9*80=720, Resulting Numbers: [720] 720,82 unequal: No Solution Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,82 unequal: No Solution Exploring Operation: 9+80=89, Resulting Numbers: [89] 89,82 unequal: No Solution Moving to Node #0,1,3 Current State: 82:[92, 3], Operations: ['33+59=92', '12-9=3'] Exploring Operation: 92*3=276, Resulting Numbers: [276] 276,82 unequal: No Solution Exploring Operation: 92+3=95, Resulting Numbers: [95] 95,82 unequal: No Solution Exploring Operation: 92-3=89, Resulting Numbers: [89] 89,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[12, 83], Operations: ['33+59=92', '92-9=83'] Exploring Operation: 12+83=95, Resulting Numbers: [95] 95,82 unequal: No Solution Exploring Operation: 12*83=996, Resulting Numbers: [996] 996,82 unequal: No Solution Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[92, 21], Operations: ['33+59=92', '12+9=21'] Exploring Operation: 92*21=1932, Resulting Numbers: [1932] 1932,82 unequal: No Solution Exploring Operation: 92-21=71, Resulting Numbers: [71] 71,82 unequal: No Solution Exploring Operation: 92+21=113, Resulting Numbers: [113] 113,82 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 #0,3 Current State: 82:[33, 59, 3], Operations: ['12-9=3'] Exploring Operation: 59-33=26, Resulting Numbers: [3, 26] Generated Node #0,3,0: 82:[3, 26] Operation: 59-33=26 Exploring Operation: 33+3=36, Resulting Numbers: [59, 36] Generated Node #0,3,1: 82:[59, 36] Operation: 33+3=36 Exploring Operation: 33+59=92, Resulting Numbers: [3, 92] Generated Node #0,3,2: 82:[3, 92] Operation: 33+59=92 Exploring Operation: 59-3=56, Resulting Numbers: [33, 56] Generated Node #0,3,3: 82:[33, 56] Operation: 59-3=56 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 82:[3, 92], Operations: ['12-9=3', '33+59=92'] Exploring Operation: 92-3=89, Resulting Numbers: [89] 89,82 unequal: No Solution Exploring Operation: 3+92=95, Resulting Numbers: [95] 95,82 unequal: No Solution Exploring Operation: 3*92=276, Resulting Numbers: [276] 276,82 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 #0,3,0 Current State: 82:[3, 26], Operations: ['12-9=3', '59-33=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,82 unequal: No Solution Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,82 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,82 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 #0,3,1 Current State: 82:[59, 36], Operations: ['12-9=3', '33+3=36'] Exploring Operation: 59*36=2124, Resulting Numbers: [2124] 2124,82 unequal: No Solution Exploring Operation: 59-36=23, Resulting Numbers: [23] 23,82 unequal: No Solution Exploring Operation: 59+36=95, Resulting Numbers: [95] 95,82 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 #0,3,3 Current State: 82:[33, 56], Operations: ['12-9=3', '59-3=56'] Exploring Operation: 33+56=89, Resulting Numbers: [89] 89,82 unequal: No Solution Exploring Operation: 33*56=1848, Resulting Numbers: [1848] 1848,82 unequal: No Solution Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,82 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 No solution found.
0
hs_4
mult_heuristic
[ 17, 76, 44, 11 ]
67
[ "17*11=187", "76+44=120", "187-120=67" ]
Current State: 67:[17, 76, 44, 11], Operations: [] Exploring Operation: 17*11=187, Resulting Numbers: [76, 44, 187] Generated Node #2: [76, 44, 187] from Operation: 17*11=187 Current State: 67:[76, 44, 187], Operations: ['17*11=187'] Exploring Operation: 76+44=120, Resulting Numbers: [187, 120] Generated Node #3: [187, 120] from Operation: 76+44=120 Current State: 67:[187, 120], Operations: ['17*11=187', '76+44=120'] Exploring Operation: 187-120=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[17, 76, 44, 11], Operations: [] Exploring Operation: 17+44=61, Resulting Numbers: [76, 11, 61] Generated Node #0,0: 67:[76, 11, 61] Operation: 17+44=61 Moving to Node #0,0 Current State: 67:[76, 11, 61], Operations: ['17+44=61'] Exploring Operation: 76-11=65, Resulting Numbers: [61, 65] Generated Node #0,0,0: 67:[61, 65] Operation: 76-11=65 Moving to Node #0,0,0 Current State: 67:[61, 65], Operations: ['17+44=61', '76-11=65'] Exploring Operation: 61+65=126, Resulting Numbers: [126] 126,67 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 10, 28, 62, 81 ]
37
[ "28-10=18", "81-62=19", "18+19=37" ]
Current State: 37:[10, 28, 62, 81], Operations: [] Exploring Operation: 28-10=18, Resulting Numbers: [62, 81, 18] Generated Node #2: [62, 81, 18] from Operation: 28-10=18 Current State: 37:[62, 81, 18], Operations: ['28-10=18'] Exploring Operation: 81-62=19, Resulting Numbers: [18, 19] Generated Node #3: [18, 19] from Operation: 81-62=19 Current State: 37:[18, 19], Operations: ['28-10=18', '81-62=19'] Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[10, 28, 62, 81], Operations: [] Exploring Operation: 81-10=71, Resulting Numbers: [28, 62, 71] Generated Node #0,0: 37:[28, 62, 71] Operation: 81-10=71 Exploring Operation: 81-62=19, Resulting Numbers: [10, 28, 19] Generated Node #0,1: 37:[10, 28, 19] Operation: 81-62=19 Exploring Operation: 62-10=52, Resulting Numbers: [28, 81, 52] Generated Node #0,2: 37:[28, 81, 52] Operation: 62-10=52 Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[10, 28, 19], Operations: ['81-62=19'] Exploring Operation: 10+19=29, Resulting Numbers: [28, 29] Generated Node #0,1,0: 37:[28, 29] Operation: 10+19=29 Exploring Operation: 28-10=18, Resulting Numbers: [19, 18] Generated Node #0,1,1: 37:[19, 18] Operation: 28-10=18 Exploring Operation: 10+28=38, Resulting Numbers: [19, 38] Generated Node #0,1,2: 37:[19, 38] Operation: 10+28=38 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 37:[28, 29], Operations: ['81-62=19', '10+19=29'] Exploring Operation: 28*29=812, Resulting Numbers: [812] 812,37 unequal: No Solution Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 28+29=57, Resulting Numbers: [57] 57,37 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:[19, 38], Operations: ['81-62=19', '10+28=38'] Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,37 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,37 unequal: No Solution Exploring Operation: 19+38=57, Resulting Numbers: [57] 57,37 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:[19, 18], Operations: ['81-62=19', '28-10=18'] Exploring Operation: 19*18=342, Resulting Numbers: [342] 342,37 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 19+18=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[10, 28, 62, 81], Operations: [] Exploring Operation: 81-62=19, Resulting Numbers: [10, 28, 19] Generated Node #0,1: 37:[10, 28, 19] Operation: 81-62=19 Moving to Node #0,1 Current State: 37:[10, 28, 19], Operations: ['81-62=19'] Exploring Operation: 28-10=18, Resulting Numbers: [19, 18] Generated Node #0,1,1: 37:[19, 18] Operation: 28-10=18 Moving to Node #0,1,1 Current State: 37:[19, 18], Operations: ['81-62=19', '28-10=18'] Exploring Operation: 19+18=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_3
mult_heuristic
[ 98, 66, 84, 96 ]
36
[ "98-96=2", "84-66=18", "2*18=36" ]
Current State: 36:[98, 66, 84, 96], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [66, 84, 2] Generated Node #2: [66, 84, 2] from Operation: 98-96=2 Current State: 36:[66, 84, 2], Operations: ['98-96=2'] Exploring Operation: 84-66=18, Resulting Numbers: [2, 18] Generated Node #3: [2, 18] from Operation: 84-66=18 Current State: 36:[2, 18], Operations: ['98-96=2', '84-66=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[98, 66, 84, 96], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [66, 84, 2] Generated Node #0,0: 36:[66, 84, 2] Operation: 98-96=2 Moving to Node #0,0 Current State: 36:[66, 84, 2], Operations: ['98-96=2'] Exploring Operation: 84-66=18, Resulting Numbers: [2, 18] Generated Node #0,0,0: 36:[2, 18] Operation: 84-66=18 Moving to Node #0,0,0 Current State: 36:[2, 18], Operations: ['98-96=2', '84-66=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[98, 66, 84, 96], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [66, 84, 2] Generated Node #0,0: 36:[66, 84, 2] Operation: 98-96=2 Moving to Node #0,0 Current State: 36:[66, 84, 2], Operations: ['98-96=2'] Exploring Operation: 84-66=18, Resulting Numbers: [2, 18] Generated Node #0,0,0: 36:[2, 18] Operation: 84-66=18 Moving to Node #0,0,0 Current State: 36:[2, 18], Operations: ['98-96=2', '84-66=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 99, 20, 6, 8 ]
97
[ "20-8=12", "12/6=2", "99-2=97" ]
Current State: 97:[99, 20, 6, 8], Operations: [] Exploring Operation: 20-8=12, Resulting Numbers: [99, 6, 12] Generated Node #2: [99, 6, 12] from Operation: 20-8=12 Current State: 97:[99, 6, 12], Operations: ['20-8=12'] Exploring Operation: 12/6=2, Resulting Numbers: [99, 2] Generated Node #3: [99, 2] from Operation: 12/6=2 Current State: 97:[99, 2], Operations: ['20-8=12', '12/6=2'] Exploring Operation: 99-2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[99, 20, 6, 8], Operations: [] Exploring Operation: 20*6=120, Resulting Numbers: [99, 8, 120] Generated Node #0,0: 97:[99, 8, 120] Operation: 20*6=120 Moving to Node #0,0 Current State: 97:[99, 8, 120], Operations: ['20*6=120'] Exploring Operation: 120-8=112, Resulting Numbers: [99, 112] Generated Node #0,0,0: 97:[99, 112] Operation: 120-8=112 Moving to Node #0,0,0 Current State: 97:[99, 112], Operations: ['20*6=120', '120-8=112'] Exploring Operation: 112-99=13, Resulting Numbers: [13] 13,97 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 98, 91, 18, 3 ]
69
[ "98+91=189", "18+189=207", "207/3=69" ]
Current State: 69:[98, 91, 18, 3], Operations: [] Exploring Operation: 98+91=189, Resulting Numbers: [18, 3, 189] Generated Node #2: [18, 3, 189] from Operation: 98+91=189 Current State: 69:[18, 3, 189], Operations: ['98+91=189'] Exploring Operation: 18+189=207, Resulting Numbers: [3, 207] Generated Node #3: [3, 207] from Operation: 18+189=207 Current State: 69:[3, 207], Operations: ['98+91=189', '18+189=207'] Exploring Operation: 207/3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[98, 91, 18, 3], Operations: [] Exploring Operation: 98-91=7, Resulting Numbers: [18, 3, 7] Generated Node #0,0: 69:[18, 3, 7] Operation: 98-91=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[18, 3, 7], Operations: ['98-91=7'] Exploring Operation: 18+7=25, Resulting Numbers: [3, 25] Generated Node #0,0,0: 69:[3, 25] Operation: 18+7=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[3, 25], Operations: ['98-91=7', '18+7=25'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,69 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
[ 22, 48, 8, 28 ]
20
[ "22+48=70", "8*70=560", "560/28=20" ]
Current State: 20:[22, 48, 8, 28], Operations: [] Exploring Operation: 22+48=70, Resulting Numbers: [8, 28, 70] Generated Node #2: [8, 28, 70] from Operation: 22+48=70 Current State: 20:[8, 28, 70], Operations: ['22+48=70'] Exploring Operation: 8*70=560, Resulting Numbers: [28, 560] Generated Node #3: [28, 560] from Operation: 8*70=560 Current State: 20:[28, 560], Operations: ['22+48=70', '8*70=560'] Exploring Operation: 560/28=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[22, 48, 8, 28], Operations: [] Exploring Operation: 28-8=20, Resulting Numbers: [22, 48, 20] Generated Node #0,0: 20:[22, 48, 20] Operation: 28-8=20 Exploring Operation: 48-22=26, Resulting Numbers: [8, 28, 26] Generated Node #0,1: 20:[8, 28, 26] Operation: 48-22=26 Exploring Operation: 48-8=40, Resulting Numbers: [22, 28, 40] Generated Node #0,2: 20:[22, 28, 40] Operation: 48-8=40 Exploring Operation: 48/8=6, Resulting Numbers: [22, 28, 6] Generated Node #0,3: 20:[22, 28, 6] Operation: 48/8=6 Exploring Operation: 48-28=20, Resulting Numbers: [22, 8, 20] Generated Node #0,4: 20:[22, 8, 20] Operation: 48-28=20 Moving to Node #0,4 Current State: 20:[22, 8, 20], Operations: ['48-28=20'] Exploring Operation: 22-8=14, Resulting Numbers: [20, 14] Generated Node #0,4,0: 20:[20, 14] Operation: 22-8=14 Exploring Operation: 22+8=30, Resulting Numbers: [20, 30] Generated Node #0,4,1: 20:[20, 30] Operation: 22+8=30 Exploring Operation: 22-20=2, Resulting Numbers: [8, 2] Generated Node #0,4,2: 20:[8, 2] Operation: 22-20=2 Exploring Operation: 8+20=28, Resulting Numbers: [22, 28] Generated Node #0,4,3: 20:[22, 28] Operation: 8+20=28 Exploring Operation: 20-8=12, Resulting Numbers: [22, 12] Generated Node #0,4,4: 20:[22, 12] Operation: 20-8=12 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 20:[8, 2], Operations: ['48-28=20', '22-20=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,20 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 #0,4,0 Current State: 20:[20, 14], Operations: ['48-28=20', '22-8=14'] Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,20 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,20 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 #0,4,4 Current State: 20:[22, 12], Operations: ['48-28=20', '20-8=12'] Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 22+12=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 22*12=264, Resulting Numbers: [264] 264,20 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 #0,4,1 Current State: 20:[20, 30], Operations: ['48-28=20', '22+8=30'] Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,20 unequal: No Solution Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,20 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,20 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 #0,4,3 Current State: 20:[22, 28], Operations: ['48-28=20', '8+20=28'] Exploring Operation: 22*28=616, Resulting Numbers: [616] 616,20 unequal: No Solution Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 22+28=50, Resulting Numbers: [50] 50,20 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: 20:[22, 28, 6], Operations: ['48/8=6'] Exploring Operation: 28-22=6, Resulting Numbers: [6, 6] Generated Node #0,3,0: 20:[6, 6] Operation: 28-22=6 Exploring Operation: 28-6=22, Resulting Numbers: [22, 22] Generated Node #0,3,1: 20:[22, 22] Operation: 28-6=22 Exploring Operation: 22-6=16, Resulting Numbers: [28, 16] Generated Node #0,3,2: 20:[28, 16] Operation: 22-6=16 Exploring Operation: 28+6=34, Resulting Numbers: [22, 34] Generated Node #0,3,3: 20:[22, 34] Operation: 28+6=34 Exploring Operation: 22+6=28, Resulting Numbers: [28, 28] Generated Node #0,3,4: 20:[28, 28] Operation: 22+6=28 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 20:[6, 6], Operations: ['48/8=6', '28-22=6'] Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,20 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,20 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,20 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 #0,3,1 Current State: 20:[22, 22], Operations: ['48/8=6', '28-6=22'] Exploring Operation: 22*22=484, Resulting Numbers: [484] 484,20 unequal: No Solution Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,20 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,20 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,20 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 #0,3,2 Current State: 20:[28, 16], Operations: ['48/8=6', '22-6=16'] Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,20 unequal: No Solution Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,20 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,20 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 #0,3,3 Current State: 20:[22, 34], Operations: ['48/8=6', '28+6=34'] Exploring Operation: 22*34=748, Resulting Numbers: [748] 748,20 unequal: No Solution Exploring Operation: 22+34=56, Resulting Numbers: [56] 56,20 unequal: No Solution Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,20 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 #0,3,4 Current State: 20:[28, 28], Operations: ['48/8=6', '22+6=28'] Exploring Operation: 28*28=784, Resulting Numbers: [784] 784,20 unequal: No Solution Exploring Operation: 28/28=1, Resulting Numbers: [1] 1,20 unequal: No Solution Exploring Operation: 28-28=0, Resulting Numbers: [0] 0,20 unequal: No Solution Exploring Operation: 28+28=56, Resulting Numbers: [56] 56,20 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: 20:[8, 28, 26], Operations: ['48-22=26'] Exploring Operation: 28-8=20, Resulting Numbers: [26, 20] Generated Node #0,1,0: 20:[26, 20] Operation: 28-8=20 Exploring Operation: 26-8=18, Resulting Numbers: [28, 18] Generated Node #0,1,1: 20:[28, 18] Operation: 26-8=18 Exploring Operation: 8+28=36, Resulting Numbers: [26, 36] Generated Node #0,1,2: 20:[26, 36] Operation: 8+28=36 Exploring Operation: 8+26=34, Resulting Numbers: [28, 34] Generated Node #0,1,3: 20:[28, 34] Operation: 8+26=34 Exploring Operation: 28-26=2, Resulting Numbers: [8, 2] Generated Node #0,1,4: 20:[8, 2] Operation: 28-26=2 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 20:[8, 2], Operations: ['48-22=26', '28-26=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,20 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 #0,1,0 Current State: 20:[26, 20], Operations: ['48-22=26', '28-8=20'] Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 26+20=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 26*20=520, Resulting Numbers: [520] 520,20 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 #0,1,1 Current State: 20:[28, 18], Operations: ['48-22=26', '26-8=18'] Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 28*18=504, Resulting Numbers: [504] 504,20 unequal: No Solution Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,20 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 #0,1,2 Current State: 20:[26, 36], Operations: ['48-22=26', '8+28=36'] Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 26+36=62, Resulting Numbers: [62] 62,20 unequal: No Solution Exploring Operation: 26*36=936, Resulting Numbers: [936] 936,20 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 #0,1,3 Current State: 20:[28, 34], Operations: ['48-22=26', '8+26=34'] Exploring Operation: 28*34=952, Resulting Numbers: [952] 952,20 unequal: No Solution Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 28+34=62, Resulting Numbers: [62] 62,20 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: 20:[22, 48, 20], Operations: ['28-8=20'] Exploring Operation: 48-22=26, Resulting Numbers: [20, 26] Generated Node #0,0,0: 20:[20, 26] Operation: 48-22=26 Exploring Operation: 22-20=2, Resulting Numbers: [48, 2] Generated Node #0,0,1: 20:[48, 2] Operation: 22-20=2 Exploring Operation: 22+48=70, Resulting Numbers: [20, 70] Generated Node #0,0,2: 20:[20, 70] Operation: 22+48=70 Exploring Operation: 48-20=28, Resulting Numbers: [22, 28] Generated Node #0,0,3: 20:[22, 28] Operation: 48-20=28 Exploring Operation: 22+20=42, Resulting Numbers: [48, 42] Generated Node #0,0,4: 20:[48, 42] Operation: 22+20=42 Moving to Node #0,2 Current State: 20:[22, 28, 40], Operations: ['48-8=40'] Exploring Operation: 40-22=18, Resulting Numbers: [28, 18] Generated Node #0,2,0: 20:[28, 18] Operation: 40-22=18 Exploring Operation: 40-28=12, Resulting Numbers: [22, 12] Generated Node #0,2,1: 20:[22, 12] Operation: 40-28=12 Exploring Operation: 22+40=62, Resulting Numbers: [28, 62] Generated Node #0,2,2: 20:[28, 62] Operation: 22+40=62 Exploring Operation: 22+28=50, Resulting Numbers: [40, 50] Generated Node #0,2,3: 20:[40, 50] Operation: 22+28=50 Exploring Operation: 28-22=6, Resulting Numbers: [40, 6] Generated Node #0,2,4: 20:[40, 6] Operation: 28-22=6 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 20:[22, 12], Operations: ['48-8=40', '40-28=12'] Exploring Operation: 22*12=264, Resulting Numbers: [264] 264,20 unequal: No Solution Exploring Operation: 22+12=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,20 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 #0,2,0 Current State: 20:[28, 18], Operations: ['48-8=40', '40-22=18'] Exploring Operation: 28*18=504, Resulting Numbers: [504] 504,20 unequal: No Solution Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,20 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 #0,2,4 Current State: 20:[40, 6], Operations: ['48-8=40', '28-22=6'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 40*6=240, Resulting Numbers: [240] 240,20 unequal: No Solution Exploring Operation: 40+6=46, Resulting Numbers: [46] 46,20 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 #0,2,2 Current State: 20:[28, 62], Operations: ['48-8=40', '22+40=62'] Exploring Operation: 62-28=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 28*62=1736, Resulting Numbers: [1736] 1736,20 unequal: No Solution Exploring Operation: 28+62=90, Resulting Numbers: [90] 90,20 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 #0,2,3 Current State: 20:[40, 50], Operations: ['48-8=40', '22+28=50'] Exploring Operation: 40+50=90, Resulting Numbers: [90] 90,20 unequal: No Solution Exploring Operation: 40*50=2000, Resulting Numbers: [2000] 2000,20 unequal: No Solution Exploring Operation: 50-40=10, Resulting Numbers: [10] 10,20 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: 20:[20, 26], Operations: ['28-8=20', '48-22=26'] Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,20 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,20 unequal: No Solution Moving to Node #0,0,3 Current State: 20:[22, 28], Operations: ['28-8=20', '48-20=28'] Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 22*28=616, Resulting Numbers: [616] 616,20 unequal: No Solution Exploring Operation: 22+28=50, Resulting Numbers: [50] 50,20 unequal: No Solution Moving to Node #0,0,1 Current State: 20:[48, 2], Operations: ['28-8=20', '22-20=2'] Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,20 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,20 unequal: No Solution Moving to Node #0,0,2 Current State: 20:[20, 70], Operations: ['28-8=20', '22+48=70'] Exploring Operation: 20+70=90, Resulting Numbers: [90] 90,20 unequal: No Solution Exploring Operation: 20*70=1400, Resulting Numbers: [1400] 1400,20 unequal: No Solution Exploring Operation: 70-20=50, Resulting Numbers: [50] 50,20 unequal: No Solution Moving to Node #0,0,4 Current State: 20:[48, 42], Operations: ['28-8=20', '22+20=42'] Exploring Operation: 48*42=2016, Resulting Numbers: [2016] 2016,20 unequal: No Solution Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 48+42=90, Resulting Numbers: [90] 90,20 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 8, 77, 39, 31 ]
93
[ "8+77=85", "39-31=8", "85+8=93" ]
Current State: 93:[8, 77, 39, 31], Operations: [] Exploring Operation: 8+77=85, Resulting Numbers: [39, 31, 85] Generated Node #2: [39, 31, 85] from Operation: 8+77=85 Current State: 93:[39, 31, 85], Operations: ['8+77=85'] Exploring Operation: 39-31=8, Resulting Numbers: [85, 8] Generated Node #3: [85, 8] from Operation: 39-31=8 Current State: 93:[85, 8], Operations: ['8+77=85', '39-31=8'] Exploring Operation: 85+8=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[8, 77, 39, 31], Operations: [] Exploring Operation: 77-39=38, Resulting Numbers: [8, 31, 38] Generated Node #0,0: 93:[8, 31, 38] Operation: 77-39=38 Exploring Operation: 8+77=85, Resulting Numbers: [39, 31, 85] Generated Node #0,1: 93:[39, 31, 85] Operation: 8+77=85 Exploring Operation: 39-8=31, Resulting Numbers: [77, 31, 31] Generated Node #0,2: 93:[77, 31, 31] Operation: 39-8=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[8, 31, 38], Operations: ['77-39=38'] Exploring Operation: 38-8=30, Resulting Numbers: [31, 30] Generated Node #0,0,0: 93:[31, 30] Operation: 38-8=30 Exploring Operation: 38-31=7, Resulting Numbers: [8, 7] Generated Node #0,0,1: 93:[8, 7] Operation: 38-31=7 Exploring Operation: 8+31=39, Resulting Numbers: [38, 39] Generated Node #0,0,2: 93:[38, 39] Operation: 8+31=39 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 93:[31, 30], Operations: ['77-39=38', '38-8=30'] Exploring Operation: 31*30=930, Resulting Numbers: [930] 930,93 unequal: No Solution Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 31+30=61, Resulting Numbers: [61] 61,93 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: 93:[8, 7], Operations: ['77-39=38', '38-31=7'] Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,93 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,93 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: 93:[38, 39], Operations: ['77-39=38', '8+31=39'] Exploring Operation: 39-38=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 38*39=1482, Resulting Numbers: [1482] 1482,93 unequal: No Solution Exploring Operation: 38+39=77, Resulting Numbers: [77] 77,93 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: 93:[39, 31, 85], Operations: ['8+77=85'] Exploring Operation: 39+31=70, Resulting Numbers: [85, 70] Generated Node #0,1,0: 93:[85, 70] Operation: 39+31=70 Exploring Operation: 39-31=8, Resulting Numbers: [85, 8] Generated Node #0,1,1: 93:[85, 8] Operation: 39-31=8 Exploring Operation: 85-39=46, Resulting Numbers: [31, 46] Generated Node #0,1,2: 93:[31, 46] Operation: 85-39=46 Moving to Node #0,1,1 Current State: 93:[85, 8], Operations: ['8+77=85', '39-31=8'] Exploring Operation: 85*8=680, Resulting Numbers: [680] 680,93 unequal: No Solution Exploring Operation: 85-8=77, Resulting Numbers: [77] 77,93 unequal: No Solution Exploring Operation: 85+8=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[8, 77, 39, 31], Operations: [] Exploring Operation: 8+77=85, Resulting Numbers: [39, 31, 85] Generated Node #0,1: 93:[39, 31, 85] Operation: 8+77=85 Moving to Node #0,1 Current State: 93:[39, 31, 85], Operations: ['8+77=85'] Exploring Operation: 39-31=8, Resulting Numbers: [85, 8] Generated Node #0,1,1: 93:[85, 8] Operation: 39-31=8 Moving to Node #0,1,1 Current State: 93:[85, 8], Operations: ['8+77=85', '39-31=8'] Exploring Operation: 85+8=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 2, 1, 92, 35 ]
74
[ "1+35=36", "36/2=18", "92-18=74" ]
Current State: 74:[2, 1, 92, 35], Operations: [] Exploring Operation: 1+35=36, Resulting Numbers: [2, 92, 36] Generated Node #2: [2, 92, 36] from Operation: 1+35=36 Current State: 74:[2, 92, 36], Operations: ['1+35=36'] Exploring Operation: 36/2=18, Resulting Numbers: [92, 18] Generated Node #3: [92, 18] from Operation: 36/2=18 Current State: 74:[92, 18], Operations: ['1+35=36', '36/2=18'] Exploring Operation: 92-18=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[2, 1, 92, 35], Operations: [] Exploring Operation: 92/2=46, Resulting Numbers: [1, 35, 46] Generated Node #0,0: 74:[1, 35, 46] Operation: 92/2=46 Exploring Operation: 92-35=57, Resulting Numbers: [2, 1, 57] Generated Node #0,1: 74:[2, 1, 57] Operation: 92-35=57 Moving to Node #0,0 Current State: 74:[1, 35, 46], Operations: ['92/2=46'] Exploring Operation: 35+46=81, Resulting Numbers: [1, 81] Generated Node #0,0,0: 74:[1, 81] Operation: 35+46=81 Exploring Operation: 1+35=36, Resulting Numbers: [46, 36] Generated Node #0,0,1: 74:[46, 36] Operation: 1+35=36 Moving to Node #0,1 Current State: 74:[2, 1, 57], Operations: ['92-35=57'] Exploring Operation: 2+57=59, Resulting Numbers: [1, 59] Generated Node #0,1,0: 74:[1, 59] Operation: 2+57=59 Exploring Operation: 1+57=58, Resulting Numbers: [2, 58] Generated Node #0,1,1: 74:[2, 58] Operation: 1+57=58 Moving to Node #0,0,0 Current State: 74:[1, 81], Operations: ['92/2=46', '35+46=81'] Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,74 unequal: No Solution Exploring Operation: 1*81=81, Resulting Numbers: [81] 81,74 unequal: No Solution Moving to Node #0,0,1 Current State: 74:[46, 36], Operations: ['92/2=46', '1+35=36'] Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,74 unequal: No Solution Exploring Operation: 46+36=82, Resulting Numbers: [82] 82,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[2, 58], Operations: ['92-35=57', '1+57=58'] Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,74 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,74 unequal: No Solution Moving to Node #0,1,0 Current State: 74:[1, 59], Operations: ['92-35=57', '2+57=59'] Exploring Operation: 1+59=60, Resulting Numbers: [60] 60,74 unequal: No Solution Exploring Operation: 1*59=59, Resulting Numbers: [59] 59,74 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 20, 11, 42, 19 ]
82
[ "20*19=380", "11*42=462", "462-380=82" ]
Current State: 82:[20, 11, 42, 19], Operations: [] Exploring Operation: 20*19=380, Resulting Numbers: [11, 42, 380] Generated Node #2: [11, 42, 380] from Operation: 20*19=380 Current State: 82:[11, 42, 380], Operations: ['20*19=380'] Exploring Operation: 11*42=462, Resulting Numbers: [380, 462] Generated Node #3: [380, 462] from Operation: 11*42=462 Current State: 82:[380, 462], Operations: ['20*19=380', '11*42=462'] Exploring Operation: 462-380=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[20, 11, 42, 19], Operations: [] Exploring Operation: 20-11=9, Resulting Numbers: [42, 19, 9] Generated Node #0,0: 82:[42, 19, 9] Operation: 20-11=9 Exploring Operation: 19-11=8, Resulting Numbers: [20, 42, 8] Generated Node #0,1: 82:[20, 42, 8] Operation: 19-11=8 Exploring Operation: 20+19=39, Resulting Numbers: [11, 42, 39] Generated Node #0,2: 82:[11, 42, 39] Operation: 20+19=39 Exploring Operation: 20-19=1, Resulting Numbers: [11, 42, 1] Generated Node #0,3: 82:[11, 42, 1] Operation: 20-19=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[11, 42, 1], Operations: ['20-19=1'] Exploring Operation: 11*1=11, Resulting Numbers: [42, 11] Generated Node #0,3,0: 82:[42, 11] Operation: 11*1=11 Exploring Operation: 11/1=11, Resulting Numbers: [42, 11] Generated Node #0,3,1: 82:[42, 11] Operation: 11/1=11 Exploring Operation: 42-1=41, Resulting Numbers: [11, 41] Generated Node #0,3,2: 82:[11, 41] Operation: 42-1=41 Exploring Operation: 11-1=10, Resulting Numbers: [42, 10] Generated Node #0,3,3: 82:[42, 10] Operation: 11-1=10 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 82:[11, 41], Operations: ['20-19=1', '42-1=41'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 11*41=451, Resulting Numbers: [451] 451,82 unequal: No Solution Exploring Operation: 11+41=52, Resulting Numbers: [52] 52,82 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 #0,3,3 Current State: 82:[42, 10], Operations: ['20-19=1', '11-1=10'] Exploring Operation: 42*10=420, Resulting Numbers: [420] 420,82 unequal: No Solution Exploring Operation: 42+10=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,82 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 #0,3,0 Current State: 82:[42, 11], Operations: ['20-19=1', '11*1=11'] Exploring Operation: 42+11=53, Resulting Numbers: [53] 53,82 unequal: No Solution Exploring Operation: 42*11=462, Resulting Numbers: [462] 462,82 unequal: No Solution Exploring Operation: 42-11=31, Resulting Numbers: [31] 31,82 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 #0,3,1 Current State: 82:[42, 11], Operations: ['20-19=1', '11/1=11'] Exploring Operation: 42+11=53, Resulting Numbers: [53] 53,82 unequal: No Solution Exploring Operation: 42*11=462, Resulting Numbers: [462] 462,82 unequal: No Solution Exploring Operation: 42-11=31, Resulting Numbers: [31] 31,82 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:[11, 42, 39], Operations: ['20+19=39'] Exploring Operation: 42-11=31, Resulting Numbers: [39, 31] Generated Node #0,2,0: 82:[39, 31] Operation: 42-11=31 Exploring Operation: 42-39=3, Resulting Numbers: [11, 3] Generated Node #0,2,1: 82:[11, 3] Operation: 42-39=3 Exploring Operation: 11+39=50, Resulting Numbers: [42, 50] Generated Node #0,2,2: 82:[42, 50] Operation: 11+39=50 Exploring Operation: 42+39=81, Resulting Numbers: [11, 81] Generated Node #0,2,3: 82:[11, 81] Operation: 42+39=81 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[11, 3], Operations: ['20+19=39', '42-39=3'] Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,82 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:[42, 50], Operations: ['20+19=39', '11+39=50'] Exploring Operation: 42*50=2100, Resulting Numbers: [2100] 2100,82 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 42+50=92, Resulting Numbers: [92] 92,82 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:[11, 81], Operations: ['20+19=39', '42+39=81'] Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,82 unequal: No Solution Exploring Operation: 11+81=92, Resulting Numbers: [92] 92,82 unequal: No Solution Exploring Operation: 11*81=891, Resulting Numbers: [891] 891,82 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:[39, 31], Operations: ['20+19=39', '42-11=31'] Exploring Operation: 39*31=1209, Resulting Numbers: [1209] 1209,82 unequal: No Solution Exploring Operation: 39+31=70, Resulting Numbers: [70] 70,82 unequal: No Solution Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,82 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 #0,0 Current State: 82:[42, 19, 9], Operations: ['20-11=9'] Exploring Operation: 42-19=23, Resulting Numbers: [9, 23] Generated Node #0,0,0: 82:[9, 23] Operation: 42-19=23 Exploring Operation: 42-9=33, Resulting Numbers: [19, 33] Generated Node #0,0,1: 82:[19, 33] Operation: 42-9=33 Exploring Operation: 19+9=28, Resulting Numbers: [42, 28] Generated Node #0,0,2: 82:[42, 28] Operation: 19+9=28 Exploring Operation: 19-9=10, Resulting Numbers: [42, 10] Generated Node #0,0,3: 82:[42, 10] Operation: 19-9=10 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 82:[42, 10], Operations: ['20-11=9', '19-9=10'] Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,82 unequal: No Solution Exploring Operation: 42+10=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 42*10=420, Resulting Numbers: [420] 420,82 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:[42, 28], Operations: ['20-11=9', '19+9=28'] Exploring Operation: 42*28=1176, Resulting Numbers: [1176] 1176,82 unequal: No Solution Exploring Operation: 42-28=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 42+28=70, Resulting Numbers: [70] 70,82 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 #0,0,0 Current State: 82:[9, 23], Operations: ['20-11=9', '42-19=23'] Exploring Operation: 9*23=207, Resulting Numbers: [207] 207,82 unequal: No Solution Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,82 unequal: No Solution Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,82 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:[19, 33], Operations: ['20-11=9', '42-9=33'] Exploring Operation: 33-19=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 19+33=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 19*33=627, Resulting Numbers: [627] 627,82 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:[20, 42, 8], Operations: ['19-11=8'] Exploring Operation: 20-8=12, Resulting Numbers: [42, 12] Generated Node #0,1,0: 82:[42, 12] Operation: 20-8=12 Exploring Operation: 20+8=28, Resulting Numbers: [42, 28] Generated Node #0,1,1: 82:[42, 28] Operation: 20+8=28 Exploring Operation: 42-8=34, Resulting Numbers: [20, 34] Generated Node #0,1,2: 82:[20, 34] Operation: 42-8=34 Exploring Operation: 42-20=22, Resulting Numbers: [8, 22] Generated Node #0,1,3: 82:[8, 22] Operation: 42-20=22 Moving to Node #0,1,0 Current State: 82:[42, 12], Operations: ['19-11=8', '20-8=12'] Exploring Operation: 42*12=504, Resulting Numbers: [504] 504,82 unequal: No Solution Exploring Operation: 42-12=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 42+12=54, Resulting Numbers: [54] 54,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[42, 28], Operations: ['19-11=8', '20+8=28'] Exploring Operation: 42*28=1176, Resulting Numbers: [1176] 1176,82 unequal: No Solution Exploring Operation: 42-28=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 42+28=70, Resulting Numbers: [70] 70,82 unequal: No Solution Moving to Node #0,1,3 Current State: 82:[8, 22], Operations: ['19-11=8', '42-20=22'] Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,82 unequal: No Solution Exploring Operation: 8+22=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 8*22=176, Resulting Numbers: [176] 176,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[20, 34], Operations: ['19-11=8', '42-8=34'] Exploring Operation: 20*34=680, Resulting Numbers: [680] 680,82 unequal: No Solution Exploring Operation: 20+34=54, Resulting Numbers: [54] 54,82 unequal: No Solution Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,82 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
