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
[ 17, 49, 3, 89 ]
25
[ "89-17=72", "72/3=24", "49-24=25" ]
Current State: 25:[17, 49, 3, 89], Operations: [] Exploring Operation: 89-17=72, Resulting Numbers: [49, 3, 72] Generated Node #2: [49, 3, 72] from Operation: 89-17=72 Current State: 25:[49, 3, 72], Operations: ['89-17=72'] Exploring Operation: 72/3=24, Resulting Numbers: [49, 24] Generated Node #3: [49, 24] from Operation: 72/3=24 Current State: 25:[49, 24], Operations: ['89-17=72', '72/3=24'] Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[17, 49, 3, 89], Operations: [] Exploring Operation: 49-17=32, Resulting Numbers: [3, 89, 32] Generated Node #0,0: 25:[3, 89, 32] Operation: 49-17=32 Exploring Operation: 89-49=40, Resulting Numbers: [17, 3, 40] Generated Node #0,1: 25:[17, 3, 40] Operation: 89-49=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[17, 3, 40], Operations: ['89-49=40'] Exploring Operation: 40-17=23, Resulting Numbers: [3, 23] Generated Node #0,1,0: 25:[3, 23] Operation: 40-17=23 Exploring Operation: 17+3=20, Resulting Numbers: [40, 20] Generated Node #0,1,1: 25:[40, 20] Operation: 17+3=20 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[3, 23], Operations: ['89-49=40', '40-17=23'] Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 25:[40, 20], Operations: ['89-49=40', '17+3=20'] Exploring Operation: 40/20=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,25 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: 25:[3, 89, 32], Operations: ['49-17=32'] Exploring Operation: 89-32=57, Resulting Numbers: [3, 57] Generated Node #0,0,0: 25:[3, 57] Operation: 89-32=57 Exploring Operation: 89-3=86, Resulting Numbers: [32, 86] Generated Node #0,0,1: 25:[32, 86] Operation: 89-3=86 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[3, 57], Operations: ['49-17=32', '89-32=57'] Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,25 unequal: No Solution Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 25:[32, 86], Operations: ['49-17=32', '89-3=86'] Exploring Operation: 86-32=54, Resulting Numbers: [54] 54,25 unequal: No Solution Exploring Operation: 32+86=118, Resulting Numbers: [118] 118,25 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
[ 89, 51, 46, 1 ]
83
[ "89-51=38", "46-1=45", "38+45=83" ]
Current State: 83:[89, 51, 46, 1], Operations: [] Exploring Operation: 89-51=38, Resulting Numbers: [46, 1, 38] Generated Node #2: [46, 1, 38] from Operation: 89-51=38 Current State: 83:[46, 1, 38], Operations: ['89-51=38'] Exploring Operation: 46-1=45, Resulting Numbers: [38, 45] Generated Node #3: [38, 45] from Operation: 46-1=45 Current State: 83:[38, 45], Operations: ['89-51=38', '46-1=45'] Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[89, 51, 46, 1], Operations: [] Exploring Operation: 46+1=47, Resulting Numbers: [89, 51, 47] Generated Node #0,0: 83:[89, 51, 47] Operation: 46+1=47 Exploring Operation: 51+1=52, Resulting Numbers: [89, 46, 52] Generated Node #0,1: 83:[89, 46, 52] Operation: 51+1=52 Exploring Operation: 89-1=88, Resulting Numbers: [51, 46, 88] Generated Node #0,2: 83:[51, 46, 88] Operation: 89-1=88 Moving to Node #0,0 Current State: 83:[89, 51, 47], Operations: ['46+1=47'] Exploring Operation: 51+47=98, Resulting Numbers: [89, 98] Generated Node #0,0,0: 83:[89, 98] Operation: 51+47=98 Exploring Operation: 89-51=38, Resulting Numbers: [47, 38] Generated Node #0,0,1: 83:[47, 38] Operation: 89-51=38 Exploring Operation: 89-47=42, Resulting Numbers: [51, 42] Generated Node #0,0,2: 83:[51, 42] Operation: 89-47=42 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[89, 98], Operations: ['46+1=47', '51+47=98'] Exploring Operation: 89+98=187, Resulting Numbers: [187] 187,83 unequal: No Solution Exploring Operation: 89*98=8722, Resulting Numbers: [8722] 8722,83 unequal: No Solution Exploring Operation: 98-89=9, Resulting Numbers: [9] 9,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[51, 42], Operations: ['46+1=47', '89-47=42'] Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,83 unequal: No Solution Exploring Operation: 51*42=2142, Resulting Numbers: [2142] 2142,83 unequal: No Solution Exploring Operation: 51+42=93, Resulting Numbers: [93] 93,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[47, 38], Operations: ['46+1=47', '89-51=38'] Exploring Operation: 47+38=85, Resulting Numbers: [85] 85,83 unequal: No Solution Exploring Operation: 47-38=9, Resulting Numbers: [9] 9,83 unequal: No Solution Exploring Operation: 47*38=1786, Resulting Numbers: [1786] 1786,83 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: 83:[89, 46, 52], Operations: ['51+1=52'] Exploring Operation: 89+46=135, Resulting Numbers: [52, 135] Generated Node #0,1,0: 83:[52, 135] Operation: 89+46=135 Exploring Operation: 89-46=43, Resulting Numbers: [52, 43] Generated Node #0,1,1: 83:[52, 43] Operation: 89-46=43 Exploring Operation: 46+52=98, Resulting Numbers: [89, 98] Generated Node #0,1,2: 83:[89, 98] Operation: 46+52=98 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 83:[89, 98], Operations: ['51+1=52', '46+52=98'] Exploring Operation: 89+98=187, Resulting Numbers: [187] 187,83 unequal: No Solution Exploring Operation: 89*98=8722, Resulting Numbers: [8722] 8722,83 unequal: No Solution Exploring Operation: 98-89=9, Resulting Numbers: [9] 9,83 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 #0,1,1 Current State: 83:[52, 43], Operations: ['51+1=52', '89-46=43'] Exploring Operation: 52+43=95, Resulting Numbers: [95] 95,83 unequal: No Solution Exploring Operation: 52*43=2236, Resulting Numbers: [2236] 2236,83 unequal: No Solution Exploring Operation: 52-43=9, Resulting Numbers: [9] 9,83 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 #0,1,0 Current State: 83:[52, 135], Operations: ['51+1=52', '89+46=135'] Exploring Operation: 52+135=187, Resulting Numbers: [187] 187,83 unequal: No Solution Exploring Operation: 135-52=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[89, 51, 46, 1], Operations: [] Exploring Operation: 51+1=52, Resulting Numbers: [89, 46, 52] Generated Node #0,1: 83:[89, 46, 52] Operation: 51+1=52 Moving to Node #0,1 Current State: 83:[89, 46, 52], Operations: ['51+1=52'] Exploring Operation: 89+46=135, Resulting Numbers: [52, 135] Generated Node #0,1,0: 83:[52, 135] Operation: 89+46=135 Moving to Node #0,1,0 Current State: 83:[52, 135], Operations: ['51+1=52', '89+46=135'] Exploring Operation: 135-52=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_3
mult_heuristic
[ 45, 50, 84, 18 ]
64
[ "50*18=900", "900/45=20", "84-20=64" ]
Current State: 64:[45, 50, 84, 18], Operations: [] Exploring Operation: 50*18=900, Resulting Numbers: [45, 84, 900] Generated Node #2: [45, 84, 900] from Operation: 50*18=900 Current State: 64:[45, 84, 900], Operations: ['50*18=900'] Exploring Operation: 900/45=20, Resulting Numbers: [84, 20] Generated Node #3: [84, 20] from Operation: 900/45=20 Current State: 64:[84, 20], Operations: ['50*18=900', '900/45=20'] Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[45, 50, 84, 18], Operations: [] Exploring Operation: 50-18=32, Resulting Numbers: [45, 84, 32] Generated Node #0,0: 64:[45, 84, 32] Operation: 50-18=32 Exploring Operation: 84-50=34, Resulting Numbers: [45, 18, 34] Generated Node #0,1: 64:[45, 18, 34] Operation: 84-50=34 Exploring Operation: 50-45=5, Resulting Numbers: [84, 18, 5] Generated Node #0,2: 64:[84, 18, 5] Operation: 50-45=5 Exploring Operation: 84-18=66, Resulting Numbers: [45, 50, 66] Generated Node #0,3: 64:[45, 50, 66] Operation: 84-18=66 Exploring Operation: 84-45=39, Resulting Numbers: [50, 18, 39] Generated Node #0,4: 64:[50, 18, 39] Operation: 84-45=39 Moving to Node #0,1 Current State: 64:[45, 18, 34], Operations: ['84-50=34'] Exploring Operation: 45-18=27, Resulting Numbers: [34, 27] Generated Node #0,1,0: 64:[34, 27] Operation: 45-18=27 Exploring Operation: 34-18=16, Resulting Numbers: [45, 16] Generated Node #0,1,1: 64:[45, 16] Operation: 34-18=16 Exploring Operation: 45+34=79, Resulting Numbers: [18, 79] Generated Node #0,1,2: 64:[18, 79] Operation: 45+34=79 Exploring Operation: 45-34=11, Resulting Numbers: [18, 11] Generated Node #0,1,3: 64:[18, 11] Operation: 45-34=11 Exploring Operation: 45+18=63, Resulting Numbers: [34, 63] Generated Node #0,1,4: 64:[34, 63] Operation: 45+18=63 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 64:[34, 63], Operations: ['84-50=34', '45+18=63'] Exploring Operation: 34*63=2142, Resulting Numbers: [2142] 2142,64 unequal: No Solution Exploring Operation: 63-34=29, Resulting Numbers: [29] 29,64 unequal: No Solution Exploring Operation: 34+63=97, Resulting Numbers: [97] 97,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 64:[18, 11], Operations: ['84-50=34', '45-34=11'] Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,64 unequal: No Solution Exploring Operation: 18*11=198, Resulting Numbers: [198] 198,64 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 64:[34, 27], Operations: ['84-50=34', '45-18=27'] Exploring Operation: 34+27=61, Resulting Numbers: [61] 61,64 unequal: No Solution Exploring Operation: 34*27=918, Resulting Numbers: [918] 918,64 unequal: No Solution Exploring Operation: 34-27=7, Resulting Numbers: [7] 7,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 64:[45, 16], Operations: ['84-50=34', '34-18=16'] Exploring Operation: 45*16=720, Resulting Numbers: [720] 720,64 unequal: No Solution Exploring Operation: 45+16=61, Resulting Numbers: [61] 61,64 unequal: No Solution Exploring Operation: 45-16=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 #0,1,2 Current State: 64:[18, 79], Operations: ['84-50=34', '45+34=79'] Exploring Operation: 18*79=1422, Resulting Numbers: [1422] 1422,64 unequal: No Solution Exploring Operation: 18+79=97, Resulting Numbers: [97] 97,64 unequal: No Solution Exploring Operation: 79-18=61, Resulting Numbers: [61] 61,64 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: 64:[50, 18, 39], Operations: ['84-45=39'] Exploring Operation: 39-18=21, Resulting Numbers: [50, 21] Generated Node #0,4,0: 64:[50, 21] Operation: 39-18=21 Exploring Operation: 50+18=68, Resulting Numbers: [39, 68] Generated Node #0,4,1: 64:[39, 68] Operation: 50+18=68 Exploring Operation: 50-18=32, Resulting Numbers: [39, 32] Generated Node #0,4,2: 64:[39, 32] Operation: 50-18=32 Exploring Operation: 50-39=11, Resulting Numbers: [18, 11] Generated Node #0,4,3: 64:[18, 11] Operation: 50-39=11 Exploring Operation: 18+39=57, Resulting Numbers: [50, 57] Generated Node #0,4,4: 64:[50, 57] Operation: 18+39=57 Moving to Node #0,2 Current State: 64:[84, 18, 5], Operations: ['50-45=5'] Exploring Operation: 18-5=13, Resulting Numbers: [84, 13] Generated Node #0,2,0: 64:[84, 13] Operation: 18-5=13 Exploring Operation: 84-5=79, Resulting Numbers: [18, 79] Generated Node #0,2,1: 64:[18, 79] Operation: 84-5=79 Exploring Operation: 84-18=66, Resulting Numbers: [5, 66] Generated Node #0,2,2: 64:[5, 66] Operation: 84-18=66 Exploring Operation: 18+5=23, Resulting Numbers: [84, 23] Generated Node #0,2,3: 64:[84, 23] Operation: 18+5=23 Exploring Operation: 84+5=89, Resulting Numbers: [18, 89] Generated Node #0,2,4: 64:[18, 89] Operation: 84+5=89 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 64:[5, 66], Operations: ['50-45=5', '84-18=66'] Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,64 unequal: No Solution Exploring Operation: 5+66=71, Resulting Numbers: [71] 71,64 unequal: No Solution Exploring Operation: 5*66=330, Resulting Numbers: [330] 330,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 64:[18, 79], Operations: ['50-45=5', '84-5=79'] Exploring Operation: 79-18=61, Resulting Numbers: [61] 61,64 unequal: No Solution Exploring Operation: 18+79=97, Resulting Numbers: [97] 97,64 unequal: No Solution Exploring Operation: 18*79=1422, Resulting Numbers: [1422] 1422,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 64:[84, 13], Operations: ['50-45=5', '18-5=13'] Exploring Operation: 84+13=97, Resulting Numbers: [97] 97,64 unequal: No Solution Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,64 unequal: No Solution Exploring Operation: 84*13=1092, Resulting Numbers: [1092] 1092,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 64:[84, 23], Operations: ['50-45=5', '18+5=23'] Exploring Operation: 84+23=107, Resulting Numbers: [107] 107,64 unequal: No Solution Exploring Operation: 84-23=61, Resulting Numbers: [61] 61,64 unequal: No Solution Exploring Operation: 84*23=1932, Resulting Numbers: [1932] 1932,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 64:[18, 89], Operations: ['50-45=5', '84+5=89'] Exploring Operation: 18*89=1602, Resulting Numbers: [1602] 1602,64 unequal: No Solution Exploring Operation: 89-18=71, Resulting Numbers: [71] 71,64 unequal: No Solution Exploring Operation: 18+89=107, Resulting Numbers: [107] 107,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 64:[45, 50, 66], Operations: ['84-18=66'] Exploring Operation: 45+66=111, Resulting Numbers: [50, 111] Generated Node #0,3,0: 64:[50, 111] Operation: 45+66=111 Exploring Operation: 66-50=16, Resulting Numbers: [45, 16] Generated Node #0,3,1: 64:[45, 16] Operation: 66-50=16 Exploring Operation: 50-45=5, Resulting Numbers: [66, 5] Generated Node #0,3,2: 64:[66, 5] Operation: 50-45=5 Exploring Operation: 66-45=21, Resulting Numbers: [50, 21] Generated Node #0,3,3: 64:[50, 21] Operation: 66-45=21 Exploring Operation: 45+50=95, Resulting Numbers: [66, 95] Generated Node #0,3,4: 64:[66, 95] Operation: 45+50=95 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 64:[66, 5], Operations: ['84-18=66', '50-45=5'] Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,64 unequal: No Solution Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,64 unequal: No Solution Exploring Operation: 66*5=330, Resulting Numbers: [330] 330,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 64:[45, 16], Operations: ['84-18=66', '66-50=16'] Exploring Operation: 45*16=720, Resulting Numbers: [720] 720,64 unequal: No Solution Exploring Operation: 45+16=61, Resulting Numbers: [61] 61,64 unequal: No Solution Exploring Operation: 45-16=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 #0,3,3 Current State: 64:[50, 21], Operations: ['84-18=66', '66-45=21'] Exploring Operation: 50+21=71, Resulting Numbers: [71] 71,64 unequal: No Solution Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,64 unequal: No Solution Exploring Operation: 50*21=1050, Resulting Numbers: [1050] 1050,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 64:[66, 95], Operations: ['84-18=66', '45+50=95'] Exploring Operation: 66*95=6270, Resulting Numbers: [6270] 6270,64 unequal: No Solution Exploring Operation: 66+95=161, Resulting Numbers: [161] 161,64 unequal: No Solution Exploring Operation: 95-66=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 #0,3,0 Current State: 64:[50, 111], Operations: ['84-18=66', '45+66=111'] Exploring Operation: 50+111=161, Resulting Numbers: [161] 161,64 unequal: No Solution Exploring Operation: 50*111=5550, Resulting Numbers: [5550] 5550,64 unequal: No Solution Exploring Operation: 111-50=61, Resulting Numbers: [61] 61,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 64:[45, 84, 32], Operations: ['50-18=32'] Exploring Operation: 84-32=52, Resulting Numbers: [45, 52] Generated Node #0,0,0: 64:[45, 52] Operation: 84-32=52 Exploring Operation: 45+84=129, Resulting Numbers: [32, 129] Generated Node #0,0,1: 64:[32, 129] Operation: 45+84=129 Exploring Operation: 45+32=77, Resulting Numbers: [84, 77] Generated Node #0,0,2: 64:[84, 77] Operation: 45+32=77 Exploring Operation: 84-45=39, Resulting Numbers: [32, 39] Generated Node #0,0,3: 64:[32, 39] Operation: 84-45=39 Exploring Operation: 45-32=13, Resulting Numbers: [84, 13] Generated Node #0,0,4: 64:[84, 13] Operation: 45-32=13 Moving to Node #0,4,3 Current State: 64:[18, 11], Operations: ['84-45=39', '50-39=11'] Exploring Operation: 18*11=198, Resulting Numbers: [198] 198,64 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,64 unequal: No Solution Moving to Node #0,0,3 Current State: 64:[32, 39], Operations: ['50-18=32', '84-45=39'] Exploring Operation: 32+39=71, Resulting Numbers: [71] 71,64 unequal: No Solution Exploring Operation: 39-32=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 32*39=1248, Resulting Numbers: [1248] 1248,64 unequal: No Solution Moving to Node #0,4,2 Current State: 64:[39, 32], Operations: ['84-45=39', '50-18=32'] Exploring Operation: 39-32=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 39*32=1248, Resulting Numbers: [1248] 1248,64 unequal: No Solution Exploring Operation: 39+32=71, Resulting Numbers: [71] 71,64 unequal: No Solution Moving to Node #0,4,1 Current State: 64:[39, 68], Operations: ['84-45=39', '50+18=68'] Exploring Operation: 39+68=107, Resulting Numbers: [107] 107,64 unequal: No Solution Exploring Operation: 39*68=2652, Resulting Numbers: [2652] 2652,64 unequal: No Solution Exploring Operation: 68-39=29, Resulting Numbers: [29] 29,64 unequal: No Solution Moving to Node #0,4,0 Current State: 64:[50, 21], Operations: ['84-45=39', '39-18=21'] Exploring Operation: 50+21=71, Resulting Numbers: [71] 71,64 unequal: No Solution Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,64 unequal: No Solution Exploring Operation: 50*21=1050, Resulting Numbers: [1050] 1050,64 unequal: No Solution Moving to Node #0,4,4 Current State: 64:[50, 57], Operations: ['84-45=39', '18+39=57'] Exploring Operation: 50*57=2850, Resulting Numbers: [2850] 2850,64 unequal: No Solution Exploring Operation: 50+57=107, Resulting Numbers: [107] 107,64 unequal: No Solution Exploring Operation: 57-50=7, Resulting Numbers: [7] 7,64 unequal: No Solution Moving to Node #0,0,4 Current State: 64:[84, 13], Operations: ['50-18=32', '45-32=13'] Exploring Operation: 84+13=97, Resulting Numbers: [97] 97,64 unequal: No Solution Exploring Operation: 84*13=1092, Resulting Numbers: [1092] 1092,64 unequal: No Solution Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,64 unequal: No Solution Moving to Node #0,0,0 Current State: 64:[45, 52], Operations: ['50-18=32', '84-32=52'] Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 45+52=97, Resulting Numbers: [97] 97,64 unequal: No Solution Exploring Operation: 45*52=2340, Resulting Numbers: [2340] 2340,64 unequal: No Solution Moving to Node #0,0,2 Current State: 64:[84, 77], Operations: ['50-18=32', '45+32=77'] Exploring Operation: 84+77=161, Resulting Numbers: [161] 161,64 unequal: No Solution Exploring Operation: 84-77=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 84*77=6468, Resulting Numbers: [6468] 6468,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[32, 129], Operations: ['50-18=32', '45+84=129'] Exploring Operation: 32*129=4128, Resulting Numbers: [4128] 4128,64 unequal: No Solution Exploring Operation: 129-32=97, Resulting Numbers: [97] 97,64 unequal: No Solution Exploring Operation: 32+129=161, Resulting Numbers: [161] 161,64 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 1, 44, 16, 18 ]
77
[ "44-1=43", "16+18=34", "43+34=77" ]
Current State: 77:[1, 44, 16, 18], Operations: [] Exploring Operation: 44-1=43, Resulting Numbers: [16, 18, 43] Generated Node #2: [16, 18, 43] from Operation: 44-1=43 Current State: 77:[16, 18, 43], Operations: ['44-1=43'] Exploring Operation: 16+18=34, Resulting Numbers: [43, 34] Generated Node #3: [43, 34] from Operation: 16+18=34 Current State: 77:[43, 34], Operations: ['44-1=43', '16+18=34'] Exploring Operation: 43+34=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[1, 44, 16, 18], Operations: [] Exploring Operation: 44-18=26, Resulting Numbers: [1, 16, 26] Generated Node #0,0: 77:[1, 16, 26] Operation: 44-18=26 Exploring Operation: 44+18=62, Resulting Numbers: [1, 16, 62] Generated Node #0,1: 77:[1, 16, 62] Operation: 44+18=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[1, 16, 26], Operations: ['44-18=26'] Exploring Operation: 26-16=10, Resulting Numbers: [1, 10] Generated Node #0,0,0: 77:[1, 10] Operation: 26-16=10 Exploring Operation: 16-1=15, Resulting Numbers: [26, 15] Generated Node #0,0,1: 77:[26, 15] Operation: 16-1=15 Moving to Node #0,0,0 Current State: 77:[1, 10], Operations: ['44-18=26', '26-16=10'] Exploring Operation: 1+10=11, Resulting Numbers: [11] 11,77 unequal: No Solution Exploring Operation: 1*10=10, Resulting Numbers: [10] 10,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[26, 15], Operations: ['44-18=26', '16-1=15'] Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,77 unequal: No Solution Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[1, 16, 62], Operations: ['44+18=62'] Exploring Operation: 16-1=15, Resulting Numbers: [62, 15] Generated Node #0,1,0: 77:[62, 15] Operation: 16-1=15 Exploring Operation: 16+62=78, Resulting Numbers: [1, 78] Generated Node #0,1,1: 77:[1, 78] Operation: 16+62=78 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 77:[1, 78], Operations: ['44+18=62', '16+62=78'] Exploring Operation: 1*78=78, Resulting Numbers: [78] 78,77 unequal: No Solution Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[1, 44, 16, 18], Operations: [] Exploring Operation: 44+18=62, Resulting Numbers: [1, 16, 62] Generated Node #0,1: 77:[1, 16, 62] Operation: 44+18=62 Moving to Node #0,1 Current State: 77:[1, 16, 62], Operations: ['44+18=62'] Exploring Operation: 16+62=78, Resulting Numbers: [1, 78] Generated Node #0,1,1: 77:[1, 78] Operation: 16+62=78 Moving to Node #0,1,1 Current State: 77:[1, 78], Operations: ['44+18=62', '16+62=78'] Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 54, 64, 21, 29 ]
16
[ "54-21=33", "33-29=4", "64/4=16" ]
Current State: 16:[54, 64, 21, 29], Operations: [] Exploring Operation: 54-21=33, Resulting Numbers: [64, 29, 33] Generated Node #2: [64, 29, 33] from Operation: 54-21=33 Current State: 16:[64, 29, 33], Operations: ['54-21=33'] Exploring Operation: 33-29=4, Resulting Numbers: [64, 4] Generated Node #3: [64, 4] from Operation: 33-29=4 Current State: 16:[64, 4], Operations: ['54-21=33', '33-29=4'] Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[54, 64, 21, 29], Operations: [] Exploring Operation: 64-54=10, Resulting Numbers: [21, 29, 10] Generated Node #0,0: 16:[21, 29, 10] Operation: 64-54=10 Moving to Node #0,0 Current State: 16:[21, 29, 10], Operations: ['64-54=10'] Exploring Operation: 29-21=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 16:[10, 8] Operation: 29-21=8 Moving to Node #0,0,0 Current State: 16:[10, 8], Operations: ['64-54=10', '29-21=8'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,16 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 33, 52, 25, 86 ]
92
[ "52-33=19", "25+86=111", "111-19=92" ]
Current State: 92:[33, 52, 25, 86], Operations: [] Exploring Operation: 52-33=19, Resulting Numbers: [25, 86, 19] Generated Node #2: [25, 86, 19] from Operation: 52-33=19 Current State: 92:[25, 86, 19], Operations: ['52-33=19'] Exploring Operation: 25+86=111, Resulting Numbers: [19, 111] Generated Node #3: [19, 111] from Operation: 25+86=111 Current State: 92:[19, 111], Operations: ['52-33=19', '25+86=111'] Exploring Operation: 111-19=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[33, 52, 25, 86], Operations: [] Exploring Operation: 52-33=19, Resulting Numbers: [25, 86, 19] Generated Node #0,0: 92:[25, 86, 19] Operation: 52-33=19 Exploring Operation: 33+52=85, Resulting Numbers: [25, 86, 85] Generated Node #0,1: 92:[25, 86, 85] Operation: 33+52=85 Moving to Node #0,0 Current State: 92:[25, 86, 19], Operations: ['52-33=19'] Exploring Operation: 25-19=6, Resulting Numbers: [86, 6] Generated Node #0,0,0: 92:[86, 6] Operation: 25-19=6 Exploring Operation: 25+19=44, Resulting Numbers: [86, 44] Generated Node #0,0,1: 92:[86, 44] Operation: 25+19=44 Moving to Node #0,1 Current State: 92:[25, 86, 85], Operations: ['33+52=85'] Exploring Operation: 86-85=1, Resulting Numbers: [25, 1] Generated Node #0,1,0: 92:[25, 1] Operation: 86-85=1 Exploring Operation: 85-25=60, Resulting Numbers: [86, 60] Generated Node #0,1,1: 92:[86, 60] Operation: 85-25=60 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[25, 1], Operations: ['33+52=85', '86-85=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[86, 60], Operations: ['33+52=85', '85-25=60'] Exploring Operation: 86+60=146, Resulting Numbers: [146] 146,92 unequal: No Solution Exploring Operation: 86-60=26, Resulting Numbers: [26] 26,92 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: 92:[86, 6], Operations: ['52-33=19', '25-19=6'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,92 unequal: No Solution Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[33, 52, 25, 86], Operations: [] Exploring Operation: 52-33=19, Resulting Numbers: [25, 86, 19] Generated Node #0,0: 92:[25, 86, 19] Operation: 52-33=19 Moving to Node #0,0 Current State: 92:[25, 86, 19], Operations: ['52-33=19'] Exploring Operation: 25-19=6, Resulting Numbers: [86, 6] Generated Node #0,0,0: 92:[86, 6] Operation: 25-19=6 Moving to Node #0,0,0 Current State: 92:[86, 6], Operations: ['52-33=19', '25-19=6'] Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 8, 54, 48, 40 ]
54
[ "8+54=62", "48-40=8", "62-8=54" ]
Current State: 54:[8, 54, 48, 40], Operations: [] Exploring Operation: 8+54=62, Resulting Numbers: [48, 40, 62] Generated Node #2: [48, 40, 62] from Operation: 8+54=62 Current State: 54:[48, 40, 62], Operations: ['8+54=62'] Exploring Operation: 48-40=8, Resulting Numbers: [62, 8] Generated Node #3: [62, 8] from Operation: 48-40=8 Current State: 54:[62, 8], Operations: ['8+54=62', '48-40=8'] Exploring Operation: 62-8=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[8, 54, 48, 40], Operations: [] Exploring Operation: 40-8=32, Resulting Numbers: [54, 48, 32] Generated Node #0,0: 54:[54, 48, 32] Operation: 40-8=32 Exploring Operation: 40/8=5, Resulting Numbers: [54, 48, 5] Generated Node #0,1: 54:[54, 48, 5] Operation: 40/8=5 Exploring Operation: 48-40=8, Resulting Numbers: [8, 54, 8] Generated Node #0,2: 54:[8, 54, 8] Operation: 48-40=8 Moving to Node #0,2 Current State: 54:[8, 54, 8], Operations: ['48-40=8'] Exploring Operation: 8+8=16, Resulting Numbers: [54, 16] Generated Node #0,2,0: 54:[54, 16] Operation: 8+8=16 Exploring Operation: 8/8=1, Resulting Numbers: [54, 1] Generated Node #0,2,1: 54:[54, 1] Operation: 8/8=1 Exploring Operation: 8-8=0, Resulting Numbers: [54, 0] Generated Node #0,2,2: 54:[54, 0] Operation: 8-8=0 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 54:[54, 1], Operations: ['48-40=8', '8/8=1'] Exploring Operation: 54/1=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[8, 54, 48, 40], Operations: [] Exploring Operation: 48-40=8, Resulting Numbers: [8, 54, 8] Generated Node #0,2: 54:[8, 54, 8] Operation: 48-40=8 Moving to Node #0,2 Current State: 54:[8, 54, 8], Operations: ['48-40=8'] Exploring Operation: 8/8=1, Resulting Numbers: [54, 1] Generated Node #0,2,1: 54:[54, 1] Operation: 8/8=1 Moving to Node #0,2,1 Current State: 54:[54, 1], Operations: ['48-40=8', '8/8=1'] Exploring Operation: 54/1=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 34, 70, 67, 82 ]
89
[ "34+70=104", "82-67=15", "104-15=89" ]
Current State: 89:[34, 70, 67, 82], Operations: [] Exploring Operation: 34+70=104, Resulting Numbers: [67, 82, 104] Generated Node #2: [67, 82, 104] from Operation: 34+70=104 Current State: 89:[67, 82, 104], Operations: ['34+70=104'] Exploring Operation: 82-67=15, Resulting Numbers: [104, 15] Generated Node #3: [104, 15] from Operation: 82-67=15 Current State: 89:[104, 15], Operations: ['34+70=104', '82-67=15'] Exploring Operation: 104-15=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[34, 70, 67, 82], Operations: [] Exploring Operation: 34+82=116, Resulting Numbers: [70, 67, 116] Generated Node #0,0: 89:[70, 67, 116] Operation: 34+82=116 Exploring Operation: 34+67=101, Resulting Numbers: [70, 82, 101] Generated Node #0,1: 89:[70, 82, 101] Operation: 34+67=101 Exploring Operation: 34+70=104, Resulting Numbers: [67, 82, 104] Generated Node #0,2: 89:[67, 82, 104] Operation: 34+70=104 Exploring Operation: 70-34=36, Resulting Numbers: [67, 82, 36] Generated Node #0,3: 89:[67, 82, 36] Operation: 70-34=36 Moving to Node #0,1 Current State: 89:[70, 82, 101], Operations: ['34+67=101'] Exploring Operation: 70+101=171, Resulting Numbers: [82, 171] Generated Node #0,1,0: 89:[82, 171] Operation: 70+101=171 Exploring Operation: 82-70=12, Resulting Numbers: [101, 12] Generated Node #0,1,1: 89:[101, 12] Operation: 82-70=12 Exploring Operation: 101-70=31, Resulting Numbers: [82, 31] Generated Node #0,1,2: 89:[82, 31] Operation: 101-70=31 Exploring Operation: 70+82=152, Resulting Numbers: [101, 152] Generated Node #0,1,3: 89:[101, 152] Operation: 70+82=152 Moving to Node #0,2 Current State: 89:[67, 82, 104], Operations: ['34+70=104'] Exploring Operation: 104-67=37, Resulting Numbers: [82, 37] Generated Node #0,2,0: 89:[82, 37] Operation: 104-67=37 Exploring Operation: 67+104=171, Resulting Numbers: [82, 171] Generated Node #0,2,1: 89:[82, 171] Operation: 67+104=171 Exploring Operation: 67+82=149, Resulting Numbers: [104, 149] Generated Node #0,2,2: 89:[104, 149] Operation: 67+82=149 Exploring Operation: 82-67=15, Resulting Numbers: [104, 15] Generated Node #0,2,3: 89:[104, 15] Operation: 82-67=15 Moving to Node #0,0 Current State: 89:[70, 67, 116], Operations: ['34+82=116'] Exploring Operation: 70+67=137, Resulting Numbers: [116, 137] Generated Node #0,0,0: 89:[116, 137] Operation: 70+67=137 Exploring Operation: 70-67=3, Resulting Numbers: [116, 3] Generated Node #0,0,1: 89:[116, 3] Operation: 70-67=3 Exploring Operation: 116-67=49, Resulting Numbers: [70, 49] Generated Node #0,0,2: 89:[70, 49] Operation: 116-67=49 Exploring Operation: 116-70=46, Resulting Numbers: [67, 46] Generated Node #0,0,3: 89:[67, 46] Operation: 116-70=46 Moving to Node #0,3 Current State: 89:[67, 82, 36], Operations: ['70-34=36'] Exploring Operation: 67-36=31, Resulting Numbers: [82, 31] Generated Node #0,3,0: 89:[82, 31] Operation: 67-36=31 Exploring Operation: 82+36=118, Resulting Numbers: [67, 118] Generated Node #0,3,1: 89:[67, 118] Operation: 82+36=118 Exploring Operation: 67+36=103, Resulting Numbers: [82, 103] Generated Node #0,3,2: 89:[82, 103] Operation: 67+36=103 Exploring Operation: 82-36=46, Resulting Numbers: [67, 46] Generated Node #0,3,3: 89:[67, 46] Operation: 82-36=46 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 89:[82, 103], Operations: ['70-34=36', '67+36=103'] Exploring Operation: 103-82=21, Resulting Numbers: [21] 21,89 unequal: No Solution Exploring Operation: 82*103=8446, Resulting Numbers: [8446] 8446,89 unequal: No Solution Exploring Operation: 82+103=185, Resulting Numbers: [185] 185,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 89:[67, 118], Operations: ['70-34=36', '82+36=118'] Exploring Operation: 118-67=51, Resulting Numbers: [51] 51,89 unequal: No Solution Exploring Operation: 67+118=185, Resulting Numbers: [185] 185,89 unequal: No Solution Exploring Operation: 67*118=7906, Resulting Numbers: [7906] 7906,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 89:[82, 31], Operations: ['70-34=36', '67-36=31'] Exploring Operation: 82-31=51, Resulting Numbers: [51] 51,89 unequal: No Solution Exploring Operation: 82*31=2542, Resulting Numbers: [2542] 2542,89 unequal: No Solution Exploring Operation: 82+31=113, Resulting Numbers: [113] 113,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 89:[67, 46], Operations: ['70-34=36', '82-36=46'] Exploring Operation: 67-46=21, Resulting Numbers: [21] 21,89 unequal: No Solution Exploring Operation: 67*46=3082, Resulting Numbers: [3082] 3082,89 unequal: No Solution Exploring Operation: 67+46=113, Resulting Numbers: [113] 113,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 89:[82, 37], Operations: ['34+70=104', '104-67=37'] Exploring Operation: 82*37=3034, Resulting Numbers: [3034] 3034,89 unequal: No Solution Exploring Operation: 82+37=119, Resulting Numbers: [119] 119,89 unequal: No Solution Exploring Operation: 82-37=45, Resulting Numbers: [45] 45,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[70, 49], Operations: ['34+82=116', '116-67=49'] Exploring Operation: 70+49=119, Resulting Numbers: [119] 119,89 unequal: No Solution Exploring Operation: 70*49=3430, Resulting Numbers: [3430] 3430,89 unequal: No Solution Exploring Operation: 70-49=21, Resulting Numbers: [21] 21,89 unequal: No Solution Moving to Node #0,0,3 Current State: 89:[67, 46], Operations: ['34+82=116', '116-70=46'] Exploring Operation: 67*46=3082, Resulting Numbers: [3082] 3082,89 unequal: No Solution Exploring Operation: 67+46=113, Resulting Numbers: [113] 113,89 unequal: No Solution Exploring Operation: 67-46=21, Resulting Numbers: [21] 21,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[82, 31], Operations: ['34+67=101', '101-70=31'] Exploring Operation: 82*31=2542, Resulting Numbers: [2542] 2542,89 unequal: No Solution Exploring Operation: 82+31=113, Resulting Numbers: [113] 113,89 unequal: No Solution Exploring Operation: 82-31=51, Resulting Numbers: [51] 51,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[104, 149], Operations: ['34+70=104', '67+82=149'] Exploring Operation: 104*149=15496, Resulting Numbers: [15496] 15496,89 unequal: No Solution Exploring Operation: 149-104=45, Resulting Numbers: [45] 45,89 unequal: No Solution Exploring Operation: 104+149=253, Resulting Numbers: [253] 253,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[116, 137], Operations: ['34+82=116', '70+67=137'] Exploring Operation: 137-116=21, Resulting Numbers: [21] 21,89 unequal: No Solution Exploring Operation: 116+137=253, Resulting Numbers: [253] 253,89 unequal: No Solution Exploring Operation: 116*137=15892, Resulting Numbers: [15892] 15892,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[101, 152], Operations: ['34+67=101', '70+82=152'] Exploring Operation: 101+152=253, Resulting Numbers: [253] 253,89 unequal: No Solution Exploring Operation: 101*152=15352, Resulting Numbers: [15352] 15352,89 unequal: No Solution Exploring Operation: 152-101=51, Resulting Numbers: [51] 51,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[82, 171], Operations: ['34+70=104', '67+104=171'] Exploring Operation: 82+171=253, Resulting Numbers: [253] 253,89 unequal: No Solution Exploring Operation: 171-82=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[34, 70, 67, 82], Operations: [] Exploring Operation: 34+70=104, Resulting Numbers: [67, 82, 104] Generated Node #0,2: 89:[67, 82, 104] Operation: 34+70=104 Moving to Node #0,2 Current State: 89:[67, 82, 104], Operations: ['34+70=104'] Exploring Operation: 67+104=171, Resulting Numbers: [82, 171] Generated Node #0,2,1: 89:[82, 171] Operation: 67+104=171 Moving to Node #0,2,1 Current State: 89:[82, 171], Operations: ['34+70=104', '67+104=171'] Exploring Operation: 171-82=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
0.948785
hs_4
mult_heuristic
[ 62, 38, 3, 66 ]
30
[ "62-38=24", "66+24=90", "90/3=30" ]
Current State: 30:[62, 38, 3, 66], Operations: [] Exploring Operation: 62-38=24, Resulting Numbers: [3, 66, 24] Generated Node #2: [3, 66, 24] from Operation: 62-38=24 Current State: 30:[3, 66, 24], Operations: ['62-38=24'] Exploring Operation: 66+24=90, Resulting Numbers: [3, 90] Generated Node #3: [3, 90] from Operation: 66+24=90 Current State: 30:[3, 90], Operations: ['62-38=24', '66+24=90'] Exploring Operation: 90/3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[62, 38, 3, 66], Operations: [] Exploring Operation: 66-38=28, Resulting Numbers: [62, 3, 28] Generated Node #0,0: 30:[62, 3, 28] Operation: 66-38=28 Exploring Operation: 66-62=4, Resulting Numbers: [38, 3, 4] Generated Node #0,1: 30:[38, 3, 4] Operation: 66-62=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[38, 3, 4], Operations: ['66-62=4'] Exploring Operation: 38-3=35, Resulting Numbers: [4, 35] Generated Node #0,1,0: 30:[4, 35] Operation: 38-3=35 Exploring Operation: 38-4=34, Resulting Numbers: [3, 34] Generated Node #0,1,1: 30:[3, 34] Operation: 38-4=34 Moving to Node #0,1,1 Current State: 30:[3, 34], Operations: ['66-62=4', '38-4=34'] Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[4, 35], Operations: ['66-62=4', '38-3=35'] Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[62, 3, 28], Operations: ['66-38=28'] Exploring Operation: 62-3=59, Resulting Numbers: [28, 59] Generated Node #0,0,0: 30:[28, 59] Operation: 62-3=59 Exploring Operation: 62-28=34, Resulting Numbers: [3, 34] Generated Node #0,0,1: 30:[3, 34] Operation: 62-28=34 Moving to Node #0,0,1 Current State: 30:[3, 34], Operations: ['66-38=28', '62-28=34'] Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[28, 59], Operations: ['66-38=28', '62-3=59'] Exploring Operation: 28+59=87, Resulting Numbers: [87] 87,30 unequal: No Solution Exploring Operation: 59-28=31, Resulting Numbers: [31] 31,30 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
[ 65, 50, 45, 72 ]
10
[ "65*50=3250", "45*72=3240", "3250-3240=10" ]
Current State: 10:[65, 50, 45, 72], Operations: [] Exploring Operation: 65*50=3250, Resulting Numbers: [45, 72, 3250] Generated Node #2: [45, 72, 3250] from Operation: 65*50=3250 Current State: 10:[45, 72, 3250], Operations: ['65*50=3250'] Exploring Operation: 45*72=3240, Resulting Numbers: [3250, 3240] Generated Node #3: [3250, 3240] from Operation: 45*72=3240 Current State: 10:[3250, 3240], Operations: ['65*50=3250', '45*72=3240'] Exploring Operation: 3250-3240=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[65, 50, 45, 72], Operations: [] Exploring Operation: 65-45=20, Resulting Numbers: [50, 72, 20] Generated Node #0,0: 10:[50, 72, 20] Operation: 65-45=20 Exploring Operation: 72-65=7, Resulting Numbers: [50, 45, 7] Generated Node #0,1: 10:[50, 45, 7] Operation: 72-65=7 Exploring Operation: 72-50=22, Resulting Numbers: [65, 45, 22] Generated Node #0,2: 10:[65, 45, 22] Operation: 72-50=22 Exploring Operation: 65-50=15, Resulting Numbers: [45, 72, 15] Generated Node #0,3: 10:[45, 72, 15] Operation: 65-50=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[50, 45, 7], Operations: ['72-65=7'] Exploring Operation: 50+7=57, Resulting Numbers: [45, 57] Generated Node #0,1,0: 10:[45, 57] Operation: 50+7=57 Exploring Operation: 50-45=5, Resulting Numbers: [7, 5] Generated Node #0,1,1: 10:[7, 5] Operation: 50-45=5 Exploring Operation: 50-7=43, Resulting Numbers: [45, 43] Generated Node #0,1,2: 10:[45, 43] Operation: 50-7=43 Exploring Operation: 45-7=38, Resulting Numbers: [50, 38] Generated Node #0,1,3: 10:[50, 38] Operation: 45-7=38 Moving to Node #0,1,1 Current State: 10:[7, 5], Operations: ['72-65=7', '50-45=5'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,10 unequal: No Solution Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,10 unequal: No Solution Moving to Node #0,1,3 Current State: 10:[50, 38], Operations: ['72-65=7', '45-7=38'] Exploring Operation: 50*38=1900, Resulting Numbers: [1900] 1900,10 unequal: No Solution Exploring Operation: 50+38=88, Resulting Numbers: [88] 88,10 unequal: No Solution Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,10 unequal: No Solution Moving to Node #0,1,2 Current State: 10:[45, 43], Operations: ['72-65=7', '50-7=43'] Exploring Operation: 45+43=88, Resulting Numbers: [88] 88,10 unequal: No Solution Exploring Operation: 45-43=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 45*43=1935, Resulting Numbers: [1935] 1935,10 unequal: No Solution Moving to Node #0,1,0 Current State: 10:[45, 57], Operations: ['72-65=7', '50+7=57'] Exploring Operation: 45*57=2565, Resulting Numbers: [2565] 2565,10 unequal: No Solution Exploring Operation: 57-45=12, Resulting Numbers: [12] 12,10 unequal: No Solution Exploring Operation: 45+57=102, Resulting Numbers: [102] 102,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 10:[65, 45, 22], Operations: ['72-50=22'] Exploring Operation: 65+45=110, Resulting Numbers: [22, 110] Generated Node #0,2,0: 10:[22, 110] Operation: 65+45=110 Exploring Operation: 65-22=43, Resulting Numbers: [45, 43] Generated Node #0,2,1: 10:[45, 43] Operation: 65-22=43 Exploring Operation: 65-45=20, Resulting Numbers: [22, 20] Generated Node #0,2,2: 10:[22, 20] Operation: 65-45=20 Exploring Operation: 45-22=23, Resulting Numbers: [65, 23] Generated Node #0,2,3: 10:[65, 23] Operation: 45-22=23 Moving to Node #0,2,2 Current State: 10:[22, 20], Operations: ['72-50=22', '65-45=20'] Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,10 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,10 unequal: No Solution Moving to Node #0,2,3 Current State: 10:[65, 23], Operations: ['72-50=22', '45-22=23'] Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 65*23=1495, Resulting Numbers: [1495] 1495,10 unequal: No Solution Exploring Operation: 65+23=88, Resulting Numbers: [88] 88,10 unequal: No Solution Moving to Node #0,2,1 Current State: 10:[45, 43], Operations: ['72-50=22', '65-22=43'] Exploring Operation: 45+43=88, Resulting Numbers: [88] 88,10 unequal: No Solution Exploring Operation: 45-43=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 45*43=1935, Resulting Numbers: [1935] 1935,10 unequal: No Solution Moving to Node #0,2,0 Current State: 10:[22, 110], Operations: ['72-50=22', '65+45=110'] Exploring Operation: 110/22=5, Resulting Numbers: [5] 5,10 unequal: No Solution Exploring Operation: 110-22=88, Resulting Numbers: [88] 88,10 unequal: No Solution Exploring Operation: 22*110=2420, Resulting Numbers: [2420] 2420,10 unequal: No Solution Exploring Operation: 22+110=132, Resulting Numbers: [132] 132,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 10:[45, 72, 15], Operations: ['65-50=15'] Exploring Operation: 45-15=30, Resulting Numbers: [72, 30] Generated Node #0,3,0: 10:[72, 30] Operation: 45-15=30 Exploring Operation: 72-15=57, Resulting Numbers: [45, 57] Generated Node #0,3,1: 10:[45, 57] Operation: 72-15=57 Exploring Operation: 45/15=3, Resulting Numbers: [72, 3] Generated Node #0,3,2: 10:[72, 3] Operation: 45/15=3 Exploring Operation: 72-45=27, Resulting Numbers: [15, 27] Generated Node #0,3,3: 10:[15, 27] Operation: 72-45=27 Moving to Node #0,3,3 Current State: 10:[15, 27], Operations: ['65-50=15', '72-45=27'] Exploring Operation: 15*27=405, Resulting Numbers: [405] 405,10 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,10 unequal: No Solution Exploring Operation: 15+27=42, Resulting Numbers: [42] 42,10 unequal: No Solution Moving to Node #0,3,2 Current State: 10:[72, 3], Operations: ['65-50=15', '45/15=3'] Exploring Operation: 72*3=216, Resulting Numbers: [216] 216,10 unequal: No Solution Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,10 unequal: No Solution Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,10 unequal: No Solution Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,10 unequal: No Solution Moving to Node #0,3,1 Current State: 10:[45, 57], Operations: ['65-50=15', '72-15=57'] Exploring Operation: 45+57=102, Resulting Numbers: [102] 102,10 unequal: No Solution Exploring Operation: 45*57=2565, Resulting Numbers: [2565] 2565,10 unequal: No Solution Exploring Operation: 57-45=12, Resulting Numbers: [12] 12,10 unequal: No Solution Moving to Node #0,3,0 Current State: 10:[72, 30], Operations: ['65-50=15', '45-15=30'] Exploring Operation: 72+30=102, Resulting Numbers: [102] 102,10 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 72*30=2160, Resulting Numbers: [2160] 2160,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[50, 72, 20], Operations: ['65-45=20'] Exploring Operation: 50+72=122, Resulting Numbers: [20, 122] Generated Node #0,0,0: 10:[20, 122] Operation: 50+72=122 Exploring Operation: 50-20=30, Resulting Numbers: [72, 30] Generated Node #0,0,1: 10:[72, 30] Operation: 50-20=30 Exploring Operation: 72-50=22, Resulting Numbers: [20, 22] Generated Node #0,0,2: 10:[20, 22] Operation: 72-50=22 Exploring Operation: 72-20=52, Resulting Numbers: [50, 52] Generated Node #0,0,3: 10:[50, 52] Operation: 72-20=52 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 10:[20, 22], Operations: ['65-45=20', '72-50=22'] Exploring Operation: 20*22=440, Resulting Numbers: [440] 440,10 unequal: No Solution Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 10:[72, 30], Operations: ['65-45=20', '50-20=30'] Exploring Operation: 72*30=2160, Resulting Numbers: [2160] 2160,10 unequal: No Solution Exploring Operation: 72+30=102, Resulting Numbers: [102] 102,10 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 10:[50, 52], Operations: ['65-45=20', '72-20=52'] Exploring Operation: 50*52=2600, Resulting Numbers: [2600] 2600,10 unequal: No Solution Exploring Operation: 50+52=102, Resulting Numbers: [102] 102,10 unequal: No Solution Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[20, 122], Operations: ['65-45=20', '50+72=122'] Exploring Operation: 20+122=142, Resulting Numbers: [142] 142,10 unequal: No Solution Exploring Operation: 122-20=102, Resulting Numbers: [102] 102,10 unequal: No Solution Exploring Operation: 20*122=2440, Resulting Numbers: [2440] 2440,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 59, 30, 50, 59 ]
81
[ "59/59=1", "30+50=80", "1+80=81" ]
Current State: 81:[59, 30, 50, 59], Operations: [] Exploring Operation: 59/59=1, Resulting Numbers: [30, 50, 1] Generated Node #2: [30, 50, 1] from Operation: 59/59=1 Current State: 81:[30, 50, 1], Operations: ['59/59=1'] Exploring Operation: 30+50=80, Resulting Numbers: [1, 80] Generated Node #3: [1, 80] from Operation: 30+50=80 Current State: 81:[1, 80], Operations: ['59/59=1', '30+50=80'] Exploring Operation: 1+80=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[59, 30, 50, 59], Operations: [] Exploring Operation: 59-50=9, Resulting Numbers: [59, 30, 9] Generated Node #0,0: 81:[59, 30, 9] Operation: 59-50=9 Exploring Operation: 59-50=9, Resulting Numbers: [30, 59, 9] Generated Node #0,1: 81:[30, 59, 9] Operation: 59-50=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[59, 30, 9], Operations: ['59-50=9'] Exploring Operation: 59+30=89, Resulting Numbers: [9, 89] Generated Node #0,0,0: 81:[9, 89] Operation: 59+30=89 Exploring Operation: 59-30=29, Resulting Numbers: [9, 29] Generated Node #0,0,1: 81:[9, 29] Operation: 59-30=29 Moving to Node #0,0,1 Current State: 81:[9, 29], Operations: ['59-50=9', '59-30=29'] Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,81 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[9, 89], Operations: ['59-50=9', '59+30=89'] Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,81 unequal: No Solution Exploring Operation: 9+89=98, Resulting Numbers: [98] 98,81 unequal: No Solution No 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: 81:[30, 59, 9], Operations: ['59-50=9'] Exploring Operation: 59-30=29, Resulting Numbers: [9, 29] Generated Node #0,1,0: 81:[9, 29] Operation: 59-30=29 Exploring Operation: 30+59=89, Resulting Numbers: [9, 89] Generated Node #0,1,1: 81:[9, 89] Operation: 30+59=89 Moving to Node #0,1,0 Current State: 81:[9, 29], Operations: ['59-50=9', '59-30=29'] Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[9, 89], Operations: ['59-50=9', '30+59=89'] Exploring Operation: 9+89=98, Resulting Numbers: [98] 98,81 unequal: No Solution Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,81 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
[ 8, 55, 82, 94 ]
51
[ "8+55=63", "94-82=12", "63-12=51" ]
Current State: 51:[8, 55, 82, 94], Operations: [] Exploring Operation: 8+55=63, Resulting Numbers: [82, 94, 63] Generated Node #2: [82, 94, 63] from Operation: 8+55=63 Current State: 51:[82, 94, 63], Operations: ['8+55=63'] Exploring Operation: 94-82=12, Resulting Numbers: [63, 12] Generated Node #3: [63, 12] from Operation: 94-82=12 Current State: 51:[63, 12], Operations: ['8+55=63', '94-82=12'] Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[8, 55, 82, 94], Operations: [] Exploring Operation: 82-8=74, Resulting Numbers: [55, 94, 74] Generated Node #0,0: 51:[55, 94, 74] Operation: 82-8=74 Exploring Operation: 94-55=39, Resulting Numbers: [8, 82, 39] Generated Node #0,1: 51:[8, 82, 39] Operation: 94-55=39 Exploring Operation: 94-82=12, Resulting Numbers: [8, 55, 12] Generated Node #0,2: 51:[8, 55, 12] Operation: 94-82=12 Exploring Operation: 82-55=27, Resulting Numbers: [8, 94, 27] Generated Node #0,3: 51:[8, 94, 27] Operation: 82-55=27 Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[8, 55, 12], Operations: ['94-82=12'] Exploring Operation: 8+12=20, Resulting Numbers: [55, 20] Generated Node #0,2,0: 51:[55, 20] Operation: 8+12=20 Exploring Operation: 55-8=47, Resulting Numbers: [12, 47] Generated Node #0,2,1: 51:[12, 47] Operation: 55-8=47 Exploring Operation: 55-12=43, Resulting Numbers: [8, 43] Generated Node #0,2,2: 51:[8, 43] Operation: 55-12=43 Exploring Operation: 12-8=4, Resulting Numbers: [55, 4] Generated Node #0,2,3: 51:[55, 4] Operation: 12-8=4 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 51:[55, 4], Operations: ['94-82=12', '12-8=4'] Exploring Operation: 55*4=220, Resulting Numbers: [220] 220,51 unequal: No Solution Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[8, 55, 82, 94], Operations: [] Exploring Operation: 94-82=12, Resulting Numbers: [8, 55, 12] Generated Node #0,2: 51:[8, 55, 12] Operation: 94-82=12 Moving to Node #0,2 Current State: 51:[8, 55, 12], Operations: ['94-82=12'] Exploring Operation: 12-8=4, Resulting Numbers: [55, 4] Generated Node #0,2,3: 51:[55, 4] Operation: 12-8=4 Moving to Node #0,2,3 Current State: 51:[55, 4], Operations: ['94-82=12', '12-8=4'] Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 5, 30, 78, 65 ]
35
[ "65/5=13", "78-30=48", "48-13=35" ]
Current State: 35:[5, 30, 78, 65], Operations: [] Exploring Operation: 65/5=13, Resulting Numbers: [30, 78, 13] Generated Node #2: [30, 78, 13] from Operation: 65/5=13 Current State: 35:[30, 78, 13], Operations: ['65/5=13'] Exploring Operation: 78-30=48, Resulting Numbers: [13, 48] Generated Node #3: [13, 48] from Operation: 78-30=48 Current State: 35:[13, 48], Operations: ['65/5=13', '78-30=48'] Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[5, 30, 78, 65], Operations: [] Exploring Operation: 78-30=48, Resulting Numbers: [5, 65, 48] Generated Node #0,0: 35:[5, 65, 48] Operation: 78-30=48 Exploring Operation: 5+30=35, Resulting Numbers: [78, 65, 35] Generated Node #0,1: 35:[78, 65, 35] Operation: 5+30=35 Exploring Operation: 78-65=13, Resulting Numbers: [5, 30, 13] Generated Node #0,2: 35:[5, 30, 13] Operation: 78-65=13 Exploring Operation: 65-30=35, Resulting Numbers: [5, 78, 35] Generated Node #0,3: 35:[5, 78, 35] Operation: 65-30=35 Exploring Operation: 65/5=13, Resulting Numbers: [30, 78, 13] Generated Node #0,4: 35:[30, 78, 13] Operation: 65/5=13 Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[5, 30, 13], Operations: ['78-65=13'] Exploring Operation: 13-5=8, Resulting Numbers: [30, 8] Generated Node #0,2,0: 35:[30, 8] Operation: 13-5=8 Exploring Operation: 30/5=6, Resulting Numbers: [13, 6] Generated Node #0,2,1: 35:[13, 6] Operation: 30/5=6 Exploring Operation: 30-13=17, Resulting Numbers: [5, 17] Generated Node #0,2,2: 35:[5, 17] Operation: 30-13=17 Exploring Operation: 5+30=35, Resulting Numbers: [13, 35] Generated Node #0,2,3: 35:[13, 35] Operation: 5+30=35 Exploring Operation: 30+13=43, Resulting Numbers: [5, 43] Generated Node #0,2,4: 35:[5, 43] Operation: 30+13=43 Moving to Node #0,2,0 Current State: 35:[30, 8], Operations: ['78-65=13', '13-5=8'] Exploring Operation: 30-8=22, Resulting Numbers: [22] 22,35 unequal: No Solution Exploring Operation: 30*8=240, Resulting Numbers: [240] 240,35 unequal: No Solution Exploring Operation: 30+8=38, Resulting Numbers: [38] 38,35 unequal: No Solution Moving to Node #0,2,3 Current State: 35:[13, 35], Operations: ['78-65=13', '5+30=35'] Exploring Operation: 13*35=455, Resulting Numbers: [455] 455,35 unequal: No Solution Exploring Operation: 13+35=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,35 unequal: No Solution Moving to Node #0,2,1 Current State: 35:[13, 6], Operations: ['78-65=13', '30/5=6'] Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,35 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,35 unequal: No Solution Moving to Node #0,2,4 Current State: 35:[5, 43], Operations: ['78-65=13', '30+13=43'] Exploring Operation: 5*43=215, Resulting Numbers: [215] 215,35 unequal: No Solution Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,35 unequal: No Solution Moving to Node #0,2,2 Current State: 35:[5, 17], Operations: ['78-65=13', '30-13=17'] Exploring Operation: 5+17=22, Resulting Numbers: [22] 22,35 unequal: No Solution Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 5*17=85, Resulting Numbers: [85] 85,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[5, 65, 48], Operations: ['78-30=48'] Exploring Operation: 65-5=60, Resulting Numbers: [48, 60] Generated Node #0,0,0: 35:[48, 60] Operation: 65-5=60 Exploring Operation: 65/5=13, Resulting Numbers: [48, 13] Generated Node #0,0,1: 35:[48, 13] Operation: 65/5=13 Exploring Operation: 48-5=43, Resulting Numbers: [65, 43] Generated Node #0,0,2: 35:[65, 43] Operation: 48-5=43 Exploring Operation: 65-48=17, Resulting Numbers: [5, 17] Generated Node #0,0,3: 35:[5, 17] Operation: 65-48=17 Exploring Operation: 5+65=70, Resulting Numbers: [48, 70] Generated Node #0,0,4: 35:[48, 70] Operation: 5+65=70 Moving to Node #0,0,3 Current State: 35:[5, 17], Operations: ['78-30=48', '65-48=17'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 5*17=85, Resulting Numbers: [85] 85,35 unequal: No Solution Exploring Operation: 5+17=22, Resulting Numbers: [22] 22,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[48, 13], Operations: ['78-30=48', '65/5=13'] Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[5, 30, 78, 65], Operations: [] Exploring Operation: 78-30=48, Resulting Numbers: [5, 65, 48] Generated Node #0,0: 35:[5, 65, 48] Operation: 78-30=48 Moving to Node #0,0 Current State: 35:[5, 65, 48], Operations: ['78-30=48'] Exploring Operation: 65/5=13, Resulting Numbers: [48, 13] Generated Node #0,0,1: 35:[48, 13] Operation: 65/5=13 Moving to Node #0,0,1 Current State: 35:[48, 13], Operations: ['78-30=48', '65/5=13'] Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
