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
[ 16, 2, 19, 20 ]
14
[ "16-2=14", "20-19=1", "14*1=14" ]
Current State: 14:[16, 2, 19, 20], Operations: [] Exploring Operation: 16-2=14, Resulting Numbers: [19, 20, 14] Generated Node #2: [19, 20, 14] from Operation: 16-2=14 Current State: 14:[19, 20, 14], Operations: ['16-2=14'] Exploring Operation: 20-19=1, Resulting Numbers: [14, 1] Generated Node #3: [14, 1] from Operation: 20-19=1 Current State: 14:[14, 1], Operations: ['16-2=14', '20-19=1'] Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[16, 2, 19, 20], Operations: [] Exploring Operation: 19-16=3, Resulting Numbers: [2, 20, 3] Generated Node #0,0: 14:[2, 20, 3] Operation: 19-16=3 Exploring Operation: 20-16=4, Resulting Numbers: [2, 19, 4] Generated Node #0,1: 14:[2, 19, 4] Operation: 20-16=4 Exploring Operation: 20/2=10, Resulting Numbers: [16, 19, 10] Generated Node #0,2: 14:[16, 19, 10] Operation: 20/2=10 Exploring Operation: 20-19=1, Resulting Numbers: [16, 2, 1] Generated Node #0,3: 14:[16, 2, 1] Operation: 20-19=1 Moving to Node #0,3 Current State: 14:[16, 2, 1], Operations: ['20-19=1'] Exploring Operation: 16/2=8, Resulting Numbers: [1, 8] Generated Node #0,3,0: 14:[1, 8] Operation: 16/2=8 Exploring Operation: 16-1=15, Resulting Numbers: [2, 15] Generated Node #0,3,1: 14:[2, 15] Operation: 16-1=15 Exploring Operation: 16-2=14, Resulting Numbers: [1, 14] Generated Node #0,3,2: 14:[1, 14] Operation: 16-2=14 Exploring Operation: 16*1=16, Resulting Numbers: [2, 16] Generated Node #0,3,3: 14:[2, 16] Operation: 16*1=16 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 14:[2, 15], Operations: ['20-19=1', '16-1=15'] Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,14 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,14 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,14 unequal: No Solution No 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: 14:[1, 14], Operations: ['20-19=1', '16-2=14'] Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,14 unequal: No Solution Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[16, 2, 19, 20], Operations: [] Exploring Operation: 20-19=1, Resulting Numbers: [16, 2, 1] Generated Node #0,3: 14:[16, 2, 1] Operation: 20-19=1 Moving to Node #0,3 Current State: 14:[16, 2, 1], Operations: ['20-19=1'] Exploring Operation: 16-2=14, Resulting Numbers: [1, 14] Generated Node #0,3,2: 14:[1, 14] Operation: 16-2=14 Moving to Node #0,3,2 Current State: 14:[1, 14], Operations: ['20-19=1', '16-2=14'] Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 92, 5, 73, 3 ]
80
[ "92-73=19", "19-3=16", "5*16=80" ]
Current State: 80:[92, 5, 73, 3], Operations: [] Exploring Operation: 92-73=19, Resulting Numbers: [5, 3, 19] Generated Node #2: [5, 3, 19] from Operation: 92-73=19 Current State: 80:[5, 3, 19], Operations: ['92-73=19'] Exploring Operation: 19-3=16, Resulting Numbers: [5, 16] Generated Node #3: [5, 16] from Operation: 19-3=16 Current State: 80:[5, 16], Operations: ['92-73=19', '19-3=16'] Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[92, 5, 73, 3], Operations: [] Exploring Operation: 92-73=19, Resulting Numbers: [5, 3, 19] Generated Node #0,0: 80:[5, 3, 19] Operation: 92-73=19 Exploring Operation: 92-3=89, Resulting Numbers: [5, 73, 89] Generated Node #0,1: 80:[5, 73, 89] Operation: 92-3=89 Exploring Operation: 73+3=76, Resulting Numbers: [92, 5, 76] Generated Node #0,2: 80:[92, 5, 76] Operation: 73+3=76 Exploring Operation: 92-5=87, Resulting Numbers: [73, 3, 87] Generated Node #0,3: 80:[73, 3, 87] Operation: 92-5=87 Exploring Operation: 5+73=78, Resulting Numbers: [92, 3, 78] Generated Node #0,4: 80:[92, 3, 78] Operation: 5+73=78 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[5, 3, 19], Operations: ['92-73=19'] Exploring Operation: 5*3=15, Resulting Numbers: [19, 15] Generated Node #0,0,0: 80:[19, 15] Operation: 5*3=15 Exploring Operation: 19-3=16, Resulting Numbers: [5, 16] Generated Node #0,0,1: 80:[5, 16] Operation: 19-3=16 Exploring Operation: 5-3=2, Resulting Numbers: [19, 2] Generated Node #0,0,2: 80:[19, 2] Operation: 5-3=2 Exploring Operation: 3+19=22, Resulting Numbers: [5, 22] Generated Node #0,0,3: 80:[5, 22] Operation: 3+19=22 Exploring Operation: 5+3=8, Resulting Numbers: [19, 8] Generated Node #0,0,4: 80:[19, 8] Operation: 5+3=8 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 80:[5, 16], Operations: ['92-73=19', '19-3=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[92, 5, 73, 3], Operations: [] Exploring Operation: 92-73=19, Resulting Numbers: [5, 3, 19] Generated Node #0,0: 80:[5, 3, 19] Operation: 92-73=19 Moving to Node #0,0 Current State: 80:[5, 3, 19], Operations: ['92-73=19'] Exploring Operation: 19-3=16, Resulting Numbers: [5, 16] Generated Node #0,0,1: 80:[5, 16] Operation: 19-3=16 Moving to Node #0,0,1 Current State: 80:[5, 16], Operations: ['92-73=19', '19-3=16'] Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 87, 63, 51, 78 ]
21
[ "87+63=150", "51+78=129", "150-129=21" ]
Current State: 21:[87, 63, 51, 78], Operations: [] Exploring Operation: 87+63=150, Resulting Numbers: [51, 78, 150] Generated Node #2: [51, 78, 150] from Operation: 87+63=150 Current State: 21:[51, 78, 150], Operations: ['87+63=150'] Exploring Operation: 51+78=129, Resulting Numbers: [150, 129] Generated Node #3: [150, 129] from Operation: 51+78=129 Current State: 21:[150, 129], Operations: ['87+63=150', '51+78=129'] Exploring Operation: 150-129=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[87, 63, 51, 78], Operations: [] Exploring Operation: 87-78=9, Resulting Numbers: [63, 51, 9] Generated Node #0,0: 21:[63, 51, 9] Operation: 87-78=9 Exploring Operation: 78-63=15, Resulting Numbers: [87, 51, 15] Generated Node #0,1: 21:[87, 51, 15] Operation: 78-63=15 Exploring Operation: 87-63=24, Resulting Numbers: [51, 78, 24] Generated Node #0,2: 21:[51, 78, 24] Operation: 87-63=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[63, 51, 9], Operations: ['87-78=9'] Exploring Operation: 63-9=54, Resulting Numbers: [51, 54] Generated Node #0,0,0: 21:[51, 54] Operation: 63-9=54 Exploring Operation: 63-51=12, Resulting Numbers: [9, 12] Generated Node #0,0,1: 21:[9, 12] Operation: 63-51=12 Exploring Operation: 63/9=7, Resulting Numbers: [51, 7] Generated Node #0,0,2: 21:[51, 7] Operation: 63/9=7 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 21:[9, 12], Operations: ['87-78=9', '63-51=12'] Exploring Operation: 9*12=108, Resulting Numbers: [108] 108,21 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 9+12=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[87, 63, 51, 78], Operations: [] Exploring Operation: 87-78=9, Resulting Numbers: [63, 51, 9] Generated Node #0,0: 21:[63, 51, 9] Operation: 87-78=9 Moving to Node #0,0 Current State: 21:[63, 51, 9], Operations: ['87-78=9'] Exploring Operation: 63-51=12, Resulting Numbers: [9, 12] Generated Node #0,0,1: 21:[9, 12] Operation: 63-51=12 Moving to Node #0,0,1 Current State: 21:[9, 12], Operations: ['87-78=9', '63-51=12'] Exploring Operation: 9+12=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 2, 33, 33, 13 ]
59
[ "33+13=46", "2*46=92", "92-33=59" ]
Current State: 59:[2, 33, 33, 13], Operations: [] Exploring Operation: 33+13=46, Resulting Numbers: [2, 46] Generated Node #2: [2, 46] from Operation: 33+13=46 Current State: 59:[2, 46], Operations: ['33+13=46'] Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,59 equal: Goal Reached Exploring Operation: 92-33=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[2, 33, 33, 13], Operations: [] Exploring Operation: 2+33=35, Resulting Numbers: [33, 13, 35] Generated Node #0,0: 59:[33, 13, 35] Operation: 2+33=35 Exploring Operation: 2*33=66, Resulting Numbers: [33, 13, 66] Generated Node #0,1: 59:[33, 13, 66] Operation: 2*33=66 Exploring Operation: 2*33=66, Resulting Numbers: [33, 13, 66] Generated Node #0,2: 59:[33, 13, 66] Operation: 2*33=66 Exploring Operation: 2*13=26, Resulting Numbers: [33, 33, 26] Generated Node #0,3: 59:[33, 33, 26] Operation: 2*13=26 Exploring Operation: 2+33=35, Resulting Numbers: [33, 13, 35] Generated Node #0,4: 59:[33, 13, 35] Operation: 2+33=35 Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[33, 13, 66], Operations: ['2*33=66'] Exploring Operation: 13+66=79, Resulting Numbers: [33, 79] Generated Node #0,1,0: 59:[33, 79] Operation: 13+66=79 Exploring Operation: 66-13=53, Resulting Numbers: [33, 53] Generated Node #0,1,1: 59:[33, 53] Operation: 66-13=53 Exploring Operation: 33-13=20, Resulting Numbers: [66, 20] Generated Node #0,1,2: 59:[66, 20] Operation: 33-13=20 Exploring Operation: 66-33=33, Resulting Numbers: [13, 33] Generated Node #0,1,3: 59:[13, 33] Operation: 66-33=33 Exploring Operation: 33+13=46, Resulting Numbers: [66, 46] Generated Node #0,1,4: 59:[66, 46] Operation: 33+13=46 Moving to Node #0,1,4 Current State: 59:[66, 46], Operations: ['2*33=66', '33+13=46'] Exploring Operation: 66*46=3036, Resulting Numbers: [3036] 3036,59 unequal: No Solution Exploring Operation: 66-46=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 66+46=112, Resulting Numbers: [112] 112,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[33, 53], Operations: ['2*33=66', '66-13=53'] Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 33*53=1749, Resulting Numbers: [1749] 1749,59 unequal: No Solution Exploring Operation: 33+53=86, Resulting Numbers: [86] 86,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[33, 79], Operations: ['2*33=66', '13+66=79'] Exploring Operation: 33*79=2607, Resulting Numbers: [2607] 2607,59 unequal: No Solution Exploring Operation: 33+79=112, Resulting Numbers: [112] 112,59 unequal: No Solution Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[66, 20], Operations: ['2*33=66', '33-13=20'] Exploring Operation: 66*20=1320, Resulting Numbers: [1320] 1320,59 unequal: No Solution Exploring Operation: 66+20=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[13, 33], Operations: ['2*33=66', '66-33=33'] Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,59 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[33, 13, 66], Operations: ['2*33=66'] Exploring Operation: 13+66=79, Resulting Numbers: [33, 79] Generated Node #0,2,0: 59:[33, 79] Operation: 13+66=79 Exploring Operation: 66-13=53, Resulting Numbers: [33, 53] Generated Node #0,2,1: 59:[33, 53] Operation: 66-13=53 Exploring Operation: 33+13=46, Resulting Numbers: [66, 46] Generated Node #0,2,2: 59:[66, 46] Operation: 33+13=46 Exploring Operation: 33-13=20, Resulting Numbers: [66, 20] Generated Node #0,2,3: 59:[66, 20] Operation: 33-13=20 Exploring Operation: 66-33=33, Resulting Numbers: [13, 33] Generated Node #0,2,4: 59:[13, 33] Operation: 66-33=33 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 59:[66, 46], Operations: ['2*33=66', '33+13=46'] Exploring Operation: 66-46=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 66+46=112, Resulting Numbers: [112] 112,59 unequal: No Solution Exploring Operation: 66*46=3036, Resulting Numbers: [3036] 3036,59 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: 59:[33, 53], Operations: ['2*33=66', '66-13=53'] Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 33+53=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 33*53=1749, Resulting Numbers: [1749] 1749,59 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: 59:[33, 79], Operations: ['2*33=66', '13+66=79'] Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 33+79=112, Resulting Numbers: [112] 112,59 unequal: No Solution Exploring Operation: 33*79=2607, Resulting Numbers: [2607] 2607,59 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: 59:[66, 20], Operations: ['2*33=66', '33-13=20'] Exploring Operation: 66*20=1320, Resulting Numbers: [1320] 1320,59 unequal: No Solution Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 66+20=86, Resulting Numbers: [86] 86,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 59:[13, 33], Operations: ['2*33=66', '66-33=33'] Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,59 unequal: No Solution Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 59:[33, 33, 26], Operations: ['2*13=26'] Exploring Operation: 33-26=7, Resulting Numbers: [33, 7] Generated Node #0,3,0: 59:[33, 7] Operation: 33-26=7 Exploring Operation: 33+33=66, Resulting Numbers: [26, 66] Generated Node #0,3,1: 59:[26, 66] Operation: 33+33=66 Exploring Operation: 33+26=59, Resulting Numbers: [33, 59] Generated Node #0,3,2: 59:[33, 59] Operation: 33+26=59 Exploring Operation: 33+26=59, Resulting Numbers: [33, 59] Generated Node #0,3,3: 59:[33, 59] Operation: 33+26=59 Exploring Operation: 33-26=7, Resulting Numbers: [33, 7] Generated Node #0,3,4: 59:[33, 7] Operation: 33-26=7 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 59:[33, 59], Operations: ['2*13=26', '33+26=59'] Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,59 unequal: No Solution Exploring Operation: 33+59=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 33*59=1947, Resulting Numbers: [1947] 1947,59 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: 59:[33, 59], Operations: ['2*13=26', '33+26=59'] Exploring Operation: 33*59=1947, Resulting Numbers: [1947] 1947,59 unequal: No Solution Exploring Operation: 33+59=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,59 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: 59:[26, 66], Operations: ['2*13=26', '33+33=66'] Exploring Operation: 26*66=1716, Resulting Numbers: [1716] 1716,59 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 26+66=92, Resulting Numbers: [92] 92,59 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: 59:[33, 7], Operations: ['2*13=26', '33-26=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,59 unequal: No Solution Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 59:[33, 7], Operations: ['2*13=26', '33-26=7'] Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,59 unequal: No Solution Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,59 unequal: No Solution Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[33, 13, 35], Operations: ['2+33=35'] Exploring Operation: 35-13=22, Resulting Numbers: [33, 22] Generated Node #0,0,0: 59:[33, 22] Operation: 35-13=22 Exploring Operation: 33+13=46, Resulting Numbers: [35, 46] Generated Node #0,0,1: 59:[35, 46] Operation: 33+13=46 Exploring Operation: 33+35=68, Resulting Numbers: [13, 68] Generated Node #0,0,2: 59:[13, 68] Operation: 33+35=68 Exploring Operation: 13+35=48, Resulting Numbers: [33, 48] Generated Node #0,0,3: 59:[33, 48] Operation: 13+35=48 Exploring Operation: 33-13=20, Resulting Numbers: [35, 20] Generated Node #0,0,4: 59:[35, 20] Operation: 33-13=20 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 59:[35, 46], Operations: ['2+33=35', '33+13=46'] Exploring Operation: 35+46=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 35*46=1610, Resulting Numbers: [1610] 1610,59 unequal: No Solution Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,59 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: 59:[33, 48], Operations: ['2+33=35', '13+35=48'] Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,59 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: 59:[13, 68], Operations: ['2+33=35', '33+35=68'] Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,59 unequal: No Solution Exploring Operation: 13*68=884, Resulting Numbers: [884] 884,59 unequal: No Solution Exploring Operation: 13+68=81, Resulting Numbers: [81] 81,59 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: 59:[33, 22], Operations: ['2+33=35', '35-13=22'] Exploring Operation: 33*22=726, Resulting Numbers: [726] 726,59 unequal: No Solution Exploring Operation: 33+22=55, Resulting Numbers: [55] 55,59 unequal: No Solution Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,59 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: 59:[35, 20], Operations: ['2+33=35', '33-13=20'] Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 35+20=55, Resulting Numbers: [55] 55,59 unequal: No Solution Exploring Operation: 35*20=700, Resulting Numbers: [700] 700,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 59:[33, 13, 35], Operations: ['2+33=35'] Exploring Operation: 35-13=22, Resulting Numbers: [33, 22] Generated Node #0,4,0: 59:[33, 22] Operation: 35-13=22 Exploring Operation: 33+13=46, Resulting Numbers: [35, 46] Generated Node #0,4,1: 59:[35, 46] Operation: 33+13=46 Exploring Operation: 33+35=68, Resulting Numbers: [13, 68] Generated Node #0,4,2: 59:[13, 68] Operation: 33+35=68 Exploring Operation: 13+35=48, Resulting Numbers: [33, 48] Generated Node #0,4,3: 59:[33, 48] Operation: 13+35=48 Exploring Operation: 33-13=20, Resulting Numbers: [35, 20] Generated Node #0,4,4: 59:[35, 20] Operation: 33-13=20 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 59:[35, 46], Operations: ['2+33=35', '33+13=46'] Exploring Operation: 35+46=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 35*46=1610, Resulting Numbers: [1610] 1610,59 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: 59:[33, 48], Operations: ['2+33=35', '13+35=48'] Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,59 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: 59:[13, 68], Operations: ['2+33=35', '33+35=68'] Exploring Operation: 13+68=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 13*68=884, Resulting Numbers: [884] 884,59 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,59 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 #0,4,0 Current State: 59:[33, 22], Operations: ['2+33=35', '35-13=22'] Exploring Operation: 33+22=55, Resulting Numbers: [55] 55,59 unequal: No Solution Exploring Operation: 33*22=726, Resulting Numbers: [726] 726,59 unequal: No Solution Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,59 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: 59:[35, 20], Operations: ['2+33=35', '33-13=20'] Exploring Operation: 35+20=55, Resulting Numbers: [55] 55,59 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 35*20=700, Resulting Numbers: [700] 700,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 49, 44, 59, 10 ]
43
[ "59-49=10", "10/10=1", "44-1=43" ]
Current State: 43:[49, 44, 59, 10], Operations: [] Exploring Operation: 59-49=10, Resulting Numbers: [44, 10, 10] Generated Node #2: [44, 10, 10] from Operation: 59-49=10 Current State: 43:[44, 10, 10], Operations: ['59-49=10'] Exploring Operation: 10/10=1, Resulting Numbers: [44, 1] Generated Node #3: [44, 1] from Operation: 10/10=1 Current State: 43:[44, 1], Operations: ['59-49=10', '10/10=1'] Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[49, 44, 59, 10], Operations: [] Exploring Operation: 49-10=39, Resulting Numbers: [44, 59, 39] Generated Node #0,0: 43:[44, 59, 39] Operation: 49-10=39 Exploring Operation: 59-10=49, Resulting Numbers: [49, 44, 49] Generated Node #0,1: 43:[49, 44, 49] Operation: 59-10=49 Moving to Node #0,1 Current State: 43:[49, 44, 49], Operations: ['59-10=49'] Exploring Operation: 49/49=1, Resulting Numbers: [44, 1] Generated Node #0,1,0: 43:[44, 1] Operation: 49/49=1 Exploring Operation: 49-44=5, Resulting Numbers: [49, 5] Generated Node #0,1,1: 43:[49, 5] Operation: 49-44=5 Moving to Node #0,0 Current State: 43:[44, 59, 39], Operations: ['49-10=39'] Exploring Operation: 59-44=15, Resulting Numbers: [39, 15] Generated Node #0,0,0: 43:[39, 15] Operation: 59-44=15 Exploring Operation: 59-39=20, Resulting Numbers: [44, 20] Generated Node #0,0,1: 43:[44, 20] Operation: 59-39=20 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 43:[44, 20], Operations: ['49-10=39', '59-39=20'] Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,43 unequal: No Solution Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,43 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 #0,0,0 Current State: 43:[39, 15], Operations: ['49-10=39', '59-44=15'] Exploring Operation: 39+15=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,43 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: 43:[44, 1], Operations: ['59-10=49', '49/49=1'] Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[49, 44, 59, 10], Operations: [] Exploring Operation: 59-10=49, Resulting Numbers: [49, 44, 49] Generated Node #0,1: 43:[49, 44, 49] Operation: 59-10=49 Moving to Node #0,1 Current State: 43:[49, 44, 49], Operations: ['59-10=49'] Exploring Operation: 49/49=1, Resulting Numbers: [44, 1] Generated Node #0,1,0: 43:[44, 1] Operation: 49/49=1 Moving to Node #0,1,0 Current State: 43:[44, 1], Operations: ['59-10=49', '49/49=1'] Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 37, 42, 81, 84 ]
69
[ "84-81=3", "37*3=111", "111-42=69" ]
Current State: 69:[37, 42, 81, 84], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [37, 42, 3] Generated Node #2: [37, 42, 3] from Operation: 84-81=3 Current State: 69:[37, 42, 3], Operations: ['84-81=3'] Exploring Operation: 37*3=111, Resulting Numbers: [42, 111] Generated Node #3: [42, 111] from Operation: 37*3=111 Current State: 69:[42, 111], Operations: ['84-81=3', '37*3=111'] Exploring Operation: 111-42=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[37, 42, 81, 84], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [37, 42, 3] Generated Node #0,0: 69:[37, 42, 3] Operation: 84-81=3 Exploring Operation: 42-37=5, Resulting Numbers: [81, 84, 5] Generated Node #0,1: 69:[81, 84, 5] Operation: 42-37=5 Exploring Operation: 37+42=79, Resulting Numbers: [81, 84, 79] Generated Node #0,2: 69:[81, 84, 79] Operation: 37+42=79 Exploring Operation: 84/42=2, Resulting Numbers: [37, 81, 2] Generated Node #0,3: 69:[37, 81, 2] Operation: 84/42=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 69:[37, 81, 2], Operations: ['84/42=2'] Exploring Operation: 37*2=74, Resulting Numbers: [81, 74] Generated Node #0,3,0: 69:[81, 74] Operation: 37*2=74 Exploring Operation: 37-2=35, Resulting Numbers: [81, 35] Generated Node #0,3,1: 69:[81, 35] Operation: 37-2=35 Exploring Operation: 81-2=79, Resulting Numbers: [37, 79] Generated Node #0,3,2: 69:[37, 79] Operation: 81-2=79 Exploring Operation: 81-37=44, Resulting Numbers: [2, 44] Generated Node #0,3,3: 69:[2, 44] Operation: 81-37=44 Moving to Node #0,3,0 Current State: 69:[81, 74], Operations: ['84/42=2', '37*2=74'] Exploring Operation: 81*74=5994, Resulting Numbers: [5994] 5994,69 unequal: No Solution Exploring Operation: 81-74=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 81+74=155, Resulting Numbers: [155] 155,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[2, 44], Operations: ['84/42=2', '81-37=44'] Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,69 unequal: No Solution Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,69 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,69 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[37, 79], Operations: ['84/42=2', '81-2=79'] Exploring Operation: 37+79=116, Resulting Numbers: [116] 116,69 unequal: No Solution Exploring Operation: 37*79=2923, Resulting Numbers: [2923] 2923,69 unequal: No Solution Exploring Operation: 79-37=42, Resulting Numbers: [42] 42,69 unequal: No Solution Moving to Node #0,3,1 Current State: 69:[81, 35], Operations: ['84/42=2', '37-2=35'] Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,69 unequal: No Solution Exploring Operation: 81+35=116, Resulting Numbers: [116] 116,69 unequal: No Solution Exploring Operation: 81*35=2835, Resulting Numbers: [2835] 2835,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[81, 84, 5], Operations: ['42-37=5'] Exploring Operation: 81+5=86, Resulting Numbers: [84, 86] Generated Node #0,1,0: 69:[84, 86] Operation: 81+5=86 Exploring Operation: 84-5=79, Resulting Numbers: [81, 79] Generated Node #0,1,1: 69:[81, 79] Operation: 84-5=79 Exploring Operation: 84-81=3, Resulting Numbers: [5, 3] Generated Node #0,1,2: 69:[5, 3] Operation: 84-81=3 Exploring Operation: 81-5=76, Resulting Numbers: [84, 76] Generated Node #0,1,3: 69:[84, 76] Operation: 81-5=76 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 69:[5, 3], Operations: ['42-37=5', '84-81=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,69 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,69 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: 69:[81, 79], Operations: ['42-37=5', '84-5=79'] Exploring Operation: 81*79=6399, Resulting Numbers: [6399] 6399,69 unequal: No Solution Exploring Operation: 81-79=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 81+79=160, Resulting Numbers: [160] 160,69 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: 69:[84, 76], Operations: ['42-37=5', '81-5=76'] Exploring Operation: 84*76=6384, Resulting Numbers: [6384] 6384,69 unequal: No Solution Exploring Operation: 84+76=160, Resulting Numbers: [160] 160,69 unequal: No Solution Exploring Operation: 84-76=8, Resulting Numbers: [8] 8,69 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: 69:[84, 86], Operations: ['42-37=5', '81+5=86'] Exploring Operation: 84+86=170, Resulting Numbers: [170] 170,69 unequal: No Solution Exploring Operation: 84*86=7224, Resulting Numbers: [7224] 7224,69 unequal: No Solution Exploring Operation: 86-84=2, Resulting Numbers: [2] 2,69 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[37, 42, 3], Operations: ['84-81=3'] Exploring Operation: 37+42=79, Resulting Numbers: [3, 79] Generated Node #0,0,0: 69:[3, 79] Operation: 37+42=79 Exploring Operation: 37-3=34, Resulting Numbers: [42, 34] Generated Node #0,0,1: 69:[42, 34] Operation: 37-3=34 Exploring Operation: 42/3=14, Resulting Numbers: [37, 14] Generated Node #0,0,2: 69:[37, 14] Operation: 42/3=14 Exploring Operation: 42-37=5, Resulting Numbers: [3, 5] Generated Node #0,0,3: 69:[3, 5] Operation: 42-37=5 Moving to Node #0,0,3 Current State: 69:[3, 5], Operations: ['84-81=3', '42-37=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[3, 79], Operations: ['84-81=3', '37+42=79'] Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 3*79=237, Resulting Numbers: [237] 237,69 unequal: No Solution Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,69 unequal: No Solution Moving to Node #0,0,2 Current State: 69:[37, 14], Operations: ['84-81=3', '42/3=14'] Exploring Operation: 37*14=518, Resulting Numbers: [518] 518,69 unequal: No Solution Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 37+14=51, Resulting Numbers: [51] 51,69 unequal: No Solution Moving to Node #0,0,1 Current State: 69:[42, 34], Operations: ['84-81=3', '37-3=34'] Exploring Operation: 42*34=1428, Resulting Numbers: [1428] 1428,69 unequal: No Solution Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,69 unequal: No Solution Exploring Operation: 42+34=76, Resulting Numbers: [76] 76,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[81, 84, 79], Operations: ['37+42=79'] Exploring Operation: 84-79=5, Resulting Numbers: [81, 5] Generated Node #0,2,0: 69:[81, 5] Operation: 84-79=5 Exploring Operation: 81+84=165, Resulting Numbers: [79, 165] Generated Node #0,2,1: 69:[79, 165] Operation: 81+84=165 Exploring Operation: 84-81=3, Resulting Numbers: [79, 3] Generated Node #0,2,2: 69:[79, 3] Operation: 84-81=3 Exploring Operation: 81-79=2, Resulting Numbers: [84, 2] Generated Node #0,2,3: 69:[84, 2] Operation: 81-79=2 Moving to Node #0,2,2 Current State: 69:[79, 3], Operations: ['37+42=79', '84-81=3'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,69 unequal: No Solution Exploring Operation: 79*3=237, Resulting Numbers: [237] 237,69 unequal: No Solution Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[81, 5], Operations: ['37+42=79', '84-79=5'] Exploring Operation: 81+5=86, Resulting Numbers: [86] 86,69 unequal: No Solution Exploring Operation: 81*5=405, Resulting Numbers: [405] 405,69 unequal: No Solution Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[84, 2], Operations: ['37+42=79', '81-79=2'] Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,69 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,69 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 84*2=168, Resulting Numbers: [168] 168,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[79, 165], Operations: ['37+42=79', '81+84=165'] Exploring Operation: 165-79=86, Resulting Numbers: [86] 86,69 unequal: No Solution Exploring Operation: 79+165=244, Resulting Numbers: [244] 244,69 unequal: No Solution Exploring Operation: 79*165=13035, Resulting Numbers: [13035] 13035,69 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
[ 76, 65, 75, 22 ]
73
[ "76-65=11", "22/11=2", "75-2=73" ]
Current State: 73:[76, 65, 75, 22], Operations: [] Exploring Operation: 76-65=11, Resulting Numbers: [75, 22, 11] Generated Node #2: [75, 22, 11] from Operation: 76-65=11 Current State: 73:[75, 22, 11], Operations: ['76-65=11'] 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: ['76-65=11', '22/11=2'] Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[76, 65, 75, 22], Operations: [] Exploring Operation: 65+22=87, Resulting Numbers: [76, 75, 87] Generated Node #0,0: 73:[76, 75, 87] Operation: 65+22=87 Exploring Operation: 76-22=54, Resulting Numbers: [65, 75, 54] Generated Node #0,1: 73:[65, 75, 54] Operation: 76-22=54 Exploring Operation: 75-22=53, Resulting Numbers: [76, 65, 53] Generated Node #0,2: 73:[76, 65, 53] Operation: 75-22=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[76, 75, 87], Operations: ['65+22=87'] Exploring Operation: 76-75=1, Resulting Numbers: [87, 1] Generated Node #0,0,0: 73:[87, 1] Operation: 76-75=1 Exploring Operation: 87-76=11, Resulting Numbers: [75, 11] Generated Node #0,0,1: 73:[75, 11] Operation: 87-76=11 Exploring Operation: 87-75=12, Resulting Numbers: [76, 12] Generated Node #0,0,2: 73:[76, 12] Operation: 87-75=12 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[75, 11], Operations: ['65+22=87', '87-76=11'] Exploring Operation: 75-11=64, Resulting Numbers: [64] 64,73 unequal: No Solution Exploring Operation: 75*11=825, Resulting Numbers: [825] 825,73 unequal: No Solution Exploring Operation: 75+11=86, Resulting Numbers: [86] 86,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 73:[76, 12], Operations: ['65+22=87', '87-75=12'] Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,73 unequal: No Solution Exploring Operation: 76+12=88, Resulting Numbers: [88] 88,73 unequal: No Solution Exploring Operation: 76*12=912, Resulting Numbers: [912] 912,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[87, 1], Operations: ['65+22=87', '76-75=1'] Exploring Operation: 87/1=87, Resulting Numbers: [87] 87,73 unequal: No Solution Exploring Operation: 87-1=86, Resulting Numbers: [86] 86,73 unequal: No Solution Exploring Operation: 87*1=87, Resulting Numbers: [87] 87,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[65, 75, 54], Operations: ['76-22=54'] Exploring Operation: 75-54=21, Resulting Numbers: [65, 21] Generated Node #0,1,0: 73:[65, 21] Operation: 75-54=21 Exploring Operation: 65+54=119, Resulting Numbers: [75, 119] Generated Node #0,1,1: 73:[75, 119] Operation: 65+54=119 Exploring Operation: 65-54=11, Resulting Numbers: [75, 11] Generated Node #0,1,2: 73:[75, 11] Operation: 65-54=11 Moving to Node #0,1,1 Current State: 73:[75, 119], Operations: ['76-22=54', '65+54=119'] Exploring Operation: 119-75=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 75*119=8925, Resulting Numbers: [8925] 8925,73 unequal: No Solution Exploring Operation: 75+119=194, Resulting Numbers: [194] 194,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[65, 21], Operations: ['76-22=54', '75-54=21'] Exploring Operation: 65*21=1365, Resulting Numbers: [1365] 1365,73 unequal: No Solution Exploring Operation: 65-21=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 65+21=86, Resulting Numbers: [86] 86,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[75, 11], Operations: ['76-22=54', '65-54=11'] Exploring Operation: 75*11=825, Resulting Numbers: [825] 825,73 unequal: No Solution Exploring Operation: 75-11=64, Resulting Numbers: [64] 64,73 unequal: No Solution Exploring Operation: 75+11=86, Resulting Numbers: [86] 86,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[76, 65, 53], Operations: ['75-22=53'] Exploring Operation: 65+53=118, Resulting Numbers: [76, 118] Generated Node #0,2,0: 73:[76, 118] Operation: 65+53=118 Exploring Operation: 76-53=23, Resulting Numbers: [65, 23] Generated Node #0,2,1: 73:[65, 23] Operation: 76-53=23 Exploring Operation: 76+53=129, Resulting Numbers: [65, 129] Generated Node #0,2,2: 73:[65, 129] Operation: 76+53=129 Moving to Node #0,2,0 Current State: 73:[76, 118], Operations: ['75-22=53', '65+53=118'] Exploring Operation: 76*118=8968, Resulting Numbers: [8968] 8968,73 unequal: No Solution Exploring Operation: 76+118=194, Resulting Numbers: [194] 194,73 unequal: No Solution Exploring Operation: 118-76=42, Resulting Numbers: [42] 42,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[65, 23], Operations: ['75-22=53', '76-53=23'] Exploring Operation: 65*23=1495, Resulting Numbers: [1495] 1495,73 unequal: No Solution Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,73 unequal: No Solution Exploring Operation: 65+23=88, Resulting Numbers: [88] 88,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[65, 129], Operations: ['75-22=53', '76+53=129'] Exploring Operation: 129-65=64, Resulting Numbers: [64] 64,73 unequal: No Solution Exploring Operation: 65+129=194, Resulting Numbers: [194] 194,73 unequal: No Solution Exploring Operation: 65*129=8385, Resulting Numbers: [8385] 8385,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 30, 32, 98, 14 ]
91
[ "32-30=2", "14/2=7", "98-7=91" ]
Current State: 91:[30, 32, 98, 14], Operations: [] Exploring Operation: 32-30=2, Resulting Numbers: [98, 14, 2] Generated Node #2: [98, 14, 2] from Operation: 32-30=2 Current State: 91:[98, 14, 2], Operations: ['32-30=2'] Exploring Operation: 14/2=7, Resulting Numbers: [98, 7] Generated Node #3: [98, 7] from Operation: 14/2=7 Current State: 91:[98, 7], Operations: ['32-30=2', '14/2=7'] Exploring Operation: 98-7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[30, 32, 98, 14], Operations: [] Exploring Operation: 98/14=7, Resulting Numbers: [30, 32, 7] Generated Node #0,0: 91:[30, 32, 7] Operation: 98/14=7 Exploring Operation: 30-14=16, Resulting Numbers: [32, 98, 16] Generated Node #0,1: 91:[32, 98, 16] Operation: 30-14=16 Exploring Operation: 32-30=2, Resulting Numbers: [98, 14, 2] Generated Node #0,2: 91:[98, 14, 2] Operation: 32-30=2 Exploring Operation: 32-14=18, Resulting Numbers: [30, 98, 18] Generated Node #0,3: 91:[30, 98, 18] Operation: 32-14=18 Moving to Node #0,2 Current State: 91:[98, 14, 2], Operations: ['32-30=2'] Exploring Operation: 98/14=7, Resulting Numbers: [2, 7] Generated Node #0,2,0: 91:[2, 7] Operation: 98/14=7 Exploring Operation: 98-2=96, Resulting Numbers: [14, 96] Generated Node #0,2,1: 91:[14, 96] Operation: 98-2=96 Exploring Operation: 14-2=12, Resulting Numbers: [98, 12] Generated Node #0,2,2: 91:[98, 12] Operation: 14-2=12 Exploring Operation: 14/2=7, Resulting Numbers: [98, 7] Generated Node #0,2,3: 91:[98, 7] Operation: 14/2=7 Moving to Node #0,3 Current State: 91:[30, 98, 18], Operations: ['32-14=18'] Exploring Operation: 98-18=80, Resulting Numbers: [30, 80] Generated Node #0,3,0: 91:[30, 80] Operation: 98-18=80 Exploring Operation: 30+98=128, Resulting Numbers: [18, 128] Generated Node #0,3,1: 91:[18, 128] Operation: 30+98=128 Exploring Operation: 98-30=68, Resulting Numbers: [18, 68] Generated Node #0,3,2: 91:[18, 68] Operation: 98-30=68 Exploring Operation: 30-18=12, Resulting Numbers: [98, 12] Generated Node #0,3,3: 91:[98, 12] Operation: 30-18=12 Moving to Node #0,1 Current State: 91:[32, 98, 16], Operations: ['30-14=16'] Exploring Operation: 98-16=82, Resulting Numbers: [32, 82] Generated Node #0,1,0: 91:[32, 82] Operation: 98-16=82 Exploring Operation: 32/16=2, Resulting Numbers: [98, 2] Generated Node #0,1,1: 91:[98, 2] Operation: 32/16=2 Exploring Operation: 32-16=16, Resulting Numbers: [98, 16] Generated Node #0,1,2: 91:[98, 16] Operation: 32-16=16 Exploring Operation: 98-32=66, Resulting Numbers: [16, 66] Generated Node #0,1,3: 91:[16, 66] Operation: 98-32=66 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 91:[98, 16], Operations: ['30-14=16', '32-16=16'] Exploring Operation: 98+16=114, Resulting Numbers: [114] 114,91 unequal: No Solution Exploring Operation: 98*16=1568, Resulting Numbers: [1568] 1568,91 unequal: No Solution Exploring Operation: 98-16=82, Resulting Numbers: [82] 82,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 91:[98, 2], Operations: ['30-14=16', '32/16=2'] Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,91 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,91 unequal: No Solution Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,91 unequal: No Solution Exploring Operation: 98*2=196, Resulting Numbers: [196] 196,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 91:[32, 82], Operations: ['30-14=16', '98-16=82'] Exploring Operation: 32+82=114, Resulting Numbers: [114] 114,91 unequal: No Solution Exploring Operation: 82-32=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 32*82=2624, Resulting Numbers: [2624] 2624,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 91:[16, 66], Operations: ['30-14=16', '98-32=66'] Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 16*66=1056, Resulting Numbers: [1056] 1056,91 unequal: No Solution Exploring Operation: 16+66=82, Resulting Numbers: [82] 82,91 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: 91:[30, 32, 7], Operations: ['98/14=7'] Exploring Operation: 30+32=62, Resulting Numbers: [7, 62] Generated Node #0,0,0: 91:[7, 62] Operation: 30+32=62 Exploring Operation: 32-7=25, Resulting Numbers: [30, 25] Generated Node #0,0,1: 91:[30, 25] Operation: 32-7=25 Exploring Operation: 32-30=2, Resulting Numbers: [7, 2] Generated Node #0,0,2: 91:[7, 2] Operation: 32-30=2 Exploring Operation: 30-7=23, Resulting Numbers: [32, 23] Generated Node #0,0,3: 91:[32, 23] Operation: 30-7=23 Moving to Node #0,2,0 Current State: 91:[2, 7], Operations: ['32-30=2', '98/14=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,91 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[7, 2], Operations: ['98/14=7', '32-30=2'] Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,91 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[14, 96], Operations: ['32-30=2', '98-2=96'] Exploring Operation: 96-14=82, Resulting Numbers: [82] 82,91 unequal: No Solution Exploring Operation: 14+96=110, Resulting Numbers: [110] 110,91 unequal: No Solution Exploring Operation: 14*96=1344, Resulting Numbers: [1344] 1344,91 unequal: No Solution Moving to Node #0,2,3 Current State: 91:[98, 7], Operations: ['32-30=2', '14/2=7'] Exploring Operation: 98*7=686, Resulting Numbers: [686] 686,91 unequal: No Solution Exploring Operation: 98-7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[30, 32, 98, 14], Operations: [] Exploring Operation: 32-30=2, Resulting Numbers: [98, 14, 2] Generated Node #0,2: 91:[98, 14, 2] Operation: 32-30=2 Moving to Node #0,2 Current State: 91:[98, 14, 2], Operations: ['32-30=2'] Exploring Operation: 14/2=7, Resulting Numbers: [98, 7] Generated Node #0,2,3: 91:[98, 7] Operation: 14/2=7 Moving to Node #0,2,3 Current State: 91:[98, 7], Operations: ['32-30=2', '14/2=7'] Exploring Operation: 98-7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
0.958333
hs_4
mult_heuristic
[ 2, 5, 33, 20 ]
65
[ "2+33=35", "5*20=100", "100-35=65" ]
Current State: 65:[2, 5, 33, 20], Operations: [] Exploring Operation: 2+33=35, Resulting Numbers: [5, 20, 35] Generated Node #2: [5, 20, 35] from Operation: 2+33=35 Current State: 65:[5, 20, 35], Operations: ['2+33=35'] Exploring Operation: 5*20=100, Resulting Numbers: [35, 100] Generated Node #3: [35, 100] from Operation: 5*20=100 Current State: 65:[35, 100], Operations: ['2+33=35', '5*20=100'] Exploring Operation: 100-35=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[2, 5, 33, 20], Operations: [] Exploring Operation: 33+20=53, Resulting Numbers: [2, 5, 53] Generated Node #0,0: 65:[2, 5, 53] Operation: 33+20=53 Exploring Operation: 20/5=4, Resulting Numbers: [2, 33, 4] Generated Node #0,1: 65:[2, 33, 4] Operation: 20/5=4 Exploring Operation: 20/2=10, Resulting Numbers: [5, 33, 10] Generated Node #0,2: 65:[5, 33, 10] Operation: 20/2=10 Exploring Operation: 33-20=13, Resulting Numbers: [2, 5, 13] Generated Node #0,3: 65:[2, 5, 13] Operation: 33-20=13 Exploring Operation: 2*33=66, Resulting Numbers: [5, 20, 66] Generated Node #0,4: 65:[5, 20, 66] Operation: 2*33=66 Moving to Node #0,3 Current State: 65:[2, 5, 13], Operations: ['33-20=13'] Exploring Operation: 5-2=3, Resulting Numbers: [13, 3] Generated Node #0,3,0: 65:[13, 3] Operation: 5-2=3 Exploring Operation: 13-2=11, Resulting Numbers: [5, 11] Generated Node #0,3,1: 65:[5, 11] Operation: 13-2=11 Exploring Operation: 2*5=10, Resulting Numbers: [13, 10] Generated Node #0,3,2: 65:[13, 10] Operation: 2*5=10 Exploring Operation: 2+5=7, Resulting Numbers: [13, 7] Generated Node #0,3,3: 65:[13, 7] Operation: 2+5=7 Exploring Operation: 2+13=15, Resulting Numbers: [5, 15] Generated Node #0,3,4: 65:[5, 15] Operation: 2+13=15 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 65:[13, 3], Operations: ['33-20=13', '5-2=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,65 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,65 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 65:[5, 11], Operations: ['33-20=13', '13-2=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 65:[13, 7], Operations: ['33-20=13', '2+5=7'] Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,65 unequal: No Solution Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,65 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 65:[5, 15], Operations: ['33-20=13', '2+13=15'] Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,65 unequal: No Solution Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,65 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 65:[13, 10], Operations: ['33-20=13', '2*5=10'] Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,65 unequal: No Solution Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,65 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: 65:[5, 20, 66], Operations: ['2*33=66'] Exploring Operation: 5+66=71, Resulting Numbers: [20, 71] Generated Node #0,4,0: 65:[20, 71] Operation: 5+66=71 Exploring Operation: 66-5=61, Resulting Numbers: [20, 61] Generated Node #0,4,1: 65:[20, 61] Operation: 66-5=61 Exploring Operation: 5+20=25, Resulting Numbers: [66, 25] Generated Node #0,4,2: 65:[66, 25] Operation: 5+20=25 Exploring Operation: 20-5=15, Resulting Numbers: [66, 15] Generated Node #0,4,3: 65:[66, 15] Operation: 20-5=15 Exploring Operation: 20/5=4, Resulting Numbers: [66, 4] Generated Node #0,4,4: 65:[66, 4] Operation: 20/5=4 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 65:[66, 4], Operations: ['2*33=66', '20/5=4'] Exploring Operation: 66*4=264, Resulting Numbers: [264] 264,65 unequal: No Solution Exploring Operation: 66+4=70, Resulting Numbers: [70] 70,65 unequal: No Solution Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 65:[66, 15], Operations: ['2*33=66', '20-5=15'] Exploring Operation: 66-15=51, Resulting Numbers: [51] 51,65 unequal: No Solution Exploring Operation: 66*15=990, Resulting Numbers: [990] 990,65 unequal: No Solution Exploring Operation: 66+15=81, Resulting Numbers: [81] 81,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 65:[20, 61], Operations: ['2*33=66', '66-5=61'] Exploring Operation: 20*61=1220, Resulting Numbers: [1220] 1220,65 unequal: No Solution Exploring Operation: 20+61=81, Resulting Numbers: [81] 81,65 unequal: No Solution Exploring Operation: 61-20=41, Resulting Numbers: [41] 41,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 65:[20, 71], Operations: ['2*33=66', '5+66=71'] Exploring Operation: 20*71=1420, Resulting Numbers: [1420] 1420,65 unequal: No Solution Exploring Operation: 71-20=51, Resulting Numbers: [51] 51,65 unequal: No Solution Exploring Operation: 20+71=91, Resulting Numbers: [91] 91,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 65:[66, 25], Operations: ['2*33=66', '5+20=25'] Exploring Operation: 66*25=1650, Resulting Numbers: [1650] 1650,65 unequal: No Solution Exploring Operation: 66-25=41, Resulting Numbers: [41] 41,65 unequal: No Solution Exploring Operation: 66+25=91, Resulting Numbers: [91] 91,65 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: 65:[2, 5, 53], Operations: ['33+20=53'] Exploring Operation: 2+5=7, Resulting Numbers: [53, 7] Generated Node #0,0,0: 65:[53, 7] Operation: 2+5=7 Exploring Operation: 5-2=3, Resulting Numbers: [53, 3] Generated Node #0,0,1: 65:[53, 3] Operation: 5-2=3 Exploring Operation: 2+53=55, Resulting Numbers: [5, 55] Generated Node #0,0,2: 65:[5, 55] Operation: 2+53=55 Exploring Operation: 5+53=58, Resulting Numbers: [2, 58] Generated Node #0,0,3: 65:[2, 58] Operation: 5+53=58 Exploring Operation: 53-2=51, Resulting Numbers: [5, 51] Generated Node #0,0,4: 65:[5, 51] Operation: 53-2=51 Moving to Node #0,2 Current State: 65:[5, 33, 10], Operations: ['20/2=10'] Exploring Operation: 33+10=43, Resulting Numbers: [5, 43] Generated Node #0,2,0: 65:[5, 43] Operation: 33+10=43 Exploring Operation: 5+10=15, Resulting Numbers: [33, 15] Generated Node #0,2,1: 65:[33, 15] Operation: 5+10=15 Exploring Operation: 33-5=28, Resulting Numbers: [10, 28] Generated Node #0,2,2: 65:[10, 28] Operation: 33-5=28 Exploring Operation: 10-5=5, Resulting Numbers: [33, 5] Generated Node #0,2,3: 65:[33, 5] Operation: 10-5=5 Exploring Operation: 33-10=23, Resulting Numbers: [5, 23] Generated Node #0,2,4: 65:[5, 23] Operation: 33-10=23 Moving to Node #0,1 Current State: 65:[2, 33, 4], Operations: ['20/5=4'] Exploring Operation: 2+33=35, Resulting Numbers: [4, 35] Generated Node #0,1,0: 65:[4, 35] Operation: 2+33=35 Exploring Operation: 33-4=29, Resulting Numbers: [2, 29] Generated Node #0,1,1: 65:[2, 29] Operation: 33-4=29 Exploring Operation: 2+4=6, Resulting Numbers: [33, 6] Generated Node #0,1,2: 65:[33, 6] Operation: 2+4=6 Exploring Operation: 33-2=31, Resulting Numbers: [4, 31] Generated Node #0,1,3: 65:[4, 31] Operation: 33-2=31 Exploring Operation: 2*33=66, Resulting Numbers: [4, 66] Generated Node #0,1,4: 65:[4, 66] Operation: 2*33=66 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 65:[4, 66], Operations: ['20/5=4', '2*33=66'] Exploring Operation: 4*66=264, Resulting Numbers: [264] 264,65 unequal: No Solution Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,65 unequal: No Solution Exploring Operation: 4+66=70, Resulting Numbers: [70] 70,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[2, 29], Operations: ['20/5=4', '33-4=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,65 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 65:[4, 31], Operations: ['20/5=4', '33-2=31'] Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,65 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[33, 6], Operations: ['20/5=4', '2+4=6'] Exploring Operation: 33+6=39, Resulting Numbers: [39] 39,65 unequal: No Solution Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 33*6=198, Resulting Numbers: [198] 198,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[4, 35], Operations: ['20/5=4', '2+33=35'] Exploring Operation: 4*35=140, Resulting Numbers: [140] 140,65 unequal: No Solution Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,65 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,65 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: 65:[5, 55], Operations: ['33+20=53', '2+53=55'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 5*55=275, Resulting Numbers: [275] 275,65 unequal: No Solution Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,65 unequal: No Solution Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,65 unequal: No Solution Moving to Node #0,2,4 Current State: 65:[5, 23], Operations: ['20/2=10', '33-10=23'] Exploring Operation: 5*23=115, Resulting Numbers: [115] 115,65 unequal: No Solution Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,65 unequal: No Solution Exploring Operation: 5+23=28, Resulting Numbers: [28] 28,65 unequal: No Solution Moving to Node #0,0,3 Current State: 65:[2, 58], Operations: ['33+20=53', '5+53=58'] Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,65 unequal: No Solution Exploring Operation: 2*58=116, Resulting Numbers: [116] 116,65 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,65 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[53, 7], Operations: ['33+20=53', '2+5=7'] Exploring Operation: 53*7=371, Resulting Numbers: [371] 371,65 unequal: No Solution Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,65 unequal: No Solution Exploring Operation: 53+7=60, Resulting Numbers: [60] 60,65 unequal: No Solution Moving to Node #0,0,4 Current State: 65:[5, 51], Operations: ['33+20=53', '53-2=51'] Exploring Operation: 5*51=255, Resulting Numbers: [255] 255,65 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,65 unequal: No Solution Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[53, 3], Operations: ['33+20=53', '5-2=3'] Exploring Operation: 53*3=159, Resulting Numbers: [159] 159,65 unequal: No Solution Exploring Operation: 53+3=56, Resulting Numbers: [56] 56,65 unequal: No Solution Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[10, 28], Operations: ['20/2=10', '33-5=28'] Exploring Operation: 10*28=280, Resulting Numbers: [280] 280,65 unequal: No Solution Exploring Operation: 10+28=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,65 unequal: No Solution Moving to Node #0,2,3 Current State: 65:[33, 5], Operations: ['20/2=10', '10-5=5'] Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,65 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[33, 15], Operations: ['20/2=10', '5+10=15'] Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,65 unequal: No Solution Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,65 unequal: No Solution Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[5, 43], Operations: ['20/2=10', '33+10=43'] Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 5*43=215, Resulting Numbers: [215] 215,65 unequal: No Solution Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,65 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 20, 61, 30, 71 ]
88
[ "61+71=132", "20*132=2640", "2640/30=88" ]
Current State: 88:[20, 61, 30, 71], Operations: [] Exploring Operation: 61+71=132, Resulting Numbers: [20, 30, 132] Generated Node #2: [20, 30, 132] from Operation: 61+71=132 Current State: 88:[20, 30, 132], Operations: ['61+71=132'] Exploring Operation: 20*132=2640, Resulting Numbers: [30, 2640] Generated Node #3: [30, 2640] from Operation: 20*132=2640 Current State: 88:[30, 2640], Operations: ['61+71=132', '20*132=2640'] Exploring Operation: 2640/30=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[20, 61, 30, 71], Operations: [] Exploring Operation: 71-61=10, Resulting Numbers: [20, 30, 10] Generated Node #0,0: 88:[20, 30, 10] Operation: 71-61=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[20, 30, 10], Operations: ['71-61=10'] Exploring Operation: 30-20=10, Resulting Numbers: [10, 10] Generated Node #0,0,0: 88:[10, 10] Operation: 30-20=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[10, 10], Operations: ['71-61=10', '30-20=10'] Exploring Operation: 10/10=1, Resulting Numbers: [1] 1,88 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
[ 97, 22, 6, 54 ]
59
[ "97+22=119", "6+54=60", "119-60=59" ]
Current State: 59:[97, 22, 6, 54], Operations: [] Exploring Operation: 97+22=119, Resulting Numbers: [6, 54, 119] Generated Node #2: [6, 54, 119] from Operation: 97+22=119 Current State: 59:[6, 54, 119], Operations: ['97+22=119'] Exploring Operation: 6+54=60, Resulting Numbers: [119, 60] Generated Node #3: [119, 60] from Operation: 6+54=60 Current State: 59:[119, 60], Operations: ['97+22=119', '6+54=60'] Exploring Operation: 119-60=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[97, 22, 6, 54], Operations: [] Exploring Operation: 97-6=91, Resulting Numbers: [22, 54, 91] Generated Node #0,0: 59:[22, 54, 91] Operation: 97-6=91 Exploring Operation: 22+6=28, Resulting Numbers: [97, 54, 28] Generated Node #0,1: 59:[97, 54, 28] Operation: 22+6=28 Exploring Operation: 97-22=75, Resulting Numbers: [6, 54, 75] Generated Node #0,2: 59:[6, 54, 75] Operation: 97-22=75 Exploring Operation: 6+54=60, Resulting Numbers: [97, 22, 60] Generated Node #0,3: 59:[97, 22, 60] Operation: 6+54=60 Moving to Node #0,0 Current State: 59:[22, 54, 91], Operations: ['97-6=91'] Exploring Operation: 54-22=32, Resulting Numbers: [91, 32] Generated Node #0,0,0: 59:[91, 32] Operation: 54-22=32 Exploring Operation: 22+54=76, Resulting Numbers: [91, 76] Generated Node #0,0,1: 59:[91, 76] Operation: 22+54=76 Exploring Operation: 91-22=69, Resulting Numbers: [54, 69] Generated Node #0,0,2: 59:[54, 69] Operation: 91-22=69 Exploring Operation: 22+91=113, Resulting Numbers: [54, 113] Generated Node #0,0,3: 59:[54, 113] Operation: 22+91=113 Moving to Node #0,2 Current State: 59:[6, 54, 75], Operations: ['97-22=75'] Exploring Operation: 54-6=48, Resulting Numbers: [75, 48] Generated Node #0,2,0: 59:[75, 48] Operation: 54-6=48 Exploring Operation: 75-6=69, Resulting Numbers: [54, 69] Generated Node #0,2,1: 59:[54, 69] Operation: 75-6=69 Exploring Operation: 6+54=60, Resulting Numbers: [75, 60] Generated Node #0,2,2: 59:[75, 60] Operation: 6+54=60 Exploring Operation: 6+75=81, Resulting Numbers: [54, 81] Generated Node #0,2,3: 59:[54, 81] Operation: 6+75=81 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[54, 69], Operations: ['97-22=75', '75-6=69'] Exploring Operation: 69-54=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 54*69=3726, Resulting Numbers: [3726] 3726,59 unequal: No Solution Exploring Operation: 54+69=123, Resulting Numbers: [123] 123,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[75, 60], Operations: ['97-22=75', '6+54=60'] Exploring Operation: 75-60=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 75+60=135, Resulting Numbers: [135] 135,59 unequal: No Solution Exploring Operation: 75*60=4500, Resulting Numbers: [4500] 4500,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[75, 48], Operations: ['97-22=75', '54-6=48'] Exploring Operation: 75*48=3600, Resulting Numbers: [3600] 3600,59 unequal: No Solution Exploring Operation: 75+48=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 75-48=27, Resulting Numbers: [27] 27,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 59:[54, 81], Operations: ['97-22=75', '6+75=81'] Exploring Operation: 54+81=135, Resulting Numbers: [135] 135,59 unequal: No Solution Exploring Operation: 54*81=4374, Resulting Numbers: [4374] 4374,59 unequal: No Solution Exploring Operation: 81-54=27, Resulting Numbers: [27] 27,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 59:[97, 54, 28], Operations: ['22+6=28'] Exploring Operation: 97+28=125, Resulting Numbers: [54, 125] Generated Node #0,1,0: 59:[54, 125] Operation: 97+28=125 Exploring Operation: 97-28=69, Resulting Numbers: [54, 69] Generated Node #0,1,1: 59:[54, 69] Operation: 97-28=69 Exploring Operation: 54+28=82, Resulting Numbers: [97, 82] Generated Node #0,1,2: 59:[97, 82] Operation: 54+28=82 Exploring Operation: 97-54=43, Resulting Numbers: [28, 43] Generated Node #0,1,3: 59:[28, 43] Operation: 97-54=43 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[54, 69], Operations: ['22+6=28', '97-28=69'] Exploring Operation: 69-54=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 54*69=3726, Resulting Numbers: [3726] 3726,59 unequal: No Solution Exploring Operation: 54+69=123, Resulting Numbers: [123] 123,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 59:[28, 43], Operations: ['22+6=28', '97-54=43'] Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 28+43=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 28*43=1204, Resulting Numbers: [1204] 1204,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[97, 82], Operations: ['22+6=28', '54+28=82'] Exploring Operation: 97+82=179, Resulting Numbers: [179] 179,59 unequal: No Solution Exploring Operation: 97-82=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 97*82=7954, Resulting Numbers: [7954] 7954,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[54, 125], Operations: ['22+6=28', '97+28=125'] Exploring Operation: 54+125=179, Resulting Numbers: [179] 179,59 unequal: No Solution Exploring Operation: 54*125=6750, Resulting Numbers: [6750] 6750,59 unequal: No Solution Exploring Operation: 125-54=71, Resulting Numbers: [71] 71,59 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: 59:[97, 22, 60], Operations: ['6+54=60'] Exploring Operation: 97-60=37, Resulting Numbers: [22, 37] Generated Node #0,3,0: 59:[22, 37] Operation: 97-60=37 Exploring Operation: 97+22=119, Resulting Numbers: [60, 119] Generated Node #0,3,1: 59:[60, 119] Operation: 97+22=119 Exploring Operation: 60-22=38, Resulting Numbers: [97, 38] Generated Node #0,3,2: 59:[97, 38] Operation: 60-22=38 Exploring Operation: 97-22=75, Resulting Numbers: [60, 75] Generated Node #0,3,3: 59:[60, 75] Operation: 97-22=75 Moving to Node #0,0,2 Current State: 59:[54, 69], Operations: ['97-6=91', '91-22=69'] Exploring Operation: 54+69=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 69-54=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 54*69=3726, Resulting Numbers: [3726] 3726,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[60, 75], Operations: ['6+54=60', '97-22=75'] Exploring Operation: 60*75=4500, Resulting Numbers: [4500] 4500,59 unequal: No Solution Exploring Operation: 60+75=135, Resulting Numbers: [135] 135,59 unequal: No Solution Exploring Operation: 75-60=15, Resulting Numbers: [15] 15,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[91, 76], Operations: ['97-6=91', '22+54=76'] Exploring Operation: 91*76=6916, Resulting Numbers: [6916] 6916,59 unequal: No Solution Exploring Operation: 91+76=167, Resulting Numbers: [167] 167,59 unequal: No Solution Exploring Operation: 91-76=15, Resulting Numbers: [15] 15,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[91, 32], Operations: ['97-6=91', '54-22=32'] Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[97, 22, 6, 54], Operations: [] Exploring Operation: 97-6=91, Resulting Numbers: [22, 54, 91] Generated Node #0,0: 59:[22, 54, 91] Operation: 97-6=91 Moving to Node #0,0 Current State: 59:[22, 54, 91], Operations: ['97-6=91'] Exploring Operation: 54-22=32, Resulting Numbers: [91, 32] Generated Node #0,0,0: 59:[91, 32] Operation: 54-22=32 Moving to Node #0,0,0 Current State: 59:[91, 32], Operations: ['97-6=91', '54-22=32'] Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
0.949653
hs_4
mult_heuristic
[ 98, 26, 82, 19 ]
78
[ "98-82=16", "19-16=3", "26*3=78" ]
Current State: 78:[98, 26, 82, 19], Operations: [] Exploring Operation: 98-82=16, Resulting Numbers: [26, 19, 16] Generated Node #2: [26, 19, 16] from Operation: 98-82=16 Current State: 78:[26, 19, 16], Operations: ['98-82=16'] Exploring Operation: 19-16=3, Resulting Numbers: [26, 3] Generated Node #3: [26, 3] from Operation: 19-16=3 Current State: 78:[26, 3], Operations: ['98-82=16', '19-16=3'] Exploring Operation: 26*3=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[98, 26, 82, 19], Operations: [] Exploring Operation: 98-26=72, Resulting Numbers: [82, 19, 72] Generated Node #0,0: 78:[82, 19, 72] Operation: 98-26=72 Exploring Operation: 98-19=79, Resulting Numbers: [26, 82, 79] Generated Node #0,1: 78:[26, 82, 79] Operation: 98-19=79 Exploring Operation: 98-82=16, Resulting Numbers: [26, 19, 16] Generated Node #0,2: 78:[26, 19, 16] Operation: 98-82=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[26, 82, 79], Operations: ['98-19=79'] Exploring Operation: 79-26=53, Resulting Numbers: [82, 53] Generated Node #0,1,0: 78:[82, 53] Operation: 79-26=53 Exploring Operation: 82-26=56, Resulting Numbers: [79, 56] Generated Node #0,1,1: 78:[79, 56] Operation: 82-26=56 Exploring Operation: 82-79=3, Resulting Numbers: [26, 3] Generated Node #0,1,2: 78:[26, 3] Operation: 82-79=3 Moving to Node #0,1,2 Current State: 78:[26, 3], Operations: ['98-19=79', '82-79=3'] Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,78 unequal: No Solution Exploring Operation: 26*3=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[98, 26, 82, 19], Operations: [] Exploring Operation: 98-19=79, Resulting Numbers: [26, 82, 79] Generated Node #0,1: 78:[26, 82, 79] Operation: 98-19=79 Moving to Node #0,1 Current State: 78:[26, 82, 79], Operations: ['98-19=79'] Exploring Operation: 82-79=3, Resulting Numbers: [26, 3] Generated Node #0,1,2: 78:[26, 3] Operation: 82-79=3 Moving to Node #0,1,2 Current State: 78:[26, 3], Operations: ['98-19=79', '82-79=3'] Exploring Operation: 26*3=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 28, 47, 31, 38 ]
26
[ "47-28=19", "38-31=7", "19+7=26" ]
Current State: 26:[28, 47, 31, 38], Operations: [] Exploring Operation: 47-28=19, Resulting Numbers: [31, 38, 19] Generated Node #2: [31, 38, 19] from Operation: 47-28=19 Current State: 26:[31, 38, 19], Operations: ['47-28=19'] Exploring Operation: 38-31=7, Resulting Numbers: [19, 7] Generated Node #3: [19, 7] from Operation: 38-31=7 Current State: 26:[19, 7], Operations: ['47-28=19', '38-31=7'] Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[28, 47, 31, 38], Operations: [] Exploring Operation: 47-38=9, Resulting Numbers: [28, 31, 9] Generated Node #0,0: 26:[28, 31, 9] Operation: 47-38=9 Exploring Operation: 47-28=19, Resulting Numbers: [31, 38, 19] Generated Node #0,1: 26:[31, 38, 19] Operation: 47-28=19 Exploring Operation: 47-31=16, Resulting Numbers: [28, 38, 16] Generated Node #0,2: 26:[28, 38, 16] Operation: 47-31=16 Moving to Node #0,0 Current State: 26:[28, 31, 9], Operations: ['47-38=9'] Exploring Operation: 28-9=19, Resulting Numbers: [31, 19] Generated Node #0,0,0: 26:[31, 19] Operation: 28-9=19 Exploring Operation: 31-9=22, Resulting Numbers: [28, 22] Generated Node #0,0,1: 26:[28, 22] Operation: 31-9=22 Exploring Operation: 31-28=3, Resulting Numbers: [9, 3] Generated Node #0,0,2: 26:[9, 3] Operation: 31-28=3 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 26:[9, 3], Operations: ['47-38=9', '31-28=3'] Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,26 unequal: No Solution No 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: 26:[28, 22], Operations: ['47-38=9', '31-9=22'] Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,26 unequal: No Solution Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,26 unequal: No Solution Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,26 unequal: No Solution No 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: 26:[31, 19], Operations: ['47-38=9', '28-9=19'] Exploring Operation: 31-19=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 31*19=589, Resulting Numbers: [589] 589,26 unequal: No Solution Exploring Operation: 31+19=50, Resulting Numbers: [50] 50,26 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: 26:[28, 38, 16], Operations: ['47-31=16'] Exploring Operation: 28-16=12, Resulting Numbers: [38, 12] Generated Node #0,2,0: 26:[38, 12] Operation: 28-16=12 Exploring Operation: 38-28=10, Resulting Numbers: [16, 10] Generated Node #0,2,1: 26:[16, 10] Operation: 38-28=10 Exploring Operation: 38-16=22, Resulting Numbers: [28, 22] Generated Node #0,2,2: 26:[28, 22] Operation: 38-16=22 Moving to Node #0,1 Current State: 26:[31, 38, 19], Operations: ['47-28=19'] Exploring Operation: 38-31=7, Resulting Numbers: [19, 7] Generated Node #0,1,0: 26:[19, 7] Operation: 38-31=7 Exploring Operation: 38-19=19, Resulting Numbers: [31, 19] Generated Node #0,1,1: 26:[31, 19] Operation: 38-19=19 Exploring Operation: 38/19=2, Resulting Numbers: [31, 2] Generated Node #0,1,2: 26:[31, 2] Operation: 38/19=2 Moving to Node #0,1,2 Current State: 26:[31, 2], Operations: ['47-28=19', '38/19=2'] Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,26 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,26 unequal: No Solution Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[16, 10], Operations: ['47-31=16', '38-28=10'] Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[28, 47, 31, 38], Operations: [] Exploring Operation: 47-31=16, Resulting Numbers: [28, 38, 16] Generated Node #0,2: 26:[28, 38, 16] Operation: 47-31=16 Moving to Node #0,2 Current State: 26:[28, 38, 16], Operations: ['47-31=16'] Exploring Operation: 38-28=10, Resulting Numbers: [16, 10] Generated Node #0,2,1: 26:[16, 10] Operation: 38-28=10 Moving to Node #0,2,1 Current State: 26:[16, 10], Operations: ['47-31=16', '38-28=10'] Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
0.974826
hs_3
sum_heuristic
[ 84, 60, 2, 31 ]
23
[ "84-31=53", "60/2=30", "53-30=23" ]
Current State: 23:[84, 60, 2, 31], Operations: [] Exploring Operation: 84-31=53, Resulting Numbers: [60, 2, 53] Generated Node #2: [60, 2, 53] from Operation: 84-31=53 Current State: 23:[60, 2, 53], Operations: ['84-31=53'] Exploring Operation: 60/2=30, Resulting Numbers: [53, 30] Generated Node #3: [53, 30] from Operation: 60/2=30 Current State: 23:[53, 30], Operations: ['84-31=53', '60/2=30'] Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[84, 60, 2, 31], Operations: [] Exploring Operation: 84/2=42, Resulting Numbers: [60, 31, 42] Generated Node #0,0: 23:[60, 31, 42] Operation: 84/2=42 Exploring Operation: 84-60=24, Resulting Numbers: [2, 31, 24] Generated Node #0,1: 23:[2, 31, 24] Operation: 84-60=24 Exploring Operation: 60/2=30, Resulting Numbers: [84, 31, 30] Generated Node #0,2: 23:[84, 31, 30] Operation: 60/2=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[2, 31, 24], Operations: ['84-60=24'] Exploring Operation: 2+31=33, Resulting Numbers: [24, 33] Generated Node #0,1,0: 23:[24, 33] Operation: 2+31=33 Exploring Operation: 31-2=29, Resulting Numbers: [24, 29] Generated Node #0,1,1: 23:[24, 29] Operation: 31-2=29 Exploring Operation: 24-2=22, Resulting Numbers: [31, 22] Generated Node #0,1,2: 23:[31, 22] Operation: 24-2=22 Moving to Node #0,1,1 Current State: 23:[24, 29], Operations: ['84-60=24', '31-2=29'] Exploring Operation: 24*29=696, Resulting Numbers: [696] 696,23 unequal: No Solution Exploring Operation: 24+29=53, Resulting Numbers: [53] 53,23 unequal: No Solution Exploring Operation: 29-24=5, Resulting Numbers: [5] 5,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[31, 22], Operations: ['84-60=24', '24-2=22'] Exploring Operation: 31-22=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 31+22=53, Resulting Numbers: [53] 53,23 unequal: No Solution Exploring Operation: 31*22=682, Resulting Numbers: [682] 682,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[24, 33], Operations: ['84-60=24', '2+31=33'] Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 24*33=792, Resulting Numbers: [792] 792,23 unequal: No Solution Exploring Operation: 24+33=57, Resulting Numbers: [57] 57,23 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 Current State: 23:[60, 31, 42], Operations: ['84/2=42'] Exploring Operation: 60-31=29, Resulting Numbers: [42, 29] Generated Node #0,0,0: 23:[42, 29] Operation: 60-31=29 Exploring Operation: 42-31=11, Resulting Numbers: [60, 11] Generated Node #0,0,1: 23:[60, 11] Operation: 42-31=11 Exploring Operation: 60-42=18, Resulting Numbers: [31, 18] Generated Node #0,0,2: 23:[31, 18] Operation: 60-42=18 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 23:[31, 18], Operations: ['84/2=42', '60-42=18'] Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,23 unequal: No Solution Exploring Operation: 31+18=49, Resulting Numbers: [49] 49,23 unequal: No Solution Exploring Operation: 31*18=558, Resulting Numbers: [558] 558,23 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: 23:[42, 29], Operations: ['84/2=42', '60-31=29'] Exploring Operation: 42+29=71, Resulting Numbers: [71] 71,23 unequal: No Solution Exploring Operation: 42*29=1218, Resulting Numbers: [1218] 1218,23 unequal: No Solution Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,23 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: 23:[60, 11], Operations: ['84/2=42', '42-31=11'] Exploring Operation: 60+11=71, Resulting Numbers: [71] 71,23 unequal: No Solution Exploring Operation: 60-11=49, Resulting Numbers: [49] 49,23 unequal: No Solution Exploring Operation: 60*11=660, Resulting Numbers: [660] 660,23 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: 23:[84, 31, 30], Operations: ['60/2=30'] Exploring Operation: 31-30=1, Resulting Numbers: [84, 1] Generated Node #0,2,0: 23:[84, 1] Operation: 31-30=1 Exploring Operation: 84-30=54, Resulting Numbers: [31, 54] Generated Node #0,2,1: 23:[31, 54] Operation: 84-30=54 Exploring Operation: 84-31=53, Resulting Numbers: [30, 53] Generated Node #0,2,2: 23:[30, 53] Operation: 84-31=53 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 23:[30, 53], Operations: ['60/2=30', '84-31=53'] Exploring Operation: 30*53=1590, Resulting Numbers: [1590] 1590,23 unequal: No Solution Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[84, 60, 2, 31], Operations: [] Exploring Operation: 60/2=30, Resulting Numbers: [84, 31, 30] Generated Node #0,2: 23:[84, 31, 30] Operation: 60/2=30 Moving to Node #0,2 Current State: 23:[84, 31, 30], Operations: ['60/2=30'] Exploring Operation: 84-31=53, Resulting Numbers: [30, 53] Generated Node #0,2,2: 23:[30, 53] Operation: 84-31=53 Moving to Node #0,2,2 Current State: 23:[30, 53], Operations: ['60/2=30', '84-31=53'] Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 59, 60, 15, 39 ]
55
[ "60-59=1", "15+39=54", "1+54=55" ]
Current State: 55:[59, 60, 15, 39], Operations: [] Exploring Operation: 60-59=1, Resulting Numbers: [15, 39, 1] Generated Node #2: [15, 39, 1] from Operation: 60-59=1 Current State: 55:[15, 39, 1], Operations: ['60-59=1'] Exploring Operation: 15+39=54, Resulting Numbers: [1, 54] Generated Node #3: [1, 54] from Operation: 15+39=54 Current State: 55:[1, 54], Operations: ['60-59=1', '15+39=54'] Exploring Operation: 1+54=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[59, 60, 15, 39], Operations: [] Exploring Operation: 15+39=54, Resulting Numbers: [59, 60, 54] Generated Node #0,0: 55:[59, 60, 54] Operation: 15+39=54 Exploring Operation: 59-39=20, Resulting Numbers: [60, 15, 20] Generated Node #0,1: 55:[60, 15, 20] Operation: 59-39=20 Exploring Operation: 60-39=21, Resulting Numbers: [59, 15, 21] Generated Node #0,2: 55:[59, 15, 21] Operation: 60-39=21 Moving to Node #0,0 Current State: 55:[59, 60, 54], Operations: ['15+39=54'] Exploring Operation: 60-54=6, Resulting Numbers: [59, 6] Generated Node #0,0,0: 55:[59, 6] Operation: 60-54=6 Exploring Operation: 60-59=1, Resulting Numbers: [54, 1] Generated Node #0,0,1: 55:[54, 1] Operation: 60-59=1 Exploring Operation: 59-54=5, Resulting Numbers: [60, 5] Generated Node #0,0,2: 55:[60, 5] Operation: 59-54=5 Moving to Node #0,1 Current State: 55:[60, 15, 20], Operations: ['59-39=20'] Exploring Operation: 60/20=3, Resulting Numbers: [15, 3] Generated Node #0,1,0: 55:[15, 3] Operation: 60/20=3 Exploring Operation: 60/15=4, Resulting Numbers: [20, 4] Generated Node #0,1,1: 55:[20, 4] Operation: 60/15=4 Exploring Operation: 20-15=5, Resulting Numbers: [60, 5] Generated Node #0,1,2: 55:[60, 5] Operation: 20-15=5 Moving to Node #0,2 Current State: 55:[59, 15, 21], Operations: ['60-39=21'] Exploring Operation: 59-21=38, Resulting Numbers: [15, 38] Generated Node #0,2,0: 55:[15, 38] Operation: 59-21=38 Exploring Operation: 21-15=6, Resulting Numbers: [59, 6] Generated Node #0,2,1: 55:[59, 6] Operation: 21-15=6 Exploring Operation: 59-15=44, Resulting Numbers: [21, 44] Generated Node #0,2,2: 55:[21, 44] Operation: 59-15=44 Moving to Node #0,0,0 Current State: 55:[59, 6], Operations: ['15+39=54', '60-54=6'] Exploring Operation: 59*6=354, Resulting Numbers: [354] 354,55 unequal: No Solution Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,55 unequal: No Solution Exploring Operation: 59+6=65, Resulting Numbers: [65] 65,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[60, 5], Operations: ['15+39=54', '59-54=5'] Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[59, 60, 15, 39], Operations: [] Exploring Operation: 15+39=54, Resulting Numbers: [59, 60, 54] Generated Node #0,0: 55:[59, 60, 54] Operation: 15+39=54 Moving to Node #0,0 Current State: 55:[59, 60, 54], Operations: ['15+39=54'] Exploring Operation: 59-54=5, Resulting Numbers: [60, 5] Generated Node #0,0,2: 55:[60, 5] Operation: 59-54=5 Moving to Node #0,0,2 Current State: 55:[60, 5], Operations: ['15+39=54', '59-54=5'] Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
0.982639
hs_3
mult_heuristic
[ 8, 15, 59, 2 ]
72
[ "8+15=23", "59-23=36", "2*36=72" ]
Current State: 72:[8, 15, 59, 2], Operations: [] Exploring Operation: 8+15=23, Resulting Numbers: [59, 2, 23] Generated Node #2: [59, 2, 23] from Operation: 8+15=23 Current State: 72:[59, 2, 23], Operations: ['8+15=23'] Exploring Operation: 59-23=36, Resulting Numbers: [2, 36] Generated Node #3: [2, 36] from Operation: 59-23=36 Current State: 72:[2, 36], Operations: ['8+15=23', '59-23=36'] Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[8, 15, 59, 2], Operations: [] Exploring Operation: 59-15=44, Resulting Numbers: [8, 2, 44] Generated Node #0,0: 72:[8, 2, 44] Operation: 59-15=44 Exploring Operation: 15+59=74, Resulting Numbers: [8, 2, 74] Generated Node #0,1: 72:[8, 2, 74] Operation: 15+59=74 Exploring Operation: 8+59=67, Resulting Numbers: [15, 2, 67] Generated Node #0,2: 72:[15, 2, 67] Operation: 8+59=67 Moving to Node #0,1 Current State: 72:[8, 2, 74], Operations: ['15+59=74'] Exploring Operation: 74-2=72, Resulting Numbers: [8, 72] Generated Node #0,1,0: 72:[8, 72] Operation: 74-2=72 Exploring Operation: 8-2=6, Resulting Numbers: [74, 6] Generated Node #0,1,1: 72:[74, 6] Operation: 8-2=6 Exploring Operation: 74/2=37, Resulting Numbers: [8, 37] Generated Node #0,1,2: 72:[8, 37] Operation: 74/2=37 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 72:[8, 72], Operations: ['15+59=74', '74-2=72'] Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,72 unequal: No Solution Exploring Operation: 8+72=80, Resulting Numbers: [80] 80,72 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,72 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:[8, 37], Operations: ['15+59=74', '74/2=37'] Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 8*37=296, Resulting Numbers: [296] 296,72 unequal: No Solution Exploring Operation: 8+37=45, Resulting Numbers: [45] 45,72 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 #0,1,1 Current State: 72:[74, 6], Operations: ['15+59=74', '8-2=6'] Exploring Operation: 74*6=444, Resulting Numbers: [444] 444,72 unequal: No Solution Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,72 unequal: No Solution Exploring Operation: 74+6=80, Resulting Numbers: [80] 80,72 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: 72:[8, 2, 44], Operations: ['59-15=44'] Exploring Operation: 44-2=42, Resulting Numbers: [8, 42] Generated Node #0,0,0: 72:[8, 42] Operation: 44-2=42 Exploring Operation: 44/2=22, Resulting Numbers: [8, 22] Generated Node #0,0,1: 72:[8, 22] Operation: 44/2=22 Exploring Operation: 44-8=36, Resulting Numbers: [2, 36] Generated Node #0,0,2: 72:[2, 36] Operation: 44-8=36 Moving to Node #0,2 Current State: 72:[15, 2, 67], Operations: ['8+59=67'] Exploring Operation: 15-2=13, Resulting Numbers: [67, 13] Generated Node #0,2,0: 72:[67, 13] Operation: 15-2=13 Exploring Operation: 2+67=69, Resulting Numbers: [15, 69] Generated Node #0,2,1: 72:[15, 69] Operation: 2+67=69 Exploring Operation: 15+2=17, Resulting Numbers: [67, 17] Generated Node #0,2,2: 72:[67, 17] Operation: 15+2=17 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 72:[67, 13], Operations: ['8+59=67', '15-2=13'] Exploring Operation: 67*13=871, Resulting Numbers: [871] 871,72 unequal: No Solution Exploring Operation: 67+13=80, Resulting Numbers: [80] 80,72 unequal: No Solution Exploring Operation: 67-13=54, Resulting Numbers: [54] 54,72 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 #0,2,1 Current State: 72:[15, 69], Operations: ['8+59=67', '2+67=69'] Exploring Operation: 15*69=1035, Resulting Numbers: [1035] 1035,72 unequal: No Solution Exploring Operation: 69-15=54, Resulting Numbers: [54] 54,72 unequal: No Solution Exploring Operation: 15+69=84, Resulting Numbers: [84] 84,72 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:[67, 17], Operations: ['8+59=67', '15+2=17'] Exploring Operation: 67+17=84, Resulting Numbers: [84] 84,72 unequal: No Solution Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,72 unequal: No Solution Exploring Operation: 67*17=1139, Resulting Numbers: [1139] 1139,72 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: 72:[2, 36], Operations: ['59-15=44', '44-8=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[8, 15, 59, 2], Operations: [] Exploring Operation: 59-15=44, Resulting Numbers: [8, 2, 44] Generated Node #0,0: 72:[8, 2, 44] Operation: 59-15=44 Moving to Node #0,0 Current State: 72:[8, 2, 44], Operations: ['59-15=44'] Exploring Operation: 44-8=36, Resulting Numbers: [2, 36] Generated Node #0,0,2: 72:[2, 36] Operation: 44-8=36 Moving to Node #0,0,2 Current State: 72:[2, 36], Operations: ['59-15=44', '44-8=36'] Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.967882
hs_3
mult_heuristic
[ 60, 2, 47, 70 ]
84
[ "70-60=10", "2*47=94", "94-10=84" ]
Current State: 84:[60, 2, 47, 70], Operations: [] Exploring Operation: 70-60=10, Resulting Numbers: [2, 47, 10] Generated Node #2: [2, 47, 10] from Operation: 70-60=10 Current State: 84:[2, 47, 10], Operations: ['70-60=10'] Exploring Operation: 2*47=94, Resulting Numbers: [10, 94] Generated Node #3: [10, 94] from Operation: 2*47=94 Current State: 84:[10, 94], Operations: ['70-60=10', '2*47=94'] Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[60, 2, 47, 70], Operations: [] Exploring Operation: 70-60=10, Resulting Numbers: [2, 47, 10] Generated Node #0,0: 84:[2, 47, 10] Operation: 70-60=10 Moving to Node #0,0 Current State: 84:[2, 47, 10], Operations: ['70-60=10'] Exploring Operation: 47-2=45, Resulting Numbers: [10, 45] Generated Node #0,0,0: 84:[10, 45] Operation: 47-2=45 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[10, 45], Operations: ['70-60=10', '47-2=45'] Exploring Operation: 45-10=35, Resulting Numbers: [35] 35,84 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
[ 3, 69, 37, 23 ]
86
[ "3+69=72", "37-23=14", "72+14=86" ]
Current State: 86:[3, 69, 37, 23], Operations: [] Exploring Operation: 3+69=72, Resulting Numbers: [37, 23, 72] Generated Node #2: [37, 23, 72] from Operation: 3+69=72 Current State: 86:[37, 23, 72], Operations: ['3+69=72'] Exploring Operation: 37-23=14, Resulting Numbers: [72, 14] Generated Node #3: [72, 14] from Operation: 37-23=14 Current State: 86:[72, 14], Operations: ['3+69=72', '37-23=14'] Exploring Operation: 72+14=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[3, 69, 37, 23], Operations: [] Exploring Operation: 69+23=92, Resulting Numbers: [3, 37, 92] Generated Node #0,0: 86:[3, 37, 92] Operation: 69+23=92 Exploring Operation: 69-23=46, Resulting Numbers: [3, 37, 46] Generated Node #0,1: 86:[3, 37, 46] Operation: 69-23=46 Exploring Operation: 69/23=3, Resulting Numbers: [3, 37, 3] Generated Node #0,2: 86:[3, 37, 3] Operation: 69/23=3 Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[3, 37, 3], Operations: ['69/23=3'] Exploring Operation: 3/3=1, Resulting Numbers: [37, 1] Generated Node #0,2,0: 86:[37, 1] Operation: 3/3=1 Exploring Operation: 3+37=40, Resulting Numbers: [3, 40] Generated Node #0,2,1: 86:[3, 40] Operation: 3+37=40 Exploring Operation: 37+3=40, Resulting Numbers: [3, 40] Generated Node #0,2,2: 86:[3, 40] Operation: 37+3=40 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 86:[3, 40], Operations: ['69/23=3', '3+37=40'] Exploring Operation: 3*40=120, Resulting Numbers: [120] 120,86 unequal: No Solution Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,86 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: 86:[3, 40], Operations: ['69/23=3', '37+3=40'] Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 3*40=120, Resulting Numbers: [120] 120,86 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,86 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: 86:[37, 1], Operations: ['69/23=3', '3/3=1'] Exploring Operation: 37*1=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 37+1=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,86 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: 86:[3, 37, 46], Operations: ['69-23=46'] Exploring Operation: 3+37=40, Resulting Numbers: [46, 40] Generated Node #0,1,0: 86:[46, 40] Operation: 3+37=40 Exploring Operation: 46-3=43, Resulting Numbers: [37, 43] Generated Node #0,1,1: 86:[37, 43] Operation: 46-3=43 Exploring Operation: 37+46=83, Resulting Numbers: [3, 83] Generated Node #0,1,2: 86:[3, 83] Operation: 37+46=83 Moving to Node #0,1,2 Current State: 86:[3, 83], Operations: ['69-23=46', '37+46=83'] Exploring Operation: 83-3=80, Resulting Numbers: [80] 80,86 unequal: No Solution Exploring Operation: 3+83=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[3, 69, 37, 23], Operations: [] Exploring Operation: 69-23=46, Resulting Numbers: [3, 37, 46] Generated Node #0,1: 86:[3, 37, 46] Operation: 69-23=46 Moving to Node #0,1 Current State: 86:[3, 37, 46], Operations: ['69-23=46'] Exploring Operation: 37+46=83, Resulting Numbers: [3, 83] Generated Node #0,1,2: 86:[3, 83] Operation: 37+46=83 Moving to Node #0,1,2 Current State: 86:[3, 83], Operations: ['69-23=46', '37+46=83'] Exploring Operation: 3+83=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 67, 22, 22, 15 ]
25
[ "67-22=45", "45/15=3", "22+3=25" ]
Current State: 25:[67, 22, 22, 15], Operations: [] Exploring Operation: 67-22=45, Resulting Numbers: [15, 45] Generated Node #2: [15, 45] from Operation: 67-22=45 Current State: 25:[15, 45], Operations: ['67-22=45'] Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,25 equal: Goal Reached Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[67, 22, 22, 15], Operations: [] Exploring Operation: 67-22=45, Resulting Numbers: [22, 15, 45] Generated Node #0,0: 25:[22, 15, 45] Operation: 67-22=45 Exploring Operation: 22-15=7, Resulting Numbers: [67, 22, 7] Generated Node #0,1: 25:[67, 22, 7] Operation: 22-15=7 Exploring Operation: 67-22=45, Resulting Numbers: [22, 15, 45] Generated Node #0,2: 25:[22, 15, 45] Operation: 67-22=45 Exploring Operation: 67-15=52, Resulting Numbers: [22, 22, 52] Generated Node #0,3: 25:[22, 22, 52] Operation: 67-15=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[22, 15, 45], Operations: ['67-22=45'] Exploring Operation: 45-15=30, Resulting Numbers: [22, 30] Generated Node #0,0,0: 25:[22, 30] Operation: 45-15=30 Exploring Operation: 22-15=7, Resulting Numbers: [45, 7] Generated Node #0,0,1: 25:[45, 7] Operation: 22-15=7 Exploring Operation: 45-22=23, Resulting Numbers: [15, 23] Generated Node #0,0,2: 25:[15, 23] Operation: 45-22=23 Exploring Operation: 45/15=3, Resulting Numbers: [22, 3] Generated Node #0,0,3: 25:[22, 3] Operation: 45/15=3 Moving to Node #0,0,3 Current State: 25:[22, 3], Operations: ['67-22=45', '45/15=3'] Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[67, 22, 22, 15], Operations: [] Exploring Operation: 67-22=45, Resulting Numbers: [22, 15, 45] Generated Node #0,0: 25:[22, 15, 45] Operation: 67-22=45 Moving to Node #0,0 Current State: 25:[22, 15, 45], Operations: ['67-22=45'] Exploring Operation: 45/15=3, Resulting Numbers: [22, 3] Generated Node #0,0,3: 25:[22, 3] Operation: 45/15=3 Moving to Node #0,0,3 Current State: 25:[22, 3], Operations: ['67-22=45', '45/15=3'] Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 4, 82, 24, 96 ]
83
[ "4*24=96", "96/96=1", "82+1=83" ]
Current State: 83:[4, 82, 24, 96], Operations: [] Exploring Operation: 4*24=96, Resulting Numbers: [82, 96, 96] Generated Node #2: [82, 96, 96] from Operation: 4*24=96 Current State: 83:[82, 96, 96], Operations: ['4*24=96'] Exploring Operation: 96/96=1, Resulting Numbers: [82, 1] Generated Node #3: [82, 1] from Operation: 96/96=1 Current State: 83:[82, 1], Operations: ['4*24=96', '96/96=1'] Exploring Operation: 82+1=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[4, 82, 24, 96], Operations: [] Exploring Operation: 4+24=28, Resulting Numbers: [82, 96, 28] Generated Node #0,0: 83:[82, 96, 28] Operation: 4+24=28 Exploring Operation: 4*24=96, Resulting Numbers: [82, 96, 96] Generated Node #0,1: 83:[82, 96, 96] Operation: 4*24=96 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[82, 96, 96], Operations: ['4*24=96'] Exploring Operation: 96-82=14, Resulting Numbers: [96, 14] Generated Node #0,1,0: 83:[96, 14] Operation: 96-82=14 Exploring Operation: 96-82=14, Resulting Numbers: [96, 14] Generated Node #0,1,1: 83:[96, 14] Operation: 96-82=14 Moving to Node #0,1,0 Current State: 83:[96, 14], Operations: ['4*24=96', '96-82=14'] Exploring Operation: 96+14=110, Resulting Numbers: [110] 110,83 unequal: No Solution Exploring Operation: 96-14=82, Resulting Numbers: [82] 82,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[96, 14], Operations: ['4*24=96', '96-82=14'] Exploring Operation: 96+14=110, Resulting Numbers: [110] 110,83 unequal: No Solution Exploring Operation: 96-14=82, Resulting Numbers: [82] 82,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[82, 96, 28], Operations: ['4+24=28'] Exploring Operation: 96-28=68, Resulting Numbers: [82, 68] Generated Node #0,0,0: 83:[82, 68] Operation: 96-28=68 Exploring Operation: 82+28=110, Resulting Numbers: [96, 110] Generated Node #0,0,1: 83:[96, 110] Operation: 82+28=110 Moving to Node #0,0,0 Current State: 83:[82, 68], Operations: ['4+24=28', '96-28=68'] Exploring Operation: 82+68=150, Resulting Numbers: [150] 150,83 unequal: No Solution Exploring Operation: 82-68=14, Resulting Numbers: [14] 14,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[96, 110], Operations: ['4+24=28', '82+28=110'] Exploring Operation: 96+110=206, Resulting Numbers: [206] 206,83 unequal: No Solution Exploring Operation: 110-96=14, Resulting Numbers: [14] 14,83 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
[ 12, 65, 33, 77 ]
34
[ "12+65=77", "77/77=1", "33+1=34" ]
Current State: 34:[12, 65, 33, 77], Operations: [] Exploring Operation: 12+65=77, Resulting Numbers: [33, 77, 77] Generated Node #2: [33, 77, 77] from Operation: 12+65=77 Current State: 34:[33, 77, 77], Operations: ['12+65=77'] Exploring Operation: 77/77=1, Resulting Numbers: [33, 1] Generated Node #3: [33, 1] from Operation: 77/77=1 Current State: 34:[33, 1], Operations: ['12+65=77', '77/77=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[12, 65, 33, 77], Operations: [] Exploring Operation: 77-65=12, Resulting Numbers: [12, 33, 12] Generated Node #0,0: 34:[12, 33, 12] Operation: 77-65=12 Moving to Node #0,0 Current State: 34:[12, 33, 12], Operations: ['77-65=12'] Exploring Operation: 12/12=1, Resulting Numbers: [33, 1] Generated Node #0,0,0: 34:[33, 1] Operation: 12/12=1 Moving to Node #0,0,0 Current State: 34:[33, 1], Operations: ['77-65=12', '12/12=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[12, 65, 33, 77], Operations: [] Exploring Operation: 77-65=12, Resulting Numbers: [12, 33, 12] Generated Node #0,0: 34:[12, 33, 12] Operation: 77-65=12 Moving to Node #0,0 Current State: 34:[12, 33, 12], Operations: ['77-65=12'] Exploring Operation: 12/12=1, Resulting Numbers: [33, 1] Generated Node #0,0,0: 34:[33, 1] Operation: 12/12=1 Moving to Node #0,0,0 Current State: 34:[33, 1], Operations: ['77-65=12', '12/12=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 16, 20, 79, 18 ]
71
[ "20-18=2", "16/2=8", "79-8=71" ]
Current State: 71:[16, 20, 79, 18], Operations: [] Exploring Operation: 20-18=2, Resulting Numbers: [16, 79, 2] Generated Node #2: [16, 79, 2] from Operation: 20-18=2 Current State: 71:[16, 79, 2], Operations: ['20-18=2'] Exploring Operation: 16/2=8, Resulting Numbers: [79, 8] Generated Node #3: [79, 8] from Operation: 16/2=8 Current State: 71:[79, 8], Operations: ['20-18=2', '16/2=8'] Exploring Operation: 79-8=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[16, 20, 79, 18], Operations: [] Exploring Operation: 16+18=34, Resulting Numbers: [20, 79, 34] Generated Node #0,0: 71:[20, 79, 34] Operation: 16+18=34 Exploring Operation: 20+18=38, Resulting Numbers: [16, 79, 38] Generated Node #0,1: 71:[16, 79, 38] Operation: 20+18=38 Exploring Operation: 16+20=36, Resulting Numbers: [79, 18, 36] Generated Node #0,2: 71:[79, 18, 36] Operation: 16+20=36 Moving to Node #0,0 Current State: 71:[20, 79, 34], Operations: ['16+18=34'] Exploring Operation: 20+34=54, Resulting Numbers: [79, 54] Generated Node #0,0,0: 71:[79, 54] Operation: 20+34=54 Exploring Operation: 79-20=59, Resulting Numbers: [34, 59] Generated Node #0,0,1: 71:[34, 59] Operation: 79-20=59 Exploring Operation: 20+79=99, Resulting Numbers: [34, 99] Generated Node #0,0,2: 71:[34, 99] Operation: 20+79=99 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[79, 54], Operations: ['16+18=34', '20+34=54'] Exploring Operation: 79-54=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 79*54=4266, Resulting Numbers: [4266] 4266,71 unequal: No Solution Exploring Operation: 79+54=133, Resulting Numbers: [133] 133,71 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 #0,0,1 Current State: 71:[34, 59], Operations: ['16+18=34', '79-20=59'] Exploring Operation: 59-34=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 34+59=93, Resulting Numbers: [93] 93,71 unequal: No Solution Exploring Operation: 34*59=2006, Resulting Numbers: [2006] 2006,71 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 #0,0,2 Current State: 71:[34, 99], Operations: ['16+18=34', '20+79=99'] Exploring Operation: 99-34=65, Resulting Numbers: [65] 65,71 unequal: No Solution Exploring Operation: 34*99=3366, Resulting Numbers: [3366] 3366,71 unequal: No Solution Exploring Operation: 34+99=133, Resulting Numbers: [133] 133,71 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: 71:[16, 79, 38], Operations: ['20+18=38'] Exploring Operation: 79-16=63, Resulting Numbers: [38, 63] Generated Node #0,1,0: 71:[38, 63] Operation: 79-16=63 Exploring Operation: 16+38=54, Resulting Numbers: [79, 54] Generated Node #0,1,1: 71:[79, 54] Operation: 16+38=54 Exploring Operation: 16+79=95, Resulting Numbers: [38, 95] Generated Node #0,1,2: 71:[38, 95] Operation: 16+79=95 Moving to Node #0,2 Current State: 71:[79, 18, 36], Operations: ['16+20=36'] Exploring Operation: 18+36=54, Resulting Numbers: [79, 54] Generated Node #0,2,0: 71:[79, 54] Operation: 18+36=54 Exploring Operation: 79+18=97, Resulting Numbers: [36, 97] Generated Node #0,2,1: 71:[36, 97] Operation: 79+18=97 Exploring Operation: 79-18=61, Resulting Numbers: [36, 61] Generated Node #0,2,2: 71:[36, 61] Operation: 79-18=61 Moving to Node #0,1,1 Current State: 71:[79, 54], Operations: ['20+18=38', '16+38=54'] Exploring Operation: 79-54=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 79*54=4266, Resulting Numbers: [4266] 4266,71 unequal: No Solution Exploring Operation: 79+54=133, Resulting Numbers: [133] 133,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[79, 54], Operations: ['16+20=36', '18+36=54'] Exploring Operation: 79*54=4266, Resulting Numbers: [4266] 4266,71 unequal: No Solution Exploring Operation: 79-54=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 79+54=133, Resulting Numbers: [133] 133,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[38, 63], Operations: ['20+18=38', '79-16=63'] Exploring Operation: 38+63=101, Resulting Numbers: [101] 101,71 unequal: No Solution Exploring Operation: 38*63=2394, Resulting Numbers: [2394] 2394,71 unequal: No Solution Exploring Operation: 63-38=25, Resulting Numbers: [25] 25,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[36, 61], Operations: ['16+20=36', '79-18=61'] Exploring Operation: 36*61=2196, Resulting Numbers: [2196] 2196,71 unequal: No Solution Exploring Operation: 36+61=97, Resulting Numbers: [97] 97,71 unequal: No Solution Exploring Operation: 61-36=25, Resulting Numbers: [25] 25,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[38, 95], Operations: ['20+18=38', '16+79=95'] Exploring Operation: 38*95=3610, Resulting Numbers: [3610] 3610,71 unequal: No Solution Exploring Operation: 38+95=133, Resulting Numbers: [133] 133,71 unequal: No Solution Exploring Operation: 95-38=57, Resulting Numbers: [57] 57,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[36, 97], Operations: ['16+20=36', '79+18=97'] Exploring Operation: 97-36=61, Resulting Numbers: [61] 61,71 unequal: No Solution Exploring Operation: 36*97=3492, Resulting Numbers: [3492] 3492,71 unequal: No Solution Exploring Operation: 36+97=133, Resulting Numbers: [133] 133,71 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 92, 15, 8, 61 ]
24
[ "92-15=77", "61-8=53", "77-53=24" ]
Current State: 24:[92, 15, 8, 61], Operations: [] Exploring Operation: 92-15=77, Resulting Numbers: [8, 61, 77] Generated Node #2: [8, 61, 77] from Operation: 92-15=77 Current State: 24:[8, 61, 77], Operations: ['92-15=77'] Exploring Operation: 61-8=53, Resulting Numbers: [77, 53] Generated Node #3: [77, 53] from Operation: 61-8=53 Current State: 24:[77, 53], Operations: ['92-15=77', '61-8=53'] Exploring Operation: 77-53=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[92, 15, 8, 61], Operations: [] Exploring Operation: 92-61=31, Resulting Numbers: [15, 8, 31] Generated Node #0,0: 24:[15, 8, 31] Operation: 92-61=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[15, 8, 31], Operations: ['92-61=31'] Exploring Operation: 31-15=16, Resulting Numbers: [8, 16] Generated Node #0,0,0: 24:[8, 16] Operation: 31-15=16 Moving to Node #0,0,0 Current State: 24:[8, 16], Operations: ['92-61=31', '31-15=16'] Exploring Operation: 8+16=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[92, 15, 8, 61], Operations: [] Exploring Operation: 92-61=31, Resulting Numbers: [15, 8, 31] Generated Node #0,0: 24:[15, 8, 31] Operation: 92-61=31 Moving to Node #0,0 Current State: 24:[15, 8, 31], Operations: ['92-61=31'] Exploring Operation: 31-15=16, Resulting Numbers: [8, 16] Generated Node #0,0,0: 24:[8, 16] Operation: 31-15=16 Moving to Node #0,0,0 Current State: 24:[8, 16], Operations: ['92-61=31', '31-15=16'] Exploring Operation: 8+16=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 35, 36, 54, 37 ]
20
[ "35+36=71", "54+37=91", "91-71=20" ]
Current State: 20:[35, 36, 54, 37], Operations: [] Exploring Operation: 35+36=71, Resulting Numbers: [54, 37, 71] Generated Node #2: [54, 37, 71] from Operation: 35+36=71 Current State: 20:[54, 37, 71], Operations: ['35+36=71'] Exploring Operation: 54+37=91, Resulting Numbers: [71, 91] Generated Node #3: [71, 91] from Operation: 54+37=91 Current State: 20:[71, 91], Operations: ['35+36=71', '54+37=91'] Exploring Operation: 91-71=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[35, 36, 54, 37], Operations: [] Exploring Operation: 54-36=18, Resulting Numbers: [35, 37, 18] Generated Node #0,0: 20:[35, 37, 18] Operation: 54-36=18 Exploring Operation: 54-35=19, Resulting Numbers: [36, 37, 19] Generated Node #0,1: 20:[36, 37, 19] Operation: 54-35=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[35, 37, 18], Operations: ['54-36=18'] Exploring Operation: 37-35=2, Resulting Numbers: [18, 2] Generated Node #0,0,0: 20:[18, 2] Operation: 37-35=2 Exploring Operation: 37-18=19, Resulting Numbers: [35, 19] Generated Node #0,0,1: 20:[35, 19] Operation: 37-18=19 Moving to Node #0,0,0 Current State: 20:[18, 2], Operations: ['54-36=18', '37-35=2'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[35, 36, 54, 37], Operations: [] Exploring Operation: 54-36=18, Resulting Numbers: [35, 37, 18] Generated Node #0,0: 20:[35, 37, 18] Operation: 54-36=18 Moving to Node #0,0 Current State: 20:[35, 37, 18], Operations: ['54-36=18'] Exploring Operation: 37-35=2, Resulting Numbers: [18, 2] Generated Node #0,0,0: 20:[18, 2] Operation: 37-35=2 Moving to Node #0,0,0 Current State: 20:[18, 2], Operations: ['54-36=18', '37-35=2'] Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 13, 51, 3, 51 ]
52
[ "51/51=1", "3+1=4", "13*4=52" ]
Current State: 52:[13, 51, 3, 51], Operations: [] Exploring Operation: 51/51=1, Resulting Numbers: [13, 3, 1] Generated Node #2: [13, 3, 1] from Operation: 51/51=1 Current State: 52:[13, 3, 1], Operations: ['51/51=1'] Exploring Operation: 3+1=4, Resulting Numbers: [13, 4] Generated Node #3: [13, 4] from Operation: 3+1=4 Current State: 52:[13, 4], Operations: ['51/51=1', '3+1=4'] Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[13, 51, 3, 51], Operations: [] Exploring Operation: 51/51=1, Resulting Numbers: [13, 3, 1] Generated Node #0,0: 52:[13, 3, 1] Operation: 51/51=1 Exploring Operation: 3+51=54, Resulting Numbers: [13, 51, 54] Generated Node #0,1: 52:[13, 51, 54] Operation: 3+51=54 Exploring Operation: 51+3=54, Resulting Numbers: [13, 51, 54] Generated Node #0,2: 52:[13, 51, 54] Operation: 51+3=54 Exploring Operation: 51-51=0, Resulting Numbers: [13, 3, 0] Generated Node #0,3: 52:[13, 3, 0] Operation: 51-51=0 Moving to Node #0,0 Current State: 52:[13, 3, 1], Operations: ['51/51=1'] Exploring Operation: 3+1=4, Resulting Numbers: [13, 4] Generated Node #0,0,0: 52:[13, 4] Operation: 3+1=4 Exploring Operation: 13/1=13, Resulting Numbers: [3, 13] Generated Node #0,0,1: 52:[3, 13] Operation: 13/1=13 Exploring Operation: 13*1=13, Resulting Numbers: [3, 13] Generated Node #0,0,2: 52:[3, 13] Operation: 13*1=13 Exploring Operation: 3-1=2, Resulting Numbers: [13, 2] Generated Node #0,0,3: 52:[13, 2] Operation: 3-1=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[13, 4], Operations: ['51/51=1', '3+1=4'] Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,52 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[13, 51, 3, 51], Operations: [] Exploring Operation: 51/51=1, Resulting Numbers: [13, 3, 1] Generated Node #0,0: 52:[13, 3, 1] Operation: 51/51=1 Moving to Node #0,0 Current State: 52:[13, 3, 1], Operations: ['51/51=1'] Exploring Operation: 3+1=4, Resulting Numbers: [13, 4] Generated Node #0,0,0: 52:[13, 4] Operation: 3+1=4 Moving to Node #0,0,0 Current State: 52:[13, 4], Operations: ['51/51=1', '3+1=4'] Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 11, 81, 94, 60 ]
67
[ "94+60=154", "154/11=14", "81-14=67" ]
Current State: 67:[11, 81, 94, 60], Operations: [] Exploring Operation: 94+60=154, Resulting Numbers: [11, 81, 154] Generated Node #2: [11, 81, 154] from Operation: 94+60=154 Current State: 67:[11, 81, 154], Operations: ['94+60=154'] Exploring Operation: 154/11=14, Resulting Numbers: [81, 14] Generated Node #3: [81, 14] from Operation: 154/11=14 Current State: 67:[81, 14], Operations: ['94+60=154', '154/11=14'] Exploring Operation: 81-14=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[11, 81, 94, 60], Operations: [] Exploring Operation: 81-11=70, Resulting Numbers: [94, 60, 70] Generated Node #0,0: 67:[94, 60, 70] Operation: 81-11=70 Exploring Operation: 11+60=71, Resulting Numbers: [81, 94, 71] Generated Node #0,1: 67:[81, 94, 71] Operation: 11+60=71 Exploring Operation: 94-11=83, Resulting Numbers: [81, 60, 83] Generated Node #0,2: 67:[81, 60, 83] Operation: 94-11=83 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[94, 60, 70], Operations: ['81-11=70'] Exploring Operation: 94-70=24, Resulting Numbers: [60, 24] Generated Node #0,0,0: 67:[60, 24] Operation: 94-70=24 Exploring Operation: 94-60=34, Resulting Numbers: [70, 34] Generated Node #0,0,1: 67:[70, 34] Operation: 94-60=34 Exploring Operation: 70-60=10, Resulting Numbers: [94, 10] Generated Node #0,0,2: 67:[94, 10] Operation: 70-60=10 Moving to Node #0,0,1 Current State: 67:[70, 34], Operations: ['81-11=70', '94-60=34'] Exploring Operation: 70*34=2380, Resulting Numbers: [2380] 2380,67 unequal: No Solution Exploring Operation: 70+34=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[60, 24], Operations: ['81-11=70', '94-70=24'] Exploring Operation: 60+24=84, Resulting Numbers: [84] 84,67 unequal: No Solution Exploring Operation: 60*24=1440, Resulting Numbers: [1440] 1440,67 unequal: No Solution Exploring Operation: 60-24=36, Resulting Numbers: [36] 36,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[94, 10], Operations: ['81-11=70', '70-60=10'] Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,67 unequal: No Solution Exploring Operation: 94*10=940, Resulting Numbers: [940] 940,67 unequal: No Solution Exploring Operation: 94+10=104, Resulting Numbers: [104] 104,67 unequal: No Solution No 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: 67:[81, 60, 83], Operations: ['94-11=83'] Exploring Operation: 81-60=21, Resulting Numbers: [83, 21] Generated Node #0,2,0: 67:[83, 21] Operation: 81-60=21 Exploring Operation: 83-81=2, Resulting Numbers: [60, 2] Generated Node #0,2,1: 67:[60, 2] Operation: 83-81=2 Exploring Operation: 83-60=23, Resulting Numbers: [81, 23] Generated Node #0,2,2: 67:[81, 23] Operation: 83-60=23 Moving to Node #0,2,2 Current State: 67:[81, 23], Operations: ['94-11=83', '83-60=23'] Exploring Operation: 81*23=1863, Resulting Numbers: [1863] 1863,67 unequal: No Solution Exploring Operation: 81+23=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 81-23=58, Resulting Numbers: [58] 58,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[83, 21], Operations: ['94-11=83', '81-60=21'] Exploring Operation: 83-21=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 83+21=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 83*21=1743, Resulting Numbers: [1743] 1743,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[60, 2], Operations: ['94-11=83', '83-81=2'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,67 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,67 unequal: No Solution Exploring Operation: 60+2=62, Resulting Numbers: [62] 62,67 unequal: No Solution No 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: 67:[81, 94, 71], Operations: ['11+60=71'] Exploring Operation: 94-71=23, Resulting Numbers: [81, 23] Generated Node #0,1,0: 67:[81, 23] Operation: 94-71=23 Exploring Operation: 81-71=10, Resulting Numbers: [94, 10] Generated Node #0,1,1: 67:[94, 10] Operation: 81-71=10 Exploring Operation: 94-81=13, Resulting Numbers: [71, 13] Generated Node #0,1,2: 67:[71, 13] Operation: 94-81=13 Moving to Node #0,1,0 Current State: 67:[81, 23], Operations: ['11+60=71', '94-71=23'] Exploring Operation: 81*23=1863, Resulting Numbers: [1863] 1863,67 unequal: No Solution Exploring Operation: 81+23=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 81-23=58, Resulting Numbers: [58] 58,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[71, 13], Operations: ['11+60=71', '94-81=13'] Exploring Operation: 71*13=923, Resulting Numbers: [923] 923,67 unequal: No Solution Exploring Operation: 71-13=58, Resulting Numbers: [58] 58,67 unequal: No Solution Exploring Operation: 71+13=84, Resulting Numbers: [84] 84,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[94, 10], Operations: ['11+60=71', '81-71=10'] Exploring Operation: 94*10=940, Resulting Numbers: [940] 940,67 unequal: No Solution Exploring Operation: 94+10=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 35, 39, 89, 87 ]
43
[ "89-87=2", "39*2=78", "78-35=43" ]
Current State: 43:[35, 39, 89, 87], Operations: [] Exploring Operation: 89-87=2, Resulting Numbers: [35, 39, 2] Generated Node #2: [35, 39, 2] from Operation: 89-87=2 Current State: 43:[35, 39, 2], Operations: ['89-87=2'] Exploring Operation: 39*2=78, Resulting Numbers: [35, 78] Generated Node #3: [35, 78] from Operation: 39*2=78 Current State: 43:[35, 78], Operations: ['89-87=2', '39*2=78'] Exploring Operation: 78-35=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[35, 39, 89, 87], Operations: [] Exploring Operation: 89-35=54, Resulting Numbers: [39, 87, 54] Generated Node #0,0: 43:[39, 87, 54] Operation: 89-35=54 Exploring Operation: 89-87=2, Resulting Numbers: [35, 39, 2] Generated Node #0,1: 43:[35, 39, 2] Operation: 89-87=2 Moving to Node #0,1 Current State: 43:[35, 39, 2], Operations: ['89-87=2'] Exploring Operation: 39+2=41, Resulting Numbers: [35, 41] Generated Node #0,1,0: 43:[35, 41] Operation: 39+2=41 Exploring Operation: 35+2=37, Resulting Numbers: [39, 37] Generated Node #0,1,1: 43:[39, 37] Operation: 35+2=37 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[35, 41], Operations: ['89-87=2', '39+2=41'] Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,43 unequal: No Solution Exploring Operation: 35+41=76, Resulting Numbers: [76] 76,43 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 #0,1,1 Current State: 43:[39, 37], Operations: ['89-87=2', '35+2=37'] Exploring Operation: 39-37=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 39+37=76, Resulting Numbers: [76] 76,43 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: 43:[39, 87, 54], Operations: ['89-35=54'] Exploring Operation: 87-54=33, Resulting Numbers: [39, 33] Generated Node #0,0,0: 43:[39, 33] Operation: 87-54=33 Exploring Operation: 87-39=48, Resulting Numbers: [54, 48] Generated Node #0,0,1: 43:[54, 48] Operation: 87-39=48 Moving to Node #0,0,0 Current State: 43:[39, 33], Operations: ['89-35=54', '87-54=33'] Exploring Operation: 39+33=72, Resulting Numbers: [72] 72,43 unequal: No Solution Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[54, 48], Operations: ['89-35=54', '87-39=48'] Exploring Operation: 54-48=6, Resulting Numbers: [6] 6,43 unequal: No Solution Exploring Operation: 54+48=102, Resulting Numbers: [102] 102,43 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 23, 19, 65, 4 ]
19
[ "23+19=42", "65-4=61", "61-42=19" ]
Current State: 19:[23, 19, 65, 4], Operations: [] Exploring Operation: 23+19=42, Resulting Numbers: [65, 4, 42] Generated Node #2: [65, 4, 42] from Operation: 23+19=42 Current State: 19:[65, 4, 42], Operations: ['23+19=42'] Exploring Operation: 65-4=61, Resulting Numbers: [42, 61] Generated Node #3: [42, 61] from Operation: 65-4=61 Current State: 19:[42, 61], Operations: ['23+19=42', '65-4=61'] Exploring Operation: 61-42=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[23, 19, 65, 4], Operations: [] Exploring Operation: 23-4=19, Resulting Numbers: [19, 65, 19] Generated Node #0,0: 19:[19, 65, 19] Operation: 23-4=19 Exploring Operation: 65-19=46, Resulting Numbers: [23, 4, 46] Generated Node #0,1: 19:[23, 4, 46] Operation: 65-19=46 Exploring Operation: 65-23=42, Resulting Numbers: [19, 4, 42] Generated Node #0,2: 19:[19, 4, 42] Operation: 65-23=42 Exploring Operation: 65-4=61, Resulting Numbers: [23, 19, 61] Generated Node #0,3: 19:[23, 19, 61] Operation: 65-4=61 Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[19, 4, 42], Operations: ['65-23=42'] Exploring Operation: 42-4=38, Resulting Numbers: [19, 38] Generated Node #0,2,0: 19:[19, 38] Operation: 42-4=38 Exploring Operation: 42-19=23, Resulting Numbers: [4, 23] Generated Node #0,2,1: 19:[4, 23] Operation: 42-19=23 Exploring Operation: 19-4=15, Resulting Numbers: [42, 15] Generated Node #0,2,2: 19:[42, 15] Operation: 19-4=15 Exploring Operation: 19+4=23, Resulting Numbers: [42, 23] Generated Node #0,2,3: 19:[42, 23] Operation: 19+4=23 Moving to Node #0,2,0 Current State: 19:[19, 38], Operations: ['65-23=42', '42-4=38'] Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[23, 19, 65, 4], Operations: [] Exploring Operation: 65-23=42, Resulting Numbers: [19, 4, 42] Generated Node #0,2: 19:[19, 4, 42] Operation: 65-23=42 Moving to Node #0,2 Current State: 19:[19, 4, 42], Operations: ['65-23=42'] Exploring Operation: 42-4=38, Resulting Numbers: [19, 38] Generated Node #0,2,0: 19:[19, 38] Operation: 42-4=38 Moving to Node #0,2,0 Current State: 19:[19, 38], Operations: ['65-23=42', '42-4=38'] Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 12, 96, 45, 54 ]
32
[ "12+45=57", "57-54=3", "96/3=32" ]
Current State: 32:[12, 96, 45, 54], Operations: [] Exploring Operation: 12+45=57, Resulting Numbers: [96, 54, 57] Generated Node #2: [96, 54, 57] from Operation: 12+45=57 Current State: 32:[96, 54, 57], Operations: ['12+45=57'] Exploring Operation: 57-54=3, Resulting Numbers: [96, 3] Generated Node #3: [96, 3] from Operation: 57-54=3 Current State: 32:[96, 3], Operations: ['12+45=57', '57-54=3'] Exploring Operation: 96/3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[12, 96, 45, 54], Operations: [] Exploring Operation: 96-54=42, Resulting Numbers: [12, 45, 42] Generated Node #0,0: 32:[12, 45, 42] Operation: 96-54=42 Exploring Operation: 54-45=9, Resulting Numbers: [12, 96, 9] Generated Node #0,1: 32:[12, 96, 9] Operation: 54-45=9 Exploring Operation: 96-12=84, Resulting Numbers: [45, 54, 84] Generated Node #0,2: 32:[45, 54, 84] Operation: 96-12=84 Exploring Operation: 96/12=8, Resulting Numbers: [45, 54, 8] Generated Node #0,3: 32:[45, 54, 8] Operation: 96/12=8 Exploring Operation: 96-45=51, Resulting Numbers: [12, 54, 51] Generated Node #0,4: 32:[12, 54, 51] Operation: 96-45=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[12, 45, 42], Operations: ['96-54=42'] Exploring Operation: 12+42=54, Resulting Numbers: [45, 54] Generated Node #0,0,0: 32:[45, 54] Operation: 12+42=54 Exploring Operation: 12+45=57, Resulting Numbers: [42, 57] Generated Node #0,0,1: 32:[42, 57] Operation: 12+45=57 Exploring Operation: 45-42=3, Resulting Numbers: [12, 3] Generated Node #0,0,2: 32:[12, 3] Operation: 45-42=3 Exploring Operation: 42-12=30, Resulting Numbers: [45, 30] Generated Node #0,0,3: 32:[45, 30] Operation: 42-12=30 Exploring Operation: 45-12=33, Resulting Numbers: [42, 33] Generated Node #0,0,4: 32:[42, 33] Operation: 45-12=33 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 32:[12, 3], Operations: ['96-54=42', '45-42=3'] Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,32 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,32 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: 32:[42, 33], Operations: ['96-54=42', '45-12=33'] Exploring Operation: 42+33=75, Resulting Numbers: [75] 75,32 unequal: No Solution Exploring Operation: 42-33=9, Resulting Numbers: [9] 9,32 unequal: No Solution Exploring Operation: 42*33=1386, Resulting Numbers: [1386] 1386,32 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: 32:[45, 30], Operations: ['96-54=42', '42-12=30'] Exploring Operation: 45-30=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 45+30=75, Resulting Numbers: [75] 75,32 unequal: No Solution Exploring Operation: 45*30=1350, Resulting Numbers: [1350] 1350,32 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: 32:[45, 54], Operations: ['96-54=42', '12+42=54'] Exploring Operation: 45+54=99, Resulting Numbers: [99] 99,32 unequal: No Solution Exploring Operation: 45*54=2430, Resulting Numbers: [2430] 2430,32 unequal: No Solution Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,32 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: 32:[42, 57], Operations: ['96-54=42', '12+45=57'] Exploring Operation: 42+57=99, Resulting Numbers: [99] 99,32 unequal: No Solution Exploring Operation: 57-42=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 42*57=2394, Resulting Numbers: [2394] 2394,32 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: 32:[45, 54, 8], Operations: ['96/12=8'] Exploring Operation: 45+8=53, Resulting Numbers: [54, 53] Generated Node #0,3,0: 32:[54, 53] Operation: 45+8=53 Exploring Operation: 54+8=62, Resulting Numbers: [45, 62] Generated Node #0,3,1: 32:[45, 62] Operation: 54+8=62 Exploring Operation: 45-8=37, Resulting Numbers: [54, 37] Generated Node #0,3,2: 32:[54, 37] Operation: 45-8=37 Exploring Operation: 54-8=46, Resulting Numbers: [45, 46] Generated Node #0,3,3: 32:[45, 46] Operation: 54-8=46 Exploring Operation: 54-45=9, Resulting Numbers: [8, 9] Generated Node #0,3,4: 32:[8, 9] Operation: 54-45=9 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 32:[8, 9], Operations: ['96/12=8', '54-45=9'] Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,32 unequal: No Solution Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,32 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: 32:[54, 37], Operations: ['96/12=8', '45-8=37'] Exploring Operation: 54-37=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 54*37=1998, Resulting Numbers: [1998] 1998,32 unequal: No Solution Exploring Operation: 54+37=91, Resulting Numbers: [91] 91,32 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: 32:[45, 46], Operations: ['96/12=8', '54-8=46'] Exploring Operation: 45+46=91, Resulting Numbers: [91] 91,32 unequal: No Solution Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,32 unequal: No Solution Exploring Operation: 45*46=2070, Resulting Numbers: [2070] 2070,32 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: 32:[54, 53], Operations: ['96/12=8', '45+8=53'] Exploring Operation: 54+53=107, Resulting Numbers: [107] 107,32 unequal: No Solution Exploring Operation: 54*53=2862, Resulting Numbers: [2862] 2862,32 unequal: No Solution Exploring Operation: 54-53=1, Resulting Numbers: [1] 1,32 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: 32:[45, 62], Operations: ['96/12=8', '54+8=62'] Exploring Operation: 45*62=2790, Resulting Numbers: [2790] 2790,32 unequal: No Solution Exploring Operation: 62-45=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 45+62=107, Resulting Numbers: [107] 107,32 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: 32:[12, 54, 51], Operations: ['96-45=51'] Exploring Operation: 54-51=3, Resulting Numbers: [12, 3] Generated Node #0,4,0: 32:[12, 3] Operation: 54-51=3 Exploring Operation: 12+54=66, Resulting Numbers: [51, 66] Generated Node #0,4,1: 32:[51, 66] Operation: 12+54=66 Exploring Operation: 54-12=42, Resulting Numbers: [51, 42] Generated Node #0,4,2: 32:[51, 42] Operation: 54-12=42 Exploring Operation: 12+51=63, Resulting Numbers: [54, 63] Generated Node #0,4,3: 32:[54, 63] Operation: 12+51=63 Exploring Operation: 51-12=39, Resulting Numbers: [54, 39] Generated Node #0,4,4: 32:[54, 39] Operation: 51-12=39 Moving to Node #0,4,0 Current State: 32:[12, 3], Operations: ['96-45=51', '54-51=3'] Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,32 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,32 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,32 unequal: No Solution Moving to Node #0,4,4 Current State: 32:[54, 39], Operations: ['96-45=51', '51-12=39'] Exploring Operation: 54*39=2106, Resulting Numbers: [2106] 2106,32 unequal: No Solution Exploring Operation: 54+39=93, Resulting Numbers: [93] 93,32 unequal: No Solution Exploring Operation: 54-39=15, Resulting Numbers: [15] 15,32 unequal: No Solution Moving to Node #0,4,2 Current State: 32:[51, 42], Operations: ['96-45=51', '54-12=42'] Exploring Operation: 51+42=93, Resulting Numbers: [93] 93,32 unequal: No Solution Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,32 unequal: No Solution Exploring Operation: 51*42=2142, Resulting Numbers: [2142] 2142,32 unequal: No Solution Moving to Node #0,4,1 Current State: 32:[51, 66], Operations: ['96-45=51', '12+54=66'] Exploring Operation: 66-51=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 51+66=117, Resulting Numbers: [117] 117,32 unequal: No Solution Exploring Operation: 51*66=3366, Resulting Numbers: [3366] 3366,32 unequal: No Solution Moving to Node #0,4,3 Current State: 32:[54, 63], Operations: ['96-45=51', '12+51=63'] Exploring Operation: 54*63=3402, Resulting Numbers: [3402] 3402,32 unequal: No Solution Exploring Operation: 63-54=9, Resulting Numbers: [9] 9,32 unequal: No Solution Exploring Operation: 54+63=117, Resulting Numbers: [117] 117,32 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 Current State: 32:[12, 96, 9], Operations: ['54-45=9'] Exploring Operation: 12-9=3, Resulting Numbers: [96, 3] Generated Node #0,1,0: 32:[96, 3] Operation: 12-9=3 Exploring Operation: 96-12=84, Resulting Numbers: [9, 84] Generated Node #0,1,1: 32:[9, 84] Operation: 96-12=84 Exploring Operation: 96-9=87, Resulting Numbers: [12, 87] Generated Node #0,1,2: 32:[12, 87] Operation: 96-9=87 Exploring Operation: 12+9=21, Resulting Numbers: [96, 21] Generated Node #0,1,3: 32:[96, 21] Operation: 12+9=21 Exploring Operation: 96/12=8, Resulting Numbers: [9, 8] Generated Node #0,1,4: 32:[9, 8] Operation: 96/12=8 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 32:[9, 8], Operations: ['54-45=9', '96/12=8'] Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,32 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,32 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: 32:[9, 84], Operations: ['54-45=9', '96-12=84'] Exploring Operation: 9+84=93, Resulting Numbers: [93] 93,32 unequal: No Solution Exploring Operation: 9*84=756, Resulting Numbers: [756] 756,32 unequal: No Solution Exploring Operation: 84-9=75, Resulting Numbers: [75] 75,32 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: 32:[12, 87], Operations: ['54-45=9', '96-9=87'] Exploring Operation: 12*87=1044, Resulting Numbers: [1044] 1044,32 unequal: No Solution Exploring Operation: 12+87=99, Resulting Numbers: [99] 99,32 unequal: No Solution Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,32 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: 32:[96, 3], Operations: ['54-45=9', '12-9=3'] Exploring Operation: 96/3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[12, 96, 45, 54], Operations: [] Exploring Operation: 54-45=9, Resulting Numbers: [12, 96, 9] Generated Node #0,1: 32:[12, 96, 9] Operation: 54-45=9 Moving to Node #0,1 Current State: 32:[12, 96, 9], Operations: ['54-45=9'] Exploring Operation: 12-9=3, Resulting Numbers: [96, 3] Generated Node #0,1,0: 32:[96, 3] Operation: 12-9=3 Moving to Node #0,1,0 Current State: 32:[96, 3], Operations: ['54-45=9', '12-9=3'] Exploring Operation: 96/3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.925347
hs_5
mult_heuristic
[ 3, 96, 1, 46 ]
46
[ "96-3=93", "1+46=47", "93-47=46" ]
Current State: 46:[3, 96, 1, 46], Operations: [] Exploring Operation: 96-3=93, Resulting Numbers: [1, 46, 93] Generated Node #2: [1, 46, 93] from Operation: 96-3=93 Current State: 46:[1, 46, 93], Operations: ['96-3=93'] Exploring Operation: 1+46=47, Resulting Numbers: [93, 47] Generated Node #3: [93, 47] from Operation: 1+46=47 Current State: 46:[93, 47], Operations: ['96-3=93', '1+46=47'] Exploring Operation: 93-47=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[3, 96, 1, 46], Operations: [] Exploring Operation: 96/3=32, Resulting Numbers: [1, 46, 32] Generated Node #0,0: 46:[1, 46, 32] Operation: 96/3=32 Exploring Operation: 96-46=50, Resulting Numbers: [3, 1, 50] Generated Node #0,1: 46:[3, 1, 50] Operation: 96-46=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[3, 1, 50], Operations: ['96-46=50'] Exploring Operation: 3-1=2, Resulting Numbers: [50, 2] Generated Node #0,1,0: 46:[50, 2] Operation: 3-1=2 Exploring Operation: 50-3=47, Resulting Numbers: [1, 47] Generated Node #0,1,1: 46:[1, 47] Operation: 50-3=47 Moving to Node #0,1,1 Current State: 46:[1, 47], Operations: ['96-46=50', '50-3=47'] Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[3, 96, 1, 46], Operations: [] Exploring Operation: 96-46=50, Resulting Numbers: [3, 1, 50] Generated Node #0,1: 46:[3, 1, 50] Operation: 96-46=50 Moving to Node #0,1 Current State: 46:[3, 1, 50], Operations: ['96-46=50'] Exploring Operation: 50-3=47, Resulting Numbers: [1, 47] Generated Node #0,1,1: 46:[1, 47] Operation: 50-3=47 Moving to Node #0,1,1 Current State: 46:[1, 47], Operations: ['96-46=50', '50-3=47'] Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 59, 25, 29, 25 ]
89
[ "59+29=88", "25/25=1", "88+1=89" ]
Current State: 89:[59, 25, 29, 25], Operations: [] Exploring Operation: 59+29=88, Resulting Numbers: [25, 25, 88] Generated Node #2: [25, 25, 88] from Operation: 59+29=88 Current State: 89:[25, 25, 88], Operations: ['59+29=88'] Exploring Operation: 25/25=1, Resulting Numbers: [88, 1] Generated Node #3: [88, 1] from Operation: 25/25=1 Current State: 89:[88, 1], Operations: ['59+29=88', '25/25=1'] Exploring Operation: 88+1=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[59, 25, 29, 25], Operations: [] Exploring Operation: 59+25=84, Resulting Numbers: [29, 25, 84] Generated Node #0,0: 89:[29, 25, 84] Operation: 59+25=84 Exploring Operation: 59+29=88, Resulting Numbers: [25, 25, 88] Generated Node #0,1: 89:[25, 25, 88] Operation: 59+29=88 Exploring Operation: 59+25=84, Resulting Numbers: [25, 29, 84] Generated Node #0,2: 89:[25, 29, 84] Operation: 59+25=84 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[29, 25, 84], Operations: ['59+25=84'] Exploring Operation: 25+84=109, Resulting Numbers: [29, 109] Generated Node #0,0,0: 89:[29, 109] Operation: 25+84=109 Exploring Operation: 29+25=54, Resulting Numbers: [84, 54] Generated Node #0,0,1: 89:[84, 54] Operation: 29+25=54 Exploring Operation: 29+84=113, Resulting Numbers: [25, 113] Generated Node #0,0,2: 89:[25, 113] Operation: 29+84=113 Moving to Node #0,0,1 Current State: 89:[84, 54], Operations: ['59+25=84', '29+25=54'] Exploring Operation: 84-54=30, Resulting Numbers: [30] 30,89 unequal: No Solution Exploring Operation: 84*54=4536, Resulting Numbers: [4536] 4536,89 unequal: No Solution Exploring Operation: 84+54=138, Resulting Numbers: [138] 138,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[29, 109], Operations: ['59+25=84', '25+84=109'] Exploring Operation: 29*109=3161, Resulting Numbers: [3161] 3161,89 unequal: No Solution Exploring Operation: 109-29=80, Resulting Numbers: [80] 80,89 unequal: No Solution Exploring Operation: 29+109=138, Resulting Numbers: [138] 138,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[25, 113], Operations: ['59+25=84', '29+84=113'] Exploring Operation: 25*113=2825, Resulting Numbers: [2825] 2825,89 unequal: No Solution Exploring Operation: 25+113=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 113-25=88, Resulting Numbers: [88] 88,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[25, 25, 88], Operations: ['59+29=88'] Exploring Operation: 25+88=113, Resulting Numbers: [25, 113] Generated Node #0,1,0: 89:[25, 113] Operation: 25+88=113 Exploring Operation: 25+88=113, Resulting Numbers: [25, 113] Generated Node #0,1,1: 89:[25, 113] Operation: 25+88=113 Exploring Operation: 25+25=50, Resulting Numbers: [88, 50] Generated Node #0,1,2: 89:[88, 50] Operation: 25+25=50 Moving to Node #0,1,2 Current State: 89:[88, 50], Operations: ['59+29=88', '25+25=50'] Exploring Operation: 88-50=38, Resulting Numbers: [38] 38,89 unequal: No Solution Exploring Operation: 88*50=4400, Resulting Numbers: [4400] 4400,89 unequal: No Solution Exploring Operation: 88+50=138, Resulting Numbers: [138] 138,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[25, 113], Operations: ['59+29=88', '25+88=113'] Exploring Operation: 113-25=88, Resulting Numbers: [88] 88,89 unequal: No Solution Exploring Operation: 25+113=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 25*113=2825, Resulting Numbers: [2825] 2825,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[25, 113], Operations: ['59+29=88', '25+88=113'] Exploring Operation: 25*113=2825, Resulting Numbers: [2825] 2825,89 unequal: No Solution Exploring Operation: 25+113=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 113-25=88, Resulting Numbers: [88] 88,89 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 Current State: 89:[25, 29, 84], Operations: ['59+25=84'] Exploring Operation: 29+84=113, Resulting Numbers: [25, 113] Generated Node #0,2,0: 89:[25, 113] Operation: 29+84=113 Exploring Operation: 25+29=54, Resulting Numbers: [84, 54] Generated Node #0,2,1: 89:[84, 54] Operation: 25+29=54 Exploring Operation: 25+84=109, Resulting Numbers: [29, 109] Generated Node #0,2,2: 89:[29, 109] Operation: 25+84=109 Moving to Node #0,2,1 Current State: 89:[84, 54], Operations: ['59+25=84', '25+29=54'] Exploring Operation: 84-54=30, Resulting Numbers: [30] 30,89 unequal: No Solution Exploring Operation: 84*54=4536, Resulting Numbers: [4536] 4536,89 unequal: No Solution Exploring Operation: 84+54=138, Resulting Numbers: [138] 138,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[29, 109], Operations: ['59+25=84', '25+84=109'] Exploring Operation: 109-29=80, Resulting Numbers: [80] 80,89 unequal: No Solution Exploring Operation: 29*109=3161, Resulting Numbers: [3161] 3161,89 unequal: No Solution Exploring Operation: 29+109=138, Resulting Numbers: [138] 138,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[25, 113], Operations: ['59+25=84', '29+84=113'] Exploring Operation: 25*113=2825, Resulting Numbers: [2825] 2825,89 unequal: No Solution Exploring Operation: 113-25=88, Resulting Numbers: [88] 88,89 unequal: No Solution Exploring Operation: 25+113=138, Resulting Numbers: [138] 138,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 18, 45, 19, 72 ]
80
[ "45-18=27", "72-19=53", "27+53=80" ]
Current State: 80:[18, 45, 19, 72], Operations: [] Exploring Operation: 45-18=27, Resulting Numbers: [19, 72, 27] Generated Node #2: [19, 72, 27] from Operation: 45-18=27 Current State: 80:[19, 72, 27], Operations: ['45-18=27'] Exploring Operation: 72-19=53, Resulting Numbers: [27, 53] Generated Node #3: [27, 53] from Operation: 72-19=53 Current State: 80:[27, 53], Operations: ['45-18=27', '72-19=53'] Exploring Operation: 27+53=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[18, 45, 19, 72], Operations: [] Exploring Operation: 19-18=1, Resulting Numbers: [45, 72, 1] Generated Node #0,0: 80:[45, 72, 1] Operation: 19-18=1 Exploring Operation: 18+19=37, Resulting Numbers: [45, 72, 37] Generated Node #0,1: 80:[45, 72, 37] Operation: 18+19=37 Exploring Operation: 72/18=4, Resulting Numbers: [45, 19, 4] Generated Node #0,2: 80:[45, 19, 4] Operation: 72/18=4 Exploring Operation: 45-18=27, Resulting Numbers: [19, 72, 27] Generated Node #0,3: 80:[19, 72, 27] Operation: 45-18=27 Exploring Operation: 72-45=27, Resulting Numbers: [18, 19, 27] Generated Node #0,4: 80:[18, 19, 27] Operation: 72-45=27 Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[45, 19, 4], Operations: ['72/18=4'] Exploring Operation: 19-4=15, Resulting Numbers: [45, 15] Generated Node #0,2,0: 80:[45, 15] Operation: 19-4=15 Exploring Operation: 45-4=41, Resulting Numbers: [19, 41] Generated Node #0,2,1: 80:[19, 41] Operation: 45-4=41 Exploring Operation: 19+4=23, Resulting Numbers: [45, 23] Generated Node #0,2,2: 80:[45, 23] Operation: 19+4=23 Exploring Operation: 19*4=76, Resulting Numbers: [45, 76] Generated Node #0,2,3: 80:[45, 76] Operation: 19*4=76 Exploring Operation: 45-19=26, Resulting Numbers: [4, 26] Generated Node #0,2,4: 80:[4, 26] Operation: 45-19=26 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 80:[19, 41], Operations: ['72/18=4', '45-4=41'] Exploring Operation: 19+41=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 19*41=779, Resulting Numbers: [779] 779,80 unequal: No Solution Exploring Operation: 41-19=22, Resulting Numbers: [22] 22,80 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 #0,2,0 Current State: 80:[45, 15], Operations: ['72/18=4', '19-4=15'] Exploring Operation: 45*15=675, Resulting Numbers: [675] 675,80 unequal: No Solution Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,80 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 45+15=60, Resulting Numbers: [60] 60,80 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 #0,2,4 Current State: 80:[4, 26], Operations: ['72/18=4', '45-19=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,80 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,80 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:[45, 23], Operations: ['72/18=4', '19+4=23'] Exploring Operation: 45+23=68, Resulting Numbers: [68] 68,80 unequal: No Solution Exploring Operation: 45*23=1035, Resulting Numbers: [1035] 1035,80 unequal: No Solution Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,80 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 #0,2,3 Current State: 80:[45, 76], Operations: ['72/18=4', '19*4=76'] Exploring Operation: 45*76=3420, Resulting Numbers: [3420] 3420,80 unequal: No Solution Exploring Operation: 76-45=31, Resulting Numbers: [31] 31,80 unequal: No Solution Exploring Operation: 45+76=121, Resulting Numbers: [121] 121,80 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 #0,4 Current State: 80:[18, 19, 27], Operations: ['72-45=27'] Exploring Operation: 27-18=9, Resulting Numbers: [19, 9] Generated Node #0,4,0: 80:[19, 9] Operation: 27-18=9 Exploring Operation: 19-18=1, Resulting Numbers: [27, 1] Generated Node #0,4,1: 80:[27, 1] Operation: 19-18=1 Exploring Operation: 27-19=8, Resulting Numbers: [18, 8] Generated Node #0,4,2: 80:[18, 8] Operation: 27-19=8 Exploring Operation: 19+27=46, Resulting Numbers: [18, 46] Generated Node #0,4,3: 80:[18, 46] Operation: 19+27=46 Exploring Operation: 18+27=45, Resulting Numbers: [19, 45] Generated Node #0,4,4: 80:[19, 45] Operation: 18+27=45 Moving to Node #0,4,0 Current State: 80:[19, 9], Operations: ['72-45=27', '27-18=9'] Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,80 unequal: No Solution Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,80 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,80 unequal: No Solution Moving to Node #0,4,2 Current State: 80:[18, 8], Operations: ['72-45=27', '27-19=8'] Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,80 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,80 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,80 unequal: No Solution Moving to Node #0,4,4 Current State: 80:[19, 45], Operations: ['72-45=27', '18+27=45'] Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,80 unequal: No Solution Exploring Operation: 19+45=64, Resulting Numbers: [64] 64,80 unequal: No Solution Exploring Operation: 19*45=855, Resulting Numbers: [855] 855,80 unequal: No Solution Moving to Node #0,4,1 Current State: 80:[27, 1], Operations: ['72-45=27', '19-18=1'] Exploring Operation: 27+1=28, Resulting Numbers: [28] 28,80 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,80 unequal: No Solution Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,80 unequal: No Solution Moving to Node #0,4,3 Current State: 80:[18, 46], Operations: ['72-45=27', '19+27=46'] Exploring Operation: 18*46=828, Resulting Numbers: [828] 828,80 unequal: No Solution Exploring Operation: 46-18=28, Resulting Numbers: [28] 28,80 unequal: No Solution Exploring Operation: 18+46=64, Resulting Numbers: [64] 64,80 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 #0,0 Current State: 80:[45, 72, 1], Operations: ['19-18=1'] Exploring Operation: 72+1=73, Resulting Numbers: [45, 73] Generated Node #0,0,0: 80:[45, 73] Operation: 72+1=73 Exploring Operation: 45*1=45, Resulting Numbers: [72, 45] Generated Node #0,0,1: 80:[72, 45] Operation: 45*1=45 Exploring Operation: 45-1=44, Resulting Numbers: [72, 44] Generated Node #0,0,2: 80:[72, 44] Operation: 45-1=44 Exploring Operation: 45/1=45, Resulting Numbers: [72, 45] Generated Node #0,0,3: 80:[72, 45] Operation: 45/1=45 Exploring Operation: 72-45=27, Resulting Numbers: [1, 27] Generated Node #0,0,4: 80:[1, 27] Operation: 72-45=27 Moving to Node #0,0,4 Current State: 80:[1, 27], Operations: ['19-18=1', '72-45=27'] Exploring Operation: 1*27=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,80 unequal: No Solution Exploring Operation: 1+27=28, Resulting Numbers: [28] 28,80 unequal: No Solution Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[72, 44], Operations: ['19-18=1', '45-1=44'] Exploring Operation: 72+44=116, Resulting Numbers: [116] 116,80 unequal: No Solution Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,80 unequal: No Solution Exploring Operation: 72*44=3168, Resulting Numbers: [3168] 3168,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[45, 73], Operations: ['19-18=1', '72+1=73'] Exploring Operation: 45+73=118, Resulting Numbers: [118] 118,80 unequal: No Solution Exploring Operation: 45*73=3285, Resulting Numbers: [3285] 3285,80 unequal: No Solution Exploring Operation: 73-45=28, Resulting Numbers: [28] 28,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[72, 45], Operations: ['19-18=1', '45*1=45'] Exploring Operation: 72+45=117, Resulting Numbers: [117] 117,80 unequal: No Solution Exploring Operation: 72-45=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 72*45=3240, Resulting Numbers: [3240] 3240,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[72, 45], Operations: ['19-18=1', '45/1=45'] Exploring Operation: 72*45=3240, Resulting Numbers: [3240] 3240,80 unequal: No Solution Exploring Operation: 72+45=117, Resulting Numbers: [117] 117,80 unequal: No Solution Exploring Operation: 72-45=27, Resulting Numbers: [27] 27,80 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:[45, 72, 37], Operations: ['18+19=37'] Exploring Operation: 72-37=35, Resulting Numbers: [45, 35] Generated Node #0,1,0: 80:[45, 35] Operation: 72-37=35 Exploring Operation: 45-37=8, Resulting Numbers: [72, 8] Generated Node #0,1,1: 80:[72, 8] Operation: 45-37=8 Exploring Operation: 72+37=109, Resulting Numbers: [45, 109] Generated Node #0,1,2: 80:[45, 109] Operation: 72+37=109 Exploring Operation: 45+37=82, Resulting Numbers: [72, 82] Generated Node #0,1,3: 80:[72, 82] Operation: 45+37=82 Exploring Operation: 72-45=27, Resulting Numbers: [37, 27] Generated Node #0,1,4: 80:[37, 27] Operation: 72-45=27 Moving to Node #0,1,1 Current State: 80:[72, 8], Operations: ['18+19=37', '45-37=8'] Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[18, 45, 19, 72], Operations: [] Exploring Operation: 18+19=37, Resulting Numbers: [45, 72, 37] Generated Node #0,1: 80:[45, 72, 37] Operation: 18+19=37 Moving to Node #0,1 Current State: 80:[45, 72, 37], Operations: ['18+19=37'] Exploring Operation: 45-37=8, Resulting Numbers: [72, 8] Generated Node #0,1,1: 80:[72, 8] Operation: 45-37=8 Moving to Node #0,1,1 Current State: 80:[72, 8], Operations: ['18+19=37', '45-37=8'] Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.932292
hs_5
mult_heuristic
[ 80, 48, 16, 64 ]
32
[ "80+48=128", "64/16=4", "128/4=32" ]
Current State: 32:[80, 48, 16, 64], Operations: [] Exploring Operation: 80+48=128, Resulting Numbers: [16, 64, 128] Generated Node #2: [16, 64, 128] from Operation: 80+48=128 Current State: 32:[16, 64, 128], Operations: ['80+48=128'] Exploring Operation: 64/16=4, Resulting Numbers: [128, 4] Generated Node #3: [128, 4] from Operation: 64/16=4 Current State: 32:[128, 4], Operations: ['80+48=128', '64/16=4'] Exploring Operation: 128/4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[80, 48, 16, 64], Operations: [] Exploring Operation: 64-48=16, Resulting Numbers: [80, 16, 16] Generated Node #0,0: 32:[80, 16, 16] Operation: 64-48=16 Exploring Operation: 80-48=32, Resulting Numbers: [16, 64, 32] Generated Node #0,1: 32:[16, 64, 32] Operation: 80-48=32 Exploring Operation: 80-64=16, Resulting Numbers: [48, 16, 16] Generated Node #0,2: 32:[48, 16, 16] Operation: 80-64=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[48, 16, 16], Operations: ['80-64=16'] Exploring Operation: 48-16=32, Resulting Numbers: [16, 32] Generated Node #0,2,0: 32:[16, 32] Operation: 48-16=32 Exploring Operation: 48-16=32, Resulting Numbers: [16, 32] Generated Node #0,2,1: 32:[16, 32] Operation: 48-16=32 Exploring Operation: 48/16=3, Resulting Numbers: [16, 3] Generated Node #0,2,2: 32:[16, 3] Operation: 48/16=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 32:[16, 32], Operations: ['80-64=16', '48-16=32'] Exploring Operation: 16+32=48, Resulting Numbers: [48] 48,32 unequal: No Solution Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,32 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: 32:[16, 32], Operations: ['80-64=16', '48-16=32'] Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 16+32=48, Resulting Numbers: [48] 48,32 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: 32:[16, 3], Operations: ['80-64=16', '48/16=3'] Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,32 unequal: No Solution Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,32 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: 32:[16, 64, 32], Operations: ['80-48=32'] Exploring Operation: 64/32=2, Resulting Numbers: [16, 2] Generated Node #0,1,0: 32:[16, 2] Operation: 64/32=2 Exploring Operation: 64-32=32, Resulting Numbers: [16, 32] Generated Node #0,1,1: 32:[16, 32] Operation: 64-32=32 Exploring Operation: 64/16=4, Resulting Numbers: [32, 4] Generated Node #0,1,2: 32:[32, 4] Operation: 64/16=4 Moving to Node #0,1,0 Current State: 32:[16, 2], Operations: ['80-48=32', '64/32=2'] Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,32 unequal: No Solution Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[80, 48, 16, 64], Operations: [] Exploring Operation: 80-48=32, Resulting Numbers: [16, 64, 32] Generated Node #0,1: 32:[16, 64, 32] Operation: 80-48=32 Moving to Node #0,1 Current State: 32:[16, 64, 32], Operations: ['80-48=32'] Exploring Operation: 64/32=2, Resulting Numbers: [16, 2] Generated Node #0,1,0: 32:[16, 2] Operation: 64/32=2 Moving to Node #0,1,0 Current State: 32:[16, 2], Operations: ['80-48=32', '64/32=2'] Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 20, 60, 48, 42 ]
58
[ "60/20=3", "48/3=16", "42+16=58" ]
Current State: 58:[20, 60, 48, 42], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [48, 42, 3] Generated Node #2: [48, 42, 3] from Operation: 60/20=3 Current State: 58:[48, 42, 3], Operations: ['60/20=3'] Exploring Operation: 48/3=16, Resulting Numbers: [42, 16] Generated Node #3: [42, 16] from Operation: 48/3=16 Current State: 58:[42, 16], Operations: ['60/20=3', '48/3=16'] Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[20, 60, 48, 42], Operations: [] Exploring Operation: 48-42=6, Resulting Numbers: [20, 60, 6] Generated Node #0,0: 58:[20, 60, 6] Operation: 48-42=6 Exploring Operation: 48-20=28, Resulting Numbers: [60, 42, 28] Generated Node #0,1: 58:[60, 42, 28] Operation: 48-20=28 Moving to Node #0,0 Current State: 58:[20, 60, 6], Operations: ['48-42=6'] Exploring Operation: 20+6=26, Resulting Numbers: [60, 26] Generated Node #0,0,0: 58:[60, 26] Operation: 20+6=26 Exploring Operation: 60/20=3, Resulting Numbers: [6, 3] Generated Node #0,0,1: 58:[6, 3] Operation: 60/20=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[60, 26], Operations: ['48-42=6', '20+6=26'] Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,58 unequal: No Solution Exploring Operation: 60+26=86, Resulting Numbers: [86] 86,58 unequal: No Solution No 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: 58:[6, 3], Operations: ['48-42=6', '60/20=3'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,58 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: 58:[60, 42, 28], Operations: ['48-20=28'] Exploring Operation: 42+28=70, Resulting Numbers: [60, 70] Generated Node #0,1,0: 58:[60, 70] Operation: 42+28=70 Exploring Operation: 60-42=18, Resulting Numbers: [28, 18] Generated Node #0,1,1: 58:[28, 18] Operation: 60-42=18 Moving to Node #0,1,1 Current State: 58:[28, 18], Operations: ['48-20=28', '60-42=18'] Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,58 unequal: No Solution Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,58 unequal: No Solution Moving to Node #0,1,0 Current State: 58:[60, 70], Operations: ['48-20=28', '42+28=70'] Exploring Operation: 60+70=130, Resulting Numbers: [130] 130,58 unequal: No Solution Exploring Operation: 70-60=10, Resulting Numbers: [10] 10,58 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 3, 14, 2, 84 ]
38
[ "84-14=70", "70/2=35", "3+35=38" ]
Current State: 38:[3, 14, 2, 84], Operations: [] Exploring Operation: 84-14=70, Resulting Numbers: [3, 2, 70] Generated Node #2: [3, 2, 70] from Operation: 84-14=70 Current State: 38:[3, 2, 70], Operations: ['84-14=70'] Exploring Operation: 70/2=35, Resulting Numbers: [3, 35] Generated Node #3: [3, 35] from Operation: 70/2=35 Current State: 38:[3, 35], Operations: ['84-14=70', '70/2=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[3, 14, 2, 84], Operations: [] Exploring Operation: 84/2=42, Resulting Numbers: [3, 14, 42] Generated Node #0,0: 38:[3, 14, 42] Operation: 84/2=42 Exploring Operation: 84/3=28, Resulting Numbers: [14, 2, 28] Generated Node #0,1: 38:[14, 2, 28] Operation: 84/3=28 Exploring Operation: 84/14=6, Resulting Numbers: [3, 2, 6] Generated Node #0,2: 38:[3, 2, 6] Operation: 84/14=6 Exploring Operation: 84-14=70, Resulting Numbers: [3, 2, 70] Generated Node #0,3: 38:[3, 2, 70] Operation: 84-14=70 Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[3, 2, 6], Operations: ['84/14=6'] Exploring Operation: 6/3=2, Resulting Numbers: [2, 2] Generated Node #0,2,0: 38:[2, 2] Operation: 6/3=2 Exploring Operation: 6-3=3, Resulting Numbers: [2, 3] Generated Node #0,2,1: 38:[2, 3] Operation: 6-3=3 Exploring Operation: 6/2=3, Resulting Numbers: [3, 3] Generated Node #0,2,2: 38:[3, 3] Operation: 6/2=3 Exploring Operation: 3*6=18, Resulting Numbers: [2, 18] Generated Node #0,2,3: 38:[2, 18] Operation: 3*6=18 Moving to Node #0,2,0 Current State: 38:[2, 2], Operations: ['84/14=6', '6/3=2'] Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,38 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,38 unequal: No Solution Moving to Node #0,2,3 Current State: 38:[2, 18], Operations: ['84/14=6', '3*6=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,38 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,38 unequal: No Solution Moving to Node #0,2,1 Current State: 38:[2, 3], Operations: ['84/14=6', '6-3=3'] Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,38 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[3, 3], Operations: ['84/14=6', '6/2=3'] Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,38 unequal: No Solution Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,38 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 #0,0 Current State: 38:[3, 14, 42], Operations: ['84/2=42'] Exploring Operation: 3*14=42, Resulting Numbers: [42, 42] Generated Node #0,0,0: 38:[42, 42] Operation: 3*14=42 Exploring Operation: 3+14=17, Resulting Numbers: [42, 17] Generated Node #0,0,1: 38:[42, 17] Operation: 3+14=17 Exploring Operation: 42/14=3, Resulting Numbers: [3, 3] Generated Node #0,0,2: 38:[3, 3] Operation: 42/14=3 Exploring Operation: 42-3=39, Resulting Numbers: [14, 39] Generated Node #0,0,3: 38:[14, 39] Operation: 42-3=39 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 38:[3, 3], Operations: ['84/2=42', '42/14=3'] Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,38 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,38 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 #0,0,1 Current State: 38:[42, 17], Operations: ['84/2=42', '3+14=17'] Exploring Operation: 42*17=714, Resulting Numbers: [714] 714,38 unequal: No Solution Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,38 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 #0,0,3 Current State: 38:[14, 39], Operations: ['84/2=42', '42-3=39'] Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 14*39=546, Resulting Numbers: [546] 546,38 unequal: No Solution Exploring Operation: 14+39=53, Resulting Numbers: [53] 53,38 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 #0,0,0 Current State: 38:[42, 42], Operations: ['84/2=42', '3*14=42'] Exploring Operation: 42*42=1764, Resulting Numbers: [1764] 1764,38 unequal: No Solution Exploring Operation: 42-42=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 42/42=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 42+42=84, Resulting Numbers: [84] 84,38 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 #0,1 Current State: 38:[14, 2, 28], Operations: ['84/3=28'] Exploring Operation: 28/14=2, Resulting Numbers: [2, 2] Generated Node #0,1,0: 38:[2, 2] Operation: 28/14=2 Exploring Operation: 28-14=14, Resulting Numbers: [2, 14] Generated Node #0,1,1: 38:[2, 14] Operation: 28-14=14 Exploring Operation: 28/2=14, Resulting Numbers: [14, 14] Generated Node #0,1,2: 38:[14, 14] Operation: 28/2=14 Exploring Operation: 14+28=42, Resulting Numbers: [2, 42] Generated Node #0,1,3: 38:[2, 42] Operation: 14+28=42 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 38:[2, 2], Operations: ['84/3=28', '28/14=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,38 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,38 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,38 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 #0,1,3 Current State: 38:[2, 42], Operations: ['84/3=28', '14+28=42'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,38 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,38 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,38 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 #0,1,1 Current State: 38:[2, 14], Operations: ['84/3=28', '28-14=14'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,38 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,38 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,38 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:[14, 14], Operations: ['84/3=28', '28/2=14'] Exploring Operation: 14+14=28, Resulting Numbers: [28] 28,38 unequal: No Solution Exploring Operation: 14/14=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 14-14=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 14*14=196, Resulting Numbers: [196] 196,38 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 #0,3 Current State: 38:[3, 2, 70], Operations: ['84-14=70'] Exploring Operation: 70/2=35, Resulting Numbers: [3, 35] Generated Node #0,3,0: 38:[3, 35] Operation: 70/2=35 Exploring Operation: 3-2=1, Resulting Numbers: [70, 1] Generated Node #0,3,1: 38:[70, 1] Operation: 3-2=1 Exploring Operation: 70-2=68, Resulting Numbers: [3, 68] Generated Node #0,3,2: 38:[3, 68] Operation: 70-2=68 Exploring Operation: 70-3=67, Resulting Numbers: [2, 67] Generated Node #0,3,3: 38:[2, 67] Operation: 70-3=67 Moving to Node #0,3,0 Current State: 38:[3, 35], Operations: ['84-14=70', '70/2=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[3, 14, 2, 84], Operations: [] Exploring Operation: 84-14=70, Resulting Numbers: [3, 2, 70] Generated Node #0,3: 38:[3, 2, 70] Operation: 84-14=70 Moving to Node #0,3 Current State: 38:[3, 2, 70], Operations: ['84-14=70'] Exploring Operation: 70/2=35, Resulting Numbers: [3, 35] Generated Node #0,3,0: 38:[3, 35] Operation: 70/2=35 Moving to Node #0,3,0 Current State: 38:[3, 35], Operations: ['84-14=70', '70/2=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.939236
hs_4
sum_heuristic
[ 47, 17, 5, 55 ]
51
[ "47+5=52", "55-52=3", "17*3=51" ]
Current State: 51:[47, 17, 5, 55], Operations: [] Exploring Operation: 47+5=52, Resulting Numbers: [17, 55, 52] Generated Node #2: [17, 55, 52] from Operation: 47+5=52 Current State: 51:[17, 55, 52], Operations: ['47+5=52'] Exploring Operation: 55-52=3, Resulting Numbers: [17, 3] Generated Node #3: [17, 3] from Operation: 55-52=3 Current State: 51:[17, 3], Operations: ['47+5=52', '55-52=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[47, 17, 5, 55], Operations: [] Exploring Operation: 47+5=52, Resulting Numbers: [17, 55, 52] Generated Node #0,0: 51:[17, 55, 52] Operation: 47+5=52 Exploring Operation: 55-5=50, Resulting Numbers: [47, 17, 50] Generated Node #0,1: 51:[47, 17, 50] Operation: 55-5=50 Moving to Node #0,0 Current State: 51:[17, 55, 52], Operations: ['47+5=52'] Exploring Operation: 55-17=38, Resulting Numbers: [52, 38] Generated Node #0,0,0: 51:[52, 38] Operation: 55-17=38 Exploring Operation: 55-52=3, Resulting Numbers: [17, 3] Generated Node #0,0,1: 51:[17, 3] Operation: 55-52=3 Moving to Node #0,1 Current State: 51:[47, 17, 50], Operations: ['55-5=50'] Exploring Operation: 47+17=64, Resulting Numbers: [50, 64] Generated Node #0,1,0: 51:[50, 64] Operation: 47+17=64 Exploring Operation: 50-47=3, Resulting Numbers: [17, 3] Generated Node #0,1,1: 51:[17, 3] Operation: 50-47=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 51:[17, 3], Operations: ['55-5=50', '50-47=3'] Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[47, 17, 5, 55], Operations: [] Exploring Operation: 55-5=50, Resulting Numbers: [47, 17, 50] Generated Node #0,1: 51:[47, 17, 50] Operation: 55-5=50 Moving to Node #0,1 Current State: 51:[47, 17, 50], Operations: ['55-5=50'] Exploring Operation: 50-47=3, Resulting Numbers: [17, 3] Generated Node #0,1,1: 51:[17, 3] Operation: 50-47=3 Moving to Node #0,1,1 Current State: 51:[17, 3], Operations: ['55-5=50', '50-47=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 61, 51, 73, 47 ]
86
[ "61+51=112", "73-47=26", "112-26=86" ]
Current State: 86:[61, 51, 73, 47], Operations: [] Exploring Operation: 61+51=112, Resulting Numbers: [73, 47, 112] Generated Node #2: [73, 47, 112] from Operation: 61+51=112 Current State: 86:[73, 47, 112], Operations: ['61+51=112'] Exploring Operation: 73-47=26, Resulting Numbers: [112, 26] Generated Node #3: [112, 26] from Operation: 73-47=26 Current State: 86:[112, 26], Operations: ['61+51=112', '73-47=26'] Exploring Operation: 112-26=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[61, 51, 73, 47], Operations: [] Exploring Operation: 61-51=10, Resulting Numbers: [73, 47, 10] Generated Node #0,0: 86:[73, 47, 10] Operation: 61-51=10 Exploring Operation: 73-61=12, Resulting Numbers: [51, 47, 12] Generated Node #0,1: 86:[51, 47, 12] Operation: 73-61=12 Exploring Operation: 61-47=14, Resulting Numbers: [51, 73, 14] Generated Node #0,2: 86:[51, 73, 14] Operation: 61-47=14 Moving to Node #0,1 Current State: 86:[51, 47, 12], Operations: ['73-61=12'] Exploring Operation: 51-47=4, Resulting Numbers: [12, 4] Generated Node #0,1,0: 86:[12, 4] Operation: 51-47=4 Exploring Operation: 47-12=35, Resulting Numbers: [51, 35] Generated Node #0,1,1: 86:[51, 35] Operation: 47-12=35 Exploring Operation: 51-12=39, Resulting Numbers: [47, 39] Generated Node #0,1,2: 86:[47, 39] Operation: 51-12=39 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[47, 39], Operations: ['73-61=12', '51-12=39'] Exploring Operation: 47+39=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[61, 51, 73, 47], Operations: [] Exploring Operation: 73-61=12, Resulting Numbers: [51, 47, 12] Generated Node #0,1: 86:[51, 47, 12] Operation: 73-61=12 Moving to Node #0,1 Current State: 86:[51, 47, 12], Operations: ['73-61=12'] Exploring Operation: 51-12=39, Resulting Numbers: [47, 39] Generated Node #0,1,2: 86:[47, 39] Operation: 51-12=39 Moving to Node #0,1,2 Current State: 86:[47, 39], Operations: ['73-61=12', '51-12=39'] Exploring Operation: 47+39=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 9, 73, 14, 1 ]
52
[ "9*14=126", "73+1=74", "126-74=52" ]
Current State: 52:[9, 73, 14, 1], Operations: [] Exploring Operation: 9*14=126, Resulting Numbers: [73, 1, 126] Generated Node #2: [73, 1, 126] from Operation: 9*14=126 Current State: 52:[73, 1, 126], Operations: ['9*14=126'] Exploring Operation: 73+1=74, Resulting Numbers: [126, 74] Generated Node #3: [126, 74] from Operation: 73+1=74 Current State: 52:[126, 74], Operations: ['9*14=126', '73+1=74'] Exploring Operation: 126-74=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[9, 73, 14, 1], Operations: [] Exploring Operation: 73-14=59, Resulting Numbers: [9, 1, 59] Generated Node #0,0: 52:[9, 1, 59] Operation: 73-14=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[9, 1, 59], Operations: ['73-14=59'] Exploring Operation: 59-9=50, Resulting Numbers: [1, 50] Generated Node #0,0,0: 52:[1, 50] Operation: 59-9=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[1, 50], Operations: ['73-14=59', '59-9=50'] Exploring Operation: 1+50=51, Resulting Numbers: [51] 51,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 15, 40, 4, 10 ]
11
[ "40-15=25", "4+10=14", "25-14=11" ]
Current State: 11:[15, 40, 4, 10], Operations: [] Exploring Operation: 40-15=25, Resulting Numbers: [4, 10, 25] Generated Node #2: [4, 10, 25] from Operation: 40-15=25 Current State: 11:[4, 10, 25], Operations: ['40-15=25'] Exploring Operation: 4+10=14, Resulting Numbers: [25, 14] Generated Node #3: [25, 14] from Operation: 4+10=14 Current State: 11:[25, 14], Operations: ['40-15=25', '4+10=14'] Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[15, 40, 4, 10], Operations: [] Exploring Operation: 40/10=4, Resulting Numbers: [15, 4, 4] Generated Node #0,0: 11:[15, 4, 4] Operation: 40/10=4 Exploring Operation: 40-15=25, Resulting Numbers: [4, 10, 25] Generated Node #0,1: 11:[4, 10, 25] Operation: 40-15=25 Exploring Operation: 40/4=10, Resulting Numbers: [15, 10, 10] Generated Node #0,2: 11:[15, 10, 10] Operation: 40/4=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 11:[15, 10, 10], Operations: ['40/4=10'] Exploring Operation: 10+10=20, Resulting Numbers: [15, 20] Generated Node #0,2,0: 11:[15, 20] Operation: 10+10=20 Exploring Operation: 15-10=5, Resulting Numbers: [10, 5] Generated Node #0,2,1: 11:[10, 5] Operation: 15-10=5 Exploring Operation: 15-10=5, Resulting Numbers: [10, 5] Generated Node #0,2,2: 11:[10, 5] Operation: 15-10=5 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 11:[10, 5], Operations: ['40/4=10', '15-10=5'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 10+5=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 11:[10, 5], Operations: ['40/4=10', '15-10=5'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,11 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 10+5=15, Resulting Numbers: [15] 15,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 11:[15, 20], Operations: ['40/4=10', '10+10=20'] Exploring Operation: 15*20=300, Resulting Numbers: [300] 300,11 unequal: No Solution Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,11 unequal: No Solution Exploring Operation: 15+20=35, Resulting Numbers: [35] 35,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[15, 4, 4], Operations: ['40/10=4'] Exploring Operation: 15-4=11, Resulting Numbers: [4, 11] Generated Node #0,0,0: 11:[4, 11] Operation: 15-4=11 Exploring Operation: 15-4=11, Resulting Numbers: [4, 11] Generated Node #0,0,1: 11:[4, 11] Operation: 15-4=11 Exploring Operation: 4+4=8, Resulting Numbers: [15, 8] Generated Node #0,0,2: 11:[15, 8] Operation: 4+4=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[4, 11], Operations: ['40/10=4', '15-4=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,11 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 11:[4, 11], Operations: ['40/10=4', '15-4=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,11 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 11:[15, 8], Operations: ['40/10=4', '4+4=8'] Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,11 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[4, 10, 25], Operations: ['40-15=25'] Exploring Operation: 4+10=14, Resulting Numbers: [25, 14] Generated Node #0,1,0: 11:[25, 14] Operation: 4+10=14 Exploring Operation: 25-4=21, Resulting Numbers: [10, 21] Generated Node #0,1,1: 11:[10, 21] Operation: 25-4=21 Exploring Operation: 25-10=15, Resulting Numbers: [4, 15] Generated Node #0,1,2: 11:[4, 15] Operation: 25-10=15 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 11:[10, 21], Operations: ['40-15=25', '25-4=21'] Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[15, 40, 4, 10], Operations: [] Exploring Operation: 40-15=25, Resulting Numbers: [4, 10, 25] Generated Node #0,1: 11:[4, 10, 25] Operation: 40-15=25 Moving to Node #0,1 Current State: 11:[4, 10, 25], Operations: ['40-15=25'] Exploring Operation: 25-4=21, Resulting Numbers: [10, 21] Generated Node #0,1,1: 11:[10, 21] Operation: 25-4=21 Moving to Node #0,1,1 Current State: 11:[10, 21], Operations: ['40-15=25', '25-4=21'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 3, 64, 80, 6 ]
72
[ "6/3=2", "64+80=144", "144/2=72" ]
Current State: 72:[3, 64, 80, 6], Operations: [] Exploring Operation: 6/3=2, Resulting Numbers: [64, 80, 2] Generated Node #2: [64, 80, 2] from Operation: 6/3=2 Current State: 72:[64, 80, 2], Operations: ['6/3=2'] Exploring Operation: 64+80=144, Resulting Numbers: [2, 144] Generated Node #3: [2, 144] from Operation: 64+80=144 Current State: 72:[2, 144], Operations: ['6/3=2', '64+80=144'] Exploring Operation: 144/2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[3, 64, 80, 6], Operations: [] Exploring Operation: 64+6=70, Resulting Numbers: [3, 80, 70] Generated Node #0,0: 72:[3, 80, 70] Operation: 64+6=70 Exploring Operation: 80-6=74, Resulting Numbers: [3, 64, 74] Generated Node #0,1: 72:[3, 64, 74] Operation: 80-6=74 Exploring Operation: 3+64=67, Resulting Numbers: [80, 6, 67] Generated Node #0,2: 72:[80, 6, 67] Operation: 3+64=67 Exploring Operation: 80-64=16, Resulting Numbers: [3, 6, 16] Generated Node #0,3: 72:[3, 6, 16] Operation: 80-64=16 Moving to Node #0,3 Current State: 72:[3, 6, 16], Operations: ['80-64=16'] Exploring Operation: 3+16=19, Resulting Numbers: [6, 19] Generated Node #0,3,0: 72:[6, 19] Operation: 3+16=19 Exploring Operation: 16-6=10, Resulting Numbers: [3, 10] Generated Node #0,3,1: 72:[3, 10] Operation: 16-6=10 Exploring Operation: 3+6=9, Resulting Numbers: [16, 9] Generated Node #0,3,2: 72:[16, 9] Operation: 3+6=9 Exploring Operation: 16-3=13, Resulting Numbers: [6, 13] Generated Node #0,3,3: 72:[6, 13] Operation: 16-3=13 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 72:[6, 19], Operations: ['80-64=16', '3+16=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,72 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,72 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 #0,3,1 Current State: 72:[3, 10], Operations: ['80-64=16', '16-6=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,72 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 #0,3,3 Current State: 72:[6, 13], Operations: ['80-64=16', '16-3=13'] Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,72 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 #0,3,2 Current State: 72:[16, 9], Operations: ['80-64=16', '3+6=9'] Exploring Operation: 16*9=144, Resulting Numbers: [144] 144,72 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,72 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:[3, 64, 74], Operations: ['80-6=74'] Exploring Operation: 64-3=61, Resulting Numbers: [74, 61] Generated Node #0,1,0: 72:[74, 61] Operation: 64-3=61 Exploring Operation: 3+64=67, Resulting Numbers: [74, 67] Generated Node #0,1,1: 72:[74, 67] Operation: 3+64=67 Exploring Operation: 74-3=71, Resulting Numbers: [64, 71] Generated Node #0,1,2: 72:[64, 71] Operation: 74-3=71 Exploring Operation: 74-64=10, Resulting Numbers: [3, 10] Generated Node #0,1,3: 72:[3, 10] Operation: 74-64=10 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 72:[3, 10], Operations: ['80-6=74', '74-64=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,72 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,72 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 #0,1,1 Current State: 72:[74, 67], Operations: ['80-6=74', '3+64=67'] Exploring Operation: 74-67=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 74+67=141, Resulting Numbers: [141] 141,72 unequal: No Solution Exploring Operation: 74*67=4958, Resulting Numbers: [4958] 4958,72 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:[64, 71], Operations: ['80-6=74', '74-3=71'] Exploring Operation: 64+71=135, Resulting Numbers: [135] 135,72 unequal: No Solution Exploring Operation: 71-64=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 64*71=4544, Resulting Numbers: [4544] 4544,72 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:[74, 61], Operations: ['80-6=74', '64-3=61'] Exploring Operation: 74-61=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 74+61=135, Resulting Numbers: [135] 135,72 unequal: No Solution Exploring Operation: 74*61=4514, Resulting Numbers: [4514] 4514,72 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: 72:[3, 80, 70], Operations: ['64+6=70'] Exploring Operation: 3+80=83, Resulting Numbers: [70, 83] Generated Node #0,0,0: 72:[70, 83] Operation: 3+80=83 Exploring Operation: 80-70=10, Resulting Numbers: [3, 10] Generated Node #0,0,1: 72:[3, 10] Operation: 80-70=10 Exploring Operation: 80-3=77, Resulting Numbers: [70, 77] Generated Node #0,0,2: 72:[70, 77] Operation: 80-3=77 Exploring Operation: 3+70=73, Resulting Numbers: [80, 73] Generated Node #0,0,3: 72:[80, 73] Operation: 3+70=73 Moving to Node #0,2 Current State: 72:[80, 6, 67], Operations: ['3+64=67'] Exploring Operation: 80-6=74, Resulting Numbers: [67, 74] Generated Node #0,2,0: 72:[67, 74] Operation: 80-6=74 Exploring Operation: 80-67=13, Resulting Numbers: [6, 13] Generated Node #0,2,1: 72:[6, 13] Operation: 80-67=13 Exploring Operation: 80+6=86, Resulting Numbers: [67, 86] Generated Node #0,2,2: 72:[67, 86] Operation: 80+6=86 Exploring Operation: 6+67=73, Resulting Numbers: [80, 73] Generated Node #0,2,3: 72:[80, 73] Operation: 6+67=73 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 72:[6, 13], Operations: ['3+64=67', '80-67=13'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,72 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,72 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 #0,2,0 Current State: 72:[67, 74], Operations: ['3+64=67', '80-6=74'] Exploring Operation: 74-67=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 67*74=4958, Resulting Numbers: [4958] 4958,72 unequal: No Solution Exploring Operation: 67+74=141, Resulting Numbers: [141] 141,72 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 #0,2,3 Current State: 72:[80, 73], Operations: ['3+64=67', '6+67=73'] Exploring Operation: 80+73=153, Resulting Numbers: [153] 153,72 unequal: No Solution Exploring Operation: 80*73=5840, Resulting Numbers: [5840] 5840,72 unequal: No Solution Exploring Operation: 80-73=7, Resulting Numbers: [7] 7,72 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:[67, 86], Operations: ['3+64=67', '80+6=86'] Exploring Operation: 67*86=5762, Resulting Numbers: [5762] 5762,72 unequal: No Solution Exploring Operation: 67+86=153, Resulting Numbers: [153] 153,72 unequal: No Solution Exploring Operation: 86-67=19, Resulting Numbers: [19] 19,72 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: 72:[3, 10], Operations: ['64+6=70', '80-70=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,72 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[70, 77], Operations: ['64+6=70', '80-3=77'] Exploring Operation: 70*77=5390, Resulting Numbers: [5390] 5390,72 unequal: No Solution Exploring Operation: 77-70=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 70+77=147, Resulting Numbers: [147] 147,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[80, 73], Operations: ['64+6=70', '3+70=73'] Exploring Operation: 80+73=153, Resulting Numbers: [153] 153,72 unequal: No Solution Exploring Operation: 80*73=5840, Resulting Numbers: [5840] 5840,72 unequal: No Solution Exploring Operation: 80-73=7, Resulting Numbers: [7] 7,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[70, 83], Operations: ['64+6=70', '3+80=83'] Exploring Operation: 70*83=5810, Resulting Numbers: [5810] 5810,72 unequal: No Solution Exploring Operation: 70+83=153, Resulting Numbers: [153] 153,72 unequal: No Solution Exploring Operation: 83-70=13, Resulting Numbers: [13] 13,72 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 27, 24, 75, 33 ]
69
[ "33-27=6", "24*6=144", "144-75=69" ]
Current State: 69:[27, 24, 75, 33], Operations: [] Exploring Operation: 33-27=6, Resulting Numbers: [24, 75, 6] Generated Node #2: [24, 75, 6] from Operation: 33-27=6 Current State: 69:[24, 75, 6], Operations: ['33-27=6'] Exploring Operation: 24*6=144, Resulting Numbers: [75, 144] Generated Node #3: [75, 144] from Operation: 24*6=144 Current State: 69:[75, 144], Operations: ['33-27=6', '24*6=144'] Exploring Operation: 144-75=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[27, 24, 75, 33], Operations: [] Exploring Operation: 27-24=3, Resulting Numbers: [75, 33, 3] Generated Node #0,0: 69:[75, 33, 3] Operation: 27-24=3 Exploring Operation: 33-27=6, Resulting Numbers: [24, 75, 6] Generated Node #0,1: 69:[24, 75, 6] Operation: 33-27=6 Exploring Operation: 27+33=60, Resulting Numbers: [24, 75, 60] Generated Node #0,2: 69:[24, 75, 60] Operation: 27+33=60 Moving to Node #0,1 Current State: 69:[24, 75, 6], Operations: ['33-27=6'] Exploring Operation: 24/6=4, Resulting Numbers: [75, 4] Generated Node #0,1,0: 69:[75, 4] Operation: 24/6=4 Exploring Operation: 24-6=18, Resulting Numbers: [75, 18] Generated Node #0,1,1: 69:[75, 18] Operation: 24-6=18 Exploring Operation: 75-6=69, Resulting Numbers: [24, 69] Generated Node #0,1,2: 69:[24, 69] Operation: 75-6=69 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[24, 69], Operations: ['33-27=6', '75-6=69'] Exploring Operation: 24+69=93, Resulting Numbers: [93] 93,69 unequal: No Solution Exploring Operation: 24*69=1656, Resulting Numbers: [1656] 1656,69 unequal: No Solution Exploring Operation: 69-24=45, Resulting Numbers: [45] 45,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[75, 4], Operations: ['33-27=6', '24/6=4'] Exploring Operation: 75+4=79, Resulting Numbers: [79] 79,69 unequal: No Solution Exploring Operation: 75*4=300, Resulting Numbers: [300] 300,69 unequal: No Solution Exploring Operation: 75-4=71, Resulting Numbers: [71] 71,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[75, 18], Operations: ['33-27=6', '24-6=18'] Exploring Operation: 75+18=93, Resulting Numbers: [93] 93,69 unequal: No Solution Exploring Operation: 75-18=57, Resulting Numbers: [57] 57,69 unequal: No Solution Exploring Operation: 75*18=1350, Resulting Numbers: [1350] 1350,69 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: 69:[75, 33, 3], Operations: ['27-24=3'] Exploring Operation: 75-3=72, Resulting Numbers: [33, 72] Generated Node #0,0,0: 69:[33, 72] Operation: 75-3=72 Exploring Operation: 75/3=25, Resulting Numbers: [33, 25] Generated Node #0,0,1: 69:[33, 25] Operation: 75/3=25 Exploring Operation: 33-3=30, Resulting Numbers: [75, 30] Generated Node #0,0,2: 69:[75, 30] Operation: 33-3=30 Moving to Node #0,2 Current State: 69:[24, 75, 60], Operations: ['27+33=60'] Exploring Operation: 60-24=36, Resulting Numbers: [75, 36] Generated Node #0,2,0: 69:[75, 36] Operation: 60-24=36 Exploring Operation: 24+60=84, Resulting Numbers: [75, 84] Generated Node #0,2,1: 69:[75, 84] Operation: 24+60=84 Exploring Operation: 75-60=15, Resulting Numbers: [24, 15] Generated Node #0,2,2: 69:[24, 15] Operation: 75-60=15 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 69:[24, 15], Operations: ['27+33=60', '75-60=15'] Exploring Operation: 24*15=360, Resulting Numbers: [360] 360,69 unequal: No Solution Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 69:[75, 36], Operations: ['27+33=60', '60-24=36'] Exploring Operation: 75*36=2700, Resulting Numbers: [2700] 2700,69 unequal: No Solution Exploring Operation: 75-36=39, Resulting Numbers: [39] 39,69 unequal: No Solution Exploring Operation: 75+36=111, Resulting Numbers: [111] 111,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 69:[75, 84], Operations: ['27+33=60', '24+60=84'] Exploring Operation: 75*84=6300, Resulting Numbers: [6300] 6300,69 unequal: No Solution Exploring Operation: 75+84=159, Resulting Numbers: [159] 159,69 unequal: No Solution Exploring Operation: 84-75=9, Resulting Numbers: [9] 9,69 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: 69:[33, 25], Operations: ['27-24=3', '75/3=25'] Exploring Operation: 33*25=825, Resulting Numbers: [825] 825,69 unequal: No Solution Exploring Operation: 33-25=8, Resulting Numbers: [8] 8,69 unequal: No Solution Exploring Operation: 33+25=58, Resulting Numbers: [58] 58,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[33, 72], Operations: ['27-24=3', '75-3=72'] Exploring Operation: 33*72=2376, Resulting Numbers: [2376] 2376,69 unequal: No Solution Exploring Operation: 33+72=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 72-33=39, Resulting Numbers: [39] 39,69 unequal: No Solution Moving to Node #0,0,2 Current State: 69:[75, 30], Operations: ['27-24=3', '33-3=30'] Exploring Operation: 75-30=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 75*30=2250, Resulting Numbers: [2250] 2250,69 unequal: No Solution Exploring Operation: 75+30=105, Resulting Numbers: [105] 105,69 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 68, 55, 73, 50 ]
36
[ "68-55=13", "73-50=23", "13+23=36" ]
Current State: 36:[68, 55, 73, 50], Operations: [] Exploring Operation: 68-55=13, Resulting Numbers: [73, 50, 13] Generated Node #2: [73, 50, 13] from Operation: 68-55=13 Current State: 36:[73, 50, 13], Operations: ['68-55=13'] Exploring Operation: 73-50=23, Resulting Numbers: [13, 23] Generated Node #3: [13, 23] from Operation: 73-50=23 Current State: 36:[13, 23], Operations: ['68-55=13', '73-50=23'] Exploring Operation: 13+23=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[68, 55, 73, 50], Operations: [] Exploring Operation: 73-55=18, Resulting Numbers: [68, 50, 18] Generated Node #0,0: 36:[68, 50, 18] Operation: 73-55=18 Exploring Operation: 73-68=5, Resulting Numbers: [55, 50, 5] Generated Node #0,1: 36:[55, 50, 5] Operation: 73-68=5 Moving to Node #0,1 Current State: 36:[55, 50, 5], Operations: ['73-68=5'] Exploring Operation: 55-50=5, Resulting Numbers: [5, 5] Generated Node #0,1,0: 36:[5, 5] Operation: 55-50=5 Exploring Operation: 55/5=11, Resulting Numbers: [50, 11] Generated Node #0,1,1: 36:[50, 11] Operation: 55/5=11 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 36:[5, 5], Operations: ['73-68=5', '55-50=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 5/5=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 #0,1,1 Current State: 36:[50, 11], Operations: ['73-68=5', '55/5=11'] Exploring Operation: 50-11=39, Resulting Numbers: [39] 39,36 unequal: No Solution Exploring Operation: 50+11=61, Resulting Numbers: [61] 61,36 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:[68, 50, 18], Operations: ['73-55=18'] Exploring Operation: 68-50=18, Resulting Numbers: [18, 18] Generated Node #0,0,0: 36:[18, 18] Operation: 68-50=18 Exploring Operation: 68-18=50, Resulting Numbers: [50, 50] Generated Node #0,0,1: 36:[50, 50] Operation: 68-18=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[18, 18], Operations: ['73-55=18', '68-50=18'] Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,36 unequal: No Solution Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[68, 55, 73, 50], Operations: [] Exploring Operation: 73-55=18, Resulting Numbers: [68, 50, 18] Generated Node #0,0: 36:[68, 50, 18] Operation: 73-55=18 Moving to Node #0,0 Current State: 36:[68, 50, 18], Operations: ['73-55=18'] Exploring Operation: 68-50=18, Resulting Numbers: [18, 18] Generated Node #0,0,0: 36:[18, 18] Operation: 68-50=18 Moving to Node #0,0,0 Current State: 36:[18, 18], Operations: ['73-55=18', '68-50=18'] Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 12, 3, 50, 30 ]
80
[ "12/3=4", "50-30=20", "4*20=80" ]
Current State: 80:[12, 3, 50, 30], Operations: [] Exploring Operation: 12/3=4, Resulting Numbers: [50, 30, 4] Generated Node #2: [50, 30, 4] from Operation: 12/3=4 Current State: 80:[50, 30, 4], Operations: ['12/3=4'] Exploring Operation: 50-30=20, Resulting Numbers: [4, 20] Generated Node #3: [4, 20] from Operation: 50-30=20 Current State: 80:[4, 20], Operations: ['12/3=4', '50-30=20'] Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[12, 3, 50, 30], Operations: [] Exploring Operation: 50-30=20, Resulting Numbers: [12, 3, 20] Generated Node #0,0: 80:[12, 3, 20] Operation: 50-30=20 Exploring Operation: 50+30=80, Resulting Numbers: [12, 3, 80] Generated Node #0,1: 80:[12, 3, 80] Operation: 50+30=80 Exploring Operation: 30/3=10, Resulting Numbers: [12, 50, 10] Generated Node #0,2: 80:[12, 50, 10] Operation: 30/3=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[12, 3, 20], Operations: ['50-30=20'] Exploring Operation: 12/3=4, Resulting Numbers: [20, 4] Generated Node #0,0,0: 80:[20, 4] Operation: 12/3=4 Exploring Operation: 12+3=15, Resulting Numbers: [20, 15] Generated Node #0,0,1: 80:[20, 15] Operation: 12+3=15 Exploring Operation: 12-3=9, Resulting Numbers: [20, 9] Generated Node #0,0,2: 80:[20, 9] Operation: 12-3=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[20, 4], Operations: ['50-30=20', '12/3=4'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[12, 3, 50, 30], Operations: [] Exploring Operation: 50-30=20, Resulting Numbers: [12, 3, 20] Generated Node #0,0: 80:[12, 3, 20] Operation: 50-30=20 Moving to Node #0,0 Current State: 80:[12, 3, 20], Operations: ['50-30=20'] Exploring Operation: 12/3=4, Resulting Numbers: [20, 4] Generated Node #0,0,0: 80:[20, 4] Operation: 12/3=4 Moving to Node #0,0,0 Current State: 80:[20, 4], Operations: ['50-30=20', '12/3=4'] Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 1, 59, 26, 63 ]
30
[ "1*59=59", "26+63=89", "89-59=30" ]
Current State: 30:[1, 59, 26, 63], Operations: [] Exploring Operation: 1*59=59, Resulting Numbers: [26, 63, 59] Generated Node #2: [26, 63, 59] from Operation: 1*59=59 Current State: 30:[26, 63, 59], Operations: ['1*59=59'] Exploring Operation: 26+63=89, Resulting Numbers: [59, 89] Generated Node #3: [59, 89] from Operation: 26+63=89 Current State: 30:[59, 89], Operations: ['1*59=59', '26+63=89'] Exploring Operation: 89-59=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[1, 59, 26, 63], Operations: [] Exploring Operation: 59-1=58, Resulting Numbers: [26, 63, 58] Generated Node #0,0: 30:[26, 63, 58] Operation: 59-1=58 Exploring Operation: 59-26=33, Resulting Numbers: [1, 63, 33] Generated Node #0,1: 30:[1, 63, 33] Operation: 59-26=33 Exploring Operation: 63-59=4, Resulting Numbers: [1, 26, 4] Generated Node #0,2: 30:[1, 26, 4] Operation: 63-59=4 Exploring Operation: 63-26=37, Resulting Numbers: [1, 59, 37] Generated Node #0,3: 30:[1, 59, 37] Operation: 63-26=37 Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[1, 26, 4], Operations: ['63-59=4'] Exploring Operation: 4-1=3, Resulting Numbers: [26, 3] Generated Node #0,2,0: 30:[26, 3] Operation: 4-1=3 Exploring Operation: 26+4=30, Resulting Numbers: [1, 30] Generated Node #0,2,1: 30:[1, 30] Operation: 26+4=30 Exploring Operation: 1+4=5, Resulting Numbers: [26, 5] Generated Node #0,2,2: 30:[26, 5] Operation: 1+4=5 Exploring Operation: 1+26=27, Resulting Numbers: [4, 27] Generated Node #0,2,3: 30:[4, 27] Operation: 1+26=27 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 30:[1, 30], Operations: ['63-59=4', '26+4=30'] Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,30 unequal: No Solution Exploring Operation: 1+30=31, Resulting Numbers: [31] 31,30 unequal: No Solution Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[1, 59, 26, 63], Operations: [] Exploring Operation: 63-59=4, Resulting Numbers: [1, 26, 4] Generated Node #0,2: 30:[1, 26, 4] Operation: 63-59=4 Moving to Node #0,2 Current State: 30:[1, 26, 4], Operations: ['63-59=4'] Exploring Operation: 26+4=30, Resulting Numbers: [1, 30] Generated Node #0,2,1: 30:[1, 30] Operation: 26+4=30 Moving to Node #0,2,1 Current State: 30:[1, 30], Operations: ['63-59=4', '26+4=30'] Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 26, 45, 45, 66 ]
39
[ "66-26=40", "45/45=1", "40-1=39" ]
Current State: 39:[26, 45, 45, 66], Operations: [] Exploring Operation: 66-26=40, Resulting Numbers: [45, 45, 40] Generated Node #2: [45, 45, 40] from Operation: 66-26=40 Current State: 39:[45, 45, 40], Operations: ['66-26=40'] Exploring Operation: 45/45=1, Resulting Numbers: [40, 1] Generated Node #3: [40, 1] from Operation: 45/45=1 Current State: 39:[40, 1], Operations: ['66-26=40', '45/45=1'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[26, 45, 45, 66], Operations: [] Exploring Operation: 66-45=21, Resulting Numbers: [26, 45, 21] Generated Node #0,0: 39:[26, 45, 21] Operation: 66-45=21 Exploring Operation: 45-26=19, Resulting Numbers: [45, 66, 19] Generated Node #0,1: 39:[45, 66, 19] Operation: 45-26=19 Exploring Operation: 66-45=21, Resulting Numbers: [26, 45, 21] Generated Node #0,2: 39:[26, 45, 21] Operation: 66-45=21 Exploring Operation: 45-26=19, Resulting Numbers: [45, 66, 19] Generated Node #0,3: 39:[45, 66, 19] Operation: 45-26=19 Exploring Operation: 66-26=40, Resulting Numbers: [45, 45, 40] Generated Node #0,4: 39:[45, 45, 40] Operation: 66-26=40 Start Sub Search at level 1: Moving to Node #0,4 Current State: 39:[45, 45, 40], Operations: ['66-26=40'] Exploring Operation: 45+45=90, Resulting Numbers: [40, 90] Generated Node #0,4,0: 39:[40, 90] Operation: 45+45=90 Exploring Operation: 45/45=1, Resulting Numbers: [40, 1] Generated Node #0,4,1: 39:[40, 1] Operation: 45/45=1 Exploring Operation: 45-40=5, Resulting Numbers: [45, 5] Generated Node #0,4,2: 39:[45, 5] Operation: 45-40=5 Exploring Operation: 45-40=5, Resulting Numbers: [45, 5] Generated Node #0,4,3: 39:[45, 5] Operation: 45-40=5 Exploring Operation: 45-45=0, Resulting Numbers: [40, 0] Generated Node #0,4,4: 39:[40, 0] Operation: 45-45=0 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 39:[40, 1], Operations: ['66-26=40', '45/45=1'] Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,39 unequal: No Solution Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,39 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[26, 45, 45, 66], Operations: [] Exploring Operation: 66-26=40, Resulting Numbers: [45, 45, 40] Generated Node #0,4: 39:[45, 45, 40] Operation: 66-26=40 Moving to Node #0,4 Current State: 39:[45, 45, 40], Operations: ['66-26=40'] Exploring Operation: 45/45=1, Resulting Numbers: [40, 1] Generated Node #0,4,1: 39:[40, 1] Operation: 45/45=1 Moving to Node #0,4,1 Current State: 39:[40, 1], Operations: ['66-26=40', '45/45=1'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 45, 49, 3, 2 ]
22
[ "49-3=46", "46/2=23", "45-23=22" ]
Current State: 22:[45, 49, 3, 2], Operations: [] Exploring Operation: 49-3=46, Resulting Numbers: [45, 2, 46] Generated Node #2: [45, 2, 46] from Operation: 49-3=46 Current State: 22:[45, 2, 46], Operations: ['49-3=46'] Exploring Operation: 46/2=23, Resulting Numbers: [45, 23] Generated Node #3: [45, 23] from Operation: 46/2=23 Current State: 22:[45, 23], Operations: ['49-3=46', '46/2=23'] Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[45, 49, 3, 2], Operations: [] Exploring Operation: 49-45=4, Resulting Numbers: [3, 2, 4] Generated Node #0,0: 22:[3, 2, 4] Operation: 49-45=4 Exploring Operation: 45-3=42, Resulting Numbers: [49, 2, 42] Generated Node #0,1: 22:[49, 2, 42] Operation: 45-3=42 Exploring Operation: 49-3=46, Resulting Numbers: [45, 2, 46] Generated Node #0,2: 22:[45, 2, 46] Operation: 49-3=46 Exploring Operation: 45/3=15, Resulting Numbers: [49, 2, 15] Generated Node #0,3: 22:[49, 2, 15] Operation: 45/3=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[3, 2, 4], Operations: ['49-45=4'] Exploring Operation: 4-2=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 22:[3, 2] Operation: 4-2=2 Exploring Operation: 3*4=12, Resulting Numbers: [2, 12] Generated Node #0,0,1: 22:[2, 12] Operation: 3*4=12 Exploring Operation: 4-3=1, Resulting Numbers: [2, 1] Generated Node #0,0,2: 22:[2, 1] Operation: 4-3=1 Exploring Operation: 4/2=2, Resulting Numbers: [3, 2] Generated Node #0,0,3: 22:[3, 2] Operation: 4/2=2 Moving to Node #0,0,0 Current State: 22:[3, 2], Operations: ['49-45=4', '4-2=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,22 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[2, 1], Operations: ['49-45=4', '4-3=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,22 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[2, 12], Operations: ['49-45=4', '3*4=12'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,22 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,22 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,22 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,22 unequal: No Solution Moving to Node #0,0,3 Current State: 22:[3, 2], Operations: ['49-45=4', '4/2=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 22:[49, 2, 15], Operations: ['45/3=15'] Exploring Operation: 49-2=47, Resulting Numbers: [15, 47] Generated Node #0,3,0: 22:[15, 47] Operation: 49-2=47 Exploring Operation: 49-15=34, Resulting Numbers: [2, 34] Generated Node #0,3,1: 22:[2, 34] Operation: 49-15=34 Exploring Operation: 2+15=17, Resulting Numbers: [49, 17] Generated Node #0,3,2: 22:[49, 17] Operation: 2+15=17 Exploring Operation: 15-2=13, Resulting Numbers: [49, 13] Generated Node #0,3,3: 22:[49, 13] Operation: 15-2=13 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 22:[2, 34], Operations: ['45/3=15', '49-15=34'] Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,22 unequal: No Solution Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,22 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,22 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,22 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: 22:[15, 47], Operations: ['45/3=15', '49-2=47'] Exploring Operation: 15*47=705, Resulting Numbers: [705] 705,22 unequal: No Solution Exploring Operation: 15+47=62, Resulting Numbers: [62] 62,22 unequal: No Solution Exploring Operation: 47-15=32, Resulting Numbers: [32] 32,22 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: 22:[49, 13], Operations: ['45/3=15', '15-2=13'] Exploring Operation: 49*13=637, Resulting Numbers: [637] 637,22 unequal: No Solution Exploring Operation: 49+13=62, Resulting Numbers: [62] 62,22 unequal: No Solution Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,22 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: 22:[49, 17], Operations: ['45/3=15', '2+15=17'] Exploring Operation: 49-17=32, Resulting Numbers: [32] 32,22 unequal: No Solution Exploring Operation: 49*17=833, Resulting Numbers: [833] 833,22 unequal: No Solution Exploring Operation: 49+17=66, Resulting Numbers: [66] 66,22 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: 22:[49, 2, 42], Operations: ['45-3=42'] Exploring Operation: 49-42=7, Resulting Numbers: [2, 7] Generated Node #0,1,0: 22:[2, 7] Operation: 49-42=7 Exploring Operation: 42-2=40, Resulting Numbers: [49, 40] Generated Node #0,1,1: 22:[49, 40] Operation: 42-2=40 Exploring Operation: 49-2=47, Resulting Numbers: [42, 47] Generated Node #0,1,2: 22:[42, 47] Operation: 49-2=47 Exploring Operation: 42/2=21, Resulting Numbers: [49, 21] Generated Node #0,1,3: 22:[49, 21] Operation: 42/2=21 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 22:[2, 7], Operations: ['45-3=42', '49-42=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,22 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,22 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,22 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: 22:[49, 21], Operations: ['45-3=42', '42/2=21'] Exploring Operation: 49-21=28, Resulting Numbers: [28] 28,22 unequal: No Solution Exploring Operation: 49+21=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 49*21=1029, Resulting Numbers: [1029] 1029,22 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: 22:[49, 40], Operations: ['45-3=42', '42-2=40'] Exploring Operation: 49+40=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 49*40=1960, Resulting Numbers: [1960] 1960,22 unequal: No Solution Exploring Operation: 49-40=9, Resulting Numbers: [9] 9,22 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: 22:[42, 47], Operations: ['45-3=42', '49-2=47'] Exploring Operation: 42+47=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 47-42=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 42*47=1974, Resulting Numbers: [1974] 1974,22 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: 22:[45, 2, 46], Operations: ['49-3=46'] Exploring Operation: 45-2=43, Resulting Numbers: [46, 43] Generated Node #0,2,0: 22:[46, 43] Operation: 45-2=43 Exploring Operation: 46/2=23, Resulting Numbers: [45, 23] Generated Node #0,2,1: 22:[45, 23] Operation: 46/2=23 Exploring Operation: 46-2=44, Resulting Numbers: [45, 44] Generated Node #0,2,2: 22:[45, 44] Operation: 46-2=44 Exploring Operation: 46-45=1, Resulting Numbers: [2, 1] Generated Node #0,2,3: 22:[2, 1] Operation: 46-45=1 Moving to Node #0,2,3 Current State: 22:[2, 1], Operations: ['49-3=46', '46-45=1'] Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,22 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,22 unequal: No Solution Moving to Node #0,2,1 Current State: 22:[45, 23], Operations: ['49-3=46', '46/2=23'] Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[45, 49, 3, 2], Operations: [] Exploring Operation: 49-3=46, Resulting Numbers: [45, 2, 46] Generated Node #0,2: 22:[45, 2, 46] Operation: 49-3=46 Moving to Node #0,2 Current State: 22:[45, 2, 46], Operations: ['49-3=46'] Exploring Operation: 46/2=23, Resulting Numbers: [45, 23] Generated Node #0,2,1: 22:[45, 23] Operation: 46/2=23 Moving to Node #0,2,1 Current State: 22:[45, 23], Operations: ['49-3=46', '46/2=23'] Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.940972
hs_4
sum_heuristic
[ 19, 5, 15, 10 ]
95
[ "15+10=25", "19*25=475", "475/5=95" ]
Current State: 95:[19, 5, 15, 10], Operations: [] Exploring Operation: 15+10=25, Resulting Numbers: [19, 5, 25] Generated Node #2: [19, 5, 25] from Operation: 15+10=25 Current State: 95:[19, 5, 25], Operations: ['15+10=25'] Exploring Operation: 19*25=475, Resulting Numbers: [5, 475] Generated Node #3: [5, 475] from Operation: 19*25=475 Current State: 95:[5, 475], Operations: ['15+10=25', '19*25=475'] Exploring Operation: 475/5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[19, 5, 15, 10], Operations: [] Exploring Operation: 19-15=4, Resulting Numbers: [5, 10, 4] Generated Node #0,0: 95:[5, 10, 4] Operation: 19-15=4 Exploring Operation: 5+15=20, Resulting Numbers: [19, 10, 20] Generated Node #0,1: 95:[19, 10, 20] Operation: 5+15=20 Exploring Operation: 15+10=25, Resulting Numbers: [19, 5, 25] Generated Node #0,2: 95:[19, 5, 25] Operation: 15+10=25 Exploring Operation: 15-10=5, Resulting Numbers: [19, 5, 5] Generated Node #0,3: 95:[19, 5, 5] Operation: 15-10=5 Exploring Operation: 10-5=5, Resulting Numbers: [19, 15, 5] Generated Node #0,4: 95:[19, 15, 5] Operation: 10-5=5 Moving to Node #0,3 Current State: 95:[19, 5, 5], Operations: ['15-10=5'] Exploring Operation: 19+5=24, Resulting Numbers: [5, 24] Generated Node #0,3,0: 95:[5, 24] Operation: 19+5=24 Exploring Operation: 19*5=95, Resulting Numbers: [5, 95] Generated Node #0,3,1: 95:[5, 95] Operation: 19*5=95 Exploring Operation: 5/5=1, Resulting Numbers: [19, 1] Generated Node #0,3,2: 95:[19, 1] Operation: 5/5=1 Exploring Operation: 19-5=14, Resulting Numbers: [5, 14] Generated Node #0,3,3: 95:[5, 14] Operation: 19-5=14 Exploring Operation: 19*5=95, Resulting Numbers: [5, 95] Generated Node #0,3,4: 95:[5, 95] Operation: 19*5=95 Moving to Node #0,4 Current State: 95:[19, 15, 5], Operations: ['10-5=5'] Exploring Operation: 19-15=4, Resulting Numbers: [5, 4] Generated Node #0,4,0: 95:[5, 4] Operation: 19-15=4 Exploring Operation: 15/5=3, Resulting Numbers: [19, 3] Generated Node #0,4,1: 95:[19, 3] Operation: 15/5=3 Exploring Operation: 15+5=20, Resulting Numbers: [19, 20] Generated Node #0,4,2: 95:[19, 20] Operation: 15+5=20 Exploring Operation: 19*5=95, Resulting Numbers: [15, 95] Generated Node #0,4,3: 95:[15, 95] Operation: 19*5=95 Exploring Operation: 15-5=10, Resulting Numbers: [19, 10] Generated Node #0,4,4: 95:[19, 10] Operation: 15-5=10 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 95:[5, 4], Operations: ['10-5=5', '19-15=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,95 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,95 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 95:[19, 20], Operations: ['10-5=5', '15+5=20'] Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,95 unequal: No Solution Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,95 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 95:[19, 3], Operations: ['10-5=5', '15/5=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,95 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 95:[15, 95], Operations: ['10-5=5', '19*5=95'] Exploring Operation: 95-15=80, Resulting Numbers: [80] 80,95 unequal: No Solution Exploring Operation: 15*95=1425, Resulting Numbers: [1425] 1425,95 unequal: No Solution Exploring Operation: 15+95=110, Resulting Numbers: [110] 110,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 95:[19, 10], Operations: ['10-5=5', '15-5=10'] Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,95 unequal: No Solution Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,95 unequal: No Solution Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,95 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: 95:[5, 10, 4], Operations: ['19-15=4'] Exploring Operation: 10/5=2, Resulting Numbers: [4, 2] Generated Node #0,0,0: 95:[4, 2] Operation: 10/5=2 Exploring Operation: 10-5=5, Resulting Numbers: [4, 5] Generated Node #0,0,1: 95:[4, 5] Operation: 10-5=5 Exploring Operation: 5+10=15, Resulting Numbers: [4, 15] Generated Node #0,0,2: 95:[4, 15] Operation: 5+10=15 Exploring Operation: 10+4=14, Resulting Numbers: [5, 14] Generated Node #0,0,3: 95:[5, 14] Operation: 10+4=14 Exploring Operation: 10-4=6, Resulting Numbers: [5, 6] Generated Node #0,0,4: 95:[5, 6] Operation: 10-4=6 Moving to Node #0,1 Current State: 95:[19, 10, 20], Operations: ['5+15=20'] Exploring Operation: 20-10=10, Resulting Numbers: [19, 10] Generated Node #0,1,0: 95:[19, 10] Operation: 20-10=10 Exploring Operation: 20-19=1, Resulting Numbers: [10, 1] Generated Node #0,1,1: 95:[10, 1] Operation: 20-19=1 Exploring Operation: 19+10=29, Resulting Numbers: [20, 29] Generated Node #0,1,2: 95:[20, 29] Operation: 19+10=29 Exploring Operation: 19-10=9, Resulting Numbers: [20, 9] Generated Node #0,1,3: 95:[20, 9] Operation: 19-10=9 Exploring Operation: 20/10=2, Resulting Numbers: [19, 2] Generated Node #0,1,4: 95:[19, 2] Operation: 20/10=2 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 95:[19, 2], Operations: ['5+15=20', '20/10=2'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,95 unequal: No Solution Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,95 unequal: No Solution Exploring Operation: 19+2=21, Resulting Numbers: [21] 21,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 95:[19, 10], Operations: ['5+15=20', '20-10=10'] Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,95 unequal: No Solution Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,95 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 95:[20, 9], Operations: ['5+15=20', '19-10=9'] Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,95 unequal: No Solution Exploring Operation: 20+9=29, Resulting Numbers: [29] 29,95 unequal: No Solution Exploring Operation: 20*9=180, Resulting Numbers: [180] 180,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 95:[10, 1], Operations: ['5+15=20', '20-19=1'] Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,95 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,95 unequal: No Solution Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 95:[20, 29], Operations: ['5+15=20', '19+10=29'] Exploring Operation: 20+29=49, Resulting Numbers: [49] 49,95 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,95 unequal: No Solution Exploring Operation: 20*29=580, Resulting Numbers: [580] 580,95 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: 95:[19, 5, 25], Operations: ['15+10=25'] Exploring Operation: 25-5=20, Resulting Numbers: [19, 20] Generated Node #0,2,0: 95:[19, 20] Operation: 25-5=20 Exploring Operation: 25-19=6, Resulting Numbers: [5, 6] Generated Node #0,2,1: 95:[5, 6] Operation: 25-19=6 Exploring Operation: 19*5=95, Resulting Numbers: [25, 95] Generated Node #0,2,2: 95:[25, 95] Operation: 19*5=95 Exploring Operation: 25/5=5, Resulting Numbers: [19, 5] Generated Node #0,2,3: 95:[19, 5] Operation: 25/5=5 Exploring Operation: 19+5=24, Resulting Numbers: [25, 24] Generated Node #0,2,4: 95:[25, 24] Operation: 19+5=24 Moving to Node #0,3,1 Current State: 95:[5, 95], Operations: ['15-10=5', '19*5=95'] Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,95 unequal: No Solution Exploring Operation: 5*95=475, Resulting Numbers: [475] 475,95 unequal: No Solution Exploring Operation: 95-5=90, Resulting Numbers: [90] 90,95 unequal: No Solution Exploring Operation: 5+95=100, Resulting Numbers: [100] 100,95 unequal: No Solution Moving to Node #0,3,4 Current State: 95:[5, 95], Operations: ['15-10=5', '19*5=95'] Exploring Operation: 95-5=90, Resulting Numbers: [90] 90,95 unequal: No Solution Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,95 unequal: No Solution Exploring Operation: 5*95=475, Resulting Numbers: [475] 475,95 unequal: No Solution Exploring Operation: 5+95=100, Resulting Numbers: [100] 100,95 unequal: No Solution Moving to Node #0,2,3 Current State: 95:[19, 5], Operations: ['15+10=25', '25/5=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[19, 5, 15, 10], Operations: [] Exploring Operation: 15+10=25, Resulting Numbers: [19, 5, 25] Generated Node #0,2: 95:[19, 5, 25] Operation: 15+10=25 Moving to Node #0,2 Current State: 95:[19, 5, 25], Operations: ['15+10=25'] Exploring Operation: 25/5=5, Resulting Numbers: [19, 5] Generated Node #0,2,3: 95:[19, 5] Operation: 25/5=5 Moving to Node #0,2,3 Current State: 95:[19, 5], Operations: ['15+10=25', '25/5=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
0.935764
hs_5
mult_heuristic
[ 93, 90, 51, 37 ]
20
[ "93-90=3", "51/3=17", "37-17=20" ]
Current State: 20:[93, 90, 51, 37], Operations: [] Exploring Operation: 93-90=3, Resulting Numbers: [51, 37, 3] Generated Node #2: [51, 37, 3] from Operation: 93-90=3 Current State: 20:[51, 37, 3], Operations: ['93-90=3'] Exploring Operation: 51/3=17, Resulting Numbers: [37, 17] Generated Node #3: [37, 17] from Operation: 51/3=17 Current State: 20:[37, 17], Operations: ['93-90=3', '51/3=17'] Exploring Operation: 37-17=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[93, 90, 51, 37], Operations: [] Exploring Operation: 90-51=39, Resulting Numbers: [93, 37, 39] Generated Node #0,0: 20:[93, 37, 39] Operation: 90-51=39 Exploring Operation: 90-37=53, Resulting Numbers: [93, 51, 53] Generated Node #0,1: 20:[93, 51, 53] Operation: 90-37=53 Exploring Operation: 93-37=56, Resulting Numbers: [90, 51, 56] Generated Node #0,2: 20:[90, 51, 56] Operation: 93-37=56 Exploring Operation: 93-90=3, Resulting Numbers: [51, 37, 3] Generated Node #0,3: 20:[51, 37, 3] Operation: 93-90=3 Exploring Operation: 93-51=42, Resulting Numbers: [90, 37, 42] Generated Node #0,4: 20:[90, 37, 42] Operation: 93-51=42 Start Sub Search at level 1: Moving to Node #0,3 Current State: 20:[51, 37, 3], Operations: ['93-90=3'] Exploring Operation: 51-3=48, Resulting Numbers: [37, 48] Generated Node #0,3,0: 20:[37, 48] Operation: 51-3=48 Exploring Operation: 37-3=34, Resulting Numbers: [51, 34] Generated Node #0,3,1: 20:[51, 34] Operation: 37-3=34 Exploring Operation: 51/3=17, Resulting Numbers: [37, 17] Generated Node #0,3,2: 20:[37, 17] Operation: 51/3=17 Exploring Operation: 51+3=54, Resulting Numbers: [37, 54] Generated Node #0,3,3: 20:[37, 54] Operation: 51+3=54 Exploring Operation: 51-37=14, Resulting Numbers: [3, 14] Generated Node #0,3,4: 20:[3, 14] Operation: 51-37=14 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 20:[3, 14], Operations: ['93-90=3', '51-37=14'] Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,20 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,20 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,20 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 #0,3,2 Current State: 20:[37, 17], Operations: ['93-90=3', '51/3=17'] Exploring Operation: 37+17=54, Resulting Numbers: [54] 54,20 unequal: No Solution Exploring Operation: 37-17=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[93, 90, 51, 37], Operations: [] Exploring Operation: 93-90=3, Resulting Numbers: [51, 37, 3] Generated Node #0,3: 20:[51, 37, 3] Operation: 93-90=3 Moving to Node #0,3 Current State: 20:[51, 37, 3], Operations: ['93-90=3'] Exploring Operation: 51/3=17, Resulting Numbers: [37, 17] Generated Node #0,3,2: 20:[37, 17] Operation: 51/3=17 Moving to Node #0,3,2 Current State: 20:[37, 17], Operations: ['93-90=3', '51/3=17'] Exploring Operation: 37-17=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 17, 11, 7, 50 ]
63
[ "17-11=6", "7+50=57", "6+57=63" ]
Current State: 63:[17, 11, 7, 50], Operations: [] Exploring Operation: 17-11=6, Resulting Numbers: [7, 50, 6] Generated Node #2: [7, 50, 6] from Operation: 17-11=6 Current State: 63:[7, 50, 6], Operations: ['17-11=6'] Exploring Operation: 7+50=57, Resulting Numbers: [6, 57] Generated Node #3: [6, 57] from Operation: 7+50=57 Current State: 63:[6, 57], Operations: ['17-11=6', '7+50=57'] Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[17, 11, 7, 50], Operations: [] Exploring Operation: 17+50=67, Resulting Numbers: [11, 7, 67] Generated Node #0,0: 63:[11, 7, 67] Operation: 17+50=67 Exploring Operation: 11+50=61, Resulting Numbers: [17, 7, 61] Generated Node #0,1: 63:[17, 7, 61] Operation: 11+50=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[11, 7, 67], Operations: ['17+50=67'] Exploring Operation: 67-7=60, Resulting Numbers: [11, 60] Generated Node #0,0,0: 63:[11, 60] Operation: 67-7=60 Exploring Operation: 11-7=4, Resulting Numbers: [67, 4] Generated Node #0,0,1: 63:[67, 4] Operation: 11-7=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[11, 60], Operations: ['17+50=67', '67-7=60'] Exploring Operation: 11+60=71, Resulting Numbers: [71] 71,63 unequal: No Solution Exploring Operation: 60-11=49, Resulting Numbers: [49] 49,63 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: 63:[67, 4], Operations: ['17+50=67', '11-7=4'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[17, 11, 7, 50], Operations: [] Exploring Operation: 17+50=67, Resulting Numbers: [11, 7, 67] Generated Node #0,0: 63:[11, 7, 67] Operation: 17+50=67 Moving to Node #0,0 Current State: 63:[11, 7, 67], Operations: ['17+50=67'] Exploring Operation: 11-7=4, Resulting Numbers: [67, 4] Generated Node #0,0,1: 63:[67, 4] Operation: 11-7=4 Moving to Node #0,0,1 Current State: 63:[67, 4], Operations: ['17+50=67', '11-7=4'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 14, 16, 88, 27 ]
66
[ "27-16=11", "14*11=154", "154-88=66" ]
Current State: 66:[14, 16, 88, 27], Operations: [] Exploring Operation: 27-16=11, Resulting Numbers: [14, 88, 11] Generated Node #2: [14, 88, 11] from Operation: 27-16=11 Current State: 66:[14, 88, 11], Operations: ['27-16=11'] Exploring Operation: 14*11=154, Resulting Numbers: [88, 154] Generated Node #3: [88, 154] from Operation: 14*11=154 Current State: 66:[88, 154], Operations: ['27-16=11', '14*11=154'] Exploring Operation: 154-88=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[14, 16, 88, 27], Operations: [] Exploring Operation: 88-27=61, Resulting Numbers: [14, 16, 61] Generated Node #0,0: 66:[14, 16, 61] Operation: 88-27=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[14, 16, 61], Operations: ['88-27=61'] Exploring Operation: 16-14=2, Resulting Numbers: [61, 2] Generated Node #0,0,0: 66:[61, 2] Operation: 16-14=2 Moving to Node #0,0,0 Current State: 66:[61, 2], Operations: ['88-27=61', '16-14=2'] Exploring Operation: 61+2=63, Resulting Numbers: [63] 63,66 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
[ 81, 47, 64, 95 ]
97
[ "81+47=128", "95-64=31", "128-31=97" ]
Current State: 97:[81, 47, 64, 95], Operations: [] Exploring Operation: 81+47=128, Resulting Numbers: [64, 95, 128] Generated Node #2: [64, 95, 128] from Operation: 81+47=128 Current State: 97:[64, 95, 128], Operations: ['81+47=128'] Exploring Operation: 95-64=31, Resulting Numbers: [128, 31] Generated Node #3: [128, 31] from Operation: 95-64=31 Current State: 97:[128, 31], Operations: ['81+47=128', '95-64=31'] Exploring Operation: 128-31=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[81, 47, 64, 95], Operations: [] Exploring Operation: 81-47=34, Resulting Numbers: [64, 95, 34] Generated Node #0,0: 97:[64, 95, 34] Operation: 81-47=34 Exploring Operation: 47+64=111, Resulting Numbers: [81, 95, 111] Generated Node #0,1: 97:[81, 95, 111] Operation: 47+64=111 Exploring Operation: 47+95=142, Resulting Numbers: [81, 64, 142] Generated Node #0,2: 97:[81, 64, 142] Operation: 47+95=142 Exploring Operation: 81+47=128, Resulting Numbers: [64, 95, 128] Generated Node #0,3: 97:[64, 95, 128] Operation: 81+47=128 Moving to Node #0,1 Current State: 97:[81, 95, 111], Operations: ['47+64=111'] Exploring Operation: 81+95=176, Resulting Numbers: [111, 176] Generated Node #0,1,0: 97:[111, 176] Operation: 81+95=176 Exploring Operation: 111-81=30, Resulting Numbers: [95, 30] Generated Node #0,1,1: 97:[95, 30] Operation: 111-81=30 Exploring Operation: 81+111=192, Resulting Numbers: [95, 192] Generated Node #0,1,2: 97:[95, 192] Operation: 81+111=192 Exploring Operation: 95-81=14, Resulting Numbers: [111, 14] Generated Node #0,1,3: 97:[111, 14] Operation: 95-81=14 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[95, 30], Operations: ['47+64=111', '111-81=30'] Exploring Operation: 95*30=2850, Resulting Numbers: [2850] 2850,97 unequal: No Solution Exploring Operation: 95-30=65, Resulting Numbers: [65] 65,97 unequal: No Solution Exploring Operation: 95+30=125, Resulting Numbers: [125] 125,97 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 #0,1,0 Current State: 97:[111, 176], Operations: ['47+64=111', '81+95=176'] Exploring Operation: 111*176=19536, Resulting Numbers: [19536] 19536,97 unequal: No Solution Exploring Operation: 111+176=287, Resulting Numbers: [287] 287,97 unequal: No Solution Exploring Operation: 176-111=65, Resulting Numbers: [65] 65,97 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 #0,1,2 Current State: 97:[95, 192], Operations: ['47+64=111', '81+111=192'] Exploring Operation: 95+192=287, Resulting Numbers: [287] 287,97 unequal: No Solution Exploring Operation: 95*192=18240, Resulting Numbers: [18240] 18240,97 unequal: No Solution Exploring Operation: 192-95=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[81, 47, 64, 95], Operations: [] Exploring Operation: 47+64=111, Resulting Numbers: [81, 95, 111] Generated Node #0,1: 97:[81, 95, 111] Operation: 47+64=111 Moving to Node #0,1 Current State: 97:[81, 95, 111], Operations: ['47+64=111'] Exploring Operation: 81+111=192, Resulting Numbers: [95, 192] Generated Node #0,1,2: 97:[95, 192] Operation: 81+111=192 Moving to Node #0,1,2 Current State: 97:[95, 192], Operations: ['47+64=111', '81+111=192'] Exploring Operation: 192-95=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 96, 63, 21, 56 ]
85
[ "96*56=5376", "5376-21=5355", "5355/63=85" ]
Current State: 85:[96, 63, 21, 56], Operations: [] Exploring Operation: 96*56=5376, Resulting Numbers: [63, 21, 5376] Generated Node #2: [63, 21, 5376] from Operation: 96*56=5376 Current State: 85:[63, 21, 5376], Operations: ['96*56=5376'] Exploring Operation: 5376-21=5355, Resulting Numbers: [63, 5355] Generated Node #3: [63, 5355] from Operation: 5376-21=5355 Current State: 85:[63, 5355], Operations: ['96*56=5376', '5376-21=5355'] Exploring Operation: 5355/63=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[96, 63, 21, 56], Operations: [] Exploring Operation: 63-56=7, Resulting Numbers: [96, 21, 7] Generated Node #0,0: 85:[96, 21, 7] Operation: 63-56=7 Moving to Node #0,0 Current State: 85:[96, 21, 7], Operations: ['63-56=7'] Exploring Operation: 96-7=89, Resulting Numbers: [21, 89] Generated Node #0,0,0: 85:[21, 89] Operation: 96-7=89 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[21, 89], Operations: ['63-56=7', '96-7=89'] Exploring Operation: 89-21=68, Resulting Numbers: [68] 68,85 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
[ 2, 90, 91, 15 ]
83
[ "91-2=89", "90/15=6", "89-6=83" ]
Current State: 83:[2, 90, 91, 15], Operations: [] Exploring Operation: 91-2=89, Resulting Numbers: [90, 15, 89] Generated Node #2: [90, 15, 89] from Operation: 91-2=89 Current State: 83:[90, 15, 89], Operations: ['91-2=89'] Exploring Operation: 90/15=6, Resulting Numbers: [89, 6] Generated Node #3: [89, 6] from Operation: 90/15=6 Current State: 83:[89, 6], Operations: ['91-2=89', '90/15=6'] Exploring Operation: 89-6=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[2, 90, 91, 15], Operations: [] Exploring Operation: 90-2=88, Resulting Numbers: [91, 15, 88] Generated Node #0,0: 83:[91, 15, 88] Operation: 90-2=88 Exploring Operation: 2*15=30, Resulting Numbers: [90, 91, 30] Generated Node #0,1: 83:[90, 91, 30] Operation: 2*15=30 Exploring Operation: 2+15=17, Resulting Numbers: [90, 91, 17] Generated Node #0,2: 83:[90, 91, 17] Operation: 2+15=17 Exploring Operation: 91-2=89, Resulting Numbers: [90, 15, 89] Generated Node #0,3: 83:[90, 15, 89] Operation: 91-2=89 Moving to Node #0,1 Current State: 83:[90, 91, 30], Operations: ['2*15=30'] Exploring Operation: 91-30=61, Resulting Numbers: [90, 61] Generated Node #0,1,0: 83:[90, 61] Operation: 91-30=61 Exploring Operation: 91+30=121, Resulting Numbers: [90, 121] Generated Node #0,1,1: 83:[90, 121] Operation: 91+30=121 Exploring Operation: 90+30=120, Resulting Numbers: [91, 120] Generated Node #0,1,2: 83:[91, 120] Operation: 90+30=120 Exploring Operation: 90-30=60, Resulting Numbers: [91, 60] Generated Node #0,1,3: 83:[91, 60] Operation: 90-30=60 Moving to Node #0,2 Current State: 83:[90, 91, 17], Operations: ['2+15=17'] Exploring Operation: 91-17=74, Resulting Numbers: [90, 74] Generated Node #0,2,0: 83:[90, 74] Operation: 91-17=74 Exploring Operation: 91+17=108, Resulting Numbers: [90, 108] Generated Node #0,2,1: 83:[90, 108] Operation: 91+17=108 Exploring Operation: 90-17=73, Resulting Numbers: [91, 73] Generated Node #0,2,2: 83:[91, 73] Operation: 90-17=73 Exploring Operation: 90+17=107, Resulting Numbers: [91, 107] Generated Node #0,2,3: 83:[91, 107] Operation: 90+17=107 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 83:[90, 74], Operations: ['2+15=17', '91-17=74'] Exploring Operation: 90*74=6660, Resulting Numbers: [6660] 6660,83 unequal: No Solution Exploring Operation: 90+74=164, Resulting Numbers: [164] 164,83 unequal: No Solution Exploring Operation: 90-74=16, Resulting Numbers: [16] 16,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 83:[91, 73], Operations: ['2+15=17', '90-17=73'] Exploring Operation: 91*73=6643, Resulting Numbers: [6643] 6643,83 unequal: No Solution Exploring Operation: 91+73=164, Resulting Numbers: [164] 164,83 unequal: No Solution Exploring Operation: 91-73=18, Resulting Numbers: [18] 18,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 83:[90, 108], Operations: ['2+15=17', '91+17=108'] Exploring Operation: 90+108=198, Resulting Numbers: [198] 198,83 unequal: No Solution Exploring Operation: 108-90=18, Resulting Numbers: [18] 18,83 unequal: No Solution Exploring Operation: 90*108=9720, Resulting Numbers: [9720] 9720,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 83:[91, 107], Operations: ['2+15=17', '90+17=107'] Exploring Operation: 107-91=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 91+107=198, Resulting Numbers: [198] 198,83 unequal: No Solution Exploring Operation: 91*107=9737, Resulting Numbers: [9737] 9737,83 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: 83:[91, 15, 88], Operations: ['90-2=88'] Exploring Operation: 15+88=103, Resulting Numbers: [91, 103] Generated Node #0,0,0: 83:[91, 103] Operation: 15+88=103 Exploring Operation: 91+15=106, Resulting Numbers: [88, 106] Generated Node #0,0,1: 83:[88, 106] Operation: 91+15=106 Exploring Operation: 91-15=76, Resulting Numbers: [88, 76] Generated Node #0,0,2: 83:[88, 76] Operation: 91-15=76 Exploring Operation: 88-15=73, Resulting Numbers: [91, 73] Generated Node #0,0,3: 83:[91, 73] Operation: 88-15=73 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[88, 76], Operations: ['90-2=88', '91-15=76'] Exploring Operation: 88+76=164, Resulting Numbers: [164] 164,83 unequal: No Solution Exploring Operation: 88*76=6688, Resulting Numbers: [6688] 6688,83 unequal: No Solution Exploring Operation: 88-76=12, Resulting Numbers: [12] 12,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 83:[91, 73], Operations: ['90-2=88', '88-15=73'] Exploring Operation: 91*73=6643, Resulting Numbers: [6643] 6643,83 unequal: No Solution Exploring Operation: 91+73=164, Resulting Numbers: [164] 164,83 unequal: No Solution Exploring Operation: 91-73=18, Resulting Numbers: [18] 18,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[91, 103], Operations: ['90-2=88', '15+88=103'] Exploring Operation: 91*103=9373, Resulting Numbers: [9373] 9373,83 unequal: No Solution Exploring Operation: 91+103=194, Resulting Numbers: [194] 194,83 unequal: No Solution Exploring Operation: 103-91=12, Resulting Numbers: [12] 12,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[88, 106], Operations: ['90-2=88', '91+15=106'] Exploring Operation: 88*106=9328, Resulting Numbers: [9328] 9328,83 unequal: No Solution Exploring Operation: 106-88=18, Resulting Numbers: [18] 18,83 unequal: No Solution Exploring Operation: 88+106=194, Resulting Numbers: [194] 194,83 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: 83:[90, 15, 89], Operations: ['91-2=89'] Exploring Operation: 90-15=75, Resulting Numbers: [89, 75] Generated Node #0,3,0: 83:[89, 75] Operation: 90-15=75 Exploring Operation: 89-15=74, Resulting Numbers: [90, 74] Generated Node #0,3,1: 83:[90, 74] Operation: 89-15=74 Exploring Operation: 15+89=104, Resulting Numbers: [90, 104] Generated Node #0,3,2: 83:[90, 104] Operation: 15+89=104 Exploring Operation: 90+15=105, Resulting Numbers: [89, 105] Generated Node #0,3,3: 83:[89, 105] Operation: 90+15=105 Moving to Node #0,3,0 Current State: 83:[89, 75], Operations: ['91-2=89', '90-15=75'] Exploring Operation: 89+75=164, Resulting Numbers: [164] 164,83 unequal: No Solution Exploring Operation: 89*75=6675, Resulting Numbers: [6675] 6675,83 unequal: No Solution Exploring Operation: 89-75=14, Resulting Numbers: [14] 14,83 unequal: No Solution Moving to Node #0,3,1 Current State: 83:[90, 74], Operations: ['91-2=89', '89-15=74'] Exploring Operation: 90-74=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 90*74=6660, Resulting Numbers: [6660] 6660,83 unequal: No Solution Exploring Operation: 90+74=164, Resulting Numbers: [164] 164,83 unequal: No Solution Moving to Node #0,3,2 Current State: 83:[90, 104], Operations: ['91-2=89', '15+89=104'] Exploring Operation: 104-90=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 90+104=194, Resulting Numbers: [194] 194,83 unequal: No Solution Exploring Operation: 90*104=9360, Resulting Numbers: [9360] 9360,83 unequal: No Solution Moving to Node #0,3,3 Current State: 83:[89, 105], Operations: ['91-2=89', '90+15=105'] Exploring Operation: 89*105=9345, Resulting Numbers: [9345] 9345,83 unequal: No Solution Exploring Operation: 105-89=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 89+105=194, Resulting Numbers: [194] 194,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[90, 61], Operations: ['2*15=30', '91-30=61'] Exploring Operation: 90+61=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 90*61=5490, Resulting Numbers: [5490] 5490,83 unequal: No Solution Exploring Operation: 90-61=29, Resulting Numbers: [29] 29,83 unequal: No Solution Moving to Node #0,1,3 Current State: 83:[91, 60], Operations: ['2*15=30', '90-30=60'] Exploring Operation: 91*60=5460, Resulting Numbers: [5460] 5460,83 unequal: No Solution Exploring Operation: 91+60=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 91-60=31, Resulting Numbers: [31] 31,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[91, 120], Operations: ['2*15=30', '90+30=120'] Exploring Operation: 91*120=10920, Resulting Numbers: [10920] 10920,83 unequal: No Solution Exploring Operation: 120-91=29, Resulting Numbers: [29] 29,83 unequal: No Solution Exploring Operation: 91+120=211, Resulting Numbers: [211] 211,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[90, 121], Operations: ['2*15=30', '91+30=121'] Exploring Operation: 90*121=10890, Resulting Numbers: [10890] 10890,83 unequal: No Solution Exploring Operation: 121-90=31, Resulting Numbers: [31] 31,83 unequal: No Solution Exploring Operation: 90+121=211, Resulting Numbers: [211] 211,83 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 89, 16, 15, 60 ]
29
[ "89-60=29", "16-15=1", "29*1=29" ]
Current State: 29:[89, 16, 15, 60], Operations: [] Exploring Operation: 89-60=29, Resulting Numbers: [16, 15, 29] Generated Node #2: [16, 15, 29] from Operation: 89-60=29 Current State: 29:[16, 15, 29], Operations: ['89-60=29'] Exploring Operation: 16-15=1, Resulting Numbers: [29, 1] Generated Node #3: [29, 1] from Operation: 16-15=1 Current State: 29:[29, 1], Operations: ['89-60=29', '16-15=1'] Exploring Operation: 29*1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[89, 16, 15, 60], Operations: [] Exploring Operation: 89-60=29, Resulting Numbers: [16, 15, 29] Generated Node #0,0: 29:[16, 15, 29] Operation: 89-60=29 Exploring Operation: 89-15=74, Resulting Numbers: [16, 60, 74] Generated Node #0,1: 29:[16, 60, 74] Operation: 89-15=74 Exploring Operation: 89-16=73, Resulting Numbers: [15, 60, 73] Generated Node #0,2: 29:[15, 60, 73] Operation: 89-16=73 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[16, 15, 29], Operations: ['89-60=29'] Exploring Operation: 16-15=1, Resulting Numbers: [29, 1] Generated Node #0,0,0: 29:[29, 1] Operation: 16-15=1 Exploring Operation: 16+15=31, Resulting Numbers: [29, 31] Generated Node #0,0,1: 29:[29, 31] Operation: 16+15=31 Exploring Operation: 15+29=44, Resulting Numbers: [16, 44] Generated Node #0,0,2: 29:[16, 44] Operation: 15+29=44 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 29:[29, 31], Operations: ['89-60=29', '16+15=31'] Exploring Operation: 29+31=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 31-29=2, Resulting Numbers: [2] 2,29 unequal: No Solution Exploring Operation: 29*31=899, Resulting Numbers: [899] 899,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[29, 1], Operations: ['89-60=29', '16-15=1'] Exploring Operation: 29+1=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 29*1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[89, 16, 15, 60], Operations: [] Exploring Operation: 89-60=29, Resulting Numbers: [16, 15, 29] Generated Node #0,0: 29:[16, 15, 29] Operation: 89-60=29 Moving to Node #0,0 Current State: 29:[16, 15, 29], Operations: ['89-60=29'] Exploring Operation: 16-15=1, Resulting Numbers: [29, 1] Generated Node #0,0,0: 29:[29, 1] Operation: 16-15=1 Moving to Node #0,0,0 Current State: 29:[29, 1], Operations: ['89-60=29', '16-15=1'] Exploring Operation: 29*1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 51, 16, 46, 26 ]
80
[ "51*26=1326", "1326-46=1280", "1280/16=80" ]
Current State: 80:[51, 16, 46, 26], Operations: [] Exploring Operation: 51*26=1326, Resulting Numbers: [16, 46, 1326] Generated Node #2: [16, 46, 1326] from Operation: 51*26=1326 Current State: 80:[16, 46, 1326], Operations: ['51*26=1326'] Exploring Operation: 1326-46=1280, Resulting Numbers: [16, 1280] Generated Node #3: [16, 1280] from Operation: 1326-46=1280 Current State: 80:[16, 1280], Operations: ['51*26=1326', '1326-46=1280'] Exploring Operation: 1280/16=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[51, 16, 46, 26], Operations: [] Exploring Operation: 51-46=5, Resulting Numbers: [16, 26, 5] Generated Node #0,0: 80:[16, 26, 5] Operation: 51-46=5 Moving to Node #0,0 Current State: 80:[16, 26, 5], Operations: ['51-46=5'] Exploring Operation: 26-16=10, Resulting Numbers: [5, 10] Generated Node #0,0,0: 80:[5, 10] Operation: 26-16=10 Moving to Node #0,0,0 Current State: 80:[5, 10], Operations: ['51-46=5', '26-16=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,80 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 62, 79, 7, 71 ]
98
[ "62+71=133", "133/7=19", "79+19=98" ]
Current State: 98:[62, 79, 7, 71], Operations: [] Exploring Operation: 62+71=133, Resulting Numbers: [79, 7, 133] Generated Node #2: [79, 7, 133] from Operation: 62+71=133 Current State: 98:[79, 7, 133], Operations: ['62+71=133'] Exploring Operation: 133/7=19, Resulting Numbers: [79, 19] Generated Node #3: [79, 19] from Operation: 133/7=19 Current State: 98:[79, 19], Operations: ['62+71=133', '133/7=19'] Exploring Operation: 79+19=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[62, 79, 7, 71], Operations: [] Exploring Operation: 79+7=86, Resulting Numbers: [62, 71, 86] Generated Node #0,0: 98:[62, 71, 86] Operation: 79+7=86 Exploring Operation: 62-7=55, Resulting Numbers: [79, 71, 55] Generated Node #0,1: 98:[79, 71, 55] Operation: 62-7=55 Exploring Operation: 79-71=8, Resulting Numbers: [62, 7, 8] Generated Node #0,2: 98:[62, 7, 8] Operation: 79-71=8 Exploring Operation: 71-62=9, Resulting Numbers: [79, 7, 9] Generated Node #0,3: 98:[79, 7, 9] Operation: 71-62=9 Exploring Operation: 79-62=17, Resulting Numbers: [7, 71, 17] Generated Node #0,4: 98:[7, 71, 17] Operation: 79-62=17 Moving to Node #0,2 Current State: 98:[62, 7, 8], Operations: ['79-71=8'] Exploring Operation: 7+8=15, Resulting Numbers: [62, 15] Generated Node #0,2,0: 98:[62, 15] Operation: 7+8=15 Exploring Operation: 62-8=54, Resulting Numbers: [7, 54] Generated Node #0,2,1: 98:[7, 54] Operation: 62-8=54 Exploring Operation: 62-7=55, Resulting Numbers: [8, 55] Generated Node #0,2,2: 98:[8, 55] Operation: 62-7=55 Exploring Operation: 8-7=1, Resulting Numbers: [62, 1] Generated Node #0,2,3: 98:[62, 1] Operation: 8-7=1 Exploring Operation: 7*8=56, Resulting Numbers: [62, 56] Generated Node #0,2,4: 98:[62, 56] Operation: 7*8=56 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 98:[7, 54], Operations: ['79-71=8', '62-8=54'] Exploring Operation: 54-7=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 7+54=61, Resulting Numbers: [61] 61,98 unequal: No Solution Exploring Operation: 7*54=378, Resulting Numbers: [378] 378,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 98:[8, 55], Operations: ['79-71=8', '62-7=55'] Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 8+55=63, Resulting Numbers: [63] 63,98 unequal: No Solution Exploring Operation: 8*55=440, Resulting Numbers: [440] 440,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 98:[62, 15], Operations: ['79-71=8', '7+8=15'] Exploring Operation: 62-15=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 62+15=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 62*15=930, Resulting Numbers: [930] 930,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 98:[62, 1], Operations: ['79-71=8', '8-7=1'] Exploring Operation: 62*1=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,98 unequal: No Solution Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 98:[62, 56], Operations: ['79-71=8', '7*8=56'] Exploring Operation: 62-56=6, Resulting Numbers: [6] 6,98 unequal: No Solution Exploring Operation: 62*56=3472, Resulting Numbers: [3472] 3472,98 unequal: No Solution Exploring Operation: 62+56=118, Resulting Numbers: [118] 118,98 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: 98:[79, 7, 9], Operations: ['71-62=9'] Exploring Operation: 9-7=2, Resulting Numbers: [79, 2] Generated Node #0,3,0: 98:[79, 2] Operation: 9-7=2 Exploring Operation: 79-9=70, Resulting Numbers: [7, 70] Generated Node #0,3,1: 98:[7, 70] Operation: 79-9=70 Exploring Operation: 79+7=86, Resulting Numbers: [9, 86] Generated Node #0,3,2: 98:[9, 86] Operation: 79+7=86 Exploring Operation: 7+9=16, Resulting Numbers: [79, 16] Generated Node #0,3,3: 98:[79, 16] Operation: 7+9=16 Exploring Operation: 79+9=88, Resulting Numbers: [7, 88] Generated Node #0,3,4: 98:[7, 88] Operation: 79+9=88 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 98:[7, 88], Operations: ['71-62=9', '79+9=88'] Exploring Operation: 7+88=95, Resulting Numbers: [95] 95,98 unequal: No Solution Exploring Operation: 88-7=81, Resulting Numbers: [81] 81,98 unequal: No Solution Exploring Operation: 7*88=616, Resulting Numbers: [616] 616,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 98:[9, 86], Operations: ['71-62=9', '79+7=86'] Exploring Operation: 9*86=774, Resulting Numbers: [774] 774,98 unequal: No Solution Exploring Operation: 9+86=95, Resulting Numbers: [95] 95,98 unequal: No Solution Exploring Operation: 86-9=77, Resulting Numbers: [77] 77,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 98:[79, 2], Operations: ['71-62=9', '9-7=2'] Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,98 unequal: No Solution Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,98 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 98:[7, 70], Operations: ['71-62=9', '79-9=70'] Exploring Operation: 7+70=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 7*70=490, Resulting Numbers: [490] 490,98 unequal: No Solution Exploring Operation: 70-7=63, Resulting Numbers: [63] 63,98 unequal: No Solution Exploring Operation: 70/7=10, Resulting Numbers: [10] 10,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 98:[79, 16], Operations: ['71-62=9', '7+9=16'] Exploring Operation: 79+16=95, Resulting Numbers: [95] 95,98 unequal: No Solution Exploring Operation: 79*16=1264, Resulting Numbers: [1264] 1264,98 unequal: No Solution Exploring Operation: 79-16=63, Resulting Numbers: [63] 63,98 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: 98:[7, 71, 17], Operations: ['79-62=17'] Exploring Operation: 71+17=88, Resulting Numbers: [7, 88] Generated Node #0,4,0: 98:[7, 88] Operation: 71+17=88 Exploring Operation: 71-7=64, Resulting Numbers: [17, 64] Generated Node #0,4,1: 98:[17, 64] Operation: 71-7=64 Exploring Operation: 7+71=78, Resulting Numbers: [17, 78] Generated Node #0,4,2: 98:[17, 78] Operation: 7+71=78 Exploring Operation: 17-7=10, Resulting Numbers: [71, 10] Generated Node #0,4,3: 98:[71, 10] Operation: 17-7=10 Exploring Operation: 71-17=54, Resulting Numbers: [7, 54] Generated Node #0,4,4: 98:[7, 54] Operation: 71-17=54 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 98:[7, 54], Operations: ['79-62=17', '71-17=54'] Exploring Operation: 7+54=61, Resulting Numbers: [61] 61,98 unequal: No Solution Exploring Operation: 54-7=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 7*54=378, Resulting Numbers: [378] 378,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 98:[7, 88], Operations: ['79-62=17', '71+17=88'] Exploring Operation: 7*88=616, Resulting Numbers: [616] 616,98 unequal: No Solution Exploring Operation: 88-7=81, Resulting Numbers: [81] 81,98 unequal: No Solution Exploring Operation: 7+88=95, Resulting Numbers: [95] 95,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 98:[17, 64], Operations: ['79-62=17', '71-7=64'] Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 17*64=1088, Resulting Numbers: [1088] 1088,98 unequal: No Solution Exploring Operation: 17+64=81, Resulting Numbers: [81] 81,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 98:[17, 78], Operations: ['79-62=17', '7+71=78'] Exploring Operation: 17*78=1326, Resulting Numbers: [1326] 1326,98 unequal: No Solution Exploring Operation: 17+78=95, Resulting Numbers: [95] 95,98 unequal: No Solution Exploring Operation: 78-17=61, Resulting Numbers: [61] 61,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 98:[71, 10], Operations: ['79-62=17', '17-7=10'] Exploring Operation: 71+10=81, Resulting Numbers: [81] 81,98 unequal: No Solution Exploring Operation: 71-10=61, Resulting Numbers: [61] 61,98 unequal: No Solution Exploring Operation: 71*10=710, Resulting Numbers: [710] 710,98 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: 98:[62, 71, 86], Operations: ['79+7=86'] Exploring Operation: 62+86=148, Resulting Numbers: [71, 148] Generated Node #0,0,0: 98:[71, 148] Operation: 62+86=148 Exploring Operation: 62+71=133, Resulting Numbers: [86, 133] Generated Node #0,0,1: 98:[86, 133] Operation: 62+71=133 Exploring Operation: 71-62=9, Resulting Numbers: [86, 9] Generated Node #0,0,2: 98:[86, 9] Operation: 71-62=9 Exploring Operation: 86-71=15, Resulting Numbers: [62, 15] Generated Node #0,0,3: 98:[62, 15] Operation: 86-71=15 Exploring Operation: 86-62=24, Resulting Numbers: [71, 24] Generated Node #0,0,4: 98:[71, 24] Operation: 86-62=24 Moving to Node #0,1 Current State: 98:[79, 71, 55], Operations: ['62-7=55'] Exploring Operation: 71-55=16, Resulting Numbers: [79, 16] Generated Node #0,1,0: 98:[79, 16] Operation: 71-55=16 Exploring Operation: 79-71=8, Resulting Numbers: [55, 8] Generated Node #0,1,1: 98:[55, 8] Operation: 79-71=8 Exploring Operation: 79+71=150, Resulting Numbers: [55, 150] Generated Node #0,1,2: 98:[55, 150] Operation: 79+71=150 Exploring Operation: 71+55=126, Resulting Numbers: [79, 126] Generated Node #0,1,3: 98:[79, 126] Operation: 71+55=126 Exploring Operation: 79-55=24, Resulting Numbers: [71, 24] Generated Node #0,1,4: 98:[71, 24] Operation: 79-55=24 Moving to Node #0,1,1 Current State: 98:[55, 8], Operations: ['62-7=55', '79-71=8'] Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 55*8=440, Resulting Numbers: [440] 440,98 unequal: No Solution Exploring Operation: 55+8=63, Resulting Numbers: [63] 63,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[86, 9], Operations: ['79+7=86', '71-62=9'] Exploring Operation: 86-9=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 86*9=774, Resulting Numbers: [774] 774,98 unequal: No Solution Exploring Operation: 86+9=95, Resulting Numbers: [95] 95,98 unequal: No Solution Moving to Node #0,0,3 Current State: 98:[62, 15], Operations: ['79+7=86', '86-71=15'] Exploring Operation: 62-15=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 62*15=930, Resulting Numbers: [930] 930,98 unequal: No Solution Exploring Operation: 62+15=77, Resulting Numbers: [77] 77,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[79, 16], Operations: ['62-7=55', '71-55=16'] Exploring Operation: 79+16=95, Resulting Numbers: [95] 95,98 unequal: No Solution Exploring Operation: 79*16=1264, Resulting Numbers: [1264] 1264,98 unequal: No Solution Exploring Operation: 79-16=63, Resulting Numbers: [63] 63,98 unequal: No Solution Moving to Node #0,0,4 Current State: 98:[71, 24], Operations: ['79+7=86', '86-62=24'] Exploring Operation: 71*24=1704, Resulting Numbers: [1704] 1704,98 unequal: No Solution Exploring Operation: 71-24=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 71+24=95, Resulting Numbers: [95] 95,98 unequal: No Solution Moving to Node #0,1,4 Current State: 98:[71, 24], Operations: ['62-7=55', '79-55=24'] Exploring Operation: 71+24=95, Resulting Numbers: [95] 95,98 unequal: No Solution Exploring Operation: 71-24=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 71*24=1704, Resulting Numbers: [1704] 1704,98 unequal: No Solution Moving to Node #0,1,3 Current State: 98:[79, 126], Operations: ['62-7=55', '71+55=126'] Exploring Operation: 126-79=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 79*126=9954, Resulting Numbers: [9954] 9954,98 unequal: No Solution Exploring Operation: 79+126=205, Resulting Numbers: [205] 205,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[86, 133], Operations: ['79+7=86', '62+71=133'] Exploring Operation: 86*133=11438, Resulting Numbers: [11438] 11438,98 unequal: No Solution Exploring Operation: 133-86=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 86+133=219, Resulting Numbers: [219] 219,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[55, 150], Operations: ['62-7=55', '79+71=150'] Exploring Operation: 55*150=8250, Resulting Numbers: [8250] 8250,98 unequal: No Solution Exploring Operation: 150-55=95, Resulting Numbers: [95] 95,98 unequal: No Solution Exploring Operation: 55+150=205, Resulting Numbers: [205] 205,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[71, 148], Operations: ['79+7=86', '62+86=148'] Exploring Operation: 71+148=219, Resulting Numbers: [219] 219,98 unequal: No Solution Exploring Operation: 71*148=10508, Resulting Numbers: [10508] 10508,98 unequal: No Solution Exploring Operation: 148-71=77, Resulting Numbers: [77] 77,98 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 18, 15, 74, 84 ]
10
[ "74-18=56", "15*56=840", "840/84=10" ]
Current State: 10:[18, 15, 74, 84], Operations: [] Exploring Operation: 74-18=56, Resulting Numbers: [15, 84, 56] Generated Node #2: [15, 84, 56] from Operation: 74-18=56 Current State: 10:[15, 84, 56], Operations: ['74-18=56'] Exploring Operation: 15*56=840, Resulting Numbers: [84, 840] Generated Node #3: [84, 840] from Operation: 15*56=840 Current State: 10:[84, 840], Operations: ['74-18=56', '15*56=840'] Exploring Operation: 840/84=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[18, 15, 74, 84], Operations: [] Exploring Operation: 84-74=10, Resulting Numbers: [18, 15, 10] Generated Node #0,0: 10:[18, 15, 10] Operation: 84-74=10 Exploring Operation: 74-18=56, Resulting Numbers: [15, 84, 56] Generated Node #0,1: 10:[15, 84, 56] Operation: 74-18=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[18, 15, 10], Operations: ['84-74=10'] Exploring Operation: 18-15=3, Resulting Numbers: [10, 3] Generated Node #0,0,0: 10:[10, 3] Operation: 18-15=3 Exploring Operation: 18-10=8, Resulting Numbers: [15, 8] Generated Node #0,0,1: 10:[15, 8] Operation: 18-10=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[10, 3], Operations: ['84-74=10', '18-15=3'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,10 unequal: No Solution Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,10 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 #0,0,1 Current State: 10:[15, 8], Operations: ['84-74=10', '18-10=8'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,10 unequal: No Solution Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,10 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: 10:[15, 84, 56], Operations: ['74-18=56'] Exploring Operation: 84-56=28, Resulting Numbers: [15, 28] Generated Node #0,1,0: 10:[15, 28] Operation: 84-56=28 Exploring Operation: 84-15=69, Resulting Numbers: [56, 69] Generated Node #0,1,1: 10:[56, 69] Operation: 84-15=69 Moving to Node #0,1,0 Current State: 10:[15, 28], Operations: ['74-18=56', '84-56=28'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,10 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,10 unequal: No Solution Moving to Node #0,1,1 Current State: 10:[56, 69], Operations: ['74-18=56', '84-15=69'] Exploring Operation: 56+69=125, Resulting Numbers: [125] 125,10 unequal: No Solution Exploring Operation: 69-56=13, Resulting Numbers: [13] 13,10 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
[ 56, 3, 70, 59 ]
42
[ "56-3=53", "70-59=11", "53-11=42" ]
Current State: 42:[56, 3, 70, 59], Operations: [] Exploring Operation: 56-3=53, Resulting Numbers: [70, 59, 53] Generated Node #2: [70, 59, 53] from Operation: 56-3=53 Current State: 42:[70, 59, 53], Operations: ['56-3=53'] Exploring Operation: 70-59=11, Resulting Numbers: [53, 11] Generated Node #3: [53, 11] from Operation: 70-59=11 Current State: 42:[53, 11], Operations: ['56-3=53', '70-59=11'] Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[56, 3, 70, 59], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [3, 70, 3] Generated Node #0,0: 42:[3, 70, 3] Operation: 59-56=3 Exploring Operation: 70-59=11, Resulting Numbers: [56, 3, 11] Generated Node #0,1: 42:[56, 3, 11] Operation: 70-59=11 Exploring Operation: 70-56=14, Resulting Numbers: [3, 59, 14] Generated Node #0,2: 42:[3, 59, 14] Operation: 70-56=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[56, 3, 11], Operations: ['70-59=11'] Exploring Operation: 56-11=45, Resulting Numbers: [3, 45] Generated Node #0,1,0: 42:[3, 45] Operation: 56-11=45 Exploring Operation: 56-3=53, Resulting Numbers: [11, 53] Generated Node #0,1,1: 42:[11, 53] Operation: 56-3=53 Exploring Operation: 3+11=14, Resulting Numbers: [56, 14] Generated Node #0,1,2: 42:[56, 14] Operation: 3+11=14 Moving to Node #0,1,0 Current State: 42:[3, 45], Operations: ['70-59=11', '56-11=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 3+45=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[56, 3, 70, 59], Operations: [] Exploring Operation: 70-59=11, Resulting Numbers: [56, 3, 11] Generated Node #0,1: 42:[56, 3, 11] Operation: 70-59=11 Moving to Node #0,1 Current State: 42:[56, 3, 11], Operations: ['70-59=11'] Exploring Operation: 56-11=45, Resulting Numbers: [3, 45] Generated Node #0,1,0: 42:[3, 45] Operation: 56-11=45 Moving to Node #0,1,0 Current State: 42:[3, 45], Operations: ['70-59=11', '56-11=45'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 41, 74, 22, 98 ]
87
[ "74-41=33", "22+98=120", "120-33=87" ]
Current State: 87:[41, 74, 22, 98], Operations: [] Exploring Operation: 74-41=33, Resulting Numbers: [22, 98, 33] Generated Node #2: [22, 98, 33] from Operation: 74-41=33 Current State: 87:[22, 98, 33], Operations: ['74-41=33'] Exploring Operation: 22+98=120, Resulting Numbers: [33, 120] Generated Node #3: [33, 120] from Operation: 22+98=120 Current State: 87:[33, 120], Operations: ['74-41=33', '22+98=120'] Exploring Operation: 120-33=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[41, 74, 22, 98], Operations: [] Exploring Operation: 74-41=33, Resulting Numbers: [22, 98, 33] Generated Node #0,0: 87:[22, 98, 33] Operation: 74-41=33 Exploring Operation: 98-74=24, Resulting Numbers: [41, 22, 24] Generated Node #0,1: 87:[41, 22, 24] Operation: 98-74=24 Moving to Node #0,0 Current State: 87:[22, 98, 33], Operations: ['74-41=33'] Exploring Operation: 98-22=76, Resulting Numbers: [33, 76] Generated Node #0,0,0: 87:[33, 76] Operation: 98-22=76 Exploring Operation: 33-22=11, Resulting Numbers: [98, 11] Generated Node #0,0,1: 87:[98, 11] Operation: 33-22=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[33, 76], Operations: ['74-41=33', '98-22=76'] Exploring Operation: 33+76=109, Resulting Numbers: [109] 109,87 unequal: No Solution Exploring Operation: 76-33=43, Resulting Numbers: [43] 43,87 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:[98, 11], Operations: ['74-41=33', '33-22=11'] Exploring Operation: 98+11=109, Resulting Numbers: [109] 109,87 unequal: No Solution Exploring Operation: 98-11=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[41, 74, 22, 98], Operations: [] Exploring Operation: 74-41=33, Resulting Numbers: [22, 98, 33] Generated Node #0,0: 87:[22, 98, 33] Operation: 74-41=33 Moving to Node #0,0 Current State: 87:[22, 98, 33], Operations: ['74-41=33'] Exploring Operation: 33-22=11, Resulting Numbers: [98, 11] Generated Node #0,0,1: 87:[98, 11] Operation: 33-22=11 Moving to Node #0,0,1 Current State: 87:[98, 11], Operations: ['74-41=33', '33-22=11'] Exploring Operation: 98-11=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 72, 63, 7, 7 ]
63
[ "72*7=504", "63*7=441", "504-441=63" ]
Current State: 63:[72, 63, 7, 7], Operations: [] Exploring Operation: 72*7=504, Resulting Numbers: [63, 504] Generated Node #2: [63, 504] from Operation: 72*7=504 Current State: 63:[63, 504], Operations: ['72*7=504'] Exploring Operation: 63*7=441, Resulting Numbers: [504, 441] Generated Node #3: [504, 441] from Operation: 63*7=441 Current State: 63:[504, 441], Operations: ['72*7=504', '63*7=441'] Exploring Operation: 504-441=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[72, 63, 7, 7], Operations: [] Exploring Operation: 72-63=9, Resulting Numbers: [7, 7, 9] Generated Node #0,0: 63:[7, 7, 9] Operation: 72-63=9 Exploring Operation: 72-7=65, Resulting Numbers: [63, 7, 65] Generated Node #0,1: 63:[63, 7, 65] Operation: 72-7=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[7, 7, 9], Operations: ['72-63=9'] Exploring Operation: 7*9=63, Resulting Numbers: [7, 63] Generated Node #0,0,0: 63:[7, 63] Operation: 7*9=63 Exploring Operation: 7*9=63, Resulting Numbers: [7, 63] Generated Node #0,0,1: 63:[7, 63] Operation: 7*9=63 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[7, 63], Operations: ['72-63=9', '7*9=63'] Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 7+63=70, Resulting Numbers: [70] 70,63 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: 63:[7, 63], Operations: ['72-63=9', '7*9=63'] Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 7+63=70, Resulting Numbers: [70] 70,63 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: 63:[63, 7, 65], Operations: ['72-7=65'] Exploring Operation: 65-63=2, Resulting Numbers: [7, 2] Generated Node #0,1,0: 63:[7, 2] Operation: 65-63=2 Exploring Operation: 63/7=9, Resulting Numbers: [65, 9] Generated Node #0,1,1: 63:[65, 9] Operation: 63/7=9 Moving to Node #0,1,0 Current State: 63:[7, 2], Operations: ['72-7=65', '65-63=2'] Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[65, 9], Operations: ['72-7=65', '63/7=9'] Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,63 unequal: No Solution Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,63 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
[ 9, 29, 40, 8 ]
69
[ "9-8=1", "29+40=69", "1*69=69" ]
Current State: 69:[9, 29, 40, 8], Operations: [] Exploring Operation: 9-8=1, Resulting Numbers: [29, 40, 1] Generated Node #2: [29, 40, 1] from Operation: 9-8=1 Current State: 69:[29, 40, 1], Operations: ['9-8=1'] Exploring Operation: 29+40=69, Resulting Numbers: [1, 69] Generated Node #3: [1, 69] from Operation: 29+40=69 Current State: 69:[1, 69], Operations: ['9-8=1', '29+40=69'] Exploring Operation: 1*69=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[9, 29, 40, 8], Operations: [] Exploring Operation: 29+40=69, Resulting Numbers: [9, 8, 69] Generated Node #0,0: 69:[9, 8, 69] Operation: 29+40=69 Moving to Node #0,0 Current State: 69:[9, 8, 69], Operations: ['29+40=69'] Exploring Operation: 9-8=1, Resulting Numbers: [69, 1] Generated Node #0,0,0: 69:[69, 1] Operation: 9-8=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[69, 1], Operations: ['29+40=69', '9-8=1'] Exploring Operation: 69*1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[9, 29, 40, 8], Operations: [] Exploring Operation: 29+40=69, Resulting Numbers: [9, 8, 69] Generated Node #0,0: 69:[9, 8, 69] Operation: 29+40=69 Moving to Node #0,0 Current State: 69:[9, 8, 69], Operations: ['29+40=69'] Exploring Operation: 9-8=1, Resulting Numbers: [69, 1] Generated Node #0,0,0: 69:[69, 1] Operation: 9-8=1 Moving to Node #0,0,0 Current State: 69:[69, 1], Operations: ['29+40=69', '9-8=1'] Exploring Operation: 69*1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 89, 64, 58, 61 ]
22
[ "89-64=25", "61-58=3", "25-3=22" ]
Current State: 22:[89, 64, 58, 61], Operations: [] Exploring Operation: 89-64=25, Resulting Numbers: [58, 61, 25] Generated Node #2: [58, 61, 25] from Operation: 89-64=25 Current State: 22:[58, 61, 25], Operations: ['89-64=25'] Exploring Operation: 61-58=3, Resulting Numbers: [25, 3] Generated Node #3: [25, 3] from Operation: 61-58=3 Current State: 22:[25, 3], Operations: ['89-64=25', '61-58=3'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[89, 64, 58, 61], Operations: [] Exploring Operation: 89-61=28, Resulting Numbers: [64, 58, 28] Generated Node #0,0: 22:[64, 58, 28] Operation: 89-61=28 Exploring Operation: 89-64=25, Resulting Numbers: [58, 61, 25] Generated Node #0,1: 22:[58, 61, 25] Operation: 89-64=25 Exploring Operation: 89-58=31, Resulting Numbers: [64, 61, 31] Generated Node #0,2: 22:[64, 61, 31] Operation: 89-58=31 Exploring Operation: 64-61=3, Resulting Numbers: [89, 58, 3] Generated Node #0,3: 22:[89, 58, 3] Operation: 64-61=3 Exploring Operation: 64-58=6, Resulting Numbers: [89, 61, 6] Generated Node #0,4: 22:[89, 61, 6] Operation: 64-58=6 Moving to Node #0,1 Current State: 22:[58, 61, 25], Operations: ['89-64=25'] Exploring Operation: 61-25=36, Resulting Numbers: [58, 36] Generated Node #0,1,0: 22:[58, 36] Operation: 61-25=36 Exploring Operation: 61-58=3, Resulting Numbers: [25, 3] Generated Node #0,1,1: 22:[25, 3] Operation: 61-58=3 Exploring Operation: 58+61=119, Resulting Numbers: [25, 119] Generated Node #0,1,2: 22:[25, 119] Operation: 58+61=119 Exploring Operation: 58+25=83, Resulting Numbers: [61, 83] Generated Node #0,1,3: 22:[61, 83] Operation: 58+25=83 Exploring Operation: 58-25=33, Resulting Numbers: [61, 33] Generated Node #0,1,4: 22:[61, 33] Operation: 58-25=33 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[25, 3], Operations: ['89-64=25', '61-58=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,22 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[89, 64, 58, 61], Operations: [] Exploring Operation: 89-64=25, Resulting Numbers: [58, 61, 25] Generated Node #0,1: 22:[58, 61, 25] Operation: 89-64=25 Moving to Node #0,1 Current State: 22:[58, 61, 25], Operations: ['89-64=25'] Exploring Operation: 61-58=3, Resulting Numbers: [25, 3] Generated Node #0,1,1: 22:[25, 3] Operation: 61-58=3 Moving to Node #0,1,1 Current State: 22:[25, 3], Operations: ['89-64=25', '61-58=3'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 19, 23, 7, 80 ]
91
[ "23-19=4", "7+80=87", "4+87=91" ]
Current State: 91:[19, 23, 7, 80], Operations: [] Exploring Operation: 23-19=4, Resulting Numbers: [7, 80, 4] Generated Node #2: [7, 80, 4] from Operation: 23-19=4 Current State: 91:[7, 80, 4], Operations: ['23-19=4'] Exploring Operation: 7+80=87, Resulting Numbers: [4, 87] Generated Node #3: [4, 87] from Operation: 7+80=87 Current State: 91:[4, 87], Operations: ['23-19=4', '7+80=87'] Exploring Operation: 4+87=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[19, 23, 7, 80], Operations: [] Exploring Operation: 23+80=103, Resulting Numbers: [19, 7, 103] Generated Node #0,0: 91:[19, 7, 103] Operation: 23+80=103 Exploring Operation: 19+80=99, Resulting Numbers: [23, 7, 99] Generated Node #0,1: 91:[23, 7, 99] Operation: 19+80=99 Exploring Operation: 23-19=4, Resulting Numbers: [7, 80, 4] Generated Node #0,2: 91:[7, 80, 4] Operation: 23-19=4 Exploring Operation: 23-7=16, Resulting Numbers: [19, 80, 16] Generated Node #0,3: 91:[19, 80, 16] Operation: 23-7=16 Moving to Node #0,2 Current State: 91:[7, 80, 4], Operations: ['23-19=4'] Exploring Operation: 7+4=11, Resulting Numbers: [80, 11] Generated Node #0,2,0: 91:[80, 11] Operation: 7+4=11 Exploring Operation: 7+80=87, Resulting Numbers: [4, 87] Generated Node #0,2,1: 91:[4, 87] Operation: 7+80=87 Exploring Operation: 80+4=84, Resulting Numbers: [7, 84] Generated Node #0,2,2: 91:[7, 84] Operation: 80+4=84 Exploring Operation: 80/4=20, Resulting Numbers: [7, 20] Generated Node #0,2,3: 91:[7, 20] Operation: 80/4=20 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 91:[4, 87], Operations: ['23-19=4', '7+80=87'] Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,91 unequal: No Solution Exploring Operation: 4+87=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[19, 23, 7, 80], Operations: [] Exploring Operation: 23-19=4, Resulting Numbers: [7, 80, 4] Generated Node #0,2: 91:[7, 80, 4] Operation: 23-19=4 Moving to Node #0,2 Current State: 91:[7, 80, 4], Operations: ['23-19=4'] Exploring Operation: 7+80=87, Resulting Numbers: [4, 87] Generated Node #0,2,1: 91:[4, 87] Operation: 7+80=87 Moving to Node #0,2,1 Current State: 91:[4, 87], Operations: ['23-19=4', '7+80=87'] Exploring Operation: 4+87=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 32, 42, 56, 16 ]
73
[ "42*56=2352", "2352-16=2336", "2336/32=73" ]
Current State: 73:[32, 42, 56, 16], Operations: [] Exploring Operation: 42*56=2352, Resulting Numbers: [32, 16, 2352] Generated Node #2: [32, 16, 2352] from Operation: 42*56=2352 Current State: 73:[32, 16, 2352], Operations: ['42*56=2352'] Exploring Operation: 2352-16=2336, Resulting Numbers: [32, 2336] Generated Node #3: [32, 2336] from Operation: 2352-16=2336 Current State: 73:[32, 2336], Operations: ['42*56=2352', '2352-16=2336'] Exploring Operation: 2336/32=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[32, 42, 56, 16], Operations: [] Exploring Operation: 42+16=58, Resulting Numbers: [32, 56, 58] Generated Node #0,0: 73:[32, 56, 58] Operation: 42+16=58 Exploring Operation: 32+42=74, Resulting Numbers: [56, 16, 74] Generated Node #0,1: 73:[56, 16, 74] Operation: 32+42=74 Exploring Operation: 56+16=72, Resulting Numbers: [32, 42, 72] Generated Node #0,2: 73:[32, 42, 72] Operation: 56+16=72 Exploring Operation: 32+16=48, Resulting Numbers: [42, 56, 48] Generated Node #0,3: 73:[42, 56, 48] Operation: 32+16=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[32, 56, 58], Operations: ['42+16=58'] Exploring Operation: 32+58=90, Resulting Numbers: [56, 90] Generated Node #0,0,0: 73:[56, 90] Operation: 32+58=90 Exploring Operation: 58-32=26, Resulting Numbers: [56, 26] Generated Node #0,0,1: 73:[56, 26] Operation: 58-32=26 Exploring Operation: 56-32=24, Resulting Numbers: [58, 24] Generated Node #0,0,2: 73:[58, 24] Operation: 56-32=24 Exploring Operation: 32+56=88, Resulting Numbers: [58, 88] Generated Node #0,0,3: 73:[58, 88] Operation: 32+56=88 Moving to Node #0,0,3 Current State: 73:[58, 88], Operations: ['42+16=58', '32+56=88'] Exploring Operation: 58+88=146, Resulting Numbers: [146] 146,73 unequal: No Solution Exploring Operation: 58*88=5104, Resulting Numbers: [5104] 5104,73 unequal: No Solution Exploring Operation: 88-58=30, Resulting Numbers: [30] 30,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[56, 90], Operations: ['42+16=58', '32+58=90'] Exploring Operation: 90-56=34, Resulting Numbers: [34] 34,73 unequal: No Solution Exploring Operation: 56+90=146, Resulting Numbers: [146] 146,73 unequal: No Solution Exploring Operation: 56*90=5040, Resulting Numbers: [5040] 5040,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[58, 24], Operations: ['42+16=58', '56-32=24'] Exploring Operation: 58+24=82, Resulting Numbers: [82] 82,73 unequal: No Solution Exploring Operation: 58-24=34, Resulting Numbers: [34] 34,73 unequal: No Solution Exploring Operation: 58*24=1392, Resulting Numbers: [1392] 1392,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[56, 26], Operations: ['42+16=58', '58-32=26'] Exploring Operation: 56-26=30, Resulting Numbers: [30] 30,73 unequal: No Solution Exploring Operation: 56*26=1456, Resulting Numbers: [1456] 1456,73 unequal: No Solution Exploring Operation: 56+26=82, Resulting Numbers: [82] 82,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[32, 42, 72], Operations: ['56+16=72'] Exploring Operation: 72-32=40, Resulting Numbers: [42, 40] Generated Node #0,2,0: 73:[42, 40] Operation: 72-32=40 Exploring Operation: 32+72=104, Resulting Numbers: [42, 104] Generated Node #0,2,1: 73:[42, 104] Operation: 32+72=104 Exploring Operation: 42-32=10, Resulting Numbers: [72, 10] Generated Node #0,2,2: 73:[72, 10] Operation: 42-32=10 Exploring Operation: 32+42=74, Resulting Numbers: [72, 74] Generated Node #0,2,3: 73:[72, 74] Operation: 32+42=74 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 73:[72, 74], Operations: ['56+16=72', '32+42=74'] Exploring Operation: 72+74=146, Resulting Numbers: [146] 146,73 unequal: No Solution Exploring Operation: 74-72=2, Resulting Numbers: [2] 2,73 unequal: No Solution Exploring Operation: 72*74=5328, Resulting Numbers: [5328] 5328,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 73:[42, 104], Operations: ['56+16=72', '32+72=104'] Exploring Operation: 42+104=146, Resulting Numbers: [146] 146,73 unequal: No Solution Exploring Operation: 104-42=62, Resulting Numbers: [62] 62,73 unequal: No Solution Exploring Operation: 42*104=4368, Resulting Numbers: [4368] 4368,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 73:[42, 40], Operations: ['56+16=72', '72-32=40'] Exploring Operation: 42+40=82, Resulting Numbers: [82] 82,73 unequal: No Solution Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,73 unequal: No Solution Exploring Operation: 42*40=1680, Resulting Numbers: [1680] 1680,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 73:[72, 10], Operations: ['56+16=72', '42-32=10'] Exploring Operation: 72-10=62, Resulting Numbers: [62] 62,73 unequal: No Solution Exploring Operation: 72*10=720, Resulting Numbers: [720] 720,73 unequal: No Solution Exploring Operation: 72+10=82, Resulting Numbers: [82] 82,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 73:[42, 56, 48], Operations: ['32+16=48'] Exploring Operation: 56-42=14, Resulting Numbers: [48, 14] Generated Node #0,3,0: 73:[48, 14] Operation: 56-42=14 Exploring Operation: 42+48=90, Resulting Numbers: [56, 90] Generated Node #0,3,1: 73:[56, 90] Operation: 42+48=90 Exploring Operation: 42+56=98, Resulting Numbers: [48, 98] Generated Node #0,3,2: 73:[48, 98] Operation: 42+56=98 Exploring Operation: 56+48=104, Resulting Numbers: [42, 104] Generated Node #0,3,3: 73:[42, 104] Operation: 56+48=104 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 73:[56, 90], Operations: ['32+16=48', '42+48=90'] Exploring Operation: 56*90=5040, Resulting Numbers: [5040] 5040,73 unequal: No Solution Exploring Operation: 90-56=34, Resulting Numbers: [34] 34,73 unequal: No Solution Exploring Operation: 56+90=146, Resulting Numbers: [146] 146,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 73:[48, 98], Operations: ['32+16=48', '42+56=98'] Exploring Operation: 48+98=146, Resulting Numbers: [146] 146,73 unequal: No Solution Exploring Operation: 48*98=4704, Resulting Numbers: [4704] 4704,73 unequal: No Solution Exploring Operation: 98-48=50, Resulting Numbers: [50] 50,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 73:[42, 104], Operations: ['32+16=48', '56+48=104'] Exploring Operation: 42*104=4368, Resulting Numbers: [4368] 4368,73 unequal: No Solution Exploring Operation: 104-42=62, Resulting Numbers: [62] 62,73 unequal: No Solution Exploring Operation: 42+104=146, Resulting Numbers: [146] 146,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 73:[48, 14], Operations: ['32+16=48', '56-42=14'] Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,73 unequal: No Solution Exploring Operation: 48+14=62, Resulting Numbers: [62] 62,73 unequal: No Solution Exploring Operation: 48*14=672, Resulting Numbers: [672] 672,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[56, 16, 74], Operations: ['32+42=74'] Exploring Operation: 56-16=40, Resulting Numbers: [74, 40] Generated Node #0,1,0: 73:[74, 40] Operation: 56-16=40 Exploring Operation: 74-16=58, Resulting Numbers: [56, 58] Generated Node #0,1,1: 73:[56, 58] Operation: 74-16=58 Exploring Operation: 16+74=90, Resulting Numbers: [56, 90] Generated Node #0,1,2: 73:[56, 90] Operation: 16+74=90 Exploring Operation: 56+16=72, Resulting Numbers: [74, 72] Generated Node #0,1,3: 73:[74, 72] Operation: 56+16=72 Moving to Node #0,1,3 Current State: 73:[74, 72], Operations: ['32+42=74', '56+16=72'] Exploring Operation: 74*72=5328, Resulting Numbers: [5328] 5328,73 unequal: No Solution Exploring Operation: 74-72=2, Resulting Numbers: [2] 2,73 unequal: No Solution Exploring Operation: 74+72=146, Resulting Numbers: [146] 146,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[56, 58], Operations: ['32+42=74', '74-16=58'] Exploring Operation: 56+58=114, Resulting Numbers: [114] 114,73 unequal: No Solution Exploring Operation: 58-56=2, Resulting Numbers: [2] 2,73 unequal: No Solution Exploring Operation: 56*58=3248, Resulting Numbers: [3248] 3248,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[56, 90], Operations: ['32+42=74', '16+74=90'] Exploring Operation: 56*90=5040, Resulting Numbers: [5040] 5040,73 unequal: No Solution Exploring Operation: 90-56=34, Resulting Numbers: [34] 34,73 unequal: No Solution Exploring Operation: 56+90=146, Resulting Numbers: [146] 146,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[74, 40], Operations: ['32+42=74', '56-16=40'] Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,73 unequal: No Solution Exploring Operation: 74+40=114, Resulting Numbers: [114] 114,73 unequal: No Solution Exploring Operation: 74*40=2960, Resulting Numbers: [2960] 2960,73 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
[ 18, 8, 98, 72 ]
26
[ "18*8=144", "98+72=170", "170-144=26" ]
Current State: 26:[18, 8, 98, 72], Operations: [] Exploring Operation: 18*8=144, Resulting Numbers: [98, 72, 144] Generated Node #2: [98, 72, 144] from Operation: 18*8=144 Current State: 26:[98, 72, 144], Operations: ['18*8=144'] Exploring Operation: 98+72=170, Resulting Numbers: [144, 170] Generated Node #3: [144, 170] from Operation: 98+72=170 Current State: 26:[144, 170], Operations: ['18*8=144', '98+72=170'] Exploring Operation: 170-144=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[18, 8, 98, 72], Operations: [] Exploring Operation: 98-72=26, Resulting Numbers: [18, 8, 26] Generated Node #0,0: 26:[18, 8, 26] Operation: 98-72=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[18, 8, 26], Operations: ['98-72=26'] Exploring Operation: 18+8=26, Resulting Numbers: [26, 26] Generated Node #0,0,0: 26:[26, 26] Operation: 18+8=26 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 26:[26, 26], Operations: ['98-72=26', '18+8=26'] Exploring Operation: 26/26=1, Resulting Numbers: [1] 1,26 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
[ 42, 32, 16, 39 ]
96
[ "42*16=672", "39-32=7", "672/7=96" ]
Current State: 96:[42, 32, 16, 39], Operations: [] Exploring Operation: 42*16=672, Resulting Numbers: [32, 39, 672] Generated Node #2: [32, 39, 672] from Operation: 42*16=672 Current State: 96:[32, 39, 672], Operations: ['42*16=672'] Exploring Operation: 39-32=7, Resulting Numbers: [672, 7] Generated Node #3: [672, 7] from Operation: 39-32=7 Current State: 96:[672, 7], Operations: ['42*16=672', '39-32=7'] Exploring Operation: 672/7=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[42, 32, 16, 39], Operations: [] Exploring Operation: 39-32=7, Resulting Numbers: [42, 16, 7] Generated Node #0,0: 96:[42, 16, 7] Operation: 39-32=7 Exploring Operation: 42-39=3, Resulting Numbers: [32, 16, 3] Generated Node #0,1: 96:[32, 16, 3] Operation: 42-39=3 Exploring Operation: 39-16=23, Resulting Numbers: [42, 32, 23] Generated Node #0,2: 96:[42, 32, 23] Operation: 39-16=23 Moving to Node #0,1 Current State: 96:[32, 16, 3], Operations: ['42-39=3'] Exploring Operation: 32/16=2, Resulting Numbers: [3, 2] Generated Node #0,1,0: 96:[3, 2] Operation: 32/16=2 Exploring Operation: 32-16=16, Resulting Numbers: [3, 16] Generated Node #0,1,1: 96:[3, 16] Operation: 32-16=16 Exploring Operation: 32+16=48, Resulting Numbers: [3, 48] Generated Node #0,1,2: 96:[3, 48] Operation: 32+16=48 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 96:[3, 2], Operations: ['42-39=3', '32/16=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,96 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 96:[3, 16], Operations: ['42-39=3', '32-16=16'] Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,96 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,96 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 96:[3, 48], Operations: ['42-39=3', '32+16=48'] Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,96 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,96 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: 96:[42, 16, 7], Operations: ['39-32=7'] Exploring Operation: 42-16=26, Resulting Numbers: [7, 26] Generated Node #0,0,0: 96:[7, 26] Operation: 42-16=26 Exploring Operation: 42+7=49, Resulting Numbers: [16, 49] Generated Node #0,0,1: 96:[16, 49] Operation: 42+7=49 Exploring Operation: 42/7=6, Resulting Numbers: [16, 6] Generated Node #0,0,2: 96:[16, 6] Operation: 42/7=6 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 96:[16, 6], Operations: ['39-32=7', '42/7=6'] Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[42, 32, 16, 39], Operations: [] Exploring Operation: 39-32=7, Resulting Numbers: [42, 16, 7] Generated Node #0,0: 96:[42, 16, 7] Operation: 39-32=7 Moving to Node #0,0 Current State: 96:[42, 16, 7], Operations: ['39-32=7'] Exploring Operation: 42/7=6, Resulting Numbers: [16, 6] Generated Node #0,0,2: 96:[16, 6] Operation: 42/7=6 Moving to Node #0,0,2 Current State: 96:[16, 6], Operations: ['39-32=7', '42/7=6'] Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 47, 97, 9, 27 ]
99
[ "47+97=144", "9*27=243", "243-144=99" ]
Current State: 99:[47, 97, 9, 27], Operations: [] Exploring Operation: 47+97=144, Resulting Numbers: [9, 27, 144] Generated Node #2: [9, 27, 144] from Operation: 47+97=144 Current State: 99:[9, 27, 144], Operations: ['47+97=144'] Exploring Operation: 9*27=243, Resulting Numbers: [144, 243] Generated Node #3: [144, 243] from Operation: 9*27=243 Current State: 99:[144, 243], Operations: ['47+97=144', '9*27=243'] Exploring Operation: 243-144=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[47, 97, 9, 27], Operations: [] Exploring Operation: 47-9=38, Resulting Numbers: [97, 27, 38] Generated Node #0,0: 99:[97, 27, 38] Operation: 47-9=38 Exploring Operation: 47-27=20, Resulting Numbers: [97, 9, 20] Generated Node #0,1: 99:[97, 9, 20] Operation: 47-27=20 Exploring Operation: 27/9=3, Resulting Numbers: [47, 97, 3] Generated Node #0,2: 99:[47, 97, 3] Operation: 27/9=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[97, 9, 20], Operations: ['47-27=20'] Exploring Operation: 20-9=11, Resulting Numbers: [97, 11] Generated Node #0,1,0: 99:[97, 11] Operation: 20-9=11 Exploring Operation: 97+9=106, Resulting Numbers: [20, 106] Generated Node #0,1,1: 99:[20, 106] Operation: 97+9=106 Exploring Operation: 9+20=29, Resulting Numbers: [97, 29] Generated Node #0,1,2: 99:[97, 29] Operation: 9+20=29 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 99:[97, 11], Operations: ['47-27=20', '20-9=11'] Exploring Operation: 97*11=1067, Resulting Numbers: [1067] 1067,99 unequal: No Solution Exploring Operation: 97-11=86, Resulting Numbers: [86] 86,99 unequal: No Solution Exploring Operation: 97+11=108, Resulting Numbers: [108] 108,99 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 #0,1,2 Current State: 99:[97, 29], Operations: ['47-27=20', '9+20=29'] Exploring Operation: 97-29=68, Resulting Numbers: [68] 68,99 unequal: No Solution Exploring Operation: 97*29=2813, Resulting Numbers: [2813] 2813,99 unequal: No Solution Exploring Operation: 97+29=126, Resulting Numbers: [126] 126,99 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 #0,1,1 Current State: 99:[20, 106], Operations: ['47-27=20', '97+9=106'] Exploring Operation: 106-20=86, Resulting Numbers: [86] 86,99 unequal: No Solution Exploring Operation: 20+106=126, Resulting Numbers: [126] 126,99 unequal: No Solution Exploring Operation: 20*106=2120, Resulting Numbers: [2120] 2120,99 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:[97, 27, 38], Operations: ['47-9=38'] Exploring Operation: 38-27=11, Resulting Numbers: [97, 11] Generated Node #0,0,0: 99:[97, 11] Operation: 38-27=11 Exploring Operation: 97+27=124, Resulting Numbers: [38, 124] Generated Node #0,0,1: 99:[38, 124] Operation: 97+27=124 Exploring Operation: 97-38=59, Resulting Numbers: [27, 59] Generated Node #0,0,2: 99:[27, 59] Operation: 97-38=59 Moving to Node #0,0,0 Current State: 99:[97, 11], Operations: ['47-9=38', '38-27=11'] Exploring Operation: 97*11=1067, Resulting Numbers: [1067] 1067,99 unequal: No Solution Exploring Operation: 97+11=108, Resulting Numbers: [108] 108,99 unequal: No Solution Exploring Operation: 97-11=86, Resulting Numbers: [86] 86,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[38, 124], Operations: ['47-9=38', '97+27=124'] Exploring Operation: 38*124=4712, Resulting Numbers: [4712] 4712,99 unequal: No Solution Exploring Operation: 124-38=86, Resulting Numbers: [86] 86,99 unequal: No Solution Exploring Operation: 38+124=162, Resulting Numbers: [162] 162,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[27, 59], Operations: ['47-9=38', '97-38=59'] Exploring Operation: 27*59=1593, Resulting Numbers: [1593] 1593,99 unequal: No Solution Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 27+59=86, Resulting Numbers: [86] 86,99 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 #0,2 Current State: 99:[47, 97, 3], Operations: ['27/9=3'] Exploring Operation: 97-47=50, Resulting Numbers: [3, 50] Generated Node #0,2,0: 99:[3, 50] Operation: 97-47=50 Exploring Operation: 47-3=44, Resulting Numbers: [97, 44] Generated Node #0,2,1: 99:[97, 44] Operation: 47-3=44 Exploring Operation: 97+3=100, Resulting Numbers: [47, 100] Generated Node #0,2,2: 99:[47, 100] Operation: 97+3=100 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 99:[97, 44], Operations: ['27/9=3', '47-3=44'] Exploring Operation: 97+44=141, Resulting Numbers: [141] 141,99 unequal: No Solution Exploring Operation: 97-44=53, Resulting Numbers: [53] 53,99 unequal: No Solution Exploring Operation: 97*44=4268, Resulting Numbers: [4268] 4268,99 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:[47, 100], Operations: ['27/9=3', '97+3=100'] Exploring Operation: 47+100=147, Resulting Numbers: [147] 147,99 unequal: No Solution Exploring Operation: 100-47=53, Resulting Numbers: [53] 53,99 unequal: No Solution Exploring Operation: 47*100=4700, Resulting Numbers: [4700] 4700,99 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:[3, 50], Operations: ['27/9=3', '97-47=50'] Exploring Operation: 3*50=150, Resulting Numbers: [150] 150,99 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,99 unequal: No Solution Exploring Operation: 3+50=53, Resulting Numbers: [53] 53,99 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 No solution found.
0
hs_3
mult_heuristic
[ 39, 6, 74, 29 ]
12
[ "39-6=33", "74-29=45", "45-33=12" ]
Current State: 12:[39, 6, 74, 29], Operations: [] Exploring Operation: 39-6=33, Resulting Numbers: [74, 29, 33] Generated Node #2: [74, 29, 33] from Operation: 39-6=33 Current State: 12:[74, 29, 33], Operations: ['39-6=33'] Exploring Operation: 74-29=45, Resulting Numbers: [33, 45] Generated Node #3: [33, 45] from Operation: 74-29=45 Current State: 12:[33, 45], Operations: ['39-6=33', '74-29=45'] Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[39, 6, 74, 29], Operations: [] Exploring Operation: 74-39=35, Resulting Numbers: [6, 29, 35] Generated Node #0,0: 12:[6, 29, 35] Operation: 74-39=35 Exploring Operation: 39-29=10, Resulting Numbers: [6, 74, 10] Generated Node #0,1: 12:[6, 74, 10] Operation: 39-29=10 Exploring Operation: 74-29=45, Resulting Numbers: [39, 6, 45] Generated Node #0,2: 12:[39, 6, 45] Operation: 74-29=45 Moving to Node #0,0 Current State: 12:[6, 29, 35], Operations: ['74-39=35'] Exploring Operation: 35-6=29, Resulting Numbers: [29, 29] Generated Node #0,0,0: 12:[29, 29] Operation: 35-6=29 Exploring Operation: 29-6=23, Resulting Numbers: [35, 23] Generated Node #0,0,1: 12:[35, 23] Operation: 29-6=23 Exploring Operation: 35-29=6, Resulting Numbers: [6, 6] Generated Node #0,0,2: 12:[6, 6] Operation: 35-29=6 Moving to Node #0,2 Current State: 12:[39, 6, 45], Operations: ['74-29=45'] Exploring Operation: 39-6=33, Resulting Numbers: [45, 33] Generated Node #0,2,0: 12:[45, 33] Operation: 39-6=33 Exploring Operation: 45-39=6, Resulting Numbers: [6, 6] Generated Node #0,2,1: 12:[6, 6] Operation: 45-39=6 Exploring Operation: 45-6=39, Resulting Numbers: [39, 39] Generated Node #0,2,2: 12:[39, 39] Operation: 45-6=39 Moving to Node #0,1 Current State: 12:[6, 74, 10], Operations: ['39-29=10'] Exploring Operation: 74-10=64, Resulting Numbers: [6, 64] Generated Node #0,1,0: 12:[6, 64] Operation: 74-10=64 Exploring Operation: 10-6=4, Resulting Numbers: [74, 4] Generated Node #0,1,1: 12:[74, 4] Operation: 10-6=4 Exploring Operation: 74-6=68, Resulting Numbers: [10, 68] Generated Node #0,1,2: 12:[10, 68] Operation: 74-6=68 Moving to Node #0,0,2 Current State: 12:[6, 6], Operations: ['74-39=35', '35-29=6'] Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,12 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[39, 6, 74, 29], Operations: [] Exploring Operation: 74-39=35, Resulting Numbers: [6, 29, 35] Generated Node #0,0: 12:[6, 29, 35] Operation: 74-39=35 Moving to Node #0,0 Current State: 12:[6, 29, 35], Operations: ['74-39=35'] Exploring Operation: 35-29=6, Resulting Numbers: [6, 6] Generated Node #0,0,2: 12:[6, 6] Operation: 35-29=6 Moving to Node #0,0,2 Current State: 12:[6, 6], Operations: ['74-39=35', '35-29=6'] Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.983507
hs_3
mult_heuristic
[ 29, 21, 98, 7 ]
20
[ "29+98=127", "21*7=147", "147-127=20" ]
Current State: 20:[29, 21, 98, 7], Operations: [] Exploring Operation: 29+98=127, Resulting Numbers: [21, 7, 127] Generated Node #2: [21, 7, 127] from Operation: 29+98=127 Current State: 20:[21, 7, 127], Operations: ['29+98=127'] Exploring Operation: 21*7=147, Resulting Numbers: [127, 147] Generated Node #3: [127, 147] from Operation: 21*7=147 Current State: 20:[127, 147], Operations: ['29+98=127', '21*7=147'] Exploring Operation: 147-127=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[29, 21, 98, 7], Operations: [] Exploring Operation: 98-29=69, Resulting Numbers: [21, 7, 69] Generated Node #0,0: 20:[21, 7, 69] Operation: 98-29=69 Exploring Operation: 98/7=14, Resulting Numbers: [29, 21, 14] Generated Node #0,1: 20:[29, 21, 14] Operation: 98/7=14 Moving to Node #0,1 Current State: 20:[29, 21, 14], Operations: ['98/7=14'] Exploring Operation: 29-21=8, Resulting Numbers: [14, 8] Generated Node #0,1,0: 20:[14, 8] Operation: 29-21=8 Exploring Operation: 29-14=15, Resulting Numbers: [21, 15] Generated Node #0,1,1: 20:[21, 15] Operation: 29-14=15 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 20:[14, 8], Operations: ['98/7=14', '29-21=8'] Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,20 unequal: No Solution Exploring Operation: 14-8=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 #0,1,1 Current State: 20:[21, 15], Operations: ['98/7=14', '29-14=15'] Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,20 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:[21, 7, 69], Operations: ['98-29=69'] Exploring Operation: 69-21=48, Resulting Numbers: [7, 48] Generated Node #0,0,0: 20:[7, 48] Operation: 69-21=48 Exploring Operation: 69-7=62, Resulting Numbers: [21, 62] Generated Node #0,0,1: 20:[21, 62] Operation: 69-7=62 Moving to Node #0,0,0 Current State: 20:[7, 48], Operations: ['98-29=69', '69-21=48'] Exploring Operation: 7+48=55, Resulting Numbers: [55] 55,20 unequal: No Solution Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,20 unequal: No Solution Moving to Node #0,0,1 Current State: 20:[21, 62], Operations: ['98-29=69', '69-7=62'] Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,20 unequal: No Solution Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,20 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 24, 16, 18, 8 ]
19
[ "24-16=8", "8/8=1", "18+1=19" ]
Current State: 19:[24, 16, 18, 8], Operations: [] Exploring Operation: 24-16=8, Resulting Numbers: [18, 8, 8] Generated Node #2: [18, 8, 8] from Operation: 24-16=8 Current State: 19:[18, 8, 8], Operations: ['24-16=8'] Exploring Operation: 8/8=1, Resulting Numbers: [18, 1] Generated Node #3: [18, 1] from Operation: 8/8=1 Current State: 19:[18, 1], Operations: ['24-16=8', '8/8=1'] Exploring Operation: 18+1=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[24, 16, 18, 8], Operations: [] Exploring Operation: 16+8=24, Resulting Numbers: [24, 18, 24] Generated Node #0,0: 19:[24, 18, 24] Operation: 16+8=24 Exploring Operation: 24-8=16, Resulting Numbers: [16, 18, 16] Generated Node #0,1: 19:[16, 18, 16] Operation: 24-8=16 Moving to Node #0,1 Current State: 19:[16, 18, 16], Operations: ['24-8=16'] Exploring Operation: 16+18=34, Resulting Numbers: [16, 34] Generated Node #0,1,0: 19:[16, 34] Operation: 16+18=34 Exploring Operation: 16+16=32, Resulting Numbers: [18, 32] Generated Node #0,1,1: 19:[18, 32] Operation: 16+16=32 Moving to Node #0,0 Current State: 19:[24, 18, 24], Operations: ['16+8=24'] Exploring Operation: 24-18=6, Resulting Numbers: [24, 6] Generated Node #0,0,0: 19:[24, 6] Operation: 24-18=6 Exploring Operation: 24-18=6, Resulting Numbers: [24, 6] Generated Node #0,0,1: 19:[24, 6] Operation: 24-18=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[24, 6], Operations: ['16+8=24', '24-18=6'] Exploring Operation: 24+6=30, Resulting Numbers: [30] 30,19 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,19 unequal: No Solution No 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: 19:[24, 6], Operations: ['16+8=24', '24-18=6'] Exploring Operation: 24+6=30, Resulting Numbers: [30] 30,19 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 19:[18, 32], Operations: ['24-8=16', '16+16=32'] Exploring Operation: 18+32=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,19 unequal: No Solution Moving to Node #0,1,0 Current State: 19:[16, 34], Operations: ['24-8=16', '16+18=34'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,19 unequal: No Solution Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,19 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 11, 68, 81, 94 ]
22
[ "68+94=162", "11*162=1782", "1782/81=22" ]
Current State: 22:[11, 68, 81, 94], Operations: [] Exploring Operation: 68+94=162, Resulting Numbers: [11, 81, 162] Generated Node #2: [11, 81, 162] from Operation: 68+94=162 Current State: 22:[11, 81, 162], Operations: ['68+94=162'] Exploring Operation: 11*162=1782, Resulting Numbers: [81, 1782] Generated Node #3: [81, 1782] from Operation: 11*162=1782 Current State: 22:[81, 1782], Operations: ['68+94=162', '11*162=1782'] Exploring Operation: 1782/81=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[11, 68, 81, 94], Operations: [] Exploring Operation: 94-68=26, Resulting Numbers: [11, 81, 26] Generated Node #0,0: 22:[11, 81, 26] Operation: 94-68=26 Exploring Operation: 94-81=13, Resulting Numbers: [11, 68, 13] Generated Node #0,1: 22:[11, 68, 13] Operation: 94-81=13 Moving to Node #0,1 Current State: 22:[11, 68, 13], Operations: ['94-81=13'] Exploring Operation: 68-13=55, Resulting Numbers: [11, 55] Generated Node #0,1,0: 22:[11, 55] Operation: 68-13=55 Exploring Operation: 68-11=57, Resulting Numbers: [13, 57] Generated Node #0,1,1: 22:[13, 57] Operation: 68-11=57 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[11, 55], Operations: ['94-81=13', '68-13=55'] Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,22 unequal: No Solution Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[13, 57], Operations: ['94-81=13', '68-11=57'] Exploring Operation: 13+57=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 57-13=44, Resulting Numbers: [44] 44,22 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: 22:[11, 81, 26], Operations: ['94-68=26'] Exploring Operation: 81-11=70, Resulting Numbers: [26, 70] Generated Node #0,0,0: 22:[26, 70] Operation: 81-11=70 Exploring Operation: 81-26=55, Resulting Numbers: [11, 55] Generated Node #0,0,1: 22:[11, 55] Operation: 81-26=55 Moving to Node #0,0,1 Current State: 22:[11, 55], Operations: ['94-68=26', '81-26=55'] Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,22 unequal: No Solution Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,22 unequal: No Solution Moving to Node #0,0,0 Current State: 22:[26, 70], Operations: ['94-68=26', '81-11=70'] Exploring Operation: 70-26=44, Resulting Numbers: [44] 44,22 unequal: No Solution Exploring Operation: 26+70=96, Resulting Numbers: [96] 96,22 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 46, 55, 92, 87 ]
16
[ "92/46=2", "87-55=32", "32/2=16" ]
Current State: 16:[46, 55, 92, 87], Operations: [] Exploring Operation: 92/46=2, Resulting Numbers: [55, 87, 2] Generated Node #2: [55, 87, 2] from Operation: 92/46=2 Current State: 16:[55, 87, 2], Operations: ['92/46=2'] Exploring Operation: 87-55=32, Resulting Numbers: [2, 32] Generated Node #3: [2, 32] from Operation: 87-55=32 Current State: 16:[2, 32], Operations: ['92/46=2', '87-55=32'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[46, 55, 92, 87], Operations: [] Exploring Operation: 92/46=2, Resulting Numbers: [55, 87, 2] Generated Node #0,0: 16:[55, 87, 2] Operation: 92/46=2 Exploring Operation: 92-87=5, Resulting Numbers: [46, 55, 5] Generated Node #0,1: 16:[46, 55, 5] Operation: 92-87=5 Exploring Operation: 92-55=37, Resulting Numbers: [46, 87, 37] Generated Node #0,2: 16:[46, 87, 37] Operation: 92-55=37 Moving to Node #0,1 Current State: 16:[46, 55, 5], Operations: ['92-87=5'] Exploring Operation: 46-5=41, Resulting Numbers: [55, 41] Generated Node #0,1,0: 16:[55, 41] Operation: 46-5=41 Exploring Operation: 55/5=11, Resulting Numbers: [46, 11] Generated Node #0,1,1: 16:[46, 11] Operation: 55/5=11 Exploring Operation: 55-46=9, Resulting Numbers: [5, 9] Generated Node #0,1,2: 16:[5, 9] Operation: 55-46=9 Moving to Node #0,0 Current State: 16:[55, 87, 2], Operations: ['92/46=2'] Exploring Operation: 87-2=85, Resulting Numbers: [55, 85] Generated Node #0,0,0: 16:[55, 85] Operation: 87-2=85 Exploring Operation: 87-55=32, Resulting Numbers: [2, 32] Generated Node #0,0,1: 16:[2, 32] Operation: 87-55=32 Exploring Operation: 55-2=53, Resulting Numbers: [87, 53] Generated Node #0,0,2: 16:[87, 53] Operation: 55-2=53 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[2, 32], Operations: ['92/46=2', '87-55=32'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[46, 55, 92, 87], Operations: [] Exploring Operation: 92/46=2, Resulting Numbers: [55, 87, 2] Generated Node #0,0: 16:[55, 87, 2] Operation: 92/46=2 Moving to Node #0,0 Current State: 16:[55, 87, 2], Operations: ['92/46=2'] Exploring Operation: 87-55=32, Resulting Numbers: [2, 32] Generated Node #0,0,1: 16:[2, 32] Operation: 87-55=32 Moving to Node #0,0,1 Current State: 16:[2, 32], Operations: ['92/46=2', '87-55=32'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 10, 7, 96, 66 ]
54
[ "10-7=3", "96+66=162", "162/3=54" ]
Current State: 54:[10, 7, 96, 66], Operations: [] Exploring Operation: 10-7=3, Resulting Numbers: [96, 66, 3] Generated Node #2: [96, 66, 3] from Operation: 10-7=3 Current State: 54:[96, 66, 3], Operations: ['10-7=3'] Exploring Operation: 96+66=162, Resulting Numbers: [3, 162] Generated Node #3: [3, 162] from Operation: 96+66=162 Current State: 54:[3, 162], Operations: ['10-7=3', '96+66=162'] Exploring Operation: 162/3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[10, 7, 96, 66], Operations: [] Exploring Operation: 66-10=56, Resulting Numbers: [7, 96, 56] Generated Node #0,0: 54:[7, 96, 56] Operation: 66-10=56 Exploring Operation: 96-7=89, Resulting Numbers: [10, 66, 89] Generated Node #0,1: 54:[10, 66, 89] Operation: 96-7=89 Exploring Operation: 96-10=86, Resulting Numbers: [7, 66, 86] Generated Node #0,2: 54:[7, 66, 86] Operation: 96-10=86 Exploring Operation: 96-66=30, Resulting Numbers: [10, 7, 30] Generated Node #0,3: 54:[10, 7, 30] Operation: 96-66=30 Start Sub Search at level 1: Moving to Node #0,3 Current State: 54:[10, 7, 30], Operations: ['96-66=30'] Exploring Operation: 10-7=3, Resulting Numbers: [30, 3] Generated Node #0,3,0: 54:[30, 3] Operation: 10-7=3 Exploring Operation: 30-10=20, Resulting Numbers: [7, 20] Generated Node #0,3,1: 54:[7, 20] Operation: 30-10=20 Exploring Operation: 30/10=3, Resulting Numbers: [7, 3] Generated Node #0,3,2: 54:[7, 3] Operation: 30/10=3 Exploring Operation: 10+7=17, Resulting Numbers: [30, 17] Generated Node #0,3,3: 54:[30, 17] Operation: 10+7=17 Moving to Node #0,3,2 Current State: 54:[7, 3], Operations: ['96-66=30', '30/10=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,54 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,54 unequal: No Solution Moving to Node #0,3,1 Current State: 54:[7, 20], Operations: ['96-66=30', '30-10=20'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,54 unequal: No Solution Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,54 unequal: No Solution Moving to Node #0,3,0 Current State: 54:[30, 3], Operations: ['96-66=30', '10-7=3'] Exploring Operation: 30*3=90, Resulting Numbers: [90] 90,54 unequal: No Solution Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,54 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,54 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,54 unequal: No Solution Moving to Node #0,3,3 Current State: 54:[30, 17], Operations: ['96-66=30', '10+7=17'] Exploring Operation: 30*17=510, Resulting Numbers: [510] 510,54 unequal: No Solution Exploring Operation: 30+17=47, Resulting Numbers: [47] 47,54 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,54 unequal: No Solution No 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: 54:[7, 96, 56], Operations: ['66-10=56'] Exploring Operation: 56-7=49, Resulting Numbers: [96, 49] Generated Node #0,0,0: 54:[96, 49] Operation: 56-7=49 Exploring Operation: 96-7=89, Resulting Numbers: [56, 89] Generated Node #0,0,1: 54:[56, 89] Operation: 96-7=89 Exploring Operation: 96-56=40, Resulting Numbers: [7, 40] Generated Node #0,0,2: 54:[7, 40] Operation: 96-56=40 Exploring Operation: 56/7=8, Resulting Numbers: [96, 8] Generated Node #0,0,3: 54:[96, 8] Operation: 56/7=8 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 54:[7, 40], Operations: ['66-10=56', '96-56=40'] Exploring Operation: 7+40=47, Resulting Numbers: [47] 47,54 unequal: No Solution Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,54 unequal: No Solution Exploring Operation: 7*40=280, Resulting Numbers: [280] 280,54 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 #0,0,1 Current State: 54:[56, 89], Operations: ['66-10=56', '96-7=89'] Exploring Operation: 89-56=33, Resulting Numbers: [33] 33,54 unequal: No Solution Exploring Operation: 56+89=145, Resulting Numbers: [145] 145,54 unequal: No Solution Exploring Operation: 56*89=4984, Resulting Numbers: [4984] 4984,54 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 #0,0,3 Current State: 54:[96, 8], Operations: ['66-10=56', '56/7=8'] Exploring Operation: 96/8=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 96*8=768, Resulting Numbers: [768] 768,54 unequal: No Solution Exploring Operation: 96+8=104, Resulting Numbers: [104] 104,54 unequal: No Solution Exploring Operation: 96-8=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 #0,0,0 Current State: 54:[96, 49], Operations: ['66-10=56', '56-7=49'] Exploring Operation: 96+49=145, Resulting Numbers: [145] 145,54 unequal: No Solution Exploring Operation: 96-49=47, Resulting Numbers: [47] 47,54 unequal: No Solution Exploring Operation: 96*49=4704, Resulting Numbers: [4704] 4704,54 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 #0,2 Current State: 54:[7, 66, 86], Operations: ['96-10=86'] Exploring Operation: 86-7=79, Resulting Numbers: [66, 79] Generated Node #0,2,0: 54:[66, 79] Operation: 86-7=79 Exploring Operation: 7+66=73, Resulting Numbers: [86, 73] Generated Node #0,2,1: 54:[86, 73] Operation: 7+66=73 Exploring Operation: 66-7=59, Resulting Numbers: [86, 59] Generated Node #0,2,2: 54:[86, 59] Operation: 66-7=59 Exploring Operation: 86-66=20, Resulting Numbers: [7, 20] Generated Node #0,2,3: 54:[7, 20] Operation: 86-66=20 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 54:[7, 20], Operations: ['96-10=86', '86-66=20'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,54 unequal: No Solution Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,54 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 #0,2,0 Current State: 54:[66, 79], Operations: ['96-10=86', '86-7=79'] Exploring Operation: 66+79=145, Resulting Numbers: [145] 145,54 unequal: No Solution Exploring Operation: 79-66=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 66*79=5214, Resulting Numbers: [5214] 5214,54 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:[86, 59], Operations: ['96-10=86', '66-7=59'] Exploring Operation: 86*59=5074, Resulting Numbers: [5074] 5074,54 unequal: No Solution Exploring Operation: 86+59=145, Resulting Numbers: [145] 145,54 unequal: No Solution Exploring Operation: 86-59=27, Resulting Numbers: [27] 27,54 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:[86, 73], Operations: ['96-10=86', '7+66=73'] Exploring Operation: 86-73=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 86+73=159, Resulting Numbers: [159] 159,54 unequal: No Solution Exploring Operation: 86*73=6278, Resulting Numbers: [6278] 6278,54 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 #0,1 Current State: 54:[10, 66, 89], Operations: ['96-7=89'] Exploring Operation: 66-10=56, Resulting Numbers: [89, 56] Generated Node #0,1,0: 54:[89, 56] Operation: 66-10=56 Exploring Operation: 89-10=79, Resulting Numbers: [66, 79] Generated Node #0,1,1: 54:[66, 79] Operation: 89-10=79 Exploring Operation: 89-66=23, Resulting Numbers: [10, 23] Generated Node #0,1,2: 54:[10, 23] Operation: 89-66=23 Exploring Operation: 10+66=76, Resulting Numbers: [89, 76] Generated Node #0,1,3: 54:[89, 76] Operation: 10+66=76 Moving to Node #0,1,2 Current State: 54:[10, 23], Operations: ['96-7=89', '89-66=23'] Exploring Operation: 10+23=33, Resulting Numbers: [33] 33,54 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 10*23=230, Resulting Numbers: [230] 230,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[66, 79], Operations: ['96-7=89', '89-10=79'] Exploring Operation: 66*79=5214, Resulting Numbers: [5214] 5214,54 unequal: No Solution Exploring Operation: 79-66=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 66+79=145, Resulting Numbers: [145] 145,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[89, 56], Operations: ['96-7=89', '66-10=56'] Exploring Operation: 89*56=4984, Resulting Numbers: [4984] 4984,54 unequal: No Solution Exploring Operation: 89+56=145, Resulting Numbers: [145] 145,54 unequal: No Solution Exploring Operation: 89-56=33, Resulting Numbers: [33] 33,54 unequal: No Solution Moving to Node #0,1,3 Current State: 54:[89, 76], Operations: ['96-7=89', '10+66=76'] Exploring Operation: 89-76=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 89*76=6764, Resulting Numbers: [6764] 6764,54 unequal: No Solution Exploring Operation: 89+76=165, Resulting Numbers: [165] 165,54 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
[ 10, 57, 8, 84 ]
61
[ "10*8=80", "57+84=141", "141-80=61" ]
Current State: 61:[10, 57, 8, 84], Operations: [] Exploring Operation: 10*8=80, Resulting Numbers: [57, 84, 80] Generated Node #2: [57, 84, 80] from Operation: 10*8=80 Current State: 61:[57, 84, 80], Operations: ['10*8=80'] Exploring Operation: 57+84=141, Resulting Numbers: [80, 141] Generated Node #3: [80, 141] from Operation: 57+84=141 Current State: 61:[80, 141], Operations: ['10*8=80', '57+84=141'] Exploring Operation: 141-80=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[10, 57, 8, 84], Operations: [] Exploring Operation: 10+8=18, Resulting Numbers: [57, 84, 18] Generated Node #0,0: 61:[57, 84, 18] Operation: 10+8=18 Exploring Operation: 10*8=80, Resulting Numbers: [57, 84, 80] Generated Node #0,1: 61:[57, 84, 80] Operation: 10*8=80 Moving to Node #0,1 Current State: 61:[57, 84, 80], Operations: ['10*8=80'] Exploring Operation: 80-57=23, Resulting Numbers: [84, 23] Generated Node #0,1,0: 61:[84, 23] Operation: 80-57=23 Exploring Operation: 84-57=27, Resulting Numbers: [80, 27] Generated Node #0,1,1: 61:[80, 27] Operation: 84-57=27 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[80, 27], Operations: ['10*8=80', '84-57=27'] Exploring Operation: 80-27=53, Resulting Numbers: [53] 53,61 unequal: No Solution Exploring Operation: 80+27=107, Resulting Numbers: [107] 107,61 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:[84, 23], Operations: ['10*8=80', '80-57=23'] Exploring Operation: 84+23=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 84-23=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[10, 57, 8, 84], Operations: [] Exploring Operation: 10*8=80, Resulting Numbers: [57, 84, 80] Generated Node #0,1: 61:[57, 84, 80] Operation: 10*8=80 Moving to Node #0,1 Current State: 61:[57, 84, 80], Operations: ['10*8=80'] Exploring Operation: 80-57=23, Resulting Numbers: [84, 23] Generated Node #0,1,0: 61:[84, 23] Operation: 80-57=23 Moving to Node #0,1,0 Current State: 61:[84, 23], Operations: ['10*8=80', '80-57=23'] Exploring Operation: 84-23=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 49, 39, 72, 68 ]
22
[ "49+39=88", "72-68=4", "88/4=22" ]
Current State: 22:[49, 39, 72, 68], Operations: [] Exploring Operation: 49+39=88, Resulting Numbers: [72, 68, 88] Generated Node #2: [72, 68, 88] from Operation: 49+39=88 Current State: 22:[72, 68, 88], Operations: ['49+39=88'] Exploring Operation: 72-68=4, Resulting Numbers: [88, 4] Generated Node #3: [88, 4] from Operation: 72-68=4 Current State: 22:[88, 4], Operations: ['49+39=88', '72-68=4'] Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[49, 39, 72, 68], Operations: [] Exploring Operation: 72-68=4, Resulting Numbers: [49, 39, 4] Generated Node #0,0: 22:[49, 39, 4] Operation: 72-68=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[49, 39, 4], Operations: ['72-68=4'] Exploring Operation: 49-39=10, Resulting Numbers: [4, 10] Generated Node #0,0,0: 22:[4, 10] Operation: 49-39=10 Moving to Node #0,0,0 Current State: 22:[4, 10], Operations: ['72-68=4', '49-39=10'] Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,22 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
[ 79, 40, 81, 41 ]
27
[ "79+41=120", "40*81=3240", "3240/120=27" ]
Current State: 27:[79, 40, 81, 41], Operations: [] Exploring Operation: 79+41=120, Resulting Numbers: [40, 81, 120] Generated Node #2: [40, 81, 120] from Operation: 79+41=120 Current State: 27:[40, 81, 120], Operations: ['79+41=120'] Exploring Operation: 40*81=3240, Resulting Numbers: [120, 3240] Generated Node #3: [120, 3240] from Operation: 40*81=3240 Current State: 27:[120, 3240], Operations: ['79+41=120', '40*81=3240'] Exploring Operation: 3240/120=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[79, 40, 81, 41], Operations: [] Exploring Operation: 81-41=40, Resulting Numbers: [79, 40, 40] Generated Node #0,0: 27:[79, 40, 40] Operation: 81-41=40 Exploring Operation: 79-41=38, Resulting Numbers: [40, 81, 38] Generated Node #0,1: 27:[40, 81, 38] Operation: 79-41=38 Exploring Operation: 81-79=2, Resulting Numbers: [40, 41, 2] Generated Node #0,2: 27:[40, 41, 2] Operation: 81-79=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[40, 41, 2], Operations: ['81-79=2'] Exploring Operation: 40/2=20, Resulting Numbers: [41, 20] Generated Node #0,2,0: 27:[41, 20] Operation: 40/2=20 Exploring Operation: 41-40=1, Resulting Numbers: [2, 1] Generated Node #0,2,1: 27:[2, 1] Operation: 41-40=1 Exploring Operation: 40-2=38, Resulting Numbers: [41, 38] Generated Node #0,2,2: 27:[41, 38] Operation: 40-2=38 Moving to Node #0,2,1 Current State: 27:[2, 1], Operations: ['81-79=2', '41-40=1'] Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,27 unequal: No Solution Moving to Node #0,2,0 Current State: 27:[41, 20], Operations: ['81-79=2', '40/2=20'] Exploring Operation: 41+20=61, Resulting Numbers: [61] 61,27 unequal: No Solution Exploring Operation: 41*20=820, Resulting Numbers: [820] 820,27 unequal: No Solution Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,27 unequal: No Solution Moving to Node #0,2,2 Current State: 27:[41, 38], Operations: ['81-79=2', '40-2=38'] Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 41*38=1558, Resulting Numbers: [1558] 1558,27 unequal: No Solution Exploring Operation: 41+38=79, Resulting Numbers: [79] 79,27 unequal: No Solution No 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: 27:[79, 40, 40], Operations: ['81-41=40'] Exploring Operation: 79-40=39, Resulting Numbers: [40, 39] Generated Node #0,0,0: 27:[40, 39] Operation: 79-40=39 Exploring Operation: 79-40=39, Resulting Numbers: [40, 39] Generated Node #0,0,1: 27:[40, 39] Operation: 79-40=39 Exploring Operation: 40/40=1, Resulting Numbers: [79, 1] Generated Node #0,0,2: 27:[79, 1] Operation: 40/40=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[40, 39], Operations: ['81-41=40', '79-40=39'] Exploring Operation: 40+39=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 40*39=1560, Resulting Numbers: [1560] 1560,27 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: 27:[40, 39], Operations: ['81-41=40', '79-40=39'] Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 40+39=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 40*39=1560, Resulting Numbers: [1560] 1560,27 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: 27:[79, 1], Operations: ['81-41=40', '40/40=1'] Exploring Operation: 79-1=78, Resulting Numbers: [78] 78,27 unequal: No Solution Exploring Operation: 79*1=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 79/1=79, Resulting Numbers: [79] 79,27 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: 27:[40, 81, 38], Operations: ['79-41=38'] Exploring Operation: 81-38=43, Resulting Numbers: [40, 43] Generated Node #0,1,0: 27:[40, 43] Operation: 81-38=43 Exploring Operation: 81-40=41, Resulting Numbers: [38, 41] Generated Node #0,1,1: 27:[38, 41] Operation: 81-40=41 Exploring Operation: 40-38=2, Resulting Numbers: [81, 2] Generated Node #0,1,2: 27:[81, 2] Operation: 40-38=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 27:[38, 41], Operations: ['79-41=38', '81-40=41'] Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 38*41=1558, Resulting Numbers: [1558] 1558,27 unequal: No Solution Exploring Operation: 38+41=79, Resulting Numbers: [79] 79,27 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: 27:[40, 43], Operations: ['79-41=38', '81-38=43'] Exploring Operation: 40+43=83, Resulting Numbers: [83] 83,27 unequal: No Solution Exploring Operation: 40*43=1720, Resulting Numbers: [1720] 1720,27 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,27 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: 27:[81, 2], Operations: ['79-41=38', '40-38=2'] Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 81+2=83, Resulting Numbers: [83] 83,27 unequal: No Solution Exploring Operation: 81*2=162, Resulting Numbers: [162] 162,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 44, 15, 71, 29 ]
13
[ "44-15=29", "71-29=42", "42-29=13" ]
Current State: 13:[44, 15, 71, 29], Operations: [] Exploring Operation: 44-15=29, Resulting Numbers: [71, 29, 29] Generated Node #2: [71, 29, 29] from Operation: 44-15=29 Current State: 13:[71, 29, 29], Operations: ['44-15=29'] Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,13 equal: Goal Reached Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[44, 15, 71, 29], Operations: [] Exploring Operation: 71-29=42, Resulting Numbers: [44, 15, 42] Generated Node #0,0: 13:[44, 15, 42] Operation: 71-29=42 Exploring Operation: 71-44=27, Resulting Numbers: [15, 29, 27] Generated Node #0,1: 13:[15, 29, 27] Operation: 71-44=27 Exploring Operation: 44-29=15, Resulting Numbers: [15, 71, 15] Generated Node #0,2: 13:[15, 71, 15] Operation: 44-29=15 Moving to Node #0,1 Current State: 13:[15, 29, 27], Operations: ['71-44=27'] Exploring Operation: 29-27=2, Resulting Numbers: [15, 2] Generated Node #0,1,0: 13:[15, 2] Operation: 29-27=2 Exploring Operation: 27-15=12, Resulting Numbers: [29, 12] Generated Node #0,1,1: 13:[29, 12] Operation: 27-15=12 Exploring Operation: 29-15=14, Resulting Numbers: [27, 14] Generated Node #0,1,2: 13:[27, 14] Operation: 29-15=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 13:[15, 2], Operations: ['71-44=27', '29-27=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[44, 15, 71, 29], Operations: [] Exploring Operation: 71-44=27, Resulting Numbers: [15, 29, 27] Generated Node #0,1: 13:[15, 29, 27] Operation: 71-44=27 Moving to Node #0,1 Current State: 13:[15, 29, 27], Operations: ['71-44=27'] Exploring Operation: 29-27=2, Resulting Numbers: [15, 2] Generated Node #0,1,0: 13:[15, 2] Operation: 29-27=2 Moving to Node #0,1,0 Current State: 13:[15, 2], Operations: ['71-44=27', '29-27=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 7, 10, 28, 52 ]
94
[ "7*10=70", "52-28=24", "70+24=94" ]
Current State: 94:[7, 10, 28, 52], Operations: [] Exploring Operation: 7*10=70, Resulting Numbers: [28, 52, 70] Generated Node #2: [28, 52, 70] from Operation: 7*10=70 Current State: 94:[28, 52, 70], Operations: ['7*10=70'] Exploring Operation: 52-28=24, Resulting Numbers: [70, 24] Generated Node #3: [70, 24] from Operation: 52-28=24 Current State: 94:[70, 24], Operations: ['7*10=70', '52-28=24'] Exploring Operation: 70+24=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[7, 10, 28, 52], Operations: [] Exploring Operation: 10+28=38, Resulting Numbers: [7, 52, 38] Generated Node #0,0: 94:[7, 52, 38] Operation: 10+28=38 Exploring Operation: 28-10=18, Resulting Numbers: [7, 52, 18] Generated Node #0,1: 94:[7, 52, 18] Operation: 28-10=18 Exploring Operation: 7+28=35, Resulting Numbers: [10, 52, 35] Generated Node #0,2: 94:[10, 52, 35] Operation: 7+28=35 Exploring Operation: 28/7=4, Resulting Numbers: [10, 52, 4] Generated Node #0,3: 94:[10, 52, 4] Operation: 28/7=4 Exploring Operation: 10-7=3, Resulting Numbers: [28, 52, 3] Generated Node #0,4: 94:[28, 52, 3] Operation: 10-7=3 Moving to Node #0,3 Current State: 94:[10, 52, 4], Operations: ['28/7=4'] Exploring Operation: 10*4=40, Resulting Numbers: [52, 40] Generated Node #0,3,0: 94:[52, 40] Operation: 10*4=40 Exploring Operation: 52-4=48, Resulting Numbers: [10, 48] Generated Node #0,3,1: 94:[10, 48] Operation: 52-4=48 Exploring Operation: 10+52=62, Resulting Numbers: [4, 62] Generated Node #0,3,2: 94:[4, 62] Operation: 10+52=62 Exploring Operation: 52-10=42, Resulting Numbers: [4, 42] Generated Node #0,3,3: 94:[4, 42] Operation: 52-10=42 Exploring Operation: 10-4=6, Resulting Numbers: [52, 6] Generated Node #0,3,4: 94:[52, 6] Operation: 10-4=6 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 94:[4, 42], Operations: ['28/7=4', '52-10=42'] Exploring Operation: 4*42=168, Resulting Numbers: [168] 168,94 unequal: No Solution Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,94 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 94:[10, 48], Operations: ['28/7=4', '52-4=48'] Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,94 unequal: No Solution Exploring Operation: 10*48=480, Resulting Numbers: [480] 480,94 unequal: No Solution Exploring Operation: 10+48=58, Resulting Numbers: [58] 58,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 94:[52, 6], Operations: ['28/7=4', '10-4=6'] Exploring Operation: 52*6=312, Resulting Numbers: [312] 312,94 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,94 unequal: No Solution Exploring Operation: 52+6=58, Resulting Numbers: [58] 58,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 94:[52, 40], Operations: ['28/7=4', '10*4=40'] Exploring Operation: 52+40=92, Resulting Numbers: [92] 92,94 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 52*40=2080, Resulting Numbers: [2080] 2080,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 94:[4, 62], Operations: ['28/7=4', '10+52=62'] Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,94 unequal: No Solution Exploring Operation: 4*62=248, Resulting Numbers: [248] 248,94 unequal: No Solution Exploring Operation: 4+62=66, Resulting Numbers: [66] 66,94 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: 94:[7, 52, 38], Operations: ['10+28=38'] Exploring Operation: 52-7=45, Resulting Numbers: [38, 45] Generated Node #0,0,0: 94:[38, 45] Operation: 52-7=45 Exploring Operation: 52+38=90, Resulting Numbers: [7, 90] Generated Node #0,0,1: 94:[7, 90] Operation: 52+38=90 Exploring Operation: 7+52=59, Resulting Numbers: [38, 59] Generated Node #0,0,2: 94:[38, 59] Operation: 7+52=59 Exploring Operation: 7+38=45, Resulting Numbers: [52, 45] Generated Node #0,0,3: 94:[52, 45] Operation: 7+38=45 Exploring Operation: 52-38=14, Resulting Numbers: [7, 14] Generated Node #0,0,4: 94:[7, 14] Operation: 52-38=14 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 94:[52, 45], Operations: ['10+28=38', '7+38=45'] Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,94 unequal: No Solution Exploring Operation: 52+45=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 52*45=2340, Resulting Numbers: [2340] 2340,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 94:[7, 90], Operations: ['10+28=38', '52+38=90'] Exploring Operation: 7*90=630, Resulting Numbers: [630] 630,94 unequal: No Solution Exploring Operation: 7+90=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[38, 45], Operations: ['10+28=38', '52-7=45'] Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,94 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,94 unequal: No Solution Exploring Operation: 38*45=1710, Resulting Numbers: [1710] 1710,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 94:[7, 14], Operations: ['10+28=38', '52-38=14'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,94 unequal: No Solution Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,94 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 94:[38, 59], Operations: ['10+28=38', '7+52=59'] Exploring Operation: 38+59=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 38*59=2242, Resulting Numbers: [2242] 2242,94 unequal: No Solution Exploring Operation: 59-38=21, Resulting Numbers: [21] 21,94 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: 94:[10, 52, 35], Operations: ['7+28=35'] Exploring Operation: 10+52=62, Resulting Numbers: [35, 62] Generated Node #0,2,0: 94:[35, 62] Operation: 10+52=62 Exploring Operation: 52-10=42, Resulting Numbers: [35, 42] Generated Node #0,2,1: 94:[35, 42] Operation: 52-10=42 Exploring Operation: 52-35=17, Resulting Numbers: [10, 17] Generated Node #0,2,2: 94:[10, 17] Operation: 52-35=17 Exploring Operation: 10+35=45, Resulting Numbers: [52, 45] Generated Node #0,2,3: 94:[52, 45] Operation: 10+35=45 Exploring Operation: 52+35=87, Resulting Numbers: [10, 87] Generated Node #0,2,4: 94:[10, 87] Operation: 52+35=87 Moving to Node #0,4 Current State: 94:[28, 52, 3], Operations: ['10-7=3'] Exploring Operation: 28*3=84, Resulting Numbers: [52, 84] Generated Node #0,4,0: 94:[52, 84] Operation: 28*3=84 Exploring Operation: 52-3=49, Resulting Numbers: [28, 49] Generated Node #0,4,1: 94:[28, 49] Operation: 52-3=49 Exploring Operation: 28+52=80, Resulting Numbers: [3, 80] Generated Node #0,4,2: 94:[3, 80] Operation: 28+52=80 Exploring Operation: 28+3=31, Resulting Numbers: [52, 31] Generated Node #0,4,3: 94:[52, 31] Operation: 28+3=31 Exploring Operation: 52-28=24, Resulting Numbers: [3, 24] Generated Node #0,4,4: 94:[3, 24] Operation: 52-28=24 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 94:[52, 84], Operations: ['10-7=3', '28*3=84'] Exploring Operation: 84-52=32, Resulting Numbers: [32] 32,94 unequal: No Solution Exploring Operation: 52*84=4368, Resulting Numbers: [4368] 4368,94 unequal: No Solution Exploring Operation: 52+84=136, Resulting Numbers: [136] 136,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 94:[3, 80], Operations: ['10-7=3', '28+52=80'] Exploring Operation: 3+80=83, Resulting Numbers: [83] 83,94 unequal: No Solution Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,94 unequal: No Solution Exploring Operation: 3*80=240, Resulting Numbers: [240] 240,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 94:[28, 49], Operations: ['10-7=3', '52-3=49'] Exploring Operation: 49-28=21, Resulting Numbers: [21] 21,94 unequal: No Solution Exploring Operation: 28*49=1372, Resulting Numbers: [1372] 1372,94 unequal: No Solution Exploring Operation: 28+49=77, Resulting Numbers: [77] 77,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 94:[52, 31], Operations: ['10-7=3', '28+3=31'] Exploring Operation: 52*31=1612, Resulting Numbers: [1612] 1612,94 unequal: No Solution Exploring Operation: 52+31=83, Resulting Numbers: [83] 83,94 unequal: No Solution Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 94:[3, 24], Operations: ['10-7=3', '52-28=24'] Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,94 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,94 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,94 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,94 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: 94:[7, 52, 18], Operations: ['28-10=18'] Exploring Operation: 18-7=11, Resulting Numbers: [52, 11] Generated Node #0,1,0: 94:[52, 11] Operation: 18-7=11 Exploring Operation: 7+18=25, Resulting Numbers: [52, 25] Generated Node #0,1,1: 94:[52, 25] Operation: 7+18=25 Exploring Operation: 7+52=59, Resulting Numbers: [18, 59] Generated Node #0,1,2: 94:[18, 59] Operation: 7+52=59 Exploring Operation: 52-7=45, Resulting Numbers: [18, 45] Generated Node #0,1,3: 94:[18, 45] Operation: 52-7=45 Exploring Operation: 52-18=34, Resulting Numbers: [7, 34] Generated Node #0,1,4: 94:[7, 34] Operation: 52-18=34 Moving to Node #0,2,3 Current State: 94:[52, 45], Operations: ['7+28=35', '10+35=45'] Exploring Operation: 52*45=2340, Resulting Numbers: [2340] 2340,94 unequal: No Solution Exploring Operation: 52+45=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[52, 11], Operations: ['28-10=18', '18-7=11'] Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,94 unequal: No Solution Exploring Operation: 52+11=63, Resulting Numbers: [63] 63,94 unequal: No Solution Exploring Operation: 52*11=572, Resulting Numbers: [572] 572,94 unequal: No Solution Moving to Node #0,2,4 Current State: 94:[10, 87], Operations: ['7+28=35', '52+35=87'] Exploring Operation: 87-10=77, Resulting Numbers: [77] 77,94 unequal: No Solution Exploring Operation: 10*87=870, Resulting Numbers: [870] 870,94 unequal: No Solution Exploring Operation: 10+87=97, Resulting Numbers: [97] 97,94 unequal: No Solution Moving to Node #0,2,1 Current State: 94:[35, 42], Operations: ['7+28=35', '52-10=42'] Exploring Operation: 35*42=1470, Resulting Numbers: [1470] 1470,94 unequal: No Solution Exploring Operation: 42-35=7, Resulting Numbers: [7] 7,94 unequal: No Solution Exploring Operation: 35+42=77, Resulting Numbers: [77] 77,94 unequal: No Solution Moving to Node #0,1,3 Current State: 94:[18, 45], Operations: ['28-10=18', '52-7=45'] Exploring Operation: 18*45=810, Resulting Numbers: [810] 810,94 unequal: No Solution Exploring Operation: 18+45=63, Resulting Numbers: [63] 63,94 unequal: No Solution Exploring Operation: 45-18=27, Resulting Numbers: [27] 27,94 unequal: No Solution Moving to Node #0,1,4 Current State: 94:[7, 34], Operations: ['28-10=18', '52-18=34'] Exploring Operation: 7*34=238, Resulting Numbers: [238] 238,94 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,94 unequal: No Solution Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[10, 17], Operations: ['7+28=35', '52-35=17'] Exploring Operation: 10*17=170, Resulting Numbers: [170] 170,94 unequal: No Solution Exploring Operation: 10+17=27, Resulting Numbers: [27] 27,94 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[52, 25], Operations: ['28-10=18', '7+18=25'] Exploring Operation: 52*25=1300, Resulting Numbers: [1300] 1300,94 unequal: No Solution Exploring Operation: 52+25=77, Resulting Numbers: [77] 77,94 unequal: No Solution Exploring Operation: 52-25=27, Resulting Numbers: [27] 27,94 unequal: No Solution Moving to Node #0,2,0 Current State: 94:[35, 62], Operations: ['7+28=35', '10+52=62'] Exploring Operation: 35+62=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 35*62=2170, Resulting Numbers: [2170] 2170,94 unequal: No Solution Exploring Operation: 62-35=27, Resulting Numbers: [27] 27,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[18, 59], Operations: ['28-10=18', '7+52=59'] Exploring Operation: 59-18=41, Resulting Numbers: [41] 41,94 unequal: No Solution Exploring Operation: 18*59=1062, Resulting Numbers: [1062] 1062,94 unequal: No Solution Exploring Operation: 18+59=77, Resulting Numbers: [77] 77,94 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 77, 76, 54, 52 ]
47
[ "77+76=153", "54+52=106", "153-106=47" ]
Current State: 47:[77, 76, 54, 52], Operations: [] Exploring Operation: 77+76=153, Resulting Numbers: [54, 52, 153] Generated Node #2: [54, 52, 153] from Operation: 77+76=153 Current State: 47:[54, 52, 153], Operations: ['77+76=153'] Exploring Operation: 54+52=106, Resulting Numbers: [153, 106] Generated Node #3: [153, 106] from Operation: 54+52=106 Current State: 47:[153, 106], Operations: ['77+76=153', '54+52=106'] Exploring Operation: 153-106=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[77, 76, 54, 52], Operations: [] Exploring Operation: 77-52=25, Resulting Numbers: [76, 54, 25] Generated Node #0,0: 47:[76, 54, 25] Operation: 77-52=25 Exploring Operation: 76-54=22, Resulting Numbers: [77, 52, 22] Generated Node #0,1: 47:[77, 52, 22] Operation: 76-54=22 Exploring Operation: 77-54=23, Resulting Numbers: [76, 52, 23] Generated Node #0,2: 47:[76, 52, 23] Operation: 77-54=23 Exploring Operation: 77-76=1, Resulting Numbers: [54, 52, 1] Generated Node #0,3: 47:[54, 52, 1] Operation: 77-76=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[76, 54, 25], Operations: ['77-52=25'] Exploring Operation: 76-25=51, Resulting Numbers: [54, 51] Generated Node #0,0,0: 47:[54, 51] Operation: 76-25=51 Exploring Operation: 76+25=101, Resulting Numbers: [54, 101] Generated Node #0,0,1: 47:[54, 101] Operation: 76+25=101 Exploring Operation: 76-54=22, Resulting Numbers: [25, 22] Generated Node #0,0,2: 47:[25, 22] Operation: 76-54=22 Exploring Operation: 54-25=29, Resulting Numbers: [76, 29] Generated Node #0,0,3: 47:[76, 29] Operation: 54-25=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[54, 51], Operations: ['77-52=25', '76-25=51'] Exploring Operation: 54+51=105, Resulting Numbers: [105] 105,47 unequal: No Solution Exploring Operation: 54-51=3, Resulting Numbers: [3] 3,47 unequal: No Solution Exploring Operation: 54*51=2754, Resulting Numbers: [2754] 2754,47 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: 47:[25, 22], Operations: ['77-52=25', '76-54=22'] Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[77, 76, 54, 52], Operations: [] Exploring Operation: 77-52=25, Resulting Numbers: [76, 54, 25] Generated Node #0,0: 47:[76, 54, 25] Operation: 77-52=25 Moving to Node #0,0 Current State: 47:[76, 54, 25], Operations: ['77-52=25'] Exploring Operation: 76-54=22, Resulting Numbers: [25, 22] Generated Node #0,0,2: 47:[25, 22] Operation: 76-54=22 Moving to Node #0,0,2 Current State: 47:[25, 22], Operations: ['77-52=25', '76-54=22'] Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 13, 73, 68, 66 ]
62
[ "73-13=60", "68-66=2", "60+2=62" ]
Current State: 62:[13, 73, 68, 66], Operations: [] Exploring Operation: 73-13=60, Resulting Numbers: [68, 66, 60] Generated Node #2: [68, 66, 60] from Operation: 73-13=60 Current State: 62:[68, 66, 60], Operations: ['73-13=60'] Exploring Operation: 68-66=2, Resulting Numbers: [60, 2] Generated Node #3: [60, 2] from Operation: 68-66=2 Current State: 62:[60, 2], Operations: ['73-13=60', '68-66=2'] Exploring Operation: 60+2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[13, 73, 68, 66], Operations: [] Exploring Operation: 73-68=5, Resulting Numbers: [13, 66, 5] Generated Node #0,0: 62:[13, 66, 5] Operation: 73-68=5 Exploring Operation: 73-13=60, Resulting Numbers: [68, 66, 60] Generated Node #0,1: 62:[68, 66, 60] Operation: 73-13=60 Moving to Node #0,1 Current State: 62:[68, 66, 60], Operations: ['73-13=60'] Exploring Operation: 68-66=2, Resulting Numbers: [60, 2] Generated Node #0,1,0: 62:[60, 2] Operation: 68-66=2 Exploring Operation: 68-60=8, Resulting Numbers: [66, 8] Generated Node #0,1,1: 62:[66, 8] Operation: 68-60=8 Moving to Node #0,0 Current State: 62:[13, 66, 5], Operations: ['73-68=5'] Exploring Operation: 13*5=65, Resulting Numbers: [66, 65] Generated Node #0,0,0: 62:[66, 65] Operation: 13*5=65 Exploring Operation: 13-5=8, Resulting Numbers: [66, 8] Generated Node #0,0,1: 62:[66, 8] Operation: 13-5=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[66, 65], Operations: ['73-68=5', '13*5=65'] Exploring Operation: 66+65=131, Resulting Numbers: [131] 131,62 unequal: No Solution Exploring Operation: 66-65=1, Resulting Numbers: [1] 1,62 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:[66, 8], Operations: ['73-68=5', '13-5=8'] Exploring Operation: 66+8=74, Resulting Numbers: [74] 74,62 unequal: No Solution Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 62:[60, 2], Operations: ['73-13=60', '68-66=2'] Exploring Operation: 60+2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[13, 73, 68, 66], Operations: [] Exploring Operation: 73-13=60, Resulting Numbers: [68, 66, 60] Generated Node #0,1: 62:[68, 66, 60] Operation: 73-13=60 Moving to Node #0,1 Current State: 62:[68, 66, 60], Operations: ['73-13=60'] Exploring Operation: 68-66=2, Resulting Numbers: [60, 2] Generated Node #0,1,0: 62:[60, 2] Operation: 68-66=2 Moving to Node #0,1,0 Current State: 62:[60, 2], Operations: ['73-13=60', '68-66=2'] Exploring Operation: 60+2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 87, 84, 68, 87 ]
39
[ "87-84=3", "87/3=29", "68-29=39" ]
Current State: 39:[87, 84, 68, 87], Operations: [] Exploring Operation: 87-84=3, Resulting Numbers: [68, 3] Generated Node #2: [68, 3] from Operation: 87-84=3 Current State: 39:[68, 3], Operations: ['87-84=3'] Exploring Operation: 87/3=29, Resulting Numbers: [68, 29] Generated Node #3: [68, 29] from Operation: 87/3=29 Current State: 39:[68, 29], Operations: ['87-84=3', '87/3=29'] Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[87, 84, 68, 87], Operations: [] Exploring Operation: 87-87=0, Resulting Numbers: [84, 68, 0] Generated Node #0,0: 39:[84, 68, 0] Operation: 87-87=0 Exploring Operation: 87-84=3, Resulting Numbers: [68, 87, 3] Generated Node #0,1: 39:[68, 87, 3] Operation: 87-84=3 Exploring Operation: 87-68=19, Resulting Numbers: [84, 87, 19] Generated Node #0,2: 39:[84, 87, 19] Operation: 87-68=19 Exploring Operation: 87-84=3, Resulting Numbers: [87, 68, 3] Generated Node #0,3: 39:[87, 68, 3] Operation: 87-84=3 Exploring Operation: 87/87=1, Resulting Numbers: [84, 68, 1] Generated Node #0,4: 39:[84, 68, 1] Operation: 87/87=1 Moving to Node #0,4 Current State: 39:[84, 68, 1], Operations: ['87/87=1'] Exploring Operation: 84-1=83, Resulting Numbers: [68, 83] Generated Node #0,4,0: 39:[68, 83] Operation: 84-1=83 Exploring Operation: 84-68=16, Resulting Numbers: [1, 16] Generated Node #0,4,1: 39:[1, 16] Operation: 84-68=16 Exploring Operation: 84/1=84, Resulting Numbers: [68, 84] Generated Node #0,4,2: 39:[68, 84] Operation: 84/1=84 Exploring Operation: 84*1=84, Resulting Numbers: [68, 84] Generated Node #0,4,3: 39:[68, 84] Operation: 84*1=84 Exploring Operation: 68-1=67, Resulting Numbers: [84, 67] Generated Node #0,4,4: 39:[84, 67] Operation: 68-1=67 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 39:[1, 16], Operations: ['87/87=1', '84-68=16'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,39 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:[68, 83], Operations: ['87/87=1', '84-1=83'] Exploring Operation: 83-68=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 68*83=5644, Resulting Numbers: [5644] 5644,39 unequal: No Solution Exploring Operation: 68+83=151, Resulting Numbers: [151] 151,39 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:[84, 67], Operations: ['87/87=1', '68-1=67'] Exploring Operation: 84*67=5628, Resulting Numbers: [5628] 5628,39 unequal: No Solution Exploring Operation: 84+67=151, Resulting Numbers: [151] 151,39 unequal: No Solution Exploring Operation: 84-67=17, Resulting Numbers: [17] 17,39 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:[68, 84], Operations: ['87/87=1', '84/1=84'] Exploring Operation: 68+84=152, Resulting Numbers: [152] 152,39 unequal: No Solution Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 68*84=5712, Resulting Numbers: [5712] 5712,39 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:[68, 84], Operations: ['87/87=1', '84*1=84'] Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 68*84=5712, Resulting Numbers: [5712] 5712,39 unequal: No Solution Exploring Operation: 68+84=152, Resulting Numbers: [152] 152,39 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:[68, 87, 3], Operations: ['87-84=3'] Exploring Operation: 87-3=84, Resulting Numbers: [68, 84] Generated Node #0,1,0: 39:[68, 84] Operation: 87-3=84 Exploring Operation: 68+3=71, Resulting Numbers: [87, 71] Generated Node #0,1,1: 39:[87, 71] Operation: 68+3=71 Exploring Operation: 68-3=65, Resulting Numbers: [87, 65] Generated Node #0,1,2: 39:[87, 65] Operation: 68-3=65 Exploring Operation: 87/3=29, Resulting Numbers: [68, 29] Generated Node #0,1,3: 39:[68, 29] Operation: 87/3=29 Exploring Operation: 87-68=19, Resulting Numbers: [3, 19] Generated Node #0,1,4: 39:[3, 19] Operation: 87-68=19 Moving to Node #0,0 Current State: 39:[84, 68, 0], Operations: ['87-87=0'] Exploring Operation: 68*0=0, Resulting Numbers: [84, 0] Generated Node #0,0,0: 39:[84, 0] Operation: 68*0=0 Exploring Operation: 84+0=84, Resulting Numbers: [68, 84] Generated Node #0,0,1: 39:[68, 84] Operation: 84+0=84 Exploring Operation: 84-0=84, Resulting Numbers: [68, 84] Generated Node #0,0,2: 39:[68, 84] Operation: 84-0=84 Exploring Operation: 84-68=16, Resulting Numbers: [0, 16] Generated Node #0,0,3: 39:[0, 16] Operation: 84-68=16 Exploring Operation: 84*0=0, Resulting Numbers: [68, 0] Generated Node #0,0,4: 39:[68, 0] Operation: 84*0=0 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 39:[0, 16], Operations: ['87-87=0', '84-68=16'] Exploring Operation: 16-0=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 0*16=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 0+16=16, Resulting Numbers: [16] 16,39 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 #0,0,4 Current State: 39:[68, 0], Operations: ['87-87=0', '84*0=0'] Exploring Operation: 68+0=68, Resulting Numbers: [68] 68,39 unequal: No Solution Exploring Operation: 68-0=68, Resulting Numbers: [68] 68,39 unequal: No Solution Exploring Operation: 68*0=0, Resulting Numbers: [0] 0,39 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 #0,0,0 Current State: 39:[84, 0], Operations: ['87-87=0', '68*0=0'] Exploring Operation: 84*0=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 84+0=84, Resulting Numbers: [84] 84,39 unequal: No Solution Exploring Operation: 84-0=84, Resulting Numbers: [84] 84,39 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 #0,0,1 Current State: 39:[68, 84], Operations: ['87-87=0', '84+0=84'] Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 68*84=5712, Resulting Numbers: [5712] 5712,39 unequal: No Solution Exploring Operation: 68+84=152, Resulting Numbers: [152] 152,39 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 #0,0,2 Current State: 39:[68, 84], Operations: ['87-87=0', '84-0=84'] Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 68+84=152, Resulting Numbers: [152] 152,39 unequal: No Solution Exploring Operation: 68*84=5712, Resulting Numbers: [5712] 5712,39 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: 39:[87, 68, 3], Operations: ['87-84=3'] Exploring Operation: 87-68=19, Resulting Numbers: [3, 19] Generated Node #0,3,0: 39:[3, 19] Operation: 87-68=19 Exploring Operation: 87-3=84, Resulting Numbers: [68, 84] Generated Node #0,3,1: 39:[68, 84] Operation: 87-3=84 Exploring Operation: 68-3=65, Resulting Numbers: [87, 65] Generated Node #0,3,2: 39:[87, 65] Operation: 68-3=65 Exploring Operation: 87/3=29, Resulting Numbers: [68, 29] Generated Node #0,3,3: 39:[68, 29] Operation: 87/3=29 Exploring Operation: 87+3=90, Resulting Numbers: [68, 90] Generated Node #0,3,4: 39:[68, 90] Operation: 87+3=90 Moving to Node #0,2 Current State: 39:[84, 87, 19], Operations: ['87-68=19'] Exploring Operation: 84+19=103, Resulting Numbers: [87, 103] Generated Node #0,2,0: 39:[87, 103] Operation: 84+19=103 Exploring Operation: 84-19=65, Resulting Numbers: [87, 65] Generated Node #0,2,1: 39:[87, 65] Operation: 84-19=65 Exploring Operation: 87-19=68, Resulting Numbers: [84, 68] Generated Node #0,2,2: 39:[84, 68] Operation: 87-19=68 Exploring Operation: 87-84=3, Resulting Numbers: [19, 3] Generated Node #0,2,3: 39:[19, 3] Operation: 87-84=3 Exploring Operation: 87+19=106, Resulting Numbers: [84, 106] Generated Node #0,2,4: 39:[84, 106] Operation: 87+19=106 Moving to Node #0,1,4 Current State: 39:[3, 19], Operations: ['87-84=3', '87-68=19'] Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,39 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,39 unequal: No Solution Moving to Node #0,3,0 Current State: 39:[3, 19], Operations: ['87-84=3', '87-68=19'] Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,39 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,39 unequal: No Solution Moving to Node #0,2,3 Current State: 39:[19, 3], Operations: ['87-68=19', '87-84=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,39 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,39 unequal: No Solution Moving to Node #0,3,3 Current State: 39:[68, 29], Operations: ['87-84=3', '87/3=29'] Exploring Operation: 68*29=1972, Resulting Numbers: [1972] 1972,39 unequal: No Solution Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[87, 84, 68, 87], Operations: [] Exploring Operation: 87-84=3, Resulting Numbers: [87, 68, 3] Generated Node #0,3: 39:[87, 68, 3] Operation: 87-84=3 Moving to Node #0,3 Current State: 39:[87, 68, 3], Operations: ['87-84=3'] Exploring Operation: 87/3=29, Resulting Numbers: [68, 29] Generated Node #0,3,3: 39:[68, 29] Operation: 87/3=29 Moving to Node #0,3,3 Current State: 39:[68, 29], Operations: ['87-84=3', '87/3=29'] Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
0.934028
hs_5
sum_heuristic
[ 20, 16, 38, 17 ]
91
[ "20+16=36", "38+17=55", "36+55=91" ]
Current State: 91:[20, 16, 38, 17], Operations: [] Exploring Operation: 20+16=36, Resulting Numbers: [38, 17, 36] Generated Node #2: [38, 17, 36] from Operation: 20+16=36 Current State: 91:[38, 17, 36], Operations: ['20+16=36'] Exploring Operation: 38+17=55, Resulting Numbers: [36, 55] Generated Node #3: [36, 55] from Operation: 38+17=55 Current State: 91:[36, 55], Operations: ['20+16=36', '38+17=55'] Exploring Operation: 36+55=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[20, 16, 38, 17], Operations: [] Exploring Operation: 38-20=18, Resulting Numbers: [16, 17, 18] Generated Node #0,0: 91:[16, 17, 18] Operation: 38-20=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[16, 17, 18], Operations: ['38-20=18'] Exploring Operation: 18-16=2, Resulting Numbers: [17, 2] Generated Node #0,0,0: 91:[17, 2] Operation: 18-16=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[17, 2], Operations: ['38-20=18', '18-16=2'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,91 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 No solution found.
0
hs_1
sum_heuristic
[ 50, 91, 13, 8 ]
46
[ "91-50=41", "13-8=5", "41+5=46" ]
Current State: 46:[50, 91, 13, 8], Operations: [] Exploring Operation: 91-50=41, Resulting Numbers: [13, 8, 41] Generated Node #2: [13, 8, 41] from Operation: 91-50=41 Current State: 46:[13, 8, 41], Operations: ['91-50=41'] Exploring Operation: 13-8=5, Resulting Numbers: [41, 5] Generated Node #3: [41, 5] from Operation: 13-8=5 Current State: 46:[41, 5], Operations: ['91-50=41', '13-8=5'] Exploring Operation: 41+5=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[50, 91, 13, 8], Operations: [] Exploring Operation: 91-50=41, Resulting Numbers: [13, 8, 41] Generated Node #0,0: 46:[13, 8, 41] Operation: 91-50=41 Exploring Operation: 91/13=7, Resulting Numbers: [50, 8, 7] Generated Node #0,1: 46:[50, 8, 7] Operation: 91/13=7 Exploring Operation: 91-13=78, Resulting Numbers: [50, 8, 78] Generated Node #0,2: 46:[50, 8, 78] Operation: 91-13=78 Exploring Operation: 91-8=83, Resulting Numbers: [50, 13, 83] Generated Node #0,3: 46:[50, 13, 83] Operation: 91-8=83 Exploring Operation: 13+8=21, Resulting Numbers: [50, 91, 21] Generated Node #0,4: 46:[50, 91, 21] Operation: 13+8=21 Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[50, 8, 7], Operations: ['91/13=7'] Exploring Operation: 8-7=1, Resulting Numbers: [50, 1] Generated Node #0,1,0: 46:[50, 1] Operation: 8-7=1 Exploring Operation: 8*7=56, Resulting Numbers: [50, 56] Generated Node #0,1,1: 46:[50, 56] Operation: 8*7=56 Exploring Operation: 50-7=43, Resulting Numbers: [8, 43] Generated Node #0,1,2: 46:[8, 43] Operation: 50-7=43 Exploring Operation: 50-8=42, Resulting Numbers: [7, 42] Generated Node #0,1,3: 46:[7, 42] Operation: 50-8=42 Exploring Operation: 8+7=15, Resulting Numbers: [50, 15] Generated Node #0,1,4: 46:[50, 15] Operation: 8+7=15 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[50, 1], Operations: ['91/13=7', '8-7=1'] Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,46 unequal: No Solution Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,46 unequal: No Solution Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,46 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: 46:[8, 43], Operations: ['91/13=7', '50-7=43'] Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,46 unequal: No Solution Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,46 unequal: No Solution Exploring Operation: 8*43=344, Resulting Numbers: [344] 344,46 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: 46:[7, 42], Operations: ['91/13=7', '50-8=42'] Exploring Operation: 7*42=294, Resulting Numbers: [294] 294,46 unequal: No Solution Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,46 unequal: No Solution Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,46 unequal: No Solution Exploring Operation: 7+42=49, Resulting Numbers: [49] 49,46 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: 46:[50, 15], Operations: ['91/13=7', '8+7=15'] Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,46 unequal: No Solution Exploring Operation: 50+15=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 50*15=750, Resulting Numbers: [750] 750,46 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: 46:[50, 56], Operations: ['91/13=7', '8*7=56'] Exploring Operation: 50*56=2800, Resulting Numbers: [2800] 2800,46 unequal: No Solution Exploring Operation: 56-50=6, Resulting Numbers: [6] 6,46 unequal: No Solution Exploring Operation: 50+56=106, Resulting Numbers: [106] 106,46 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[13, 8, 41], Operations: ['91-50=41'] Exploring Operation: 13+41=54, Resulting Numbers: [8, 54] Generated Node #0,0,0: 46:[8, 54] Operation: 13+41=54 Exploring Operation: 13+8=21, Resulting Numbers: [41, 21] Generated Node #0,0,1: 46:[41, 21] Operation: 13+8=21 Exploring Operation: 13-8=5, Resulting Numbers: [41, 5] Generated Node #0,0,2: 46:[41, 5] Operation: 13-8=5 Exploring Operation: 8+41=49, Resulting Numbers: [13, 49] Generated Node #0,0,3: 46:[13, 49] Operation: 8+41=49 Exploring Operation: 41-13=28, Resulting Numbers: [8, 28] Generated Node #0,0,4: 46:[8, 28] Operation: 41-13=28 Moving to Node #0,0,1 Current State: 46:[41, 21], Operations: ['91-50=41', '13+8=21'] Exploring Operation: 41*21=861, Resulting Numbers: [861] 861,46 unequal: No Solution Exploring Operation: 41+21=62, Resulting Numbers: [62] 62,46 unequal: No Solution Exploring Operation: 41-21=20, Resulting Numbers: [20] 20,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[41, 5], Operations: ['91-50=41', '13-8=5'] Exploring Operation: 41*5=205, Resulting Numbers: [205] 205,46 unequal: No Solution Exploring Operation: 41+5=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[50, 91, 13, 8], Operations: [] Exploring Operation: 91-50=41, Resulting Numbers: [13, 8, 41] Generated Node #0,0: 46:[13, 8, 41] Operation: 91-50=41 Moving to Node #0,0 Current State: 46:[13, 8, 41], Operations: ['91-50=41'] Exploring Operation: 13-8=5, Resulting Numbers: [41, 5] Generated Node #0,0,2: 46:[41, 5] Operation: 13-8=5 Moving to Node #0,0,2 Current State: 46:[41, 5], Operations: ['91-50=41', '13-8=5'] Exploring Operation: 41+5=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 13, 35, 28, 72 ]
77
[ "35*72=2520", "2520/28=90", "90-13=77" ]
Current State: 77:[13, 35, 28, 72], Operations: [] Exploring Operation: 35*72=2520, Resulting Numbers: [13, 28, 2520] Generated Node #2: [13, 28, 2520] from Operation: 35*72=2520 Current State: 77:[13, 28, 2520], Operations: ['35*72=2520'] Exploring Operation: 2520/28=90, Resulting Numbers: [13, 90] Generated Node #3: [13, 90] from Operation: 2520/28=90 Current State: 77:[13, 90], Operations: ['35*72=2520', '2520/28=90'] Exploring Operation: 90-13=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[13, 35, 28, 72], Operations: [] Exploring Operation: 35-13=22, Resulting Numbers: [28, 72, 22] Generated Node #0,0: 77:[28, 72, 22] Operation: 35-13=22 Exploring Operation: 35-28=7, Resulting Numbers: [13, 72, 7] Generated Node #0,1: 77:[13, 72, 7] Operation: 35-28=7 Exploring Operation: 35+28=63, Resulting Numbers: [13, 72, 63] Generated Node #0,2: 77:[13, 72, 63] Operation: 35+28=63 Exploring Operation: 28-13=15, Resulting Numbers: [35, 72, 15] Generated Node #0,3: 77:[35, 72, 15] Operation: 28-13=15 Moving to Node #0,1 Current State: 77:[13, 72, 7], Operations: ['35-28=7'] Exploring Operation: 72+7=79, Resulting Numbers: [13, 79] Generated Node #0,1,0: 77:[13, 79] Operation: 72+7=79 Exploring Operation: 13-7=6, Resulting Numbers: [72, 6] Generated Node #0,1,1: 77:[72, 6] Operation: 13-7=6 Exploring Operation: 13+72=85, Resulting Numbers: [7, 85] Generated Node #0,1,2: 77:[7, 85] Operation: 13+72=85 Exploring Operation: 13+7=20, Resulting Numbers: [72, 20] Generated Node #0,1,3: 77:[72, 20] Operation: 13+7=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 77:[13, 79], Operations: ['35-28=7', '72+7=79'] Exploring Operation: 79-13=66, Resulting Numbers: [66] 66,77 unequal: No Solution Exploring Operation: 13+79=92, Resulting Numbers: [92] 92,77 unequal: No Solution Exploring Operation: 13*79=1027, Resulting Numbers: [1027] 1027,77 unequal: No Solution No 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: 77:[72, 6], Operations: ['35-28=7', '13-7=6'] Exploring Operation: 72-6=66, Resulting Numbers: [66] 66,77 unequal: No Solution Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,77 unequal: No Solution Exploring Operation: 72+6=78, Resulting Numbers: [78] 78,77 unequal: No Solution Exploring Operation: 72*6=432, Resulting Numbers: [432] 432,77 unequal: No Solution No 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: 77:[7, 85], Operations: ['35-28=7', '13+72=85'] Exploring Operation: 7+85=92, Resulting Numbers: [92] 92,77 unequal: No Solution Exploring Operation: 7*85=595, Resulting Numbers: [595] 595,77 unequal: No Solution Exploring Operation: 85-7=78, Resulting Numbers: [78] 78,77 unequal: No Solution No 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: 77:[72, 20], Operations: ['35-28=7', '13+7=20'] Exploring Operation: 72*20=1440, Resulting Numbers: [1440] 1440,77 unequal: No Solution Exploring Operation: 72-20=52, Resulting Numbers: [52] 52,77 unequal: No Solution Exploring Operation: 72+20=92, Resulting Numbers: [92] 92,77 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: 77:[13, 72, 63], Operations: ['35+28=63'] Exploring Operation: 72-13=59, Resulting Numbers: [63, 59] Generated Node #0,2,0: 77:[63, 59] Operation: 72-13=59 Exploring Operation: 13+63=76, Resulting Numbers: [72, 76] Generated Node #0,2,1: 77:[72, 76] Operation: 13+63=76 Exploring Operation: 13+72=85, Resulting Numbers: [63, 85] Generated Node #0,2,2: 77:[63, 85] Operation: 13+72=85 Exploring Operation: 72-63=9, Resulting Numbers: [13, 9] Generated Node #0,2,3: 77:[13, 9] Operation: 72-63=9 Moving to Node #0,3 Current State: 77:[35, 72, 15], Operations: ['28-13=15'] Exploring Operation: 35-15=20, Resulting Numbers: [72, 20] Generated Node #0,3,0: 77:[72, 20] Operation: 35-15=20 Exploring Operation: 35+72=107, Resulting Numbers: [15, 107] Generated Node #0,3,1: 77:[15, 107] Operation: 35+72=107 Exploring Operation: 35+15=50, Resulting Numbers: [72, 50] Generated Node #0,3,2: 77:[72, 50] Operation: 35+15=50 Exploring Operation: 72-35=37, Resulting Numbers: [15, 37] Generated Node #0,3,3: 77:[15, 37] Operation: 72-35=37 Moving to Node #0,0 Current State: 77:[28, 72, 22], Operations: ['35-13=22'] Exploring Operation: 28-22=6, Resulting Numbers: [72, 6] Generated Node #0,0,0: 77:[72, 6] Operation: 28-22=6 Exploring Operation: 72+22=94, Resulting Numbers: [28, 94] Generated Node #0,0,1: 77:[28, 94] Operation: 72+22=94 Exploring Operation: 28+22=50, Resulting Numbers: [72, 50] Generated Node #0,0,2: 77:[72, 50] Operation: 28+22=50 Exploring Operation: 28+72=100, Resulting Numbers: [22, 100] Generated Node #0,0,3: 77:[22, 100] Operation: 28+72=100 Moving to Node #0,2,3 Current State: 77:[13, 9], Operations: ['35+28=63', '72-63=9'] Exploring Operation: 13*9=117, Resulting Numbers: [117] 117,77 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,77 unequal: No Solution Moving to Node #0,2,1 Current State: 77:[72, 76], Operations: ['35+28=63', '13+63=76'] Exploring Operation: 76-72=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 72+76=148, Resulting Numbers: [148] 148,77 unequal: No Solution Exploring Operation: 72*76=5472, Resulting Numbers: [5472] 5472,77 unequal: No Solution Moving to Node #0,0,0 Current State: 77:[72, 6], Operations: ['35-13=22', '28-22=6'] Exploring Operation: 72-6=66, Resulting Numbers: [66] 66,77 unequal: No Solution Exploring Operation: 72*6=432, Resulting Numbers: [432] 432,77 unequal: No Solution Exploring Operation: 72+6=78, Resulting Numbers: [78] 78,77 unequal: No Solution Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,77 unequal: No Solution Moving to Node #0,3,0 Current State: 77:[72, 20], Operations: ['28-13=15', '35-15=20'] Exploring Operation: 72*20=1440, Resulting Numbers: [1440] 1440,77 unequal: No Solution Exploring Operation: 72+20=92, Resulting Numbers: [92] 92,77 unequal: No Solution Exploring Operation: 72-20=52, Resulting Numbers: [52] 52,77 unequal: No Solution Moving to Node #0,2,2 Current State: 77:[63, 85], Operations: ['35+28=63', '13+72=85'] Exploring Operation: 85-63=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 63+85=148, Resulting Numbers: [148] 148,77 unequal: No Solution Exploring Operation: 63*85=5355, Resulting Numbers: [5355] 5355,77 unequal: No Solution Moving to Node #0,3,3 Current State: 77:[15, 37], Operations: ['28-13=15', '72-35=37'] Exploring Operation: 15*37=555, Resulting Numbers: [555] 555,77 unequal: No Solution Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 15+37=52, Resulting Numbers: [52] 52,77 unequal: No Solution Moving to Node #0,3,2 Current State: 77:[72, 50], Operations: ['28-13=15', '35+15=50'] Exploring Operation: 72-50=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 72*50=3600, Resulting Numbers: [3600] 3600,77 unequal: No Solution Exploring Operation: 72+50=122, Resulting Numbers: [122] 122,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[72, 50], Operations: ['35-13=22', '28+22=50'] Exploring Operation: 72-50=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 72+50=122, Resulting Numbers: [122] 122,77 unequal: No Solution Exploring Operation: 72*50=3600, Resulting Numbers: [3600] 3600,77 unequal: No Solution Moving to Node #0,2,0 Current State: 77:[63, 59], Operations: ['35+28=63', '72-13=59'] Exploring Operation: 63-59=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 63*59=3717, Resulting Numbers: [3717] 3717,77 unequal: No Solution Exploring Operation: 63+59=122, Resulting Numbers: [122] 122,77 unequal: No Solution Moving to Node #0,0,3 Current State: 77:[22, 100], Operations: ['35-13=22', '28+72=100'] Exploring Operation: 22*100=2200, Resulting Numbers: [2200] 2200,77 unequal: No Solution Exploring Operation: 22+100=122, Resulting Numbers: [122] 122,77 unequal: No Solution Exploring Operation: 100-22=78, Resulting Numbers: [78] 78,77 unequal: No Solution Moving to Node #0,3,1 Current State: 77:[15, 107], Operations: ['28-13=15', '35+72=107'] Exploring Operation: 15+107=122, Resulting Numbers: [122] 122,77 unequal: No Solution Exploring Operation: 107-15=92, Resulting Numbers: [92] 92,77 unequal: No Solution Exploring Operation: 15*107=1605, Resulting Numbers: [1605] 1605,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[28, 94], Operations: ['35-13=22', '72+22=94'] Exploring Operation: 28+94=122, Resulting Numbers: [122] 122,77 unequal: No Solution Exploring Operation: 28*94=2632, Resulting Numbers: [2632] 2632,77 unequal: No Solution Exploring Operation: 94-28=66, Resulting Numbers: [66] 66,77 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 56, 17, 25, 20 ]
87
[ "56*25=1400", "1400/20=70", "17+70=87" ]
Current State: 87:[56, 17, 25, 20], Operations: [] Exploring Operation: 56*25=1400, Resulting Numbers: [17, 20, 1400] Generated Node #2: [17, 20, 1400] from Operation: 56*25=1400 Current State: 87:[17, 20, 1400], Operations: ['56*25=1400'] Exploring Operation: 1400/20=70, Resulting Numbers: [17, 70] Generated Node #3: [17, 70] from Operation: 1400/20=70 Current State: 87:[17, 70], Operations: ['56*25=1400', '1400/20=70'] Exploring Operation: 17+70=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[56, 17, 25, 20], Operations: [] Exploring Operation: 56-25=31, Resulting Numbers: [17, 20, 31] Generated Node #0,0: 87:[17, 20, 31] Operation: 56-25=31 Exploring Operation: 56-17=39, Resulting Numbers: [25, 20, 39] Generated Node #0,1: 87:[25, 20, 39] Operation: 56-17=39 Exploring Operation: 56-20=36, Resulting Numbers: [17, 25, 36] Generated Node #0,2: 87:[17, 25, 36] Operation: 56-20=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[17, 20, 31], Operations: ['56-25=31'] Exploring Operation: 31-17=14, Resulting Numbers: [20, 14] Generated Node #0,0,0: 87:[20, 14] Operation: 31-17=14 Exploring Operation: 20-17=3, Resulting Numbers: [31, 3] Generated Node #0,0,1: 87:[31, 3] Operation: 20-17=3 Exploring Operation: 17+20=37, Resulting Numbers: [31, 37] Generated Node #0,0,2: 87:[31, 37] Operation: 17+20=37 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[31, 3], Operations: ['56-25=31', '20-17=3'] Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,87 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,87 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: 87:[31, 37], Operations: ['56-25=31', '17+20=37'] Exploring Operation: 31+37=68, Resulting Numbers: [68] 68,87 unequal: No Solution Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 31*37=1147, Resulting Numbers: [1147] 1147,87 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: 87:[20, 14], Operations: ['56-25=31', '31-17=14'] Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,87 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,87 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: 87:[25, 20, 39], Operations: ['56-17=39'] Exploring Operation: 39-25=14, Resulting Numbers: [20, 14] Generated Node #0,1,0: 87:[20, 14] Operation: 39-25=14 Exploring Operation: 39-20=19, Resulting Numbers: [25, 19] Generated Node #0,1,1: 87:[25, 19] Operation: 39-20=19 Exploring Operation: 25-20=5, Resulting Numbers: [39, 5] Generated Node #0,1,2: 87:[39, 5] Operation: 25-20=5 Moving to Node #0,1,2 Current State: 87:[39, 5], Operations: ['56-17=39', '25-20=5'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,87 unequal: No Solution Exploring Operation: 39*5=195, Resulting Numbers: [195] 195,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[25, 19], Operations: ['56-17=39', '39-20=19'] Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,87 unequal: No Solution Exploring Operation: 25*19=475, Resulting Numbers: [475] 475,87 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[20, 14], Operations: ['56-17=39', '39-25=14'] Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,87 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 #0,2 Current State: 87:[17, 25, 36], Operations: ['56-20=36'] Exploring Operation: 25-17=8, Resulting Numbers: [36, 8] Generated Node #0,2,0: 87:[36, 8] Operation: 25-17=8 Exploring Operation: 36-17=19, Resulting Numbers: [25, 19] Generated Node #0,2,1: 87:[25, 19] Operation: 36-17=19 Exploring Operation: 17+25=42, Resulting Numbers: [36, 42] Generated Node #0,2,2: 87:[36, 42] Operation: 17+25=42 Moving to Node #0,2,0 Current State: 87:[36, 8], Operations: ['56-20=36', '25-17=8'] Exploring Operation: 36+8=44, Resulting Numbers: [44] 44,87 unequal: No Solution Exploring Operation: 36*8=288, Resulting Numbers: [288] 288,87 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,87 unequal: No Solution Moving to Node #0,2,1 Current State: 87:[25, 19], Operations: ['56-20=36', '36-17=19'] Exploring Operation: 25*19=475, Resulting Numbers: [475] 475,87 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,87 unequal: No Solution Moving to Node #0,2,2 Current State: 87:[36, 42], Operations: ['56-20=36', '17+25=42'] Exploring Operation: 36*42=1512, Resulting Numbers: [1512] 1512,87 unequal: No Solution Exploring Operation: 36+42=78, Resulting Numbers: [78] 78,87 unequal: No Solution Exploring Operation: 42-36=6, Resulting Numbers: [6] 6,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 49, 45, 19, 88 ]
25
[ "49+45=94", "88-19=69", "94-69=25" ]
Current State: 25:[49, 45, 19, 88], Operations: [] Exploring Operation: 49+45=94, Resulting Numbers: [19, 88, 94] Generated Node #2: [19, 88, 94] from Operation: 49+45=94 Current State: 25:[19, 88, 94], Operations: ['49+45=94'] Exploring Operation: 88-19=69, Resulting Numbers: [94, 69] Generated Node #3: [94, 69] from Operation: 88-19=69 Current State: 25:[94, 69], Operations: ['49+45=94', '88-19=69'] Exploring Operation: 94-69=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[49, 45, 19, 88], Operations: [] Exploring Operation: 88-45=43, Resulting Numbers: [49, 19, 43] Generated Node #0,0: 25:[49, 19, 43] Operation: 88-45=43 Exploring Operation: 49-19=30, Resulting Numbers: [45, 88, 30] Generated Node #0,1: 25:[45, 88, 30] Operation: 49-19=30 Exploring Operation: 49-45=4, Resulting Numbers: [19, 88, 4] Generated Node #0,2: 25:[19, 88, 4] Operation: 49-45=4 Exploring Operation: 88-49=39, Resulting Numbers: [45, 19, 39] Generated Node #0,3: 25:[45, 19, 39] Operation: 88-49=39 Moving to Node #0,3 Current State: 25:[45, 19, 39], Operations: ['88-49=39'] Exploring Operation: 45-19=26, Resulting Numbers: [39, 26] Generated Node #0,3,0: 25:[39, 26] Operation: 45-19=26 Exploring Operation: 45-39=6, Resulting Numbers: [19, 6] Generated Node #0,3,1: 25:[19, 6] Operation: 45-39=6 Exploring Operation: 45+19=64, Resulting Numbers: [39, 64] Generated Node #0,3,2: 25:[39, 64] Operation: 45+19=64 Exploring Operation: 39-19=20, Resulting Numbers: [45, 20] Generated Node #0,3,3: 25:[45, 20] Operation: 39-19=20 Moving to Node #0,0 Current State: 25:[49, 19, 43], Operations: ['88-45=43'] Exploring Operation: 49-43=6, Resulting Numbers: [19, 6] Generated Node #0,0,0: 25:[19, 6] Operation: 49-43=6 Exploring Operation: 49-19=30, Resulting Numbers: [43, 30] Generated Node #0,0,1: 25:[43, 30] Operation: 49-19=30 Exploring Operation: 49+19=68, Resulting Numbers: [43, 68] Generated Node #0,0,2: 25:[43, 68] Operation: 49+19=68 Exploring Operation: 43-19=24, Resulting Numbers: [49, 24] Generated Node #0,0,3: 25:[49, 24] Operation: 43-19=24 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[19, 6], Operations: ['88-45=43', '49-43=6'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,25 unequal: No Solution Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[49, 45, 19, 88], Operations: [] Exploring Operation: 88-45=43, Resulting Numbers: [49, 19, 43] Generated Node #0,0: 25:[49, 19, 43] Operation: 88-45=43 Moving to Node #0,0 Current State: 25:[49, 19, 43], Operations: ['88-45=43'] Exploring Operation: 49-43=6, Resulting Numbers: [19, 6] Generated Node #0,0,0: 25:[19, 6] Operation: 49-43=6 Moving to Node #0,0,0 Current State: 25:[19, 6], Operations: ['88-45=43', '49-43=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 63, 43, 25, 26 ]
11
[ "25*26=650", "43+650=693", "693/63=11" ]
Current State: 11:[63, 43, 25, 26], Operations: [] Exploring Operation: 25*26=650, Resulting Numbers: [63, 43, 650] Generated Node #2: [63, 43, 650] from Operation: 25*26=650 Current State: 11:[63, 43, 650], Operations: ['25*26=650'] Exploring Operation: 43+650=693, Resulting Numbers: [63, 693] Generated Node #3: [63, 693] from Operation: 43+650=693 Current State: 11:[63, 693], Operations: ['25*26=650', '43+650=693'] Exploring Operation: 693/63=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[63, 43, 25, 26], Operations: [] Exploring Operation: 43-26=17, Resulting Numbers: [63, 25, 17] Generated Node #0,0: 11:[63, 25, 17] Operation: 43-26=17 Exploring Operation: 63-43=20, Resulting Numbers: [25, 26, 20] Generated Node #0,1: 11:[25, 26, 20] Operation: 63-43=20 Exploring Operation: 63-25=38, Resulting Numbers: [43, 26, 38] Generated Node #0,2: 11:[43, 26, 38] Operation: 63-25=38 Exploring Operation: 63-26=37, Resulting Numbers: [43, 25, 37] Generated Node #0,3: 11:[43, 25, 37] Operation: 63-26=37 Moving to Node #0,1 Current State: 11:[25, 26, 20], Operations: ['63-43=20'] Exploring Operation: 25-20=5, Resulting Numbers: [26, 5] Generated Node #0,1,0: 11:[26, 5] Operation: 25-20=5 Exploring Operation: 26-20=6, Resulting Numbers: [25, 6] Generated Node #0,1,1: 11:[25, 6] Operation: 26-20=6 Exploring Operation: 26-25=1, Resulting Numbers: [20, 1] Generated Node #0,1,2: 11:[20, 1] Operation: 26-25=1 Exploring Operation: 25+26=51, Resulting Numbers: [20, 51] Generated Node #0,1,3: 11:[20, 51] Operation: 25+26=51 Moving to Node #0,3 Current State: 11:[43, 25, 37], Operations: ['63-26=37'] Exploring Operation: 43+25=68, Resulting Numbers: [37, 68] Generated Node #0,3,0: 11:[37, 68] Operation: 43+25=68 Exploring Operation: 43-37=6, Resulting Numbers: [25, 6] Generated Node #0,3,1: 11:[25, 6] Operation: 43-37=6 Exploring Operation: 43-25=18, Resulting Numbers: [37, 18] Generated Node #0,3,2: 11:[37, 18] Operation: 43-25=18 Exploring Operation: 37-25=12, Resulting Numbers: [43, 12] Generated Node #0,3,3: 11:[43, 12] Operation: 37-25=12 Moving to Node #0,0 Current State: 11:[63, 25, 17], Operations: ['43-26=17'] Exploring Operation: 63+25=88, Resulting Numbers: [17, 88] Generated Node #0,0,0: 11:[17, 88] Operation: 63+25=88 Exploring Operation: 63-17=46, Resulting Numbers: [25, 46] Generated Node #0,0,1: 11:[25, 46] Operation: 63-17=46 Exploring Operation: 63-25=38, Resulting Numbers: [17, 38] Generated Node #0,0,2: 11:[17, 38] Operation: 63-25=38 Exploring Operation: 25-17=8, Resulting Numbers: [63, 8] Generated Node #0,0,3: 11:[63, 8] Operation: 25-17=8 Moving to Node #0,2 Current State: 11:[43, 26, 38], Operations: ['63-25=38'] Exploring Operation: 43-38=5, Resulting Numbers: [26, 5] Generated Node #0,2,0: 11:[26, 5] Operation: 43-38=5 Exploring Operation: 43-26=17, Resulting Numbers: [38, 17] Generated Node #0,2,1: 11:[38, 17] Operation: 43-26=17 Exploring Operation: 38-26=12, Resulting Numbers: [43, 12] Generated Node #0,2,2: 11:[43, 12] Operation: 38-26=12 Exploring Operation: 43+26=69, Resulting Numbers: [38, 69] Generated Node #0,2,3: 11:[38, 69] Operation: 43+26=69 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[26, 5], Operations: ['63-25=38', '43-38=5'] Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,11 unequal: No Solution Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,11 unequal: No Solution No 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: 11:[38, 17], Operations: ['63-25=38', '43-26=17'] Exploring Operation: 38*17=646, Resulting Numbers: [646] 646,11 unequal: No Solution Exploring Operation: 38+17=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 38-17=21, Resulting Numbers: [21] 21,11 unequal: No Solution No 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: 11:[43, 12], Operations: ['63-25=38', '38-26=12'] Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 43*12=516, Resulting Numbers: [516] 516,11 unequal: No Solution Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,11 unequal: No Solution No 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: 11:[38, 69], Operations: ['63-25=38', '43+26=69'] Exploring Operation: 38*69=2622, Resulting Numbers: [2622] 2622,11 unequal: No Solution Exploring Operation: 38+69=107, Resulting Numbers: [107] 107,11 unequal: No Solution Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 11:[25, 6], Operations: ['63-43=20', '26-20=6'] Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,11 unequal: No Solution Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[20, 1], Operations: ['63-43=20', '26-25=1'] Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,11 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,11 unequal: No Solution Moving to Node #0,3,1 Current State: 11:[25, 6], Operations: ['63-26=37', '43-37=6'] Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,11 unequal: No Solution Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[26, 5], Operations: ['63-43=20', '25-20=5'] Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,11 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,11 unequal: No Solution Moving to Node #0,3,3 Current State: 11:[43, 12], Operations: ['63-26=37', '37-25=12'] Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 43*12=516, Resulting Numbers: [516] 516,11 unequal: No Solution Moving to Node #0,3,2 Current State: 11:[37, 18], Operations: ['63-26=37', '43-25=18'] Exploring Operation: 37*18=666, Resulting Numbers: [666] 666,11 unequal: No Solution Exploring Operation: 37+18=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[17, 38], Operations: ['43-26=17', '63-25=38'] Exploring Operation: 38-17=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 17+38=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 17*38=646, Resulting Numbers: [646] 646,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[25, 46], Operations: ['43-26=17', '63-17=46'] Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 25+46=71, Resulting Numbers: [71] 71,11 unequal: No Solution Exploring Operation: 25*46=1150, Resulting Numbers: [1150] 1150,11 unequal: No Solution Moving to Node #0,1,3 Current State: 11:[20, 51], Operations: ['63-43=20', '25+26=51'] Exploring Operation: 20+51=71, Resulting Numbers: [71] 71,11 unequal: No Solution Exploring Operation: 20*51=1020, Resulting Numbers: [1020] 1020,11 unequal: No Solution Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,11 unequal: No Solution Moving to Node #0,0,3 Current State: 11:[63, 8], Operations: ['43-26=17', '25-17=8'] Exploring Operation: 63*8=504, Resulting Numbers: [504] 504,11 unequal: No Solution Exploring Operation: 63+8=71, Resulting Numbers: [71] 71,11 unequal: No Solution Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,11 unequal: No Solution Moving to Node #0,3,0 Current State: 11:[37, 68], Operations: ['63-26=37', '43+25=68'] Exploring Operation: 37*68=2516, Resulting Numbers: [2516] 2516,11 unequal: No Solution Exploring Operation: 37+68=105, Resulting Numbers: [105] 105,11 unequal: No Solution Exploring Operation: 68-37=31, Resulting Numbers: [31] 31,11 unequal: No Solution Moving to Node #0,0,0 Current State: 11:[17, 88], Operations: ['43-26=17', '63+25=88'] Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,11 unequal: No Solution Exploring Operation: 17+88=105, Resulting Numbers: [105] 105,11 unequal: No Solution Exploring Operation: 17*88=1496, Resulting Numbers: [1496] 1496,11 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 1, 7, 70, 35 ]
14
[ "1*7=7", "70/35=2", "7*2=14" ]
Current State: 14:[1, 7, 70, 35], Operations: [] Exploring Operation: 1*7=7, Resulting Numbers: [70, 35, 7] Generated Node #2: [70, 35, 7] from Operation: 1*7=7 Current State: 14:[70, 35, 7], Operations: ['1*7=7'] Exploring Operation: 70/35=2, Resulting Numbers: [7, 2] Generated Node #3: [7, 2] from Operation: 70/35=2 Current State: 14:[7, 2], Operations: ['1*7=7', '70/35=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[1, 7, 70, 35], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [1, 7, 2] Generated Node #0,0: 14:[1, 7, 2] Operation: 70/35=2 Exploring Operation: 70-35=35, Resulting Numbers: [1, 7, 35] Generated Node #0,1: 14:[1, 7, 35] Operation: 70-35=35 Moving to Node #0,0 Current State: 14:[1, 7, 2], Operations: ['70/35=2'] Exploring Operation: 1*7=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 14:[2, 7] Operation: 1*7=7 Exploring Operation: 7/1=7, Resulting Numbers: [2, 7] Generated Node #0,0,1: 14:[2, 7] Operation: 7/1=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[2, 7], Operations: ['70/35=2', '1*7=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,14 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[1, 7, 70, 35], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [1, 7, 2] Generated Node #0,0: 14:[1, 7, 2] Operation: 70/35=2 Moving to Node #0,0 Current State: 14:[1, 7, 2], Operations: ['70/35=2'] Exploring Operation: 1*7=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 14:[2, 7] Operation: 1*7=7 Moving to Node #0,0,0 Current State: 14:[2, 7], Operations: ['70/35=2', '1*7=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 27, 63, 15, 95 ]
20
[ "27+63=90", "15+95=110", "110-90=20" ]
Current State: 20:[27, 63, 15, 95], Operations: [] Exploring Operation: 27+63=90, Resulting Numbers: [15, 95, 90] Generated Node #2: [15, 95, 90] from Operation: 27+63=90 Current State: 20:[15, 95, 90], Operations: ['27+63=90'] Exploring Operation: 15+95=110, Resulting Numbers: [90, 110] Generated Node #3: [90, 110] from Operation: 15+95=110 Current State: 20:[90, 110], Operations: ['27+63=90', '15+95=110'] Exploring Operation: 110-90=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[27, 63, 15, 95], Operations: [] Exploring Operation: 63-15=48, Resulting Numbers: [27, 95, 48] Generated Node #0,0: 20:[27, 95, 48] Operation: 63-15=48 Exploring Operation: 63-27=36, Resulting Numbers: [15, 95, 36] Generated Node #0,1: 20:[15, 95, 36] Operation: 63-27=36 Exploring Operation: 95-27=68, Resulting Numbers: [63, 15, 68] Generated Node #0,2: 20:[63, 15, 68] Operation: 95-27=68 Exploring Operation: 95-63=32, Resulting Numbers: [27, 15, 32] Generated Node #0,3: 20:[27, 15, 32] Operation: 95-63=32 Moving to Node #0,3 Current State: 20:[27, 15, 32], Operations: ['95-63=32'] Exploring Operation: 27-15=12, Resulting Numbers: [32, 12] Generated Node #0,3,0: 20:[32, 12] Operation: 27-15=12 Exploring Operation: 32-27=5, Resulting Numbers: [15, 5] Generated Node #0,3,1: 20:[15, 5] Operation: 32-27=5 Exploring Operation: 32-15=17, Resulting Numbers: [27, 17] Generated Node #0,3,2: 20:[27, 17] Operation: 32-15=17 Exploring Operation: 27+15=42, Resulting Numbers: [32, 42] Generated Node #0,3,3: 20:[32, 42] Operation: 27+15=42 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 20:[15, 5], Operations: ['95-63=32', '32-27=5'] Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[27, 63, 15, 95], Operations: [] Exploring Operation: 95-63=32, Resulting Numbers: [27, 15, 32] Generated Node #0,3: 20:[27, 15, 32] Operation: 95-63=32 Moving to Node #0,3 Current State: 20:[27, 15, 32], Operations: ['95-63=32'] Exploring Operation: 32-27=5, Resulting Numbers: [15, 5] Generated Node #0,3,1: 20:[15, 5] Operation: 32-27=5 Moving to Node #0,3,1 Current State: 20:[15, 5], Operations: ['95-63=32', '32-27=5'] Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 31, 35, 38, 36 ]
68
[ "31+35=66", "38-36=2", "66+2=68" ]
Current State: 68:[31, 35, 38, 36], Operations: [] Exploring Operation: 31+35=66, Resulting Numbers: [38, 36, 66] Generated Node #2: [38, 36, 66] from Operation: 31+35=66 Current State: 68:[38, 36, 66], Operations: ['31+35=66'] Exploring Operation: 38-36=2, Resulting Numbers: [66, 2] Generated Node #3: [66, 2] from Operation: 38-36=2 Current State: 68:[66, 2], Operations: ['31+35=66', '38-36=2'] Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[31, 35, 38, 36], Operations: [] Exploring Operation: 31+38=69, Resulting Numbers: [35, 36, 69] Generated Node #0,0: 68:[35, 36, 69] Operation: 31+38=69 Exploring Operation: 38-36=2, Resulting Numbers: [31, 35, 2] Generated Node #0,1: 68:[31, 35, 2] Operation: 38-36=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[35, 36, 69], Operations: ['31+38=69'] Exploring Operation: 36-35=1, Resulting Numbers: [69, 1] Generated Node #0,0,0: 68:[69, 1] Operation: 36-35=1 Exploring Operation: 69-35=34, Resulting Numbers: [36, 34] Generated Node #0,0,1: 68:[36, 34] Operation: 69-35=34 Moving to Node #0,0,0 Current State: 68:[69, 1], Operations: ['31+38=69', '36-35=1'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[31, 35, 38, 36], Operations: [] Exploring Operation: 31+38=69, Resulting Numbers: [35, 36, 69] Generated Node #0,0: 68:[35, 36, 69] Operation: 31+38=69 Moving to Node #0,0 Current State: 68:[35, 36, 69], Operations: ['31+38=69'] Exploring Operation: 36-35=1, Resulting Numbers: [69, 1] Generated Node #0,0,0: 68:[69, 1] Operation: 36-35=1 Moving to Node #0,0,0 Current State: 68:[69, 1], Operations: ['31+38=69', '36-35=1'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 3, 21, 4, 45 ]
56
[ "21/3=7", "4+45=49", "7+49=56" ]
Current State: 56:[3, 21, 4, 45], Operations: [] Exploring Operation: 21/3=7, Resulting Numbers: [4, 45, 7] Generated Node #2: [4, 45, 7] from Operation: 21/3=7 Current State: 56:[4, 45, 7], Operations: ['21/3=7'] Exploring Operation: 4+45=49, Resulting Numbers: [7, 49] Generated Node #3: [7, 49] from Operation: 4+45=49 Current State: 56:[7, 49], Operations: ['21/3=7', '4+45=49'] Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[3, 21, 4, 45], Operations: [] Exploring Operation: 45/3=15, Resulting Numbers: [21, 4, 15] Generated Node #0,0: 56:[21, 4, 15] Operation: 45/3=15 Exploring Operation: 45-21=24, Resulting Numbers: [3, 4, 24] Generated Node #0,1: 56:[3, 4, 24] Operation: 45-21=24 Moving to Node #0,1 Current State: 56:[3, 4, 24], Operations: ['45-21=24'] Exploring Operation: 24/3=8, Resulting Numbers: [4, 8] Generated Node #0,1,0: 56:[4, 8] Operation: 24/3=8 Exploring Operation: 3+24=27, Resulting Numbers: [4, 27] Generated Node #0,1,1: 56:[4, 27] Operation: 3+24=27 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 56:[4, 8], Operations: ['45-21=24', '24/3=8'] Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,56 unequal: No Solution No 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: 56:[4, 27], Operations: ['45-21=24', '3+24=27'] Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,56 unequal: No Solution Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,56 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: 56:[21, 4, 15], Operations: ['45/3=15'] Exploring Operation: 21-15=6, Resulting Numbers: [4, 6] Generated Node #0,0,0: 56:[4, 6] Operation: 21-15=6 Exploring Operation: 21+4=25, Resulting Numbers: [15, 25] Generated Node #0,0,1: 56:[15, 25] Operation: 21+4=25 Moving to Node #0,0,0 Current State: 56:[4, 6], Operations: ['45/3=15', '21-15=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,56 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[15, 25], Operations: ['45/3=15', '21+4=25'] Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,56 unequal: No Solution Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,56 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 78, 39, 51, 27 ]
76
[ "78/39=2", "51+27=78", "78-2=76" ]
Current State: 76:[78, 39, 51, 27], Operations: [] Exploring Operation: 78/39=2, Resulting Numbers: [51, 27, 2] Generated Node #2: [51, 27, 2] from Operation: 78/39=2 Current State: 76:[51, 27, 2], Operations: ['78/39=2'] Exploring Operation: 51+27=78, Resulting Numbers: [2, 78] Generated Node #3: [2, 78] from Operation: 51+27=78 Current State: 76:[2, 78], Operations: ['78/39=2', '51+27=78'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[78, 39, 51, 27], Operations: [] Exploring Operation: 51-27=24, Resulting Numbers: [78, 39, 24] Generated Node #0,0: 76:[78, 39, 24] Operation: 51-27=24 Exploring Operation: 51+27=78, Resulting Numbers: [78, 39, 78] Generated Node #0,1: 76:[78, 39, 78] Operation: 51+27=78 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[78, 39, 78], Operations: ['51+27=78'] Exploring Operation: 78/78=1, Resulting Numbers: [39, 1] Generated Node #0,1,0: 76:[39, 1] Operation: 78/78=1 Exploring Operation: 78/39=2, Resulting Numbers: [78, 2] Generated Node #0,1,1: 76:[78, 2] Operation: 78/39=2 Moving to Node #0,1,0 Current State: 76:[39, 1], Operations: ['51+27=78', '78/78=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,76 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[78, 2], Operations: ['51+27=78', '78/39=2'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,76 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[78, 39, 51, 27], Operations: [] Exploring Operation: 51+27=78, Resulting Numbers: [78, 39, 78] Generated Node #0,1: 76:[78, 39, 78] Operation: 51+27=78 Moving to Node #0,1 Current State: 76:[78, 39, 78], Operations: ['51+27=78'] Exploring Operation: 78/39=2, Resulting Numbers: [78, 2] Generated Node #0,1,1: 76:[78, 2] Operation: 78/39=2 Moving to Node #0,1,1 Current State: 76:[78, 2], Operations: ['51+27=78', '78/39=2'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 40, 38, 40, 34 ]
71
[ "40/40=1", "38+34=72", "72-1=71" ]
Current State: 71:[40, 38, 40, 34], Operations: [] Exploring Operation: 40/40=1, Resulting Numbers: [38, 34, 1] Generated Node #2: [38, 34, 1] from Operation: 40/40=1 Current State: 71:[38, 34, 1], Operations: ['40/40=1'] Exploring Operation: 38+34=72, Resulting Numbers: [1, 72] Generated Node #3: [1, 72] from Operation: 38+34=72 Current State: 71:[1, 72], Operations: ['40/40=1', '38+34=72'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[40, 38, 40, 34], Operations: [] Exploring Operation: 40+34=74, Resulting Numbers: [38, 40, 74] Generated Node #0,0: 71:[38, 40, 74] Operation: 40+34=74 Exploring Operation: 40+38=78, Resulting Numbers: [40, 34, 78] Generated Node #0,1: 71:[40, 34, 78] Operation: 40+38=78 Exploring Operation: 38+34=72, Resulting Numbers: [40, 40, 72] Generated Node #0,2: 71:[40, 40, 72] Operation: 38+34=72 Exploring Operation: 40+34=74, Resulting Numbers: [40, 38, 74] Generated Node #0,3: 71:[40, 38, 74] Operation: 40+34=74 Exploring Operation: 38+40=78, Resulting Numbers: [40, 34, 78] Generated Node #0,4: 71:[40, 34, 78] Operation: 38+40=78 Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[40, 40, 72], Operations: ['38+34=72'] Exploring Operation: 40-40=0, Resulting Numbers: [72, 0] Generated Node #0,2,0: 71:[72, 0] Operation: 40-40=0 Exploring Operation: 72-40=32, Resulting Numbers: [40, 32] Generated Node #0,2,1: 71:[40, 32] Operation: 72-40=32 Exploring Operation: 40+40=80, Resulting Numbers: [72, 80] Generated Node #0,2,2: 71:[72, 80] Operation: 40+40=80 Exploring Operation: 72-40=32, Resulting Numbers: [40, 32] Generated Node #0,2,3: 71:[40, 32] Operation: 72-40=32 Exploring Operation: 40/40=1, Resulting Numbers: [72, 1] Generated Node #0,2,4: 71:[72, 1] Operation: 40/40=1 Moving to Node #0,2,2 Current State: 71:[72, 80], Operations: ['38+34=72', '40+40=80'] Exploring Operation: 72*80=5760, Resulting Numbers: [5760] 5760,71 unequal: No Solution Exploring Operation: 72+80=152, Resulting Numbers: [152] 152,71 unequal: No Solution Exploring Operation: 80-72=8, Resulting Numbers: [8] 8,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[40, 32], Operations: ['38+34=72', '72-40=32'] Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,71 unequal: No Solution Exploring Operation: 40+32=72, Resulting Numbers: [72] 72,71 unequal: No Solution Exploring Operation: 40*32=1280, Resulting Numbers: [1280] 1280,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[40, 32], Operations: ['38+34=72', '72-40=32'] Exploring Operation: 40+32=72, Resulting Numbers: [72] 72,71 unequal: No Solution Exploring Operation: 40*32=1280, Resulting Numbers: [1280] 1280,71 unequal: No Solution Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,71 unequal: No Solution Moving to Node #0,2,4 Current State: 71:[72, 1], Operations: ['38+34=72', '40/40=1'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[40, 38, 40, 34], Operations: [] Exploring Operation: 38+34=72, Resulting Numbers: [40, 40, 72] Generated Node #0,2: 71:[40, 40, 72] Operation: 38+34=72 Moving to Node #0,2 Current State: 71:[40, 40, 72], Operations: ['38+34=72'] Exploring Operation: 40/40=1, Resulting Numbers: [72, 1] Generated Node #0,2,4: 71:[72, 1] Operation: 40/40=1 Moving to Node #0,2,4 Current State: 71:[72, 1], Operations: ['38+34=72', '40/40=1'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_5
sum_heuristic
[ 71, 79, 21, 71 ]
58
[ "71+79=150", "21+71=92", "150-92=58" ]
Current State: 58:[71, 79, 21, 71], Operations: [] Exploring Operation: 71+79=150, Resulting Numbers: [21, 150] Generated Node #2: [21, 150] from Operation: 71+79=150 Current State: 58:[21, 150], Operations: ['71+79=150'] Exploring Operation: 21+71=92, Resulting Numbers: [150, 92] Generated Node #3: [150, 92] from Operation: 21+71=92 Current State: 58:[150, 92], Operations: ['71+79=150', '21+71=92'] Exploring Operation: 150-92=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[71, 79, 21, 71], Operations: [] Exploring Operation: 79-71=8, Resulting Numbers: [21, 71, 8] Generated Node #0,0: 58:[21, 71, 8] Operation: 79-71=8 Exploring Operation: 79-71=8, Resulting Numbers: [71, 21, 8] Generated Node #0,1: 58:[71, 21, 8] Operation: 79-71=8 Exploring Operation: 79-21=58, Resulting Numbers: [71, 71, 58] Generated Node #0,2: 58:[71, 71, 58] Operation: 79-21=58 Exploring Operation: 71/71=1, Resulting Numbers: [79, 21, 1] Generated Node #0,3: 58:[79, 21, 1] Operation: 71/71=1 Moving to Node #0,2 Current State: 58:[71, 71, 58], Operations: ['79-21=58'] Exploring Operation: 71-71=0, Resulting Numbers: [58, 0] Generated Node #0,2,0: 58:[58, 0] Operation: 71-71=0 Exploring Operation: 71/71=1, Resulting Numbers: [58, 1] Generated Node #0,2,1: 58:[58, 1] Operation: 71/71=1 Exploring Operation: 71-58=13, Resulting Numbers: [71, 13] Generated Node #0,2,2: 58:[71, 13] Operation: 71-58=13 Exploring Operation: 71-58=13, Resulting Numbers: [71, 13] Generated Node #0,2,3: 58:[71, 13] Operation: 71-58=13 Moving to Node #0,1 Current State: 58:[71, 21, 8], Operations: ['79-71=8'] Exploring Operation: 71-8=63, Resulting Numbers: [21, 63] Generated Node #0,1,0: 58:[21, 63] Operation: 71-8=63 Exploring Operation: 71-21=50, Resulting Numbers: [8, 50] Generated Node #0,1,1: 58:[8, 50] Operation: 71-21=50 Exploring Operation: 21+8=29, Resulting Numbers: [71, 29] Generated Node #0,1,2: 58:[71, 29] Operation: 21+8=29 Exploring Operation: 21-8=13, Resulting Numbers: [71, 13] Generated Node #0,1,3: 58:[71, 13] Operation: 21-8=13 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 58:[21, 63], Operations: ['79-71=8', '71-8=63'] Exploring Operation: 21*63=1323, Resulting Numbers: [1323] 1323,58 unequal: No Solution Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 21+63=84, Resulting Numbers: [84] 84,58 unequal: No Solution Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,58 unequal: No Solution No 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: 58:[71, 29], Operations: ['79-71=8', '21+8=29'] Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,58 unequal: No Solution Exploring Operation: 71+29=100, Resulting Numbers: [100] 100,58 unequal: No Solution Exploring Operation: 71*29=2059, Resulting Numbers: [2059] 2059,58 unequal: No Solution No 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: 58:[8, 50], Operations: ['79-71=8', '71-21=50'] Exploring Operation: 8+50=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[71, 79, 21, 71], Operations: [] Exploring Operation: 79-71=8, Resulting Numbers: [71, 21, 8] Generated Node #0,1: 58:[71, 21, 8] Operation: 79-71=8 Moving to Node #0,1 Current State: 58:[71, 21, 8], Operations: ['79-71=8'] Exploring Operation: 71-21=50, Resulting Numbers: [8, 50] Generated Node #0,1,1: 58:[8, 50] Operation: 71-21=50 Moving to Node #0,1,1 Current State: 58:[8, 50], Operations: ['79-71=8', '71-21=50'] Exploring Operation: 8+50=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_4
mult_heuristic
[ 88, 27, 31, 4 ]
87
[ "31-27=4", "4/4=1", "88-1=87" ]
Current State: 87:[88, 27, 31, 4], Operations: [] Exploring Operation: 31-27=4, Resulting Numbers: [88, 4, 4] Generated Node #2: [88, 4, 4] from Operation: 31-27=4 Current State: 87:[88, 4, 4], Operations: ['31-27=4'] Exploring Operation: 4/4=1, Resulting Numbers: [88, 1] Generated Node #3: [88, 1] from Operation: 4/4=1 Current State: 87:[88, 1], Operations: ['31-27=4', '4/4=1'] Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[88, 27, 31, 4], Operations: [] Exploring Operation: 31-27=4, Resulting Numbers: [88, 4, 4] Generated Node #0,0: 87:[88, 4, 4] Operation: 31-27=4 Exploring Operation: 27+4=31, Resulting Numbers: [88, 31, 31] Generated Node #0,1: 87:[88, 31, 31] Operation: 27+4=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[88, 4, 4], Operations: ['31-27=4'] Exploring Operation: 88-4=84, Resulting Numbers: [4, 84] Generated Node #0,0,0: 87:[4, 84] Operation: 88-4=84 Exploring Operation: 4/4=1, Resulting Numbers: [88, 1] Generated Node #0,0,1: 87:[88, 1] Operation: 4/4=1 Moving to Node #0,0,1 Current State: 87:[88, 1], Operations: ['31-27=4', '4/4=1'] Exploring Operation: 88*1=88, Resulting Numbers: [88] 88,87 unequal: No Solution Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[88, 27, 31, 4], Operations: [] Exploring Operation: 31-27=4, Resulting Numbers: [88, 4, 4] Generated Node #0,0: 87:[88, 4, 4] Operation: 31-27=4 Moving to Node #0,0 Current State: 87:[88, 4, 4], Operations: ['31-27=4'] Exploring Operation: 4/4=1, Resulting Numbers: [88, 1] Generated Node #0,0,1: 87:[88, 1] Operation: 4/4=1 Moving to Node #0,0,1 Current State: 87:[88, 1], Operations: ['31-27=4', '4/4=1'] Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 96, 88, 81, 21 ]
24
[ "88*21=1848", "96+1848=1944", "1944/81=24" ]
Current State: 24:[96, 88, 81, 21], Operations: [] Exploring Operation: 88*21=1848, Resulting Numbers: [96, 81, 1848] Generated Node #2: [96, 81, 1848] from Operation: 88*21=1848 Current State: 24:[96, 81, 1848], Operations: ['88*21=1848'] Exploring Operation: 96+1848=1944, Resulting Numbers: [81, 1944] Generated Node #3: [81, 1944] from Operation: 96+1848=1944 Current State: 24:[81, 1944], Operations: ['88*21=1848', '96+1848=1944'] Exploring Operation: 1944/81=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[96, 88, 81, 21], Operations: [] Exploring Operation: 96-88=8, Resulting Numbers: [81, 21, 8] Generated Node #0,0: 24:[81, 21, 8] Operation: 96-88=8 Exploring Operation: 88-81=7, Resulting Numbers: [96, 21, 7] Generated Node #0,1: 24:[96, 21, 7] Operation: 88-81=7 Exploring Operation: 96-81=15, Resulting Numbers: [88, 21, 15] Generated Node #0,2: 24:[88, 21, 15] Operation: 96-81=15 Moving to Node #0,0 Current State: 24:[81, 21, 8], Operations: ['96-88=8'] Exploring Operation: 21-8=13, Resulting Numbers: [81, 13] Generated Node #0,0,0: 24:[81, 13] Operation: 21-8=13 Exploring Operation: 81-8=73, Resulting Numbers: [21, 73] Generated Node #0,0,1: 24:[21, 73] Operation: 81-8=73 Exploring Operation: 81-21=60, Resulting Numbers: [8, 60] Generated Node #0,0,2: 24:[8, 60] Operation: 81-21=60 Moving to Node #0,2 Current State: 24:[88, 21, 15], Operations: ['96-81=15'] Exploring Operation: 88-21=67, Resulting Numbers: [15, 67] Generated Node #0,2,0: 24:[15, 67] Operation: 88-21=67 Exploring Operation: 88-15=73, Resulting Numbers: [21, 73] Generated Node #0,2,1: 24:[21, 73] Operation: 88-15=73 Exploring Operation: 21-15=6, Resulting Numbers: [88, 6] Generated Node #0,2,2: 24:[88, 6] Operation: 21-15=6 Moving to Node #0,1 Current State: 24:[96, 21, 7], Operations: ['88-81=7'] Exploring Operation: 21/7=3, Resulting Numbers: [96, 3] Generated Node #0,1,0: 24:[96, 3] Operation: 21/7=3 Exploring Operation: 96-21=75, Resulting Numbers: [7, 75] Generated Node #0,1,1: 24:[7, 75] Operation: 96-21=75 Exploring Operation: 96-7=89, Resulting Numbers: [21, 89] Generated Node #0,1,2: 24:[21, 89] Operation: 96-7=89 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 24:[7, 75], Operations: ['88-81=7', '96-21=75'] Exploring Operation: 7*75=525, Resulting Numbers: [525] 525,24 unequal: No Solution Exploring Operation: 7+75=82, Resulting Numbers: [82] 82,24 unequal: No Solution Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,24 unequal: No Solution No 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: 24:[21, 89], Operations: ['88-81=7', '96-7=89'] Exploring Operation: 89-21=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 21*89=1869, Resulting Numbers: [1869] 1869,24 unequal: No Solution Exploring Operation: 21+89=110, Resulting Numbers: [110] 110,24 unequal: No Solution No 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: 24:[96, 3], Operations: ['88-81=7', '21/7=3'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,24 unequal: No Solution Exploring Operation: 96/3=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 96+3=99, Resulting Numbers: [99] 99,24 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: 24:[8, 60], Operations: ['96-88=8', '81-21=60'] Exploring Operation: 8+60=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 60-8=52, Resulting Numbers: [52] 52,24 unequal: No Solution Exploring Operation: 8*60=480, Resulting Numbers: [480] 480,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[15, 67], Operations: ['96-81=15', '88-21=67'] Exploring Operation: 67-15=52, Resulting Numbers: [52] 52,24 unequal: No Solution Exploring Operation: 15*67=1005, Resulting Numbers: [1005] 1005,24 unequal: No Solution Exploring Operation: 15+67=82, Resulting Numbers: [82] 82,24 unequal: No Solution Moving to Node #0,2,1 Current State: 24:[21, 73], Operations: ['96-81=15', '88-15=73'] Exploring Operation: 21+73=94, Resulting Numbers: [94] 94,24 unequal: No Solution Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,24 unequal: No Solution Exploring Operation: 21*73=1533, Resulting Numbers: [1533] 1533,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[21, 73], Operations: ['96-88=8', '81-8=73'] Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,24 unequal: No Solution Exploring Operation: 21*73=1533, Resulting Numbers: [1533] 1533,24 unequal: No Solution Exploring Operation: 21+73=94, Resulting Numbers: [94] 94,24 unequal: No Solution Moving to Node #0,0,0 Current State: 24:[81, 13], Operations: ['96-88=8', '21-8=13'] Exploring Operation: 81-13=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 81*13=1053, Resulting Numbers: [1053] 1053,24 unequal: No Solution Exploring Operation: 81+13=94, Resulting Numbers: [94] 94,24 unequal: No Solution Moving to Node #0,2,2 Current State: 24:[88, 6], Operations: ['96-81=15', '21-15=6'] Exploring Operation: 88*6=528, Resulting Numbers: [528] 528,24 unequal: No Solution Exploring Operation: 88+6=94, Resulting Numbers: [94] 94,24 unequal: No Solution Exploring Operation: 88-6=82, Resulting Numbers: [82] 82,24 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 19, 8, 43, 17 ]
71
[ "19-8=11", "43+17=60", "11+60=71" ]
Current State: 71:[19, 8, 43, 17], Operations: [] Exploring Operation: 19-8=11, Resulting Numbers: [43, 17, 11] Generated Node #2: [43, 17, 11] from Operation: 19-8=11 Current State: 71:[43, 17, 11], Operations: ['19-8=11'] Exploring Operation: 43+17=60, Resulting Numbers: [11, 60] Generated Node #3: [11, 60] from Operation: 43+17=60 Current State: 71:[11, 60], Operations: ['19-8=11', '43+17=60'] Exploring Operation: 11+60=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[19, 8, 43, 17], Operations: [] Exploring Operation: 19+43=62, Resulting Numbers: [8, 17, 62] Generated Node #0,0: 71:[8, 17, 62] Operation: 19+43=62 Exploring Operation: 19+8=27, Resulting Numbers: [43, 17, 27] Generated Node #0,1: 71:[43, 17, 27] Operation: 19+8=27 Exploring Operation: 19+17=36, Resulting Numbers: [8, 43, 36] Generated Node #0,2: 71:[8, 43, 36] Operation: 19+17=36 Moving to Node #0,0 Current State: 71:[8, 17, 62], Operations: ['19+43=62'] Exploring Operation: 17-8=9, Resulting Numbers: [62, 9] Generated Node #0,0,0: 71:[62, 9] Operation: 17-8=9 Exploring Operation: 8+62=70, Resulting Numbers: [17, 70] Generated Node #0,0,1: 71:[17, 70] Operation: 8+62=70 Exploring Operation: 8+17=25, Resulting Numbers: [62, 25] Generated Node #0,0,2: 71:[62, 25] Operation: 8+17=25 Moving to Node #0,1 Current State: 71:[43, 17, 27], Operations: ['19+8=27'] Exploring Operation: 43+27=70, Resulting Numbers: [17, 70] Generated Node #0,1,0: 71:[17, 70] Operation: 43+27=70 Exploring Operation: 17+27=44, Resulting Numbers: [43, 44] Generated Node #0,1,1: 71:[43, 44] Operation: 17+27=44 Exploring Operation: 43+17=60, Resulting Numbers: [27, 60] Generated Node #0,1,2: 71:[27, 60] Operation: 43+17=60 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 71:[17, 70], Operations: ['19+8=27', '43+27=70'] Exploring Operation: 70-17=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 17+70=87, Resulting Numbers: [87] 87,71 unequal: No Solution Exploring Operation: 17*70=1190, Resulting Numbers: [1190] 1190,71 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 #0,1,1 Current State: 71:[43, 44], Operations: ['19+8=27', '17+27=44'] Exploring Operation: 44-43=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 43*44=1892, Resulting Numbers: [1892] 1892,71 unequal: No Solution Exploring Operation: 43+44=87, Resulting Numbers: [87] 87,71 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 #0,1,2 Current State: 71:[27, 60], Operations: ['19+8=27', '43+17=60'] Exploring Operation: 27+60=87, Resulting Numbers: [87] 87,71 unequal: No Solution Exploring Operation: 27*60=1620, Resulting Numbers: [1620] 1620,71 unequal: No Solution Exploring Operation: 60-27=33, Resulting Numbers: [33] 33,71 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: 71:[8, 43, 36], Operations: ['19+17=36'] Exploring Operation: 43-8=35, Resulting Numbers: [36, 35] Generated Node #0,2,0: 71:[36, 35] Operation: 43-8=35 Exploring Operation: 8+36=44, Resulting Numbers: [43, 44] Generated Node #0,2,1: 71:[43, 44] Operation: 8+36=44 Exploring Operation: 8+43=51, Resulting Numbers: [36, 51] Generated Node #0,2,2: 71:[36, 51] Operation: 8+43=51 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 71:[43, 44], Operations: ['19+17=36', '8+36=44'] Exploring Operation: 44-43=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 43+44=87, Resulting Numbers: [87] 87,71 unequal: No Solution Exploring Operation: 43*44=1892, Resulting Numbers: [1892] 1892,71 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 #0,2,2 Current State: 71:[36, 51], Operations: ['19+17=36', '8+43=51'] Exploring Operation: 51-36=15, Resulting Numbers: [15] 15,71 unequal: No Solution Exploring Operation: 36+51=87, Resulting Numbers: [87] 87,71 unequal: No Solution Exploring Operation: 36*51=1836, Resulting Numbers: [1836] 1836,71 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 #0,2,0 Current State: 71:[36, 35], Operations: ['19+17=36', '43-8=35'] Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 36+35=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[19, 8, 43, 17], Operations: [] Exploring Operation: 19+17=36, Resulting Numbers: [8, 43, 36] Generated Node #0,2: 71:[8, 43, 36] Operation: 19+17=36 Moving to Node #0,2 Current State: 71:[8, 43, 36], Operations: ['19+17=36'] Exploring Operation: 43-8=35, Resulting Numbers: [36, 35] Generated Node #0,2,0: 71:[36, 35] Operation: 43-8=35 Moving to Node #0,2,0 Current State: 71:[36, 35], Operations: ['19+17=36', '43-8=35'] Exploring Operation: 36+35=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_3
mult_heuristic
[ 63, 21, 77, 46 ]
28
[ "63/21=3", "77-46=31", "31-3=28" ]
Current State: 28:[63, 21, 77, 46], Operations: [] Exploring Operation: 63/21=3, Resulting Numbers: [77, 46, 3] Generated Node #2: [77, 46, 3] from Operation: 63/21=3 Current State: 28:[77, 46, 3], Operations: ['63/21=3'] Exploring Operation: 77-46=31, Resulting Numbers: [3, 31] Generated Node #3: [3, 31] from Operation: 77-46=31 Current State: 28:[3, 31], Operations: ['63/21=3', '77-46=31'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[63, 21, 77, 46], Operations: [] Exploring Operation: 77-63=14, Resulting Numbers: [21, 46, 14] Generated Node #0,0: 28:[21, 46, 14] Operation: 77-63=14 Exploring Operation: 77-46=31, Resulting Numbers: [63, 21, 31] Generated Node #0,1: 28:[63, 21, 31] Operation: 77-46=31 Exploring Operation: 63-46=17, Resulting Numbers: [21, 77, 17] Generated Node #0,2: 28:[21, 77, 17] Operation: 63-46=17 Moving to Node #0,0 Current State: 28:[21, 46, 14], Operations: ['77-63=14'] Exploring Operation: 21-14=7, Resulting Numbers: [46, 7] Generated Node #0,0,0: 28:[46, 7] Operation: 21-14=7 Exploring Operation: 46-21=25, Resulting Numbers: [14, 25] Generated Node #0,0,1: 28:[14, 25] Operation: 46-21=25 Exploring Operation: 46-14=32, Resulting Numbers: [21, 32] Generated Node #0,0,2: 28:[21, 32] Operation: 46-14=32 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 28:[14, 25], Operations: ['77-63=14', '46-21=25'] Exploring Operation: 14*25=350, Resulting Numbers: [350] 350,28 unequal: No Solution Exploring Operation: 14+25=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,28 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 #0,0,2 Current State: 28:[21, 32], Operations: ['77-63=14', '46-14=32'] Exploring Operation: 21+32=53, Resulting Numbers: [53] 53,28 unequal: No Solution Exploring Operation: 21*32=672, Resulting Numbers: [672] 672,28 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,28 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 #0,0,0 Current State: 28:[46, 7], Operations: ['77-63=14', '21-14=7'] Exploring Operation: 46*7=322, Resulting Numbers: [322] 322,28 unequal: No Solution Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 46+7=53, Resulting Numbers: [53] 53,28 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: 28:[63, 21, 31], Operations: ['77-46=31'] Exploring Operation: 63/21=3, Resulting Numbers: [31, 3] Generated Node #0,1,0: 28:[31, 3] Operation: 63/21=3 Exploring Operation: 63-31=32, Resulting Numbers: [21, 32] Generated Node #0,1,1: 28:[21, 32] Operation: 63-31=32 Exploring Operation: 63-21=42, Resulting Numbers: [31, 42] Generated Node #0,1,2: 28:[31, 42] Operation: 63-21=42 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 28:[31, 3], Operations: ['77-46=31', '63/21=3'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[63, 21, 77, 46], Operations: [] Exploring Operation: 77-46=31, Resulting Numbers: [63, 21, 31] Generated Node #0,1: 28:[63, 21, 31] Operation: 77-46=31 Moving to Node #0,1 Current State: 28:[63, 21, 31], Operations: ['77-46=31'] Exploring Operation: 63/21=3, Resulting Numbers: [31, 3] Generated Node #0,1,0: 28:[31, 3] Operation: 63/21=3 Moving to Node #0,1,0 Current State: 28:[31, 3], Operations: ['77-46=31', '63/21=3'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 27, 9, 35, 46 ]
54
[ "9+35=44", "46-44=2", "27*2=54" ]
Current State: 54:[27, 9, 35, 46], Operations: [] Exploring Operation: 9+35=44, Resulting Numbers: [27, 46, 44] Generated Node #2: [27, 46, 44] from Operation: 9+35=44 Current State: 54:[27, 46, 44], Operations: ['9+35=44'] Exploring Operation: 46-44=2, Resulting Numbers: [27, 2] Generated Node #3: [27, 2] from Operation: 46-44=2 Current State: 54:[27, 2], Operations: ['9+35=44', '46-44=2'] Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[27, 9, 35, 46], Operations: [] Exploring Operation: 46-27=19, Resulting Numbers: [9, 35, 19] Generated Node #0,0: 54:[9, 35, 19] Operation: 46-27=19 Exploring Operation: 35-27=8, Resulting Numbers: [9, 46, 8] Generated Node #0,1: 54:[9, 46, 8] Operation: 35-27=8 Exploring Operation: 46-35=11, Resulting Numbers: [27, 9, 11] Generated Node #0,2: 54:[27, 9, 11] Operation: 46-35=11 Exploring Operation: 35-9=26, Resulting Numbers: [27, 46, 26] Generated Node #0,3: 54:[27, 46, 26] Operation: 35-9=26 Moving to Node #0,2 Current State: 54:[27, 9, 11], Operations: ['46-35=11'] Exploring Operation: 27-9=18, Resulting Numbers: [11, 18] Generated Node #0,2,0: 54:[11, 18] Operation: 27-9=18 Exploring Operation: 27/9=3, Resulting Numbers: [11, 3] Generated Node #0,2,1: 54:[11, 3] Operation: 27/9=3 Exploring Operation: 27-11=16, Resulting Numbers: [9, 16] Generated Node #0,2,2: 54:[9, 16] Operation: 27-11=16 Exploring Operation: 11-9=2, Resulting Numbers: [27, 2] Generated Node #0,2,3: 54:[27, 2] Operation: 11-9=2 Moving to Node #0,1 Current State: 54:[9, 46, 8], Operations: ['35-27=8'] Exploring Operation: 9-8=1, Resulting Numbers: [46, 1] Generated Node #0,1,0: 54:[46, 1] Operation: 9-8=1 Exploring Operation: 9+8=17, Resulting Numbers: [46, 17] Generated Node #0,1,1: 54:[46, 17] Operation: 9+8=17 Exploring Operation: 9+46=55, Resulting Numbers: [8, 55] Generated Node #0,1,2: 54:[8, 55] Operation: 9+46=55 Exploring Operation: 46+8=54, Resulting Numbers: [9, 54] Generated Node #0,1,3: 54:[9, 54] Operation: 46+8=54 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 54:[9, 54], Operations: ['35-27=8', '46+8=54'] Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,54 unequal: No Solution Exploring Operation: 9+54=63, Resulting Numbers: [63] 63,54 unequal: No Solution Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 9*54=486, Resulting Numbers: [486] 486,54 unequal: No Solution No 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: 54:[8, 55], Operations: ['35-27=8', '9+46=55'] Exploring Operation: 8*55=440, Resulting Numbers: [440] 440,54 unequal: No Solution Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,54 unequal: No Solution Exploring Operation: 8+55=63, Resulting Numbers: [63] 63,54 unequal: No Solution No 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: 54:[46, 1], Operations: ['35-27=8', '9-8=1'] Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,54 unequal: No Solution Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 46+1=47, Resulting Numbers: [47] 47,54 unequal: No Solution No 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: 54:[46, 17], Operations: ['35-27=8', '9+8=17'] Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,54 unequal: No Solution Exploring Operation: 46*17=782, Resulting Numbers: [782] 782,54 unequal: No Solution Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,54 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: 54:[9, 35, 19], Operations: ['46-27=19'] Exploring Operation: 9+19=28, Resulting Numbers: [35, 28] Generated Node #0,0,0: 54:[35, 28] Operation: 9+19=28 Exploring Operation: 35-9=26, Resulting Numbers: [19, 26] Generated Node #0,0,1: 54:[19, 26] Operation: 35-9=26 Exploring Operation: 35+19=54, Resulting Numbers: [9, 54] Generated Node #0,0,2: 54:[9, 54] Operation: 35+19=54 Exploring Operation: 35-19=16, Resulting Numbers: [9, 16] Generated Node #0,0,3: 54:[9, 16] Operation: 35-19=16 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 54:[9, 54], Operations: ['46-27=19', '35+19=54'] Exploring Operation: 9*54=486, Resulting Numbers: [486] 486,54 unequal: No Solution Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 9+54=63, Resulting Numbers: [63] 63,54 unequal: No Solution Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,54 unequal: No Solution No 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: 54:[19, 26], Operations: ['46-27=19', '35-9=26'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,54 unequal: No Solution Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,54 unequal: No Solution No 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: 54:[9, 16], Operations: ['46-27=19', '35-19=16'] Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,54 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,54 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,54 unequal: No Solution No 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: 54:[35, 28], Operations: ['46-27=19', '9+19=28'] Exploring Operation: 35*28=980, Resulting Numbers: [980] 980,54 unequal: No Solution Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 35+28=63, Resulting Numbers: [63] 63,54 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: 54:[27, 46, 26], Operations: ['35-9=26'] Exploring Operation: 27-26=1, Resulting Numbers: [46, 1] Generated Node #0,3,0: 54:[46, 1] Operation: 27-26=1 Exploring Operation: 46-26=20, Resulting Numbers: [27, 20] Generated Node #0,3,1: 54:[27, 20] Operation: 46-26=20 Exploring Operation: 27+26=53, Resulting Numbers: [46, 53] Generated Node #0,3,2: 54:[46, 53] Operation: 27+26=53 Exploring Operation: 46-27=19, Resulting Numbers: [26, 19] Generated Node #0,3,3: 54:[26, 19] Operation: 46-27=19 Moving to Node #0,2,3 Current State: 54:[27, 2], Operations: ['46-35=11', '11-9=2'] Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[27, 9, 35, 46], Operations: [] Exploring Operation: 46-35=11, Resulting Numbers: [27, 9, 11] Generated Node #0,2: 54:[27, 9, 11] Operation: 46-35=11 Moving to Node #0,2 Current State: 54:[27, 9, 11], Operations: ['46-35=11'] Exploring Operation: 11-9=2, Resulting Numbers: [27, 2] Generated Node #0,2,3: 54:[27, 2] Operation: 11-9=2 Moving to Node #0,2,3 Current State: 54:[27, 2], Operations: ['46-35=11', '11-9=2'] Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
0.954861
hs_4
mult_heuristic
[ 15, 51, 68, 63 ]
69
[ "68*63=4284", "4284/51=84", "84-15=69" ]
Current State: 69:[15, 51, 68, 63], Operations: [] Exploring Operation: 68*63=4284, Resulting Numbers: [15, 51, 4284] Generated Node #2: [15, 51, 4284] from Operation: 68*63=4284 Current State: 69:[15, 51, 4284], Operations: ['68*63=4284'] Exploring Operation: 4284/51=84, Resulting Numbers: [15, 84] Generated Node #3: [15, 84] from Operation: 4284/51=84 Current State: 69:[15, 84], Operations: ['68*63=4284', '4284/51=84'] Exploring Operation: 84-15=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[15, 51, 68, 63], Operations: [] Exploring Operation: 63-51=12, Resulting Numbers: [15, 68, 12] Generated Node #0,0: 69:[15, 68, 12] Operation: 63-51=12 Exploring Operation: 15+51=66, Resulting Numbers: [68, 63, 66] Generated Node #0,1: 69:[68, 63, 66] Operation: 15+51=66 Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[68, 63, 66], Operations: ['15+51=66'] Exploring Operation: 66-63=3, Resulting Numbers: [68, 3] Generated Node #0,1,0: 69:[68, 3] Operation: 66-63=3 Exploring Operation: 68-63=5, Resulting Numbers: [66, 5] Generated Node #0,1,1: 69:[66, 5] Operation: 68-63=5 Moving to Node #0,1,0 Current State: 69:[68, 3], Operations: ['15+51=66', '66-63=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,69 unequal: No Solution Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[66, 5], Operations: ['15+51=66', '68-63=5'] Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,69 unequal: No Solution Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[15, 68, 12], Operations: ['63-51=12'] Exploring Operation: 15+12=27, Resulting Numbers: [68, 27] Generated Node #0,0,0: 69:[68, 27] Operation: 15+12=27 Exploring Operation: 15-12=3, Resulting Numbers: [68, 3] Generated Node #0,0,1: 69:[68, 3] Operation: 15-12=3 Moving to Node #0,0,1 Current State: 69:[68, 3], Operations: ['63-51=12', '15-12=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,69 unequal: No Solution Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[68, 27], Operations: ['63-51=12', '15+12=27'] Exploring Operation: 68+27=95, Resulting Numbers: [95] 95,69 unequal: No Solution Exploring Operation: 68-27=41, Resulting Numbers: [41] 41,69 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