[ 65, 80, 13, 15 ]
43
[ "80-65=15", "13+15=28", "15+28=43" ]
Current State: 43:[65, 80, 13, 15], Operations: [] Exploring Operation: 80-65=15, Resulting Numbers: [13, 15, 15] Generated Node #2: [13, 15, 15] from Operation: 80-65=15 Current State: 43:[13, 15, 15], Operations: ['80-65=15'] Exploring Operation: 13+15=28, Resulting Numbers: [28] 28,43 equal: Goal Reached Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[65, 80, 13, 15], Operations: [] Exploring Operation: 80-15=65, Resulting Numbers: [65, 13, 65] Generated Node #0,0: 43:[65, 13, 65] Operation: 80-15=65 Exploring Operation: 80-13=67, Resulting Numbers: [65, 15, 67] Generated Node #0,1: 43:[65, 15, 67] Operation: 80-13=67 Exploring Operation: 65-13=52, Resulting Numbers: [80, 15, 52] Generated Node #0,2: 43:[80, 15, 52] Operation: 65-13=52 Exploring Operation: 13+15=28, Resulting Numbers: [65, 80, 28] Generated Node #0,3: 43:[65, 80, 28] Operation: 13+15=28 Exploring Operation: 65-15=50, Resulting Numbers: [80, 13, 50] Generated Node #0,4: 43:[80, 13, 50] Operation: 65-15=50 Moving to Node #0,0 Current State: 43:[65, 13, 65], Operations: ['80-15=65'] Exploring Operation: 65+13=78, Resulting Numbers: [65, 78] Generated Node #0,0,0: 43:[65, 78] Operation: 65+13=78 Exploring Operation: 65-13=52, Resulting Numbers: [65, 52] Generated Node #0,0,1: 43:[65, 52] Operation: 65-13=52 Exploring Operation: 65-13=52, Resulting Numbers: [65, 52] Generated Node #0,0,2: 43:[65, 52] Operation: 65-13=52 Exploring Operation: 65/13=5, Resulting Numbers: [65, 5] Generated Node #0,0,3: 43:[65, 5] Operation: 65/13=5 Exploring Operation: 13+65=78, Resulting Numbers: [65, 78] Generated Node #0,0,4: 43:[65, 78] Operation: 13+65=78 Moving to Node #0,2 Current State: 43:[80, 15, 52], Operations: ['65-13=52'] Exploring Operation: 80-52=28, Resulting Numbers: [15, 28] Generated Node #0,2,0: 43:[15, 28] Operation: 80-52=28 Exploring Operation: 80-15=65, Resulting Numbers: [52, 65] Generated Node #0,2,1: 43:[52, 65] Operation: 80-15=65 Exploring Operation: 15+52=67, Resulting Numbers: [80, 67] Generated Node #0,2,2: 43:[80, 67] Operation: 15+52=67 Exploring Operation: 52-15=37, Resulting Numbers: [80, 37] Generated Node #0,2,3: 43:[80, 37] Operation: 52-15=37 Exploring Operation: 80+15=95, Resulting Numbers: [52, 95] Generated Node #0,2,4: 43:[52, 95] Operation: 80+15=95 Moving to Node #0,4 Current State: 43:[80, 13, 50], Operations: ['65-15=50'] Exploring Operation: 80-13=67, Resulting Numbers: [50, 67] Generated Node #0,4,0: 43:[50, 67] Operation: 80-13=67 Exploring Operation: 50-13=37, Resulting Numbers: [80, 37] Generated Node #0,4,1: 43:[80, 37] Operation: 50-13=37 Exploring Operation: 80+13=93, Resulting Numbers: [50, 93] Generated Node #0,4,2: 43:[50, 93] Operation: 80+13=93 Exploring Operation: 80-50=30, Resulting Numbers: [13, 30] Generated Node #0,4,3: 43:[13, 30] Operation: 80-50=30 Exploring Operation: 13+50=63, Resulting Numbers: [80, 63] Generated Node #0,4,4: 43:[80, 63] Operation: 13+50=63 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 43:[50, 67], Operations: ['65-15=50', '80-13=67'] Exploring Operation: 50*67=3350, Resulting Numbers: [3350] 3350,43 unequal: No Solution Exploring Operation: 67-50=17, Resulting Numbers: [17] 17,43 unequal: No Solution Exploring Operation: 50+67=117, Resulting Numbers: [117] 117,43 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: 43:[80, 37], Operations: ['65-15=50', '50-13=37'] Exploring Operation: 80+37=117, Resulting Numbers: [117] 117,43 unequal: No Solution Exploring Operation: 80*37=2960, Resulting Numbers: [2960] 2960,43 unequal: No Solution Exploring Operation: 80-37=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[65, 80, 13, 15], Operations: [] Exploring Operation: 65-15=50, Resulting Numbers: [80, 13, 50] Generated Node #0,4: 43:[80, 13, 50] Operation: 65-15=50 Moving to Node #0,4 Current State: 43:[80, 13, 50], Operations: ['65-15=50'] Exploring Operation: 50-13=37, Resulting Numbers: [80, 37] Generated Node #0,4,1: 43:[80, 37] Operation: 50-13=37 Moving to Node #0,4,1 Current State: 43:[80, 37], Operations: ['65-15=50', '50-13=37'] Exploring Operation: 80-37=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_5
sum_heuristic
[ 18, 70, 51, 14 ]
62
[ "18*51=918", "70*14=980", "980-918=62" ]
Current State: 62:[18, 70, 51, 14], Operations: [] Exploring Operation: 18*51=918, Resulting Numbers: [70, 14, 918] Generated Node #2: [70, 14, 918] from Operation: 18*51=918 Current State: 62:[70, 14, 918], Operations: ['18*51=918'] Exploring Operation: 70*14=980, Resulting Numbers: [918, 980] Generated Node #3: [918, 980] from Operation: 70*14=980 Current State: 62:[918, 980], Operations: ['18*51=918', '70*14=980'] Exploring Operation: 980-918=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[18, 70, 51, 14], Operations: [] Exploring Operation: 18-14=4, Resulting Numbers: [70, 51, 4] Generated Node #0,0: 62:[70, 51, 4] Operation: 18-14=4 Exploring Operation: 18+14=32, Resulting Numbers: [70, 51, 32] Generated Node #0,1: 62:[70, 51, 32] Operation: 18+14=32 Moving to Node #0,1 Current State: 62:[70, 51, 32], Operations: ['18+14=32'] Exploring Operation: 70-51=19, Resulting Numbers: [32, 19] Generated Node #0,1,0: 62:[32, 19] Operation: 70-51=19 Exploring Operation: 70-32=38, Resulting Numbers: [51, 38] Generated Node #0,1,1: 62:[51, 38] Operation: 70-32=38 Moving to Node #0,0 Current State: 62:[70, 51, 4], Operations: ['18-14=4'] Exploring Operation: 70-51=19, Resulting Numbers: [4, 19] Generated Node #0,0,0: 62:[4, 19] Operation: 70-51=19 Exploring Operation: 70-4=66, Resulting Numbers: [51, 66] Generated Node #0,0,1: 62:[51, 66] Operation: 70-4=66 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[4, 19], Operations: ['18-14=4', '70-51=19'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,62 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 #0,0,1 Current State: 62:[51, 66], Operations: ['18-14=4', '70-4=66'] Exploring Operation: 66-51=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 51+66=117, Resulting Numbers: [117] 117,62 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: 62:[32, 19], Operations: ['18+14=32', '70-51=19'] Exploring Operation: 32+19=51, Resulting Numbers: [51] 51,62 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,62 unequal: No Solution Moving to Node #0,1,1 Current State: 62:[51, 38], Operations: ['18+14=32', '70-32=38'] Exploring Operation: 51-38=13, Resulting Numbers: [13] 13,62 unequal: No Solution Exploring Operation: 51+38=89, Resulting Numbers: [89] 89,62 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 12, 20, 55, 18 ]
61
[ "20-18=2", "12/2=6", "55+6=61" ]
Current State: 61:[12, 20, 55, 18], Operations: [] Exploring Operation: 20-18=2, Resulting Numbers: [12, 55, 2] Generated Node #2: [12, 55, 2] from Operation: 20-18=2 Current State: 61:[12, 55, 2], Operations: ['20-18=2'] Exploring Operation: 12/2=6, Resulting Numbers: [55, 6] Generated Node #3: [55, 6] from Operation: 12/2=6 Current State: 61:[55, 6], Operations: ['20-18=2', '12/2=6'] Exploring Operation: 55+6=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[12, 20, 55, 18], Operations: [] Exploring Operation: 12+20=32, Resulting Numbers: [55, 18, 32] Generated Node #0,0: 61:[55, 18, 32] Operation: 12+20=32 Exploring Operation: 12+18=30, Resulting Numbers: [20, 55, 30] Generated Node #0,1: 61:[20, 55, 30] Operation: 12+18=30 Moving to Node #0,0 Current State: 61:[55, 18, 32], Operations: ['12+20=32'] Exploring Operation: 18+32=50, Resulting Numbers: [55, 50] Generated Node #0,0,0: 61:[55, 50] Operation: 18+32=50 Exploring Operation: 55+18=73, Resulting Numbers: [32, 73] Generated Node #0,0,1: 61:[32, 73] Operation: 55+18=73 Moving to Node #0,1 Current State: 61:[20, 55, 30], Operations: ['12+18=30'] Exploring Operation: 20+30=50, Resulting Numbers: [55, 50] Generated Node #0,1,0: 61:[55, 50] Operation: 20+30=50 Exploring Operation: 20+55=75, Resulting Numbers: [30, 75] Generated Node #0,1,1: 61:[30, 75] Operation: 20+55=75 Moving to Node #0,0,0 Current State: 61:[55, 50], Operations: ['12+20=32', '18+32=50'] Exploring Operation: 55+50=105, Resulting Numbers: [105] 105,61 unequal: No Solution Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[55, 50], Operations: ['12+18=30', '20+30=50'] Exploring Operation: 55+50=105, Resulting Numbers: [105] 105,61 unequal: No Solution Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[32, 73], Operations: ['12+20=32', '55+18=73'] Exploring Operation: 32+73=105, Resulting Numbers: [105] 105,61 unequal: No Solution Exploring Operation: 73-32=41, Resulting Numbers: [41] 41,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[30, 75], Operations: ['12+18=30', '20+55=75'] Exploring Operation: 75-30=45, Resulting Numbers: [45] 45,61 unequal: No Solution Exploring Operation: 30+75=105, Resulting Numbers: [105] 105,61 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 3, 91, 48, 76 ]
23
[ "3*48=144", "91+76=167", "167-144=23" ]
Current State: 23:[3, 91, 48, 76], Operations: [] Exploring Operation: 3*48=144, Resulting Numbers: [91, 76, 144] Generated Node #2: [91, 76, 144] from Operation: 3*48=144 Current State: 23:[91, 76, 144], Operations: ['3*48=144'] Exploring Operation: 91+76=167, Resulting Numbers: [144, 167] Generated Node #3: [144, 167] from Operation: 91+76=167 Current State: 23:[144, 167], Operations: ['3*48=144', '91+76=167'] Exploring Operation: 167-144=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[3, 91, 48, 76], Operations: [] Exploring Operation: 76-48=28, Resulting Numbers: [3, 91, 28] Generated Node #0,0: 23:[3, 91, 28] Operation: 76-48=28 Exploring Operation: 91-48=43, Resulting Numbers: [3, 76, 43] Generated Node #0,1: 23:[3, 76, 43] Operation: 91-48=43 Exploring Operation: 91-76=15, Resulting Numbers: [3, 48, 15] Generated Node #0,2: 23:[3, 48, 15] Operation: 91-76=15 Moving to Node #0,2 Current State: 23:[3, 48, 15], Operations: ['91-76=15'] Exploring Operation: 3+15=18, Resulting Numbers: [48, 18] Generated Node #0,2,0: 23:[48, 18] Operation: 3+15=18 Exploring Operation: 48/3=16, Resulting Numbers: [15, 16] Generated Node #0,2,1: 23:[15, 16] Operation: 48/3=16 Exploring Operation: 48-3=45, Resulting Numbers: [15, 45] Generated Node #0,2,2: 23:[15, 45] Operation: 48-3=45 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[15, 16], Operations: ['91-76=15', '48/3=16'] Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,23 unequal: No Solution Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,23 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,23 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: 23:[48, 18], Operations: ['91-76=15', '3+15=18'] Exploring Operation: 48+18=66, Resulting Numbers: [66] 66,23 unequal: No Solution Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 48*18=864, Resulting Numbers: [864] 864,23 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: 23:[15, 45], Operations: ['91-76=15', '48-3=45'] Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 15+45=60, Resulting Numbers: [60] 60,23 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: 23:[3, 91, 28], Operations: ['76-48=28'] Exploring Operation: 91-28=63, Resulting Numbers: [3, 63] Generated Node #0,0,0: 23:[3, 63] Operation: 91-28=63 Exploring Operation: 91-3=88, Resulting Numbers: [28, 88] Generated Node #0,0,1: 23:[28, 88] Operation: 91-3=88 Exploring Operation: 28-3=25, Resulting Numbers: [91, 25] Generated Node #0,0,2: 23:[91, 25] Operation: 28-3=25 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 23:[3, 63], Operations: ['76-48=28', '91-28=63'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 3+63=66, Resulting Numbers: [66] 66,23 unequal: No Solution Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,23 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: 23:[28, 88], Operations: ['76-48=28', '91-3=88'] Exploring Operation: 88-28=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 28*88=2464, Resulting Numbers: [2464] 2464,23 unequal: No Solution Exploring Operation: 28+88=116, Resulting Numbers: [116] 116,23 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: 23:[91, 25], Operations: ['76-48=28', '28-3=25'] Exploring Operation: 91-25=66, Resulting Numbers: [66] 66,23 unequal: No Solution Exploring Operation: 91+25=116, Resulting Numbers: [116] 116,23 unequal: No Solution Exploring Operation: 91*25=2275, Resulting Numbers: [2275] 2275,23 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: 23:[3, 76, 43], Operations: ['91-48=43'] Exploring Operation: 76-3=73, Resulting Numbers: [43, 73] Generated Node #0,1,0: 23:[43, 73] Operation: 76-3=73 Exploring Operation: 43-3=40, Resulting Numbers: [76, 40] Generated Node #0,1,1: 23:[76, 40] Operation: 43-3=40 Exploring Operation: 76-43=33, Resulting Numbers: [3, 33] Generated Node #0,1,2: 23:[3, 33] Operation: 76-43=33 Moving to Node #0,1,2 Current State: 23:[3, 33], Operations: ['91-48=43', '76-43=33'] Exploring Operation: 3+33=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[43, 73], Operations: ['91-48=43', '76-3=73'] Exploring Operation: 43+73=116, Resulting Numbers: [116] 116,23 unequal: No Solution Exploring Operation: 43*73=3139, Resulting Numbers: [3139] 3139,23 unequal: No Solution Exploring Operation: 73-43=30, Resulting Numbers: [30] 30,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[76, 40], Operations: ['91-48=43', '43-3=40'] Exploring Operation: 76+40=116, Resulting Numbers: [116] 116,23 unequal: No Solution Exploring Operation: 76-40=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 76*40=3040, Resulting Numbers: [3040] 3040,23 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 70, 96, 12, 15 ]
18
[ "96-12=84", "15*84=1260", "1260/70=18" ]
Current State: 18:[70, 96, 12, 15], Operations: [] Exploring Operation: 96-12=84, Resulting Numbers: [70, 15, 84] Generated Node #2: [70, 15, 84] from Operation: 96-12=84 Current State: 18:[70, 15, 84], Operations: ['96-12=84'] Exploring Operation: 15*84=1260, Resulting Numbers: [70, 1260] Generated Node #3: [70, 1260] from Operation: 15*84=1260 Current State: 18:[70, 1260], Operations: ['96-12=84', '15*84=1260'] Exploring Operation: 1260/70=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[70, 96, 12, 15], Operations: [] Exploring Operation: 96-70=26, Resulting Numbers: [12, 15, 26] Generated Node #0,0: 18:[12, 15, 26] Operation: 96-70=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[12, 15, 26], Operations: ['96-70=26'] Exploring Operation: 26-15=11, Resulting Numbers: [12, 11] Generated Node #0,0,0: 18:[12, 11] Operation: 26-15=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[12, 11], Operations: ['96-70=26', '26-15=11'] Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,18 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
[ 75, 4, 22, 39 ]
54
[ "75-4=71", "39-22=17", "71-17=54" ]
Current State: 54:[75, 4, 22, 39], Operations: [] Exploring Operation: 75-4=71, Resulting Numbers: [22, 39, 71] Generated Node #2: [22, 39, 71] from Operation: 75-4=71 Current State: 54:[22, 39, 71], Operations: ['75-4=71'] Exploring Operation: 39-22=17, Resulting Numbers: [71, 17] Generated Node #3: [71, 17] from Operation: 39-22=17 Current State: 54:[71, 17], Operations: ['75-4=71', '39-22=17'] Exploring Operation: 71-17=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[75, 4, 22, 39], Operations: [] Exploring Operation: 39-22=17, Resulting Numbers: [75, 4, 17] Generated Node #0,0: 54:[75, 4, 17] Operation: 39-22=17 Exploring Operation: 22+39=61, Resulting Numbers: [75, 4, 61] Generated Node #0,1: 54:[75, 4, 61] Operation: 22+39=61 Exploring Operation: 75-22=53, Resulting Numbers: [4, 39, 53] Generated Node #0,2: 54:[4, 39, 53] Operation: 75-22=53 Exploring Operation: 75-39=36, Resulting Numbers: [4, 22, 36] Generated Node #0,3: 54:[4, 22, 36] Operation: 75-39=36 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[4, 39, 53], Operations: ['75-22=53'] Exploring Operation: 53-39=14, Resulting Numbers: [4, 14] Generated Node #0,2,0: 54:[4, 14] Operation: 53-39=14 Exploring Operation: 4+39=43, Resulting Numbers: [53, 43] Generated Node #0,2,1: 54:[53, 43] Operation: 4+39=43 Exploring Operation: 39-4=35, Resulting Numbers: [53, 35] Generated Node #0,2,2: 54:[53, 35] Operation: 39-4=35 Exploring Operation: 4+53=57, Resulting Numbers: [39, 57] Generated Node #0,2,3: 54:[39, 57] Operation: 4+53=57 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 54:[4, 14], Operations: ['75-22=53', '53-39=14'] Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,54 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,54 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: 54:[53, 35], Operations: ['75-22=53', '39-4=35'] Exploring Operation: 53*35=1855, Resulting Numbers: [1855] 1855,54 unequal: No Solution Exploring Operation: 53-35=18, Resulting Numbers: [18] 18,54 unequal: No Solution Exploring Operation: 53+35=88, Resulting Numbers: [88] 88,54 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: 54:[53, 43], Operations: ['75-22=53', '4+39=43'] Exploring Operation: 53*43=2279, Resulting Numbers: [2279] 2279,54 unequal: No Solution Exploring Operation: 53+43=96, Resulting Numbers: [96] 96,54 unequal: No Solution Exploring Operation: 53-43=10, Resulting Numbers: [10] 10,54 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: 54:[39, 57], Operations: ['75-22=53', '4+53=57'] Exploring Operation: 39*57=2223, Resulting Numbers: [2223] 2223,54 unequal: No Solution Exploring Operation: 39+57=96, Resulting Numbers: [96] 96,54 unequal: No Solution Exploring Operation: 57-39=18, Resulting Numbers: [18] 18,54 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: 54:[4, 22, 36], Operations: ['75-39=36'] Exploring Operation: 36-22=14, Resulting Numbers: [4, 14] Generated Node #0,3,0: 54:[4, 14] Operation: 36-22=14 Exploring Operation: 36/4=9, Resulting Numbers: [22, 9] Generated Node #0,3,1: 54:[22, 9] Operation: 36/4=9 Exploring Operation: 22-4=18, Resulting Numbers: [36, 18] Generated Node #0,3,2: 54:[36, 18] Operation: 22-4=18 Exploring Operation: 22+36=58, Resulting Numbers: [4, 58] Generated Node #0,3,3: 54:[4, 58] Operation: 22+36=58 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 54:[22, 9], Operations: ['75-39=36', '36/4=9'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,54 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,54 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: 54:[4, 14], Operations: ['75-39=36', '36-22=14'] Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,54 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,54 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: 54:[4, 58], Operations: ['75-39=36', '22+36=58'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[75, 4, 22, 39], Operations: [] Exploring Operation: 75-39=36, Resulting Numbers: [4, 22, 36] Generated Node #0,3: 54:[4, 22, 36] Operation: 75-39=36 Moving to Node #0,3 Current State: 54:[4, 22, 36], Operations: ['75-39=36'] Exploring Operation: 22+36=58, Resulting Numbers: [4, 58] Generated Node #0,3,3: 54:[4, 58] Operation: 22+36=58 Moving to Node #0,3,3 Current State: 54:[4, 58], Operations: ['75-39=36', '22+36=58'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_4
mult_heuristic
[ 6, 89, 10, 15 ]
61
[ "10+15=25", "6*25=150", "150-89=61" ]
Current State: 61:[6, 89, 10, 15], Operations: [] Exploring Operation: 10+15=25, Resulting Numbers: [6, 89, 25] Generated Node #2: [6, 89, 25] from Operation: 10+15=25 Current State: 61:[6, 89, 25], Operations: ['10+15=25'] Exploring Operation: 6*25=150, Resulting Numbers: [89, 150] Generated Node #3: [89, 150] from Operation: 6*25=150 Current State: 61:[89, 150], Operations: ['10+15=25', '6*25=150'] Exploring Operation: 150-89=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[6, 89, 10, 15], Operations: [] Exploring Operation: 6*10=60, Resulting Numbers: [89, 15, 60] Generated Node #0,0: 61:[89, 15, 60] Operation: 6*10=60 Exploring Operation: 6*15=90, Resulting Numbers: [89, 10, 90] Generated Node #0,1: 61:[89, 10, 90] Operation: 6*15=90 Exploring Operation: 6+15=21, Resulting Numbers: [89, 10, 21] Generated Node #0,2: 61:[89, 10, 21] Operation: 6+15=21 Exploring Operation: 6+10=16, Resulting Numbers: [89, 15, 16] Generated Node #0,3: 61:[89, 15, 16] Operation: 6+10=16 Exploring Operation: 89-6=83, Resulting Numbers: [10, 15, 83] Generated Node #0,4: 61:[10, 15, 83] Operation: 89-6=83 Moving to Node #0,0 Current State: 61:[89, 15, 60], Operations: ['6*10=60'] Exploring Operation: 89+15=104, Resulting Numbers: [60, 104] Generated Node #0,0,0: 61:[60, 104] Operation: 89+15=104 Exploring Operation: 60-15=45, Resulting Numbers: [89, 45] Generated Node #0,0,1: 61:[89, 45] Operation: 60-15=45 Exploring Operation: 89-15=74, Resulting Numbers: [60, 74] Generated Node #0,0,2: 61:[60, 74] Operation: 89-15=74 Exploring Operation: 89-60=29, Resulting Numbers: [15, 29] Generated Node #0,0,3: 61:[15, 29] Operation: 89-60=29 Exploring Operation: 15+60=75, Resulting Numbers: [89, 75] Generated Node #0,0,4: 61:[89, 75] Operation: 15+60=75 Moving to Node #0,1 Current State: 61:[89, 10, 90], Operations: ['6*15=90'] Exploring Operation: 90/10=9, Resulting Numbers: [89, 9] Generated Node #0,1,0: 61:[89, 9] Operation: 90/10=9 Exploring Operation: 90-10=80, Resulting Numbers: [89, 80] Generated Node #0,1,1: 61:[89, 80] Operation: 90-10=80 Exploring Operation: 89-10=79, Resulting Numbers: [90, 79] Generated Node #0,1,2: 61:[90, 79] Operation: 89-10=79 Exploring Operation: 89+10=99, Resulting Numbers: [90, 99] Generated Node #0,1,3: 61:[90, 99] Operation: 89+10=99 Exploring Operation: 10+90=100, Resulting Numbers: [89, 100] Generated Node #0,1,4: 61:[89, 100] Operation: 10+90=100 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[89, 80], Operations: ['6*15=90', '90-10=80'] Exploring Operation: 89+80=169, Resulting Numbers: [169] 169,61 unequal: No Solution Exploring Operation: 89*80=7120, Resulting Numbers: [7120] 7120,61 unequal: No Solution Exploring Operation: 89-80=9, Resulting Numbers: [9] 9,61 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 #0,1,2 Current State: 61:[90, 79], Operations: ['6*15=90', '89-10=79'] Exploring Operation: 90-79=11, Resulting Numbers: [11] 11,61 unequal: No Solution Exploring Operation: 90+79=169, Resulting Numbers: [169] 169,61 unequal: No Solution Exploring Operation: 90*79=7110, Resulting Numbers: [7110] 7110,61 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 #0,1,3 Current State: 61:[90, 99], Operations: ['6*15=90', '89+10=99'] Exploring Operation: 90+99=189, Resulting Numbers: [189] 189,61 unequal: No Solution Exploring Operation: 90*99=8910, Resulting Numbers: [8910] 8910,61 unequal: No Solution Exploring Operation: 99-90=9, Resulting Numbers: [9] 9,61 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 #0,1,4 Current State: 61:[89, 100], Operations: ['6*15=90', '10+90=100'] Exploring Operation: 100-89=11, Resulting Numbers: [11] 11,61 unequal: No Solution Exploring Operation: 89+100=189, Resulting Numbers: [189] 189,61 unequal: No Solution Exploring Operation: 89*100=8900, Resulting Numbers: [8900] 8900,61 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 #0,1,0 Current State: 61:[89, 9], Operations: ['6*15=90', '90/10=9'] Exploring Operation: 89*9=801, Resulting Numbers: [801] 801,61 unequal: No Solution Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,61 unequal: No Solution Exploring Operation: 89+9=98, Resulting Numbers: [98] 98,61 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: 61:[89, 10, 21], Operations: ['6+15=21'] Exploring Operation: 89+10=99, Resulting Numbers: [21, 99] Generated Node #0,2,0: 61:[21, 99] Operation: 89+10=99 Exploring Operation: 89-10=79, Resulting Numbers: [21, 79] Generated Node #0,2,1: 61:[21, 79] Operation: 89-10=79 Exploring Operation: 21-10=11, Resulting Numbers: [89, 11] Generated Node #0,2,2: 61:[89, 11] Operation: 21-10=11 Exploring Operation: 10+21=31, Resulting Numbers: [89, 31] Generated Node #0,2,3: 61:[89, 31] Operation: 10+21=31 Exploring Operation: 89-21=68, Resulting Numbers: [10, 68] Generated Node #0,2,4: 61:[10, 68] Operation: 89-21=68 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 61:[21, 79], Operations: ['6+15=21', '89-10=79'] Exploring Operation: 21+79=100, Resulting Numbers: [100] 100,61 unequal: No Solution Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,61 unequal: No Solution Exploring Operation: 21*79=1659, Resulting Numbers: [1659] 1659,61 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 #0,2,3 Current State: 61:[89, 31], Operations: ['6+15=21', '10+21=31'] Exploring Operation: 89-31=58, Resulting Numbers: [58] 58,61 unequal: No Solution Exploring Operation: 89*31=2759, Resulting Numbers: [2759] 2759,61 unequal: No Solution Exploring Operation: 89+31=120, Resulting Numbers: [120] 120,61 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:[10, 68], Operations: ['6+15=21', '89-21=68'] Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,61 unequal: No Solution Exploring Operation: 10*68=680, Resulting Numbers: [680] 680,61 unequal: No Solution Exploring Operation: 10+68=78, Resulting Numbers: [78] 78,61 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:[21, 99], Operations: ['6+15=21', '89+10=99'] Exploring Operation: 21+99=120, Resulting Numbers: [120] 120,61 unequal: No Solution Exploring Operation: 21*99=2079, Resulting Numbers: [2079] 2079,61 unequal: No Solution Exploring Operation: 99-21=78, Resulting Numbers: [78] 78,61 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:[89, 11], Operations: ['6+15=21', '21-10=11'] Exploring Operation: 89-11=78, Resulting Numbers: [78] 78,61 unequal: No Solution Exploring Operation: 89*11=979, Resulting Numbers: [979] 979,61 unequal: No Solution Exploring Operation: 89+11=100, Resulting Numbers: [100] 100,61 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: 61:[89, 15, 16], Operations: ['6+10=16'] Exploring Operation: 89+15=104, Resulting Numbers: [16, 104] Generated Node #0,3,0: 61:[16, 104] Operation: 89+15=104 Exploring Operation: 89-16=73, Resulting Numbers: [15, 73] Generated Node #0,3,1: 61:[15, 73] Operation: 89-16=73 Exploring Operation: 16-15=1, Resulting Numbers: [89, 1] Generated Node #0,3,2: 61:[89, 1] Operation: 16-15=1 Exploring Operation: 15+16=31, Resulting Numbers: [89, 31] Generated Node #0,3,3: 61:[89, 31] Operation: 15+16=31 Exploring Operation: 89-15=74, Resulting Numbers: [16, 74] Generated Node #0,3,4: 61:[16, 74] Operation: 89-15=74 Moving to Node #0,4 Current State: 61:[10, 15, 83], Operations: ['89-6=83'] Exploring Operation: 10+83=93, Resulting Numbers: [15, 93] Generated Node #0,4,0: 61:[15, 93] Operation: 10+83=93 Exploring Operation: 10+15=25, Resulting Numbers: [83, 25] Generated Node #0,4,1: 61:[83, 25] Operation: 10+15=25 Exploring Operation: 83-15=68, Resulting Numbers: [10, 68] Generated Node #0,4,2: 61:[10, 68] Operation: 83-15=68 Exploring Operation: 15-10=5, Resulting Numbers: [83, 5] Generated Node #0,4,3: 61:[83, 5] Operation: 15-10=5 Exploring Operation: 83-10=73, Resulting Numbers: [15, 73] Generated Node #0,4,4: 61:[15, 73] Operation: 83-10=73 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 61:[83, 25], Operations: ['89-6=83', '10+15=25'] Exploring Operation: 83*25=2075, Resulting Numbers: [2075] 2075,61 unequal: No Solution Exploring Operation: 83-25=58, Resulting Numbers: [58] 58,61 unequal: No Solution Exploring Operation: 83+25=108, Resulting Numbers: [108] 108,61 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 #0,4,2 Current State: 61:[10, 68], Operations: ['89-6=83', '83-15=68'] Exploring Operation: 10+68=78, Resulting Numbers: [78] 78,61 unequal: No Solution Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,61 unequal: No Solution Exploring Operation: 10*68=680, Resulting Numbers: [680] 680,61 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:[15, 73], Operations: ['89-6=83', '83-10=73'] Exploring Operation: 15*73=1095, Resulting Numbers: [1095] 1095,61 unequal: No Solution Exploring Operation: 15+73=88, Resulting Numbers: [88] 88,61 unequal: No Solution Exploring Operation: 73-15=58, Resulting Numbers: [58] 58,61 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:[15, 93], Operations: ['89-6=83', '10+83=93'] Exploring Operation: 93-15=78, Resulting Numbers: [78] 78,61 unequal: No Solution Exploring Operation: 15*93=1395, Resulting Numbers: [1395] 1395,61 unequal: No Solution Exploring Operation: 15+93=108, Resulting Numbers: [108] 108,61 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:[83, 5], Operations: ['89-6=83', '15-10=5'] Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,61 unequal: No Solution Exploring Operation: 83*5=415, Resulting Numbers: [415] 415,61 unequal: No Solution Exploring Operation: 83+5=88, Resulting Numbers: [88] 88,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 61:[60, 74], Operations: ['6*10=60', '89-15=74'] Exploring Operation: 60+74=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 60*74=4440, Resulting Numbers: [4440] 4440,61 unequal: No Solution Exploring Operation: 74-60=14, Resulting Numbers: [14] 14,61 unequal: No Solution Moving to Node #0,0,4 Current State: 61:[89, 75], Operations: ['6*10=60', '15+60=75'] Exploring Operation: 89+75=164, Resulting Numbers: [164] 164,61 unequal: No Solution Exploring Operation: 89*75=6675, Resulting Numbers: [6675] 6675,61 unequal: No Solution Exploring Operation: 89-75=14, Resulting Numbers: [14] 14,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[60, 104], Operations: ['6*10=60', '89+15=104'] Exploring Operation: 60+104=164, Resulting Numbers: [164] 164,61 unequal: No Solution Exploring Operation: 60*104=6240, Resulting Numbers: [6240] 6240,61 unequal: No Solution Exploring Operation: 104-60=44, Resulting Numbers: [44] 44,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[89, 45], Operations: ['6*10=60', '60-15=45'] Exploring Operation: 89+45=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 89-45=44, Resulting Numbers: [44] 44,61 unequal: No Solution Exploring Operation: 89*45=4005, Resulting Numbers: [4005] 4005,61 unequal: No Solution Moving to Node #0,3,3 Current State: 61:[89, 31], Operations: ['6+10=16', '15+16=31'] Exploring Operation: 89+31=120, Resulting Numbers: [120] 120,61 unequal: No Solution Exploring Operation: 89-31=58, Resulting Numbers: [58] 58,61 unequal: No Solution Exploring Operation: 89*31=2759, Resulting Numbers: [2759] 2759,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[15, 73], Operations: ['6+10=16', '89-16=73'] Exploring Operation: 73-15=58, Resulting Numbers: [58] 58,61 unequal: No Solution Exploring Operation: 15+73=88, Resulting Numbers: [88] 88,61 unequal: No Solution Exploring Operation: 15*73=1095, Resulting Numbers: [1095] 1095,61 unequal: No Solution Moving to Node #0,3,4 Current State: 61:[16, 74], Operations: ['6+10=16', '89-15=74'] Exploring Operation: 74-16=58, Resulting Numbers: [58] 58,61 unequal: No Solution Exploring Operation: 16*74=1184, Resulting Numbers: [1184] 1184,61 unequal: No Solution Exploring Operation: 16+74=90, Resulting Numbers: [90] 90,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[15, 29], Operations: ['6*10=60', '89-60=29'] Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,61 unequal: No Solution Exploring Operation: 15*29=435, Resulting Numbers: [435] 435,61 unequal: No Solution Exploring Operation: 15+29=44, Resulting Numbers: [44] 44,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[89, 1], Operations: ['6+10=16', '16-15=1'] Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,61 unequal: No Solution Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,61 unequal: No Solution Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,61 unequal: No Solution Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[16, 104], Operations: ['6+10=16', '89+15=104'] Exploring Operation: 104-16=88, Resulting Numbers: [88] 88,61 unequal: No Solution Exploring Operation: 16*104=1664, Resulting Numbers: [1664] 1664,61 unequal: No Solution Exploring Operation: 16+104=120, Resulting Numbers: [120] 120,61 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 64, 67, 8, 47 ]
23
[ "67-64=3", "8*3=24", "47-24=23" ]
Current State: 23:[64, 67, 8, 47], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [8, 47, 3] Generated Node #2: [8, 47, 3] from Operation: 67-64=3 Current State: 23:[8, 47, 3], Operations: ['67-64=3'] Exploring Operation: 8*3=24, Resulting Numbers: [47, 24] Generated Node #3: [47, 24] from Operation: 8*3=24 Current State: 23:[47, 24], Operations: ['67-64=3', '8*3=24'] Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[64, 67, 8, 47], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [8, 47, 3] Generated Node #0,0: 23:[8, 47, 3] Operation: 67-64=3 Exploring Operation: 67-47=20, Resulting Numbers: [64, 8, 20] Generated Node #0,1: 23:[64, 8, 20] Operation: 67-47=20 Moving to Node #0,0 Current State: 23:[8, 47, 3], Operations: ['67-64=3'] Exploring Operation: 8*3=24, Resulting Numbers: [47, 24] Generated Node #0,0,0: 23:[47, 24] Operation: 8*3=24 Exploring Operation: 47-8=39, Resulting Numbers: [3, 39] Generated Node #0,0,1: 23:[3, 39] Operation: 47-8=39 Moving to Node #0,1 Current State: 23:[64, 8, 20], Operations: ['67-47=20'] Exploring Operation: 64/8=8, Resulting Numbers: [20, 8] Generated Node #0,1,0: 23:[20, 8] Operation: 64/8=8 Exploring Operation: 64-8=56, Resulting Numbers: [20, 56] Generated Node #0,1,1: 23:[20, 56] Operation: 64-8=56 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[20, 8], Operations: ['67-47=20', '64/8=8'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 20+8=28, Resulting Numbers: [28] 28,23 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: 23:[20, 56], Operations: ['67-47=20', '64-8=56'] Exploring Operation: 56-20=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 20+56=76, Resulting Numbers: [76] 76,23 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: 23:[47, 24], Operations: ['67-64=3', '8*3=24'] Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,23 unequal: No Solution Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[64, 67, 8, 47], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [8, 47, 3] Generated Node #0,0: 23:[8, 47, 3] Operation: 67-64=3 Moving to Node #0,0 Current State: 23:[8, 47, 3], Operations: ['67-64=3'] Exploring Operation: 8*3=24, Resulting Numbers: [47, 24] Generated Node #0,0,0: 23:[47, 24] Operation: 8*3=24 Moving to Node #0,0,0 Current State: 23:[47, 24], Operations: ['67-64=3', '8*3=24'] Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 17, 61, 78, 85 ]
37
[ "61-17=44", "85-78=7", "44-7=37" ]
Current State: 37:[17, 61, 78, 85], Operations: [] Exploring Operation: 61-17=44, Resulting Numbers: [78, 85, 44] Generated Node #2: [78, 85, 44] from Operation: 61-17=44 Current State: 37:[78, 85, 44], Operations: ['61-17=44'] Exploring Operation: 85-78=7, Resulting Numbers: [44, 7] Generated Node #3: [44, 7] from Operation: 85-78=7 Current State: 37:[44, 7], Operations: ['61-17=44', '85-78=7'] Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[17, 61, 78, 85], Operations: [] Exploring Operation: 78-61=17, Resulting Numbers: [17, 85, 17] Generated Node #0,0: 37:[17, 85, 17] Operation: 78-61=17 Exploring Operation: 61-17=44, Resulting Numbers: [78, 85, 44] Generated Node #0,1: 37:[78, 85, 44] Operation: 61-17=44 Exploring Operation: 85-61=24, Resulting Numbers: [17, 78, 24] Generated Node #0,2: 37:[17, 78, 24] Operation: 85-61=24 Exploring Operation: 85-78=7, Resulting Numbers: [17, 61, 7] Generated Node #0,3: 37:[17, 61, 7] Operation: 85-78=7 Exploring Operation: 78-17=61, Resulting Numbers: [61, 85, 61] Generated Node #0,4: 37:[61, 85, 61] Operation: 78-17=61 Moving to Node #0,2 Current State: 37:[17, 78, 24], Operations: ['85-61=24'] Exploring Operation: 17+78=95, Resulting Numbers: [24, 95] Generated Node #0,2,0: 37:[24, 95] Operation: 17+78=95 Exploring Operation: 78-17=61, Resulting Numbers: [24, 61] Generated Node #0,2,1: 37:[24, 61] Operation: 78-17=61 Exploring Operation: 17+24=41, Resulting Numbers: [78, 41] Generated Node #0,2,2: 37:[78, 41] Operation: 17+24=41 Exploring Operation: 24-17=7, Resulting Numbers: [78, 7] Generated Node #0,2,3: 37:[78, 7] Operation: 24-17=7 Exploring Operation: 78-24=54, Resulting Numbers: [17, 54] Generated Node #0,2,4: 37:[17, 54] Operation: 78-24=54 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 37:[24, 61], Operations: ['85-61=24', '78-17=61'] Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[17, 61, 78, 85], Operations: [] Exploring Operation: 85-61=24, Resulting Numbers: [17, 78, 24] Generated Node #0,2: 37:[17, 78, 24] Operation: 85-61=24 Moving to Node #0,2 Current State: 37:[17, 78, 24], Operations: ['85-61=24'] Exploring Operation: 78-17=61, Resulting Numbers: [24, 61] Generated Node #0,2,1: 37:[24, 61] Operation: 78-17=61 Moving to Node #0,2,1 Current State: 37:[24, 61], Operations: ['85-61=24', '78-17=61'] Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 24, 28, 64, 29 ]
41
[ "24+28=52", "64+29=93", "93-52=41" ]
Current State: 41:[24, 28, 64, 29], Operations: [] Exploring Operation: 24+28=52, Resulting Numbers: [64, 29, 52] Generated Node #2: [64, 29, 52] from Operation: 24+28=52 Current State: 41:[64, 29, 52], Operations: ['24+28=52'] Exploring Operation: 64+29=93, Resulting Numbers: [52, 93] Generated Node #3: [52, 93] from Operation: 64+29=93 Current State: 41:[52, 93], Operations: ['24+28=52', '64+29=93'] Exploring Operation: 93-52=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[24, 28, 64, 29], Operations: [] Exploring Operation: 64-28=36, Resulting Numbers: [24, 29, 36] Generated Node #0,0: 41:[24, 29, 36] Operation: 64-28=36 Exploring Operation: 64-24=40, Resulting Numbers: [28, 29, 40] Generated Node #0,1: 41:[28, 29, 40] Operation: 64-24=40 Moving to Node #0,1 Current State: 41:[28, 29, 40], Operations: ['64-24=40'] Exploring Operation: 28+29=57, Resulting Numbers: [40, 57] Generated Node #0,1,0: 41:[40, 57] Operation: 28+29=57 Exploring Operation: 28+40=68, Resulting Numbers: [29, 68] Generated Node #0,1,1: 41:[29, 68] Operation: 28+40=68 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[40, 57], Operations: ['64-24=40', '28+29=57'] Exploring Operation: 40+57=97, Resulting Numbers: [97] 97,41 unequal: No Solution Exploring Operation: 57-40=17, Resulting Numbers: [17] 17,41 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: 41:[29, 68], Operations: ['64-24=40', '28+40=68'] Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 29+68=97, Resulting Numbers: [97] 97,41 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: 41:[24, 29, 36], Operations: ['64-28=36'] Exploring Operation: 24+29=53, Resulting Numbers: [36, 53] Generated Node #0,0,0: 41:[36, 53] Operation: 24+29=53 Exploring Operation: 24+36=60, Resulting Numbers: [29, 60] Generated Node #0,0,1: 41:[29, 60] Operation: 24+36=60 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[36, 53], Operations: ['64-28=36', '24+29=53'] Exploring Operation: 36+53=89, Resulting Numbers: [89] 89,41 unequal: No Solution Exploring Operation: 53-36=17, Resulting Numbers: [17] 17,41 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: 41:[29, 60], Operations: ['64-28=36', '24+36=60'] Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 29+60=89, Resulting Numbers: [89] 89,41 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
[ 38, 43, 68, 2 ]
20
[ "38+68=106", "43*2=86", "106-86=20" ]
Current State: 20:[38, 43, 68, 2], Operations: [] Exploring Operation: 38+68=106, Resulting Numbers: [43, 2, 106] Generated Node #2: [43, 2, 106] from Operation: 38+68=106 Current State: 20:[43, 2, 106], Operations: ['38+68=106'] Exploring Operation: 43*2=86, Resulting Numbers: [106, 86] Generated Node #3: [106, 86] from Operation: 43*2=86 Current State: 20:[106, 86], Operations: ['38+68=106', '43*2=86'] Exploring Operation: 106-86=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[38, 43, 68, 2], Operations: [] Exploring Operation: 68-43=25, Resulting Numbers: [38, 2, 25] Generated Node #0,0: 20:[38, 2, 25] Operation: 68-43=25 Moving to Node #0,0 Current State: 20:[38, 2, 25], Operations: ['68-43=25'] Exploring Operation: 38-25=13, Resulting Numbers: [2, 13] Generated Node #0,0,0: 20:[2, 13] Operation: 38-25=13 Moving to Node #0,0,0 Current State: 20:[2, 13], Operations: ['68-43=25', '38-25=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,20 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 32, 34, 9, 32 ]
46
[ "34-32=2", "32-9=23", "2*23=46" ]
Current State: 46:[32, 34, 9, 32], Operations: [] Exploring Operation: 34-32=2, Resulting Numbers: [9, 2] Generated Node #2: [9, 2] from Operation: 34-32=2 Current State: 46:[9, 2], Operations: ['34-32=2'] Exploring Operation: 32-9=23, Resulting Numbers: [2, 23] Generated Node #3: [2, 23] from Operation: 32-9=23 Current State: 46:[2, 23], Operations: ['34-32=2', '32-9=23'] Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[32, 34, 9, 32], Operations: [] Exploring Operation: 32-9=23, Resulting Numbers: [34, 32, 23] Generated Node #0,0: 46:[34, 32, 23] Operation: 32-9=23 Exploring Operation: 34-32=2, Resulting Numbers: [32, 9, 2] Generated Node #0,1: 46:[32, 9, 2] Operation: 34-32=2 Exploring Operation: 34-32=2, Resulting Numbers: [9, 32, 2] Generated Node #0,2: 46:[9, 32, 2] Operation: 34-32=2 Exploring Operation: 32/32=1, Resulting Numbers: [34, 9, 1] Generated Node #0,3: 46:[34, 9, 1] Operation: 32/32=1 Moving to Node #0,1 Current State: 46:[32, 9, 2], Operations: ['34-32=2'] Exploring Operation: 32-2=30, Resulting Numbers: [9, 30] Generated Node #0,1,0: 46:[9, 30] Operation: 32-2=30 Exploring Operation: 32+9=41, Resulting Numbers: [2, 41] Generated Node #0,1,1: 46:[2, 41] Operation: 32+9=41 Exploring Operation: 32-9=23, Resulting Numbers: [2, 23] Generated Node #0,1,2: 46:[2, 23] Operation: 32-9=23 Exploring Operation: 32/2=16, Resulting Numbers: [9, 16] Generated Node #0,1,3: 46:[9, 16] Operation: 32/2=16 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 46:[2, 23], Operations: ['34-32=2', '32-9=23'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,46 unequal: No Solution Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[32, 34, 9, 32], Operations: [] Exploring Operation: 34-32=2, Resulting Numbers: [32, 9, 2] Generated Node #0,1: 46:[32, 9, 2] Operation: 34-32=2 Moving to Node #0,1 Current State: 46:[32, 9, 2], Operations: ['34-32=2'] Exploring Operation: 32-9=23, Resulting Numbers: [2, 23] Generated Node #0,1,2: 46:[2, 23] Operation: 32-9=23 Moving to Node #0,1,2 Current State: 46:[2, 23], Operations: ['34-32=2', '32-9=23'] Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 34, 19, 80, 5 ]
71
[ "34*5=170", "19+80=99", "170-99=71" ]
Current State: 71:[34, 19, 80, 5], Operations: [] Exploring Operation: 34*5=170, Resulting Numbers: [19, 80, 170] Generated Node #2: [19, 80, 170] from Operation: 34*5=170 Current State: 71:[19, 80, 170], Operations: ['34*5=170'] Exploring Operation: 19+80=99, Resulting Numbers: [170, 99] Generated Node #3: [170, 99] from Operation: 19+80=99 Current State: 71:[170, 99], Operations: ['34*5=170', '19+80=99'] Exploring Operation: 170-99=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[34, 19, 80, 5], Operations: [] Exploring Operation: 34+5=39, Resulting Numbers: [19, 80, 39] Generated Node #0,0: 71:[19, 80, 39] Operation: 34+5=39 Exploring Operation: 34+19=53, Resulting Numbers: [80, 5, 53] Generated Node #0,1: 71:[80, 5, 53] Operation: 34+19=53 Exploring Operation: 19*5=95, Resulting Numbers: [34, 80, 95] Generated Node #0,2: 71:[34, 80, 95] Operation: 19*5=95 Exploring Operation: 19+5=24, Resulting Numbers: [34, 80, 24] Generated Node #0,3: 71:[34, 80, 24] Operation: 19+5=24 Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[34, 80, 95], Operations: ['19*5=95'] Exploring Operation: 34+80=114, Resulting Numbers: [95, 114] Generated Node #0,2,0: 71:[95, 114] Operation: 34+80=114 Exploring Operation: 34+95=129, Resulting Numbers: [80, 129] Generated Node #0,2,1: 71:[80, 129] Operation: 34+95=129 Exploring Operation: 80-34=46, Resulting Numbers: [95, 46] Generated Node #0,2,2: 71:[95, 46] Operation: 80-34=46 Exploring Operation: 95-34=61, Resulting Numbers: [80, 61] Generated Node #0,2,3: 71:[80, 61] Operation: 95-34=61 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 71:[80, 61], Operations: ['19*5=95', '95-34=61'] Exploring Operation: 80-61=19, Resulting Numbers: [19] 19,71 unequal: No Solution Exploring Operation: 80+61=141, Resulting Numbers: [141] 141,71 unequal: No Solution Exploring Operation: 80*61=4880, Resulting Numbers: [4880] 4880,71 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: 71:[95, 46], Operations: ['19*5=95', '80-34=46'] Exploring Operation: 95-46=49, Resulting Numbers: [49] 49,71 unequal: No Solution Exploring Operation: 95*46=4370, Resulting Numbers: [4370] 4370,71 unequal: No Solution Exploring Operation: 95+46=141, Resulting Numbers: [141] 141,71 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: 71:[95, 114], Operations: ['19*5=95', '34+80=114'] Exploring Operation: 95+114=209, Resulting Numbers: [209] 209,71 unequal: No Solution Exploring Operation: 95*114=10830, Resulting Numbers: [10830] 10830,71 unequal: No Solution Exploring Operation: 114-95=19, Resulting Numbers: [19] 19,71 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: 71:[80, 129], Operations: ['19*5=95', '34+95=129'] Exploring Operation: 129-80=49, Resulting Numbers: [49] 49,71 unequal: No Solution Exploring Operation: 80*129=10320, Resulting Numbers: [10320] 10320,71 unequal: No Solution Exploring Operation: 80+129=209, Resulting Numbers: [209] 209,71 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: 71:[19, 80, 39], Operations: ['34+5=39'] Exploring Operation: 19+39=58, Resulting Numbers: [80, 58] Generated Node #0,0,0: 71:[80, 58] Operation: 19+39=58 Exploring Operation: 19+80=99, Resulting Numbers: [39, 99] Generated Node #0,0,1: 71:[39, 99] Operation: 19+80=99 Exploring Operation: 39-19=20, Resulting Numbers: [80, 20] Generated Node #0,0,2: 71:[80, 20] Operation: 39-19=20 Exploring Operation: 80-19=61, Resulting Numbers: [39, 61] Generated Node #0,0,3: 71:[39, 61] Operation: 80-19=61 Moving to Node #0,0,0 Current State: 71:[80, 58], Operations: ['34+5=39', '19+39=58'] Exploring Operation: 80*58=4640, Resulting Numbers: [4640] 4640,71 unequal: No Solution Exploring Operation: 80+58=138, Resulting Numbers: [138] 138,71 unequal: No Solution Exploring Operation: 80-58=22, Resulting Numbers: [22] 22,71 unequal: No Solution Moving to Node #0,0,3 Current State: 71:[39, 61], Operations: ['34+5=39', '80-19=61'] Exploring Operation: 61-39=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 39+61=100, Resulting Numbers: [100] 100,71 unequal: No Solution Exploring Operation: 39*61=2379, Resulting Numbers: [2379] 2379,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[80, 20], Operations: ['34+5=39', '39-19=20'] Exploring Operation: 80*20=1600, Resulting Numbers: [1600] 1600,71 unequal: No Solution Exploring Operation: 80+20=100, Resulting Numbers: [100] 100,71 unequal: No Solution Exploring Operation: 80/20=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 80-20=60, Resulting Numbers: [60] 60,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[39, 99], Operations: ['34+5=39', '19+80=99'] Exploring Operation: 99-39=60, Resulting Numbers: [60] 60,71 unequal: No Solution Exploring Operation: 39+99=138, Resulting Numbers: [138] 138,71 unequal: No Solution Exploring Operation: 39*99=3861, Resulting Numbers: [3861] 3861,71 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: 71:[80, 5, 53], Operations: ['34+19=53'] Exploring Operation: 53-5=48, Resulting Numbers: [80, 48] Generated Node #0,1,0: 71:[80, 48] Operation: 53-5=48 Exploring Operation: 80+5=85, Resulting Numbers: [53, 85] Generated Node #0,1,1: 71:[53, 85] Operation: 80+5=85 Exploring Operation: 5+53=58, Resulting Numbers: [80, 58] Generated Node #0,1,2: 71:[80, 58] Operation: 5+53=58 Exploring Operation: 80-5=75, Resulting Numbers: [53, 75] Generated Node #0,1,3: 71:[53, 75] Operation: 80-5=75 Moving to Node #0,1,2 Current State: 71:[80, 58], Operations: ['34+19=53', '5+53=58'] Exploring Operation: 80-58=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 80+58=138, Resulting Numbers: [138] 138,71 unequal: No Solution Exploring Operation: 80*58=4640, Resulting Numbers: [4640] 4640,71 unequal: No Solution Moving to Node #0,1,3 Current State: 71:[53, 75], Operations: ['34+19=53', '80-5=75'] Exploring Operation: 75-53=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 53*75=3975, Resulting Numbers: [3975] 3975,71 unequal: No Solution Exploring Operation: 53+75=128, Resulting Numbers: [128] 128,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[53, 85], Operations: ['34+19=53', '80+5=85'] Exploring Operation: 53*85=4505, Resulting Numbers: [4505] 4505,71 unequal: No Solution Exploring Operation: 85-53=32, Resulting Numbers: [32] 32,71 unequal: No Solution Exploring Operation: 53+85=138, Resulting Numbers: [138] 138,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[80, 48], Operations: ['34+19=53', '53-5=48'] Exploring Operation: 80+48=128, Resulting Numbers: [128] 128,71 unequal: No Solution Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,71 unequal: No Solution Exploring Operation: 80*48=3840, Resulting Numbers: [3840] 3840,71 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: 71:[34, 80, 24], Operations: ['19+5=24'] Exploring Operation: 80+24=104, Resulting Numbers: [34, 104] Generated Node #0,3,0: 71:[34, 104] Operation: 80+24=104 Exploring Operation: 34-24=10, Resulting Numbers: [80, 10] Generated Node #0,3,1: 71:[80, 10] Operation: 34-24=10 Exploring Operation: 80-24=56, Resulting Numbers: [34, 56] Generated Node #0,3,2: 71:[34, 56] Operation: 80-24=56 Exploring Operation: 34+24=58, Resulting Numbers: [80, 58] Generated Node #0,3,3: 71:[80, 58] Operation: 34+24=58 Moving to Node #0,3,3 Current State: 71:[80, 58], Operations: ['19+5=24', '34+24=58'] Exploring Operation: 80+58=138, Resulting Numbers: [138] 138,71 unequal: No Solution Exploring Operation: 80-58=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 80*58=4640, Resulting Numbers: [4640] 4640,71 unequal: No Solution Moving to Node #0,3,2 Current State: 71:[34, 56], Operations: ['19+5=24', '80-24=56'] Exploring Operation: 34*56=1904, Resulting Numbers: [1904] 1904,71 unequal: No Solution Exploring Operation: 34+56=90, Resulting Numbers: [90] 90,71 unequal: No Solution Exploring Operation: 56-34=22, Resulting Numbers: [22] 22,71 unequal: No Solution Moving to Node #0,3,1 Current State: 71:[80, 10], Operations: ['19+5=24', '34-24=10'] Exploring Operation: 80/10=8, Resulting Numbers: [8] 8,71 unequal: No Solution Exploring Operation: 80*10=800, Resulting Numbers: [800] 800,71 unequal: No Solution Exploring Operation: 80-10=70, Resulting Numbers: [70] 70,71 unequal: No Solution Exploring Operation: 80+10=90, Resulting Numbers: [90] 90,71 unequal: No Solution Moving to Node #0,3,0 Current State: 71:[34, 104], Operations: ['19+5=24', '80+24=104'] Exploring Operation: 104-34=70, Resulting Numbers: [70] 70,71 unequal: No Solution Exploring Operation: 34+104=138, Resulting Numbers: [138] 138,71 unequal: No Solution Exploring Operation: 34*104=3536, Resulting Numbers: [3536] 3536,71 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
[ 23, 21, 44, 89 ]
43
[ "23-21=2", "89-44=45", "45-2=43" ]
Current State: 43:[23, 21, 44, 89], Operations: [] Exploring Operation: 23-21=2, Resulting Numbers: [44, 89, 2] Generated Node #2: [44, 89, 2] from Operation: 23-21=2 Current State: 43:[44, 89, 2], Operations: ['23-21=2'] Exploring Operation: 89-44=45, Resulting Numbers: [2, 45] Generated Node #3: [2, 45] from Operation: 89-44=45 Current State: 43:[2, 45], Operations: ['23-21=2', '89-44=45'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[23, 21, 44, 89], Operations: [] Exploring Operation: 89-44=45, Resulting Numbers: [23, 21, 45] Generated Node #0,0: 43:[23, 21, 45] Operation: 89-44=45 Exploring Operation: 23+21=44, Resulting Numbers: [44, 89, 44] Generated Node #0,1: 43:[44, 89, 44] Operation: 23+21=44 Exploring Operation: 89-23=66, Resulting Numbers: [21, 44, 66] Generated Node #0,2: 43:[21, 44, 66] Operation: 89-23=66 Exploring Operation: 89-21=68, Resulting Numbers: [23, 44, 68] Generated Node #0,3: 43:[23, 44, 68] Operation: 89-21=68 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[23, 21, 45], Operations: ['89-44=45'] Exploring Operation: 45-21=24, Resulting Numbers: [23, 24] Generated Node #0,0,0: 43:[23, 24] Operation: 45-21=24 Exploring Operation: 45-23=22, Resulting Numbers: [21, 22] Generated Node #0,0,1: 43:[21, 22] Operation: 45-23=22 Exploring Operation: 23+21=44, Resulting Numbers: [45, 44] Generated Node #0,0,2: 43:[45, 44] Operation: 23+21=44 Exploring Operation: 23-21=2, Resulting Numbers: [45, 2] Generated Node #0,0,3: 43:[45, 2] Operation: 23-21=2 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 43:[45, 44], Operations: ['89-44=45', '23+21=44'] Exploring Operation: 45*44=1980, Resulting Numbers: [1980] 1980,43 unequal: No Solution Exploring Operation: 45+44=89, Resulting Numbers: [89] 89,43 unequal: No Solution Exploring Operation: 45-44=1, Resulting Numbers: [1] 1,43 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: 43:[23, 24], Operations: ['89-44=45', '45-21=24'] Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,43 unequal: No Solution Exploring Operation: 23*24=552, Resulting Numbers: [552] 552,43 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: 43:[21, 22], Operations: ['89-44=45', '45-23=22'] Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 21*22=462, Resulting Numbers: [462] 462,43 unequal: No Solution Exploring Operation: 21+22=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[23, 21, 44, 89], Operations: [] Exploring Operation: 89-44=45, Resulting Numbers: [23, 21, 45] Generated Node #0,0: 43:[23, 21, 45] Operation: 89-44=45 Moving to Node #0,0 Current State: 43:[23, 21, 45], Operations: ['89-44=45'] Exploring Operation: 45-23=22, Resulting Numbers: [21, 22] Generated Node #0,0,1: 43:[21, 22] Operation: 45-23=22 Moving to Node #0,0,1 Current State: 43:[21, 22], Operations: ['89-44=45', '45-23=22'] Exploring Operation: 21+22=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 74, 31, 66, 31 ]
66
[ "31-31=0", "74*0=0", "66+0=66" ]
Current State: 66:[74, 31, 66, 31], Operations: [] Exploring Operation: 31-31=0, Resulting Numbers: [74, 66, 0] Generated Node #2: [74, 66, 0] from Operation: 31-31=0 Current State: 66:[74, 66, 0], Operations: ['31-31=0'] Exploring Operation: 74*0=0, Resulting Numbers: [66, 0] Generated Node #3: [66, 0] from Operation: 74*0=0 Current State: 66:[66, 0], Operations: ['31-31=0', '74*0=0'] Exploring Operation: 66+0=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[74, 31, 66, 31], Operations: [] Exploring Operation: 74-31=43, Resulting Numbers: [31, 66, 43] Generated Node #0,0: 66:[31, 66, 43] Operation: 74-31=43 Exploring Operation: 31/31=1, Resulting Numbers: [74, 66, 1] Generated Node #0,1: 66:[74, 66, 1] Operation: 31/31=1 Exploring Operation: 74-66=8, Resulting Numbers: [31, 31, 8] Generated Node #0,2: 66:[31, 31, 8] Operation: 74-66=8 Exploring Operation: 31-31=0, Resulting Numbers: [74, 66, 0] Generated Node #0,3: 66:[74, 66, 0] Operation: 31-31=0 Exploring Operation: 74-31=43, Resulting Numbers: [66, 31, 43] Generated Node #0,4: 66:[66, 31, 43] Operation: 74-31=43 Moving to Node #0,2 Current State: 66:[31, 31, 8], Operations: ['74-66=8'] Exploring Operation: 31-31=0, Resulting Numbers: [8, 0] Generated Node #0,2,0: 66:[8, 0] Operation: 31-31=0 Exploring Operation: 31+31=62, Resulting Numbers: [8, 62] Generated Node #0,2,1: 66:[8, 62] Operation: 31+31=62 Exploring Operation: 31/31=1, Resulting Numbers: [8, 1] Generated Node #0,2,2: 66:[8, 1] Operation: 31/31=1 Exploring Operation: 31-8=23, Resulting Numbers: [31, 23] Generated Node #0,2,3: 66:[31, 23] Operation: 31-8=23 Exploring Operation: 31-8=23, Resulting Numbers: [31, 23] Generated Node #0,2,4: 66:[31, 23] Operation: 31-8=23 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 66:[8, 1], Operations: ['74-66=8', '31/31=1'] Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,66 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,66 unequal: No Solution Exploring Operation: 8+1=9, Resulting Numbers: [9] 9,66 unequal: No Solution Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,66 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: 66:[31, 23], Operations: ['74-66=8', '31-8=23'] Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,66 unequal: No Solution Exploring Operation: 31*23=713, Resulting Numbers: [713] 713,66 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,66 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: 66:[31, 23], Operations: ['74-66=8', '31-8=23'] Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,66 unequal: No Solution Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,66 unequal: No Solution Exploring Operation: 31*23=713, Resulting Numbers: [713] 713,66 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: 66:[8, 0], Operations: ['74-66=8', '31-31=0'] Exploring Operation: 8*0=0, Resulting Numbers: [0] 0,66 unequal: No Solution Exploring Operation: 8-0=8, Resulting Numbers: [8] 8,66 unequal: No Solution Exploring Operation: 8+0=8, Resulting Numbers: [8] 8,66 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: 66:[8, 62], Operations: ['74-66=8', '31+31=62'] Exploring Operation: 8+62=70, Resulting Numbers: [70] 70,66 unequal: No Solution Exploring Operation: 8*62=496, Resulting Numbers: [496] 496,66 unequal: No Solution Exploring Operation: 62-8=54, Resulting Numbers: [54] 54,66 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: 66:[74, 66, 1], Operations: ['31/31=1'] Exploring Operation: 74/1=74, Resulting Numbers: [66, 74] Generated Node #0,1,0: 66:[66, 74] Operation: 74/1=74 Exploring Operation: 66*1=66, Resulting Numbers: [74, 66] Generated Node #0,1,1: 66:[74, 66] Operation: 66*1=66 Exploring Operation: 74-1=73, Resulting Numbers: [66, 73] Generated Node #0,1,2: 66:[66, 73] Operation: 74-1=73 Exploring Operation: 74*1=74, Resulting Numbers: [66, 74] Generated Node #0,1,3: 66:[66, 74] Operation: 74*1=74 Exploring Operation: 74-66=8, Resulting Numbers: [1, 8] Generated Node #0,1,4: 66:[1, 8] Operation: 74-66=8 Moving to Node #0,3 Current State: 66:[74, 66, 0], Operations: ['31-31=0'] Exploring Operation: 74-0=74, Resulting Numbers: [66, 74] Generated Node #0,3,0: 66:[66, 74] Operation: 74-0=74 Exploring Operation: 74*0=0, Resulting Numbers: [66, 0] Generated Node #0,3,1: 66:[66, 0] Operation: 74*0=0 Exploring Operation: 74-66=8, Resulting Numbers: [0, 8] Generated Node #0,3,2: 66:[0, 8] Operation: 74-66=8 Exploring Operation: 74+0=74, Resulting Numbers: [66, 74] Generated Node #0,3,3: 66:[66, 74] Operation: 74+0=74 Exploring Operation: 66+0=66, Resulting Numbers: [74, 66] Generated Node #0,3,4: 66:[74, 66] Operation: 66+0=66 Moving to Node #0,0 Current State: 66:[31, 66, 43], Operations: ['74-31=43'] Exploring Operation: 31+43=74, Resulting Numbers: [66, 74] Generated Node #0,0,0: 66:[66, 74] Operation: 31+43=74 Exploring Operation: 66-31=35, Resulting Numbers: [43, 35] Generated Node #0,0,1: 66:[43, 35] Operation: 66-31=35 Exploring Operation: 66-43=23, Resulting Numbers: [31, 23] Generated Node #0,0,2: 66:[31, 23] Operation: 66-43=23 Exploring Operation: 43-31=12, Resulting Numbers: [66, 12] Generated Node #0,0,3: 66:[66, 12] Operation: 43-31=12 Exploring Operation: 31+66=97, Resulting Numbers: [43, 97] Generated Node #0,0,4: 66:[43, 97] Operation: 31+66=97 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 66:[66, 12], Operations: ['74-31=43', '43-31=12'] Exploring Operation: 66*12=792, Resulting Numbers: [792] 792,66 unequal: No Solution Exploring Operation: 66-12=54, Resulting Numbers: [54] 54,66 unequal: No Solution Exploring Operation: 66+12=78, Resulting Numbers: [78] 78,66 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: 66:[31, 23], Operations: ['74-31=43', '66-43=23'] Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,66 unequal: No Solution Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,66 unequal: No Solution Exploring Operation: 31*23=713, Resulting Numbers: [713] 713,66 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: 66:[66, 74], Operations: ['74-31=43', '31+43=74'] Exploring Operation: 74-66=8, Resulting Numbers: [8] 8,66 unequal: No Solution Exploring Operation: 66+74=140, Resulting Numbers: [140] 140,66 unequal: No Solution Exploring Operation: 66*74=4884, Resulting Numbers: [4884] 4884,66 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: 66:[43, 35], Operations: ['74-31=43', '66-31=35'] Exploring Operation: 43-35=8, Resulting Numbers: [8] 8,66 unequal: No Solution Exploring Operation: 43*35=1505, Resulting Numbers: [1505] 1505,66 unequal: No Solution Exploring Operation: 43+35=78, Resulting Numbers: [78] 78,66 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: 66:[43, 97], Operations: ['74-31=43', '31+66=97'] Exploring Operation: 43+97=140, Resulting Numbers: [140] 140,66 unequal: No Solution Exploring Operation: 43*97=4171, Resulting Numbers: [4171] 4171,66 unequal: No Solution Exploring Operation: 97-43=54, Resulting Numbers: [54] 54,66 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: 66:[66, 31, 43], Operations: ['74-31=43'] Exploring Operation: 66-31=35, Resulting Numbers: [43, 35] Generated Node #0,4,0: 66:[43, 35] Operation: 66-31=35 Exploring Operation: 31+43=74, Resulting Numbers: [66, 74] Generated Node #0,4,1: 66:[66, 74] Operation: 31+43=74 Exploring Operation: 66-43=23, Resulting Numbers: [31, 23] Generated Node #0,4,2: 66:[31, 23] Operation: 66-43=23 Exploring Operation: 66+31=97, Resulting Numbers: [43, 97] Generated Node #0,4,3: 66:[43, 97] Operation: 66+31=97 Exploring Operation: 43-31=12, Resulting Numbers: [66, 12] Generated Node #0,4,4: 66:[66, 12] Operation: 43-31=12 Moving to Node #0,4,4 Current State: 66:[66, 12], Operations: ['74-31=43', '43-31=12'] Exploring Operation: 66-12=54, Resulting Numbers: [54] 54,66 unequal: No Solution Exploring Operation: 66*12=792, Resulting Numbers: [792] 792,66 unequal: No Solution Exploring Operation: 66+12=78, Resulting Numbers: [78] 78,66 unequal: No Solution Moving to Node #0,3,1 Current State: 66:[66, 0], Operations: ['31-31=0', '74*0=0'] Exploring Operation: 66*0=0, Resulting Numbers: [0] 0,66 unequal: No Solution Exploring Operation: 66-0=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[74, 31, 66, 31], Operations: [] Exploring Operation: 31-31=0, Resulting Numbers: [74, 66, 0] Generated Node #0,3: 66:[74, 66, 0] Operation: 31-31=0 Moving to Node #0,3 Current State: 66:[74, 66, 0], Operations: ['31-31=0'] Exploring Operation: 74*0=0, Resulting Numbers: [66, 0] Generated Node #0,3,1: 66:[66, 0] Operation: 74*0=0 Moving to Node #0,3,1 Current State: 66:[66, 0], Operations: ['31-31=0', '74*0=0'] Exploring Operation: 66-0=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
0.939236
hs_5
mult_heuristic
[ 25, 4, 8, 42 ]
46
[ "8/4=2", "42/2=21", "25+21=46" ]
Current State: 46:[25, 4, 8, 42], Operations: [] Exploring Operation: 8/4=2, Resulting Numbers: [25, 42, 2] Generated Node #2: [25, 42, 2] from Operation: 8/4=2 Current State: 46:[25, 42, 2], Operations: ['8/4=2'] Exploring Operation: 42/2=21, Resulting Numbers: [25, 21] Generated Node #3: [25, 21] from Operation: 42/2=21 Current State: 46:[25, 21], Operations: ['8/4=2', '42/2=21'] Exploring Operation: 25+21=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[25, 4, 8, 42], Operations: [] Exploring Operation: 8/4=2, Resulting Numbers: [25, 42, 2] Generated Node #0,0: 46:[25, 42, 2] Operation: 8/4=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[25, 42, 2], Operations: ['8/4=2'] Exploring Operation: 25-2=23, Resulting Numbers: [42, 23] Generated Node #0,0,0: 46:[42, 23] Operation: 25-2=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[42, 23], Operations: ['8/4=2', '25-2=23'] Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,46 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
[ 24, 12, 41, 89 ]
28
[ "89-41=48", "48/12=4", "24+4=28" ]
Current State: 28:[24, 12, 41, 89], Operations: [] Exploring Operation: 89-41=48, Resulting Numbers: [24, 12, 48] Generated Node #2: [24, 12, 48] from Operation: 89-41=48 Current State: 28:[24, 12, 48], Operations: ['89-41=48'] Exploring Operation: 48/12=4, Resulting Numbers: [24, 4] Generated Node #3: [24, 4] from Operation: 48/12=4 Current State: 28:[24, 4], Operations: ['89-41=48', '48/12=4'] Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[24, 12, 41, 89], Operations: [] Exploring Operation: 41-24=17, Resulting Numbers: [12, 89, 17] Generated Node #0,0: 28:[12, 89, 17] Operation: 41-24=17 Exploring Operation: 89-24=65, Resulting Numbers: [12, 41, 65] Generated Node #0,1: 28:[12, 41, 65] Operation: 89-24=65 Exploring Operation: 89-41=48, Resulting Numbers: [24, 12, 48] Generated Node #0,2: 28:[24, 12, 48] Operation: 89-41=48 Start Sub Search at level 1: Moving to Node #0,2 Current State: 28:[24, 12, 48], Operations: ['89-41=48'] Exploring Operation: 48-24=24, Resulting Numbers: [12, 24] Generated Node #0,2,0: 28:[12, 24] Operation: 48-24=24 Exploring Operation: 48/12=4, Resulting Numbers: [24, 4] Generated Node #0,2,1: 28:[24, 4] Operation: 48/12=4 Exploring Operation: 48/24=2, Resulting Numbers: [12, 2] Generated Node #0,2,2: 28:[12, 2] Operation: 48/24=2 Moving to Node #0,2,2 Current State: 28:[12, 2], Operations: ['89-41=48', '48/24=2'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,28 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,28 unequal: No Solution Moving to Node #0,2,1 Current State: 28:[24, 4], Operations: ['89-41=48', '48/12=4'] Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[24, 12, 41, 89], Operations: [] Exploring Operation: 89-41=48, Resulting Numbers: [24, 12, 48] Generated Node #0,2: 28:[24, 12, 48] Operation: 89-41=48 Moving to Node #0,2 Current State: 28:[24, 12, 48], Operations: ['89-41=48'] Exploring Operation: 48/12=4, Resulting Numbers: [24, 4] Generated Node #0,2,1: 28:[24, 4] Operation: 48/12=4 Moving to Node #0,2,1 Current State: 28:[24, 4], Operations: ['89-41=48', '48/12=4'] Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 5, 17, 86, 30 ]
31
[ "5*17=85", "86+30=116", "116-85=31" ]
Current State: 31:[5, 17, 86, 30], Operations: [] Exploring Operation: 5*17=85, Resulting Numbers: [86, 30, 85] Generated Node #2: [86, 30, 85] from Operation: 5*17=85 Current State: 31:[86, 30, 85], Operations: ['5*17=85'] Exploring Operation: 86+30=116, Resulting Numbers: [85, 116] Generated Node #3: [85, 116] from Operation: 86+30=116 Current State: 31:[85, 116], Operations: ['5*17=85', '86+30=116'] Exploring Operation: 116-85=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[5, 17, 86, 30], Operations: [] Exploring Operation: 5+17=22, Resulting Numbers: [86, 30, 22] Generated Node #0,0: 31:[86, 30, 22] Operation: 5+17=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[86, 30, 22], Operations: ['5+17=22'] Exploring Operation: 86-30=56, Resulting Numbers: [22, 56] Generated Node #0,0,0: 31:[22, 56] Operation: 86-30=56 Moving to Node #0,0,0 Current State: 31:[22, 56], Operations: ['5+17=22', '86-30=56'] Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,31 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
[ 58, 8, 36, 9 ]
56
[ "8*9=72", "72/36=2", "58-2=56" ]
Current State: 56:[58, 8, 36, 9], Operations: [] Exploring Operation: 8*9=72, Resulting Numbers: [58, 36, 72] Generated Node #2: [58, 36, 72] from Operation: 8*9=72 Current State: 56:[58, 36, 72], Operations: ['8*9=72'] Exploring Operation: 72/36=2, Resulting Numbers: [58, 2] Generated Node #3: [58, 2] from Operation: 72/36=2 Current State: 56:[58, 2], Operations: ['8*9=72', '72/36=2'] Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[58, 8, 36, 9], Operations: [] Exploring Operation: 36/9=4, Resulting Numbers: [58, 8, 4] Generated Node #0,0: 56:[58, 8, 4] Operation: 36/9=4 Exploring Operation: 36-9=27, Resulting Numbers: [58, 8, 27] Generated Node #0,1: 56:[58, 8, 27] Operation: 36-9=27 Exploring Operation: 58-36=22, Resulting Numbers: [8, 9, 22] Generated Node #0,2: 56:[8, 9, 22] Operation: 58-36=22 Exploring Operation: 36-8=28, Resulting Numbers: [58, 9, 28] Generated Node #0,3: 56:[58, 9, 28] Operation: 36-8=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[58, 8, 4], Operations: ['36/9=4'] Exploring Operation: 58-4=54, Resulting Numbers: [8, 54] Generated Node #0,0,0: 56:[8, 54] Operation: 58-4=54 Exploring Operation: 8+4=12, Resulting Numbers: [58, 12] Generated Node #0,0,1: 56:[58, 12] Operation: 8+4=12 Exploring Operation: 8/4=2, Resulting Numbers: [58, 2] Generated Node #0,0,2: 56:[58, 2] Operation: 8/4=2 Exploring Operation: 8-4=4, Resulting Numbers: [58, 4] Generated Node #0,0,3: 56:[58, 4] Operation: 8-4=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[8, 54], Operations: ['36/9=4', '58-4=54'] Exploring Operation: 8+54=62, Resulting Numbers: [62] 62,56 unequal: No Solution Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,56 unequal: No Solution Exploring Operation: 8*54=432, Resulting Numbers: [432] 432,56 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: 56:[58, 2], Operations: ['36/9=4', '8/4=2'] Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,56 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[58, 8, 36, 9], Operations: [] Exploring Operation: 36/9=4, Resulting Numbers: [58, 8, 4] Generated Node #0,0: 56:[58, 8, 4] Operation: 36/9=4 Moving to Node #0,0 Current State: 56:[58, 8, 4], Operations: ['36/9=4'] Exploring Operation: 8/4=2, Resulting Numbers: [58, 2] Generated Node #0,0,2: 56:[58, 2] Operation: 8/4=2 Moving to Node #0,0,2 Current State: 56:[58, 2], Operations: ['36/9=4', '8/4=2'] Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 62, 36, 34, 48 ]
34
[ "62+34=96", "96/48=2", "36-2=34" ]
Current State: 34:[62, 36, 34, 48], Operations: [] Exploring Operation: 62+34=96, Resulting Numbers: [36, 48, 96] Generated Node #2: [36, 48, 96] from Operation: 62+34=96 Current State: 34:[36, 48, 96], Operations: ['62+34=96'] Exploring Operation: 96/48=2, Resulting Numbers: [36, 2] Generated Node #3: [36, 2] from Operation: 96/48=2 Current State: 34:[36, 2], Operations: ['62+34=96', '96/48=2'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[62, 36, 34, 48], Operations: [] Exploring Operation: 62-34=28, Resulting Numbers: [36, 48, 28] Generated Node #0,0: 34:[36, 48, 28] Operation: 62-34=28 Exploring Operation: 62-48=14, Resulting Numbers: [36, 34, 14] Generated Node #0,1: 34:[36, 34, 14] Operation: 62-48=14 Exploring Operation: 62-36=26, Resulting Numbers: [34, 48, 26] Generated Node #0,2: 34:[34, 48, 26] Operation: 62-36=26 Exploring Operation: 48-36=12, Resulting Numbers: [62, 34, 12] Generated Node #0,3: 34:[62, 34, 12] Operation: 48-36=12 Moving to Node #0,1 Current State: 34:[36, 34, 14], Operations: ['62-48=14'] Exploring Operation: 36-34=2, Resulting Numbers: [14, 2] Generated Node #0,1,0: 34:[14, 2] Operation: 36-34=2 Exploring Operation: 36+14=50, Resulting Numbers: [34, 50] Generated Node #0,1,1: 34:[34, 50] Operation: 36+14=50 Exploring Operation: 36-14=22, Resulting Numbers: [34, 22] Generated Node #0,1,2: 34:[34, 22] Operation: 36-14=22 Exploring Operation: 34-14=20, Resulting Numbers: [36, 20] Generated Node #0,1,3: 34:[36, 20] Operation: 34-14=20 Moving to Node #0,2 Current State: 34:[34, 48, 26], Operations: ['62-36=26'] Exploring Operation: 48-26=22, Resulting Numbers: [34, 22] Generated Node #0,2,0: 34:[34, 22] Operation: 48-26=22 Exploring Operation: 34+26=60, Resulting Numbers: [48, 60] Generated Node #0,2,1: 34:[48, 60] Operation: 34+26=60 Exploring Operation: 34-26=8, Resulting Numbers: [48, 8] Generated Node #0,2,2: 34:[48, 8] Operation: 34-26=8 Exploring Operation: 48-34=14, Resulting Numbers: [26, 14] Generated Node #0,2,3: 34:[26, 14] Operation: 48-34=14 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 34:[34, 22], Operations: ['62-36=26', '48-26=22'] Exploring Operation: 34*22=748, Resulting Numbers: [748] 748,34 unequal: No Solution Exploring Operation: 34+22=56, Resulting Numbers: [56] 56,34 unequal: No Solution Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,34 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: 34:[26, 14], Operations: ['62-36=26', '48-34=14'] Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,34 unequal: No Solution Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,34 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: 34:[48, 8], Operations: ['62-36=26', '34-26=8'] Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,34 unequal: No Solution Exploring Operation: 48*8=384, Resulting Numbers: [384] 384,34 unequal: No Solution Exploring Operation: 48+8=56, Resulting Numbers: [56] 56,34 unequal: No Solution Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,34 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: 34:[48, 60], Operations: ['62-36=26', '34+26=60'] Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,34 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,34 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: 34:[36, 48, 28], Operations: ['62-34=28'] Exploring Operation: 48-36=12, Resulting Numbers: [28, 12] Generated Node #0,0,0: 34:[28, 12] Operation: 48-36=12 Exploring Operation: 36-28=8, Resulting Numbers: [48, 8] Generated Node #0,0,1: 34:[48, 8] Operation: 36-28=8 Exploring Operation: 48-28=20, Resulting Numbers: [36, 20] Generated Node #0,0,2: 34:[36, 20] Operation: 48-28=20 Exploring Operation: 36+28=64, Resulting Numbers: [48, 64] Generated Node #0,0,3: 34:[48, 64] Operation: 36+28=64 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 34:[36, 20], Operations: ['62-34=28', '48-28=20'] Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,34 unequal: No Solution Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,34 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: 34:[28, 12], Operations: ['62-34=28', '48-36=12'] Exploring Operation: 28*12=336, Resulting Numbers: [336] 336,34 unequal: No Solution Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,34 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,34 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: 34:[48, 8], Operations: ['62-34=28', '36-28=8'] Exploring Operation: 48+8=56, Resulting Numbers: [56] 56,34 unequal: No Solution Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,34 unequal: No Solution Exploring Operation: 48*8=384, Resulting Numbers: [384] 384,34 unequal: No Solution Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,34 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: 34:[48, 64], Operations: ['62-34=28', '36+28=64'] Exploring Operation: 48*64=3072, Resulting Numbers: [3072] 3072,34 unequal: No Solution Exploring Operation: 64-48=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 48+64=112, Resulting Numbers: [112] 112,34 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: 34:[62, 34, 12], Operations: ['48-36=12'] Exploring Operation: 62+12=74, Resulting Numbers: [34, 74] Generated Node #0,3,0: 34:[34, 74] Operation: 62+12=74 Exploring Operation: 62-34=28, Resulting Numbers: [12, 28] Generated Node #0,3,1: 34:[12, 28] Operation: 62-34=28 Exploring Operation: 34-12=22, Resulting Numbers: [62, 22] Generated Node #0,3,2: 34:[62, 22] Operation: 34-12=22 Exploring Operation: 62-12=50, Resulting Numbers: [34, 50] Generated Node #0,3,3: 34:[34, 50] Operation: 62-12=50 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 34:[12, 28], Operations: ['48-36=12', '62-34=28'] Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 12*28=336, Resulting Numbers: [336] 336,34 unequal: No Solution Exploring Operation: 12+28=40, Resulting Numbers: [40] 40,34 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: 34:[34, 50], Operations: ['48-36=12', '62-12=50'] Exploring Operation: 34*50=1700, Resulting Numbers: [1700] 1700,34 unequal: No Solution Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 34+50=84, Resulting Numbers: [84] 84,34 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: 34:[62, 22], Operations: ['48-36=12', '34-12=22'] Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,34 unequal: No Solution Exploring Operation: 62+22=84, Resulting Numbers: [84] 84,34 unequal: No Solution Exploring Operation: 62*22=1364, Resulting Numbers: [1364] 1364,34 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: 34:[34, 74], Operations: ['48-36=12', '62+12=74'] Exploring Operation: 74-34=40, Resulting Numbers: [40] 40,34 unequal: No Solution Exploring Operation: 34+74=108, Resulting Numbers: [108] 108,34 unequal: No Solution Exploring Operation: 34*74=2516, Resulting Numbers: [2516] 2516,34 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: 34:[14, 2], Operations: ['62-48=14', '36-34=2'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,34 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,34 unequal: No Solution Moving to Node #0,1,3 Current State: 34:[36, 20], Operations: ['62-48=14', '34-14=20'] Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,34 unequal: No Solution Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[34, 22], Operations: ['62-48=14', '36-14=22'] Exploring Operation: 34*22=748, Resulting Numbers: [748] 748,34 unequal: No Solution Exploring Operation: 34+22=56, Resulting Numbers: [56] 56,34 unequal: No Solution Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[34, 50], Operations: ['62-48=14', '36+14=50'] Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 34+50=84, Resulting Numbers: [84] 84,34 unequal: No Solution Exploring Operation: 34*50=1700, Resulting Numbers: [1700] 1700,34 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 77, 83, 39, 79 ]
34
[ "83-77=6", "79-39=40", "40-6=34" ]
Current State: 34:[77, 83, 39, 79], Operations: [] Exploring Operation: 83-77=6, Resulting Numbers: [39, 79, 6] Generated Node #2: [39, 79, 6] from Operation: 83-77=6 Current State: 34:[39, 79, 6], Operations: ['83-77=6'] Exploring Operation: 79-39=40, Resulting Numbers: [6, 40] Generated Node #3: [6, 40] from Operation: 79-39=40 Current State: 34:[6, 40], Operations: ['83-77=6', '79-39=40'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[77, 83, 39, 79], Operations: [] Exploring Operation: 83-79=4, Resulting Numbers: [77, 39, 4] Generated Node #0,0: 34:[77, 39, 4] Operation: 83-79=4 Exploring Operation: 83-77=6, Resulting Numbers: [39, 79, 6] Generated Node #0,1: 34:[39, 79, 6] Operation: 83-77=6 Exploring Operation: 79-77=2, Resulting Numbers: [83, 39, 2] Generated Node #0,2: 34:[83, 39, 2] Operation: 79-77=2 Moving to Node #0,0 Current State: 34:[77, 39, 4], Operations: ['83-79=4'] Exploring Operation: 77-39=38, Resulting Numbers: [4, 38] Generated Node #0,0,0: 34:[4, 38] Operation: 77-39=38 Exploring Operation: 77-4=73, Resulting Numbers: [39, 73] Generated Node #0,0,1: 34:[39, 73] Operation: 77-4=73 Exploring Operation: 39-4=35, Resulting Numbers: [77, 35] Generated Node #0,0,2: 34:[77, 35] Operation: 39-4=35 Moving to Node #0,1 Current State: 34:[39, 79, 6], Operations: ['83-77=6'] Exploring Operation: 39-6=33, Resulting Numbers: [79, 33] Generated Node #0,1,0: 34:[79, 33] Operation: 39-6=33 Exploring Operation: 79-39=40, Resulting Numbers: [6, 40] Generated Node #0,1,1: 34:[6, 40] Operation: 79-39=40 Exploring Operation: 79-6=73, Resulting Numbers: [39, 73] Generated Node #0,1,2: 34:[39, 73] Operation: 79-6=73 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 34:[6, 40], Operations: ['83-77=6', '79-39=40'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[77, 83, 39, 79], Operations: [] Exploring Operation: 83-77=6, Resulting Numbers: [39, 79, 6] Generated Node #0,1: 34:[39, 79, 6] Operation: 83-77=6 Moving to Node #0,1 Current State: 34:[39, 79, 6], Operations: ['83-77=6'] Exploring Operation: 79-39=40, Resulting Numbers: [6, 40] Generated Node #0,1,1: 34:[6, 40] Operation: 79-39=40 Moving to Node #0,1,1 Current State: 34:[6, 40], Operations: ['83-77=6', '79-39=40'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 63, 80, 63, 11 ]
76
[ "63+80=143", "143/11=13", "63+13=76" ]
Current State: 76:[63, 80, 63, 11], Operations: [] Exploring Operation: 63+80=143, Resulting Numbers: [11, 143] Generated Node #2: [11, 143] from Operation: 63+80=143 Current State: 76:[11, 143], Operations: ['63+80=143'] Exploring Operation: 143/11=13, Resulting Numbers: [13] 13,76 equal: Goal Reached Exploring Operation: 63+13=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[63, 80, 63, 11], Operations: [] Exploring Operation: 80-63=17, Resulting Numbers: [63, 11, 17] Generated Node #0,0: 76:[63, 11, 17] Operation: 80-63=17 Exploring Operation: 63/63=1, Resulting Numbers: [80, 11, 1] Generated Node #0,1: 76:[80, 11, 1] Operation: 63/63=1 Exploring Operation: 63+11=74, Resulting Numbers: [80, 63, 74] Generated Node #0,2: 76:[80, 63, 74] Operation: 63+11=74 Exploring Operation: 63+11=74, Resulting Numbers: [63, 80, 74] Generated Node #0,3: 76:[63, 80, 74] Operation: 63+11=74 Exploring Operation: 63-63=0, Resulting Numbers: [80, 11, 0] Generated Node #0,4: 76:[80, 11, 0] Operation: 63-63=0 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[80, 11, 1], Operations: ['63/63=1'] Exploring Operation: 80-11=69, Resulting Numbers: [1, 69] Generated Node #0,1,0: 76:[1, 69] Operation: 80-11=69 Exploring Operation: 11-1=10, Resulting Numbers: [80, 10] Generated Node #0,1,1: 76:[80, 10] Operation: 11-1=10 Exploring Operation: 80*1=80, Resulting Numbers: [11, 80] Generated Node #0,1,2: 76:[11, 80] Operation: 80*1=80 Exploring Operation: 80-1=79, Resulting Numbers: [11, 79] Generated Node #0,1,3: 76:[11, 79] Operation: 80-1=79 Exploring Operation: 80/1=80, Resulting Numbers: [11, 80] Generated Node #0,1,4: 76:[11, 80] Operation: 80/1=80 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 76:[1, 69], Operations: ['63/63=1', '80-11=69'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 1*69=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 1+69=70, Resulting Numbers: [70] 70,76 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: 76:[80, 10], Operations: ['63/63=1', '11-1=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=800, Resulting Numbers: [800] 800,76 unequal: No Solution Exploring Operation: 80-10=70, Resulting Numbers: [70] 70,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 76:[11, 79], Operations: ['63/63=1', '80-1=79'] Exploring Operation: 79-11=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 11*79=869, Resulting Numbers: [869] 869,76 unequal: No Solution Exploring Operation: 11+79=90, Resulting Numbers: [90] 90,76 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: 76:[11, 80], Operations: ['63/63=1', '80*1=80'] Exploring Operation: 11*80=880, Resulting Numbers: [880] 880,76 unequal: No Solution Exploring Operation: 11+80=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,76 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: 76:[11, 80], Operations: ['63/63=1', '80/1=80'] Exploring Operation: 11+80=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 11*80=880, Resulting Numbers: [880] 880,76 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: 76:[80, 11, 0], Operations: ['63-63=0'] Exploring Operation: 11*0=0, Resulting Numbers: [80, 0] Generated Node #0,4,0: 76:[80, 0] Operation: 11*0=0 Exploring Operation: 80*0=0, Resulting Numbers: [11, 0] Generated Node #0,4,1: 76:[11, 0] Operation: 80*0=0 Exploring Operation: 80-11=69, Resulting Numbers: [0, 69] Generated Node #0,4,2: 76:[0, 69] Operation: 80-11=69 Exploring Operation: 80-0=80, Resulting Numbers: [11, 80] Generated Node #0,4,3: 76:[11, 80] Operation: 80-0=80 Exploring Operation: 80+0=80, Resulting Numbers: [11, 80] Generated Node #0,4,4: 76:[11, 80] Operation: 80+0=80 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 76:[80, 0], Operations: ['63-63=0', '11*0=0'] Exploring Operation: 80*0=0, Resulting Numbers: [0] 0,76 unequal: No Solution Exploring Operation: 80-0=80, Resulting Numbers: [80] 80,76 unequal: No Solution Exploring Operation: 80+0=80, Resulting Numbers: [80] 80,76 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: 76:[11, 0], Operations: ['63-63=0', '80*0=0'] Exploring Operation: 11-0=11, Resulting Numbers: [11] 11,76 unequal: No Solution Exploring Operation: 11*0=0, Resulting Numbers: [0] 0,76 unequal: No Solution Exploring Operation: 11+0=11, Resulting Numbers: [11] 11,76 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: 76:[0, 69], Operations: ['63-63=0', '80-11=69'] Exploring Operation: 69-0=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 0+69=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 0*69=0, Resulting Numbers: [0] 0,76 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: 76:[11, 80], Operations: ['63-63=0', '80-0=80'] Exploring Operation: 11*80=880, Resulting Numbers: [880] 880,76 unequal: No Solution Exploring Operation: 11+80=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,76 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: 76:[11, 80], Operations: ['63-63=0', '80+0=80'] Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 11*80=880, Resulting Numbers: [880] 880,76 unequal: No Solution Exploring Operation: 11+80=91, Resulting Numbers: [91] 91,76 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: 76:[80, 63, 74], Operations: ['63+11=74'] Exploring Operation: 74-63=11, Resulting Numbers: [80, 11] Generated Node #0,2,0: 76:[80, 11] Operation: 74-63=11 Exploring Operation: 80-63=17, Resulting Numbers: [74, 17] Generated Node #0,2,1: 76:[74, 17] Operation: 80-63=17 Exploring Operation: 80-74=6, Resulting Numbers: [63, 6] Generated Node #0,2,2: 76:[63, 6] Operation: 80-74=6 Exploring Operation: 63+74=137, Resulting Numbers: [80, 137] Generated Node #0,2,3: 76:[80, 137] Operation: 63+74=137 Exploring Operation: 80+63=143, Resulting Numbers: [74, 143] Generated Node #0,2,4: 76:[74, 143] Operation: 80+63=143 Moving to Node #0,2,1 Current State: 76:[74, 17], Operations: ['63+11=74', '80-63=17'] Exploring Operation: 74+17=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 74*17=1258, Resulting Numbers: [1258] 1258,76 unequal: No Solution Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[80, 11], Operations: ['63+11=74', '74-63=11'] Exploring Operation: 80*11=880, Resulting Numbers: [880] 880,76 unequal: No Solution Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 80+11=91, Resulting Numbers: [91] 91,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[63, 6], Operations: ['63+11=74', '80-74=6'] Exploring Operation: 63*6=378, Resulting Numbers: [378] 378,76 unequal: No Solution Exploring Operation: 63+6=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,76 unequal: No Solution Moving to Node #0,2,3 Current State: 76:[80, 137], Operations: ['63+11=74', '63+74=137'] Exploring Operation: 80+137=217, Resulting Numbers: [217] 217,76 unequal: No Solution Exploring Operation: 80*137=10960, Resulting Numbers: [10960] 10960,76 unequal: No Solution Exploring Operation: 137-80=57, Resulting Numbers: [57] 57,76 unequal: No Solution Moving to Node #0,2,4 Current State: 76:[74, 143], Operations: ['63+11=74', '80+63=143'] Exploring Operation: 143-74=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 74*143=10582, Resulting Numbers: [10582] 10582,76 unequal: No Solution Exploring Operation: 74+143=217, Resulting Numbers: [217] 217,76 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 Current State: 76:[63, 80, 74], Operations: ['63+11=74'] Exploring Operation: 80-74=6, Resulting Numbers: [63, 6] Generated Node #0,3,0: 76:[63, 6] Operation: 80-74=6 Exploring Operation: 63+80=143, Resulting Numbers: [74, 143] Generated Node #0,3,1: 76:[74, 143] Operation: 63+80=143 Exploring Operation: 74-63=11, Resulting Numbers: [80, 11] Generated Node #0,3,2: 76:[80, 11] Operation: 74-63=11 Exploring Operation: 63+74=137, Resulting Numbers: [80, 137] Generated Node #0,3,3: 76:[80, 137] Operation: 63+74=137 Exploring Operation: 80-63=17, Resulting Numbers: [74, 17] Generated Node #0,3,4: 76:[74, 17] Operation: 80-63=17 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 76:[74, 17], Operations: ['63+11=74', '80-63=17'] Exploring Operation: 74+17=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 74*17=1258, Resulting Numbers: [1258] 1258,76 unequal: No Solution Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,76 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: 76:[80, 11], Operations: ['63+11=74', '74-63=11'] Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 80*11=880, Resulting Numbers: [880] 880,76 unequal: No Solution Exploring Operation: 80+11=91, Resulting Numbers: [91] 91,76 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: 76:[63, 6], Operations: ['63+11=74', '80-74=6'] Exploring Operation: 63+6=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,76 unequal: No Solution Exploring Operation: 63*6=378, Resulting Numbers: [378] 378,76 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: 76:[80, 137], Operations: ['63+11=74', '63+74=137'] Exploring Operation: 137-80=57, Resulting Numbers: [57] 57,76 unequal: No Solution Exploring Operation: 80+137=217, Resulting Numbers: [217] 217,76 unequal: No Solution Exploring Operation: 80*137=10960, Resulting Numbers: [10960] 10960,76 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: 76:[74, 143], Operations: ['63+11=74', '63+80=143'] Exploring Operation: 143-74=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 74+143=217, Resulting Numbers: [217] 217,76 unequal: No Solution Exploring Operation: 74*143=10582, Resulting Numbers: [10582] 10582,76 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: 76:[63, 11, 17], Operations: ['80-63=17'] Exploring Operation: 63+17=80, Resulting Numbers: [11, 80] Generated Node #0,0,0: 76:[11, 80] Operation: 63+17=80 Exploring Operation: 17-11=6, Resulting Numbers: [63, 6] Generated Node #0,0,1: 76:[63, 6] Operation: 17-11=6 Exploring Operation: 63+11=74, Resulting Numbers: [17, 74] Generated Node #0,0,2: 76:[17, 74] Operation: 63+11=74 Exploring Operation: 63-17=46, Resulting Numbers: [11, 46] Generated Node #0,0,3: 76:[11, 46] Operation: 63-17=46 Exploring Operation: 63-11=52, Resulting Numbers: [17, 52] Generated Node #0,0,4: 76:[17, 52] Operation: 63-11=52 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 76:[17, 74], Operations: ['80-63=17', '63+11=74'] Exploring Operation: 17*74=1258, Resulting Numbers: [1258] 1258,76 unequal: No Solution Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,76 unequal: No Solution Exploring Operation: 17+74=91, Resulting Numbers: [91] 91,76 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: 76:[11, 80], Operations: ['80-63=17', '63+17=80'] Exploring Operation: 11*80=880, Resulting Numbers: [880] 880,76 unequal: No Solution Exploring Operation: 11+80=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,76 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: 76:[63, 6], Operations: ['80-63=17', '17-11=6'] Exploring Operation: 63*6=378, Resulting Numbers: [378] 378,76 unequal: No Solution Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,76 unequal: No Solution Exploring Operation: 63+6=69, Resulting Numbers: [69] 69,76 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: 76:[11, 46], Operations: ['80-63=17', '63-17=46'] Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 11+46=57, Resulting Numbers: [57] 57,76 unequal: No Solution Exploring Operation: 11*46=506, Resulting Numbers: [506] 506,76 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: 76:[17, 52], Operations: ['80-63=17', '63-11=52'] Exploring Operation: 17+52=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 17*52=884, Resulting Numbers: [884] 884,76 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
[ 77, 2, 72, 32 ]
21
[ "77-72=5", "32/2=16", "5+16=21" ]
Current State: 21:[77, 2, 72, 32], Operations: [] Exploring Operation: 77-72=5, Resulting Numbers: [2, 32, 5] Generated Node #2: [2, 32, 5] from Operation: 77-72=5 Current State: 21:[2, 32, 5], Operations: ['77-72=5'] Exploring Operation: 32/2=16, Resulting Numbers: [5, 16] Generated Node #3: [5, 16] from Operation: 32/2=16 Current State: 21:[5, 16], Operations: ['77-72=5', '32/2=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[77, 2, 72, 32], Operations: [] Exploring Operation: 77-72=5, Resulting Numbers: [2, 32, 5] Generated Node #0,0: 21:[2, 32, 5] Operation: 77-72=5 Exploring Operation: 77-32=45, Resulting Numbers: [2, 72, 45] Generated Node #0,1: 21:[2, 72, 45] Operation: 77-32=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[2, 32, 5], Operations: ['77-72=5'] Exploring Operation: 32/2=16, Resulting Numbers: [5, 16] Generated Node #0,0,0: 21:[5, 16] Operation: 32/2=16 Exploring Operation: 32-5=27, Resulting Numbers: [2, 27] Generated Node #0,0,1: 21:[2, 27] Operation: 32-5=27 Moving to Node #0,0,0 Current State: 21:[5, 16], Operations: ['77-72=5', '32/2=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[77, 2, 72, 32], Operations: [] Exploring Operation: 77-72=5, Resulting Numbers: [2, 32, 5] Generated Node #0,0: 21:[2, 32, 5] Operation: 77-72=5 Moving to Node #0,0 Current State: 21:[2, 32, 5], Operations: ['77-72=5'] Exploring Operation: 32/2=16, Resulting Numbers: [5, 16] Generated Node #0,0,0: 21:[5, 16] Operation: 32/2=16 Moving to Node #0,0,0 Current State: 21:[5, 16], Operations: ['77-72=5', '32/2=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 13, 3, 74, 20 ]
27
[ "13+74=87", "3*20=60", "87-60=27" ]
Current State: 27:[13, 3, 74, 20], Operations: [] Exploring Operation: 13+74=87, Resulting Numbers: [3, 20, 87] Generated Node #2: [3, 20, 87] from Operation: 13+74=87 Current State: 27:[3, 20, 87], Operations: ['13+74=87'] Exploring Operation: 3*20=60, Resulting Numbers: [87, 60] Generated Node #3: [87, 60] from Operation: 3*20=60 Current State: 27:[87, 60], Operations: ['13+74=87', '3*20=60'] Exploring Operation: 87-60=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[13, 3, 74, 20], Operations: [] Exploring Operation: 74-20=54, Resulting Numbers: [13, 3, 54] Generated Node #0,0: 27:[13, 3, 54] Operation: 74-20=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[13, 3, 54], Operations: ['74-20=54'] Exploring Operation: 54/3=18, Resulting Numbers: [13, 18] Generated Node #0,0,0: 27:[13, 18] Operation: 54/3=18 Moving to Node #0,0,0 Current State: 27:[13, 18], Operations: ['74-20=54', '54/3=18'] Exploring Operation: 18-13=5, Resulting Numbers: [5] 5,27 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
[ 21, 17, 62, 70 ]
32
[ "21-17=4", "70-62=8", "4*8=32" ]
Current State: 32:[21, 17, 62, 70], Operations: [] Exploring Operation: 21-17=4, Resulting Numbers: [62, 70, 4] Generated Node #2: [62, 70, 4] from Operation: 21-17=4 Current State: 32:[62, 70, 4], Operations: ['21-17=4'] Exploring Operation: 70-62=8, Resulting Numbers: [4, 8] Generated Node #3: [4, 8] from Operation: 70-62=8 Current State: 32:[4, 8], Operations: ['21-17=4', '70-62=8'] Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[21, 17, 62, 70], Operations: [] Exploring Operation: 70-62=8, Resulting Numbers: [21, 17, 8] Generated Node #0,0: 32:[21, 17, 8] Operation: 70-62=8 Exploring Operation: 62-21=41, Resulting Numbers: [17, 70, 41] Generated Node #0,1: 32:[17, 70, 41] Operation: 62-21=41 Exploring Operation: 70-21=49, Resulting Numbers: [17, 62, 49] Generated Node #0,2: 32:[17, 62, 49] Operation: 70-21=49 Moving to Node #0,0 Current State: 32:[21, 17, 8], Operations: ['70-62=8'] Exploring Operation: 21+8=29, Resulting Numbers: [17, 29] Generated Node #0,0,0: 32:[17, 29] Operation: 21+8=29 Exploring Operation: 21-8=13, Resulting Numbers: [17, 13] Generated Node #0,0,1: 32:[17, 13] Operation: 21-8=13 Exploring Operation: 21-17=4, Resulting Numbers: [8, 4] Generated Node #0,0,2: 32:[8, 4] Operation: 21-17=4 Moving to Node #0,1 Current State: 32:[17, 70, 41], Operations: ['62-21=41'] Exploring Operation: 70-17=53, Resulting Numbers: [41, 53] Generated Node #0,1,0: 32:[41, 53] Operation: 70-17=53 Exploring Operation: 70-41=29, Resulting Numbers: [17, 29] Generated Node #0,1,1: 32:[17, 29] Operation: 70-41=29 Exploring Operation: 41-17=24, Resulting Numbers: [70, 24] Generated Node #0,1,2: 32:[70, 24] Operation: 41-17=24 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[17, 29], Operations: ['62-21=41', '70-41=29'] Exploring Operation: 17*29=493, Resulting Numbers: [493] 493,32 unequal: No Solution Exploring Operation: 17+29=46, Resulting Numbers: [46] 46,32 unequal: No Solution Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,32 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: 32:[41, 53], Operations: ['62-21=41', '70-17=53'] Exploring Operation: 41*53=2173, Resulting Numbers: [2173] 2173,32 unequal: No Solution Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,32 unequal: No Solution Exploring Operation: 41+53=94, Resulting Numbers: [94] 94,32 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: 32:[70, 24], Operations: ['62-21=41', '41-17=24'] Exploring Operation: 70+24=94, Resulting Numbers: [94] 94,32 unequal: No Solution Exploring Operation: 70*24=1680, Resulting Numbers: [1680] 1680,32 unequal: No Solution Exploring Operation: 70-24=46, Resulting Numbers: [46] 46,32 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: 32:[17, 62, 49], Operations: ['70-21=49'] Exploring Operation: 62-49=13, Resulting Numbers: [17, 13] Generated Node #0,2,0: 32:[17, 13] Operation: 62-49=13 Exploring Operation: 62-17=45, Resulting Numbers: [49, 45] Generated Node #0,2,1: 32:[49, 45] Operation: 62-17=45 Exploring Operation: 49-17=32, Resulting Numbers: [62, 32] Generated Node #0,2,2: 32:[62, 32] Operation: 49-17=32 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 32:[17, 13], Operations: ['70-21=49', '62-49=13'] Exploring Operation: 17*13=221, Resulting Numbers: [221] 221,32 unequal: No Solution Exploring Operation: 17+13=30, Resulting Numbers: [30] 30,32 unequal: No Solution Exploring Operation: 17-13=4, Resulting Numbers: [4] 4,32 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: 32:[49, 45], Operations: ['70-21=49', '62-17=45'] Exploring Operation: 49-45=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 49+45=94, Resulting Numbers: [94] 94,32 unequal: No Solution Exploring Operation: 49*45=2205, Resulting Numbers: [2205] 2205,32 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: 32:[62, 32], Operations: ['70-21=49', '49-17=32'] Exploring Operation: 62*32=1984, Resulting Numbers: [1984] 1984,32 unequal: No Solution Exploring Operation: 62-32=30, Resulting Numbers: [30] 30,32 unequal: No Solution Exploring Operation: 62+32=94, Resulting Numbers: [94] 94,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 32:[8, 4], Operations: ['70-62=8', '21-17=4'] Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[21, 17, 62, 70], Operations: [] Exploring Operation: 70-62=8, Resulting Numbers: [21, 17, 8] Generated Node #0,0: 32:[21, 17, 8] Operation: 70-62=8 Moving to Node #0,0 Current State: 32:[21, 17, 8], Operations: ['70-62=8'] Exploring Operation: 21-17=4, Resulting Numbers: [8, 4] Generated Node #0,0,2: 32:[8, 4] Operation: 21-17=4 Moving to Node #0,0,2 Current State: 32:[8, 4], Operations: ['70-62=8', '21-17=4'] Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.96875
hs_3
sum_heuristic
[ 63, 57, 76, 21 ]
50
[ "63-57=6", "21*6=126", "126-76=50" ]
Current State: 50:[63, 57, 76, 21], Operations: [] Exploring Operation: 63-57=6, Resulting Numbers: [76, 21, 6] Generated Node #2: [76, 21, 6] from Operation: 63-57=6 Current State: 50:[76, 21, 6], Operations: ['63-57=6'] Exploring Operation: 21*6=126, Resulting Numbers: [76, 126] Generated Node #3: [76, 126] from Operation: 21*6=126 Current State: 50:[76, 126], Operations: ['63-57=6', '21*6=126'] Exploring Operation: 126-76=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[63, 57, 76, 21], Operations: [] Exploring Operation: 76-21=55, Resulting Numbers: [63, 57, 55] Generated Node #0,0: 50:[63, 57, 55] Operation: 76-21=55 Exploring Operation: 76-57=19, Resulting Numbers: [63, 21, 19] Generated Node #0,1: 50:[63, 21, 19] Operation: 76-57=19 Exploring Operation: 76-63=13, Resulting Numbers: [57, 21, 13] Generated Node #0,2: 50:[57, 21, 13] Operation: 76-63=13 Exploring Operation: 63-57=6, Resulting Numbers: [76, 21, 6] Generated Node #0,3: 50:[76, 21, 6] Operation: 63-57=6 Start Sub Search at level 1: Moving to Node #0,2 Current State: 50:[57, 21, 13], Operations: ['76-63=13'] Exploring Operation: 21-13=8, Resulting Numbers: [57, 8] Generated Node #0,2,0: 50:[57, 8] Operation: 21-13=8 Exploring Operation: 21+13=34, Resulting Numbers: [57, 34] Generated Node #0,2,1: 50:[57, 34] Operation: 21+13=34 Exploring Operation: 57-21=36, Resulting Numbers: [13, 36] Generated Node #0,2,2: 50:[13, 36] Operation: 57-21=36 Exploring Operation: 57-13=44, Resulting Numbers: [21, 44] Generated Node #0,2,3: 50:[21, 44] Operation: 57-13=44 Moving to Node #0,2,0 Current State: 50:[57, 8], Operations: ['76-63=13', '21-13=8'] Exploring Operation: 57-8=49, Resulting Numbers: [49] 49,50 unequal: No Solution Exploring Operation: 57*8=456, Resulting Numbers: [456] 456,50 unequal: No Solution Exploring Operation: 57+8=65, Resulting Numbers: [65] 65,50 unequal: No Solution Moving to Node #0,2,3 Current State: 50:[21, 44], Operations: ['76-63=13', '57-13=44'] Exploring Operation: 21*44=924, Resulting Numbers: [924] 924,50 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 21+44=65, Resulting Numbers: [65] 65,50 unequal: No Solution Moving to Node #0,2,2 Current State: 50:[13, 36], Operations: ['76-63=13', '57-21=36'] Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 13*36=468, Resulting Numbers: [468] 468,50 unequal: No Solution Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,50 unequal: No Solution Moving to Node #0,2,1 Current State: 50:[57, 34], Operations: ['76-63=13', '21+13=34'] Exploring Operation: 57+34=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 57*34=1938, Resulting Numbers: [1938] 1938,50 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 Current State: 50:[63, 21, 19], Operations: ['76-57=19'] Exploring Operation: 21-19=2, Resulting Numbers: [63, 2] Generated Node #0,1,0: 50:[63, 2] Operation: 21-19=2 Exploring Operation: 63-21=42, Resulting Numbers: [19, 42] Generated Node #0,1,1: 50:[19, 42] Operation: 63-21=42 Exploring Operation: 63-19=44, Resulting Numbers: [21, 44] Generated Node #0,1,2: 50:[21, 44] Operation: 63-19=44 Exploring Operation: 63/21=3, Resulting Numbers: [19, 3] Generated Node #0,1,3: 50:[19, 3] Operation: 63/21=3 Moving to Node #0,1,3 Current State: 50:[19, 3], Operations: ['76-57=19', '63/21=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,50 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,50 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,50 unequal: No Solution Moving to Node #0,1,2 Current State: 50:[21, 44], Operations: ['76-57=19', '63-19=44'] Exploring Operation: 21*44=924, Resulting Numbers: [924] 924,50 unequal: No Solution Exploring Operation: 21+44=65, Resulting Numbers: [65] 65,50 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,50 unequal: No Solution Moving to Node #0,1,0 Current State: 50:[63, 2], Operations: ['76-57=19', '21-19=2'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,50 unequal: No Solution Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,50 unequal: No Solution Exploring Operation: 63*2=126, Resulting Numbers: [126] 126,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[19, 42], Operations: ['76-57=19', '63-21=42'] Exploring Operation: 19+42=61, Resulting Numbers: [61] 61,50 unequal: No Solution Exploring Operation: 42-19=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 19*42=798, Resulting Numbers: [798] 798,50 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 #0,0 Current State: 50:[63, 57, 55], Operations: ['76-21=55'] Exploring Operation: 63-55=8, Resulting Numbers: [57, 8] Generated Node #0,0,0: 50:[57, 8] Operation: 63-55=8 Exploring Operation: 63-57=6, Resulting Numbers: [55, 6] Generated Node #0,0,1: 50:[55, 6] Operation: 63-57=6 Exploring Operation: 63+57=120, Resulting Numbers: [55, 120] Generated Node #0,0,2: 50:[55, 120] Operation: 63+57=120 Exploring Operation: 57-55=2, Resulting Numbers: [63, 2] Generated Node #0,0,3: 50:[63, 2] Operation: 57-55=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 50:[55, 6], Operations: ['76-21=55', '63-57=6'] Exploring Operation: 55+6=61, Resulting Numbers: [61] 61,50 unequal: No Solution Exploring Operation: 55-6=49, Resulting Numbers: [49] 49,50 unequal: No Solution Exploring Operation: 55*6=330, Resulting Numbers: [330] 330,50 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: 50:[57, 8], Operations: ['76-21=55', '63-55=8'] Exploring Operation: 57*8=456, Resulting Numbers: [456] 456,50 unequal: No Solution Exploring Operation: 57-8=49, Resulting Numbers: [49] 49,50 unequal: No Solution Exploring Operation: 57+8=65, Resulting Numbers: [65] 65,50 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: 50:[63, 2], Operations: ['76-21=55', '57-55=2'] Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,50 unequal: No Solution Exploring Operation: 63*2=126, Resulting Numbers: [126] 126,50 unequal: No Solution Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,50 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: 50:[55, 120], Operations: ['76-21=55', '63+57=120'] Exploring Operation: 55+120=175, Resulting Numbers: [175] 175,50 unequal: No Solution Exploring Operation: 120-55=65, Resulting Numbers: [65] 65,50 unequal: No Solution Exploring Operation: 55*120=6600, Resulting Numbers: [6600] 6600,50 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: 50:[76, 21, 6], Operations: ['63-57=6'] Exploring Operation: 21+6=27, Resulting Numbers: [76, 27] Generated Node #0,3,0: 50:[76, 27] Operation: 21+6=27 Exploring Operation: 76-21=55, Resulting Numbers: [6, 55] Generated Node #0,3,1: 50:[6, 55] Operation: 76-21=55 Exploring Operation: 21-6=15, Resulting Numbers: [76, 15] Generated Node #0,3,2: 50:[76, 15] Operation: 21-6=15 Exploring Operation: 76-6=70, Resulting Numbers: [21, 70] Generated Node #0,3,3: 50:[21, 70] Operation: 76-6=70 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 50:[6, 55], Operations: ['63-57=6', '76-21=55'] Exploring Operation: 6*55=330, Resulting Numbers: [330] 330,50 unequal: No Solution Exploring Operation: 6+55=61, Resulting Numbers: [61] 61,50 unequal: No Solution Exploring Operation: 55-6=49, Resulting Numbers: [49] 49,50 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: 50:[21, 70], Operations: ['63-57=6', '76-6=70'] Exploring Operation: 21*70=1470, Resulting Numbers: [1470] 1470,50 unequal: No Solution Exploring Operation: 21+70=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 70-21=49, Resulting Numbers: [49] 49,50 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: 50:[76, 27], Operations: ['63-57=6', '21+6=27'] Exploring Operation: 76*27=2052, Resulting Numbers: [2052] 2052,50 unequal: No Solution Exploring Operation: 76+27=103, Resulting Numbers: [103] 103,50 unequal: No Solution Exploring Operation: 76-27=49, Resulting Numbers: [49] 49,50 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: 50:[76, 15], Operations: ['63-57=6', '21-6=15'] Exploring Operation: 76*15=1140, Resulting Numbers: [1140] 1140,50 unequal: No Solution Exploring Operation: 76+15=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 76-15=61, Resulting Numbers: [61] 61,50 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
[ 29, 36, 95, 17 ]
16
[ "36-29=7", "95+17=112", "112/7=16" ]
Current State: 16:[29, 36, 95, 17], Operations: [] Exploring Operation: 36-29=7, Resulting Numbers: [95, 17, 7] Generated Node #2: [95, 17, 7] from Operation: 36-29=7 Current State: 16:[95, 17, 7], Operations: ['36-29=7'] Exploring Operation: 95+17=112, Resulting Numbers: [7, 112] Generated Node #3: [7, 112] from Operation: 95+17=112 Current State: 16:[7, 112], Operations: ['36-29=7', '95+17=112'] Exploring Operation: 112/7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[29, 36, 95, 17], Operations: [] Exploring Operation: 95-29=66, Resulting Numbers: [36, 17, 66] Generated Node #0,0: 16:[36, 17, 66] Operation: 95-29=66 Exploring Operation: 36-29=7, Resulting Numbers: [95, 17, 7] Generated Node #0,1: 16:[95, 17, 7] Operation: 36-29=7 Exploring Operation: 95-36=59, Resulting Numbers: [29, 17, 59] Generated Node #0,2: 16:[29, 17, 59] Operation: 95-36=59 Moving to Node #0,2 Current State: 16:[29, 17, 59], Operations: ['95-36=59'] Exploring Operation: 59-17=42, Resulting Numbers: [29, 42] Generated Node #0,2,0: 16:[29, 42] Operation: 59-17=42 Exploring Operation: 29-17=12, Resulting Numbers: [59, 12] Generated Node #0,2,1: 16:[59, 12] Operation: 29-17=12 Exploring Operation: 59-29=30, Resulting Numbers: [17, 30] Generated Node #0,2,2: 16:[17, 30] Operation: 59-29=30 Moving to Node #0,0 Current State: 16:[36, 17, 66], Operations: ['95-29=66'] Exploring Operation: 36-17=19, Resulting Numbers: [66, 19] Generated Node #0,0,0: 16:[66, 19] Operation: 36-17=19 Exploring Operation: 66-17=49, Resulting Numbers: [36, 49] Generated Node #0,0,1: 16:[36, 49] Operation: 66-17=49 Exploring Operation: 66-36=30, Resulting Numbers: [17, 30] Generated Node #0,0,2: 16:[17, 30] Operation: 66-36=30 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[17, 30], Operations: ['95-29=66', '66-36=30'] Exploring Operation: 17*30=510, Resulting Numbers: [510] 510,16 unequal: No Solution Exploring Operation: 17+30=47, Resulting Numbers: [47] 47,16 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,16 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: 16:[66, 19], Operations: ['95-29=66', '36-17=19'] Exploring Operation: 66+19=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 66-19=47, Resulting Numbers: [47] 47,16 unequal: No Solution Exploring Operation: 66*19=1254, Resulting Numbers: [1254] 1254,16 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: 16:[36, 49], Operations: ['95-29=66', '66-17=49'] Exploring Operation: 49-36=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 36*49=1764, Resulting Numbers: [1764] 1764,16 unequal: No Solution Exploring Operation: 36+49=85, Resulting Numbers: [85] 85,16 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: 16:[95, 17, 7], Operations: ['36-29=7'] Exploring Operation: 95-7=88, Resulting Numbers: [17, 88] Generated Node #0,1,0: 16:[17, 88] Operation: 95-7=88 Exploring Operation: 17-7=10, Resulting Numbers: [95, 10] Generated Node #0,1,1: 16:[95, 10] Operation: 17-7=10 Exploring Operation: 95-17=78, Resulting Numbers: [7, 78] Generated Node #0,1,2: 16:[7, 78] Operation: 95-17=78 Moving to Node #0,2,2 Current State: 16:[17, 30], Operations: ['95-36=59', '59-29=30'] Exploring Operation: 17*30=510, Resulting Numbers: [510] 510,16 unequal: No Solution Exploring Operation: 17+30=47, Resulting Numbers: [47] 47,16 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[29, 42], Operations: ['95-36=59', '59-17=42'] Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 29*42=1218, Resulting Numbers: [1218] 1218,16 unequal: No Solution Exploring Operation: 29+42=71, Resulting Numbers: [71] 71,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[59, 12], Operations: ['95-36=59', '29-17=12'] Exploring Operation: 59*12=708, Resulting Numbers: [708] 708,16 unequal: No Solution Exploring Operation: 59-12=47, Resulting Numbers: [47] 47,16 unequal: No Solution Exploring Operation: 59+12=71, Resulting Numbers: [71] 71,16 unequal: No Solution Moving to Node #0,1,2 Current State: 16:[7, 78], Operations: ['36-29=7', '95-17=78'] Exploring Operation: 7*78=546, Resulting Numbers: [546] 546,16 unequal: No Solution Exploring Operation: 78-7=71, Resulting Numbers: [71] 71,16 unequal: No Solution Exploring Operation: 7+78=85, Resulting Numbers: [85] 85,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[17, 88], Operations: ['36-29=7', '95-7=88'] Exploring Operation: 17*88=1496, Resulting Numbers: [1496] 1496,16 unequal: No Solution Exploring Operation: 17+88=105, Resulting Numbers: [105] 105,16 unequal: No Solution Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[95, 10], Operations: ['36-29=7', '17-7=10'] Exploring Operation: 95*10=950, Resulting Numbers: [950] 950,16 unequal: No Solution Exploring Operation: 95-10=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 95+10=105, Resulting Numbers: [105] 105,16 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 22, 15, 42, 34 ]
28
[ "22-15=7", "42/7=6", "34-6=28" ]
Current State: 28:[22, 15, 42, 34], Operations: [] Exploring Operation: 22-15=7, Resulting Numbers: [42, 34, 7] Generated Node #2: [42, 34, 7] from Operation: 22-15=7 Current State: 28:[42, 34, 7], Operations: ['22-15=7'] Exploring Operation: 42/7=6, Resulting Numbers: [34, 6] Generated Node #3: [34, 6] from Operation: 42/7=6 Current State: 28:[34, 6], Operations: ['22-15=7', '42/7=6'] Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[22, 15, 42, 34], Operations: [] Exploring Operation: 42-22=20, Resulting Numbers: [15, 34, 20] Generated Node #0,0: 28:[15, 34, 20] Operation: 42-22=20 Exploring Operation: 42-34=8, Resulting Numbers: [22, 15, 8] Generated Node #0,1: 28:[22, 15, 8] Operation: 42-34=8 Moving to Node #0,1 Current State: 28:[22, 15, 8], Operations: ['42-34=8'] Exploring Operation: 22-15=7, Resulting Numbers: [8, 7] Generated Node #0,1,0: 28:[8, 7] Operation: 22-15=7 Exploring Operation: 22-8=14, Resulting Numbers: [15, 14] Generated Node #0,1,1: 28:[15, 14] Operation: 22-8=14 Moving to Node #0,0 Current State: 28:[15, 34, 20], Operations: ['42-22=20'] Exploring Operation: 34-20=14, Resulting Numbers: [15, 14] Generated Node #0,0,0: 28:[15, 14] Operation: 34-20=14 Exploring Operation: 20-15=5, Resulting Numbers: [34, 5] Generated Node #0,0,1: 28:[34, 5] Operation: 20-15=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 28:[15, 14], Operations: ['42-22=20', '34-20=14'] Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,28 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: 28:[34, 5], Operations: ['42-22=20', '20-15=5'] Exploring Operation: 34+5=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,28 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: 28:[8, 7], Operations: ['42-34=8', '22-15=7'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,28 unequal: No Solution Moving to Node #0,1,1 Current State: 28:[15, 14], Operations: ['42-34=8', '22-8=14'] Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,28 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 48, 33, 97, 30 ]
99
[ "48-33=15", "30/15=2", "97+2=99" ]
Current State: 99:[48, 33, 97, 30], Operations: [] Exploring Operation: 48-33=15, Resulting Numbers: [97, 30, 15] Generated Node #2: [97, 30, 15] from Operation: 48-33=15 Current State: 99:[97, 30, 15], Operations: ['48-33=15'] Exploring Operation: 30/15=2, Resulting Numbers: [97, 2] Generated Node #3: [97, 2] from Operation: 30/15=2 Current State: 99:[97, 2], Operations: ['48-33=15', '30/15=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[48, 33, 97, 30], Operations: [] Exploring Operation: 48+33=81, Resulting Numbers: [97, 30, 81] Generated Node #0,0: 99:[97, 30, 81] Operation: 48+33=81 Exploring Operation: 48-30=18, Resulting Numbers: [33, 97, 18] Generated Node #0,1: 99:[33, 97, 18] Operation: 48-30=18 Exploring Operation: 97-48=49, Resulting Numbers: [33, 30, 49] Generated Node #0,2: 99:[33, 30, 49] Operation: 97-48=49 Exploring Operation: 48-33=15, Resulting Numbers: [97, 30, 15] Generated Node #0,3: 99:[97, 30, 15] Operation: 48-33=15 Exploring Operation: 33-30=3, Resulting Numbers: [48, 97, 3] Generated Node #0,4: 99:[48, 97, 3] Operation: 33-30=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[33, 97, 18], Operations: ['48-30=18'] Exploring Operation: 33+97=130, Resulting Numbers: [18, 130] Generated Node #0,1,0: 99:[18, 130] Operation: 33+97=130 Exploring Operation: 97-18=79, Resulting Numbers: [33, 79] Generated Node #0,1,1: 99:[33, 79] Operation: 97-18=79 Exploring Operation: 33+18=51, Resulting Numbers: [97, 51] Generated Node #0,1,2: 99:[97, 51] Operation: 33+18=51 Exploring Operation: 33-18=15, Resulting Numbers: [97, 15] Generated Node #0,1,3: 99:[97, 15] Operation: 33-18=15 Exploring Operation: 97+18=115, Resulting Numbers: [33, 115] Generated Node #0,1,4: 99:[33, 115] Operation: 97+18=115 Moving to Node #0,1,3 Current State: 99:[97, 15], Operations: ['48-30=18', '33-18=15'] Exploring Operation: 97*15=1455, Resulting Numbers: [1455] 1455,99 unequal: No Solution Exploring Operation: 97+15=112, Resulting Numbers: [112] 112,99 unequal: No Solution Exploring Operation: 97-15=82, Resulting Numbers: [82] 82,99 unequal: No Solution Moving to Node #0,1,4 Current State: 99:[33, 115], Operations: ['48-30=18', '97+18=115'] Exploring Operation: 33*115=3795, Resulting Numbers: [3795] 3795,99 unequal: No Solution Exploring Operation: 33+115=148, Resulting Numbers: [148] 148,99 unequal: No Solution Exploring Operation: 115-33=82, Resulting Numbers: [82] 82,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[33, 79], Operations: ['48-30=18', '97-18=79'] Exploring Operation: 33*79=2607, Resulting Numbers: [2607] 2607,99 unequal: No Solution Exploring Operation: 33+79=112, Resulting Numbers: [112] 112,99 unequal: No Solution Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[97, 51], Operations: ['48-30=18', '33+18=51'] Exploring Operation: 97-51=46, Resulting Numbers: [46] 46,99 unequal: No Solution Exploring Operation: 97*51=4947, Resulting Numbers: [4947] 4947,99 unequal: No Solution Exploring Operation: 97+51=148, Resulting Numbers: [148] 148,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[18, 130], Operations: ['48-30=18', '33+97=130'] Exploring Operation: 18+130=148, Resulting Numbers: [148] 148,99 unequal: No Solution Exploring Operation: 130-18=112, Resulting Numbers: [112] 112,99 unequal: No Solution Exploring Operation: 18*130=2340, Resulting Numbers: [2340] 2340,99 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: 99:[97, 30, 15], Operations: ['48-33=15'] Exploring Operation: 30/15=2, Resulting Numbers: [97, 2] Generated Node #0,3,0: 99:[97, 2] Operation: 30/15=2 Exploring Operation: 97+15=112, Resulting Numbers: [30, 112] Generated Node #0,3,1: 99:[30, 112] Operation: 97+15=112 Exploring Operation: 97-15=82, Resulting Numbers: [30, 82] Generated Node #0,3,2: 99:[30, 82] Operation: 97-15=82 Exploring Operation: 30+15=45, Resulting Numbers: [97, 45] Generated Node #0,3,3: 99:[97, 45] Operation: 30+15=45 Exploring Operation: 30-15=15, Resulting Numbers: [97, 15] Generated Node #0,3,4: 99:[97, 15] Operation: 30-15=15 Moving to Node #0,3,0 Current State: 99:[97, 2], Operations: ['48-33=15', '30/15=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[48, 33, 97, 30], Operations: [] Exploring Operation: 48-33=15, Resulting Numbers: [97, 30, 15] Generated Node #0,3: 99:[97, 30, 15] Operation: 48-33=15 Moving to Node #0,3 Current State: 99:[97, 30, 15], Operations: ['48-33=15'] Exploring Operation: 30/15=2, Resulting Numbers: [97, 2] Generated Node #0,3,0: 99:[97, 2] Operation: 30/15=2 Moving to Node #0,3,0 Current State: 99:[97, 2], Operations: ['48-33=15', '30/15=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
mult_heuristic
[ 90, 56, 1, 29 ]
53
[ "1+29=30", "90/30=3", "56-3=53" ]
Current State: 53:[90, 56, 1, 29], Operations: [] Exploring Operation: 1+29=30, Resulting Numbers: [90, 56, 30] Generated Node #2: [90, 56, 30] from Operation: 1+29=30 Current State: 53:[90, 56, 30], Operations: ['1+29=30'] Exploring Operation: 90/30=3, Resulting Numbers: [56, 3] Generated Node #3: [56, 3] from Operation: 90/30=3 Current State: 53:[56, 3], Operations: ['1+29=30', '90/30=3'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[90, 56, 1, 29], Operations: [] Exploring Operation: 56-1=55, Resulting Numbers: [90, 29, 55] Generated Node #0,0: 53:[90, 29, 55] Operation: 56-1=55 Exploring Operation: 90-29=61, Resulting Numbers: [56, 1, 61] Generated Node #0,1: 53:[56, 1, 61] Operation: 90-29=61 Exploring Operation: 90-1=89, Resulting Numbers: [56, 29, 89] Generated Node #0,2: 53:[56, 29, 89] Operation: 90-1=89 Exploring Operation: 90*1=90, Resulting Numbers: [56, 29, 90] Generated Node #0,3: 53:[56, 29, 90] Operation: 90*1=90 Exploring Operation: 1+29=30, Resulting Numbers: [90, 56, 30] Generated Node #0,4: 53:[90, 56, 30] Operation: 1+29=30 Moving to Node #0,0 Current State: 53:[90, 29, 55], Operations: ['56-1=55'] Exploring Operation: 90+29=119, Resulting Numbers: [55, 119] Generated Node #0,0,0: 53:[55, 119] Operation: 90+29=119 Exploring Operation: 90-55=35, Resulting Numbers: [29, 35] Generated Node #0,0,1: 53:[29, 35] Operation: 90-55=35 Exploring Operation: 29+55=84, Resulting Numbers: [90, 84] Generated Node #0,0,2: 53:[90, 84] Operation: 29+55=84 Exploring Operation: 55-29=26, Resulting Numbers: [90, 26] Generated Node #0,0,3: 53:[90, 26] Operation: 55-29=26 Exploring Operation: 90-29=61, Resulting Numbers: [55, 61] Generated Node #0,0,4: 53:[55, 61] Operation: 90-29=61 Moving to Node #0,2 Current State: 53:[56, 29, 89], Operations: ['90-1=89'] Exploring Operation: 89-29=60, Resulting Numbers: [56, 60] Generated Node #0,2,0: 53:[56, 60] Operation: 89-29=60 Exploring Operation: 89-56=33, Resulting Numbers: [29, 33] Generated Node #0,2,1: 53:[29, 33] Operation: 89-56=33 Exploring Operation: 29+89=118, Resulting Numbers: [56, 118] Generated Node #0,2,2: 53:[56, 118] Operation: 29+89=118 Exploring Operation: 56-29=27, Resulting Numbers: [89, 27] Generated Node #0,2,3: 53:[89, 27] Operation: 56-29=27 Exploring Operation: 56+29=85, Resulting Numbers: [89, 85] Generated Node #0,2,4: 53:[89, 85] Operation: 56+29=85 Moving to Node #0,1 Current State: 53:[56, 1, 61], Operations: ['90-29=61'] Exploring Operation: 1*61=61, Resulting Numbers: [56, 61] Generated Node #0,1,0: 53:[56, 61] Operation: 1*61=61 Exploring Operation: 56-1=55, Resulting Numbers: [61, 55] Generated Node #0,1,1: 53:[61, 55] Operation: 56-1=55 Exploring Operation: 56*1=56, Resulting Numbers: [61, 56] Generated Node #0,1,2: 53:[61, 56] Operation: 56*1=56 Exploring Operation: 61-1=60, Resulting Numbers: [56, 60] Generated Node #0,1,3: 53:[56, 60] Operation: 61-1=60 Exploring Operation: 56/1=56, Resulting Numbers: [61, 56] Generated Node #0,1,4: 53:[61, 56] Operation: 56/1=56 Moving to Node #0,4 Current State: 53:[90, 56, 30], Operations: ['1+29=30'] Exploring Operation: 90-30=60, Resulting Numbers: [56, 60] Generated Node #0,4,0: 53:[56, 60] Operation: 90-30=60 Exploring Operation: 90+30=120, Resulting Numbers: [56, 120] Generated Node #0,4,1: 53:[56, 120] Operation: 90+30=120 Exploring Operation: 56-30=26, Resulting Numbers: [90, 26] Generated Node #0,4,2: 53:[90, 26] Operation: 56-30=26 Exploring Operation: 90-56=34, Resulting Numbers: [30, 34] Generated Node #0,4,3: 53:[30, 34] Operation: 90-56=34 Exploring Operation: 90/30=3, Resulting Numbers: [56, 3] Generated Node #0,4,4: 53:[56, 3] Operation: 90/30=3 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 53:[56, 60], Operations: ['1+29=30', '90-30=60'] Exploring Operation: 56+60=116, Resulting Numbers: [116] 116,53 unequal: No Solution Exploring Operation: 56*60=3360, Resulting Numbers: [3360] 3360,53 unequal: No Solution Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,53 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 #0,4,3 Current State: 53:[30, 34], Operations: ['1+29=30', '90-56=34'] Exploring Operation: 30+34=64, Resulting Numbers: [64] 64,53 unequal: No Solution Exploring Operation: 34-30=4, Resulting Numbers: [4] 4,53 unequal: No Solution Exploring Operation: 30*34=1020, Resulting Numbers: [1020] 1020,53 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 #0,4,4 Current State: 53:[56, 3], Operations: ['1+29=30', '90/30=3'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[90, 56, 1, 29], Operations: [] Exploring Operation: 1+29=30, Resulting Numbers: [90, 56, 30] Generated Node #0,4: 53:[90, 56, 30] Operation: 1+29=30 Moving to Node #0,4 Current State: 53:[90, 56, 30], Operations: ['1+29=30'] Exploring Operation: 90/30=3, Resulting Numbers: [56, 3] Generated Node #0,4,4: 53:[56, 3] Operation: 90/30=3 Moving to Node #0,4,4 Current State: 53:[56, 3], Operations: ['1+29=30', '90/30=3'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
sum_heuristic
[ 9, 60, 34, 75 ]
20
[ "34-9=25", "60*25=1500", "1500/75=20" ]
Current State: 20:[9, 60, 34, 75], Operations: [] Exploring Operation: 34-9=25, Resulting Numbers: [60, 75, 25] Generated Node #2: [60, 75, 25] from Operation: 34-9=25 Current State: 20:[60, 75, 25], Operations: ['34-9=25'] Exploring Operation: 60*25=1500, Resulting Numbers: [75, 1500] Generated Node #3: [75, 1500] from Operation: 60*25=1500 Current State: 20:[75, 1500], Operations: ['34-9=25', '60*25=1500'] Exploring Operation: 1500/75=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[9, 60, 34, 75], Operations: [] Exploring Operation: 75-60=15, Resulting Numbers: [9, 34, 15] Generated Node #0,0: 20:[9, 34, 15] Operation: 75-60=15 Exploring Operation: 75-34=41, Resulting Numbers: [9, 60, 41] Generated Node #0,1: 20:[9, 60, 41] Operation: 75-34=41 Exploring Operation: 60-34=26, Resulting Numbers: [9, 75, 26] Generated Node #0,2: 20:[9, 75, 26] Operation: 60-34=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[9, 34, 15], Operations: ['75-60=15'] Exploring Operation: 34-15=19, Resulting Numbers: [9, 19] Generated Node #0,0,0: 20:[9, 19] Operation: 34-15=19 Exploring Operation: 34-9=25, Resulting Numbers: [15, 25] Generated Node #0,0,1: 20:[15, 25] Operation: 34-9=25 Exploring Operation: 15-9=6, Resulting Numbers: [34, 6] Generated Node #0,0,2: 20:[34, 6] Operation: 15-9=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 20:[9, 19], Operations: ['75-60=15', '34-15=19'] Exploring Operation: 9*19=171, Resulting Numbers: [171] 171,20 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 9+19=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 #0,0,1 Current State: 20:[15, 25], Operations: ['75-60=15', '34-9=25'] Exploring Operation: 15*25=375, Resulting Numbers: [375] 375,20 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,20 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:[34, 6], Operations: ['75-60=15', '15-9=6'] Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,20 unequal: No Solution Exploring Operation: 34*6=204, Resulting Numbers: [204] 204,20 unequal: No Solution Exploring Operation: 34+6=40, Resulting Numbers: [40] 40,20 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:[9, 60, 41], Operations: ['75-34=41'] Exploring Operation: 60-41=19, Resulting Numbers: [9, 19] Generated Node #0,1,0: 20:[9, 19] Operation: 60-41=19 Exploring Operation: 60-9=51, Resulting Numbers: [41, 51] Generated Node #0,1,1: 20:[41, 51] Operation: 60-9=51 Exploring Operation: 41-9=32, Resulting Numbers: [60, 32] Generated Node #0,1,2: 20:[60, 32] Operation: 41-9=32 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 20:[9, 19], Operations: ['75-34=41', '60-41=19'] Exploring Operation: 9+19=28, Resulting Numbers: [28] 28,20 unequal: No Solution Exploring Operation: 9*19=171, Resulting Numbers: [171] 171,20 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,20 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:[41, 51], Operations: ['75-34=41', '60-9=51'] Exploring Operation: 41+51=92, Resulting Numbers: [92] 92,20 unequal: No Solution Exploring Operation: 51-41=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 41*51=2091, Resulting Numbers: [2091] 2091,20 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 #0,1,2 Current State: 20:[60, 32], Operations: ['75-34=41', '41-9=32'] Exploring Operation: 60-32=28, Resulting Numbers: [28] 28,20 unequal: No Solution Exploring Operation: 60*32=1920, Resulting Numbers: [1920] 1920,20 unequal: No Solution Exploring Operation: 60+32=92, Resulting Numbers: [92] 92,20 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:[9, 75, 26], Operations: ['60-34=26'] Exploring Operation: 26-9=17, Resulting Numbers: [75, 17] Generated Node #0,2,0: 20:[75, 17] Operation: 26-9=17 Exploring Operation: 75-9=66, Resulting Numbers: [26, 66] Generated Node #0,2,1: 20:[26, 66] Operation: 75-9=66 Exploring Operation: 75-26=49, Resulting Numbers: [9, 49] Generated Node #0,2,2: 20:[9, 49] Operation: 75-26=49 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 20:[9, 49], Operations: ['60-34=26', '75-26=49'] Exploring Operation: 9*49=441, Resulting Numbers: [441] 441,20 unequal: No Solution Exploring Operation: 49-9=40, Resulting Numbers: [40] 40,20 unequal: No Solution Exploring Operation: 9+49=58, Resulting Numbers: [58] 58,20 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 #0,2,1 Current State: 20:[26, 66], Operations: ['60-34=26', '75-9=66'] Exploring Operation: 26*66=1716, Resulting Numbers: [1716] 1716,20 unequal: No Solution Exploring Operation: 26+66=92, Resulting Numbers: [92] 92,20 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,20 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 #0,2,0 Current State: 20:[75, 17], Operations: ['60-34=26', '26-9=17'] Exploring Operation: 75-17=58, Resulting Numbers: [58] 58,20 unequal: No Solution Exploring Operation: 75+17=92, Resulting Numbers: [92] 92,20 unequal: No Solution Exploring Operation: 75*17=1275, Resulting Numbers: [1275] 1275,20 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 No solution found.
0
hs_3
sum_heuristic
[ 12, 30, 6, 30 ]
37
[ "12+30=42", "30/6=5", "42-5=37" ]
Current State: 37:[12, 30, 6, 30], Operations: [] Exploring Operation: 12+30=42, Resulting Numbers: [6, 42] Generated Node #2: [6, 42] from Operation: 12+30=42 Current State: 37:[6, 42], Operations: ['12+30=42'] Exploring Operation: 30/6=5, Resulting Numbers: [42, 5] Generated Node #3: [42, 5] from Operation: 30/6=5 Current State: 37:[42, 5], Operations: ['12+30=42', '30/6=5'] Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[12, 30, 6, 30], Operations: [] Exploring Operation: 12+6=18, Resulting Numbers: [30, 30, 18] Generated Node #0,0: 37:[30, 30, 18] Operation: 12+6=18 Exploring Operation: 30+6=36, Resulting Numbers: [12, 30, 36] Generated Node #0,1: 37:[12, 30, 36] Operation: 30+6=36 Moving to Node #0,0 Current State: 37:[30, 30, 18], Operations: ['12+6=18'] Exploring Operation: 30+18=48, Resulting Numbers: [30, 48] Generated Node #0,0,0: 37:[30, 48] Operation: 30+18=48 Exploring Operation: 30+18=48, Resulting Numbers: [30, 48] Generated Node #0,0,1: 37:[30, 48] Operation: 30+18=48 Moving to Node #0,1 Current State: 37:[12, 30, 36], Operations: ['30+6=36'] Exploring Operation: 12+30=42, Resulting Numbers: [36, 42] Generated Node #0,1,0: 37:[36, 42] Operation: 12+30=42 Exploring Operation: 12+36=48, Resulting Numbers: [30, 48] Generated Node #0,1,1: 37:[30, 48] Operation: 12+36=48 Moving to Node #0,1,0 Current State: 37:[36, 42], Operations: ['30+6=36', '12+30=42'] Exploring Operation: 42-36=6, Resulting Numbers: [6] 6,37 unequal: No Solution Exploring Operation: 36+42=78, Resulting Numbers: [78] 78,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[30, 48], Operations: ['12+6=18', '30+18=48'] Exploring Operation: 30+48=78, Resulting Numbers: [78] 78,37 unequal: No Solution Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[30, 48], Operations: ['12+6=18', '30+18=48'] Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,37 unequal: No Solution Exploring Operation: 30+48=78, Resulting Numbers: [78] 78,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[30, 48], Operations: ['30+6=36', '12+36=48'] Exploring Operation: 30+48=78, Resulting Numbers: [78] 78,37 unequal: No Solution Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,37 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 82, 14, 76, 65 ]
72
[ "76-65=11", "14*11=154", "154-82=72" ]
Current State: 72:[82, 14, 76, 65], Operations: [] Exploring Operation: 76-65=11, Resulting Numbers: [82, 14, 11] Generated Node #2: [82, 14, 11] from Operation: 76-65=11 Current State: 72:[82, 14, 11], Operations: ['76-65=11'] Exploring Operation: 14*11=154, Resulting Numbers: [82, 154] Generated Node #3: [82, 154] from Operation: 14*11=154 Current State: 72:[82, 154], Operations: ['76-65=11', '14*11=154'] Exploring Operation: 154-82=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[82, 14, 76, 65], Operations: [] Exploring Operation: 82-76=6, Resulting Numbers: [14, 65, 6] Generated Node #0,0: 72:[14, 65, 6] Operation: 82-76=6 Exploring Operation: 76-65=11, Resulting Numbers: [82, 14, 11] Generated Node #0,1: 72:[82, 14, 11] Operation: 76-65=11 Exploring Operation: 82-65=17, Resulting Numbers: [14, 76, 17] Generated Node #0,2: 72:[14, 76, 17] Operation: 82-65=17 Moving to Node #0,2 Current State: 72:[14, 76, 17], Operations: ['82-65=17'] Exploring Operation: 17-14=3, Resulting Numbers: [76, 3] Generated Node #0,2,0: 72:[76, 3] Operation: 17-14=3 Exploring Operation: 14+17=31, Resulting Numbers: [76, 31] Generated Node #0,2,1: 72:[76, 31] Operation: 14+17=31 Exploring Operation: 76-14=62, Resulting Numbers: [17, 62] Generated Node #0,2,2: 72:[17, 62] Operation: 76-14=62 Moving to Node #0,0 Current State: 72:[14, 65, 6], Operations: ['82-76=6'] Exploring Operation: 14+65=79, Resulting Numbers: [6, 79] Generated Node #0,0,0: 72:[6, 79] Operation: 14+65=79 Exploring Operation: 65+6=71, Resulting Numbers: [14, 71] Generated Node #0,0,1: 72:[14, 71] Operation: 65+6=71 Exploring Operation: 14-6=8, Resulting Numbers: [65, 8] Generated Node #0,0,2: 72:[65, 8] Operation: 14-6=8 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[14, 71], Operations: ['82-76=6', '65+6=71'] Exploring Operation: 71-14=57, Resulting Numbers: [57] 57,72 unequal: No Solution Exploring Operation: 14*71=994, Resulting Numbers: [994] 994,72 unequal: No Solution Exploring Operation: 14+71=85, Resulting Numbers: [85] 85,72 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: 72:[6, 79], Operations: ['82-76=6', '14+65=79'] Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,72 unequal: No Solution Exploring Operation: 6+79=85, Resulting Numbers: [85] 85,72 unequal: No Solution Exploring Operation: 6*79=474, Resulting Numbers: [474] 474,72 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: 72:[65, 8], Operations: ['82-76=6', '14-6=8'] Exploring Operation: 65*8=520, Resulting Numbers: [520] 520,72 unequal: No Solution Exploring Operation: 65+8=73, Resulting Numbers: [73] 73,72 unequal: No Solution Exploring Operation: 65-8=57, Resulting Numbers: [57] 57,72 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: 72:[82, 14, 11], Operations: ['76-65=11'] Exploring Operation: 82-14=68, Resulting Numbers: [11, 68] Generated Node #0,1,0: 72:[11, 68] Operation: 82-14=68 Exploring Operation: 82-11=71, Resulting Numbers: [14, 71] Generated Node #0,1,1: 72:[14, 71] Operation: 82-11=71 Exploring Operation: 14-11=3, Resulting Numbers: [82, 3] Generated Node #0,1,2: 72:[82, 3] Operation: 14-11=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 72:[14, 71], Operations: ['76-65=11', '82-11=71'] Exploring Operation: 14+71=85, Resulting Numbers: [85] 85,72 unequal: No Solution Exploring Operation: 14*71=994, Resulting Numbers: [994] 994,72 unequal: No Solution Exploring Operation: 71-14=57, Resulting Numbers: [57] 57,72 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: 72:[11, 68], Operations: ['76-65=11', '82-14=68'] Exploring Operation: 11+68=79, Resulting Numbers: [79] 79,72 unequal: No Solution Exploring Operation: 68-11=57, Resulting Numbers: [57] 57,72 unequal: No Solution Exploring Operation: 11*68=748, Resulting Numbers: [748] 748,72 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: 72:[82, 3], Operations: ['76-65=11', '14-11=3'] Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,72 unequal: No Solution Exploring Operation: 82+3=85, Resulting Numbers: [85] 85,72 unequal: No Solution Exploring Operation: 82*3=246, Resulting Numbers: [246] 246,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 72:[76, 3], Operations: ['82-65=17', '17-14=3'] Exploring Operation: 76*3=228, Resulting Numbers: [228] 228,72 unequal: No Solution Exploring Operation: 76-3=73, Resulting Numbers: [73] 73,72 unequal: No Solution Exploring Operation: 76+3=79, Resulting Numbers: [79] 79,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[76, 31], Operations: ['82-65=17', '14+17=31'] Exploring Operation: 76*31=2356, Resulting Numbers: [2356] 2356,72 unequal: No Solution Exploring Operation: 76-31=45, Resulting Numbers: [45] 45,72 unequal: No Solution Exploring Operation: 76+31=107, Resulting Numbers: [107] 107,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[17, 62], Operations: ['82-65=17', '76-14=62'] Exploring Operation: 17*62=1054, Resulting Numbers: [1054] 1054,72 unequal: No Solution Exploring Operation: 17+62=79, Resulting Numbers: [79] 79,72 unequal: No Solution Exploring Operation: 62-17=45, Resulting Numbers: [45] 45,72 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 21, 73, 21, 10 ]
21
[ "73-21=52", "21+10=31", "52-31=21" ]
Current State: 21:[21, 73, 21, 10], Operations: [] Exploring Operation: 73-21=52, Resulting Numbers: [10, 52] Generated Node #2: [10, 52] from Operation: 73-21=52 Current State: 21:[10, 52], Operations: ['73-21=52'] Exploring Operation: 21+10=31, Resulting Numbers: [52, 31] Generated Node #3: [52, 31] from Operation: 21+10=31 Current State: 21:[52, 31], Operations: ['73-21=52', '21+10=31'] Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[21, 73, 21, 10], Operations: [] Exploring Operation: 73-21=52, Resulting Numbers: [21, 10, 52] Generated Node #0,0: 21:[21, 10, 52] Operation: 73-21=52 Exploring Operation: 21-10=11, Resulting Numbers: [21, 73, 11] Generated Node #0,1: 21:[21, 73, 11] Operation: 21-10=11 Exploring Operation: 21-10=11, Resulting Numbers: [73, 21, 11] Generated Node #0,2: 21:[73, 21, 11] Operation: 21-10=11 Exploring Operation: 73-10=63, Resulting Numbers: [21, 21, 63] Generated Node #0,3: 21:[21, 21, 63] Operation: 73-10=63 Exploring Operation: 73-21=52, Resulting Numbers: [21, 10, 52] Generated Node #0,4: 21:[21, 10, 52] Operation: 73-21=52 Moving to Node #0,0 Current State: 21:[21, 10, 52], Operations: ['73-21=52'] Exploring Operation: 21+10=31, Resulting Numbers: [52, 31] Generated Node #0,0,0: 21:[52, 31] Operation: 21+10=31 Exploring Operation: 52-10=42, Resulting Numbers: [21, 42] Generated Node #0,0,1: 21:[21, 42] Operation: 52-10=42 Exploring Operation: 21-10=11, Resulting Numbers: [52, 11] Generated Node #0,0,2: 21:[52, 11] Operation: 21-10=11 Exploring Operation: 52-21=31, Resulting Numbers: [10, 31] Generated Node #0,0,3: 21:[10, 31] Operation: 52-21=31 Exploring Operation: 10+52=62, Resulting Numbers: [21, 62] Generated Node #0,0,4: 21:[21, 62] Operation: 10+52=62 Moving to Node #0,4 Current State: 21:[21, 10, 52], Operations: ['73-21=52'] Exploring Operation: 21-10=11, Resulting Numbers: [52, 11] Generated Node #0,4,0: 21:[52, 11] Operation: 21-10=11 Exploring Operation: 52-10=42, Resulting Numbers: [21, 42] Generated Node #0,4,1: 21:[21, 42] Operation: 52-10=42 Exploring Operation: 10+52=62, Resulting Numbers: [21, 62] Generated Node #0,4,2: 21:[21, 62] Operation: 10+52=62 Exploring Operation: 52-21=31, Resulting Numbers: [10, 31] Generated Node #0,4,3: 21:[10, 31] Operation: 52-21=31 Exploring Operation: 21+10=31, Resulting Numbers: [52, 31] Generated Node #0,4,4: 21:[52, 31] Operation: 21+10=31 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 21:[10, 31], Operations: ['73-21=52', '52-21=31'] Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[21, 73, 21, 10], Operations: [] Exploring Operation: 73-21=52, Resulting Numbers: [21, 10, 52] Generated Node #0,4: 21:[21, 10, 52] Operation: 73-21=52 Moving to Node #0,4 Current State: 21:[21, 10, 52], Operations: ['73-21=52'] Exploring Operation: 52-21=31, Resulting Numbers: [10, 31] Generated Node #0,4,3: 21:[10, 31] Operation: 52-21=31 Moving to Node #0,4,3 Current State: 21:[10, 31], Operations: ['73-21=52', '52-21=31'] Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 29, 84, 56, 14 ]
39
[ "84+56=140", "140/14=10", "29+10=39" ]
Current State: 39:[29, 84, 56, 14], Operations: [] Exploring Operation: 84+56=140, Resulting Numbers: [29, 14, 140] Generated Node #2: [29, 14, 140] from Operation: 84+56=140 Current State: 39:[29, 14, 140], Operations: ['84+56=140'] Exploring Operation: 140/14=10, Resulting Numbers: [29, 10] Generated Node #3: [29, 10] from Operation: 140/14=10 Current State: 39:[29, 10], Operations: ['84+56=140', '140/14=10'] Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[29, 84, 56, 14], Operations: [] Exploring Operation: 84/14=6, Resulting Numbers: [29, 56, 6] Generated Node #0,0: 39:[29, 56, 6] Operation: 84/14=6 Exploring Operation: 56-29=27, Resulting Numbers: [84, 14, 27] Generated Node #0,1: 39:[84, 14, 27] Operation: 56-29=27 Exploring Operation: 84-56=28, Resulting Numbers: [29, 14, 28] Generated Node #0,2: 39:[29, 14, 28] Operation: 84-56=28 Exploring Operation: 84-29=55, Resulting Numbers: [56, 14, 55] Generated Node #0,3: 39:[56, 14, 55] Operation: 84-29=55 Exploring Operation: 56/14=4, Resulting Numbers: [29, 84, 4] Generated Node #0,4: 39:[29, 84, 4] Operation: 56/14=4 Moving to Node #0,2 Current State: 39:[29, 14, 28], Operations: ['84-56=28'] Exploring Operation: 28/14=2, Resulting Numbers: [29, 2] Generated Node #0,2,0: 39:[29, 2] Operation: 28/14=2 Exploring Operation: 29-14=15, Resulting Numbers: [28, 15] Generated Node #0,2,1: 39:[28, 15] Operation: 29-14=15 Exploring Operation: 28-14=14, Resulting Numbers: [29, 14] Generated Node #0,2,2: 39:[29, 14] Operation: 28-14=14 Exploring Operation: 29-28=1, Resulting Numbers: [14, 1] Generated Node #0,2,3: 39:[14, 1] Operation: 29-28=1 Exploring Operation: 14+28=42, Resulting Numbers: [29, 42] Generated Node #0,2,4: 39:[29, 42] Operation: 14+28=42 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 39:[14, 1], Operations: ['84-56=28', '29-28=1'] Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,39 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,39 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,39 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: 39:[29, 2], Operations: ['84-56=28', '28/14=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,39 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: 39:[29, 14], Operations: ['84-56=28', '28-14=14'] Exploring Operation: 29+14=43, Resulting Numbers: [43] 43,39 unequal: No Solution Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 29*14=406, Resulting Numbers: [406] 406,39 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: 39:[28, 15], Operations: ['84-56=28', '29-14=15'] Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,39 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,39 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: 39:[29, 42], Operations: ['84-56=28', '14+28=42'] Exploring Operation: 29+42=71, Resulting Numbers: [71] 71,39 unequal: No Solution Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 29*42=1218, Resulting Numbers: [1218] 1218,39 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: 39:[29, 56, 6], Operations: ['84/14=6'] Exploring Operation: 29+6=35, Resulting Numbers: [56, 35] Generated Node #0,0,0: 39:[56, 35] Operation: 29+6=35 Exploring Operation: 56-29=27, Resulting Numbers: [6, 27] Generated Node #0,0,1: 39:[6, 27] Operation: 56-29=27 Exploring Operation: 56-6=50, Resulting Numbers: [29, 50] Generated Node #0,0,2: 39:[29, 50] Operation: 56-6=50 Exploring Operation: 56+6=62, Resulting Numbers: [29, 62] Generated Node #0,0,3: 39:[29, 62] Operation: 56+6=62 Exploring Operation: 29-6=23, Resulting Numbers: [56, 23] Generated Node #0,0,4: 39:[56, 23] Operation: 29-6=23 Moving to Node #0,3 Current State: 39:[56, 14, 55], Operations: ['84-29=55'] Exploring Operation: 56/14=4, Resulting Numbers: [55, 4] Generated Node #0,3,0: 39:[55, 4] Operation: 56/14=4 Exploring Operation: 56+14=70, Resulting Numbers: [55, 70] Generated Node #0,3,1: 39:[55, 70] Operation: 56+14=70 Exploring Operation: 56-14=42, Resulting Numbers: [55, 42] Generated Node #0,3,2: 39:[55, 42] Operation: 56-14=42 Exploring Operation: 56-55=1, Resulting Numbers: [14, 1] Generated Node #0,3,3: 39:[14, 1] Operation: 56-55=1 Exploring Operation: 55-14=41, Resulting Numbers: [56, 41] Generated Node #0,3,4: 39:[56, 41] Operation: 55-14=41 Moving to Node #0,4 Current State: 39:[29, 84, 4], Operations: ['56/14=4'] Exploring Operation: 84-4=80, Resulting Numbers: [29, 80] Generated Node #0,4,0: 39:[29, 80] Operation: 84-4=80 Exploring Operation: 84-29=55, Resulting Numbers: [4, 55] Generated Node #0,4,1: 39:[4, 55] Operation: 84-29=55 Exploring Operation: 29+4=33, Resulting Numbers: [84, 33] Generated Node #0,4,2: 39:[84, 33] Operation: 29+4=33 Exploring Operation: 29-4=25, Resulting Numbers: [84, 25] Generated Node #0,4,3: 39:[84, 25] Operation: 29-4=25 Exploring Operation: 84/4=21, Resulting Numbers: [29, 21] Generated Node #0,4,4: 39:[29, 21] Operation: 84/4=21 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 39:[4, 55], Operations: ['56/14=4', '84-29=55'] Exploring Operation: 4+55=59, Resulting Numbers: [59] 59,39 unequal: No Solution Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,39 unequal: No Solution Exploring Operation: 4*55=220, Resulting Numbers: [220] 220,39 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: 39:[29, 21], Operations: ['56/14=4', '84/4=21'] Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,39 unequal: No Solution Exploring Operation: 29+21=50, Resulting Numbers: [50] 50,39 unequal: No Solution Exploring Operation: 29*21=609, Resulting Numbers: [609] 609,39 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: 39:[29, 80], Operations: ['56/14=4', '84-4=80'] Exploring Operation: 29*80=2320, Resulting Numbers: [2320] 2320,39 unequal: No Solution Exploring Operation: 29+80=109, Resulting Numbers: [109] 109,39 unequal: No Solution Exploring Operation: 80-29=51, Resulting Numbers: [51] 51,39 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: 39:[84, 33], Operations: ['56/14=4', '29+4=33'] Exploring Operation: 84-33=51, Resulting Numbers: [51] 51,39 unequal: No Solution Exploring Operation: 84*33=2772, Resulting Numbers: [2772] 2772,39 unequal: No Solution Exploring Operation: 84+33=117, Resulting Numbers: [117] 117,39 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: 39:[84, 25], Operations: ['56/14=4', '29-4=25'] Exploring Operation: 84*25=2100, Resulting Numbers: [2100] 2100,39 unequal: No Solution Exploring Operation: 84+25=109, Resulting Numbers: [109] 109,39 unequal: No Solution Exploring Operation: 84-25=59, Resulting Numbers: [59] 59,39 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: 39:[84, 14, 27], Operations: ['56-29=27'] Exploring Operation: 84-14=70, Resulting Numbers: [27, 70] Generated Node #0,1,0: 39:[27, 70] Operation: 84-14=70 Exploring Operation: 27-14=13, Resulting Numbers: [84, 13] Generated Node #0,1,1: 39:[84, 13] Operation: 27-14=13 Exploring Operation: 84-27=57, Resulting Numbers: [14, 57] Generated Node #0,1,2: 39:[14, 57] Operation: 84-27=57 Exploring Operation: 14+27=41, Resulting Numbers: [84, 41] Generated Node #0,1,3: 39:[84, 41] Operation: 14+27=41 Exploring Operation: 84/14=6, Resulting Numbers: [27, 6] Generated Node #0,1,4: 39:[27, 6] Operation: 84/14=6 Moving to Node #0,3,3 Current State: 39:[14, 1], Operations: ['84-29=55', '56-55=1'] Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,39 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[6, 27], Operations: ['84/14=6', '56-29=27'] Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 6*27=162, Resulting Numbers: [162] 162,39 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,39 unequal: No Solution Moving to Node #0,1,4 Current State: 39:[27, 6], Operations: ['56-29=27', '84/14=6'] Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,39 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,39 unequal: No Solution Moving to Node #0,3,0 Current State: 39:[55, 4], Operations: ['84-29=55', '56/14=4'] Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,39 unequal: No Solution Exploring Operation: 55*4=220, Resulting Numbers: [220] 220,39 unequal: No Solution Exploring Operation: 55+4=59, Resulting Numbers: [59] 59,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[14, 57], Operations: ['56-29=27', '84-27=57'] Exploring Operation: 57-14=43, Resulting Numbers: [43] 43,39 unequal: No Solution Exploring Operation: 14+57=71, Resulting Numbers: [71] 71,39 unequal: No Solution Exploring Operation: 14*57=798, Resulting Numbers: [798] 798,39 unequal: No Solution Moving to Node #0,3,2 Current State: 39:[55, 42], Operations: ['84-29=55', '56-14=42'] Exploring Operation: 55+42=97, Resulting Numbers: [97] 97,39 unequal: No Solution Exploring Operation: 55-42=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 55*42=2310, Resulting Numbers: [2310] 2310,39 unequal: No Solution Moving to Node #0,3,4 Current State: 39:[56, 41], Operations: ['84-29=55', '55-14=41'] Exploring Operation: 56+41=97, Resulting Numbers: [97] 97,39 unequal: No Solution Exploring Operation: 56*41=2296, Resulting Numbers: [2296] 2296,39 unequal: No Solution Exploring Operation: 56-41=15, Resulting Numbers: [15] 15,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[29, 50], Operations: ['84/14=6', '56-6=50'] Exploring Operation: 29+50=79, Resulting Numbers: [79] 79,39 unequal: No Solution Exploring Operation: 29*50=1450, Resulting Numbers: [1450] 1450,39 unequal: No Solution Exploring Operation: 50-29=21, Resulting Numbers: [21] 21,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[56, 35], Operations: ['84/14=6', '29+6=35'] Exploring Operation: 56-35=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 56+35=91, Resulting Numbers: [91] 91,39 unequal: No Solution Exploring Operation: 56*35=1960, Resulting Numbers: [1960] 1960,39 unequal: No Solution Moving to Node #0,0,4 Current State: 39:[56, 23], Operations: ['84/14=6', '29-6=23'] Exploring Operation: 56*23=1288, Resulting Numbers: [1288] 1288,39 unequal: No Solution Exploring Operation: 56+23=79, Resulting Numbers: [79] 79,39 unequal: No Solution Exploring Operation: 56-23=33, Resulting Numbers: [33] 33,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[29, 62], Operations: ['84/14=6', '56+6=62'] Exploring Operation: 29+62=91, Resulting Numbers: [91] 91,39 unequal: No Solution Exploring Operation: 62-29=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 29*62=1798, Resulting Numbers: [1798] 1798,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[27, 70], Operations: ['56-29=27', '84-14=70'] Exploring Operation: 70-27=43, Resulting Numbers: [43] 43,39 unequal: No Solution Exploring Operation: 27+70=97, Resulting Numbers: [97] 97,39 unequal: No Solution Exploring Operation: 27*70=1890, Resulting Numbers: [1890] 1890,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[84, 13], Operations: ['56-29=27', '27-14=13'] Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,39 unequal: No Solution Exploring Operation: 84*13=1092, Resulting Numbers: [1092] 1092,39 unequal: No Solution Exploring Operation: 84+13=97, Resulting Numbers: [97] 97,39 unequal: No Solution Moving to Node #0,3,1 Current State: 39:[55, 70], Operations: ['84-29=55', '56+14=70'] Exploring Operation: 55*70=3850, Resulting Numbers: [3850] 3850,39 unequal: No Solution Exploring Operation: 55+70=125, Resulting Numbers: [125] 125,39 unequal: No Solution Exploring Operation: 70-55=15, Resulting Numbers: [15] 15,39 unequal: No Solution Moving to Node #0,1,3 Current State: 39:[84, 41], Operations: ['56-29=27', '14+27=41'] Exploring Operation: 84+41=125, Resulting Numbers: [125] 125,39 unequal: No Solution Exploring Operation: 84*41=3444, Resulting Numbers: [3444] 3444,39 unequal: No Solution Exploring Operation: 84-41=43, Resulting Numbers: [43] 43,39 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 68, 69, 7, 74 ]
82
[ "69-68=1", "7+74=81", "1+81=82" ]
Current State: 82:[68, 69, 7, 74], Operations: [] Exploring Operation: 69-68=1, Resulting Numbers: [7, 74, 1] Generated Node #2: [7, 74, 1] from Operation: 69-68=1 Current State: 82:[7, 74, 1], Operations: ['69-68=1'] Exploring Operation: 7+74=81, Resulting Numbers: [1, 81] Generated Node #3: [1, 81] from Operation: 7+74=81 Current State: 82:[1, 81], Operations: ['69-68=1', '7+74=81'] Exploring Operation: 1+81=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[68, 69, 7, 74], Operations: [] Exploring Operation: 69-68=1, Resulting Numbers: [7, 74, 1] Generated Node #0,0: 82:[7, 74, 1] Operation: 69-68=1 Exploring Operation: 74-68=6, Resulting Numbers: [69, 7, 6] Generated Node #0,1: 82:[69, 7, 6] Operation: 74-68=6 Exploring Operation: 74-69=5, Resulting Numbers: [68, 7, 5] Generated Node #0,2: 82:[68, 7, 5] Operation: 74-69=5 Exploring Operation: 68+7=75, Resulting Numbers: [69, 74, 75] Generated Node #0,3: 82:[69, 74, 75] Operation: 68+7=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[7, 74, 1], Operations: ['69-68=1'] Exploring Operation: 7*1=7, Resulting Numbers: [74, 7] Generated Node #0,0,0: 82:[74, 7] Operation: 7*1=7 Exploring Operation: 7-1=6, Resulting Numbers: [74, 6] Generated Node #0,0,1: 82:[74, 6] Operation: 7-1=6 Exploring Operation: 7+74=81, Resulting Numbers: [1, 81] Generated Node #0,0,2: 82:[1, 81] Operation: 7+74=81 Exploring Operation: 74+1=75, Resulting Numbers: [7, 75] Generated Node #0,0,3: 82:[7, 75] Operation: 74+1=75 Moving to Node #0,0,2 Current State: 82:[1, 81], Operations: ['69-68=1', '7+74=81'] Exploring Operation: 81/1=81, Resulting Numbers: [81] 81,82 unequal: No Solution Exploring Operation: 1+81=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[68, 69, 7, 74], Operations: [] Exploring Operation: 69-68=1, Resulting Numbers: [7, 74, 1] Generated Node #0,0: 82:[7, 74, 1] Operation: 69-68=1 Moving to Node #0,0 Current State: 82:[7, 74, 1], Operations: ['69-68=1'] Exploring Operation: 7+74=81, Resulting Numbers: [1, 81] Generated Node #0,0,2: 82:[1, 81] Operation: 7+74=81 Moving to Node #0,0,2 Current State: 82:[1, 81], Operations: ['69-68=1', '7+74=81'] Exploring Operation: 1+81=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 81, 60, 97, 12 ]
45
[ "97-81=16", "60*12=720", "720/16=45" ]
Current State: 45:[81, 60, 97, 12], Operations: [] Exploring Operation: 97-81=16, Resulting Numbers: [60, 12, 16] Generated Node #2: [60, 12, 16] from Operation: 97-81=16 Current State: 45:[60, 12, 16], Operations: ['97-81=16'] Exploring Operation: 60*12=720, Resulting Numbers: [16, 720] Generated Node #3: [16, 720] from Operation: 60*12=720 Current State: 45:[16, 720], Operations: ['97-81=16', '60*12=720'] Exploring Operation: 720/16=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[81, 60, 97, 12], Operations: [] Exploring Operation: 97-81=16, Resulting Numbers: [60, 12, 16] Generated Node #0,0: 45:[60, 12, 16] Operation: 97-81=16 Moving to Node #0,0 Current State: 45:[60, 12, 16], Operations: ['97-81=16'] Exploring Operation: 60/12=5, Resulting Numbers: [16, 5] Generated Node #0,0,0: 45:[16, 5] Operation: 60/12=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[16, 5], Operations: ['97-81=16', '60/12=5'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,45 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
[ 62, 48, 96, 78 ]
32
[ "62-48=14", "96-78=18", "14+18=32" ]
Current State: 32:[62, 48, 96, 78], Operations: [] Exploring Operation: 62-48=14, Resulting Numbers: [96, 78, 14] Generated Node #2: [96, 78, 14] from Operation: 62-48=14 Current State: 32:[96, 78, 14], Operations: ['62-48=14'] Exploring Operation: 96-78=18, Resulting Numbers: [14, 18] Generated Node #3: [14, 18] from Operation: 96-78=18 Current State: 32:[14, 18], Operations: ['62-48=14', '96-78=18'] Exploring Operation: 14+18=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[62, 48, 96, 78], Operations: [] Exploring Operation: 96/48=2, Resulting Numbers: [62, 78, 2] Generated Node #0,0: 32:[62, 78, 2] Operation: 96/48=2 Exploring Operation: 96-78=18, Resulting Numbers: [62, 48, 18] Generated Node #0,1: 32:[62, 48, 18] Operation: 96-78=18 Exploring Operation: 96-62=34, Resulting Numbers: [48, 78, 34] Generated Node #0,2: 32:[48, 78, 34] Operation: 96-62=34 Moving to Node #0,1 Current State: 32:[62, 48, 18], Operations: ['96-78=18'] Exploring Operation: 48-18=30, Resulting Numbers: [62, 30] Generated Node #0,1,0: 32:[62, 30] Operation: 48-18=30 Exploring Operation: 62-18=44, Resulting Numbers: [48, 44] Generated Node #0,1,1: 32:[48, 44] Operation: 62-18=44 Exploring Operation: 62-48=14, Resulting Numbers: [18, 14] Generated Node #0,1,2: 32:[18, 14] Operation: 62-48=14 Moving to Node #0,2 Current State: 32:[48, 78, 34], Operations: ['96-62=34'] Exploring Operation: 78-34=44, Resulting Numbers: [48, 44] Generated Node #0,2,0: 32:[48, 44] Operation: 78-34=44 Exploring Operation: 78-48=30, Resulting Numbers: [34, 30] Generated Node #0,2,1: 32:[34, 30] Operation: 78-48=30 Exploring Operation: 48-34=14, Resulting Numbers: [78, 14] Generated Node #0,2,2: 32:[78, 14] Operation: 48-34=14 Moving to Node #0,0 Current State: 32:[62, 78, 2], Operations: ['96/48=2'] Exploring Operation: 78-62=16, Resulting Numbers: [2, 16] Generated Node #0,0,0: 32:[2, 16] Operation: 78-62=16 Exploring Operation: 78/2=39, Resulting Numbers: [62, 39] Generated Node #0,0,1: 32:[62, 39] Operation: 78/2=39 Exploring Operation: 62/2=31, Resulting Numbers: [78, 31] Generated Node #0,0,2: 32:[78, 31] Operation: 62/2=31 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[2, 16], Operations: ['96/48=2', '78-62=16'] Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,32 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[62, 48, 96, 78], Operations: [] Exploring Operation: 96/48=2, Resulting Numbers: [62, 78, 2] Generated Node #0,0: 32:[62, 78, 2] Operation: 96/48=2 Moving to Node #0,0 Current State: 32:[62, 78, 2], Operations: ['96/48=2'] Exploring Operation: 78-62=16, Resulting Numbers: [2, 16] Generated Node #0,0,0: 32:[2, 16] Operation: 78-62=16 Moving to Node #0,0,0 Current State: 32:[2, 16], Operations: ['96/48=2', '78-62=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 93, 78, 3, 39 ]
80
[ "93-39=54", "78/3=26", "54+26=80" ]
Current State: 80:[93, 78, 3, 39], Operations: [] Exploring Operation: 93-39=54, Resulting Numbers: [78, 3, 54] Generated Node #2: [78, 3, 54] from Operation: 93-39=54 Current State: 80:[78, 3, 54], Operations: ['93-39=54'] Exploring Operation: 78/3=26, Resulting Numbers: [54, 26] Generated Node #3: [54, 26] from Operation: 78/3=26 Current State: 80:[54, 26], Operations: ['93-39=54', '78/3=26'] Exploring Operation: 54+26=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[93, 78, 3, 39], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [78, 39, 31] Generated Node #0,0: 80:[78, 39, 31] Operation: 93/3=31 Exploring Operation: 93-3=90, Resulting Numbers: [78, 39, 90] Generated Node #0,1: 80:[78, 39, 90] Operation: 93-3=90 Exploring Operation: 93-78=15, Resulting Numbers: [3, 39, 15] Generated Node #0,2: 80:[3, 39, 15] Operation: 93-78=15 Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[3, 39, 15], Operations: ['93-78=15'] Exploring Operation: 15/3=5, Resulting Numbers: [39, 5] Generated Node #0,2,0: 80:[39, 5] Operation: 15/3=5 Exploring Operation: 3+15=18, Resulting Numbers: [39, 18] Generated Node #0,2,1: 80:[39, 18] Operation: 3+15=18 Exploring Operation: 3+39=42, Resulting Numbers: [15, 42] Generated Node #0,2,2: 80:[15, 42] Operation: 3+39=42 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 80:[39, 5], Operations: ['93-78=15', '15/3=5'] Exploring Operation: 39*5=195, Resulting Numbers: [195] 195,80 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,80 unequal: No Solution Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,80 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: 80:[39, 18], Operations: ['93-78=15', '3+15=18'] Exploring Operation: 39*18=702, Resulting Numbers: [702] 702,80 unequal: No Solution Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,80 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: 80:[15, 42], Operations: ['93-78=15', '3+39=42'] Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 15*42=630, Resulting Numbers: [630] 630,80 unequal: No Solution Exploring Operation: 15+42=57, Resulting Numbers: [57] 57,80 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: 80:[78, 39, 31], Operations: ['93/3=31'] Exploring Operation: 39-31=8, Resulting Numbers: [78, 8] Generated Node #0,0,0: 80:[78, 8] Operation: 39-31=8 Exploring Operation: 78-31=47, Resulting Numbers: [39, 47] Generated Node #0,0,1: 80:[39, 47] Operation: 78-31=47 Exploring Operation: 78/39=2, Resulting Numbers: [31, 2] Generated Node #0,0,2: 80:[31, 2] Operation: 78/39=2 Moving to Node #0,0,0 Current State: 80:[78, 8], Operations: ['93/3=31', '39-31=8'] Exploring Operation: 78-8=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 78*8=624, Resulting Numbers: [624] 624,80 unequal: No Solution Exploring Operation: 78+8=86, Resulting Numbers: [86] 86,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[39, 47], Operations: ['93/3=31', '78-31=47'] Exploring Operation: 39+47=86, Resulting Numbers: [86] 86,80 unequal: No Solution Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 39*47=1833, Resulting Numbers: [1833] 1833,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[31, 2], Operations: ['93/3=31', '78/39=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,80 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: 80:[78, 39, 90], Operations: ['93-3=90'] Exploring Operation: 90-78=12, Resulting Numbers: [39, 12] Generated Node #0,1,0: 80:[39, 12] Operation: 90-78=12 Exploring Operation: 78/39=2, Resulting Numbers: [90, 2] Generated Node #0,1,1: 80:[90, 2] Operation: 78/39=2 Exploring Operation: 78-39=39, Resulting Numbers: [90, 39] Generated Node #0,1,2: 80:[90, 39] Operation: 78-39=39 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 80:[39, 12], Operations: ['93-3=90', '90-78=12'] Exploring Operation: 39-12=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 39*12=468, Resulting Numbers: [468] 468,80 unequal: No Solution Exploring Operation: 39+12=51, Resulting Numbers: [51] 51,80 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: 80:[90, 2], Operations: ['93-3=90', '78/39=2'] Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,80 unequal: No Solution Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,80 unequal: No Solution Exploring Operation: 90+2=92, Resulting Numbers: [92] 92,80 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: 80:[90, 39], Operations: ['93-3=90', '78-39=39'] Exploring Operation: 90+39=129, Resulting Numbers: [129] 129,80 unequal: No Solution Exploring Operation: 90*39=3510, Resulting Numbers: [3510] 3510,80 unequal: No Solution Exploring Operation: 90-39=51, Resulting Numbers: [51] 51,80 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
[ 21, 11, 27, 55 ]
18
[ "21-11=10", "55-27=28", "28-10=18" ]
Current State: 18:[21, 11, 27, 55], Operations: [] Exploring Operation: 21-11=10, Resulting Numbers: [27, 55, 10] Generated Node #2: [27, 55, 10] from Operation: 21-11=10 Current State: 18:[27, 55, 10], Operations: ['21-11=10'] Exploring Operation: 55-27=28, Resulting Numbers: [10, 28] Generated Node #3: [10, 28] from Operation: 55-27=28 Current State: 18:[10, 28], Operations: ['21-11=10', '55-27=28'] Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[21, 11, 27, 55], Operations: [] Exploring Operation: 55-11=44, Resulting Numbers: [21, 27, 44] Generated Node #0,0: 18:[21, 27, 44] Operation: 55-11=44 Exploring Operation: 55-27=28, Resulting Numbers: [21, 11, 28] Generated Node #0,1: 18:[21, 11, 28] Operation: 55-27=28 Exploring Operation: 55-21=34, Resulting Numbers: [11, 27, 34] Generated Node #0,2: 18:[11, 27, 34] Operation: 55-21=34 Exploring Operation: 55/11=5, Resulting Numbers: [21, 27, 5] Generated Node #0,3: 18:[21, 27, 5] Operation: 55/11=5 Moving to Node #0,3 Current State: 18:[21, 27, 5], Operations: ['55/11=5'] Exploring Operation: 21+5=26, Resulting Numbers: [27, 26] Generated Node #0,3,0: 18:[27, 26] Operation: 21+5=26 Exploring Operation: 21-5=16, Resulting Numbers: [27, 16] Generated Node #0,3,1: 18:[27, 16] Operation: 21-5=16 Exploring Operation: 27-5=22, Resulting Numbers: [21, 22] Generated Node #0,3,2: 18:[21, 22] Operation: 27-5=22 Exploring Operation: 27-21=6, Resulting Numbers: [5, 6] Generated Node #0,3,3: 18:[5, 6] Operation: 27-21=6 Moving to Node #0,1 Current State: 18:[21, 11, 28], Operations: ['55-27=28'] Exploring Operation: 21+11=32, Resulting Numbers: [28, 32] Generated Node #0,1,0: 18:[28, 32] Operation: 21+11=32 Exploring Operation: 21-11=10, Resulting Numbers: [28, 10] Generated Node #0,1,1: 18:[28, 10] Operation: 21-11=10 Exploring Operation: 28-11=17, Resulting Numbers: [21, 17] Generated Node #0,1,2: 18:[21, 17] Operation: 28-11=17 Exploring Operation: 28-21=7, Resulting Numbers: [11, 7] Generated Node #0,1,3: 18:[11, 7] Operation: 28-21=7 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[11, 7], Operations: ['55-27=28', '28-21=7'] Exploring Operation: 11*7=77, Resulting Numbers: [77] 77,18 unequal: No Solution Exploring Operation: 11+7=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[21, 11, 27, 55], Operations: [] Exploring Operation: 55-27=28, Resulting Numbers: [21, 11, 28] Generated Node #0,1: 18:[21, 11, 28] Operation: 55-27=28 Moving to Node #0,1 Current State: 18:[21, 11, 28], Operations: ['55-27=28'] Exploring Operation: 28-21=7, Resulting Numbers: [11, 7] Generated Node #0,1,3: 18:[11, 7] Operation: 28-21=7 Moving to Node #0,1,3 Current State: 18:[11, 7], Operations: ['55-27=28', '28-21=7'] Exploring Operation: 11+7=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 25, 18, 22, 54 ]
97
[ "25*54=1350", "1350/18=75", "22+75=97" ]
Current State: 97:[25, 18, 22, 54], Operations: [] Exploring Operation: 25*54=1350, Resulting Numbers: [18, 22, 1350] Generated Node #2: [18, 22, 1350] from Operation: 25*54=1350 Current State: 97:[18, 22, 1350], Operations: ['25*54=1350'] Exploring Operation: 1350/18=75, Resulting Numbers: [22, 75] Generated Node #3: [22, 75] from Operation: 1350/18=75 Current State: 97:[22, 75], Operations: ['25*54=1350', '1350/18=75'] Exploring Operation: 22+75=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[25, 18, 22, 54], Operations: [] Exploring Operation: 18+54=72, Resulting Numbers: [25, 22, 72] Generated Node #0,0: 97:[25, 22, 72] Operation: 18+54=72 Exploring Operation: 25+22=47, Resulting Numbers: [18, 54, 47] Generated Node #0,1: 97:[18, 54, 47] Operation: 25+22=47 Exploring Operation: 25+54=79, Resulting Numbers: [18, 22, 79] Generated Node #0,2: 97:[18, 22, 79] Operation: 25+54=79 Exploring Operation: 18+22=40, Resulting Numbers: [25, 54, 40] Generated Node #0,3: 97:[25, 54, 40] Operation: 18+22=40 Exploring Operation: 25+18=43, Resulting Numbers: [22, 54, 43] Generated Node #0,4: 97:[22, 54, 43] Operation: 25+18=43 Moving to Node #0,0 Current State: 97:[25, 22, 72], Operations: ['18+54=72'] Exploring Operation: 25+22=47, Resulting Numbers: [72, 47] Generated Node #0,0,0: 97:[72, 47] Operation: 25+22=47 Exploring Operation: 25-22=3, Resulting Numbers: [72, 3] Generated Node #0,0,1: 97:[72, 3] Operation: 25-22=3 Exploring Operation: 22+72=94, Resulting Numbers: [25, 94] Generated Node #0,0,2: 97:[25, 94] Operation: 22+72=94 Exploring Operation: 72-22=50, Resulting Numbers: [25, 50] Generated Node #0,0,3: 97:[25, 50] Operation: 72-22=50 Exploring Operation: 25+72=97, Resulting Numbers: [22, 97] Generated Node #0,0,4: 97:[22, 97] Operation: 25+72=97 Moving to Node #0,2 Current State: 97:[18, 22, 79], Operations: ['25+54=79'] Exploring Operation: 22+79=101, Resulting Numbers: [18, 101] Generated Node #0,2,0: 97:[18, 101] Operation: 22+79=101 Exploring Operation: 18+79=97, Resulting Numbers: [22, 97] Generated Node #0,2,1: 97:[22, 97] Operation: 18+79=97 Exploring Operation: 18+22=40, Resulting Numbers: [79, 40] Generated Node #0,2,2: 97:[79, 40] Operation: 18+22=40 Exploring Operation: 22-18=4, Resulting Numbers: [79, 4] Generated Node #0,2,3: 97:[79, 4] Operation: 22-18=4 Exploring Operation: 79-18=61, Resulting Numbers: [22, 61] Generated Node #0,2,4: 97:[22, 61] Operation: 79-18=61 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[22, 97], Operations: ['25+54=79', '18+79=97'] Exploring Operation: 22*97=2134, Resulting Numbers: [2134] 2134,97 unequal: No Solution Exploring Operation: 97-22=75, Resulting Numbers: [75] 75,97 unequal: No Solution Exploring Operation: 22+97=119, Resulting Numbers: [119] 119,97 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: 97:[79, 40], Operations: ['25+54=79', '18+22=40'] Exploring Operation: 79*40=3160, Resulting Numbers: [3160] 3160,97 unequal: No Solution Exploring Operation: 79+40=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 79-40=39, Resulting Numbers: [39] 39,97 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: 97:[18, 101], Operations: ['25+54=79', '22+79=101'] Exploring Operation: 101-18=83, Resulting Numbers: [83] 83,97 unequal: No Solution Exploring Operation: 18+101=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 18*101=1818, Resulting Numbers: [1818] 1818,97 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: 97:[79, 4], Operations: ['25+54=79', '22-18=4'] Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,97 unequal: No Solution Exploring Operation: 79*4=316, Resulting Numbers: [316] 316,97 unequal: No Solution Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,97 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: 97:[22, 61], Operations: ['25+54=79', '79-18=61'] Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,97 unequal: No Solution Exploring Operation: 22+61=83, Resulting Numbers: [83] 83,97 unequal: No Solution Exploring Operation: 22*61=1342, Resulting Numbers: [1342] 1342,97 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: 97:[22, 54, 43], Operations: ['25+18=43'] Exploring Operation: 54-22=32, Resulting Numbers: [43, 32] Generated Node #0,4,0: 97:[43, 32] Operation: 54-22=32 Exploring Operation: 22+43=65, Resulting Numbers: [54, 65] Generated Node #0,4,1: 97:[54, 65] Operation: 22+43=65 Exploring Operation: 43-22=21, Resulting Numbers: [54, 21] Generated Node #0,4,2: 97:[54, 21] Operation: 43-22=21 Exploring Operation: 22+54=76, Resulting Numbers: [43, 76] Generated Node #0,4,3: 97:[43, 76] Operation: 22+54=76 Exploring Operation: 54+43=97, Resulting Numbers: [22, 97] Generated Node #0,4,4: 97:[22, 97] Operation: 54+43=97 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 97:[54, 65], Operations: ['25+18=43', '22+43=65'] Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,97 unequal: No Solution Exploring Operation: 54*65=3510, Resulting Numbers: [3510] 3510,97 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: 97:[43, 76], Operations: ['25+18=43', '22+54=76'] Exploring Operation: 43+76=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,97 unequal: No Solution Exploring Operation: 43*76=3268, Resulting Numbers: [3268] 3268,97 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: 97:[22, 97], Operations: ['25+18=43', '54+43=97'] Exploring Operation: 22+97=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 97-22=75, Resulting Numbers: [75] 75,97 unequal: No Solution Exploring Operation: 22*97=2134, Resulting Numbers: [2134] 2134,97 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: 97:[43, 32], Operations: ['25+18=43', '54-22=32'] Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,97 unequal: No Solution Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,97 unequal: No Solution Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,97 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: 97:[54, 21], Operations: ['25+18=43', '43-22=21'] Exploring Operation: 54+21=75, Resulting Numbers: [75] 75,97 unequal: No Solution Exploring Operation: 54*21=1134, Resulting Numbers: [1134] 1134,97 unequal: No Solution Exploring Operation: 54-21=33, Resulting Numbers: [33] 33,97 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: 97:[18, 54, 47], Operations: ['25+22=47'] Exploring Operation: 47-18=29, Resulting Numbers: [54, 29] Generated Node #0,1,0: 97:[54, 29] Operation: 47-18=29 Exploring Operation: 54+47=101, Resulting Numbers: [18, 101] Generated Node #0,1,1: 97:[18, 101] Operation: 54+47=101 Exploring Operation: 18+47=65, Resulting Numbers: [54, 65] Generated Node #0,1,2: 97:[54, 65] Operation: 18+47=65 Exploring Operation: 18+54=72, Resulting Numbers: [47, 72] Generated Node #0,1,3: 97:[47, 72] Operation: 18+54=72 Exploring Operation: 54-18=36, Resulting Numbers: [47, 36] Generated Node #0,1,4: 97:[47, 36] Operation: 54-18=36 Moving to Node #0,3 Current State: 97:[25, 54, 40], Operations: ['18+22=40'] Exploring Operation: 25+54=79, Resulting Numbers: [40, 79] Generated Node #0,3,0: 97:[40, 79] Operation: 25+54=79 Exploring Operation: 40-25=15, Resulting Numbers: [54, 15] Generated Node #0,3,1: 97:[54, 15] Operation: 40-25=15 Exploring Operation: 54-25=29, Resulting Numbers: [40, 29] Generated Node #0,3,2: 97:[40, 29] Operation: 54-25=29 Exploring Operation: 54+40=94, Resulting Numbers: [25, 94] Generated Node #0,3,3: 97:[25, 94] Operation: 54+40=94 Exploring Operation: 25+40=65, Resulting Numbers: [54, 65] Generated Node #0,3,4: 97:[54, 65] Operation: 25+40=65 Moving to Node #0,0,0 Current State: 97:[72, 47], Operations: ['18+54=72', '25+22=47'] Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,97 unequal: No Solution Exploring Operation: 72*47=3384, Resulting Numbers: [3384] 3384,97 unequal: No Solution Exploring Operation: 72+47=119, Resulting Numbers: [119] 119,97 unequal: No Solution Moving to Node #0,0,4 Current State: 97:[22, 97], Operations: ['18+54=72', '25+72=97'] Exploring Operation: 97-22=75, Resulting Numbers: [75] 75,97 unequal: No Solution Exploring Operation: 22+97=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 22*97=2134, Resulting Numbers: [2134] 2134,97 unequal: No Solution Moving to Node #0,1,3 Current State: 97:[47, 72], Operations: ['25+22=47', '18+54=72'] Exploring Operation: 47*72=3384, Resulting Numbers: [3384] 3384,97 unequal: No Solution Exploring Operation: 47+72=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[54, 65], Operations: ['25+22=47', '18+47=65'] Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,97 unequal: No Solution Exploring Operation: 54*65=3510, Resulting Numbers: [3510] 3510,97 unequal: No Solution Moving to Node #0,3,4 Current State: 97:[54, 65], Operations: ['18+22=40', '25+40=65'] Exploring Operation: 54*65=3510, Resulting Numbers: [3510] 3510,97 unequal: No Solution Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,97 unequal: No Solution Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,97 unequal: No Solution Moving to Node #0,3,3 Current State: 97:[25, 94], Operations: ['18+22=40', '54+40=94'] Exploring Operation: 94-25=69, Resulting Numbers: [69] 69,97 unequal: No Solution Exploring Operation: 25+94=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 25*94=2350, Resulting Numbers: [2350] 2350,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[25, 94], Operations: ['18+54=72', '22+72=94'] Exploring Operation: 25*94=2350, Resulting Numbers: [2350] 2350,97 unequal: No Solution Exploring Operation: 94-25=69, Resulting Numbers: [69] 69,97 unequal: No Solution Exploring Operation: 25+94=119, Resulting Numbers: [119] 119,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[40, 79], Operations: ['18+22=40', '25+54=79'] Exploring Operation: 79-40=39, Resulting Numbers: [39] 39,97 unequal: No Solution Exploring Operation: 40+79=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 40*79=3160, Resulting Numbers: [3160] 3160,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[18, 101], Operations: ['25+22=47', '54+47=101'] Exploring Operation: 101-18=83, Resulting Numbers: [83] 83,97 unequal: No Solution Exploring Operation: 18*101=1818, Resulting Numbers: [1818] 1818,97 unequal: No Solution Exploring Operation: 18+101=119, Resulting Numbers: [119] 119,97 unequal: No Solution Moving to Node #0,1,4 Current State: 97:[47, 36], Operations: ['25+22=47', '54-18=36'] Exploring Operation: 47+36=83, Resulting Numbers: [83] 83,97 unequal: No Solution Exploring Operation: 47-36=11, Resulting Numbers: [11] 11,97 unequal: No Solution Exploring Operation: 47*36=1692, Resulting Numbers: [1692] 1692,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[54, 29], Operations: ['25+22=47', '47-18=29'] Exploring Operation: 54-29=25, Resulting Numbers: [25] 25,97 unequal: No Solution Exploring Operation: 54*29=1566, Resulting Numbers: [1566] 1566,97 unequal: No Solution Exploring Operation: 54+29=83, Resulting Numbers: [83] 83,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[25, 50], Operations: ['18+54=72', '72-22=50'] Exploring Operation: 25*50=1250, Resulting Numbers: [1250] 1250,97 unequal: No Solution Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,97 unequal: No Solution Exploring Operation: 25+50=75, Resulting Numbers: [75] 75,97 unequal: No Solution Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[72, 3], Operations: ['18+54=72', '25-22=3'] Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,97 unequal: No Solution Exploring Operation: 72*3=216, Resulting Numbers: [216] 216,97 unequal: No Solution Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,97 unequal: No Solution Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,97 unequal: No Solution Moving to Node #0,3,1 Current State: 97:[54, 15], Operations: ['18+22=40', '40-25=15'] Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,97 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,97 unequal: No Solution Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,97 unequal: No Solution Moving to Node #0,3,2 Current State: 97:[40, 29], Operations: ['18+22=40', '54-25=29'] Exploring Operation: 40-29=11, Resulting Numbers: [11] 11,97 unequal: No Solution Exploring Operation: 40*29=1160, Resulting Numbers: [1160] 1160,97 unequal: No Solution Exploring Operation: 40+29=69, Resulting Numbers: [69] 69,97 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 91, 82, 86, 26 ]
14
[ "86-82=4", "91*4=364", "364/26=14" ]
Current State: 14:[91, 82, 86, 26], Operations: [] Exploring Operation: 86-82=4, Resulting Numbers: [91, 26, 4] Generated Node #2: [91, 26, 4] from Operation: 86-82=4 Current State: 14:[91, 26, 4], Operations: ['86-82=4'] Exploring Operation: 91*4=364, Resulting Numbers: [26, 364] Generated Node #3: [26, 364] from Operation: 91*4=364 Current State: 14:[26, 364], Operations: ['86-82=4', '91*4=364'] Exploring Operation: 364/26=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[91, 82, 86, 26], Operations: [] Exploring Operation: 91-86=5, Resulting Numbers: [82, 26, 5] Generated Node #0,0: 14:[82, 26, 5] Operation: 91-86=5 Moving to Node #0,0 Current State: 14:[82, 26, 5], Operations: ['91-86=5'] Exploring Operation: 82-26=56, Resulting Numbers: [5, 56] Generated Node #0,0,0: 14:[5, 56] Operation: 82-26=56 Moving to Node #0,0,0 Current State: 14:[5, 56], Operations: ['91-86=5', '82-26=56'] Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,14 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 28, 31, 51, 55 ]
47
[ "28+31=59", "51+55=106", "106-59=47" ]
Current State: 47:[28, 31, 51, 55], Operations: [] Exploring Operation: 28+31=59, Resulting Numbers: [51, 55, 59] Generated Node #2: [51, 55, 59] from Operation: 28+31=59 Current State: 47:[51, 55, 59], Operations: ['28+31=59'] Exploring Operation: 51+55=106, Resulting Numbers: [59, 106] Generated Node #3: [59, 106] from Operation: 51+55=106 Current State: 47:[59, 106], Operations: ['28+31=59', '51+55=106'] Exploring Operation: 106-59=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[28, 31, 51, 55], Operations: [] Exploring Operation: 28+31=59, Resulting Numbers: [51, 55, 59] Generated Node #0,0: 47:[51, 55, 59] Operation: 28+31=59 Exploring Operation: 55-31=24, Resulting Numbers: [28, 51, 24] Generated Node #0,1: 47:[28, 51, 24] Operation: 55-31=24 Exploring Operation: 55-28=27, Resulting Numbers: [31, 51, 27] Generated Node #0,2: 47:[31, 51, 27] Operation: 55-28=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[51, 55, 59], Operations: ['28+31=59'] Exploring Operation: 55-51=4, Resulting Numbers: [59, 4] Generated Node #0,0,0: 47:[59, 4] Operation: 55-51=4 Exploring Operation: 59-55=4, Resulting Numbers: [51, 4] Generated Node #0,0,1: 47:[51, 4] Operation: 59-55=4 Exploring Operation: 59-51=8, Resulting Numbers: [55, 8] Generated Node #0,0,2: 47:[55, 8] Operation: 59-51=8 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 47:[51, 4], Operations: ['28+31=59', '59-55=4'] Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[28, 31, 51, 55], Operations: [] Exploring Operation: 28+31=59, Resulting Numbers: [51, 55, 59] Generated Node #0,0: 47:[51, 55, 59] Operation: 28+31=59 Moving to Node #0,0 Current State: 47:[51, 55, 59], Operations: ['28+31=59'] Exploring Operation: 59-55=4, Resulting Numbers: [51, 4] Generated Node #0,0,1: 47:[51, 4] Operation: 59-55=4 Moving to Node #0,0,1 Current State: 47:[51, 4], Operations: ['28+31=59', '59-55=4'] Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 16, 36, 55, 7 ]
28
[ "36-16=20", "55-7=48", "48-20=28" ]
Current State: 28:[16, 36, 55, 7], Operations: [] Exploring Operation: 36-16=20, Resulting Numbers: [55, 7, 20] Generated Node #2: [55, 7, 20] from Operation: 36-16=20 Current State: 28:[55, 7, 20], Operations: ['36-16=20'] Exploring Operation: 55-7=48, Resulting Numbers: [20, 48] Generated Node #3: [20, 48] from Operation: 55-7=48 Current State: 28:[20, 48], Operations: ['36-16=20', '55-7=48'] Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[16, 36, 55, 7], Operations: [] Exploring Operation: 55-36=19, Resulting Numbers: [16, 7, 19] Generated Node #0,0: 28:[16, 7, 19] Operation: 55-36=19 Exploring Operation: 55-16=39, Resulting Numbers: [36, 7, 39] Generated Node #0,1: 28:[36, 7, 39] Operation: 55-16=39 Moving to Node #0,0 Current State: 28:[16, 7, 19], Operations: ['55-36=19'] Exploring Operation: 7+19=26, Resulting Numbers: [16, 26] Generated Node #0,0,0: 28:[16, 26] Operation: 7+19=26 Exploring Operation: 19-16=3, Resulting Numbers: [7, 3] Generated Node #0,0,1: 28:[7, 3] Operation: 19-16=3 Moving to Node #0,1 Current State: 28:[36, 7, 39], Operations: ['55-16=39'] Exploring Operation: 39-36=3, Resulting Numbers: [7, 3] Generated Node #0,1,0: 28:[7, 3] Operation: 39-36=3 Exploring Operation: 36-7=29, Resulting Numbers: [39, 29] Generated Node #0,1,1: 28:[39, 29] Operation: 36-7=29 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 28:[7, 3], Operations: ['55-16=39', '39-36=3'] Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,28 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,28 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: 28:[39, 29], Operations: ['55-16=39', '36-7=29'] Exploring Operation: 39-29=10, Resulting Numbers: [10] 10,28 unequal: No Solution Exploring Operation: 39+29=68, Resulting Numbers: [68] 68,28 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: 28:[7, 3], Operations: ['55-36=19', '19-16=3'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,28 unequal: No Solution Moving to Node #0,0,0 Current State: 28:[16, 26], Operations: ['55-36=19', '7+19=26'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,28 unequal: No Solution Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,28 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 12, 4, 35, 52 ]
92
[ "12*35=420", "420-52=368", "368/4=92" ]
Current State: 92:[12, 4, 35, 52], Operations: [] Exploring Operation: 12*35=420, Resulting Numbers: [4, 52, 420] Generated Node #2: [4, 52, 420] from Operation: 12*35=420 Current State: 92:[4, 52, 420], Operations: ['12*35=420'] Exploring Operation: 420-52=368, Resulting Numbers: [4, 368] Generated Node #3: [4, 368] from Operation: 420-52=368 Current State: 92:[4, 368], Operations: ['12*35=420', '420-52=368'] Exploring Operation: 368/4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[12, 4, 35, 52], Operations: [] Exploring Operation: 52-35=17, Resulting Numbers: [12, 4, 17] Generated Node #0,0: 92:[12, 4, 17] Operation: 52-35=17 Exploring Operation: 35-12=23, Resulting Numbers: [4, 52, 23] Generated Node #0,1: 92:[4, 52, 23] Operation: 35-12=23 Exploring Operation: 12+35=47, Resulting Numbers: [4, 52, 47] Generated Node #0,2: 92:[4, 52, 47] Operation: 12+35=47 Exploring Operation: 35+52=87, Resulting Numbers: [12, 4, 87] Generated Node #0,3: 92:[12, 4, 87] Operation: 35+52=87 Moving to Node #0,1 Current State: 92:[4, 52, 23], Operations: ['35-12=23'] Exploring Operation: 4*23=92, Resulting Numbers: [52, 92] Generated Node #0,1,0: 92:[52, 92] Operation: 4*23=92 Exploring Operation: 52/4=13, Resulting Numbers: [23, 13] Generated Node #0,1,1: 92:[23, 13] Operation: 52/4=13 Exploring Operation: 52-4=48, Resulting Numbers: [23, 48] Generated Node #0,1,2: 92:[23, 48] Operation: 52-4=48 Exploring Operation: 52-23=29, Resulting Numbers: [4, 29] Generated Node #0,1,3: 92:[4, 29] Operation: 52-23=29 Moving to Node #0,2 Current State: 92:[4, 52, 47], Operations: ['12+35=47'] Exploring Operation: 52-47=5, Resulting Numbers: [4, 5] Generated Node #0,2,0: 92:[4, 5] Operation: 52-47=5 Exploring Operation: 47-4=43, Resulting Numbers: [52, 43] Generated Node #0,2,1: 92:[52, 43] Operation: 47-4=43 Exploring Operation: 52-4=48, Resulting Numbers: [47, 48] Generated Node #0,2,2: 92:[47, 48] Operation: 52-4=48 Exploring Operation: 52+47=99, Resulting Numbers: [4, 99] Generated Node #0,2,3: 92:[4, 99] Operation: 52+47=99 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 92:[4, 5], Operations: ['12+35=47', '52-47=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,92 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,92 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 #0,2,2 Current State: 92:[47, 48], Operations: ['12+35=47', '52-4=48'] Exploring Operation: 48-47=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 47*48=2256, Resulting Numbers: [2256] 2256,92 unequal: No Solution Exploring Operation: 47+48=95, Resulting Numbers: [95] 95,92 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 #0,2,3 Current State: 92:[4, 99], Operations: ['12+35=47', '52+47=99'] Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,92 unequal: No Solution Exploring Operation: 4*99=396, Resulting Numbers: [396] 396,92 unequal: No Solution Exploring Operation: 4+99=103, Resulting Numbers: [103] 103,92 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 #0,2,1 Current State: 92:[52, 43], Operations: ['12+35=47', '47-4=43'] Exploring Operation: 52-43=9, Resulting Numbers: [9] 9,92 unequal: No Solution Exploring Operation: 52*43=2236, Resulting Numbers: [2236] 2236,92 unequal: No Solution Exploring Operation: 52+43=95, Resulting Numbers: [95] 95,92 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: 92:[12, 4, 87], Operations: ['35+52=87'] Exploring Operation: 12*4=48, Resulting Numbers: [87, 48] Generated Node #0,3,0: 92:[87, 48] Operation: 12*4=48 Exploring Operation: 12+87=99, Resulting Numbers: [4, 99] Generated Node #0,3,1: 92:[4, 99] Operation: 12+87=99 Exploring Operation: 12/4=3, Resulting Numbers: [87, 3] Generated Node #0,3,2: 92:[87, 3] Operation: 12/4=3 Exploring Operation: 12-4=8, Resulting Numbers: [87, 8] Generated Node #0,3,3: 92:[87, 8] Operation: 12-4=8 Moving to Node #0,0 Current State: 92:[12, 4, 17], Operations: ['52-35=17'] Exploring Operation: 12/4=3, Resulting Numbers: [17, 3] Generated Node #0,0,0: 92:[17, 3] Operation: 12/4=3 Exploring Operation: 12*4=48, Resulting Numbers: [17, 48] Generated Node #0,0,1: 92:[17, 48] Operation: 12*4=48 Exploring Operation: 12+17=29, Resulting Numbers: [4, 29] Generated Node #0,0,2: 92:[4, 29] Operation: 12+17=29 Exploring Operation: 17-12=5, Resulting Numbers: [4, 5] Generated Node #0,0,3: 92:[4, 5] Operation: 17-12=5 Moving to Node #0,0,3 Current State: 92:[4, 5], Operations: ['52-35=17', '17-12=5'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,92 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,92 unequal: No Solution Moving to Node #0,1,2 Current State: 92:[23, 48], Operations: ['35-12=23', '52-4=48'] Exploring Operation: 23*48=1104, Resulting Numbers: [1104] 1104,92 unequal: No Solution Exploring Operation: 48-23=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 23+48=71, Resulting Numbers: [71] 71,92 unequal: No Solution Moving to Node #0,1,3 Current State: 92:[4, 29], Operations: ['35-12=23', '52-23=29'] Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,92 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,92 unequal: No Solution Moving to Node #0,3,2 Current State: 92:[87, 3], Operations: ['35+52=87', '12/4=3'] Exploring Operation: 87/3=29, Resulting Numbers: [29] 29,92 unequal: No Solution Exploring Operation: 87-3=84, Resulting Numbers: [84] 84,92 unequal: No Solution Exploring Operation: 87*3=261, Resulting Numbers: [261] 261,92 unequal: No Solution Exploring Operation: 87+3=90, Resulting Numbers: [90] 90,92 unequal: No Solution Moving to Node #0,0,2 Current State: 92:[4, 29], Operations: ['52-35=17', '12+17=29'] Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,92 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[52, 92], Operations: ['35-12=23', '4*23=92'] Exploring Operation: 92-52=40, Resulting Numbers: [40] 40,92 unequal: No Solution Exploring Operation: 52+92=144, Resulting Numbers: [144] 144,92 unequal: No Solution Exploring Operation: 52*92=4784, Resulting Numbers: [4784] 4784,92 unequal: No Solution Moving to Node #0,3,1 Current State: 92:[4, 99], Operations: ['35+52=87', '12+87=99'] Exploring Operation: 4*99=396, Resulting Numbers: [396] 396,92 unequal: No Solution Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,92 unequal: No Solution Exploring Operation: 4+99=103, Resulting Numbers: [103] 103,92 unequal: No Solution Moving to Node #0,3,0 Current State: 92:[87, 48], Operations: ['35+52=87', '12*4=48'] Exploring Operation: 87-48=39, Resulting Numbers: [39] 39,92 unequal: No Solution Exploring Operation: 87*48=4176, Resulting Numbers: [4176] 4176,92 unequal: No Solution Exploring Operation: 87+48=135, Resulting Numbers: [135] 135,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[17, 3], Operations: ['52-35=17', '12/4=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,92 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,92 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[17, 48], Operations: ['52-35=17', '12*4=48'] Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,92 unequal: No Solution Exploring Operation: 17*48=816, Resulting Numbers: [816] 816,92 unequal: No Solution Exploring Operation: 17+48=65, Resulting Numbers: [65] 65,92 unequal: No Solution Moving to Node #0,3,3 Current State: 92:[87, 8], Operations: ['35+52=87', '12-4=8'] Exploring Operation: 87*8=696, Resulting Numbers: [696] 696,92 unequal: No Solution Exploring Operation: 87+8=95, Resulting Numbers: [95] 95,92 unequal: No Solution Exploring Operation: 87-8=79, Resulting Numbers: [79] 79,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[23, 13], Operations: ['35-12=23', '52/4=13'] Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,92 unequal: No Solution Exploring Operation: 23*13=299, Resulting Numbers: [299] 299,92 unequal: No Solution Exploring Operation: 23+13=36, Resulting Numbers: [36] 36,92 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 82, 20, 85, 81 ]
47
[ "85-82=3", "81/3=27", "20+27=47" ]
Current State: 47:[82, 20, 85, 81], Operations: [] Exploring Operation: 85-82=3, Resulting Numbers: [20, 81, 3] Generated Node #2: [20, 81, 3] from Operation: 85-82=3 Current State: 47:[20, 81, 3], Operations: ['85-82=3'] Exploring Operation: 81/3=27, Resulting Numbers: [20, 27] Generated Node #3: [20, 27] from Operation: 81/3=27 Current State: 47:[20, 27], Operations: ['85-82=3', '81/3=27'] Exploring Operation: 20+27=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[82, 20, 85, 81], Operations: [] Exploring Operation: 82-20=62, Resulting Numbers: [85, 81, 62] Generated Node #0,0: 47:[85, 81, 62] Operation: 82-20=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[85, 81, 62], Operations: ['82-20=62'] Exploring Operation: 85-81=4, Resulting Numbers: [62, 4] Generated Node #0,0,0: 47:[62, 4] Operation: 85-81=4 Moving to Node #0,0,0 Current State: 47:[62, 4], Operations: ['82-20=62', '85-81=4'] Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,47 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
[ 75, 30, 8, 11 ]
73
[ "30-8=22", "22/11=2", "75-2=73" ]
Current State: 73:[75, 30, 8, 11], Operations: [] Exploring Operation: 30-8=22, Resulting Numbers: [75, 11, 22] Generated Node #2: [75, 11, 22] from Operation: 30-8=22 Current State: 73:[75, 11, 22], Operations: ['30-8=22'] Exploring Operation: 22/11=2, Resulting Numbers: [75, 2] Generated Node #3: [75, 2] from Operation: 22/11=2 Current State: 73:[75, 2], Operations: ['30-8=22', '22/11=2'] Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[75, 30, 8, 11], Operations: [] Exploring Operation: 30+8=38, Resulting Numbers: [75, 11, 38] Generated Node #0,0: 73:[75, 11, 38] Operation: 30+8=38 Exploring Operation: 30+11=41, Resulting Numbers: [75, 8, 41] Generated Node #0,1: 73:[75, 8, 41] Operation: 30+11=41 Exploring Operation: 8*11=88, Resulting Numbers: [75, 30, 88] Generated Node #0,2: 73:[75, 30, 88] Operation: 8*11=88 Moving to Node #0,2 Current State: 73:[75, 30, 88], Operations: ['8*11=88'] Exploring Operation: 75+30=105, Resulting Numbers: [88, 105] Generated Node #0,2,0: 73:[88, 105] Operation: 75+30=105 Exploring Operation: 75-30=45, Resulting Numbers: [88, 45] Generated Node #0,2,1: 73:[88, 45] Operation: 75-30=45 Exploring Operation: 88-30=58, Resulting Numbers: [75, 58] Generated Node #0,2,2: 73:[75, 58] Operation: 88-30=58 Moving to Node #0,0 Current State: 73:[75, 11, 38], Operations: ['30+8=38'] Exploring Operation: 11+38=49, Resulting Numbers: [75, 49] Generated Node #0,0,0: 73:[75, 49] Operation: 11+38=49 Exploring Operation: 75+11=86, Resulting Numbers: [38, 86] Generated Node #0,0,1: 73:[38, 86] Operation: 75+11=86 Exploring Operation: 75-11=64, Resulting Numbers: [38, 64] Generated Node #0,0,2: 73:[38, 64] Operation: 75-11=64 Moving to Node #0,1 Current State: 73:[75, 8, 41], Operations: ['30+11=41'] Exploring Operation: 75+8=83, Resulting Numbers: [41, 83] Generated Node #0,1,0: 73:[41, 83] Operation: 75+8=83 Exploring Operation: 8+41=49, Resulting Numbers: [75, 49] Generated Node #0,1,1: 73:[75, 49] Operation: 8+41=49 Exploring Operation: 75-8=67, Resulting Numbers: [41, 67] Generated Node #0,1,2: 73:[41, 67] Operation: 75-8=67 Moving to Node #0,2,2 Current State: 73:[75, 58], Operations: ['8*11=88', '88-30=58'] Exploring Operation: 75+58=133, Resulting Numbers: [133] 133,73 unequal: No Solution Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,73 unequal: No Solution Exploring Operation: 75*58=4350, Resulting Numbers: [4350] 4350,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[75, 49], Operations: ['30+11=41', '8+41=49'] Exploring Operation: 75-49=26, Resulting Numbers: [26] 26,73 unequal: No Solution Exploring Operation: 75*49=3675, Resulting Numbers: [3675] 3675,73 unequal: No Solution Exploring Operation: 75+49=124, Resulting Numbers: [124] 124,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[75, 49], Operations: ['30+8=38', '11+38=49'] Exploring Operation: 75*49=3675, Resulting Numbers: [3675] 3675,73 unequal: No Solution Exploring Operation: 75-49=26, Resulting Numbers: [26] 26,73 unequal: No Solution Exploring Operation: 75+49=124, Resulting Numbers: [124] 124,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[41, 67], Operations: ['30+11=41', '75-8=67'] Exploring Operation: 41*67=2747, Resulting Numbers: [2747] 2747,73 unequal: No Solution Exploring Operation: 41+67=108, Resulting Numbers: [108] 108,73 unequal: No Solution Exploring Operation: 67-41=26, Resulting Numbers: [26] 26,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[41, 83], Operations: ['30+11=41', '75+8=83'] Exploring Operation: 41+83=124, Resulting Numbers: [124] 124,73 unequal: No Solution Exploring Operation: 83-41=42, Resulting Numbers: [42] 42,73 unequal: No Solution Exploring Operation: 41*83=3403, Resulting Numbers: [3403] 3403,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[88, 45], Operations: ['8*11=88', '75-30=45'] Exploring Operation: 88+45=133, Resulting Numbers: [133] 133,73 unequal: No Solution Exploring Operation: 88*45=3960, Resulting Numbers: [3960] 3960,73 unequal: No Solution Exploring Operation: 88-45=43, Resulting Numbers: [43] 43,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[38, 64], Operations: ['30+8=38', '75-11=64'] Exploring Operation: 64-38=26, Resulting Numbers: [26] 26,73 unequal: No Solution Exploring Operation: 38+64=102, Resulting Numbers: [102] 102,73 unequal: No Solution Exploring Operation: 38*64=2432, Resulting Numbers: [2432] 2432,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[88, 105], Operations: ['8*11=88', '75+30=105'] Exploring Operation: 88+105=193, Resulting Numbers: [193] 193,73 unequal: No Solution Exploring Operation: 88*105=9240, Resulting Numbers: [9240] 9240,73 unequal: No Solution Exploring Operation: 105-88=17, Resulting Numbers: [17] 17,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[38, 86], Operations: ['30+8=38', '75+11=86'] Exploring Operation: 38+86=124, Resulting Numbers: [124] 124,73 unequal: No Solution Exploring Operation: 38*86=3268, Resulting Numbers: [3268] 3268,73 unequal: No Solution Exploring Operation: 86-38=48, Resulting Numbers: [48] 48,73 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 34, 25, 11, 30 ]
78
[ "34+25=59", "30-11=19", "59+19=78" ]
Current State: 78:[34, 25, 11, 30], Operations: [] Exploring Operation: 34+25=59, Resulting Numbers: [11, 30, 59] Generated Node #2: [11, 30, 59] from Operation: 34+25=59 Current State: 78:[11, 30, 59], Operations: ['34+25=59'] Exploring Operation: 30-11=19, Resulting Numbers: [59, 19] Generated Node #3: [59, 19] from Operation: 30-11=19 Current State: 78:[59, 19], Operations: ['34+25=59', '30-11=19'] Exploring Operation: 59+19=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[34, 25, 11, 30], Operations: [] Exploring Operation: 34-30=4, Resulting Numbers: [25, 11, 4] Generated Node #0,0: 78:[25, 11, 4] Operation: 34-30=4 Exploring Operation: 34-11=23, Resulting Numbers: [25, 30, 23] Generated Node #0,1: 78:[25, 30, 23] Operation: 34-11=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[25, 11, 4], Operations: ['34-30=4'] Exploring Operation: 11-4=7, Resulting Numbers: [25, 7] Generated Node #0,0,0: 78:[25, 7] Operation: 11-4=7 Exploring Operation: 25-11=14, Resulting Numbers: [4, 14] Generated Node #0,0,1: 78:[4, 14] Operation: 25-11=14 Moving to Node #0,0,0 Current State: 78:[25, 7], Operations: ['34-30=4', '11-4=7'] Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,78 unequal: No Solution Moving to Node #0,0,1 Current State: 78:[4, 14], Operations: ['34-30=4', '25-11=14'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,78 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,78 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: 78:[25, 30, 23], Operations: ['34-11=23'] Exploring Operation: 30-23=7, Resulting Numbers: [25, 7] Generated Node #0,1,0: 78:[25, 7] Operation: 30-23=7 Exploring Operation: 30-25=5, Resulting Numbers: [23, 5] Generated Node #0,1,1: 78:[23, 5] Operation: 30-25=5 Moving to Node #0,1,0 Current State: 78:[25, 7], Operations: ['34-11=23', '30-23=7'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,78 unequal: No Solution Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[23, 5], Operations: ['34-11=23', '30-25=5'] Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,78 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
[ 8, 34, 51, 27 ]
80
[ "51-34=17", "27-17=10", "8*10=80" ]
Current State: 80:[8, 34, 51, 27], Operations: [] Exploring Operation: 51-34=17, Resulting Numbers: [8, 27, 17] Generated Node #2: [8, 27, 17] from Operation: 51-34=17 Current State: 80:[8, 27, 17], Operations: ['51-34=17'] Exploring Operation: 27-17=10, Resulting Numbers: [8, 10] Generated Node #3: [8, 10] from Operation: 27-17=10 Current State: 80:[8, 10], Operations: ['51-34=17', '27-17=10'] Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[8, 34, 51, 27], Operations: [] Exploring Operation: 51-27=24, Resulting Numbers: [8, 34, 24] Generated Node #0,0: 80:[8, 34, 24] Operation: 51-27=24 Exploring Operation: 34+51=85, Resulting Numbers: [8, 27, 85] Generated Node #0,1: 80:[8, 27, 85] Operation: 34+51=85 Exploring Operation: 51-34=17, Resulting Numbers: [8, 27, 17] Generated Node #0,2: 80:[8, 27, 17] Operation: 51-34=17 Exploring Operation: 51+27=78, Resulting Numbers: [8, 34, 78] Generated Node #0,3: 80:[8, 34, 78] Operation: 51+27=78 Moving to Node #0,2 Current State: 80:[8, 27, 17], Operations: ['51-34=17'] Exploring Operation: 27-17=10, Resulting Numbers: [8, 10] Generated Node #0,2,0: 80:[8, 10] Operation: 27-17=10 Exploring Operation: 27-8=19, Resulting Numbers: [17, 19] Generated Node #0,2,1: 80:[17, 19] Operation: 27-8=19 Exploring Operation: 8+27=35, Resulting Numbers: [17, 35] Generated Node #0,2,2: 80:[17, 35] Operation: 8+27=35 Exploring Operation: 27+17=44, Resulting Numbers: [8, 44] Generated Node #0,2,3: 80:[8, 44] Operation: 27+17=44 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[8, 10], Operations: ['51-34=17', '27-17=10'] Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[8, 34, 51, 27], Operations: [] Exploring Operation: 51-34=17, Resulting Numbers: [8, 27, 17] Generated Node #0,2: 80:[8, 27, 17] Operation: 51-34=17 Moving to Node #0,2 Current State: 80:[8, 27, 17], Operations: ['51-34=17'] Exploring Operation: 27-17=10, Resulting Numbers: [8, 10] Generated Node #0,2,0: 80:[8, 10] Operation: 27-17=10 Moving to Node #0,2,0 Current State: 80:[8, 10], Operations: ['51-34=17', '27-17=10'] Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 62, 3, 94, 66 ]
10
[ "94-62=32", "66/3=22", "32-22=10" ]
Current State: 10:[62, 3, 94, 66], Operations: [] Exploring Operation: 94-62=32, Resulting Numbers: [3, 66, 32] Generated Node #2: [3, 66, 32] from Operation: 94-62=32 Current State: 10:[3, 66, 32], Operations: ['94-62=32'] Exploring Operation: 66/3=22, Resulting Numbers: [32, 22] Generated Node #3: [32, 22] from Operation: 66/3=22 Current State: 10:[32, 22], Operations: ['94-62=32', '66/3=22'] Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[62, 3, 94, 66], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [3, 94, 4] Generated Node #0,0: 10:[3, 94, 4] Operation: 66-62=4 Exploring Operation: 94-62=32, Resulting Numbers: [3, 66, 32] Generated Node #0,1: 10:[3, 66, 32] Operation: 94-62=32 Exploring Operation: 94-66=28, Resulting Numbers: [62, 3, 28] Generated Node #0,2: 10:[62, 3, 28] Operation: 94-66=28 Start Sub Search at level 1: Moving to Node #0,2 Current State: 10:[62, 3, 28], Operations: ['94-66=28'] Exploring Operation: 28-3=25, Resulting Numbers: [62, 25] Generated Node #0,2,0: 10:[62, 25] Operation: 28-3=25 Exploring Operation: 62-3=59, Resulting Numbers: [28, 59] Generated Node #0,2,1: 10:[28, 59] Operation: 62-3=59 Exploring Operation: 62-28=34, Resulting Numbers: [3, 34] Generated Node #0,2,2: 10:[3, 34] Operation: 62-28=34 Moving to Node #0,2,2 Current State: 10:[3, 34], Operations: ['94-66=28', '62-28=34'] Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,10 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,10 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,10 unequal: No Solution Moving to Node #0,2,0 Current State: 10:[62, 25], Operations: ['94-66=28', '28-3=25'] Exploring Operation: 62+25=87, Resulting Numbers: [87] 87,10 unequal: No Solution Exploring Operation: 62*25=1550, Resulting Numbers: [1550] 1550,10 unequal: No Solution Exploring Operation: 62-25=37, Resulting Numbers: [37] 37,10 unequal: No Solution Moving to Node #0,2,1 Current State: 10:[28, 59], Operations: ['94-66=28', '62-3=59'] Exploring Operation: 28*59=1652, Resulting Numbers: [1652] 1652,10 unequal: No Solution Exploring Operation: 59-28=31, Resulting Numbers: [31] 31,10 unequal: No Solution Exploring Operation: 28+59=87, Resulting Numbers: [87] 87,10 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: 10:[3, 66, 32], Operations: ['94-62=32'] Exploring Operation: 66-3=63, Resulting Numbers: [32, 63] Generated Node #0,1,0: 10:[32, 63] Operation: 66-3=63 Exploring Operation: 66-32=34, Resulting Numbers: [3, 34] Generated Node #0,1,1: 10:[3, 34] Operation: 66-32=34 Exploring Operation: 66/3=22, Resulting Numbers: [32, 22] Generated Node #0,1,2: 10:[32, 22] Operation: 66/3=22 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 10:[3, 34], Operations: ['94-62=32', '66-32=34'] Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,10 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,10 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,10 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: 10:[32, 22], Operations: ['94-62=32', '66/3=22'] Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[62, 3, 94, 66], Operations: [] Exploring Operation: 94-62=32, Resulting Numbers: [3, 66, 32] Generated Node #0,1: 10:[3, 66, 32] Operation: 94-62=32 Moving to Node #0,1 Current State: 10:[3, 66, 32], Operations: ['94-62=32'] Exploring Operation: 66/3=22, Resulting Numbers: [32, 22] Generated Node #0,1,2: 10:[32, 22] Operation: 66/3=22 Moving to Node #0,1,2 Current State: 10:[32, 22], Operations: ['94-62=32', '66/3=22'] Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.977431
hs_3
sum_heuristic
[ 20, 58, 18, 18 ]
16
[ "58-18=40", "40/20=2", "18-2=16" ]
Current State: 16:[20, 58, 18, 18], Operations: [] Exploring Operation: 58-18=40, Resulting Numbers: [20, 40] Generated Node #2: [20, 40] from Operation: 58-18=40 Current State: 16:[20, 40], Operations: ['58-18=40'] Exploring Operation: 40/20=2, Resulting Numbers: [2] 2,16 equal: Goal Reached Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[20, 58, 18, 18], Operations: [] Exploring Operation: 58-18=40, Resulting Numbers: [20, 18, 40] Generated Node #0,0: 16:[20, 18, 40] Operation: 58-18=40 Exploring Operation: 58-20=38, Resulting Numbers: [18, 18, 38] Generated Node #0,1: 16:[18, 18, 38] Operation: 58-20=38 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[18, 18, 38], Operations: ['58-20=38'] Exploring Operation: 38-18=20, Resulting Numbers: [18, 20] Generated Node #0,1,0: 16:[18, 20] Operation: 38-18=20 Exploring Operation: 38-18=20, Resulting Numbers: [18, 20] Generated Node #0,1,1: 16:[18, 20] Operation: 38-18=20 Moving to Node #0,1,0 Current State: 16:[18, 20], Operations: ['58-20=38', '38-18=20'] Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,16 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[18, 20], Operations: ['58-20=38', '38-18=20'] Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,16 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,16 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: 16:[20, 18, 40], Operations: ['58-18=40'] Exploring Operation: 40-20=20, Resulting Numbers: [18, 20] Generated Node #0,0,0: 16:[18, 20] Operation: 40-20=20 Exploring Operation: 40/20=2, Resulting Numbers: [18, 2] Generated Node #0,0,1: 16:[18, 2] Operation: 40/20=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 16:[18, 2], Operations: ['58-18=40', '40/20=2'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[20, 58, 18, 18], Operations: [] Exploring Operation: 58-18=40, Resulting Numbers: [20, 18, 40] Generated Node #0,0: 16:[20, 18, 40] Operation: 58-18=40 Moving to Node #0,0 Current State: 16:[20, 18, 40], Operations: ['58-18=40'] Exploring Operation: 40/20=2, Resulting Numbers: [18, 2] Generated Node #0,0,1: 16:[18, 2] Operation: 40/20=2 Moving to Node #0,0,1 Current State: 16:[18, 2], Operations: ['58-18=40', '40/20=2'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 7, 33, 70, 76 ]
99
[ "70/7=10", "33+76=109", "109-10=99" ]
Current State: 99:[7, 33, 70, 76], Operations: [] Exploring Operation: 70/7=10, Resulting Numbers: [33, 76, 10] Generated Node #2: [33, 76, 10] from Operation: 70/7=10 Current State: 99:[33, 76, 10], Operations: ['70/7=10'] Exploring Operation: 33+76=109, Resulting Numbers: [10, 109] Generated Node #3: [10, 109] from Operation: 33+76=109 Current State: 99:[10, 109], Operations: ['70/7=10', '33+76=109'] Exploring Operation: 109-10=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[7, 33, 70, 76], Operations: [] Exploring Operation: 70/7=10, Resulting Numbers: [33, 76, 10] Generated Node #0,0: 99:[33, 76, 10] Operation: 70/7=10 Exploring Operation: 33+70=103, Resulting Numbers: [7, 76, 103] Generated Node #0,1: 99:[7, 76, 103] Operation: 33+70=103 Exploring Operation: 76-70=6, Resulting Numbers: [7, 33, 6] Generated Node #0,2: 99:[7, 33, 6] Operation: 76-70=6 Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[7, 33, 6], Operations: ['76-70=6'] Exploring Operation: 33+6=39, Resulting Numbers: [7, 39] Generated Node #0,2,0: 99:[7, 39] Operation: 33+6=39 Exploring Operation: 7-6=1, Resulting Numbers: [33, 1] Generated Node #0,2,1: 99:[33, 1] Operation: 7-6=1 Exploring Operation: 7+6=13, Resulting Numbers: [33, 13] Generated Node #0,2,2: 99:[33, 13] Operation: 7+6=13 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 99:[33, 1], Operations: ['76-70=6', '7-6=1'] Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,99 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: 99:[33, 13], Operations: ['76-70=6', '7+6=13'] Exploring Operation: 33+13=46, Resulting Numbers: [46] 46,99 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,99 unequal: No Solution Exploring Operation: 33*13=429, Resulting Numbers: [429] 429,99 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: 99:[7, 39], Operations: ['76-70=6', '33+6=39'] Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 7*39=273, Resulting Numbers: [273] 273,99 unequal: No Solution Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,99 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: 99:[33, 76, 10], Operations: ['70/7=10'] Exploring Operation: 76+10=86, Resulting Numbers: [33, 86] Generated Node #0,0,0: 99:[33, 86] Operation: 76+10=86 Exploring Operation: 76-33=43, Resulting Numbers: [10, 43] Generated Node #0,0,1: 99:[10, 43] Operation: 76-33=43 Exploring Operation: 33+76=109, Resulting Numbers: [10, 109] Generated Node #0,0,2: 99:[10, 109] Operation: 33+76=109 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 99:[10, 43], Operations: ['70/7=10', '76-33=43'] Exploring Operation: 10*43=430, Resulting Numbers: [430] 430,99 unequal: No Solution Exploring Operation: 43-10=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 10+43=53, Resulting Numbers: [53] 53,99 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: 99:[10, 109], Operations: ['70/7=10', '33+76=109'] Exploring Operation: 10*109=1090, Resulting Numbers: [1090] 1090,99 unequal: No Solution Exploring Operation: 10+109=119, Resulting Numbers: [119] 119,99 unequal: No Solution Exploring Operation: 109-10=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[7, 33, 70, 76], Operations: [] Exploring Operation: 70/7=10, Resulting Numbers: [33, 76, 10] Generated Node #0,0: 99:[33, 76, 10] Operation: 70/7=10 Moving to Node #0,0 Current State: 99:[33, 76, 10], Operations: ['70/7=10'] Exploring Operation: 33+76=109, Resulting Numbers: [10, 109] Generated Node #0,0,2: 99:[10, 109] Operation: 33+76=109 Moving to Node #0,0,2 Current State: 99:[10, 109], Operations: ['70/7=10', '33+76=109'] Exploring Operation: 109-10=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.975694
hs_3
sum_heuristic
[ 40, 8, 27, 19 ]
94
[ "40+8=48", "27+19=46", "48+46=94" ]
Current State: 94:[40, 8, 27, 19], Operations: [] Exploring Operation: 40+8=48, Resulting Numbers: [27, 19, 48] Generated Node #2: [27, 19, 48] from Operation: 40+8=48 Current State: 94:[27, 19, 48], Operations: ['40+8=48'] Exploring Operation: 27+19=46, Resulting Numbers: [48, 46] Generated Node #3: [48, 46] from Operation: 27+19=46 Current State: 94:[48, 46], Operations: ['40+8=48', '27+19=46'] Exploring Operation: 48+46=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[40, 8, 27, 19], Operations: [] Exploring Operation: 40-27=13, Resulting Numbers: [8, 19, 13] Generated Node #0,0: 94:[8, 19, 13] Operation: 40-27=13 Exploring Operation: 8+27=35, Resulting Numbers: [40, 19, 35] Generated Node #0,1: 94:[40, 19, 35] Operation: 8+27=35 Exploring Operation: 27-19=8, Resulting Numbers: [40, 8, 8] Generated Node #0,2: 94:[40, 8, 8] Operation: 27-19=8 Exploring Operation: 27+19=46, Resulting Numbers: [40, 8, 46] Generated Node #0,3: 94:[40, 8, 46] Operation: 27+19=46 Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[40, 8, 46], Operations: ['27+19=46'] Exploring Operation: 40/8=5, Resulting Numbers: [46, 5] Generated Node #0,3,0: 94:[46, 5] Operation: 40/8=5 Exploring Operation: 46-40=6, Resulting Numbers: [8, 6] Generated Node #0,3,1: 94:[8, 6] Operation: 46-40=6 Exploring Operation: 40+8=48, Resulting Numbers: [46, 48] Generated Node #0,3,2: 94:[46, 48] Operation: 40+8=48 Exploring Operation: 40+46=86, Resulting Numbers: [8, 86] Generated Node #0,3,3: 94:[8, 86] Operation: 40+46=86 Moving to Node #0,3,2 Current State: 94:[46, 48], Operations: ['27+19=46', '40+8=48'] Exploring Operation: 48-46=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 46*48=2208, Resulting Numbers: [2208] 2208,94 unequal: No Solution Exploring Operation: 46+48=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[40, 8, 27, 19], Operations: [] Exploring Operation: 27+19=46, Resulting Numbers: [40, 8, 46] Generated Node #0,3: 94:[40, 8, 46] Operation: 27+19=46 Moving to Node #0,3 Current State: 94:[40, 8, 46], Operations: ['27+19=46'] Exploring Operation: 40+8=48, Resulting Numbers: [46, 48] Generated Node #0,3,2: 94:[46, 48] Operation: 40+8=48 Moving to Node #0,3,2 Current State: 94:[46, 48], Operations: ['27+19=46', '40+8=48'] Exploring Operation: 46+48=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 76, 78, 7, 93 ]
98
[ "78-76=2", "7+93=100", "100-2=98" ]
Current State: 98:[76, 78, 7, 93], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [7, 93, 2] Generated Node #2: [7, 93, 2] from Operation: 78-76=2 Current State: 98:[7, 93, 2], Operations: ['78-76=2'] Exploring Operation: 7+93=100, Resulting Numbers: [2, 100] Generated Node #3: [2, 100] from Operation: 7+93=100 Current State: 98:[2, 100], Operations: ['78-76=2', '7+93=100'] Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[76, 78, 7, 93], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [7, 93, 2] Generated Node #0,0: 98:[7, 93, 2] Operation: 78-76=2 Exploring Operation: 93-78=15, Resulting Numbers: [76, 7, 15] Generated Node #0,1: 98:[76, 7, 15] Operation: 93-78=15 Exploring Operation: 93-76=17, Resulting Numbers: [78, 7, 17] Generated Node #0,2: 98:[78, 7, 17] Operation: 93-76=17 Moving to Node #0,0 Current State: 98:[7, 93, 2], Operations: ['78-76=2'] Exploring Operation: 7+93=100, Resulting Numbers: [2, 100] Generated Node #0,0,0: 98:[2, 100] Operation: 7+93=100 Exploring Operation: 93+2=95, Resulting Numbers: [7, 95] Generated Node #0,0,1: 98:[7, 95] Operation: 93+2=95 Exploring Operation: 7*2=14, Resulting Numbers: [93, 14] Generated Node #0,0,2: 98:[93, 14] Operation: 7*2=14 Moving to Node #0,1 Current State: 98:[76, 7, 15], Operations: ['93-78=15'] Exploring Operation: 76+15=91, Resulting Numbers: [7, 91] Generated Node #0,1,0: 98:[7, 91] Operation: 76+15=91 Exploring Operation: 76-15=61, Resulting Numbers: [7, 61] Generated Node #0,1,1: 98:[7, 61] Operation: 76-15=61 Exploring Operation: 76+7=83, Resulting Numbers: [15, 83] Generated Node #0,1,2: 98:[15, 83] Operation: 76+7=83 Moving to Node #0,2 Current State: 98:[78, 7, 17], Operations: ['93-76=17'] Exploring Operation: 78+7=85, Resulting Numbers: [17, 85] Generated Node #0,2,0: 98:[17, 85] Operation: 78+7=85 Exploring Operation: 78-17=61, Resulting Numbers: [7, 61] Generated Node #0,2,1: 98:[7, 61] Operation: 78-17=61 Exploring Operation: 78+17=95, Resulting Numbers: [7, 95] Generated Node #0,2,2: 98:[7, 95] Operation: 78+17=95 Moving to Node #0,0,0 Current State: 98:[2, 100], Operations: ['78-76=2', '7+93=100'] Exploring Operation: 100/2=50, Resulting Numbers: [50] 50,98 unequal: No Solution Exploring Operation: 2+100=102, Resulting Numbers: [102] 102,98 unequal: No Solution Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[76, 78, 7, 93], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [7, 93, 2] Generated Node #0,0: 98:[7, 93, 2] Operation: 78-76=2 Moving to Node #0,0 Current State: 98:[7, 93, 2], Operations: ['78-76=2'] Exploring Operation: 7+93=100, Resulting Numbers: [2, 100] Generated Node #0,0,0: 98:[2, 100] Operation: 7+93=100 Moving to Node #0,0,0 Current State: 98:[2, 100], Operations: ['78-76=2', '7+93=100'] Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
0.983507
hs_3
mult_heuristic
[ 52, 34, 44, 66 ]
44
[ "52*44=2288", "34*66=2244", "2288-2244=44" ]
Current State: 44:[52, 34, 44, 66], Operations: [] Exploring Operation: 52*44=2288, Resulting Numbers: [34, 66, 2288] Generated Node #2: [34, 66, 2288] from Operation: 52*44=2288 Current State: 44:[34, 66, 2288], Operations: ['52*44=2288'] Exploring Operation: 34*66=2244, Resulting Numbers: [2288, 2244] Generated Node #3: [2288, 2244] from Operation: 34*66=2244 Current State: 44:[2288, 2244], Operations: ['52*44=2288', '34*66=2244'] Exploring Operation: 2288-2244=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[52, 34, 44, 66], Operations: [] Exploring Operation: 66-34=32, Resulting Numbers: [52, 44, 32] Generated Node #0,0: 44:[52, 44, 32] Operation: 66-34=32 Exploring Operation: 66-52=14, Resulting Numbers: [34, 44, 14] Generated Node #0,1: 44:[34, 44, 14] Operation: 66-52=14 Moving to Node #0,1 Current State: 44:[34, 44, 14], Operations: ['66-52=14'] Exploring Operation: 34-14=20, Resulting Numbers: [44, 20] Generated Node #0,1,0: 44:[44, 20] Operation: 34-14=20 Exploring Operation: 44-34=10, Resulting Numbers: [14, 10] Generated Node #0,1,1: 44:[14, 10] Operation: 44-34=10 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 44:[44, 20], Operations: ['66-52=14', '34-14=20'] Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,44 unequal: No Solution Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,44 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: 44:[14, 10], Operations: ['66-52=14', '44-34=10'] Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 14+10=24, Resulting Numbers: [24] 24,44 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: 44:[52, 44, 32], Operations: ['66-34=32'] Exploring Operation: 44-32=12, Resulting Numbers: [52, 12] Generated Node #0,0,0: 44:[52, 12] Operation: 44-32=12 Exploring Operation: 52-32=20, Resulting Numbers: [44, 20] Generated Node #0,0,1: 44:[44, 20] Operation: 52-32=20 Moving to Node #0,0,1 Current State: 44:[44, 20], Operations: ['66-34=32', '52-32=20'] Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,44 unequal: No Solution Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,44 unequal: No Solution Moving to Node #0,0,0 Current State: 44:[52, 12], Operations: ['66-34=32', '44-32=12'] Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,44 unequal: No Solution Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,44 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 40, 38, 1, 13 ]
66
[ "40+38=78", "13-1=12", "78-12=66" ]
Current State: 66:[40, 38, 1, 13], Operations: [] Exploring Operation: 40+38=78, Resulting Numbers: [1, 13, 78] Generated Node #2: [1, 13, 78] from Operation: 40+38=78 Current State: 66:[1, 13, 78], Operations: ['40+38=78'] Exploring Operation: 13-1=12, Resulting Numbers: [78, 12] Generated Node #3: [78, 12] from Operation: 13-1=12 Current State: 66:[78, 12], Operations: ['40+38=78', '13-1=12'] Exploring Operation: 78-12=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[40, 38, 1, 13], Operations: [] Exploring Operation: 40-38=2, Resulting Numbers: [1, 13, 2] Generated Node #0,0: 66:[1, 13, 2] Operation: 40-38=2 Moving to Node #0,0 Current State: 66:[1, 13, 2], Operations: ['40-38=2'] Exploring Operation: 13-1=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 66:[2, 12] Operation: 13-1=12 Moving to Node #0,0,0 Current State: 66:[2, 12], Operations: ['40-38=2', '13-1=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,66 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 86, 83, 11, 9 ]
38
[ "86-83=3", "9*3=27", "11+27=38" ]
Current State: 38:[86, 83, 11, 9], Operations: [] Exploring Operation: 86-83=3, Resulting Numbers: [11, 9, 3] Generated Node #2: [11, 9, 3] from Operation: 86-83=3 Current State: 38:[11, 9, 3], Operations: ['86-83=3'] Exploring Operation: 9*3=27, Resulting Numbers: [11, 27] Generated Node #3: [11, 27] from Operation: 9*3=27 Current State: 38:[11, 27], Operations: ['86-83=3', '9*3=27'] Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[86, 83, 11, 9], Operations: [] Exploring Operation: 86-11=75, Resulting Numbers: [83, 9, 75] Generated Node #0,0: 38:[83, 9, 75] Operation: 86-11=75 Exploring Operation: 86-83=3, Resulting Numbers: [11, 9, 3] Generated Node #0,1: 38:[11, 9, 3] Operation: 86-83=3 Exploring Operation: 83-11=72, Resulting Numbers: [86, 9, 72] Generated Node #0,2: 38:[86, 9, 72] Operation: 83-11=72 Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[11, 9, 3], Operations: ['86-83=3'] Exploring Operation: 11+9=20, Resulting Numbers: [3, 20] Generated Node #0,1,0: 38:[3, 20] Operation: 11+9=20 Exploring Operation: 11-9=2, Resulting Numbers: [3, 2] Generated Node #0,1,1: 38:[3, 2] Operation: 11-9=2 Exploring Operation: 9/3=3, Resulting Numbers: [11, 3] Generated Node #0,1,2: 38:[11, 3] Operation: 9/3=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 38:[3, 2], Operations: ['86-83=3', '11-9=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,38 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,38 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: 38:[3, 20], Operations: ['86-83=3', '11+9=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,38 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,38 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,38 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: 38:[11, 3], Operations: ['86-83=3', '9/3=3'] Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,38 unequal: No Solution Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,38 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: 38:[83, 9, 75], Operations: ['86-11=75'] Exploring Operation: 83-9=74, Resulting Numbers: [75, 74] Generated Node #0,0,0: 38:[75, 74] Operation: 83-9=74 Exploring Operation: 83-75=8, Resulting Numbers: [9, 8] Generated Node #0,0,1: 38:[9, 8] Operation: 83-75=8 Exploring Operation: 75-9=66, Resulting Numbers: [83, 66] Generated Node #0,0,2: 38:[83, 66] Operation: 75-9=66 Moving to Node #0,0,1 Current State: 38:[9, 8], Operations: ['86-11=75', '83-75=8'] Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,38 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,38 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[75, 74], Operations: ['86-11=75', '83-9=74'] Exploring Operation: 75-74=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 75+74=149, Resulting Numbers: [149] 149,38 unequal: No Solution Exploring Operation: 75*74=5550, Resulting Numbers: [5550] 5550,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[83, 66], Operations: ['86-11=75', '75-9=66'] Exploring Operation: 83-66=17, Resulting Numbers: [17] 17,38 unequal: No Solution Exploring Operation: 83*66=5478, Resulting Numbers: [5478] 5478,38 unequal: No Solution Exploring Operation: 83+66=149, Resulting Numbers: [149] 149,38 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: 38:[86, 9, 72], Operations: ['83-11=72'] Exploring Operation: 86-9=77, Resulting Numbers: [72, 77] Generated Node #0,2,0: 38:[72, 77] Operation: 86-9=77 Exploring Operation: 86-72=14, Resulting Numbers: [9, 14] Generated Node #0,2,1: 38:[9, 14] Operation: 86-72=14 Exploring Operation: 72/9=8, Resulting Numbers: [86, 8] Generated Node #0,2,2: 38:[86, 8] Operation: 72/9=8 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 38:[9, 14], Operations: ['83-11=72', '86-72=14'] Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,38 unequal: No Solution Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,38 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: 38:[86, 8], Operations: ['83-11=72', '72/9=8'] Exploring Operation: 86-8=78, Resulting Numbers: [78] 78,38 unequal: No Solution Exploring Operation: 86+8=94, Resulting Numbers: [94] 94,38 unequal: No Solution Exploring Operation: 86*8=688, Resulting Numbers: [688] 688,38 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: 38:[72, 77], Operations: ['83-11=72', '86-9=77'] Exploring Operation: 72*77=5544, Resulting Numbers: [5544] 5544,38 unequal: No Solution Exploring Operation: 77-72=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 72+77=149, Resulting Numbers: [149] 149,38 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