mult_heuristic
[ 46, 20, 39, 42 ]
44
[ "46-42=4", "20/4=5", "39+5=44" ]
Current State: 44:[46, 20, 39, 42], Operations: [] Exploring Operation: 46-42=4, Resulting Numbers: [20, 39, 4] Generated Node #2: [20, 39, 4] from Operation: 46-42=4 Current State: 44:[20, 39, 4], Operations: ['46-42=4'] Exploring Operation: 20/4=5, Resulting Numbers: [39, 5] Generated Node #3: [39, 5] from Operation: 20/4=5 Current State: 44:[39, 5], Operations: ['46-42=4', '20/4=5'] Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[46, 20, 39, 42], Operations: [] Exploring Operation: 42-39=3, Resulting Numbers: [46, 20, 3] Generated Node #0,0: 44:[46, 20, 3] Operation: 42-39=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[46, 20, 3], Operations: ['42-39=3'] Exploring Operation: 46-3=43, Resulting Numbers: [20, 43] Generated Node #0,0,0: 44:[20, 43] Operation: 46-3=43 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[20, 43], Operations: ['42-39=3', '46-3=43'] Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,44 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
[ 58, 17, 18, 53 ]
60
[ "53-17=36", "36/18=2", "58+2=60" ]
Current State: 60:[58, 17, 18, 53], Operations: [] Exploring Operation: 53-17=36, Resulting Numbers: [58, 18, 36] Generated Node #2: [58, 18, 36] from Operation: 53-17=36 Current State: 60:[58, 18, 36], Operations: ['53-17=36'] Exploring Operation: 36/18=2, Resulting Numbers: [58, 2] Generated Node #3: [58, 2] from Operation: 36/18=2 Current State: 60:[58, 2], Operations: ['53-17=36', '36/18=2'] Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[58, 17, 18, 53], Operations: [] Exploring Operation: 53-17=36, Resulting Numbers: [58, 18, 36] Generated Node #0,0: 60:[58, 18, 36] Operation: 53-17=36 Exploring Operation: 17+18=35, Resulting Numbers: [58, 53, 35] Generated Node #0,1: 60:[58, 53, 35] Operation: 17+18=35 Exploring Operation: 53-18=35, Resulting Numbers: [58, 17, 35] Generated Node #0,2: 60:[58, 17, 35] Operation: 53-18=35 Exploring Operation: 58-53=5, Resulting Numbers: [17, 18, 5] Generated Node #0,3: 60:[17, 18, 5] Operation: 58-53=5 Exploring Operation: 18-17=1, Resulting Numbers: [58, 53, 1] Generated Node #0,4: 60:[58, 53, 1] Operation: 18-17=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 60:[17, 18, 5], Operations: ['58-53=5'] Exploring Operation: 17+5=22, Resulting Numbers: [18, 22] Generated Node #0,3,0: 60:[18, 22] Operation: 17+5=22 Exploring Operation: 17-5=12, Resulting Numbers: [18, 12] Generated Node #0,3,1: 60:[18, 12] Operation: 17-5=12 Exploring Operation: 18-5=13, Resulting Numbers: [17, 13] Generated Node #0,3,2: 60:[17, 13] Operation: 18-5=13 Exploring Operation: 18-17=1, Resulting Numbers: [5, 1] Generated Node #0,3,3: 60:[5, 1] Operation: 18-17=1 Exploring Operation: 17+18=35, Resulting Numbers: [5, 35] Generated Node #0,3,4: 60:[5, 35] Operation: 17+18=35 Moving to Node #0,3,3 Current State: 60:[5, 1], Operations: ['58-53=5', '18-17=1'] Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,60 unequal: No Solution Moving to Node #0,3,1 Current State: 60:[18, 12], Operations: ['58-53=5', '17-5=12'] Exploring Operation: 18*12=216, Resulting Numbers: [216] 216,60 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,60 unequal: No Solution Moving to Node #0,3,2 Current State: 60:[17, 13], Operations: ['58-53=5', '18-5=13'] Exploring Operation: 17*13=221, Resulting Numbers: [221] 221,60 unequal: No Solution Exploring Operation: 17-13=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 17+13=30, Resulting Numbers: [30] 30,60 unequal: No Solution Moving to Node #0,3,0 Current State: 60:[18, 22], Operations: ['58-53=5', '17+5=22'] Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,60 unequal: No Solution Exploring Operation: 18*22=396, Resulting Numbers: [396] 396,60 unequal: No Solution Moving to Node #0,3,4 Current State: 60:[5, 35], Operations: ['58-53=5', '17+18=35'] Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 5*35=175, Resulting Numbers: [175] 175,60 unequal: No Solution Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,60 unequal: No Solution Exploring Operation: 5+35=40, Resulting Numbers: [40] 40,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 60:[58, 17, 35], Operations: ['53-18=35'] Exploring Operation: 35-17=18, Resulting Numbers: [58, 18] Generated Node #0,2,0: 60:[58, 18] Operation: 35-17=18 Exploring Operation: 58+17=75, Resulting Numbers: [35, 75] Generated Node #0,2,1: 60:[35, 75] Operation: 58+17=75 Exploring Operation: 58-17=41, Resulting Numbers: [35, 41] Generated Node #0,2,2: 60:[35, 41] Operation: 58-17=41 Exploring Operation: 17+35=52, Resulting Numbers: [58, 52] Generated Node #0,2,3: 60:[58, 52] Operation: 17+35=52 Exploring Operation: 58-35=23, Resulting Numbers: [17, 23] Generated Node #0,2,4: 60:[17, 23] Operation: 58-35=23 Moving to Node #0,2,0 Current State: 60:[58, 18], Operations: ['53-18=35', '35-17=18'] Exploring Operation: 58-18=40, Resulting Numbers: [40] 40,60 unequal: No Solution Exploring Operation: 58+18=76, Resulting Numbers: [76] 76,60 unequal: No Solution Exploring Operation: 58*18=1044, Resulting Numbers: [1044] 1044,60 unequal: No Solution Moving to Node #0,2,4 Current State: 60:[17, 23], Operations: ['53-18=35', '58-35=23'] Exploring Operation: 17+23=40, Resulting Numbers: [40] 40,60 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 17*23=391, Resulting Numbers: [391] 391,60 unequal: No Solution Moving to Node #0,2,3 Current State: 60:[58, 52], Operations: ['53-18=35', '17+35=52'] Exploring Operation: 58+52=110, Resulting Numbers: [110] 110,60 unequal: No Solution Exploring Operation: 58*52=3016, Resulting Numbers: [3016] 3016,60 unequal: No Solution Exploring Operation: 58-52=6, Resulting Numbers: [6] 6,60 unequal: No Solution Moving to Node #0,2,2 Current State: 60:[35, 41], Operations: ['53-18=35', '58-17=41'] Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 35*41=1435, Resulting Numbers: [1435] 1435,60 unequal: No Solution Exploring Operation: 35+41=76, Resulting Numbers: [76] 76,60 unequal: No Solution Moving to Node #0,2,1 Current State: 60:[35, 75], Operations: ['53-18=35', '58+17=75'] Exploring Operation: 75-35=40, Resulting Numbers: [40] 40,60 unequal: No Solution Exploring Operation: 35+75=110, Resulting Numbers: [110] 110,60 unequal: No Solution Exploring Operation: 35*75=2625, Resulting Numbers: [2625] 2625,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[58, 18, 36], Operations: ['53-17=36'] Exploring Operation: 18+36=54, Resulting Numbers: [58, 54] Generated Node #0,0,0: 60:[58, 54] Operation: 18+36=54 Exploring Operation: 36/18=2, Resulting Numbers: [58, 2] Generated Node #0,0,1: 60:[58, 2] Operation: 36/18=2 Exploring Operation: 36-18=18, Resulting Numbers: [58, 18] Generated Node #0,0,2: 60:[58, 18] Operation: 36-18=18 Exploring Operation: 58-36=22, Resulting Numbers: [18, 22] Generated Node #0,0,3: 60:[18, 22] Operation: 58-36=22 Exploring Operation: 58-18=40, Resulting Numbers: [36, 40] Generated Node #0,0,4: 60:[36, 40] Operation: 58-18=40 Moving to Node #0,0,1 Current State: 60:[58, 2], Operations: ['53-17=36', '36/18=2'] Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,60 unequal: No Solution Exploring Operation: 58*2=116, Resulting Numbers: [116] 116,60 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[58, 17, 18, 53], Operations: [] Exploring Operation: 53-17=36, Resulting Numbers: [58, 18, 36] Generated Node #0,0: 60:[58, 18, 36] Operation: 53-17=36 Moving to Node #0,0 Current State: 60:[58, 18, 36], Operations: ['53-17=36'] Exploring Operation: 36/18=2, Resulting Numbers: [58, 2] Generated Node #0,0,1: 60:[58, 2] Operation: 36/18=2 Moving to Node #0,0,1 Current State: 60:[58, 2], Operations: ['53-17=36', '36/18=2'] Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.947917
hs_5
sum_heuristic
[ 75, 28, 34, 37 ]
24
[ "75-28=47", "34+37=71", "71-47=24" ]
Current State: 24:[75, 28, 34, 37], Operations: [] Exploring Operation: 75-28=47, Resulting Numbers: [34, 37, 47] Generated Node #2: [34, 37, 47] from Operation: 75-28=47 Current State: 24:[34, 37, 47], Operations: ['75-28=47'] Exploring Operation: 34+37=71, Resulting Numbers: [47, 71] Generated Node #3: [47, 71] from Operation: 34+37=71 Current State: 24:[47, 71], Operations: ['75-28=47', '34+37=71'] Exploring Operation: 71-47=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[75, 28, 34, 37], Operations: [] Exploring Operation: 37-34=3, Resulting Numbers: [75, 28, 3] Generated Node #0,0: 24:[75, 28, 3] Operation: 37-34=3 Exploring Operation: 75-34=41, Resulting Numbers: [28, 37, 41] Generated Node #0,1: 24:[28, 37, 41] Operation: 75-34=41 Exploring Operation: 75-37=38, Resulting Numbers: [28, 34, 38] Generated Node #0,2: 24:[28, 34, 38] Operation: 75-37=38 Exploring Operation: 37-28=9, Resulting Numbers: [75, 34, 9] Generated Node #0,3: 24:[75, 34, 9] Operation: 37-28=9 Exploring Operation: 75-28=47, Resulting Numbers: [34, 37, 47] Generated Node #0,4: 24:[34, 37, 47] Operation: 75-28=47 Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[28, 34, 38], Operations: ['75-37=38'] Exploring Operation: 38-28=10, Resulting Numbers: [34, 10] Generated Node #0,2,0: 24:[34, 10] Operation: 38-28=10 Exploring Operation: 28+34=62, Resulting Numbers: [38, 62] Generated Node #0,2,1: 24:[38, 62] Operation: 28+34=62 Exploring Operation: 34-28=6, Resulting Numbers: [38, 6] Generated Node #0,2,2: 24:[38, 6] Operation: 34-28=6 Exploring Operation: 38-34=4, Resulting Numbers: [28, 4] Generated Node #0,2,3: 24:[28, 4] Operation: 38-34=4 Exploring Operation: 28+38=66, Resulting Numbers: [34, 66] Generated Node #0,2,4: 24:[34, 66] Operation: 28+38=66 Moving to Node #0,2,3 Current State: 24:[28, 4], Operations: ['75-37=38', '38-34=4'] Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,24 unequal: No Solution Exploring Operation: 28*4=112, Resulting Numbers: [112] 112,24 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[75, 28, 34, 37], Operations: [] Exploring Operation: 75-37=38, Resulting Numbers: [28, 34, 38] Generated Node #0,2: 24:[28, 34, 38] Operation: 75-37=38 Moving to Node #0,2 Current State: 24:[28, 34, 38], Operations: ['75-37=38'] Exploring Operation: 38-34=4, Resulting Numbers: [28, 4] Generated Node #0,2,3: 24:[28, 4] Operation: 38-34=4 Moving to Node #0,2,3 Current State: 24:[28, 4], Operations: ['75-37=38', '38-34=4'] Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 23, 91, 3, 35 ]
52
[ "23-3=20", "91*20=1820", "1820/35=52" ]
Current State: 52:[23, 91, 3, 35], Operations: [] Exploring Operation: 23-3=20, Resulting Numbers: [91, 35, 20] Generated Node #2: [91, 35, 20] from Operation: 23-3=20 Current State: 52:[91, 35, 20], Operations: ['23-3=20'] Exploring Operation: 91*20=1820, Resulting Numbers: [35, 1820] Generated Node #3: [35, 1820] from Operation: 91*20=1820 Current State: 52:[35, 1820], Operations: ['23-3=20', '91*20=1820'] Exploring Operation: 1820/35=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[23, 91, 3, 35], Operations: [] Exploring Operation: 23+35=58, Resulting Numbers: [91, 3, 58] Generated Node #0,0: 52:[91, 3, 58] Operation: 23+35=58 Exploring Operation: 91-23=68, Resulting Numbers: [3, 35, 68] Generated Node #0,1: 52:[3, 35, 68] Operation: 91-23=68 Exploring Operation: 91-35=56, Resulting Numbers: [23, 3, 56] Generated Node #0,2: 52:[23, 3, 56] Operation: 91-35=56 Exploring Operation: 35-23=12, Resulting Numbers: [91, 3, 12] Generated Node #0,3: 52:[91, 3, 12] Operation: 35-23=12 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[23, 3, 56], Operations: ['91-35=56'] Exploring Operation: 56-23=33, Resulting Numbers: [3, 33] Generated Node #0,2,0: 52:[3, 33] Operation: 56-23=33 Exploring Operation: 23+3=26, Resulting Numbers: [56, 26] Generated Node #0,2,1: 52:[56, 26] Operation: 23+3=26 Exploring Operation: 23-3=20, Resulting Numbers: [56, 20] Generated Node #0,2,2: 52:[56, 20] Operation: 23-3=20 Exploring Operation: 56-3=53, Resulting Numbers: [23, 53] Generated Node #0,2,3: 52:[23, 53] Operation: 56-3=53 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 52:[56, 26], Operations: ['91-35=56', '23+3=26'] Exploring Operation: 56-26=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 56*26=1456, Resulting Numbers: [1456] 1456,52 unequal: No Solution Exploring Operation: 56+26=82, Resulting Numbers: [82] 82,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 52:[23, 53], Operations: ['91-35=56', '56-3=53'] Exploring Operation: 23+53=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 23*53=1219, Resulting Numbers: [1219] 1219,52 unequal: No Solution Exploring Operation: 53-23=30, Resulting Numbers: [30] 30,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 52:[3, 33], Operations: ['91-35=56', '56-23=33'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 3+33=36, Resulting Numbers: [36] 36,52 unequal: No Solution Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,52 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 52:[56, 20], Operations: ['91-35=56', '23-3=20'] Exploring Operation: 56*20=1120, Resulting Numbers: [1120] 1120,52 unequal: No Solution Exploring Operation: 56-20=36, Resulting Numbers: [36] 36,52 unequal: No Solution Exploring Operation: 56+20=76, Resulting Numbers: [76] 76,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[3, 35, 68], Operations: ['91-23=68'] Exploring Operation: 68-35=33, Resulting Numbers: [3, 33] Generated Node #0,1,0: 52:[3, 33] Operation: 68-35=33 Exploring Operation: 68-3=65, Resulting Numbers: [35, 65] Generated Node #0,1,1: 52:[35, 65] Operation: 68-3=65 Exploring Operation: 3+35=38, Resulting Numbers: [68, 38] Generated Node #0,1,2: 52:[68, 38] Operation: 3+35=38 Exploring Operation: 35-3=32, Resulting Numbers: [68, 32] Generated Node #0,1,3: 52:[68, 32] Operation: 35-3=32 Moving to Node #0,1,0 Current State: 52:[3, 33], Operations: ['91-23=68', '68-35=33'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 3+33=36, Resulting Numbers: [36] 36,52 unequal: No Solution Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,52 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,52 unequal: No Solution Moving to Node #0,1,3 Current State: 52:[68, 32], Operations: ['91-23=68', '35-3=32'] Exploring Operation: 68*32=2176, Resulting Numbers: [2176] 2176,52 unequal: No Solution Exploring Operation: 68+32=100, Resulting Numbers: [100] 100,52 unequal: No Solution Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[35, 65], Operations: ['91-23=68', '68-3=65'] Exploring Operation: 35*65=2275, Resulting Numbers: [2275] 2275,52 unequal: No Solution Exploring Operation: 65-35=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 35+65=100, Resulting Numbers: [100] 100,52 unequal: No Solution Moving to Node #0,1,2 Current State: 52:[68, 38], Operations: ['91-23=68', '3+35=38'] Exploring Operation: 68+38=106, Resulting Numbers: [106] 106,52 unequal: No Solution Exploring Operation: 68-38=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 68*38=2584, Resulting Numbers: [2584] 2584,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[91, 3, 12], Operations: ['35-23=12'] Exploring Operation: 12/3=4, Resulting Numbers: [91, 4] Generated Node #0,3,0: 52:[91, 4] Operation: 12/3=4 Exploring Operation: 3+12=15, Resulting Numbers: [91, 15] Generated Node #0,3,1: 52:[91, 15] Operation: 3+12=15 Exploring Operation: 91-3=88, Resulting Numbers: [12, 88] Generated Node #0,3,2: 52:[12, 88] Operation: 91-3=88 Exploring Operation: 91-12=79, Resulting Numbers: [3, 79] Generated Node #0,3,3: 52:[3, 79] Operation: 91-12=79 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 52:[3, 79], Operations: ['35-23=12', '91-12=79'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 3*79=237, Resulting Numbers: [237] 237,52 unequal: No Solution Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 52:[12, 88], Operations: ['35-23=12', '91-3=88'] Exploring Operation: 12*88=1056, Resulting Numbers: [1056] 1056,52 unequal: No Solution Exploring Operation: 88-12=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 12+88=100, Resulting Numbers: [100] 100,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 52:[91, 4], Operations: ['35-23=12', '12/3=4'] Exploring Operation: 91-4=87, Resulting Numbers: [87] 87,52 unequal: No Solution Exploring Operation: 91+4=95, Resulting Numbers: [95] 95,52 unequal: No Solution Exploring Operation: 91*4=364, Resulting Numbers: [364] 364,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 52:[91, 15], Operations: ['35-23=12', '3+12=15'] Exploring Operation: 91*15=1365, Resulting Numbers: [1365] 1365,52 unequal: No Solution Exploring Operation: 91+15=106, Resulting Numbers: [106] 106,52 unequal: No Solution Exploring Operation: 91-15=76, Resulting Numbers: [76] 76,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[91, 3, 58], Operations: ['23+35=58'] Exploring Operation: 91-3=88, Resulting Numbers: [58, 88] Generated Node #0,0,0: 52:[58, 88] Operation: 91-3=88 Exploring Operation: 91+3=94, Resulting Numbers: [58, 94] Generated Node #0,0,1: 52:[58, 94] Operation: 91+3=94 Exploring Operation: 91-58=33, Resulting Numbers: [3, 33] Generated Node #0,0,2: 52:[3, 33] Operation: 91-58=33 Exploring Operation: 58-3=55, Resulting Numbers: [91, 55] Generated Node #0,0,3: 52:[91, 55] Operation: 58-3=55 Moving to Node #0,0,2 Current State: 52:[3, 33], Operations: ['23+35=58', '91-58=33'] Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,52 unequal: No Solution Exploring Operation: 3+33=36, Resulting Numbers: [36] 36,52 unequal: No Solution Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,52 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,52 unequal: No Solution Moving to Node #0,0,3 Current State: 52:[91, 55], Operations: ['23+35=58', '58-3=55'] Exploring Operation: 91*55=5005, Resulting Numbers: [5005] 5005,52 unequal: No Solution Exploring Operation: 91-55=36, Resulting Numbers: [36] 36,52 unequal: No Solution Exploring Operation: 91+55=146, Resulting Numbers: [146] 146,52 unequal: No Solution Moving to Node #0,0,0 Current State: 52:[58, 88], Operations: ['23+35=58', '91-3=88'] Exploring Operation: 58+88=146, Resulting Numbers: [146] 146,52 unequal: No Solution Exploring Operation: 58*88=5104, Resulting Numbers: [5104] 5104,52 unequal: No Solution Exploring Operation: 88-58=30, Resulting Numbers: [30] 30,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[58, 94], Operations: ['23+35=58', '91+3=94'] Exploring Operation: 94-58=36, Resulting Numbers: [36] 36,52 unequal: No Solution Exploring Operation: 58+94=152, Resulting Numbers: [152] 152,52 unequal: No Solution Exploring Operation: 58*94=5452, Resulting Numbers: [5452] 5452,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 14, 98, 73, 13 ]
79
[ "98/14=7", "73+13=86", "86-7=79" ]
Current State: 79:[14, 98, 73, 13], Operations: [] Exploring Operation: 98/14=7, Resulting Numbers: [73, 13, 7] Generated Node #2: [73, 13, 7] from Operation: 98/14=7 Current State: 79:[73, 13, 7], Operations: ['98/14=7'] Exploring Operation: 73+13=86, Resulting Numbers: [7, 86] Generated Node #3: [7, 86] from Operation: 73+13=86 Current State: 79:[7, 86], Operations: ['98/14=7', '73+13=86'] Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[14, 98, 73, 13], Operations: [] Exploring Operation: 98-13=85, Resulting Numbers: [14, 73, 85] Generated Node #0,0: 79:[14, 73, 85] Operation: 98-13=85 Exploring Operation: 98-14=84, Resulting Numbers: [73, 13, 84] Generated Node #0,1: 79:[73, 13, 84] Operation: 98-14=84 Exploring Operation: 14+13=27, Resulting Numbers: [98, 73, 27] Generated Node #0,2: 79:[98, 73, 27] Operation: 14+13=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[14, 73, 85], Operations: ['98-13=85'] Exploring Operation: 85-14=71, Resulting Numbers: [73, 71] Generated Node #0,0,0: 79:[73, 71] Operation: 85-14=71 Exploring Operation: 14+73=87, Resulting Numbers: [85, 87] Generated Node #0,0,1: 79:[85, 87] Operation: 14+73=87 Exploring Operation: 73-14=59, Resulting Numbers: [85, 59] Generated Node #0,0,2: 79:[85, 59] Operation: 73-14=59 Moving to Node #0,0,0 Current State: 79:[73, 71], Operations: ['98-13=85', '85-14=71'] Exploring Operation: 73+71=144, Resulting Numbers: [144] 144,79 unequal: No Solution Exploring Operation: 73-71=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 73*71=5183, Resulting Numbers: [5183] 5183,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[85, 87], Operations: ['98-13=85', '14+73=87'] Exploring Operation: 85+87=172, Resulting Numbers: [172] 172,79 unequal: No Solution Exploring Operation: 85*87=7395, Resulting Numbers: [7395] 7395,79 unequal: No Solution Exploring Operation: 87-85=2, Resulting Numbers: [2] 2,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[85, 59], Operations: ['98-13=85', '73-14=59'] Exploring Operation: 85-59=26, Resulting Numbers: [26] 26,79 unequal: No Solution Exploring Operation: 85*59=5015, Resulting Numbers: [5015] 5015,79 unequal: No Solution Exploring Operation: 85+59=144, Resulting Numbers: [144] 144,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[73, 13, 84], Operations: ['98-14=84'] Exploring Operation: 73+13=86, Resulting Numbers: [84, 86] Generated Node #0,1,0: 79:[84, 86] Operation: 73+13=86 Exploring Operation: 84-13=71, Resulting Numbers: [73, 71] Generated Node #0,1,1: 79:[73, 71] Operation: 84-13=71 Exploring Operation: 73-13=60, Resulting Numbers: [84, 60] Generated Node #0,1,2: 79:[84, 60] Operation: 73-13=60 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 79:[84, 86], Operations: ['98-14=84', '73+13=86'] Exploring Operation: 86-84=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 84*86=7224, Resulting Numbers: [7224] 7224,79 unequal: No Solution Exploring Operation: 84+86=170, Resulting Numbers: [170] 170,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 79:[73, 71], Operations: ['98-14=84', '84-13=71'] Exploring Operation: 73+71=144, Resulting Numbers: [144] 144,79 unequal: No Solution Exploring Operation: 73*71=5183, Resulting Numbers: [5183] 5183,79 unequal: No Solution Exploring Operation: 73-71=2, Resulting Numbers: [2] 2,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 79:[84, 60], Operations: ['98-14=84', '73-13=60'] Exploring Operation: 84*60=5040, Resulting Numbers: [5040] 5040,79 unequal: No Solution Exploring Operation: 84-60=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 84+60=144, Resulting Numbers: [144] 144,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[98, 73, 27], Operations: ['14+13=27'] Exploring Operation: 98-27=71, Resulting Numbers: [73, 71] Generated Node #0,2,0: 79:[73, 71] Operation: 98-27=71 Exploring Operation: 98+27=125, Resulting Numbers: [73, 125] Generated Node #0,2,1: 79:[73, 125] Operation: 98+27=125 Exploring Operation: 73+27=100, Resulting Numbers: [98, 100] Generated Node #0,2,2: 79:[98, 100] Operation: 73+27=100 Moving to Node #0,2,0 Current State: 79:[73, 71], Operations: ['14+13=27', '98-27=71'] Exploring Operation: 73+71=144, Resulting Numbers: [144] 144,79 unequal: No Solution Exploring Operation: 73*71=5183, Resulting Numbers: [5183] 5183,79 unequal: No Solution Exploring Operation: 73-71=2, Resulting Numbers: [2] 2,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[98, 100], Operations: ['14+13=27', '73+27=100'] Exploring Operation: 100-98=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 98+100=198, Resulting Numbers: [198] 198,79 unequal: No Solution Exploring Operation: 98*100=9800, Resulting Numbers: [9800] 9800,79 unequal: No Solution Moving to Node #0,2,1 Current State: 79:[73, 125], Operations: ['14+13=27', '98+27=125'] Exploring Operation: 73+125=198, Resulting Numbers: [198] 198,79 unequal: No Solution Exploring Operation: 125-73=52, Resulting Numbers: [52] 52,79 unequal: No Solution Exploring Operation: 73*125=9125, Resulting Numbers: [9125] 9125,79 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
[ 38, 6, 2, 7 ]
17
[ "6/2=3", "7*3=21", "38-21=17" ]
Current State: 17:[38, 6, 2, 7], Operations: [] Exploring Operation: 6/2=3, Resulting Numbers: [38, 7, 3] Generated Node #2: [38, 7, 3] from Operation: 6/2=3 Current State: 17:[38, 7, 3], Operations: ['6/2=3'] Exploring Operation: 7*3=21, Resulting Numbers: [38, 21] Generated Node #3: [38, 21] from Operation: 7*3=21 Current State: 17:[38, 21], Operations: ['6/2=3', '7*3=21'] Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[38, 6, 2, 7], Operations: [] Exploring Operation: 38/2=19, Resulting Numbers: [6, 7, 19] Generated Node #0,0: 17:[6, 7, 19] Operation: 38/2=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[6, 7, 19], Operations: ['38/2=19'] Exploring Operation: 6+7=13, Resulting Numbers: [19, 13] Generated Node #0,0,0: 17:[19, 13] Operation: 6+7=13 Moving to Node #0,0,0 Current State: 17:[19, 13], Operations: ['38/2=19', '6+7=13'] Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,17 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
[ 30, 30, 6, 15 ]
39
[ "30+30=60", "6+15=21", "60-21=39" ]
Current State: 39:[30, 30, 6, 15], Operations: [] Exploring Operation: 30+30=60, Resulting Numbers: [6, 15, 60] Generated Node #2: [6, 15, 60] from Operation: 30+30=60 Current State: 39:[6, 15, 60], Operations: ['30+30=60'] Exploring Operation: 6+15=21, Resulting Numbers: [60, 21] Generated Node #3: [60, 21] from Operation: 6+15=21 Current State: 39:[60, 21], Operations: ['30+30=60', '6+15=21'] Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[30, 30, 6, 15], Operations: [] Exploring Operation: 30-30=0, Resulting Numbers: [6, 15, 0] Generated Node #0,0: 39:[6, 15, 0] Operation: 30-30=0 Exploring Operation: 30/6=5, Resulting Numbers: [30, 15, 5] Generated Node #0,1: 39:[30, 15, 5] Operation: 30/6=5 Exploring Operation: 30/30=1, Resulting Numbers: [6, 15, 1] Generated Node #0,2: 39:[6, 15, 1] Operation: 30/30=1 Moving to Node #0,2 Current State: 39:[6, 15, 1], Operations: ['30/30=1'] Exploring Operation: 6-1=5, Resulting Numbers: [15, 5] Generated Node #0,2,0: 39:[15, 5] Operation: 6-1=5 Exploring Operation: 6*1=6, Resulting Numbers: [15, 6] Generated Node #0,2,1: 39:[15, 6] Operation: 6*1=6 Exploring Operation: 15-1=14, Resulting Numbers: [6, 14] Generated Node #0,2,2: 39:[6, 14] Operation: 15-1=14 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[15, 5], Operations: ['30/30=1', '6-1=5'] Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,39 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 39:[6, 14], Operations: ['30/30=1', '15-1=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,39 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,39 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 39:[15, 6], Operations: ['30/30=1', '6*1=6'] Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,39 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 39:[6, 15, 0], Operations: ['30-30=0'] Exploring Operation: 6+0=6, Resulting Numbers: [15, 6] Generated Node #0,0,0: 39:[15, 6] Operation: 6+0=6 Exploring Operation: 6-0=6, Resulting Numbers: [15, 6] Generated Node #0,0,1: 39:[15, 6] Operation: 6-0=6 Exploring Operation: 6*0=0, Resulting Numbers: [15, 0] Generated Node #0,0,2: 39:[15, 0] Operation: 6*0=0 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[15, 6], Operations: ['30-30=0', '6+0=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,39 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 39:[15, 6], Operations: ['30-30=0', '6-0=6'] Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,39 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 39:[15, 0], Operations: ['30-30=0', '6*0=0'] Exploring Operation: 15*0=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 15-0=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 15+0=15, Resulting Numbers: [15] 15,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 39:[30, 15, 5], Operations: ['30/6=5'] Exploring Operation: 30/5=6, Resulting Numbers: [15, 6] Generated Node #0,1,0: 39:[15, 6] Operation: 30/5=6 Exploring Operation: 30-15=15, Resulting Numbers: [5, 15] Generated Node #0,1,1: 39:[5, 15] Operation: 30-15=15 Exploring Operation: 30/15=2, Resulting Numbers: [5, 2] Generated Node #0,1,2: 39:[5, 2] Operation: 30/15=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 39:[5, 2], Operations: ['30/6=5', '30/15=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[5, 15], Operations: ['30/6=5', '30-15=15'] Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,39 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[15, 6], Operations: ['30/6=5', '30/5=6'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,39 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
[ 7, 39, 61, 65 ]
42
[ "7+39=46", "65-61=4", "46-4=42" ]
Current State: 42:[7, 39, 61, 65], Operations: [] Exploring Operation: 7+39=46, Resulting Numbers: [61, 65, 46] Generated Node #2: [61, 65, 46] from Operation: 7+39=46 Current State: 42:[61, 65, 46], Operations: ['7+39=46'] Exploring Operation: 65-61=4, Resulting Numbers: [46, 4] Generated Node #3: [46, 4] from Operation: 65-61=4 Current State: 42:[46, 4], Operations: ['7+39=46', '65-61=4'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[7, 39, 61, 65], Operations: [] Exploring Operation: 65-61=4, Resulting Numbers: [7, 39, 4] Generated Node #0,0: 42:[7, 39, 4] Operation: 65-61=4 Exploring Operation: 65-39=26, Resulting Numbers: [7, 61, 26] Generated Node #0,1: 42:[7, 61, 26] Operation: 65-39=26 Exploring Operation: 61-39=22, Resulting Numbers: [7, 65, 22] Generated Node #0,2: 42:[7, 65, 22] Operation: 61-39=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[7, 39, 4], Operations: ['65-61=4'] Exploring Operation: 7+39=46, Resulting Numbers: [4, 46] Generated Node #0,0,0: 42:[4, 46] Operation: 7+39=46 Exploring Operation: 7-4=3, Resulting Numbers: [39, 3] Generated Node #0,0,1: 42:[39, 3] Operation: 7-4=3 Exploring Operation: 39+4=43, Resulting Numbers: [7, 43] Generated Node #0,0,2: 42:[7, 43] Operation: 39+4=43 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 42:[7, 43], Operations: ['65-61=4', '39+4=43'] Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,42 unequal: No Solution Exploring Operation: 7+43=50, Resulting Numbers: [50] 50,42 unequal: No Solution Exploring Operation: 7*43=301, Resulting Numbers: [301] 301,42 unequal: No Solution No 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: 42:[39, 3], Operations: ['65-61=4', '7-4=3'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,42 unequal: No Solution Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[7, 39, 61, 65], Operations: [] Exploring Operation: 65-61=4, Resulting Numbers: [7, 39, 4] Generated Node #0,0: 42:[7, 39, 4] Operation: 65-61=4 Moving to Node #0,0 Current State: 42:[7, 39, 4], Operations: ['65-61=4'] Exploring Operation: 7-4=3, Resulting Numbers: [39, 3] Generated Node #0,0,1: 42:[39, 3] Operation: 7-4=3 Moving to Node #0,0,1 Current State: 42:[39, 3], Operations: ['65-61=4', '7-4=3'] Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 21, 4, 10, 67 ]
13
[ "67-4=63", "63/21=3", "10+3=13" ]
Current State: 13:[21, 4, 10, 67], Operations: [] Exploring Operation: 67-4=63, Resulting Numbers: [21, 10, 63] Generated Node #2: [21, 10, 63] from Operation: 67-4=63 Current State: 13:[21, 10, 63], Operations: ['67-4=63'] Exploring Operation: 63/21=3, Resulting Numbers: [10, 3] Generated Node #3: [10, 3] from Operation: 63/21=3 Current State: 13:[10, 3], Operations: ['67-4=63', '63/21=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[21, 4, 10, 67], Operations: [] Exploring Operation: 4+10=14, Resulting Numbers: [21, 67, 14] Generated Node #0,0: 13:[21, 67, 14] Operation: 4+10=14 Exploring Operation: 67-21=46, Resulting Numbers: [4, 10, 46] Generated Node #0,1: 13:[4, 10, 46] Operation: 67-21=46 Exploring Operation: 21-4=17, Resulting Numbers: [10, 67, 17] Generated Node #0,2: 13:[10, 67, 17] Operation: 21-4=17 Exploring Operation: 67-4=63, Resulting Numbers: [21, 10, 63] Generated Node #0,3: 13:[21, 10, 63] Operation: 67-4=63 Exploring Operation: 67-10=57, Resulting Numbers: [21, 4, 57] Generated Node #0,4: 13:[21, 4, 57] Operation: 67-10=57 Moving to Node #0,1 Current State: 13:[4, 10, 46], Operations: ['67-21=46'] Exploring Operation: 46-4=42, Resulting Numbers: [10, 42] Generated Node #0,1,0: 13:[10, 42] Operation: 46-4=42 Exploring Operation: 10-4=6, Resulting Numbers: [46, 6] Generated Node #0,1,1: 13:[46, 6] Operation: 10-4=6 Exploring Operation: 4+46=50, Resulting Numbers: [10, 50] Generated Node #0,1,2: 13:[10, 50] Operation: 4+46=50 Exploring Operation: 46-10=36, Resulting Numbers: [4, 36] Generated Node #0,1,3: 13:[4, 36] Operation: 46-10=36 Exploring Operation: 4+10=14, Resulting Numbers: [46, 14] Generated Node #0,1,4: 13:[46, 14] Operation: 4+10=14 Moving to Node #0,3 Current State: 13:[21, 10, 63], Operations: ['67-4=63'] Exploring Operation: 21+10=31, Resulting Numbers: [63, 31] Generated Node #0,3,0: 13:[63, 31] Operation: 21+10=31 Exploring Operation: 21-10=11, Resulting Numbers: [63, 11] Generated Node #0,3,1: 13:[63, 11] Operation: 21-10=11 Exploring Operation: 63/21=3, Resulting Numbers: [10, 3] Generated Node #0,3,2: 13:[10, 3] Operation: 63/21=3 Exploring Operation: 63-21=42, Resulting Numbers: [10, 42] Generated Node #0,3,3: 13:[10, 42] Operation: 63-21=42 Exploring Operation: 63-10=53, Resulting Numbers: [21, 53] Generated Node #0,3,4: 13:[21, 53] Operation: 63-10=53 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 13:[10, 3], Operations: ['67-4=63', '63/21=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[21, 4, 10, 67], Operations: [] Exploring Operation: 67-4=63, Resulting Numbers: [21, 10, 63] Generated Node #0,3: 13:[21, 10, 63] Operation: 67-4=63 Moving to Node #0,3 Current State: 13:[21, 10, 63], Operations: ['67-4=63'] Exploring Operation: 63/21=3, Resulting Numbers: [10, 3] Generated Node #0,3,2: 13:[10, 3] Operation: 63/21=3 Moving to Node #0,3,2 Current State: 13:[10, 3], Operations: ['67-4=63', '63/21=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 30, 99, 94, 27 ]
16
[ "30*99=2970", "2970/27=110", "110-94=16" ]
Current State: 16:[30, 99, 94, 27], Operations: [] Exploring Operation: 30*99=2970, Resulting Numbers: [94, 27, 2970] Generated Node #2: [94, 27, 2970] from Operation: 30*99=2970 Current State: 16:[94, 27, 2970], Operations: ['30*99=2970'] Exploring Operation: 2970/27=110, Resulting Numbers: [94, 110] Generated Node #3: [94, 110] from Operation: 2970/27=110 Current State: 16:[94, 110], Operations: ['30*99=2970', '2970/27=110'] Exploring Operation: 110-94=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[30, 99, 94, 27], Operations: [] Exploring Operation: 99-27=72, Resulting Numbers: [30, 94, 72] Generated Node #0,0: 16:[30, 94, 72] Operation: 99-27=72 Exploring Operation: 99-30=69, Resulting Numbers: [94, 27, 69] Generated Node #0,1: 16:[94, 27, 69] Operation: 99-30=69 Exploring Operation: 99-94=5, Resulting Numbers: [30, 27, 5] Generated Node #0,2: 16:[30, 27, 5] Operation: 99-94=5 Exploring Operation: 94-27=67, Resulting Numbers: [30, 99, 67] Generated Node #0,3: 16:[30, 99, 67] Operation: 94-27=67 Exploring Operation: 94-30=64, Resulting Numbers: [99, 27, 64] Generated Node #0,4: 16:[99, 27, 64] Operation: 94-30=64 Moving to Node #0,2 Current State: 16:[30, 27, 5], Operations: ['99-94=5'] Exploring Operation: 27-5=22, Resulting Numbers: [30, 22] Generated Node #0,2,0: 16:[30, 22] Operation: 27-5=22 Exploring Operation: 30-5=25, Resulting Numbers: [27, 25] Generated Node #0,2,1: 16:[27, 25] Operation: 30-5=25 Exploring Operation: 30/5=6, Resulting Numbers: [27, 6] Generated Node #0,2,2: 16:[27, 6] Operation: 30/5=6 Exploring Operation: 30-27=3, Resulting Numbers: [5, 3] Generated Node #0,2,3: 16:[5, 3] Operation: 30-27=3 Exploring Operation: 30+5=35, Resulting Numbers: [27, 35] Generated Node #0,2,4: 16:[27, 35] Operation: 30+5=35 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 16:[5, 3], Operations: ['99-94=5', '30-27=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,16 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 16:[27, 6], Operations: ['99-94=5', '30/5=6'] Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,16 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,16 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,16 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 #0,2,0 Current State: 16:[30, 22], Operations: ['99-94=5', '27-5=22'] Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 30*22=660, Resulting Numbers: [660] 660,16 unequal: No Solution Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,16 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 #0,2,1 Current State: 16:[27, 25], Operations: ['99-94=5', '30-5=25'] Exploring Operation: 27+25=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 27*25=675, Resulting Numbers: [675] 675,16 unequal: No Solution Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 16:[27, 35], Operations: ['99-94=5', '30+5=35'] Exploring Operation: 27*35=945, Resulting Numbers: [945] 945,16 unequal: No Solution Exploring Operation: 27+35=62, Resulting Numbers: [62] 62,16 unequal: No Solution Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,16 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: 16:[99, 27, 64], Operations: ['94-30=64'] Exploring Operation: 99-64=35, Resulting Numbers: [27, 35] Generated Node #0,4,0: 16:[27, 35] Operation: 99-64=35 Exploring Operation: 99-27=72, Resulting Numbers: [64, 72] Generated Node #0,4,1: 16:[64, 72] Operation: 99-27=72 Exploring Operation: 99+27=126, Resulting Numbers: [64, 126] Generated Node #0,4,2: 16:[64, 126] Operation: 99+27=126 Exploring Operation: 64-27=37, Resulting Numbers: [99, 37] Generated Node #0,4,3: 16:[99, 37] Operation: 64-27=37 Exploring Operation: 99+64=163, Resulting Numbers: [27, 163] Generated Node #0,4,4: 16:[27, 163] Operation: 99+64=163 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 16:[27, 35], Operations: ['94-30=64', '99-64=35'] Exploring Operation: 27+35=62, Resulting Numbers: [62] 62,16 unequal: No Solution Exploring Operation: 27*35=945, Resulting Numbers: [945] 945,16 unequal: No Solution Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,16 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 #0,4,1 Current State: 16:[64, 72], Operations: ['94-30=64', '99-27=72'] Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 64+72=136, Resulting Numbers: [136] 136,16 unequal: No Solution Exploring Operation: 64*72=4608, Resulting Numbers: [4608] 4608,16 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 #0,4,3 Current State: 16:[99, 37], Operations: ['94-30=64', '64-27=37'] Exploring Operation: 99+37=136, Resulting Numbers: [136] 136,16 unequal: No Solution Exploring Operation: 99-37=62, Resulting Numbers: [62] 62,16 unequal: No Solution Exploring Operation: 99*37=3663, Resulting Numbers: [3663] 3663,16 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 #0,4,2 Current State: 16:[64, 126], Operations: ['94-30=64', '99+27=126'] Exploring Operation: 126-64=62, Resulting Numbers: [62] 62,16 unequal: No Solution Exploring Operation: 64+126=190, Resulting Numbers: [190] 190,16 unequal: No Solution Exploring Operation: 64*126=8064, Resulting Numbers: [8064] 8064,16 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 #0,4,4 Current State: 16:[27, 163], Operations: ['94-30=64', '99+64=163'] Exploring Operation: 163-27=136, Resulting Numbers: [136] 136,16 unequal: No Solution Exploring Operation: 27+163=190, Resulting Numbers: [190] 190,16 unequal: No Solution Exploring Operation: 27*163=4401, Resulting Numbers: [4401] 4401,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 16:[94, 27, 69], Operations: ['99-30=69'] Exploring Operation: 94-69=25, Resulting Numbers: [27, 25] Generated Node #0,1,0: 16:[27, 25] Operation: 94-69=25 Exploring Operation: 69-27=42, Resulting Numbers: [94, 42] Generated Node #0,1,1: 16:[94, 42] Operation: 69-27=42 Exploring Operation: 94+69=163, Resulting Numbers: [27, 163] Generated Node #0,1,2: 16:[27, 163] Operation: 94+69=163 Exploring Operation: 94+27=121, Resulting Numbers: [69, 121] Generated Node #0,1,3: 16:[69, 121] Operation: 94+27=121 Exploring Operation: 94-27=67, Resulting Numbers: [69, 67] Generated Node #0,1,4: 16:[69, 67] Operation: 94-27=67 Moving to Node #0,0 Current State: 16:[30, 94, 72], Operations: ['99-27=72'] Exploring Operation: 72-30=42, Resulting Numbers: [94, 42] Generated Node #0,0,0: 16:[94, 42] Operation: 72-30=42 Exploring Operation: 30+72=102, Resulting Numbers: [94, 102] Generated Node #0,0,1: 16:[94, 102] Operation: 30+72=102 Exploring Operation: 94-30=64, Resulting Numbers: [72, 64] Generated Node #0,0,2: 16:[72, 64] Operation: 94-30=64 Exploring Operation: 30+94=124, Resulting Numbers: [72, 124] Generated Node #0,0,3: 16:[72, 124] Operation: 30+94=124 Exploring Operation: 94-72=22, Resulting Numbers: [30, 22] Generated Node #0,0,4: 16:[30, 22] Operation: 94-72=22 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 16:[30, 22], Operations: ['99-27=72', '94-72=22'] Exploring Operation: 30*22=660, Resulting Numbers: [660] 660,16 unequal: No Solution Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[94, 42], Operations: ['99-27=72', '72-30=42'] Exploring Operation: 94-42=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 94*42=3948, Resulting Numbers: [3948] 3948,16 unequal: No Solution Exploring Operation: 94+42=136, Resulting Numbers: [136] 136,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[72, 64], Operations: ['99-27=72', '94-30=64'] Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 72+64=136, Resulting Numbers: [136] 136,16 unequal: No Solution Exploring Operation: 72*64=4608, Resulting Numbers: [4608] 4608,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[94, 102], Operations: ['99-27=72', '30+72=102'] Exploring Operation: 102-94=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 94+102=196, Resulting Numbers: [196] 196,16 unequal: No Solution Exploring Operation: 94*102=9588, Resulting Numbers: [9588] 9588,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 16:[72, 124], Operations: ['99-27=72', '30+94=124'] Exploring Operation: 72+124=196, Resulting Numbers: [196] 196,16 unequal: No Solution Exploring Operation: 72*124=8928, Resulting Numbers: [8928] 8928,16 unequal: No Solution Exploring Operation: 124-72=52, Resulting Numbers: [52] 52,16 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: 16:[30, 99, 67], Operations: ['94-27=67'] Exploring Operation: 99-67=32, Resulting Numbers: [30, 32] Generated Node #0,3,0: 16:[30, 32] Operation: 99-67=32 Exploring Operation: 99-30=69, Resulting Numbers: [67, 69] Generated Node #0,3,1: 16:[67, 69] Operation: 99-30=69 Exploring Operation: 30+67=97, Resulting Numbers: [99, 97] Generated Node #0,3,2: 16:[99, 97] Operation: 30+67=97 Exploring Operation: 30+99=129, Resulting Numbers: [67, 129] Generated Node #0,3,3: 16:[67, 129] Operation: 30+99=129 Exploring Operation: 67-30=37, Resulting Numbers: [99, 37] Generated Node #0,3,4: 16:[99, 37] Operation: 67-30=37 Moving to Node #0,1,0 Current State: 16:[27, 25], Operations: ['99-30=69', '94-69=25'] Exploring Operation: 27+25=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 27*25=675, Resulting Numbers: [675] 675,16 unequal: No Solution Moving to Node #0,3,0 Current State: 16:[30, 32], Operations: ['94-27=67', '99-67=32'] Exploring Operation: 30*32=960, Resulting Numbers: [960] 960,16 unequal: No Solution Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,16 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,16 unequal: No Solution Moving to Node #0,3,1 Current State: 16:[67, 69], Operations: ['94-27=67', '99-30=69'] Exploring Operation: 67*69=4623, Resulting Numbers: [4623] 4623,16 unequal: No Solution Exploring Operation: 69-67=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 67+69=136, Resulting Numbers: [136] 136,16 unequal: No Solution Moving to Node #0,1,4 Current State: 16:[69, 67], Operations: ['99-30=69', '94-27=67'] Exploring Operation: 69*67=4623, Resulting Numbers: [4623] 4623,16 unequal: No Solution Exploring Operation: 69+67=136, Resulting Numbers: [136] 136,16 unequal: No Solution Exploring Operation: 69-67=2, Resulting Numbers: [2] 2,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[94, 42], Operations: ['99-30=69', '69-27=42'] Exploring Operation: 94-42=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 94+42=136, Resulting Numbers: [136] 136,16 unequal: No Solution Exploring Operation: 94*42=3948, Resulting Numbers: [3948] 3948,16 unequal: No Solution Moving to Node #0,3,4 Current State: 16:[99, 37], Operations: ['94-27=67', '67-30=37'] Exploring Operation: 99*37=3663, Resulting Numbers: [3663] 3663,16 unequal: No Solution Exploring Operation: 99-37=62, Resulting Numbers: [62] 62,16 unequal: No Solution Exploring Operation: 99+37=136, Resulting Numbers: [136] 136,16 unequal: No Solution Moving to Node #0,1,2 Current State: 16:[27, 163], Operations: ['99-30=69', '94+69=163'] Exploring Operation: 163-27=136, Resulting Numbers: [136] 136,16 unequal: No Solution Exploring Operation: 27+163=190, Resulting Numbers: [190] 190,16 unequal: No Solution Exploring Operation: 27*163=4401, Resulting Numbers: [4401] 4401,16 unequal: No Solution Moving to Node #0,1,3 Current State: 16:[69, 121], Operations: ['99-30=69', '94+27=121'] Exploring Operation: 69*121=8349, Resulting Numbers: [8349] 8349,16 unequal: No Solution Exploring Operation: 121-69=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 69+121=190, Resulting Numbers: [190] 190,16 unequal: No Solution Moving to Node #0,3,3 Current State: 16:[67, 129], Operations: ['94-27=67', '30+99=129'] Exploring Operation: 129-67=62, Resulting Numbers: [62] 62,16 unequal: No Solution Exploring Operation: 67+129=196, Resulting Numbers: [196] 196,16 unequal: No Solution Exploring Operation: 67*129=8643, Resulting Numbers: [8643] 8643,16 unequal: No Solution Moving to Node #0,3,2 Current State: 16:[99, 97], Operations: ['94-27=67', '30+67=97'] Exploring Operation: 99-97=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 99*97=9603, Resulting Numbers: [9603] 9603,16 unequal: No Solution Exploring Operation: 99+97=196, Resulting Numbers: [196] 196,16 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 49, 39, 3, 77 ]
47
[ "49-39=10", "3*10=30", "77-30=47" ]
Current State: 47:[49, 39, 3, 77], Operations: [] Exploring Operation: 49-39=10, Resulting Numbers: [3, 77, 10] Generated Node #2: [3, 77, 10] from Operation: 49-39=10 Current State: 47:[3, 77, 10], Operations: ['49-39=10'] Exploring Operation: 3*10=30, Resulting Numbers: [77, 30] Generated Node #3: [77, 30] from Operation: 3*10=30 Current State: 47:[77, 30], Operations: ['49-39=10', '3*10=30'] Exploring Operation: 77-30=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[49, 39, 3, 77], Operations: [] Exploring Operation: 77-3=74, Resulting Numbers: [49, 39, 74] Generated Node #0,0: 47:[49, 39, 74] Operation: 77-3=74 Exploring Operation: 39+3=42, Resulting Numbers: [49, 77, 42] Generated Node #0,1: 47:[49, 77, 42] Operation: 39+3=42 Moving to Node #0,0 Current State: 47:[49, 39, 74], Operations: ['77-3=74'] Exploring Operation: 74-39=35, Resulting Numbers: [49, 35] Generated Node #0,0,0: 47:[49, 35] Operation: 74-39=35 Exploring Operation: 74-49=25, Resulting Numbers: [39, 25] Generated Node #0,0,1: 47:[39, 25] Operation: 74-49=25 Moving to Node #0,1 Current State: 47:[49, 77, 42], Operations: ['39+3=42'] Exploring Operation: 77-49=28, Resulting Numbers: [42, 28] Generated Node #0,1,0: 47:[42, 28] Operation: 77-49=28 Exploring Operation: 77-42=35, Resulting Numbers: [49, 35] Generated Node #0,1,1: 47:[49, 35] Operation: 77-42=35 Moving to Node #0,0,0 Current State: 47:[49, 35], Operations: ['77-3=74', '74-39=35'] Exploring Operation: 49+35=84, Resulting Numbers: [84] 84,47 unequal: No Solution Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[49, 35], Operations: ['39+3=42', '77-42=35'] Exploring Operation: 49+35=84, Resulting Numbers: [84] 84,47 unequal: No Solution Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[42, 28], Operations: ['39+3=42', '77-49=28'] Exploring Operation: 42-28=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 42+28=70, Resulting Numbers: [70] 70,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[39, 25], Operations: ['77-3=74', '74-49=25'] Exploring Operation: 39+25=64, Resulting Numbers: [64] 64,47 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,47 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 37, 28, 15, 66 ]
31
[ "37-15=22", "66/22=3", "28+3=31" ]
Current State: 31:[37, 28, 15, 66], Operations: [] Exploring Operation: 37-15=22, Resulting Numbers: [28, 66, 22] Generated Node #2: [28, 66, 22] from Operation: 37-15=22 Current State: 31:[28, 66, 22], Operations: ['37-15=22'] Exploring Operation: 66/22=3, Resulting Numbers: [28, 3] Generated Node #3: [28, 3] from Operation: 66/22=3 Current State: 31:[28, 3], Operations: ['37-15=22', '66/22=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[37, 28, 15, 66], Operations: [] Exploring Operation: 66-28=38, Resulting Numbers: [37, 15, 38] Generated Node #0,0: 31:[37, 15, 38] Operation: 66-28=38 Exploring Operation: 66-37=29, Resulting Numbers: [28, 15, 29] Generated Node #0,1: 31:[28, 15, 29] Operation: 66-37=29 Exploring Operation: 66-15=51, Resulting Numbers: [37, 28, 51] Generated Node #0,2: 31:[37, 28, 51] Operation: 66-15=51 Moving to Node #0,1 Current State: 31:[28, 15, 29], Operations: ['66-37=29'] Exploring Operation: 28-15=13, Resulting Numbers: [29, 13] Generated Node #0,1,0: 31:[29, 13] Operation: 28-15=13 Exploring Operation: 15+29=44, Resulting Numbers: [28, 44] Generated Node #0,1,1: 31:[28, 44] Operation: 15+29=44 Exploring Operation: 28+15=43, Resulting Numbers: [29, 43] Generated Node #0,1,2: 31:[29, 43] Operation: 28+15=43 Moving to Node #0,0 Current State: 31:[37, 15, 38], Operations: ['66-28=38'] Exploring Operation: 37+15=52, Resulting Numbers: [38, 52] Generated Node #0,0,0: 31:[38, 52] Operation: 37+15=52 Exploring Operation: 37-15=22, Resulting Numbers: [38, 22] Generated Node #0,0,1: 31:[38, 22] Operation: 37-15=22 Exploring Operation: 38-15=23, Resulting Numbers: [37, 23] Generated Node #0,0,2: 31:[37, 23] Operation: 38-15=23 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 31:[37, 23], Operations: ['66-28=38', '38-15=23'] Exploring Operation: 37*23=851, Resulting Numbers: [851] 851,31 unequal: No Solution Exploring Operation: 37+23=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,31 unequal: No Solution No 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: 31:[38, 22], Operations: ['66-28=38', '37-15=22'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,31 unequal: No Solution Exploring Operation: 38+22=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 38*22=836, Resulting Numbers: [836] 836,31 unequal: No Solution No 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: 31:[38, 52], Operations: ['66-28=38', '37+15=52'] Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 38+52=90, Resulting Numbers: [90] 90,31 unequal: No Solution Exploring Operation: 38*52=1976, Resulting Numbers: [1976] 1976,31 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: 31:[37, 28, 51], Operations: ['66-15=51'] Exploring Operation: 51-37=14, Resulting Numbers: [28, 14] Generated Node #0,2,0: 31:[28, 14] Operation: 51-37=14 Exploring Operation: 51-28=23, Resulting Numbers: [37, 23] Generated Node #0,2,1: 31:[37, 23] Operation: 51-28=23 Exploring Operation: 37-28=9, Resulting Numbers: [51, 9] Generated Node #0,2,2: 31:[51, 9] Operation: 37-28=9 Moving to Node #0,1,2 Current State: 31:[29, 43], Operations: ['66-37=29', '28+15=43'] Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 29*43=1247, Resulting Numbers: [1247] 1247,31 unequal: No Solution Exploring Operation: 29+43=72, Resulting Numbers: [72] 72,31 unequal: No Solution Moving to Node #0,2,1 Current State: 31:[37, 23], Operations: ['66-15=51', '51-28=23'] Exploring Operation: 37+23=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 37*23=851, Resulting Numbers: [851] 851,31 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[28, 44], Operations: ['66-37=29', '15+29=44'] Exploring Operation: 28+44=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,31 unequal: No Solution Exploring Operation: 28*44=1232, Resulting Numbers: [1232] 1232,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[29, 13], Operations: ['66-37=29', '28-15=13'] Exploring Operation: 29*13=377, Resulting Numbers: [377] 377,31 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,31 unequal: No Solution Exploring Operation: 29+13=42, Resulting Numbers: [42] 42,31 unequal: No Solution Moving to Node #0,2,0 Current State: 31:[28, 14], Operations: ['66-15=51', '51-37=14'] Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[51, 9], Operations: ['66-15=51', '37-28=9'] Exploring Operation: 51*9=459, Resulting Numbers: [459] 459,31 unequal: No Solution Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 51+9=60, Resulting Numbers: [60] 60,31 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 74, 97, 49, 92 ]
66
[ "97-74=23", "92-49=43", "23+43=66" ]
Current State: 66:[74, 97, 49, 92], Operations: [] Exploring Operation: 97-74=23, Resulting Numbers: [49, 92, 23] Generated Node #2: [49, 92, 23] from Operation: 97-74=23 Current State: 66:[49, 92, 23], Operations: ['97-74=23'] Exploring Operation: 92-49=43, Resulting Numbers: [23, 43] Generated Node #3: [23, 43] from Operation: 92-49=43 Current State: 66:[23, 43], Operations: ['97-74=23', '92-49=43'] Exploring Operation: 23+43=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[74, 97, 49, 92], Operations: [] Exploring Operation: 92-49=43, Resulting Numbers: [74, 97, 43] Generated Node #0,0: 66:[74, 97, 43] Operation: 92-49=43 Exploring Operation: 92-74=18, Resulting Numbers: [97, 49, 18] Generated Node #0,1: 66:[97, 49, 18] Operation: 92-74=18 Exploring Operation: 97-49=48, Resulting Numbers: [74, 92, 48] Generated Node #0,2: 66:[74, 92, 48] Operation: 97-49=48 Exploring Operation: 97-92=5, Resulting Numbers: [74, 49, 5] Generated Node #0,3: 66:[74, 49, 5] Operation: 97-92=5 Exploring Operation: 97-74=23, Resulting Numbers: [49, 92, 23] Generated Node #0,4: 66:[49, 92, 23] Operation: 97-74=23 Moving to Node #0,3 Current State: 66:[74, 49, 5], Operations: ['97-92=5'] Exploring Operation: 49+5=54, Resulting Numbers: [74, 54] Generated Node #0,3,0: 66:[74, 54] Operation: 49+5=54 Exploring Operation: 74-5=69, Resulting Numbers: [49, 69] Generated Node #0,3,1: 66:[49, 69] Operation: 74-5=69 Exploring Operation: 49-5=44, Resulting Numbers: [74, 44] Generated Node #0,3,2: 66:[74, 44] Operation: 49-5=44 Exploring Operation: 74+5=79, Resulting Numbers: [49, 79] Generated Node #0,3,3: 66:[49, 79] Operation: 74+5=79 Exploring Operation: 74-49=25, Resulting Numbers: [5, 25] Generated Node #0,3,4: 66:[5, 25] Operation: 74-49=25 Moving to Node #0,4 Current State: 66:[49, 92, 23], Operations: ['97-74=23'] Exploring Operation: 49+23=72, Resulting Numbers: [92, 72] Generated Node #0,4,0: 66:[92, 72] Operation: 49+23=72 Exploring Operation: 92-49=43, Resulting Numbers: [23, 43] Generated Node #0,4,1: 66:[23, 43] Operation: 92-49=43 Exploring Operation: 92/23=4, Resulting Numbers: [49, 4] Generated Node #0,4,2: 66:[49, 4] Operation: 92/23=4 Exploring Operation: 92-23=69, Resulting Numbers: [49, 69] Generated Node #0,4,3: 66:[49, 69] Operation: 92-23=69 Exploring Operation: 49-23=26, Resulting Numbers: [92, 26] Generated Node #0,4,4: 66:[92, 26] Operation: 49-23=26 Moving to Node #0,0 Current State: 66:[74, 97, 43], Operations: ['92-49=43'] Exploring Operation: 74+43=117, Resulting Numbers: [97, 117] Generated Node #0,0,0: 66:[97, 117] Operation: 74+43=117 Exploring Operation: 97-43=54, Resulting Numbers: [74, 54] Generated Node #0,0,1: 66:[74, 54] Operation: 97-43=54 Exploring Operation: 74-43=31, Resulting Numbers: [97, 31] Generated Node #0,0,2: 66:[97, 31] Operation: 74-43=31 Exploring Operation: 97+43=140, Resulting Numbers: [74, 140] Generated Node #0,0,3: 66:[74, 140] Operation: 97+43=140 Exploring Operation: 97-74=23, Resulting Numbers: [43, 23] Generated Node #0,0,4: 66:[43, 23] Operation: 97-74=23 Moving to Node #0,2 Current State: 66:[74, 92, 48], Operations: ['97-49=48'] Exploring Operation: 92-48=44, Resulting Numbers: [74, 44] Generated Node #0,2,0: 66:[74, 44] Operation: 92-48=44 Exploring Operation: 92-74=18, Resulting Numbers: [48, 18] Generated Node #0,2,1: 66:[48, 18] Operation: 92-74=18 Exploring Operation: 92+48=140, Resulting Numbers: [74, 140] Generated Node #0,2,2: 66:[74, 140] Operation: 92+48=140 Exploring Operation: 74-48=26, Resulting Numbers: [92, 26] Generated Node #0,2,3: 66:[92, 26] Operation: 74-48=26 Exploring Operation: 74+48=122, Resulting Numbers: [92, 122] Generated Node #0,2,4: 66:[92, 122] Operation: 74+48=122 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 66:[74, 44], Operations: ['97-49=48', '92-48=44'] Exploring Operation: 74*44=3256, Resulting Numbers: [3256] 3256,66 unequal: No Solution Exploring Operation: 74+44=118, Resulting Numbers: [118] 118,66 unequal: No Solution Exploring Operation: 74-44=30, Resulting Numbers: [30] 30,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 66:[48, 18], Operations: ['97-49=48', '92-74=18'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 48*18=864, Resulting Numbers: [864] 864,66 unequal: No Solution Exploring Operation: 48+18=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[74, 97, 49, 92], Operations: [] Exploring Operation: 97-49=48, Resulting Numbers: [74, 92, 48] Generated Node #0,2: 66:[74, 92, 48] Operation: 97-49=48 Moving to Node #0,2 Current State: 66:[74, 92, 48], Operations: ['97-49=48'] Exploring Operation: 92-74=18, Resulting Numbers: [48, 18] Generated Node #0,2,1: 66:[48, 18] Operation: 92-74=18 Moving to Node #0,2,1 Current State: 66:[48, 18], Operations: ['97-49=48', '92-74=18'] Exploring Operation: 48+18=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
sum_heuristic
[ 24, 39, 71, 36 ]
96
[ "71-39=32", "36-32=4", "24*4=96" ]
Current State: 96:[24, 39, 71, 36], Operations: [] Exploring Operation: 71-39=32, Resulting Numbers: [24, 36, 32] Generated Node #2: [24, 36, 32] from Operation: 71-39=32 Current State: 96:[24, 36, 32], Operations: ['71-39=32'] Exploring Operation: 36-32=4, Resulting Numbers: [24, 4] Generated Node #3: [24, 4] from Operation: 36-32=4 Current State: 96:[24, 4], Operations: ['71-39=32', '36-32=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[24, 39, 71, 36], Operations: [] Exploring Operation: 71-24=47, Resulting Numbers: [39, 36, 47] Generated Node #0,0: 96:[39, 36, 47] Operation: 71-24=47 Exploring Operation: 71-36=35, Resulting Numbers: [24, 39, 35] Generated Node #0,1: 96:[24, 39, 35] Operation: 71-36=35 Exploring Operation: 24+71=95, Resulting Numbers: [39, 36, 95] Generated Node #0,2: 96:[39, 36, 95] Operation: 24+71=95 Exploring Operation: 39+71=110, Resulting Numbers: [24, 36, 110] Generated Node #0,3: 96:[24, 36, 110] Operation: 39+71=110 Exploring Operation: 71-39=32, Resulting Numbers: [24, 36, 32] Generated Node #0,4: 96:[24, 36, 32] Operation: 71-39=32 Moving to Node #0,4 Current State: 96:[24, 36, 32], Operations: ['71-39=32'] Exploring Operation: 32-24=8, Resulting Numbers: [36, 8] Generated Node #0,4,0: 96:[36, 8] Operation: 32-24=8 Exploring Operation: 24+36=60, Resulting Numbers: [32, 60] Generated Node #0,4,1: 96:[32, 60] Operation: 24+36=60 Exploring Operation: 24+32=56, Resulting Numbers: [36, 56] Generated Node #0,4,2: 96:[36, 56] Operation: 24+32=56 Exploring Operation: 36-32=4, Resulting Numbers: [24, 4] Generated Node #0,4,3: 96:[24, 4] Operation: 36-32=4 Exploring Operation: 36-24=12, Resulting Numbers: [32, 12] Generated Node #0,4,4: 96:[32, 12] Operation: 36-24=12 Moving to Node #0,1 Current State: 96:[24, 39, 35], Operations: ['71-36=35'] Exploring Operation: 24+35=59, Resulting Numbers: [39, 59] Generated Node #0,1,0: 96:[39, 59] Operation: 24+35=59 Exploring Operation: 39-35=4, Resulting Numbers: [24, 4] Generated Node #0,1,1: 96:[24, 4] Operation: 39-35=4 Exploring Operation: 24+39=63, Resulting Numbers: [35, 63] Generated Node #0,1,2: 96:[35, 63] Operation: 24+39=63 Exploring Operation: 35-24=11, Resulting Numbers: [39, 11] Generated Node #0,1,3: 96:[39, 11] Operation: 35-24=11 Exploring Operation: 39-24=15, Resulting Numbers: [35, 15] Generated Node #0,1,4: 96:[35, 15] Operation: 39-24=15 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 96:[24, 4], Operations: ['71-36=35', '39-35=4'] Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,96 unequal: No Solution Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[24, 39, 71, 36], Operations: [] Exploring Operation: 71-36=35, Resulting Numbers: [24, 39, 35] Generated Node #0,1: 96:[24, 39, 35] Operation: 71-36=35 Moving to Node #0,1 Current State: 96:[24, 39, 35], Operations: ['71-36=35'] Exploring Operation: 39-35=4, Resulting Numbers: [24, 4] Generated Node #0,1,1: 96:[24, 4] Operation: 39-35=4 Moving to Node #0,1,1 Current State: 96:[24, 4], Operations: ['71-36=35', '39-35=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 92, 24, 86, 42 ]
72
[ "92+24=116", "86-42=44", "116-44=72" ]
Current State: 72:[92, 24, 86, 42], Operations: [] Exploring Operation: 92+24=116, Resulting Numbers: [86, 42, 116] Generated Node #2: [86, 42, 116] from Operation: 92+24=116 Current State: 72:[86, 42, 116], Operations: ['92+24=116'] Exploring Operation: 86-42=44, Resulting Numbers: [116, 44] Generated Node #3: [116, 44] from Operation: 86-42=44 Current State: 72:[116, 44], Operations: ['92+24=116', '86-42=44'] Exploring Operation: 116-44=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[92, 24, 86, 42], Operations: [] Exploring Operation: 92-42=50, Resulting Numbers: [24, 86, 50] Generated Node #0,0: 72:[24, 86, 50] Operation: 92-42=50 Exploring Operation: 92-86=6, Resulting Numbers: [24, 42, 6] Generated Node #0,1: 72:[24, 42, 6] Operation: 92-86=6 Exploring Operation: 92-24=68, Resulting Numbers: [86, 42, 68] Generated Node #0,2: 72:[86, 42, 68] Operation: 92-24=68 Exploring Operation: 86-42=44, Resulting Numbers: [92, 24, 44] Generated Node #0,3: 72:[92, 24, 44] Operation: 86-42=44 Exploring Operation: 42-24=18, Resulting Numbers: [92, 86, 18] Generated Node #0,4: 72:[92, 86, 18] Operation: 42-24=18 Moving to Node #0,1 Current State: 72:[24, 42, 6], Operations: ['92-86=6'] Exploring Operation: 42-24=18, Resulting Numbers: [6, 18] Generated Node #0,1,0: 72:[6, 18] Operation: 42-24=18 Exploring Operation: 42-6=36, Resulting Numbers: [24, 36] Generated Node #0,1,1: 72:[24, 36] Operation: 42-6=36 Exploring Operation: 42/6=7, Resulting Numbers: [24, 7] Generated Node #0,1,2: 72:[24, 7] Operation: 42/6=7 Exploring Operation: 24+42=66, Resulting Numbers: [6, 66] Generated Node #0,1,3: 72:[6, 66] Operation: 24+42=66 Exploring Operation: 24-6=18, Resulting Numbers: [42, 18] Generated Node #0,1,4: 72:[42, 18] Operation: 24-6=18 Moving to Node #0,2 Current State: 72:[86, 42, 68], Operations: ['92-24=68'] Exploring Operation: 86+42=128, Resulting Numbers: [68, 128] Generated Node #0,2,0: 72:[68, 128] Operation: 86+42=128 Exploring Operation: 42+68=110, Resulting Numbers: [86, 110] Generated Node #0,2,1: 72:[86, 110] Operation: 42+68=110 Exploring Operation: 86-42=44, Resulting Numbers: [68, 44] Generated Node #0,2,2: 72:[68, 44] Operation: 86-42=44 Exploring Operation: 68-42=26, Resulting Numbers: [86, 26] Generated Node #0,2,3: 72:[86, 26] Operation: 68-42=26 Exploring Operation: 86-68=18, Resulting Numbers: [42, 18] Generated Node #0,2,4: 72:[42, 18] Operation: 86-68=18 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 72:[42, 18], Operations: ['92-24=68', '86-68=18'] Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,72 unequal: No Solution Exploring Operation: 42+18=60, Resulting Numbers: [60] 60,72 unequal: No Solution Exploring Operation: 42*18=756, Resulting Numbers: [756] 756,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 72:[68, 44], Operations: ['92-24=68', '86-42=44'] Exploring Operation: 68*44=2992, Resulting Numbers: [2992] 2992,72 unequal: No Solution Exploring Operation: 68-44=24, Resulting Numbers: [24] 24,72 unequal: No Solution Exploring Operation: 68+44=112, Resulting Numbers: [112] 112,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 72:[86, 26], Operations: ['92-24=68', '68-42=26'] Exploring Operation: 86*26=2236, Resulting Numbers: [2236] 2236,72 unequal: No Solution Exploring Operation: 86+26=112, Resulting Numbers: [112] 112,72 unequal: No Solution Exploring Operation: 86-26=60, Resulting Numbers: [60] 60,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 72:[86, 110], Operations: ['92-24=68', '42+68=110'] Exploring Operation: 110-86=24, Resulting Numbers: [24] 24,72 unequal: No Solution Exploring Operation: 86+110=196, Resulting Numbers: [196] 196,72 unequal: No Solution Exploring Operation: 86*110=9460, Resulting Numbers: [9460] 9460,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 72:[68, 128], Operations: ['92-24=68', '86+42=128'] Exploring Operation: 68*128=8704, Resulting Numbers: [8704] 8704,72 unequal: No Solution Exploring Operation: 128-68=60, Resulting Numbers: [60] 60,72 unequal: No Solution Exploring Operation: 68+128=196, Resulting Numbers: [196] 196,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 72:[24, 86, 50], Operations: ['92-42=50'] Exploring Operation: 24+86=110, Resulting Numbers: [50, 110] Generated Node #0,0,0: 72:[50, 110] Operation: 24+86=110 Exploring Operation: 50-24=26, Resulting Numbers: [86, 26] Generated Node #0,0,1: 72:[86, 26] Operation: 50-24=26 Exploring Operation: 24+50=74, Resulting Numbers: [86, 74] Generated Node #0,0,2: 72:[86, 74] Operation: 24+50=74 Exploring Operation: 86-50=36, Resulting Numbers: [24, 36] Generated Node #0,0,3: 72:[24, 36] Operation: 86-50=36 Exploring Operation: 86-24=62, Resulting Numbers: [50, 62] Generated Node #0,0,4: 72:[50, 62] Operation: 86-24=62 Moving to Node #0,3 Current State: 72:[92, 24, 44], Operations: ['86-42=44'] Exploring Operation: 92-44=48, Resulting Numbers: [24, 48] Generated Node #0,3,0: 72:[24, 48] Operation: 92-44=48 Exploring Operation: 24+44=68, Resulting Numbers: [92, 68] Generated Node #0,3,1: 72:[92, 68] Operation: 24+44=68 Exploring Operation: 44-24=20, Resulting Numbers: [92, 20] Generated Node #0,3,2: 72:[92, 20] Operation: 44-24=20 Exploring Operation: 92-24=68, Resulting Numbers: [44, 68] Generated Node #0,3,3: 72:[44, 68] Operation: 92-24=68 Exploring Operation: 92+24=116, Resulting Numbers: [44, 116] Generated Node #0,3,4: 72:[44, 116] Operation: 92+24=116 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 72:[24, 48], Operations: ['86-42=44', '92-44=48'] Exploring Operation: 24*48=1152, Resulting Numbers: [1152] 1152,72 unequal: No Solution Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,72 unequal: No Solution Exploring Operation: 24+48=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[92, 24, 86, 42], Operations: [] Exploring Operation: 86-42=44, Resulting Numbers: [92, 24, 44] Generated Node #0,3: 72:[92, 24, 44] Operation: 86-42=44 Moving to Node #0,3 Current State: 72:[92, 24, 44], Operations: ['86-42=44'] Exploring Operation: 92-44=48, Resulting Numbers: [24, 48] Generated Node #0,3,0: 72:[24, 48] Operation: 92-44=48 Moving to Node #0,3,0 Current State: 72:[24, 48], Operations: ['86-42=44', '92-44=48'] Exploring Operation: 24+48=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
sum_heuristic
[ 10, 40, 25, 37 ]
42
[ "40-10=30", "37-25=12", "30+12=42" ]
Current State: 42:[10, 40, 25, 37], Operations: [] Exploring Operation: 40-10=30, Resulting Numbers: [25, 37, 30] Generated Node #2: [25, 37, 30] from Operation: 40-10=30 Current State: 42:[25, 37, 30], Operations: ['40-10=30'] Exploring Operation: 37-25=12, Resulting Numbers: [30, 12] Generated Node #3: [30, 12] from Operation: 37-25=12 Current State: 42:[30, 12], Operations: ['40-10=30', '37-25=12'] Exploring Operation: 30+12=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[10, 40, 25, 37], Operations: [] Exploring Operation: 40-37=3, Resulting Numbers: [10, 25, 3] Generated Node #0,0: 42:[10, 25, 3] Operation: 40-37=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[10, 25, 3], Operations: ['40-37=3'] Exploring Operation: 25-10=15, Resulting Numbers: [3, 15] Generated Node #0,0,0: 42:[3, 15] Operation: 25-10=15 Moving to Node #0,0,0 Current State: 42:[3, 15], Operations: ['40-37=3', '25-10=15'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 68, 89, 84, 90 ]
17
[ "68+89=157", "84+90=174", "174-157=17" ]
Current State: 17:[68, 89, 84, 90], Operations: [] Exploring Operation: 68+89=157, Resulting Numbers: [84, 90, 157] Generated Node #2: [84, 90, 157] from Operation: 68+89=157 Current State: 17:[84, 90, 157], Operations: ['68+89=157'] Exploring Operation: 84+90=174, Resulting Numbers: [157, 174] Generated Node #3: [157, 174] from Operation: 84+90=174 Current State: 17:[157, 174], Operations: ['68+89=157', '84+90=174'] Exploring Operation: 174-157=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[68, 89, 84, 90], Operations: [] Exploring Operation: 89-84=5, Resulting Numbers: [68, 90, 5] Generated Node #0,0: 17:[68, 90, 5] Operation: 89-84=5 Exploring Operation: 90-89=1, Resulting Numbers: [68, 84, 1] Generated Node #0,1: 17:[68, 84, 1] Operation: 90-89=1 Exploring Operation: 90-84=6, Resulting Numbers: [68, 89, 6] Generated Node #0,2: 17:[68, 89, 6] Operation: 90-84=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[68, 84, 1], Operations: ['90-89=1'] Exploring Operation: 68-1=67, Resulting Numbers: [84, 67] Generated Node #0,1,0: 17:[84, 67] Operation: 68-1=67 Exploring Operation: 84-68=16, Resulting Numbers: [1, 16] Generated Node #0,1,1: 17:[1, 16] Operation: 84-68=16 Exploring Operation: 84-1=83, Resulting Numbers: [68, 83] Generated Node #0,1,2: 17:[68, 83] Operation: 84-1=83 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 17:[1, 16], Operations: ['90-89=1', '84-68=16'] Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[68, 89, 84, 90], Operations: [] Exploring Operation: 90-89=1, Resulting Numbers: [68, 84, 1] Generated Node #0,1: 17:[68, 84, 1] Operation: 90-89=1 Moving to Node #0,1 Current State: 17:[68, 84, 1], Operations: ['90-89=1'] Exploring Operation: 84-68=16, Resulting Numbers: [1, 16] Generated Node #0,1,1: 17:[1, 16] Operation: 84-68=16 Moving to Node #0,1,1 Current State: 17:[1, 16], Operations: ['90-89=1', '84-68=16'] Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 21, 52, 49, 23 ]
55
[ "23-21=2", "52*2=104", "104-49=55" ]
Current State: 55:[21, 52, 49, 23], Operations: [] Exploring Operation: 23-21=2, Resulting Numbers: [52, 49, 2] Generated Node #2: [52, 49, 2] from Operation: 23-21=2 Current State: 55:[52, 49, 2], Operations: ['23-21=2'] Exploring Operation: 52*2=104, Resulting Numbers: [49, 104] Generated Node #3: [49, 104] from Operation: 52*2=104 Current State: 55:[49, 104], Operations: ['23-21=2', '52*2=104'] Exploring Operation: 104-49=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[21, 52, 49, 23], Operations: [] Exploring Operation: 52-49=3, Resulting Numbers: [21, 23, 3] Generated Node #0,0: 55:[21, 23, 3] Operation: 52-49=3 Exploring Operation: 21+23=44, Resulting Numbers: [52, 49, 44] Generated Node #0,1: 55:[52, 49, 44] Operation: 21+23=44 Exploring Operation: 23-21=2, Resulting Numbers: [52, 49, 2] Generated Node #0,2: 55:[52, 49, 2] Operation: 23-21=2 Exploring Operation: 49-23=26, Resulting Numbers: [21, 52, 26] Generated Node #0,3: 55:[21, 52, 26] Operation: 49-23=26 Moving to Node #0,2 Current State: 55:[52, 49, 2], Operations: ['23-21=2'] Exploring Operation: 52-49=3, Resulting Numbers: [2, 3] Generated Node #0,2,0: 55:[2, 3] Operation: 52-49=3 Exploring Operation: 49+2=51, Resulting Numbers: [52, 51] Generated Node #0,2,1: 55:[52, 51] Operation: 49+2=51 Exploring Operation: 52-2=50, Resulting Numbers: [49, 50] Generated Node #0,2,2: 55:[49, 50] Operation: 52-2=50 Exploring Operation: 52+2=54, Resulting Numbers: [49, 54] Generated Node #0,2,3: 55:[49, 54] Operation: 52+2=54 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 55:[2, 3], Operations: ['23-21=2', '52-49=3'] Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,55 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,55 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:[52, 51], Operations: ['23-21=2', '49+2=51'] Exploring Operation: 52+51=103, Resulting Numbers: [103] 103,55 unequal: No Solution Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 52*51=2652, Resulting Numbers: [2652] 2652,55 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:[49, 54], Operations: ['23-21=2', '52+2=54'] Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 49*54=2646, Resulting Numbers: [2646] 2646,55 unequal: No Solution Exploring Operation: 49+54=103, Resulting Numbers: [103] 103,55 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 #0,2,2 Current State: 55:[49, 50], Operations: ['23-21=2', '52-2=50'] Exploring Operation: 49+50=99, Resulting Numbers: [99] 99,55 unequal: No Solution Exploring Operation: 50-49=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 49*50=2450, Resulting Numbers: [2450] 2450,55 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: 55:[52, 49, 44], Operations: ['21+23=44'] Exploring Operation: 49-44=5, Resulting Numbers: [52, 5] Generated Node #0,1,0: 55:[52, 5] Operation: 49-44=5 Exploring Operation: 52-44=8, Resulting Numbers: [49, 8] Generated Node #0,1,1: 55:[49, 8] Operation: 52-44=8 Exploring Operation: 49+44=93, Resulting Numbers: [52, 93] Generated Node #0,1,2: 55:[52, 93] Operation: 49+44=93 Exploring Operation: 52-49=3, Resulting Numbers: [44, 3] Generated Node #0,1,3: 55:[44, 3] Operation: 52-49=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[52, 5], Operations: ['21+23=44', '49-44=5'] Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,55 unequal: No Solution Exploring Operation: 52+5=57, Resulting Numbers: [57] 57,55 unequal: No Solution Exploring Operation: 52*5=260, Resulting Numbers: [260] 260,55 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 #0,1,1 Current State: 55:[49, 8], Operations: ['21+23=44', '52-44=8'] Exploring Operation: 49*8=392, Resulting Numbers: [392] 392,55 unequal: No Solution Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,55 unequal: No Solution Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,55 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 #0,1,3 Current State: 55:[44, 3], Operations: ['21+23=44', '52-49=3'] Exploring Operation: 44*3=132, Resulting Numbers: [132] 132,55 unequal: No Solution Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,55 unequal: No Solution Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,55 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 #0,1,2 Current State: 55:[52, 93], Operations: ['21+23=44', '49+44=93'] Exploring Operation: 52+93=145, Resulting Numbers: [145] 145,55 unequal: No Solution Exploring Operation: 52*93=4836, Resulting Numbers: [4836] 4836,55 unequal: No Solution Exploring Operation: 93-52=41, Resulting Numbers: [41] 41,55 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: 55:[21, 23, 3], Operations: ['52-49=3'] Exploring Operation: 21/3=7, Resulting Numbers: [23, 7] Generated Node #0,0,0: 55:[23, 7] Operation: 21/3=7 Exploring Operation: 21-3=18, Resulting Numbers: [23, 18] Generated Node #0,0,1: 55:[23, 18] Operation: 21-3=18 Exploring Operation: 23-21=2, Resulting Numbers: [3, 2] Generated Node #0,0,2: 55:[3, 2] Operation: 23-21=2 Exploring Operation: 21+23=44, Resulting Numbers: [3, 44] Generated Node #0,0,3: 55:[3, 44] Operation: 21+23=44 Moving to Node #0,3 Current State: 55:[21, 52, 26], Operations: ['49-23=26'] Exploring Operation: 21+26=47, Resulting Numbers: [52, 47] Generated Node #0,3,0: 55:[52, 47] Operation: 21+26=47 Exploring Operation: 26-21=5, Resulting Numbers: [52, 5] Generated Node #0,3,1: 55:[52, 5] Operation: 26-21=5 Exploring Operation: 52-26=26, Resulting Numbers: [21, 26] Generated Node #0,3,2: 55:[21, 26] Operation: 52-26=26 Exploring Operation: 52/26=2, Resulting Numbers: [21, 2] Generated Node #0,3,3: 55:[21, 2] Operation: 52/26=2 Moving to Node #0,3,1 Current State: 55:[52, 5], Operations: ['49-23=26', '26-21=5'] Exploring Operation: 52*5=260, Resulting Numbers: [260] 260,55 unequal: No Solution Exploring Operation: 52+5=57, Resulting Numbers: [57] 57,55 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[3, 2], Operations: ['52-49=3', '23-21=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,55 unequal: No Solution Moving to Node #0,3,0 Current State: 55:[52, 47], Operations: ['49-23=26', '21+26=47'] Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 52*47=2444, Resulting Numbers: [2444] 2444,55 unequal: No Solution Exploring Operation: 52+47=99, Resulting Numbers: [99] 99,55 unequal: No Solution Moving to Node #0,3,3 Current State: 55:[21, 2], Operations: ['49-23=26', '52/26=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,55 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,55 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,55 unequal: No Solution Moving to Node #0,0,3 Current State: 55:[3, 44], Operations: ['52-49=3', '21+23=44'] Exploring Operation: 3+44=47, Resulting Numbers: [47] 47,55 unequal: No Solution Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,55 unequal: No Solution Exploring Operation: 3*44=132, Resulting Numbers: [132] 132,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[23, 7], Operations: ['52-49=3', '21/3=7'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,55 unequal: No Solution Exploring Operation: 23*7=161, Resulting Numbers: [161] 161,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[23, 18], Operations: ['52-49=3', '21-3=18'] Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 23*18=414, Resulting Numbers: [414] 414,55 unequal: No Solution Exploring Operation: 23+18=41, Resulting Numbers: [41] 41,55 unequal: No Solution Moving to Node #0,3,2 Current State: 55:[21, 26], Operations: ['49-23=26', '52-26=26'] Exploring Operation: 21+26=47, Resulting Numbers: [47] 47,55 unequal: No Solution Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 21*26=546, Resulting Numbers: [546] 546,55 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 5, 68, 12, 26 ]
49
[ "68-5=63", "26-12=14", "63-14=49" ]
Current State: 49:[5, 68, 12, 26], Operations: [] Exploring Operation: 68-5=63, Resulting Numbers: [12, 26, 63] Generated Node #2: [12, 26, 63] from Operation: 68-5=63 Current State: 49:[12, 26, 63], Operations: ['68-5=63'] Exploring Operation: 26-12=14, Resulting Numbers: [63, 14] Generated Node #3: [63, 14] from Operation: 26-12=14 Current State: 49:[63, 14], Operations: ['68-5=63', '26-12=14'] Exploring Operation: 63-14=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[5, 68, 12, 26], Operations: [] Exploring Operation: 68-12=56, Resulting Numbers: [5, 26, 56] Generated Node #0,0: 49:[5, 26, 56] Operation: 68-12=56 Exploring Operation: 26-12=14, Resulting Numbers: [5, 68, 14] Generated Node #0,1: 49:[5, 68, 14] Operation: 26-12=14 Exploring Operation: 68-26=42, Resulting Numbers: [5, 12, 42] Generated Node #0,2: 49:[5, 12, 42] Operation: 68-26=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[5, 12, 42], Operations: ['68-26=42'] Exploring Operation: 5+42=47, Resulting Numbers: [12, 47] Generated Node #0,2,0: 49:[12, 47] Operation: 5+42=47 Exploring Operation: 12+42=54, Resulting Numbers: [5, 54] Generated Node #0,2,1: 49:[5, 54] Operation: 12+42=54 Exploring Operation: 12-5=7, Resulting Numbers: [42, 7] Generated Node #0,2,2: 49:[42, 7] Operation: 12-5=7 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 49:[12, 47], Operations: ['68-26=42', '5+42=47'] Exploring Operation: 12+47=59, Resulting Numbers: [59] 59,49 unequal: No Solution Exploring Operation: 12*47=564, Resulting Numbers: [564] 564,49 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,49 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 #0,2,1 Current State: 49:[5, 54], Operations: ['68-26=42', '12+42=54'] Exploring Operation: 5*54=270, Resulting Numbers: [270] 270,49 unequal: No Solution Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[5, 68, 12, 26], Operations: [] Exploring Operation: 68-26=42, Resulting Numbers: [5, 12, 42] Generated Node #0,2: 49:[5, 12, 42] Operation: 68-26=42 Moving to Node #0,2 Current State: 49:[5, 12, 42], Operations: ['68-26=42'] Exploring Operation: 12+42=54, Resulting Numbers: [5, 54] Generated Node #0,2,1: 49:[5, 54] Operation: 12+42=54 Moving to Node #0,2,1 Current State: 49:[5, 54], Operations: ['68-26=42', '12+42=54'] Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 14, 80, 81, 16 ]
79
[ "16-14=2", "80*2=160", "160-81=79" ]
Current State: 79:[14, 80, 81, 16], Operations: [] Exploring Operation: 16-14=2, Resulting Numbers: [80, 81, 2] Generated Node #2: [80, 81, 2] from Operation: 16-14=2 Current State: 79:[80, 81, 2], Operations: ['16-14=2'] Exploring Operation: 80*2=160, Resulting Numbers: [81, 160] Generated Node #3: [81, 160] from Operation: 80*2=160 Current State: 79:[81, 160], Operations: ['16-14=2', '80*2=160'] Exploring Operation: 160-81=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[14, 80, 81, 16], Operations: [] Exploring Operation: 14+81=95, Resulting Numbers: [80, 16, 95] Generated Node #0,0: 79:[80, 16, 95] Operation: 14+81=95 Exploring Operation: 14+80=94, Resulting Numbers: [81, 16, 94] Generated Node #0,1: 79:[81, 16, 94] Operation: 14+80=94 Exploring Operation: 81-14=67, Resulting Numbers: [80, 16, 67] Generated Node #0,2: 79:[80, 16, 67] Operation: 81-14=67 Exploring Operation: 14+16=30, Resulting Numbers: [80, 81, 30] Generated Node #0,3: 79:[80, 81, 30] Operation: 14+16=30 Exploring Operation: 80-14=66, Resulting Numbers: [81, 16, 66] Generated Node #0,4: 79:[81, 16, 66] Operation: 80-14=66 Moving to Node #0,3 Current State: 79:[80, 81, 30], Operations: ['14+16=30'] Exploring Operation: 81-30=51, Resulting Numbers: [80, 51] Generated Node #0,3,0: 79:[80, 51] Operation: 81-30=51 Exploring Operation: 80-30=50, Resulting Numbers: [81, 50] Generated Node #0,3,1: 79:[81, 50] Operation: 80-30=50 Exploring Operation: 81-80=1, Resulting Numbers: [30, 1] Generated Node #0,3,2: 79:[30, 1] Operation: 81-80=1 Exploring Operation: 81+30=111, Resulting Numbers: [80, 111] Generated Node #0,3,3: 79:[80, 111] Operation: 81+30=111 Exploring Operation: 80+30=110, Resulting Numbers: [81, 110] Generated Node #0,3,4: 79:[81, 110] Operation: 80+30=110 Moving to Node #0,2 Current State: 79:[80, 16, 67], Operations: ['81-14=67'] Exploring Operation: 80+16=96, Resulting Numbers: [67, 96] Generated Node #0,2,0: 79:[67, 96] Operation: 80+16=96 Exploring Operation: 16+67=83, Resulting Numbers: [80, 83] Generated Node #0,2,1: 79:[80, 83] Operation: 16+67=83 Exploring Operation: 80-16=64, Resulting Numbers: [67, 64] Generated Node #0,2,2: 79:[67, 64] Operation: 80-16=64 Exploring Operation: 80/16=5, Resulting Numbers: [67, 5] Generated Node #0,2,3: 79:[67, 5] Operation: 80/16=5 Exploring Operation: 67-16=51, Resulting Numbers: [80, 51] Generated Node #0,2,4: 79:[80, 51] Operation: 67-16=51 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[80, 83], Operations: ['81-14=67', '16+67=83'] Exploring Operation: 83-80=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 80+83=163, Resulting Numbers: [163] 163,79 unequal: No Solution Exploring Operation: 80*83=6640, Resulting Numbers: [6640] 6640,79 unequal: No Solution No 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: 79:[67, 64], Operations: ['81-14=67', '80-16=64'] Exploring Operation: 67+64=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 67*64=4288, Resulting Numbers: [4288] 4288,79 unequal: No Solution Exploring Operation: 67-64=3, Resulting Numbers: [3] 3,79 unequal: No Solution No 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: 79:[67, 96], Operations: ['81-14=67', '80+16=96'] Exploring Operation: 67*96=6432, Resulting Numbers: [6432] 6432,79 unequal: No Solution Exploring Operation: 67+96=163, Resulting Numbers: [163] 163,79 unequal: No Solution Exploring Operation: 96-67=29, Resulting Numbers: [29] 29,79 unequal: No Solution No 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: 79:[80, 51], Operations: ['81-14=67', '67-16=51'] Exploring Operation: 80-51=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 80+51=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 80*51=4080, Resulting Numbers: [4080] 4080,79 unequal: No Solution No 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: 79:[67, 5], Operations: ['81-14=67', '80/16=5'] Exploring Operation: 67+5=72, Resulting Numbers: [72] 72,79 unequal: No Solution Exploring Operation: 67*5=335, Resulting Numbers: [335] 335,79 unequal: No Solution Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,79 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: 79:[81, 16, 66], Operations: ['80-14=66'] Exploring Operation: 66-16=50, Resulting Numbers: [81, 50] Generated Node #0,4,0: 79:[81, 50] Operation: 66-16=50 Exploring Operation: 16+66=82, Resulting Numbers: [81, 82] Generated Node #0,4,1: 79:[81, 82] Operation: 16+66=82 Exploring Operation: 81-16=65, Resulting Numbers: [66, 65] Generated Node #0,4,2: 79:[66, 65] Operation: 81-16=65 Exploring Operation: 81+16=97, Resulting Numbers: [66, 97] Generated Node #0,4,3: 79:[66, 97] Operation: 81+16=97 Exploring Operation: 81-66=15, Resulting Numbers: [16, 15] Generated Node #0,4,4: 79:[16, 15] Operation: 81-66=15 Moving to Node #0,0 Current State: 79:[80, 16, 95], Operations: ['14+81=95'] Exploring Operation: 80/16=5, Resulting Numbers: [95, 5] Generated Node #0,0,0: 79:[95, 5] Operation: 80/16=5 Exploring Operation: 95-16=79, Resulting Numbers: [80, 79] Generated Node #0,0,1: 79:[80, 79] Operation: 95-16=79 Exploring Operation: 80+16=96, Resulting Numbers: [95, 96] Generated Node #0,0,2: 79:[95, 96] Operation: 80+16=96 Exploring Operation: 16+95=111, Resulting Numbers: [80, 111] Generated Node #0,0,3: 79:[80, 111] Operation: 16+95=111 Exploring Operation: 80-16=64, Resulting Numbers: [95, 64] Generated Node #0,0,4: 79:[95, 64] Operation: 80-16=64 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[80, 79], Operations: ['14+81=95', '95-16=79'] Exploring Operation: 80+79=159, Resulting Numbers: [159] 159,79 unequal: No Solution Exploring Operation: 80*79=6320, Resulting Numbers: [6320] 6320,79 unequal: No Solution Exploring Operation: 80-79=1, Resulting Numbers: [1] 1,79 unequal: No Solution No 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: 79:[95, 64], Operations: ['14+81=95', '80-16=64'] Exploring Operation: 95+64=159, Resulting Numbers: [159] 159,79 unequal: No Solution Exploring Operation: 95*64=6080, Resulting Numbers: [6080] 6080,79 unequal: No Solution Exploring Operation: 95-64=31, Resulting Numbers: [31] 31,79 unequal: No Solution No 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: 79:[95, 96], Operations: ['14+81=95', '80+16=96'] Exploring Operation: 96-95=1, Resulting Numbers: [1] 1,79 unequal: No Solution Exploring Operation: 95+96=191, Resulting Numbers: [191] 191,79 unequal: No Solution Exploring Operation: 95*96=9120, Resulting Numbers: [9120] 9120,79 unequal: No Solution No 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: 79:[80, 111], Operations: ['14+81=95', '16+95=111'] Exploring Operation: 111-80=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 80*111=8880, Resulting Numbers: [8880] 8880,79 unequal: No Solution Exploring Operation: 80+111=191, Resulting Numbers: [191] 191,79 unequal: No Solution No 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: 79:[95, 5], Operations: ['14+81=95', '80/16=5'] Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,79 unequal: No Solution Exploring Operation: 95-5=90, Resulting Numbers: [90] 90,79 unequal: No Solution Exploring Operation: 95*5=475, Resulting Numbers: [475] 475,79 unequal: No Solution Exploring Operation: 95+5=100, Resulting Numbers: [100] 100,79 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: 79:[81, 16, 94], Operations: ['14+80=94'] Exploring Operation: 94-81=13, Resulting Numbers: [16, 13] Generated Node #0,1,0: 79:[16, 13] Operation: 94-81=13 Exploring Operation: 81-16=65, Resulting Numbers: [94, 65] Generated Node #0,1,1: 79:[94, 65] Operation: 81-16=65 Exploring Operation: 94-16=78, Resulting Numbers: [81, 78] Generated Node #0,1,2: 79:[81, 78] Operation: 94-16=78 Exploring Operation: 16+94=110, Resulting Numbers: [81, 110] Generated Node #0,1,3: 79:[81, 110] Operation: 16+94=110 Exploring Operation: 81+16=97, Resulting Numbers: [94, 97] Generated Node #0,1,4: 79:[94, 97] Operation: 81+16=97 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[81, 78], Operations: ['14+80=94', '94-16=78'] Exploring Operation: 81-78=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 81*78=6318, Resulting Numbers: [6318] 6318,79 unequal: No Solution Exploring Operation: 81+78=159, Resulting Numbers: [159] 159,79 unequal: No Solution No 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: 79:[94, 65], Operations: ['14+80=94', '81-16=65'] Exploring Operation: 94*65=6110, Resulting Numbers: [6110] 6110,79 unequal: No Solution Exploring Operation: 94-65=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 94+65=159, Resulting Numbers: [159] 159,79 unequal: No Solution No 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: 79:[81, 110], Operations: ['14+80=94', '16+94=110'] Exploring Operation: 110-81=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 81+110=191, Resulting Numbers: [191] 191,79 unequal: No Solution Exploring Operation: 81*110=8910, Resulting Numbers: [8910] 8910,79 unequal: No Solution No 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: 79:[94, 97], Operations: ['14+80=94', '81+16=97'] Exploring Operation: 97-94=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 94*97=9118, Resulting Numbers: [9118] 9118,79 unequal: No Solution Exploring Operation: 94+97=191, Resulting Numbers: [191] 191,79 unequal: No Solution No 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: 79:[16, 13], Operations: ['14+80=94', '94-81=13'] Exploring Operation: 16+13=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 16*13=208, Resulting Numbers: [208] 208,79 unequal: No Solution Exploring Operation: 16-13=3, Resulting Numbers: [3] 3,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,1 Current State: 79:[81, 82], Operations: ['80-14=66', '16+66=82'] Exploring Operation: 82-81=1, Resulting Numbers: [1] 1,79 unequal: No Solution Exploring Operation: 81*82=6642, Resulting Numbers: [6642] 6642,79 unequal: No Solution Exploring Operation: 81+82=163, Resulting Numbers: [163] 163,79 unequal: No Solution Moving to Node #0,4,2 Current State: 79:[66, 65], Operations: ['80-14=66', '81-16=65'] Exploring Operation: 66+65=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 66*65=4290, Resulting Numbers: [4290] 4290,79 unequal: No Solution Exploring Operation: 66-65=1, Resulting Numbers: [1] 1,79 unequal: No Solution Moving to Node #0,3,0 Current State: 79:[80, 51], Operations: ['14+16=30', '81-30=51'] Exploring Operation: 80-51=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 80+51=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 80*51=4080, Resulting Numbers: [4080] 4080,79 unequal: No Solution Moving to Node #0,4,3 Current State: 79:[66, 97], Operations: ['80-14=66', '81+16=97'] Exploring Operation: 97-66=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 66+97=163, Resulting Numbers: [163] 163,79 unequal: No Solution Exploring Operation: 66*97=6402, Resulting Numbers: [6402] 6402,79 unequal: No Solution Moving to Node #0,3,1 Current State: 79:[81, 50], Operations: ['14+16=30', '80-30=50'] Exploring Operation: 81*50=4050, Resulting Numbers: [4050] 4050,79 unequal: No Solution Exploring Operation: 81+50=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 81-50=31, Resulting Numbers: [31] 31,79 unequal: No Solution Moving to Node #0,4,0 Current State: 79:[81, 50], Operations: ['80-14=66', '66-16=50'] Exploring Operation: 81+50=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 81*50=4050, Resulting Numbers: [4050] 4050,79 unequal: No Solution Exploring Operation: 81-50=31, Resulting Numbers: [31] 31,79 unequal: No Solution Moving to Node #0,3,3 Current State: 79:[80, 111], Operations: ['14+16=30', '81+30=111'] Exploring Operation: 80*111=8880, Resulting Numbers: [8880] 8880,79 unequal: No Solution Exploring Operation: 111-80=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 80+111=191, Resulting Numbers: [191] 191,79 unequal: No Solution Moving to Node #0,3,4 Current State: 79:[81, 110], Operations: ['14+16=30', '80+30=110'] Exploring Operation: 81+110=191, Resulting Numbers: [191] 191,79 unequal: No Solution Exploring Operation: 110-81=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 81*110=8910, Resulting Numbers: [8910] 8910,79 unequal: No Solution Moving to Node #0,4,4 Current State: 79:[16, 15], Operations: ['80-14=66', '81-66=15'] Exploring Operation: 16*15=240, Resulting Numbers: [240] 240,79 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,79 unequal: No Solution Exploring Operation: 16+15=31, Resulting Numbers: [31] 31,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[30, 1], Operations: ['14+16=30', '81-80=1'] Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 30/1=30, Resulting Numbers: [30] 30,79 unequal: No Solution Exploring Operation: 30*1=30, Resulting Numbers: [30] 30,79 unequal: No Solution Exploring Operation: 30+1=31, Resulting Numbers: [31] 31,79 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 35, 59, 5, 42 ]
78
[ "59-35=24", "5*24=120", "120-42=78" ]
Current State: 78:[35, 59, 5, 42], Operations: [] Exploring Operation: 59-35=24, Resulting Numbers: [5, 42, 24] Generated Node #2: [5, 42, 24] from Operation: 59-35=24 Current State: 78:[5, 42, 24], Operations: ['59-35=24'] Exploring Operation: 5*24=120, Resulting Numbers: [42, 120] Generated Node #3: [42, 120] from Operation: 5*24=120 Current State: 78:[42, 120], Operations: ['59-35=24', '5*24=120'] Exploring Operation: 120-42=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[35, 59, 5, 42], Operations: [] Exploring Operation: 59-35=24, Resulting Numbers: [5, 42, 24] Generated Node #0,0: 78:[5, 42, 24] Operation: 59-35=24 Moving to Node #0,0 Current State: 78:[5, 42, 24], Operations: ['59-35=24'] Exploring Operation: 42-5=37, Resulting Numbers: [24, 37] Generated Node #0,0,0: 78:[24, 37] Operation: 42-5=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[24, 37], Operations: ['59-35=24', '42-5=37'] Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,78 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
[ 4, 49, 93, 56 ]
31
[ "4+49=53", "56-53=3", "93/3=31" ]
Current State: 31:[4, 49, 93, 56], Operations: [] Exploring Operation: 4+49=53, Resulting Numbers: [93, 56, 53] Generated Node #2: [93, 56, 53] from Operation: 4+49=53 Current State: 31:[93, 56, 53], Operations: ['4+49=53'] Exploring Operation: 56-53=3, Resulting Numbers: [93, 3] Generated Node #3: [93, 3] from Operation: 56-53=3 Current State: 31:[93, 3], Operations: ['4+49=53', '56-53=3'] Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[4, 49, 93, 56], Operations: [] Exploring Operation: 93-56=37, Resulting Numbers: [4, 49, 37] Generated Node #0,0: 31:[4, 49, 37] Operation: 93-56=37 Moving to Node #0,0 Current State: 31:[4, 49, 37], Operations: ['93-56=37'] Exploring Operation: 49-4=45, Resulting Numbers: [37, 45] Generated Node #0,0,0: 31:[37, 45] Operation: 49-4=45 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[37, 45], Operations: ['93-56=37', '49-4=45'] Exploring Operation: 45-37=8, Resulting Numbers: [8] 8,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 61, 12, 79, 76 ]
82
[ "61+12=73", "79+76=155", "155-73=82" ]
Current State: 82:[61, 12, 79, 76], Operations: [] Exploring Operation: 61+12=73, Resulting Numbers: [79, 76, 73] Generated Node #2: [79, 76, 73] from Operation: 61+12=73 Current State: 82:[79, 76, 73], Operations: ['61+12=73'] Exploring Operation: 79+76=155, Resulting Numbers: [73, 155] Generated Node #3: [73, 155] from Operation: 79+76=155 Current State: 82:[73, 155], Operations: ['61+12=73', '79+76=155'] Exploring Operation: 155-73=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[61, 12, 79, 76], Operations: [] Exploring Operation: 76-61=15, Resulting Numbers: [12, 79, 15] Generated Node #0,0: 82:[12, 79, 15] Operation: 76-61=15 Exploring Operation: 12+76=88, Resulting Numbers: [61, 79, 88] Generated Node #0,1: 82:[61, 79, 88] Operation: 12+76=88 Exploring Operation: 61-12=49, Resulting Numbers: [79, 76, 49] Generated Node #0,2: 82:[79, 76, 49] Operation: 61-12=49 Exploring Operation: 61+12=73, Resulting Numbers: [79, 76, 73] Generated Node #0,3: 82:[79, 76, 73] Operation: 61+12=73 Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[79, 76, 49], Operations: ['61-12=49'] Exploring Operation: 79-49=30, Resulting Numbers: [76, 30] Generated Node #0,2,0: 82:[76, 30] Operation: 79-49=30 Exploring Operation: 76-49=27, Resulting Numbers: [79, 27] Generated Node #0,2,1: 82:[79, 27] Operation: 76-49=27 Exploring Operation: 76+49=125, Resulting Numbers: [79, 125] Generated Node #0,2,2: 82:[79, 125] Operation: 76+49=125 Exploring Operation: 79-76=3, Resulting Numbers: [49, 3] Generated Node #0,2,3: 82:[49, 3] Operation: 79-76=3 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 82:[49, 3], Operations: ['61-12=49', '79-76=3'] Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,82 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[76, 30], Operations: ['61-12=49', '79-49=30'] Exploring Operation: 76*30=2280, Resulting Numbers: [2280] 2280,82 unequal: No Solution Exploring Operation: 76-30=46, Resulting Numbers: [46] 46,82 unequal: No Solution Exploring Operation: 76+30=106, Resulting Numbers: [106] 106,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[79, 27], Operations: ['61-12=49', '76-49=27'] Exploring Operation: 79-27=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 79+27=106, Resulting Numbers: [106] 106,82 unequal: No Solution Exploring Operation: 79*27=2133, Resulting Numbers: [2133] 2133,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 82:[79, 125], Operations: ['61-12=49', '76+49=125'] Exploring Operation: 79+125=204, Resulting Numbers: [204] 204,82 unequal: No Solution Exploring Operation: 79*125=9875, Resulting Numbers: [9875] 9875,82 unequal: No Solution Exploring Operation: 125-79=46, Resulting Numbers: [46] 46,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[79, 76, 73], Operations: ['61+12=73'] Exploring Operation: 76+73=149, Resulting Numbers: [79, 149] Generated Node #0,3,0: 82:[79, 149] Operation: 76+73=149 Exploring Operation: 79-73=6, Resulting Numbers: [76, 6] Generated Node #0,3,1: 82:[76, 6] Operation: 79-73=6 Exploring Operation: 79-76=3, Resulting Numbers: [73, 3] Generated Node #0,3,2: 82:[73, 3] Operation: 79-76=3 Exploring Operation: 76-73=3, Resulting Numbers: [79, 3] Generated Node #0,3,3: 82:[79, 3] Operation: 76-73=3 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 82:[79, 3], Operations: ['61+12=73', '76-73=3'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,82 unequal: No Solution Exploring Operation: 79*3=237, Resulting Numbers: [237] 237,82 unequal: No Solution Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[61, 12, 79, 76], Operations: [] Exploring Operation: 61+12=73, Resulting Numbers: [79, 76, 73] Generated Node #0,3: 82:[79, 76, 73] Operation: 61+12=73 Moving to Node #0,3 Current State: 82:[79, 76, 73], Operations: ['61+12=73'] Exploring Operation: 76-73=3, Resulting Numbers: [79, 3] Generated Node #0,3,3: 82:[79, 3] Operation: 76-73=3 Moving to Node #0,3,3 Current State: 82:[79, 3], Operations: ['61+12=73', '76-73=3'] Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 88, 24, 28, 39 ]
43
[ "88+24=112", "112/28=4", "39+4=43" ]
Current State: 43:[88, 24, 28, 39], Operations: [] Exploring Operation: 88+24=112, Resulting Numbers: [28, 39, 112] Generated Node #2: [28, 39, 112] from Operation: 88+24=112 Current State: 43:[28, 39, 112], Operations: ['88+24=112'] Exploring Operation: 112/28=4, Resulting Numbers: [39, 4] Generated Node #3: [39, 4] from Operation: 112/28=4 Current State: 43:[39, 4], Operations: ['88+24=112', '112/28=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[88, 24, 28, 39], Operations: [] Exploring Operation: 88-24=64, Resulting Numbers: [28, 39, 64] Generated Node #0,0: 43:[28, 39, 64] Operation: 88-24=64 Exploring Operation: 88-28=60, Resulting Numbers: [24, 39, 60] Generated Node #0,1: 43:[24, 39, 60] Operation: 88-28=60 Exploring Operation: 88-39=49, Resulting Numbers: [24, 28, 49] Generated Node #0,2: 43:[24, 28, 49] Operation: 88-39=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[28, 39, 64], Operations: ['88-24=64'] Exploring Operation: 28+39=67, Resulting Numbers: [64, 67] Generated Node #0,0,0: 43:[64, 67] Operation: 28+39=67 Exploring Operation: 64-28=36, Resulting Numbers: [39, 36] Generated Node #0,0,1: 43:[39, 36] Operation: 64-28=36 Exploring Operation: 64-39=25, Resulting Numbers: [28, 25] Generated Node #0,0,2: 43:[28, 25] Operation: 64-39=25 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 43:[39, 36], Operations: ['88-24=64', '64-28=36'] Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 39+36=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 39*36=1404, Resulting Numbers: [1404] 1404,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 43:[28, 25], Operations: ['88-24=64', '64-39=25'] Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 28+25=53, Resulting Numbers: [53] 53,43 unequal: No Solution Exploring Operation: 28*25=700, Resulting Numbers: [700] 700,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[64, 67], Operations: ['88-24=64', '28+39=67'] Exploring Operation: 64*67=4288, Resulting Numbers: [4288] 4288,43 unequal: No Solution Exploring Operation: 67-64=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 64+67=131, Resulting Numbers: [131] 131,43 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: 43:[24, 39, 60], Operations: ['88-28=60'] Exploring Operation: 60-24=36, Resulting Numbers: [39, 36] Generated Node #0,1,0: 43:[39, 36] Operation: 60-24=36 Exploring Operation: 60-39=21, Resulting Numbers: [24, 21] Generated Node #0,1,1: 43:[24, 21] Operation: 60-39=21 Exploring Operation: 24+39=63, Resulting Numbers: [60, 63] Generated Node #0,1,2: 43:[60, 63] Operation: 24+39=63 Moving to Node #0,1,0 Current State: 43:[39, 36], Operations: ['88-28=60', '60-24=36'] Exploring Operation: 39+36=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 39*36=1404, Resulting Numbers: [1404] 1404,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[60, 63], Operations: ['88-28=60', '24+39=63'] Exploring Operation: 60+63=123, Resulting Numbers: [123] 123,43 unequal: No Solution Exploring Operation: 60*63=3780, Resulting Numbers: [3780] 3780,43 unequal: No Solution Exploring Operation: 63-60=3, Resulting Numbers: [3] 3,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[24, 21], Operations: ['88-28=60', '60-39=21'] Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,43 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 43:[24, 28, 49], Operations: ['88-39=49'] Exploring Operation: 24+28=52, Resulting Numbers: [49, 52] Generated Node #0,2,0: 43:[49, 52] Operation: 24+28=52 Exploring Operation: 49-28=21, Resulting Numbers: [24, 21] Generated Node #0,2,1: 43:[24, 21] Operation: 49-28=21 Exploring Operation: 49-24=25, Resulting Numbers: [28, 25] Generated Node #0,2,2: 43:[28, 25] Operation: 49-24=25 Moving to Node #0,2,0 Current State: 43:[49, 52], Operations: ['88-39=49', '24+28=52'] Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,43 unequal: No Solution Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 49*52=2548, Resulting Numbers: [2548] 2548,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[28, 25], Operations: ['88-39=49', '49-24=25'] Exploring Operation: 28*25=700, Resulting Numbers: [700] 700,43 unequal: No Solution Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 28+25=53, Resulting Numbers: [53] 53,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[24, 21], Operations: ['88-39=49', '49-28=21'] Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,43 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,43 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
[ 8, 62, 17, 1 ]
88
[ "8+62=70", "17+1=18", "70+18=88" ]
Current State: 88:[8, 62, 17, 1], Operations: [] Exploring Operation: 8+62=70, Resulting Numbers: [17, 1, 70] Generated Node #2: [17, 1, 70] from Operation: 8+62=70 Current State: 88:[17, 1, 70], Operations: ['8+62=70'] Exploring Operation: 17+1=18, Resulting Numbers: [70, 18] Generated Node #3: [70, 18] from Operation: 17+1=18 Current State: 88:[70, 18], Operations: ['8+62=70', '17+1=18'] Exploring Operation: 70+18=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[8, 62, 17, 1], Operations: [] Exploring Operation: 62+17=79, Resulting Numbers: [8, 1, 79] Generated Node #0,0: 88:[8, 1, 79] Operation: 62+17=79 Exploring Operation: 62-8=54, Resulting Numbers: [17, 1, 54] Generated Node #0,1: 88:[17, 1, 54] Operation: 62-8=54 Exploring Operation: 62-17=45, Resulting Numbers: [8, 1, 45] Generated Node #0,2: 88:[8, 1, 45] Operation: 62-17=45 Moving to Node #0,2 Current State: 88:[8, 1, 45], Operations: ['62-17=45'] Exploring Operation: 8*1=8, Resulting Numbers: [45, 8] Generated Node #0,2,0: 88:[45, 8] Operation: 8*1=8 Exploring Operation: 8/1=8, Resulting Numbers: [45, 8] Generated Node #0,2,1: 88:[45, 8] Operation: 8/1=8 Exploring Operation: 45-1=44, Resulting Numbers: [8, 44] Generated Node #0,2,2: 88:[8, 44] Operation: 45-1=44 Moving to Node #0,0 Current State: 88:[8, 1, 79], Operations: ['62+17=79'] Exploring Operation: 8+79=87, Resulting Numbers: [1, 87] Generated Node #0,0,0: 88:[1, 87] Operation: 8+79=87 Exploring Operation: 1+79=80, Resulting Numbers: [8, 80] Generated Node #0,0,1: 88:[8, 80] Operation: 1+79=80 Exploring Operation: 8*1=8, Resulting Numbers: [79, 8] Generated Node #0,0,2: 88:[79, 8] Operation: 8*1=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[1, 87], Operations: ['62+17=79', '8+79=87'] Exploring Operation: 1*87=87, Resulting Numbers: [87] 87,88 unequal: No Solution Exploring Operation: 87/1=87, Resulting Numbers: [87] 87,88 unequal: No Solution Exploring Operation: 1+87=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[8, 62, 17, 1], Operations: [] Exploring Operation: 62+17=79, Resulting Numbers: [8, 1, 79] Generated Node #0,0: 88:[8, 1, 79] Operation: 62+17=79 Moving to Node #0,0 Current State: 88:[8, 1, 79], Operations: ['62+17=79'] Exploring Operation: 8+79=87, Resulting Numbers: [1, 87] Generated Node #0,0,0: 88:[1, 87] Operation: 8+79=87 Moving to Node #0,0,0 Current State: 88:[1, 87], Operations: ['62+17=79', '8+79=87'] Exploring Operation: 1+87=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 30, 97, 17, 68 ]
23
[ "30*68=2040", "2040/17=120", "120-97=23" ]
Current State: 23:[30, 97, 17, 68], Operations: [] Exploring Operation: 30*68=2040, Resulting Numbers: [97, 17, 2040] Generated Node #2: [97, 17, 2040] from Operation: 30*68=2040 Current State: 23:[97, 17, 2040], Operations: ['30*68=2040'] Exploring Operation: 2040/17=120, Resulting Numbers: [97, 120] Generated Node #3: [97, 120] from Operation: 2040/17=120 Current State: 23:[97, 120], Operations: ['30*68=2040', '2040/17=120'] Exploring Operation: 120-97=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[30, 97, 17, 68], Operations: [] Exploring Operation: 68/17=4, Resulting Numbers: [30, 97, 4] Generated Node #0,0: 23:[30, 97, 4] Operation: 68/17=4 Exploring Operation: 97-30=67, Resulting Numbers: [17, 68, 67] Generated Node #0,1: 23:[17, 68, 67] Operation: 97-30=67 Exploring Operation: 68-30=38, Resulting Numbers: [97, 17, 38] Generated Node #0,2: 23:[97, 17, 38] Operation: 68-30=38 Exploring Operation: 97-68=29, Resulting Numbers: [30, 17, 29] Generated Node #0,3: 23:[30, 17, 29] Operation: 97-68=29 Exploring Operation: 97-17=80, Resulting Numbers: [30, 68, 80] Generated Node #0,4: 23:[30, 68, 80] Operation: 97-17=80 Start Sub Search at level 1: Moving to Node #0,3 Current State: 23:[30, 17, 29], Operations: ['97-68=29'] Exploring Operation: 30-17=13, Resulting Numbers: [29, 13] Generated Node #0,3,0: 23:[29, 13] Operation: 30-17=13 Exploring Operation: 30+17=47, Resulting Numbers: [29, 47] Generated Node #0,3,1: 23:[29, 47] Operation: 30+17=47 Exploring Operation: 29-17=12, Resulting Numbers: [30, 12] Generated Node #0,3,2: 23:[30, 12] Operation: 29-17=12 Exploring Operation: 17+29=46, Resulting Numbers: [30, 46] Generated Node #0,3,3: 23:[30, 46] Operation: 17+29=46 Exploring Operation: 30-29=1, Resulting Numbers: [17, 1] Generated Node #0,3,4: 23:[17, 1] Operation: 30-29=1 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 23:[29, 13], Operations: ['97-68=29', '30-17=13'] Exploring Operation: 29+13=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 29*13=377, Resulting Numbers: [377] 377,23 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 23:[30, 12], Operations: ['97-68=29', '29-17=12'] Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 30+12=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 30*12=360, Resulting Numbers: [360] 360,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 23:[17, 1], Operations: ['97-68=29', '30-29=1'] Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 23:[29, 47], Operations: ['97-68=29', '30+17=47'] Exploring Operation: 29+47=76, Resulting Numbers: [76] 76,23 unequal: No Solution Exploring Operation: 29*47=1363, Resulting Numbers: [1363] 1363,23 unequal: No Solution Exploring Operation: 47-29=18, Resulting Numbers: [18] 18,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 23:[30, 46], Operations: ['97-68=29', '17+29=46'] Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 30+46=76, Resulting Numbers: [76] 76,23 unequal: No Solution Exploring Operation: 30*46=1380, Resulting Numbers: [1380] 1380,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[17, 68, 67], Operations: ['97-30=67'] Exploring Operation: 67-17=50, Resulting Numbers: [68, 50] Generated Node #0,1,0: 23:[68, 50] Operation: 67-17=50 Exploring Operation: 68-67=1, Resulting Numbers: [17, 1] Generated Node #0,1,1: 23:[17, 1] Operation: 68-67=1 Exploring Operation: 68-17=51, Resulting Numbers: [67, 51] Generated Node #0,1,2: 23:[67, 51] Operation: 68-17=51 Exploring Operation: 17+68=85, Resulting Numbers: [67, 85] Generated Node #0,1,3: 23:[67, 85] Operation: 17+68=85 Exploring Operation: 68/17=4, Resulting Numbers: [67, 4] Generated Node #0,1,4: 23:[67, 4] Operation: 68/17=4 Moving to Node #0,1,1 Current State: 23:[17, 1], Operations: ['97-30=67', '68-67=1'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,23 unequal: No Solution Moving to Node #0,1,4 Current State: 23:[67, 4], Operations: ['97-30=67', '68/17=4'] Exploring Operation: 67*4=268, Resulting Numbers: [268] 268,23 unequal: No Solution Exploring Operation: 67+4=71, Resulting Numbers: [71] 71,23 unequal: No Solution Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[68, 50], Operations: ['97-30=67', '67-17=50'] Exploring Operation: 68*50=3400, Resulting Numbers: [3400] 3400,23 unequal: No Solution Exploring Operation: 68+50=118, Resulting Numbers: [118] 118,23 unequal: No Solution Exploring Operation: 68-50=18, Resulting Numbers: [18] 18,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[67, 51], Operations: ['97-30=67', '68-17=51'] Exploring Operation: 67+51=118, Resulting Numbers: [118] 118,23 unequal: No Solution Exploring Operation: 67-51=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 67*51=3417, Resulting Numbers: [3417] 3417,23 unequal: No Solution Moving to Node #0,1,3 Current State: 23:[67, 85], Operations: ['97-30=67', '17+68=85'] Exploring Operation: 67*85=5695, Resulting Numbers: [5695] 5695,23 unequal: No Solution Exploring Operation: 85-67=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 67+85=152, Resulting Numbers: [152] 152,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[97, 17, 38], Operations: ['68-30=38'] Exploring Operation: 17+38=55, Resulting Numbers: [97, 55] Generated Node #0,2,0: 23:[97, 55] Operation: 17+38=55 Exploring Operation: 97-17=80, Resulting Numbers: [38, 80] Generated Node #0,2,1: 23:[38, 80] Operation: 97-17=80 Exploring Operation: 97-38=59, Resulting Numbers: [17, 59] Generated Node #0,2,2: 23:[17, 59] Operation: 97-38=59 Exploring Operation: 97+17=114, Resulting Numbers: [38, 114] Generated Node #0,2,3: 23:[38, 114] Operation: 97+17=114 Exploring Operation: 38-17=21, Resulting Numbers: [97, 21] Generated Node #0,2,4: 23:[97, 21] Operation: 38-17=21 Moving to Node #0,2,2 Current State: 23:[17, 59], Operations: ['68-30=38', '97-38=59'] Exploring Operation: 17*59=1003, Resulting Numbers: [1003] 1003,23 unequal: No Solution Exploring Operation: 17+59=76, Resulting Numbers: [76] 76,23 unequal: No Solution Exploring Operation: 59-17=42, Resulting Numbers: [42] 42,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[38, 80], Operations: ['68-30=38', '97-17=80'] Exploring Operation: 38+80=118, Resulting Numbers: [118] 118,23 unequal: No Solution Exploring Operation: 38*80=3040, Resulting Numbers: [3040] 3040,23 unequal: No Solution Exploring Operation: 80-38=42, Resulting Numbers: [42] 42,23 unequal: No Solution Moving to Node #0,2,4 Current State: 23:[97, 21], Operations: ['68-30=38', '38-17=21'] Exploring Operation: 97+21=118, Resulting Numbers: [118] 118,23 unequal: No Solution Exploring Operation: 97-21=76, Resulting Numbers: [76] 76,23 unequal: No Solution Exploring Operation: 97*21=2037, Resulting Numbers: [2037] 2037,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[97, 55], Operations: ['68-30=38', '17+38=55'] Exploring Operation: 97-55=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 97+55=152, Resulting Numbers: [152] 152,23 unequal: No Solution Exploring Operation: 97*55=5335, Resulting Numbers: [5335] 5335,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[38, 114], Operations: ['68-30=38', '97+17=114'] Exploring Operation: 38*114=4332, Resulting Numbers: [4332] 4332,23 unequal: No Solution Exploring Operation: 38+114=152, Resulting Numbers: [152] 152,23 unequal: No Solution Exploring Operation: 114/38=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 114-38=76, Resulting Numbers: [76] 76,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[30, 97, 4], Operations: ['68/17=4'] Exploring Operation: 30+4=34, Resulting Numbers: [97, 34] Generated Node #0,0,0: 23:[97, 34] Operation: 30+4=34 Exploring Operation: 97-4=93, Resulting Numbers: [30, 93] Generated Node #0,0,1: 23:[30, 93] Operation: 97-4=93 Exploring Operation: 30-4=26, Resulting Numbers: [97, 26] Generated Node #0,0,2: 23:[97, 26] Operation: 30-4=26 Exploring Operation: 97-30=67, Resulting Numbers: [4, 67] Generated Node #0,0,3: 23:[4, 67] Operation: 97-30=67 Exploring Operation: 97+4=101, Resulting Numbers: [30, 101] Generated Node #0,0,4: 23:[30, 101] Operation: 97+4=101 Moving to Node #0,0,3 Current State: 23:[4, 67], Operations: ['68/17=4', '97-30=67'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 4*67=268, Resulting Numbers: [268] 268,23 unequal: No Solution Exploring Operation: 4+67=71, Resulting Numbers: [71] 71,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[97, 26], Operations: ['68/17=4', '30-4=26'] Exploring Operation: 97*26=2522, Resulting Numbers: [2522] 2522,23 unequal: No Solution Exploring Operation: 97+26=123, Resulting Numbers: [123] 123,23 unequal: No Solution Exploring Operation: 97-26=71, Resulting Numbers: [71] 71,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[30, 93], Operations: ['68/17=4', '97-4=93'] Exploring Operation: 30*93=2790, Resulting Numbers: [2790] 2790,23 unequal: No Solution Exploring Operation: 30+93=123, Resulting Numbers: [123] 123,23 unequal: No Solution Exploring Operation: 93-30=63, Resulting Numbers: [63] 63,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[97, 34], Operations: ['68/17=4', '30+4=34'] Exploring Operation: 97+34=131, Resulting Numbers: [131] 131,23 unequal: No Solution Exploring Operation: 97*34=3298, Resulting Numbers: [3298] 3298,23 unequal: No Solution Exploring Operation: 97-34=63, Resulting Numbers: [63] 63,23 unequal: No Solution Moving to Node #0,0,4 Current State: 23:[30, 101], Operations: ['68/17=4', '97+4=101'] Exploring Operation: 30*101=3030, Resulting Numbers: [3030] 3030,23 unequal: No Solution Exploring Operation: 101-30=71, Resulting Numbers: [71] 71,23 unequal: No Solution Exploring Operation: 30+101=131, Resulting Numbers: [131] 131,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 23:[30, 68, 80], Operations: ['97-17=80'] Exploring Operation: 30+80=110, Resulting Numbers: [68, 110] Generated Node #0,4,0: 23:[68, 110] Operation: 30+80=110 Exploring Operation: 68-30=38, Resulting Numbers: [80, 38] Generated Node #0,4,1: 23:[80, 38] Operation: 68-30=38 Exploring Operation: 80-30=50, Resulting Numbers: [68, 50] Generated Node #0,4,2: 23:[68, 50] Operation: 80-30=50 Exploring Operation: 30+68=98, Resulting Numbers: [80, 98] Generated Node #0,4,3: 23:[80, 98] Operation: 30+68=98 Exploring Operation: 80-68=12, Resulting Numbers: [30, 12] Generated Node #0,4,4: 23:[30, 12] Operation: 80-68=12 Moving to Node #0,4,4 Current State: 23:[30, 12], Operations: ['97-17=80', '80-68=12'] Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 30*12=360, Resulting Numbers: [360] 360,23 unequal: No Solution Exploring Operation: 30+12=42, Resulting Numbers: [42] 42,23 unequal: No Solution Moving to Node #0,4,2 Current State: 23:[68, 50], Operations: ['97-17=80', '80-30=50'] Exploring Operation: 68*50=3400, Resulting Numbers: [3400] 3400,23 unequal: No Solution Exploring Operation: 68+50=118, Resulting Numbers: [118] 118,23 unequal: No Solution Exploring Operation: 68-50=18, Resulting Numbers: [18] 18,23 unequal: No Solution Moving to Node #0,4,1 Current State: 23:[80, 38], Operations: ['97-17=80', '68-30=38'] Exploring Operation: 80-38=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 80*38=3040, Resulting Numbers: [3040] 3040,23 unequal: No Solution Exploring Operation: 80+38=118, Resulting Numbers: [118] 118,23 unequal: No Solution Moving to Node #0,4,0 Current State: 23:[68, 110], Operations: ['97-17=80', '30+80=110'] Exploring Operation: 68+110=178, Resulting Numbers: [178] 178,23 unequal: No Solution Exploring Operation: 68*110=7480, Resulting Numbers: [7480] 7480,23 unequal: No Solution Exploring Operation: 110-68=42, Resulting Numbers: [42] 42,23 unequal: No Solution Moving to Node #0,4,3 Current State: 23:[80, 98], Operations: ['97-17=80', '30+68=98'] Exploring Operation: 80+98=178, Resulting Numbers: [178] 178,23 unequal: No Solution Exploring Operation: 80*98=7840, Resulting Numbers: [7840] 7840,23 unequal: No Solution Exploring Operation: 98-80=18, Resulting Numbers: [18] 18,23 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
[ 14, 32, 3, 55 ]
43
[ "32+55=87", "87/3=29", "14+29=43" ]
Current State: 43:[14, 32, 3, 55], Operations: [] Exploring Operation: 32+55=87, Resulting Numbers: [14, 3, 87] Generated Node #2: [14, 3, 87] from Operation: 32+55=87 Current State: 43:[14, 3, 87], Operations: ['32+55=87'] Exploring Operation: 87/3=29, Resulting Numbers: [14, 29] Generated Node #3: [14, 29] from Operation: 87/3=29 Current State: 43:[14, 29], Operations: ['32+55=87', '87/3=29'] Exploring Operation: 14+29=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[14, 32, 3, 55], Operations: [] Exploring Operation: 14+3=17, Resulting Numbers: [32, 55, 17] Generated Node #0,0: 43:[32, 55, 17] Operation: 14+3=17 Exploring Operation: 14*3=42, Resulting Numbers: [32, 55, 42] Generated Node #0,1: 43:[32, 55, 42] Operation: 14*3=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[32, 55, 42], Operations: ['14*3=42'] Exploring Operation: 55-32=23, Resulting Numbers: [42, 23] Generated Node #0,1,0: 43:[42, 23] Operation: 55-32=23 Exploring Operation: 55-42=13, Resulting Numbers: [32, 13] Generated Node #0,1,1: 43:[32, 13] Operation: 55-42=13 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 43:[42, 23], Operations: ['14*3=42', '55-32=23'] Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,43 unequal: No Solution Exploring Operation: 42+23=65, Resulting Numbers: [65] 65,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 43:[32, 13], Operations: ['14*3=42', '55-42=13'] Exploring Operation: 32-13=19, Resulting Numbers: [19] 19,43 unequal: No Solution Exploring Operation: 32+13=45, Resulting Numbers: [45] 45,43 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: 43:[32, 55, 17], Operations: ['14+3=17'] Exploring Operation: 55-17=38, Resulting Numbers: [32, 38] Generated Node #0,0,0: 43:[32, 38] Operation: 55-17=38 Exploring Operation: 32+17=49, Resulting Numbers: [55, 49] Generated Node #0,0,1: 43:[55, 49] Operation: 32+17=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[32, 38], Operations: ['14+3=17', '55-17=38'] Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,43 unequal: No Solution Exploring Operation: 32+38=70, Resulting Numbers: [70] 70,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 43:[55, 49], Operations: ['14+3=17', '32+17=49'] Exploring Operation: 55+49=104, Resulting Numbers: [104] 104,43 unequal: No Solution Exploring Operation: 55-49=6, Resulting Numbers: [6] 6,43 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
[ 36, 12, 18, 63 ]
39
[ "36*12=432", "432/18=24", "63-24=39" ]
Current State: 39:[36, 12, 18, 63], Operations: [] Exploring Operation: 36*12=432, Resulting Numbers: [18, 63, 432] Generated Node #2: [18, 63, 432] from Operation: 36*12=432 Current State: 39:[18, 63, 432], Operations: ['36*12=432'] Exploring Operation: 432/18=24, Resulting Numbers: [63, 24] Generated Node #3: [63, 24] from Operation: 432/18=24 Current State: 39:[63, 24], Operations: ['36*12=432', '432/18=24'] Exploring Operation: 63-24=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[36, 12, 18, 63], Operations: [] Exploring Operation: 63-18=45, Resulting Numbers: [36, 12, 45] Generated Node #0,0: 39:[36, 12, 45] Operation: 63-18=45 Exploring Operation: 63-36=27, Resulting Numbers: [12, 18, 27] Generated Node #0,1: 39:[12, 18, 27] Operation: 63-36=27 Exploring Operation: 63-12=51, Resulting Numbers: [36, 18, 51] Generated Node #0,2: 39:[36, 18, 51] Operation: 63-12=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[36, 12, 45], Operations: ['63-18=45'] Exploring Operation: 45-12=33, Resulting Numbers: [36, 33] Generated Node #0,0,0: 39:[36, 33] Operation: 45-12=33 Exploring Operation: 36/12=3, Resulting Numbers: [45, 3] Generated Node #0,0,1: 39:[45, 3] Operation: 36/12=3 Exploring Operation: 45-36=9, Resulting Numbers: [12, 9] Generated Node #0,0,2: 39:[12, 9] Operation: 45-36=9 Moving to Node #0,0,2 Current State: 39:[12, 9], Operations: ['63-18=45', '45-36=9'] Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 12*9=108, Resulting Numbers: [108] 108,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[45, 3], Operations: ['63-18=45', '36/12=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,39 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,39 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[36, 33], Operations: ['63-18=45', '45-12=33'] Exploring Operation: 36+33=69, Resulting Numbers: [69] 69,39 unequal: No Solution Exploring Operation: 36*33=1188, Resulting Numbers: [1188] 1188,39 unequal: No Solution Exploring Operation: 36-33=3, Resulting Numbers: [3] 3,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[12, 18, 27], Operations: ['63-36=27'] Exploring Operation: 27-12=15, Resulting Numbers: [18, 15] Generated Node #0,1,0: 39:[18, 15] Operation: 27-12=15 Exploring Operation: 12+27=39, Resulting Numbers: [18, 39] Generated Node #0,1,1: 39:[18, 39] Operation: 12+27=39 Exploring Operation: 27-18=9, Resulting Numbers: [12, 9] Generated Node #0,1,2: 39:[12, 9] Operation: 27-18=9 Moving to Node #0,1,1 Current State: 39:[18, 39], Operations: ['63-36=27', '12+27=39'] Exploring Operation: 18*39=702, Resulting Numbers: [702] 702,39 unequal: No Solution Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 18+39=57, Resulting Numbers: [57] 57,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[12, 9], Operations: ['63-36=27', '27-18=9'] Exploring Operation: 12*9=108, Resulting Numbers: [108] 108,39 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[18, 15], Operations: ['63-36=27', '27-12=15'] Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[36, 18, 51], Operations: ['63-12=51'] Exploring Operation: 51-36=15, Resulting Numbers: [18, 15] Generated Node #0,2,0: 39:[18, 15] Operation: 51-36=15 Exploring Operation: 36/18=2, Resulting Numbers: [51, 2] Generated Node #0,2,1: 39:[51, 2] Operation: 36/18=2 Exploring Operation: 51-18=33, Resulting Numbers: [36, 33] Generated Node #0,2,2: 39:[36, 33] Operation: 51-18=33 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 39:[18, 15], Operations: ['63-12=51', '51-36=15'] Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,39 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 39:[36, 33], Operations: ['63-12=51', '51-18=33'] Exploring Operation: 36-33=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 36+33=69, Resulting Numbers: [69] 69,39 unequal: No Solution Exploring Operation: 36*33=1188, Resulting Numbers: [1188] 1188,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 39:[51, 2], Operations: ['63-12=51', '36/18=2'] Exploring Operation: 51*2=102, Resulting Numbers: [102] 102,39 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,39 unequal: No Solution Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 62, 60, 51, 59 ]
12
[ "62+60=122", "51+59=110", "122-110=12" ]
Current State: 12:[62, 60, 51, 59], Operations: [] Exploring Operation: 62+60=122, Resulting Numbers: [51, 59, 122] Generated Node #2: [51, 59, 122] from Operation: 62+60=122 Current State: 12:[51, 59, 122], Operations: ['62+60=122'] Exploring Operation: 51+59=110, Resulting Numbers: [122, 110] Generated Node #3: [122, 110] from Operation: 51+59=110 Current State: 12:[122, 110], Operations: ['62+60=122', '51+59=110'] Exploring Operation: 122-110=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[62, 60, 51, 59], Operations: [] Exploring Operation: 62-60=2, Resulting Numbers: [51, 59, 2] Generated Node #0,0: 12:[51, 59, 2] Operation: 62-60=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[51, 59, 2], Operations: ['62-60=2'] Exploring Operation: 59-51=8, Resulting Numbers: [2, 8] Generated Node #0,0,0: 12:[2, 8] Operation: 59-51=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[2, 8], Operations: ['62-60=2', '59-51=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,12 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
[ 43, 44, 3, 89 ]
87
[ "44-43=1", "89-3=86", "1+86=87" ]
Current State: 87:[43, 44, 3, 89], Operations: [] Exploring Operation: 44-43=1, Resulting Numbers: [3, 89, 1] Generated Node #2: [3, 89, 1] from Operation: 44-43=1 Current State: 87:[3, 89, 1], Operations: ['44-43=1'] Exploring Operation: 89-3=86, Resulting Numbers: [1, 86] Generated Node #3: [1, 86] from Operation: 89-3=86 Current State: 87:[1, 86], Operations: ['44-43=1', '89-3=86'] Exploring Operation: 1+86=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[43, 44, 3, 89], Operations: [] Exploring Operation: 44-43=1, Resulting Numbers: [3, 89, 1] Generated Node #0,0: 87:[3, 89, 1] Operation: 44-43=1 Exploring Operation: 44-3=41, Resulting Numbers: [43, 89, 41] Generated Node #0,1: 87:[43, 89, 41] Operation: 44-3=41 Exploring Operation: 43+44=87, Resulting Numbers: [3, 89, 87] Generated Node #0,2: 87:[3, 89, 87] Operation: 43+44=87 Exploring Operation: 43-3=40, Resulting Numbers: [44, 89, 40] Generated Node #0,3: 87:[44, 89, 40] Operation: 43-3=40 Moving to Node #0,2 Current State: 87:[3, 89, 87], Operations: ['43+44=87'] Exploring Operation: 89-3=86, Resulting Numbers: [87, 86] Generated Node #0,2,0: 87:[87, 86] Operation: 89-3=86 Exploring Operation: 3+89=92, Resulting Numbers: [87, 92] Generated Node #0,2,1: 87:[87, 92] Operation: 3+89=92 Exploring Operation: 87/3=29, Resulting Numbers: [89, 29] Generated Node #0,2,2: 87:[89, 29] Operation: 87/3=29 Exploring Operation: 89-87=2, Resulting Numbers: [3, 2] Generated Node #0,2,3: 87:[3, 2] Operation: 89-87=2 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 87:[87, 86], Operations: ['43+44=87', '89-3=86'] Exploring Operation: 87-86=1, Resulting Numbers: [1] 1,87 unequal: No Solution Exploring Operation: 87*86=7482, Resulting Numbers: [7482] 7482,87 unequal: No Solution Exploring Operation: 87+86=173, Resulting Numbers: [173] 173,87 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 #0,2,3 Current State: 87:[3, 2], Operations: ['43+44=87', '89-87=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,87 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,87 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:[89, 29], Operations: ['43+44=87', '87/3=29'] Exploring Operation: 89+29=118, Resulting Numbers: [118] 118,87 unequal: No Solution Exploring Operation: 89*29=2581, Resulting Numbers: [2581] 2581,87 unequal: No Solution Exploring Operation: 89-29=60, Resulting Numbers: [60] 60,87 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:[87, 92], Operations: ['43+44=87', '3+89=92'] Exploring Operation: 87+92=179, Resulting Numbers: [179] 179,87 unequal: No Solution Exploring Operation: 92-87=5, Resulting Numbers: [5] 5,87 unequal: No Solution Exploring Operation: 87*92=8004, Resulting Numbers: [8004] 8004,87 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:[3, 89, 1], Operations: ['44-43=1'] Exploring Operation: 3*1=3, Resulting Numbers: [89, 3] Generated Node #0,0,0: 87:[89, 3] Operation: 3*1=3 Exploring Operation: 89-1=88, Resulting Numbers: [3, 88] Generated Node #0,0,1: 87:[3, 88] Operation: 89-1=88 Exploring Operation: 89*1=89, Resulting Numbers: [3, 89] Generated Node #0,0,2: 87:[3, 89] Operation: 89*1=89 Exploring Operation: 3/1=3, Resulting Numbers: [89, 3] Generated Node #0,0,3: 87:[89, 3] Operation: 3/1=3 Moving to Node #0,3 Current State: 87:[44, 89, 40], Operations: ['43-3=40'] Exploring Operation: 89-40=49, Resulting Numbers: [44, 49] Generated Node #0,3,0: 87:[44, 49] Operation: 89-40=49 Exploring Operation: 89-44=45, Resulting Numbers: [40, 45] Generated Node #0,3,1: 87:[40, 45] Operation: 89-44=45 Exploring Operation: 44-40=4, Resulting Numbers: [89, 4] Generated Node #0,3,2: 87:[89, 4] Operation: 44-40=4 Exploring Operation: 44+40=84, Resulting Numbers: [89, 84] Generated Node #0,3,3: 87:[89, 84] Operation: 44+40=84 Moving to Node #0,1 Current State: 87:[43, 89, 41], Operations: ['44-3=41'] Exploring Operation: 89-43=46, Resulting Numbers: [41, 46] Generated Node #0,1,0: 87:[41, 46] Operation: 89-43=46 Exploring Operation: 89-41=48, Resulting Numbers: [43, 48] Generated Node #0,1,1: 87:[43, 48] Operation: 89-41=48 Exploring Operation: 43+41=84, Resulting Numbers: [89, 84] Generated Node #0,1,2: 87:[89, 84] Operation: 43+41=84 Exploring Operation: 43-41=2, Resulting Numbers: [89, 2] Generated Node #0,1,3: 87:[89, 2] Operation: 43-41=2 Moving to Node #0,0,1 Current State: 87:[3, 88], Operations: ['44-43=1', '89-1=88'] Exploring Operation: 3+88=91, Resulting Numbers: [91] 91,87 unequal: No Solution Exploring Operation: 3*88=264, Resulting Numbers: [264] 264,87 unequal: No Solution Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,87 unequal: No Solution Moving to Node #0,0,2 Current State: 87:[3, 89], Operations: ['44-43=1', '89*1=89'] Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,87 unequal: No Solution Exploring Operation: 3*89=267, Resulting Numbers: [267] 267,87 unequal: No Solution Exploring Operation: 3+89=92, Resulting Numbers: [92] 92,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[89, 3], Operations: ['44-43=1', '3*1=3'] Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,87 unequal: No Solution Exploring Operation: 89*3=267, Resulting Numbers: [267] 267,87 unequal: No Solution Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,87 unequal: No Solution Moving to Node #0,0,3 Current State: 87:[89, 3], Operations: ['44-43=1', '3/1=3'] Exploring Operation: 89*3=267, Resulting Numbers: [267] 267,87 unequal: No Solution Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,87 unequal: No Solution Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,87 unequal: No Solution Moving to Node #0,3,2 Current State: 87:[89, 4], Operations: ['43-3=40', '44-40=4'] Exploring Operation: 89*4=356, Resulting Numbers: [356] 356,87 unequal: No Solution Exploring Operation: 89+4=93, Resulting Numbers: [93] 93,87 unequal: No Solution Exploring Operation: 89-4=85, Resulting Numbers: [85] 85,87 unequal: No Solution Moving to Node #0,1,3 Current State: 87:[89, 2], Operations: ['44-3=41', '43-41=2'] Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[43, 44, 3, 89], Operations: [] Exploring Operation: 44-3=41, Resulting Numbers: [43, 89, 41] Generated Node #0,1: 87:[43, 89, 41] Operation: 44-3=41 Moving to Node #0,1 Current State: 87:[43, 89, 41], Operations: ['44-3=41'] Exploring Operation: 43-41=2, Resulting Numbers: [89, 2] Generated Node #0,1,3: 87:[89, 2] Operation: 43-41=2 Moving to Node #0,1,3 Current State: 87:[89, 2], Operations: ['44-3=41', '43-41=2'] Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
0.954861
hs_4
mult_heuristic
[ 22, 63, 25, 9 ]
25
[ "63-22=41", "25-9=16", "41-16=25" ]
Current State: 25:[22, 63, 25, 9], Operations: [] Exploring Operation: 63-22=41, Resulting Numbers: [25, 9, 41] Generated Node #2: [25, 9, 41] from Operation: 63-22=41 Current State: 25:[25, 9, 41], Operations: ['63-22=41'] Exploring Operation: 25-9=16, Resulting Numbers: [41, 16] Generated Node #3: [41, 16] from Operation: 25-9=16 Current State: 25:[41, 16], Operations: ['63-22=41', '25-9=16'] Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[22, 63, 25, 9], Operations: [] Exploring Operation: 63/9=7, Resulting Numbers: [22, 25, 7] Generated Node #0,0: 25:[22, 25, 7] Operation: 63/9=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[22, 25, 7], Operations: ['63/9=7'] Exploring Operation: 25-22=3, Resulting Numbers: [7, 3] Generated Node #0,0,0: 25:[7, 3] Operation: 25-22=3 Moving to Node #0,0,0 Current State: 25:[7, 3], Operations: ['63/9=7', '25-22=3'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,25 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
[ 59, 89, 7, 63 ]
78
[ "59+89=148", "7+63=70", "148-70=78" ]
Current State: 78:[59, 89, 7, 63], Operations: [] Exploring Operation: 59+89=148, Resulting Numbers: [7, 63, 148] Generated Node #2: [7, 63, 148] from Operation: 59+89=148 Current State: 78:[7, 63, 148], Operations: ['59+89=148'] Exploring Operation: 7+63=70, Resulting Numbers: [148, 70] Generated Node #3: [148, 70] from Operation: 7+63=70 Current State: 78:[148, 70], Operations: ['59+89=148', '7+63=70'] Exploring Operation: 148-70=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[59, 89, 7, 63], Operations: [] Exploring Operation: 63-59=4, Resulting Numbers: [89, 7, 4] Generated Node #0,0: 78:[89, 7, 4] Operation: 63-59=4 Exploring Operation: 89-59=30, Resulting Numbers: [7, 63, 30] Generated Node #0,1: 78:[7, 63, 30] Operation: 89-59=30 Exploring Operation: 89-63=26, Resulting Numbers: [59, 7, 26] Generated Node #0,2: 78:[59, 7, 26] Operation: 89-63=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[89, 7, 4], Operations: ['63-59=4'] Exploring Operation: 7-4=3, Resulting Numbers: [89, 3] Generated Node #0,0,0: 78:[89, 3] Operation: 7-4=3 Exploring Operation: 89-7=82, Resulting Numbers: [4, 82] Generated Node #0,0,1: 78:[4, 82] Operation: 89-7=82 Exploring Operation: 89-4=85, Resulting Numbers: [7, 85] Generated Node #0,0,2: 78:[7, 85] Operation: 89-4=85 Moving to Node #0,0,1 Current State: 78:[4, 82], Operations: ['63-59=4', '89-7=82'] Exploring Operation: 4+82=86, Resulting Numbers: [86] 86,78 unequal: No Solution Exploring Operation: 4*82=328, Resulting Numbers: [328] 328,78 unequal: No Solution Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[59, 89, 7, 63], Operations: [] Exploring Operation: 63-59=4, Resulting Numbers: [89, 7, 4] Generated Node #0,0: 78:[89, 7, 4] Operation: 63-59=4 Moving to Node #0,0 Current State: 78:[89, 7, 4], Operations: ['63-59=4'] Exploring Operation: 89-7=82, Resulting Numbers: [4, 82] Generated Node #0,0,1: 78:[4, 82] Operation: 89-7=82 Moving to Node #0,0,1 Current State: 78:[4, 82], Operations: ['63-59=4', '89-7=82'] Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 23, 41, 80, 69 ]
16
[ "23+41=64", "69-64=5", "80/5=16" ]
Current State: 16:[23, 41, 80, 69], Operations: [] Exploring Operation: 23+41=64, Resulting Numbers: [80, 69, 64] Generated Node #2: [80, 69, 64] from Operation: 23+41=64 Current State: 16:[80, 69, 64], Operations: ['23+41=64'] Exploring Operation: 69-64=5, Resulting Numbers: [80, 5] Generated Node #3: [80, 5] from Operation: 69-64=5 Current State: 16:[80, 5], Operations: ['23+41=64', '69-64=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[23, 41, 80, 69], Operations: [] Exploring Operation: 69-41=28, Resulting Numbers: [23, 80, 28] Generated Node #0,0: 16:[23, 80, 28] Operation: 69-41=28 Exploring Operation: 80-69=11, Resulting Numbers: [23, 41, 11] Generated Node #0,1: 16:[23, 41, 11] Operation: 80-69=11 Exploring Operation: 80-41=39, Resulting Numbers: [23, 69, 39] Generated Node #0,2: 16:[23, 69, 39] Operation: 80-41=39 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[23, 41, 11], Operations: ['80-69=11'] Exploring Operation: 41-11=30, Resulting Numbers: [23, 30] Generated Node #0,1,0: 16:[23, 30] Operation: 41-11=30 Exploring Operation: 41-23=18, Resulting Numbers: [11, 18] Generated Node #0,1,1: 16:[11, 18] Operation: 41-23=18 Exploring Operation: 23-11=12, Resulting Numbers: [41, 12] Generated Node #0,1,2: 16:[41, 12] Operation: 23-11=12 Moving to Node #0,1,1 Current State: 16:[11, 18], Operations: ['80-69=11', '41-23=18'] Exploring Operation: 11*18=198, Resulting Numbers: [198] 198,16 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 11+18=29, Resulting Numbers: [29] 29,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[23, 30], Operations: ['80-69=11', '41-11=30'] Exploring Operation: 23*30=690, Resulting Numbers: [690] 690,16 unequal: No Solution Exploring Operation: 23+30=53, Resulting Numbers: [53] 53,16 unequal: No Solution Exploring Operation: 30-23=7, Resulting Numbers: [7] 7,16 unequal: No Solution Moving to Node #0,1,2 Current State: 16:[41, 12], Operations: ['80-69=11', '23-11=12'] Exploring Operation: 41*12=492, Resulting Numbers: [492] 492,16 unequal: No Solution Exploring Operation: 41-12=29, Resulting Numbers: [29] 29,16 unequal: No Solution Exploring Operation: 41+12=53, Resulting Numbers: [53] 53,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[23, 80, 28], Operations: ['69-41=28'] Exploring Operation: 80-23=57, Resulting Numbers: [28, 57] Generated Node #0,0,0: 16:[28, 57] Operation: 80-23=57 Exploring Operation: 28-23=5, Resulting Numbers: [80, 5] Generated Node #0,0,1: 16:[80, 5] Operation: 28-23=5 Exploring Operation: 80-28=52, Resulting Numbers: [23, 52] Generated Node #0,0,2: 16:[23, 52] Operation: 80-28=52 Moving to Node #0,0,2 Current State: 16:[23, 52], Operations: ['69-41=28', '80-28=52'] Exploring Operation: 23*52=1196, Resulting Numbers: [1196] 1196,16 unequal: No Solution Exploring Operation: 23+52=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 52-23=29, Resulting Numbers: [29] 29,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[28, 57], Operations: ['69-41=28', '80-23=57'] Exploring Operation: 28*57=1596, Resulting Numbers: [1596] 1596,16 unequal: No Solution Exploring Operation: 28+57=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 57-28=29, Resulting Numbers: [29] 29,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[80, 5], Operations: ['69-41=28', '28-23=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=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[23, 41, 80, 69], Operations: [] Exploring Operation: 69-41=28, Resulting Numbers: [23, 80, 28] Generated Node #0,0: 16:[23, 80, 28] Operation: 69-41=28 Moving to Node #0,0 Current State: 16:[23, 80, 28], Operations: ['69-41=28'] Exploring Operation: 28-23=5, Resulting Numbers: [80, 5] Generated Node #0,0,1: 16:[80, 5] Operation: 28-23=5 Moving to Node #0,0,1 Current State: 16:[80, 5], Operations: ['69-41=28', '28-23=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_3
sum_heuristic
[ 30, 9, 46, 18 ]
33
[ "9+46=55", "18*55=990", "990/30=33" ]
Current State: 33:[30, 9, 46, 18], Operations: [] Exploring Operation: 9+46=55, Resulting Numbers: [30, 18, 55] Generated Node #2: [30, 18, 55] from Operation: 9+46=55 Current State: 33:[30, 18, 55], Operations: ['9+46=55'] Exploring Operation: 18*55=990, Resulting Numbers: [30, 990] Generated Node #3: [30, 990] from Operation: 18*55=990 Current State: 33:[30, 990], Operations: ['9+46=55', '18*55=990'] Exploring Operation: 990/30=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[30, 9, 46, 18], Operations: [] Exploring Operation: 46-18=28, Resulting Numbers: [30, 9, 28] Generated Node #0,0: 33:[30, 9, 28] Operation: 46-18=28 Moving to Node #0,0 Current State: 33:[30, 9, 28], Operations: ['46-18=28'] Exploring Operation: 30-28=2, Resulting Numbers: [9, 2] Generated Node #0,0,0: 33:[9, 2] Operation: 30-28=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[9, 2], Operations: ['46-18=28', '30-28=2'] Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,33 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
[ 9, 6, 77, 78 ]
45
[ "6+77=83", "83-78=5", "9*5=45" ]
Current State: 45:[9, 6, 77, 78], Operations: [] Exploring Operation: 6+77=83, Resulting Numbers: [9, 78, 83] Generated Node #2: [9, 78, 83] from Operation: 6+77=83 Current State: 45:[9, 78, 83], Operations: ['6+77=83'] Exploring Operation: 83-78=5, Resulting Numbers: [9, 5] Generated Node #3: [9, 5] from Operation: 83-78=5 Current State: 45:[9, 5], Operations: ['6+77=83', '83-78=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[9, 6, 77, 78], Operations: [] Exploring Operation: 78/6=13, Resulting Numbers: [9, 77, 13] Generated Node #0,0: 45:[9, 77, 13] Operation: 78/6=13 Exploring Operation: 78-9=69, Resulting Numbers: [6, 77, 69] Generated Node #0,1: 45:[6, 77, 69] Operation: 78-9=69 Exploring Operation: 77-9=68, Resulting Numbers: [6, 78, 68] Generated Node #0,2: 45:[6, 78, 68] Operation: 77-9=68 Exploring Operation: 78-77=1, Resulting Numbers: [9, 6, 1] Generated Node #0,3: 45:[9, 6, 1] Operation: 78-77=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 45:[9, 6, 1], Operations: ['78-77=1'] Exploring Operation: 6-1=5, Resulting Numbers: [9, 5] Generated Node #0,3,0: 45:[9, 5] Operation: 6-1=5 Exploring Operation: 9*1=9, Resulting Numbers: [6, 9] Generated Node #0,3,1: 45:[6, 9] Operation: 9*1=9 Exploring Operation: 6*1=6, Resulting Numbers: [9, 6] Generated Node #0,3,2: 45:[9, 6] Operation: 6*1=6 Exploring Operation: 9/1=9, Resulting Numbers: [6, 9] Generated Node #0,3,3: 45:[6, 9] Operation: 9/1=9 Moving to Node #0,3,0 Current State: 45:[9, 5], Operations: ['78-77=1', '6-1=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[9, 6, 77, 78], Operations: [] Exploring Operation: 78-77=1, Resulting Numbers: [9, 6, 1] Generated Node #0,3: 45:[9, 6, 1] Operation: 78-77=1 Moving to Node #0,3 Current State: 45:[9, 6, 1], Operations: ['78-77=1'] Exploring Operation: 6-1=5, Resulting Numbers: [9, 5] Generated Node #0,3,0: 45:[9, 5] Operation: 6-1=5 Moving to Node #0,3,0 Current State: 45:[9, 5], Operations: ['78-77=1', '6-1=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 15, 59, 80, 20 ]
56
[ "59-15=44", "80+20=100", "100-44=56" ]
Current State: 56:[15, 59, 80, 20], Operations: [] Exploring Operation: 59-15=44, Resulting Numbers: [80, 20, 44] Generated Node #2: [80, 20, 44] from Operation: 59-15=44 Current State: 56:[80, 20, 44], Operations: ['59-15=44'] Exploring Operation: 80+20=100, Resulting Numbers: [44, 100] Generated Node #3: [44, 100] from Operation: 80+20=100 Current State: 56:[44, 100], Operations: ['59-15=44', '80+20=100'] Exploring Operation: 100-44=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[15, 59, 80, 20], Operations: [] Exploring Operation: 80-20=60, Resulting Numbers: [15, 59, 60] Generated Node #0,0: 56:[15, 59, 60] Operation: 80-20=60 Exploring Operation: 80/20=4, Resulting Numbers: [15, 59, 4] Generated Node #0,1: 56:[15, 59, 4] Operation: 80/20=4 Exploring Operation: 80-59=21, Resulting Numbers: [15, 20, 21] Generated Node #0,2: 56:[15, 20, 21] Operation: 80-59=21 Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[15, 59, 4], Operations: ['80/20=4'] Exploring Operation: 15-4=11, Resulting Numbers: [59, 11] Generated Node #0,1,0: 56:[59, 11] Operation: 15-4=11 Exploring Operation: 59-4=55, Resulting Numbers: [15, 55] Generated Node #0,1,1: 56:[15, 55] Operation: 59-4=55 Exploring Operation: 15*4=60, Resulting Numbers: [59, 60] Generated Node #0,1,2: 56:[59, 60] Operation: 15*4=60 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 56:[15, 55], Operations: ['80/20=4', '59-4=55'] Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,56 unequal: No Solution Exploring Operation: 15*55=825, Resulting Numbers: [825] 825,56 unequal: No Solution Exploring Operation: 15+55=70, Resulting Numbers: [70] 70,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 56:[59, 11], Operations: ['80/20=4', '15-4=11'] Exploring Operation: 59*11=649, Resulting Numbers: [649] 649,56 unequal: No Solution Exploring Operation: 59+11=70, Resulting Numbers: [70] 70,56 unequal: No Solution Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 56:[59, 60], Operations: ['80/20=4', '15*4=60'] Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 59+60=119, Resulting Numbers: [119] 119,56 unequal: No Solution Exploring Operation: 59*60=3540, Resulting Numbers: [3540] 3540,56 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: 56:[15, 59, 60], Operations: ['80-20=60'] Exploring Operation: 60-59=1, Resulting Numbers: [15, 1] Generated Node #0,0,0: 56:[15, 1] Operation: 60-59=1 Exploring Operation: 60-15=45, Resulting Numbers: [59, 45] Generated Node #0,0,1: 56:[59, 45] Operation: 60-15=45 Exploring Operation: 60/15=4, Resulting Numbers: [59, 4] Generated Node #0,0,2: 56:[59, 4] Operation: 60/15=4 Moving to Node #0,0,0 Current State: 56:[15, 1], Operations: ['80-20=60', '60-59=1'] Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,56 unequal: No Solution Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,56 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,56 unequal: No Solution Moving to Node #0,0,2 Current State: 56:[59, 4], Operations: ['80-20=60', '60/15=4'] Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 59+4=63, Resulting Numbers: [63] 63,56 unequal: No Solution Exploring Operation: 59*4=236, Resulting Numbers: [236] 236,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[59, 45], Operations: ['80-20=60', '60-15=45'] Exploring Operation: 59+45=104, Resulting Numbers: [104] 104,56 unequal: No Solution Exploring Operation: 59-45=14, Resulting Numbers: [14] 14,56 unequal: No Solution Exploring Operation: 59*45=2655, Resulting Numbers: [2655] 2655,56 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 Current State: 56:[15, 20, 21], Operations: ['80-59=21'] Exploring Operation: 20-15=5, Resulting Numbers: [21, 5] Generated Node #0,2,0: 56:[21, 5] Operation: 20-15=5 Exploring Operation: 21-15=6, Resulting Numbers: [20, 6] Generated Node #0,2,1: 56:[20, 6] Operation: 21-15=6 Exploring Operation: 21-20=1, Resulting Numbers: [15, 1] Generated Node #0,2,2: 56:[15, 1] Operation: 21-20=1 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 56:[15, 1], Operations: ['80-59=21', '21-20=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,56 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,56 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 56:[20, 6], Operations: ['80-59=21', '21-15=6'] Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,56 unequal: No Solution Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,56 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 56:[21, 5], Operations: ['80-59=21', '20-15=5'] Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,56 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,56 unequal: No Solution Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,56 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
[ 98, 2, 49, 15 ]
36
[ "98+2=100", "49+15=64", "100-64=36" ]
Current State: 36:[98, 2, 49, 15], Operations: [] Exploring Operation: 98+2=100, Resulting Numbers: [49, 15, 100] Generated Node #2: [49, 15, 100] from Operation: 98+2=100 Current State: 36:[49, 15, 100], Operations: ['98+2=100'] Exploring Operation: 49+15=64, Resulting Numbers: [100, 64] Generated Node #3: [100, 64] from Operation: 49+15=64 Current State: 36:[100, 64], Operations: ['98+2=100', '49+15=64'] Exploring Operation: 100-64=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[98, 2, 49, 15], Operations: [] Exploring Operation: 98/49=2, Resulting Numbers: [2, 15, 2] Generated Node #0,0: 36:[2, 15, 2] Operation: 98/49=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[2, 15, 2], Operations: ['98/49=2'] Exploring Operation: 2+15=17, Resulting Numbers: [2, 17] Generated Node #0,0,0: 36:[2, 17] Operation: 2+15=17 Moving to Node #0,0,0 Current State: 36:[2, 17], Operations: ['98/49=2', '2+15=17'] Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,36 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
[ 94, 72, 31, 62 ]
28
[ "31*62=1922", "94+1922=2016", "2016/72=28" ]
Current State: 28:[94, 72, 31, 62], Operations: [] Exploring Operation: 31*62=1922, Resulting Numbers: [94, 72, 1922] Generated Node #2: [94, 72, 1922] from Operation: 31*62=1922 Current State: 28:[94, 72, 1922], Operations: ['31*62=1922'] Exploring Operation: 94+1922=2016, Resulting Numbers: [72, 2016] Generated Node #3: [72, 2016] from Operation: 94+1922=2016 Current State: 28:[72, 2016], Operations: ['31*62=1922', '94+1922=2016'] Exploring Operation: 2016/72=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[94, 72, 31, 62], Operations: [] Exploring Operation: 94-62=32, Resulting Numbers: [72, 31, 32] Generated Node #0,0: 28:[72, 31, 32] Operation: 94-62=32 Exploring Operation: 94-72=22, Resulting Numbers: [31, 62, 22] Generated Node #0,1: 28:[31, 62, 22] Operation: 94-72=22 Exploring Operation: 72-62=10, Resulting Numbers: [94, 31, 10] Generated Node #0,2: 28:[94, 31, 10] Operation: 72-62=10 Moving to Node #0,1 Current State: 28:[31, 62, 22], Operations: ['94-72=22'] Exploring Operation: 62/31=2, Resulting Numbers: [22, 2] Generated Node #0,1,0: 28:[22, 2] Operation: 62/31=2 Exploring Operation: 62-31=31, Resulting Numbers: [22, 31] Generated Node #0,1,1: 28:[22, 31] Operation: 62-31=31 Exploring Operation: 62-22=40, Resulting Numbers: [31, 40] Generated Node #0,1,2: 28:[31, 40] Operation: 62-22=40 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 28:[22, 2], Operations: ['94-72=22', '62/31=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,28 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,28 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 28:[22, 31], Operations: ['94-72=22', '62-31=31'] Exploring Operation: 22+31=53, Resulting Numbers: [53] 53,28 unequal: No Solution Exploring Operation: 31-22=9, Resulting Numbers: [9] 9,28 unequal: No Solution Exploring Operation: 22*31=682, Resulting Numbers: [682] 682,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 28:[31, 40], Operations: ['94-72=22', '62-22=40'] Exploring Operation: 31+40=71, Resulting Numbers: [71] 71,28 unequal: No Solution Exploring Operation: 40-31=9, Resulting Numbers: [9] 9,28 unequal: No Solution Exploring Operation: 31*40=1240, Resulting Numbers: [1240] 1240,28 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: 28:[72, 31, 32], Operations: ['94-62=32'] Exploring Operation: 72-32=40, Resulting Numbers: [31, 40] Generated Node #0,0,0: 28:[31, 40] Operation: 72-32=40 Exploring Operation: 72-31=41, Resulting Numbers: [32, 41] Generated Node #0,0,1: 28:[32, 41] Operation: 72-31=41 Exploring Operation: 32-31=1, Resulting Numbers: [72, 1] Generated Node #0,0,2: 28:[72, 1] Operation: 32-31=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 28:[31, 40], Operations: ['94-62=32', '72-32=40'] Exploring Operation: 40-31=9, Resulting Numbers: [9] 9,28 unequal: No Solution Exploring Operation: 31*40=1240, Resulting Numbers: [1240] 1240,28 unequal: No Solution Exploring Operation: 31+40=71, Resulting Numbers: [71] 71,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 28:[32, 41], Operations: ['94-62=32', '72-31=41'] Exploring Operation: 32+41=73, Resulting Numbers: [73] 73,28 unequal: No Solution Exploring Operation: 32*41=1312, Resulting Numbers: [1312] 1312,28 unequal: No Solution Exploring Operation: 41-32=9, Resulting Numbers: [9] 9,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 28:[72, 1], Operations: ['94-62=32', '32-31=1'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,28 unequal: No Solution Exploring Operation: 72*1=72, Resulting Numbers: [72] 72,28 unequal: No Solution Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,28 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: 28:[94, 31, 10], Operations: ['72-62=10'] Exploring Operation: 31-10=21, Resulting Numbers: [94, 21] Generated Node #0,2,0: 28:[94, 21] Operation: 31-10=21 Exploring Operation: 94-31=63, Resulting Numbers: [10, 63] Generated Node #0,2,1: 28:[10, 63] Operation: 94-31=63 Exploring Operation: 94-10=84, Resulting Numbers: [31, 84] Generated Node #0,2,2: 28:[31, 84] Operation: 94-10=84 Moving to Node #0,2,1 Current State: 28:[10, 63], Operations: ['72-62=10', '94-31=63'] Exploring Operation: 63-10=53, Resulting Numbers: [53] 53,28 unequal: No Solution Exploring Operation: 10+63=73, Resulting Numbers: [73] 73,28 unequal: No Solution Exploring Operation: 10*63=630, Resulting Numbers: [630] 630,28 unequal: No Solution Moving to Node #0,2,2 Current State: 28:[31, 84], Operations: ['72-62=10', '94-10=84'] Exploring Operation: 31*84=2604, Resulting Numbers: [2604] 2604,28 unequal: No Solution Exploring Operation: 31+84=115, Resulting Numbers: [115] 115,28 unequal: No Solution Exploring Operation: 84-31=53, Resulting Numbers: [53] 53,28 unequal: No Solution Moving to Node #0,2,0 Current State: 28:[94, 21], Operations: ['72-62=10', '31-10=21'] Exploring Operation: 94+21=115, Resulting Numbers: [115] 115,28 unequal: No Solution Exploring Operation: 94*21=1974, Resulting Numbers: [1974] 1974,28 unequal: No Solution Exploring Operation: 94-21=73, Resulting Numbers: [73] 73,28 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 52, 2, 84, 68 ]
10
[ "52/2=26", "84-68=16", "26-16=10" ]
Current State: 10:[52, 2, 84, 68], Operations: [] Exploring Operation: 52/2=26, Resulting Numbers: [84, 68, 26] Generated Node #2: [84, 68, 26] from Operation: 52/2=26 Current State: 10:[84, 68, 26], Operations: ['52/2=26'] Exploring Operation: 84-68=16, Resulting Numbers: [26, 16] Generated Node #3: [26, 16] from Operation: 84-68=16 Current State: 10:[26, 16], Operations: ['52/2=26', '84-68=16'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[52, 2, 84, 68], Operations: [] Exploring Operation: 84-68=16, Resulting Numbers: [52, 2, 16] Generated Node #0,0: 10:[52, 2, 16] Operation: 84-68=16 Exploring Operation: 68-52=16, Resulting Numbers: [2, 84, 16] Generated Node #0,1: 10:[2, 84, 16] Operation: 68-52=16 Exploring Operation: 68/2=34, Resulting Numbers: [52, 84, 34] Generated Node #0,2: 10:[52, 84, 34] Operation: 68/2=34 Exploring Operation: 84-52=32, Resulting Numbers: [2, 68, 32] Generated Node #0,3: 10:[2, 68, 32] Operation: 84-52=32 Exploring Operation: 84/2=42, Resulting Numbers: [52, 68, 42] Generated Node #0,4: 10:[52, 68, 42] Operation: 84/2=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[52, 2, 16], Operations: ['84-68=16'] Exploring Operation: 52-2=50, Resulting Numbers: [16, 50] Generated Node #0,0,0: 10:[16, 50] Operation: 52-2=50 Exploring Operation: 52-16=36, Resulting Numbers: [2, 36] Generated Node #0,0,1: 10:[2, 36] Operation: 52-16=36 Exploring Operation: 16/2=8, Resulting Numbers: [52, 8] Generated Node #0,0,2: 10:[52, 8] Operation: 16/2=8 Exploring Operation: 52/2=26, Resulting Numbers: [16, 26] Generated Node #0,0,3: 10:[16, 26] Operation: 52/2=26 Exploring Operation: 16-2=14, Resulting Numbers: [52, 14] Generated Node #0,0,4: 10:[52, 14] Operation: 16-2=14 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 10:[16, 26], Operations: ['84-68=16', '52/2=26'] Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,10 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[52, 2, 84, 68], Operations: [] Exploring Operation: 84-68=16, Resulting Numbers: [52, 2, 16] Generated Node #0,0: 10:[52, 2, 16] Operation: 84-68=16 Moving to Node #0,0 Current State: 10:[52, 2, 16], Operations: ['84-68=16'] Exploring Operation: 52/2=26, Resulting Numbers: [16, 26] Generated Node #0,0,3: 10:[16, 26] Operation: 52/2=26 Moving to Node #0,0,3 Current State: 10:[16, 26], Operations: ['84-68=16', '52/2=26'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 48, 83, 65, 18 ]
49
[ "83-65=18", "18/18=1", "48+1=49" ]
Current State: 49:[48, 83, 65, 18], Operations: [] Exploring Operation: 83-65=18, Resulting Numbers: [48, 18, 18] Generated Node #2: [48, 18, 18] from Operation: 83-65=18 Current State: 49:[48, 18, 18], Operations: ['83-65=18'] Exploring Operation: 18/18=1, Resulting Numbers: [48, 1] Generated Node #3: [48, 1] from Operation: 18/18=1 Current State: 49:[48, 1], Operations: ['83-65=18', '18/18=1'] Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[48, 83, 65, 18], Operations: [] Exploring Operation: 83-65=18, Resulting Numbers: [48, 18, 18] Generated Node #0,0: 49:[48, 18, 18] Operation: 83-65=18 Exploring Operation: 65-18=47, Resulting Numbers: [48, 83, 47] Generated Node #0,1: 49:[48, 83, 47] Operation: 65-18=47 Exploring Operation: 83-18=65, Resulting Numbers: [48, 65, 65] Generated Node #0,2: 49:[48, 65, 65] Operation: 83-18=65 Moving to Node #0,0 Current State: 49:[48, 18, 18], Operations: ['83-65=18'] Exploring Operation: 18+18=36, Resulting Numbers: [48, 36] Generated Node #0,0,0: 49:[48, 36] Operation: 18+18=36 Exploring Operation: 18/18=1, Resulting Numbers: [48, 1] Generated Node #0,0,1: 49:[48, 1] Operation: 18/18=1 Exploring Operation: 18-18=0, Resulting Numbers: [48, 0] Generated Node #0,0,2: 49:[48, 0] Operation: 18-18=0 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 49:[48, 1], Operations: ['83-65=18', '18/18=1'] Exploring Operation: 48/1=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 48*1=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[48, 83, 65, 18], Operations: [] Exploring Operation: 83-65=18, Resulting Numbers: [48, 18, 18] Generated Node #0,0: 49:[48, 18, 18] Operation: 83-65=18 Moving to Node #0,0 Current State: 49:[48, 18, 18], Operations: ['83-65=18'] Exploring Operation: 18/18=1, Resulting Numbers: [48, 1] Generated Node #0,0,1: 49:[48, 1] Operation: 18/18=1 Moving to Node #0,0,1 Current State: 49:[48, 1], Operations: ['83-65=18', '18/18=1'] Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 38, 21, 16, 67 ]
21
[ "38+67=105", "21-16=5", "105/5=21" ]
Current State: 21:[38, 21, 16, 67], Operations: [] Exploring Operation: 38+67=105, Resulting Numbers: [21, 16, 105] Generated Node #2: [21, 16, 105] from Operation: 38+67=105 Current State: 21:[21, 16, 105], Operations: ['38+67=105'] Exploring Operation: 21-16=5, Resulting Numbers: [105, 5] Generated Node #3: [105, 5] from Operation: 21-16=5 Current State: 21:[105, 5], Operations: ['38+67=105', '21-16=5'] Exploring Operation: 105/5=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[38, 21, 16, 67], Operations: [] Exploring Operation: 67-38=29, Resulting Numbers: [21, 16, 29] Generated Node #0,0: 21:[21, 16, 29] Operation: 67-38=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[21, 16, 29], Operations: ['67-38=29'] Exploring Operation: 29-21=8, Resulting Numbers: [16, 8] Generated Node #0,0,0: 21:[16, 8] Operation: 29-21=8 Moving to Node #0,0,0 Current State: 21:[16, 8], Operations: ['67-38=29', '29-21=8'] Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,21 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
[ 44, 49, 57, 36 ]
88
[ "49-44=5", "57+36=93", "93-5=88" ]
Current State: 88:[44, 49, 57, 36], Operations: [] Exploring Operation: 49-44=5, Resulting Numbers: [57, 36, 5] Generated Node #2: [57, 36, 5] from Operation: 49-44=5 Current State: 88:[57, 36, 5], Operations: ['49-44=5'] Exploring Operation: 57+36=93, Resulting Numbers: [5, 93] Generated Node #3: [5, 93] from Operation: 57+36=93 Current State: 88:[5, 93], Operations: ['49-44=5', '57+36=93'] Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[44, 49, 57, 36], Operations: [] Exploring Operation: 57-49=8, Resulting Numbers: [44, 36, 8] Generated Node #0,0: 88:[44, 36, 8] Operation: 57-49=8 Exploring Operation: 57-36=21, Resulting Numbers: [44, 49, 21] Generated Node #0,1: 88:[44, 49, 21] Operation: 57-36=21 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[44, 49, 21], Operations: ['57-36=21'] Exploring Operation: 44+49=93, Resulting Numbers: [21, 93] Generated Node #0,1,0: 88:[21, 93] Operation: 44+49=93 Exploring Operation: 49-44=5, Resulting Numbers: [21, 5] Generated Node #0,1,1: 88:[21, 5] Operation: 49-44=5 Moving to Node #0,1,1 Current State: 88:[21, 5], Operations: ['57-36=21', '49-44=5'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,88 unequal: No Solution Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[21, 93], Operations: ['57-36=21', '44+49=93'] Exploring Operation: 21+93=114, Resulting Numbers: [114] 114,88 unequal: No Solution Exploring Operation: 93-21=72, Resulting Numbers: [72] 72,88 unequal: No Solution No 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: 88:[44, 36, 8], Operations: ['57-49=8'] Exploring Operation: 36+8=44, Resulting Numbers: [44, 44] Generated Node #0,0,0: 88:[44, 44] Operation: 36+8=44 Exploring Operation: 44-36=8, Resulting Numbers: [8, 8] Generated Node #0,0,1: 88:[8, 8] Operation: 44-36=8 Moving to Node #0,0,0 Current State: 88:[44, 44], Operations: ['57-49=8', '36+8=44'] Exploring Operation: 44/44=1, Resulting Numbers: [1] 1,88 unequal: No Solution Exploring Operation: 44+44=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[44, 49, 57, 36], Operations: [] Exploring Operation: 57-49=8, Resulting Numbers: [44, 36, 8] Generated Node #0,0: 88:[44, 36, 8] Operation: 57-49=8 Moving to Node #0,0 Current State: 88:[44, 36, 8], Operations: ['57-49=8'] Exploring Operation: 36+8=44, Resulting Numbers: [44, 44] Generated Node #0,0,0: 88:[44, 44] Operation: 36+8=44 Moving to Node #0,0,0 Current State: 88:[44, 44], Operations: ['57-49=8', '36+8=44'] Exploring Operation: 44+44=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 20, 18, 37, 11 ]
50
[ "20-18=2", "37+11=48", "2+48=50" ]
Current State: 50:[20, 18, 37, 11], Operations: [] Exploring Operation: 20-18=2, Resulting Numbers: [37, 11, 2] Generated Node #2: [37, 11, 2] from Operation: 20-18=2 Current State: 50:[37, 11, 2], Operations: ['20-18=2'] Exploring Operation: 37+11=48, Resulting Numbers: [2, 48] Generated Node #3: [2, 48] from Operation: 37+11=48 Current State: 50:[2, 48], Operations: ['20-18=2', '37+11=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[20, 18, 37, 11], Operations: [] Exploring Operation: 37-18=19, Resulting Numbers: [20, 11, 19] Generated Node #0,0: 50:[20, 11, 19] Operation: 37-18=19 Exploring Operation: 18+37=55, Resulting Numbers: [20, 11, 55] Generated Node #0,1: 50:[20, 11, 55] Operation: 18+37=55 Exploring Operation: 20-18=2, Resulting Numbers: [37, 11, 2] Generated Node #0,2: 50:[37, 11, 2] Operation: 20-18=2 Moving to Node #0,1 Current State: 50:[20, 11, 55], Operations: ['18+37=55'] Exploring Operation: 55/11=5, Resulting Numbers: [20, 5] Generated Node #0,1,0: 50:[20, 5] Operation: 55/11=5 Exploring Operation: 20-11=9, Resulting Numbers: [55, 9] Generated Node #0,1,1: 50:[55, 9] Operation: 20-11=9 Exploring Operation: 20+11=31, Resulting Numbers: [55, 31] Generated Node #0,1,2: 50:[55, 31] Operation: 20+11=31 Moving to Node #0,0 Current State: 50:[20, 11, 19], Operations: ['37-18=19'] Exploring Operation: 20-11=9, Resulting Numbers: [19, 9] Generated Node #0,0,0: 50:[19, 9] Operation: 20-11=9 Exploring Operation: 19-11=8, Resulting Numbers: [20, 8] Generated Node #0,0,1: 50:[20, 8] Operation: 19-11=8 Exploring Operation: 20-19=1, Resulting Numbers: [11, 1] Generated Node #0,0,2: 50:[11, 1] Operation: 20-19=1 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 50:[11, 1], Operations: ['37-18=19', '20-19=1'] Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,50 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,50 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[19, 9], Operations: ['37-18=19', '20-11=9'] Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,50 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 50:[20, 8], Operations: ['37-18=19', '19-11=8'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,50 unequal: No Solution Exploring Operation: 20+8=28, Resulting Numbers: [28] 28,50 unequal: No Solution Exploring Operation: 20*8=160, Resulting Numbers: [160] 160,50 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: 50:[37, 11, 2], Operations: ['20-18=2'] Exploring Operation: 37+11=48, Resulting Numbers: [2, 48] Generated Node #0,2,0: 50:[2, 48] Operation: 37+11=48 Exploring Operation: 37-2=35, Resulting Numbers: [11, 35] Generated Node #0,2,1: 50:[11, 35] Operation: 37-2=35 Exploring Operation: 37-11=26, Resulting Numbers: [2, 26] Generated Node #0,2,2: 50:[2, 26] Operation: 37-11=26 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 50:[2, 26], Operations: ['20-18=2', '37-11=26'] Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,50 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,50 unequal: No Solution Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 50:[2, 48], Operations: ['20-18=2', '37+11=48'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,50 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,50 unequal: No Solution Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[20, 18, 37, 11], Operations: [] Exploring Operation: 20-18=2, Resulting Numbers: [37, 11, 2] Generated Node #0,2: 50:[37, 11, 2] Operation: 20-18=2 Moving to Node #0,2 Current State: 50:[37, 11, 2], Operations: ['20-18=2'] Exploring Operation: 37+11=48, Resulting Numbers: [2, 48] Generated Node #0,2,0: 50:[2, 48] Operation: 37+11=48 Moving to Node #0,2,0 Current State: 50:[2, 48], Operations: ['20-18=2', '37+11=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_3
sum_heuristic
[ 83, 6, 16, 62 ]
49
[ "83+62=145", "6*16=96", "145-96=49" ]
Current State: 49:[83, 6, 16, 62], Operations: [] Exploring Operation: 83+62=145, Resulting Numbers: [6, 16, 145] Generated Node #2: [6, 16, 145] from Operation: 83+62=145 Current State: 49:[6, 16, 145], Operations: ['83+62=145'] Exploring Operation: 6*16=96, Resulting Numbers: [145, 96] Generated Node #3: [145, 96] from Operation: 6*16=96 Current State: 49:[145, 96], Operations: ['83+62=145', '6*16=96'] Exploring Operation: 145-96=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[83, 6, 16, 62], Operations: [] Exploring Operation: 83-62=21, Resulting Numbers: [6, 16, 21] Generated Node #0,0: 49:[6, 16, 21] Operation: 83-62=21 Exploring Operation: 83-16=67, Resulting Numbers: [6, 62, 67] Generated Node #0,1: 49:[6, 62, 67] Operation: 83-16=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[6, 16, 21], Operations: ['83-62=21'] Exploring Operation: 16+21=37, Resulting Numbers: [6, 37] Generated Node #0,0,0: 49:[6, 37] Operation: 16+21=37 Exploring Operation: 21-16=5, Resulting Numbers: [6, 5] Generated Node #0,0,1: 49:[6, 5] Operation: 21-16=5 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 49:[6, 5], Operations: ['83-62=21', '21-16=5'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,49 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 #0,0,0 Current State: 49:[6, 37], Operations: ['83-62=21', '16+21=37'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,49 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:[6, 62, 67], Operations: ['83-16=67'] Exploring Operation: 62-6=56, Resulting Numbers: [67, 56] Generated Node #0,1,0: 49:[67, 56] Operation: 62-6=56 Exploring Operation: 67-62=5, Resulting Numbers: [6, 5] Generated Node #0,1,1: 49:[6, 5] Operation: 67-62=5 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 49:[6, 5], Operations: ['83-16=67', '67-62=5'] Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,49 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 #0,1,0 Current State: 49:[67, 56], Operations: ['83-16=67', '62-6=56'] Exploring Operation: 67+56=123, Resulting Numbers: [123] 123,49 unequal: No Solution Exploring Operation: 67-56=11, Resulting Numbers: [11] 11,49 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_2
sum_heuristic
[ 49, 49, 72, 25 ]
96
[ "49/49=1", "72+25=97", "97-1=96" ]
Current State: 96:[49, 49, 72, 25], Operations: [] Exploring Operation: 49/49=1, Resulting Numbers: [72, 25, 1] Generated Node #2: [72, 25, 1] from Operation: 49/49=1 Current State: 96:[72, 25, 1], Operations: ['49/49=1'] Exploring Operation: 72+25=97, Resulting Numbers: [1, 97] Generated Node #3: [1, 97] from Operation: 72+25=97 Current State: 96:[1, 97], Operations: ['49/49=1', '72+25=97'] Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[49, 49, 72, 25], Operations: [] Exploring Operation: 72+25=97, Resulting Numbers: [49, 49, 97] Generated Node #0,0: 96:[49, 49, 97] Operation: 72+25=97 Exploring Operation: 49-25=24, Resulting Numbers: [49, 72, 24] Generated Node #0,1: 96:[49, 72, 24] Operation: 49-25=24 Exploring Operation: 72-25=47, Resulting Numbers: [49, 49, 47] Generated Node #0,2: 96:[49, 49, 47] Operation: 72-25=47 Exploring Operation: 72-49=23, Resulting Numbers: [49, 25, 23] Generated Node #0,3: 96:[49, 25, 23] Operation: 72-49=23 Exploring Operation: 72-49=23, Resulting Numbers: [49, 25, 23] Generated Node #0,4: 96:[49, 25, 23] Operation: 72-49=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[49, 49, 97], Operations: ['72+25=97'] Exploring Operation: 97-49=48, Resulting Numbers: [49, 48] Generated Node #0,0,0: 96:[49, 48] Operation: 97-49=48 Exploring Operation: 97-49=48, Resulting Numbers: [49, 48] Generated Node #0,0,1: 96:[49, 48] Operation: 97-49=48 Exploring Operation: 49-49=0, Resulting Numbers: [97, 0] Generated Node #0,0,2: 96:[97, 0] Operation: 49-49=0 Exploring Operation: 49/49=1, Resulting Numbers: [97, 1] Generated Node #0,0,3: 96:[97, 1] Operation: 49/49=1 Exploring Operation: 49+49=98, Resulting Numbers: [97, 98] Generated Node #0,0,4: 96:[97, 98] Operation: 49+49=98 Moving to Node #0,0,0 Current State: 96:[49, 48], Operations: ['72+25=97', '97-49=48'] Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,96 unequal: No Solution Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[49, 48], Operations: ['72+25=97', '97-49=48'] Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,96 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[97, 1], Operations: ['72+25=97', '49/49=1'] Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[49, 49, 72, 25], Operations: [] Exploring Operation: 72+25=97, Resulting Numbers: [49, 49, 97] Generated Node #0,0: 96:[49, 49, 97] Operation: 72+25=97 Moving to Node #0,0 Current State: 96:[49, 49, 97], Operations: ['72+25=97'] Exploring Operation: 49/49=1, Resulting Numbers: [97, 1] Generated Node #0,0,3: 96:[97, 1] Operation: 49/49=1 Moving to Node #0,0,3 Current State: 96:[97, 1], Operations: ['72+25=97', '49/49=1'] Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 38, 16, 3, 12 ]
58
[ "38+16=54", "12/3=4", "54+4=58" ]
Current State: 58:[38, 16, 3, 12], Operations: [] Exploring Operation: 38+16=54, Resulting Numbers: [3, 12, 54] Generated Node #2: [3, 12, 54] from Operation: 38+16=54 Current State: 58:[3, 12, 54], Operations: ['38+16=54'] Exploring Operation: 12/3=4, Resulting Numbers: [54, 4] Generated Node #3: [54, 4] from Operation: 12/3=4 Current State: 58:[54, 4], Operations: ['38+16=54', '12/3=4'] Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[38, 16, 3, 12], Operations: [] Exploring Operation: 38-16=22, Resulting Numbers: [3, 12, 22] Generated Node #0,0: 58:[3, 12, 22] Operation: 38-16=22 Exploring Operation: 38+16=54, Resulting Numbers: [3, 12, 54] Generated Node #0,1: 58:[3, 12, 54] Operation: 38+16=54 Exploring Operation: 38-12=26, Resulting Numbers: [16, 3, 26] Generated Node #0,2: 58:[16, 3, 26] Operation: 38-12=26 Exploring Operation: 16-12=4, Resulting Numbers: [38, 3, 4] Generated Node #0,3: 58:[38, 3, 4] Operation: 16-12=4 Exploring Operation: 16+12=28, Resulting Numbers: [38, 3, 28] Generated Node #0,4: 58:[38, 3, 28] Operation: 16+12=28 Start Sub Search at level 1: Moving to Node #0,4 Current State: 58:[38, 3, 28], Operations: ['16+12=28'] Exploring Operation: 38+3=41, Resulting Numbers: [28, 41] Generated Node #0,4,0: 58:[28, 41] Operation: 38+3=41 Exploring Operation: 38-3=35, Resulting Numbers: [28, 35] Generated Node #0,4,1: 58:[28, 35] Operation: 38-3=35 Exploring Operation: 38+28=66, Resulting Numbers: [3, 66] Generated Node #0,4,2: 58:[3, 66] Operation: 38+28=66 Exploring Operation: 38-28=10, Resulting Numbers: [3, 10] Generated Node #0,4,3: 58:[3, 10] Operation: 38-28=10 Exploring Operation: 3+28=31, Resulting Numbers: [38, 31] Generated Node #0,4,4: 58:[38, 31] Operation: 3+28=31 Moving to Node #0,4,1 Current State: 58:[28, 35], Operations: ['16+12=28', '38-3=35'] Exploring Operation: 28*35=980, Resulting Numbers: [980] 980,58 unequal: No Solution Exploring Operation: 28+35=63, Resulting Numbers: [63] 63,58 unequal: No Solution Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,58 unequal: No Solution Moving to Node #0,4,3 Current State: 58:[3, 10], Operations: ['16+12=28', '38-28=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,58 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,58 unequal: No Solution Moving to Node #0,4,2 Current State: 58:[3, 66], Operations: ['16+12=28', '38+28=66'] Exploring Operation: 3+66=69, Resulting Numbers: [69] 69,58 unequal: No Solution Exploring Operation: 66-3=63, Resulting Numbers: [63] 63,58 unequal: No Solution Exploring Operation: 3*66=198, Resulting Numbers: [198] 198,58 unequal: No Solution Exploring Operation: 66/3=22, Resulting Numbers: [22] 22,58 unequal: No Solution Moving to Node #0,4,4 Current State: 58:[38, 31], Operations: ['16+12=28', '3+28=31'] Exploring Operation: 38*31=1178, Resulting Numbers: [1178] 1178,58 unequal: No Solution Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,58 unequal: No Solution Exploring Operation: 38+31=69, Resulting Numbers: [69] 69,58 unequal: No Solution Moving to Node #0,4,0 Current State: 58:[28, 41], Operations: ['16+12=28', '38+3=41'] Exploring Operation: 28*41=1148, Resulting Numbers: [1148] 1148,58 unequal: No Solution Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 28+41=69, Resulting Numbers: [69] 69,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[38, 3, 4], Operations: ['16-12=4'] Exploring Operation: 38-3=35, Resulting Numbers: [4, 35] Generated Node #0,3,0: 58:[4, 35] Operation: 38-3=35 Exploring Operation: 38-4=34, Resulting Numbers: [3, 34] Generated Node #0,3,1: 58:[3, 34] Operation: 38-4=34 Exploring Operation: 38+3=41, Resulting Numbers: [4, 41] Generated Node #0,3,2: 58:[4, 41] Operation: 38+3=41 Exploring Operation: 4-3=1, Resulting Numbers: [38, 1] Generated Node #0,3,3: 58:[38, 1] Operation: 4-3=1 Exploring Operation: 38+4=42, Resulting Numbers: [3, 42] Generated Node #0,3,4: 58:[3, 42] Operation: 38+4=42 Moving to Node #0,3,1 Current State: 58:[3, 34], Operations: ['16-12=4', '38-4=34'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,58 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,58 unequal: No Solution Moving to Node #0,3,0 Current State: 58:[4, 35], Operations: ['16-12=4', '38-3=35'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 4*35=140, Resulting Numbers: [140] 140,58 unequal: No Solution Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,58 unequal: No Solution Moving to Node #0,3,3 Current State: 58:[38, 1], Operations: ['16-12=4', '4-3=1'] Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,58 unequal: No Solution Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,58 unequal: No Solution Exploring Operation: 38+1=39, Resulting Numbers: [39] 39,58 unequal: No Solution Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,58 unequal: No Solution Moving to Node #0,3,2 Current State: 58:[4, 41], Operations: ['16-12=4', '38+3=41'] Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,58 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,58 unequal: No Solution Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,58 unequal: No Solution Moving to Node #0,3,4 Current State: 58:[3, 42], Operations: ['16-12=4', '38+4=42'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,58 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,58 unequal: No Solution Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[3, 12, 54], Operations: ['38+16=54'] Exploring Operation: 3*12=36, Resulting Numbers: [54, 36] Generated Node #0,1,0: 58:[54, 36] Operation: 3*12=36 Exploring Operation: 3+54=57, Resulting Numbers: [12, 57] Generated Node #0,1,1: 58:[12, 57] Operation: 3+54=57 Exploring Operation: 12+54=66, Resulting Numbers: [3, 66] Generated Node #0,1,2: 58:[3, 66] Operation: 12+54=66 Exploring Operation: 12/3=4, Resulting Numbers: [54, 4] Generated Node #0,1,3: 58:[54, 4] Operation: 12/3=4 Exploring Operation: 12-3=9, Resulting Numbers: [54, 9] Generated Node #0,1,4: 58:[54, 9] Operation: 12-3=9 Moving to Node #0,1,3 Current State: 58:[54, 4], Operations: ['38+16=54', '12/3=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,58 unequal: No Solution Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[38, 16, 3, 12], Operations: [] Exploring Operation: 38+16=54, Resulting Numbers: [3, 12, 54] Generated Node #0,1: 58:[3, 12, 54] Operation: 38+16=54 Moving to Node #0,1 Current State: 58:[3, 12, 54], Operations: ['38+16=54'] Exploring Operation: 12/3=4, Resulting Numbers: [54, 4] Generated Node #0,1,3: 58:[54, 4] Operation: 12/3=4 Moving to Node #0,1,3 Current State: 58:[54, 4], Operations: ['38+16=54', '12/3=4'] Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.948785
hs_5
mult_heuristic
[ 56, 56, 9, 8 ]
18
[ "56/56=1", "9+8=17", "1+17=18" ]
Current State: 18:[56, 56, 9, 8], Operations: [] Exploring Operation: 56/56=1, Resulting Numbers: [9, 8, 1] Generated Node #2: [9, 8, 1] from Operation: 56/56=1 Current State: 18:[9, 8, 1], Operations: ['56/56=1'] Exploring Operation: 9+8=17, Resulting Numbers: [1, 17] Generated Node #3: [1, 17] from Operation: 9+8=17 Current State: 18:[1, 17], Operations: ['56/56=1', '9+8=17'] Exploring Operation: 1+17=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[56, 56, 9, 8], Operations: [] Exploring Operation: 56-56=0, Resulting Numbers: [9, 8, 0] Generated Node #0,0: 18:[9, 8, 0] Operation: 56-56=0 Exploring Operation: 56/56=1, Resulting Numbers: [9, 8, 1] Generated Node #0,1: 18:[9, 8, 1] Operation: 56/56=1 Moving to Node #0,1 Current State: 18:[9, 8, 1], Operations: ['56/56=1'] Exploring Operation: 8+1=9, Resulting Numbers: [9, 9] Generated Node #0,1,0: 18:[9, 9] Operation: 8+1=9 Exploring Operation: 9*1=9, Resulting Numbers: [8, 9] Generated Node #0,1,1: 18:[8, 9] Operation: 9*1=9 Moving to Node #0,0 Current State: 18:[9, 8, 0], Operations: ['56-56=0'] Exploring Operation: 9-0=9, Resulting Numbers: [8, 9] Generated Node #0,0,0: 18:[8, 9] Operation: 9-0=9 Exploring Operation: 9+0=9, Resulting Numbers: [8, 9] Generated Node #0,0,1: 18:[8, 9] Operation: 9+0=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[8, 9], Operations: ['56-56=0', '9-0=9'] Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,18 unequal: No Solution No 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: 18:[8, 9], Operations: ['56-56=0', '9+0=9'] Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 18:[9, 9], Operations: ['56/56=1', '8+1=9'] Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[56, 56, 9, 8], Operations: [] Exploring Operation: 56/56=1, Resulting Numbers: [9, 8, 1] Generated Node #0,1: 18:[9, 8, 1] Operation: 56/56=1 Moving to Node #0,1 Current State: 18:[9, 8, 1], Operations: ['56/56=1'] Exploring Operation: 8+1=9, Resulting Numbers: [9, 9] Generated Node #0,1,0: 18:[9, 9] Operation: 8+1=9 Moving to Node #0,1,0 Current State: 18:[9, 9], Operations: ['56/56=1', '8+1=9'] Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 4, 62, 26, 56 ]
88
[ "62-4=58", "56-26=30", "58+30=88" ]
Current State: 88:[4, 62, 26, 56], Operations: [] Exploring Operation: 62-4=58, Resulting Numbers: [26, 56, 58] Generated Node #2: [26, 56, 58] from Operation: 62-4=58 Current State: 88:[26, 56, 58], Operations: ['62-4=58'] Exploring Operation: 56-26=30, Resulting Numbers: [58, 30] Generated Node #3: [58, 30] from Operation: 56-26=30 Current State: 88:[58, 30], Operations: ['62-4=58', '56-26=30'] Exploring Operation: 58+30=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[4, 62, 26, 56], Operations: [] Exploring Operation: 62-56=6, Resulting Numbers: [4, 26, 6] Generated Node #0,0: 88:[4, 26, 6] Operation: 62-56=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[4, 26, 6], Operations: ['62-56=6'] Exploring Operation: 26-4=22, Resulting Numbers: [6, 22] Generated Node #0,0,0: 88:[6, 22] Operation: 26-4=22 Moving to Node #0,0,0 Current State: 88:[6, 22], Operations: ['62-56=6', '26-4=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,88 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
[ 33, 57, 6, 92 ]
15
[ "6*92=552", "552-57=495", "495/33=15" ]
Current State: 15:[33, 57, 6, 92], Operations: [] Exploring Operation: 6*92=552, Resulting Numbers: [33, 57, 552] Generated Node #2: [33, 57, 552] from Operation: 6*92=552 Current State: 15:[33, 57, 552], Operations: ['6*92=552'] Exploring Operation: 552-57=495, Resulting Numbers: [33, 495] Generated Node #3: [33, 495] from Operation: 552-57=495 Current State: 15:[33, 495], Operations: ['6*92=552', '552-57=495'] Exploring Operation: 495/33=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[33, 57, 6, 92], Operations: [] Exploring Operation: 92-57=35, Resulting Numbers: [33, 6, 35] Generated Node #0,0: 15:[33, 6, 35] Operation: 92-57=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[33, 6, 35], Operations: ['92-57=35'] Exploring Operation: 35-33=2, Resulting Numbers: [6, 2] Generated Node #0,0,0: 15:[6, 2] Operation: 35-33=2 Moving to Node #0,0,0 Current State: 15:[6, 2], Operations: ['92-57=35', '35-33=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,15 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
[ 69, 29, 52, 26 ]
87
[ "29-26=3", "52*3=156", "156-69=87" ]
Current State: 87:[69, 29, 52, 26], Operations: [] Exploring Operation: 29-26=3, Resulting Numbers: [69, 52, 3] Generated Node #2: [69, 52, 3] from Operation: 29-26=3 Current State: 87:[69, 52, 3], Operations: ['29-26=3'] Exploring Operation: 52*3=156, Resulting Numbers: [69, 156] Generated Node #3: [69, 156] from Operation: 52*3=156 Current State: 87:[69, 156], Operations: ['29-26=3', '52*3=156'] Exploring Operation: 156-69=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[69, 29, 52, 26], Operations: [] Exploring Operation: 52-26=26, Resulting Numbers: [69, 29, 26] Generated Node #0,0: 87:[69, 29, 26] Operation: 52-26=26 Exploring Operation: 29+52=81, Resulting Numbers: [69, 26, 81] Generated Node #0,1: 87:[69, 26, 81] Operation: 29+52=81 Exploring Operation: 52/26=2, Resulting Numbers: [69, 29, 2] Generated Node #0,2: 87:[69, 29, 2] Operation: 52/26=2 Exploring Operation: 69-52=17, Resulting Numbers: [29, 26, 17] Generated Node #0,3: 87:[29, 26, 17] Operation: 69-52=17 Start Sub Search at level 1: Moving to Node #0,3 Current State: 87:[29, 26, 17], Operations: ['69-52=17'] Exploring Operation: 29-26=3, Resulting Numbers: [17, 3] Generated Node #0,3,0: 87:[17, 3] Operation: 29-26=3 Exploring Operation: 26+17=43, Resulting Numbers: [29, 43] Generated Node #0,3,1: 87:[29, 43] Operation: 26+17=43 Exploring Operation: 29-17=12, Resulting Numbers: [26, 12] Generated Node #0,3,2: 87:[26, 12] Operation: 29-17=12 Exploring Operation: 26-17=9, Resulting Numbers: [29, 9] Generated Node #0,3,3: 87:[29, 9] Operation: 26-17=9 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 87:[29, 9], Operations: ['69-52=17', '26-17=9'] Exploring Operation: 29+9=38, Resulting Numbers: [38] 38,87 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 29*9=261, Resulting Numbers: [261] 261,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 87:[17, 3], Operations: ['69-52=17', '29-26=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,87 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 87:[26, 12], Operations: ['69-52=17', '29-17=12'] Exploring Operation: 26+12=38, Resulting Numbers: [38] 38,87 unequal: No Solution Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,87 unequal: No Solution Exploring Operation: 26*12=312, Resulting Numbers: [312] 312,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 87:[29, 43], Operations: ['69-52=17', '26+17=43'] Exploring Operation: 29+43=72, Resulting Numbers: [72] 72,87 unequal: No Solution Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,87 unequal: No Solution Exploring Operation: 29*43=1247, Resulting Numbers: [1247] 1247,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[69, 29, 2], Operations: ['52/26=2'] Exploring Operation: 69+29=98, Resulting Numbers: [2, 98] Generated Node #0,2,0: 87:[2, 98] Operation: 69+29=98 Exploring Operation: 69-29=40, Resulting Numbers: [2, 40] Generated Node #0,2,1: 87:[2, 40] Operation: 69-29=40 Exploring Operation: 69+2=71, Resulting Numbers: [29, 71] Generated Node #0,2,2: 87:[29, 71] Operation: 69+2=71 Exploring Operation: 69-2=67, Resulting Numbers: [29, 67] Generated Node #0,2,3: 87:[29, 67] Operation: 69-2=67 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 87:[2, 98], Operations: ['52/26=2', '69+29=98'] Exploring Operation: 2*98=196, Resulting Numbers: [196] 196,87 unequal: No Solution Exploring Operation: 2+98=100, Resulting Numbers: [100] 100,87 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,87 unequal: No Solution Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 87:[2, 40], Operations: ['52/26=2', '69-29=40'] Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,87 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,87 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,87 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 87:[29, 71], Operations: ['52/26=2', '69+2=71'] Exploring Operation: 29+71=100, Resulting Numbers: [100] 100,87 unequal: No Solution Exploring Operation: 29*71=2059, Resulting Numbers: [2059] 2059,87 unequal: No Solution Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 87:[29, 67], Operations: ['52/26=2', '69-2=67'] Exploring Operation: 29+67=96, Resulting Numbers: [96] 96,87 unequal: No Solution Exploring Operation: 67-29=38, Resulting Numbers: [38] 38,87 unequal: No Solution Exploring Operation: 29*67=1943, Resulting Numbers: [1943] 1943,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[69, 29, 26], Operations: ['52-26=26'] Exploring Operation: 69+26=95, Resulting Numbers: [29, 95] Generated Node #0,0,0: 87:[29, 95] Operation: 69+26=95 Exploring Operation: 69+29=98, Resulting Numbers: [26, 98] Generated Node #0,0,1: 87:[26, 98] Operation: 69+29=98 Exploring Operation: 69-29=40, Resulting Numbers: [26, 40] Generated Node #0,0,2: 87:[26, 40] Operation: 69-29=40 Exploring Operation: 69-26=43, Resulting Numbers: [29, 43] Generated Node #0,0,3: 87:[29, 43] Operation: 69-26=43 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[29, 95], Operations: ['52-26=26', '69+26=95'] Exploring Operation: 29+95=124, Resulting Numbers: [124] 124,87 unequal: No Solution Exploring Operation: 29*95=2755, Resulting Numbers: [2755] 2755,87 unequal: No Solution Exploring Operation: 95-29=66, Resulting Numbers: [66] 66,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[26, 98], Operations: ['52-26=26', '69+29=98'] Exploring Operation: 98-26=72, Resulting Numbers: [72] 72,87 unequal: No Solution Exploring Operation: 26+98=124, Resulting Numbers: [124] 124,87 unequal: No Solution Exploring Operation: 26*98=2548, Resulting Numbers: [2548] 2548,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 87:[26, 40], Operations: ['52-26=26', '69-29=40'] Exploring Operation: 26*40=1040, Resulting Numbers: [1040] 1040,87 unequal: No Solution Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,87 unequal: No Solution Exploring Operation: 26+40=66, Resulting Numbers: [66] 66,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 87:[29, 43], Operations: ['52-26=26', '69-26=43'] Exploring Operation: 29*43=1247, Resulting Numbers: [1247] 1247,87 unequal: No Solution Exploring Operation: 29+43=72, Resulting Numbers: [72] 72,87 unequal: No Solution Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[69, 26, 81], Operations: ['29+52=81'] Exploring Operation: 26+81=107, Resulting Numbers: [69, 107] Generated Node #0,1,0: 87:[69, 107] Operation: 26+81=107 Exploring Operation: 69+26=95, Resulting Numbers: [81, 95] Generated Node #0,1,1: 87:[81, 95] Operation: 69+26=95 Exploring Operation: 81-69=12, Resulting Numbers: [26, 12] Generated Node #0,1,2: 87:[26, 12] Operation: 81-69=12 Exploring Operation: 69-26=43, Resulting Numbers: [81, 43] Generated Node #0,1,3: 87:[81, 43] Operation: 69-26=43 Moving to Node #0,1,2 Current State: 87:[26, 12], Operations: ['29+52=81', '81-69=12'] Exploring Operation: 26+12=38, Resulting Numbers: [38] 38,87 unequal: No Solution Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,87 unequal: No Solution Exploring Operation: 26*12=312, Resulting Numbers: [312] 312,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[81, 95], Operations: ['29+52=81', '69+26=95'] Exploring Operation: 95-81=14, Resulting Numbers: [14] 14,87 unequal: No Solution Exploring Operation: 81*95=7695, Resulting Numbers: [7695] 7695,87 unequal: No Solution Exploring Operation: 81+95=176, Resulting Numbers: [176] 176,87 unequal: No Solution Moving to Node #0,1,3 Current State: 87:[81, 43], Operations: ['29+52=81', '69-26=43'] Exploring Operation: 81+43=124, Resulting Numbers: [124] 124,87 unequal: No Solution Exploring Operation: 81-43=38, Resulting Numbers: [38] 38,87 unequal: No Solution Exploring Operation: 81*43=3483, Resulting Numbers: [3483] 3483,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[69, 107], Operations: ['29+52=81', '26+81=107'] Exploring Operation: 107-69=38, Resulting Numbers: [38] 38,87 unequal: No Solution Exploring Operation: 69+107=176, Resulting Numbers: [176] 176,87 unequal: No Solution Exploring Operation: 69*107=7383, Resulting Numbers: [7383] 7383,87 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
[ 95, 30, 23, 3 ]
99
[ "95+30=125", "23+3=26", "125-26=99" ]
Current State: 99:[95, 30, 23, 3], Operations: [] Exploring Operation: 95+30=125, Resulting Numbers: [23, 3, 125] Generated Node #2: [23, 3, 125] from Operation: 95+30=125 Current State: 99:[23, 3, 125], Operations: ['95+30=125'] Exploring Operation: 23+3=26, Resulting Numbers: [125, 26] Generated Node #3: [125, 26] from Operation: 23+3=26 Current State: 99:[125, 26], Operations: ['95+30=125', '23+3=26'] Exploring Operation: 125-26=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[95, 30, 23, 3], Operations: [] Exploring Operation: 30-23=7, Resulting Numbers: [95, 3, 7] Generated Node #0,0: 99:[95, 3, 7] Operation: 30-23=7 Moving to Node #0,0 Current State: 99:[95, 3, 7], Operations: ['30-23=7'] Exploring Operation: 95+3=98, Resulting Numbers: [7, 98] Generated Node #0,0,0: 99:[7, 98] Operation: 95+3=98 Moving to Node #0,0,0 Current State: 99:[7, 98], Operations: ['30-23=7', '95+3=98'] Exploring Operation: 98/7=14, Resulting Numbers: [14] 14,99 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 80, 8, 61, 13 ]
40
[ "80+8=88", "61-13=48", "88-48=40" ]
Current State: 40:[80, 8, 61, 13], Operations: [] Exploring Operation: 80+8=88, Resulting Numbers: [61, 13, 88] Generated Node #2: [61, 13, 88] from Operation: 80+8=88 Current State: 40:[61, 13, 88], Operations: ['80+8=88'] Exploring Operation: 61-13=48, Resulting Numbers: [88, 48] Generated Node #3: [88, 48] from Operation: 61-13=48 Current State: 40:[88, 48], Operations: ['80+8=88', '61-13=48'] Exploring Operation: 88-48=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[80, 8, 61, 13], Operations: [] Exploring Operation: 80-61=19, Resulting Numbers: [8, 13, 19] Generated Node #0,0: 40:[8, 13, 19] Operation: 80-61=19 Exploring Operation: 80/8=10, Resulting Numbers: [61, 13, 10] Generated Node #0,1: 40:[61, 13, 10] Operation: 80/8=10 Moving to Node #0,0 Current State: 40:[8, 13, 19], Operations: ['80-61=19'] Exploring Operation: 13-8=5, Resulting Numbers: [19, 5] Generated Node #0,0,0: 40:[19, 5] Operation: 13-8=5 Exploring Operation: 19-13=6, Resulting Numbers: [8, 6] Generated Node #0,0,1: 40:[8, 6] Operation: 19-13=6 Moving to Node #0,1 Current State: 40:[61, 13, 10], Operations: ['80/8=10'] Exploring Operation: 61-13=48, Resulting Numbers: [10, 48] Generated Node #0,1,0: 40:[10, 48] Operation: 61-13=48 Exploring Operation: 61-10=51, Resulting Numbers: [13, 51] Generated Node #0,1,1: 40:[13, 51] Operation: 61-10=51 Moving to Node #0,0,0 Current State: 40:[19, 5], Operations: ['80-61=19', '13-8=5'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,40 unequal: No Solution Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[8, 6], Operations: ['80-61=19', '19-13=6'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,40 unequal: No Solution Moving to Node #0,1,0 Current State: 40:[10, 48], Operations: ['80/8=10', '61-13=48'] Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,40 unequal: No Solution Exploring Operation: 10+48=58, Resulting Numbers: [58] 58,40 unequal: No Solution Moving to Node #0,1,1 Current State: 40:[13, 51], Operations: ['80/8=10', '61-10=51'] Exploring Operation: 51-13=38, Resulting Numbers: [38] 38,40 unequal: No Solution Exploring Operation: 13+51=64, Resulting Numbers: [64] 64,40 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 70, 4, 1, 64 ]
86
[ "70*1=70", "64/4=16", "70+16=86" ]
Current State: 86:[70, 4, 1, 64], Operations: [] Exploring Operation: 70*1=70, Resulting Numbers: [4, 64, 70] Generated Node #2: [4, 64, 70] from Operation: 70*1=70 Current State: 86:[4, 64, 70], Operations: ['70*1=70'] Exploring Operation: 64/4=16, Resulting Numbers: [70, 16] Generated Node #3: [70, 16] from Operation: 64/4=16 Current State: 86:[70, 16], Operations: ['70*1=70', '64/4=16'] Exploring Operation: 70+16=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[70, 4, 1, 64], Operations: [] Exploring Operation: 64/4=16, Resulting Numbers: [70, 1, 16] Generated Node #0,0: 86:[70, 1, 16] Operation: 64/4=16 Exploring Operation: 70-64=6, Resulting Numbers: [4, 1, 6] Generated Node #0,1: 86:[4, 1, 6] Operation: 70-64=6 Exploring Operation: 70+4=74, Resulting Numbers: [1, 64, 74] Generated Node #0,2: 86:[1, 64, 74] Operation: 70+4=74 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[4, 1, 6], Operations: ['70-64=6'] Exploring Operation: 6-1=5, Resulting Numbers: [4, 5] Generated Node #0,1,0: 86:[4, 5] Operation: 6-1=5 Exploring Operation: 6-4=2, Resulting Numbers: [1, 2] Generated Node #0,1,1: 86:[1, 2] Operation: 6-4=2 Exploring Operation: 4-1=3, Resulting Numbers: [6, 3] Generated Node #0,1,2: 86:[6, 3] Operation: 4-1=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 86:[1, 2], Operations: ['70-64=6', '6-4=2'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,86 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:[4, 5], Operations: ['70-64=6', '6-1=5'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,86 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,86 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,86 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 #0,1,2 Current State: 86:[6, 3], Operations: ['70-64=6', '4-1=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,86 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:[70, 1, 16], Operations: ['64/4=16'] Exploring Operation: 70-16=54, Resulting Numbers: [1, 54] Generated Node #0,0,0: 86:[1, 54] Operation: 70-16=54 Exploring Operation: 70+16=86, Resulting Numbers: [1, 86] Generated Node #0,0,1: 86:[1, 86] Operation: 70+16=86 Exploring Operation: 70+1=71, Resulting Numbers: [16, 71] Generated Node #0,0,2: 86:[16, 71] Operation: 70+1=71 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[1, 86], Operations: ['64/4=16', '70+16=86'] Exploring Operation: 1+86=87, Resulting Numbers: [87] 87,86 unequal: No Solution Exploring Operation: 86/1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[70, 4, 1, 64], Operations: [] Exploring Operation: 64/4=16, Resulting Numbers: [70, 1, 16] Generated Node #0,0: 86:[70, 1, 16] Operation: 64/4=16 Moving to Node #0,0 Current State: 86:[70, 1, 16], Operations: ['64/4=16'] Exploring Operation: 70+16=86, Resulting Numbers: [1, 86] Generated Node #0,0,1: 86:[1, 86] Operation: 70+16=86 Moving to Node #0,0,1 Current State: 86:[1, 86], Operations: ['64/4=16', '70+16=86'] Exploring Operation: 86/1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 64, 77, 8, 77 ]
72
[ "64+77=141", "77-8=69", "141-69=72" ]
Current State: 72:[64, 77, 8, 77], Operations: [] Exploring Operation: 64+77=141, Resulting Numbers: [8, 141] Generated Node #2: [8, 141] from Operation: 64+77=141 Current State: 72:[8, 141], Operations: ['64+77=141'] Exploring Operation: 77-8=69, Resulting Numbers: [141, 69] Generated Node #3: [141, 69] from Operation: 77-8=69 Current State: 72:[141, 69], Operations: ['64+77=141', '77-8=69'] Exploring Operation: 141-69=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[64, 77, 8, 77], Operations: [] Exploring Operation: 77/77=1, Resulting Numbers: [64, 8, 1] Generated Node #0,0: 72:[64, 8, 1] Operation: 77/77=1 Exploring Operation: 77-64=13, Resulting Numbers: [8, 77, 13] Generated Node #0,1: 72:[8, 77, 13] Operation: 77-64=13 Exploring Operation: 64+8=72, Resulting Numbers: [77, 77, 72] Generated Node #0,2: 72:[77, 77, 72] Operation: 64+8=72 Exploring Operation: 77-64=13, Resulting Numbers: [77, 8, 13] Generated Node #0,3: 72:[77, 8, 13] Operation: 77-64=13 Moving to Node #0,1 Current State: 72:[8, 77, 13], Operations: ['77-64=13'] Exploring Operation: 77-13=64, Resulting Numbers: [8, 64] Generated Node #0,1,0: 72:[8, 64] Operation: 77-13=64 Exploring Operation: 77-8=69, Resulting Numbers: [13, 69] Generated Node #0,1,1: 72:[13, 69] Operation: 77-8=69 Exploring Operation: 8+13=21, Resulting Numbers: [77, 21] Generated Node #0,1,2: 72:[77, 21] Operation: 8+13=21 Exploring Operation: 13-8=5, Resulting Numbers: [77, 5] Generated Node #0,1,3: 72:[77, 5] Operation: 13-8=5 Moving to Node #0,3 Current State: 72:[77, 8, 13], Operations: ['77-64=13'] Exploring Operation: 77-13=64, Resulting Numbers: [8, 64] Generated Node #0,3,0: 72:[8, 64] Operation: 77-13=64 Exploring Operation: 8+13=21, Resulting Numbers: [77, 21] Generated Node #0,3,1: 72:[77, 21] Operation: 8+13=21 Exploring Operation: 13-8=5, Resulting Numbers: [77, 5] Generated Node #0,3,2: 72:[77, 5] Operation: 13-8=5 Exploring Operation: 77-8=69, Resulting Numbers: [13, 69] Generated Node #0,3,3: 72:[13, 69] Operation: 77-8=69 Moving to Node #0,0 Current State: 72:[64, 8, 1], Operations: ['77/77=1'] Exploring Operation: 64/8=8, Resulting Numbers: [1, 8] Generated Node #0,0,0: 72:[1, 8] Operation: 64/8=8 Exploring Operation: 64+1=65, Resulting Numbers: [8, 65] Generated Node #0,0,1: 72:[8, 65] Operation: 64+1=65 Exploring Operation: 64+8=72, Resulting Numbers: [1, 72] Generated Node #0,0,2: 72:[1, 72] Operation: 64+8=72 Exploring Operation: 64*1=64, Resulting Numbers: [8, 64] Generated Node #0,0,3: 72:[8, 64] Operation: 64*1=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[1, 8], Operations: ['77/77=1', '64/8=8'] Exploring Operation: 1*8=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 1+8=9, Resulting Numbers: [9] 9,72 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 72:[1, 72], Operations: ['77/77=1', '64+8=72'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,72 unequal: No Solution Exploring Operation: 1+72=73, Resulting Numbers: [73] 73,72 unequal: No Solution Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[64, 77, 8, 77], Operations: [] Exploring Operation: 77/77=1, Resulting Numbers: [64, 8, 1] Generated Node #0,0: 72:[64, 8, 1] Operation: 77/77=1 Moving to Node #0,0 Current State: 72:[64, 8, 1], Operations: ['77/77=1'] Exploring Operation: 64+8=72, Resulting Numbers: [1, 72] Generated Node #0,0,2: 72:[1, 72] Operation: 64+8=72 Moving to Node #0,0,2 Current State: 72:[1, 72], Operations: ['77/77=1', '64+8=72'] Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_4
sum_heuristic
[ 18, 36, 54, 2 ]
50
[ "36/18=2", "54-2=52", "52-2=50" ]
Current State: 50:[18, 36, 54, 2], Operations: [] Exploring Operation: 36/18=2, Resulting Numbers: [54, 2, 2] Generated Node #2: [54, 2, 2] from Operation: 36/18=2 Current State: 50:[54, 2, 2], Operations: ['36/18=2'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,50 equal: Goal Reached Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[18, 36, 54, 2], Operations: [] Exploring Operation: 36/18=2, Resulting Numbers: [54, 2, 2] Generated Node #0,0: 50:[54, 2, 2] Operation: 36/18=2 Exploring Operation: 18+36=54, Resulting Numbers: [54, 2, 54] Generated Node #0,1: 50:[54, 2, 54] Operation: 18+36=54 Moving to Node #0,0 Current State: 50:[54, 2, 2], Operations: ['36/18=2'] Exploring Operation: 54/2=27, Resulting Numbers: [2, 27] Generated Node #0,0,0: 50:[2, 27] Operation: 54/2=27 Exploring Operation: 54-2=52, Resulting Numbers: [2, 52] Generated Node #0,0,1: 50:[2, 52] Operation: 54-2=52 Moving to Node #0,1 Current State: 50:[54, 2, 54], Operations: ['18+36=54'] Exploring Operation: 54-54=0, Resulting Numbers: [2, 0] Generated Node #0,1,0: 50:[2, 0] Operation: 54-54=0 Exploring Operation: 54/54=1, Resulting Numbers: [2, 1] Generated Node #0,1,1: 50:[2, 1] Operation: 54/54=1 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 50:[2, 1], Operations: ['18+36=54', '54/54=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[2, 0], Operations: ['18+36=54', '54-54=0'] Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,50 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: 50:[2, 27], Operations: ['36/18=2', '54/2=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,50 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[2, 52], Operations: ['36/18=2', '54-2=52'] Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[18, 36, 54, 2], Operations: [] Exploring Operation: 36/18=2, Resulting Numbers: [54, 2, 2] Generated Node #0,0: 50:[54, 2, 2] Operation: 36/18=2 Moving to Node #0,0 Current State: 50:[54, 2, 2], Operations: ['36/18=2'] Exploring Operation: 54-2=52, Resulting Numbers: [2, 52] Generated Node #0,0,1: 50:[2, 52] Operation: 54-2=52 Moving to Node #0,0,1 Current State: 50:[2, 52], Operations: ['36/18=2', '54-2=52'] Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
0.984375
hs_2
mult_heuristic
[ 78, 53, 26, 14 ]
95
[ "78/26=3", "14*3=42", "53+42=95" ]
Current State: 95:[78, 53, 26, 14], Operations: [] Exploring Operation: 78/26=3, Resulting Numbers: [53, 14, 3] Generated Node #2: [53, 14, 3] from Operation: 78/26=3 Current State: 95:[53, 14, 3], Operations: ['78/26=3'] Exploring Operation: 14*3=42, Resulting Numbers: [53, 42] Generated Node #3: [53, 42] from Operation: 14*3=42 Current State: 95:[53, 42], Operations: ['78/26=3', '14*3=42'] Exploring Operation: 53+42=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[78, 53, 26, 14], Operations: [] Exploring Operation: 78/26=3, Resulting Numbers: [53, 14, 3] Generated Node #0,0: 95:[53, 14, 3] Operation: 78/26=3 Exploring Operation: 53+26=79, Resulting Numbers: [78, 14, 79] Generated Node #0,1: 95:[78, 14, 79] Operation: 53+26=79 Exploring Operation: 53-26=27, Resulting Numbers: [78, 14, 27] Generated Node #0,2: 95:[78, 14, 27] Operation: 53-26=27 Exploring Operation: 78-53=25, Resulting Numbers: [26, 14, 25] Generated Node #0,3: 95:[26, 14, 25] Operation: 78-53=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 95:[26, 14, 25], Operations: ['78-53=25'] Exploring Operation: 26-25=1, Resulting Numbers: [14, 1] Generated Node #0,3,0: 95:[14, 1] Operation: 26-25=1 Exploring Operation: 25-14=11, Resulting Numbers: [26, 11] Generated Node #0,3,1: 95:[26, 11] Operation: 25-14=11 Exploring Operation: 26-14=12, Resulting Numbers: [25, 12] Generated Node #0,3,2: 95:[25, 12] Operation: 26-14=12 Exploring Operation: 26+14=40, Resulting Numbers: [25, 40] Generated Node #0,3,3: 95:[25, 40] Operation: 26+14=40 Moving to Node #0,3,0 Current State: 95:[14, 1], Operations: ['78-53=25', '26-25=1'] Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,95 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,95 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,95 unequal: No Solution Moving to Node #0,3,2 Current State: 95:[25, 12], Operations: ['78-53=25', '26-14=12'] Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,95 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,95 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,95 unequal: No Solution Moving to Node #0,3,1 Current State: 95:[26, 11], Operations: ['78-53=25', '25-14=11'] Exploring Operation: 26*11=286, Resulting Numbers: [286] 286,95 unequal: No Solution Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,95 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,95 unequal: No Solution Moving to Node #0,3,3 Current State: 95:[25, 40], Operations: ['78-53=25', '26+14=40'] Exploring Operation: 25*40=1000, Resulting Numbers: [1000] 1000,95 unequal: No Solution Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 95:[78, 14, 27], Operations: ['53-26=27'] Exploring Operation: 78-27=51, Resulting Numbers: [14, 51] Generated Node #0,2,0: 95:[14, 51] Operation: 78-27=51 Exploring Operation: 78+27=105, Resulting Numbers: [14, 105] Generated Node #0,2,1: 95:[14, 105] Operation: 78+27=105 Exploring Operation: 78+14=92, Resulting Numbers: [27, 92] Generated Node #0,2,2: 95:[27, 92] Operation: 78+14=92 Exploring Operation: 27-14=13, Resulting Numbers: [78, 13] Generated Node #0,2,3: 95:[78, 13] Operation: 27-14=13 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 95:[27, 92], Operations: ['53-26=27', '78+14=92'] Exploring Operation: 27+92=119, Resulting Numbers: [119] 119,95 unequal: No Solution Exploring Operation: 92-27=65, Resulting Numbers: [65] 65,95 unequal: No Solution Exploring Operation: 27*92=2484, Resulting Numbers: [2484] 2484,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 95:[14, 105], Operations: ['53-26=27', '78+27=105'] Exploring Operation: 105-14=91, Resulting Numbers: [91] 91,95 unequal: No Solution Exploring Operation: 14+105=119, Resulting Numbers: [119] 119,95 unequal: No Solution Exploring Operation: 14*105=1470, Resulting Numbers: [1470] 1470,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 95:[78, 13], Operations: ['53-26=27', '27-14=13'] Exploring Operation: 78+13=91, Resulting Numbers: [91] 91,95 unequal: No Solution Exploring Operation: 78*13=1014, Resulting Numbers: [1014] 1014,95 unequal: No Solution Exploring Operation: 78-13=65, Resulting Numbers: [65] 65,95 unequal: No Solution Exploring Operation: 78/13=6, Resulting Numbers: [6] 6,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 95:[14, 51], Operations: ['53-26=27', '78-27=51'] Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,95 unequal: No Solution Exploring Operation: 14*51=714, Resulting Numbers: [714] 714,95 unequal: No Solution Exploring Operation: 14+51=65, Resulting Numbers: [65] 65,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[78, 14, 79], Operations: ['53+26=79'] Exploring Operation: 14+79=93, Resulting Numbers: [78, 93] Generated Node #0,1,0: 95:[78, 93] Operation: 14+79=93 Exploring Operation: 79-78=1, Resulting Numbers: [14, 1] Generated Node #0,1,1: 95:[14, 1] Operation: 79-78=1 Exploring Operation: 78+14=92, Resulting Numbers: [79, 92] Generated Node #0,1,2: 95:[79, 92] Operation: 78+14=92 Exploring Operation: 78-14=64, Resulting Numbers: [79, 64] Generated Node #0,1,3: 95:[79, 64] Operation: 78-14=64 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 95:[14, 1], Operations: ['53+26=79', '79-78=1'] Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,95 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,95 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 95:[78, 93], Operations: ['53+26=79', '14+79=93'] Exploring Operation: 93-78=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 78*93=7254, Resulting Numbers: [7254] 7254,95 unequal: No Solution Exploring Operation: 78+93=171, Resulting Numbers: [171] 171,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 95:[79, 92], Operations: ['53+26=79', '78+14=92'] Exploring Operation: 92-79=13, Resulting Numbers: [13] 13,95 unequal: No Solution Exploring Operation: 79*92=7268, Resulting Numbers: [7268] 7268,95 unequal: No Solution Exploring Operation: 79+92=171, Resulting Numbers: [171] 171,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 95:[79, 64], Operations: ['53+26=79', '78-14=64'] Exploring Operation: 79+64=143, Resulting Numbers: [143] 143,95 unequal: No Solution Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 79*64=5056, Resulting Numbers: [5056] 5056,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[53, 14, 3], Operations: ['78/26=3'] Exploring Operation: 14+3=17, Resulting Numbers: [53, 17] Generated Node #0,0,0: 95:[53, 17] Operation: 14+3=17 Exploring Operation: 53-3=50, Resulting Numbers: [14, 50] Generated Node #0,0,1: 95:[14, 50] Operation: 53-3=50 Exploring Operation: 53+14=67, Resulting Numbers: [3, 67] Generated Node #0,0,2: 95:[3, 67] Operation: 53+14=67 Exploring Operation: 53-14=39, Resulting Numbers: [3, 39] Generated Node #0,0,3: 95:[3, 39] Operation: 53-14=39 Moving to Node #0,0,3 Current State: 95:[3, 39], Operations: ['78/26=3', '53-14=39'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,95 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,95 unequal: No Solution Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,95 unequal: No Solution Exploring Operation: 3*39=117, Resulting Numbers: [117] 117,95 unequal: No Solution Moving to Node #0,0,2 Current State: 95:[3, 67], Operations: ['78/26=3', '53+14=67'] Exploring Operation: 3+67=70, Resulting Numbers: [70] 70,95 unequal: No Solution Exploring Operation: 3*67=201, Resulting Numbers: [201] 201,95 unequal: No Solution Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[14, 50], Operations: ['78/26=3', '53-3=50'] Exploring Operation: 50-14=36, Resulting Numbers: [36] 36,95 unequal: No Solution Exploring Operation: 14*50=700, Resulting Numbers: [700] 700,95 unequal: No Solution Exploring Operation: 14+50=64, Resulting Numbers: [64] 64,95 unequal: No Solution Moving to Node #0,0,0 Current State: 95:[53, 17], Operations: ['78/26=3', '14+3=17'] Exploring Operation: 53*17=901, Resulting Numbers: [901] 901,95 unequal: No Solution Exploring Operation: 53-17=36, Resulting Numbers: [36] 36,95 unequal: No Solution Exploring Operation: 53+17=70, Resulting Numbers: [70] 70,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 12, 52, 80, 39 ]
51
[ "80-12=68", "39*68=2652", "2652/52=51" ]
Current State: 51:[12, 52, 80, 39], Operations: [] Exploring Operation: 80-12=68, Resulting Numbers: [52, 39, 68] Generated Node #2: [52, 39, 68] from Operation: 80-12=68 Current State: 51:[52, 39, 68], Operations: ['80-12=68'] Exploring Operation: 39*68=2652, Resulting Numbers: [52, 2652] Generated Node #3: [52, 2652] from Operation: 39*68=2652 Current State: 51:[52, 2652], Operations: ['80-12=68', '39*68=2652'] Exploring Operation: 2652/52=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[12, 52, 80, 39], Operations: [] Exploring Operation: 80-52=28, Resulting Numbers: [12, 39, 28] Generated Node #0,0: 51:[12, 39, 28] Operation: 80-52=28 Exploring Operation: 80-39=41, Resulting Numbers: [12, 52, 41] Generated Node #0,1: 51:[12, 52, 41] Operation: 80-39=41 Exploring Operation: 52-39=13, Resulting Numbers: [12, 80, 13] Generated Node #0,2: 51:[12, 80, 13] Operation: 52-39=13 Exploring Operation: 80-12=68, Resulting Numbers: [52, 39, 68] Generated Node #0,3: 51:[52, 39, 68] Operation: 80-12=68 Exploring Operation: 12+39=51, Resulting Numbers: [52, 80, 51] Generated Node #0,4: 51:[52, 80, 51] Operation: 12+39=51 Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[12, 52, 41], Operations: ['80-39=41'] Exploring Operation: 12+52=64, Resulting Numbers: [41, 64] Generated Node #0,1,0: 51:[41, 64] Operation: 12+52=64 Exploring Operation: 41-12=29, Resulting Numbers: [52, 29] Generated Node #0,1,1: 51:[52, 29] Operation: 41-12=29 Exploring Operation: 12+41=53, Resulting Numbers: [52, 53] Generated Node #0,1,2: 51:[52, 53] Operation: 12+41=53 Exploring Operation: 52-41=11, Resulting Numbers: [12, 11] Generated Node #0,1,3: 51:[12, 11] Operation: 52-41=11 Exploring Operation: 52-12=40, Resulting Numbers: [41, 40] Generated Node #0,1,4: 51:[41, 40] Operation: 52-12=40 Moving to Node #0,1,2 Current State: 51:[52, 53], Operations: ['80-39=41', '12+41=53'] Exploring Operation: 52*53=2756, Resulting Numbers: [2756] 2756,51 unequal: No Solution Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 52+53=105, Resulting Numbers: [105] 105,51 unequal: No Solution Moving to Node #0,1,3 Current State: 51:[12, 11], Operations: ['80-39=41', '52-41=11'] Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 12*11=132, Resulting Numbers: [132] 132,51 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[52, 29], Operations: ['80-39=41', '41-12=29'] Exploring Operation: 52*29=1508, Resulting Numbers: [1508] 1508,51 unequal: No Solution Exploring Operation: 52-29=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 52+29=81, Resulting Numbers: [81] 81,51 unequal: No Solution Moving to Node #0,1,4 Current State: 51:[41, 40], Operations: ['80-39=41', '52-12=40'] Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 41*40=1640, Resulting Numbers: [1640] 1640,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[41, 64], Operations: ['80-39=41', '12+52=64'] Exploring Operation: 41+64=105, Resulting Numbers: [105] 105,51 unequal: No Solution Exploring Operation: 41*64=2624, Resulting Numbers: [2624] 2624,51 unequal: No Solution Exploring Operation: 64-41=23, Resulting Numbers: [23] 23,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[12, 39, 28], Operations: ['80-52=28'] Exploring Operation: 39-12=27, Resulting Numbers: [28, 27] Generated Node #0,0,0: 51:[28, 27] Operation: 39-12=27 Exploring Operation: 39-28=11, Resulting Numbers: [12, 11] Generated Node #0,0,1: 51:[12, 11] Operation: 39-28=11 Exploring Operation: 28-12=16, Resulting Numbers: [39, 16] Generated Node #0,0,2: 51:[39, 16] Operation: 28-12=16 Exploring Operation: 39+28=67, Resulting Numbers: [12, 67] Generated Node #0,0,3: 51:[12, 67] Operation: 39+28=67 Exploring Operation: 12+39=51, Resulting Numbers: [28, 51] Generated Node #0,0,4: 51:[28, 51] Operation: 12+39=51 Moving to Node #0,0,1 Current State: 51:[12, 11], Operations: ['80-52=28', '39-28=11'] Exploring Operation: 12*11=132, Resulting Numbers: [132] 132,51 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,51 unequal: No Solution Moving to Node #0,0,4 Current State: 51:[28, 51], Operations: ['80-52=28', '12+39=51'] Exploring Operation: 28*51=1428, Resulting Numbers: [1428] 1428,51 unequal: No Solution Exploring Operation: 28+51=79, Resulting Numbers: [79] 79,51 unequal: No Solution Exploring Operation: 51-28=23, Resulting Numbers: [23] 23,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[39, 16], Operations: ['80-52=28', '28-12=16'] Exploring Operation: 39*16=624, Resulting Numbers: [624] 624,51 unequal: No Solution Exploring Operation: 39-16=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 39+16=55, Resulting Numbers: [55] 55,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[28, 27], Operations: ['80-52=28', '39-12=27'] Exploring Operation: 28*27=756, Resulting Numbers: [756] 756,51 unequal: No Solution Exploring Operation: 28+27=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,51 unequal: No Solution Moving to Node #0,0,3 Current State: 51:[12, 67], Operations: ['80-52=28', '39+28=67'] Exploring Operation: 12+67=79, Resulting Numbers: [79] 79,51 unequal: No Solution Exploring Operation: 67-12=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 12*67=804, Resulting Numbers: [804] 804,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[52, 39, 68], Operations: ['80-12=68'] Exploring Operation: 39+68=107, Resulting Numbers: [52, 107] Generated Node #0,3,0: 51:[52, 107] Operation: 39+68=107 Exploring Operation: 52-39=13, Resulting Numbers: [68, 13] Generated Node #0,3,1: 51:[68, 13] Operation: 52-39=13 Exploring Operation: 68-39=29, Resulting Numbers: [52, 29] Generated Node #0,3,2: 51:[52, 29] Operation: 68-39=29 Exploring Operation: 52+39=91, Resulting Numbers: [68, 91] Generated Node #0,3,3: 51:[68, 91] Operation: 52+39=91 Exploring Operation: 68-52=16, Resulting Numbers: [39, 16] Generated Node #0,3,4: 51:[39, 16] Operation: 68-52=16 Moving to Node #0,3,2 Current State: 51:[52, 29], Operations: ['80-12=68', '68-39=29'] Exploring Operation: 52+29=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 52-29=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 52*29=1508, Resulting Numbers: [1508] 1508,51 unequal: No Solution Moving to Node #0,3,4 Current State: 51:[39, 16], Operations: ['80-12=68', '68-52=16'] Exploring Operation: 39*16=624, Resulting Numbers: [624] 624,51 unequal: No Solution Exploring Operation: 39+16=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 39-16=23, Resulting Numbers: [23] 23,51 unequal: No Solution Moving to Node #0,3,1 Current State: 51:[68, 13], Operations: ['80-12=68', '52-39=13'] Exploring Operation: 68+13=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 68*13=884, Resulting Numbers: [884] 884,51 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,51 unequal: No Solution Moving to Node #0,3,0 Current State: 51:[52, 107], Operations: ['80-12=68', '39+68=107'] Exploring Operation: 52+107=159, Resulting Numbers: [159] 159,51 unequal: No Solution Exploring Operation: 107-52=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 52*107=5564, Resulting Numbers: [5564] 5564,51 unequal: No Solution Moving to Node #0,3,3 Current State: 51:[68, 91], Operations: ['80-12=68', '52+39=91'] Exploring Operation: 91-68=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 68+91=159, Resulting Numbers: [159] 159,51 unequal: No Solution Exploring Operation: 68*91=6188, Resulting Numbers: [6188] 6188,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 51:[52, 80, 51], Operations: ['12+39=51'] Exploring Operation: 80-52=28, Resulting Numbers: [51, 28] Generated Node #0,4,0: 51:[51, 28] Operation: 80-52=28 Exploring Operation: 80-51=29, Resulting Numbers: [52, 29] Generated Node #0,4,1: 51:[52, 29] Operation: 80-51=29 Exploring Operation: 52+80=132, Resulting Numbers: [51, 132] Generated Node #0,4,2: 51:[51, 132] Operation: 52+80=132 Exploring Operation: 52-51=1, Resulting Numbers: [80, 1] Generated Node #0,4,3: 51:[80, 1] Operation: 52-51=1 Exploring Operation: 52+51=103, Resulting Numbers: [80, 103] Generated Node #0,4,4: 51:[80, 103] Operation: 52+51=103 Moving to Node #0,4,0 Current State: 51:[51, 28], Operations: ['12+39=51', '80-52=28'] Exploring Operation: 51*28=1428, Resulting Numbers: [1428] 1428,51 unequal: No Solution Exploring Operation: 51-28=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 51+28=79, Resulting Numbers: [79] 79,51 unequal: No Solution Moving to Node #0,4,1 Current State: 51:[52, 29], Operations: ['12+39=51', '80-51=29'] Exploring Operation: 52*29=1508, Resulting Numbers: [1508] 1508,51 unequal: No Solution Exploring Operation: 52-29=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 52+29=81, Resulting Numbers: [81] 81,51 unequal: No Solution Moving to Node #0,4,3 Current State: 51:[80, 1], Operations: ['12+39=51', '52-51=1'] Exploring Operation: 80/1=80, Resulting Numbers: [80] 80,51 unequal: No Solution Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,51 unequal: No Solution Exploring Operation: 80*1=80, Resulting Numbers: [80] 80,51 unequal: No Solution Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,51 unequal: No Solution Moving to Node #0,4,2 Current State: 51:[51, 132], Operations: ['12+39=51', '52+80=132'] Exploring Operation: 132-51=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 51+132=183, Resulting Numbers: [183] 183,51 unequal: No Solution Exploring Operation: 51*132=6732, Resulting Numbers: [6732] 6732,51 unequal: No Solution Moving to Node #0,4,4 Current State: 51:[80, 103], Operations: ['12+39=51', '52+51=103'] Exploring Operation: 80*103=8240, Resulting Numbers: [8240] 8240,51 unequal: No Solution Exploring Operation: 103-80=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 80+103=183, Resulting Numbers: [183] 183,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[12, 80, 13], Operations: ['52-39=13'] Exploring Operation: 12+80=92, Resulting Numbers: [13, 92] Generated Node #0,2,0: 51:[13, 92] Operation: 12+80=92 Exploring Operation: 13-12=1, Resulting Numbers: [80, 1] Generated Node #0,2,1: 51:[80, 1] Operation: 13-12=1 Exploring Operation: 80-13=67, Resulting Numbers: [12, 67] Generated Node #0,2,2: 51:[12, 67] Operation: 80-13=67 Exploring Operation: 80-12=68, Resulting Numbers: [13, 68] Generated Node #0,2,3: 51:[13, 68] Operation: 80-12=68 Exploring Operation: 12+13=25, Resulting Numbers: [80, 25] Generated Node #0,2,4: 51:[80, 25] Operation: 12+13=25 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 51:[12, 67], Operations: ['52-39=13', '80-13=67'] Exploring Operation: 67-12=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 12+67=79, Resulting Numbers: [79] 79,51 unequal: No Solution Exploring Operation: 12*67=804, Resulting Numbers: [804] 804,51 unequal: No Solution No 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: 51:[13, 68], Operations: ['52-39=13', '80-12=68'] Exploring Operation: 13*68=884, Resulting Numbers: [884] 884,51 unequal: No Solution Exploring Operation: 13+68=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,51 unequal: No Solution No 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: 51:[80, 1], Operations: ['52-39=13', '13-12=1'] Exploring Operation: 80*1=80, Resulting Numbers: [80] 80,51 unequal: No Solution Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,51 unequal: No Solution Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 80/1=80, Resulting Numbers: [80] 80,51 unequal: No Solution No 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: 51:[80, 25], Operations: ['52-39=13', '12+13=25'] Exploring Operation: 80*25=2000, Resulting Numbers: [2000] 2000,51 unequal: No Solution Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 80+25=105, Resulting Numbers: [105] 105,51 unequal: No Solution No 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: 51:[13, 92], Operations: ['52-39=13', '12+80=92'] Exploring Operation: 13*92=1196, Resulting Numbers: [1196] 1196,51 unequal: No Solution Exploring Operation: 13+92=105, Resulting Numbers: [105] 105,51 unequal: No Solution Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,51 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
[ 62, 50, 14, 39 ]
60
[ "39-14=25", "50/25=2", "62-2=60" ]
Current State: 60:[62, 50, 14, 39], Operations: [] Exploring Operation: 39-14=25, Resulting Numbers: [62, 50, 25] Generated Node #2: [62, 50, 25] from Operation: 39-14=25 Current State: 60:[62, 50, 25], Operations: ['39-14=25'] Exploring Operation: 50/25=2, Resulting Numbers: [62, 2] Generated Node #3: [62, 2] from Operation: 50/25=2 Current State: 60:[62, 2], Operations: ['39-14=25', '50/25=2'] Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[62, 50, 14, 39], Operations: [] Exploring Operation: 50-39=11, Resulting Numbers: [62, 14, 11] Generated Node #0,0: 60:[62, 14, 11] Operation: 50-39=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[62, 14, 11], Operations: ['50-39=11'] Exploring Operation: 14-11=3, Resulting Numbers: [62, 3] Generated Node #0,0,0: 60:[62, 3] Operation: 14-11=3 Moving to Node #0,0,0 Current State: 60:[62, 3], Operations: ['50-39=11', '14-11=3'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,60 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
[ 69, 90, 73, 6 ]
24
[ "73-69=4", "90+6=96", "96/4=24" ]
Current State: 24:[69, 90, 73, 6], Operations: [] Exploring Operation: 73-69=4, Resulting Numbers: [90, 6, 4] Generated Node #2: [90, 6, 4] from Operation: 73-69=4 Current State: 24:[90, 6, 4], Operations: ['73-69=4'] Exploring Operation: 90+6=96, Resulting Numbers: [4, 96] Generated Node #3: [4, 96] from Operation: 90+6=96 Current State: 24:[4, 96], Operations: ['73-69=4', '90+6=96'] Exploring Operation: 96/4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[69, 90, 73, 6], Operations: [] Exploring Operation: 90-73=17, Resulting Numbers: [69, 6, 17] Generated Node #0,0: 24:[69, 6, 17] Operation: 90-73=17 Exploring Operation: 69-6=63, Resulting Numbers: [90, 73, 63] Generated Node #0,1: 24:[90, 73, 63] Operation: 69-6=63 Exploring Operation: 73-69=4, Resulting Numbers: [90, 6, 4] Generated Node #0,2: 24:[90, 6, 4] Operation: 73-69=4 Exploring Operation: 90-69=21, Resulting Numbers: [73, 6, 21] Generated Node #0,3: 24:[73, 6, 21] Operation: 90-69=21 Exploring Operation: 90/6=15, Resulting Numbers: [69, 73, 15] Generated Node #0,4: 24:[69, 73, 15] Operation: 90/6=15 Moving to Node #0,0 Current State: 24:[69, 6, 17], Operations: ['90-73=17'] Exploring Operation: 69-17=52, Resulting Numbers: [6, 52] Generated Node #0,0,0: 24:[6, 52] Operation: 69-17=52 Exploring Operation: 17-6=11, Resulting Numbers: [69, 11] Generated Node #0,0,1: 24:[69, 11] Operation: 17-6=11 Exploring Operation: 69+6=75, Resulting Numbers: [17, 75] Generated Node #0,0,2: 24:[17, 75] Operation: 69+6=75 Exploring Operation: 69-6=63, Resulting Numbers: [17, 63] Generated Node #0,0,3: 24:[17, 63] Operation: 69-6=63 Exploring Operation: 6+17=23, Resulting Numbers: [69, 23] Generated Node #0,0,4: 24:[69, 23] Operation: 6+17=23 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 24:[6, 52], Operations: ['90-73=17', '69-17=52'] Exploring Operation: 6*52=312, Resulting Numbers: [312] 312,24 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,24 unequal: No Solution Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 24:[17, 63], Operations: ['90-73=17', '69-6=63'] Exploring Operation: 17+63=80, Resulting Numbers: [80] 80,24 unequal: No Solution Exploring Operation: 63-17=46, Resulting Numbers: [46] 46,24 unequal: No Solution Exploring Operation: 17*63=1071, Resulting Numbers: [1071] 1071,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[69, 11], Operations: ['90-73=17', '17-6=11'] Exploring Operation: 69-11=58, Resulting Numbers: [58] 58,24 unequal: No Solution Exploring Operation: 69*11=759, Resulting Numbers: [759] 759,24 unequal: No Solution Exploring Operation: 69+11=80, Resulting Numbers: [80] 80,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 24:[69, 23], Operations: ['90-73=17', '6+17=23'] Exploring Operation: 69*23=1587, Resulting Numbers: [1587] 1587,24 unequal: No Solution Exploring Operation: 69+23=92, Resulting Numbers: [92] 92,24 unequal: No Solution Exploring Operation: 69-23=46, Resulting Numbers: [46] 46,24 unequal: No Solution Exploring Operation: 69/23=3, Resulting Numbers: [3] 3,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 24:[17, 75], Operations: ['90-73=17', '69+6=75'] Exploring Operation: 17*75=1275, Resulting Numbers: [1275] 1275,24 unequal: No Solution Exploring Operation: 17+75=92, Resulting Numbers: [92] 92,24 unequal: No Solution Exploring Operation: 75-17=58, Resulting Numbers: [58] 58,24 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: 24:[73, 6, 21], Operations: ['90-69=21'] Exploring Operation: 73+6=79, Resulting Numbers: [21, 79] Generated Node #0,3,0: 24:[21, 79] Operation: 73+6=79 Exploring Operation: 73-21=52, Resulting Numbers: [6, 52] Generated Node #0,3,1: 24:[6, 52] Operation: 73-21=52 Exploring Operation: 21-6=15, Resulting Numbers: [73, 15] Generated Node #0,3,2: 24:[73, 15] Operation: 21-6=15 Exploring Operation: 73-6=67, Resulting Numbers: [21, 67] Generated Node #0,3,3: 24:[21, 67] Operation: 73-6=67 Exploring Operation: 6+21=27, Resulting Numbers: [73, 27] Generated Node #0,3,4: 24:[73, 27] Operation: 6+21=27 Moving to Node #0,2 Current State: 24:[90, 6, 4], Operations: ['73-69=4'] Exploring Operation: 6-4=2, Resulting Numbers: [90, 2] Generated Node #0,2,0: 24:[90, 2] Operation: 6-4=2 Exploring Operation: 90/6=15, Resulting Numbers: [4, 15] Generated Node #0,2,1: 24:[4, 15] Operation: 90/6=15 Exploring Operation: 6*4=24, Resulting Numbers: [90, 24] Generated Node #0,2,2: 24:[90, 24] Operation: 6*4=24 Exploring Operation: 90-6=84, Resulting Numbers: [4, 84] Generated Node #0,2,3: 24:[4, 84] Operation: 90-6=84 Exploring Operation: 90-4=86, Resulting Numbers: [6, 86] Generated Node #0,2,4: 24:[6, 86] Operation: 90-4=86 Moving to Node #0,4 Current State: 24:[69, 73, 15], Operations: ['90/6=15'] Exploring Operation: 73+15=88, Resulting Numbers: [69, 88] Generated Node #0,4,0: 24:[69, 88] Operation: 73+15=88 Exploring Operation: 73-15=58, Resulting Numbers: [69, 58] Generated Node #0,4,1: 24:[69, 58] Operation: 73-15=58 Exploring Operation: 69-15=54, Resulting Numbers: [73, 54] Generated Node #0,4,2: 24:[73, 54] Operation: 69-15=54 Exploring Operation: 69+15=84, Resulting Numbers: [73, 84] Generated Node #0,4,3: 24:[73, 84] Operation: 69+15=84 Exploring Operation: 73-69=4, Resulting Numbers: [15, 4] Generated Node #0,4,4: 24:[15, 4] Operation: 73-69=4 Moving to Node #0,1 Current State: 24:[90, 73, 63], Operations: ['69-6=63'] Exploring Operation: 73-63=10, Resulting Numbers: [90, 10] Generated Node #0,1,0: 24:[90, 10] Operation: 73-63=10 Exploring Operation: 90-73=17, Resulting Numbers: [63, 17] Generated Node #0,1,1: 24:[63, 17] Operation: 90-73=17 Exploring Operation: 90+63=153, Resulting Numbers: [73, 153] Generated Node #0,1,2: 24:[73, 153] Operation: 90+63=153 Exploring Operation: 90+73=163, Resulting Numbers: [63, 163] Generated Node #0,1,3: 24:[63, 163] Operation: 90+73=163 Exploring Operation: 90-63=27, Resulting Numbers: [73, 27] Generated Node #0,1,4: 24:[73, 27] Operation: 90-63=27 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 24:[63, 17], Operations: ['69-6=63', '90-73=17'] Exploring Operation: 63-17=46, Resulting Numbers: [46] 46,24 unequal: No Solution Exploring Operation: 63*17=1071, Resulting Numbers: [1071] 1071,24 unequal: No Solution Exploring Operation: 63+17=80, Resulting Numbers: [80] 80,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 24:[73, 27], Operations: ['69-6=63', '90-63=27'] Exploring Operation: 73+27=100, Resulting Numbers: [100] 100,24 unequal: No Solution Exploring Operation: 73-27=46, Resulting Numbers: [46] 46,24 unequal: No Solution Exploring Operation: 73*27=1971, Resulting Numbers: [1971] 1971,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[90, 10], Operations: ['69-6=63', '73-63=10'] Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,24 unequal: No Solution Exploring Operation: 90*10=900, Resulting Numbers: [900] 900,24 unequal: No Solution Exploring Operation: 90+10=100, Resulting Numbers: [100] 100,24 unequal: No Solution Exploring Operation: 90/10=9, Resulting Numbers: [9] 9,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[73, 153], Operations: ['69-6=63', '90+63=153'] Exploring Operation: 73*153=11169, Resulting Numbers: [11169] 11169,24 unequal: No Solution Exploring Operation: 153-73=80, Resulting Numbers: [80] 80,24 unequal: No Solution Exploring Operation: 73+153=226, Resulting Numbers: [226] 226,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 24:[63, 163], Operations: ['69-6=63', '90+73=163'] Exploring Operation: 63+163=226, Resulting Numbers: [226] 226,24 unequal: No Solution Exploring Operation: 63*163=10269, Resulting Numbers: [10269] 10269,24 unequal: No Solution Exploring Operation: 163-63=100, Resulting Numbers: [100] 100,24 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: 24:[4, 15], Operations: ['73-69=4', '90/6=15'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,24 unequal: No Solution Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,24 unequal: No Solution Moving to Node #0,4,4 Current State: 24:[15, 4], Operations: ['90/6=15', '73-69=4'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,24 unequal: No Solution Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,24 unequal: No Solution Moving to Node #0,3,1 Current State: 24:[6, 52], Operations: ['90-69=21', '73-21=52'] Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,24 unequal: No Solution Exploring Operation: 6*52=312, Resulting Numbers: [312] 312,24 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,24 unequal: No Solution Moving to Node #0,3,3 Current State: 24:[21, 67], Operations: ['90-69=21', '73-6=67'] Exploring Operation: 21*67=1407, Resulting Numbers: [1407] 1407,24 unequal: No Solution Exploring Operation: 21+67=88, Resulting Numbers: [88] 88,24 unequal: No Solution Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[73, 15], Operations: ['90-69=21', '21-6=15'] Exploring Operation: 73*15=1095, Resulting Numbers: [1095] 1095,24 unequal: No Solution Exploring Operation: 73-15=58, Resulting Numbers: [58] 58,24 unequal: No Solution Exploring Operation: 73+15=88, Resulting Numbers: [88] 88,24 unequal: No Solution Moving to Node #0,3,4 Current State: 24:[73, 27], Operations: ['90-69=21', '6+21=27'] Exploring Operation: 73*27=1971, Resulting Numbers: [1971] 1971,24 unequal: No Solution Exploring Operation: 73+27=100, Resulting Numbers: [100] 100,24 unequal: No Solution Exploring Operation: 73-27=46, Resulting Numbers: [46] 46,24 unequal: No Solution Moving to Node #0,3,0 Current State: 24:[21, 79], Operations: ['90-69=21', '73+6=79'] Exploring Operation: 21+79=100, Resulting Numbers: [100] 100,24 unequal: No Solution Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,24 unequal: No Solution Exploring Operation: 21*79=1659, Resulting Numbers: [1659] 1659,24 unequal: No Solution Moving to Node #0,2,3 Current State: 24:[4, 84], Operations: ['73-69=4', '90-6=84'] Exploring Operation: 4*84=336, Resulting Numbers: [336] 336,24 unequal: No Solution Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,24 unequal: No Solution Exploring Operation: 4+84=88, Resulting Numbers: [88] 88,24 unequal: No Solution Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,24 unequal: No Solution Moving to Node #0,2,4 Current State: 24:[6, 86], Operations: ['73-69=4', '90-4=86'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,24 unequal: No Solution Exploring Operation: 6*86=516, Resulting Numbers: [516] 516,24 unequal: No Solution Exploring Operation: 6+86=92, Resulting Numbers: [92] 92,24 unequal: No Solution Moving to Node #0,2,2 Current State: 24:[90, 24], Operations: ['73-69=4', '6*4=24'] Exploring Operation: 90*24=2160, Resulting Numbers: [2160] 2160,24 unequal: No Solution Exploring Operation: 90-24=66, Resulting Numbers: [66] 66,24 unequal: No Solution Exploring Operation: 90+24=114, Resulting Numbers: [114] 114,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[90, 2], Operations: ['73-69=4', '6-4=2'] Exploring Operation: 90+2=92, Resulting Numbers: [92] 92,24 unequal: No Solution Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,24 unequal: No Solution Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 90*2=180, Resulting Numbers: [180] 180,24 unequal: No Solution Moving to Node #0,4,1 Current State: 24:[69, 58], Operations: ['90/6=15', '73-15=58'] Exploring Operation: 69*58=4002, Resulting Numbers: [4002] 4002,24 unequal: No Solution Exploring Operation: 69-58=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 69+58=127, Resulting Numbers: [127] 127,24 unequal: No Solution Moving to Node #0,4,2 Current State: 24:[73, 54], Operations: ['90/6=15', '69-15=54'] Exploring Operation: 73*54=3942, Resulting Numbers: [3942] 3942,24 unequal: No Solution Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,24 unequal: No Solution Exploring Operation: 73+54=127, Resulting Numbers: [127] 127,24 unequal: No Solution Moving to Node #0,4,3 Current State: 24:[73, 84], Operations: ['90/6=15', '69+15=84'] Exploring Operation: 73*84=6132, Resulting Numbers: [6132] 6132,24 unequal: No Solution Exploring Operation: 84-73=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 73+84=157, Resulting Numbers: [157] 157,24 unequal: No Solution Moving to Node #0,4,0 Current State: 24:[69, 88], Operations: ['90/6=15', '73+15=88'] Exploring Operation: 69*88=6072, Resulting Numbers: [6072] 6072,24 unequal: No Solution Exploring Operation: 69+88=157, Resulting Numbers: [157] 157,24 unequal: No Solution Exploring Operation: 88-69=19, Resulting Numbers: [19] 19,24 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 69, 2, 6, 61 ]
83
[ "69*2=138", "61-6=55", "138-55=83" ]
Current State: 83:[69, 2, 6, 61], Operations: [] Exploring Operation: 69*2=138, Resulting Numbers: [6, 61, 138] Generated Node #2: [6, 61, 138] from Operation: 69*2=138 Current State: 83:[6, 61, 138], Operations: ['69*2=138'] Exploring Operation: 61-6=55, Resulting Numbers: [138, 55] Generated Node #3: [138, 55] from Operation: 61-6=55 Current State: 83:[138, 55], Operations: ['69*2=138', '61-6=55'] Exploring Operation: 138-55=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[69, 2, 6, 61], Operations: [] Exploring Operation: 2*6=12, Resulting Numbers: [69, 61, 12] Generated Node #0,0: 83:[69, 61, 12] Operation: 2*6=12 Exploring Operation: 69+2=71, Resulting Numbers: [6, 61, 71] Generated Node #0,1: 83:[6, 61, 71] Operation: 69+2=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[69, 61, 12], Operations: ['2*6=12'] Exploring Operation: 61+12=73, Resulting Numbers: [69, 73] Generated Node #0,0,0: 83:[69, 73] Operation: 61+12=73 Exploring Operation: 69+12=81, Resulting Numbers: [61, 81] Generated Node #0,0,1: 83:[61, 81] Operation: 69+12=81 Moving to Node #0,0,0 Current State: 83:[69, 73], Operations: ['2*6=12', '61+12=73'] Exploring Operation: 73-69=4, Resulting Numbers: [4] 4,83 unequal: No Solution Exploring Operation: 69+73=142, Resulting Numbers: [142] 142,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[61, 81], Operations: ['2*6=12', '69+12=81'] Exploring Operation: 61+81=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 81-61=20, Resulting Numbers: [20] 20,83 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 #0,1 Current State: 83:[6, 61, 71], Operations: ['69+2=71'] Exploring Operation: 6+71=77, Resulting Numbers: [61, 77] Generated Node #0,1,0: 83:[61, 77] Operation: 6+71=77 Exploring Operation: 6+61=67, Resulting Numbers: [71, 67] Generated Node #0,1,1: 83:[71, 67] Operation: 6+61=67 Moving to Node #0,1,0 Current State: 83:[61, 77], Operations: ['69+2=71', '6+71=77'] Exploring Operation: 61+77=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 77-61=16, Resulting Numbers: [16] 16,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[71, 67], Operations: ['69+2=71', '6+61=67'] Exploring Operation: 71+67=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 71-67=4, Resulting Numbers: [4] 4,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 4, 17, 90, 8 ]
54
[ "17-8=9", "4*9=36", "90-36=54" ]
Current State: 54:[4, 17, 90, 8], Operations: [] Exploring Operation: 17-8=9, Resulting Numbers: [4, 90, 9] Generated Node #2: [4, 90, 9] from Operation: 17-8=9 Current State: 54:[4, 90, 9], Operations: ['17-8=9'] Exploring Operation: 4*9=36, Resulting Numbers: [90, 36] Generated Node #3: [90, 36] from Operation: 4*9=36 Current State: 54:[90, 36], Operations: ['17-8=9', '4*9=36'] Exploring Operation: 90-36=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[4, 17, 90, 8], Operations: [] Exploring Operation: 90-4=86, Resulting Numbers: [17, 8, 86] Generated Node #0,0: 54:[17, 8, 86] Operation: 90-4=86 Exploring Operation: 90-8=82, Resulting Numbers: [4, 17, 82] Generated Node #0,1: 54:[4, 17, 82] Operation: 90-8=82 Exploring Operation: 17-8=9, Resulting Numbers: [4, 90, 9] Generated Node #0,2: 54:[4, 90, 9] Operation: 17-8=9 Exploring Operation: 8/4=2, Resulting Numbers: [17, 90, 2] Generated Node #0,3: 54:[17, 90, 2] Operation: 8/4=2 Exploring Operation: 90-17=73, Resulting Numbers: [4, 8, 73] Generated Node #0,4: 54:[4, 8, 73] Operation: 90-17=73 Start Sub Search at level 1: Moving to Node #0,4 Current State: 54:[4, 8, 73], Operations: ['90-17=73'] Exploring Operation: 8-4=4, Resulting Numbers: [73, 4] Generated Node #0,4,0: 54:[73, 4] Operation: 8-4=4 Exploring Operation: 4+8=12, Resulting Numbers: [73, 12] Generated Node #0,4,1: 54:[73, 12] Operation: 4+8=12 Exploring Operation: 73-8=65, Resulting Numbers: [4, 65] Generated Node #0,4,2: 54:[4, 65] Operation: 73-8=65 Exploring Operation: 8/4=2, Resulting Numbers: [73, 2] Generated Node #0,4,3: 54:[73, 2] Operation: 8/4=2 Exploring Operation: 73-4=69, Resulting Numbers: [8, 69] Generated Node #0,4,4: 54:[8, 69] Operation: 73-4=69 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 54:[4, 65], Operations: ['90-17=73', '73-8=65'] Exploring Operation: 4*65=260, Resulting Numbers: [260] 260,54 unequal: No Solution Exploring Operation: 4+65=69, Resulting Numbers: [69] 69,54 unequal: No Solution Exploring Operation: 65-4=61, Resulting Numbers: [61] 61,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 54:[8, 69], Operations: ['90-17=73', '73-4=69'] Exploring Operation: 8*69=552, Resulting Numbers: [552] 552,54 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,54 unequal: No Solution Exploring Operation: 8+69=77, Resulting Numbers: [77] 77,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 54:[73, 2], Operations: ['90-17=73', '8/4=2'] Exploring Operation: 73*2=146, Resulting Numbers: [146] 146,54 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,54 unequal: No Solution Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 54:[73, 4], Operations: ['90-17=73', '8-4=4'] Exploring Operation: 73+4=77, Resulting Numbers: [77] 77,54 unequal: No Solution Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,54 unequal: No Solution Exploring Operation: 73*4=292, Resulting Numbers: [292] 292,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 54:[73, 12], Operations: ['90-17=73', '4+8=12'] Exploring Operation: 73-12=61, Resulting Numbers: [61] 61,54 unequal: No Solution Exploring Operation: 73*12=876, Resulting Numbers: [876] 876,54 unequal: No Solution Exploring Operation: 73+12=85, Resulting Numbers: [85] 85,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[4, 17, 82], Operations: ['90-8=82'] Exploring Operation: 82-17=65, Resulting Numbers: [4, 65] Generated Node #0,1,0: 54:[4, 65] Operation: 82-17=65 Exploring Operation: 17-4=13, Resulting Numbers: [82, 13] Generated Node #0,1,1: 54:[82, 13] Operation: 17-4=13 Exploring Operation: 4+17=21, Resulting Numbers: [82, 21] Generated Node #0,1,2: 54:[82, 21] Operation: 4+17=21 Exploring Operation: 82-4=78, Resulting Numbers: [17, 78] Generated Node #0,1,3: 54:[17, 78] Operation: 82-4=78 Exploring Operation: 4+82=86, Resulting Numbers: [17, 86] Generated Node #0,1,4: 54:[17, 86] Operation: 4+82=86 Moving to Node #0,1,0 Current State: 54:[4, 65], Operations: ['90-8=82', '82-17=65'] Exploring Operation: 4+65=69, Resulting Numbers: [69] 69,54 unequal: No Solution Exploring Operation: 65-4=61, Resulting Numbers: [61] 61,54 unequal: No Solution Exploring Operation: 4*65=260, Resulting Numbers: [260] 260,54 unequal: No Solution Moving to Node #0,1,3 Current State: 54:[17, 78], Operations: ['90-8=82', '82-4=78'] Exploring Operation: 17+78=95, Resulting Numbers: [95] 95,54 unequal: No Solution Exploring Operation: 17*78=1326, Resulting Numbers: [1326] 1326,54 unequal: No Solution Exploring Operation: 78-17=61, Resulting Numbers: [61] 61,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[82, 21], Operations: ['90-8=82', '4+17=21'] Exploring Operation: 82+21=103, Resulting Numbers: [103] 103,54 unequal: No Solution Exploring Operation: 82*21=1722, Resulting Numbers: [1722] 1722,54 unequal: No Solution Exploring Operation: 82-21=61, Resulting Numbers: [61] 61,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[82, 13], Operations: ['90-8=82', '17-4=13'] Exploring Operation: 82-13=69, Resulting Numbers: [69] 69,54 unequal: No Solution Exploring Operation: 82+13=95, Resulting Numbers: [95] 95,54 unequal: No Solution Exploring Operation: 82*13=1066, Resulting Numbers: [1066] 1066,54 unequal: No Solution Moving to Node #0,1,4 Current State: 54:[17, 86], Operations: ['90-8=82', '4+82=86'] Exploring Operation: 17+86=103, Resulting Numbers: [103] 103,54 unequal: No Solution Exploring Operation: 17*86=1462, Resulting Numbers: [1462] 1462,54 unequal: No Solution Exploring Operation: 86-17=69, Resulting Numbers: [69] 69,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[17, 8, 86], Operations: ['90-4=86'] Exploring Operation: 8+86=94, Resulting Numbers: [17, 94] Generated Node #0,0,0: 54:[17, 94] Operation: 8+86=94 Exploring Operation: 17-8=9, Resulting Numbers: [86, 9] Generated Node #0,0,1: 54:[86, 9] Operation: 17-8=9 Exploring Operation: 86-17=69, Resulting Numbers: [8, 69] Generated Node #0,0,2: 54:[8, 69] Operation: 86-17=69 Exploring Operation: 17+8=25, Resulting Numbers: [86, 25] Generated Node #0,0,3: 54:[86, 25] Operation: 17+8=25 Exploring Operation: 86-8=78, Resulting Numbers: [17, 78] Generated Node #0,0,4: 54:[17, 78] Operation: 86-8=78 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 54:[8, 69], Operations: ['90-4=86', '86-17=69'] Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,54 unequal: No Solution Exploring Operation: 8+69=77, Resulting Numbers: [77] 77,54 unequal: No Solution Exploring Operation: 8*69=552, Resulting Numbers: [552] 552,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 54:[17, 78], Operations: ['90-4=86', '86-8=78'] Exploring Operation: 17+78=95, Resulting Numbers: [95] 95,54 unequal: No Solution Exploring Operation: 17*78=1326, Resulting Numbers: [1326] 1326,54 unequal: No Solution Exploring Operation: 78-17=61, Resulting Numbers: [61] 61,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 54:[86, 9], Operations: ['90-4=86', '17-8=9'] Exploring Operation: 86+9=95, Resulting Numbers: [95] 95,54 unequal: No Solution Exploring Operation: 86*9=774, Resulting Numbers: [774] 774,54 unequal: No Solution Exploring Operation: 86-9=77, Resulting Numbers: [77] 77,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 54:[86, 25], Operations: ['90-4=86', '17+8=25'] Exploring Operation: 86+25=111, Resulting Numbers: [111] 111,54 unequal: No Solution Exploring Operation: 86*25=2150, Resulting Numbers: [2150] 2150,54 unequal: No Solution Exploring Operation: 86-25=61, Resulting Numbers: [61] 61,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[17, 94], Operations: ['90-4=86', '8+86=94'] Exploring Operation: 17+94=111, Resulting Numbers: [111] 111,54 unequal: No Solution Exploring Operation: 94-17=77, Resulting Numbers: [77] 77,54 unequal: No Solution Exploring Operation: 17*94=1598, Resulting Numbers: [1598] 1598,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[4, 90, 9], Operations: ['17-8=9'] Exploring Operation: 90-9=81, Resulting Numbers: [4, 81] Generated Node #0,2,0: 54:[4, 81] Operation: 90-9=81 Exploring Operation: 9-4=5, Resulting Numbers: [90, 5] Generated Node #0,2,1: 54:[90, 5] Operation: 9-4=5 Exploring Operation: 4+90=94, Resulting Numbers: [9, 94] Generated Node #0,2,2: 54:[9, 94] Operation: 4+90=94 Exploring Operation: 90-4=86, Resulting Numbers: [9, 86] Generated Node #0,2,3: 54:[9, 86] Operation: 90-4=86 Exploring Operation: 90/9=10, Resulting Numbers: [4, 10] Generated Node #0,2,4: 54:[4, 10] Operation: 90/9=10 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 54:[4, 10], Operations: ['17-8=9', '90/9=10'] Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,54 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 54:[4, 81], Operations: ['17-8=9', '90-9=81'] Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,54 unequal: No Solution Exploring Operation: 4*81=324, Resulting Numbers: [324] 324,54 unequal: No Solution Exploring Operation: 4+81=85, Resulting Numbers: [85] 85,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 54:[9, 86], Operations: ['17-8=9', '90-4=86'] Exploring Operation: 86-9=77, Resulting Numbers: [77] 77,54 unequal: No Solution Exploring Operation: 9+86=95, Resulting Numbers: [95] 95,54 unequal: No Solution Exploring Operation: 9*86=774, Resulting Numbers: [774] 774,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 54:[90, 5], Operations: ['17-8=9', '9-4=5'] Exploring Operation: 90+5=95, Resulting Numbers: [95] 95,54 unequal: No Solution Exploring Operation: 90-5=85, Resulting Numbers: [85] 85,54 unequal: No Solution Exploring Operation: 90*5=450, Resulting Numbers: [450] 450,54 unequal: No Solution Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 54:[9, 94], Operations: ['17-8=9', '4+90=94'] Exploring Operation: 9+94=103, Resulting Numbers: [103] 103,54 unequal: No Solution Exploring Operation: 94-9=85, Resulting Numbers: [85] 85,54 unequal: No Solution Exploring Operation: 9*94=846, Resulting Numbers: [846] 846,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 54:[17, 90, 2], Operations: ['8/4=2'] Exploring Operation: 90-2=88, Resulting Numbers: [17, 88] Generated Node #0,3,0: 54:[17, 88] Operation: 90-2=88 Exploring Operation: 17+2=19, Resulting Numbers: [90, 19] Generated Node #0,3,1: 54:[90, 19] Operation: 17+2=19 Exploring Operation: 17-2=15, Resulting Numbers: [90, 15] Generated Node #0,3,2: 54:[90, 15] Operation: 17-2=15 Exploring Operation: 90/2=45, Resulting Numbers: [17, 45] Generated Node #0,3,3: 54:[17, 45] Operation: 90/2=45 Exploring Operation: 90-17=73, Resulting Numbers: [2, 73] Generated Node #0,3,4: 54:[2, 73] Operation: 90-17=73 Moving to Node #0,3,3 Current State: 54:[17, 45], Operations: ['8/4=2', '90/2=45'] Exploring Operation: 17*45=765, Resulting Numbers: [765] 765,54 unequal: No Solution Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 17+45=62, Resulting Numbers: [62] 62,54 unequal: No Solution Moving to Node #0,3,4 Current State: 54:[2, 73], Operations: ['8/4=2', '90-17=73'] Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,54 unequal: No Solution Exploring Operation: 2*73=146, Resulting Numbers: [146] 146,54 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,54 unequal: No Solution Moving to Node #0,3,0 Current State: 54:[17, 88], Operations: ['8/4=2', '90-2=88'] Exploring Operation: 17*88=1496, Resulting Numbers: [1496] 1496,54 unequal: No Solution Exploring Operation: 17+88=105, Resulting Numbers: [105] 105,54 unequal: No Solution Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,54 unequal: No Solution Moving to Node #0,3,1 Current State: 54:[90, 19], Operations: ['8/4=2', '17+2=19'] Exploring Operation: 90+19=109, Resulting Numbers: [109] 109,54 unequal: No Solution Exploring Operation: 90*19=1710, Resulting Numbers: [1710] 1710,54 unequal: No Solution Exploring Operation: 90-19=71, Resulting Numbers: [71] 71,54 unequal: No Solution Moving to Node #0,3,2 Current State: 54:[90, 15], Operations: ['8/4=2', '17-2=15'] Exploring Operation: 90-15=75, Resulting Numbers: [75] 75,54 unequal: No Solution Exploring Operation: 90/15=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 90+15=105, Resulting Numbers: [105] 105,54 unequal: No Solution Exploring Operation: 90*15=1350, Resulting Numbers: [1350] 1350,54 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
[ 71, 59, 1, 4 ]
41
[ "71+1=72", "72/4=18", "59-18=41" ]
Current State: 41:[71, 59, 1, 4], Operations: [] Exploring Operation: 71+1=72, Resulting Numbers: [59, 4, 72] Generated Node #2: [59, 4, 72] from Operation: 71+1=72 Current State: 41:[59, 4, 72], Operations: ['71+1=72'] Exploring Operation: 72/4=18, Resulting Numbers: [59, 18] Generated Node #3: [59, 18] from Operation: 72/4=18 Current State: 41:[59, 18], Operations: ['71+1=72', '72/4=18'] Exploring Operation: 59-18=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[71, 59, 1, 4], Operations: [] Exploring Operation: 59-1=58, Resulting Numbers: [71, 4, 58] Generated Node #0,0: 41:[71, 4, 58] Operation: 59-1=58 Exploring Operation: 59-4=55, Resulting Numbers: [71, 1, 55] Generated Node #0,1: 41:[71, 1, 55] Operation: 59-4=55 Exploring Operation: 71-4=67, Resulting Numbers: [59, 1, 67] Generated Node #0,2: 41:[59, 1, 67] Operation: 71-4=67 Exploring Operation: 71-1=70, Resulting Numbers: [59, 4, 70] Generated Node #0,3: 41:[59, 4, 70] Operation: 71-1=70 Moving to Node #0,0 Current State: 41:[71, 4, 58], Operations: ['59-1=58'] Exploring Operation: 71+4=75, Resulting Numbers: [58, 75] Generated Node #0,0,0: 41:[58, 75] Operation: 71+4=75 Exploring Operation: 71-4=67, Resulting Numbers: [58, 67] Generated Node #0,0,1: 41:[58, 67] Operation: 71-4=67 Exploring Operation: 4+58=62, Resulting Numbers: [71, 62] Generated Node #0,0,2: 41:[71, 62] Operation: 4+58=62 Exploring Operation: 58-4=54, Resulting Numbers: [71, 54] Generated Node #0,0,3: 41:[71, 54] Operation: 58-4=54 Moving to Node #0,2 Current State: 41:[59, 1, 67], Operations: ['71-4=67'] Exploring Operation: 59-1=58, Resulting Numbers: [67, 58] Generated Node #0,2,0: 41:[67, 58] Operation: 59-1=58 Exploring Operation: 59/1=59, Resulting Numbers: [67, 59] Generated Node #0,2,1: 41:[67, 59] Operation: 59/1=59 Exploring Operation: 59*1=59, Resulting Numbers: [67, 59] Generated Node #0,2,2: 41:[67, 59] Operation: 59*1=59 Exploring Operation: 67-1=66, Resulting Numbers: [59, 66] Generated Node #0,2,3: 41:[59, 66] Operation: 67-1=66 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 41:[67, 58], Operations: ['71-4=67', '59-1=58'] Exploring Operation: 67*58=3886, Resulting Numbers: [3886] 3886,41 unequal: No Solution Exploring Operation: 67-58=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 67+58=125, Resulting Numbers: [125] 125,41 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 #0,2,3 Current State: 41:[59, 66], Operations: ['71-4=67', '67-1=66'] Exploring Operation: 59*66=3894, Resulting Numbers: [3894] 3894,41 unequal: No Solution Exploring Operation: 59+66=125, Resulting Numbers: [125] 125,41 unequal: No Solution Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,41 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 #0,2,1 Current State: 41:[67, 59], Operations: ['71-4=67', '59/1=59'] Exploring Operation: 67*59=3953, Resulting Numbers: [3953] 3953,41 unequal: No Solution Exploring Operation: 67-59=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 67+59=126, Resulting Numbers: [126] 126,41 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 #0,2,2 Current State: 41:[67, 59], Operations: ['71-4=67', '59*1=59'] Exploring Operation: 67-59=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 67+59=126, Resulting Numbers: [126] 126,41 unequal: No Solution Exploring Operation: 67*59=3953, Resulting Numbers: [3953] 3953,41 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: 41:[71, 1, 55], Operations: ['59-4=55'] Exploring Operation: 71/1=71, Resulting Numbers: [55, 71] Generated Node #0,1,0: 41:[55, 71] Operation: 71/1=71 Exploring Operation: 71-1=70, Resulting Numbers: [55, 70] Generated Node #0,1,1: 41:[55, 70] Operation: 71-1=70 Exploring Operation: 55-1=54, Resulting Numbers: [71, 54] Generated Node #0,1,2: 41:[71, 54] Operation: 55-1=54 Exploring Operation: 71*1=71, Resulting Numbers: [55, 71] Generated Node #0,1,3: 41:[55, 71] Operation: 71*1=71 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[55, 70], Operations: ['59-4=55', '71-1=70'] Exploring Operation: 55+70=125, Resulting Numbers: [125] 125,41 unequal: No Solution Exploring Operation: 70-55=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 55*70=3850, Resulting Numbers: [3850] 3850,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 41:[71, 54], Operations: ['59-4=55', '55-1=54'] Exploring Operation: 71+54=125, Resulting Numbers: [125] 125,41 unequal: No Solution Exploring Operation: 71*54=3834, Resulting Numbers: [3834] 3834,41 unequal: No Solution Exploring Operation: 71-54=17, Resulting Numbers: [17] 17,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[55, 71], Operations: ['59-4=55', '71/1=71'] Exploring Operation: 71-55=16, Resulting Numbers: [16] 16,41 unequal: No Solution Exploring Operation: 55+71=126, Resulting Numbers: [126] 126,41 unequal: No Solution Exploring Operation: 55*71=3905, Resulting Numbers: [3905] 3905,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 41:[55, 71], Operations: ['59-4=55', '71*1=71'] Exploring Operation: 55*71=3905, Resulting Numbers: [3905] 3905,41 unequal: No Solution Exploring Operation: 71-55=16, Resulting Numbers: [16] 16,41 unequal: No Solution Exploring Operation: 55+71=126, Resulting Numbers: [126] 126,41 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: 41:[59, 4, 70], Operations: ['71-1=70'] Exploring Operation: 59-4=55, Resulting Numbers: [70, 55] Generated Node #0,3,0: 41:[70, 55] Operation: 59-4=55 Exploring Operation: 59+4=63, Resulting Numbers: [70, 63] Generated Node #0,3,1: 41:[70, 63] Operation: 59+4=63 Exploring Operation: 4+70=74, Resulting Numbers: [59, 74] Generated Node #0,3,2: 41:[59, 74] Operation: 4+70=74 Exploring Operation: 70-4=66, Resulting Numbers: [59, 66] Generated Node #0,3,3: 41:[59, 66] Operation: 70-4=66 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 41:[70, 55], Operations: ['71-1=70', '59-4=55'] Exploring Operation: 70+55=125, Resulting Numbers: [125] 125,41 unequal: No Solution Exploring Operation: 70-55=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 70*55=3850, Resulting Numbers: [3850] 3850,41 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 #0,3,3 Current State: 41:[59, 66], Operations: ['71-1=70', '70-4=66'] Exploring Operation: 59+66=125, Resulting Numbers: [125] 125,41 unequal: No Solution Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,41 unequal: No Solution Exploring Operation: 59*66=3894, Resulting Numbers: [3894] 3894,41 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 #0,3,1 Current State: 41:[70, 63], Operations: ['71-1=70', '59+4=63'] Exploring Operation: 70+63=133, Resulting Numbers: [133] 133,41 unequal: No Solution Exploring Operation: 70*63=4410, Resulting Numbers: [4410] 4410,41 unequal: No Solution Exploring Operation: 70-63=7, Resulting Numbers: [7] 7,41 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 #0,3,2 Current State: 41:[59, 74], Operations: ['71-1=70', '4+70=74'] Exploring Operation: 59+74=133, Resulting Numbers: [133] 133,41 unequal: No Solution Exploring Operation: 74-59=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 59*74=4366, Resulting Numbers: [4366] 4366,41 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: 41:[58, 67], Operations: ['59-1=58', '71-4=67'] Exploring Operation: 67-58=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 58*67=3886, Resulting Numbers: [3886] 3886,41 unequal: No Solution Exploring Operation: 58+67=125, Resulting Numbers: [125] 125,41 unequal: No Solution Moving to Node #0,0,3 Current State: 41:[71, 54], Operations: ['59-1=58', '58-4=54'] Exploring Operation: 71+54=125, Resulting Numbers: [125] 125,41 unequal: No Solution Exploring Operation: 71*54=3834, Resulting Numbers: [3834] 3834,41 unequal: No Solution Exploring Operation: 71-54=17, Resulting Numbers: [17] 17,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[71, 62], Operations: ['59-1=58', '4+58=62'] Exploring Operation: 71+62=133, Resulting Numbers: [133] 133,41 unequal: No Solution Exploring Operation: 71*62=4402, Resulting Numbers: [4402] 4402,41 unequal: No Solution Exploring Operation: 71-62=9, Resulting Numbers: [9] 9,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[58, 75], Operations: ['59-1=58', '71+4=75'] Exploring Operation: 58*75=4350, Resulting Numbers: [4350] 4350,41 unequal: No Solution Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,41 unequal: No Solution Exploring Operation: 58+75=133, Resulting Numbers: [133] 133,41 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 41, 5, 1, 59 ]
90
[ "41*1=41", "59-41=18", "5*18=90" ]
Current State: 90:[41, 5, 1, 59], Operations: [] Exploring Operation: 41*1=41, Resulting Numbers: [5, 59, 41] Generated Node #2: [5, 59, 41] from Operation: 41*1=41 Current State: 90:[5, 59, 41], Operations: ['41*1=41'] Exploring Operation: 59-41=18, Resulting Numbers: [5, 18] Generated Node #3: [5, 18] from Operation: 59-41=18 Current State: 90:[5, 18], Operations: ['41*1=41', '59-41=18'] Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[41, 5, 1, 59], Operations: [] Exploring Operation: 59-41=18, Resulting Numbers: [5, 1, 18] Generated Node #0,0: 90:[5, 1, 18] Operation: 59-41=18 Moving to Node #0,0 Current State: 90:[5, 1, 18], Operations: ['59-41=18'] Exploring Operation: 5+1=6, Resulting Numbers: [18, 6] Generated Node #0,0,0: 90:[18, 6] Operation: 5+1=6 Moving to Node #0,0,0 Current State: 90:[18, 6], Operations: ['59-41=18', '5+1=6'] Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,90 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 88, 97, 2, 49 ]
92
[ "88/2=44", "97-49=48", "44+48=92" ]
Current State: 92:[88, 97, 2, 49], Operations: [] Exploring Operation: 88/2=44, Resulting Numbers: [97, 49, 44] Generated Node #2: [97, 49, 44] from Operation: 88/2=44 Current State: 92:[97, 49, 44], Operations: ['88/2=44'] Exploring Operation: 97-49=48, Resulting Numbers: [44, 48] Generated Node #3: [44, 48] from Operation: 97-49=48 Current State: 92:[44, 48], Operations: ['88/2=44', '97-49=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[88, 97, 2, 49], Operations: [] Exploring Operation: 97-88=9, Resulting Numbers: [2, 49, 9] Generated Node #0,0: 92:[2, 49, 9] Operation: 97-88=9 Exploring Operation: 97-2=95, Resulting Numbers: [88, 49, 95] Generated Node #0,1: 92:[88, 49, 95] Operation: 97-2=95 Exploring Operation: 88/2=44, Resulting Numbers: [97, 49, 44] Generated Node #0,2: 92:[97, 49, 44] Operation: 88/2=44 Exploring Operation: 88+2=90, Resulting Numbers: [97, 49, 90] Generated Node #0,3: 92:[97, 49, 90] Operation: 88+2=90 Exploring Operation: 97-49=48, Resulting Numbers: [88, 2, 48] Generated Node #0,4: 92:[88, 2, 48] Operation: 97-49=48 Moving to Node #0,4 Current State: 92:[88, 2, 48], Operations: ['97-49=48'] Exploring Operation: 88+2=90, Resulting Numbers: [48, 90] Generated Node #0,4,0: 92:[48, 90] Operation: 88+2=90 Exploring Operation: 48-2=46, Resulting Numbers: [88, 46] Generated Node #0,4,1: 92:[88, 46] Operation: 48-2=46 Exploring Operation: 88-48=40, Resulting Numbers: [2, 40] Generated Node #0,4,2: 92:[2, 40] Operation: 88-48=40 Exploring Operation: 48/2=24, Resulting Numbers: [88, 24] Generated Node #0,4,3: 92:[88, 24] Operation: 48/2=24 Exploring Operation: 88/2=44, Resulting Numbers: [48, 44] Generated Node #0,4,4: 92:[48, 44] Operation: 88/2=44 Moving to Node #0,0 Current State: 92:[2, 49, 9], Operations: ['97-88=9'] Exploring Operation: 2+49=51, Resulting Numbers: [9, 51] Generated Node #0,0,0: 92:[9, 51] Operation: 2+49=51 Exploring Operation: 49-2=47, Resulting Numbers: [9, 47] Generated Node #0,0,1: 92:[9, 47] Operation: 49-2=47 Exploring Operation: 2*9=18, Resulting Numbers: [49, 18] Generated Node #0,0,2: 92:[49, 18] Operation: 2*9=18 Exploring Operation: 9-2=7, Resulting Numbers: [49, 7] Generated Node #0,0,3: 92:[49, 7] Operation: 9-2=7 Exploring Operation: 49-9=40, Resulting Numbers: [2, 40] Generated Node #0,0,4: 92:[2, 40] Operation: 49-9=40 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[9, 47], Operations: ['97-88=9', '49-2=47'] Exploring Operation: 9*47=423, Resulting Numbers: [423] 423,92 unequal: No Solution Exploring Operation: 9+47=56, Resulting Numbers: [56] 56,92 unequal: No Solution Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,92 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 #0,0,3 Current State: 92:[49, 7], Operations: ['97-88=9', '9-2=7'] Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,92 unequal: No Solution Exploring Operation: 49*7=343, Resulting Numbers: [343] 343,92 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,92 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 #0,0,4 Current State: 92:[2, 40], Operations: ['97-88=9', '49-9=40'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,92 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,92 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 92:[49, 18], Operations: ['97-88=9', '2*9=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 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[9, 51], Operations: ['97-88=9', '2+49=51'] Exploring Operation: 9+51=60, Resulting Numbers: [60] 60,92 unequal: No Solution Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 9*51=459, Resulting Numbers: [459] 459,92 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: 92:[88, 49, 95], Operations: ['97-2=95'] Exploring Operation: 88+49=137, Resulting Numbers: [95, 137] Generated Node #0,1,0: 92:[95, 137] Operation: 88+49=137 Exploring Operation: 49+95=144, Resulting Numbers: [88, 144] Generated Node #0,1,1: 92:[88, 144] Operation: 49+95=144 Exploring Operation: 95-49=46, Resulting Numbers: [88, 46] Generated Node #0,1,2: 92:[88, 46] Operation: 95-49=46 Exploring Operation: 88-49=39, Resulting Numbers: [95, 39] Generated Node #0,1,3: 92:[95, 39] Operation: 88-49=39 Exploring Operation: 95-88=7, Resulting Numbers: [49, 7] Generated Node #0,1,4: 92:[49, 7] Operation: 95-88=7 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 92:[88, 46], Operations: ['97-2=95', '95-49=46'] Exploring Operation: 88+46=134, Resulting Numbers: [134] 134,92 unequal: No Solution Exploring Operation: 88*46=4048, Resulting Numbers: [4048] 4048,92 unequal: No Solution Exploring Operation: 88-46=42, Resulting Numbers: [42] 42,92 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 #0,1,4 Current State: 92:[49, 7], Operations: ['97-2=95', '95-88=7'] Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 49*7=343, Resulting Numbers: [343] 343,92 unequal: No Solution Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,92 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,92 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 #0,1,3 Current State: 92:[95, 39], Operations: ['97-2=95', '88-49=39'] Exploring Operation: 95*39=3705, Resulting Numbers: [3705] 3705,92 unequal: No Solution Exploring Operation: 95-39=56, Resulting Numbers: [56] 56,92 unequal: No Solution Exploring Operation: 95+39=134, Resulting Numbers: [134] 134,92 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:[95, 137], Operations: ['97-2=95', '88+49=137'] Exploring Operation: 95+137=232, Resulting Numbers: [232] 232,92 unequal: No Solution Exploring Operation: 137-95=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 95*137=13015, Resulting Numbers: [13015] 13015,92 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 #0,1,1 Current State: 92:[88, 144], Operations: ['97-2=95', '49+95=144'] Exploring Operation: 88+144=232, Resulting Numbers: [232] 232,92 unequal: No Solution Exploring Operation: 144-88=56, Resulting Numbers: [56] 56,92 unequal: No Solution Exploring Operation: 88*144=12672, Resulting Numbers: [12672] 12672,92 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:[97, 49, 44], Operations: ['88/2=44'] Exploring Operation: 97+44=141, Resulting Numbers: [49, 141] Generated Node #0,2,0: 92:[49, 141] Operation: 97+44=141 Exploring Operation: 97-44=53, Resulting Numbers: [49, 53] Generated Node #0,2,1: 92:[49, 53] Operation: 97-44=53 Exploring Operation: 49+44=93, Resulting Numbers: [97, 93] Generated Node #0,2,2: 92:[97, 93] Operation: 49+44=93 Exploring Operation: 49-44=5, Resulting Numbers: [97, 5] Generated Node #0,2,3: 92:[97, 5] Operation: 49-44=5 Exploring Operation: 97-49=48, Resulting Numbers: [44, 48] Generated Node #0,2,4: 92:[44, 48] Operation: 97-49=48 Moving to Node #0,3 Current State: 92:[97, 49, 90], Operations: ['88+2=90'] Exploring Operation: 97+49=146, Resulting Numbers: [90, 146] Generated Node #0,3,0: 92:[90, 146] Operation: 97+49=146 Exploring Operation: 90-49=41, Resulting Numbers: [97, 41] Generated Node #0,3,1: 92:[97, 41] Operation: 90-49=41 Exploring Operation: 97-49=48, Resulting Numbers: [90, 48] Generated Node #0,3,2: 92:[90, 48] Operation: 97-49=48 Exploring Operation: 97-90=7, Resulting Numbers: [49, 7] Generated Node #0,3,3: 92:[49, 7] Operation: 97-90=7 Exploring Operation: 49+90=139, Resulting Numbers: [97, 139] Generated Node #0,3,4: 92:[97, 139] Operation: 49+90=139 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 92:[90, 48], Operations: ['88+2=90', '97-49=48'] Exploring Operation: 90*48=4320, Resulting Numbers: [4320] 4320,92 unequal: No Solution Exploring Operation: 90+48=138, Resulting Numbers: [138] 138,92 unequal: No Solution Exploring Operation: 90-48=42, Resulting Numbers: [42] 42,92 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 #0,3,3 Current State: 92:[49, 7], Operations: ['88+2=90', '97-90=7'] Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,92 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,92 unequal: No Solution Exploring Operation: 49*7=343, Resulting Numbers: [343] 343,92 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 #0,3,1 Current State: 92:[97, 41], Operations: ['88+2=90', '90-49=41'] Exploring Operation: 97+41=138, Resulting Numbers: [138] 138,92 unequal: No Solution Exploring Operation: 97*41=3977, Resulting Numbers: [3977] 3977,92 unequal: No Solution Exploring Operation: 97-41=56, Resulting Numbers: [56] 56,92 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 #0,3,4 Current State: 92:[97, 139], Operations: ['88+2=90', '49+90=139'] Exploring Operation: 97*139=13483, Resulting Numbers: [13483] 13483,92 unequal: No Solution Exploring Operation: 97+139=236, Resulting Numbers: [236] 236,92 unequal: No Solution Exploring Operation: 139-97=42, Resulting Numbers: [42] 42,92 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 #0,3,0 Current State: 92:[90, 146], Operations: ['88+2=90', '97+49=146'] Exploring Operation: 90+146=236, Resulting Numbers: [236] 236,92 unequal: No Solution Exploring Operation: 146-90=56, Resulting Numbers: [56] 56,92 unequal: No Solution Exploring Operation: 90*146=13140, Resulting Numbers: [13140] 13140,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,0 Current State: 92:[48, 90], Operations: ['97-49=48', '88+2=90'] Exploring Operation: 48+90=138, Resulting Numbers: [138] 138,92 unequal: No Solution Exploring Operation: 90-48=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 48*90=4320, Resulting Numbers: [4320] 4320,92 unequal: No Solution Moving to Node #0,4,4 Current State: 92:[48, 44], Operations: ['97-49=48', '88/2=44'] Exploring Operation: 48*44=2112, Resulting Numbers: [2112] 2112,92 unequal: No Solution Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[88, 97, 2, 49], Operations: [] Exploring Operation: 97-49=48, Resulting Numbers: [88, 2, 48] Generated Node #0,4: 92:[88, 2, 48] Operation: 97-49=48 Moving to Node #0,4 Current State: 92:[88, 2, 48], Operations: ['97-49=48'] Exploring Operation: 88/2=44, Resulting Numbers: [48, 44] Generated Node #0,4,4: 92:[48, 44] Operation: 88/2=44 Moving to Node #0,4,4 Current State: 92:[48, 44], Operations: ['97-49=48', '88/2=44'] Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
0.922743
hs_5
mult_heuristic
[ 55, 79, 10, 86 ]
58
[ "55+79=134", "86-10=76", "134-76=58" ]
Current State: 58:[55, 79, 10, 86], Operations: [] Exploring Operation: 55+79=134, Resulting Numbers: [10, 86, 134] Generated Node #2: [10, 86, 134] from Operation: 55+79=134 Current State: 58:[10, 86, 134], Operations: ['55+79=134'] Exploring Operation: 86-10=76, Resulting Numbers: [134, 76] Generated Node #3: [134, 76] from Operation: 86-10=76 Current State: 58:[134, 76], Operations: ['55+79=134', '86-10=76'] Exploring Operation: 134-76=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[55, 79, 10, 86], Operations: [] Exploring Operation: 79-55=24, Resulting Numbers: [10, 86, 24] Generated Node #0,0: 58:[10, 86, 24] Operation: 79-55=24 Exploring Operation: 79-10=69, Resulting Numbers: [55, 86, 69] Generated Node #0,1: 58:[55, 86, 69] Operation: 79-10=69 Exploring Operation: 86-79=7, Resulting Numbers: [55, 10, 7] Generated Node #0,2: 58:[55, 10, 7] Operation: 86-79=7 Exploring Operation: 86-55=31, Resulting Numbers: [79, 10, 31] Generated Node #0,3: 58:[79, 10, 31] Operation: 86-55=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[55, 10, 7], Operations: ['86-79=7'] Exploring Operation: 55+10=65, Resulting Numbers: [7, 65] Generated Node #0,2,0: 58:[7, 65] Operation: 55+10=65 Exploring Operation: 55+7=62, Resulting Numbers: [10, 62] Generated Node #0,2,1: 58:[10, 62] Operation: 55+7=62 Exploring Operation: 10+7=17, Resulting Numbers: [55, 17] Generated Node #0,2,2: 58:[55, 17] Operation: 10+7=17 Exploring Operation: 10-7=3, Resulting Numbers: [55, 3] Generated Node #0,2,3: 58:[55, 3] Operation: 10-7=3 Moving to Node #0,2,3 Current State: 58:[55, 3], Operations: ['86-79=7', '10-7=3'] Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,58 unequal: No Solution Exploring Operation: 55*3=165, Resulting Numbers: [165] 165,58 unequal: No Solution Exploring Operation: 55+3=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[55, 79, 10, 86], Operations: [] Exploring Operation: 86-79=7, Resulting Numbers: [55, 10, 7] Generated Node #0,2: 58:[55, 10, 7] Operation: 86-79=7 Moving to Node #0,2 Current State: 58:[55, 10, 7], Operations: ['86-79=7'] Exploring Operation: 10-7=3, Resulting Numbers: [55, 3] Generated Node #0,2,3: 58:[55, 3] Operation: 10-7=3 Moving to Node #0,2,3 Current State: 58:[55, 3], Operations: ['86-79=7', '10-7=3'] Exploring Operation: 55+3=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 96, 72, 72, 98 ]
50
[ "96-72=24", "98-72=26", "24+26=50" ]
Current State: 50:[96, 72, 72, 98], Operations: [] Exploring Operation: 96-72=24, Resulting Numbers: [98, 24] Generated Node #2: [98, 24] from Operation: 96-72=24 Current State: 50:[98, 24], Operations: ['96-72=24'] Exploring Operation: 98-72=26, Resulting Numbers: [24, 26] Generated Node #3: [24, 26] from Operation: 98-72=26 Current State: 50:[24, 26], Operations: ['96-72=24', '98-72=26'] Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[96, 72, 72, 98], Operations: [] Exploring Operation: 98-72=26, Resulting Numbers: [96, 72, 26] Generated Node #0,0: 50:[96, 72, 26] Operation: 98-72=26 Exploring Operation: 98-96=2, Resulting Numbers: [72, 72, 2] Generated Node #0,1: 50:[72, 72, 2] Operation: 98-96=2 Exploring Operation: 98-72=26, Resulting Numbers: [96, 72, 26] Generated Node #0,2: 50:[96, 72, 26] Operation: 98-72=26 Exploring Operation: 96-72=24, Resulting Numbers: [72, 98, 24] Generated Node #0,3: 50:[72, 98, 24] Operation: 96-72=24 Moving to Node #0,1 Current State: 50:[72, 72, 2], Operations: ['98-96=2'] Exploring Operation: 72-72=0, Resulting Numbers: [2, 0] Generated Node #0,1,0: 50:[2, 0] Operation: 72-72=0 Exploring Operation: 72/2=36, Resulting Numbers: [72, 36] Generated Node #0,1,1: 50:[72, 36] Operation: 72/2=36 Exploring Operation: 72/72=1, Resulting Numbers: [2, 1] Generated Node #0,1,2: 50:[2, 1] Operation: 72/72=1 Exploring Operation: 72/2=36, Resulting Numbers: [72, 36] Generated Node #0,1,3: 50:[72, 36] Operation: 72/2=36 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 50:[2, 1], Operations: ['98-96=2', '72/72=1'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[2, 0], Operations: ['98-96=2', '72-72=0'] Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 50:[72, 36], Operations: ['98-96=2', '72/2=36'] Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 72+36=108, Resulting Numbers: [108] 108,50 unequal: No Solution Exploring Operation: 72*36=2592, Resulting Numbers: [2592] 2592,50 unequal: No Solution Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 50:[72, 36], Operations: ['98-96=2', '72/2=36'] Exploring Operation: 72+36=108, Resulting Numbers: [108] 108,50 unequal: No Solution Exploring Operation: 72*36=2592, Resulting Numbers: [2592] 2592,50 unequal: No Solution Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,50 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,50 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: 50:[96, 72, 26], Operations: ['98-72=26'] Exploring Operation: 96-72=24, Resulting Numbers: [26, 24] Generated Node #0,2,0: 50:[26, 24] Operation: 96-72=24 Exploring Operation: 72-26=46, Resulting Numbers: [96, 46] Generated Node #0,2,1: 50:[96, 46] Operation: 72-26=46 Exploring Operation: 96+26=122, Resulting Numbers: [72, 122] Generated Node #0,2,2: 50:[72, 122] Operation: 96+26=122 Exploring Operation: 96-26=70, Resulting Numbers: [72, 70] Generated Node #0,2,3: 50:[72, 70] Operation: 96-26=70 Moving to Node #0,0 Current State: 50:[96, 72, 26], Operations: ['98-72=26'] Exploring Operation: 96+26=122, Resulting Numbers: [72, 122] Generated Node #0,0,0: 50:[72, 122] Operation: 96+26=122 Exploring Operation: 96-72=24, Resulting Numbers: [26, 24] Generated Node #0,0,1: 50:[26, 24] Operation: 96-72=24 Exploring Operation: 72-26=46, Resulting Numbers: [96, 46] Generated Node #0,0,2: 50:[96, 46] Operation: 72-26=46 Exploring Operation: 96-26=70, Resulting Numbers: [72, 70] Generated Node #0,0,3: 50:[72, 70] Operation: 96-26=70 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 50:[26, 24], Operations: ['98-72=26', '96-72=24'] Exploring Operation: 26*24=624, Resulting Numbers: [624] 624,50 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 26+24=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[96, 72, 72, 98], Operations: [] Exploring Operation: 98-72=26, Resulting Numbers: [96, 72, 26] Generated Node #0,0: 50:[96, 72, 26] Operation: 98-72=26 Moving to Node #0,0 Current State: 50:[96, 72, 26], Operations: ['98-72=26'] Exploring Operation: 96-72=24, Resulting Numbers: [26, 24] Generated Node #0,0,1: 50:[26, 24] Operation: 96-72=24 Moving to Node #0,0,1 Current State: 50:[26, 24], Operations: ['98-72=26', '96-72=24'] Exploring Operation: 26+24=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_4
mult_heuristic
[ 52, 18, 7, 25 ]
63
[ "52-18=34", "34-25=9", "7*9=63" ]
Current State: 63:[52, 18, 7, 25], Operations: [] Exploring Operation: 52-18=34, Resulting Numbers: [7, 25, 34] Generated Node #2: [7, 25, 34] from Operation: 52-18=34 Current State: 63:[7, 25, 34], Operations: ['52-18=34'] Exploring Operation: 34-25=9, Resulting Numbers: [7, 9] Generated Node #3: [7, 9] from Operation: 34-25=9 Current State: 63:[7, 9], Operations: ['52-18=34', '34-25=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[52, 18, 7, 25], Operations: [] Exploring Operation: 52-25=27, Resulting Numbers: [18, 7, 27] Generated Node #0,0: 63:[18, 7, 27] Operation: 52-25=27 Moving to Node #0,0 Current State: 63:[18, 7, 27], Operations: ['52-25=27'] Exploring Operation: 27-18=9, Resulting Numbers: [7, 9] Generated Node #0,0,0: 63:[7, 9] Operation: 27-18=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[7, 9], Operations: ['52-25=27', '27-18=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[52, 18, 7, 25], Operations: [] Exploring Operation: 52-25=27, Resulting Numbers: [18, 7, 27] Generated Node #0,0: 63:[18, 7, 27] Operation: 52-25=27 Moving to Node #0,0 Current State: 63:[18, 7, 27], Operations: ['52-25=27'] Exploring Operation: 27-18=9, Resulting Numbers: [7, 9] Generated Node #0,0,0: 63:[7, 9] Operation: 27-18=9 Moving to Node #0,0,0 Current State: 63:[7, 9], Operations: ['52-25=27', '27-18=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 21, 81, 87, 56 ]
18
[ "81+87=168", "168/56=3", "21-3=18" ]
Current State: 18:[21, 81, 87, 56], Operations: [] Exploring Operation: 81+87=168, Resulting Numbers: [21, 56, 168] Generated Node #2: [21, 56, 168] from Operation: 81+87=168 Current State: 18:[21, 56, 168], Operations: ['81+87=168'] Exploring Operation: 168/56=3, Resulting Numbers: [21, 3] Generated Node #3: [21, 3] from Operation: 168/56=3 Current State: 18:[21, 3], Operations: ['81+87=168', '168/56=3'] Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[21, 81, 87, 56], Operations: [] Exploring Operation: 81-56=25, Resulting Numbers: [21, 87, 25] Generated Node #0,0: 18:[21, 87, 25] Operation: 81-56=25 Exploring Operation: 87-81=6, Resulting Numbers: [21, 56, 6] Generated Node #0,1: 18:[21, 56, 6] Operation: 87-81=6 Exploring Operation: 81-21=60, Resulting Numbers: [87, 56, 60] Generated Node #0,2: 18:[87, 56, 60] Operation: 81-21=60 Exploring Operation: 87-21=66, Resulting Numbers: [81, 56, 66] Generated Node #0,3: 18:[81, 56, 66] Operation: 87-21=66 Exploring Operation: 87-56=31, Resulting Numbers: [21, 81, 31] Generated Node #0,4: 18:[21, 81, 31] Operation: 87-56=31 Moving to Node #0,1 Current State: 18:[21, 56, 6], Operations: ['87-81=6'] Exploring Operation: 21+6=27, Resulting Numbers: [56, 27] Generated Node #0,1,0: 18:[56, 27] Operation: 21+6=27 Exploring Operation: 56+6=62, Resulting Numbers: [21, 62] Generated Node #0,1,1: 18:[21, 62] Operation: 56+6=62 Exploring Operation: 56-6=50, Resulting Numbers: [21, 50] Generated Node #0,1,2: 18:[21, 50] Operation: 56-6=50 Exploring Operation: 21-6=15, Resulting Numbers: [56, 15] Generated Node #0,1,3: 18:[56, 15] Operation: 21-6=15 Exploring Operation: 56-21=35, Resulting Numbers: [6, 35] Generated Node #0,1,4: 18:[6, 35] Operation: 56-21=35 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 18:[6, 35], Operations: ['87-81=6', '56-21=35'] Exploring Operation: 6+35=41, Resulting Numbers: [41] 41,18 unequal: No Solution Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,18 unequal: No Solution Exploring Operation: 6*35=210, Resulting Numbers: [210] 210,18 unequal: No Solution No 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: 18:[21, 50], Operations: ['87-81=6', '56-6=50'] Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,18 unequal: No Solution Exploring Operation: 21*50=1050, Resulting Numbers: [1050] 1050,18 unequal: No Solution Exploring Operation: 21+50=71, Resulting Numbers: [71] 71,18 unequal: No Solution No 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: 18:[56, 15], Operations: ['87-81=6', '21-6=15'] Exploring Operation: 56*15=840, Resulting Numbers: [840] 840,18 unequal: No Solution Exploring Operation: 56-15=41, Resulting Numbers: [41] 41,18 unequal: No Solution Exploring Operation: 56+15=71, Resulting Numbers: [71] 71,18 unequal: No Solution No 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: 18:[56, 27], Operations: ['87-81=6', '21+6=27'] Exploring Operation: 56+27=83, Resulting Numbers: [83] 83,18 unequal: No Solution Exploring Operation: 56-27=29, Resulting Numbers: [29] 29,18 unequal: No Solution Exploring Operation: 56*27=1512, Resulting Numbers: [1512] 1512,18 unequal: No Solution No 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: 18:[21, 62], Operations: ['87-81=6', '56+6=62'] Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,18 unequal: No Solution Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,18 unequal: No Solution Exploring Operation: 21*62=1302, Resulting Numbers: [1302] 1302,18 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: 18:[21, 81, 31], Operations: ['87-56=31'] Exploring Operation: 31-21=10, Resulting Numbers: [81, 10] Generated Node #0,4,0: 18:[81, 10] Operation: 31-21=10 Exploring Operation: 81-31=50, Resulting Numbers: [21, 50] Generated Node #0,4,1: 18:[21, 50] Operation: 81-31=50 Exploring Operation: 81-21=60, Resulting Numbers: [31, 60] Generated Node #0,4,2: 18:[31, 60] Operation: 81-21=60 Exploring Operation: 21+81=102, Resulting Numbers: [31, 102] Generated Node #0,4,3: 18:[31, 102] Operation: 21+81=102 Exploring Operation: 21+31=52, Resulting Numbers: [81, 52] Generated Node #0,4,4: 18:[81, 52] Operation: 21+31=52 Moving to Node #0,0 Current State: 18:[21, 87, 25], Operations: ['81-56=25'] Exploring Operation: 87-21=66, Resulting Numbers: [25, 66] Generated Node #0,0,0: 18:[25, 66] Operation: 87-21=66 Exploring Operation: 21+87=108, Resulting Numbers: [25, 108] Generated Node #0,0,1: 18:[25, 108] Operation: 21+87=108 Exploring Operation: 21+25=46, Resulting Numbers: [87, 46] Generated Node #0,0,2: 18:[87, 46] Operation: 21+25=46 Exploring Operation: 87-25=62, Resulting Numbers: [21, 62] Generated Node #0,0,3: 18:[21, 62] Operation: 87-25=62 Exploring Operation: 25-21=4, Resulting Numbers: [87, 4] Generated Node #0,0,4: 18:[87, 4] Operation: 25-21=4 Moving to Node #0,2 Current State: 18:[87, 56, 60], Operations: ['81-21=60'] Exploring Operation: 87+60=147, Resulting Numbers: [56, 147] Generated Node #0,2,0: 18:[56, 147] Operation: 87+60=147 Exploring Operation: 87-56=31, Resulting Numbers: [60, 31] Generated Node #0,2,1: 18:[60, 31] Operation: 87-56=31 Exploring Operation: 87+56=143, Resulting Numbers: [60, 143] Generated Node #0,2,2: 18:[60, 143] Operation: 87+56=143 Exploring Operation: 60-56=4, Resulting Numbers: [87, 4] Generated Node #0,2,3: 18:[87, 4] Operation: 60-56=4 Exploring Operation: 87-60=27, Resulting Numbers: [56, 27] Generated Node #0,2,4: 18:[56, 27] Operation: 87-60=27 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 18:[56, 27], Operations: ['81-21=60', '87-60=27'] Exploring Operation: 56+27=83, Resulting Numbers: [83] 83,18 unequal: No Solution Exploring Operation: 56*27=1512, Resulting Numbers: [1512] 1512,18 unequal: No Solution Exploring Operation: 56-27=29, Resulting Numbers: [29] 29,18 unequal: No Solution No 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: 18:[60, 31], Operations: ['81-21=60', '87-56=31'] Exploring Operation: 60+31=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 60-31=29, Resulting Numbers: [29] 29,18 unequal: No Solution Exploring Operation: 60*31=1860, Resulting Numbers: [1860] 1860,18 unequal: No Solution No 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: 18:[87, 4], Operations: ['81-21=60', '60-56=4'] Exploring Operation: 87*4=348, Resulting Numbers: [348] 348,18 unequal: No Solution Exploring Operation: 87+4=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,18 unequal: No Solution No 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: 18:[56, 147], Operations: ['81-21=60', '87+60=147'] Exploring Operation: 56*147=8232, Resulting Numbers: [8232] 8232,18 unequal: No Solution Exploring Operation: 147-56=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 56+147=203, Resulting Numbers: [203] 203,18 unequal: No Solution No 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: 18:[60, 143], Operations: ['81-21=60', '87+56=143'] Exploring Operation: 60*143=8580, Resulting Numbers: [8580] 8580,18 unequal: No Solution Exploring Operation: 143-60=83, Resulting Numbers: [83] 83,18 unequal: No Solution Exploring Operation: 60+143=203, Resulting Numbers: [203] 203,18 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: 18:[81, 56, 66], Operations: ['87-21=66'] Exploring Operation: 81-66=15, Resulting Numbers: [56, 15] Generated Node #0,3,0: 18:[56, 15] Operation: 81-66=15 Exploring Operation: 66-56=10, Resulting Numbers: [81, 10] Generated Node #0,3,1: 18:[81, 10] Operation: 66-56=10 Exploring Operation: 81+66=147, Resulting Numbers: [56, 147] Generated Node #0,3,2: 18:[56, 147] Operation: 81+66=147 Exploring Operation: 81+56=137, Resulting Numbers: [66, 137] Generated Node #0,3,3: 18:[66, 137] Operation: 81+56=137 Exploring Operation: 81-56=25, Resulting Numbers: [66, 25] Generated Node #0,3,4: 18:[66, 25] Operation: 81-56=25 Moving to Node #0,4,1 Current State: 18:[21, 50], Operations: ['87-56=31', '81-31=50'] Exploring Operation: 21+50=71, Resulting Numbers: [71] 71,18 unequal: No Solution Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,18 unequal: No Solution Exploring Operation: 21*50=1050, Resulting Numbers: [1050] 1050,18 unequal: No Solution Moving to Node #0,3,0 Current State: 18:[56, 15], Operations: ['87-21=66', '81-66=15'] Exploring Operation: 56+15=71, Resulting Numbers: [71] 71,18 unequal: No Solution Exploring Operation: 56*15=840, Resulting Numbers: [840] 840,18 unequal: No Solution Exploring Operation: 56-15=41, Resulting Numbers: [41] 41,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[21, 62], Operations: ['81-56=25', '87-25=62'] Exploring Operation: 21*62=1302, Resulting Numbers: [1302] 1302,18 unequal: No Solution Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,18 unequal: No Solution Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[25, 66], Operations: ['81-56=25', '87-21=66'] Exploring Operation: 25*66=1650, Resulting Numbers: [1650] 1650,18 unequal: No Solution Exploring Operation: 25+66=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 66-25=41, Resulting Numbers: [41] 41,18 unequal: No Solution Moving to Node #0,3,4 Current State: 18:[66, 25], Operations: ['87-21=66', '81-56=25'] Exploring Operation: 66*25=1650, Resulting Numbers: [1650] 1650,18 unequal: No Solution Exploring Operation: 66+25=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 66-25=41, Resulting Numbers: [41] 41,18 unequal: No Solution Moving to Node #0,4,2 Current State: 18:[31, 60], Operations: ['87-56=31', '81-21=60'] Exploring Operation: 60-31=29, Resulting Numbers: [29] 29,18 unequal: No Solution Exploring Operation: 31*60=1860, Resulting Numbers: [1860] 1860,18 unequal: No Solution Exploring Operation: 31+60=91, Resulting Numbers: [91] 91,18 unequal: No Solution Moving to Node #0,4,0 Current State: 18:[81, 10], Operations: ['87-56=31', '31-21=10'] Exploring Operation: 81+10=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 81*10=810, Resulting Numbers: [810] 810,18 unequal: No Solution Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,18 unequal: No Solution Moving to Node #0,3,1 Current State: 18:[81, 10], Operations: ['87-21=66', '66-56=10'] Exploring Operation: 81*10=810, Resulting Numbers: [810] 810,18 unequal: No Solution Exploring Operation: 81+10=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,18 unequal: No Solution Moving to Node #0,0,4 Current State: 18:[87, 4], Operations: ['81-56=25', '25-21=4'] Exploring Operation: 87*4=348, Resulting Numbers: [348] 348,18 unequal: No Solution Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,18 unequal: No Solution Exploring Operation: 87+4=91, Resulting Numbers: [91] 91,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[87, 46], Operations: ['81-56=25', '21+25=46'] Exploring Operation: 87+46=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 87-46=41, Resulting Numbers: [41] 41,18 unequal: No Solution Exploring Operation: 87*46=4002, Resulting Numbers: [4002] 4002,18 unequal: No Solution Moving to Node #0,4,4 Current State: 18:[81, 52], Operations: ['87-56=31', '21+31=52'] Exploring Operation: 81+52=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 81-52=29, Resulting Numbers: [29] 29,18 unequal: No Solution Exploring Operation: 81*52=4212, Resulting Numbers: [4212] 4212,18 unequal: No Solution Moving to Node #0,4,3 Current State: 18:[31, 102], Operations: ['87-56=31', '21+81=102'] Exploring Operation: 31+102=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 31*102=3162, Resulting Numbers: [3162] 3162,18 unequal: No Solution Exploring Operation: 102-31=71, Resulting Numbers: [71] 71,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[25, 108], Operations: ['81-56=25', '21+87=108'] Exploring Operation: 25*108=2700, Resulting Numbers: [2700] 2700,18 unequal: No Solution Exploring Operation: 25+108=133, Resulting Numbers: [133] 133,18 unequal: No Solution Exploring Operation: 108-25=83, Resulting Numbers: [83] 83,18 unequal: No Solution Moving to Node #0,3,2 Current State: 18:[56, 147], Operations: ['87-21=66', '81+66=147'] Exploring Operation: 56*147=8232, Resulting Numbers: [8232] 8232,18 unequal: No Solution Exploring Operation: 147-56=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 56+147=203, Resulting Numbers: [203] 203,18 unequal: No Solution Moving to Node #0,3,3 Current State: 18:[66, 137], Operations: ['87-21=66', '81+56=137'] Exploring Operation: 137-66=71, Resulting Numbers: [71] 71,18 unequal: No Solution Exploring Operation: 66+137=203, Resulting Numbers: [203] 203,18 unequal: No Solution Exploring Operation: 66*137=9042, Resulting Numbers: [9042] 9042,18 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 17, 13, 84, 30 ]
84
[ "17+13=30", "84+30=114", "114-30=84" ]
Current State: 84:[17, 13, 84, 30], Operations: [] Exploring Operation: 17+13=30, Resulting Numbers: [84, 30, 30] Generated Node #2: [84, 30, 30] from Operation: 17+13=30 Current State: 84:[84, 30, 30], Operations: ['17+13=30'] Exploring Operation: 84+30=114, Resulting Numbers: [114] 114,84 equal: Goal Reached Exploring Operation: 114-30=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[17, 13, 84, 30], Operations: [] Exploring Operation: 13+30=43, Resulting Numbers: [17, 84, 43] Generated Node #0,0: 84:[17, 84, 43] Operation: 13+30=43 Exploring Operation: 17-13=4, Resulting Numbers: [84, 30, 4] Generated Node #0,1: 84:[84, 30, 4] Operation: 17-13=4 Exploring Operation: 17+13=30, Resulting Numbers: [84, 30, 30] Generated Node #0,2: 84:[84, 30, 30] Operation: 17+13=30 Exploring Operation: 30-17=13, Resulting Numbers: [13, 84, 13] Generated Node #0,3: 84:[13, 84, 13] Operation: 30-17=13 Exploring Operation: 17+30=47, Resulting Numbers: [13, 84, 47] Generated Node #0,4: 84:[13, 84, 47] Operation: 17+30=47 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[84, 30, 4], Operations: ['17-13=4'] Exploring Operation: 84+4=88, Resulting Numbers: [30, 88] Generated Node #0,1,0: 84:[30, 88] Operation: 84+4=88 Exploring Operation: 30-4=26, Resulting Numbers: [84, 26] Generated Node #0,1,1: 84:[84, 26] Operation: 30-4=26 Exploring Operation: 30+4=34, Resulting Numbers: [84, 34] Generated Node #0,1,2: 84:[84, 34] Operation: 30+4=34 Exploring Operation: 84-4=80, Resulting Numbers: [30, 80] Generated Node #0,1,3: 84:[30, 80] Operation: 84-4=80 Exploring Operation: 84/4=21, Resulting Numbers: [30, 21] Generated Node #0,1,4: 84:[30, 21] Operation: 84/4=21 Moving to Node #0,1,1 Current State: 84:[84, 26], Operations: ['17-13=4', '30-4=26'] Exploring Operation: 84+26=110, Resulting Numbers: [110] 110,84 unequal: No Solution Exploring Operation: 84-26=58, Resulting Numbers: [58] 58,84 unequal: No Solution Exploring Operation: 84*26=2184, Resulting Numbers: [2184] 2184,84 unequal: No Solution Moving to Node #0,1,4 Current State: 84:[30, 21], Operations: ['17-13=4', '84/4=21'] Exploring Operation: 30-21=9, Resulting Numbers: [9] 9,84 unequal: No Solution Exploring Operation: 30*21=630, Resulting Numbers: [630] 630,84 unequal: No Solution Exploring Operation: 30+21=51, Resulting Numbers: [51] 51,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[30, 88], Operations: ['17-13=4', '84+4=88'] Exploring Operation: 30+88=118, Resulting Numbers: [118] 118,84 unequal: No Solution Exploring Operation: 30*88=2640, Resulting Numbers: [2640] 2640,84 unequal: No Solution Exploring Operation: 88-30=58, Resulting Numbers: [58] 58,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[84, 34], Operations: ['17-13=4', '30+4=34'] Exploring Operation: 84*34=2856, Resulting Numbers: [2856] 2856,84 unequal: No Solution Exploring Operation: 84+34=118, Resulting Numbers: [118] 118,84 unequal: No Solution Exploring Operation: 84-34=50, Resulting Numbers: [50] 50,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[30, 80], Operations: ['17-13=4', '84-4=80'] Exploring Operation: 30+80=110, Resulting Numbers: [110] 110,84 unequal: No Solution Exploring Operation: 80-30=50, Resulting Numbers: [50] 50,84 unequal: No Solution Exploring Operation: 30*80=2400, Resulting Numbers: [2400] 2400,84 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 #0,3 Current State: 84:[13, 84, 13], Operations: ['30-17=13'] Exploring Operation: 13+84=97, Resulting Numbers: [13, 97] Generated Node #0,3,0: 84:[13, 97] Operation: 13+84=97 Exploring Operation: 13+13=26, Resulting Numbers: [84, 26] Generated Node #0,3,1: 84:[84, 26] Operation: 13+13=26 Exploring Operation: 13/13=1, Resulting Numbers: [84, 1] Generated Node #0,3,2: 84:[84, 1] Operation: 13/13=1 Exploring Operation: 13-13=0, Resulting Numbers: [84, 0] Generated Node #0,3,3: 84:[84, 0] Operation: 13-13=0 Exploring Operation: 84-13=71, Resulting Numbers: [13, 71] Generated Node #0,3,4: 84:[13, 71] Operation: 84-13=71 Moving to Node #0,3,2 Current State: 84:[84, 1], Operations: ['30-17=13', '13/13=1'] Exploring Operation: 84+1=85, Resulting Numbers: [85] 85,84 unequal: No Solution Exploring Operation: 84*1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[17, 13, 84, 30], Operations: [] Exploring Operation: 30-17=13, Resulting Numbers: [13, 84, 13] Generated Node #0,3: 84:[13, 84, 13] Operation: 30-17=13 Moving to Node #0,3 Current State: 84:[13, 84, 13], Operations: ['30-17=13'] Exploring Operation: 13/13=1, Resulting Numbers: [84, 1] Generated Node #0,3,2: 84:[84, 1] Operation: 13/13=1 Moving to Node #0,3,2 Current State: 84:[84, 1], Operations: ['30-17=13', '13/13=1'] Exploring Operation: 84*1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 93, 58, 43, 14 ]
91
[ "43-14=29", "58/29=2", "93-2=91" ]
Current State: 91:[93, 58, 43, 14], Operations: [] Exploring Operation: 43-14=29, Resulting Numbers: [93, 58, 29] Generated Node #2: [93, 58, 29] from Operation: 43-14=29 Current State: 91:[93, 58, 29], Operations: ['43-14=29'] Exploring Operation: 58/29=2, Resulting Numbers: [93, 2] Generated Node #3: [93, 2] from Operation: 58/29=2 Current State: 91:[93, 2], Operations: ['43-14=29', '58/29=2'] Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[93, 58, 43, 14], Operations: [] Exploring Operation: 58+14=72, Resulting Numbers: [93, 43, 72] Generated Node #0,0: 91:[93, 43, 72] Operation: 58+14=72 Exploring Operation: 43-14=29, Resulting Numbers: [93, 58, 29] Generated Node #0,1: 91:[93, 58, 29] Operation: 43-14=29 Exploring Operation: 58-43=15, Resulting Numbers: [93, 14, 15] Generated Node #0,2: 91:[93, 14, 15] Operation: 58-43=15 Exploring Operation: 93-58=35, Resulting Numbers: [43, 14, 35] Generated Node #0,3: 91:[43, 14, 35] Operation: 93-58=35 Exploring Operation: 58+43=101, Resulting Numbers: [93, 14, 101] Generated Node #0,4: 91:[93, 14, 101] Operation: 58+43=101 Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[93, 14, 15], Operations: ['58-43=15'] Exploring Operation: 93-15=78, Resulting Numbers: [14, 78] Generated Node #0,2,0: 91:[14, 78] Operation: 93-15=78 Exploring Operation: 15-14=1, Resulting Numbers: [93, 1] Generated Node #0,2,1: 91:[93, 1] Operation: 15-14=1 Exploring Operation: 93-14=79, Resulting Numbers: [15, 79] Generated Node #0,2,2: 91:[15, 79] Operation: 93-14=79 Exploring Operation: 93+15=108, Resulting Numbers: [14, 108] Generated Node #0,2,3: 91:[14, 108] Operation: 93+15=108 Exploring Operation: 93+14=107, Resulting Numbers: [15, 107] Generated Node #0,2,4: 91:[15, 107] Operation: 93+14=107 Moving to Node #0,2,1 Current State: 91:[93, 1], Operations: ['58-43=15', '15-14=1'] Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,91 unequal: No Solution Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,91 unequal: No Solution Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,91 unequal: No Solution Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[15, 79], Operations: ['58-43=15', '93-14=79'] Exploring Operation: 15+79=94, Resulting Numbers: [94] 94,91 unequal: No Solution Exploring Operation: 79-15=64, Resulting Numbers: [64] 64,91 unequal: No Solution Exploring Operation: 15*79=1185, Resulting Numbers: [1185] 1185,91 unequal: No Solution Moving to Node #0,2,0 Current State: 91:[14, 78], Operations: ['58-43=15', '93-15=78'] Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,91 unequal: No Solution Exploring Operation: 14*78=1092, Resulting Numbers: [1092] 1092,91 unequal: No Solution Exploring Operation: 14+78=92, Resulting Numbers: [92] 92,91 unequal: No Solution Moving to Node #0,2,3 Current State: 91:[14, 108], Operations: ['58-43=15', '93+15=108'] Exploring Operation: 14*108=1512, Resulting Numbers: [1512] 1512,91 unequal: No Solution Exploring Operation: 108-14=94, Resulting Numbers: [94] 94,91 unequal: No Solution Exploring Operation: 14+108=122, Resulting Numbers: [122] 122,91 unequal: No Solution Moving to Node #0,2,4 Current State: 91:[15, 107], Operations: ['58-43=15', '93+14=107'] Exploring Operation: 107-15=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 15*107=1605, Resulting Numbers: [1605] 1605,91 unequal: No Solution Exploring Operation: 15+107=122, Resulting Numbers: [122] 122,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 91:[93, 14, 101], Operations: ['58+43=101'] Exploring Operation: 101-14=87, Resulting Numbers: [93, 87] Generated Node #0,4,0: 91:[93, 87] Operation: 101-14=87 Exploring Operation: 14+101=115, Resulting Numbers: [93, 115] Generated Node #0,4,1: 91:[93, 115] Operation: 14+101=115 Exploring Operation: 101-93=8, Resulting Numbers: [14, 8] Generated Node #0,4,2: 91:[14, 8] Operation: 101-93=8 Exploring Operation: 93+14=107, Resulting Numbers: [101, 107] Generated Node #0,4,3: 91:[101, 107] Operation: 93+14=107 Exploring Operation: 93-14=79, Resulting Numbers: [101, 79] Generated Node #0,4,4: 91:[101, 79] Operation: 93-14=79 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 91:[14, 8], Operations: ['58+43=101', '101-93=8'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,91 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 91:[93, 87], Operations: ['58+43=101', '101-14=87'] Exploring Operation: 93-87=6, Resulting Numbers: [6] 6,91 unequal: No Solution Exploring Operation: 93*87=8091, Resulting Numbers: [8091] 8091,91 unequal: No Solution Exploring Operation: 93+87=180, Resulting Numbers: [180] 180,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 91:[101, 79], Operations: ['58+43=101', '93-14=79'] Exploring Operation: 101+79=180, Resulting Numbers: [180] 180,91 unequal: No Solution Exploring Operation: 101-79=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 101*79=7979, Resulting Numbers: [7979] 7979,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 91:[93, 115], Operations: ['58+43=101', '14+101=115'] Exploring Operation: 93+115=208, Resulting Numbers: [208] 208,91 unequal: No Solution Exploring Operation: 93*115=10695, Resulting Numbers: [10695] 10695,91 unequal: No Solution Exploring Operation: 115-93=22, Resulting Numbers: [22] 22,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 91:[101, 107], Operations: ['58+43=101', '93+14=107'] Exploring Operation: 107-101=6, Resulting Numbers: [6] 6,91 unequal: No Solution Exploring Operation: 101*107=10807, Resulting Numbers: [10807] 10807,91 unequal: No Solution Exploring Operation: 101+107=208, Resulting Numbers: [208] 208,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[93, 43, 72], Operations: ['58+14=72'] Exploring Operation: 72-43=29, Resulting Numbers: [93, 29] Generated Node #0,0,0: 91:[93, 29] Operation: 72-43=29 Exploring Operation: 43+72=115, Resulting Numbers: [93, 115] Generated Node #0,0,1: 91:[93, 115] Operation: 43+72=115 Exploring Operation: 93-72=21, Resulting Numbers: [43, 21] Generated Node #0,0,2: 91:[43, 21] Operation: 93-72=21 Exploring Operation: 93+43=136, Resulting Numbers: [72, 136] Generated Node #0,0,3: 91:[72, 136] Operation: 93+43=136 Exploring Operation: 93-43=50, Resulting Numbers: [72, 50] Generated Node #0,0,4: 91:[72, 50] Operation: 93-43=50 Moving to Node #0,0,0 Current State: 91:[93, 29], Operations: ['58+14=72', '72-43=29'] Exploring Operation: 93-29=64, Resulting Numbers: [64] 64,91 unequal: No Solution Exploring Operation: 93+29=122, Resulting Numbers: [122] 122,91 unequal: No Solution Exploring Operation: 93*29=2697, Resulting Numbers: [2697] 2697,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[93, 115], Operations: ['58+14=72', '43+72=115'] Exploring Operation: 115-93=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 93*115=10695, Resulting Numbers: [10695] 10695,91 unequal: No Solution Exploring Operation: 93+115=208, Resulting Numbers: [208] 208,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[43, 21], Operations: ['58+14=72', '93-72=21'] Exploring Operation: 43*21=903, Resulting Numbers: [903] 903,91 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 43+21=64, Resulting Numbers: [64] 64,91 unequal: No Solution Moving to Node #0,0,4 Current State: 91:[72, 50], Operations: ['58+14=72', '93-43=50'] Exploring Operation: 72*50=3600, Resulting Numbers: [3600] 3600,91 unequal: No Solution Exploring Operation: 72-50=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 72+50=122, Resulting Numbers: [122] 122,91 unequal: No Solution Moving to Node #0,0,3 Current State: 91:[72, 136], Operations: ['58+14=72', '93+43=136'] Exploring Operation: 136-72=64, Resulting Numbers: [64] 64,91 unequal: No Solution Exploring Operation: 72*136=9792, Resulting Numbers: [9792] 9792,91 unequal: No Solution Exploring Operation: 72+136=208, Resulting Numbers: [208] 208,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[93, 58, 29], Operations: ['43-14=29'] Exploring Operation: 58-29=29, Resulting Numbers: [93, 29] Generated Node #0,1,0: 91:[93, 29] Operation: 58-29=29 Exploring Operation: 58/29=2, Resulting Numbers: [93, 2] Generated Node #0,1,1: 91:[93, 2] Operation: 58/29=2 Exploring Operation: 93-58=35, Resulting Numbers: [29, 35] Generated Node #0,1,2: 91:[29, 35] Operation: 93-58=35 Exploring Operation: 93-29=64, Resulting Numbers: [58, 64] Generated Node #0,1,3: 91:[58, 64] Operation: 93-29=64 Exploring Operation: 58+29=87, Resulting Numbers: [93, 87] Generated Node #0,1,4: 91:[93, 87] Operation: 58+29=87 Moving to Node #0,1,4 Current State: 91:[93, 87], Operations: ['43-14=29', '58+29=87'] Exploring Operation: 93*87=8091, Resulting Numbers: [8091] 8091,91 unequal: No Solution Exploring Operation: 93-87=6, Resulting Numbers: [6] 6,91 unequal: No Solution Exploring Operation: 93+87=180, Resulting Numbers: [180] 180,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[93, 2], Operations: ['43-14=29', '58/29=2'] Exploring Operation: 93*2=186, Resulting Numbers: [186] 186,91 unequal: No Solution Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,91 unequal: No Solution Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[93, 58, 43, 14], Operations: [] Exploring Operation: 43-14=29, Resulting Numbers: [93, 58, 29] Generated Node #0,1: 91:[93, 58, 29] Operation: 43-14=29 Moving to Node #0,1 Current State: 91:[93, 58, 29], Operations: ['43-14=29'] Exploring Operation: 58/29=2, Resulting Numbers: [93, 2] Generated Node #0,1,1: 91:[93, 2] Operation: 58/29=2 Moving to Node #0,1,1 Current State: 91:[93, 2], Operations: ['43-14=29', '58/29=2'] Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.929688
hs_5
sum_heuristic
[ 50, 58, 25, 8 ]
92
[ "50+58=108", "25*8=200", "200-108=92" ]
Current State: 92:[50, 58, 25, 8], Operations: [] Exploring Operation: 50+58=108, Resulting Numbers: [25, 8, 108] Generated Node #2: [25, 8, 108] from Operation: 50+58=108 Current State: 92:[25, 8, 108], Operations: ['50+58=108'] Exploring Operation: 25*8=200, Resulting Numbers: [108, 200] Generated Node #3: [108, 200] from Operation: 25*8=200 Current State: 92:[108, 200], Operations: ['50+58=108', '25*8=200'] Exploring Operation: 200-108=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[50, 58, 25, 8], Operations: [] Exploring Operation: 58-8=50, Resulting Numbers: [50, 25, 50] Generated Node #0,0: 92:[50, 25, 50] Operation: 58-8=50 Exploring Operation: 58-50=8, Resulting Numbers: [25, 8, 8] Generated Node #0,1: 92:[25, 8, 8] Operation: 58-50=8 Moving to Node #0,0 Current State: 92:[50, 25, 50], Operations: ['58-8=50'] Exploring Operation: 50/25=2, Resulting Numbers: [50, 2] Generated Node #0,0,0: 92:[50, 2] Operation: 50/25=2 Exploring Operation: 50/50=1, Resulting Numbers: [25, 1] Generated Node #0,0,1: 92:[25, 1] Operation: 50/50=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[25, 1], Operations: ['58-8=50', '50/50=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[50, 2], Operations: ['58-8=50', '50/25=2'] Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,92 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,92 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: 92:[25, 8, 8], Operations: ['58-50=8'] Exploring Operation: 8/8=1, Resulting Numbers: [25, 1] Generated Node #0,1,0: 92:[25, 1] Operation: 8/8=1 Exploring Operation: 8-8=0, Resulting Numbers: [25, 0] Generated Node #0,1,1: 92:[25, 0] Operation: 8-8=0 Moving to Node #0,1,0 Current State: 92:[25, 1], Operations: ['58-50=8', '8/8=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[25, 0], Operations: ['58-50=8', '8-8=0'] Exploring Operation: 25+0=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 25*0=0, Resulting Numbers: [0] 0,92 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 49, 12, 86, 73 ]
84
[ "73-49=24", "24/12=2", "86-2=84" ]
Current State: 84:[49, 12, 86, 73], Operations: [] Exploring Operation: 73-49=24, Resulting Numbers: [12, 86, 24] Generated Node #2: [12, 86, 24] from Operation: 73-49=24 Current State: 84:[12, 86, 24], Operations: ['73-49=24'] Exploring Operation: 24/12=2, Resulting Numbers: [86, 2] Generated Node #3: [86, 2] from Operation: 24/12=2 Current State: 84:[86, 2], Operations: ['73-49=24', '24/12=2'] Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[49, 12, 86, 73], Operations: [] Exploring Operation: 86-73=13, Resulting Numbers: [49, 12, 13] Generated Node #0,0: 84:[49, 12, 13] Operation: 86-73=13 Exploring Operation: 73-49=24, Resulting Numbers: [12, 86, 24] Generated Node #0,1: 84:[12, 86, 24] Operation: 73-49=24 Exploring Operation: 12+73=85, Resulting Numbers: [49, 86, 85] Generated Node #0,2: 84:[49, 86, 85] Operation: 12+73=85 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[12, 86, 24], Operations: ['73-49=24'] Exploring Operation: 24-12=12, Resulting Numbers: [86, 12] Generated Node #0,1,0: 84:[86, 12] Operation: 24-12=12 Exploring Operation: 12+24=36, Resulting Numbers: [86, 36] Generated Node #0,1,1: 84:[86, 36] Operation: 12+24=36 Exploring Operation: 24/12=2, Resulting Numbers: [86, 2] Generated Node #0,1,2: 84:[86, 2] Operation: 24/12=2 Moving to Node #0,1,0 Current State: 84:[86, 12], Operations: ['73-49=24', '24-12=12'] Exploring Operation: 86*12=1032, Resulting Numbers: [1032] 1032,84 unequal: No Solution Exploring Operation: 86-12=74, Resulting Numbers: [74] 74,84 unequal: No Solution Exploring Operation: 86+12=98, Resulting Numbers: [98] 98,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[86, 2], Operations: ['73-49=24', '24/12=2'] Exploring Operation: 86+2=88, Resulting Numbers: [88] 88,84 unequal: No Solution Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,84 unequal: No Solution Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[49, 12, 86, 73], Operations: [] Exploring Operation: 73-49=24, Resulting Numbers: [12, 86, 24] Generated Node #0,1: 84:[12, 86, 24] Operation: 73-49=24 Moving to Node #0,1 Current State: 84:[12, 86, 24], Operations: ['73-49=24'] Exploring Operation: 24/12=2, Resulting Numbers: [86, 2] Generated Node #0,1,2: 84:[86, 2] Operation: 24/12=2 Moving to Node #0,1,2 Current State: 84:[86, 2], Operations: ['73-49=24', '24/12=2'] Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 82, 2, 68, 28 ]
65
[ "82+2=84", "84/28=3", "68-3=65" ]
Current State: 65:[82, 2, 68, 28], Operations: [] Exploring Operation: 82+2=84, Resulting Numbers: [68, 28, 84] Generated Node #2: [68, 28, 84] from Operation: 82+2=84 Current State: 65:[68, 28, 84], Operations: ['82+2=84'] Exploring Operation: 84/28=3, Resulting Numbers: [68, 3] Generated Node #3: [68, 3] from Operation: 84/28=3 Current State: 65:[68, 3], Operations: ['82+2=84', '84/28=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[82, 2, 68, 28], Operations: [] Exploring Operation: 82-68=14, Resulting Numbers: [2, 28, 14] Generated Node #0,0: 65:[2, 28, 14] Operation: 82-68=14 Exploring Operation: 82-28=54, Resulting Numbers: [2, 68, 54] Generated Node #0,1: 65:[2, 68, 54] Operation: 82-28=54 Moving to Node #0,1 Current State: 65:[2, 68, 54], Operations: ['82-28=54'] Exploring Operation: 68-2=66, Resulting Numbers: [54, 66] Generated Node #0,1,0: 65:[54, 66] Operation: 68-2=66 Exploring Operation: 68-54=14, Resulting Numbers: [2, 14] Generated Node #0,1,1: 65:[2, 14] Operation: 68-54=14 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[2, 14], Operations: ['82-28=54', '68-54=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,65 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[54, 66], Operations: ['82-28=54', '68-2=66'] Exploring Operation: 66-54=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 54+66=120, Resulting Numbers: [120] 120,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 65:[2, 28, 14], Operations: ['82-68=14'] Exploring Operation: 28-14=14, Resulting Numbers: [2, 14] Generated Node #0,0,0: 65:[2, 14] Operation: 28-14=14 Exploring Operation: 28/2=14, Resulting Numbers: [14, 14] Generated Node #0,0,1: 65:[14, 14] Operation: 28/2=14 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 65:[14, 14], Operations: ['82-68=14', '28/2=14'] Exploring Operation: 14/14=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 14-14=0, Resulting Numbers: [0] 0,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[2, 14], Operations: ['82-68=14', '28-14=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,65 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,65 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
[ 89, 54, 30, 3 ]
91
[ "30-3=27", "54/27=2", "89+2=91" ]
Current State: 91:[89, 54, 30, 3], Operations: [] Exploring Operation: 30-3=27, Resulting Numbers: [89, 54, 27] Generated Node #2: [89, 54, 27] from Operation: 30-3=27 Current State: 91:[89, 54, 27], Operations: ['30-3=27'] Exploring Operation: 54/27=2, Resulting Numbers: [89, 2] Generated Node #3: [89, 2] from Operation: 54/27=2 Current State: 91:[89, 2], Operations: ['30-3=27', '54/27=2'] Exploring Operation: 89+2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[89, 54, 30, 3], Operations: [] Exploring Operation: 54+30=84, Resulting Numbers: [89, 3, 84] Generated Node #0,0: 91:[89, 3, 84] Operation: 54+30=84 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[89, 3, 84], Operations: ['54+30=84'] Exploring Operation: 89-84=5, Resulting Numbers: [3, 5] Generated Node #0,0,0: 91:[3, 5] Operation: 89-84=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[3, 5], Operations: ['54+30=84', '89-84=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 78, 41, 29, 13 ]
53
[ "78-41=37", "29-13=16", "37+16=53" ]
Current State: 53:[78, 41, 29, 13], Operations: [] Exploring Operation: 78-41=37, Resulting Numbers: [29, 13, 37] Generated Node #2: [29, 13, 37] from Operation: 78-41=37 Current State: 53:[29, 13, 37], Operations: ['78-41=37'] Exploring Operation: 29-13=16, Resulting Numbers: [37, 16] Generated Node #3: [37, 16] from Operation: 29-13=16 Current State: 53:[37, 16], Operations: ['78-41=37', '29-13=16'] Exploring Operation: 37+16=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[78, 41, 29, 13], Operations: [] Exploring Operation: 78-13=65, Resulting Numbers: [41, 29, 65] Generated Node #0,0: 53:[41, 29, 65] Operation: 78-13=65 Exploring Operation: 29+13=42, Resulting Numbers: [78, 41, 42] Generated Node #0,1: 53:[78, 41, 42] Operation: 29+13=42 Exploring Operation: 41+13=54, Resulting Numbers: [78, 29, 54] Generated Node #0,2: 53:[78, 29, 54] Operation: 41+13=54 Exploring Operation: 78-29=49, Resulting Numbers: [41, 13, 49] Generated Node #0,3: 53:[41, 13, 49] Operation: 78-29=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[41, 29, 65], Operations: ['78-13=65'] Exploring Operation: 65-41=24, Resulting Numbers: [29, 24] Generated Node #0,0,0: 53:[29, 24] Operation: 65-41=24 Exploring Operation: 41-29=12, Resulting Numbers: [65, 12] Generated Node #0,0,1: 53:[65, 12] Operation: 41-29=12 Exploring Operation: 41+29=70, Resulting Numbers: [65, 70] Generated Node #0,0,2: 53:[65, 70] Operation: 41+29=70 Exploring Operation: 65-29=36, Resulting Numbers: [41, 36] Generated Node #0,0,3: 53:[41, 36] Operation: 65-29=36 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 53:[65, 70], Operations: ['78-13=65', '41+29=70'] Exploring Operation: 70-65=5, Resulting Numbers: [5] 5,53 unequal: No Solution Exploring Operation: 65*70=4550, Resulting Numbers: [4550] 4550,53 unequal: No Solution Exploring Operation: 65+70=135, Resulting Numbers: [135] 135,53 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 #0,0,3 Current State: 53:[41, 36], Operations: ['78-13=65', '65-29=36'] Exploring Operation: 41*36=1476, Resulting Numbers: [1476] 1476,53 unequal: No Solution Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,53 unequal: No Solution Exploring Operation: 41+36=77, Resulting Numbers: [77] 77,53 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 #0,0,0 Current State: 53:[29, 24], Operations: ['78-13=65', '65-41=24'] Exploring Operation: 29+24=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[78, 41, 29, 13], Operations: [] Exploring Operation: 78-13=65, Resulting Numbers: [41, 29, 65] Generated Node #0,0: 53:[41, 29, 65] Operation: 78-13=65 Moving to Node #0,0 Current State: 53:[41, 29, 65], Operations: ['78-13=65'] Exploring Operation: 65-41=24, Resulting Numbers: [29, 24] Generated Node #0,0,0: 53:[29, 24] Operation: 65-41=24 Moving to Node #0,0,0 Current State: 53:[29, 24], Operations: ['78-13=65', '65-41=24'] Exploring Operation: 29+24=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 7, 59, 70, 4 ]
49
[ "70-59=11", "11-4=7", "7*7=49" ]
Current State: 49:[7, 59, 70, 4], Operations: [] Exploring Operation: 70-59=11, Resulting Numbers: [7, 4, 11] Generated Node #2: [7, 4, 11] from Operation: 70-59=11 Current State: 49:[7, 4, 11], Operations: ['70-59=11'] Exploring Operation: 11-4=7, Resulting Numbers: [7, 7] Generated Node #3: [7, 7] from Operation: 11-4=7 Current State: 49:[7, 7], Operations: ['70-59=11', '11-4=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[7, 59, 70, 4], Operations: [] Exploring Operation: 70-7=63, Resulting Numbers: [59, 4, 63] Generated Node #0,0: 49:[59, 4, 63] Operation: 70-7=63 Exploring Operation: 59-4=55, Resulting Numbers: [7, 70, 55] Generated Node #0,1: 49:[7, 70, 55] Operation: 59-4=55 Exploring Operation: 70-59=11, Resulting Numbers: [7, 4, 11] Generated Node #0,2: 49:[7, 4, 11] Operation: 70-59=11 Exploring Operation: 59-7=52, Resulting Numbers: [70, 4, 52] Generated Node #0,3: 49:[70, 4, 52] Operation: 59-7=52 Exploring Operation: 70/7=10, Resulting Numbers: [59, 4, 10] Generated Node #0,4: 49:[59, 4, 10] Operation: 70/7=10 Moving to Node #0,2 Current State: 49:[7, 4, 11], Operations: ['70-59=11'] Exploring Operation: 7+4=11, Resulting Numbers: [11, 11] Generated Node #0,2,0: 49:[11, 11] Operation: 7+4=11 Exploring Operation: 11-4=7, Resulting Numbers: [7, 7] Generated Node #0,2,1: 49:[7, 7] Operation: 11-4=7 Exploring Operation: 11-7=4, Resulting Numbers: [4, 4] Generated Node #0,2,2: 49:[4, 4] Operation: 11-7=4 Exploring Operation: 7-4=3, Resulting Numbers: [11, 3] Generated Node #0,2,3: 49:[11, 3] Operation: 7-4=3 Exploring Operation: 4*11=44, Resulting Numbers: [7, 44] Generated Node #0,2,4: 49:[7, 44] Operation: 4*11=44 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 49:[7, 7], Operations: ['70-59=11', '11-4=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[7, 59, 70, 4], Operations: [] Exploring Operation: 70-59=11, Resulting Numbers: [7, 4, 11] Generated Node #0,2: 49:[7, 4, 11] Operation: 70-59=11 Moving to Node #0,2 Current State: 49:[7, 4, 11], Operations: ['70-59=11'] Exploring Operation: 11-4=7, Resulting Numbers: [7, 7] Generated Node #0,2,1: 49:[7, 7] Operation: 11-4=7 Moving to Node #0,2,1 Current State: 49:[7, 7], Operations: ['70-59=11', '11-4=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 16, 51, 57, 81 ]
59
[ "51-16=35", "81-57=24", "35+24=59" ]
Current State: 59:[16, 51, 57, 81], Operations: [] Exploring Operation: 51-16=35, Resulting Numbers: [57, 81, 35] Generated Node #2: [57, 81, 35] from Operation: 51-16=35 Current State: 59:[57, 81, 35], Operations: ['51-16=35'] Exploring Operation: 81-57=24, Resulting Numbers: [35, 24] Generated Node #3: [35, 24] from Operation: 81-57=24 Current State: 59:[35, 24], Operations: ['51-16=35', '81-57=24'] Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[16, 51, 57, 81], Operations: [] Exploring Operation: 16+51=67, Resulting Numbers: [57, 81, 67] Generated Node #0,0: 59:[57, 81, 67] Operation: 16+51=67 Exploring Operation: 81-16=65, Resulting Numbers: [51, 57, 65] Generated Node #0,1: 59:[51, 57, 65] Operation: 81-16=65 Exploring Operation: 16+57=73, Resulting Numbers: [51, 81, 73] Generated Node #0,2: 59:[51, 81, 73] Operation: 16+57=73 Exploring Operation: 57-16=41, Resulting Numbers: [51, 81, 41] Generated Node #0,3: 59:[51, 81, 41] Operation: 57-16=41 Exploring Operation: 51-16=35, Resulting Numbers: [57, 81, 35] Generated Node #0,4: 59:[57, 81, 35] Operation: 51-16=35 Moving to Node #0,1 Current State: 59:[51, 57, 65], Operations: ['81-16=65'] Exploring Operation: 65-57=8, Resulting Numbers: [51, 8] Generated Node #0,1,0: 59:[51, 8] Operation: 65-57=8 Exploring Operation: 51+57=108, Resulting Numbers: [65, 108] Generated Node #0,1,1: 59:[65, 108] Operation: 51+57=108 Exploring Operation: 57-51=6, Resulting Numbers: [65, 6] Generated Node #0,1,2: 59:[65, 6] Operation: 57-51=6 Exploring Operation: 65-51=14, Resulting Numbers: [57, 14] Generated Node #0,1,3: 59:[57, 14] Operation: 65-51=14 Exploring Operation: 51+65=116, Resulting Numbers: [57, 116] Generated Node #0,1,4: 59:[57, 116] Operation: 51+65=116 Moving to Node #0,0 Current State: 59:[57, 81, 67], Operations: ['16+51=67'] Exploring Operation: 57+67=124, Resulting Numbers: [81, 124] Generated Node #0,0,0: 59:[81, 124] Operation: 57+67=124 Exploring Operation: 67-57=10, Resulting Numbers: [81, 10] Generated Node #0,0,1: 59:[81, 10] Operation: 67-57=10 Exploring Operation: 57+81=138, Resulting Numbers: [67, 138] Generated Node #0,0,2: 59:[67, 138] Operation: 57+81=138 Exploring Operation: 81-57=24, Resulting Numbers: [67, 24] Generated Node #0,0,3: 59:[67, 24] Operation: 81-57=24 Exploring Operation: 81-67=14, Resulting Numbers: [57, 14] Generated Node #0,0,4: 59:[57, 14] Operation: 81-67=14 Moving to Node #0,2 Current State: 59:[51, 81, 73], Operations: ['16+57=73'] Exploring Operation: 51+81=132, Resulting Numbers: [73, 132] Generated Node #0,2,0: 59:[73, 132] Operation: 51+81=132 Exploring Operation: 51+73=124, Resulting Numbers: [81, 124] Generated Node #0,2,1: 59:[81, 124] Operation: 51+73=124 Exploring Operation: 81-51=30, Resulting Numbers: [73, 30] Generated Node #0,2,2: 59:[73, 30] Operation: 81-51=30 Exploring Operation: 81-73=8, Resulting Numbers: [51, 8] Generated Node #0,2,3: 59:[51, 8] Operation: 81-73=8 Exploring Operation: 73-51=22, Resulting Numbers: [81, 22] Generated Node #0,2,4: 59:[81, 22] Operation: 73-51=22 Moving to Node #0,3 Current State: 59:[51, 81, 41], Operations: ['57-16=41'] Exploring Operation: 81-51=30, Resulting Numbers: [41, 30] Generated Node #0,3,0: 59:[41, 30] Operation: 81-51=30 Exploring Operation: 81-41=40, Resulting Numbers: [51, 40] Generated Node #0,3,1: 59:[51, 40] Operation: 81-41=40 Exploring Operation: 81+41=122, Resulting Numbers: [51, 122] Generated Node #0,3,2: 59:[51, 122] Operation: 81+41=122 Exploring Operation: 51+41=92, Resulting Numbers: [81, 92] Generated Node #0,3,3: 59:[81, 92] Operation: 51+41=92 Exploring Operation: 51-41=10, Resulting Numbers: [81, 10] Generated Node #0,3,4: 59:[81, 10] Operation: 51-41=10 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 59:[51, 40], Operations: ['57-16=41', '81-41=40'] Exploring Operation: 51*40=2040, Resulting Numbers: [2040] 2040,59 unequal: No Solution Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 51+40=91, Resulting Numbers: [91] 91,59 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 #0,3,0 Current State: 59:[41, 30], Operations: ['57-16=41', '81-51=30'] Exploring Operation: 41+30=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 41-30=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 41*30=1230, Resulting Numbers: [1230] 1230,59 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 #0,3,3 Current State: 59:[81, 92], Operations: ['57-16=41', '51+41=92'] Exploring Operation: 92-81=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 81*92=7452, Resulting Numbers: [7452] 7452,59 unequal: No Solution Exploring Operation: 81+92=173, Resulting Numbers: [173] 173,59 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 #0,3,2 Current State: 59:[51, 122], Operations: ['57-16=41', '81+41=122'] Exploring Operation: 122-51=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 51+122=173, Resulting Numbers: [173] 173,59 unequal: No Solution Exploring Operation: 51*122=6222, Resulting Numbers: [6222] 6222,59 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 #0,3,4 Current State: 59:[81, 10], Operations: ['57-16=41', '51-41=10'] Exploring Operation: 81+10=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 81*10=810, Resulting Numbers: [810] 810,59 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: 59:[57, 81, 35], Operations: ['51-16=35'] Exploring Operation: 81-35=46, Resulting Numbers: [57, 46] Generated Node #0,4,0: 59:[57, 46] Operation: 81-35=46 Exploring Operation: 81-57=24, Resulting Numbers: [35, 24] Generated Node #0,4,1: 59:[35, 24] Operation: 81-57=24 Exploring Operation: 57+35=92, Resulting Numbers: [81, 92] Generated Node #0,4,2: 59:[81, 92] Operation: 57+35=92 Exploring Operation: 81+35=116, Resulting Numbers: [57, 116] Generated Node #0,4,3: 59:[57, 116] Operation: 81+35=116 Exploring Operation: 57-35=22, Resulting Numbers: [81, 22] Generated Node #0,4,4: 59:[81, 22] Operation: 57-35=22 Moving to Node #0,4,0 Current State: 59:[57, 46], Operations: ['51-16=35', '81-35=46'] Exploring Operation: 57+46=103, Resulting Numbers: [103] 103,59 unequal: No Solution Exploring Operation: 57*46=2622, Resulting Numbers: [2622] 2622,59 unequal: No Solution Exploring Operation: 57-46=11, Resulting Numbers: [11] 11,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[67, 24], Operations: ['16+51=67', '81-57=24'] Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 67+24=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 67*24=1608, Resulting Numbers: [1608] 1608,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[73, 30], Operations: ['16+57=73', '81-51=30'] Exploring Operation: 73*30=2190, Resulting Numbers: [2190] 2190,59 unequal: No Solution Exploring Operation: 73-30=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 73+30=103, Resulting Numbers: [103] 103,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[57, 14], Operations: ['81-16=65', '65-51=14'] Exploring Operation: 57*14=798, Resulting Numbers: [798] 798,59 unequal: No Solution Exploring Operation: 57+14=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 57-14=43, Resulting Numbers: [43] 43,59 unequal: No Solution Moving to Node #0,0,4 Current State: 59:[57, 14], Operations: ['16+51=67', '81-67=14'] Exploring Operation: 57-14=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 57+14=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 57*14=798, Resulting Numbers: [798] 798,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[65, 108], Operations: ['81-16=65', '51+57=108'] Exploring Operation: 65*108=7020, Resulting Numbers: [7020] 7020,59 unequal: No Solution Exploring Operation: 108-65=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 65+108=173, Resulting Numbers: [173] 173,59 unequal: No Solution Moving to Node #0,4,2 Current State: 59:[81, 92], Operations: ['51-16=35', '57+35=92'] Exploring Operation: 81*92=7452, Resulting Numbers: [7452] 7452,59 unequal: No Solution Exploring Operation: 81+92=173, Resulting Numbers: [173] 173,59 unequal: No Solution Exploring Operation: 92-81=11, Resulting Numbers: [11] 11,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[51, 8], Operations: ['81-16=65', '65-57=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[16, 51, 57, 81], Operations: [] Exploring Operation: 81-16=65, Resulting Numbers: [51, 57, 65] Generated Node #0,1: 59:[51, 57, 65] Operation: 81-16=65 Moving to Node #0,1 Current State: 59:[51, 57, 65], Operations: ['81-16=65'] Exploring Operation: 65-57=8, Resulting Numbers: [51, 8] Generated Node #0,1,0: 59:[51, 8] Operation: 65-57=8 Moving to Node #0,1,0 Current State: 59:[51, 8], Operations: ['81-16=65', '65-57=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
0.938368
hs_5
sum_heuristic
[ 59, 54, 56, 69 ]
45
[ "59-56=3", "69-54=15", "3*15=45" ]
Current State: 45:[59, 54, 56, 69], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [54, 69, 3] Generated Node #2: [54, 69, 3] from Operation: 59-56=3 Current State: 45:[54, 69, 3], Operations: ['59-56=3'] Exploring Operation: 69-54=15, Resulting Numbers: [3, 15] Generated Node #3: [3, 15] from Operation: 69-54=15 Current State: 45:[3, 15], Operations: ['59-56=3', '69-54=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[59, 54, 56, 69], Operations: [] Exploring Operation: 69-54=15, Resulting Numbers: [59, 56, 15] Generated Node #0,0: 45:[59, 56, 15] Operation: 69-54=15 Exploring Operation: 69-56=13, Resulting Numbers: [59, 54, 13] Generated Node #0,1: 45:[59, 54, 13] Operation: 69-56=13 Exploring Operation: 69-59=10, Resulting Numbers: [54, 56, 10] Generated Node #0,2: 45:[54, 56, 10] Operation: 69-59=10 Moving to Node #0,2 Current State: 45:[54, 56, 10], Operations: ['69-59=10'] Exploring Operation: 56-10=46, Resulting Numbers: [54, 46] Generated Node #0,2,0: 45:[54, 46] Operation: 56-10=46 Exploring Operation: 56-54=2, Resulting Numbers: [10, 2] Generated Node #0,2,1: 45:[10, 2] Operation: 56-54=2 Exploring Operation: 54-10=44, Resulting Numbers: [56, 44] Generated Node #0,2,2: 45:[56, 44] Operation: 54-10=44 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 45:[10, 2], Operations: ['69-59=10', '56-54=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,45 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 45:[54, 46], Operations: ['69-59=10', '56-10=46'] Exploring Operation: 54*46=2484, Resulting Numbers: [2484] 2484,45 unequal: No Solution Exploring Operation: 54+46=100, Resulting Numbers: [100] 100,45 unequal: No Solution Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 45:[56, 44], Operations: ['69-59=10', '54-10=44'] Exploring Operation: 56*44=2464, Resulting Numbers: [2464] 2464,45 unequal: No Solution Exploring Operation: 56-44=12, Resulting Numbers: [12] 12,45 unequal: No Solution Exploring Operation: 56+44=100, Resulting Numbers: [100] 100,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 45:[59, 56, 15], Operations: ['69-54=15'] Exploring Operation: 56-15=41, Resulting Numbers: [59, 41] Generated Node #0,0,0: 45:[59, 41] Operation: 56-15=41 Exploring Operation: 59-56=3, Resulting Numbers: [15, 3] Generated Node #0,0,1: 45:[15, 3] Operation: 59-56=3 Exploring Operation: 59-15=44, Resulting Numbers: [56, 44] Generated Node #0,0,2: 45:[56, 44] Operation: 59-15=44 Moving to Node #0,1 Current State: 45:[59, 54, 13], Operations: ['69-56=13'] Exploring Operation: 54-13=41, Resulting Numbers: [59, 41] Generated Node #0,1,0: 45:[59, 41] Operation: 54-13=41 Exploring Operation: 59-54=5, Resulting Numbers: [13, 5] Generated Node #0,1,1: 45:[13, 5] Operation: 59-54=5 Exploring Operation: 59-13=46, Resulting Numbers: [54, 46] Generated Node #0,1,2: 45:[54, 46] Operation: 59-13=46 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[13, 5], Operations: ['69-56=13', '59-54=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,45 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[54, 46], Operations: ['69-56=13', '59-13=46'] Exploring Operation: 54*46=2484, Resulting Numbers: [2484] 2484,45 unequal: No Solution Exploring Operation: 54+46=100, Resulting Numbers: [100] 100,45 unequal: No Solution Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[59, 41], Operations: ['69-56=13', '54-13=41'] Exploring Operation: 59+41=100, Resulting Numbers: [100] 100,45 unequal: No Solution Exploring Operation: 59-41=18, Resulting Numbers: [18] 18,45 unequal: No Solution Exploring Operation: 59*41=2419, Resulting Numbers: [2419] 2419,45 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: 45:[15, 3], Operations: ['69-54=15', '59-56=3'] Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,45 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[59, 54, 56, 69], Operations: [] Exploring Operation: 69-54=15, Resulting Numbers: [59, 56, 15] Generated Node #0,0: 45:[59, 56, 15] Operation: 69-54=15 Moving to Node #0,0 Current State: 45:[59, 56, 15], Operations: ['69-54=15'] Exploring Operation: 59-56=3, Resulting Numbers: [15, 3] Generated Node #0,0,1: 45:[15, 3] Operation: 59-56=3 Moving to Node #0,0,1 Current State: 45:[15, 3], Operations: ['69-54=15', '59-56=3'] Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
0.967882
hs_3
sum_heuristic
[ 78, 15, 14, 6 ]
90
[ "78+6=84", "15*84=1260", "1260/14=90" ]
Current State: 90:[78, 15, 14, 6], Operations: [] Exploring Operation: 78+6=84, Resulting Numbers: [15, 14, 84] Generated Node #2: [15, 14, 84] from Operation: 78+6=84 Current State: 90:[15, 14, 84], Operations: ['78+6=84'] Exploring Operation: 15*84=1260, Resulting Numbers: [14, 1260] Generated Node #3: [14, 1260] from Operation: 15*84=1260 Current State: 90:[14, 1260], Operations: ['78+6=84', '15*84=1260'] Exploring Operation: 1260/14=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[78, 15, 14, 6], Operations: [] Exploring Operation: 78/6=13, Resulting Numbers: [15, 14, 13] Generated Node #0,0: 90:[15, 14, 13] Operation: 78/6=13 Exploring Operation: 78+15=93, Resulting Numbers: [14, 6, 93] Generated Node #0,1: 90:[14, 6, 93] Operation: 78+15=93 Exploring Operation: 78+6=84, Resulting Numbers: [15, 14, 84] Generated Node #0,2: 90:[15, 14, 84] Operation: 78+6=84 Exploring Operation: 78+14=92, Resulting Numbers: [15, 6, 92] Generated Node #0,3: 90:[15, 6, 92] Operation: 78+14=92 Moving to Node #0,3 Current State: 90:[15, 6, 92], Operations: ['78+14=92'] Exploring Operation: 15+6=21, Resulting Numbers: [92, 21] Generated Node #0,3,0: 90:[92, 21] Operation: 15+6=21 Exploring Operation: 15-6=9, Resulting Numbers: [92, 9] Generated Node #0,3,1: 90:[92, 9] Operation: 15-6=9 Exploring Operation: 15*6=90, Resulting Numbers: [92, 90] Generated Node #0,3,2: 90:[92, 90] Operation: 15*6=90 Exploring Operation: 92-6=86, Resulting Numbers: [15, 86] Generated Node #0,3,3: 90:[15, 86] Operation: 92-6=86 Moving to Node #0,0 Current State: 90:[15, 14, 13], Operations: ['78/6=13'] Exploring Operation: 15-13=2, Resulting Numbers: [14, 2] Generated Node #0,0,0: 90:[14, 2] Operation: 15-13=2 Exploring Operation: 15+14=29, Resulting Numbers: [13, 29] Generated Node #0,0,1: 90:[13, 29] Operation: 15+14=29 Exploring Operation: 15-14=1, Resulting Numbers: [13, 1] Generated Node #0,0,2: 90:[13, 1] Operation: 15-14=1 Exploring Operation: 14-13=1, Resulting Numbers: [15, 1] Generated Node #0,0,3: 90:[15, 1] Operation: 14-13=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[14, 2], Operations: ['78/6=13', '15-13=2'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,90 unequal: No Solution Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,90 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 90:[15, 1], Operations: ['78/6=13', '14-13=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 15+1=16, Resulting Numbers: [16] 16,90 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[13, 29], Operations: ['78/6=13', '15+14=29'] Exploring Operation: 13*29=377, Resulting Numbers: [377] 377,90 unequal: No Solution Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,90 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[13, 1], Operations: ['78/6=13', '15-14=1'] Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,90 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,90 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: 90:[14, 6, 93], Operations: ['78+15=93'] Exploring Operation: 93-6=87, Resulting Numbers: [14, 87] Generated Node #0,1,0: 90:[14, 87] Operation: 93-6=87 Exploring Operation: 14+6=20, Resulting Numbers: [93, 20] Generated Node #0,1,1: 90:[93, 20] Operation: 14+6=20 Exploring Operation: 14-6=8, Resulting Numbers: [93, 8] Generated Node #0,1,2: 90:[93, 8] Operation: 14-6=8 Exploring Operation: 14*6=84, Resulting Numbers: [93, 84] Generated Node #0,1,3: 90:[93, 84] Operation: 14*6=84 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[14, 87], Operations: ['78+15=93', '93-6=87'] Exploring Operation: 14+87=101, Resulting Numbers: [101] 101,90 unequal: No Solution Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,90 unequal: No Solution Exploring Operation: 14*87=1218, Resulting Numbers: [1218] 1218,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 90:[93, 8], Operations: ['78+15=93', '14-6=8'] Exploring Operation: 93*8=744, Resulting Numbers: [744] 744,90 unequal: No Solution Exploring Operation: 93+8=101, Resulting Numbers: [101] 101,90 unequal: No Solution Exploring Operation: 93-8=85, Resulting Numbers: [85] 85,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[93, 20], Operations: ['78+15=93', '14+6=20'] Exploring Operation: 93-20=73, Resulting Numbers: [73] 73,90 unequal: No Solution Exploring Operation: 93+20=113, Resulting Numbers: [113] 113,90 unequal: No Solution Exploring Operation: 93*20=1860, Resulting Numbers: [1860] 1860,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 90:[93, 84], Operations: ['78+15=93', '14*6=84'] Exploring Operation: 93+84=177, Resulting Numbers: [177] 177,90 unequal: No Solution Exploring Operation: 93*84=7812, Resulting Numbers: [7812] 7812,90 unequal: No Solution Exploring Operation: 93-84=9, Resulting Numbers: [9] 9,90 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: 90:[15, 14, 84], Operations: ['78+6=84'] Exploring Operation: 14+84=98, Resulting Numbers: [15, 98] Generated Node #0,2,0: 90:[15, 98] Operation: 14+84=98 Exploring Operation: 15+14=29, Resulting Numbers: [84, 29] Generated Node #0,2,1: 90:[84, 29] Operation: 15+14=29 Exploring Operation: 15-14=1, Resulting Numbers: [84, 1] Generated Node #0,2,2: 90:[84, 1] Operation: 15-14=1 Exploring Operation: 84/14=6, Resulting Numbers: [15, 6] Generated Node #0,2,3: 90:[15, 6] Operation: 84/14=6 Moving to Node #0,2,3 Current State: 90:[15, 6], Operations: ['78+6=84', '84/14=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,90 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[78, 15, 14, 6], Operations: [] Exploring Operation: 78+6=84, Resulting Numbers: [15, 14, 84] Generated Node #0,2: 90:[15, 14, 84] Operation: 78+6=84 Moving to Node #0,2 Current State: 90:[15, 14, 84], Operations: ['78+6=84'] Exploring Operation: 84/14=6, Resulting Numbers: [15, 6] Generated Node #0,2,3: 90:[15, 6] Operation: 84/14=6 Moving to Node #0,2,3 Current State: 90:[15, 6], Operations: ['78+6=84', '84/14=6'] Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
0.953125
hs_4
sum_heuristic
[ 92, 58, 98, 30 ]
63
[ "98-92=6", "30/6=5", "58+5=63" ]
Current State: 63:[92, 58, 98, 30], Operations: [] Exploring Operation: 98-92=6, Resulting Numbers: [58, 30, 6] Generated Node #2: [58, 30, 6] from Operation: 98-92=6 Current State: 63:[58, 30, 6], Operations: ['98-92=6'] Exploring Operation: 30/6=5, Resulting Numbers: [58, 5] Generated Node #3: [58, 5] from Operation: 30/6=5 Current State: 63:[58, 5], Operations: ['98-92=6', '30/6=5'] Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[92, 58, 98, 30], Operations: [] Exploring Operation: 98-92=6, Resulting Numbers: [58, 30, 6] Generated Node #0,0: 63:[58, 30, 6] Operation: 98-92=6 Moving to Node #0,0 Current State: 63:[58, 30, 6], Operations: ['98-92=6'] Exploring Operation: 30/6=5, Resulting Numbers: [58, 5] Generated Node #0,0,0: 63:[58, 5] Operation: 30/6=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[58, 5], Operations: ['98-92=6', '30/6=5'] Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[92, 58, 98, 30], Operations: [] Exploring Operation: 98-92=6, Resulting Numbers: [58, 30, 6] Generated Node #0,0: 63:[58, 30, 6] Operation: 98-92=6 Moving to Node #0,0 Current State: 63:[58, 30, 6], Operations: ['98-92=6'] Exploring Operation: 30/6=5, Resulting Numbers: [58, 5] Generated Node #0,0,0: 63:[58, 5] Operation: 30/6=5 Moving to Node #0,0,0 Current State: 63:[58, 5], Operations: ['98-92=6', '30/6=5'] Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 61, 53, 11, 2 ]
92
[ "61+53=114", "11*2=22", "114-22=92" ]
Current State: 92:[61, 53, 11, 2], Operations: [] Exploring Operation: 61+53=114, Resulting Numbers: [11, 2, 114] Generated Node #2: [11, 2, 114] from Operation: 61+53=114 Current State: 92:[11, 2, 114], Operations: ['61+53=114'] Exploring Operation: 11*2=22, Resulting Numbers: [114, 22] Generated Node #3: [114, 22] from Operation: 11*2=22 Current State: 92:[114, 22], Operations: ['61+53=114', '11*2=22'] Exploring Operation: 114-22=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[61, 53, 11, 2], Operations: [] Exploring Operation: 11*2=22, Resulting Numbers: [61, 53, 22] Generated Node #0,0: 92:[61, 53, 22] Operation: 11*2=22 Exploring Operation: 61-11=50, Resulting Numbers: [53, 2, 50] Generated Node #0,1: 92:[53, 2, 50] Operation: 61-11=50 Exploring Operation: 61-53=8, Resulting Numbers: [11, 2, 8] Generated Node #0,2: 92:[11, 2, 8] Operation: 61-53=8 Exploring Operation: 53-11=42, Resulting Numbers: [61, 2, 42] Generated Node #0,3: 92:[61, 2, 42] Operation: 53-11=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[53, 2, 50], Operations: ['61-11=50'] Exploring Operation: 50/2=25, Resulting Numbers: [53, 25] Generated Node #0,1,0: 92:[53, 25] Operation: 50/2=25 Exploring Operation: 53-2=51, Resulting Numbers: [50, 51] Generated Node #0,1,1: 92:[50, 51] Operation: 53-2=51 Exploring Operation: 50-2=48, Resulting Numbers: [53, 48] Generated Node #0,1,2: 92:[53, 48] Operation: 50-2=48 Exploring Operation: 53-50=3, Resulting Numbers: [2, 3] Generated Node #0,1,3: 92:[2, 3] Operation: 53-50=3 Moving to Node #0,1,3 Current State: 92:[2, 3], Operations: ['61-11=50', '53-50=3'] Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,92 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[50, 51], Operations: ['61-11=50', '53-2=51'] Exploring Operation: 50+51=101, Resulting Numbers: [101] 101,92 unequal: No Solution Exploring Operation: 50*51=2550, Resulting Numbers: [2550] 2550,92 unequal: No Solution Exploring Operation: 51-50=1, Resulting Numbers: [1] 1,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[53, 25], Operations: ['61-11=50', '50/2=25'] Exploring Operation: 53+25=78, Resulting Numbers: [78] 78,92 unequal: No Solution Exploring Operation: 53*25=1325, Resulting Numbers: [1325] 1325,92 unequal: No Solution Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,92 unequal: No Solution Moving to Node #0,1,2 Current State: 92:[53, 48], Operations: ['61-11=50', '50-2=48'] Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 53*48=2544, Resulting Numbers: [2544] 2544,92 unequal: No Solution Exploring Operation: 53+48=101, Resulting Numbers: [101] 101,92 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 Current State: 92:[11, 2, 8], Operations: ['61-53=8'] Exploring Operation: 11-8=3, Resulting Numbers: [2, 3] Generated Node #0,2,0: 92:[2, 3] Operation: 11-8=3 Exploring Operation: 11*2=22, Resulting Numbers: [8, 22] Generated Node #0,2,1: 92:[8, 22] Operation: 11*2=22 Exploring Operation: 11*8=88, Resulting Numbers: [2, 88] Generated Node #0,2,2: 92:[2, 88] Operation: 11*8=88 Exploring Operation: 11+8=19, Resulting Numbers: [2, 19] Generated Node #0,2,3: 92:[2, 19] Operation: 11+8=19 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 92:[2, 3], Operations: ['61-53=8', '11-8=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,92 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 92:[2, 88], Operations: ['61-53=8', '11*8=88'] Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,92 unequal: No Solution Exploring Operation: 2+88=90, Resulting Numbers: [90] 90,92 unequal: No Solution Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,92 unequal: No Solution Exploring Operation: 2*88=176, Resulting Numbers: [176] 176,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 92:[2, 19], Operations: ['61-53=8', '11+8=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,92 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,92 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 92:[8, 22], Operations: ['61-53=8', '11*2=22'] Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,92 unequal: No Solution Exploring Operation: 8+22=30, Resulting Numbers: [30] 30,92 unequal: No Solution Exploring Operation: 8*22=176, Resulting Numbers: [176] 176,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 92:[61, 2, 42], Operations: ['53-11=42'] Exploring Operation: 61-2=59, Resulting Numbers: [42, 59] Generated Node #0,3,0: 92:[42, 59] Operation: 61-2=59 Exploring Operation: 61-42=19, Resulting Numbers: [2, 19] Generated Node #0,3,1: 92:[2, 19] Operation: 61-42=19 Exploring Operation: 61+42=103, Resulting Numbers: [2, 103] Generated Node #0,3,2: 92:[2, 103] Operation: 61+42=103 Exploring Operation: 2+42=44, Resulting Numbers: [61, 44] Generated Node #0,3,3: 92:[61, 44] Operation: 2+42=44 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 92:[2, 19], Operations: ['53-11=42', '61-42=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,92 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,92 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 92:[2, 103], Operations: ['53-11=42', '61+42=103'] Exploring Operation: 2+103=105, Resulting Numbers: [105] 105,92 unequal: No Solution Exploring Operation: 2*103=206, Resulting Numbers: [206] 206,92 unequal: No Solution Exploring Operation: 103-2=101, Resulting Numbers: [101] 101,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 92:[42, 59], Operations: ['53-11=42', '61-2=59'] Exploring Operation: 42+59=101, Resulting Numbers: [101] 101,92 unequal: No Solution Exploring Operation: 42*59=2478, Resulting Numbers: [2478] 2478,92 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 92:[61, 44], Operations: ['53-11=42', '2+42=44'] Exploring Operation: 61*44=2684, Resulting Numbers: [2684] 2684,92 unequal: No Solution Exploring Operation: 61+44=105, Resulting Numbers: [105] 105,92 unequal: No Solution Exploring Operation: 61-44=17, Resulting Numbers: [17] 17,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[61, 53, 22], Operations: ['11*2=22'] Exploring Operation: 61+22=83, Resulting Numbers: [53, 83] Generated Node #0,0,0: 92:[53, 83] Operation: 61+22=83 Exploring Operation: 61-22=39, Resulting Numbers: [53, 39] Generated Node #0,0,1: 92:[53, 39] Operation: 61-22=39 Exploring Operation: 61-53=8, Resulting Numbers: [22, 8] Generated Node #0,0,2: 92:[22, 8] Operation: 61-53=8 Exploring Operation: 61+53=114, Resulting Numbers: [22, 114] Generated Node #0,0,3: 92:[22, 114] Operation: 61+53=114 Moving to Node #0,0,2 Current State: 92:[22, 8], Operations: ['11*2=22', '61-53=8'] Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,92 unequal: No Solution Exploring Operation: 22*8=176, Resulting Numbers: [176] 176,92 unequal: No Solution Exploring Operation: 22+8=30, Resulting Numbers: [30] 30,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[53, 39], Operations: ['11*2=22', '61-22=39'] Exploring Operation: 53*39=2067, Resulting Numbers: [2067] 2067,92 unequal: No Solution Exploring Operation: 53+39=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[61, 53, 11, 2], Operations: [] Exploring Operation: 11*2=22, Resulting Numbers: [61, 53, 22] Generated Node #0,0: 92:[61, 53, 22] Operation: 11*2=22 Moving to Node #0,0 Current State: 92:[61, 53, 22], Operations: ['11*2=22'] Exploring Operation: 61-22=39, Resulting Numbers: [53, 39] Generated Node #0,0,1: 92:[53, 39] Operation: 61-22=39 Moving to Node #0,0,1 Current State: 92:[53, 39], Operations: ['11*2=22', '61-22=39'] Exploring Operation: 53+39=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.942708
hs_4
mult_heuristic
[ 72, 80, 59, 70 ]
88
[ "80-72=8", "70-59=11", "8*11=88" ]
Current State: 88:[72, 80, 59, 70], Operations: [] Exploring Operation: 80-72=8, Resulting Numbers: [59, 70, 8] Generated Node #2: [59, 70, 8] from Operation: 80-72=8 Current State: 88:[59, 70, 8], Operations: ['80-72=8'] Exploring Operation: 70-59=11, Resulting Numbers: [8, 11] Generated Node #3: [8, 11] from Operation: 70-59=11 Current State: 88:[8, 11], Operations: ['80-72=8', '70-59=11'] Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[72, 80, 59, 70], Operations: [] Exploring Operation: 72-59=13, Resulting Numbers: [80, 70, 13] Generated Node #0,0: 88:[80, 70, 13] Operation: 72-59=13 Exploring Operation: 80-70=10, Resulting Numbers: [72, 59, 10] Generated Node #0,1: 88:[72, 59, 10] Operation: 80-70=10 Exploring Operation: 72-70=2, Resulting Numbers: [80, 59, 2] Generated Node #0,2: 88:[80, 59, 2] Operation: 72-70=2 Exploring Operation: 70-59=11, Resulting Numbers: [72, 80, 11] Generated Node #0,3: 88:[72, 80, 11] Operation: 70-59=11 Moving to Node #0,2 Current State: 88:[80, 59, 2], Operations: ['72-70=2'] Exploring Operation: 59-2=57, Resulting Numbers: [80, 57] Generated Node #0,2,0: 88:[80, 57] Operation: 59-2=57 Exploring Operation: 80/2=40, Resulting Numbers: [59, 40] Generated Node #0,2,1: 88:[59, 40] Operation: 80/2=40 Exploring Operation: 80+2=82, Resulting Numbers: [59, 82] Generated Node #0,2,2: 88:[59, 82] Operation: 80+2=82 Exploring Operation: 80-59=21, Resulting Numbers: [2, 21] Generated Node #0,2,3: 88:[2, 21] Operation: 80-59=21 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 88:[2, 21], Operations: ['72-70=2', '80-59=21'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,88 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,88 unequal: No Solution Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,88 unequal: No Solution No 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: 88:[59, 40], Operations: ['72-70=2', '80/2=40'] Exploring Operation: 59*40=2360, Resulting Numbers: [2360] 2360,88 unequal: No Solution Exploring Operation: 59+40=99, Resulting Numbers: [99] 99,88 unequal: No Solution Exploring Operation: 59-40=19, Resulting Numbers: [19] 19,88 unequal: No Solution No 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: 88:[80, 57], Operations: ['72-70=2', '59-2=57'] Exploring Operation: 80-57=23, Resulting Numbers: [23] 23,88 unequal: No Solution Exploring Operation: 80*57=4560, Resulting Numbers: [4560] 4560,88 unequal: No Solution Exploring Operation: 80+57=137, Resulting Numbers: [137] 137,88 unequal: No Solution No 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: 88:[59, 82], Operations: ['72-70=2', '80+2=82'] Exploring Operation: 59*82=4838, Resulting Numbers: [4838] 4838,88 unequal: No Solution Exploring Operation: 59+82=141, Resulting Numbers: [141] 141,88 unequal: No Solution Exploring Operation: 82-59=23, Resulting Numbers: [23] 23,88 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: 88:[72, 80, 11], Operations: ['70-59=11'] Exploring Operation: 80-72=8, Resulting Numbers: [11, 8] Generated Node #0,3,0: 88:[11, 8] Operation: 80-72=8 Exploring Operation: 80+11=91, Resulting Numbers: [72, 91] Generated Node #0,3,1: 88:[72, 91] Operation: 80+11=91 Exploring Operation: 72+11=83, Resulting Numbers: [80, 83] Generated Node #0,3,2: 88:[80, 83] Operation: 72+11=83 Exploring Operation: 72-11=61, Resulting Numbers: [80, 61] Generated Node #0,3,3: 88:[80, 61] Operation: 72-11=61 Moving to Node #0,0 Current State: 88:[80, 70, 13], Operations: ['72-59=13'] Exploring Operation: 70-13=57, Resulting Numbers: [80, 57] Generated Node #0,0,0: 88:[80, 57] Operation: 70-13=57 Exploring Operation: 80-70=10, Resulting Numbers: [13, 10] Generated Node #0,0,1: 88:[13, 10] Operation: 80-70=10 Exploring Operation: 70+13=83, Resulting Numbers: [80, 83] Generated Node #0,0,2: 88:[80, 83] Operation: 70+13=83 Exploring Operation: 80+13=93, Resulting Numbers: [70, 93] Generated Node #0,0,3: 88:[70, 93] Operation: 80+13=93 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 88:[13, 10], Operations: ['72-59=13', '80-70=10'] Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,88 unequal: No Solution Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,88 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,88 unequal: No Solution No 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: 88:[80, 83], Operations: ['72-59=13', '70+13=83'] Exploring Operation: 83-80=3, Resulting Numbers: [3] 3,88 unequal: No Solution Exploring Operation: 80*83=6640, Resulting Numbers: [6640] 6640,88 unequal: No Solution Exploring Operation: 80+83=163, Resulting Numbers: [163] 163,88 unequal: No Solution No 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: 88:[80, 57], Operations: ['72-59=13', '70-13=57'] Exploring Operation: 80-57=23, Resulting Numbers: [23] 23,88 unequal: No Solution Exploring Operation: 80+57=137, Resulting Numbers: [137] 137,88 unequal: No Solution Exploring Operation: 80*57=4560, Resulting Numbers: [4560] 4560,88 unequal: No Solution No 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: 88:[70, 93], Operations: ['72-59=13', '80+13=93'] Exploring Operation: 70*93=6510, Resulting Numbers: [6510] 6510,88 unequal: No Solution Exploring Operation: 93-70=23, Resulting Numbers: [23] 23,88 unequal: No Solution Exploring Operation: 70+93=163, Resulting Numbers: [163] 163,88 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: 88:[72, 59, 10], Operations: ['80-70=10'] Exploring Operation: 72+10=82, Resulting Numbers: [59, 82] Generated Node #0,1,0: 88:[59, 82] Operation: 72+10=82 Exploring Operation: 59-10=49, Resulting Numbers: [72, 49] Generated Node #0,1,1: 88:[72, 49] Operation: 59-10=49 Exploring Operation: 72-10=62, Resulting Numbers: [59, 62] Generated Node #0,1,2: 88:[59, 62] Operation: 72-10=62 Exploring Operation: 72-59=13, Resulting Numbers: [10, 13] Generated Node #0,1,3: 88:[10, 13] Operation: 72-59=13 Moving to Node #0,3,0 Current State: 88:[11, 8], Operations: ['70-59=11', '80-72=8'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,88 unequal: No Solution Exploring Operation: 11+8=19, Resulting Numbers: [19] 19,88 unequal: No Solution Exploring Operation: 11*8=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[72, 80, 59, 70], Operations: [] Exploring Operation: 70-59=11, Resulting Numbers: [72, 80, 11] Generated Node #0,3: 88:[72, 80, 11] Operation: 70-59=11 Moving to Node #0,3 Current State: 88:[72, 80, 11], Operations: ['70-59=11'] Exploring Operation: 80-72=8, Resulting Numbers: [11, 8] Generated Node #0,3,0: 88:[11, 8] Operation: 80-72=8 Moving to Node #0,3,0 Current State: 88:[11, 8], Operations: ['70-59=11', '80-72=8'] Exploring Operation: 11*8=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.955729
hs_4
sum_heuristic
[ 9, 7, 98, 45 ]
68
[ "9+45=54", "98/7=14", "54+14=68" ]
Current State: 68:[9, 7, 98, 45], Operations: [] Exploring Operation: 9+45=54, Resulting Numbers: [7, 98, 54] Generated Node #2: [7, 98, 54] from Operation: 9+45=54 Current State: 68:[7, 98, 54], Operations: ['9+45=54'] Exploring Operation: 98/7=14, Resulting Numbers: [54, 14] Generated Node #3: [54, 14] from Operation: 98/7=14 Current State: 68:[54, 14], Operations: ['9+45=54', '98/7=14'] Exploring Operation: 54+14=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[9, 7, 98, 45], Operations: [] Exploring Operation: 98/7=14, Resulting Numbers: [9, 45, 14] Generated Node #0,0: 68:[9, 45, 14] Operation: 98/7=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[9, 45, 14], Operations: ['98/7=14'] Exploring Operation: 45/9=5, Resulting Numbers: [14, 5] Generated Node #0,0,0: 68:[14, 5] Operation: 45/9=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[14, 5], Operations: ['98/7=14', '45/9=5'] Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,68 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
[ 2, 88, 73, 69 ]
35
[ "88-69=19", "2*19=38", "73-38=35" ]
Current State: 35:[2, 88, 73, 69], Operations: [] Exploring Operation: 88-69=19, Resulting Numbers: [2, 73, 19] Generated Node #2: [2, 73, 19] from Operation: 88-69=19 Current State: 35:[2, 73, 19], Operations: ['88-69=19'] Exploring Operation: 2*19=38, Resulting Numbers: [73, 38] Generated Node #3: [73, 38] from Operation: 2*19=38 Current State: 35:[73, 38], Operations: ['88-69=19', '2*19=38'] Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[2, 88, 73, 69], Operations: [] Exploring Operation: 73-69=4, Resulting Numbers: [2, 88, 4] Generated Node #0,0: 35:[2, 88, 4] Operation: 73-69=4 Exploring Operation: 88-69=19, Resulting Numbers: [2, 73, 19] Generated Node #0,1: 35:[2, 73, 19] Operation: 88-69=19 Exploring Operation: 88-73=15, Resulting Numbers: [2, 69, 15] Generated Node #0,2: 35:[2, 69, 15] Operation: 88-73=15 Exploring Operation: 88/2=44, Resulting Numbers: [73, 69, 44] Generated Node #0,3: 35:[73, 69, 44] Operation: 88/2=44 Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[2, 69, 15], Operations: ['88-73=15'] Exploring Operation: 2*15=30, Resulting Numbers: [69, 30] Generated Node #0,2,0: 35:[69, 30] Operation: 2*15=30 Exploring Operation: 69-15=54, Resulting Numbers: [2, 54] Generated Node #0,2,1: 35:[2, 54] Operation: 69-15=54 Exploring Operation: 15-2=13, Resulting Numbers: [69, 13] Generated Node #0,2,2: 35:[69, 13] Operation: 15-2=13 Exploring Operation: 69-2=67, Resulting Numbers: [15, 67] Generated Node #0,2,3: 35:[15, 67] Operation: 69-2=67 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 35:[2, 54], Operations: ['88-73=15', '69-15=54'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,35 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 2+54=56, Resulting Numbers: [56] 56,35 unequal: No Solution Exploring Operation: 2*54=108, Resulting Numbers: [108] 108,35 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 #0,2,0 Current State: 35:[69, 30], Operations: ['88-73=15', '2*15=30'] Exploring Operation: 69+30=99, Resulting Numbers: [99] 99,35 unequal: No Solution Exploring Operation: 69*30=2070, Resulting Numbers: [2070] 2070,35 unequal: No Solution Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,35 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 #0,2,2 Current State: 35:[69, 13], Operations: ['88-73=15', '15-2=13'] Exploring Operation: 69+13=82, Resulting Numbers: [82] 82,35 unequal: No Solution Exploring Operation: 69-13=56, Resulting Numbers: [56] 56,35 unequal: No Solution Exploring Operation: 69*13=897, Resulting Numbers: [897] 897,35 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 #0,2,3 Current State: 35:[15, 67], Operations: ['88-73=15', '69-2=67'] Exploring Operation: 15*67=1005, Resulting Numbers: [1005] 1005,35 unequal: No Solution Exploring Operation: 67-15=52, Resulting Numbers: [52] 52,35 unequal: No Solution Exploring Operation: 15+67=82, Resulting Numbers: [82] 82,35 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:[2, 73, 19], Operations: ['88-69=19'] Exploring Operation: 19-2=17, Resulting Numbers: [73, 17] Generated Node #0,1,0: 35:[73, 17] Operation: 19-2=17 Exploring Operation: 2*19=38, Resulting Numbers: [73, 38] Generated Node #0,1,1: 35:[73, 38] Operation: 2*19=38 Exploring Operation: 73-2=71, Resulting Numbers: [19, 71] Generated Node #0,1,2: 35:[19, 71] Operation: 73-2=71 Exploring Operation: 73-19=54, Resulting Numbers: [2, 54] Generated Node #0,1,3: 35:[2, 54] Operation: 73-19=54 Moving to Node #0,1,3 Current State: 35:[2, 54], Operations: ['88-69=19', '73-19=54'] Exploring Operation: 2*54=108, Resulting Numbers: [108] 108,35 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,35 unequal: No Solution Exploring Operation: 2+54=56, Resulting Numbers: [56] 56,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[73, 38], Operations: ['88-69=19', '2*19=38'] Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[2, 88, 73, 69], Operations: [] Exploring Operation: 88-69=19, Resulting Numbers: [2, 73, 19] Generated Node #0,1: 35:[2, 73, 19] Operation: 88-69=19 Moving to Node #0,1 Current State: 35:[2, 73, 19], Operations: ['88-69=19'] Exploring Operation: 2*19=38, Resulting Numbers: [73, 38] Generated Node #0,1,1: 35:[73, 38] Operation: 2*19=38 Moving to Node #0,1,1 Current State: 35:[73, 38], Operations: ['88-69=19', '2*19=38'] Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
sum_heuristic
[ 2, 36, 3, 1 ]
75
[ "2*36=72", "3*1=3", "72+3=75" ]
Current State: 75:[2, 36, 3, 1], Operations: [] Exploring Operation: 2*36=72, Resulting Numbers: [3, 1, 72] Generated Node #2: [3, 1, 72] from Operation: 2*36=72 Current State: 75:[3, 1, 72], Operations: ['2*36=72'] Exploring Operation: 3*1=3, Resulting Numbers: [72, 3] Generated Node #3: [72, 3] from Operation: 3*1=3 Current State: 75:[72, 3], Operations: ['2*36=72', '3*1=3'] Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[2, 36, 3, 1], Operations: [] Exploring Operation: 36-2=34, Resulting Numbers: [3, 1, 34] Generated Node #0,0: 75:[3, 1, 34] Operation: 36-2=34 Exploring Operation: 2*36=72, Resulting Numbers: [3, 1, 72] Generated Node #0,1: 75:[3, 1, 72] Operation: 2*36=72 Exploring Operation: 36/3=12, Resulting Numbers: [2, 1, 12] Generated Node #0,2: 75:[2, 1, 12] Operation: 36/3=12 Exploring Operation: 36/2=18, Resulting Numbers: [3, 1, 18] Generated Node #0,3: 75:[3, 1, 18] Operation: 36/2=18 Moving to Node #0,1 Current State: 75:[3, 1, 72], Operations: ['2*36=72'] Exploring Operation: 3*1=3, Resulting Numbers: [72, 3] Generated Node #0,1,0: 75:[72, 3] Operation: 3*1=3 Exploring Operation: 3+72=75, Resulting Numbers: [1, 75] Generated Node #0,1,1: 75:[1, 75] Operation: 3+72=75 Exploring Operation: 3/1=3, Resulting Numbers: [72, 3] Generated Node #0,1,2: 75:[72, 3] Operation: 3/1=3 Exploring Operation: 1+72=73, Resulting Numbers: [3, 73] Generated Node #0,1,3: 75:[3, 73] Operation: 1+72=73 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 75:[1, 75], Operations: ['2*36=72', '3+72=75'] Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[2, 36, 3, 1], Operations: [] Exploring Operation: 2*36=72, Resulting Numbers: [3, 1, 72] Generated Node #0,1: 75:[3, 1, 72] Operation: 2*36=72 Moving to Node #0,1 Current State: 75:[3, 1, 72], Operations: ['2*36=72'] Exploring Operation: 3+72=75, Resulting Numbers: [1, 75] Generated Node #0,1,1: 75:[1, 75] Operation: 3+72=75 Moving to Node #0,1,1 Current State: 75:[1, 75], Operations: ['2*36=72', '3+72=75'] Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 29, 7, 48, 50 ]
51
[ "50-29=21", "21/7=3", "48+3=51" ]
Current State: 51:[29, 7, 48, 50], Operations: [] Exploring Operation: 50-29=21, Resulting Numbers: [7, 48, 21] Generated Node #2: [7, 48, 21] from Operation: 50-29=21 Current State: 51:[7, 48, 21], Operations: ['50-29=21'] Exploring Operation: 21/7=3, Resulting Numbers: [48, 3] Generated Node #3: [48, 3] from Operation: 21/7=3 Current State: 51:[48, 3], Operations: ['50-29=21', '21/7=3'] Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[29, 7, 48, 50], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [29, 7, 2] Generated Node #0,0: 51:[29, 7, 2] Operation: 50-48=2 Exploring Operation: 50-29=21, Resulting Numbers: [7, 48, 21] Generated Node #0,1: 51:[7, 48, 21] Operation: 50-29=21 Exploring Operation: 29-7=22, Resulting Numbers: [48, 50, 22] Generated Node #0,2: 51:[48, 50, 22] Operation: 29-7=22 Exploring Operation: 7+48=55, Resulting Numbers: [29, 50, 55] Generated Node #0,3: 51:[29, 50, 55] Operation: 7+48=55 Exploring Operation: 48-29=19, Resulting Numbers: [7, 50, 19] Generated Node #0,4: 51:[7, 50, 19] Operation: 48-29=19 Start Sub Search at level 1: Moving to Node #0,4 Current State: 51:[7, 50, 19], Operations: ['48-29=19'] Exploring Operation: 19-7=12, Resulting Numbers: [50, 12] Generated Node #0,4,0: 51:[50, 12] Operation: 19-7=12 Exploring Operation: 7+19=26, Resulting Numbers: [50, 26] Generated Node #0,4,1: 51:[50, 26] Operation: 7+19=26 Exploring Operation: 50-19=31, Resulting Numbers: [7, 31] Generated Node #0,4,2: 51:[7, 31] Operation: 50-19=31 Exploring Operation: 50-7=43, Resulting Numbers: [19, 43] Generated Node #0,4,3: 51:[19, 43] Operation: 50-7=43 Exploring Operation: 7+50=57, Resulting Numbers: [19, 57] Generated Node #0,4,4: 51:[19, 57] Operation: 7+50=57 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 51:[50, 12], Operations: ['48-29=19', '19-7=12'] Exploring Operation: 50*12=600, Resulting Numbers: [600] 600,51 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,51 unequal: No Solution Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,51 unequal: No Solution No 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: 51:[19, 57], Operations: ['48-29=19', '7+50=57'] Exploring Operation: 57-19=38, Resulting Numbers: [38] 38,51 unequal: No Solution Exploring Operation: 57/19=3, Resulting Numbers: [3] 3,51 unequal: No Solution Exploring Operation: 19*57=1083, Resulting Numbers: [1083] 1083,51 unequal: No Solution Exploring Operation: 19+57=76, Resulting Numbers: [76] 76,51 unequal: No Solution No 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: 51:[50, 26], Operations: ['48-29=19', '7+19=26'] Exploring Operation: 50*26=1300, Resulting Numbers: [1300] 1300,51 unequal: No Solution Exploring Operation: 50-26=24, Resulting Numbers: [24] 24,51 unequal: No Solution Exploring Operation: 50+26=76, Resulting Numbers: [76] 76,51 unequal: No Solution No 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: 51:[19, 43], Operations: ['48-29=19', '50-7=43'] Exploring Operation: 19*43=817, Resulting Numbers: [817] 817,51 unequal: No Solution Exploring Operation: 43-19=24, Resulting Numbers: [24] 24,51 unequal: No Solution Exploring Operation: 19+43=62, Resulting Numbers: [62] 62,51 unequal: No Solution No 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: 51:[7, 31], Operations: ['48-29=19', '50-19=31'] Exploring Operation: 7*31=217, Resulting Numbers: [217] 217,51 unequal: No Solution Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,51 unequal: No Solution Exploring Operation: 7+31=38, Resulting Numbers: [38] 38,51 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: 51:[48, 50, 22], Operations: ['29-7=22'] Exploring Operation: 50+22=72, Resulting Numbers: [48, 72] Generated Node #0,2,0: 51:[48, 72] Operation: 50+22=72 Exploring Operation: 50-22=28, Resulting Numbers: [48, 28] Generated Node #0,2,1: 51:[48, 28] Operation: 50-22=28 Exploring Operation: 50-48=2, Resulting Numbers: [22, 2] Generated Node #0,2,2: 51:[22, 2] Operation: 50-48=2 Exploring Operation: 48-22=26, Resulting Numbers: [50, 26] Generated Node #0,2,3: 51:[50, 26] Operation: 48-22=26 Exploring Operation: 48+22=70, Resulting Numbers: [50, 70] Generated Node #0,2,4: 51:[50, 70] Operation: 48+22=70 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 51:[22, 2], Operations: ['29-7=22', '50-48=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,51 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,51 unequal: No Solution No 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: 51:[50, 26], Operations: ['29-7=22', '48-22=26'] Exploring Operation: 50-26=24, Resulting Numbers: [24] 24,51 unequal: No Solution Exploring Operation: 50*26=1300, Resulting Numbers: [1300] 1300,51 unequal: No Solution Exploring Operation: 50+26=76, Resulting Numbers: [76] 76,51 unequal: No Solution No 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: 51:[48, 28], Operations: ['29-7=22', '50-22=28'] Exploring Operation: 48-28=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 48*28=1344, Resulting Numbers: [1344] 1344,51 unequal: No Solution Exploring Operation: 48+28=76, Resulting Numbers: [76] 76,51 unequal: No Solution No 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: 51:[50, 70], Operations: ['29-7=22', '48+22=70'] Exploring Operation: 50*70=3500, Resulting Numbers: [3500] 3500,51 unequal: No Solution Exploring Operation: 70-50=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 50+70=120, Resulting Numbers: [120] 120,51 unequal: No Solution No 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: 51:[48, 72], Operations: ['29-7=22', '50+22=72'] Exploring Operation: 72-48=24, Resulting Numbers: [24] 24,51 unequal: No Solution Exploring Operation: 48+72=120, Resulting Numbers: [120] 120,51 unequal: No Solution Exploring Operation: 48*72=3456, Resulting Numbers: [3456] 3456,51 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: 51:[7, 48, 21], Operations: ['50-29=21'] Exploring Operation: 21-7=14, Resulting Numbers: [48, 14] Generated Node #0,1,0: 51:[48, 14] Operation: 21-7=14 Exploring Operation: 21/7=3, Resulting Numbers: [48, 3] Generated Node #0,1,1: 51:[48, 3] Operation: 21/7=3 Exploring Operation: 7+21=28, Resulting Numbers: [48, 28] Generated Node #0,1,2: 51:[48, 28] Operation: 7+21=28 Exploring Operation: 7+48=55, Resulting Numbers: [21, 55] Generated Node #0,1,3: 51:[21, 55] Operation: 7+48=55 Exploring Operation: 48-7=41, Resulting Numbers: [21, 41] Generated Node #0,1,4: 51:[21, 41] Operation: 48-7=41 Moving to Node #0,1,1 Current State: 51:[48, 3], Operations: ['50-29=21', '21/7=3'] Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,51 unequal: No Solution Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[29, 7, 48, 50], Operations: [] Exploring Operation: 50-29=21, Resulting Numbers: [7, 48, 21] Generated Node #0,1: 51:[7, 48, 21] Operation: 50-29=21 Moving to Node #0,1 Current State: 51:[7, 48, 21], Operations: ['50-29=21'] Exploring Operation: 21/7=3, Resulting Numbers: [48, 3] Generated Node #0,1,1: 51:[48, 3] Operation: 21/7=3 Moving to Node #0,1,1 Current State: 51:[48, 3], Operations: ['50-29=21', '21/7=3'] Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.949653
hs_5
mult_heuristic
[ 55, 96, 35, 59 ]
57
[ "55+96=151", "35+59=94", "151-94=57" ]
Current State: 57:[55, 96, 35, 59], Operations: [] Exploring Operation: 55+96=151, Resulting Numbers: [35, 59, 151] Generated Node #2: [35, 59, 151] from Operation: 55+96=151 Current State: 57:[35, 59, 151], Operations: ['55+96=151'] Exploring Operation: 35+59=94, Resulting Numbers: [151, 94] Generated Node #3: [151, 94] from Operation: 35+59=94 Current State: 57:[151, 94], Operations: ['55+96=151', '35+59=94'] Exploring Operation: 151-94=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[55, 96, 35, 59], Operations: [] Exploring Operation: 96-59=37, Resulting Numbers: [55, 35, 37] Generated Node #0,0: 57:[55, 35, 37] Operation: 96-59=37 Exploring Operation: 96-35=61, Resulting Numbers: [55, 59, 61] Generated Node #0,1: 57:[55, 59, 61] Operation: 96-35=61 Exploring Operation: 96-55=41, Resulting Numbers: [35, 59, 41] Generated Node #0,2: 57:[35, 59, 41] Operation: 96-55=41 Moving to Node #0,1 Current State: 57:[55, 59, 61], Operations: ['96-35=61'] Exploring Operation: 61-59=2, Resulting Numbers: [55, 2] Generated Node #0,1,0: 57:[55, 2] Operation: 61-59=2 Exploring Operation: 61-55=6, Resulting Numbers: [59, 6] Generated Node #0,1,1: 57:[59, 6] Operation: 61-55=6 Exploring Operation: 59-55=4, Resulting Numbers: [61, 4] Generated Node #0,1,2: 57:[61, 4] Operation: 59-55=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[55, 2], Operations: ['96-35=61', '61-59=2'] Exploring Operation: 55*2=110, Resulting Numbers: [110] 110,57 unequal: No Solution Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[55, 96, 35, 59], Operations: [] Exploring Operation: 96-35=61, Resulting Numbers: [55, 59, 61] Generated Node #0,1: 57:[55, 59, 61] Operation: 96-35=61 Moving to Node #0,1 Current State: 57:[55, 59, 61], Operations: ['96-35=61'] Exploring Operation: 61-59=2, Resulting Numbers: [55, 2] Generated Node #0,1,0: 57:[55, 2] Operation: 61-59=2 Moving to Node #0,1,0 Current State: 57:[55, 2], Operations: ['96-35=61', '61-59=2'] Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic