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
[ 51, 49, 38, 95 ]
19
[ "51-49=2", "38*2=76", "95-76=19" ]
Current State: 19:[51, 49, 38, 95], Operations: [] Exploring Operation: 51-49=2, Resulting Numbers: [38, 95, 2] Generated Node #2: [38, 95, 2] from Operation: 51-49=2 Current State: 19:[38, 95, 2], Operations: ['51-49=2'] Exploring Operation: 38*2=76, Resulting Numbers: [95, 76] Generated Node #3: [95, 76] from Operation: 38*2=76 Current State: 19:[95, 76], Operations: ['51-49=2', '38*2=76'] Exploring Operation: 95-76=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[51, 49, 38, 95], Operations: [] Exploring Operation: 95-38=57, Resulting Numbers: [51, 49, 57] Generated Node #0,0: 19:[51, 49, 57] Operation: 95-38=57 Exploring Operation: 95-49=46, Resulting Numbers: [51, 38, 46] Generated Node #0,1: 19:[51, 38, 46] Operation: 95-49=46 Exploring Operation: 95-51=44, Resulting Numbers: [49, 38, 44] Generated Node #0,2: 19:[49, 38, 44] Operation: 95-51=44 Exploring Operation: 51-49=2, Resulting Numbers: [38, 95, 2] Generated Node #0,3: 19:[38, 95, 2] Operation: 51-49=2 Moving to Node #0,2 Current State: 19:[49, 38, 44], Operations: ['95-51=44'] Exploring Operation: 44-38=6, Resulting Numbers: [49, 6] Generated Node #0,2,0: 19:[49, 6] Operation: 44-38=6 Exploring Operation: 49-38=11, Resulting Numbers: [44, 11] Generated Node #0,2,1: 19:[44, 11] Operation: 49-38=11 Exploring Operation: 49+38=87, Resulting Numbers: [44, 87] Generated Node #0,2,2: 19:[44, 87] Operation: 49+38=87 Exploring Operation: 49-44=5, Resulting Numbers: [38, 5] Generated Node #0,2,3: 19:[38, 5] Operation: 49-44=5 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 19:[44, 11], Operations: ['95-51=44', '49-38=11'] Exploring Operation: 44+11=55, Resulting Numbers: [55] 55,19 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,19 unequal: No Solution Exploring Operation: 44*11=484, Resulting Numbers: [484] 484,19 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 #0,2,3 Current State: 19:[38, 5], Operations: ['95-51=44', '49-44=5'] Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,19 unequal: No Solution Exploring Operation: 38*5=190, Resulting Numbers: [190] 190,19 unequal: No Solution Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,19 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 #0,2,0 Current State: 19:[49, 6], Operations: ['95-51=44', '44-38=6'] Exploring Operation: 49*6=294, Resulting Numbers: [294] 294,19 unequal: No Solution Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,19 unequal: No Solution Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,19 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 #0,2,2 Current State: 19:[44, 87], Operations: ['95-51=44', '49+38=87'] Exploring Operation: 44*87=3828, Resulting Numbers: [3828] 3828,19 unequal: No Solution Exploring Operation: 44+87=131, Resulting Numbers: [131] 131,19 unequal: No Solution Exploring Operation: 87-44=43, Resulting Numbers: [43] 43,19 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: 19:[51, 38, 46], Operations: ['95-49=46'] Exploring Operation: 51+38=89, Resulting Numbers: [46, 89] Generated Node #0,1,0: 19:[46, 89] Operation: 51+38=89 Exploring Operation: 46-38=8, Resulting Numbers: [51, 8] Generated Node #0,1,1: 19:[51, 8] Operation: 46-38=8 Exploring Operation: 51-38=13, Resulting Numbers: [46, 13] Generated Node #0,1,2: 19:[46, 13] Operation: 51-38=13 Exploring Operation: 51-46=5, Resulting Numbers: [38, 5] Generated Node #0,1,3: 19:[38, 5] Operation: 51-46=5 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 19:[46, 13], Operations: ['95-49=46', '51-38=13'] Exploring Operation: 46-13=33, Resulting Numbers: [33] 33,19 unequal: No Solution Exploring Operation: 46+13=59, Resulting Numbers: [59] 59,19 unequal: No Solution Exploring Operation: 46*13=598, Resulting Numbers: [598] 598,19 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 #0,1,3 Current State: 19:[38, 5], Operations: ['95-49=46', '51-46=5'] Exploring Operation: 38*5=190, Resulting Numbers: [190] 190,19 unequal: No Solution Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,19 unequal: No Solution Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,19 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 #0,1,1 Current State: 19:[51, 8], Operations: ['95-49=46', '46-38=8'] Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,19 unequal: No Solution Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,19 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,19 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 #0,1,0 Current State: 19:[46, 89], Operations: ['95-49=46', '51+38=89'] Exploring Operation: 89-46=43, Resulting Numbers: [43] 43,19 unequal: No Solution Exploring Operation: 46+89=135, Resulting Numbers: [135] 135,19 unequal: No Solution Exploring Operation: 46*89=4094, Resulting Numbers: [4094] 4094,19 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: 19:[51, 49, 57], Operations: ['95-38=57'] Exploring Operation: 57-49=8, Resulting Numbers: [51, 8] Generated Node #0,0,0: 19:[51, 8] Operation: 57-49=8 Exploring Operation: 51+49=100, Resulting Numbers: [57, 100] Generated Node #0,0,1: 19:[57, 100] Operation: 51+49=100 Exploring Operation: 51-49=2, Resulting Numbers: [57, 2] Generated Node #0,0,2: 19:[57, 2] Operation: 51-49=2 Exploring Operation: 57-51=6, Resulting Numbers: [49, 6] Generated Node #0,0,3: 19:[49, 6] Operation: 57-51=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[51, 8], Operations: ['95-38=57', '57-49=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,19 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,19 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,19 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 #0,0,3 Current State: 19:[49, 6], Operations: ['95-38=57', '57-51=6'] Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,19 unequal: No Solution Exploring Operation: 49*6=294, Resulting Numbers: [294] 294,19 unequal: No Solution Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,19 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 #0,0,2 Current State: 19:[57, 2], Operations: ['95-38=57', '51-49=2'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,19 unequal: No Solution Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,19 unequal: No Solution Exploring Operation: 57*2=114, Resulting Numbers: [114] 114,19 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:[57, 100], Operations: ['95-38=57', '51+49=100'] Exploring Operation: 100-57=43, Resulting Numbers: [43] 43,19 unequal: No Solution Exploring Operation: 57+100=157, Resulting Numbers: [157] 157,19 unequal: No Solution Exploring Operation: 57*100=5700, Resulting Numbers: [5700] 5700,19 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: 19:[38, 95, 2], Operations: ['51-49=2'] Exploring Operation: 38-2=36, Resulting Numbers: [95, 36] Generated Node #0,3,0: 19:[95, 36] Operation: 38-2=36 Exploring Operation: 95-2=93, Resulting Numbers: [38, 93] Generated Node #0,3,1: 19:[38, 93] Operation: 95-2=93 Exploring Operation: 95-38=57, Resulting Numbers: [2, 57] Generated Node #0,3,2: 19:[2, 57] Operation: 95-38=57 Exploring Operation: 38/2=19, Resulting Numbers: [95, 19] Generated Node #0,3,3: 19:[95, 19] Operation: 38/2=19 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 19:[2, 57], Operations: ['51-49=2', '95-38=57'] Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,19 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,19 unequal: No Solution Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,19 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 #0,3,3 Current State: 19:[95, 19], Operations: ['51-49=2', '38/2=19'] Exploring Operation: 95*19=1805, Resulting Numbers: [1805] 1805,19 unequal: No Solution Exploring Operation: 95-19=76, Resulting Numbers: [76] 76,19 unequal: No Solution Exploring Operation: 95+19=114, Resulting Numbers: [114] 114,19 unequal: No Solution Exploring Operation: 95/19=5, Resulting Numbers: [5] 5,19 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 #0,3,0 Current State: 19:[95, 36], Operations: ['51-49=2', '38-2=36'] Exploring Operation: 95-36=59, Resulting Numbers: [59] 59,19 unequal: No Solution Exploring Operation: 95+36=131, Resulting Numbers: [131] 131,19 unequal: No Solution Exploring Operation: 95*36=3420, Resulting Numbers: [3420] 3420,19 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 #0,3,1 Current State: 19:[38, 93], Operations: ['51-49=2', '95-2=93'] Exploring Operation: 38*93=3534, Resulting Numbers: [3534] 3534,19 unequal: No Solution Exploring Operation: 38+93=131, Resulting Numbers: [131] 131,19 unequal: No Solution Exploring Operation: 93-38=55, Resulting Numbers: [55] 55,19 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
[ 66, 81, 6, 2 ]
38
[ "81*2=162", "66+162=228", "228/6=38" ]
Current State: 38:[66, 81, 6, 2], Operations: [] Exploring Operation: 81*2=162, Resulting Numbers: [66, 6, 162] Generated Node #2: [66, 6, 162] from Operation: 81*2=162 Current State: 38:[66, 6, 162], Operations: ['81*2=162'] Exploring Operation: 66+162=228, Resulting Numbers: [6, 228] Generated Node #3: [6, 228] from Operation: 66+162=228 Current State: 38:[6, 228], Operations: ['81*2=162', '66+162=228'] Exploring Operation: 228/6=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[66, 81, 6, 2], Operations: [] Exploring Operation: 81-66=15, Resulting Numbers: [6, 2, 15] Generated Node #0,0: 38:[6, 2, 15] Operation: 81-66=15 Exploring Operation: 66/2=33, Resulting Numbers: [81, 6, 33] Generated Node #0,1: 38:[81, 6, 33] Operation: 66/2=33 Exploring Operation: 81-6=75, Resulting Numbers: [66, 2, 75] Generated Node #0,2: 38:[66, 2, 75] Operation: 81-6=75 Exploring Operation: 66-6=60, Resulting Numbers: [81, 2, 60] Generated Node #0,3: 38:[81, 2, 60] Operation: 66-6=60 Exploring Operation: 66/6=11, Resulting Numbers: [81, 2, 11] Generated Node #0,4: 38:[81, 2, 11] Operation: 66/6=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[6, 2, 15], Operations: ['81-66=15'] Exploring Operation: 6-2=4, Resulting Numbers: [15, 4] Generated Node #0,0,0: 38:[15, 4] Operation: 6-2=4 Exploring Operation: 15-6=9, Resulting Numbers: [2, 9] Generated Node #0,0,1: 38:[2, 9] Operation: 15-6=9 Exploring Operation: 6+15=21, Resulting Numbers: [2, 21] Generated Node #0,0,2: 38:[2, 21] Operation: 6+15=21 Exploring Operation: 6/2=3, Resulting Numbers: [15, 3] Generated Node #0,0,3: 38:[15, 3] Operation: 6/2=3 Exploring Operation: 2+15=17, Resulting Numbers: [6, 17] Generated Node #0,0,4: 38:[6, 17] Operation: 2+15=17 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 38:[2, 21], Operations: ['81-66=15', '6+15=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,38 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,38 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,38 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:[15, 3], Operations: ['81-66=15', '6/2=3'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,38 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,38 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:[15, 4], Operations: ['81-66=15', '6-2=4'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 38:[6, 17], Operations: ['81-66=15', '2+15=17'] Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 6+17=23, Resulting Numbers: [23] 23,38 unequal: No Solution Exploring Operation: 6*17=102, Resulting Numbers: [102] 102,38 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:[2, 9], Operations: ['81-66=15', '15-6=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,38 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 #0,4 Current State: 38:[81, 2, 11], Operations: ['66/6=11'] Exploring Operation: 81-2=79, Resulting Numbers: [11, 79] Generated Node #0,4,0: 38:[11, 79] Operation: 81-2=79 Exploring Operation: 2*11=22, Resulting Numbers: [81, 22] Generated Node #0,4,1: 38:[81, 22] Operation: 2*11=22 Exploring Operation: 2+11=13, Resulting Numbers: [81, 13] Generated Node #0,4,2: 38:[81, 13] Operation: 2+11=13 Exploring Operation: 81-11=70, Resulting Numbers: [2, 70] Generated Node #0,4,3: 38:[2, 70] Operation: 81-11=70 Exploring Operation: 11-2=9, Resulting Numbers: [81, 9] Generated Node #0,4,4: 38:[81, 9] Operation: 11-2=9 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 38:[2, 70], Operations: ['66/6=11', '81-11=70'] Exploring Operation: 2*70=140, Resulting Numbers: [140] 140,38 unequal: No Solution Exploring Operation: 2+70=72, Resulting Numbers: [72] 72,38 unequal: No Solution Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,38 unequal: No Solution Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,38 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 #0,4,1 Current State: 38:[81, 22], Operations: ['66/6=11', '2*11=22'] Exploring Operation: 81+22=103, Resulting Numbers: [103] 103,38 unequal: No Solution Exploring Operation: 81*22=1782, Resulting Numbers: [1782] 1782,38 unequal: No Solution Exploring Operation: 81-22=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 #0,4,0 Current State: 38:[11, 79], Operations: ['66/6=11', '81-2=79'] Exploring Operation: 11+79=90, Resulting Numbers: [90] 90,38 unequal: No Solution Exploring Operation: 11*79=869, Resulting Numbers: [869] 869,38 unequal: No Solution Exploring Operation: 79-11=68, Resulting Numbers: [68] 68,38 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 #0,4,2 Current State: 38:[81, 13], Operations: ['66/6=11', '2+11=13'] Exploring Operation: 81*13=1053, Resulting Numbers: [1053] 1053,38 unequal: No Solution Exploring Operation: 81+13=94, Resulting Numbers: [94] 94,38 unequal: No Solution Exploring Operation: 81-13=68, Resulting Numbers: [68] 68,38 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 #0,4,4 Current State: 38:[81, 9], Operations: ['66/6=11', '11-2=9'] Exploring Operation: 81/9=9, Resulting Numbers: [9] 9,38 unequal: No Solution Exploring Operation: 81+9=90, Resulting Numbers: [90] 90,38 unequal: No Solution Exploring Operation: 81-9=72, Resulting Numbers: [72] 72,38 unequal: No Solution Exploring Operation: 81*9=729, Resulting Numbers: [729] 729,38 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:[81, 6, 33], Operations: ['66/2=33'] Exploring Operation: 81-6=75, Resulting Numbers: [33, 75] Generated Node #0,1,0: 38:[33, 75] Operation: 81-6=75 Exploring Operation: 33-6=27, Resulting Numbers: [81, 27] Generated Node #0,1,1: 38:[81, 27] Operation: 33-6=27 Exploring Operation: 81-33=48, Resulting Numbers: [6, 48] Generated Node #0,1,2: 38:[6, 48] Operation: 81-33=48 Exploring Operation: 81+6=87, Resulting Numbers: [33, 87] Generated Node #0,1,3: 38:[33, 87] Operation: 81+6=87 Exploring Operation: 6+33=39, Resulting Numbers: [81, 39] Generated Node #0,1,4: 38:[81, 39] Operation: 6+33=39 Moving to Node #0,1,2 Current State: 38:[6, 48], Operations: ['66/2=33', '81-33=48'] Exploring Operation: 6*48=288, Resulting Numbers: [288] 288,38 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,38 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[33, 75], Operations: ['66/2=33', '81-6=75'] Exploring Operation: 33+75=108, Resulting Numbers: [108] 108,38 unequal: No Solution Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,38 unequal: No Solution Exploring Operation: 33*75=2475, Resulting Numbers: [2475] 2475,38 unequal: No Solution Moving to Node #0,1,4 Current State: 38:[81, 39], Operations: ['66/2=33', '6+33=39'] Exploring Operation: 81-39=42, Resulting Numbers: [42] 42,38 unequal: No Solution Exploring Operation: 81+39=120, Resulting Numbers: [120] 120,38 unequal: No Solution Exploring Operation: 81*39=3159, Resulting Numbers: [3159] 3159,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[81, 27], Operations: ['66/2=33', '33-6=27'] Exploring Operation: 81+27=108, Resulting Numbers: [108] 108,38 unequal: No Solution Exploring Operation: 81/27=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 81-27=54, Resulting Numbers: [54] 54,38 unequal: No Solution Exploring Operation: 81*27=2187, Resulting Numbers: [2187] 2187,38 unequal: No Solution Moving to Node #0,1,3 Current State: 38:[33, 87], Operations: ['66/2=33', '81+6=87'] Exploring Operation: 33+87=120, Resulting Numbers: [120] 120,38 unequal: No Solution Exploring Operation: 33*87=2871, Resulting Numbers: [2871] 2871,38 unequal: No Solution Exploring Operation: 87-33=54, Resulting Numbers: [54] 54,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[66, 2, 75], Operations: ['81-6=75'] Exploring Operation: 66+2=68, Resulting Numbers: [75, 68] Generated Node #0,2,0: 38:[75, 68] Operation: 66+2=68 Exploring Operation: 66-2=64, Resulting Numbers: [75, 64] Generated Node #0,2,1: 38:[75, 64] Operation: 66-2=64 Exploring Operation: 66/2=33, Resulting Numbers: [75, 33] Generated Node #0,2,2: 38:[75, 33] Operation: 66/2=33 Exploring Operation: 75-2=73, Resulting Numbers: [66, 73] Generated Node #0,2,3: 38:[66, 73] Operation: 75-2=73 Exploring Operation: 75-66=9, Resulting Numbers: [2, 9] Generated Node #0,2,4: 38:[2, 9] Operation: 75-66=9 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 38:[2, 9], Operations: ['81-6=75', '75-66=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 38:[75, 33], Operations: ['81-6=75', '66/2=33'] Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,38 unequal: No Solution Exploring Operation: 75+33=108, Resulting Numbers: [108] 108,38 unequal: No Solution Exploring Operation: 75*33=2475, Resulting Numbers: [2475] 2475,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 38:[75, 64], Operations: ['81-6=75', '66-2=64'] Exploring Operation: 75*64=4800, Resulting Numbers: [4800] 4800,38 unequal: No Solution Exploring Operation: 75+64=139, Resulting Numbers: [139] 139,38 unequal: No Solution Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 38:[66, 73], Operations: ['81-6=75', '75-2=73'] Exploring Operation: 66*73=4818, Resulting Numbers: [4818] 4818,38 unequal: No Solution Exploring Operation: 66+73=139, Resulting Numbers: [139] 139,38 unequal: No Solution Exploring Operation: 73-66=7, Resulting Numbers: [7] 7,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 38:[75, 68], Operations: ['81-6=75', '66+2=68'] Exploring Operation: 75-68=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 75*68=5100, Resulting Numbers: [5100] 5100,38 unequal: No Solution Exploring Operation: 75+68=143, Resulting Numbers: [143] 143,38 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:[81, 2, 60], Operations: ['66-6=60'] Exploring Operation: 60-2=58, Resulting Numbers: [81, 58] Generated Node #0,3,0: 38:[81, 58] Operation: 60-2=58 Exploring Operation: 81-2=79, Resulting Numbers: [60, 79] Generated Node #0,3,1: 38:[60, 79] Operation: 81-2=79 Exploring Operation: 81-60=21, Resulting Numbers: [2, 21] Generated Node #0,3,2: 38:[2, 21] Operation: 81-60=21 Exploring Operation: 81+2=83, Resulting Numbers: [60, 83] Generated Node #0,3,3: 38:[60, 83] Operation: 81+2=83 Exploring Operation: 60/2=30, Resulting Numbers: [81, 30] Generated Node #0,3,4: 38:[81, 30] Operation: 60/2=30 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 38:[2, 21], Operations: ['66-6=60', '81-60=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,38 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,38 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,38 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 #0,3,4 Current State: 38:[81, 30], Operations: ['66-6=60', '60/2=30'] Exploring Operation: 81-30=51, Resulting Numbers: [51] 51,38 unequal: No Solution Exploring Operation: 81+30=111, Resulting Numbers: [111] 111,38 unequal: No Solution Exploring Operation: 81*30=2430, Resulting Numbers: [2430] 2430,38 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 #0,3,0 Current State: 38:[81, 58], Operations: ['66-6=60', '60-2=58'] Exploring Operation: 81-58=23, Resulting Numbers: [23] 23,38 unequal: No Solution Exploring Operation: 81*58=4698, Resulting Numbers: [4698] 4698,38 unequal: No Solution Exploring Operation: 81+58=139, Resulting Numbers: [139] 139,38 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 #0,3,1 Current State: 38:[60, 79], Operations: ['66-6=60', '81-2=79'] Exploring Operation: 60*79=4740, Resulting Numbers: [4740] 4740,38 unequal: No Solution Exploring Operation: 60+79=139, Resulting Numbers: [139] 139,38 unequal: No Solution Exploring Operation: 79-60=19, Resulting Numbers: [19] 19,38 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 #0,3,3 Current State: 38:[60, 83], Operations: ['66-6=60', '81+2=83'] Exploring Operation: 60*83=4980, Resulting Numbers: [4980] 4980,38 unequal: No Solution Exploring Operation: 83-60=23, Resulting Numbers: [23] 23,38 unequal: No Solution Exploring Operation: 60+83=143, Resulting Numbers: [143] 143,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 48, 73, 44, 92 ]
76
[ "48-44=4", "92-73=19", "4*19=76" ]
Current State: 76:[48, 73, 44, 92], Operations: [] Exploring Operation: 48-44=4, Resulting Numbers: [73, 92, 4] Generated Node #2: [73, 92, 4] from Operation: 48-44=4 Current State: 76:[73, 92, 4], Operations: ['48-44=4'] Exploring Operation: 92-73=19, Resulting Numbers: [4, 19] Generated Node #3: [4, 19] from Operation: 92-73=19 Current State: 76:[4, 19], Operations: ['48-44=4', '92-73=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[48, 73, 44, 92], Operations: [] Exploring Operation: 92-73=19, Resulting Numbers: [48, 44, 19] Generated Node #0,0: 76:[48, 44, 19] Operation: 92-73=19 Exploring Operation: 48-44=4, Resulting Numbers: [73, 92, 4] Generated Node #0,1: 76:[73, 92, 4] Operation: 48-44=4 Exploring Operation: 92-48=44, Resulting Numbers: [73, 44, 44] Generated Node #0,2: 76:[73, 44, 44] Operation: 92-48=44 Exploring Operation: 92-44=48, Resulting Numbers: [48, 73, 48] Generated Node #0,3: 76:[48, 73, 48] Operation: 92-44=48 Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[73, 44, 44], Operations: ['92-48=44'] Exploring Operation: 73-44=29, Resulting Numbers: [44, 29] Generated Node #0,2,0: 76:[44, 29] Operation: 73-44=29 Exploring Operation: 44/44=1, Resulting Numbers: [73, 1] Generated Node #0,2,1: 76:[73, 1] Operation: 44/44=1 Exploring Operation: 44-44=0, Resulting Numbers: [73, 0] Generated Node #0,2,2: 76:[73, 0] Operation: 44-44=0 Exploring Operation: 73-44=29, Resulting Numbers: [44, 29] Generated Node #0,2,3: 76:[44, 29] Operation: 73-44=29 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 76:[73, 1], Operations: ['92-48=44', '44/44=1'] Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,76 unequal: No Solution Exploring Operation: 73*1=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 73/1=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 73+1=74, Resulting Numbers: [74] 74,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 76:[73, 0], Operations: ['92-48=44', '44-44=0'] Exploring Operation: 73-0=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 73*0=0, Resulting Numbers: [0] 0,76 unequal: No Solution Exploring Operation: 73+0=73, Resulting Numbers: [73] 73,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 76:[44, 29], Operations: ['92-48=44', '73-44=29'] Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,76 unequal: No Solution Exploring Operation: 44+29=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 44*29=1276, Resulting Numbers: [1276] 1276,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 76:[44, 29], Operations: ['92-48=44', '73-44=29'] Exploring Operation: 44+29=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 44*29=1276, Resulting Numbers: [1276] 1276,76 unequal: No Solution Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[48, 44, 19], Operations: ['92-73=19'] Exploring Operation: 48+44=92, Resulting Numbers: [19, 92] Generated Node #0,0,0: 76:[19, 92] Operation: 48+44=92 Exploring Operation: 48+19=67, Resulting Numbers: [44, 67] Generated Node #0,0,1: 76:[44, 67] Operation: 48+19=67 Exploring Operation: 48-19=29, Resulting Numbers: [44, 29] Generated Node #0,0,2: 76:[44, 29] Operation: 48-19=29 Exploring Operation: 48-44=4, Resulting Numbers: [19, 4] Generated Node #0,0,3: 76:[19, 4] Operation: 48-44=4 Moving to Node #0,0,3 Current State: 76:[19, 4], Operations: ['92-73=19', '48-44=4'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,76 unequal: No Solution Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[48, 73, 44, 92], Operations: [] Exploring Operation: 92-73=19, Resulting Numbers: [48, 44, 19] Generated Node #0,0: 76:[48, 44, 19] Operation: 92-73=19 Moving to Node #0,0 Current State: 76:[48, 44, 19], Operations: ['92-73=19'] Exploring Operation: 48-44=4, Resulting Numbers: [19, 4] Generated Node #0,0,3: 76:[19, 4] Operation: 48-44=4 Moving to Node #0,0,3 Current State: 76:[19, 4], Operations: ['92-73=19', '48-44=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 65, 97, 8, 47 ]
83
[ "65+47=112", "112/8=14", "97-14=83" ]
Current State: 83:[65, 97, 8, 47], Operations: [] Exploring Operation: 65+47=112, Resulting Numbers: [97, 8, 112] Generated Node #2: [97, 8, 112] from Operation: 65+47=112 Current State: 83:[97, 8, 112], Operations: ['65+47=112'] Exploring Operation: 112/8=14, Resulting Numbers: [97, 14] Generated Node #3: [97, 14] from Operation: 112/8=14 Current State: 83:[97, 14], Operations: ['65+47=112', '112/8=14'] Exploring Operation: 97-14=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[65, 97, 8, 47], Operations: [] Exploring Operation: 8+47=55, Resulting Numbers: [65, 97, 55] Generated Node #0,0: 83:[65, 97, 55] Operation: 8+47=55 Exploring Operation: 97+8=105, Resulting Numbers: [65, 47, 105] Generated Node #0,1: 83:[65, 47, 105] Operation: 97+8=105 Exploring Operation: 97-8=89, Resulting Numbers: [65, 47, 89] Generated Node #0,2: 83:[65, 47, 89] Operation: 97-8=89 Exploring Operation: 65+8=73, Resulting Numbers: [97, 47, 73] Generated Node #0,3: 83:[97, 47, 73] Operation: 65+8=73 Exploring Operation: 65-8=57, Resulting Numbers: [97, 47, 57] Generated Node #0,4: 83:[97, 47, 57] Operation: 65-8=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[65, 97, 55], Operations: ['8+47=55'] Exploring Operation: 97+55=152, Resulting Numbers: [65, 152] Generated Node #0,0,0: 83:[65, 152] Operation: 97+55=152 Exploring Operation: 65+55=120, Resulting Numbers: [97, 120] Generated Node #0,0,1: 83:[97, 120] Operation: 65+55=120 Exploring Operation: 97-65=32, Resulting Numbers: [55, 32] Generated Node #0,0,2: 83:[55, 32] Operation: 97-65=32 Exploring Operation: 65-55=10, Resulting Numbers: [97, 10] Generated Node #0,0,3: 83:[97, 10] Operation: 65-55=10 Exploring Operation: 97-55=42, Resulting Numbers: [65, 42] Generated Node #0,0,4: 83:[65, 42] Operation: 97-55=42 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[97, 120], Operations: ['8+47=55', '65+55=120'] Exploring Operation: 97*120=11640, Resulting Numbers: [11640] 11640,83 unequal: No Solution Exploring Operation: 97+120=217, Resulting Numbers: [217] 217,83 unequal: No Solution Exploring Operation: 120-97=23, Resulting Numbers: [23] 23,83 unequal: No Solution No 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: 83:[65, 42], Operations: ['8+47=55', '97-55=42'] Exploring Operation: 65-42=23, Resulting Numbers: [23] 23,83 unequal: No Solution Exploring Operation: 65+42=107, Resulting Numbers: [107] 107,83 unequal: No Solution Exploring Operation: 65*42=2730, Resulting Numbers: [2730] 2730,83 unequal: No Solution No 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: 83:[55, 32], Operations: ['8+47=55', '97-65=32'] Exploring Operation: 55-32=23, Resulting Numbers: [23] 23,83 unequal: No Solution Exploring Operation: 55+32=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 55*32=1760, Resulting Numbers: [1760] 1760,83 unequal: No Solution No 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: 83:[65, 152], Operations: ['8+47=55', '97+55=152'] Exploring Operation: 65+152=217, Resulting Numbers: [217] 217,83 unequal: No Solution Exploring Operation: 65*152=9880, Resulting Numbers: [9880] 9880,83 unequal: No Solution Exploring Operation: 152-65=87, Resulting Numbers: [87] 87,83 unequal: No Solution No 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: 83:[97, 10], Operations: ['8+47=55', '65-55=10'] Exploring Operation: 97-10=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 97+10=107, Resulting Numbers: [107] 107,83 unequal: No Solution Exploring Operation: 97*10=970, Resulting Numbers: [970] 970,83 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: 83:[65, 47, 89], Operations: ['97-8=89'] Exploring Operation: 89-47=42, Resulting Numbers: [65, 42] Generated Node #0,2,0: 83:[65, 42] Operation: 89-47=42 Exploring Operation: 65+47=112, Resulting Numbers: [89, 112] Generated Node #0,2,1: 83:[89, 112] Operation: 65+47=112 Exploring Operation: 47+89=136, Resulting Numbers: [65, 136] Generated Node #0,2,2: 83:[65, 136] Operation: 47+89=136 Exploring Operation: 65-47=18, Resulting Numbers: [89, 18] Generated Node #0,2,3: 83:[89, 18] Operation: 65-47=18 Exploring Operation: 89-65=24, Resulting Numbers: [47, 24] Generated Node #0,2,4: 83:[47, 24] Operation: 89-65=24 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[89, 112], Operations: ['97-8=89', '65+47=112'] Exploring Operation: 89+112=201, Resulting Numbers: [201] 201,83 unequal: No Solution Exploring Operation: 112-89=23, Resulting Numbers: [23] 23,83 unequal: No Solution Exploring Operation: 89*112=9968, Resulting Numbers: [9968] 9968,83 unequal: No Solution No 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: 83:[65, 42], Operations: ['97-8=89', '89-47=42'] Exploring Operation: 65-42=23, Resulting Numbers: [23] 23,83 unequal: No Solution Exploring Operation: 65+42=107, Resulting Numbers: [107] 107,83 unequal: No Solution Exploring Operation: 65*42=2730, Resulting Numbers: [2730] 2730,83 unequal: No Solution No 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: 83:[65, 136], Operations: ['97-8=89', '47+89=136'] Exploring Operation: 65*136=8840, Resulting Numbers: [8840] 8840,83 unequal: No Solution Exploring Operation: 136-65=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 65+136=201, Resulting Numbers: [201] 201,83 unequal: No Solution No 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: 83:[89, 18], Operations: ['97-8=89', '65-47=18'] Exploring Operation: 89+18=107, Resulting Numbers: [107] 107,83 unequal: No Solution Exploring Operation: 89-18=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 89*18=1602, Resulting Numbers: [1602] 1602,83 unequal: No Solution No 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: 83:[47, 24], Operations: ['97-8=89', '89-65=24'] Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,83 unequal: No Solution Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 47*24=1128, Resulting Numbers: [1128] 1128,83 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: 83:[97, 47, 73], Operations: ['65+8=73'] Exploring Operation: 97-73=24, Resulting Numbers: [47, 24] Generated Node #0,3,0: 83:[47, 24] Operation: 97-73=24 Exploring Operation: 97-47=50, Resulting Numbers: [73, 50] Generated Node #0,3,1: 83:[73, 50] Operation: 97-47=50 Exploring Operation: 73-47=26, Resulting Numbers: [97, 26] Generated Node #0,3,2: 83:[97, 26] Operation: 73-47=26 Exploring Operation: 47+73=120, Resulting Numbers: [97, 120] Generated Node #0,3,3: 83:[97, 120] Operation: 47+73=120 Exploring Operation: 97+47=144, Resulting Numbers: [73, 144] Generated Node #0,3,4: 83:[73, 144] Operation: 97+47=144 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 83:[73, 50], Operations: ['65+8=73', '97-47=50'] Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,83 unequal: No Solution Exploring Operation: 73+50=123, Resulting Numbers: [123] 123,83 unequal: No Solution Exploring Operation: 73*50=3650, Resulting Numbers: [3650] 3650,83 unequal: No Solution No 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: 83:[97, 120], Operations: ['65+8=73', '47+73=120'] Exploring Operation: 120-97=23, Resulting Numbers: [23] 23,83 unequal: No Solution Exploring Operation: 97*120=11640, Resulting Numbers: [11640] 11640,83 unequal: No Solution Exploring Operation: 97+120=217, Resulting Numbers: [217] 217,83 unequal: No Solution No 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: 83:[97, 26], Operations: ['65+8=73', '73-47=26'] Exploring Operation: 97-26=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 97*26=2522, Resulting Numbers: [2522] 2522,83 unequal: No Solution Exploring Operation: 97+26=123, Resulting Numbers: [123] 123,83 unequal: No Solution No 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: 83:[73, 144], Operations: ['65+8=73', '97+47=144'] Exploring Operation: 144-73=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 73*144=10512, Resulting Numbers: [10512] 10512,83 unequal: No Solution Exploring Operation: 73+144=217, Resulting Numbers: [217] 217,83 unequal: No Solution No 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: 83:[47, 24], Operations: ['65+8=73', '97-73=24'] Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 47*24=1128, Resulting Numbers: [1128] 1128,83 unequal: No Solution Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,83 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: 83:[65, 47, 105], Operations: ['97+8=105'] Exploring Operation: 65-47=18, Resulting Numbers: [105, 18] Generated Node #0,1,0: 83:[105, 18] Operation: 65-47=18 Exploring Operation: 65+47=112, Resulting Numbers: [105, 112] Generated Node #0,1,1: 83:[105, 112] Operation: 65+47=112 Exploring Operation: 105-47=58, Resulting Numbers: [65, 58] Generated Node #0,1,2: 83:[65, 58] Operation: 105-47=58 Exploring Operation: 105-65=40, Resulting Numbers: [47, 40] Generated Node #0,1,3: 83:[47, 40] Operation: 105-65=40 Exploring Operation: 47+105=152, Resulting Numbers: [65, 152] Generated Node #0,1,4: 83:[65, 152] Operation: 47+105=152 Moving to Node #0,1,2 Current State: 83:[65, 58], Operations: ['97+8=105', '105-47=58'] Exploring Operation: 65-58=7, Resulting Numbers: [7] 7,83 unequal: No Solution Exploring Operation: 65*58=3770, Resulting Numbers: [3770] 3770,83 unequal: No Solution Exploring Operation: 65+58=123, Resulting Numbers: [123] 123,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[105, 112], Operations: ['97+8=105', '65+47=112'] Exploring Operation: 112-105=7, Resulting Numbers: [7] 7,83 unequal: No Solution Exploring Operation: 105+112=217, Resulting Numbers: [217] 217,83 unequal: No Solution Exploring Operation: 105*112=11760, Resulting Numbers: [11760] 11760,83 unequal: No Solution Moving to Node #0,1,3 Current State: 83:[47, 40], Operations: ['97+8=105', '105-65=40'] Exploring Operation: 47*40=1880, Resulting Numbers: [1880] 1880,83 unequal: No Solution Exploring Operation: 47-40=7, Resulting Numbers: [7] 7,83 unequal: No Solution Exploring Operation: 47+40=87, Resulting Numbers: [87] 87,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[105, 18], Operations: ['97+8=105', '65-47=18'] Exploring Operation: 105-18=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 105+18=123, Resulting Numbers: [123] 123,83 unequal: No Solution Exploring Operation: 105*18=1890, Resulting Numbers: [1890] 1890,83 unequal: No Solution Moving to Node #0,1,4 Current State: 83:[65, 152], Operations: ['97+8=105', '47+105=152'] Exploring Operation: 65*152=9880, Resulting Numbers: [9880] 9880,83 unequal: No Solution Exploring Operation: 152-65=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 65+152=217, Resulting Numbers: [217] 217,83 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 #0,4 Current State: 83:[97, 47, 57], Operations: ['65-8=57'] Exploring Operation: 57-47=10, Resulting Numbers: [97, 10] Generated Node #0,4,0: 83:[97, 10] Operation: 57-47=10 Exploring Operation: 97-57=40, Resulting Numbers: [47, 40] Generated Node #0,4,1: 83:[47, 40] Operation: 97-57=40 Exploring Operation: 47+57=104, Resulting Numbers: [97, 104] Generated Node #0,4,2: 83:[97, 104] Operation: 47+57=104 Exploring Operation: 97+47=144, Resulting Numbers: [57, 144] Generated Node #0,4,3: 83:[57, 144] Operation: 97+47=144 Exploring Operation: 97-47=50, Resulting Numbers: [57, 50] Generated Node #0,4,4: 83:[57, 50] Operation: 97-47=50 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 83:[97, 104], Operations: ['65-8=57', '47+57=104'] Exploring Operation: 104-97=7, Resulting Numbers: [7] 7,83 unequal: No Solution Exploring Operation: 97*104=10088, Resulting Numbers: [10088] 10088,83 unequal: No Solution Exploring Operation: 97+104=201, Resulting Numbers: [201] 201,83 unequal: No Solution No 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: 83:[57, 50], Operations: ['65-8=57', '97-47=50'] Exploring Operation: 57-50=7, Resulting Numbers: [7] 7,83 unequal: No Solution Exploring Operation: 57+50=107, Resulting Numbers: [107] 107,83 unequal: No Solution Exploring Operation: 57*50=2850, Resulting Numbers: [2850] 2850,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 83:[47, 40], Operations: ['65-8=57', '97-57=40'] Exploring Operation: 47*40=1880, Resulting Numbers: [1880] 1880,83 unequal: No Solution Exploring Operation: 47+40=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 47-40=7, Resulting Numbers: [7] 7,83 unequal: No Solution No 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: 83:[97, 10], Operations: ['65-8=57', '57-47=10'] Exploring Operation: 97+10=107, Resulting Numbers: [107] 107,83 unequal: No Solution Exploring Operation: 97*10=970, Resulting Numbers: [970] 970,83 unequal: No Solution Exploring Operation: 97-10=87, Resulting Numbers: [87] 87,83 unequal: No Solution No 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: 83:[57, 144], Operations: ['65-8=57', '97+47=144'] Exploring Operation: 57*144=8208, Resulting Numbers: [8208] 8208,83 unequal: No Solution Exploring Operation: 144-57=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 57+144=201, Resulting Numbers: [201] 201,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 61, 26, 79, 93 ]
73
[ "61+26=87", "93-79=14", "87-14=73" ]
Current State: 73:[61, 26, 79, 93], Operations: [] Exploring Operation: 61+26=87, Resulting Numbers: [79, 93, 87] Generated Node #2: [79, 93, 87] from Operation: 61+26=87 Current State: 73:[79, 93, 87], Operations: ['61+26=87'] Exploring Operation: 93-79=14, Resulting Numbers: [87, 14] Generated Node #3: [87, 14] from Operation: 93-79=14 Current State: 73:[87, 14], Operations: ['61+26=87', '93-79=14'] Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[61, 26, 79, 93], Operations: [] Exploring Operation: 79-26=53, Resulting Numbers: [61, 93, 53] Generated Node #0,0: 73:[61, 93, 53] Operation: 79-26=53 Exploring Operation: 61+26=87, Resulting Numbers: [79, 93, 87] Generated Node #0,1: 73:[79, 93, 87] Operation: 61+26=87 Exploring Operation: 93-26=67, Resulting Numbers: [61, 79, 67] Generated Node #0,2: 73:[61, 79, 67] Operation: 93-26=67 Moving to Node #0,2 Current State: 73:[61, 79, 67], Operations: ['93-26=67'] Exploring Operation: 61+79=140, Resulting Numbers: [67, 140] Generated Node #0,2,0: 73:[67, 140] Operation: 61+79=140 Exploring Operation: 79-61=18, Resulting Numbers: [67, 18] Generated Node #0,2,1: 73:[67, 18] Operation: 79-61=18 Exploring Operation: 61+67=128, Resulting Numbers: [79, 128] Generated Node #0,2,2: 73:[79, 128] Operation: 61+67=128 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 73:[67, 18], Operations: ['93-26=67', '79-61=18'] Exploring Operation: 67+18=85, Resulting Numbers: [85] 85,73 unequal: No Solution Exploring Operation: 67*18=1206, Resulting Numbers: [1206] 1206,73 unequal: No Solution Exploring Operation: 67-18=49, Resulting Numbers: [49] 49,73 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 #0,2,2 Current State: 73:[79, 128], Operations: ['93-26=67', '61+67=128'] Exploring Operation: 79+128=207, Resulting Numbers: [207] 207,73 unequal: No Solution Exploring Operation: 128-79=49, Resulting Numbers: [49] 49,73 unequal: No Solution Exploring Operation: 79*128=10112, Resulting Numbers: [10112] 10112,73 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 #0,2,0 Current State: 73:[67, 140], Operations: ['93-26=67', '61+79=140'] Exploring Operation: 140-67=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[61, 26, 79, 93], Operations: [] Exploring Operation: 93-26=67, Resulting Numbers: [61, 79, 67] Generated Node #0,2: 73:[61, 79, 67] Operation: 93-26=67 Moving to Node #0,2 Current State: 73:[61, 79, 67], Operations: ['93-26=67'] Exploring Operation: 61+79=140, Resulting Numbers: [67, 140] Generated Node #0,2,0: 73:[67, 140] Operation: 61+79=140 Moving to Node #0,2,0 Current State: 73:[67, 140], Operations: ['93-26=67', '61+79=140'] Exploring Operation: 140-67=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 49, 42, 32, 77 ]
21
[ "49-42=7", "77/7=11", "32-11=21" ]
Current State: 21:[49, 42, 32, 77], Operations: [] Exploring Operation: 49-42=7, Resulting Numbers: [32, 77, 7] Generated Node #2: [32, 77, 7] from Operation: 49-42=7 Current State: 21:[32, 77, 7], Operations: ['49-42=7'] Exploring Operation: 77/7=11, Resulting Numbers: [32, 11] Generated Node #3: [32, 11] from Operation: 77/7=11 Current State: 21:[32, 11], Operations: ['49-42=7', '77/7=11'] Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[49, 42, 32, 77], Operations: [] Exploring Operation: 77-32=45, Resulting Numbers: [49, 42, 45] Generated Node #0,0: 21:[49, 42, 45] Operation: 77-32=45 Exploring Operation: 49-42=7, Resulting Numbers: [32, 77, 7] Generated Node #0,1: 21:[32, 77, 7] Operation: 49-42=7 Exploring Operation: 77-49=28, Resulting Numbers: [42, 32, 28] Generated Node #0,2: 21:[42, 32, 28] Operation: 77-49=28 Exploring Operation: 49-32=17, Resulting Numbers: [42, 77, 17] Generated Node #0,3: 21:[42, 77, 17] Operation: 49-32=17 Exploring Operation: 77-42=35, Resulting Numbers: [49, 32, 35] Generated Node #0,4: 21:[49, 32, 35] Operation: 77-42=35 Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[42, 32, 28], Operations: ['77-49=28'] Exploring Operation: 42+28=70, Resulting Numbers: [32, 70] Generated Node #0,2,0: 21:[32, 70] Operation: 42+28=70 Exploring Operation: 42+32=74, Resulting Numbers: [28, 74] Generated Node #0,2,1: 21:[28, 74] Operation: 42+32=74 Exploring Operation: 42-32=10, Resulting Numbers: [28, 10] Generated Node #0,2,2: 21:[28, 10] Operation: 42-32=10 Exploring Operation: 42-28=14, Resulting Numbers: [32, 14] Generated Node #0,2,3: 21:[32, 14] Operation: 42-28=14 Exploring Operation: 32-28=4, Resulting Numbers: [42, 4] Generated Node #0,2,4: 21:[42, 4] Operation: 32-28=4 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 21:[28, 10], Operations: ['77-49=28', '42-32=10'] Exploring Operation: 28+10=38, Resulting Numbers: [38] 38,21 unequal: No Solution Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 28*10=280, Resulting Numbers: [280] 280,21 unequal: No Solution No 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: 21:[32, 14], Operations: ['77-49=28', '42-28=14'] Exploring Operation: 32*14=448, Resulting Numbers: [448] 448,21 unequal: No Solution Exploring Operation: 32+14=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,21 unequal: No Solution No 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: 21:[42, 4], Operations: ['77-49=28', '32-28=4'] Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,21 unequal: No Solution Exploring Operation: 42*4=168, Resulting Numbers: [168] 168,21 unequal: No Solution No 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: 21:[32, 70], Operations: ['77-49=28', '42+28=70'] Exploring Operation: 70-32=38, Resulting Numbers: [38] 38,21 unequal: No Solution Exploring Operation: 32+70=102, Resulting Numbers: [102] 102,21 unequal: No Solution Exploring Operation: 32*70=2240, Resulting Numbers: [2240] 2240,21 unequal: No Solution No 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: 21:[28, 74], Operations: ['77-49=28', '42+32=74'] Exploring Operation: 28+74=102, Resulting Numbers: [102] 102,21 unequal: No Solution Exploring Operation: 28*74=2072, Resulting Numbers: [2072] 2072,21 unequal: No Solution Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,21 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: 21:[49, 32, 35], Operations: ['77-42=35'] Exploring Operation: 49+35=84, Resulting Numbers: [32, 84] Generated Node #0,4,0: 21:[32, 84] Operation: 49+35=84 Exploring Operation: 49-32=17, Resulting Numbers: [35, 17] Generated Node #0,4,1: 21:[35, 17] Operation: 49-32=17 Exploring Operation: 49+32=81, Resulting Numbers: [35, 81] Generated Node #0,4,2: 21:[35, 81] Operation: 49+32=81 Exploring Operation: 35-32=3, Resulting Numbers: [49, 3] Generated Node #0,4,3: 21:[49, 3] Operation: 35-32=3 Exploring Operation: 49-35=14, Resulting Numbers: [32, 14] Generated Node #0,4,4: 21:[32, 14] Operation: 49-35=14 Moving to Node #0,4,1 Current State: 21:[35, 17], Operations: ['77-42=35', '49-32=17'] Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 35+17=52, Resulting Numbers: [52] 52,21 unequal: No Solution Exploring Operation: 35*17=595, Resulting Numbers: [595] 595,21 unequal: No Solution Moving to Node #0,4,4 Current State: 21:[32, 14], Operations: ['77-42=35', '49-35=14'] Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 32*14=448, Resulting Numbers: [448] 448,21 unequal: No Solution Exploring Operation: 32+14=46, Resulting Numbers: [46] 46,21 unequal: No Solution Moving to Node #0,4,3 Current State: 21:[49, 3], Operations: ['77-42=35', '35-32=3'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,21 unequal: No Solution Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,21 unequal: No Solution Moving to Node #0,4,0 Current State: 21:[32, 84], Operations: ['77-42=35', '49+35=84'] Exploring Operation: 32+84=116, Resulting Numbers: [116] 116,21 unequal: No Solution Exploring Operation: 32*84=2688, Resulting Numbers: [2688] 2688,21 unequal: No Solution Exploring Operation: 84-32=52, Resulting Numbers: [52] 52,21 unequal: No Solution Moving to Node #0,4,2 Current State: 21:[35, 81], Operations: ['77-42=35', '49+32=81'] Exploring Operation: 35*81=2835, Resulting Numbers: [2835] 2835,21 unequal: No Solution Exploring Operation: 35+81=116, Resulting Numbers: [116] 116,21 unequal: No Solution Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[32, 77, 7], Operations: ['49-42=7'] Exploring Operation: 77-32=45, Resulting Numbers: [7, 45] Generated Node #0,1,0: 21:[7, 45] Operation: 77-32=45 Exploring Operation: 77-7=70, Resulting Numbers: [32, 70] Generated Node #0,1,1: 21:[32, 70] Operation: 77-7=70 Exploring Operation: 77/7=11, Resulting Numbers: [32, 11] Generated Node #0,1,2: 21:[32, 11] Operation: 77/7=11 Exploring Operation: 32-7=25, Resulting Numbers: [77, 25] Generated Node #0,1,3: 21:[77, 25] Operation: 32-7=25 Exploring Operation: 32+7=39, Resulting Numbers: [77, 39] Generated Node #0,1,4: 21:[77, 39] Operation: 32+7=39 Moving to Node #0,1,2 Current State: 21:[32, 11], Operations: ['49-42=7', '77/7=11'] Exploring Operation: 32+11=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 32*11=352, Resulting Numbers: [352] 352,21 unequal: No Solution Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[49, 42, 32, 77], Operations: [] Exploring Operation: 49-42=7, Resulting Numbers: [32, 77, 7] Generated Node #0,1: 21:[32, 77, 7] Operation: 49-42=7 Moving to Node #0,1 Current State: 21:[32, 77, 7], Operations: ['49-42=7'] Exploring Operation: 77/7=11, Resulting Numbers: [32, 11] Generated Node #0,1,2: 21:[32, 11] Operation: 77/7=11 Moving to Node #0,1,2 Current State: 21:[32, 11], Operations: ['49-42=7', '77/7=11'] Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.950521
hs_5
mult_heuristic
[ 48, 48, 5, 38 ]
63
[ "48+48=96", "38-5=33", "96-33=63" ]
Current State: 63:[48, 48, 5, 38], Operations: [] Exploring Operation: 48+48=96, Resulting Numbers: [5, 38, 96] Generated Node #2: [5, 38, 96] from Operation: 48+48=96 Current State: 63:[5, 38, 96], Operations: ['48+48=96'] Exploring Operation: 38-5=33, Resulting Numbers: [96, 33] Generated Node #3: [96, 33] from Operation: 38-5=33 Current State: 63:[96, 33], Operations: ['48+48=96', '38-5=33'] Exploring Operation: 96-33=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[48, 48, 5, 38], Operations: [] Exploring Operation: 48-38=10, Resulting Numbers: [48, 5, 10] Generated Node #0,0: 63:[48, 5, 10] Operation: 48-38=10 Exploring Operation: 48-38=10, Resulting Numbers: [48, 5, 10] Generated Node #0,1: 63:[48, 5, 10] Operation: 48-38=10 Moving to Node #0,0 Current State: 63:[48, 5, 10], Operations: ['48-38=10'] Exploring Operation: 48+10=58, Resulting Numbers: [5, 58] Generated Node #0,0,0: 63:[5, 58] Operation: 48+10=58 Exploring Operation: 48+5=53, Resulting Numbers: [10, 53] Generated Node #0,0,1: 63:[10, 53] Operation: 48+5=53 Moving to Node #0,1 Current State: 63:[48, 5, 10], Operations: ['48-38=10'] Exploring Operation: 48+10=58, Resulting Numbers: [5, 58] Generated Node #0,1,0: 63:[5, 58] Operation: 48+10=58 Exploring Operation: 48+5=53, Resulting Numbers: [10, 53] Generated Node #0,1,1: 63:[10, 53] Operation: 48+5=53 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 63:[5, 58], Operations: ['48-38=10', '48+10=58'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,63 unequal: No Solution Exploring Operation: 5+58=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[48, 48, 5, 38], Operations: [] Exploring Operation: 48-38=10, Resulting Numbers: [48, 5, 10] Generated Node #0,1: 63:[48, 5, 10] Operation: 48-38=10 Moving to Node #0,1 Current State: 63:[48, 5, 10], Operations: ['48-38=10'] Exploring Operation: 48+10=58, Resulting Numbers: [5, 58] Generated Node #0,1,0: 63:[5, 58] Operation: 48+10=58 Moving to Node #0,1,0 Current State: 63:[5, 58], Operations: ['48-38=10', '48+10=58'] Exploring Operation: 5+58=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 32, 17, 48, 46 ]
86
[ "48*46=2208", "2208/32=69", "17+69=86" ]
Current State: 86:[32, 17, 48, 46], Operations: [] Exploring Operation: 48*46=2208, Resulting Numbers: [32, 17, 2208] Generated Node #2: [32, 17, 2208] from Operation: 48*46=2208 Current State: 86:[32, 17, 2208], Operations: ['48*46=2208'] Exploring Operation: 2208/32=69, Resulting Numbers: [17, 69] Generated Node #3: [17, 69] from Operation: 2208/32=69 Current State: 86:[17, 69], Operations: ['48*46=2208', '2208/32=69'] Exploring Operation: 17+69=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[32, 17, 48, 46], Operations: [] Exploring Operation: 32-17=15, Resulting Numbers: [48, 46, 15] Generated Node #0,0: 86:[48, 46, 15] Operation: 32-17=15 Exploring Operation: 32+17=49, Resulting Numbers: [48, 46, 49] Generated Node #0,1: 86:[48, 46, 49] Operation: 32+17=49 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[48, 46, 49], Operations: ['32+17=49'] Exploring Operation: 48-46=2, Resulting Numbers: [49, 2] Generated Node #0,1,0: 86:[49, 2] Operation: 48-46=2 Exploring Operation: 49-48=1, Resulting Numbers: [46, 1] Generated Node #0,1,1: 86:[46, 1] Operation: 49-48=1 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 86:[46, 1], Operations: ['32+17=49', '49-48=1'] Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,86 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,86 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 #0,1,0 Current State: 86:[49, 2], Operations: ['32+17=49', '48-46=2'] Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,86 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,86 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 #0,0 Current State: 86:[48, 46, 15], Operations: ['32-17=15'] Exploring Operation: 48-15=33, Resulting Numbers: [46, 33] Generated Node #0,0,0: 86:[46, 33] Operation: 48-15=33 Exploring Operation: 48-46=2, Resulting Numbers: [15, 2] Generated Node #0,0,1: 86:[15, 2] Operation: 48-46=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[46, 33], Operations: ['32-17=15', '48-15=33'] Exploring Operation: 46+33=79, Resulting Numbers: [79] 79,86 unequal: No Solution Exploring Operation: 46-33=13, Resulting Numbers: [13] 13,86 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 #0,0,1 Current State: 86:[15, 2], Operations: ['32-17=15', '48-46=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,86 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 No solution found.
0
hs_2
mult_heuristic
[ 28, 6, 76, 2 ]
93
[ "28+6=34", "34/2=17", "76+17=93" ]
Current State: 93:[28, 6, 76, 2], Operations: [] Exploring Operation: 28+6=34, Resulting Numbers: [76, 2, 34] Generated Node #2: [76, 2, 34] from Operation: 28+6=34 Current State: 93:[76, 2, 34], Operations: ['28+6=34'] Exploring Operation: 34/2=17, Resulting Numbers: [76, 17] Generated Node #3: [76, 17] from Operation: 34/2=17 Current State: 93:[76, 17], Operations: ['28+6=34', '34/2=17'] Exploring Operation: 76+17=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[28, 6, 76, 2], Operations: [] Exploring Operation: 6+76=82, Resulting Numbers: [28, 2, 82] Generated Node #0,0: 93:[28, 2, 82] Operation: 6+76=82 Exploring Operation: 28+76=104, Resulting Numbers: [6, 2, 104] Generated Node #0,1: 93:[6, 2, 104] Operation: 28+76=104 Exploring Operation: 76/2=38, Resulting Numbers: [28, 6, 38] Generated Node #0,2: 93:[28, 6, 38] Operation: 76/2=38 Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[28, 6, 38], Operations: ['76/2=38'] Exploring Operation: 38-28=10, Resulting Numbers: [6, 10] Generated Node #0,2,0: 93:[6, 10] Operation: 38-28=10 Exploring Operation: 28+6=34, Resulting Numbers: [38, 34] Generated Node #0,2,1: 93:[38, 34] Operation: 28+6=34 Exploring Operation: 38-6=32, Resulting Numbers: [28, 32] Generated Node #0,2,2: 93:[28, 32] Operation: 38-6=32 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 93:[28, 32], Operations: ['76/2=38', '38-6=32'] Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,93 unequal: No Solution Exploring Operation: 28*32=896, Resulting Numbers: [896] 896,93 unequal: No Solution Exploring Operation: 28+32=60, Resulting Numbers: [60] 60,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 93:[6, 10], Operations: ['76/2=38', '38-28=10'] Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,93 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,93 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 93:[38, 34], Operations: ['76/2=38', '28+6=34'] Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,93 unequal: No Solution Exploring Operation: 38+34=72, Resulting Numbers: [72] 72,93 unequal: No Solution Exploring Operation: 38*34=1292, Resulting Numbers: [1292] 1292,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[28, 2, 82], Operations: ['6+76=82'] Exploring Operation: 2+82=84, Resulting Numbers: [28, 84] Generated Node #0,0,0: 93:[28, 84] Operation: 2+82=84 Exploring Operation: 28+2=30, Resulting Numbers: [82, 30] Generated Node #0,0,1: 93:[82, 30] Operation: 28+2=30 Exploring Operation: 82/2=41, Resulting Numbers: [28, 41] Generated Node #0,0,2: 93:[28, 41] Operation: 82/2=41 Moving to Node #0,0,0 Current State: 93:[28, 84], Operations: ['6+76=82', '2+82=84'] Exploring Operation: 84/28=3, Resulting Numbers: [3] 3,93 unequal: No Solution Exploring Operation: 84-28=56, Resulting Numbers: [56] 56,93 unequal: No Solution Exploring Operation: 28+84=112, Resulting Numbers: [112] 112,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[82, 30], Operations: ['6+76=82', '28+2=30'] Exploring Operation: 82+30=112, Resulting Numbers: [112] 112,93 unequal: No Solution Exploring Operation: 82*30=2460, Resulting Numbers: [2460] 2460,93 unequal: No Solution Exploring Operation: 82-30=52, Resulting Numbers: [52] 52,93 unequal: No Solution Moving to Node #0,0,2 Current State: 93:[28, 41], Operations: ['6+76=82', '82/2=41'] Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,93 unequal: No Solution Exploring Operation: 28+41=69, Resulting Numbers: [69] 69,93 unequal: No Solution Exploring Operation: 28*41=1148, Resulting Numbers: [1148] 1148,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[6, 2, 104], Operations: ['28+76=104'] Exploring Operation: 104-6=98, Resulting Numbers: [2, 98] Generated Node #0,1,0: 93:[2, 98] Operation: 104-6=98 Exploring Operation: 6-2=4, Resulting Numbers: [104, 4] Generated Node #0,1,1: 93:[104, 4] Operation: 6-2=4 Exploring Operation: 6/2=3, Resulting Numbers: [104, 3] Generated Node #0,1,2: 93:[104, 3] Operation: 6/2=3 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 93:[2, 98], Operations: ['28+76=104', '104-6=98'] Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,93 unequal: No Solution Exploring Operation: 2+98=100, Resulting Numbers: [100] 100,93 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 93:[104, 3], Operations: ['28+76=104', '6/2=3'] Exploring Operation: 104-3=101, Resulting Numbers: [101] 101,93 unequal: No Solution Exploring Operation: 104*3=312, Resulting Numbers: [312] 312,93 unequal: No Solution Exploring Operation: 104+3=107, Resulting Numbers: [107] 107,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 93:[104, 4], Operations: ['28+76=104', '6-2=4'] Exploring Operation: 104+4=108, Resulting Numbers: [108] 108,93 unequal: No Solution Exploring Operation: 104/4=26, Resulting Numbers: [26] 26,93 unequal: No Solution Exploring Operation: 104-4=100, Resulting Numbers: [100] 100,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 16, 54, 21, 2 ]
71
[ "16+21=37", "54*2=108", "108-37=71" ]
Current State: 71:[16, 54, 21, 2], Operations: [] Exploring Operation: 16+21=37, Resulting Numbers: [54, 2, 37] Generated Node #2: [54, 2, 37] from Operation: 16+21=37 Current State: 71:[54, 2, 37], Operations: ['16+21=37'] Exploring Operation: 54*2=108, Resulting Numbers: [37, 108] Generated Node #3: [37, 108] from Operation: 54*2=108 Current State: 71:[37, 108], Operations: ['16+21=37', '54*2=108'] Exploring Operation: 108-37=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[16, 54, 21, 2], Operations: [] Exploring Operation: 21*2=42, Resulting Numbers: [16, 54, 42] Generated Node #0,0: 71:[16, 54, 42] Operation: 21*2=42 Moving to Node #0,0 Current State: 71:[16, 54, 42], Operations: ['21*2=42'] Exploring Operation: 16+54=70, Resulting Numbers: [42, 70] Generated Node #0,0,0: 71:[42, 70] Operation: 16+54=70 Moving to Node #0,0,0 Current State: 71:[42, 70], Operations: ['21*2=42', '16+54=70'] Exploring Operation: 42+70=112, Resulting Numbers: [112] 112,71 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 89, 27, 7, 92 ]
60
[ "92-89=3", "27-7=20", "3*20=60" ]
Current State: 60:[89, 27, 7, 92], Operations: [] Exploring Operation: 92-89=3, Resulting Numbers: [27, 7, 3] Generated Node #2: [27, 7, 3] from Operation: 92-89=3 Current State: 60:[27, 7, 3], Operations: ['92-89=3'] Exploring Operation: 27-7=20, Resulting Numbers: [3, 20] Generated Node #3: [3, 20] from Operation: 27-7=20 Current State: 60:[3, 20], Operations: ['92-89=3', '27-7=20'] Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[89, 27, 7, 92], Operations: [] Exploring Operation: 92-89=3, Resulting Numbers: [27, 7, 3] Generated Node #0,0: 60:[27, 7, 3] Operation: 92-89=3 Exploring Operation: 92-27=65, Resulting Numbers: [89, 7, 65] Generated Node #0,1: 60:[89, 7, 65] Operation: 92-27=65 Exploring Operation: 89-27=62, Resulting Numbers: [7, 92, 62] Generated Node #0,2: 60:[7, 92, 62] Operation: 89-27=62 Moving to Node #0,0 Current State: 60:[27, 7, 3], Operations: ['92-89=3'] Exploring Operation: 27-7=20, Resulting Numbers: [3, 20] Generated Node #0,0,0: 60:[3, 20] Operation: 27-7=20 Exploring Operation: 27/3=9, Resulting Numbers: [7, 9] Generated Node #0,0,1: 60:[7, 9] Operation: 27/3=9 Exploring Operation: 27+3=30, Resulting Numbers: [7, 30] Generated Node #0,0,2: 60:[7, 30] Operation: 27+3=30 Moving to Node #0,1 Current State: 60:[89, 7, 65], Operations: ['92-27=65'] Exploring Operation: 89-7=82, Resulting Numbers: [65, 82] Generated Node #0,1,0: 60:[65, 82] Operation: 89-7=82 Exploring Operation: 65-7=58, Resulting Numbers: [89, 58] Generated Node #0,1,1: 60:[89, 58] Operation: 65-7=58 Exploring Operation: 89-65=24, Resulting Numbers: [7, 24] Generated Node #0,1,2: 60:[7, 24] Operation: 89-65=24 Moving to Node #0,2 Current State: 60:[7, 92, 62], Operations: ['89-27=62'] Exploring Operation: 92-7=85, Resulting Numbers: [62, 85] Generated Node #0,2,0: 60:[62, 85] Operation: 92-7=85 Exploring Operation: 92-62=30, Resulting Numbers: [7, 30] Generated Node #0,2,1: 60:[7, 30] Operation: 92-62=30 Exploring Operation: 62-7=55, Resulting Numbers: [92, 55] Generated Node #0,2,2: 60:[92, 55] Operation: 62-7=55 Moving to Node #0,0,0 Current State: 60:[3, 20], Operations: ['92-89=3', '27-7=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[89, 27, 7, 92], Operations: [] Exploring Operation: 92-89=3, Resulting Numbers: [27, 7, 3] Generated Node #0,0: 60:[27, 7, 3] Operation: 92-89=3 Moving to Node #0,0 Current State: 60:[27, 7, 3], Operations: ['92-89=3'] Exploring Operation: 27-7=20, Resulting Numbers: [3, 20] Generated Node #0,0,0: 60:[3, 20] Operation: 27-7=20 Moving to Node #0,0,0 Current State: 60:[3, 20], Operations: ['92-89=3', '27-7=20'] Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
0.983507
hs_3
mult_heuristic
[ 45, 92, 4, 37 ]
23
[ "45-4=41", "41-37=4", "92/4=23" ]
Current State: 23:[45, 92, 4, 37], Operations: [] Exploring Operation: 45-4=41, Resulting Numbers: [92, 37, 41] Generated Node #2: [92, 37, 41] from Operation: 45-4=41 Current State: 23:[92, 37, 41], Operations: ['45-4=41'] Exploring Operation: 41-37=4, Resulting Numbers: [92, 4] Generated Node #3: [92, 4] from Operation: 41-37=4 Current State: 23:[92, 4], Operations: ['45-4=41', '41-37=4'] Exploring Operation: 92/4=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[45, 92, 4, 37], Operations: [] Exploring Operation: 92/4=23, Resulting Numbers: [45, 37, 23] Generated Node #0,0: 23:[45, 37, 23] Operation: 92/4=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[45, 37, 23], Operations: ['92/4=23'] Exploring Operation: 45-37=8, Resulting Numbers: [23, 8] Generated Node #0,0,0: 23:[23, 8] Operation: 45-37=8 Moving to Node #0,0,0 Current State: 23:[23, 8], Operations: ['92/4=23', '45-37=8'] Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,23 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
[ 50, 2, 48, 33 ]
64
[ "50-48=2", "2*33=66", "66-2=64" ]
Current State: 64:[50, 2, 48, 33], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [2, 33, 2] Generated Node #2: [2, 33, 2] from Operation: 50-48=2 Current State: 64:[2, 33, 2], Operations: ['50-48=2'] Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,64 equal: Goal Reached Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[50, 2, 48, 33], Operations: [] Exploring Operation: 48/2=24, Resulting Numbers: [50, 33, 24] Generated Node #0,0: 64:[50, 33, 24] Operation: 48/2=24 Exploring Operation: 50/2=25, Resulting Numbers: [48, 33, 25] Generated Node #0,1: 64:[48, 33, 25] Operation: 50/2=25 Exploring Operation: 50-33=17, Resulting Numbers: [2, 48, 17] Generated Node #0,2: 64:[2, 48, 17] Operation: 50-33=17 Exploring Operation: 48-33=15, Resulting Numbers: [50, 2, 15] Generated Node #0,3: 64:[50, 2, 15] Operation: 48-33=15 Exploring Operation: 50-48=2, Resulting Numbers: [2, 33, 2] Generated Node #0,4: 64:[2, 33, 2] Operation: 50-48=2 Moving to Node #0,4 Current State: 64:[2, 33, 2], Operations: ['50-48=2'] Exploring Operation: 2+2=4, Resulting Numbers: [33, 4] Generated Node #0,4,0: 64:[33, 4] Operation: 2+2=4 Exploring Operation: 2*33=66, Resulting Numbers: [2, 66] Generated Node #0,4,1: 64:[2, 66] Operation: 2*33=66 Exploring Operation: 33-2=31, Resulting Numbers: [2, 31] Generated Node #0,4,2: 64:[2, 31] Operation: 33-2=31 Exploring Operation: 33-2=31, Resulting Numbers: [2, 31] Generated Node #0,4,3: 64:[2, 31] Operation: 33-2=31 Exploring Operation: 2*2=4, Resulting Numbers: [33, 4] Generated Node #0,4,4: 64:[33, 4] Operation: 2*2=4 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 64:[33, 4], Operations: ['50-48=2', '2+2=4'] Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,64 unequal: No Solution Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,64 unequal: No Solution Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 64:[2, 31], Operations: ['50-48=2', '33-2=31'] Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,64 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,64 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 64:[2, 31], Operations: ['50-48=2', '33-2=31'] Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,64 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,64 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 64:[33, 4], Operations: ['50-48=2', '2*2=4'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,64 unequal: No Solution Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,64 unequal: No Solution Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 64:[2, 66], Operations: ['50-48=2', '2*33=66'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,64 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[50, 2, 48, 33], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [2, 33, 2] Generated Node #0,4: 64:[2, 33, 2] Operation: 50-48=2 Moving to Node #0,4 Current State: 64:[2, 33, 2], Operations: ['50-48=2'] Exploring Operation: 2*33=66, Resulting Numbers: [2, 66] Generated Node #0,4,1: 64:[2, 66] Operation: 2*33=66 Moving to Node #0,4,1 Current State: 64:[2, 66], Operations: ['50-48=2', '2*33=66'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_5
sum_heuristic
[ 48, 26, 96, 44 ]
31
[ "48*26=1248", "1248/96=13", "44-13=31" ]
Current State: 31:[48, 26, 96, 44], Operations: [] Exploring Operation: 48*26=1248, Resulting Numbers: [96, 44, 1248] Generated Node #2: [96, 44, 1248] from Operation: 48*26=1248 Current State: 31:[96, 44, 1248], Operations: ['48*26=1248'] Exploring Operation: 1248/96=13, Resulting Numbers: [44, 13] Generated Node #3: [44, 13] from Operation: 1248/96=13 Current State: 31:[44, 13], Operations: ['48*26=1248', '1248/96=13'] Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[48, 26, 96, 44], Operations: [] Exploring Operation: 96-48=48, Resulting Numbers: [26, 44, 48] Generated Node #0,0: 31:[26, 44, 48] Operation: 96-48=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[26, 44, 48], Operations: ['96-48=48'] Exploring Operation: 48-26=22, Resulting Numbers: [44, 22] Generated Node #0,0,0: 31:[44, 22] Operation: 48-26=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[44, 22], Operations: ['96-48=48', '48-26=22'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,31 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
[ 68, 97, 52, 32 ]
61
[ "97*32=3104", "68+3104=3172", "3172/52=61" ]
Current State: 61:[68, 97, 52, 32], Operations: [] Exploring Operation: 97*32=3104, Resulting Numbers: [68, 52, 3104] Generated Node #2: [68, 52, 3104] from Operation: 97*32=3104 Current State: 61:[68, 52, 3104], Operations: ['97*32=3104'] Exploring Operation: 68+3104=3172, Resulting Numbers: [52, 3172] Generated Node #3: [52, 3172] from Operation: 68+3104=3172 Current State: 61:[52, 3172], Operations: ['97*32=3104', '68+3104=3172'] Exploring Operation: 3172/52=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[68, 97, 52, 32], Operations: [] Exploring Operation: 97-32=65, Resulting Numbers: [68, 52, 65] Generated Node #0,0: 61:[68, 52, 65] Operation: 97-32=65 Exploring Operation: 52+32=84, Resulting Numbers: [68, 97, 84] Generated Node #0,1: 61:[68, 97, 84] Operation: 52+32=84 Exploring Operation: 97-52=45, Resulting Numbers: [68, 32, 45] Generated Node #0,2: 61:[68, 32, 45] Operation: 97-52=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[68, 52, 65], Operations: ['97-32=65'] Exploring Operation: 68+52=120, Resulting Numbers: [65, 120] Generated Node #0,0,0: 61:[65, 120] Operation: 68+52=120 Exploring Operation: 68-52=16, Resulting Numbers: [65, 16] Generated Node #0,0,1: 61:[65, 16] Operation: 68-52=16 Exploring Operation: 65-52=13, Resulting Numbers: [68, 13] Generated Node #0,0,2: 61:[68, 13] Operation: 65-52=13 Moving to Node #0,0,1 Current State: 61:[65, 16], Operations: ['97-32=65', '68-52=16'] Exploring Operation: 65+16=81, Resulting Numbers: [81] 81,61 unequal: No Solution Exploring Operation: 65*16=1040, Resulting Numbers: [1040] 1040,61 unequal: No Solution Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[68, 13], Operations: ['97-32=65', '65-52=13'] Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,61 unequal: No Solution Exploring Operation: 68*13=884, Resulting Numbers: [884] 884,61 unequal: No Solution Exploring Operation: 68+13=81, Resulting Numbers: [81] 81,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[65, 120], Operations: ['97-32=65', '68+52=120'] Exploring Operation: 65*120=7800, Resulting Numbers: [7800] 7800,61 unequal: No Solution Exploring Operation: 65+120=185, Resulting Numbers: [185] 185,61 unequal: No Solution Exploring Operation: 120-65=55, Resulting Numbers: [55] 55,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[68, 32, 45], Operations: ['97-52=45'] Exploring Operation: 32+45=77, Resulting Numbers: [68, 77] Generated Node #0,2,0: 61:[68, 77] Operation: 32+45=77 Exploring Operation: 68+32=100, Resulting Numbers: [45, 100] Generated Node #0,2,1: 61:[45, 100] Operation: 68+32=100 Exploring Operation: 68-32=36, Resulting Numbers: [45, 36] Generated Node #0,2,2: 61:[45, 36] Operation: 68-32=36 Moving to Node #0,2,0 Current State: 61:[68, 77], Operations: ['97-52=45', '32+45=77'] Exploring Operation: 68*77=5236, Resulting Numbers: [5236] 5236,61 unequal: No Solution Exploring Operation: 77-68=9, Resulting Numbers: [9] 9,61 unequal: No Solution Exploring Operation: 68+77=145, Resulting Numbers: [145] 145,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[45, 36], Operations: ['97-52=45', '68-32=36'] Exploring Operation: 45*36=1620, Resulting Numbers: [1620] 1620,61 unequal: No Solution Exploring Operation: 45-36=9, Resulting Numbers: [9] 9,61 unequal: No Solution Exploring Operation: 45+36=81, Resulting Numbers: [81] 81,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[45, 100], Operations: ['97-52=45', '68+32=100'] Exploring Operation: 45*100=4500, Resulting Numbers: [4500] 4500,61 unequal: No Solution Exploring Operation: 100-45=55, Resulting Numbers: [55] 55,61 unequal: No Solution Exploring Operation: 45+100=145, Resulting Numbers: [145] 145,61 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 Current State: 61:[68, 97, 84], Operations: ['52+32=84'] Exploring Operation: 84-68=16, Resulting Numbers: [97, 16] Generated Node #0,1,0: 61:[97, 16] Operation: 84-68=16 Exploring Operation: 97-84=13, Resulting Numbers: [68, 13] Generated Node #0,1,1: 61:[68, 13] Operation: 97-84=13 Exploring Operation: 97-68=29, Resulting Numbers: [84, 29] Generated Node #0,1,2: 61:[84, 29] Operation: 97-68=29 Moving to Node #0,1,1 Current State: 61:[68, 13], Operations: ['52+32=84', '97-84=13'] Exploring Operation: 68*13=884, Resulting Numbers: [884] 884,61 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,61 unequal: No Solution Exploring Operation: 68+13=81, Resulting Numbers: [81] 81,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[84, 29], Operations: ['52+32=84', '97-68=29'] Exploring Operation: 84-29=55, Resulting Numbers: [55] 55,61 unequal: No Solution Exploring Operation: 84+29=113, Resulting Numbers: [113] 113,61 unequal: No Solution Exploring Operation: 84*29=2436, Resulting Numbers: [2436] 2436,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[97, 16], Operations: ['52+32=84', '84-68=16'] Exploring Operation: 97-16=81, Resulting Numbers: [81] 81,61 unequal: No Solution Exploring Operation: 97+16=113, Resulting Numbers: [113] 113,61 unequal: No Solution Exploring Operation: 97*16=1552, Resulting Numbers: [1552] 1552,61 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
[ 75, 45, 45, 45 ]
73
[ "45+45=90", "90/45=2", "75-2=73" ]
Current State: 73:[75, 45, 45, 45], Operations: [] Exploring Operation: 45+45=90, Resulting Numbers: [75, 90] Generated Node #2: [75, 90] from Operation: 45+45=90 Current State: 73:[75, 90], Operations: ['45+45=90'] Exploring Operation: 90/45=2, Resulting Numbers: [75, 2] Generated Node #3: [75, 2] from Operation: 90/45=2 Current State: 73:[75, 2], Operations: ['45+45=90', '90/45=2'] Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[75, 45, 45, 45], Operations: [] Exploring Operation: 45+45=90, Resulting Numbers: [75, 45, 90] Generated Node #0,0: 73:[75, 45, 90] Operation: 45+45=90 Moving to Node #0,0 Current State: 73:[75, 45, 90], Operations: ['45+45=90'] Exploring Operation: 90-45=45, Resulting Numbers: [75, 45] Generated Node #0,0,0: 73:[75, 45] Operation: 90-45=45 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[75, 45], Operations: ['45+45=90', '90-45=45'] Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 87, 88, 73, 32 ]
42
[ "88-87=1", "73-32=41", "1+41=42" ]
Current State: 42:[87, 88, 73, 32], Operations: [] Exploring Operation: 88-87=1, Resulting Numbers: [73, 32, 1] Generated Node #2: [73, 32, 1] from Operation: 88-87=1 Current State: 42:[73, 32, 1], Operations: ['88-87=1'] Exploring Operation: 73-32=41, Resulting Numbers: [1, 41] Generated Node #3: [1, 41] from Operation: 73-32=41 Current State: 42:[1, 41], Operations: ['88-87=1', '73-32=41'] Exploring Operation: 1+41=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[87, 88, 73, 32], Operations: [] Exploring Operation: 88-73=15, Resulting Numbers: [87, 32, 15] Generated Node #0,0: 42:[87, 32, 15] Operation: 88-73=15 Exploring Operation: 88-87=1, Resulting Numbers: [73, 32, 1] Generated Node #0,1: 42:[73, 32, 1] Operation: 88-87=1 Exploring Operation: 87-32=55, Resulting Numbers: [88, 73, 55] Generated Node #0,2: 42:[88, 73, 55] Operation: 87-32=55 Exploring Operation: 87-73=14, Resulting Numbers: [88, 32, 14] Generated Node #0,3: 42:[88, 32, 14] Operation: 87-73=14 Moving to Node #0,1 Current State: 42:[73, 32, 1], Operations: ['88-87=1'] Exploring Operation: 73*1=73, Resulting Numbers: [32, 73] Generated Node #0,1,0: 42:[32, 73] Operation: 73*1=73 Exploring Operation: 73-1=72, Resulting Numbers: [32, 72] Generated Node #0,1,1: 42:[32, 72] Operation: 73-1=72 Exploring Operation: 73-32=41, Resulting Numbers: [1, 41] Generated Node #0,1,2: 42:[1, 41] Operation: 73-32=41 Exploring Operation: 32+1=33, Resulting Numbers: [73, 33] Generated Node #0,1,3: 42:[73, 33] Operation: 32+1=33 Moving to Node #0,3 Current State: 42:[88, 32, 14], Operations: ['87-73=14'] Exploring Operation: 88-14=74, Resulting Numbers: [32, 74] Generated Node #0,3,0: 42:[32, 74] Operation: 88-14=74 Exploring Operation: 88-32=56, Resulting Numbers: [14, 56] Generated Node #0,3,1: 42:[14, 56] Operation: 88-32=56 Exploring Operation: 32-14=18, Resulting Numbers: [88, 18] Generated Node #0,3,2: 42:[88, 18] Operation: 32-14=18 Exploring Operation: 32+14=46, Resulting Numbers: [88, 46] Generated Node #0,3,3: 42:[88, 46] Operation: 32+14=46 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 42:[14, 56], Operations: ['87-73=14', '88-32=56'] Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 14*56=784, Resulting Numbers: [784] 784,42 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[87, 88, 73, 32], Operations: [] Exploring Operation: 87-73=14, Resulting Numbers: [88, 32, 14] Generated Node #0,3: 42:[88, 32, 14] Operation: 87-73=14 Moving to Node #0,3 Current State: 42:[88, 32, 14], Operations: ['87-73=14'] Exploring Operation: 88-32=56, Resulting Numbers: [14, 56] Generated Node #0,3,1: 42:[14, 56] Operation: 88-32=56 Moving to Node #0,3,1 Current State: 42:[14, 56], Operations: ['87-73=14', '88-32=56'] Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 1, 22, 68, 66 ]
46
[ "1+22=23", "68-66=2", "23*2=46" ]
Current State: 46:[1, 22, 68, 66], Operations: [] Exploring Operation: 1+22=23, Resulting Numbers: [68, 66, 23] Generated Node #2: [68, 66, 23] from Operation: 1+22=23 Current State: 46:[68, 66, 23], Operations: ['1+22=23'] Exploring Operation: 68-66=2, Resulting Numbers: [23, 2] Generated Node #3: [23, 2] from Operation: 68-66=2 Current State: 46:[23, 2], Operations: ['1+22=23', '68-66=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[1, 22, 68, 66], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [1, 22, 2] Generated Node #0,0: 46:[1, 22, 2] Operation: 68-66=2 Moving to Node #0,0 Current State: 46:[1, 22, 2], Operations: ['68-66=2'] Exploring Operation: 1+22=23, Resulting Numbers: [2, 23] Generated Node #0,0,0: 46:[2, 23] Operation: 1+22=23 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 46:[2, 23], Operations: ['68-66=2', '1+22=23'] Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[1, 22, 68, 66], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [1, 22, 2] Generated Node #0,0: 46:[1, 22, 2] Operation: 68-66=2 Moving to Node #0,0 Current State: 46:[1, 22, 2], Operations: ['68-66=2'] Exploring Operation: 1+22=23, Resulting Numbers: [2, 23] Generated Node #0,0,0: 46:[2, 23] Operation: 1+22=23 Moving to Node #0,0,0 Current State: 46:[2, 23], Operations: ['68-66=2', '1+22=23'] Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 23, 94, 47, 69 ]
94
[ "94-23=71", "71-69=2", "47*2=94" ]
Current State: 94:[23, 94, 47, 69], Operations: [] Exploring Operation: 94-23=71, Resulting Numbers: [47, 69, 71] Generated Node #2: [47, 69, 71] from Operation: 94-23=71 Current State: 94:[47, 69, 71], Operations: ['94-23=71'] Exploring Operation: 71-69=2, Resulting Numbers: [47, 2] Generated Node #3: [47, 2] from Operation: 71-69=2 Current State: 94:[47, 2], Operations: ['94-23=71', '71-69=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[23, 94, 47, 69], Operations: [] Exploring Operation: 69-23=46, Resulting Numbers: [94, 47, 46] Generated Node #0,0: 94:[94, 47, 46] Operation: 69-23=46 Exploring Operation: 69/23=3, Resulting Numbers: [94, 47, 3] Generated Node #0,1: 94:[94, 47, 3] Operation: 69/23=3 Moving to Node #0,0 Current State: 94:[94, 47, 46], Operations: ['69-23=46'] Exploring Operation: 94-47=47, Resulting Numbers: [46, 47] Generated Node #0,0,0: 94:[46, 47] Operation: 94-47=47 Exploring Operation: 94/47=2, Resulting Numbers: [46, 2] Generated Node #0,0,1: 94:[46, 2] Operation: 94/47=2 Moving to Node #0,1 Current State: 94:[94, 47, 3], Operations: ['69/23=3'] Exploring Operation: 94-47=47, Resulting Numbers: [3, 47] Generated Node #0,1,0: 94:[3, 47] Operation: 94-47=47 Exploring Operation: 94/47=2, Resulting Numbers: [3, 2] Generated Node #0,1,1: 94:[3, 2] Operation: 94/47=2 Moving to Node #0,0,0 Current State: 94:[46, 47], Operations: ['69-23=46', '94-47=47'] Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 46+47=93, Resulting Numbers: [93] 93,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[3, 47], Operations: ['69/23=3', '94-47=47'] Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[46, 2], Operations: ['69-23=46', '94/47=2'] Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,94 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[3, 2], Operations: ['69/23=3', '94/47=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,94 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 69, 2, 94, 12 ]
61
[ "2+94=96", "96/12=8", "69-8=61" ]
Current State: 61:[69, 2, 94, 12], Operations: [] Exploring Operation: 2+94=96, Resulting Numbers: [69, 12, 96] Generated Node #2: [69, 12, 96] from Operation: 2+94=96 Current State: 61:[69, 12, 96], Operations: ['2+94=96'] Exploring Operation: 96/12=8, Resulting Numbers: [69, 8] Generated Node #3: [69, 8] from Operation: 96/12=8 Current State: 61:[69, 8], Operations: ['2+94=96', '96/12=8'] Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[69, 2, 94, 12], Operations: [] Exploring Operation: 94/2=47, Resulting Numbers: [69, 12, 47] Generated Node #0,0: 61:[69, 12, 47] Operation: 94/2=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[69, 12, 47], Operations: ['94/2=47'] Exploring Operation: 12+47=59, Resulting Numbers: [69, 59] Generated Node #0,0,0: 61:[69, 59] Operation: 12+47=59 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[69, 59], Operations: ['94/2=47', '12+47=59'] Exploring Operation: 69-59=10, Resulting Numbers: [10] 10,61 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
[ 14, 97, 5, 89 ]
78
[ "14*5=70", "97-89=8", "70+8=78" ]
Current State: 78:[14, 97, 5, 89], Operations: [] Exploring Operation: 14*5=70, Resulting Numbers: [97, 89, 70] Generated Node #2: [97, 89, 70] from Operation: 14*5=70 Current State: 78:[97, 89, 70], Operations: ['14*5=70'] Exploring Operation: 97-89=8, Resulting Numbers: [70, 8] Generated Node #3: [70, 8] from Operation: 97-89=8 Current State: 78:[70, 8], Operations: ['14*5=70', '97-89=8'] Exploring Operation: 70+8=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[14, 97, 5, 89], Operations: [] Exploring Operation: 89-5=84, Resulting Numbers: [14, 97, 84] Generated Node #0,0: 78:[14, 97, 84] Operation: 89-5=84 Exploring Operation: 89-14=75, Resulting Numbers: [97, 5, 75] Generated Node #0,1: 78:[97, 5, 75] Operation: 89-14=75 Exploring Operation: 97-14=83, Resulting Numbers: [5, 89, 83] Generated Node #0,2: 78:[5, 89, 83] Operation: 97-14=83 Exploring Operation: 97-5=92, Resulting Numbers: [14, 89, 92] Generated Node #0,3: 78:[14, 89, 92] Operation: 97-5=92 Exploring Operation: 97-89=8, Resulting Numbers: [14, 5, 8] Generated Node #0,4: 78:[14, 5, 8] Operation: 97-89=8 Moving to Node #0,4 Current State: 78:[14, 5, 8], Operations: ['97-89=8'] Exploring Operation: 14-5=9, Resulting Numbers: [8, 9] Generated Node #0,4,0: 78:[8, 9] Operation: 14-5=9 Exploring Operation: 14-8=6, Resulting Numbers: [5, 6] Generated Node #0,4,1: 78:[5, 6] Operation: 14-8=6 Exploring Operation: 8-5=3, Resulting Numbers: [14, 3] Generated Node #0,4,2: 78:[14, 3] Operation: 8-5=3 Exploring Operation: 5*8=40, Resulting Numbers: [14, 40] Generated Node #0,4,3: 78:[14, 40] Operation: 5*8=40 Exploring Operation: 5+8=13, Resulting Numbers: [14, 13] Generated Node #0,4,4: 78:[14, 13] Operation: 5+8=13 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 78:[5, 6], Operations: ['97-89=8', '14-8=6'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 78:[14, 3], Operations: ['97-89=8', '8-5=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 78:[14, 13], Operations: ['97-89=8', '5+8=13'] Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,78 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 78:[14, 40], Operations: ['97-89=8', '5*8=40'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 14+40=54, Resulting Numbers: [54] 54,78 unequal: No Solution Exploring Operation: 14*40=560, Resulting Numbers: [560] 560,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 78:[8, 9], Operations: ['97-89=8', '14-5=9'] Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,78 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: 78:[5, 89, 83], Operations: ['97-14=83'] Exploring Operation: 89-5=84, Resulting Numbers: [83, 84] Generated Node #0,2,0: 78:[83, 84] Operation: 89-5=84 Exploring Operation: 5+89=94, Resulting Numbers: [83, 94] Generated Node #0,2,1: 78:[83, 94] Operation: 5+89=94 Exploring Operation: 89-83=6, Resulting Numbers: [5, 6] Generated Node #0,2,2: 78:[5, 6] Operation: 89-83=6 Exploring Operation: 5+83=88, Resulting Numbers: [89, 88] Generated Node #0,2,3: 78:[89, 88] Operation: 5+83=88 Exploring Operation: 83-5=78, Resulting Numbers: [89, 78] Generated Node #0,2,4: 78:[89, 78] Operation: 83-5=78 Moving to Node #0,1 Current State: 78:[97, 5, 75], Operations: ['89-14=75'] Exploring Operation: 97+5=102, Resulting Numbers: [75, 102] Generated Node #0,1,0: 78:[75, 102] Operation: 97+5=102 Exploring Operation: 5+75=80, Resulting Numbers: [97, 80] Generated Node #0,1,1: 78:[97, 80] Operation: 5+75=80 Exploring Operation: 97-5=92, Resulting Numbers: [75, 92] Generated Node #0,1,2: 78:[75, 92] Operation: 97-5=92 Exploring Operation: 97-75=22, Resulting Numbers: [5, 22] Generated Node #0,1,3: 78:[5, 22] Operation: 97-75=22 Exploring Operation: 75/5=15, Resulting Numbers: [97, 15] Generated Node #0,1,4: 78:[97, 15] Operation: 75/5=15 Moving to Node #0,0 Current State: 78:[14, 97, 84], Operations: ['89-5=84'] Exploring Operation: 14+97=111, Resulting Numbers: [84, 111] Generated Node #0,0,0: 78:[84, 111] Operation: 14+97=111 Exploring Operation: 84-14=70, Resulting Numbers: [97, 70] Generated Node #0,0,1: 78:[97, 70] Operation: 84-14=70 Exploring Operation: 97-14=83, Resulting Numbers: [84, 83] Generated Node #0,0,2: 78:[84, 83] Operation: 97-14=83 Exploring Operation: 84/14=6, Resulting Numbers: [97, 6] Generated Node #0,0,3: 78:[97, 6] Operation: 84/14=6 Exploring Operation: 97-84=13, Resulting Numbers: [14, 13] Generated Node #0,0,4: 78:[14, 13] Operation: 97-84=13 Moving to Node #0,3 Current State: 78:[14, 89, 92], Operations: ['97-5=92'] Exploring Operation: 14+89=103, Resulting Numbers: [92, 103] Generated Node #0,3,0: 78:[92, 103] Operation: 14+89=103 Exploring Operation: 92-89=3, Resulting Numbers: [14, 3] Generated Node #0,3,1: 78:[14, 3] Operation: 92-89=3 Exploring Operation: 89-14=75, Resulting Numbers: [92, 75] Generated Node #0,3,2: 78:[92, 75] Operation: 89-14=75 Exploring Operation: 14+92=106, Resulting Numbers: [89, 106] Generated Node #0,3,3: 78:[89, 106] Operation: 14+92=106 Exploring Operation: 92-14=78, Resulting Numbers: [89, 78] Generated Node #0,3,4: 78:[89, 78] Operation: 92-14=78 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 78:[14, 3], Operations: ['97-5=92', '92-89=3'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,78 unequal: No Solution Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 78:[89, 78], Operations: ['97-5=92', '92-14=78'] Exploring Operation: 89-78=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 89+78=167, Resulting Numbers: [167] 167,78 unequal: No Solution Exploring Operation: 89*78=6942, Resulting Numbers: [6942] 6942,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 78:[92, 75], Operations: ['97-5=92', '89-14=75'] Exploring Operation: 92-75=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 92+75=167, Resulting Numbers: [167] 167,78 unequal: No Solution Exploring Operation: 92*75=6900, Resulting Numbers: [6900] 6900,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 78:[92, 103], Operations: ['97-5=92', '14+89=103'] Exploring Operation: 92*103=9476, Resulting Numbers: [9476] 9476,78 unequal: No Solution Exploring Operation: 103-92=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 92+103=195, Resulting Numbers: [195] 195,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 78:[89, 106], Operations: ['97-5=92', '14+92=106'] Exploring Operation: 106-89=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 89*106=9434, Resulting Numbers: [9434] 9434,78 unequal: No Solution Exploring Operation: 89+106=195, Resulting Numbers: [195] 195,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 78:[5, 6], Operations: ['97-14=83', '89-83=6'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,78 unequal: No Solution Moving to Node #0,0,4 Current State: 78:[14, 13], Operations: ['89-5=84', '97-84=13'] Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,78 unequal: No Solution Moving to Node #0,1,3 Current State: 78:[5, 22], Operations: ['89-14=75', '97-75=22'] Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,78 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,78 unequal: No Solution Moving to Node #0,2,4 Current State: 78:[89, 78], Operations: ['97-14=83', '83-5=78'] Exploring Operation: 89-78=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 89*78=6942, Resulting Numbers: [6942] 6942,78 unequal: No Solution Exploring Operation: 89+78=167, Resulting Numbers: [167] 167,78 unequal: No Solution Moving to Node #0,0,2 Current State: 78:[84, 83], Operations: ['89-5=84', '97-14=83'] Exploring Operation: 84+83=167, Resulting Numbers: [167] 167,78 unequal: No Solution Exploring Operation: 84-83=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 84*83=6972, Resulting Numbers: [6972] 6972,78 unequal: No Solution Moving to Node #0,2,0 Current State: 78:[83, 84], Operations: ['97-14=83', '89-5=84'] Exploring Operation: 83+84=167, Resulting Numbers: [167] 167,78 unequal: No Solution Exploring Operation: 83*84=6972, Resulting Numbers: [6972] 6972,78 unequal: No Solution Exploring Operation: 84-83=1, Resulting Numbers: [1] 1,78 unequal: No Solution Moving to Node #0,1,2 Current State: 78:[75, 92], Operations: ['89-14=75', '97-5=92'] Exploring Operation: 92-75=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 75+92=167, Resulting Numbers: [167] 167,78 unequal: No Solution Exploring Operation: 75*92=6900, Resulting Numbers: [6900] 6900,78 unequal: No Solution Moving to Node #0,0,3 Current State: 78:[97, 6], Operations: ['89-5=84', '84/14=6'] Exploring Operation: 97+6=103, Resulting Numbers: [103] 103,78 unequal: No Solution Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,78 unequal: No Solution Exploring Operation: 97*6=582, Resulting Numbers: [582] 582,78 unequal: No Solution Moving to Node #0,1,4 Current State: 78:[97, 15], Operations: ['89-14=75', '75/5=15'] Exploring Operation: 97*15=1455, Resulting Numbers: [1455] 1455,78 unequal: No Solution Exploring Operation: 97-15=82, Resulting Numbers: [82] 82,78 unequal: No Solution Exploring Operation: 97+15=112, Resulting Numbers: [112] 112,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[97, 80], Operations: ['89-14=75', '5+75=80'] Exploring Operation: 97-80=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 97*80=7760, Resulting Numbers: [7760] 7760,78 unequal: No Solution Exploring Operation: 97+80=177, Resulting Numbers: [177] 177,78 unequal: No Solution Moving to Node #0,2,3 Current State: 78:[89, 88], Operations: ['97-14=83', '5+83=88'] Exploring Operation: 89*88=7832, Resulting Numbers: [7832] 7832,78 unequal: No Solution Exploring Operation: 89+88=177, Resulting Numbers: [177] 177,78 unequal: No Solution Exploring Operation: 89-88=1, Resulting Numbers: [1] 1,78 unequal: No Solution Moving to Node #0,2,1 Current State: 78:[83, 94], Operations: ['97-14=83', '5+89=94'] Exploring Operation: 83+94=177, Resulting Numbers: [177] 177,78 unequal: No Solution Exploring Operation: 94-83=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 83*94=7802, Resulting Numbers: [7802] 7802,78 unequal: No Solution Moving to Node #0,0,1 Current State: 78:[97, 70], Operations: ['89-5=84', '84-14=70'] Exploring Operation: 97*70=6790, Resulting Numbers: [6790] 6790,78 unequal: No Solution Exploring Operation: 97-70=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 97+70=167, Resulting Numbers: [167] 167,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[75, 102], Operations: ['89-14=75', '97+5=102'] Exploring Operation: 75*102=7650, Resulting Numbers: [7650] 7650,78 unequal: No Solution Exploring Operation: 75+102=177, Resulting Numbers: [177] 177,78 unequal: No Solution Exploring Operation: 102-75=27, Resulting Numbers: [27] 27,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[84, 111], Operations: ['89-5=84', '14+97=111'] Exploring Operation: 111-84=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 84*111=9324, Resulting Numbers: [9324] 9324,78 unequal: No Solution Exploring Operation: 84+111=195, Resulting Numbers: [195] 195,78 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 48, 69, 52, 56 ]
81
[ "56-52=4", "48/4=12", "69+12=81" ]
Current State: 81:[48, 69, 52, 56], Operations: [] Exploring Operation: 56-52=4, Resulting Numbers: [48, 69, 4] Generated Node #2: [48, 69, 4] from Operation: 56-52=4 Current State: 81:[48, 69, 4], Operations: ['56-52=4'] Exploring Operation: 48/4=12, Resulting Numbers: [69, 12] Generated Node #3: [69, 12] from Operation: 48/4=12 Current State: 81:[69, 12], Operations: ['56-52=4', '48/4=12'] Exploring Operation: 69+12=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[48, 69, 52, 56], Operations: [] Exploring Operation: 56-48=8, Resulting Numbers: [69, 52, 8] Generated Node #0,0: 81:[69, 52, 8] Operation: 56-48=8 Exploring Operation: 56-52=4, Resulting Numbers: [48, 69, 4] Generated Node #0,1: 81:[48, 69, 4] Operation: 56-52=4 Exploring Operation: 52-48=4, Resulting Numbers: [69, 56, 4] Generated Node #0,2: 81:[69, 56, 4] Operation: 52-48=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[48, 69, 4], Operations: ['56-52=4'] Exploring Operation: 48-4=44, Resulting Numbers: [69, 44] Generated Node #0,1,0: 81:[69, 44] Operation: 48-4=44 Exploring Operation: 69-48=21, Resulting Numbers: [4, 21] Generated Node #0,1,1: 81:[4, 21] Operation: 69-48=21 Exploring Operation: 48/4=12, Resulting Numbers: [69, 12] Generated Node #0,1,2: 81:[69, 12] Operation: 48/4=12 Moving to Node #0,1,1 Current State: 81:[4, 21], Operations: ['56-52=4', '69-48=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,81 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,81 unequal: No Solution Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,81 unequal: No Solution Moving to Node #0,1,2 Current State: 81:[69, 12], Operations: ['56-52=4', '48/4=12'] Exploring Operation: 69+12=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[48, 69, 52, 56], Operations: [] Exploring Operation: 56-52=4, Resulting Numbers: [48, 69, 4] Generated Node #0,1: 81:[48, 69, 4] Operation: 56-52=4 Moving to Node #0,1 Current State: 81:[48, 69, 4], Operations: ['56-52=4'] Exploring Operation: 48/4=12, Resulting Numbers: [69, 12] Generated Node #0,1,2: 81:[69, 12] Operation: 48/4=12 Moving to Node #0,1,2 Current State: 81:[69, 12], Operations: ['56-52=4', '48/4=12'] Exploring Operation: 69+12=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 70, 35, 2, 42 ]
86
[ "70/35=2", "2*42=84", "2+84=86" ]
Current State: 86:[70, 35, 2, 42], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [2, 42, 2] Generated Node #2: [2, 42, 2] from Operation: 70/35=2 Current State: 86:[2, 42, 2], Operations: ['70/35=2'] Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,86 equal: Goal Reached Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[70, 35, 2, 42], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [2, 42, 2] Generated Node #0,0: 86:[2, 42, 2] Operation: 70/35=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[2, 42, 2], Operations: ['70/35=2'] Exploring Operation: 2+42=44, Resulting Numbers: [2, 44] Generated Node #0,0,0: 86:[2, 44] Operation: 2+42=44 Moving to Node #0,0,0 Current State: 86:[2, 44], Operations: ['70/35=2', '2+42=44'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,86 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
[ 95, 77, 42, 88 ]
42
[ "95+77=172", "42+88=130", "172-130=42" ]
Current State: 42:[95, 77, 42, 88], Operations: [] Exploring Operation: 95+77=172, Resulting Numbers: [42, 88, 172] Generated Node #2: [42, 88, 172] from Operation: 95+77=172 Current State: 42:[42, 88, 172], Operations: ['95+77=172'] Exploring Operation: 42+88=130, Resulting Numbers: [172, 130] Generated Node #3: [172, 130] from Operation: 42+88=130 Current State: 42:[172, 130], Operations: ['95+77=172', '42+88=130'] Exploring Operation: 172-130=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[95, 77, 42, 88], Operations: [] Exploring Operation: 88-42=46, Resulting Numbers: [95, 77, 46] Generated Node #0,0: 42:[95, 77, 46] Operation: 88-42=46 Exploring Operation: 95-88=7, Resulting Numbers: [77, 42, 7] Generated Node #0,1: 42:[77, 42, 7] Operation: 95-88=7 Exploring Operation: 95-77=18, Resulting Numbers: [42, 88, 18] Generated Node #0,2: 42:[42, 88, 18] Operation: 95-77=18 Exploring Operation: 88-77=11, Resulting Numbers: [95, 42, 11] Generated Node #0,3: 42:[95, 42, 11] Operation: 88-77=11 Exploring Operation: 95-42=53, Resulting Numbers: [77, 88, 53] Generated Node #0,4: 42:[77, 88, 53] Operation: 95-42=53 Moving to Node #0,1 Current State: 42:[77, 42, 7], Operations: ['95-88=7'] Exploring Operation: 77-7=70, Resulting Numbers: [42, 70] Generated Node #0,1,0: 42:[42, 70] Operation: 77-7=70 Exploring Operation: 77/7=11, Resulting Numbers: [42, 11] Generated Node #0,1,1: 42:[42, 11] Operation: 77/7=11 Exploring Operation: 42/7=6, Resulting Numbers: [77, 6] Generated Node #0,1,2: 42:[77, 6] Operation: 42/7=6 Exploring Operation: 77+7=84, Resulting Numbers: [42, 84] Generated Node #0,1,3: 42:[42, 84] Operation: 77+7=84 Exploring Operation: 77-42=35, Resulting Numbers: [7, 35] Generated Node #0,1,4: 42:[7, 35] Operation: 77-42=35 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 42:[42, 11], Operations: ['95-88=7', '77/7=11'] Exploring Operation: 42+11=53, Resulting Numbers: [53] 53,42 unequal: No Solution Exploring Operation: 42*11=462, Resulting Numbers: [462] 462,42 unequal: No Solution Exploring Operation: 42-11=31, Resulting Numbers: [31] 31,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 42:[7, 35], Operations: ['95-88=7', '77-42=35'] Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[95, 77, 42, 88], Operations: [] Exploring Operation: 95-88=7, Resulting Numbers: [77, 42, 7] Generated Node #0,1: 42:[77, 42, 7] Operation: 95-88=7 Moving to Node #0,1 Current State: 42:[77, 42, 7], Operations: ['95-88=7'] Exploring Operation: 77-42=35, Resulting Numbers: [7, 35] Generated Node #0,1,4: 42:[7, 35] Operation: 77-42=35 Moving to Node #0,1,4 Current State: 42:[7, 35], Operations: ['95-88=7', '77-42=35'] Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 3, 11, 23, 6 ]
75
[ "23-11=12", "6*12=72", "3+72=75" ]
Current State: 75:[3, 11, 23, 6], Operations: [] Exploring Operation: 23-11=12, Resulting Numbers: [3, 6, 12] Generated Node #2: [3, 6, 12] from Operation: 23-11=12 Current State: 75:[3, 6, 12], Operations: ['23-11=12'] Exploring Operation: 6*12=72, Resulting Numbers: [3, 72] Generated Node #3: [3, 72] from Operation: 6*12=72 Current State: 75:[3, 72], Operations: ['23-11=12', '6*12=72'] Exploring Operation: 3+72=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[3, 11, 23, 6], Operations: [] Exploring Operation: 11+6=17, Resulting Numbers: [3, 23, 17] Generated Node #0,0: 75:[3, 23, 17] Operation: 11+6=17 Exploring Operation: 23-11=12, Resulting Numbers: [3, 6, 12] Generated Node #0,1: 75:[3, 6, 12] Operation: 23-11=12 Exploring Operation: 11-6=5, Resulting Numbers: [3, 23, 5] Generated Node #0,2: 75:[3, 23, 5] Operation: 11-6=5 Exploring Operation: 3+11=14, Resulting Numbers: [23, 6, 14] Generated Node #0,3: 75:[23, 6, 14] Operation: 3+11=14 Moving to Node #0,2 Current State: 75:[3, 23, 5], Operations: ['11-6=5'] Exploring Operation: 5-3=2, Resulting Numbers: [23, 2] Generated Node #0,2,0: 75:[23, 2] Operation: 5-3=2 Exploring Operation: 3*5=15, Resulting Numbers: [23, 15] Generated Node #0,2,1: 75:[23, 15] Operation: 3*5=15 Exploring Operation: 3+23=26, Resulting Numbers: [5, 26] Generated Node #0,2,2: 75:[5, 26] Operation: 3+23=26 Exploring Operation: 23+5=28, Resulting Numbers: [3, 28] Generated Node #0,2,3: 75:[3, 28] Operation: 23+5=28 Moving to Node #0,1 Current State: 75:[3, 6, 12], Operations: ['23-11=12'] Exploring Operation: 3+12=15, Resulting Numbers: [6, 15] Generated Node #0,1,0: 75:[6, 15] Operation: 3+12=15 Exploring Operation: 12/3=4, Resulting Numbers: [6, 4] Generated Node #0,1,1: 75:[6, 4] Operation: 12/3=4 Exploring Operation: 12-6=6, Resulting Numbers: [3, 6] Generated Node #0,1,2: 75:[3, 6] Operation: 12-6=6 Exploring Operation: 12/6=2, Resulting Numbers: [3, 2] Generated Node #0,1,3: 75:[3, 2] Operation: 12/6=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 75:[6, 15], Operations: ['23-11=12', '3+12=15'] Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,75 unequal: No Solution Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,75 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,75 unequal: No Solution No 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: 75:[3, 6], Operations: ['23-11=12', '12-6=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,75 unequal: No Solution No 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: 75:[3, 2], Operations: ['23-11=12', '12/6=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,75 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,75 unequal: No Solution No 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: 75:[6, 4], Operations: ['23-11=12', '12/3=4'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,75 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,75 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: 75:[3, 23, 17], Operations: ['11+6=17'] Exploring Operation: 17-3=14, Resulting Numbers: [23, 14] Generated Node #0,0,0: 75:[23, 14] Operation: 17-3=14 Exploring Operation: 23-17=6, Resulting Numbers: [3, 6] Generated Node #0,0,1: 75:[3, 6] Operation: 23-17=6 Exploring Operation: 23-3=20, Resulting Numbers: [17, 20] Generated Node #0,0,2: 75:[17, 20] Operation: 23-3=20 Exploring Operation: 3+23=26, Resulting Numbers: [17, 26] Generated Node #0,0,3: 75:[17, 26] Operation: 3+23=26 Moving to Node #0,3 Current State: 75:[23, 6, 14], Operations: ['3+11=14'] Exploring Operation: 23-6=17, Resulting Numbers: [14, 17] Generated Node #0,3,0: 75:[14, 17] Operation: 23-6=17 Exploring Operation: 23-14=9, Resulting Numbers: [6, 9] Generated Node #0,3,1: 75:[6, 9] Operation: 23-14=9 Exploring Operation: 14-6=8, Resulting Numbers: [23, 8] Generated Node #0,3,2: 75:[23, 8] Operation: 14-6=8 Exploring Operation: 23+6=29, Resulting Numbers: [14, 29] Generated Node #0,3,3: 75:[14, 29] Operation: 23+6=29 Moving to Node #0,2,2 Current State: 75:[5, 26], Operations: ['11-6=5', '3+23=26'] Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,75 unequal: No Solution Exploring Operation: 5*26=130, Resulting Numbers: [130] 130,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[3, 6], Operations: ['11+6=17', '23-17=6'] Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,75 unequal: No Solution Moving to Node #0,2,1 Current State: 75:[23, 15], Operations: ['11-6=5', '3*5=15'] Exploring Operation: 23+15=38, Resulting Numbers: [38] 38,75 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 23*15=345, Resulting Numbers: [345] 345,75 unequal: No Solution Moving to Node #0,2,0 Current State: 75:[23, 2], Operations: ['11-6=5', '5-3=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,75 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,75 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,75 unequal: No Solution Moving to Node #0,0,3 Current State: 75:[17, 26], Operations: ['11+6=17', '3+23=26'] Exploring Operation: 17*26=442, Resulting Numbers: [442] 442,75 unequal: No Solution Exploring Operation: 17+26=43, Resulting Numbers: [43] 43,75 unequal: No Solution Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[23, 14], Operations: ['11+6=17', '17-3=14'] Exploring Operation: 23*14=322, Resulting Numbers: [322] 322,75 unequal: No Solution Exploring Operation: 23+14=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 23-14=9, Resulting Numbers: [9] 9,75 unequal: No Solution Moving to Node #0,2,3 Current State: 75:[3, 28], Operations: ['11-6=5', '23+5=28'] Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,75 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,75 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,75 unequal: No Solution Moving to Node #0,3,0 Current State: 75:[14, 17], Operations: ['3+11=14', '23-6=17'] Exploring Operation: 14*17=238, Resulting Numbers: [238] 238,75 unequal: No Solution Exploring Operation: 14+17=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,75 unequal: No Solution Moving to Node #0,3,1 Current State: 75:[6, 9], Operations: ['3+11=14', '23-14=9'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,75 unequal: No Solution Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,75 unequal: No Solution Moving to Node #0,3,3 Current State: 75:[14, 29], Operations: ['3+11=14', '23+6=29'] Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 14*29=406, Resulting Numbers: [406] 406,75 unequal: No Solution Exploring Operation: 14+29=43, Resulting Numbers: [43] 43,75 unequal: No Solution Moving to Node #0,3,2 Current State: 75:[23, 8], Operations: ['3+11=14', '14-6=8'] Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,75 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[17, 20], Operations: ['11+6=17', '23-3=20'] Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 17*20=340, Resulting Numbers: [340] 340,75 unequal: No Solution Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,75 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 95, 64, 50, 98 ]
11
[ "95+64=159", "50+98=148", "159-148=11" ]
Current State: 11:[95, 64, 50, 98], Operations: [] Exploring Operation: 95+64=159, Resulting Numbers: [50, 98, 159] Generated Node #2: [50, 98, 159] from Operation: 95+64=159 Current State: 11:[50, 98, 159], Operations: ['95+64=159'] Exploring Operation: 50+98=148, Resulting Numbers: [159, 148] Generated Node #3: [159, 148] from Operation: 50+98=148 Current State: 11:[159, 148], Operations: ['95+64=159', '50+98=148'] Exploring Operation: 159-148=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[95, 64, 50, 98], Operations: [] Exploring Operation: 98-64=34, Resulting Numbers: [95, 50, 34] Generated Node #0,0: 11:[95, 50, 34] Operation: 98-64=34 Exploring Operation: 95-50=45, Resulting Numbers: [64, 98, 45] Generated Node #0,1: 11:[64, 98, 45] Operation: 95-50=45 Exploring Operation: 95-64=31, Resulting Numbers: [50, 98, 31] Generated Node #0,2: 11:[50, 98, 31] Operation: 95-64=31 Exploring Operation: 98-95=3, Resulting Numbers: [64, 50, 3] Generated Node #0,3: 11:[64, 50, 3] Operation: 98-95=3 Exploring Operation: 64-50=14, Resulting Numbers: [95, 98, 14] Generated Node #0,4: 11:[95, 98, 14] Operation: 64-50=14 Moving to Node #0,3 Current State: 11:[64, 50, 3], Operations: ['98-95=3'] Exploring Operation: 50+3=53, Resulting Numbers: [64, 53] Generated Node #0,3,0: 11:[64, 53] Operation: 50+3=53 Exploring Operation: 64-50=14, Resulting Numbers: [3, 14] Generated Node #0,3,1: 11:[3, 14] Operation: 64-50=14 Exploring Operation: 64-3=61, Resulting Numbers: [50, 61] Generated Node #0,3,2: 11:[50, 61] Operation: 64-3=61 Exploring Operation: 64+3=67, Resulting Numbers: [50, 67] Generated Node #0,3,3: 11:[50, 67] Operation: 64+3=67 Exploring Operation: 50-3=47, Resulting Numbers: [64, 47] Generated Node #0,3,4: 11:[64, 47] Operation: 50-3=47 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 11:[3, 14], Operations: ['98-95=3', '64-50=14'] Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[95, 64, 50, 98], Operations: [] Exploring Operation: 98-95=3, Resulting Numbers: [64, 50, 3] Generated Node #0,3: 11:[64, 50, 3] Operation: 98-95=3 Moving to Node #0,3 Current State: 11:[64, 50, 3], Operations: ['98-95=3'] Exploring Operation: 64-50=14, Resulting Numbers: [3, 14] Generated Node #0,3,1: 11:[3, 14] Operation: 64-50=14 Moving to Node #0,3,1 Current State: 11:[3, 14], Operations: ['98-95=3', '64-50=14'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 63, 26, 30, 84 ]
25
[ "63+26=89", "30+84=114", "114-89=25" ]
Current State: 25:[63, 26, 30, 84], Operations: [] Exploring Operation: 63+26=89, Resulting Numbers: [30, 84, 89] Generated Node #2: [30, 84, 89] from Operation: 63+26=89 Current State: 25:[30, 84, 89], Operations: ['63+26=89'] Exploring Operation: 30+84=114, Resulting Numbers: [89, 114] Generated Node #3: [89, 114] from Operation: 30+84=114 Current State: 25:[89, 114], Operations: ['63+26=89', '30+84=114'] Exploring Operation: 114-89=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[63, 26, 30, 84], Operations: [] Exploring Operation: 84-63=21, Resulting Numbers: [26, 30, 21] Generated Node #0,0: 25:[26, 30, 21] Operation: 84-63=21 Exploring Operation: 84-30=54, Resulting Numbers: [63, 26, 54] Generated Node #0,1: 25:[63, 26, 54] Operation: 84-30=54 Exploring Operation: 63-30=33, Resulting Numbers: [26, 84, 33] Generated Node #0,2: 25:[26, 84, 33] Operation: 63-30=33 Exploring Operation: 63-26=37, Resulting Numbers: [30, 84, 37] Generated Node #0,3: 25:[30, 84, 37] Operation: 63-26=37 Moving to Node #0,0 Current State: 25:[26, 30, 21], Operations: ['84-63=21'] Exploring Operation: 26+21=47, Resulting Numbers: [30, 47] Generated Node #0,0,0: 25:[30, 47] Operation: 26+21=47 Exploring Operation: 30-26=4, Resulting Numbers: [21, 4] Generated Node #0,0,1: 25:[21, 4] Operation: 30-26=4 Exploring Operation: 26-21=5, Resulting Numbers: [30, 5] Generated Node #0,0,2: 25:[30, 5] Operation: 26-21=5 Exploring Operation: 30-21=9, Resulting Numbers: [26, 9] Generated Node #0,0,3: 25:[26, 9] Operation: 30-21=9 Moving to Node #0,2 Current State: 25:[26, 84, 33], Operations: ['63-30=33'] Exploring Operation: 84-26=58, Resulting Numbers: [33, 58] Generated Node #0,2,0: 25:[33, 58] Operation: 84-26=58 Exploring Operation: 33-26=7, Resulting Numbers: [84, 7] Generated Node #0,2,1: 25:[84, 7] Operation: 33-26=7 Exploring Operation: 84-33=51, Resulting Numbers: [26, 51] Generated Node #0,2,2: 25:[26, 51] Operation: 84-33=51 Exploring Operation: 26+84=110, Resulting Numbers: [33, 110] Generated Node #0,2,3: 25:[33, 110] Operation: 26+84=110 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 25:[26, 51], Operations: ['63-30=33', '84-33=51'] Exploring Operation: 26*51=1326, Resulting Numbers: [1326] 1326,25 unequal: No Solution Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[63, 26, 30, 84], Operations: [] Exploring Operation: 63-30=33, Resulting Numbers: [26, 84, 33] Generated Node #0,2: 25:[26, 84, 33] Operation: 63-30=33 Moving to Node #0,2 Current State: 25:[26, 84, 33], Operations: ['63-30=33'] Exploring Operation: 84-33=51, Resulting Numbers: [26, 51] Generated Node #0,2,2: 25:[26, 51] Operation: 84-33=51 Moving to Node #0,2,2 Current State: 25:[26, 51], Operations: ['63-30=33', '84-33=51'] Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 35, 34, 27, 54 ]
67
[ "35+34=69", "54/27=2", "69-2=67" ]
Current State: 67:[35, 34, 27, 54], Operations: [] Exploring Operation: 35+34=69, Resulting Numbers: [27, 54, 69] Generated Node #2: [27, 54, 69] from Operation: 35+34=69 Current State: 67:[27, 54, 69], Operations: ['35+34=69'] Exploring Operation: 54/27=2, Resulting Numbers: [69, 2] Generated Node #3: [69, 2] from Operation: 54/27=2 Current State: 67:[69, 2], Operations: ['35+34=69', '54/27=2'] Exploring Operation: 69-2=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[35, 34, 27, 54], Operations: [] Exploring Operation: 34+27=61, Resulting Numbers: [35, 54, 61] Generated Node #0,0: 67:[35, 54, 61] Operation: 34+27=61 Exploring Operation: 35+27=62, Resulting Numbers: [34, 54, 62] Generated Node #0,1: 67:[34, 54, 62] Operation: 35+27=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[35, 54, 61], Operations: ['34+27=61'] Exploring Operation: 35+61=96, Resulting Numbers: [54, 96] Generated Node #0,0,0: 67:[54, 96] Operation: 35+61=96 Exploring Operation: 35+54=89, Resulting Numbers: [61, 89] Generated Node #0,0,1: 67:[61, 89] Operation: 35+54=89 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 67:[61, 89], Operations: ['34+27=61', '35+54=89'] Exploring Operation: 89-61=28, Resulting Numbers: [28] 28,67 unequal: No Solution Exploring Operation: 61+89=150, Resulting Numbers: [150] 150,67 unequal: No Solution No 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: 67:[54, 96], Operations: ['34+27=61', '35+61=96'] Exploring Operation: 96-54=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 54+96=150, Resulting Numbers: [150] 150,67 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: 67:[34, 54, 62], Operations: ['35+27=62'] Exploring Operation: 34+54=88, Resulting Numbers: [62, 88] Generated Node #0,1,0: 67:[62, 88] Operation: 34+54=88 Exploring Operation: 34+62=96, Resulting Numbers: [54, 96] Generated Node #0,1,1: 67:[54, 96] Operation: 34+62=96 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 67:[62, 88], Operations: ['35+27=62', '34+54=88'] Exploring Operation: 62+88=150, Resulting Numbers: [150] 150,67 unequal: No Solution Exploring Operation: 88-62=26, Resulting Numbers: [26] 26,67 unequal: No Solution No 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: 67:[54, 96], Operations: ['35+27=62', '34+62=96'] Exploring Operation: 96-54=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 54+96=150, Resulting Numbers: [150] 150,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 88, 10, 2, 6 ]
56
[ "10+6=16", "2*16=32", "88-32=56" ]
Current State: 56:[88, 10, 2, 6], Operations: [] Exploring Operation: 10+6=16, Resulting Numbers: [88, 2, 16] Generated Node #2: [88, 2, 16] from Operation: 10+6=16 Current State: 56:[88, 2, 16], Operations: ['10+6=16'] Exploring Operation: 2*16=32, Resulting Numbers: [88, 32] Generated Node #3: [88, 32] from Operation: 2*16=32 Current State: 56:[88, 32], Operations: ['10+6=16', '2*16=32'] Exploring Operation: 88-32=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[88, 10, 2, 6], Operations: [] Exploring Operation: 88-6=82, Resulting Numbers: [10, 2, 82] Generated Node #0,0: 56:[10, 2, 82] Operation: 88-6=82 Exploring Operation: 10-6=4, Resulting Numbers: [88, 2, 4] Generated Node #0,1: 56:[88, 2, 4] Operation: 10-6=4 Exploring Operation: 88-10=78, Resulting Numbers: [2, 6, 78] Generated Node #0,2: 56:[2, 6, 78] Operation: 88-10=78 Exploring Operation: 88/2=44, Resulting Numbers: [10, 6, 44] Generated Node #0,3: 56:[10, 6, 44] Operation: 88/2=44 Moving to Node #0,3 Current State: 56:[10, 6, 44], Operations: ['88/2=44'] Exploring Operation: 44-10=34, Resulting Numbers: [6, 34] Generated Node #0,3,0: 56:[6, 34] Operation: 44-10=34 Exploring Operation: 6+44=50, Resulting Numbers: [10, 50] Generated Node #0,3,1: 56:[10, 50] Operation: 6+44=50 Exploring Operation: 10+44=54, Resulting Numbers: [6, 54] Generated Node #0,3,2: 56:[6, 54] Operation: 10+44=54 Exploring Operation: 10-6=4, Resulting Numbers: [44, 4] Generated Node #0,3,3: 56:[44, 4] Operation: 10-6=4 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 56:[6, 54], Operations: ['88/2=44', '10+44=54'] Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,56 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,56 unequal: No Solution Exploring Operation: 6*54=324, Resulting Numbers: [324] 324,56 unequal: No Solution Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,56 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 #0,3,0 Current State: 56:[6, 34], Operations: ['88/2=44', '44-10=34'] Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 6*34=204, Resulting Numbers: [204] 204,56 unequal: No Solution Exploring Operation: 6+34=40, Resulting Numbers: [40] 40,56 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 #0,3,1 Current State: 56:[10, 50], Operations: ['88/2=44', '6+44=50'] Exploring Operation: 10+50=60, Resulting Numbers: [60] 60,56 unequal: No Solution Exploring Operation: 50/10=5, Resulting Numbers: [5] 5,56 unequal: No Solution Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,56 unequal: No Solution Exploring Operation: 10*50=500, Resulting Numbers: [500] 500,56 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 #0,3,3 Current State: 56:[44, 4], Operations: ['88/2=44', '10-6=4'] Exploring Operation: 44+4=48, Resulting Numbers: [48] 48,56 unequal: No Solution Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,56 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,56 unequal: No Solution Exploring Operation: 44*4=176, Resulting Numbers: [176] 176,56 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: 56:[2, 6, 78], Operations: ['88-10=78'] Exploring Operation: 78-6=72, Resulting Numbers: [2, 72] Generated Node #0,2,0: 56:[2, 72] Operation: 78-6=72 Exploring Operation: 78-2=76, Resulting Numbers: [6, 76] Generated Node #0,2,1: 56:[6, 76] Operation: 78-2=76 Exploring Operation: 78/6=13, Resulting Numbers: [2, 13] Generated Node #0,2,2: 56:[2, 13] Operation: 78/6=13 Exploring Operation: 78/2=39, Resulting Numbers: [6, 39] Generated Node #0,2,3: 56:[6, 39] Operation: 78/2=39 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 56:[2, 13], Operations: ['88-10=78', '78/6=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,56 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,56 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,56 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 #0,2,3 Current State: 56:[6, 39], Operations: ['88-10=78', '78/2=39'] Exploring Operation: 6+39=45, Resulting Numbers: [45] 45,56 unequal: No Solution Exploring Operation: 6*39=234, Resulting Numbers: [234] 234,56 unequal: No Solution Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,56 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 #0,2,0 Current State: 56:[2, 72], Operations: ['88-10=78', '78-6=72'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,56 unequal: No Solution Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,56 unequal: No Solution Exploring Operation: 2*72=144, Resulting Numbers: [144] 144,56 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,56 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 #0,2,1 Current State: 56:[6, 76], Operations: ['88-10=78', '78-2=76'] Exploring Operation: 6*76=456, Resulting Numbers: [456] 456,56 unequal: No Solution Exploring Operation: 6+76=82, Resulting Numbers: [82] 82,56 unequal: No Solution Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,56 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:[10, 2, 82], Operations: ['88-6=82'] Exploring Operation: 82-10=72, Resulting Numbers: [2, 72] Generated Node #0,0,0: 56:[2, 72] Operation: 82-10=72 Exploring Operation: 82/2=41, Resulting Numbers: [10, 41] Generated Node #0,0,1: 56:[10, 41] Operation: 82/2=41 Exploring Operation: 82-2=80, Resulting Numbers: [10, 80] Generated Node #0,0,2: 56:[10, 80] Operation: 82-2=80 Exploring Operation: 10-2=8, Resulting Numbers: [82, 8] Generated Node #0,0,3: 56:[82, 8] Operation: 10-2=8 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 56:[10, 41], Operations: ['88-6=82', '82/2=41'] Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 10*41=410, Resulting Numbers: [410] 410,56 unequal: No Solution Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,56 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 #0,0,0 Current State: 56:[2, 72], Operations: ['88-6=82', '82-10=72'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,56 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,56 unequal: No Solution Exploring Operation: 2*72=144, Resulting Numbers: [144] 144,56 unequal: No Solution Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,56 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 #0,0,2 Current State: 56:[10, 80], Operations: ['88-6=82', '82-2=80'] Exploring Operation: 80/10=8, Resulting Numbers: [8] 8,56 unequal: No Solution Exploring Operation: 10*80=800, Resulting Numbers: [800] 800,56 unequal: No Solution Exploring Operation: 80-10=70, Resulting Numbers: [70] 70,56 unequal: No Solution Exploring Operation: 10+80=90, Resulting Numbers: [90] 90,56 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 #0,0,3 Current State: 56:[82, 8], Operations: ['88-6=82', '10-2=8'] Exploring Operation: 82-8=74, Resulting Numbers: [74] 74,56 unequal: No Solution Exploring Operation: 82+8=90, Resulting Numbers: [90] 90,56 unequal: No Solution Exploring Operation: 82*8=656, Resulting Numbers: [656] 656,56 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: 56:[88, 2, 4], Operations: ['10-6=4'] Exploring Operation: 88/4=22, Resulting Numbers: [2, 22] Generated Node #0,1,0: 56:[2, 22] Operation: 88/4=22 Exploring Operation: 88/2=44, Resulting Numbers: [4, 44] Generated Node #0,1,1: 56:[4, 44] Operation: 88/2=44 Exploring Operation: 88-4=84, Resulting Numbers: [2, 84] Generated Node #0,1,2: 56:[2, 84] Operation: 88-4=84 Exploring Operation: 88-2=86, Resulting Numbers: [4, 86] Generated Node #0,1,3: 56:[4, 86] Operation: 88-2=86 Moving to Node #0,1,0 Current State: 56:[2, 22], Operations: ['10-6=4', '88/4=22'] Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,56 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,56 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[4, 44], Operations: ['10-6=4', '88/2=44'] Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,56 unequal: No Solution Exploring Operation: 4*44=176, Resulting Numbers: [176] 176,56 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,56 unequal: No Solution Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,56 unequal: No Solution Moving to Node #0,1,2 Current State: 56:[2, 84], Operations: ['10-6=4', '88-4=84'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,56 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,56 unequal: No Solution Exploring Operation: 2*84=168, Resulting Numbers: [168] 168,56 unequal: No Solution Moving to Node #0,1,3 Current State: 56:[4, 86], Operations: ['10-6=4', '88-2=86'] Exploring Operation: 86-4=82, Resulting Numbers: [82] 82,56 unequal: No Solution Exploring Operation: 4+86=90, Resulting Numbers: [90] 90,56 unequal: No Solution Exploring Operation: 4*86=344, Resulting Numbers: [344] 344,56 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 87, 62, 7, 24 ]
89
[ "7+24=31", "62/31=2", "87+2=89" ]
Current State: 89:[87, 62, 7, 24], Operations: [] Exploring Operation: 7+24=31, Resulting Numbers: [87, 62, 31] Generated Node #2: [87, 62, 31] from Operation: 7+24=31 Current State: 89:[87, 62, 31], Operations: ['7+24=31'] Exploring Operation: 62/31=2, Resulting Numbers: [87, 2] Generated Node #3: [87, 2] from Operation: 62/31=2 Current State: 89:[87, 2], Operations: ['7+24=31', '62/31=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[87, 62, 7, 24], Operations: [] Exploring Operation: 62+7=69, Resulting Numbers: [87, 24, 69] Generated Node #0,0: 89:[87, 24, 69] Operation: 62+7=69 Exploring Operation: 62+24=86, Resulting Numbers: [87, 7, 86] Generated Node #0,1: 89:[87, 7, 86] Operation: 62+24=86 Moving to Node #0,0 Current State: 89:[87, 24, 69], Operations: ['62+7=69'] Exploring Operation: 24+69=93, Resulting Numbers: [87, 93] Generated Node #0,0,0: 89:[87, 93] Operation: 24+69=93 Exploring Operation: 87+24=111, Resulting Numbers: [69, 111] Generated Node #0,0,1: 89:[69, 111] Operation: 87+24=111 Moving to Node #0,1 Current State: 89:[87, 7, 86], Operations: ['62+24=86'] Exploring Operation: 87+7=94, Resulting Numbers: [86, 94] Generated Node #0,1,0: 89:[86, 94] Operation: 87+7=94 Exploring Operation: 7+86=93, Resulting Numbers: [87, 93] Generated Node #0,1,1: 89:[87, 93] Operation: 7+86=93 Moving to Node #0,0,0 Current State: 89:[87, 93], Operations: ['62+7=69', '24+69=93'] Exploring Operation: 93-87=6, Resulting Numbers: [6] 6,89 unequal: No Solution Exploring Operation: 87+93=180, Resulting Numbers: [180] 180,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[87, 93], Operations: ['62+24=86', '7+86=93'] Exploring Operation: 93-87=6, Resulting Numbers: [6] 6,89 unequal: No Solution Exploring Operation: 87+93=180, Resulting Numbers: [180] 180,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[86, 94], Operations: ['62+24=86', '87+7=94'] Exploring Operation: 86+94=180, Resulting Numbers: [180] 180,89 unequal: No Solution Exploring Operation: 94-86=8, Resulting Numbers: [8] 8,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[69, 111], Operations: ['62+7=69', '87+24=111'] Exploring Operation: 111-69=42, Resulting Numbers: [42] 42,89 unequal: No Solution Exploring Operation: 69+111=180, Resulting Numbers: [180] 180,89 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 2, 47, 94, 17 ]
62
[ "2+47=49", "94+17=111", "111-49=62" ]
Current State: 62:[2, 47, 94, 17], Operations: [] Exploring Operation: 2+47=49, Resulting Numbers: [94, 17, 49] Generated Node #2: [94, 17, 49] from Operation: 2+47=49 Current State: 62:[94, 17, 49], Operations: ['2+47=49'] Exploring Operation: 94+17=111, Resulting Numbers: [49, 111] Generated Node #3: [49, 111] from Operation: 94+17=111 Current State: 62:[49, 111], Operations: ['2+47=49', '94+17=111'] Exploring Operation: 111-49=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[2, 47, 94, 17], Operations: [] Exploring Operation: 94-47=47, Resulting Numbers: [2, 17, 47] Generated Node #0,0: 62:[2, 17, 47] Operation: 94-47=47 Exploring Operation: 94/47=2, Resulting Numbers: [2, 17, 2] Generated Node #0,1: 62:[2, 17, 2] Operation: 94/47=2 Moving to Node #0,1 Current State: 62:[2, 17, 2], Operations: ['94/47=2'] Exploring Operation: 2*17=34, Resulting Numbers: [2, 34] Generated Node #0,1,0: 62:[2, 34] Operation: 2*17=34 Exploring Operation: 17*2=34, Resulting Numbers: [2, 34] Generated Node #0,1,1: 62:[2, 34] Operation: 17*2=34 Moving to Node #0,0 Current State: 62:[2, 17, 47], Operations: ['94-47=47'] Exploring Operation: 47-17=30, Resulting Numbers: [2, 30] Generated Node #0,0,0: 62:[2, 30] Operation: 47-17=30 Exploring Operation: 17+47=64, Resulting Numbers: [2, 64] Generated Node #0,0,1: 62:[2, 64] Operation: 17+47=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[2, 30], Operations: ['94-47=47', '47-17=30'] Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,62 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,62 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:[2, 64], Operations: ['94-47=47', '17+47=64'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[2, 47, 94, 17], Operations: [] Exploring Operation: 94-47=47, Resulting Numbers: [2, 17, 47] Generated Node #0,0: 62:[2, 17, 47] Operation: 94-47=47 Moving to Node #0,0 Current State: 62:[2, 17, 47], Operations: ['94-47=47'] Exploring Operation: 17+47=64, Resulting Numbers: [2, 64] Generated Node #0,0,1: 62:[2, 64] Operation: 17+47=64 Moving to Node #0,0,1 Current State: 62:[2, 64], Operations: ['94-47=47', '17+47=64'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_2
sum_heuristic
[ 35, 9, 91, 6 ]
84
[ "35+91=126", "126/9=14", "6*14=84" ]
Current State: 84:[35, 9, 91, 6], Operations: [] Exploring Operation: 35+91=126, Resulting Numbers: [9, 6, 126] Generated Node #2: [9, 6, 126] from Operation: 35+91=126 Current State: 84:[9, 6, 126], Operations: ['35+91=126'] Exploring Operation: 126/9=14, Resulting Numbers: [6, 14] Generated Node #3: [6, 14] from Operation: 126/9=14 Current State: 84:[6, 14], Operations: ['35+91=126', '126/9=14'] Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[35, 9, 91, 6], Operations: [] Exploring Operation: 35+9=44, Resulting Numbers: [91, 6, 44] Generated Node #0,0: 84:[91, 6, 44] Operation: 35+9=44 Exploring Operation: 35-9=26, Resulting Numbers: [91, 6, 26] Generated Node #0,1: 84:[91, 6, 26] Operation: 35-9=26 Exploring Operation: 91-9=82, Resulting Numbers: [35, 6, 82] Generated Node #0,2: 84:[35, 6, 82] Operation: 91-9=82 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[91, 6, 44], Operations: ['35+9=44'] Exploring Operation: 44-6=38, Resulting Numbers: [91, 38] Generated Node #0,0,0: 84:[91, 38] Operation: 44-6=38 Exploring Operation: 91-44=47, Resulting Numbers: [6, 47] Generated Node #0,0,1: 84:[6, 47] Operation: 91-44=47 Exploring Operation: 91-6=85, Resulting Numbers: [44, 85] Generated Node #0,0,2: 84:[44, 85] Operation: 91-6=85 Moving to Node #0,0,2 Current State: 84:[44, 85], Operations: ['35+9=44', '91-6=85'] Exploring Operation: 44+85=129, Resulting Numbers: [129] 129,84 unequal: No Solution Exploring Operation: 85-44=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 44*85=3740, Resulting Numbers: [3740] 3740,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[6, 47], Operations: ['35+9=44', '91-44=47'] Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,84 unequal: No Solution Exploring Operation: 6*47=282, Resulting Numbers: [282] 282,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[91, 38], Operations: ['35+9=44', '44-6=38'] Exploring Operation: 91*38=3458, Resulting Numbers: [3458] 3458,84 unequal: No Solution Exploring Operation: 91+38=129, Resulting Numbers: [129] 129,84 unequal: No Solution Exploring Operation: 91-38=53, Resulting Numbers: [53] 53,84 unequal: No Solution No 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: 84:[91, 6, 26], Operations: ['35-9=26'] Exploring Operation: 26-6=20, Resulting Numbers: [91, 20] Generated Node #0,1,0: 84:[91, 20] Operation: 26-6=20 Exploring Operation: 91-6=85, Resulting Numbers: [26, 85] Generated Node #0,1,1: 84:[26, 85] Operation: 91-6=85 Exploring Operation: 6+26=32, Resulting Numbers: [91, 32] Generated Node #0,1,2: 84:[91, 32] Operation: 6+26=32 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 84:[26, 85], Operations: ['35-9=26', '91-6=85'] Exploring Operation: 26*85=2210, Resulting Numbers: [2210] 2210,84 unequal: No Solution Exploring Operation: 85-26=59, Resulting Numbers: [59] 59,84 unequal: No Solution Exploring Operation: 26+85=111, Resulting Numbers: [111] 111,84 unequal: No Solution No 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: 84:[91, 20], Operations: ['35-9=26', '26-6=20'] Exploring Operation: 91*20=1820, Resulting Numbers: [1820] 1820,84 unequal: No Solution Exploring Operation: 91-20=71, Resulting Numbers: [71] 71,84 unequal: No Solution Exploring Operation: 91+20=111, Resulting Numbers: [111] 111,84 unequal: No Solution No 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: 84:[91, 32], Operations: ['35-9=26', '6+26=32'] Exploring Operation: 91*32=2912, Resulting Numbers: [2912] 2912,84 unequal: No Solution Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,84 unequal: No Solution Exploring Operation: 91+32=123, Resulting Numbers: [123] 123,84 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: 84:[35, 6, 82], Operations: ['91-9=82'] Exploring Operation: 35+6=41, Resulting Numbers: [82, 41] Generated Node #0,2,0: 84:[82, 41] Operation: 35+6=41 Exploring Operation: 82-35=47, Resulting Numbers: [6, 47] Generated Node #0,2,1: 84:[6, 47] Operation: 82-35=47 Exploring Operation: 35-6=29, Resulting Numbers: [82, 29] Generated Node #0,2,2: 84:[82, 29] Operation: 35-6=29 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 84:[82, 41], Operations: ['91-9=82', '35+6=41'] Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 82+41=123, Resulting Numbers: [123] 123,84 unequal: No Solution Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,84 unequal: No Solution No 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: 84:[82, 29], Operations: ['91-9=82', '35-6=29'] Exploring Operation: 82-29=53, Resulting Numbers: [53] 53,84 unequal: No Solution Exploring Operation: 82+29=111, Resulting Numbers: [111] 111,84 unequal: No Solution Exploring Operation: 82*29=2378, Resulting Numbers: [2378] 2378,84 unequal: No Solution No 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: 84:[6, 47], Operations: ['91-9=82', '82-35=47'] Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,84 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 6*47=282, Resulting Numbers: [282] 282,84 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
[ 12, 87, 20, 45 ]
34
[ "12+87=99", "20+45=65", "99-65=34" ]
Current State: 34:[12, 87, 20, 45], Operations: [] Exploring Operation: 12+87=99, Resulting Numbers: [20, 45, 99] Generated Node #2: [20, 45, 99] from Operation: 12+87=99 Current State: 34:[20, 45, 99], Operations: ['12+87=99'] Exploring Operation: 20+45=65, Resulting Numbers: [99, 65] Generated Node #3: [99, 65] from Operation: 20+45=65 Current State: 34:[99, 65], Operations: ['12+87=99', '20+45=65'] Exploring Operation: 99-65=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[12, 87, 20, 45], Operations: [] Exploring Operation: 87-45=42, Resulting Numbers: [12, 20, 42] Generated Node #0,0: 34:[12, 20, 42] Operation: 87-45=42 Exploring Operation: 87-20=67, Resulting Numbers: [12, 45, 67] Generated Node #0,1: 34:[12, 45, 67] Operation: 87-20=67 Exploring Operation: 45-12=33, Resulting Numbers: [87, 20, 33] Generated Node #0,2: 34:[87, 20, 33] Operation: 45-12=33 Exploring Operation: 87-12=75, Resulting Numbers: [20, 45, 75] Generated Node #0,3: 34:[20, 45, 75] Operation: 87-12=75 Exploring Operation: 12+20=32, Resulting Numbers: [87, 45, 32] Generated Node #0,4: 34:[87, 45, 32] Operation: 12+20=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[12, 20, 42], Operations: ['87-45=42'] Exploring Operation: 12+20=32, Resulting Numbers: [42, 32] Generated Node #0,0,0: 34:[42, 32] Operation: 12+20=32 Exploring Operation: 42-12=30, Resulting Numbers: [20, 30] Generated Node #0,0,1: 34:[20, 30] Operation: 42-12=30 Exploring Operation: 12+42=54, Resulting Numbers: [20, 54] Generated Node #0,0,2: 34:[20, 54] Operation: 12+42=54 Exploring Operation: 42-20=22, Resulting Numbers: [12, 22] Generated Node #0,0,3: 34:[12, 22] Operation: 42-20=22 Exploring Operation: 20-12=8, Resulting Numbers: [42, 8] Generated Node #0,0,4: 34:[42, 8] Operation: 20-12=8 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 34:[20, 30], Operations: ['87-45=42', '42-12=30'] Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,34 unequal: No Solution Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,34 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,34 unequal: No Solution No 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: 34:[42, 32], Operations: ['87-45=42', '12+20=32'] Exploring Operation: 42-32=10, Resulting Numbers: [10] 10,34 unequal: No Solution Exploring Operation: 42*32=1344, Resulting Numbers: [1344] 1344,34 unequal: No Solution Exploring Operation: 42+32=74, Resulting Numbers: [74] 74,34 unequal: No Solution No 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: 34:[12, 22], Operations: ['87-45=42', '42-20=22'] Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,34 unequal: No Solution Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[12, 87, 20, 45], Operations: [] Exploring Operation: 87-45=42, Resulting Numbers: [12, 20, 42] Generated Node #0,0: 34:[12, 20, 42] Operation: 87-45=42 Moving to Node #0,0 Current State: 34:[12, 20, 42], Operations: ['87-45=42'] Exploring Operation: 42-20=22, Resulting Numbers: [12, 22] Generated Node #0,0,3: 34:[12, 22] Operation: 42-20=22 Moving to Node #0,0,3 Current State: 34:[12, 22], Operations: ['87-45=42', '42-20=22'] Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 33, 45, 20, 2 ]
49
[ "33+45=78", "20+78=98", "98/2=49" ]
Current State: 49:[33, 45, 20, 2], Operations: [] Exploring Operation: 33+45=78, Resulting Numbers: [20, 2, 78] Generated Node #2: [20, 2, 78] from Operation: 33+45=78 Current State: 49:[20, 2, 78], Operations: ['33+45=78'] Exploring Operation: 20+78=98, Resulting Numbers: [2, 98] Generated Node #3: [2, 98] from Operation: 20+78=98 Current State: 49:[2, 98], Operations: ['33+45=78', '20+78=98'] Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[33, 45, 20, 2], Operations: [] Exploring Operation: 33-20=13, Resulting Numbers: [45, 2, 13] Generated Node #0,0: 49:[45, 2, 13] Operation: 33-20=13 Exploring Operation: 45-33=12, Resulting Numbers: [20, 2, 12] Generated Node #0,1: 49:[20, 2, 12] Operation: 45-33=12 Exploring Operation: 33+20=53, Resulting Numbers: [45, 2, 53] Generated Node #0,2: 49:[45, 2, 53] Operation: 33+20=53 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[45, 2, 53], Operations: ['33+20=53'] Exploring Operation: 53-2=51, Resulting Numbers: [45, 51] Generated Node #0,2,0: 49:[45, 51] Operation: 53-2=51 Exploring Operation: 45+2=47, Resulting Numbers: [53, 47] Generated Node #0,2,1: 49:[53, 47] Operation: 45+2=47 Exploring Operation: 53-45=8, Resulting Numbers: [2, 8] Generated Node #0,2,2: 49:[2, 8] Operation: 53-45=8 Moving to Node #0,2,0 Current State: 49:[45, 51], Operations: ['33+20=53', '53-2=51'] Exploring Operation: 45+51=96, Resulting Numbers: [96] 96,49 unequal: No Solution Exploring Operation: 45*51=2295, Resulting Numbers: [2295] 2295,49 unequal: No Solution Exploring Operation: 51-45=6, Resulting Numbers: [6] 6,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[53, 47], Operations: ['33+20=53', '45+2=47'] Exploring Operation: 53*47=2491, Resulting Numbers: [2491] 2491,49 unequal: No Solution Exploring Operation: 53+47=100, Resulting Numbers: [100] 100,49 unequal: No Solution Exploring Operation: 53-47=6, Resulting Numbers: [6] 6,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[2, 8], Operations: ['33+20=53', '53-45=8'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,49 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,49 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,49 unequal: No Solution No 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: 49:[45, 2, 13], Operations: ['33-20=13'] Exploring Operation: 45+2=47, Resulting Numbers: [13, 47] Generated Node #0,0,0: 49:[13, 47] Operation: 45+2=47 Exploring Operation: 45-2=43, Resulting Numbers: [13, 43] Generated Node #0,0,1: 49:[13, 43] Operation: 45-2=43 Exploring Operation: 13-2=11, Resulting Numbers: [45, 11] Generated Node #0,0,2: 49:[45, 11] Operation: 13-2=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[13, 47], Operations: ['33-20=13', '45+2=47'] Exploring Operation: 13*47=611, Resulting Numbers: [611] 611,49 unequal: No Solution Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,49 unequal: No Solution Exploring Operation: 13+47=60, Resulting Numbers: [60] 60,49 unequal: No Solution No 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: 49:[45, 11], Operations: ['33-20=13', '13-2=11'] Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,49 unequal: No Solution Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,49 unequal: No Solution Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,49 unequal: No Solution No 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: 49:[13, 43], Operations: ['33-20=13', '45-2=43'] Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,49 unequal: No Solution Exploring Operation: 13*43=559, Resulting Numbers: [559] 559,49 unequal: No Solution Exploring Operation: 13+43=56, Resulting Numbers: [56] 56,49 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: 49:[20, 2, 12], Operations: ['45-33=12'] Exploring Operation: 20-12=8, Resulting Numbers: [2, 8] Generated Node #0,1,0: 49:[2, 8] Operation: 20-12=8 Exploring Operation: 20*2=40, Resulting Numbers: [12, 40] Generated Node #0,1,1: 49:[12, 40] Operation: 20*2=40 Exploring Operation: 20/2=10, Resulting Numbers: [12, 10] Generated Node #0,1,2: 49:[12, 10] Operation: 20/2=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 49:[2, 8], Operations: ['45-33=12', '20-12=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,49 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,49 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,49 unequal: No Solution No 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: 49:[12, 10], Operations: ['45-33=12', '20/2=10'] Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,49 unequal: No Solution Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 12*10=120, Resulting Numbers: [120] 120,49 unequal: No Solution No 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: 49:[12, 40], Operations: ['45-33=12', '20*2=40'] Exploring Operation: 12*40=480, Resulting Numbers: [480] 480,49 unequal: No Solution Exploring Operation: 12+40=52, Resulting Numbers: [52] 52,49 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 31, 62, 22, 15 ]
73
[ "31-22=9", "15*9=135", "135-62=73" ]
Current State: 73:[31, 62, 22, 15], Operations: [] Exploring Operation: 31-22=9, Resulting Numbers: [62, 15, 9] Generated Node #2: [62, 15, 9] from Operation: 31-22=9 Current State: 73:[62, 15, 9], Operations: ['31-22=9'] Exploring Operation: 15*9=135, Resulting Numbers: [62, 135] Generated Node #3: [62, 135] from Operation: 15*9=135 Current State: 73:[62, 135], Operations: ['31-22=9', '15*9=135'] Exploring Operation: 135-62=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[31, 62, 22, 15], Operations: [] Exploring Operation: 31+22=53, Resulting Numbers: [62, 15, 53] Generated Node #0,0: 73:[62, 15, 53] Operation: 31+22=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[62, 15, 53], Operations: ['31+22=53'] Exploring Operation: 15+53=68, Resulting Numbers: [62, 68] Generated Node #0,0,0: 73:[62, 68] Operation: 15+53=68 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[62, 68], Operations: ['31+22=53', '15+53=68'] Exploring Operation: 62+68=130, Resulting Numbers: [130] 130,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 18, 73, 97, 83 ]
63
[ "97+83=180", "180/18=10", "73-10=63" ]
Current State: 63:[18, 73, 97, 83], Operations: [] Exploring Operation: 97+83=180, Resulting Numbers: [18, 73, 180] Generated Node #2: [18, 73, 180] from Operation: 97+83=180 Current State: 63:[18, 73, 180], Operations: ['97+83=180'] Exploring Operation: 180/18=10, Resulting Numbers: [73, 10] Generated Node #3: [73, 10] from Operation: 180/18=10 Current State: 63:[73, 10], Operations: ['97+83=180', '180/18=10'] Exploring Operation: 73-10=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[18, 73, 97, 83], Operations: [] Exploring Operation: 97-73=24, Resulting Numbers: [18, 83, 24] Generated Node #0,0: 63:[18, 83, 24] Operation: 97-73=24 Exploring Operation: 97-83=14, Resulting Numbers: [18, 73, 14] Generated Node #0,1: 63:[18, 73, 14] Operation: 97-83=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[18, 73, 14], Operations: ['97-83=14'] Exploring Operation: 73-14=59, Resulting Numbers: [18, 59] Generated Node #0,1,0: 63:[18, 59] Operation: 73-14=59 Exploring Operation: 18-14=4, Resulting Numbers: [73, 4] Generated Node #0,1,1: 63:[73, 4] Operation: 18-14=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 63:[18, 59], Operations: ['97-83=14', '73-14=59'] Exploring Operation: 18+59=77, Resulting Numbers: [77] 77,63 unequal: No Solution Exploring Operation: 59-18=41, Resulting Numbers: [41] 41,63 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 #0,1,1 Current State: 63:[73, 4], Operations: ['97-83=14', '18-14=4'] Exploring Operation: 73+4=77, Resulting Numbers: [77] 77,63 unequal: No Solution Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,63 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 #0,0 Current State: 63:[18, 83, 24], Operations: ['97-73=24'] Exploring Operation: 83-18=65, Resulting Numbers: [24, 65] Generated Node #0,0,0: 63:[24, 65] Operation: 83-18=65 Exploring Operation: 83-24=59, Resulting Numbers: [18, 59] Generated Node #0,0,1: 63:[18, 59] Operation: 83-24=59 Moving to Node #0,0,0 Current State: 63:[24, 65], Operations: ['97-73=24', '83-18=65'] Exploring Operation: 24+65=89, Resulting Numbers: [89] 89,63 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[18, 59], Operations: ['97-73=24', '83-24=59'] Exploring Operation: 18+59=77, Resulting Numbers: [77] 77,63 unequal: No Solution Exploring Operation: 59-18=41, Resulting Numbers: [41] 41,63 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
[ 4, 46, 37, 58 ]
40
[ "58-46=12", "12/4=3", "37+3=40" ]
Current State: 40:[4, 46, 37, 58], Operations: [] Exploring Operation: 58-46=12, Resulting Numbers: [4, 37, 12] Generated Node #2: [4, 37, 12] from Operation: 58-46=12 Current State: 40:[4, 37, 12], Operations: ['58-46=12'] Exploring Operation: 12/4=3, Resulting Numbers: [37, 3] Generated Node #3: [37, 3] from Operation: 12/4=3 Current State: 40:[37, 3], Operations: ['58-46=12', '12/4=3'] Exploring Operation: 37+3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[4, 46, 37, 58], Operations: [] Exploring Operation: 58-37=21, Resulting Numbers: [4, 46, 21] Generated Node #0,0: 40:[4, 46, 21] Operation: 58-37=21 Exploring Operation: 58-46=12, Resulting Numbers: [4, 37, 12] Generated Node #0,1: 40:[4, 37, 12] Operation: 58-46=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[4, 37, 12], Operations: ['58-46=12'] Exploring Operation: 12-4=8, Resulting Numbers: [37, 8] Generated Node #0,1,0: 40:[37, 8] Operation: 12-4=8 Exploring Operation: 4+37=41, Resulting Numbers: [12, 41] Generated Node #0,1,1: 40:[12, 41] Operation: 4+37=41 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 40:[37, 8], Operations: ['58-46=12', '12-4=8'] Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,40 unequal: No Solution Exploring Operation: 37+8=45, Resulting Numbers: [45] 45,40 unequal: No Solution No 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: 40:[12, 41], Operations: ['58-46=12', '4+37=41'] Exploring Operation: 12+41=53, Resulting Numbers: [53] 53,40 unequal: No Solution Exploring Operation: 41-12=29, Resulting Numbers: [29] 29,40 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: 40:[4, 46, 21], Operations: ['58-37=21'] Exploring Operation: 46-4=42, Resulting Numbers: [21, 42] Generated Node #0,0,0: 40:[21, 42] Operation: 46-4=42 Exploring Operation: 46-21=25, Resulting Numbers: [4, 25] Generated Node #0,0,1: 40:[4, 25] Operation: 46-21=25 Moving to Node #0,0,0 Current State: 40:[21, 42], Operations: ['58-37=21', '46-4=42'] Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,40 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[4, 25], Operations: ['58-37=21', '46-21=25'] Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,40 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,40 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
[ 20, 18, 22, 64 ]
59
[ "20*64=1280", "18+1280=1298", "1298/22=59" ]
Current State: 59:[20, 18, 22, 64], Operations: [] Exploring Operation: 20*64=1280, Resulting Numbers: [18, 22, 1280] Generated Node #2: [18, 22, 1280] from Operation: 20*64=1280 Current State: 59:[18, 22, 1280], Operations: ['20*64=1280'] Exploring Operation: 18+1280=1298, Resulting Numbers: [22, 1298] Generated Node #3: [22, 1298] from Operation: 18+1280=1298 Current State: 59:[22, 1298], Operations: ['20*64=1280', '18+1280=1298'] Exploring Operation: 1298/22=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[20, 18, 22, 64], Operations: [] Exploring Operation: 20+18=38, Resulting Numbers: [22, 64, 38] Generated Node #0,0: 59:[22, 64, 38] Operation: 20+18=38 Exploring Operation: 20+22=42, Resulting Numbers: [18, 64, 42] Generated Node #0,1: 59:[18, 64, 42] Operation: 20+22=42 Moving to Node #0,0 Current State: 59:[22, 64, 38], Operations: ['20+18=38'] Exploring Operation: 64-22=42, Resulting Numbers: [38, 42] Generated Node #0,0,0: 59:[38, 42] Operation: 64-22=42 Exploring Operation: 22+38=60, Resulting Numbers: [64, 60] Generated Node #0,0,1: 59:[64, 60] Operation: 22+38=60 Moving to Node #0,1 Current State: 59:[18, 64, 42], Operations: ['20+22=42'] Exploring Operation: 18+42=60, Resulting Numbers: [64, 60] Generated Node #0,1,0: 59:[64, 60] Operation: 18+42=60 Exploring Operation: 64-18=46, Resulting Numbers: [42, 46] Generated Node #0,1,1: 59:[42, 46] Operation: 64-18=46 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[64, 60], Operations: ['20+22=42', '18+42=60'] Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 64+60=124, Resulting Numbers: [124] 124,59 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 #0,1,1 Current State: 59:[42, 46], Operations: ['20+22=42', '64-18=46'] Exploring Operation: 42+46=88, Resulting Numbers: [88] 88,59 unequal: No Solution Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,59 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: 59:[64, 60], Operations: ['20+18=38', '22+38=60'] Exploring Operation: 64+60=124, Resulting Numbers: [124] 124,59 unequal: No Solution Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[38, 42], Operations: ['20+18=38', '64-22=42'] Exploring Operation: 42-38=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 38+42=80, Resulting Numbers: [80] 80,59 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 8, 14, 35, 10 ]
41
[ "14*35=490", "490/10=49", "49-8=41" ]
Current State: 41:[8, 14, 35, 10], Operations: [] Exploring Operation: 14*35=490, Resulting Numbers: [8, 10, 490] Generated Node #2: [8, 10, 490] from Operation: 14*35=490 Current State: 41:[8, 10, 490], Operations: ['14*35=490'] Exploring Operation: 490/10=49, Resulting Numbers: [8, 49] Generated Node #3: [8, 49] from Operation: 490/10=49 Current State: 41:[8, 49], Operations: ['14*35=490', '490/10=49'] Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[8, 14, 35, 10], Operations: [] Exploring Operation: 14+10=24, Resulting Numbers: [8, 35, 24] Generated Node #0,0: 41:[8, 35, 24] Operation: 14+10=24 Exploring Operation: 8+10=18, Resulting Numbers: [14, 35, 18] Generated Node #0,1: 41:[14, 35, 18] Operation: 8+10=18 Exploring Operation: 8+14=22, Resulting Numbers: [35, 10, 22] Generated Node #0,2: 41:[35, 10, 22] Operation: 8+14=22 Exploring Operation: 8+35=43, Resulting Numbers: [14, 10, 43] Generated Node #0,3: 41:[14, 10, 43] Operation: 8+35=43 Exploring Operation: 35+10=45, Resulting Numbers: [8, 14, 45] Generated Node #0,4: 41:[8, 14, 45] Operation: 35+10=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[8, 35, 24], Operations: ['14+10=24'] Exploring Operation: 8+35=43, Resulting Numbers: [24, 43] Generated Node #0,0,0: 41:[24, 43] Operation: 8+35=43 Exploring Operation: 8+24=32, Resulting Numbers: [35, 32] Generated Node #0,0,1: 41:[35, 32] Operation: 8+24=32 Exploring Operation: 35-8=27, Resulting Numbers: [24, 27] Generated Node #0,0,2: 41:[24, 27] Operation: 35-8=27 Exploring Operation: 24-8=16, Resulting Numbers: [35, 16] Generated Node #0,0,3: 41:[35, 16] Operation: 24-8=16 Exploring Operation: 24/8=3, Resulting Numbers: [35, 3] Generated Node #0,0,4: 41:[35, 3] Operation: 24/8=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[35, 32], Operations: ['14+10=24', '8+24=32'] Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 35+32=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 35*32=1120, Resulting Numbers: [1120] 1120,41 unequal: No Solution No 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: 41:[24, 43], Operations: ['14+10=24', '8+35=43'] Exploring Operation: 24*43=1032, Resulting Numbers: [1032] 1032,41 unequal: No Solution Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,41 unequal: No Solution No 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: 41:[24, 27], Operations: ['14+10=24', '35-8=27'] Exploring Operation: 24+27=51, Resulting Numbers: [51] 51,41 unequal: No Solution Exploring Operation: 24*27=648, Resulting Numbers: [648] 648,41 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,41 unequal: No Solution No 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: 41:[35, 16], Operations: ['14+10=24', '24-8=16'] Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,41 unequal: No Solution Exploring Operation: 35*16=560, Resulting Numbers: [560] 560,41 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,41 unequal: No Solution No 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: 41:[35, 3], Operations: ['14+10=24', '24/8=3'] Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,41 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,41 unequal: No Solution Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,41 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: 41:[14, 35, 18], Operations: ['8+10=18'] Exploring Operation: 35-14=21, Resulting Numbers: [18, 21] Generated Node #0,1,0: 41:[18, 21] Operation: 35-14=21 Exploring Operation: 14+18=32, Resulting Numbers: [35, 32] Generated Node #0,1,1: 41:[35, 32] Operation: 14+18=32 Exploring Operation: 14+35=49, Resulting Numbers: [18, 49] Generated Node #0,1,2: 41:[18, 49] Operation: 14+35=49 Exploring Operation: 18-14=4, Resulting Numbers: [35, 4] Generated Node #0,1,3: 41:[35, 4] Operation: 18-14=4 Exploring Operation: 35+18=53, Resulting Numbers: [14, 53] Generated Node #0,1,4: 41:[14, 53] Operation: 35+18=53 Moving to Node #0,1,1 Current State: 41:[35, 32], Operations: ['8+10=18', '14+18=32'] Exploring Operation: 35*32=1120, Resulting Numbers: [1120] 1120,41 unequal: No Solution Exploring Operation: 35+32=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[18, 49], Operations: ['8+10=18', '14+35=49'] Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 18+49=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 18*49=882, Resulting Numbers: [882] 882,41 unequal: No Solution Moving to Node #0,1,4 Current State: 41:[14, 53], Operations: ['8+10=18', '35+18=53'] Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 14*53=742, Resulting Numbers: [742] 742,41 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[18, 21], Operations: ['8+10=18', '35-14=21'] Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 18*21=378, Resulting Numbers: [378] 378,41 unequal: No Solution Exploring Operation: 18+21=39, Resulting Numbers: [39] 39,41 unequal: No Solution Moving to Node #0,1,3 Current State: 41:[35, 4], Operations: ['8+10=18', '18-14=4'] Exploring Operation: 35*4=140, Resulting Numbers: [140] 140,41 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[35, 10, 22], Operations: ['8+14=22'] Exploring Operation: 10+22=32, Resulting Numbers: [35, 32] Generated Node #0,2,0: 41:[35, 32] Operation: 10+22=32 Exploring Operation: 35-10=25, Resulting Numbers: [22, 25] Generated Node #0,2,1: 41:[22, 25] Operation: 35-10=25 Exploring Operation: 35+22=57, Resulting Numbers: [10, 57] Generated Node #0,2,2: 41:[10, 57] Operation: 35+22=57 Exploring Operation: 35+10=45, Resulting Numbers: [22, 45] Generated Node #0,2,3: 41:[22, 45] Operation: 35+10=45 Exploring Operation: 22-10=12, Resulting Numbers: [35, 12] Generated Node #0,2,4: 41:[35, 12] Operation: 22-10=12 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 41:[35, 32], Operations: ['8+14=22', '10+22=32'] Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 35*32=1120, Resulting Numbers: [1120] 1120,41 unequal: No Solution Exploring Operation: 35+32=67, Resulting Numbers: [67] 67,41 unequal: No Solution No 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: 41:[22, 45], Operations: ['8+14=22', '35+10=45'] Exploring Operation: 22+45=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 22*45=990, Resulting Numbers: [990] 990,41 unequal: No Solution Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,41 unequal: No Solution No 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: 41:[22, 25], Operations: ['8+14=22', '35-10=25'] Exploring Operation: 22*25=550, Resulting Numbers: [550] 550,41 unequal: No Solution Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 22+25=47, Resulting Numbers: [47] 47,41 unequal: No Solution No 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: 41:[35, 12], Operations: ['8+14=22', '22-10=12'] Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,41 unequal: No Solution Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,41 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,41 unequal: No Solution No 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: 41:[10, 57], Operations: ['8+14=22', '35+22=57'] Exploring Operation: 10+57=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 57-10=47, Resulting Numbers: [47] 47,41 unequal: No Solution Exploring Operation: 10*57=570, Resulting Numbers: [570] 570,41 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: 41:[14, 10, 43], Operations: ['8+35=43'] Exploring Operation: 43-10=33, Resulting Numbers: [14, 33] Generated Node #0,3,0: 41:[14, 33] Operation: 43-10=33 Exploring Operation: 10+43=53, Resulting Numbers: [14, 53] Generated Node #0,3,1: 41:[14, 53] Operation: 10+43=53 Exploring Operation: 14-10=4, Resulting Numbers: [43, 4] Generated Node #0,3,2: 41:[43, 4] Operation: 14-10=4 Exploring Operation: 43-14=29, Resulting Numbers: [10, 29] Generated Node #0,3,3: 41:[10, 29] Operation: 43-14=29 Exploring Operation: 14+10=24, Resulting Numbers: [43, 24] Generated Node #0,3,4: 41:[43, 24] Operation: 14+10=24 Moving to Node #0,3,4 Current State: 41:[43, 24], Operations: ['8+35=43', '14+10=24'] Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 43*24=1032, Resulting Numbers: [1032] 1032,41 unequal: No Solution Moving to Node #0,3,0 Current State: 41:[14, 33], Operations: ['8+35=43', '43-10=33'] Exploring Operation: 14*33=462, Resulting Numbers: [462] 462,41 unequal: No Solution Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 14+33=47, Resulting Numbers: [47] 47,41 unequal: No Solution Moving to Node #0,3,1 Current State: 41:[14, 53], Operations: ['8+35=43', '10+43=53'] Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 14*53=742, Resulting Numbers: [742] 742,41 unequal: No Solution Moving to Node #0,3,2 Current State: 41:[43, 4], Operations: ['8+35=43', '14-10=4'] Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,41 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,41 unequal: No Solution Moving to Node #0,3,3 Current State: 41:[10, 29], Operations: ['8+35=43', '43-14=29'] Exploring Operation: 10+29=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 10*29=290, Resulting Numbers: [290] 290,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 41:[8, 14, 45], Operations: ['35+10=45'] Exploring Operation: 45-14=31, Resulting Numbers: [8, 31] Generated Node #0,4,0: 41:[8, 31] Operation: 45-14=31 Exploring Operation: 8+45=53, Resulting Numbers: [14, 53] Generated Node #0,4,1: 41:[14, 53] Operation: 8+45=53 Exploring Operation: 8+14=22, Resulting Numbers: [45, 22] Generated Node #0,4,2: 41:[45, 22] Operation: 8+14=22 Exploring Operation: 14-8=6, Resulting Numbers: [45, 6] Generated Node #0,4,3: 41:[45, 6] Operation: 14-8=6 Exploring Operation: 45-8=37, Resulting Numbers: [14, 37] Generated Node #0,4,4: 41:[14, 37] Operation: 45-8=37 Moving to Node #0,4,2 Current State: 41:[45, 22], Operations: ['35+10=45', '8+14=22'] Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 45+22=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 45*22=990, Resulting Numbers: [990] 990,41 unequal: No Solution Moving to Node #0,4,4 Current State: 41:[14, 37], Operations: ['35+10=45', '45-8=37'] Exploring Operation: 14+37=51, Resulting Numbers: [51] 51,41 unequal: No Solution Exploring Operation: 14*37=518, Resulting Numbers: [518] 518,41 unequal: No Solution Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,41 unequal: No Solution Moving to Node #0,4,1 Current State: 41:[14, 53], Operations: ['35+10=45', '8+45=53'] Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 14*53=742, Resulting Numbers: [742] 742,41 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,41 unequal: No Solution Moving to Node #0,4,3 Current State: 41:[45, 6], Operations: ['35+10=45', '14-8=6'] Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,41 unequal: No Solution Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,41 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,41 unequal: No Solution Moving to Node #0,4,0 Current State: 41:[8, 31], Operations: ['35+10=45', '45-14=31'] Exploring Operation: 8+31=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 8*31=248, Resulting Numbers: [248] 248,41 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 40, 24, 31, 41 ]
74
[ "40+24=64", "41-31=10", "64+10=74" ]
Current State: 74:[40, 24, 31, 41], Operations: [] Exploring Operation: 40+24=64, Resulting Numbers: [31, 41, 64] Generated Node #2: [31, 41, 64] from Operation: 40+24=64 Current State: 74:[31, 41, 64], Operations: ['40+24=64'] Exploring Operation: 41-31=10, Resulting Numbers: [64, 10] Generated Node #3: [64, 10] from Operation: 41-31=10 Current State: 74:[64, 10], Operations: ['40+24=64', '41-31=10'] Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[40, 24, 31, 41], Operations: [] Exploring Operation: 24+41=65, Resulting Numbers: [40, 31, 65] Generated Node #0,0: 74:[40, 31, 65] Operation: 24+41=65 Exploring Operation: 31-24=7, Resulting Numbers: [40, 41, 7] Generated Node #0,1: 74:[40, 41, 7] Operation: 31-24=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[40, 41, 7], Operations: ['31-24=7'] Exploring Operation: 41-7=34, Resulting Numbers: [40, 34] Generated Node #0,1,0: 74:[40, 34] Operation: 41-7=34 Exploring Operation: 41-40=1, Resulting Numbers: [7, 1] Generated Node #0,1,1: 74:[7, 1] Operation: 41-40=1 Moving to Node #0,1,0 Current State: 74:[40, 34], Operations: ['31-24=7', '41-7=34'] Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[40, 24, 31, 41], Operations: [] Exploring Operation: 31-24=7, Resulting Numbers: [40, 41, 7] Generated Node #0,1: 74:[40, 41, 7] Operation: 31-24=7 Moving to Node #0,1 Current State: 74:[40, 41, 7], Operations: ['31-24=7'] Exploring Operation: 41-7=34, Resulting Numbers: [40, 34] Generated Node #0,1,0: 74:[40, 34] Operation: 41-7=34 Moving to Node #0,1,0 Current State: 74:[40, 34], Operations: ['31-24=7', '41-7=34'] Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 38, 6, 31, 70 ]
83
[ "38+6=44", "70-31=39", "44+39=83" ]
Current State: 83:[38, 6, 31, 70], Operations: [] Exploring Operation: 38+6=44, Resulting Numbers: [31, 70, 44] Generated Node #2: [31, 70, 44] from Operation: 38+6=44 Current State: 83:[31, 70, 44], Operations: ['38+6=44'] Exploring Operation: 70-31=39, Resulting Numbers: [44, 39] Generated Node #3: [44, 39] from Operation: 70-31=39 Current State: 83:[44, 39], Operations: ['38+6=44', '70-31=39'] Exploring Operation: 44+39=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[38, 6, 31, 70], Operations: [] Exploring Operation: 38+6=44, Resulting Numbers: [31, 70, 44] Generated Node #0,0: 83:[31, 70, 44] Operation: 38+6=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[31, 70, 44], Operations: ['38+6=44'] Exploring Operation: 31+44=75, Resulting Numbers: [70, 75] Generated Node #0,0,0: 83:[70, 75] Operation: 31+44=75 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[70, 75], Operations: ['38+6=44', '31+44=75'] Exploring Operation: 70+75=145, Resulting Numbers: [145] 145,83 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
[ 62, 7, 45, 79 ]
69
[ "62-7=55", "45+79=124", "124-55=69" ]
Current State: 69:[62, 7, 45, 79], Operations: [] Exploring Operation: 62-7=55, Resulting Numbers: [45, 79, 55] Generated Node #2: [45, 79, 55] from Operation: 62-7=55 Current State: 69:[45, 79, 55], Operations: ['62-7=55'] Exploring Operation: 45+79=124, Resulting Numbers: [55, 124] Generated Node #3: [55, 124] from Operation: 45+79=124 Current State: 69:[55, 124], Operations: ['62-7=55', '45+79=124'] Exploring Operation: 124-55=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[62, 7, 45, 79], Operations: [] Exploring Operation: 62+7=69, Resulting Numbers: [45, 79, 69] Generated Node #0,0: 69:[45, 79, 69] Operation: 62+7=69 Exploring Operation: 45-7=38, Resulting Numbers: [62, 79, 38] Generated Node #0,1: 69:[62, 79, 38] Operation: 45-7=38 Exploring Operation: 79-45=34, Resulting Numbers: [62, 7, 34] Generated Node #0,2: 69:[62, 7, 34] Operation: 79-45=34 Exploring Operation: 62-45=17, Resulting Numbers: [7, 79, 17] Generated Node #0,3: 69:[7, 79, 17] Operation: 62-45=17 Exploring Operation: 79-62=17, Resulting Numbers: [7, 45, 17] Generated Node #0,4: 69:[7, 45, 17] Operation: 79-62=17 Moving to Node #0,3 Current State: 69:[7, 79, 17], Operations: ['62-45=17'] Exploring Operation: 7+17=24, Resulting Numbers: [79, 24] Generated Node #0,3,0: 69:[79, 24] Operation: 7+17=24 Exploring Operation: 79-17=62, Resulting Numbers: [7, 62] Generated Node #0,3,1: 69:[7, 62] Operation: 79-17=62 Exploring Operation: 79-7=72, Resulting Numbers: [17, 72] Generated Node #0,3,2: 69:[17, 72] Operation: 79-7=72 Exploring Operation: 17-7=10, Resulting Numbers: [79, 10] Generated Node #0,3,3: 69:[79, 10] Operation: 17-7=10 Exploring Operation: 7+79=86, Resulting Numbers: [17, 86] Generated Node #0,3,4: 69:[17, 86] Operation: 7+79=86 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 69:[17, 72], Operations: ['62-45=17', '79-7=72'] Exploring Operation: 72-17=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 17*72=1224, Resulting Numbers: [1224] 1224,69 unequal: No Solution Exploring Operation: 17+72=89, Resulting Numbers: [89] 89,69 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 #0,3,0 Current State: 69:[79, 24], Operations: ['62-45=17', '7+17=24'] Exploring Operation: 79-24=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 79*24=1896, Resulting Numbers: [1896] 1896,69 unequal: No Solution Exploring Operation: 79+24=103, Resulting Numbers: [103] 103,69 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 #0,3,1 Current State: 69:[7, 62], Operations: ['62-45=17', '79-17=62'] Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 7+62=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[62, 7, 45, 79], Operations: [] Exploring Operation: 62-45=17, Resulting Numbers: [7, 79, 17] Generated Node #0,3: 69:[7, 79, 17] Operation: 62-45=17 Moving to Node #0,3 Current State: 69:[7, 79, 17], Operations: ['62-45=17'] Exploring Operation: 79-17=62, Resulting Numbers: [7, 62] Generated Node #0,3,1: 69:[7, 62] Operation: 79-17=62 Moving to Node #0,3,1 Current State: 69:[7, 62], Operations: ['62-45=17', '79-17=62'] Exploring Operation: 7+62=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 18, 50, 27, 3 ]
53
[ "27-18=9", "9/3=3", "50+3=53" ]
Current State: 53:[18, 50, 27, 3], Operations: [] Exploring Operation: 27-18=9, Resulting Numbers: [50, 3, 9] Generated Node #2: [50, 3, 9] from Operation: 27-18=9 Current State: 53:[50, 3, 9], Operations: ['27-18=9'] Exploring Operation: 9/3=3, Resulting Numbers: [50, 3] Generated Node #3: [50, 3] from Operation: 9/3=3 Current State: 53:[50, 3], Operations: ['27-18=9', '9/3=3'] Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[18, 50, 27, 3], Operations: [] Exploring Operation: 18*3=54, Resulting Numbers: [50, 27, 54] Generated Node #0,0: 53:[50, 27, 54] Operation: 18*3=54 Exploring Operation: 27+3=30, Resulting Numbers: [18, 50, 30] Generated Node #0,1: 53:[18, 50, 30] Operation: 27+3=30 Exploring Operation: 50+3=53, Resulting Numbers: [18, 27, 53] Generated Node #0,2: 53:[18, 27, 53] Operation: 50+3=53 Exploring Operation: 18+3=21, Resulting Numbers: [50, 27, 21] Generated Node #0,3: 53:[50, 27, 21] Operation: 18+3=21 Exploring Operation: 18+27=45, Resulting Numbers: [50, 3, 45] Generated Node #0,4: 53:[50, 3, 45] Operation: 18+27=45 Moving to Node #0,0 Current State: 53:[50, 27, 54], Operations: ['18*3=54'] Exploring Operation: 50+27=77, Resulting Numbers: [54, 77] Generated Node #0,0,0: 53:[54, 77] Operation: 50+27=77 Exploring Operation: 50-27=23, Resulting Numbers: [54, 23] Generated Node #0,0,1: 53:[54, 23] Operation: 50-27=23 Exploring Operation: 54-27=27, Resulting Numbers: [50, 27] Generated Node #0,0,2: 53:[50, 27] Operation: 54-27=27 Exploring Operation: 27+54=81, Resulting Numbers: [50, 81] Generated Node #0,0,3: 53:[50, 81] Operation: 27+54=81 Exploring Operation: 54/27=2, Resulting Numbers: [50, 2] Generated Node #0,0,4: 53:[50, 2] Operation: 54/27=2 Moving to Node #0,2 Current State: 53:[18, 27, 53], Operations: ['50+3=53'] Exploring Operation: 27-18=9, Resulting Numbers: [53, 9] Generated Node #0,2,0: 53:[53, 9] Operation: 27-18=9 Exploring Operation: 27+53=80, Resulting Numbers: [18, 80] Generated Node #0,2,1: 53:[18, 80] Operation: 27+53=80 Exploring Operation: 18+53=71, Resulting Numbers: [27, 71] Generated Node #0,2,2: 53:[27, 71] Operation: 18+53=71 Exploring Operation: 53-18=35, Resulting Numbers: [27, 35] Generated Node #0,2,3: 53:[27, 35] Operation: 53-18=35 Exploring Operation: 18+27=45, Resulting Numbers: [53, 45] Generated Node #0,2,4: 53:[53, 45] Operation: 18+27=45 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 53:[53, 45], Operations: ['50+3=53', '18+27=45'] Exploring Operation: 53*45=2385, Resulting Numbers: [2385] 2385,53 unequal: No Solution Exploring Operation: 53-45=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 53+45=98, Resulting Numbers: [98] 98,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 53:[53, 9], Operations: ['50+3=53', '27-18=9'] Exploring Operation: 53*9=477, Resulting Numbers: [477] 477,53 unequal: No Solution Exploring Operation: 53-9=44, Resulting Numbers: [44] 44,53 unequal: No Solution Exploring Operation: 53+9=62, Resulting Numbers: [62] 62,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 53:[27, 71], Operations: ['50+3=53', '18+53=71'] Exploring Operation: 27*71=1917, Resulting Numbers: [1917] 1917,53 unequal: No Solution Exploring Operation: 27+71=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 71-27=44, Resulting Numbers: [44] 44,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 53:[27, 35], Operations: ['50+3=53', '53-18=35'] Exploring Operation: 27*35=945, Resulting Numbers: [945] 945,53 unequal: No Solution Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 27+35=62, Resulting Numbers: [62] 62,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 53:[18, 80], Operations: ['50+3=53', '27+53=80'] Exploring Operation: 18*80=1440, Resulting Numbers: [1440] 1440,53 unequal: No Solution Exploring Operation: 18+80=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,53 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: 53:[50, 3, 45], Operations: ['18+27=45'] Exploring Operation: 3+45=48, Resulting Numbers: [50, 48] Generated Node #0,4,0: 53:[50, 48] Operation: 3+45=48 Exploring Operation: 45-3=42, Resulting Numbers: [50, 42] Generated Node #0,4,1: 53:[50, 42] Operation: 45-3=42 Exploring Operation: 50-3=47, Resulting Numbers: [45, 47] Generated Node #0,4,2: 53:[45, 47] Operation: 50-3=47 Exploring Operation: 45/3=15, Resulting Numbers: [50, 15] Generated Node #0,4,3: 53:[50, 15] Operation: 45/3=15 Exploring Operation: 50+3=53, Resulting Numbers: [45, 53] Generated Node #0,4,4: 53:[45, 53] Operation: 50+3=53 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 53:[50, 48], Operations: ['18+27=45', '3+45=48'] Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,53 unequal: No Solution Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 53:[45, 53], Operations: ['18+27=45', '50+3=53'] Exploring Operation: 45*53=2385, Resulting Numbers: [2385] 2385,53 unequal: No Solution Exploring Operation: 45+53=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 53-45=8, Resulting Numbers: [8] 8,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 53:[50, 42], Operations: ['18+27=45', '45-3=42'] Exploring Operation: 50*42=2100, Resulting Numbers: [2100] 2100,53 unequal: No Solution Exploring Operation: 50+42=92, Resulting Numbers: [92] 92,53 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 53:[45, 47], Operations: ['18+27=45', '50-3=47'] Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 45*47=2115, Resulting Numbers: [2115] 2115,53 unequal: No Solution Exploring Operation: 45+47=92, Resulting Numbers: [92] 92,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 53:[50, 15], Operations: ['18+27=45', '45/3=15'] Exploring Operation: 50*15=750, Resulting Numbers: [750] 750,53 unequal: No Solution Exploring Operation: 50+15=65, Resulting Numbers: [65] 65,53 unequal: No Solution Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,53 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: 53:[18, 50, 30], Operations: ['27+3=30'] Exploring Operation: 18+50=68, Resulting Numbers: [30, 68] Generated Node #0,1,0: 53:[30, 68] Operation: 18+50=68 Exploring Operation: 30-18=12, Resulting Numbers: [50, 12] Generated Node #0,1,1: 53:[50, 12] Operation: 30-18=12 Exploring Operation: 18+30=48, Resulting Numbers: [50, 48] Generated Node #0,1,2: 53:[50, 48] Operation: 18+30=48 Exploring Operation: 50-18=32, Resulting Numbers: [30, 32] Generated Node #0,1,3: 53:[30, 32] Operation: 50-18=32 Exploring Operation: 50+30=80, Resulting Numbers: [18, 80] Generated Node #0,1,4: 53:[18, 80] Operation: 50+30=80 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 53:[50, 48], Operations: ['27+3=30', '18+30=48'] Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,53 unequal: No Solution Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[30, 68], Operations: ['27+3=30', '18+50=68'] Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 30+68=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 30*68=2040, Resulting Numbers: [2040] 2040,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 53:[50, 12], Operations: ['27+3=30', '30-18=12'] Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,53 unequal: No Solution Exploring Operation: 50*12=600, Resulting Numbers: [600] 600,53 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 53:[30, 32], Operations: ['27+3=30', '50-18=32'] Exploring Operation: 30*32=960, Resulting Numbers: [960] 960,53 unequal: No Solution Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,53 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 53:[18, 80], Operations: ['27+3=30', '50+30=80'] Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,53 unequal: No Solution Exploring Operation: 18*80=1440, Resulting Numbers: [1440] 1440,53 unequal: No Solution Exploring Operation: 18+80=98, Resulting Numbers: [98] 98,53 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: 53:[50, 27, 21], Operations: ['18+3=21'] Exploring Operation: 50+27=77, Resulting Numbers: [21, 77] Generated Node #0,3,0: 53:[21, 77] Operation: 50+27=77 Exploring Operation: 50-21=29, Resulting Numbers: [27, 29] Generated Node #0,3,1: 53:[27, 29] Operation: 50-21=29 Exploring Operation: 27+21=48, Resulting Numbers: [50, 48] Generated Node #0,3,2: 53:[50, 48] Operation: 27+21=48 Exploring Operation: 50+21=71, Resulting Numbers: [27, 71] Generated Node #0,3,3: 53:[27, 71] Operation: 50+21=71 Exploring Operation: 27-21=6, Resulting Numbers: [50, 6] Generated Node #0,3,4: 53:[50, 6] Operation: 27-21=6 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 53:[50, 48], Operations: ['18+3=21', '27+21=48'] Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 53:[27, 71], Operations: ['18+3=21', '50+21=71'] Exploring Operation: 71-27=44, Resulting Numbers: [44] 44,53 unequal: No Solution Exploring Operation: 27+71=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 27*71=1917, Resulting Numbers: [1917] 1917,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 53:[27, 29], Operations: ['18+3=21', '50-21=29'] Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,53 unequal: No Solution Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 53:[50, 6], Operations: ['18+3=21', '27-21=6'] Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,53 unequal: No Solution Exploring Operation: 50+6=56, Resulting Numbers: [56] 56,53 unequal: No Solution Exploring Operation: 50*6=300, Resulting Numbers: [300] 300,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 53:[21, 77], Operations: ['18+3=21', '50+27=77'] Exploring Operation: 21+77=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 21*77=1617, Resulting Numbers: [1617] 1617,53 unequal: No Solution Exploring Operation: 77-21=56, Resulting Numbers: [56] 56,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 53:[54, 77], Operations: ['18*3=54', '50+27=77'] Exploring Operation: 54*77=4158, Resulting Numbers: [4158] 4158,53 unequal: No Solution Exploring Operation: 54+77=131, Resulting Numbers: [131] 131,53 unequal: No Solution Exploring Operation: 77-54=23, Resulting Numbers: [23] 23,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[50, 27], Operations: ['18*3=54', '54-27=27'] Exploring Operation: 50-27=23, Resulting Numbers: [23] 23,53 unequal: No Solution Exploring Operation: 50+27=77, Resulting Numbers: [77] 77,53 unequal: No Solution Exploring Operation: 50*27=1350, Resulting Numbers: [1350] 1350,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[54, 23], Operations: ['18*3=54', '50-27=23'] Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,53 unequal: No Solution Exploring Operation: 54+23=77, Resulting Numbers: [77] 77,53 unequal: No Solution Exploring Operation: 54*23=1242, Resulting Numbers: [1242] 1242,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[50, 81], Operations: ['18*3=54', '27+54=81'] Exploring Operation: 50*81=4050, Resulting Numbers: [4050] 4050,53 unequal: No Solution Exploring Operation: 50+81=131, Resulting Numbers: [131] 131,53 unequal: No Solution Exploring Operation: 81-50=31, Resulting Numbers: [31] 31,53 unequal: No Solution Moving to Node #0,0,4 Current State: 53:[50, 2], Operations: ['18*3=54', '54/27=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,53 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,53 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,53 unequal: No Solution Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,53 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 12, 2, 16, 5 ]
66
[ "12+2=14", "16*5=80", "80-14=66" ]
Current State: 66:[12, 2, 16, 5], Operations: [] Exploring Operation: 12+2=14, Resulting Numbers: [16, 5, 14] Generated Node #2: [16, 5, 14] from Operation: 12+2=14 Current State: 66:[16, 5, 14], Operations: ['12+2=14'] Exploring Operation: 16*5=80, Resulting Numbers: [14, 80] Generated Node #3: [14, 80] from Operation: 16*5=80 Current State: 66:[14, 80], Operations: ['12+2=14', '16*5=80'] Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[12, 2, 16, 5], Operations: [] Exploring Operation: 16+5=21, Resulting Numbers: [12, 2, 21] Generated Node #0,0: 66:[12, 2, 21] Operation: 16+5=21 Exploring Operation: 16-5=11, Resulting Numbers: [12, 2, 11] Generated Node #0,1: 66:[12, 2, 11] Operation: 16-5=11 Exploring Operation: 16-12=4, Resulting Numbers: [2, 5, 4] Generated Node #0,2: 66:[2, 5, 4] Operation: 16-12=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[12, 2, 11], Operations: ['16-5=11'] Exploring Operation: 12+11=23, Resulting Numbers: [2, 23] Generated Node #0,1,0: 66:[2, 23] Operation: 12+11=23 Exploring Operation: 12/2=6, Resulting Numbers: [11, 6] Generated Node #0,1,1: 66:[11, 6] Operation: 12/2=6 Exploring Operation: 12-2=10, Resulting Numbers: [11, 10] Generated Node #0,1,2: 66:[11, 10] Operation: 12-2=10 Moving to Node #0,1,1 Current State: 66:[11, 6], Operations: ['16-5=11', '12/2=6'] Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[12, 2, 16, 5], Operations: [] Exploring Operation: 16-5=11, Resulting Numbers: [12, 2, 11] Generated Node #0,1: 66:[12, 2, 11] Operation: 16-5=11 Moving to Node #0,1 Current State: 66:[12, 2, 11], Operations: ['16-5=11'] Exploring Operation: 12/2=6, Resulting Numbers: [11, 6] Generated Node #0,1,1: 66:[11, 6] Operation: 12/2=6 Moving to Node #0,1,1 Current State: 66:[11, 6], Operations: ['16-5=11', '12/2=6'] Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 35, 5, 10, 4 ]
44
[ "35-5=30", "10+4=14", "30+14=44" ]
Current State: 44:[35, 5, 10, 4], Operations: [] Exploring Operation: 35-5=30, Resulting Numbers: [10, 4, 30] Generated Node #2: [10, 4, 30] from Operation: 35-5=30 Current State: 44:[10, 4, 30], Operations: ['35-5=30'] Exploring Operation: 10+4=14, Resulting Numbers: [30, 14] Generated Node #3: [30, 14] from Operation: 10+4=14 Current State: 44:[30, 14], Operations: ['35-5=30', '10+4=14'] Exploring Operation: 30+14=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[35, 5, 10, 4], Operations: [] Exploring Operation: 35+10=45, Resulting Numbers: [5, 4, 45] Generated Node #0,0: 44:[5, 4, 45] Operation: 35+10=45 Exploring Operation: 35/5=7, Resulting Numbers: [10, 4, 7] Generated Node #0,1: 44:[10, 4, 7] Operation: 35/5=7 Exploring Operation: 35-10=25, Resulting Numbers: [5, 4, 25] Generated Node #0,2: 44:[5, 4, 25] Operation: 35-10=25 Moving to Node #0,0 Current State: 44:[5, 4, 45], Operations: ['35+10=45'] Exploring Operation: 5+4=9, Resulting Numbers: [45, 9] Generated Node #0,0,0: 44:[45, 9] Operation: 5+4=9 Exploring Operation: 5-4=1, Resulting Numbers: [45, 1] Generated Node #0,0,1: 44:[45, 1] Operation: 5-4=1 Exploring Operation: 45/5=9, Resulting Numbers: [4, 9] Generated Node #0,0,2: 44:[4, 9] Operation: 45/5=9 Moving to Node #0,1 Current State: 44:[10, 4, 7], Operations: ['35/5=7'] Exploring Operation: 10-7=3, Resulting Numbers: [4, 3] Generated Node #0,1,0: 44:[4, 3] Operation: 10-7=3 Exploring Operation: 4+7=11, Resulting Numbers: [10, 11] Generated Node #0,1,1: 44:[10, 11] Operation: 4+7=11 Exploring Operation: 7-4=3, Resulting Numbers: [10, 3] Generated Node #0,1,2: 44:[10, 3] Operation: 7-4=3 Moving to Node #0,2 Current State: 44:[5, 4, 25], Operations: ['35-10=25'] Exploring Operation: 25/5=5, Resulting Numbers: [4, 5] Generated Node #0,2,0: 44:[4, 5] Operation: 25/5=5 Exploring Operation: 25-5=20, Resulting Numbers: [4, 20] Generated Node #0,2,1: 44:[4, 20] Operation: 25-5=20 Exploring Operation: 25-4=21, Resulting Numbers: [5, 21] Generated Node #0,2,2: 44:[5, 21] Operation: 25-4=21 Moving to Node #0,1,0 Current State: 44:[4, 3], Operations: ['35/5=7', '10-7=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,44 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,44 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,44 unequal: No Solution Moving to Node #0,2,0 Current State: 44:[4, 5], Operations: ['35-10=25', '25/5=5'] Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,44 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[10, 11], Operations: ['35/5=7', '4+7=11'] Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,44 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,44 unequal: No Solution Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,44 unequal: No Solution Moving to Node #0,1,2 Current State: 44:[10, 3], Operations: ['35/5=7', '7-4=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,44 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,44 unequal: No Solution Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,44 unequal: No Solution Moving to Node #0,2,2 Current State: 44:[5, 21], Operations: ['35-10=25', '25-4=21'] Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,44 unequal: No Solution Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,44 unequal: No Solution Moving to Node #0,0,1 Current State: 44:[45, 1], Operations: ['35+10=45', '5-4=1'] Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,44 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[35, 5, 10, 4], Operations: [] Exploring Operation: 35+10=45, Resulting Numbers: [5, 4, 45] Generated Node #0,0: 44:[5, 4, 45] Operation: 35+10=45 Moving to Node #0,0 Current State: 44:[5, 4, 45], Operations: ['35+10=45'] Exploring Operation: 5-4=1, Resulting Numbers: [45, 1] Generated Node #0,0,1: 44:[45, 1] Operation: 5-4=1 Moving to Node #0,0,1 Current State: 44:[45, 1], Operations: ['35+10=45', '5-4=1'] Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
0.971354
hs_3
sum_heuristic
[ 27, 4, 72, 87 ]
87
[ "87-27=60", "60/4=15", "72+15=87" ]
Current State: 87:[27, 4, 72, 87], Operations: [] Exploring Operation: 87-27=60, Resulting Numbers: [4, 72, 60] Generated Node #2: [4, 72, 60] from Operation: 87-27=60 Current State: 87:[4, 72, 60], Operations: ['87-27=60'] Exploring Operation: 60/4=15, Resulting Numbers: [72, 15] Generated Node #3: [72, 15] from Operation: 60/4=15 Current State: 87:[72, 15], Operations: ['87-27=60', '60/4=15'] Exploring Operation: 72+15=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[27, 4, 72, 87], Operations: [] Exploring Operation: 27+72=99, Resulting Numbers: [4, 87, 99] Generated Node #0,0: 87:[4, 87, 99] Operation: 27+72=99 Moving to Node #0,0 Current State: 87:[4, 87, 99], Operations: ['27+72=99'] Exploring Operation: 99-4=95, Resulting Numbers: [87, 95] Generated Node #0,0,0: 87:[87, 95] Operation: 99-4=95 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[87, 95], Operations: ['27+72=99', '99-4=95'] Exploring Operation: 95-87=8, Resulting Numbers: [8] 8,87 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
[ 84, 40, 10, 3 ]
28
[ "10-3=7", "84/7=12", "40-12=28" ]
Current State: 28:[84, 40, 10, 3], Operations: [] Exploring Operation: 10-3=7, Resulting Numbers: [84, 40, 7] Generated Node #2: [84, 40, 7] from Operation: 10-3=7 Current State: 28:[84, 40, 7], Operations: ['10-3=7'] Exploring Operation: 84/7=12, Resulting Numbers: [40, 12] Generated Node #3: [40, 12] from Operation: 84/7=12 Current State: 28:[40, 12], Operations: ['10-3=7', '84/7=12'] Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[84, 40, 10, 3], Operations: [] Exploring Operation: 84/3=28, Resulting Numbers: [40, 10, 28] Generated Node #0,0: 28:[40, 10, 28] Operation: 84/3=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[40, 10, 28], Operations: ['84/3=28'] Exploring Operation: 40/10=4, Resulting Numbers: [28, 4] Generated Node #0,0,0: 28:[28, 4] Operation: 40/10=4 Moving to Node #0,0,0 Current State: 28:[28, 4], Operations: ['84/3=28', '40/10=4'] Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 17, 24, 5, 30 ]
97
[ "30-24=6", "17*6=102", "102-5=97" ]
Current State: 97:[17, 24, 5, 30], Operations: [] Exploring Operation: 30-24=6, Resulting Numbers: [17, 5, 6] Generated Node #2: [17, 5, 6] from Operation: 30-24=6 Current State: 97:[17, 5, 6], Operations: ['30-24=6'] Exploring Operation: 17*6=102, Resulting Numbers: [5, 102] Generated Node #3: [5, 102] from Operation: 17*6=102 Current State: 97:[5, 102], Operations: ['30-24=6', '17*6=102'] Exploring Operation: 102-5=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[17, 24, 5, 30], Operations: [] Exploring Operation: 17*5=85, Resulting Numbers: [24, 30, 85] Generated Node #0,0: 97:[24, 30, 85] Operation: 17*5=85 Exploring Operation: 17+24=41, Resulting Numbers: [5, 30, 41] Generated Node #0,1: 97:[5, 30, 41] Operation: 17+24=41 Exploring Operation: 24*5=120, Resulting Numbers: [17, 30, 120] Generated Node #0,2: 97:[17, 30, 120] Operation: 24*5=120 Exploring Operation: 5*30=150, Resulting Numbers: [17, 24, 150] Generated Node #0,3: 97:[17, 24, 150] Operation: 5*30=150 Moving to Node #0,0 Current State: 97:[24, 30, 85], Operations: ['17*5=85'] Exploring Operation: 30-24=6, Resulting Numbers: [85, 6] Generated Node #0,0,0: 97:[85, 6] Operation: 30-24=6 Exploring Operation: 24+30=54, Resulting Numbers: [85, 54] Generated Node #0,0,1: 97:[85, 54] Operation: 24+30=54 Exploring Operation: 30+85=115, Resulting Numbers: [24, 115] Generated Node #0,0,2: 97:[24, 115] Operation: 30+85=115 Exploring Operation: 24+85=109, Resulting Numbers: [30, 109] Generated Node #0,0,3: 97:[30, 109] Operation: 24+85=109 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 97:[85, 54], Operations: ['17*5=85', '24+30=54'] Exploring Operation: 85+54=139, Resulting Numbers: [139] 139,97 unequal: No Solution Exploring Operation: 85-54=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 85*54=4590, Resulting Numbers: [4590] 4590,97 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 #0,0,3 Current State: 97:[30, 109], Operations: ['17*5=85', '24+85=109'] Exploring Operation: 109-30=79, Resulting Numbers: [79] 79,97 unequal: No Solution Exploring Operation: 30*109=3270, Resulting Numbers: [3270] 3270,97 unequal: No Solution Exploring Operation: 30+109=139, Resulting Numbers: [139] 139,97 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 #0,0,2 Current State: 97:[24, 115], Operations: ['17*5=85', '30+85=115'] Exploring Operation: 24*115=2760, Resulting Numbers: [2760] 2760,97 unequal: No Solution Exploring Operation: 24+115=139, Resulting Numbers: [139] 139,97 unequal: No Solution Exploring Operation: 115-24=91, Resulting Numbers: [91] 91,97 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 #0,0,0 Current State: 97:[85, 6], Operations: ['17*5=85', '30-24=6'] Exploring Operation: 85*6=510, Resulting Numbers: [510] 510,97 unequal: No Solution Exploring Operation: 85+6=91, Resulting Numbers: [91] 91,97 unequal: No Solution Exploring Operation: 85-6=79, Resulting Numbers: [79] 79,97 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: 97:[17, 30, 120], Operations: ['24*5=120'] Exploring Operation: 30-17=13, Resulting Numbers: [120, 13] Generated Node #0,2,0: 97:[120, 13] Operation: 30-17=13 Exploring Operation: 120-17=103, Resulting Numbers: [30, 103] Generated Node #0,2,1: 97:[30, 103] Operation: 120-17=103 Exploring Operation: 17+30=47, Resulting Numbers: [120, 47] Generated Node #0,2,2: 97:[120, 47] Operation: 17+30=47 Exploring Operation: 120-30=90, Resulting Numbers: [17, 90] Generated Node #0,2,3: 97:[17, 90] Operation: 120-30=90 Moving to Node #0,3 Current State: 97:[17, 24, 150], Operations: ['5*30=150'] Exploring Operation: 150-17=133, Resulting Numbers: [24, 133] Generated Node #0,3,0: 97:[24, 133] Operation: 150-17=133 Exploring Operation: 150-24=126, Resulting Numbers: [17, 126] Generated Node #0,3,1: 97:[17, 126] Operation: 150-24=126 Exploring Operation: 24-17=7, Resulting Numbers: [150, 7] Generated Node #0,3,2: 97:[150, 7] Operation: 24-17=7 Exploring Operation: 17+24=41, Resulting Numbers: [150, 41] Generated Node #0,3,3: 97:[150, 41] Operation: 17+24=41 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 97:[24, 133], Operations: ['5*30=150', '150-17=133'] Exploring Operation: 24+133=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 24*133=3192, Resulting Numbers: [3192] 3192,97 unequal: No Solution Exploring Operation: 133-24=109, Resulting Numbers: [109] 109,97 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 #0,3,1 Current State: 97:[17, 126], Operations: ['5*30=150', '150-24=126'] Exploring Operation: 17*126=2142, Resulting Numbers: [2142] 2142,97 unequal: No Solution Exploring Operation: 126-17=109, Resulting Numbers: [109] 109,97 unequal: No Solution Exploring Operation: 17+126=143, Resulting Numbers: [143] 143,97 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 #0,3,3 Current State: 97:[150, 41], Operations: ['5*30=150', '17+24=41'] Exploring Operation: 150*41=6150, Resulting Numbers: [6150] 6150,97 unequal: No Solution Exploring Operation: 150+41=191, Resulting Numbers: [191] 191,97 unequal: No Solution Exploring Operation: 150-41=109, Resulting Numbers: [109] 109,97 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 #0,3,2 Current State: 97:[150, 7], Operations: ['5*30=150', '24-17=7'] Exploring Operation: 150*7=1050, Resulting Numbers: [1050] 1050,97 unequal: No Solution Exploring Operation: 150+7=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 150-7=143, Resulting Numbers: [143] 143,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 97:[5, 30, 41], Operations: ['17+24=41'] Exploring Operation: 5*30=150, Resulting Numbers: [41, 150] Generated Node #0,1,0: 97:[41, 150] Operation: 5*30=150 Exploring Operation: 5+41=46, Resulting Numbers: [30, 46] Generated Node #0,1,1: 97:[30, 46] Operation: 5+41=46 Exploring Operation: 5+30=35, Resulting Numbers: [41, 35] Generated Node #0,1,2: 97:[41, 35] Operation: 5+30=35 Exploring Operation: 30+41=71, Resulting Numbers: [5, 71] Generated Node #0,1,3: 97:[5, 71] Operation: 30+41=71 Moving to Node #0,2,1 Current State: 97:[30, 103], Operations: ['24*5=120', '120-17=103'] Exploring Operation: 103-30=73, Resulting Numbers: [73] 73,97 unequal: No Solution Exploring Operation: 30+103=133, Resulting Numbers: [133] 133,97 unequal: No Solution Exploring Operation: 30*103=3090, Resulting Numbers: [3090] 3090,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[120, 47], Operations: ['24*5=120', '17+30=47'] Exploring Operation: 120-47=73, Resulting Numbers: [73] 73,97 unequal: No Solution Exploring Operation: 120+47=167, Resulting Numbers: [167] 167,97 unequal: No Solution Exploring Operation: 120*47=5640, Resulting Numbers: [5640] 5640,97 unequal: No Solution Moving to Node #0,2,3 Current State: 97:[17, 90], Operations: ['24*5=120', '120-30=90'] Exploring Operation: 17+90=107, Resulting Numbers: [107] 107,97 unequal: No Solution Exploring Operation: 90-17=73, Resulting Numbers: [73] 73,97 unequal: No Solution Exploring Operation: 17*90=1530, Resulting Numbers: [1530] 1530,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[120, 13], Operations: ['24*5=120', '30-17=13'] Exploring Operation: 120-13=107, Resulting Numbers: [107] 107,97 unequal: No Solution Exploring Operation: 120*13=1560, Resulting Numbers: [1560] 1560,97 unequal: No Solution Exploring Operation: 120+13=133, Resulting Numbers: [133] 133,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[41, 150], Operations: ['17+24=41', '5*30=150'] Exploring Operation: 41*150=6150, Resulting Numbers: [6150] 6150,97 unequal: No Solution Exploring Operation: 150-41=109, Resulting Numbers: [109] 109,97 unequal: No Solution Exploring Operation: 41+150=191, Resulting Numbers: [191] 191,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[30, 46], Operations: ['17+24=41', '5+41=46'] Exploring Operation: 30+46=76, Resulting Numbers: [76] 76,97 unequal: No Solution Exploring Operation: 30*46=1380, Resulting Numbers: [1380] 1380,97 unequal: No Solution Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,97 unequal: No Solution Moving to Node #0,1,3 Current State: 97:[5, 71], Operations: ['17+24=41', '30+41=71'] Exploring Operation: 5*71=355, Resulting Numbers: [355] 355,97 unequal: No Solution Exploring Operation: 5+71=76, Resulting Numbers: [76] 76,97 unequal: No Solution Exploring Operation: 71-5=66, Resulting Numbers: [66] 66,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[41, 35], Operations: ['17+24=41', '5+30=35'] Exploring Operation: 41+35=76, Resulting Numbers: [76] 76,97 unequal: No Solution Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,97 unequal: No Solution Exploring Operation: 41*35=1435, Resulting Numbers: [1435] 1435,97 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 74, 4, 52, 59 ]
41
[ "74-4=70", "52+59=111", "111-70=41" ]
Current State: 41:[74, 4, 52, 59], Operations: [] Exploring Operation: 74-4=70, Resulting Numbers: [52, 59, 70] Generated Node #2: [52, 59, 70] from Operation: 74-4=70 Current State: 41:[52, 59, 70], Operations: ['74-4=70'] Exploring Operation: 52+59=111, Resulting Numbers: [70, 111] Generated Node #3: [70, 111] from Operation: 52+59=111 Current State: 41:[70, 111], Operations: ['74-4=70', '52+59=111'] Exploring Operation: 111-70=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[74, 4, 52, 59], Operations: [] Exploring Operation: 74-4=70, Resulting Numbers: [52, 59, 70] Generated Node #0,0: 41:[52, 59, 70] Operation: 74-4=70 Exploring Operation: 74+4=78, Resulting Numbers: [52, 59, 78] Generated Node #0,1: 41:[52, 59, 78] Operation: 74+4=78 Exploring Operation: 52-4=48, Resulting Numbers: [74, 59, 48] Generated Node #0,2: 41:[74, 59, 48] Operation: 52-4=48 Exploring Operation: 4+52=56, Resulting Numbers: [74, 59, 56] Generated Node #0,3: 41:[74, 59, 56] Operation: 4+52=56 Exploring Operation: 59-4=55, Resulting Numbers: [74, 52, 55] Generated Node #0,4: 41:[74, 52, 55] Operation: 59-4=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[52, 59, 70], Operations: ['74-4=70'] Exploring Operation: 70-59=11, Resulting Numbers: [52, 11] Generated Node #0,0,0: 41:[52, 11] Operation: 70-59=11 Exploring Operation: 52+70=122, Resulting Numbers: [59, 122] Generated Node #0,0,1: 41:[59, 122] Operation: 52+70=122 Exploring Operation: 70-52=18, Resulting Numbers: [59, 18] Generated Node #0,0,2: 41:[59, 18] Operation: 70-52=18 Exploring Operation: 52+59=111, Resulting Numbers: [70, 111] Generated Node #0,0,3: 41:[70, 111] Operation: 52+59=111 Exploring Operation: 59-52=7, Resulting Numbers: [70, 7] Generated Node #0,0,4: 41:[70, 7] Operation: 59-52=7 Moving to Node #0,0,0 Current State: 41:[52, 11], Operations: ['74-4=70', '70-59=11'] Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[74, 4, 52, 59], Operations: [] Exploring Operation: 74-4=70, Resulting Numbers: [52, 59, 70] Generated Node #0,0: 41:[52, 59, 70] Operation: 74-4=70 Moving to Node #0,0 Current State: 41:[52, 59, 70], Operations: ['74-4=70'] Exploring Operation: 70-59=11, Resulting Numbers: [52, 11] Generated Node #0,0,0: 41:[52, 11] Operation: 70-59=11 Moving to Node #0,0,0 Current State: 41:[52, 11], Operations: ['74-4=70', '70-59=11'] Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 42, 96, 25, 8 ]
37
[ "96-42=54", "25-8=17", "54-17=37" ]
Current State: 37:[42, 96, 25, 8], Operations: [] Exploring Operation: 96-42=54, Resulting Numbers: [25, 8, 54] Generated Node #2: [25, 8, 54] from Operation: 96-42=54 Current State: 37:[25, 8, 54], Operations: ['96-42=54'] Exploring Operation: 25-8=17, Resulting Numbers: [54, 17] Generated Node #3: [54, 17] from Operation: 25-8=17 Current State: 37:[54, 17], Operations: ['96-42=54', '25-8=17'] Exploring Operation: 54-17=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[42, 96, 25, 8], Operations: [] Exploring Operation: 96/8=12, Resulting Numbers: [42, 25, 12] Generated Node #0,0: 37:[42, 25, 12] Operation: 96/8=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[42, 25, 12], Operations: ['96/8=12'] Exploring Operation: 25+12=37, Resulting Numbers: [42, 37] Generated Node #0,0,0: 37:[42, 37] Operation: 25+12=37 Moving to Node #0,0,0 Current State: 37:[42, 37], Operations: ['96/8=12', '25+12=37'] Exploring Operation: 42-37=5, Resulting Numbers: [5] 5,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 75, 80, 6, 2 ]
91
[ "75-6=69", "80*2=160", "160-69=91" ]
Current State: 91:[75, 80, 6, 2], Operations: [] Exploring Operation: 75-6=69, Resulting Numbers: [80, 2, 69] Generated Node #2: [80, 2, 69] from Operation: 75-6=69 Current State: 91:[80, 2, 69], Operations: ['75-6=69'] Exploring Operation: 80*2=160, Resulting Numbers: [69, 160] Generated Node #3: [69, 160] from Operation: 80*2=160 Current State: 91:[69, 160], Operations: ['75-6=69', '80*2=160'] Exploring Operation: 160-69=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[75, 80, 6, 2], Operations: [] Exploring Operation: 80-75=5, Resulting Numbers: [6, 2, 5] Generated Node #0,0: 91:[6, 2, 5] Operation: 80-75=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[6, 2, 5], Operations: ['80-75=5'] Exploring Operation: 2+5=7, Resulting Numbers: [6, 7] Generated Node #0,0,0: 91:[6, 7] Operation: 2+5=7 Moving to Node #0,0,0 Current State: 91:[6, 7], Operations: ['80-75=5', '2+5=7'] Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 37, 38, 2, 63 ]
24
[ "37+38=75", "75-63=12", "2*12=24" ]
Current State: 24:[37, 38, 2, 63], Operations: [] Exploring Operation: 37+38=75, Resulting Numbers: [2, 63, 75] Generated Node #2: [2, 63, 75] from Operation: 37+38=75 Current State: 24:[2, 63, 75], Operations: ['37+38=75'] Exploring Operation: 75-63=12, Resulting Numbers: [2, 12] Generated Node #3: [2, 12] from Operation: 75-63=12 Current State: 24:[2, 12], Operations: ['37+38=75', '75-63=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[37, 38, 2, 63], Operations: [] Exploring Operation: 63-38=25, Resulting Numbers: [37, 2, 25] Generated Node #0,0: 24:[37, 2, 25] Operation: 63-38=25 Moving to Node #0,0 Current State: 24:[37, 2, 25], Operations: ['63-38=25'] Exploring Operation: 37-25=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 24:[2, 12] Operation: 37-25=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 24:[2, 12], Operations: ['63-38=25', '37-25=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[37, 38, 2, 63], Operations: [] Exploring Operation: 63-38=25, Resulting Numbers: [37, 2, 25] Generated Node #0,0: 24:[37, 2, 25] Operation: 63-38=25 Moving to Node #0,0 Current State: 24:[37, 2, 25], Operations: ['63-38=25'] Exploring Operation: 37-25=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 24:[2, 12] Operation: 37-25=12 Moving to Node #0,0,0 Current State: 24:[2, 12], Operations: ['63-38=25', '37-25=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 40, 37, 45, 84 ]
43
[ "40-37=3", "45+84=129", "129/3=43" ]
Current State: 43:[40, 37, 45, 84], Operations: [] Exploring Operation: 40-37=3, Resulting Numbers: [45, 84, 3] Generated Node #2: [45, 84, 3] from Operation: 40-37=3 Current State: 43:[45, 84, 3], Operations: ['40-37=3'] Exploring Operation: 45+84=129, Resulting Numbers: [3, 129] Generated Node #3: [3, 129] from Operation: 45+84=129 Current State: 43:[3, 129], Operations: ['40-37=3', '45+84=129'] Exploring Operation: 129/3=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[40, 37, 45, 84], Operations: [] Exploring Operation: 84-40=44, Resulting Numbers: [37, 45, 44] Generated Node #0,0: 43:[37, 45, 44] Operation: 84-40=44 Moving to Node #0,0 Current State: 43:[37, 45, 44], Operations: ['84-40=44'] Exploring Operation: 45-37=8, Resulting Numbers: [44, 8] Generated Node #0,0,0: 43:[44, 8] Operation: 45-37=8 Moving to Node #0,0,0 Current State: 43:[44, 8], Operations: ['84-40=44', '45-37=8'] Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,43 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 72, 13, 26, 48 ]
11
[ "72+13=85", "26+48=74", "85-74=11" ]
Current State: 11:[72, 13, 26, 48], Operations: [] Exploring Operation: 72+13=85, Resulting Numbers: [26, 48, 85] Generated Node #2: [26, 48, 85] from Operation: 72+13=85 Current State: 11:[26, 48, 85], Operations: ['72+13=85'] Exploring Operation: 26+48=74, Resulting Numbers: [85, 74] Generated Node #3: [85, 74] from Operation: 26+48=74 Current State: 11:[85, 74], Operations: ['72+13=85', '26+48=74'] Exploring Operation: 85-74=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[72, 13, 26, 48], Operations: [] Exploring Operation: 72-26=46, Resulting Numbers: [13, 48, 46] Generated Node #0,0: 11:[13, 48, 46] Operation: 72-26=46 Exploring Operation: 72-48=24, Resulting Numbers: [13, 26, 24] Generated Node #0,1: 11:[13, 26, 24] Operation: 72-48=24 Moving to Node #0,1 Current State: 11:[13, 26, 24], Operations: ['72-48=24'] Exploring Operation: 26-24=2, Resulting Numbers: [13, 2] Generated Node #0,1,0: 11:[13, 2] Operation: 26-24=2 Exploring Operation: 26-13=13, Resulting Numbers: [24, 13] Generated Node #0,1,1: 11:[24, 13] Operation: 26-13=13 Moving to Node #0,0 Current State: 11:[13, 48, 46], Operations: ['72-26=46'] Exploring Operation: 48-13=35, Resulting Numbers: [46, 35] Generated Node #0,0,0: 11:[46, 35] Operation: 48-13=35 Exploring Operation: 48-46=2, Resulting Numbers: [13, 2] Generated Node #0,0,1: 11:[13, 2] Operation: 48-46=2 Moving to Node #0,1,0 Current State: 11:[13, 2], Operations: ['72-48=24', '26-24=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[72, 13, 26, 48], Operations: [] Exploring Operation: 72-48=24, Resulting Numbers: [13, 26, 24] Generated Node #0,1: 11:[13, 26, 24] Operation: 72-48=24 Moving to Node #0,1 Current State: 11:[13, 26, 24], Operations: ['72-48=24'] Exploring Operation: 26-24=2, Resulting Numbers: [13, 2] Generated Node #0,1,0: 11:[13, 2] Operation: 26-24=2 Moving to Node #0,1,0 Current State: 11:[13, 2], Operations: ['72-48=24', '26-24=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
0.990451
hs_2
mult_heuristic
[ 5, 37, 40, 4 ]
35
[ "40/5=8", "8/4=2", "37-2=35" ]
Current State: 35:[5, 37, 40, 4], Operations: [] Exploring Operation: 40/5=8, Resulting Numbers: [37, 4, 8] Generated Node #2: [37, 4, 8] from Operation: 40/5=8 Current State: 35:[37, 4, 8], Operations: ['40/5=8'] Exploring Operation: 8/4=2, Resulting Numbers: [37, 2] Generated Node #3: [37, 2] from Operation: 8/4=2 Current State: 35:[37, 2], Operations: ['40/5=8', '8/4=2'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[5, 37, 40, 4], Operations: [] Exploring Operation: 40-5=35, Resulting Numbers: [37, 4, 35] Generated Node #0,0: 35:[37, 4, 35] Operation: 40-5=35 Exploring Operation: 40-37=3, Resulting Numbers: [5, 4, 3] Generated Node #0,1: 35:[5, 4, 3] Operation: 40-37=3 Exploring Operation: 40-4=36, Resulting Numbers: [5, 37, 36] Generated Node #0,2: 35:[5, 37, 36] Operation: 40-4=36 Exploring Operation: 40/5=8, Resulting Numbers: [37, 4, 8] Generated Node #0,3: 35:[37, 4, 8] Operation: 40/5=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[37, 4, 35], Operations: ['40-5=35'] Exploring Operation: 37+4=41, Resulting Numbers: [35, 41] Generated Node #0,0,0: 35:[35, 41] Operation: 37+4=41 Exploring Operation: 37-4=33, Resulting Numbers: [35, 33] Generated Node #0,0,1: 35:[35, 33] Operation: 37-4=33 Exploring Operation: 4+35=39, Resulting Numbers: [37, 39] Generated Node #0,0,2: 35:[37, 39] Operation: 4+35=39 Exploring Operation: 37-35=2, Resulting Numbers: [4, 2] Generated Node #0,0,3: 35:[4, 2] Operation: 37-35=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 35:[35, 33], Operations: ['40-5=35', '37-4=33'] Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 35*33=1155, Resulting Numbers: [1155] 1155,35 unequal: No Solution Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 35:[4, 2], Operations: ['40-5=35', '37-35=2'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[35, 41], Operations: ['40-5=35', '37+4=41'] Exploring Operation: 35+41=76, Resulting Numbers: [76] 76,35 unequal: No Solution Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 35*41=1435, Resulting Numbers: [1435] 1435,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 35:[37, 39], Operations: ['40-5=35', '4+35=39'] Exploring Operation: 37+39=76, Resulting Numbers: [76] 76,35 unequal: No Solution Exploring Operation: 37*39=1443, Resulting Numbers: [1443] 1443,35 unequal: No Solution Exploring Operation: 39-37=2, Resulting Numbers: [2] 2,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[5, 4, 3], Operations: ['40-37=3'] Exploring Operation: 5+4=9, Resulting Numbers: [3, 9] Generated Node #0,1,0: 35:[3, 9] Operation: 5+4=9 Exploring Operation: 5-3=2, Resulting Numbers: [4, 2] Generated Node #0,1,1: 35:[4, 2] Operation: 5-3=2 Exploring Operation: 5+3=8, Resulting Numbers: [4, 8] Generated Node #0,1,2: 35:[4, 8] Operation: 5+3=8 Exploring Operation: 4+3=7, Resulting Numbers: [5, 7] Generated Node #0,1,3: 35:[5, 7] Operation: 4+3=7 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 35:[5, 7], Operations: ['40-37=3', '4+3=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[5, 37, 40, 4], Operations: [] Exploring Operation: 40-37=3, Resulting Numbers: [5, 4, 3] Generated Node #0,1: 35:[5, 4, 3] Operation: 40-37=3 Moving to Node #0,1 Current State: 35:[5, 4, 3], Operations: ['40-37=3'] Exploring Operation: 4+3=7, Resulting Numbers: [5, 7] Generated Node #0,1,3: 35:[5, 7] Operation: 4+3=7 Moving to Node #0,1,3 Current State: 35:[5, 7], Operations: ['40-37=3', '4+3=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 35, 95, 92, 62 ]
100
[ "35+95=130", "92-62=30", "130-30=100" ]
Current State: 100:[35, 95, 92, 62], Operations: [] Exploring Operation: 35+95=130, Resulting Numbers: [92, 62, 130] Generated Node #2: [92, 62, 130] from Operation: 35+95=130 Current State: 100:[92, 62, 130], Operations: ['35+95=130'] Exploring Operation: 92-62=30, Resulting Numbers: [130, 30] Generated Node #3: [130, 30] from Operation: 92-62=30 Current State: 100:[130, 30], Operations: ['35+95=130', '92-62=30'] Exploring Operation: 130-30=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[35, 95, 92, 62], Operations: [] Exploring Operation: 62-35=27, Resulting Numbers: [95, 92, 27] Generated Node #0,0: 100:[95, 92, 27] Operation: 62-35=27 Exploring Operation: 92-62=30, Resulting Numbers: [35, 95, 30] Generated Node #0,1: 100:[35, 95, 30] Operation: 92-62=30 Exploring Operation: 35+62=97, Resulting Numbers: [95, 92, 97] Generated Node #0,2: 100:[95, 92, 97] Operation: 35+62=97 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[95, 92, 27], Operations: ['62-35=27'] Exploring Operation: 92-27=65, Resulting Numbers: [95, 65] Generated Node #0,0,0: 100:[95, 65] Operation: 92-27=65 Exploring Operation: 92+27=119, Resulting Numbers: [95, 119] Generated Node #0,0,1: 100:[95, 119] Operation: 92+27=119 Exploring Operation: 95-92=3, Resulting Numbers: [27, 3] Generated Node #0,0,2: 100:[27, 3] Operation: 95-92=3 Moving to Node #0,0,2 Current State: 100:[27, 3], Operations: ['62-35=27', '95-92=3'] Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,100 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[95, 65], Operations: ['62-35=27', '92-27=65'] Exploring Operation: 95-65=30, Resulting Numbers: [30] 30,100 unequal: No Solution Exploring Operation: 95+65=160, Resulting Numbers: [160] 160,100 unequal: No Solution Exploring Operation: 95*65=6175, Resulting Numbers: [6175] 6175,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[95, 119], Operations: ['62-35=27', '92+27=119'] Exploring Operation: 95*119=11305, Resulting Numbers: [11305] 11305,100 unequal: No Solution Exploring Operation: 95+119=214, Resulting Numbers: [214] 214,100 unequal: No Solution Exploring Operation: 119-95=24, Resulting Numbers: [24] 24,100 unequal: No Solution No 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: 100:[95, 92, 97], Operations: ['35+62=97'] Exploring Operation: 95-92=3, Resulting Numbers: [97, 3] Generated Node #0,2,0: 100:[97, 3] Operation: 95-92=3 Exploring Operation: 97-92=5, Resulting Numbers: [95, 5] Generated Node #0,2,1: 100:[95, 5] Operation: 97-92=5 Exploring Operation: 97-95=2, Resulting Numbers: [92, 2] Generated Node #0,2,2: 100:[92, 2] Operation: 97-95=2 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 100:[97, 3], Operations: ['35+62=97', '95-92=3'] Exploring Operation: 97+3=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[35, 95, 92, 62], Operations: [] Exploring Operation: 35+62=97, Resulting Numbers: [95, 92, 97] Generated Node #0,2: 100:[95, 92, 97] Operation: 35+62=97 Moving to Node #0,2 Current State: 100:[95, 92, 97], Operations: ['35+62=97'] Exploring Operation: 95-92=3, Resulting Numbers: [97, 3] Generated Node #0,2,0: 100:[97, 3] Operation: 95-92=3 Moving to Node #0,2,0 Current State: 100:[97, 3], Operations: ['35+62=97', '95-92=3'] Exploring Operation: 97+3=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 19, 32, 71, 2 ]
91
[ "19+32=51", "71*2=142", "142-51=91" ]
Current State: 91:[19, 32, 71, 2], Operations: [] Exploring Operation: 19+32=51, Resulting Numbers: [71, 2, 51] Generated Node #2: [71, 2, 51] from Operation: 19+32=51 Current State: 91:[71, 2, 51], Operations: ['19+32=51'] Exploring Operation: 71*2=142, Resulting Numbers: [51, 142] Generated Node #3: [51, 142] from Operation: 71*2=142 Current State: 91:[51, 142], Operations: ['19+32=51', '71*2=142'] Exploring Operation: 142-51=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[19, 32, 71, 2], Operations: [] Exploring Operation: 32+71=103, Resulting Numbers: [19, 2, 103] Generated Node #0,0: 91:[19, 2, 103] Operation: 32+71=103 Moving to Node #0,0 Current State: 91:[19, 2, 103], Operations: ['32+71=103'] Exploring Operation: 103-19=84, Resulting Numbers: [2, 84] Generated Node #0,0,0: 91:[2, 84] Operation: 103-19=84 Moving to Node #0,0,0 Current State: 91:[2, 84], Operations: ['32+71=103', '103-19=84'] Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,91 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 35, 96, 90, 1 ]
29
[ "96-35=61", "90*1=90", "90-61=29" ]
Current State: 29:[35, 96, 90, 1], Operations: [] Exploring Operation: 96-35=61, Resulting Numbers: [90, 1, 61] Generated Node #2: [90, 1, 61] from Operation: 96-35=61 Current State: 29:[90, 1, 61], Operations: ['96-35=61'] Exploring Operation: 90*1=90, Resulting Numbers: [61, 90] Generated Node #3: [61, 90] from Operation: 90*1=90 Current State: 29:[61, 90], Operations: ['96-35=61', '90*1=90'] Exploring Operation: 90-61=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[35, 96, 90, 1], Operations: [] Exploring Operation: 96-90=6, Resulting Numbers: [35, 1, 6] Generated Node #0,0: 29:[35, 1, 6] Operation: 96-90=6 Exploring Operation: 90-35=55, Resulting Numbers: [96, 1, 55] Generated Node #0,1: 29:[96, 1, 55] Operation: 90-35=55 Exploring Operation: 96-35=61, Resulting Numbers: [90, 1, 61] Generated Node #0,2: 29:[90, 1, 61] Operation: 96-35=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[35, 1, 6], Operations: ['96-90=6'] Exploring Operation: 1+6=7, Resulting Numbers: [35, 7] Generated Node #0,0,0: 29:[35, 7] Operation: 1+6=7 Exploring Operation: 35-1=34, Resulting Numbers: [6, 34] Generated Node #0,0,1: 29:[6, 34] Operation: 35-1=34 Exploring Operation: 35-6=29, Resulting Numbers: [1, 29] Generated Node #0,0,2: 29:[1, 29] Operation: 35-6=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[35, 7], Operations: ['96-90=6', '1+6=7'] Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 35+7=42, Resulting Numbers: [42] 42,29 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,29 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 #0,0,1 Current State: 29:[6, 34], Operations: ['96-90=6', '35-1=34'] Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 6*34=204, Resulting Numbers: [204] 204,29 unequal: No Solution Exploring Operation: 6+34=40, Resulting Numbers: [40] 40,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 29:[1, 29], Operations: ['96-90=6', '35-6=29'] Exploring Operation: 29/1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[35, 96, 90, 1], Operations: [] Exploring Operation: 96-90=6, Resulting Numbers: [35, 1, 6] Generated Node #0,0: 29:[35, 1, 6] Operation: 96-90=6 Moving to Node #0,0 Current State: 29:[35, 1, 6], Operations: ['96-90=6'] Exploring Operation: 35-6=29, Resulting Numbers: [1, 29] Generated Node #0,0,2: 29:[1, 29] Operation: 35-6=29 Moving to Node #0,0,2 Current State: 29:[1, 29], Operations: ['96-90=6', '35-6=29'] 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
0.985243
hs_3
mult_heuristic
[ 40, 71, 81, 33 ]
63
[ "40+71=111", "81-33=48", "111-48=63" ]
Current State: 63:[40, 71, 81, 33], Operations: [] Exploring Operation: 40+71=111, Resulting Numbers: [81, 33, 111] Generated Node #2: [81, 33, 111] from Operation: 40+71=111 Current State: 63:[81, 33, 111], Operations: ['40+71=111'] Exploring Operation: 81-33=48, Resulting Numbers: [111, 48] Generated Node #3: [111, 48] from Operation: 81-33=48 Current State: 63:[111, 48], Operations: ['40+71=111', '81-33=48'] Exploring Operation: 111-48=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[40, 71, 81, 33], Operations: [] Exploring Operation: 81-71=10, Resulting Numbers: [40, 33, 10] Generated Node #0,0: 63:[40, 33, 10] Operation: 81-71=10 Exploring Operation: 40-33=7, Resulting Numbers: [71, 81, 7] Generated Node #0,1: 63:[71, 81, 7] Operation: 40-33=7 Moving to Node #0,1 Current State: 63:[71, 81, 7], Operations: ['40-33=7'] Exploring Operation: 71-7=64, Resulting Numbers: [81, 64] Generated Node #0,1,0: 63:[81, 64] Operation: 71-7=64 Exploring Operation: 81-71=10, Resulting Numbers: [7, 10] Generated Node #0,1,1: 63:[7, 10] Operation: 81-71=10 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 63:[7, 10], Operations: ['40-33=7', '81-71=10'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 63:[81, 64], Operations: ['40-33=7', '71-7=64'] Exploring Operation: 81+64=145, Resulting Numbers: [145] 145,63 unequal: No Solution Exploring Operation: 81-64=17, Resulting Numbers: [17] 17,63 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: 63:[40, 33, 10], Operations: ['81-71=10'] Exploring Operation: 40-33=7, Resulting Numbers: [10, 7] Generated Node #0,0,0: 63:[10, 7] Operation: 40-33=7 Exploring Operation: 40+33=73, Resulting Numbers: [10, 73] Generated Node #0,0,1: 63:[10, 73] Operation: 40+33=73 Moving to Node #0,0,0 Current State: 63:[10, 7], Operations: ['81-71=10', '40-33=7'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[10, 73], Operations: ['81-71=10', '40+33=73'] Exploring Operation: 73-10=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[40, 71, 81, 33], Operations: [] Exploring Operation: 81-71=10, Resulting Numbers: [40, 33, 10] Generated Node #0,0: 63:[40, 33, 10] Operation: 81-71=10 Moving to Node #0,0 Current State: 63:[40, 33, 10], Operations: ['81-71=10'] Exploring Operation: 40+33=73, Resulting Numbers: [10, 73] Generated Node #0,0,1: 63:[10, 73] Operation: 40+33=73 Moving to Node #0,0,1 Current State: 63:[10, 73], Operations: ['81-71=10', '40+33=73'] Exploring Operation: 73-10=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
0.985243
hs_2
mult_heuristic
[ 76, 38, 85, 74 ]
94
[ "76-74=2", "85-38=47", "2*47=94" ]
Current State: 94:[76, 38, 85, 74], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [38, 85, 2] Generated Node #2: [38, 85, 2] from Operation: 76-74=2 Current State: 94:[38, 85, 2], Operations: ['76-74=2'] Exploring Operation: 85-38=47, Resulting Numbers: [2, 47] Generated Node #3: [2, 47] from Operation: 85-38=47 Current State: 94:[2, 47], Operations: ['76-74=2', '85-38=47'] Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[76, 38, 85, 74], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [85, 74, 2] Generated Node #0,0: 94:[85, 74, 2] Operation: 76/38=2 Exploring Operation: 76-74=2, Resulting Numbers: [38, 85, 2] Generated Node #0,1: 94:[38, 85, 2] Operation: 76-74=2 Moving to Node #0,1 Current State: 94:[38, 85, 2], Operations: ['76-74=2'] Exploring Operation: 38+2=40, Resulting Numbers: [85, 40] Generated Node #0,1,0: 94:[85, 40] Operation: 38+2=40 Exploring Operation: 85-38=47, Resulting Numbers: [2, 47] Generated Node #0,1,1: 94:[2, 47] Operation: 85-38=47 Moving to Node #0,0 Current State: 94:[85, 74, 2], Operations: ['76/38=2'] Exploring Operation: 74/2=37, Resulting Numbers: [85, 37] Generated Node #0,0,0: 94:[85, 37] Operation: 74/2=37 Exploring Operation: 85-74=11, Resulting Numbers: [2, 11] Generated Node #0,0,1: 94:[2, 11] Operation: 85-74=11 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 94:[2, 11], Operations: ['76/38=2', '85-74=11'] Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,94 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,94 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:[85, 37], Operations: ['76/38=2', '74/2=37'] Exploring Operation: 85+37=122, Resulting Numbers: [122] 122,94 unequal: No Solution Exploring Operation: 85-37=48, Resulting Numbers: [48] 48,94 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: 94:[2, 47], Operations: ['76-74=2', '85-38=47'] Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[76, 38, 85, 74], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [38, 85, 2] Generated Node #0,1: 94:[38, 85, 2] Operation: 76-74=2 Moving to Node #0,1 Current State: 94:[38, 85, 2], Operations: ['76-74=2'] Exploring Operation: 85-38=47, Resulting Numbers: [2, 47] Generated Node #0,1,1: 94:[2, 47] Operation: 85-38=47 Moving to Node #0,1,1 Current State: 94:[2, 47], Operations: ['76-74=2', '85-38=47'] Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 83, 16, 78, 63 ]
52
[ "83-16=67", "78-63=15", "67-15=52" ]
Current State: 52:[83, 16, 78, 63], Operations: [] Exploring Operation: 83-16=67, Resulting Numbers: [78, 63, 67] Generated Node #2: [78, 63, 67] from Operation: 83-16=67 Current State: 52:[78, 63, 67], Operations: ['83-16=67'] Exploring Operation: 78-63=15, Resulting Numbers: [67, 15] Generated Node #3: [67, 15] from Operation: 78-63=15 Current State: 52:[67, 15], Operations: ['83-16=67', '78-63=15'] Exploring Operation: 67-15=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[83, 16, 78, 63], Operations: [] Exploring Operation: 83-16=67, Resulting Numbers: [78, 63, 67] Generated Node #0,0: 52:[78, 63, 67] Operation: 83-16=67 Exploring Operation: 83-78=5, Resulting Numbers: [16, 63, 5] Generated Node #0,1: 52:[16, 63, 5] Operation: 83-78=5 Exploring Operation: 78-63=15, Resulting Numbers: [83, 16, 15] Generated Node #0,2: 52:[83, 16, 15] Operation: 78-63=15 Exploring Operation: 83-63=20, Resulting Numbers: [16, 78, 20] Generated Node #0,3: 52:[16, 78, 20] Operation: 83-63=20 Moving to Node #0,1 Current State: 52:[16, 63, 5], Operations: ['83-78=5'] Exploring Operation: 16-5=11, Resulting Numbers: [63, 11] Generated Node #0,1,0: 52:[63, 11] Operation: 16-5=11 Exploring Operation: 63-5=58, Resulting Numbers: [16, 58] Generated Node #0,1,1: 52:[16, 58] Operation: 63-5=58 Exploring Operation: 63-16=47, Resulting Numbers: [5, 47] Generated Node #0,1,2: 52:[5, 47] Operation: 63-16=47 Exploring Operation: 16+5=21, Resulting Numbers: [63, 21] Generated Node #0,1,3: 52:[63, 21] Operation: 16+5=21 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 52:[5, 47], Operations: ['83-78=5', '63-16=47'] Exploring Operation: 5*47=235, Resulting Numbers: [235] 235,52 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,52 unequal: No Solution Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[83, 16, 78, 63], Operations: [] Exploring Operation: 83-78=5, Resulting Numbers: [16, 63, 5] Generated Node #0,1: 52:[16, 63, 5] Operation: 83-78=5 Moving to Node #0,1 Current State: 52:[16, 63, 5], Operations: ['83-78=5'] Exploring Operation: 63-16=47, Resulting Numbers: [5, 47] Generated Node #0,1,2: 52:[5, 47] Operation: 63-16=47 Moving to Node #0,1,2 Current State: 52:[5, 47], Operations: ['83-78=5', '63-16=47'] Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 46, 72, 38, 54 ]
66
[ "72-46=26", "38+54=92", "92-26=66" ]
Current State: 66:[46, 72, 38, 54], Operations: [] Exploring Operation: 72-46=26, Resulting Numbers: [38, 54, 26] Generated Node #2: [38, 54, 26] from Operation: 72-46=26 Current State: 66:[38, 54, 26], Operations: ['72-46=26'] Exploring Operation: 38+54=92, Resulting Numbers: [26, 92] Generated Node #3: [26, 92] from Operation: 38+54=92 Current State: 66:[26, 92], Operations: ['72-46=26', '38+54=92'] Exploring Operation: 92-26=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[46, 72, 38, 54], Operations: [] Exploring Operation: 54-46=8, Resulting Numbers: [72, 38, 8] Generated Node #0,0: 66:[72, 38, 8] Operation: 54-46=8 Exploring Operation: 72-46=26, Resulting Numbers: [38, 54, 26] Generated Node #0,1: 66:[38, 54, 26] Operation: 72-46=26 Exploring Operation: 46-38=8, Resulting Numbers: [72, 54, 8] Generated Node #0,2: 66:[72, 54, 8] Operation: 46-38=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[72, 38, 8], Operations: ['54-46=8'] Exploring Operation: 72-8=64, Resulting Numbers: [38, 64] Generated Node #0,0,0: 66:[38, 64] Operation: 72-8=64 Exploring Operation: 72/8=9, Resulting Numbers: [38, 9] Generated Node #0,0,1: 66:[38, 9] Operation: 72/8=9 Exploring Operation: 72-38=34, Resulting Numbers: [8, 34] Generated Node #0,0,2: 66:[8, 34] Operation: 72-38=34 Moving to Node #0,0,2 Current State: 66:[8, 34], Operations: ['54-46=8', '72-38=34'] Exploring Operation: 8*34=272, Resulting Numbers: [272] 272,66 unequal: No Solution Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,66 unequal: No Solution Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,66 unequal: No Solution Moving to Node #0,0,0 Current State: 66:[38, 64], Operations: ['54-46=8', '72-8=64'] Exploring Operation: 38*64=2432, Resulting Numbers: [2432] 2432,66 unequal: No Solution Exploring Operation: 38+64=102, Resulting Numbers: [102] 102,66 unequal: No Solution Exploring Operation: 64-38=26, Resulting Numbers: [26] 26,66 unequal: No Solution Moving to Node #0,0,1 Current State: 66:[38, 9], Operations: ['54-46=8', '72/8=9'] Exploring Operation: 38+9=47, Resulting Numbers: [47] 47,66 unequal: No Solution Exploring Operation: 38*9=342, Resulting Numbers: [342] 342,66 unequal: No Solution Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 66:[72, 54, 8], Operations: ['46-38=8'] Exploring Operation: 54+8=62, Resulting Numbers: [72, 62] Generated Node #0,2,0: 66:[72, 62] Operation: 54+8=62 Exploring Operation: 72-8=64, Resulting Numbers: [54, 64] Generated Node #0,2,1: 66:[54, 64] Operation: 72-8=64 Exploring Operation: 72-54=18, Resulting Numbers: [8, 18] Generated Node #0,2,2: 66:[8, 18] Operation: 72-54=18 Moving to Node #0,2,2 Current State: 66:[8, 18], Operations: ['46-38=8', '72-54=18'] Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,66 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,66 unequal: No Solution Moving to Node #0,2,0 Current State: 66:[72, 62], Operations: ['46-38=8', '54+8=62'] Exploring Operation: 72*62=4464, Resulting Numbers: [4464] 4464,66 unequal: No Solution Exploring Operation: 72+62=134, Resulting Numbers: [134] 134,66 unequal: No Solution Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,66 unequal: No Solution Moving to Node #0,2,1 Current State: 66:[54, 64], Operations: ['46-38=8', '72-8=64'] Exploring Operation: 54+64=118, Resulting Numbers: [118] 118,66 unequal: No Solution Exploring Operation: 64-54=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 54*64=3456, Resulting Numbers: [3456] 3456,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[38, 54, 26], Operations: ['72-46=26'] Exploring Operation: 38-26=12, Resulting Numbers: [54, 12] Generated Node #0,1,0: 66:[54, 12] Operation: 38-26=12 Exploring Operation: 54-26=28, Resulting Numbers: [38, 28] Generated Node #0,1,1: 66:[38, 28] Operation: 54-26=28 Exploring Operation: 54-38=16, Resulting Numbers: [26, 16] Generated Node #0,1,2: 66:[26, 16] Operation: 54-38=16 Moving to Node #0,1,2 Current State: 66:[26, 16], Operations: ['72-46=26', '54-38=16'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 26*16=416, Resulting Numbers: [416] 416,66 unequal: No Solution Exploring Operation: 26+16=42, Resulting Numbers: [42] 42,66 unequal: No Solution Moving to Node #0,1,1 Current State: 66:[38, 28], Operations: ['72-46=26', '54-26=28'] Exploring Operation: 38-28=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 38*28=1064, Resulting Numbers: [1064] 1064,66 unequal: No Solution Exploring Operation: 38+28=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[46, 72, 38, 54], Operations: [] Exploring Operation: 72-46=26, Resulting Numbers: [38, 54, 26] Generated Node #0,1: 66:[38, 54, 26] Operation: 72-46=26 Moving to Node #0,1 Current State: 66:[38, 54, 26], Operations: ['72-46=26'] Exploring Operation: 54-26=28, Resulting Numbers: [38, 28] Generated Node #0,1,1: 66:[38, 28] Operation: 54-26=28 Moving to Node #0,1,1 Current State: 66:[38, 28], Operations: ['72-46=26', '54-26=28'] Exploring Operation: 38+28=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_3
mult_heuristic
[ 28, 12, 54, 30 ]
64
[ "28+12=40", "54-30=24", "40+24=64" ]
Current State: 64:[28, 12, 54, 30], Operations: [] Exploring Operation: 28+12=40, Resulting Numbers: [54, 30, 40] Generated Node #2: [54, 30, 40] from Operation: 28+12=40 Current State: 64:[54, 30, 40], Operations: ['28+12=40'] Exploring Operation: 54-30=24, Resulting Numbers: [40, 24] Generated Node #3: [40, 24] from Operation: 54-30=24 Current State: 64:[40, 24], Operations: ['28+12=40', '54-30=24'] Exploring Operation: 40+24=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[28, 12, 54, 30], Operations: [] Exploring Operation: 28-12=16, Resulting Numbers: [54, 30, 16] Generated Node #0,0: 64:[54, 30, 16] Operation: 28-12=16 Exploring Operation: 12+54=66, Resulting Numbers: [28, 30, 66] Generated Node #0,1: 64:[28, 30, 66] Operation: 12+54=66 Exploring Operation: 54-28=26, Resulting Numbers: [12, 30, 26] Generated Node #0,2: 64:[12, 30, 26] Operation: 54-28=26 Moving to Node #0,1 Current State: 64:[28, 30, 66], Operations: ['12+54=66'] Exploring Operation: 28+30=58, Resulting Numbers: [66, 58] Generated Node #0,1,0: 64:[66, 58] Operation: 28+30=58 Exploring Operation: 66-28=38, Resulting Numbers: [30, 38] Generated Node #0,1,1: 64:[30, 38] Operation: 66-28=38 Exploring Operation: 30-28=2, Resulting Numbers: [66, 2] Generated Node #0,1,2: 64:[66, 2] Operation: 30-28=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 64:[66, 2], Operations: ['12+54=66', '30-28=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[28, 12, 54, 30], Operations: [] Exploring Operation: 12+54=66, Resulting Numbers: [28, 30, 66] Generated Node #0,1: 64:[28, 30, 66] Operation: 12+54=66 Moving to Node #0,1 Current State: 64:[28, 30, 66], Operations: ['12+54=66'] Exploring Operation: 30-28=2, Resulting Numbers: [66, 2] Generated Node #0,1,2: 64:[66, 2] Operation: 30-28=2 Moving to Node #0,1,2 Current State: 64:[66, 2], Operations: ['12+54=66', '30-28=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 20, 2, 39, 21 ]
19
[ "20+39=59", "59-21=38", "38/2=19" ]
Current State: 19:[20, 2, 39, 21], Operations: [] Exploring Operation: 20+39=59, Resulting Numbers: [2, 21, 59] Generated Node #2: [2, 21, 59] from Operation: 20+39=59 Current State: 19:[2, 21, 59], Operations: ['20+39=59'] Exploring Operation: 59-21=38, Resulting Numbers: [2, 38] Generated Node #3: [2, 38] from Operation: 59-21=38 Current State: 19:[2, 38], Operations: ['20+39=59', '59-21=38'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[20, 2, 39, 21], Operations: [] Exploring Operation: 39-20=19, Resulting Numbers: [2, 21, 19] Generated Node #0,0: 19:[2, 21, 19] Operation: 39-20=19 Exploring Operation: 39-2=37, Resulting Numbers: [20, 21, 37] Generated Node #0,1: 19:[20, 21, 37] Operation: 39-2=37 Exploring Operation: 39-21=18, Resulting Numbers: [20, 2, 18] Generated Node #0,2: 19:[20, 2, 18] Operation: 39-21=18 Exploring Operation: 21-2=19, Resulting Numbers: [20, 39, 19] Generated Node #0,3: 19:[20, 39, 19] Operation: 21-2=19 Moving to Node #0,0 Current State: 19:[2, 21, 19], Operations: ['39-20=19'] Exploring Operation: 19-2=17, Resulting Numbers: [21, 17] Generated Node #0,0,0: 19:[21, 17] Operation: 19-2=17 Exploring Operation: 2+21=23, Resulting Numbers: [19, 23] Generated Node #0,0,1: 19:[19, 23] Operation: 2+21=23 Exploring Operation: 21-2=19, Resulting Numbers: [19, 19] Generated Node #0,0,2: 19:[19, 19] Operation: 21-2=19 Exploring Operation: 2+19=21, Resulting Numbers: [21, 21] Generated Node #0,0,3: 19:[21, 21] Operation: 2+19=21 Moving to Node #0,2 Current State: 19:[20, 2, 18], Operations: ['39-21=18'] Exploring Operation: 20-2=18, Resulting Numbers: [18, 18] Generated Node #0,2,0: 19:[18, 18] Operation: 20-2=18 Exploring Operation: 2+18=20, Resulting Numbers: [20, 20] Generated Node #0,2,1: 19:[20, 20] Operation: 2+18=20 Exploring Operation: 18-2=16, Resulting Numbers: [20, 16] Generated Node #0,2,2: 19:[20, 16] Operation: 18-2=16 Exploring Operation: 20+2=22, Resulting Numbers: [18, 22] Generated Node #0,2,3: 19:[18, 22] Operation: 20+2=22 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 19:[18, 18], Operations: ['39-21=18', '20-2=18'] Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 18-18=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 18*18=324, Resulting Numbers: [324] 324,19 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 #0,2,1 Current State: 19:[20, 20], Operations: ['39-21=18', '2+18=20'] Exploring Operation: 20*20=400, Resulting Numbers: [400] 400,19 unequal: No Solution Exploring Operation: 20-20=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 20/20=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 20+20=40, Resulting Numbers: [40] 40,19 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 #0,2,2 Current State: 19:[20, 16], Operations: ['39-21=18', '18-2=16'] Exploring Operation: 20+16=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 20*16=320, Resulting Numbers: [320] 320,19 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 #0,2,3 Current State: 19:[18, 22], Operations: ['39-21=18', '20+2=22'] Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 18*22=396, Resulting Numbers: [396] 396,19 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: 19:[20, 39, 19], Operations: ['21-2=19'] Exploring Operation: 39-20=19, Resulting Numbers: [19, 19] Generated Node #0,3,0: 19:[19, 19] Operation: 39-20=19 Exploring Operation: 20+39=59, Resulting Numbers: [19, 59] Generated Node #0,3,1: 19:[19, 59] Operation: 20+39=59 Exploring Operation: 20-19=1, Resulting Numbers: [39, 1] Generated Node #0,3,2: 19:[39, 1] Operation: 20-19=1 Exploring Operation: 39-19=20, Resulting Numbers: [20, 20] Generated Node #0,3,3: 19:[20, 20] Operation: 39-19=20 Moving to Node #0,1 Current State: 19:[20, 21, 37], Operations: ['39-2=37'] Exploring Operation: 37-20=17, Resulting Numbers: [21, 17] Generated Node #0,1,0: 19:[21, 17] Operation: 37-20=17 Exploring Operation: 21-20=1, Resulting Numbers: [37, 1] Generated Node #0,1,1: 19:[37, 1] Operation: 21-20=1 Exploring Operation: 20+21=41, Resulting Numbers: [37, 41] Generated Node #0,1,2: 19:[37, 41] Operation: 20+21=41 Exploring Operation: 37-21=16, Resulting Numbers: [20, 16] Generated Node #0,1,3: 19:[20, 16] Operation: 37-21=16 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 19:[21, 17], Operations: ['39-2=37', '37-20=17'] Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 21*17=357, Resulting Numbers: [357] 357,19 unequal: No Solution Exploring Operation: 21+17=38, Resulting Numbers: [38] 38,19 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 #0,1,3 Current State: 19:[20, 16], Operations: ['39-2=37', '37-21=16'] Exploring Operation: 20+16=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 20*16=320, Resulting Numbers: [320] 320,19 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 #0,1,1 Current State: 19:[37, 1], Operations: ['39-2=37', '21-20=1'] Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,19 unequal: No Solution Exploring Operation: 37*1=37, Resulting Numbers: [37] 37,19 unequal: No Solution Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 37+1=38, Resulting Numbers: [38] 38,19 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 #0,1,2 Current State: 19:[37, 41], Operations: ['39-2=37', '20+21=41'] Exploring Operation: 37+41=78, Resulting Numbers: [78] 78,19 unequal: No Solution Exploring Operation: 37*41=1517, Resulting Numbers: [1517] 1517,19 unequal: No Solution Exploring Operation: 41-37=4, Resulting Numbers: [4] 4,19 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: 19:[19, 19], Operations: ['39-20=19', '21-2=19'] Exploring Operation: 19*19=361, Resulting Numbers: [361] 361,19 unequal: No Solution Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 19-19=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,19 unequal: No Solution Moving to Node #0,3,0 Current State: 19:[19, 19], Operations: ['21-2=19', '39-20=19'] Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,19 unequal: No Solution Exploring Operation: 19-19=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 19*19=361, Resulting Numbers: [361] 361,19 unequal: No Solution Moving to Node #0,3,3 Current State: 19:[20, 20], Operations: ['21-2=19', '39-19=20'] Exploring Operation: 20-20=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 20*20=400, Resulting Numbers: [400] 400,19 unequal: No Solution Exploring Operation: 20+20=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 20/20=1, Resulting Numbers: [1] 1,19 unequal: No Solution Moving to Node #0,0,1 Current State: 19:[19, 23], Operations: ['39-20=19', '2+21=23'] Exploring Operation: 19*23=437, Resulting Numbers: [437] 437,19 unequal: No Solution Exploring Operation: 19+23=42, Resulting Numbers: [42] 42,19 unequal: No Solution Exploring Operation: 23-19=4, Resulting Numbers: [4] 4,19 unequal: No Solution Moving to Node #0,0,0 Current State: 19:[21, 17], Operations: ['39-20=19', '19-2=17'] Exploring Operation: 21+17=38, Resulting Numbers: [38] 38,19 unequal: No Solution Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 21*17=357, Resulting Numbers: [357] 357,19 unequal: No Solution Moving to Node #0,0,3 Current State: 19:[21, 21], Operations: ['39-20=19', '2+19=21'] Exploring Operation: 21*21=441, Resulting Numbers: [441] 441,19 unequal: No Solution Exploring Operation: 21-21=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 21/21=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 21+21=42, Resulting Numbers: [42] 42,19 unequal: No Solution Moving to Node #0,3,2 Current State: 19:[39, 1], Operations: ['21-2=19', '20-19=1'] Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,19 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,19 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,19 unequal: No Solution Moving to Node #0,3,1 Current State: 19:[19, 59], Operations: ['21-2=19', '20+39=59'] Exploring Operation: 19+59=78, Resulting Numbers: [78] 78,19 unequal: No Solution Exploring Operation: 19*59=1121, Resulting Numbers: [1121] 1121,19 unequal: No Solution Exploring Operation: 59-19=40, Resulting Numbers: [40] 40,19 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 33, 26, 88, 29 ]
52
[ "33-26=7", "88-29=59", "59-7=52" ]
Current State: 52:[33, 26, 88, 29], Operations: [] Exploring Operation: 33-26=7, Resulting Numbers: [88, 29, 7] Generated Node #2: [88, 29, 7] from Operation: 33-26=7 Current State: 52:[88, 29, 7], Operations: ['33-26=7'] Exploring Operation: 88-29=59, Resulting Numbers: [7, 59] Generated Node #3: [7, 59] from Operation: 88-29=59 Current State: 52:[7, 59], Operations: ['33-26=7', '88-29=59'] Exploring Operation: 59-7=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[33, 26, 88, 29], Operations: [] Exploring Operation: 88-33=55, Resulting Numbers: [26, 29, 55] Generated Node #0,0: 52:[26, 29, 55] Operation: 88-33=55 Exploring Operation: 88-29=59, Resulting Numbers: [33, 26, 59] Generated Node #0,1: 52:[33, 26, 59] Operation: 88-29=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[26, 29, 55], Operations: ['88-33=55'] Exploring Operation: 55-29=26, Resulting Numbers: [26, 26] Generated Node #0,0,0: 52:[26, 26] Operation: 55-29=26 Exploring Operation: 29-26=3, Resulting Numbers: [55, 3] Generated Node #0,0,1: 52:[55, 3] Operation: 29-26=3 Moving to Node #0,0,0 Current State: 52:[26, 26], Operations: ['88-33=55', '55-29=26'] Exploring Operation: 26/26=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 26+26=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[33, 26, 88, 29], Operations: [] Exploring Operation: 88-33=55, Resulting Numbers: [26, 29, 55] Generated Node #0,0: 52:[26, 29, 55] Operation: 88-33=55 Moving to Node #0,0 Current State: 52:[26, 29, 55], Operations: ['88-33=55'] Exploring Operation: 55-29=26, Resulting Numbers: [26, 26] Generated Node #0,0,0: 52:[26, 26] Operation: 55-29=26 Moving to Node #0,0,0 Current State: 52:[26, 26], Operations: ['88-33=55', '55-29=26'] Exploring Operation: 26+26=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 25, 24, 15, 13 ]
75
[ "24+15=39", "25*39=975", "975/13=75" ]
Current State: 75:[25, 24, 15, 13], Operations: [] Exploring Operation: 24+15=39, Resulting Numbers: [25, 13, 39] Generated Node #2: [25, 13, 39] from Operation: 24+15=39 Current State: 75:[25, 13, 39], Operations: ['24+15=39'] Exploring Operation: 25*39=975, Resulting Numbers: [13, 975] Generated Node #3: [13, 975] from Operation: 25*39=975 Current State: 75:[13, 975], Operations: ['24+15=39', '25*39=975'] Exploring Operation: 975/13=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[25, 24, 15, 13], Operations: [] Exploring Operation: 15-13=2, Resulting Numbers: [25, 24, 2] Generated Node #0,0: 75:[25, 24, 2] Operation: 15-13=2 Moving to Node #0,0 Current State: 75:[25, 24, 2], Operations: ['15-13=2'] Exploring Operation: 24+2=26, Resulting Numbers: [25, 26] Generated Node #0,0,0: 75:[25, 26] Operation: 24+2=26 Moving to Node #0,0,0 Current State: 75:[25, 26], Operations: ['15-13=2', '24+2=26'] Exploring Operation: 26-25=1, Resulting Numbers: [1] 1,75 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 6, 72, 5, 29 ]
72
[ "6*5=30", "30-29=1", "72*1=72" ]
Current State: 72:[6, 72, 5, 29], Operations: [] Exploring Operation: 6*5=30, Resulting Numbers: [72, 29, 30] Generated Node #2: [72, 29, 30] from Operation: 6*5=30 Current State: 72:[72, 29, 30], Operations: ['6*5=30'] Exploring Operation: 30-29=1, Resulting Numbers: [72, 1] Generated Node #3: [72, 1] from Operation: 30-29=1 Current State: 72:[72, 1], Operations: ['6*5=30', '30-29=1'] Exploring Operation: 72*1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[6, 72, 5, 29], Operations: [] Exploring Operation: 29-5=24, Resulting Numbers: [6, 72, 24] Generated Node #0,0: 72:[6, 72, 24] Operation: 29-5=24 Exploring Operation: 6+29=35, Resulting Numbers: [72, 5, 35] Generated Node #0,1: 72:[72, 5, 35] Operation: 6+29=35 Exploring Operation: 5+29=34, Resulting Numbers: [6, 72, 34] Generated Node #0,2: 72:[6, 72, 34] Operation: 5+29=34 Exploring Operation: 29-6=23, Resulting Numbers: [72, 5, 23] Generated Node #0,3: 72:[72, 5, 23] Operation: 29-6=23 Moving to Node #0,0 Current State: 72:[6, 72, 24], Operations: ['29-5=24'] Exploring Operation: 72/24=3, Resulting Numbers: [6, 3] Generated Node #0,0,0: 72:[6, 3] Operation: 72/24=3 Exploring Operation: 72/6=12, Resulting Numbers: [24, 12] Generated Node #0,0,1: 72:[24, 12] Operation: 72/6=12 Exploring Operation: 24/6=4, Resulting Numbers: [72, 4] Generated Node #0,0,2: 72:[72, 4] Operation: 24/6=4 Exploring Operation: 24-6=18, Resulting Numbers: [72, 18] Generated Node #0,0,3: 72:[72, 18] Operation: 24-6=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[6, 3], Operations: ['29-5=24', '72/24=3'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,72 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,72 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[24, 12], Operations: ['29-5=24', '72/6=12'] Exploring Operation: 24+12=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 24*12=288, Resulting Numbers: [288] 288,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 72:[72, 4], Operations: ['29-5=24', '24/6=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,72 unequal: No Solution Exploring Operation: 72*4=288, Resulting Numbers: [288] 288,72 unequal: No Solution Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 72:[72, 18], Operations: ['29-5=24', '24-6=18'] Exploring Operation: 72*18=1296, Resulting Numbers: [1296] 1296,72 unequal: No Solution Exploring Operation: 72-18=54, Resulting Numbers: [54] 54,72 unequal: No Solution Exploring Operation: 72+18=90, Resulting Numbers: [90] 90,72 unequal: No Solution Exploring Operation: 72/18=4, Resulting Numbers: [4] 4,72 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: 72:[6, 72, 34], Operations: ['5+29=34'] Exploring Operation: 34-6=28, Resulting Numbers: [72, 28] Generated Node #0,2,0: 72:[72, 28] Operation: 34-6=28 Exploring Operation: 72/6=12, Resulting Numbers: [34, 12] Generated Node #0,2,1: 72:[34, 12] Operation: 72/6=12 Exploring Operation: 6+34=40, Resulting Numbers: [72, 40] Generated Node #0,2,2: 72:[72, 40] Operation: 6+34=40 Exploring Operation: 72-34=38, Resulting Numbers: [6, 38] Generated Node #0,2,3: 72:[6, 38] Operation: 72-34=38 Moving to Node #0,1 Current State: 72:[72, 5, 35], Operations: ['6+29=35'] Exploring Operation: 5+35=40, Resulting Numbers: [72, 40] Generated Node #0,1,0: 72:[72, 40] Operation: 5+35=40 Exploring Operation: 72-35=37, Resulting Numbers: [5, 37] Generated Node #0,1,1: 72:[5, 37] Operation: 72-35=37 Exploring Operation: 72+5=77, Resulting Numbers: [35, 77] Generated Node #0,1,2: 72:[35, 77] Operation: 72+5=77 Exploring Operation: 35/5=7, Resulting Numbers: [72, 7] Generated Node #0,1,3: 72:[72, 7] Operation: 35/5=7 Moving to Node #0,3 Current State: 72:[72, 5, 23], Operations: ['29-6=23'] Exploring Operation: 5+23=28, Resulting Numbers: [72, 28] Generated Node #0,3,0: 72:[72, 28] Operation: 5+23=28 Exploring Operation: 72+5=77, Resulting Numbers: [23, 77] Generated Node #0,3,1: 72:[23, 77] Operation: 72+5=77 Exploring Operation: 72-5=67, Resulting Numbers: [23, 67] Generated Node #0,3,2: 72:[23, 67] Operation: 72-5=67 Exploring Operation: 23-5=18, Resulting Numbers: [72, 18] Generated Node #0,3,3: 72:[72, 18] Operation: 23-5=18 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 72:[72, 18], Operations: ['29-6=23', '23-5=18'] Exploring Operation: 72*18=1296, Resulting Numbers: [1296] 1296,72 unequal: No Solution Exploring Operation: 72+18=90, Resulting Numbers: [90] 90,72 unequal: No Solution Exploring Operation: 72-18=54, Resulting Numbers: [54] 54,72 unequal: No Solution Exploring Operation: 72/18=4, Resulting Numbers: [4] 4,72 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 #0,3,0 Current State: 72:[72, 28], Operations: ['29-6=23', '5+23=28'] Exploring Operation: 72*28=2016, Resulting Numbers: [2016] 2016,72 unequal: No Solution Exploring Operation: 72+28=100, Resulting Numbers: [100] 100,72 unequal: No Solution Exploring Operation: 72-28=44, Resulting Numbers: [44] 44,72 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:[23, 77], Operations: ['29-6=23', '72+5=77'] Exploring Operation: 23*77=1771, Resulting Numbers: [1771] 1771,72 unequal: No Solution Exploring Operation: 23+77=100, Resulting Numbers: [100] 100,72 unequal: No Solution Exploring Operation: 77-23=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 #0,3,2 Current State: 72:[23, 67], Operations: ['29-6=23', '72-5=67'] Exploring Operation: 23*67=1541, Resulting Numbers: [1541] 1541,72 unequal: No Solution Exploring Operation: 23+67=90, Resulting Numbers: [90] 90,72 unequal: No Solution Exploring Operation: 67-23=44, Resulting Numbers: [44] 44,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 72:[72, 7], Operations: ['6+29=35', '35/5=7'] Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,72 unequal: No Solution Exploring Operation: 72*7=504, Resulting Numbers: [504] 504,72 unequal: No Solution Exploring Operation: 72+7=79, Resulting Numbers: [79] 79,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[5, 37], Operations: ['6+29=35', '72-35=37'] Exploring Operation: 5+37=42, Resulting Numbers: [42] 42,72 unequal: No Solution Exploring Operation: 5*37=185, Resulting Numbers: [185] 185,72 unequal: No Solution Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[34, 12], Operations: ['5+29=34', '72/6=12'] Exploring Operation: 34+12=46, Resulting Numbers: [46] 46,72 unequal: No Solution Exploring Operation: 34*12=408, Resulting Numbers: [408] 408,72 unequal: No Solution Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,72 unequal: No Solution Moving to Node #0,2,3 Current State: 72:[6, 38], Operations: ['5+29=34', '72-34=38'] Exploring Operation: 6*38=228, Resulting Numbers: [228] 228,72 unequal: No Solution Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,72 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[72, 40], Operations: ['6+29=35', '5+35=40'] Exploring Operation: 72*40=2880, Resulting Numbers: [2880] 2880,72 unequal: No Solution Exploring Operation: 72+40=112, Resulting Numbers: [112] 112,72 unequal: No Solution Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[72, 40], Operations: ['5+29=34', '6+34=40'] Exploring Operation: 72*40=2880, Resulting Numbers: [2880] 2880,72 unequal: No Solution Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,72 unequal: No Solution Exploring Operation: 72+40=112, Resulting Numbers: [112] 112,72 unequal: No Solution Moving to Node #0,2,0 Current State: 72:[72, 28], Operations: ['5+29=34', '34-6=28'] Exploring Operation: 72+28=100, Resulting Numbers: [100] 100,72 unequal: No Solution Exploring Operation: 72-28=44, Resulting Numbers: [44] 44,72 unequal: No Solution Exploring Operation: 72*28=2016, Resulting Numbers: [2016] 2016,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[35, 77], Operations: ['6+29=35', '72+5=77'] Exploring Operation: 77-35=42, Resulting Numbers: [42] 42,72 unequal: No Solution Exploring Operation: 35*77=2695, Resulting Numbers: [2695] 2695,72 unequal: No Solution Exploring Operation: 35+77=112, Resulting Numbers: [112] 112,72 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 63, 31, 48, 5 ]
51
[ "63+31=94", "48-5=43", "94-43=51" ]
Current State: 51:[63, 31, 48, 5], Operations: [] Exploring Operation: 63+31=94, Resulting Numbers: [48, 5, 94] Generated Node #2: [48, 5, 94] from Operation: 63+31=94 Current State: 51:[48, 5, 94], Operations: ['63+31=94'] Exploring Operation: 48-5=43, Resulting Numbers: [94, 43] Generated Node #3: [94, 43] from Operation: 48-5=43 Current State: 51:[94, 43], Operations: ['63+31=94', '48-5=43'] Exploring Operation: 94-43=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[63, 31, 48, 5], Operations: [] Exploring Operation: 63-48=15, Resulting Numbers: [31, 5, 15] Generated Node #0,0: 51:[31, 5, 15] Operation: 63-48=15 Exploring Operation: 48-31=17, Resulting Numbers: [63, 5, 17] Generated Node #0,1: 51:[63, 5, 17] Operation: 48-31=17 Exploring Operation: 63-31=32, Resulting Numbers: [48, 5, 32] Generated Node #0,2: 51:[48, 5, 32] Operation: 63-31=32 Moving to Node #0,1 Current State: 51:[63, 5, 17], Operations: ['48-31=17'] Exploring Operation: 63+5=68, Resulting Numbers: [17, 68] Generated Node #0,1,0: 51:[17, 68] Operation: 63+5=68 Exploring Operation: 63-17=46, Resulting Numbers: [5, 46] Generated Node #0,1,1: 51:[5, 46] Operation: 63-17=46 Exploring Operation: 63-5=58, Resulting Numbers: [17, 58] Generated Node #0,1,2: 51:[17, 58] Operation: 63-5=58 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 51:[5, 46], Operations: ['48-31=17', '63-17=46'] Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,51 unequal: No Solution Exploring Operation: 5*46=230, Resulting Numbers: [230] 230,51 unequal: No Solution Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[63, 31, 48, 5], Operations: [] Exploring Operation: 48-31=17, Resulting Numbers: [63, 5, 17] Generated Node #0,1: 51:[63, 5, 17] Operation: 48-31=17 Moving to Node #0,1 Current State: 51:[63, 5, 17], Operations: ['48-31=17'] Exploring Operation: 63-17=46, Resulting Numbers: [5, 46] Generated Node #0,1,1: 51:[5, 46] Operation: 63-17=46 Moving to Node #0,1,1 Current State: 51:[5, 46], Operations: ['48-31=17', '63-17=46'] Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 56, 59, 29, 9 ]
87
[ "59-56=3", "29*9=261", "261/3=87" ]
Current State: 87:[56, 59, 29, 9], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [29, 9, 3] Generated Node #2: [29, 9, 3] from Operation: 59-56=3 Current State: 87:[29, 9, 3], Operations: ['59-56=3'] Exploring Operation: 29*9=261, Resulting Numbers: [3, 261] Generated Node #3: [3, 261] from Operation: 29*9=261 Current State: 87:[3, 261], Operations: ['59-56=3', '29*9=261'] Exploring Operation: 261/3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[56, 59, 29, 9], Operations: [] Exploring Operation: 59-29=30, Resulting Numbers: [56, 9, 30] Generated Node #0,0: 87:[56, 9, 30] Operation: 59-29=30 Exploring Operation: 56+59=115, Resulting Numbers: [29, 9, 115] Generated Node #0,1: 87:[29, 9, 115] Operation: 56+59=115 Exploring Operation: 56+29=85, Resulting Numbers: [59, 9, 85] Generated Node #0,2: 87:[59, 9, 85] Operation: 56+29=85 Exploring Operation: 59-56=3, Resulting Numbers: [29, 9, 3] Generated Node #0,3: 87:[29, 9, 3] Operation: 59-56=3 Exploring Operation: 59+29=88, Resulting Numbers: [56, 9, 88] Generated Node #0,4: 87:[56, 9, 88] Operation: 59+29=88 Moving to Node #0,3 Current State: 87:[29, 9, 3], Operations: ['59-56=3'] Exploring Operation: 29+9=38, Resulting Numbers: [3, 38] Generated Node #0,3,0: 87:[3, 38] Operation: 29+9=38 Exploring Operation: 9/3=3, Resulting Numbers: [29, 3] Generated Node #0,3,1: 87:[29, 3] Operation: 9/3=3 Exploring Operation: 29*3=87, Resulting Numbers: [9, 87] Generated Node #0,3,2: 87:[9, 87] Operation: 29*3=87 Exploring Operation: 9-3=6, Resulting Numbers: [29, 6] Generated Node #0,3,3: 87:[29, 6] Operation: 9-3=6 Exploring Operation: 9*3=27, Resulting Numbers: [29, 27] Generated Node #0,3,4: 87:[29, 27] Operation: 9*3=27 Moving to Node #0,1 Current State: 87:[29, 9, 115], Operations: ['56+59=115'] Exploring Operation: 115-9=106, Resulting Numbers: [29, 106] Generated Node #0,1,0: 87:[29, 106] Operation: 115-9=106 Exploring Operation: 29-9=20, Resulting Numbers: [115, 20] Generated Node #0,1,1: 87:[115, 20] Operation: 29-9=20 Exploring Operation: 9+115=124, Resulting Numbers: [29, 124] Generated Node #0,1,2: 87:[29, 124] Operation: 9+115=124 Exploring Operation: 115-29=86, Resulting Numbers: [9, 86] Generated Node #0,1,3: 87:[9, 86] Operation: 115-29=86 Exploring Operation: 29+9=38, Resulting Numbers: [115, 38] Generated Node #0,1,4: 87:[115, 38] Operation: 29+9=38 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 87:[9, 86], Operations: ['56+59=115', '115-29=86'] Exploring Operation: 9*86=774, Resulting Numbers: [774] 774,87 unequal: No Solution Exploring Operation: 86-9=77, Resulting Numbers: [77] 77,87 unequal: No Solution Exploring Operation: 9+86=95, Resulting Numbers: [95] 95,87 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 #0,1,0 Current State: 87:[29, 106], Operations: ['56+59=115', '115-9=106'] Exploring Operation: 106-29=77, Resulting Numbers: [77] 77,87 unequal: No Solution Exploring Operation: 29+106=135, Resulting Numbers: [135] 135,87 unequal: No Solution Exploring Operation: 29*106=3074, Resulting Numbers: [3074] 3074,87 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 #0,1,1 Current State: 87:[115, 20], Operations: ['56+59=115', '29-9=20'] Exploring Operation: 115*20=2300, Resulting Numbers: [2300] 2300,87 unequal: No Solution Exploring Operation: 115-20=95, Resulting Numbers: [95] 95,87 unequal: No Solution Exploring Operation: 115+20=135, Resulting Numbers: [135] 135,87 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 #0,1,2 Current State: 87:[29, 124], Operations: ['56+59=115', '9+115=124'] Exploring Operation: 29*124=3596, Resulting Numbers: [3596] 3596,87 unequal: No Solution Exploring Operation: 124-29=95, Resulting Numbers: [95] 95,87 unequal: No Solution Exploring Operation: 29+124=153, Resulting Numbers: [153] 153,87 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 #0,1,4 Current State: 87:[115, 38], Operations: ['56+59=115', '29+9=38'] Exploring Operation: 115-38=77, Resulting Numbers: [77] 77,87 unequal: No Solution Exploring Operation: 115+38=153, Resulting Numbers: [153] 153,87 unequal: No Solution Exploring Operation: 115*38=4370, Resulting Numbers: [4370] 4370,87 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: 87:[56, 9, 30], Operations: ['59-29=30'] Exploring Operation: 56-9=47, Resulting Numbers: [30, 47] Generated Node #0,0,0: 87:[30, 47] Operation: 56-9=47 Exploring Operation: 56-30=26, Resulting Numbers: [9, 26] Generated Node #0,0,1: 87:[9, 26] Operation: 56-30=26 Exploring Operation: 30-9=21, Resulting Numbers: [56, 21] Generated Node #0,0,2: 87:[56, 21] Operation: 30-9=21 Exploring Operation: 56+9=65, Resulting Numbers: [30, 65] Generated Node #0,0,3: 87:[30, 65] Operation: 56+9=65 Exploring Operation: 56+30=86, Resulting Numbers: [9, 86] Generated Node #0,0,4: 87:[9, 86] Operation: 56+30=86 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 87:[9, 86], Operations: ['59-29=30', '56+30=86'] Exploring Operation: 9+86=95, Resulting Numbers: [95] 95,87 unequal: No Solution Exploring Operation: 9*86=774, Resulting Numbers: [774] 774,87 unequal: No Solution Exploring Operation: 86-9=77, Resulting Numbers: [77] 77,87 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:[9, 26], Operations: ['59-29=30', '56-30=26'] Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,87 unequal: No Solution Exploring Operation: 9*26=234, Resulting Numbers: [234] 234,87 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 #0,0,0 Current State: 87:[30, 47], Operations: ['59-29=30', '56-9=47'] Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 30+47=77, Resulting Numbers: [77] 77,87 unequal: No Solution Exploring Operation: 30*47=1410, Resulting Numbers: [1410] 1410,87 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 #0,0,3 Current State: 87:[30, 65], Operations: ['59-29=30', '56+9=65'] Exploring Operation: 30*65=1950, Resulting Numbers: [1950] 1950,87 unequal: No Solution Exploring Operation: 65-30=35, Resulting Numbers: [35] 35,87 unequal: No Solution Exploring Operation: 30+65=95, Resulting Numbers: [95] 95,87 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 #0,0,2 Current State: 87:[56, 21], Operations: ['59-29=30', '30-9=21'] Exploring Operation: 56+21=77, Resulting Numbers: [77] 77,87 unequal: No Solution Exploring Operation: 56*21=1176, Resulting Numbers: [1176] 1176,87 unequal: No Solution Exploring Operation: 56-21=35, Resulting Numbers: [35] 35,87 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: 87:[56, 9, 88], Operations: ['59+29=88'] Exploring Operation: 9+88=97, Resulting Numbers: [56, 97] Generated Node #0,4,0: 87:[56, 97] Operation: 9+88=97 Exploring Operation: 56+9=65, Resulting Numbers: [88, 65] Generated Node #0,4,1: 87:[88, 65] Operation: 56+9=65 Exploring Operation: 56-9=47, Resulting Numbers: [88, 47] Generated Node #0,4,2: 87:[88, 47] Operation: 56-9=47 Exploring Operation: 88-9=79, Resulting Numbers: [56, 79] Generated Node #0,4,3: 87:[56, 79] Operation: 88-9=79 Exploring Operation: 88-56=32, Resulting Numbers: [9, 32] Generated Node #0,4,4: 87:[9, 32] Operation: 88-56=32 Moving to Node #0,2 Current State: 87:[59, 9, 85], Operations: ['56+29=85'] Exploring Operation: 59+9=68, Resulting Numbers: [85, 68] Generated Node #0,2,0: 87:[85, 68] Operation: 59+9=68 Exploring Operation: 85-9=76, Resulting Numbers: [59, 76] Generated Node #0,2,1: 87:[59, 76] Operation: 85-9=76 Exploring Operation: 59-9=50, Resulting Numbers: [85, 50] Generated Node #0,2,2: 87:[85, 50] Operation: 59-9=50 Exploring Operation: 85-59=26, Resulting Numbers: [9, 26] Generated Node #0,2,3: 87:[9, 26] Operation: 85-59=26 Exploring Operation: 9+85=94, Resulting Numbers: [59, 94] Generated Node #0,2,4: 87:[59, 94] Operation: 9+85=94 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 87:[9, 26], Operations: ['56+29=85', '85-59=26'] Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,87 unequal: No Solution Exploring Operation: 9*26=234, Resulting Numbers: [234] 234,87 unequal: No Solution Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,87 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 #0,2,0 Current State: 87:[85, 68], Operations: ['56+29=85', '59+9=68'] Exploring Operation: 85*68=5780, Resulting Numbers: [5780] 5780,87 unequal: No Solution Exploring Operation: 85-68=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 85+68=153, Resulting Numbers: [153] 153,87 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 #0,2,2 Current State: 87:[85, 50], Operations: ['56+29=85', '59-9=50'] Exploring Operation: 85*50=4250, Resulting Numbers: [4250] 4250,87 unequal: No Solution Exploring Operation: 85-50=35, Resulting Numbers: [35] 35,87 unequal: No Solution Exploring Operation: 85+50=135, Resulting Numbers: [135] 135,87 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 #0,2,4 Current State: 87:[59, 94], Operations: ['56+29=85', '9+85=94'] Exploring Operation: 59*94=5546, Resulting Numbers: [5546] 5546,87 unequal: No Solution Exploring Operation: 59+94=153, Resulting Numbers: [153] 153,87 unequal: No Solution Exploring Operation: 94-59=35, Resulting Numbers: [35] 35,87 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 #0,2,1 Current State: 87:[59, 76], Operations: ['56+29=85', '85-9=76'] Exploring Operation: 76-59=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 59+76=135, Resulting Numbers: [135] 135,87 unequal: No Solution Exploring Operation: 59*76=4484, Resulting Numbers: [4484] 4484,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 87:[29, 3], Operations: ['59-56=3', '9/3=3'] Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[56, 59, 29, 9], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [29, 9, 3] Generated Node #0,3: 87:[29, 9, 3] Operation: 59-56=3 Moving to Node #0,3 Current State: 87:[29, 9, 3], Operations: ['59-56=3'] Exploring Operation: 9/3=3, Resulting Numbers: [29, 3] Generated Node #0,3,1: 87:[29, 3] Operation: 9/3=3 Moving to Node #0,3,1 Current State: 87:[29, 3], Operations: ['59-56=3', '9/3=3'] Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
0.930556
hs_5
mult_heuristic
[ 8, 12, 34, 22 ]
73
[ "12*34=408", "408/8=51", "22+51=73" ]
Current State: 73:[8, 12, 34, 22], Operations: [] Exploring Operation: 12*34=408, Resulting Numbers: [8, 22, 408] Generated Node #2: [8, 22, 408] from Operation: 12*34=408 Current State: 73:[8, 22, 408], Operations: ['12*34=408'] Exploring Operation: 408/8=51, Resulting Numbers: [22, 51] Generated Node #3: [22, 51] from Operation: 408/8=51 Current State: 73:[22, 51], Operations: ['12*34=408', '408/8=51'] Exploring Operation: 22+51=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[8, 12, 34, 22], Operations: [] Exploring Operation: 8+34=42, Resulting Numbers: [12, 22, 42] Generated Node #0,0: 73:[12, 22, 42] Operation: 8+34=42 Exploring Operation: 8+22=30, Resulting Numbers: [12, 34, 30] Generated Node #0,1: 73:[12, 34, 30] Operation: 8+22=30 Exploring Operation: 8*12=96, Resulting Numbers: [34, 22, 96] Generated Node #0,2: 73:[34, 22, 96] Operation: 8*12=96 Exploring Operation: 8+12=20, Resulting Numbers: [34, 22, 20] Generated Node #0,3: 73:[34, 22, 20] Operation: 8+12=20 Moving to Node #0,2 Current State: 73:[34, 22, 96], Operations: ['8*12=96'] Exploring Operation: 34-22=12, Resulting Numbers: [96, 12] Generated Node #0,2,0: 73:[96, 12] Operation: 34-22=12 Exploring Operation: 96-22=74, Resulting Numbers: [34, 74] Generated Node #0,2,1: 73:[34, 74] Operation: 96-22=74 Exploring Operation: 34+22=56, Resulting Numbers: [96, 56] Generated Node #0,2,2: 73:[96, 56] Operation: 34+22=56 Exploring Operation: 96-34=62, Resulting Numbers: [22, 62] Generated Node #0,2,3: 73:[22, 62] Operation: 96-34=62 Moving to Node #0,1 Current State: 73:[12, 34, 30], Operations: ['8+22=30'] Exploring Operation: 34+30=64, Resulting Numbers: [12, 64] Generated Node #0,1,0: 73:[12, 64] Operation: 34+30=64 Exploring Operation: 12+30=42, Resulting Numbers: [34, 42] Generated Node #0,1,1: 73:[34, 42] Operation: 12+30=42 Exploring Operation: 12+34=46, Resulting Numbers: [30, 46] Generated Node #0,1,2: 73:[30, 46] Operation: 12+34=46 Exploring Operation: 34-12=22, Resulting Numbers: [30, 22] Generated Node #0,1,3: 73:[30, 22] Operation: 34-12=22 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[12, 64], Operations: ['8+22=30', '34+30=64'] Exploring Operation: 64-12=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 12+64=76, Resulting Numbers: [76] 76,73 unequal: No Solution Exploring Operation: 12*64=768, Resulting Numbers: [768] 768,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[34, 42], Operations: ['8+22=30', '12+30=42'] Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 34*42=1428, Resulting Numbers: [1428] 1428,73 unequal: No Solution Exploring Operation: 34+42=76, Resulting Numbers: [76] 76,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 73:[30, 46], Operations: ['8+22=30', '12+34=46'] Exploring Operation: 30+46=76, Resulting Numbers: [76] 76,73 unequal: No Solution Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 30*46=1380, Resulting Numbers: [1380] 1380,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 73:[30, 22], Operations: ['8+22=30', '34-12=22'] Exploring Operation: 30*22=660, Resulting Numbers: [660] 660,73 unequal: No Solution Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,73 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: 73:[12, 22, 42], Operations: ['8+34=42'] Exploring Operation: 12+42=54, Resulting Numbers: [22, 54] Generated Node #0,0,0: 73:[22, 54] Operation: 12+42=54 Exploring Operation: 22-12=10, Resulting Numbers: [42, 10] Generated Node #0,0,1: 73:[42, 10] Operation: 22-12=10 Exploring Operation: 12+22=34, Resulting Numbers: [42, 34] Generated Node #0,0,2: 73:[42, 34] Operation: 12+22=34 Exploring Operation: 22+42=64, Resulting Numbers: [12, 64] Generated Node #0,0,3: 73:[12, 64] Operation: 22+42=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[22, 54], Operations: ['8+34=42', '12+42=54'] Exploring Operation: 22+54=76, Resulting Numbers: [76] 76,73 unequal: No Solution Exploring Operation: 22*54=1188, Resulting Numbers: [1188] 1188,73 unequal: No Solution Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,73 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 #0,0,2 Current State: 73:[42, 34], Operations: ['8+34=42', '12+22=34'] Exploring Operation: 42+34=76, Resulting Numbers: [76] 76,73 unequal: No Solution Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 42*34=1428, Resulting Numbers: [1428] 1428,73 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 #0,0,3 Current State: 73:[12, 64], Operations: ['8+34=42', '22+42=64'] Exploring Operation: 12+64=76, Resulting Numbers: [76] 76,73 unequal: No Solution Exploring Operation: 64-12=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 12*64=768, Resulting Numbers: [768] 768,73 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 #0,0,1 Current State: 73:[42, 10], Operations: ['8+34=42', '22-12=10'] Exploring Operation: 42*10=420, Resulting Numbers: [420] 420,73 unequal: No Solution Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,73 unequal: No Solution Exploring Operation: 42+10=52, Resulting Numbers: [52] 52,73 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: 73:[34, 22, 20], Operations: ['8+12=20'] Exploring Operation: 34-20=14, Resulting Numbers: [22, 14] Generated Node #0,3,0: 73:[22, 14] Operation: 34-20=14 Exploring Operation: 34+20=54, Resulting Numbers: [22, 54] Generated Node #0,3,1: 73:[22, 54] Operation: 34+20=54 Exploring Operation: 22+20=42, Resulting Numbers: [34, 42] Generated Node #0,3,2: 73:[34, 42] Operation: 22+20=42 Exploring Operation: 34+22=56, Resulting Numbers: [20, 56] Generated Node #0,3,3: 73:[20, 56] Operation: 34+22=56 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 73:[22, 54], Operations: ['8+12=20', '34+20=54'] Exploring Operation: 22*54=1188, Resulting Numbers: [1188] 1188,73 unequal: No Solution Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,73 unequal: No Solution Exploring Operation: 22+54=76, Resulting Numbers: [76] 76,73 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 #0,3,2 Current State: 73:[34, 42], Operations: ['8+12=20', '22+20=42'] Exploring Operation: 34+42=76, Resulting Numbers: [76] 76,73 unequal: No Solution Exploring Operation: 34*42=1428, Resulting Numbers: [1428] 1428,73 unequal: No Solution Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,73 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 #0,3,3 Current State: 73:[20, 56], Operations: ['8+12=20', '34+22=56'] Exploring Operation: 56-20=36, Resulting Numbers: [36] 36,73 unequal: No Solution Exploring Operation: 20*56=1120, Resulting Numbers: [1120] 1120,73 unequal: No Solution Exploring Operation: 20+56=76, Resulting Numbers: [76] 76,73 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 #0,3,0 Current State: 73:[22, 14], Operations: ['8+12=20', '34-20=14'] Exploring Operation: 22+14=36, Resulting Numbers: [36] 36,73 unequal: No Solution Exploring Operation: 22*14=308, Resulting Numbers: [308] 308,73 unequal: No Solution Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 73:[34, 74], Operations: ['8*12=96', '96-22=74'] Exploring Operation: 34*74=2516, Resulting Numbers: [2516] 2516,73 unequal: No Solution Exploring Operation: 34+74=108, Resulting Numbers: [108] 108,73 unequal: No Solution Exploring Operation: 74-34=40, Resulting Numbers: [40] 40,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[96, 56], Operations: ['8*12=96', '34+22=56'] Exploring Operation: 96+56=152, Resulting Numbers: [152] 152,73 unequal: No Solution Exploring Operation: 96-56=40, Resulting Numbers: [40] 40,73 unequal: No Solution Exploring Operation: 96*56=5376, Resulting Numbers: [5376] 5376,73 unequal: No Solution Moving to Node #0,2,3 Current State: 73:[22, 62], Operations: ['8*12=96', '96-34=62'] Exploring Operation: 22+62=84, Resulting Numbers: [84] 84,73 unequal: No Solution Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,73 unequal: No Solution Exploring Operation: 22*62=1364, Resulting Numbers: [1364] 1364,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[96, 12], Operations: ['8*12=96', '34-22=12'] Exploring Operation: 96*12=1152, Resulting Numbers: [1152] 1152,73 unequal: No Solution Exploring Operation: 96+12=108, Resulting Numbers: [108] 108,73 unequal: No Solution Exploring Operation: 96/12=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 96-12=84, Resulting Numbers: [84] 84,73 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 47, 94, 32, 46 ]
76
[ "94/47=2", "32+46=78", "78-2=76" ]
Current State: 76:[47, 94, 32, 46], Operations: [] Exploring Operation: 94/47=2, Resulting Numbers: [32, 46, 2] Generated Node #2: [32, 46, 2] from Operation: 94/47=2 Current State: 76:[32, 46, 2], Operations: ['94/47=2'] Exploring Operation: 32+46=78, Resulting Numbers: [2, 78] Generated Node #3: [2, 78] from Operation: 32+46=78 Current State: 76:[2, 78], Operations: ['94/47=2', '32+46=78'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[47, 94, 32, 46], Operations: [] Exploring Operation: 47-46=1, Resulting Numbers: [94, 32, 1] Generated Node #0,0: 76:[94, 32, 1] Operation: 47-46=1 Exploring Operation: 94-47=47, Resulting Numbers: [32, 46, 47] Generated Node #0,1: 76:[32, 46, 47] Operation: 94-47=47 Exploring Operation: 94/47=2, Resulting Numbers: [32, 46, 2] Generated Node #0,2: 76:[32, 46, 2] Operation: 94/47=2 Moving to Node #0,2 Current State: 76:[32, 46, 2], Operations: ['94/47=2'] Exploring Operation: 32+46=78, Resulting Numbers: [2, 78] Generated Node #0,2,0: 76:[2, 78] Operation: 32+46=78 Exploring Operation: 46-32=14, Resulting Numbers: [2, 14] Generated Node #0,2,1: 76:[2, 14] Operation: 46-32=14 Exploring Operation: 46/2=23, Resulting Numbers: [32, 23] Generated Node #0,2,2: 76:[32, 23] Operation: 46/2=23 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 76:[2, 78], Operations: ['94/47=2', '32+46=78'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[47, 94, 32, 46], Operations: [] Exploring Operation: 94/47=2, Resulting Numbers: [32, 46, 2] Generated Node #0,2: 76:[32, 46, 2] Operation: 94/47=2 Moving to Node #0,2 Current State: 76:[32, 46, 2], Operations: ['94/47=2'] Exploring Operation: 32+46=78, Resulting Numbers: [2, 78] Generated Node #0,2,0: 76:[2, 78] Operation: 32+46=78 Moving to Node #0,2,0 Current State: 76:[2, 78], Operations: ['94/47=2', '32+46=78'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 5, 15, 10, 9 ]
18
[ "5+15=20", "20/10=2", "9*2=18" ]
Current State: 18:[5, 15, 10, 9], Operations: [] Exploring Operation: 5+15=20, Resulting Numbers: [10, 9, 20] Generated Node #2: [10, 9, 20] from Operation: 5+15=20 Current State: 18:[10, 9, 20], Operations: ['5+15=20'] Exploring Operation: 20/10=2, Resulting Numbers: [9, 2] Generated Node #3: [9, 2] from Operation: 20/10=2 Current State: 18:[9, 2], Operations: ['5+15=20', '20/10=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[5, 15, 10, 9], Operations: [] Exploring Operation: 15/5=3, Resulting Numbers: [10, 9, 3] Generated Node #0,0: 18:[10, 9, 3] Operation: 15/5=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[10, 9, 3], Operations: ['15/5=3'] Exploring Operation: 10+9=19, Resulting Numbers: [3, 19] Generated Node #0,0,0: 18:[3, 19] Operation: 10+9=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[3, 19], Operations: ['15/5=3', '10+9=19'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 87, 92, 7, 94 ]
40
[ "87-7=80", "94-92=2", "80/2=40" ]
Current State: 40:[87, 92, 7, 94], Operations: [] Exploring Operation: 87-7=80, Resulting Numbers: [92, 94, 80] Generated Node #2: [92, 94, 80] from Operation: 87-7=80 Current State: 40:[92, 94, 80], Operations: ['87-7=80'] Exploring Operation: 94-92=2, Resulting Numbers: [80, 2] Generated Node #3: [80, 2] from Operation: 94-92=2 Current State: 40:[80, 2], Operations: ['87-7=80', '94-92=2'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[87, 92, 7, 94], Operations: [] Exploring Operation: 94-87=7, Resulting Numbers: [92, 7, 7] Generated Node #0,0: 40:[92, 7, 7] Operation: 94-87=7 Exploring Operation: 92-87=5, Resulting Numbers: [7, 94, 5] Generated Node #0,1: 40:[7, 94, 5] Operation: 92-87=5 Exploring Operation: 94-92=2, Resulting Numbers: [87, 7, 2] Generated Node #0,2: 40:[87, 7, 2] Operation: 94-92=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[87, 7, 2], Operations: ['94-92=2'] Exploring Operation: 87-7=80, Resulting Numbers: [2, 80] Generated Node #0,2,0: 40:[2, 80] Operation: 87-7=80 Exploring Operation: 7-2=5, Resulting Numbers: [87, 5] Generated Node #0,2,1: 40:[87, 5] Operation: 7-2=5 Exploring Operation: 87-2=85, Resulting Numbers: [7, 85] Generated Node #0,2,2: 40:[7, 85] Operation: 87-2=85 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 40:[2, 80], Operations: ['94-92=2', '87-7=80'] Exploring Operation: 2+80=82, Resulting Numbers: [82] 82,40 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,40 unequal: No Solution Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[87, 92, 7, 94], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [87, 7, 2] Generated Node #0,2: 40:[87, 7, 2] Operation: 94-92=2 Moving to Node #0,2 Current State: 40:[87, 7, 2], Operations: ['94-92=2'] Exploring Operation: 87-7=80, Resulting Numbers: [2, 80] Generated Node #0,2,0: 40:[2, 80] Operation: 87-7=80 Moving to Node #0,2,0 Current State: 40:[2, 80], Operations: ['94-92=2', '87-7=80'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 33, 37, 30, 27 ]
78
[ "37-33=4", "27*4=108", "108-30=78" ]
Current State: 78:[33, 37, 30, 27], Operations: [] Exploring Operation: 37-33=4, Resulting Numbers: [30, 27, 4] Generated Node #2: [30, 27, 4] from Operation: 37-33=4 Current State: 78:[30, 27, 4], Operations: ['37-33=4'] Exploring Operation: 27*4=108, Resulting Numbers: [30, 108] Generated Node #3: [30, 108] from Operation: 27*4=108 Current State: 78:[30, 108], Operations: ['37-33=4', '27*4=108'] Exploring Operation: 108-30=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[33, 37, 30, 27], Operations: [] Exploring Operation: 30-27=3, Resulting Numbers: [33, 37, 3] Generated Node #0,0: 78:[33, 37, 3] Operation: 30-27=3 Exploring Operation: 33-30=3, Resulting Numbers: [37, 27, 3] Generated Node #0,1: 78:[37, 27, 3] Operation: 33-30=3 Exploring Operation: 37-33=4, Resulting Numbers: [30, 27, 4] Generated Node #0,2: 78:[30, 27, 4] Operation: 37-33=4 Exploring Operation: 37-30=7, Resulting Numbers: [33, 27, 7] Generated Node #0,3: 78:[33, 27, 7] Operation: 37-30=7 Exploring Operation: 33-27=6, Resulting Numbers: [37, 30, 6] Generated Node #0,4: 78:[37, 30, 6] Operation: 33-27=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[37, 27, 3], Operations: ['33-30=3'] Exploring Operation: 37-27=10, Resulting Numbers: [3, 10] Generated Node #0,1,0: 78:[3, 10] Operation: 37-27=10 Exploring Operation: 27-3=24, Resulting Numbers: [37, 24] Generated Node #0,1,1: 78:[37, 24] Operation: 27-3=24 Exploring Operation: 27*3=81, Resulting Numbers: [37, 81] Generated Node #0,1,2: 78:[37, 81] Operation: 27*3=81 Exploring Operation: 37+3=40, Resulting Numbers: [27, 40] Generated Node #0,1,3: 78:[27, 40] Operation: 37+3=40 Exploring Operation: 27/3=9, Resulting Numbers: [37, 9] Generated Node #0,1,4: 78:[37, 9] Operation: 27/3=9 Moving to Node #0,1,3 Current State: 78:[27, 40], Operations: ['33-30=3', '37+3=40'] Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 27*40=1080, Resulting Numbers: [1080] 1080,78 unequal: No Solution Exploring Operation: 27+40=67, Resulting Numbers: [67] 67,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[3, 10], Operations: ['33-30=3', '37-27=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,78 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[37, 24], Operations: ['33-30=3', '27-3=24'] Exploring Operation: 37*24=888, Resulting Numbers: [888] 888,78 unequal: No Solution Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,78 unequal: No Solution Moving to Node #0,1,2 Current State: 78:[37, 81], Operations: ['33-30=3', '27*3=81'] Exploring Operation: 37*81=2997, Resulting Numbers: [2997] 2997,78 unequal: No Solution Exploring Operation: 37+81=118, Resulting Numbers: [118] 118,78 unequal: No Solution Exploring Operation: 81-37=44, Resulting Numbers: [44] 44,78 unequal: No Solution Moving to Node #0,1,4 Current State: 78:[37, 9], Operations: ['33-30=3', '27/3=9'] Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 37+9=46, Resulting Numbers: [46] 46,78 unequal: No Solution Exploring Operation: 37*9=333, Resulting Numbers: [333] 333,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 78:[30, 27, 4], Operations: ['37-33=4'] Exploring Operation: 27-4=23, Resulting Numbers: [30, 23] Generated Node #0,2,0: 78:[30, 23] Operation: 27-4=23 Exploring Operation: 30-27=3, Resulting Numbers: [4, 3] Generated Node #0,2,1: 78:[4, 3] Operation: 30-27=3 Exploring Operation: 30-4=26, Resulting Numbers: [27, 26] Generated Node #0,2,2: 78:[27, 26] Operation: 30-4=26 Exploring Operation: 27+4=31, Resulting Numbers: [30, 31] Generated Node #0,2,3: 78:[30, 31] Operation: 27+4=31 Exploring Operation: 30+4=34, Resulting Numbers: [27, 34] Generated Node #0,2,4: 78:[27, 34] Operation: 30+4=34 Moving to Node #0,2,1 Current State: 78:[4, 3], Operations: ['37-33=4', '30-27=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,78 unequal: No Solution Moving to Node #0,2,2 Current State: 78:[27, 26], Operations: ['37-33=4', '30-4=26'] Exploring Operation: 27*26=702, Resulting Numbers: [702] 702,78 unequal: No Solution Exploring Operation: 27+26=53, Resulting Numbers: [53] 53,78 unequal: No Solution Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,78 unequal: No Solution Moving to Node #0,2,4 Current State: 78:[27, 34], Operations: ['37-33=4', '30+4=34'] Exploring Operation: 27*34=918, Resulting Numbers: [918] 918,78 unequal: No Solution Exploring Operation: 27+34=61, Resulting Numbers: [61] 61,78 unequal: No Solution Exploring Operation: 34-27=7, Resulting Numbers: [7] 7,78 unequal: No Solution Moving to Node #0,2,0 Current State: 78:[30, 23], Operations: ['37-33=4', '27-4=23'] Exploring Operation: 30*23=690, Resulting Numbers: [690] 690,78 unequal: No Solution Exploring Operation: 30-23=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 30+23=53, Resulting Numbers: [53] 53,78 unequal: No Solution Moving to Node #0,2,3 Current State: 78:[30, 31], Operations: ['37-33=4', '27+4=31'] Exploring Operation: 30+31=61, Resulting Numbers: [61] 61,78 unequal: No Solution Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 30*31=930, Resulting Numbers: [930] 930,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 78:[37, 30, 6], Operations: ['33-27=6'] Exploring Operation: 30-6=24, Resulting Numbers: [37, 24] Generated Node #0,4,0: 78:[37, 24] Operation: 30-6=24 Exploring Operation: 30+6=36, Resulting Numbers: [37, 36] Generated Node #0,4,1: 78:[37, 36] Operation: 30+6=36 Exploring Operation: 37+6=43, Resulting Numbers: [30, 43] Generated Node #0,4,2: 78:[30, 43] Operation: 37+6=43 Exploring Operation: 30/6=5, Resulting Numbers: [37, 5] Generated Node #0,4,3: 78:[37, 5] Operation: 30/6=5 Exploring Operation: 37-30=7, Resulting Numbers: [6, 7] Generated Node #0,4,4: 78:[6, 7] Operation: 37-30=7 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 78:[6, 7], Operations: ['33-27=6', '37-30=7'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,78 unequal: No Solution No 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: 78:[37, 5], Operations: ['33-27=6', '30/6=5'] Exploring Operation: 37+5=42, Resulting Numbers: [42] 42,78 unequal: No Solution Exploring Operation: 37*5=185, Resulting Numbers: [185] 185,78 unequal: No Solution Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,78 unequal: No Solution No 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: 78:[37, 24], Operations: ['33-27=6', '30-6=24'] Exploring Operation: 37*24=888, Resulting Numbers: [888] 888,78 unequal: No Solution Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 78:[37, 36], Operations: ['33-27=6', '30+6=36'] Exploring Operation: 37*36=1332, Resulting Numbers: [1332] 1332,78 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 37+36=73, Resulting Numbers: [73] 73,78 unequal: No Solution No 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: 78:[30, 43], Operations: ['33-27=6', '37+6=43'] Exploring Operation: 43-30=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 30+43=73, Resulting Numbers: [73] 73,78 unequal: No Solution Exploring Operation: 30*43=1290, Resulting Numbers: [1290] 1290,78 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: 78:[33, 37, 3], Operations: ['30-27=3'] Exploring Operation: 37-33=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 78:[3, 4] Operation: 37-33=4 Exploring Operation: 37+3=40, Resulting Numbers: [33, 40] Generated Node #0,0,1: 78:[33, 40] Operation: 37+3=40 Exploring Operation: 33/3=11, Resulting Numbers: [37, 11] Generated Node #0,0,2: 78:[37, 11] Operation: 33/3=11 Exploring Operation: 33-3=30, Resulting Numbers: [37, 30] Generated Node #0,0,3: 78:[37, 30] Operation: 33-3=30 Exploring Operation: 33+3=36, Resulting Numbers: [37, 36] Generated Node #0,0,4: 78:[37, 36] Operation: 33+3=36 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 78:[3, 4], Operations: ['30-27=3', '37-33=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,78 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,78 unequal: No Solution No 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: 78:[37, 11], Operations: ['30-27=3', '33/3=11'] Exploring Operation: 37+11=48, Resulting Numbers: [48] 48,78 unequal: No Solution Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 37*11=407, Resulting Numbers: [407] 407,78 unequal: No Solution No 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: 78:[37, 36], Operations: ['30-27=3', '33+3=36'] Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 37*36=1332, Resulting Numbers: [1332] 1332,78 unequal: No Solution Exploring Operation: 37+36=73, Resulting Numbers: [73] 73,78 unequal: No Solution No 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: 78:[37, 30], Operations: ['30-27=3', '33-3=30'] Exploring Operation: 37*30=1110, Resulting Numbers: [1110] 1110,78 unequal: No Solution Exploring Operation: 37-30=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 37+30=67, Resulting Numbers: [67] 67,78 unequal: No Solution No 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: 78:[33, 40], Operations: ['30-27=3', '37+3=40'] Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 33+40=73, Resulting Numbers: [73] 73,78 unequal: No Solution Exploring Operation: 33*40=1320, Resulting Numbers: [1320] 1320,78 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: 78:[33, 27, 7], Operations: ['37-30=7'] Exploring Operation: 27-7=20, Resulting Numbers: [33, 20] Generated Node #0,3,0: 78:[33, 20] Operation: 27-7=20 Exploring Operation: 33-27=6, Resulting Numbers: [7, 6] Generated Node #0,3,1: 78:[7, 6] Operation: 33-27=6 Exploring Operation: 33+7=40, Resulting Numbers: [27, 40] Generated Node #0,3,2: 78:[27, 40] Operation: 33+7=40 Exploring Operation: 27+7=34, Resulting Numbers: [33, 34] Generated Node #0,3,3: 78:[33, 34] Operation: 27+7=34 Exploring Operation: 33-7=26, Resulting Numbers: [27, 26] Generated Node #0,3,4: 78:[27, 26] Operation: 33-7=26 Moving to Node #0,3,1 Current State: 78:[7, 6], Operations: ['37-30=7', '33-27=6'] Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,78 unequal: No Solution Moving to Node #0,3,4 Current State: 78:[27, 26], Operations: ['37-30=7', '33-7=26'] Exploring Operation: 27*26=702, Resulting Numbers: [702] 702,78 unequal: No Solution Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 27+26=53, Resulting Numbers: [53] 53,78 unequal: No Solution Moving to Node #0,3,2 Current State: 78:[27, 40], Operations: ['37-30=7', '33+7=40'] Exploring Operation: 27*40=1080, Resulting Numbers: [1080] 1080,78 unequal: No Solution Exploring Operation: 27+40=67, Resulting Numbers: [67] 67,78 unequal: No Solution Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,78 unequal: No Solution Moving to Node #0,3,3 Current State: 78:[33, 34], Operations: ['37-30=7', '27+7=34'] Exploring Operation: 33*34=1122, Resulting Numbers: [1122] 1122,78 unequal: No Solution Exploring Operation: 33+34=67, Resulting Numbers: [67] 67,78 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,78 unequal: No Solution Moving to Node #0,3,0 Current State: 78:[33, 20], Operations: ['37-30=7', '27-7=20'] Exploring Operation: 33*20=660, Resulting Numbers: [660] 660,78 unequal: No Solution Exploring Operation: 33-20=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 33+20=53, Resulting Numbers: [53] 53,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 28, 79, 51, 22 ]
80
[ "79-28=51", "51-22=29", "51+29=80" ]
Current State: 80:[28, 79, 51, 22], Operations: [] Exploring Operation: 79-28=51, Resulting Numbers: [51, 22, 51] Generated Node #2: [51, 22, 51] from Operation: 79-28=51 Current State: 80:[51, 22, 51], Operations: ['79-28=51'] Exploring Operation: 51-22=29, Resulting Numbers: [29] 29,80 equal: Goal Reached Exploring Operation: 51+29=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[28, 79, 51, 22], Operations: [] Exploring Operation: 51-28=23, Resulting Numbers: [79, 22, 23] Generated Node #0,0: 80:[79, 22, 23] Operation: 51-28=23 Exploring Operation: 28+51=79, Resulting Numbers: [79, 22, 79] Generated Node #0,1: 80:[79, 22, 79] Operation: 28+51=79 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[79, 22, 79], Operations: ['28+51=79'] Exploring Operation: 79-79=0, Resulting Numbers: [22, 0] Generated Node #0,1,0: 80:[22, 0] Operation: 79-79=0 Exploring Operation: 79/79=1, Resulting Numbers: [22, 1] Generated Node #0,1,1: 80:[22, 1] Operation: 79/79=1 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 80:[22, 1], Operations: ['28+51=79', '79/79=1'] Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 22*1=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 #0,1,0 Current State: 80:[22, 0], Operations: ['28+51=79', '79-79=0'] Exploring Operation: 22+0=22, Resulting Numbers: [22] 22,80 unequal: No Solution Exploring Operation: 22*0=0, Resulting Numbers: [0] 0,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[79, 22, 23], Operations: ['51-28=23'] Exploring Operation: 22+23=45, Resulting Numbers: [79, 45] Generated Node #0,0,0: 80:[79, 45] Operation: 22+23=45 Exploring Operation: 23-22=1, Resulting Numbers: [79, 1] Generated Node #0,0,1: 80:[79, 1] Operation: 23-22=1 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 80:[79, 1], Operations: ['51-28=23', '23-22=1'] Exploring Operation: 79+1=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[28, 79, 51, 22], Operations: [] Exploring Operation: 51-28=23, Resulting Numbers: [79, 22, 23] Generated Node #0,0: 80:[79, 22, 23] Operation: 51-28=23 Moving to Node #0,0 Current State: 80:[79, 22, 23], Operations: ['51-28=23'] Exploring Operation: 23-22=1, Resulting Numbers: [79, 1] Generated Node #0,0,1: 80:[79, 1] Operation: 23-22=1 Moving to Node #0,0,1 Current State: 80:[79, 1], Operations: ['51-28=23', '23-22=1'] Exploring Operation: 79+1=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 80, 74, 98, 47 ]
57
[ "80-74=6", "98-47=51", "6+51=57" ]
Current State: 57:[80, 74, 98, 47], Operations: [] Exploring Operation: 80-74=6, Resulting Numbers: [98, 47, 6] Generated Node #2: [98, 47, 6] from Operation: 80-74=6 Current State: 57:[98, 47, 6], Operations: ['80-74=6'] Exploring Operation: 98-47=51, Resulting Numbers: [6, 51] Generated Node #3: [6, 51] from Operation: 98-47=51 Current State: 57:[6, 51], Operations: ['80-74=6', '98-47=51'] Exploring Operation: 6+51=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[80, 74, 98, 47], Operations: [] Exploring Operation: 98-74=24, Resulting Numbers: [80, 47, 24] Generated Node #0,0: 57:[80, 47, 24] Operation: 98-74=24 Exploring Operation: 98-80=18, Resulting Numbers: [74, 47, 18] Generated Node #0,1: 57:[74, 47, 18] Operation: 98-80=18 Moving to Node #0,1 Current State: 57:[74, 47, 18], Operations: ['98-80=18'] Exploring Operation: 74-47=27, Resulting Numbers: [18, 27] Generated Node #0,1,0: 57:[18, 27] Operation: 74-47=27 Exploring Operation: 74-18=56, Resulting Numbers: [47, 56] Generated Node #0,1,1: 57:[47, 56] Operation: 74-18=56 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[18, 27], Operations: ['98-80=18', '74-47=27'] Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 57:[47, 56], Operations: ['98-80=18', '74-18=56'] Exploring Operation: 47+56=103, Resulting Numbers: [103] 103,57 unequal: No Solution Exploring Operation: 56-47=9, Resulting Numbers: [9] 9,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 57:[80, 47, 24], Operations: ['98-74=24'] Exploring Operation: 80-47=33, Resulting Numbers: [24, 33] Generated Node #0,0,0: 57:[24, 33] Operation: 80-47=33 Exploring Operation: 80-24=56, Resulting Numbers: [47, 56] Generated Node #0,0,1: 57:[47, 56] Operation: 80-24=56 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 57:[47, 56], Operations: ['98-74=24', '80-24=56'] Exploring Operation: 47+56=103, Resulting Numbers: [103] 103,57 unequal: No Solution Exploring Operation: 56-47=9, Resulting Numbers: [9] 9,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[24, 33], Operations: ['98-74=24', '80-47=33'] Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 24+33=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[80, 74, 98, 47], Operations: [] Exploring Operation: 98-74=24, Resulting Numbers: [80, 47, 24] Generated Node #0,0: 57:[80, 47, 24] Operation: 98-74=24 Moving to Node #0,0 Current State: 57:[80, 47, 24], Operations: ['98-74=24'] Exploring Operation: 80-47=33, Resulting Numbers: [24, 33] Generated Node #0,0,0: 57:[24, 33] Operation: 80-47=33 Moving to Node #0,0,0 Current State: 57:[24, 33], Operations: ['98-74=24', '80-47=33'] Exploring Operation: 24+33=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 69, 78, 63, 13 ]
20
[ "78-69=9", "63/9=7", "13+7=20" ]
Current State: 20:[69, 78, 63, 13], Operations: [] Exploring Operation: 78-69=9, Resulting Numbers: [63, 13, 9] Generated Node #2: [63, 13, 9] from Operation: 78-69=9 Current State: 20:[63, 13, 9], Operations: ['78-69=9'] Exploring Operation: 63/9=7, Resulting Numbers: [13, 7] Generated Node #3: [13, 7] from Operation: 63/9=7 Current State: 20:[13, 7], Operations: ['78-69=9', '63/9=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[69, 78, 63, 13], Operations: [] Exploring Operation: 78-69=9, Resulting Numbers: [63, 13, 9] Generated Node #0,0: 20:[63, 13, 9] Operation: 78-69=9 Exploring Operation: 78-63=15, Resulting Numbers: [69, 13, 15] Generated Node #0,1: 20:[69, 13, 15] Operation: 78-63=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[63, 13, 9], Operations: ['78-69=9'] Exploring Operation: 63/9=7, Resulting Numbers: [13, 7] Generated Node #0,0,0: 20:[13, 7] Operation: 63/9=7 Exploring Operation: 63-13=50, Resulting Numbers: [9, 50] Generated Node #0,0,1: 20:[9, 50] Operation: 63-13=50 Moving to Node #0,0,0 Current State: 20:[13, 7], Operations: ['78-69=9', '63/9=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[69, 78, 63, 13], Operations: [] Exploring Operation: 78-69=9, Resulting Numbers: [63, 13, 9] Generated Node #0,0: 20:[63, 13, 9] Operation: 78-69=9 Moving to Node #0,0 Current State: 20:[63, 13, 9], Operations: ['78-69=9'] Exploring Operation: 63/9=7, Resulting Numbers: [13, 7] Generated Node #0,0,0: 20:[13, 7] Operation: 63/9=7 Moving to Node #0,0,0 Current State: 20:[13, 7], Operations: ['78-69=9', '63/9=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 13, 93, 33, 2 ]
86
[ "13+93=106", "106/2=53", "33+53=86" ]
Current State: 86:[13, 93, 33, 2], Operations: [] Exploring Operation: 13+93=106, Resulting Numbers: [33, 2, 106] Generated Node #2: [33, 2, 106] from Operation: 13+93=106 Current State: 86:[33, 2, 106], Operations: ['13+93=106'] Exploring Operation: 106/2=53, Resulting Numbers: [33, 53] Generated Node #3: [33, 53] from Operation: 106/2=53 Current State: 86:[33, 53], Operations: ['13+93=106', '106/2=53'] Exploring Operation: 33+53=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[13, 93, 33, 2], Operations: [] Exploring Operation: 13+33=46, Resulting Numbers: [93, 2, 46] Generated Node #0,0: 86:[93, 2, 46] Operation: 13+33=46 Moving to Node #0,0 Current State: 86:[93, 2, 46], Operations: ['13+33=46'] Exploring Operation: 93-46=47, Resulting Numbers: [2, 47] Generated Node #0,0,0: 86:[2, 47] Operation: 93-46=47 Moving to Node #0,0,0 Current State: 86:[2, 47], Operations: ['13+33=46', '93-46=47'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,86 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 89, 10, 59, 21 ]
41
[ "89-10=79", "59-21=38", "79-38=41" ]
Current State: 41:[89, 10, 59, 21], Operations: [] Exploring Operation: 89-10=79, Resulting Numbers: [59, 21, 79] Generated Node #2: [59, 21, 79] from Operation: 89-10=79 Current State: 41:[59, 21, 79], Operations: ['89-10=79'] Exploring Operation: 59-21=38, Resulting Numbers: [79, 38] Generated Node #3: [79, 38] from Operation: 59-21=38 Current State: 41:[79, 38], Operations: ['89-10=79', '59-21=38'] Exploring Operation: 79-38=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[89, 10, 59, 21], Operations: [] Exploring Operation: 89-10=79, Resulting Numbers: [59, 21, 79] Generated Node #0,0: 41:[59, 21, 79] Operation: 89-10=79 Exploring Operation: 89-59=30, Resulting Numbers: [10, 21, 30] Generated Node #0,1: 41:[10, 21, 30] Operation: 89-59=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[10, 21, 30], Operations: ['89-59=30'] Exploring Operation: 10+21=31, Resulting Numbers: [30, 31] Generated Node #0,1,0: 41:[30, 31] Operation: 10+21=31 Exploring Operation: 10+30=40, Resulting Numbers: [21, 40] Generated Node #0,1,1: 41:[21, 40] Operation: 10+30=40 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[30, 31], Operations: ['89-59=30', '10+21=31'] Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 30+31=61, Resulting Numbers: [61] 61,41 unequal: No Solution No 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: 41:[21, 40], Operations: ['89-59=30', '10+30=40'] Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 21+40=61, Resulting Numbers: [61] 61,41 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: 41:[59, 21, 79], Operations: ['89-10=79'] Exploring Operation: 59-21=38, Resulting Numbers: [79, 38] Generated Node #0,0,0: 41:[79, 38] Operation: 59-21=38 Exploring Operation: 79-21=58, Resulting Numbers: [59, 58] Generated Node #0,0,1: 41:[59, 58] Operation: 79-21=58 Moving to Node #0,0,1 Current State: 41:[59, 58], Operations: ['89-10=79', '79-21=58'] Exploring Operation: 59+58=117, Resulting Numbers: [117] 117,41 unequal: No Solution Exploring Operation: 59-58=1, Resulting Numbers: [1] 1,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[79, 38], Operations: ['89-10=79', '59-21=38'] Exploring Operation: 79+38=117, Resulting Numbers: [117] 117,41 unequal: No Solution Exploring Operation: 79-38=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[89, 10, 59, 21], Operations: [] Exploring Operation: 89-10=79, Resulting Numbers: [59, 21, 79] Generated Node #0,0: 41:[59, 21, 79] Operation: 89-10=79 Moving to Node #0,0 Current State: 41:[59, 21, 79], Operations: ['89-10=79'] Exploring Operation: 59-21=38, Resulting Numbers: [79, 38] Generated Node #0,0,0: 41:[79, 38] Operation: 59-21=38 Moving to Node #0,0,0 Current State: 41:[79, 38], Operations: ['89-10=79', '59-21=38'] Exploring Operation: 79-38=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_2
sum_heuristic
[ 61, 90, 22, 66 ]
15
[ "90-61=29", "66-22=44", "44-29=15" ]
Current State: 15:[61, 90, 22, 66], Operations: [] Exploring Operation: 90-61=29, Resulting Numbers: [22, 66, 29] Generated Node #2: [22, 66, 29] from Operation: 90-61=29 Current State: 15:[22, 66, 29], Operations: ['90-61=29'] Exploring Operation: 66-22=44, Resulting Numbers: [29, 44] Generated Node #3: [29, 44] from Operation: 66-22=44 Current State: 15:[29, 44], Operations: ['90-61=29', '66-22=44'] Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[61, 90, 22, 66], Operations: [] Exploring Operation: 66-61=5, Resulting Numbers: [90, 22, 5] Generated Node #0,0: 15:[90, 22, 5] Operation: 66-61=5 Exploring Operation: 90-66=24, Resulting Numbers: [61, 22, 24] Generated Node #0,1: 15:[61, 22, 24] Operation: 90-66=24 Exploring Operation: 90-61=29, Resulting Numbers: [22, 66, 29] Generated Node #0,2: 15:[22, 66, 29] Operation: 90-61=29 Exploring Operation: 66/22=3, Resulting Numbers: [61, 90, 3] Generated Node #0,3: 15:[61, 90, 3] Operation: 66/22=3 Moving to Node #0,1 Current State: 15:[61, 22, 24], Operations: ['90-66=24'] Exploring Operation: 61-24=37, Resulting Numbers: [22, 37] Generated Node #0,1,0: 15:[22, 37] Operation: 61-24=37 Exploring Operation: 61+22=83, Resulting Numbers: [24, 83] Generated Node #0,1,1: 15:[24, 83] Operation: 61+22=83 Exploring Operation: 61-22=39, Resulting Numbers: [24, 39] Generated Node #0,1,2: 15:[24, 39] Operation: 61-22=39 Exploring Operation: 24-22=2, Resulting Numbers: [61, 2] Generated Node #0,1,3: 15:[61, 2] Operation: 24-22=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 15:[22, 37], Operations: ['90-66=24', '61-24=37'] Exploring Operation: 22*37=814, Resulting Numbers: [814] 814,15 unequal: No Solution Exploring Operation: 22+37=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[61, 90, 22, 66], Operations: [] Exploring Operation: 90-66=24, Resulting Numbers: [61, 22, 24] Generated Node #0,1: 15:[61, 22, 24] Operation: 90-66=24 Moving to Node #0,1 Current State: 15:[61, 22, 24], Operations: ['90-66=24'] Exploring Operation: 61-24=37, Resulting Numbers: [22, 37] Generated Node #0,1,0: 15:[22, 37] Operation: 61-24=37 Moving to Node #0,1,0 Current State: 15:[22, 37], Operations: ['90-66=24', '61-24=37'] Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 9, 13, 5, 64 ]
73
[ "13-9=4", "5+64=69", "4+69=73" ]
Current State: 73:[9, 13, 5, 64], Operations: [] Exploring Operation: 13-9=4, Resulting Numbers: [5, 64, 4] Generated Node #2: [5, 64, 4] from Operation: 13-9=4 Current State: 73:[5, 64, 4], Operations: ['13-9=4'] Exploring Operation: 5+64=69, Resulting Numbers: [4, 69] Generated Node #3: [4, 69] from Operation: 5+64=69 Current State: 73:[4, 69], Operations: ['13-9=4', '5+64=69'] Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[9, 13, 5, 64], Operations: [] Exploring Operation: 13*5=65, Resulting Numbers: [9, 64, 65] Generated Node #0,0: 73:[9, 64, 65] Operation: 13*5=65 Exploring Operation: 9*5=45, Resulting Numbers: [13, 64, 45] Generated Node #0,1: 73:[13, 64, 45] Operation: 9*5=45 Moving to Node #0,0 Current State: 73:[9, 64, 65], Operations: ['13*5=65'] Exploring Operation: 9+65=74, Resulting Numbers: [64, 74] Generated Node #0,0,0: 73:[64, 74] Operation: 9+65=74 Exploring Operation: 9+64=73, Resulting Numbers: [65, 73] Generated Node #0,0,1: 73:[65, 73] Operation: 9+64=73 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[65, 73], Operations: ['13*5=65', '9+64=73'] Exploring Operation: 65+73=138, Resulting Numbers: [138] 138,73 unequal: No Solution Exploring Operation: 73-65=8, Resulting Numbers: [8] 8,73 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 #0,0,0 Current State: 73:[64, 74], Operations: ['13*5=65', '9+65=74'] Exploring Operation: 74-64=10, Resulting Numbers: [10] 10,73 unequal: No Solution Exploring Operation: 64+74=138, Resulting Numbers: [138] 138,73 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: 73:[13, 64, 45], Operations: ['9*5=45'] Exploring Operation: 13+64=77, Resulting Numbers: [45, 77] Generated Node #0,1,0: 73:[45, 77] Operation: 13+64=77 Exploring Operation: 13+45=58, Resulting Numbers: [64, 58] Generated Node #0,1,1: 73:[64, 58] Operation: 13+45=58 Moving to Node #0,1,1 Current State: 73:[64, 58], Operations: ['9*5=45', '13+45=58'] Exploring Operation: 64+58=122, Resulting Numbers: [122] 122,73 unequal: No Solution Exploring Operation: 64-58=6, Resulting Numbers: [6] 6,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[45, 77], Operations: ['9*5=45', '13+64=77'] Exploring Operation: 77-45=32, Resulting Numbers: [32] 32,73 unequal: No Solution Exploring Operation: 45+77=122, Resulting Numbers: [122] 122,73 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 4, 28, 21, 53 ]
15
[ "28-21=7", "53+7=60", "60/4=15" ]
Current State: 15:[4, 28, 21, 53], Operations: [] Exploring Operation: 28-21=7, Resulting Numbers: [4, 53, 7] Generated Node #2: [4, 53, 7] from Operation: 28-21=7 Current State: 15:[4, 53, 7], Operations: ['28-21=7'] Exploring Operation: 53+7=60, Resulting Numbers: [4, 60] Generated Node #3: [4, 60] from Operation: 53+7=60 Current State: 15:[4, 60], Operations: ['28-21=7', '53+7=60'] Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[4, 28, 21, 53], Operations: [] Exploring Operation: 28-21=7, Resulting Numbers: [4, 53, 7] Generated Node #0,0: 15:[4, 53, 7] Operation: 28-21=7 Exploring Operation: 53-21=32, Resulting Numbers: [4, 28, 32] Generated Node #0,1: 15:[4, 28, 32] Operation: 53-21=32 Exploring Operation: 53-28=25, Resulting Numbers: [4, 21, 25] Generated Node #0,2: 15:[4, 21, 25] Operation: 53-28=25 Exploring Operation: 28/4=7, Resulting Numbers: [21, 53, 7] Generated Node #0,3: 15:[21, 53, 7] Operation: 28/4=7 Exploring Operation: 28-4=24, Resulting Numbers: [21, 53, 24] Generated Node #0,4: 15:[21, 53, 24] Operation: 28-4=24 Moving to Node #0,2 Current State: 15:[4, 21, 25], Operations: ['53-28=25'] Exploring Operation: 25-21=4, Resulting Numbers: [4, 4] Generated Node #0,2,0: 15:[4, 4] Operation: 25-21=4 Exploring Operation: 21-4=17, Resulting Numbers: [25, 17] Generated Node #0,2,1: 15:[25, 17] Operation: 21-4=17 Exploring Operation: 4+25=29, Resulting Numbers: [21, 29] Generated Node #0,2,2: 15:[21, 29] Operation: 4+25=29 Exploring Operation: 25-4=21, Resulting Numbers: [21, 21] Generated Node #0,2,3: 15:[21, 21] Operation: 25-4=21 Exploring Operation: 4+21=25, Resulting Numbers: [25, 25] Generated Node #0,2,4: 15:[25, 25] Operation: 4+21=25 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 15:[4, 4], Operations: ['53-28=25', '25-21=4'] Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,15 unequal: No Solution Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,15 unequal: No Solution No 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: 15:[25, 17], Operations: ['53-28=25', '21-4=17'] Exploring Operation: 25*17=425, Resulting Numbers: [425] 425,15 unequal: No Solution Exploring Operation: 25+17=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,15 unequal: No Solution No 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: 15:[21, 21], Operations: ['53-28=25', '25-4=21'] Exploring Operation: 21+21=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 21/21=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 21*21=441, Resulting Numbers: [441] 441,15 unequal: No Solution Exploring Operation: 21-21=0, Resulting Numbers: [0] 0,15 unequal: No Solution No 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: 15:[21, 29], Operations: ['53-28=25', '4+25=29'] Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 21*29=609, Resulting Numbers: [609] 609,15 unequal: No Solution Exploring Operation: 21+29=50, Resulting Numbers: [50] 50,15 unequal: No Solution No 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: 15:[25, 25], Operations: ['53-28=25', '4+21=25'] Exploring Operation: 25*25=625, Resulting Numbers: [625] 625,15 unequal: No Solution Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 25/25=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 25-25=0, Resulting Numbers: [0] 0,15 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: 15:[4, 28, 32], Operations: ['53-21=32'] Exploring Operation: 28-4=24, Resulting Numbers: [32, 24] Generated Node #0,1,0: 15:[32, 24] Operation: 28-4=24 Exploring Operation: 28/4=7, Resulting Numbers: [32, 7] Generated Node #0,1,1: 15:[32, 7] Operation: 28/4=7 Exploring Operation: 32-28=4, Resulting Numbers: [4, 4] Generated Node #0,1,2: 15:[4, 4] Operation: 32-28=4 Exploring Operation: 32/4=8, Resulting Numbers: [28, 8] Generated Node #0,1,3: 15:[28, 8] Operation: 32/4=8 Exploring Operation: 32-4=28, Resulting Numbers: [28, 28] Generated Node #0,1,4: 15:[28, 28] Operation: 32-4=28 Moving to Node #0,0 Current State: 15:[4, 53, 7], Operations: ['28-21=7'] Exploring Operation: 4+7=11, Resulting Numbers: [53, 11] Generated Node #0,0,0: 15:[53, 11] Operation: 4+7=11 Exploring Operation: 4+53=57, Resulting Numbers: [7, 57] Generated Node #0,0,1: 15:[7, 57] Operation: 4+53=57 Exploring Operation: 7-4=3, Resulting Numbers: [53, 3] Generated Node #0,0,2: 15:[53, 3] Operation: 7-4=3 Exploring Operation: 53-7=46, Resulting Numbers: [4, 46] Generated Node #0,0,3: 15:[4, 46] Operation: 53-7=46 Exploring Operation: 53-4=49, Resulting Numbers: [7, 49] Generated Node #0,0,4: 15:[7, 49] Operation: 53-4=49 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 15:[4, 46], Operations: ['28-21=7', '53-7=46'] Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,15 unequal: No Solution Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,15 unequal: No Solution No 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: 15:[7, 49], Operations: ['28-21=7', '53-4=49'] Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 7*49=343, Resulting Numbers: [343] 343,15 unequal: No Solution Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,15 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,15 unequal: No Solution No 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: 15:[53, 3], Operations: ['28-21=7', '7-4=3'] Exploring Operation: 53*3=159, Resulting Numbers: [159] 159,15 unequal: No Solution Exploring Operation: 53+3=56, Resulting Numbers: [56] 56,15 unequal: No Solution Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,15 unequal: No Solution No 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: 15:[53, 11], Operations: ['28-21=7', '4+7=11'] Exploring Operation: 53*11=583, Resulting Numbers: [583] 583,15 unequal: No Solution Exploring Operation: 53+11=64, Resulting Numbers: [64] 64,15 unequal: No Solution Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,15 unequal: No Solution No 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: 15:[7, 57], Operations: ['28-21=7', '4+53=57'] Exploring Operation: 7+57=64, Resulting Numbers: [64] 64,15 unequal: No Solution Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 7*57=399, Resulting Numbers: [399] 399,15 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: 15:[21, 53, 7], Operations: ['28/4=7'] Exploring Operation: 53-21=32, Resulting Numbers: [7, 32] Generated Node #0,3,0: 15:[7, 32] Operation: 53-21=32 Exploring Operation: 53-7=46, Resulting Numbers: [21, 46] Generated Node #0,3,1: 15:[21, 46] Operation: 53-7=46 Exploring Operation: 21+7=28, Resulting Numbers: [53, 28] Generated Node #0,3,2: 15:[53, 28] Operation: 21+7=28 Exploring Operation: 21/7=3, Resulting Numbers: [53, 3] Generated Node #0,3,3: 15:[53, 3] Operation: 21/7=3 Exploring Operation: 21-7=14, Resulting Numbers: [53, 14] Generated Node #0,3,4: 15:[53, 14] Operation: 21-7=14 Moving to Node #0,4 Current State: 15:[21, 53, 24], Operations: ['28-4=24'] Exploring Operation: 21+53=74, Resulting Numbers: [24, 74] Generated Node #0,4,0: 15:[24, 74] Operation: 21+53=74 Exploring Operation: 21+24=45, Resulting Numbers: [53, 45] Generated Node #0,4,1: 15:[53, 45] Operation: 21+24=45 Exploring Operation: 53-21=32, Resulting Numbers: [24, 32] Generated Node #0,4,2: 15:[24, 32] Operation: 53-21=32 Exploring Operation: 24-21=3, Resulting Numbers: [53, 3] Generated Node #0,4,3: 15:[53, 3] Operation: 24-21=3 Exploring Operation: 53-24=29, Resulting Numbers: [21, 29] Generated Node #0,4,4: 15:[21, 29] Operation: 53-24=29 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 15:[21, 29], Operations: ['28-4=24', '53-24=29'] Exploring Operation: 21+29=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 21*29=609, Resulting Numbers: [609] 609,15 unequal: No Solution Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,15 unequal: No Solution No 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: 15:[24, 32], Operations: ['28-4=24', '53-21=32'] Exploring Operation: 24*32=768, Resulting Numbers: [768] 768,15 unequal: No Solution Exploring Operation: 24+32=56, Resulting Numbers: [56] 56,15 unequal: No Solution Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,15 unequal: No Solution No 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: 15:[53, 3], Operations: ['28-4=24', '24-21=3'] Exploring Operation: 53+3=56, Resulting Numbers: [56] 56,15 unequal: No Solution Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 53*3=159, Resulting Numbers: [159] 159,15 unequal: No Solution No 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: 15:[24, 74], Operations: ['28-4=24', '21+53=74'] Exploring Operation: 24*74=1776, Resulting Numbers: [1776] 1776,15 unequal: No Solution Exploring Operation: 24+74=98, Resulting Numbers: [98] 98,15 unequal: No Solution Exploring Operation: 74-24=50, Resulting Numbers: [50] 50,15 unequal: No Solution No 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: 15:[53, 45], Operations: ['28-4=24', '21+24=45'] Exploring Operation: 53-45=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 53*45=2385, Resulting Numbers: [2385] 2385,15 unequal: No Solution Exploring Operation: 53+45=98, Resulting Numbers: [98] 98,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 15:[4, 4], Operations: ['53-21=32', '32-28=4'] Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,15 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[28, 8], Operations: ['53-21=32', '32/4=8'] Exploring Operation: 28*8=224, Resulting Numbers: [224] 224,15 unequal: No Solution Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,15 unequal: No Solution Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[32, 7], Operations: ['53-21=32', '28/4=7'] Exploring Operation: 32*7=224, Resulting Numbers: [224] 224,15 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,15 unequal: No Solution Exploring Operation: 32+7=39, Resulting Numbers: [39] 39,15 unequal: No Solution Moving to Node #0,3,0 Current State: 15:[7, 32], Operations: ['28/4=7', '53-21=32'] Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,15 unequal: No Solution Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,15 unequal: No Solution Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,15 unequal: No Solution Moving to Node #0,1,4 Current State: 15:[28, 28], Operations: ['53-21=32', '32-4=28'] Exploring Operation: 28+28=56, Resulting Numbers: [56] 56,15 unequal: No Solution Exploring Operation: 28*28=784, Resulting Numbers: [784] 784,15 unequal: No Solution Exploring Operation: 28/28=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 28-28=0, Resulting Numbers: [0] 0,15 unequal: No Solution Moving to Node #0,1,0 Current State: 15:[32, 24], Operations: ['53-21=32', '28-4=24'] Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 32*24=768, Resulting Numbers: [768] 768,15 unequal: No Solution Exploring Operation: 32+24=56, Resulting Numbers: [56] 56,15 unequal: No Solution Moving to Node #0,3,1 Current State: 15:[21, 46], Operations: ['28/4=7', '53-7=46'] Exploring Operation: 21+46=67, Resulting Numbers: [67] 67,15 unequal: No Solution Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,15 unequal: No Solution Exploring Operation: 21*46=966, Resulting Numbers: [966] 966,15 unequal: No Solution Moving to Node #0,3,3 Current State: 15:[53, 3], Operations: ['28/4=7', '21/7=3'] Exploring Operation: 53*3=159, Resulting Numbers: [159] 159,15 unequal: No Solution Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 53+3=56, Resulting Numbers: [56] 56,15 unequal: No Solution Moving to Node #0,3,4 Current State: 15:[53, 14], Operations: ['28/4=7', '21-7=14'] Exploring Operation: 53+14=67, Resulting Numbers: [67] 67,15 unequal: No Solution Exploring Operation: 53*14=742, Resulting Numbers: [742] 742,15 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,15 unequal: No Solution Moving to Node #0,3,2 Current State: 15:[53, 28], Operations: ['28/4=7', '21+7=28'] Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,15 unequal: No Solution Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,15 unequal: No Solution Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,15 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 41, 53, 89, 67 ]
98
[ "41*89=3649", "53*67=3551", "3649-3551=98" ]
Current State: 98:[41, 53, 89, 67], Operations: [] Exploring Operation: 41*89=3649, Resulting Numbers: [53, 67, 3649] Generated Node #2: [53, 67, 3649] from Operation: 41*89=3649 Current State: 98:[53, 67, 3649], Operations: ['41*89=3649'] Exploring Operation: 53*67=3551, Resulting Numbers: [3649, 3551] Generated Node #3: [3649, 3551] from Operation: 53*67=3551 Current State: 98:[3649, 3551], Operations: ['41*89=3649', '53*67=3551'] Exploring Operation: 3649-3551=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[41, 53, 89, 67], Operations: [] Exploring Operation: 89-67=22, Resulting Numbers: [41, 53, 22] Generated Node #0,0: 98:[41, 53, 22] Operation: 89-67=22 Exploring Operation: 89-41=48, Resulting Numbers: [53, 67, 48] Generated Node #0,1: 98:[53, 67, 48] Operation: 89-41=48 Exploring Operation: 41+67=108, Resulting Numbers: [53, 89, 108] Generated Node #0,2: 98:[53, 89, 108] Operation: 41+67=108 Exploring Operation: 67-53=14, Resulting Numbers: [41, 89, 14] Generated Node #0,3: 98:[41, 89, 14] Operation: 67-53=14 Exploring Operation: 67-41=26, Resulting Numbers: [53, 89, 26] Generated Node #0,4: 98:[53, 89, 26] Operation: 67-41=26 Start Sub Search at level 1: Moving to Node #0,3 Current State: 98:[41, 89, 14], Operations: ['67-53=14'] Exploring Operation: 89-14=75, Resulting Numbers: [41, 75] Generated Node #0,3,0: 98:[41, 75] Operation: 89-14=75 Exploring Operation: 89-41=48, Resulting Numbers: [14, 48] Generated Node #0,3,1: 98:[14, 48] Operation: 89-41=48 Exploring Operation: 41+14=55, Resulting Numbers: [89, 55] Generated Node #0,3,2: 98:[89, 55] Operation: 41+14=55 Exploring Operation: 41-14=27, Resulting Numbers: [89, 27] Generated Node #0,3,3: 98:[89, 27] Operation: 41-14=27 Exploring Operation: 89+14=103, Resulting Numbers: [41, 103] Generated Node #0,3,4: 98:[41, 103] Operation: 89+14=103 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 98:[14, 48], Operations: ['67-53=14', '89-41=48'] Exploring Operation: 14*48=672, Resulting Numbers: [672] 672,98 unequal: No Solution Exploring Operation: 14+48=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,98 unequal: No Solution No 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: 98:[41, 103], Operations: ['67-53=14', '89+14=103'] Exploring Operation: 41*103=4223, Resulting Numbers: [4223] 4223,98 unequal: No Solution Exploring Operation: 103-41=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 41+103=144, Resulting Numbers: [144] 144,98 unequal: No Solution No 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: 98:[89, 55], Operations: ['67-53=14', '41+14=55'] Exploring Operation: 89+55=144, Resulting Numbers: [144] 144,98 unequal: No Solution Exploring Operation: 89*55=4895, Resulting Numbers: [4895] 4895,98 unequal: No Solution Exploring Operation: 89-55=34, Resulting Numbers: [34] 34,98 unequal: No Solution No 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: 98:[89, 27], Operations: ['67-53=14', '41-14=27'] Exploring Operation: 89+27=116, Resulting Numbers: [116] 116,98 unequal: No Solution Exploring Operation: 89-27=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 89*27=2403, Resulting Numbers: [2403] 2403,98 unequal: No Solution No 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: 98:[41, 75], Operations: ['67-53=14', '89-14=75'] Exploring Operation: 41+75=116, Resulting Numbers: [116] 116,98 unequal: No Solution Exploring Operation: 41*75=3075, Resulting Numbers: [3075] 3075,98 unequal: No Solution Exploring Operation: 75-41=34, Resulting Numbers: [34] 34,98 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: 98:[41, 53, 22], Operations: ['89-67=22'] Exploring Operation: 53-41=12, Resulting Numbers: [22, 12] Generated Node #0,0,0: 98:[22, 12] Operation: 53-41=12 Exploring Operation: 53-22=31, Resulting Numbers: [41, 31] Generated Node #0,0,1: 98:[41, 31] Operation: 53-22=31 Exploring Operation: 41-22=19, Resulting Numbers: [53, 19] Generated Node #0,0,2: 98:[53, 19] Operation: 41-22=19 Exploring Operation: 41+22=63, Resulting Numbers: [53, 63] Generated Node #0,0,3: 98:[53, 63] Operation: 41+22=63 Exploring Operation: 41+53=94, Resulting Numbers: [22, 94] Generated Node #0,0,4: 98:[22, 94] Operation: 41+53=94 Moving to Node #0,0,2 Current State: 98:[53, 19], Operations: ['89-67=22', '41-22=19'] Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,98 unequal: No Solution Exploring Operation: 53*19=1007, Resulting Numbers: [1007] 1007,98 unequal: No Solution Exploring Operation: 53+19=72, Resulting Numbers: [72] 72,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[22, 12], Operations: ['89-67=22', '53-41=12'] Exploring Operation: 22*12=264, Resulting Numbers: [264] 264,98 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,98 unequal: No Solution Exploring Operation: 22+12=34, Resulting Numbers: [34] 34,98 unequal: No Solution Moving to Node #0,0,4 Current State: 98:[22, 94], Operations: ['89-67=22', '41+53=94'] Exploring Operation: 22+94=116, Resulting Numbers: [116] 116,98 unequal: No Solution Exploring Operation: 94-22=72, Resulting Numbers: [72] 72,98 unequal: No Solution Exploring Operation: 22*94=2068, Resulting Numbers: [2068] 2068,98 unequal: No Solution Moving to Node #0,0,3 Current State: 98:[53, 63], Operations: ['89-67=22', '41+22=63'] Exploring Operation: 53+63=116, Resulting Numbers: [116] 116,98 unequal: No Solution Exploring Operation: 63-53=10, Resulting Numbers: [10] 10,98 unequal: No Solution Exploring Operation: 53*63=3339, Resulting Numbers: [3339] 3339,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[41, 31], Operations: ['89-67=22', '53-22=31'] Exploring Operation: 41-31=10, Resulting Numbers: [10] 10,98 unequal: No Solution Exploring Operation: 41+31=72, Resulting Numbers: [72] 72,98 unequal: No Solution Exploring Operation: 41*31=1271, Resulting Numbers: [1271] 1271,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[53, 67, 48], Operations: ['89-41=48'] Exploring Operation: 67-48=19, Resulting Numbers: [53, 19] Generated Node #0,1,0: 98:[53, 19] Operation: 67-48=19 Exploring Operation: 67+48=115, Resulting Numbers: [53, 115] Generated Node #0,1,1: 98:[53, 115] Operation: 67+48=115 Exploring Operation: 53-48=5, Resulting Numbers: [67, 5] Generated Node #0,1,2: 98:[67, 5] Operation: 53-48=5 Exploring Operation: 53+48=101, Resulting Numbers: [67, 101] Generated Node #0,1,3: 98:[67, 101] Operation: 53+48=101 Exploring Operation: 67-53=14, Resulting Numbers: [48, 14] Generated Node #0,1,4: 98:[48, 14] Operation: 67-53=14 Moving to Node #0,1,4 Current State: 98:[48, 14], Operations: ['89-41=48', '67-53=14'] Exploring Operation: 48+14=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 48*14=672, Resulting Numbers: [672] 672,98 unequal: No Solution Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[53, 19], Operations: ['89-41=48', '67-48=19'] Exploring Operation: 53+19=72, Resulting Numbers: [72] 72,98 unequal: No Solution Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,98 unequal: No Solution Exploring Operation: 53*19=1007, Resulting Numbers: [1007] 1007,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[67, 5], Operations: ['89-41=48', '53-48=5'] Exploring Operation: 67*5=335, Resulting Numbers: [335] 335,98 unequal: No Solution Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 67+5=72, Resulting Numbers: [72] 72,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[53, 115], Operations: ['89-41=48', '67+48=115'] Exploring Operation: 53+115=168, Resulting Numbers: [168] 168,98 unequal: No Solution Exploring Operation: 115-53=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 53*115=6095, Resulting Numbers: [6095] 6095,98 unequal: No Solution Moving to Node #0,1,3 Current State: 98:[67, 101], Operations: ['89-41=48', '53+48=101'] Exploring Operation: 67*101=6767, Resulting Numbers: [6767] 6767,98 unequal: No Solution Exploring Operation: 67+101=168, Resulting Numbers: [168] 168,98 unequal: No Solution Exploring Operation: 101-67=34, Resulting Numbers: [34] 34,98 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 Current State: 98:[53, 89, 108], Operations: ['41+67=108'] Exploring Operation: 89-53=36, Resulting Numbers: [108, 36] Generated Node #0,2,0: 98:[108, 36] Operation: 89-53=36 Exploring Operation: 53+108=161, Resulting Numbers: [89, 161] Generated Node #0,2,1: 98:[89, 161] Operation: 53+108=161 Exploring Operation: 53+89=142, Resulting Numbers: [108, 142] Generated Node #0,2,2: 98:[108, 142] Operation: 53+89=142 Exploring Operation: 108-53=55, Resulting Numbers: [89, 55] Generated Node #0,2,3: 98:[89, 55] Operation: 108-53=55 Exploring Operation: 108-89=19, Resulting Numbers: [53, 19] Generated Node #0,2,4: 98:[53, 19] Operation: 108-89=19 Moving to Node #0,2,4 Current State: 98:[53, 19], Operations: ['41+67=108', '108-89=19'] Exploring Operation: 53*19=1007, Resulting Numbers: [1007] 1007,98 unequal: No Solution Exploring Operation: 53+19=72, Resulting Numbers: [72] 72,98 unequal: No Solution Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,98 unequal: No Solution Moving to Node #0,2,3 Current State: 98:[89, 55], Operations: ['41+67=108', '108-53=55'] Exploring Operation: 89*55=4895, Resulting Numbers: [4895] 4895,98 unequal: No Solution Exploring Operation: 89+55=144, Resulting Numbers: [144] 144,98 unequal: No Solution Exploring Operation: 89-55=34, Resulting Numbers: [34] 34,98 unequal: No Solution Moving to Node #0,2,0 Current State: 98:[108, 36], Operations: ['41+67=108', '89-53=36'] Exploring Operation: 108-36=72, Resulting Numbers: [72] 72,98 unequal: No Solution Exploring Operation: 108/36=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 108*36=3888, Resulting Numbers: [3888] 3888,98 unequal: No Solution Exploring Operation: 108+36=144, Resulting Numbers: [144] 144,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[108, 142], Operations: ['41+67=108', '53+89=142'] Exploring Operation: 142-108=34, Resulting Numbers: [34] 34,98 unequal: No Solution Exploring Operation: 108*142=15336, Resulting Numbers: [15336] 15336,98 unequal: No Solution Exploring Operation: 108+142=250, Resulting Numbers: [250] 250,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[89, 161], Operations: ['41+67=108', '53+108=161'] Exploring Operation: 161-89=72, Resulting Numbers: [72] 72,98 unequal: No Solution Exploring Operation: 89+161=250, Resulting Numbers: [250] 250,98 unequal: No Solution Exploring Operation: 89*161=14329, Resulting Numbers: [14329] 14329,98 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 Current State: 98:[53, 89, 26], Operations: ['67-41=26'] Exploring Operation: 89-53=36, Resulting Numbers: [26, 36] Generated Node #0,4,0: 98:[26, 36] Operation: 89-53=36 Exploring Operation: 53-26=27, Resulting Numbers: [89, 27] Generated Node #0,4,1: 98:[89, 27] Operation: 53-26=27 Exploring Operation: 89-26=63, Resulting Numbers: [53, 63] Generated Node #0,4,2: 98:[53, 63] Operation: 89-26=63 Exploring Operation: 53+26=79, Resulting Numbers: [89, 79] Generated Node #0,4,3: 98:[89, 79] Operation: 53+26=79 Exploring Operation: 89+26=115, Resulting Numbers: [53, 115] Generated Node #0,4,4: 98:[53, 115] Operation: 89+26=115 Moving to Node #0,4,2 Current State: 98:[53, 63], Operations: ['67-41=26', '89-26=63'] Exploring Operation: 53+63=116, Resulting Numbers: [116] 116,98 unequal: No Solution Exploring Operation: 63-53=10, Resulting Numbers: [10] 10,98 unequal: No Solution Exploring Operation: 53*63=3339, Resulting Numbers: [3339] 3339,98 unequal: No Solution Moving to Node #0,4,4 Current State: 98:[53, 115], Operations: ['67-41=26', '89+26=115'] Exploring Operation: 53*115=6095, Resulting Numbers: [6095] 6095,98 unequal: No Solution Exploring Operation: 115-53=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 53+115=168, Resulting Numbers: [168] 168,98 unequal: No Solution Moving to Node #0,4,1 Current State: 98:[89, 27], Operations: ['67-41=26', '53-26=27'] Exploring Operation: 89-27=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 89+27=116, Resulting Numbers: [116] 116,98 unequal: No Solution Exploring Operation: 89*27=2403, Resulting Numbers: [2403] 2403,98 unequal: No Solution Moving to Node #0,4,0 Current State: 98:[26, 36], Operations: ['67-41=26', '89-53=36'] Exploring Operation: 26+36=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 26*36=936, Resulting Numbers: [936] 936,98 unequal: No Solution Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,98 unequal: No Solution Moving to Node #0,4,3 Current State: 98:[89, 79], Operations: ['67-41=26', '53+26=79'] Exploring Operation: 89+79=168, Resulting Numbers: [168] 168,98 unequal: No Solution Exploring Operation: 89-79=10, Resulting Numbers: [10] 10,98 unequal: No Solution Exploring Operation: 89*79=7031, Resulting Numbers: [7031] 7031,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 10, 90, 28, 88 ]
66
[ "90-88=2", "28*2=56", "10+56=66" ]
Current State: 66:[10, 90, 28, 88], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [10, 28, 2] Generated Node #2: [10, 28, 2] from Operation: 90-88=2 Current State: 66:[10, 28, 2], Operations: ['90-88=2'] Exploring Operation: 28*2=56, Resulting Numbers: [10, 56] Generated Node #3: [10, 56] from Operation: 28*2=56 Current State: 66:[10, 56], Operations: ['90-88=2', '28*2=56'] Exploring Operation: 10+56=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[10, 90, 28, 88], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [10, 28, 2] Generated Node #0,0: 66:[10, 28, 2] Operation: 90-88=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[10, 28, 2], Operations: ['90-88=2'] Exploring Operation: 28-10=18, Resulting Numbers: [2, 18] Generated Node #0,0,0: 66:[2, 18] Operation: 28-10=18 Moving to Node #0,0,0 Current State: 66:[2, 18], Operations: ['90-88=2', '28-10=18'] Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,66 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
[ 6, 44, 70, 14 ]
18
[ "44-6=38", "70-14=56", "56-38=18" ]
Current State: 18:[6, 44, 70, 14], Operations: [] Exploring Operation: 44-6=38, Resulting Numbers: [70, 14, 38] Generated Node #2: [70, 14, 38] from Operation: 44-6=38 Current State: 18:[70, 14, 38], Operations: ['44-6=38'] Exploring Operation: 70-14=56, Resulting Numbers: [38, 56] Generated Node #3: [38, 56] from Operation: 70-14=56 Current State: 18:[38, 56], Operations: ['44-6=38', '70-14=56'] Exploring Operation: 56-38=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[6, 44, 70, 14], Operations: [] Exploring Operation: 44-14=30, Resulting Numbers: [6, 70, 30] Generated Node #0,0: 18:[6, 70, 30] Operation: 44-14=30 Exploring Operation: 70-44=26, Resulting Numbers: [6, 14, 26] Generated Node #0,1: 18:[6, 14, 26] Operation: 70-44=26 Exploring Operation: 70/14=5, Resulting Numbers: [6, 44, 5] Generated Node #0,2: 18:[6, 44, 5] Operation: 70/14=5 Exploring Operation: 70-14=56, Resulting Numbers: [6, 44, 56] Generated Node #0,3: 18:[6, 44, 56] Operation: 70-14=56 Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[6, 14, 26], Operations: ['70-44=26'] Exploring Operation: 26-6=20, Resulting Numbers: [14, 20] Generated Node #0,1,0: 18:[14, 20] Operation: 26-6=20 Exploring Operation: 26-14=12, Resulting Numbers: [6, 12] Generated Node #0,1,1: 18:[6, 12] Operation: 26-14=12 Exploring Operation: 14-6=8, Resulting Numbers: [26, 8] Generated Node #0,1,2: 18:[26, 8] Operation: 14-6=8 Exploring Operation: 6+14=20, Resulting Numbers: [26, 20] Generated Node #0,1,3: 18:[26, 20] Operation: 6+14=20 Moving to Node #0,1,1 Current State: 18:[6, 12], Operations: ['70-44=26', '26-14=12'] Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[6, 44, 70, 14], Operations: [] Exploring Operation: 70-44=26, Resulting Numbers: [6, 14, 26] Generated Node #0,1: 18:[6, 14, 26] Operation: 70-44=26 Moving to Node #0,1 Current State: 18:[6, 14, 26], Operations: ['70-44=26'] Exploring Operation: 26-14=12, Resulting Numbers: [6, 12] Generated Node #0,1,1: 18:[6, 12] Operation: 26-14=12 Moving to Node #0,1,1 Current State: 18:[6, 12], Operations: ['70-44=26', '26-14=12'] Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 16, 38, 2, 11 ]
92
[ "16+11=27", "2*27=54", "38+54=92" ]
Current State: 92:[16, 38, 2, 11], Operations: [] Exploring Operation: 16+11=27, Resulting Numbers: [38, 2, 27] Generated Node #2: [38, 2, 27] from Operation: 16+11=27 Current State: 92:[38, 2, 27], Operations: ['16+11=27'] Exploring Operation: 2*27=54, Resulting Numbers: [38, 54] Generated Node #3: [38, 54] from Operation: 2*27=54 Current State: 92:[38, 54], Operations: ['16+11=27', '2*27=54'] Exploring Operation: 38+54=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[16, 38, 2, 11], Operations: [] Exploring Operation: 38+11=49, Resulting Numbers: [16, 2, 49] Generated Node #0,0: 92:[16, 2, 49] Operation: 38+11=49 Exploring Operation: 38-16=22, Resulting Numbers: [2, 11, 22] Generated Node #0,1: 92:[2, 11, 22] Operation: 38-16=22 Exploring Operation: 16-11=5, Resulting Numbers: [38, 2, 5] Generated Node #0,2: 92:[38, 2, 5] Operation: 16-11=5 Moving to Node #0,1 Current State: 92:[2, 11, 22], Operations: ['38-16=22'] Exploring Operation: 2*11=22, Resulting Numbers: [22, 22] Generated Node #0,1,0: 92:[22, 22] Operation: 2*11=22 Exploring Operation: 22/11=2, Resulting Numbers: [2, 2] Generated Node #0,1,1: 92:[2, 2] Operation: 22/11=2 Exploring Operation: 11-2=9, Resulting Numbers: [22, 9] Generated Node #0,1,2: 92:[22, 9] Operation: 11-2=9 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[2, 2], Operations: ['38-16=22', '22/11=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[22, 22], Operations: ['38-16=22', '2*11=22'] Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,92 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 92:[22, 9], Operations: ['38-16=22', '11-2=9'] Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,92 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,92 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,92 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: 92:[38, 2, 5], Operations: ['16-11=5'] Exploring Operation: 38+5=43, Resulting Numbers: [2, 43] Generated Node #0,2,0: 92:[2, 43] Operation: 38+5=43 Exploring Operation: 38/2=19, Resulting Numbers: [5, 19] Generated Node #0,2,1: 92:[5, 19] Operation: 38/2=19 Exploring Operation: 38+2=40, Resulting Numbers: [5, 40] Generated Node #0,2,2: 92:[5, 40] Operation: 38+2=40 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 92:[2, 43], Operations: ['16-11=5', '38+5=43'] Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,92 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,92 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 92:[5, 19], Operations: ['16-11=5', '38/2=19'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,92 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 92:[5, 40], Operations: ['16-11=5', '38+2=40'] Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,92 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,92 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 92:[16, 2, 49], Operations: ['38+11=49'] Exploring Operation: 49-2=47, Resulting Numbers: [16, 47] Generated Node #0,0,0: 92:[16, 47] Operation: 49-2=47 Exploring Operation: 16/2=8, Resulting Numbers: [49, 8] Generated Node #0,0,1: 92:[49, 8] Operation: 16/2=8 Exploring Operation: 16+2=18, Resulting Numbers: [49, 18] Generated Node #0,0,2: 92:[49, 18] Operation: 16+2=18 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[49, 8], Operations: ['38+11=49', '16/2=8'] Exploring Operation: 49*8=392, Resulting Numbers: [392] 392,92 unequal: No Solution Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,92 unequal: No Solution Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[16, 47], Operations: ['38+11=49', '49-2=47'] Exploring Operation: 16*47=752, Resulting Numbers: [752] 752,92 unequal: No Solution Exploring Operation: 16+47=63, Resulting Numbers: [63] 63,92 unequal: No Solution Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 92:[49, 18], Operations: ['38+11=49', '16+2=18'] Exploring Operation: 49+18=67, Resulting Numbers: [67] 67,92 unequal: No Solution Exploring Operation: 49*18=882, Resulting Numbers: [882] 882,92 unequal: No Solution Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,92 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
[ 46, 81, 34, 33 ]
35
[ "81-46=35", "34-33=1", "35*1=35" ]
Current State: 35:[46, 81, 34, 33], Operations: [] Exploring Operation: 81-46=35, Resulting Numbers: [34, 33, 35] Generated Node #2: [34, 33, 35] from Operation: 81-46=35 Current State: 35:[34, 33, 35], Operations: ['81-46=35'] Exploring Operation: 34-33=1, Resulting Numbers: [35, 1] Generated Node #3: [35, 1] from Operation: 34-33=1 Current State: 35:[35, 1], Operations: ['81-46=35', '34-33=1'] Exploring Operation: 35*1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[46, 81, 34, 33], Operations: [] Exploring Operation: 81-46=35, Resulting Numbers: [34, 33, 35] Generated Node #0,0: 35:[34, 33, 35] Operation: 81-46=35 Exploring Operation: 81-34=47, Resulting Numbers: [46, 33, 47] Generated Node #0,1: 35:[46, 33, 47] Operation: 81-34=47 Moving to Node #0,0 Current State: 35:[34, 33, 35], Operations: ['81-46=35'] Exploring Operation: 34-33=1, Resulting Numbers: [35, 1] Generated Node #0,0,0: 35:[35, 1] Operation: 34-33=1 Exploring Operation: 35-33=2, Resulting Numbers: [34, 2] Generated Node #0,0,1: 35:[34, 2] Operation: 35-33=2 Moving to Node #0,1 Current State: 35:[46, 33, 47], Operations: ['81-34=47'] Exploring Operation: 46-33=13, Resulting Numbers: [47, 13] Generated Node #0,1,0: 35:[47, 13] Operation: 46-33=13 Exploring Operation: 47-46=1, Resulting Numbers: [33, 1] Generated Node #0,1,1: 35:[33, 1] Operation: 47-46=1 Moving to Node #0,0,0 Current State: 35:[35, 1], Operations: ['81-46=35', '34-33=1'] Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[46, 81, 34, 33], Operations: [] Exploring Operation: 81-46=35, Resulting Numbers: [34, 33, 35] Generated Node #0,0: 35:[34, 33, 35] Operation: 81-46=35 Moving to Node #0,0 Current State: 35:[34, 33, 35], Operations: ['81-46=35'] Exploring Operation: 34-33=1, Resulting Numbers: [35, 1] Generated Node #0,0,0: 35:[35, 1] Operation: 34-33=1 Moving to Node #0,0,0 Current State: 35:[35, 1], Operations: ['81-46=35', '34-33=1'] Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 63, 47, 25, 23 ]
55
[ "63+47=110", "25-23=2", "110/2=55" ]
Current State: 55:[63, 47, 25, 23], Operations: [] Exploring Operation: 63+47=110, Resulting Numbers: [25, 23, 110] Generated Node #2: [25, 23, 110] from Operation: 63+47=110 Current State: 55:[25, 23, 110], Operations: ['63+47=110'] Exploring Operation: 25-23=2, Resulting Numbers: [110, 2] Generated Node #3: [110, 2] from Operation: 25-23=2 Current State: 55:[110, 2], Operations: ['63+47=110', '25-23=2'] Exploring Operation: 110/2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[63, 47, 25, 23], Operations: [] Exploring Operation: 25-23=2, Resulting Numbers: [63, 47, 2] Generated Node #0,0: 55:[63, 47, 2] Operation: 25-23=2 Exploring Operation: 25+23=48, Resulting Numbers: [63, 47, 48] Generated Node #0,1: 55:[63, 47, 48] Operation: 25+23=48 Exploring Operation: 47-25=22, Resulting Numbers: [63, 23, 22] Generated Node #0,2: 55:[63, 23, 22] Operation: 47-25=22 Exploring Operation: 63-47=16, Resulting Numbers: [25, 23, 16] Generated Node #0,3: 55:[25, 23, 16] Operation: 63-47=16 Exploring Operation: 47-23=24, Resulting Numbers: [63, 25, 24] Generated Node #0,4: 55:[63, 25, 24] Operation: 47-23=24 Moving to Node #0,0 Current State: 55:[63, 47, 2], Operations: ['25-23=2'] Exploring Operation: 47-2=45, Resulting Numbers: [63, 45] Generated Node #0,0,0: 55:[63, 45] Operation: 47-2=45 Exploring Operation: 63-47=16, Resulting Numbers: [2, 16] Generated Node #0,0,1: 55:[2, 16] Operation: 63-47=16 Exploring Operation: 47+2=49, Resulting Numbers: [63, 49] Generated Node #0,0,2: 55:[63, 49] Operation: 47+2=49 Exploring Operation: 63-2=61, Resulting Numbers: [47, 61] Generated Node #0,0,3: 55:[47, 61] Operation: 63-2=61 Exploring Operation: 63+2=65, Resulting Numbers: [47, 65] Generated Node #0,0,4: 55:[47, 65] Operation: 63+2=65 Moving to Node #0,1 Current State: 55:[63, 47, 48], Operations: ['25+23=48'] Exploring Operation: 48-47=1, Resulting Numbers: [63, 1] Generated Node #0,1,0: 55:[63, 1] Operation: 48-47=1 Exploring Operation: 63+47=110, Resulting Numbers: [48, 110] Generated Node #0,1,1: 55:[48, 110] Operation: 63+47=110 Exploring Operation: 63-48=15, Resulting Numbers: [47, 15] Generated Node #0,1,2: 55:[47, 15] Operation: 63-48=15 Exploring Operation: 47+48=95, Resulting Numbers: [63, 95] Generated Node #0,1,3: 55:[63, 95] Operation: 47+48=95 Exploring Operation: 63-47=16, Resulting Numbers: [48, 16] Generated Node #0,1,4: 55:[48, 16] Operation: 63-47=16 Moving to Node #0,2 Current State: 55:[63, 23, 22], Operations: ['47-25=22'] Exploring Operation: 63-22=41, Resulting Numbers: [23, 41] Generated Node #0,2,0: 55:[23, 41] Operation: 63-22=41 Exploring Operation: 23+22=45, Resulting Numbers: [63, 45] Generated Node #0,2,1: 55:[63, 45] Operation: 23+22=45 Exploring Operation: 23-22=1, Resulting Numbers: [63, 1] Generated Node #0,2,2: 55:[63, 1] Operation: 23-22=1 Exploring Operation: 63+23=86, Resulting Numbers: [22, 86] Generated Node #0,2,3: 55:[22, 86] Operation: 63+23=86 Exploring Operation: 63-23=40, Resulting Numbers: [22, 40] Generated Node #0,2,4: 55:[22, 40] Operation: 63-23=40 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 55:[63, 1], Operations: ['47-25=22', '23-22=1'] Exploring Operation: 63+1=64, Resulting Numbers: [64] 64,55 unequal: No Solution Exploring Operation: 63*1=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 55:[63, 45], Operations: ['47-25=22', '23+22=45'] Exploring Operation: 63-45=18, Resulting Numbers: [18] 18,55 unequal: No Solution Exploring Operation: 63*45=2835, Resulting Numbers: [2835] 2835,55 unequal: No Solution Exploring Operation: 63+45=108, Resulting Numbers: [108] 108,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 55:[23, 41], Operations: ['47-25=22', '63-22=41'] Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,55 unequal: No Solution Exploring Operation: 23*41=943, Resulting Numbers: [943] 943,55 unequal: No Solution Exploring Operation: 23+41=64, Resulting Numbers: [64] 64,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 55:[22, 40], Operations: ['47-25=22', '63-23=40'] Exploring Operation: 22+40=62, Resulting Numbers: [62] 62,55 unequal: No Solution Exploring Operation: 22*40=880, Resulting Numbers: [880] 880,55 unequal: No Solution Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 55:[22, 86], Operations: ['47-25=22', '63+23=86'] Exploring Operation: 22+86=108, Resulting Numbers: [108] 108,55 unequal: No Solution Exploring Operation: 86-22=64, Resulting Numbers: [64] 64,55 unequal: No Solution Exploring Operation: 22*86=1892, Resulting Numbers: [1892] 1892,55 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: 55:[25, 23, 16], Operations: ['63-47=16'] Exploring Operation: 23-16=7, Resulting Numbers: [25, 7] Generated Node #0,3,0: 55:[25, 7] Operation: 23-16=7 Exploring Operation: 25+23=48, Resulting Numbers: [16, 48] Generated Node #0,3,1: 55:[16, 48] Operation: 25+23=48 Exploring Operation: 25+16=41, Resulting Numbers: [23, 41] Generated Node #0,3,2: 55:[23, 41] Operation: 25+16=41 Exploring Operation: 25-16=9, Resulting Numbers: [23, 9] Generated Node #0,3,3: 55:[23, 9] Operation: 25-16=9 Exploring Operation: 25-23=2, Resulting Numbers: [16, 2] Generated Node #0,3,4: 55:[16, 2] Operation: 25-23=2 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 55:[16, 2], Operations: ['63-47=16', '25-23=2'] Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,55 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 55:[16, 48], Operations: ['63-47=16', '25+23=48'] Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 48/16=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 16*48=768, Resulting Numbers: [768] 768,55 unequal: No Solution Exploring Operation: 16+48=64, Resulting Numbers: [64] 64,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 55:[23, 9], Operations: ['63-47=16', '25-16=9'] Exploring Operation: 23*9=207, Resulting Numbers: [207] 207,55 unequal: No Solution Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 23+9=32, Resulting Numbers: [32] 32,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 55:[25, 7], Operations: ['63-47=16', '23-16=7'] Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,55 unequal: No Solution Exploring Operation: 25*7=175, Resulting Numbers: [175] 175,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 55:[23, 41], Operations: ['63-47=16', '25+16=41'] Exploring Operation: 23+41=64, Resulting Numbers: [64] 64,55 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,55 unequal: No Solution Exploring Operation: 23*41=943, Resulting Numbers: [943] 943,55 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: 55:[63, 25, 24], Operations: ['47-23=24'] Exploring Operation: 63+25=88, Resulting Numbers: [24, 88] Generated Node #0,4,0: 55:[24, 88] Operation: 63+25=88 Exploring Operation: 63-25=38, Resulting Numbers: [24, 38] Generated Node #0,4,1: 55:[24, 38] Operation: 63-25=38 Exploring Operation: 25-24=1, Resulting Numbers: [63, 1] Generated Node #0,4,2: 55:[63, 1] Operation: 25-24=1 Exploring Operation: 25+24=49, Resulting Numbers: [63, 49] Generated Node #0,4,3: 55:[63, 49] Operation: 25+24=49 Exploring Operation: 63-24=39, Resulting Numbers: [25, 39] Generated Node #0,4,4: 55:[25, 39] Operation: 63-24=39 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 55:[63, 1], Operations: ['47-23=24', '25-24=1'] Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 63+1=64, Resulting Numbers: [64] 64,55 unequal: No Solution Exploring Operation: 63*1=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 55:[63, 49], Operations: ['47-23=24', '25+24=49'] Exploring Operation: 63*49=3087, Resulting Numbers: [3087] 3087,55 unequal: No Solution Exploring Operation: 63-49=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 63+49=112, Resulting Numbers: [112] 112,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 55:[24, 38], Operations: ['47-23=24', '63-25=38'] Exploring Operation: 24+38=62, Resulting Numbers: [62] 62,55 unequal: No Solution Exploring Operation: 24*38=912, Resulting Numbers: [912] 912,55 unequal: No Solution Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 55:[25, 39], Operations: ['47-23=24', '63-24=39'] Exploring Operation: 25*39=975, Resulting Numbers: [975] 975,55 unequal: No Solution Exploring Operation: 25+39=64, Resulting Numbers: [64] 64,55 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 55:[24, 88], Operations: ['47-23=24', '63+25=88'] Exploring Operation: 88-24=64, Resulting Numbers: [64] 64,55 unequal: No Solution Exploring Operation: 24*88=2112, Resulting Numbers: [2112] 2112,55 unequal: No Solution Exploring Operation: 24+88=112, Resulting Numbers: [112] 112,55 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: 55:[2, 16], Operations: ['25-23=2', '63-47=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,55 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,55 unequal: No Solution Moving to Node #0,1,0 Current State: 55:[63, 1], Operations: ['25+23=48', '48-47=1'] Exploring Operation: 63+1=64, Resulting Numbers: [64] 64,55 unequal: No Solution Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,55 unequal: No Solution Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 63*1=63, Resulting Numbers: [63] 63,55 unequal: No Solution Moving to Node #0,1,2 Current State: 55:[47, 15], Operations: ['25+23=48', '63-48=15'] Exploring Operation: 47-15=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 47*15=705, Resulting Numbers: [705] 705,55 unequal: No Solution Exploring Operation: 47+15=62, Resulting Numbers: [62] 62,55 unequal: No Solution Moving to Node #0,1,4 Current State: 55:[48, 16], Operations: ['25+23=48', '63-47=16'] Exploring Operation: 48*16=768, Resulting Numbers: [768] 768,55 unequal: No Solution Exploring Operation: 48+16=64, Resulting Numbers: [64] 64,55 unequal: No Solution Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 48/16=3, Resulting Numbers: [3] 3,55 unequal: No Solution Moving to Node #0,0,3 Current State: 55:[47, 61], Operations: ['25-23=2', '63-2=61'] Exploring Operation: 47+61=108, Resulting Numbers: [108] 108,55 unequal: No Solution Exploring Operation: 47*61=2867, Resulting Numbers: [2867] 2867,55 unequal: No Solution Exploring Operation: 61-47=14, Resulting Numbers: [14] 14,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[63, 49], Operations: ['25-23=2', '47+2=49'] Exploring Operation: 63-49=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 63+49=112, Resulting Numbers: [112] 112,55 unequal: No Solution Exploring Operation: 63*49=3087, Resulting Numbers: [3087] 3087,55 unequal: No Solution Moving to Node #0,0,4 Current State: 55:[47, 65], Operations: ['25-23=2', '63+2=65'] Exploring Operation: 47+65=112, Resulting Numbers: [112] 112,55 unequal: No Solution Exploring Operation: 47*65=3055, Resulting Numbers: [3055] 3055,55 unequal: No Solution Exploring Operation: 65-47=18, Resulting Numbers: [18] 18,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[63, 45], Operations: ['25-23=2', '47-2=45'] Exploring Operation: 63+45=108, Resulting Numbers: [108] 108,55 unequal: No Solution Exploring Operation: 63*45=2835, Resulting Numbers: [2835] 2835,55 unequal: No Solution Exploring Operation: 63-45=18, Resulting Numbers: [18] 18,55 unequal: No Solution Moving to Node #0,1,3 Current State: 55:[63, 95], Operations: ['25+23=48', '47+48=95'] Exploring Operation: 63*95=5985, Resulting Numbers: [5985] 5985,55 unequal: No Solution Exploring Operation: 95-63=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 63+95=158, Resulting Numbers: [158] 158,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[48, 110], Operations: ['25+23=48', '63+47=110'] Exploring Operation: 48+110=158, Resulting Numbers: [158] 158,55 unequal: No Solution Exploring Operation: 48*110=5280, Resulting Numbers: [5280] 5280,55 unequal: No Solution Exploring Operation: 110-48=62, Resulting Numbers: [62] 62,55 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 78, 41, 13, 47 ]
94
[ "78/13=6", "41+47=88", "6+88=94" ]
Current State: 94:[78, 41, 13, 47], Operations: [] Exploring Operation: 78/13=6, Resulting Numbers: [41, 47, 6] Generated Node #2: [41, 47, 6] from Operation: 78/13=6 Current State: 94:[41, 47, 6], Operations: ['78/13=6'] Exploring Operation: 41+47=88, Resulting Numbers: [6, 88] Generated Node #3: [6, 88] from Operation: 41+47=88 Current State: 94:[6, 88], Operations: ['78/13=6', '41+47=88'] Exploring Operation: 6+88=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[78, 41, 13, 47], Operations: [] Exploring Operation: 78+13=91, Resulting Numbers: [41, 47, 91] Generated Node #0,0: 94:[41, 47, 91] Operation: 78+13=91 Exploring Operation: 78/13=6, Resulting Numbers: [41, 47, 6] Generated Node #0,1: 94:[41, 47, 6] Operation: 78/13=6 Exploring Operation: 78-41=37, Resulting Numbers: [13, 47, 37] Generated Node #0,2: 94:[13, 47, 37] Operation: 78-41=37 Moving to Node #0,0 Current State: 94:[41, 47, 91], Operations: ['78+13=91'] Exploring Operation: 41+47=88, Resulting Numbers: [91, 88] Generated Node #0,0,0: 94:[91, 88] Operation: 41+47=88 Exploring Operation: 47-41=6, Resulting Numbers: [91, 6] Generated Node #0,0,1: 94:[91, 6] Operation: 47-41=6 Exploring Operation: 91-41=50, Resulting Numbers: [47, 50] Generated Node #0,0,2: 94:[47, 50] Operation: 91-41=50 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 94:[47, 50], Operations: ['78+13=91', '91-41=50'] Exploring Operation: 47+50=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 50-47=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 47*50=2350, Resulting Numbers: [2350] 2350,94 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:[91, 6], Operations: ['78+13=91', '47-41=6'] Exploring Operation: 91*6=546, Resulting Numbers: [546] 546,94 unequal: No Solution Exploring Operation: 91+6=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 91-6=85, Resulting Numbers: [85] 85,94 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:[91, 88], Operations: ['78+13=91', '41+47=88'] Exploring Operation: 91+88=179, Resulting Numbers: [179] 179,94 unequal: No Solution Exploring Operation: 91-88=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 91*88=8008, Resulting Numbers: [8008] 8008,94 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:[41, 47, 6], Operations: ['78/13=6'] Exploring Operation: 41+47=88, Resulting Numbers: [6, 88] Generated Node #0,1,0: 94:[6, 88] Operation: 41+47=88 Exploring Operation: 41+6=47, Resulting Numbers: [47, 47] Generated Node #0,1,1: 94:[47, 47] Operation: 41+6=47 Exploring Operation: 47-41=6, Resulting Numbers: [6, 6] Generated Node #0,1,2: 94:[6, 6] Operation: 47-41=6 Moving to Node #0,2 Current State: 94:[13, 47, 37], Operations: ['78-41=37'] Exploring Operation: 13+37=50, Resulting Numbers: [47, 50] Generated Node #0,2,0: 94:[47, 50] Operation: 13+37=50 Exploring Operation: 47-37=10, Resulting Numbers: [13, 10] Generated Node #0,2,1: 94:[13, 10] Operation: 47-37=10 Exploring Operation: 47+37=84, Resulting Numbers: [13, 84] Generated Node #0,2,2: 94:[13, 84] Operation: 47+37=84 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 94:[47, 50], Operations: ['78-41=37', '13+37=50'] Exploring Operation: 47+50=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 47*50=2350, Resulting Numbers: [2350] 2350,94 unequal: No Solution Exploring Operation: 50-47=3, Resulting Numbers: [3] 3,94 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 #0,2,1 Current State: 94:[13, 10], Operations: ['78-41=37', '47-37=10'] Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,94 unequal: No Solution Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,94 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,94 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 #0,2,2 Current State: 94:[13, 84], Operations: ['78-41=37', '47+37=84'] Exploring Operation: 13+84=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,94 unequal: No Solution Exploring Operation: 13*84=1092, Resulting Numbers: [1092] 1092,94 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: 94:[47, 47], Operations: ['78/13=6', '41+6=47'] Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[78, 41, 13, 47], Operations: [] Exploring Operation: 78/13=6, Resulting Numbers: [41, 47, 6] Generated Node #0,1: 94:[41, 47, 6] Operation: 78/13=6 Moving to Node #0,1 Current State: 94:[41, 47, 6], Operations: ['78/13=6'] Exploring Operation: 41+6=47, Resulting Numbers: [47, 47] Generated Node #0,1,1: 94:[47, 47] Operation: 41+6=47 Moving to Node #0,1,1 Current State: 94:[47, 47], Operations: ['78/13=6', '41+6=47'] Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.969618
hs_3
sum_heuristic
[ 7, 46, 71, 69 ]
52
[ "7+71=78", "46*78=3588", "3588/69=52" ]
Current State: 52:[7, 46, 71, 69], Operations: [] Exploring Operation: 7+71=78, Resulting Numbers: [46, 69, 78] Generated Node #2: [46, 69, 78] from Operation: 7+71=78 Current State: 52:[46, 69, 78], Operations: ['7+71=78'] Exploring Operation: 46*78=3588, Resulting Numbers: [69, 3588] Generated Node #3: [69, 3588] from Operation: 46*78=3588 Current State: 52:[69, 3588], Operations: ['7+71=78', '46*78=3588'] Exploring Operation: 3588/69=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[7, 46, 71, 69], Operations: [] Exploring Operation: 71-69=2, Resulting Numbers: [7, 46, 2] Generated Node #0,0: 52:[7, 46, 2] Operation: 71-69=2 Exploring Operation: 71-46=25, Resulting Numbers: [7, 69, 25] Generated Node #0,1: 52:[7, 69, 25] Operation: 71-46=25 Exploring Operation: 69-46=23, Resulting Numbers: [7, 71, 23] Generated Node #0,2: 52:[7, 71, 23] Operation: 69-46=23 Moving to Node #0,0 Current State: 52:[7, 46, 2], Operations: ['71-69=2'] Exploring Operation: 7+46=53, Resulting Numbers: [2, 53] Generated Node #0,0,0: 52:[2, 53] Operation: 7+46=53 Exploring Operation: 7*2=14, Resulting Numbers: [46, 14] Generated Node #0,0,1: 52:[46, 14] Operation: 7*2=14 Exploring Operation: 46/2=23, Resulting Numbers: [7, 23] Generated Node #0,0,2: 52:[7, 23] Operation: 46/2=23 Moving to Node #0,1 Current State: 52:[7, 69, 25], Operations: ['71-46=25'] Exploring Operation: 69-25=44, Resulting Numbers: [7, 44] Generated Node #0,1,0: 52:[7, 44] Operation: 69-25=44 Exploring Operation: 69-7=62, Resulting Numbers: [25, 62] Generated Node #0,1,1: 52:[25, 62] Operation: 69-7=62 Exploring Operation: 25-7=18, Resulting Numbers: [69, 18] Generated Node #0,1,2: 52:[69, 18] Operation: 25-7=18 Moving to Node #0,2 Current State: 52:[7, 71, 23], Operations: ['69-46=23'] Exploring Operation: 71-7=64, Resulting Numbers: [23, 64] Generated Node #0,2,0: 52:[23, 64] Operation: 71-7=64 Exploring Operation: 23-7=16, Resulting Numbers: [71, 16] Generated Node #0,2,1: 52:[71, 16] Operation: 23-7=16 Exploring Operation: 71-23=48, Resulting Numbers: [7, 48] Generated Node #0,2,2: 52:[7, 48] Operation: 71-23=48 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 52:[7, 48], Operations: ['69-46=23', '71-23=48'] Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,52 unequal: No Solution Exploring Operation: 7+48=55, Resulting Numbers: [55] 55,52 unequal: No Solution Exploring Operation: 7*48=336, Resulting Numbers: [336] 336,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 52:[23, 64], Operations: ['69-46=23', '71-7=64'] Exploring Operation: 23+64=87, Resulting Numbers: [87] 87,52 unequal: No Solution Exploring Operation: 64-23=41, Resulting Numbers: [41] 41,52 unequal: No Solution Exploring Operation: 23*64=1472, Resulting Numbers: [1472] 1472,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 52:[71, 16], Operations: ['69-46=23', '23-7=16'] Exploring Operation: 71*16=1136, Resulting Numbers: [1136] 1136,52 unequal: No Solution Exploring Operation: 71+16=87, Resulting Numbers: [87] 87,52 unequal: No Solution Exploring Operation: 71-16=55, Resulting Numbers: [55] 55,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 52:[2, 53], Operations: ['71-69=2', '7+46=53'] Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,52 unequal: No Solution Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,52 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[7, 23], Operations: ['71-69=2', '46/2=23'] Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 7*23=161, Resulting Numbers: [161] 161,52 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[46, 14], Operations: ['71-69=2', '7*2=14'] Exploring Operation: 46*14=644, Resulting Numbers: [644] 644,52 unequal: No Solution Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,52 unequal: No Solution Exploring Operation: 46+14=60, Resulting Numbers: [60] 60,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[25, 62], Operations: ['71-46=25', '69-7=62'] Exploring Operation: 25+62=87, Resulting Numbers: [87] 87,52 unequal: No Solution Exploring Operation: 25*62=1550, Resulting Numbers: [1550] 1550,52 unequal: No Solution Exploring Operation: 62-25=37, Resulting Numbers: [37] 37,52 unequal: No Solution Moving to Node #0,1,0 Current State: 52:[7, 44], Operations: ['71-46=25', '69-25=44'] Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,52 unequal: No Solution Exploring Operation: 7*44=308, Resulting Numbers: [308] 308,52 unequal: No Solution Exploring Operation: 7+44=51, Resulting Numbers: [51] 51,52 unequal: No Solution Moving to Node #0,1,2 Current State: 52:[69, 18], Operations: ['71-46=25', '25-7=18'] Exploring Operation: 69-18=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 69+18=87, Resulting Numbers: [87] 87,52 unequal: No Solution Exploring Operation: 69*18=1242, Resulting Numbers: [1242] 1242,52 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 35, 33, 94, 85 ]
38
[ "35-33=2", "94/2=47", "85-47=38" ]
Current State: 38:[35, 33, 94, 85], Operations: [] Exploring Operation: 35-33=2, Resulting Numbers: [94, 85, 2] Generated Node #2: [94, 85, 2] from Operation: 35-33=2 Current State: 38:[94, 85, 2], Operations: ['35-33=2'] Exploring Operation: 94/2=47, Resulting Numbers: [85, 47] Generated Node #3: [85, 47] from Operation: 94/2=47 Current State: 38:[85, 47], Operations: ['35-33=2', '94/2=47'] Exploring Operation: 85-47=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[35, 33, 94, 85], Operations: [] Exploring Operation: 94-35=59, Resulting Numbers: [33, 85, 59] Generated Node #0,0: 38:[33, 85, 59] Operation: 94-35=59 Exploring Operation: 85-35=50, Resulting Numbers: [33, 94, 50] Generated Node #0,1: 38:[33, 94, 50] Operation: 85-35=50 Exploring Operation: 94-33=61, Resulting Numbers: [35, 85, 61] Generated Node #0,2: 38:[35, 85, 61] Operation: 94-33=61 Exploring Operation: 94-85=9, Resulting Numbers: [35, 33, 9] Generated Node #0,3: 38:[35, 33, 9] Operation: 94-85=9 Exploring Operation: 85-33=52, Resulting Numbers: [35, 94, 52] Generated Node #0,4: 38:[35, 94, 52] Operation: 85-33=52 Start Sub Search at level 1: Moving to Node #0,3 Current State: 38:[35, 33, 9], Operations: ['94-85=9'] Exploring Operation: 33-9=24, Resulting Numbers: [35, 24] Generated Node #0,3,0: 38:[35, 24] Operation: 33-9=24 Exploring Operation: 33+9=42, Resulting Numbers: [35, 42] Generated Node #0,3,1: 38:[35, 42] Operation: 33+9=42 Exploring Operation: 35-9=26, Resulting Numbers: [33, 26] Generated Node #0,3,2: 38:[33, 26] Operation: 35-9=26 Exploring Operation: 35+9=44, Resulting Numbers: [33, 44] Generated Node #0,3,3: 38:[33, 44] Operation: 35+9=44 Exploring Operation: 35-33=2, Resulting Numbers: [9, 2] Generated Node #0,3,4: 38:[9, 2] Operation: 35-33=2 Moving to Node #0,3,1 Current State: 38:[35, 42], Operations: ['94-85=9', '33+9=42'] Exploring Operation: 42-35=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 35*42=1470, Resulting Numbers: [1470] 1470,38 unequal: No Solution Exploring Operation: 35+42=77, Resulting Numbers: [77] 77,38 unequal: No Solution Moving to Node #0,3,4 Current State: 38:[9, 2], Operations: ['94-85=9', '35-33=2'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,38 unequal: No Solution Moving to Node #0,3,0 Current State: 38:[35, 24], Operations: ['94-85=9', '33-9=24'] Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 35*24=840, Resulting Numbers: [840] 840,38 unequal: No Solution Moving to Node #0,3,3 Current State: 38:[33, 44], Operations: ['94-85=9', '35+9=44'] Exploring Operation: 33+44=77, Resulting Numbers: [77] 77,38 unequal: No Solution Exploring Operation: 33*44=1452, Resulting Numbers: [1452] 1452,38 unequal: No Solution Exploring Operation: 44-33=11, Resulting Numbers: [11] 11,38 unequal: No Solution Moving to Node #0,3,2 Current State: 38:[33, 26], Operations: ['94-85=9', '35-9=26'] Exploring Operation: 33+26=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 33-26=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 33*26=858, Resulting Numbers: [858] 858,38 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:[33, 85, 59], Operations: ['94-35=59'] Exploring Operation: 33+59=92, Resulting Numbers: [85, 92] Generated Node #0,0,0: 38:[85, 92] Operation: 33+59=92 Exploring Operation: 33+85=118, Resulting Numbers: [59, 118] Generated Node #0,0,1: 38:[59, 118] Operation: 33+85=118 Exploring Operation: 85-33=52, Resulting Numbers: [59, 52] Generated Node #0,0,2: 38:[59, 52] Operation: 85-33=52 Exploring Operation: 59-33=26, Resulting Numbers: [85, 26] Generated Node #0,0,3: 38:[85, 26] Operation: 59-33=26 Exploring Operation: 85-59=26, Resulting Numbers: [33, 26] Generated Node #0,0,4: 38:[33, 26] Operation: 85-59=26 Moving to Node #0,0,4 Current State: 38:[33, 26], Operations: ['94-35=59', '85-59=26'] Exploring Operation: 33-26=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 33*26=858, Resulting Numbers: [858] 858,38 unequal: No Solution Exploring Operation: 33+26=59, Resulting Numbers: [59] 59,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[59, 52], Operations: ['94-35=59', '85-33=52'] Exploring Operation: 59+52=111, Resulting Numbers: [111] 111,38 unequal: No Solution Exploring Operation: 59*52=3068, Resulting Numbers: [3068] 3068,38 unequal: No Solution Exploring Operation: 59-52=7, Resulting Numbers: [7] 7,38 unequal: No Solution Moving to Node #0,0,3 Current State: 38:[85, 26], Operations: ['94-35=59', '59-33=26'] Exploring Operation: 85*26=2210, Resulting Numbers: [2210] 2210,38 unequal: No Solution Exploring Operation: 85-26=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 85+26=111, Resulting Numbers: [111] 111,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[85, 92], Operations: ['94-35=59', '33+59=92'] Exploring Operation: 85+92=177, Resulting Numbers: [177] 177,38 unequal: No Solution Exploring Operation: 85*92=7820, Resulting Numbers: [7820] 7820,38 unequal: No Solution Exploring Operation: 92-85=7, Resulting Numbers: [7] 7,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[59, 118], Operations: ['94-35=59', '33+85=118'] Exploring Operation: 118-59=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 59+118=177, Resulting Numbers: [177] 177,38 unequal: No Solution Exploring Operation: 59*118=6962, Resulting Numbers: [6962] 6962,38 unequal: No Solution Exploring Operation: 118/59=2, Resulting Numbers: [2] 2,38 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 #0,1 Current State: 38:[33, 94, 50], Operations: ['85-35=50'] Exploring Operation: 94-50=44, Resulting Numbers: [33, 44] Generated Node #0,1,0: 38:[33, 44] Operation: 94-50=44 Exploring Operation: 33+50=83, Resulting Numbers: [94, 83] Generated Node #0,1,1: 38:[94, 83] Operation: 33+50=83 Exploring Operation: 33+94=127, Resulting Numbers: [50, 127] Generated Node #0,1,2: 38:[50, 127] Operation: 33+94=127 Exploring Operation: 50-33=17, Resulting Numbers: [94, 17] Generated Node #0,1,3: 38:[94, 17] Operation: 50-33=17 Exploring Operation: 94-33=61, Resulting Numbers: [50, 61] Generated Node #0,1,4: 38:[50, 61] Operation: 94-33=61 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 38:[33, 44], Operations: ['85-35=50', '94-50=44'] Exploring Operation: 44-33=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 33*44=1452, Resulting Numbers: [1452] 1452,38 unequal: No Solution Exploring Operation: 33+44=77, Resulting Numbers: [77] 77,38 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 #0,1,4 Current State: 38:[50, 61], Operations: ['85-35=50', '94-33=61'] Exploring Operation: 50+61=111, Resulting Numbers: [111] 111,38 unequal: No Solution Exploring Operation: 50*61=3050, Resulting Numbers: [3050] 3050,38 unequal: No Solution Exploring Operation: 61-50=11, Resulting Numbers: [11] 11,38 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:[94, 17], Operations: ['85-35=50', '50-33=17'] Exploring Operation: 94*17=1598, Resulting Numbers: [1598] 1598,38 unequal: No Solution Exploring Operation: 94-17=77, Resulting Numbers: [77] 77,38 unequal: No Solution Exploring Operation: 94+17=111, Resulting Numbers: [111] 111,38 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:[94, 83], Operations: ['85-35=50', '33+50=83'] Exploring Operation: 94+83=177, Resulting Numbers: [177] 177,38 unequal: No Solution Exploring Operation: 94-83=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 94*83=7802, Resulting Numbers: [7802] 7802,38 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:[50, 127], Operations: ['85-35=50', '33+94=127'] Exploring Operation: 127-50=77, Resulting Numbers: [77] 77,38 unequal: No Solution Exploring Operation: 50*127=6350, Resulting Numbers: [6350] 6350,38 unequal: No Solution Exploring Operation: 50+127=177, Resulting Numbers: [177] 177,38 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 #0,2 Current State: 38:[35, 85, 61], Operations: ['94-33=61'] Exploring Operation: 85-61=24, Resulting Numbers: [35, 24] Generated Node #0,2,0: 38:[35, 24] Operation: 85-61=24 Exploring Operation: 61-35=26, Resulting Numbers: [85, 26] Generated Node #0,2,1: 38:[85, 26] Operation: 61-35=26 Exploring Operation: 85-35=50, Resulting Numbers: [61, 50] Generated Node #0,2,2: 38:[61, 50] Operation: 85-35=50 Exploring Operation: 35+61=96, Resulting Numbers: [85, 96] Generated Node #0,2,3: 38:[85, 96] Operation: 35+61=96 Exploring Operation: 35+85=120, Resulting Numbers: [61, 120] Generated Node #0,2,4: 38:[61, 120] Operation: 35+85=120 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 38:[35, 24], Operations: ['94-33=61', '85-61=24'] Exploring Operation: 35*24=840, Resulting Numbers: [840] 840,38 unequal: No Solution Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 35+24=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 #0,2,2 Current State: 38:[61, 50], Operations: ['94-33=61', '85-35=50'] Exploring Operation: 61*50=3050, Resulting Numbers: [3050] 3050,38 unequal: No Solution Exploring Operation: 61-50=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 61+50=111, Resulting Numbers: [111] 111,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 38:[85, 26], Operations: ['94-33=61', '61-35=26'] Exploring Operation: 85+26=111, Resulting Numbers: [111] 111,38 unequal: No Solution Exploring Operation: 85-26=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 85*26=2210, Resulting Numbers: [2210] 2210,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 38:[85, 96], Operations: ['94-33=61', '35+61=96'] Exploring Operation: 96-85=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 85+96=181, Resulting Numbers: [181] 181,38 unequal: No Solution Exploring Operation: 85*96=8160, Resulting Numbers: [8160] 8160,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 38:[61, 120], Operations: ['94-33=61', '35+85=120'] Exploring Operation: 61+120=181, Resulting Numbers: [181] 181,38 unequal: No Solution Exploring Operation: 61*120=7320, Resulting Numbers: [7320] 7320,38 unequal: No Solution Exploring Operation: 120-61=59, Resulting Numbers: [59] 59,38 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 #0,4 Current State: 38:[35, 94, 52], Operations: ['85-33=52'] Exploring Operation: 35+52=87, Resulting Numbers: [94, 87] Generated Node #0,4,0: 38:[94, 87] Operation: 35+52=87 Exploring Operation: 94-35=59, Resulting Numbers: [52, 59] Generated Node #0,4,1: 38:[52, 59] Operation: 94-35=59 Exploring Operation: 94-52=42, Resulting Numbers: [35, 42] Generated Node #0,4,2: 38:[35, 42] Operation: 94-52=42 Exploring Operation: 35+94=129, Resulting Numbers: [52, 129] Generated Node #0,4,3: 38:[52, 129] Operation: 35+94=129 Exploring Operation: 52-35=17, Resulting Numbers: [94, 17] Generated Node #0,4,4: 38:[94, 17] Operation: 52-35=17 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 38:[35, 42], Operations: ['85-33=52', '94-52=42'] Exploring Operation: 35*42=1470, Resulting Numbers: [1470] 1470,38 unequal: No Solution Exploring Operation: 35+42=77, Resulting Numbers: [77] 77,38 unequal: No Solution Exploring Operation: 42-35=7, Resulting Numbers: [7] 7,38 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 #0,4,1 Current State: 38:[52, 59], Operations: ['85-33=52', '94-35=59'] Exploring Operation: 52+59=111, Resulting Numbers: [111] 111,38 unequal: No Solution Exploring Operation: 52*59=3068, Resulting Numbers: [3068] 3068,38 unequal: No Solution Exploring Operation: 59-52=7, Resulting Numbers: [7] 7,38 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 #0,4,4 Current State: 38:[94, 17], Operations: ['85-33=52', '52-35=17'] Exploring Operation: 94+17=111, Resulting Numbers: [111] 111,38 unequal: No Solution Exploring Operation: 94-17=77, Resulting Numbers: [77] 77,38 unequal: No Solution Exploring Operation: 94*17=1598, Resulting Numbers: [1598] 1598,38 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 #0,4,0 Current State: 38:[94, 87], Operations: ['85-33=52', '35+52=87'] Exploring Operation: 94+87=181, Resulting Numbers: [181] 181,38 unequal: No Solution Exploring Operation: 94-87=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 94*87=8178, Resulting Numbers: [8178] 8178,38 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 #0,4,3 Current State: 38:[52, 129], Operations: ['85-33=52', '35+94=129'] Exploring Operation: 52*129=6708, Resulting Numbers: [6708] 6708,38 unequal: No Solution Exploring Operation: 129-52=77, Resulting Numbers: [77] 77,38 unequal: No Solution Exploring Operation: 52+129=181, Resulting Numbers: [181] 181,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 50, 71, 3, 10 ]
91
[ "50+71=121", "3*10=30", "121-30=91" ]
Current State: 91:[50, 71, 3, 10], Operations: [] Exploring Operation: 50+71=121, Resulting Numbers: [3, 10, 121] Generated Node #2: [3, 10, 121] from Operation: 50+71=121 Current State: 91:[3, 10, 121], Operations: ['50+71=121'] Exploring Operation: 3*10=30, Resulting Numbers: [121, 30] Generated Node #3: [121, 30] from Operation: 3*10=30 Current State: 91:[121, 30], Operations: ['50+71=121', '3*10=30'] Exploring Operation: 121-30=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[50, 71, 3, 10], Operations: [] Exploring Operation: 71-50=21, Resulting Numbers: [3, 10, 21] Generated Node #0,0: 91:[3, 10, 21] Operation: 71-50=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[3, 10, 21], Operations: ['71-50=21'] Exploring Operation: 21/3=7, Resulting Numbers: [10, 7] Generated Node #0,0,0: 91:[10, 7] Operation: 21/3=7 Moving to Node #0,0,0 Current State: 91:[10, 7], Operations: ['71-50=21', '21/3=7'] Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 28, 59, 65, 85 ]
51
[ "59-28=31", "85-65=20", "31+20=51" ]
Current State: 51:[28, 59, 65, 85], Operations: [] Exploring Operation: 59-28=31, Resulting Numbers: [65, 85, 31] Generated Node #2: [65, 85, 31] from Operation: 59-28=31 Current State: 51:[65, 85, 31], Operations: ['59-28=31'] Exploring Operation: 85-65=20, Resulting Numbers: [31, 20] Generated Node #3: [31, 20] from Operation: 85-65=20 Current State: 51:[31, 20], Operations: ['59-28=31', '85-65=20'] Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[28, 59, 65, 85], Operations: [] Exploring Operation: 85-65=20, Resulting Numbers: [28, 59, 20] Generated Node #0,0: 51:[28, 59, 20] Operation: 85-65=20 Exploring Operation: 85-28=57, Resulting Numbers: [59, 65, 57] Generated Node #0,1: 51:[59, 65, 57] Operation: 85-28=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[28, 59, 20], Operations: ['85-65=20'] Exploring Operation: 28+20=48, Resulting Numbers: [59, 48] Generated Node #0,0,0: 51:[59, 48] Operation: 28+20=48 Exploring Operation: 28-20=8, Resulting Numbers: [59, 8] Generated Node #0,0,1: 51:[59, 8] Operation: 28-20=8 Moving to Node #0,0,0 Current State: 51:[59, 48], Operations: ['85-65=20', '28+20=48'] Exploring Operation: 59-48=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 59+48=107, Resulting Numbers: [107] 107,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[59, 8], Operations: ['85-65=20', '28-20=8'] Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[28, 59, 65, 85], Operations: [] Exploring Operation: 85-65=20, Resulting Numbers: [28, 59, 20] Generated Node #0,0: 51:[28, 59, 20] Operation: 85-65=20 Moving to Node #0,0 Current State: 51:[28, 59, 20], Operations: ['85-65=20'] Exploring Operation: 28-20=8, Resulting Numbers: [59, 8] Generated Node #0,0,1: 51:[59, 8] Operation: 28-20=8 Moving to Node #0,0,1 Current State: 51:[59, 8], Operations: ['85-65=20', '28-20=8'] Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 7, 69, 8, 44 ]
25
[ "8-7=1", "69-44=25", "1*25=25" ]
Current State: 25:[7, 69, 8, 44], Operations: [] Exploring Operation: 8-7=1, Resulting Numbers: [69, 44, 1] Generated Node #2: [69, 44, 1] from Operation: 8-7=1 Current State: 25:[69, 44, 1], Operations: ['8-7=1'] Exploring Operation: 69-44=25, Resulting Numbers: [1, 25] Generated Node #3: [1, 25] from Operation: 69-44=25 Current State: 25:[1, 25], Operations: ['8-7=1', '69-44=25'] Exploring Operation: 1*25=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[7, 69, 8, 44], Operations: [] Exploring Operation: 69-44=25, Resulting Numbers: [7, 8, 25] Generated Node #0,0: 25:[7, 8, 25] Operation: 69-44=25 Exploring Operation: 69-7=62, Resulting Numbers: [8, 44, 62] Generated Node #0,1: 25:[8, 44, 62] Operation: 69-7=62 Exploring Operation: 69-8=61, Resulting Numbers: [7, 44, 61] Generated Node #0,2: 25:[7, 44, 61] Operation: 69-8=61 Exploring Operation: 44-8=36, Resulting Numbers: [7, 69, 36] Generated Node #0,3: 25:[7, 69, 36] Operation: 44-8=36 Exploring Operation: 44-7=37, Resulting Numbers: [69, 8, 37] Generated Node #0,4: 25:[69, 8, 37] Operation: 44-7=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[7, 8, 25], Operations: ['69-44=25'] Exploring Operation: 7+25=32, Resulting Numbers: [8, 32] Generated Node #0,0,0: 25:[8, 32] Operation: 7+25=32 Exploring Operation: 25-7=18, Resulting Numbers: [8, 18] Generated Node #0,0,1: 25:[8, 18] Operation: 25-7=18 Exploring Operation: 7+8=15, Resulting Numbers: [25, 15] Generated Node #0,0,2: 25:[25, 15] Operation: 7+8=15 Exploring Operation: 8+25=33, Resulting Numbers: [7, 33] Generated Node #0,0,3: 25:[7, 33] Operation: 8+25=33 Exploring Operation: 8-7=1, Resulting Numbers: [25, 1] Generated Node #0,0,4: 25:[25, 1] Operation: 8-7=1 Moving to Node #0,0,4 Current State: 25:[25, 1], Operations: ['69-44=25', '8-7=1'] Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[7, 69, 8, 44], Operations: [] Exploring Operation: 69-44=25, Resulting Numbers: [7, 8, 25] Generated Node #0,0: 25:[7, 8, 25] Operation: 69-44=25 Moving to Node #0,0 Current State: 25:[7, 8, 25], Operations: ['69-44=25'] Exploring Operation: 8-7=1, Resulting Numbers: [25, 1] Generated Node #0,0,4: 25:[25, 1] Operation: 8-7=1 Moving to Node #0,0,4 Current State: 25:[25, 1], Operations: ['69-44=25', '8-7=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 71, 35, 71, 54 ]
53
[ "71-35=36", "71-54=17", "36+17=53" ]
Current State: 53:[71, 35, 71, 54], Operations: [] Exploring Operation: 71-35=36, Resulting Numbers: [54, 36] Generated Node #2: [54, 36] from Operation: 71-35=36 Current State: 53:[54, 36], Operations: ['71-35=36'] Exploring Operation: 71-54=17, Resulting Numbers: [36, 17] Generated Node #3: [36, 17] from Operation: 71-54=17 Current State: 53:[36, 17], Operations: ['71-35=36', '71-54=17'] Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[71, 35, 71, 54], Operations: [] Exploring Operation: 54-35=19, Resulting Numbers: [71, 71, 19] Generated Node #0,0: 53:[71, 71, 19] Operation: 54-35=19 Exploring Operation: 71-35=36, Resulting Numbers: [71, 54, 36] Generated Node #0,1: 53:[71, 54, 36] Operation: 71-35=36 Exploring Operation: 71-35=36, Resulting Numbers: [71, 54, 36] Generated Node #0,2: 53:[71, 54, 36] Operation: 71-35=36 Exploring Operation: 71/71=1, Resulting Numbers: [35, 54, 1] Generated Node #0,3: 53:[35, 54, 1] Operation: 71/71=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[71, 54, 36], Operations: ['71-35=36'] Exploring Operation: 54-36=18, Resulting Numbers: [71, 18] Generated Node #0,1,0: 53:[71, 18] Operation: 54-36=18 Exploring Operation: 71-36=35, Resulting Numbers: [54, 35] Generated Node #0,1,1: 53:[54, 35] Operation: 71-36=35 Exploring Operation: 71-54=17, Resulting Numbers: [36, 17] Generated Node #0,1,2: 53:[36, 17] Operation: 71-54=17 Exploring Operation: 71+36=107, Resulting Numbers: [54, 107] Generated Node #0,1,3: 53:[54, 107] Operation: 71+36=107 Moving to Node #0,1,1 Current State: 53:[54, 35], Operations: ['71-35=36', '71-36=35'] Exploring Operation: 54*35=1890, Resulting Numbers: [1890] 1890,53 unequal: No Solution Exploring Operation: 54-35=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 54+35=89, Resulting Numbers: [89] 89,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[36, 17], Operations: ['71-35=36', '71-54=17'] Exploring Operation: 36*17=612, Resulting Numbers: [612] 612,53 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[71, 35, 71, 54], Operations: [] Exploring Operation: 71-35=36, Resulting Numbers: [71, 54, 36] Generated Node #0,1: 53:[71, 54, 36] Operation: 71-35=36 Moving to Node #0,1 Current State: 53:[71, 54, 36], Operations: ['71-35=36'] Exploring Operation: 71-54=17, Resulting Numbers: [36, 17] Generated Node #0,1,2: 53:[36, 17] Operation: 71-54=17 Moving to Node #0,1,2 Current State: 53:[36, 17], Operations: ['71-35=36', '71-54=17'] Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 23, 47, 43, 72 ]
53
[ "47-23=24", "72-43=29", "24+29=53" ]
Current State: 53:[23, 47, 43, 72], Operations: [] Exploring Operation: 47-23=24, Resulting Numbers: [43, 72, 24] Generated Node #2: [43, 72, 24] from Operation: 47-23=24 Current State: 53:[43, 72, 24], Operations: ['47-23=24'] Exploring Operation: 72-43=29, Resulting Numbers: [24, 29] Generated Node #3: [24, 29] from Operation: 72-43=29 Current State: 53:[24, 29], Operations: ['47-23=24', '72-43=29'] Exploring Operation: 24+29=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[23, 47, 43, 72], Operations: [] Exploring Operation: 23+47=70, Resulting Numbers: [43, 72, 70] Generated Node #0,0: 53:[43, 72, 70] Operation: 23+47=70 Exploring Operation: 47-23=24, Resulting Numbers: [43, 72, 24] Generated Node #0,1: 53:[43, 72, 24] Operation: 47-23=24 Exploring Operation: 72-23=49, Resulting Numbers: [47, 43, 49] Generated Node #0,2: 53:[47, 43, 49] Operation: 72-23=49 Exploring Operation: 43-23=20, Resulting Numbers: [47, 72, 20] Generated Node #0,3: 53:[47, 72, 20] Operation: 43-23=20 Exploring Operation: 23+43=66, Resulting Numbers: [47, 72, 66] Generated Node #0,4: 53:[47, 72, 66] Operation: 23+43=66 Start Sub Search at level 1: Moving to Node #0,2 Current State: 53:[47, 43, 49], Operations: ['72-23=49'] Exploring Operation: 43+49=92, Resulting Numbers: [47, 92] Generated Node #0,2,0: 53:[47, 92] Operation: 43+49=92 Exploring Operation: 47+49=96, Resulting Numbers: [43, 96] Generated Node #0,2,1: 53:[43, 96] Operation: 47+49=96 Exploring Operation: 47-43=4, Resulting Numbers: [49, 4] Generated Node #0,2,2: 53:[49, 4] Operation: 47-43=4 Exploring Operation: 47+43=90, Resulting Numbers: [49, 90] Generated Node #0,2,3: 53:[49, 90] Operation: 47+43=90 Exploring Operation: 49-43=6, Resulting Numbers: [47, 6] Generated Node #0,2,4: 53:[47, 6] Operation: 49-43=6 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 53:[49, 90], Operations: ['72-23=49', '47+43=90'] Exploring Operation: 49*90=4410, Resulting Numbers: [4410] 4410,53 unequal: No Solution Exploring Operation: 49+90=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 90-49=41, Resulting Numbers: [41] 41,53 unequal: No Solution No 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: 53:[47, 92], Operations: ['72-23=49', '43+49=92'] Exploring Operation: 92-47=45, Resulting Numbers: [45] 45,53 unequal: No Solution Exploring Operation: 47+92=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 47*92=4324, Resulting Numbers: [4324] 4324,53 unequal: No Solution No 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: 53:[43, 96], Operations: ['72-23=49', '47+49=96'] Exploring Operation: 43*96=4128, Resulting Numbers: [4128] 4128,53 unequal: No Solution Exploring Operation: 96-43=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[23, 47, 43, 72], Operations: [] Exploring Operation: 72-23=49, Resulting Numbers: [47, 43, 49] Generated Node #0,2: 53:[47, 43, 49] Operation: 72-23=49 Moving to Node #0,2 Current State: 53:[47, 43, 49], Operations: ['72-23=49'] Exploring Operation: 47+49=96, Resulting Numbers: [43, 96] Generated Node #0,2,1: 53:[43, 96] Operation: 47+49=96 Moving to Node #0,2,1 Current State: 53:[43, 96], Operations: ['72-23=49', '47+49=96'] Exploring Operation: 96-43=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 79, 81, 80, 9 ]
73
[ "81-79=2", "80-9=71", "2+71=73" ]
Current State: 73:[79, 81, 80, 9], Operations: [] Exploring Operation: 81-79=2, Resulting Numbers: [80, 9, 2] Generated Node #2: [80, 9, 2] from Operation: 81-79=2 Current State: 73:[80, 9, 2], Operations: ['81-79=2'] Exploring Operation: 80-9=71, Resulting Numbers: [2, 71] Generated Node #3: [2, 71] from Operation: 80-9=71 Current State: 73:[2, 71], Operations: ['81-79=2', '80-9=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[79, 81, 80, 9], Operations: [] Exploring Operation: 81-9=72, Resulting Numbers: [79, 80, 72] Generated Node #0,0: 73:[79, 80, 72] Operation: 81-9=72 Exploring Operation: 79+9=88, Resulting Numbers: [81, 80, 88] Generated Node #0,1: 73:[81, 80, 88] Operation: 79+9=88 Exploring Operation: 79-9=70, Resulting Numbers: [81, 80, 70] Generated Node #0,2: 73:[81, 80, 70] Operation: 79-9=70 Exploring Operation: 81+9=90, Resulting Numbers: [79, 80, 90] Generated Node #0,3: 73:[79, 80, 90] Operation: 81+9=90 Exploring Operation: 80-9=71, Resulting Numbers: [79, 81, 71] Generated Node #0,4: 73:[79, 81, 71] Operation: 80-9=71 Moving to Node #0,0 Current State: 73:[79, 80, 72], Operations: ['81-9=72'] Exploring Operation: 79+72=151, Resulting Numbers: [80, 151] Generated Node #0,0,0: 73:[80, 151] Operation: 79+72=151 Exploring Operation: 80-79=1, Resulting Numbers: [72, 1] Generated Node #0,0,1: 73:[72, 1] Operation: 80-79=1 Exploring Operation: 79-72=7, Resulting Numbers: [80, 7] Generated Node #0,0,2: 73:[80, 7] Operation: 79-72=7 Exploring Operation: 80+72=152, Resulting Numbers: [79, 152] Generated Node #0,0,3: 73:[79, 152] Operation: 80+72=152 Exploring Operation: 80-72=8, Resulting Numbers: [79, 8] Generated Node #0,0,4: 73:[79, 8] Operation: 80-72=8 Moving to Node #0,4 Current State: 73:[79, 81, 71], Operations: ['80-9=71'] Exploring Operation: 81-79=2, Resulting Numbers: [71, 2] Generated Node #0,4,0: 73:[71, 2] Operation: 81-79=2 Exploring Operation: 81+71=152, Resulting Numbers: [79, 152] Generated Node #0,4,1: 73:[79, 152] Operation: 81+71=152 Exploring Operation: 79+71=150, Resulting Numbers: [81, 150] Generated Node #0,4,2: 73:[81, 150] Operation: 79+71=150 Exploring Operation: 81-71=10, Resulting Numbers: [79, 10] Generated Node #0,4,3: 73:[79, 10] Operation: 81-71=10 Exploring Operation: 79-71=8, Resulting Numbers: [81, 8] Generated Node #0,4,4: 73:[81, 8] Operation: 79-71=8 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 73:[79, 10], Operations: ['80-9=71', '81-71=10'] Exploring Operation: 79+10=89, Resulting Numbers: [89] 89,73 unequal: No Solution Exploring Operation: 79*10=790, Resulting Numbers: [790] 790,73 unequal: No Solution Exploring Operation: 79-10=69, Resulting Numbers: [69] 69,73 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 #0,4,0 Current State: 73:[71, 2], Operations: ['80-9=71', '81-79=2'] Exploring Operation: 71*2=142, Resulting Numbers: [142] 142,73 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[79, 81, 80, 9], Operations: [] Exploring Operation: 80-9=71, Resulting Numbers: [79, 81, 71] Generated Node #0,4: 73:[79, 81, 71] Operation: 80-9=71 Moving to Node #0,4 Current State: 73:[79, 81, 71], Operations: ['80-9=71'] Exploring Operation: 81-79=2, Resulting Numbers: [71, 2] Generated Node #0,4,0: 73:[71, 2] Operation: 81-79=2 Moving to Node #0,4,0 Current State: 73:[71, 2], Operations: ['80-9=71', '81-79=2'] Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_5
sum_heuristic
[ 2, 9, 18, 45 ]
34
[ "9-2=7", "45-18=27", "7+27=34" ]
Current State: 34:[2, 9, 18, 45], Operations: [] Exploring Operation: 9-2=7, Resulting Numbers: [18, 45, 7] Generated Node #2: [18, 45, 7] from Operation: 9-2=7 Current State: 34:[18, 45, 7], Operations: ['9-2=7'] Exploring Operation: 45-18=27, Resulting Numbers: [7, 27] Generated Node #3: [7, 27] from Operation: 45-18=27 Current State: 34:[7, 27], Operations: ['9-2=7', '45-18=27'] Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[2, 9, 18, 45], Operations: [] Exploring Operation: 45-9=36, Resulting Numbers: [2, 18, 36] Generated Node #0,0: 34:[2, 18, 36] Operation: 45-9=36 Exploring Operation: 18/9=2, Resulting Numbers: [2, 45, 2] Generated Node #0,1: 34:[2, 45, 2] Operation: 18/9=2 Exploring Operation: 45/9=5, Resulting Numbers: [2, 18, 5] Generated Node #0,2: 34:[2, 18, 5] Operation: 45/9=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[2, 18, 36], Operations: ['45-9=36'] Exploring Operation: 36-2=34, Resulting Numbers: [18, 34] Generated Node #0,0,0: 34:[18, 34] Operation: 36-2=34 Exploring Operation: 36/18=2, Resulting Numbers: [2, 2] Generated Node #0,0,1: 34:[2, 2] Operation: 36/18=2 Exploring Operation: 36-18=18, Resulting Numbers: [2, 18] Generated Node #0,0,2: 34:[2, 18] Operation: 36-18=18 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 34:[2, 2], Operations: ['45-9=36', '36/18=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,34 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,34 unequal: No Solution No 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: 34:[18, 34], Operations: ['45-9=36', '36-2=34'] Exploring Operation: 18*34=612, Resulting Numbers: [612] 612,34 unequal: No Solution Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 18+34=52, Resulting Numbers: [52] 52,34 unequal: No Solution No 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: 34:[2, 18], Operations: ['45-9=36', '36-18=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,34 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,34 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: 34:[2, 18, 5], Operations: ['45/9=5'] Exploring Operation: 18-5=13, Resulting Numbers: [2, 13] Generated Node #0,2,0: 34:[2, 13] Operation: 18-5=13 Exploring Operation: 18-2=16, Resulting Numbers: [5, 16] Generated Node #0,2,1: 34:[5, 16] Operation: 18-2=16 Exploring Operation: 5-2=3, Resulting Numbers: [18, 3] Generated Node #0,2,2: 34:[18, 3] Operation: 5-2=3 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 34:[18, 3], Operations: ['45/9=5', '5-2=3'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,34 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,34 unequal: No Solution No 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: 34:[2, 13], Operations: ['45/9=5', '18-5=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,34 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,34 unequal: No Solution No 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: 34:[5, 16], Operations: ['45/9=5', '18-2=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,34 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,34 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: 34:[2, 45, 2], Operations: ['18/9=2'] Exploring Operation: 45-2=43, Resulting Numbers: [2, 43] Generated Node #0,1,0: 34:[2, 43] Operation: 45-2=43 Exploring Operation: 2/2=1, Resulting Numbers: [45, 1] Generated Node #0,1,1: 34:[45, 1] Operation: 2/2=1 Exploring Operation: 45-2=43, Resulting Numbers: [2, 43] Generated Node #0,1,2: 34:[2, 43] Operation: 45-2=43 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 34:[2, 43], Operations: ['18/9=2', '45-2=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,34 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,34 unequal: No Solution No 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: 34:[2, 43], Operations: ['18/9=2', '45-2=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,34 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,34 unequal: No Solution No 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: 34:[45, 1], Operations: ['18/9=2', '2/2=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,34 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,34 unequal: No Solution Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,34 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
[ 72, 32, 35, 80 ]
16
[ "72-32=40", "40-35=5", "80/5=16" ]
Current State: 16:[72, 32, 35, 80], Operations: [] Exploring Operation: 72-32=40, Resulting Numbers: [35, 80, 40] Generated Node #2: [35, 80, 40] from Operation: 72-32=40 Current State: 16:[35, 80, 40], Operations: ['72-32=40'] Exploring Operation: 40-35=5, Resulting Numbers: [80, 5] Generated Node #3: [80, 5] from Operation: 40-35=5 Current State: 16:[80, 5], Operations: ['72-32=40', '40-35=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[72, 32, 35, 80], Operations: [] Exploring Operation: 80-72=8, Resulting Numbers: [32, 35, 8] Generated Node #0,0: 16:[32, 35, 8] Operation: 80-72=8 Exploring Operation: 72-32=40, Resulting Numbers: [35, 80, 40] Generated Node #0,1: 16:[35, 80, 40] Operation: 72-32=40 Exploring Operation: 80-32=48, Resulting Numbers: [72, 35, 48] Generated Node #0,2: 16:[72, 35, 48] Operation: 80-32=48 Exploring Operation: 80-35=45, Resulting Numbers: [72, 32, 45] Generated Node #0,3: 16:[72, 32, 45] Operation: 80-35=45 Exploring Operation: 72-35=37, Resulting Numbers: [32, 80, 37] Generated Node #0,4: 16:[32, 80, 37] Operation: 72-35=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[32, 35, 8], Operations: ['80-72=8'] Exploring Operation: 32/8=4, Resulting Numbers: [35, 4] Generated Node #0,0,0: 16:[35, 4] Operation: 32/8=4 Exploring Operation: 32-8=24, Resulting Numbers: [35, 24] Generated Node #0,0,1: 16:[35, 24] Operation: 32-8=24 Exploring Operation: 35-32=3, Resulting Numbers: [8, 3] Generated Node #0,0,2: 16:[8, 3] Operation: 35-32=3 Exploring Operation: 35-8=27, Resulting Numbers: [32, 27] Generated Node #0,0,3: 16:[32, 27] Operation: 35-8=27 Exploring Operation: 32+8=40, Resulting Numbers: [35, 40] Generated Node #0,0,4: 16:[35, 40] Operation: 32+8=40 Moving to Node #0,0,2 Current State: 16:[8, 3], Operations: ['80-72=8', '35-32=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,16 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[35, 4], Operations: ['80-72=8', '32/8=4'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,16 unequal: No Solution Exploring Operation: 35*4=140, Resulting Numbers: [140] 140,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[35, 24], Operations: ['80-72=8', '32-8=24'] Exploring Operation: 35*24=840, Resulting Numbers: [840] 840,16 unequal: No Solution Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,16 unequal: No Solution Moving to Node #0,0,3 Current State: 16:[32, 27], Operations: ['80-72=8', '35-8=27'] Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,16 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,16 unequal: No Solution Moving to Node #0,0,4 Current State: 16:[35, 40], Operations: ['80-72=8', '32+8=40'] Exploring Operation: 35*40=1400, Resulting Numbers: [1400] 1400,16 unequal: No Solution Exploring Operation: 40-35=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 35+40=75, Resulting Numbers: [75] 75,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 16:[72, 32, 45], Operations: ['80-35=45'] Exploring Operation: 72-45=27, Resulting Numbers: [32, 27] Generated Node #0,3,0: 16:[32, 27] Operation: 72-45=27 Exploring Operation: 45-32=13, Resulting Numbers: [72, 13] Generated Node #0,3,1: 16:[72, 13] Operation: 45-32=13 Exploring Operation: 72+45=117, Resulting Numbers: [32, 117] Generated Node #0,3,2: 16:[32, 117] Operation: 72+45=117 Exploring Operation: 72+32=104, Resulting Numbers: [45, 104] Generated Node #0,3,3: 16:[45, 104] Operation: 72+32=104 Exploring Operation: 72-32=40, Resulting Numbers: [45, 40] Generated Node #0,3,4: 16:[45, 40] Operation: 72-32=40 Moving to Node #0,3,0 Current State: 16:[32, 27], Operations: ['80-35=45', '72-45=27'] Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,16 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,16 unequal: No Solution Moving to Node #0,3,4 Current State: 16:[45, 40], Operations: ['80-35=45', '72-32=40'] Exploring Operation: 45*40=1800, Resulting Numbers: [1800] 1800,16 unequal: No Solution Exploring Operation: 45-40=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 45+40=85, Resulting Numbers: [85] 85,16 unequal: No Solution Moving to Node #0,3,1 Current State: 16:[72, 13], Operations: ['80-35=45', '45-32=13'] Exploring Operation: 72+13=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 72*13=936, Resulting Numbers: [936] 936,16 unequal: No Solution Exploring Operation: 72-13=59, Resulting Numbers: [59] 59,16 unequal: No Solution Moving to Node #0,3,2 Current State: 16:[32, 117], Operations: ['80-35=45', '72+45=117'] Exploring Operation: 32+117=149, Resulting Numbers: [149] 149,16 unequal: No Solution Exploring Operation: 32*117=3744, Resulting Numbers: [3744] 3744,16 unequal: No Solution Exploring Operation: 117-32=85, Resulting Numbers: [85] 85,16 unequal: No Solution Moving to Node #0,3,3 Current State: 16:[45, 104], Operations: ['80-35=45', '72+32=104'] Exploring Operation: 45+104=149, Resulting Numbers: [149] 149,16 unequal: No Solution Exploring Operation: 104-45=59, Resulting Numbers: [59] 59,16 unequal: No Solution Exploring Operation: 45*104=4680, Resulting Numbers: [4680] 4680,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 16:[32, 80, 37], Operations: ['72-35=37'] Exploring Operation: 32+37=69, Resulting Numbers: [80, 69] Generated Node #0,4,0: 16:[80, 69] Operation: 32+37=69 Exploring Operation: 37-32=5, Resulting Numbers: [80, 5] Generated Node #0,4,1: 16:[80, 5] Operation: 37-32=5 Exploring Operation: 80-37=43, Resulting Numbers: [32, 43] Generated Node #0,4,2: 16:[32, 43] Operation: 80-37=43 Exploring Operation: 32+80=112, Resulting Numbers: [37, 112] Generated Node #0,4,3: 16:[37, 112] Operation: 32+80=112 Exploring Operation: 80-32=48, Resulting Numbers: [37, 48] Generated Node #0,4,4: 16:[37, 48] Operation: 80-32=48 Moving to Node #0,4,2 Current State: 16:[32, 43], Operations: ['72-35=37', '80-37=43'] Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 32*43=1376, Resulting Numbers: [1376] 1376,16 unequal: No Solution Exploring Operation: 32+43=75, Resulting Numbers: [75] 75,16 unequal: No Solution Moving to Node #0,4,4 Current State: 16:[37, 48], Operations: ['72-35=37', '80-32=48'] Exploring Operation: 48-37=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 37*48=1776, Resulting Numbers: [1776] 1776,16 unequal: No Solution Exploring Operation: 37+48=85, Resulting Numbers: [85] 85,16 unequal: No Solution Moving to Node #0,4,1 Current State: 16:[80, 5], Operations: ['72-35=37', '37-32=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 80*5=400, Resulting Numbers: [400] 400,16 unequal: No Solution Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[72, 32, 35, 80], Operations: [] Exploring Operation: 72-35=37, Resulting Numbers: [32, 80, 37] Generated Node #0,4: 16:[32, 80, 37] Operation: 72-35=37 Moving to Node #0,4 Current State: 16:[32, 80, 37], Operations: ['72-35=37'] Exploring Operation: 37-32=5, Resulting Numbers: [80, 5] Generated Node #0,4,1: 16:[80, 5] Operation: 37-32=5 Moving to Node #0,4,1 Current State: 16:[80, 5], Operations: ['72-35=37', '37-32=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.944444
hs_5
sum_heuristic
[ 16, 70, 13, 1 ]
40
[ "70-16=54", "13+1=14", "54-14=40" ]
Current State: 40:[16, 70, 13, 1], Operations: [] Exploring Operation: 70-16=54, Resulting Numbers: [13, 1, 54] Generated Node #2: [13, 1, 54] from Operation: 70-16=54 Current State: 40:[13, 1, 54], Operations: ['70-16=54'] Exploring Operation: 13+1=14, Resulting Numbers: [54, 14] Generated Node #3: [54, 14] from Operation: 13+1=14 Current State: 40:[54, 14], Operations: ['70-16=54', '13+1=14'] Exploring Operation: 54-14=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[16, 70, 13, 1], Operations: [] Exploring Operation: 70-13=57, Resulting Numbers: [16, 1, 57] Generated Node #0,0: 40:[16, 1, 57] Operation: 70-13=57 Exploring Operation: 16-13=3, Resulting Numbers: [70, 1, 3] Generated Node #0,1: 40:[70, 1, 3] Operation: 16-13=3 Exploring Operation: 16+1=17, Resulting Numbers: [70, 13, 17] Generated Node #0,2: 40:[70, 13, 17] Operation: 16+1=17 Exploring Operation: 70-16=54, Resulting Numbers: [13, 1, 54] Generated Node #0,3: 40:[13, 1, 54] Operation: 70-16=54 Start Sub Search at level 1: Moving to Node #0,3 Current State: 40:[13, 1, 54], Operations: ['70-16=54'] Exploring Operation: 13-1=12, Resulting Numbers: [54, 12] Generated Node #0,3,0: 40:[54, 12] Operation: 13-1=12 Exploring Operation: 54-1=53, Resulting Numbers: [13, 53] Generated Node #0,3,1: 40:[13, 53] Operation: 54-1=53 Exploring Operation: 13*1=13, Resulting Numbers: [54, 13] Generated Node #0,3,2: 40:[54, 13] Operation: 13*1=13 Exploring Operation: 54-13=41, Resulting Numbers: [1, 41] Generated Node #0,3,3: 40:[1, 41] Operation: 54-13=41 Moving to Node #0,3,3 Current State: 40:[1, 41], Operations: ['70-16=54', '54-13=41'] Exploring Operation: 1+41=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,40 unequal: No Solution Exploring Operation: 1*41=41, Resulting Numbers: [41] 41,40 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[16, 70, 13, 1], Operations: [] Exploring Operation: 70-16=54, Resulting Numbers: [13, 1, 54] Generated Node #0,3: 40:[13, 1, 54] Operation: 70-16=54 Moving to Node #0,3 Current State: 40:[13, 1, 54], Operations: ['70-16=54'] Exploring Operation: 54-13=41, Resulting Numbers: [1, 41] Generated Node #0,3,3: 40:[1, 41] Operation: 54-13=41 Moving to Node #0,3,3 Current State: 40:[1, 41], Operations: ['70-16=54', '54-13=41'] Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic