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
[ 46, 94, 11, 83 ]
47
[ "94-11=83", "83/83=1", "46+1=47" ]
Current State: 47:[46, 94, 11, 83], Operations: [] Exploring Operation: 94-11=83, Resulting Numbers: [46, 83, 83] Generated Node #2: [46, 83, 83] from Operation: 94-11=83 Current State: 47:[46, 83, 83], Operations: ['94-11=83'] Exploring Operation: 83/83=1, Resulting Numbers: [46, 1] Generated Node #3: [46, 1] from Operation: 83/83=1 Current State: 47:[46, 1], Operations: ['94-11=83', '83/83=1'] Exploring Operation: 46+1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[46, 94, 11, 83], Operations: [] Exploring Operation: 94-46=48, Resulting Numbers: [11, 83, 48] Generated Node #0,0: 47:[11, 83, 48] Operation: 94-46=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[11, 83, 48], Operations: ['94-46=48'] Exploring Operation: 83-11=72, Resulting Numbers: [48, 72] Generated Node #0,0,0: 47:[48, 72] Operation: 83-11=72 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[48, 72], Operations: ['94-46=48', '83-11=72'] Exploring Operation: 72-48=24, Resulting Numbers: [24] 24,47 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
[ 71, 47, 21, 33 ]
36
[ "71-47=24", "33-21=12", "24+12=36" ]
Current State: 36:[71, 47, 21, 33], Operations: [] Exploring Operation: 71-47=24, Resulting Numbers: [21, 33, 24] Generated Node #2: [21, 33, 24] from Operation: 71-47=24 Current State: 36:[21, 33, 24], Operations: ['71-47=24'] Exploring Operation: 33-21=12, Resulting Numbers: [24, 12] Generated Node #3: [24, 12] from Operation: 33-21=12 Current State: 36:[24, 12], Operations: ['71-47=24', '33-21=12'] Exploring Operation: 24+12=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[71, 47, 21, 33], Operations: [] Exploring Operation: 71-47=24, Resulting Numbers: [21, 33, 24] Generated Node #0,0: 36:[21, 33, 24] Operation: 71-47=24 Exploring Operation: 71-33=38, Resulting Numbers: [47, 21, 38] Generated Node #0,1: 36:[47, 21, 38] Operation: 71-33=38 Moving to Node #0,0 Current State: 36:[21, 33, 24], Operations: ['71-47=24'] Exploring Operation: 24-21=3, Resulting Numbers: [33, 3] Generated Node #0,0,0: 36:[33, 3] Operation: 24-21=3 Exploring Operation: 33-24=9, Resulting Numbers: [21, 9] Generated Node #0,0,1: 36:[21, 9] Operation: 33-24=9 Moving to Node #0,1 Current State: 36:[47, 21, 38], Operations: ['71-33=38'] Exploring Operation: 47-21=26, Resulting Numbers: [38, 26] Generated Node #0,1,0: 36:[38, 26] Operation: 47-21=26 Exploring Operation: 47-38=9, Resulting Numbers: [21, 9] Generated Node #0,1,1: 36:[21, 9] Operation: 47-38=9 Moving to Node #0,0,0 Current State: 36:[33, 3], Operations: ['71-47=24', '24-21=3'] Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[71, 47, 21, 33], Operations: [] Exploring Operation: 71-47=24, Resulting Numbers: [21, 33, 24] Generated Node #0,0: 36:[21, 33, 24] Operation: 71-47=24 Moving to Node #0,0 Current State: 36:[21, 33, 24], Operations: ['71-47=24'] Exploring Operation: 24-21=3, Resulting Numbers: [33, 3] Generated Node #0,0,0: 36:[33, 3] Operation: 24-21=3 Moving to Node #0,0,0 Current State: 36:[33, 3], Operations: ['71-47=24', '24-21=3'] Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
0.989583
hs_2
mult_heuristic
[ 12, 33, 12, 19 ]
28
[ "33-12=21", "19-12=7", "21+7=28" ]
Current State: 28:[12, 33, 12, 19], Operations: [] Exploring Operation: 33-12=21, Resulting Numbers: [19, 21] Generated Node #2: [19, 21] from Operation: 33-12=21 Current State: 28:[19, 21], Operations: ['33-12=21'] Exploring Operation: 19-12=7, Resulting Numbers: [21, 7] Generated Node #3: [21, 7] from Operation: 19-12=7 Current State: 28:[21, 7], Operations: ['33-12=21', '19-12=7'] Exploring Operation: 21+7=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[12, 33, 12, 19], Operations: [] Exploring Operation: 12+19=31, Resulting Numbers: [12, 33, 31] Generated Node #0,0: 28:[12, 33, 31] Operation: 12+19=31 Exploring Operation: 19-12=7, Resulting Numbers: [12, 33, 7] Generated Node #0,1: 28:[12, 33, 7] Operation: 19-12=7 Exploring Operation: 12+19=31, Resulting Numbers: [33, 12, 31] Generated Node #0,2: 28:[33, 12, 31] Operation: 12+19=31 Exploring Operation: 19-12=7, Resulting Numbers: [33, 12, 7] Generated Node #0,3: 28:[33, 12, 7] Operation: 19-12=7 Exploring Operation: 33-19=14, Resulting Numbers: [12, 12, 14] Generated Node #0,4: 28:[12, 12, 14] Operation: 33-19=14 Moving to Node #0,4 Current State: 28:[12, 12, 14], Operations: ['33-19=14'] Exploring Operation: 14-12=2, Resulting Numbers: [12, 2] Generated Node #0,4,0: 28:[12, 2] Operation: 14-12=2 Exploring Operation: 12/12=1, Resulting Numbers: [14, 1] Generated Node #0,4,1: 28:[14, 1] Operation: 12/12=1 Exploring Operation: 12-12=0, Resulting Numbers: [14, 0] Generated Node #0,4,2: 28:[14, 0] Operation: 12-12=0 Exploring Operation: 14-12=2, Resulting Numbers: [12, 2] Generated Node #0,4,3: 28:[12, 2] Operation: 14-12=2 Exploring Operation: 12+12=24, Resulting Numbers: [14, 24] Generated Node #0,4,4: 28:[14, 24] Operation: 12+12=24 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 28:[14, 1], Operations: ['33-19=14', '12/12=1'] Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,28 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,28 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 #0,4,0 Current State: 28:[12, 2], Operations: ['33-19=14', '14-12=2'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,28 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,28 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,28 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 #0,4,2 Current State: 28:[14, 0], Operations: ['33-19=14', '12-12=0'] Exploring Operation: 14-0=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 14+0=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 14*0=0, Resulting Numbers: [0] 0,28 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 #0,4,3 Current State: 28:[12, 2], Operations: ['33-19=14', '14-12=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,28 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,28 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 #0,4,4 Current State: 28:[14, 24], Operations: ['33-19=14', '12+12=24'] Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,28 unequal: No Solution Exploring Operation: 14+24=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 14*24=336, Resulting Numbers: [336] 336,28 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: 28:[33, 12, 7], Operations: ['19-12=7'] Exploring Operation: 33+7=40, Resulting Numbers: [12, 40] Generated Node #0,3,0: 28:[12, 40] Operation: 33+7=40 Exploring Operation: 12-7=5, Resulting Numbers: [33, 5] Generated Node #0,3,1: 28:[33, 5] Operation: 12-7=5 Exploring Operation: 33-12=21, Resulting Numbers: [7, 21] Generated Node #0,3,2: 28:[7, 21] Operation: 33-12=21 Exploring Operation: 33-7=26, Resulting Numbers: [12, 26] Generated Node #0,3,3: 28:[12, 26] Operation: 33-7=26 Exploring Operation: 12+7=19, Resulting Numbers: [33, 19] Generated Node #0,3,4: 28:[33, 19] Operation: 12+7=19 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 28:[12, 26], Operations: ['19-12=7', '33-7=26'] Exploring Operation: 12+26=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 12*26=312, Resulting Numbers: [312] 312,28 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 #0,3,1 Current State: 28:[33, 5], Operations: ['19-12=7', '12-7=5'] Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,28 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[12, 33, 12, 19], Operations: [] Exploring Operation: 19-12=7, Resulting Numbers: [33, 12, 7] Generated Node #0,3: 28:[33, 12, 7] Operation: 19-12=7 Moving to Node #0,3 Current State: 28:[33, 12, 7], Operations: ['19-12=7'] Exploring Operation: 12-7=5, Resulting Numbers: [33, 5] Generated Node #0,3,1: 28:[33, 5] Operation: 12-7=5 Moving to Node #0,3,1 Current State: 28:[33, 5], Operations: ['19-12=7', '12-7=5'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic
[ 47, 78, 81, 79 ]
16
[ "81-79=2", "47*2=94", "94-78=16" ]
Current State: 16:[47, 78, 81, 79], Operations: [] Exploring Operation: 81-79=2, Resulting Numbers: [47, 78, 2] Generated Node #2: [47, 78, 2] from Operation: 81-79=2 Current State: 16:[47, 78, 2], Operations: ['81-79=2'] Exploring Operation: 47*2=94, Resulting Numbers: [78, 94] Generated Node #3: [78, 94] from Operation: 47*2=94 Current State: 16:[78, 94], Operations: ['81-79=2', '47*2=94'] Exploring Operation: 94-78=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[47, 78, 81, 79], Operations: [] Exploring Operation: 79-78=1, Resulting Numbers: [47, 81, 1] Generated Node #0,0: 16:[47, 81, 1] Operation: 79-78=1 Exploring Operation: 81-79=2, Resulting Numbers: [47, 78, 2] Generated Node #0,1: 16:[47, 78, 2] Operation: 81-79=2 Exploring Operation: 81-78=3, Resulting Numbers: [47, 79, 3] Generated Node #0,2: 16:[47, 79, 3] Operation: 81-78=3 Moving to Node #0,1 Current State: 16:[47, 78, 2], Operations: ['81-79=2'] Exploring Operation: 78/2=39, Resulting Numbers: [47, 39] Generated Node #0,1,0: 16:[47, 39] Operation: 78/2=39 Exploring Operation: 78-47=31, Resulting Numbers: [2, 31] Generated Node #0,1,1: 16:[2, 31] Operation: 78-47=31 Exploring Operation: 47-2=45, Resulting Numbers: [78, 45] Generated Node #0,1,2: 16:[78, 45] Operation: 47-2=45 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 16:[2, 31], Operations: ['81-79=2', '78-47=31'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,16 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,16 unequal: No Solution Exploring Operation: 2+31=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 #0,1,0 Current State: 16:[47, 39], Operations: ['81-79=2', '78/2=39'] Exploring Operation: 47+39=86, Resulting Numbers: [86] 86,16 unequal: No Solution Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 47*39=1833, Resulting Numbers: [1833] 1833,16 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 #0,1,2 Current State: 16:[78, 45], Operations: ['81-79=2', '47-2=45'] Exploring Operation: 78*45=3510, Resulting Numbers: [3510] 3510,16 unequal: No Solution Exploring Operation: 78+45=123, Resulting Numbers: [123] 123,16 unequal: No Solution Exploring Operation: 78-45=33, Resulting Numbers: [33] 33,16 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: 16:[47, 79, 3], Operations: ['81-78=3'] Exploring Operation: 79-3=76, Resulting Numbers: [47, 76] Generated Node #0,2,0: 16:[47, 76] Operation: 79-3=76 Exploring Operation: 47-3=44, Resulting Numbers: [79, 44] Generated Node #0,2,1: 16:[79, 44] Operation: 47-3=44 Exploring Operation: 79-47=32, Resulting Numbers: [3, 32] Generated Node #0,2,2: 16:[3, 32] Operation: 79-47=32 Moving to Node #0,0 Current State: 16:[47, 81, 1], Operations: ['79-78=1'] Exploring Operation: 47-1=46, Resulting Numbers: [81, 46] Generated Node #0,0,0: 16:[81, 46] Operation: 47-1=46 Exploring Operation: 81-1=80, Resulting Numbers: [47, 80] Generated Node #0,0,1: 16:[47, 80] Operation: 81-1=80 Exploring Operation: 81-47=34, Resulting Numbers: [1, 34] Generated Node #0,0,2: 16:[1, 34] Operation: 81-47=34 Moving to Node #0,2,2 Current State: 16:[3, 32], Operations: ['81-78=3', '79-47=32'] Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,16 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,16 unequal: No Solution Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,16 unequal: No Solution Moving to Node #0,0,2 Current State: 16:[1, 34], Operations: ['79-78=1', '81-47=34'] Exploring Operation: 1*34=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[79, 44], Operations: ['81-78=3', '47-3=44'] Exploring Operation: 79*44=3476, Resulting Numbers: [3476] 3476,16 unequal: No Solution Exploring Operation: 79-44=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 79+44=123, Resulting Numbers: [123] 123,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[47, 76], Operations: ['81-78=3', '79-3=76'] Exploring Operation: 47+76=123, Resulting Numbers: [123] 123,16 unequal: No Solution Exploring Operation: 47*76=3572, Resulting Numbers: [3572] 3572,16 unequal: No Solution Exploring Operation: 76-47=29, Resulting Numbers: [29] 29,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[47, 80], Operations: ['79-78=1', '81-1=80'] Exploring Operation: 47+80=127, Resulting Numbers: [127] 127,16 unequal: No Solution Exploring Operation: 47*80=3760, Resulting Numbers: [3760] 3760,16 unequal: No Solution Exploring Operation: 80-47=33, Resulting Numbers: [33] 33,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[81, 46], Operations: ['79-78=1', '47-1=46'] Exploring Operation: 81*46=3726, Resulting Numbers: [3726] 3726,16 unequal: No Solution Exploring Operation: 81-46=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 81+46=127, Resulting Numbers: [127] 127,16 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 88, 32, 40, 3 ]
68
[ "88-3=85", "32*85=2720", "2720/40=68" ]
Current State: 68:[88, 32, 40, 3], Operations: [] Exploring Operation: 88-3=85, Resulting Numbers: [32, 40, 85] Generated Node #2: [32, 40, 85] from Operation: 88-3=85 Current State: 68:[32, 40, 85], Operations: ['88-3=85'] Exploring Operation: 32*85=2720, Resulting Numbers: [40, 2720] Generated Node #3: [40, 2720] from Operation: 32*85=2720 Current State: 68:[40, 2720], Operations: ['88-3=85', '32*85=2720'] Exploring Operation: 2720/40=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[88, 32, 40, 3], Operations: [] Exploring Operation: 88-40=48, Resulting Numbers: [32, 3, 48] Generated Node #0,0: 68:[32, 3, 48] Operation: 88-40=48 Moving to Node #0,0 Current State: 68:[32, 3, 48], Operations: ['88-40=48'] Exploring Operation: 48-32=16, Resulting Numbers: [3, 16] Generated Node #0,0,0: 68:[3, 16] Operation: 48-32=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[3, 16], Operations: ['88-40=48', '48-32=16'] Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,68 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
[ 31, 83, 1, 38 ]
76
[ "31+83=114", "1*38=38", "114-38=76" ]
Current State: 76:[31, 83, 1, 38], Operations: [] Exploring Operation: 31+83=114, Resulting Numbers: [1, 38, 114] Generated Node #2: [1, 38, 114] from Operation: 31+83=114 Current State: 76:[1, 38, 114], Operations: ['31+83=114'] Exploring Operation: 1*38=38, Resulting Numbers: [114, 38] Generated Node #3: [114, 38] from Operation: 1*38=38 Current State: 76:[114, 38], Operations: ['31+83=114', '1*38=38'] Exploring Operation: 114-38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[31, 83, 1, 38], Operations: [] Exploring Operation: 31+1=32, Resulting Numbers: [83, 38, 32] Generated Node #0,0: 76:[83, 38, 32] Operation: 31+1=32 Exploring Operation: 38-31=7, Resulting Numbers: [83, 1, 7] Generated Node #0,1: 76:[83, 1, 7] Operation: 38-31=7 Moving to Node #0,1 Current State: 76:[83, 1, 7], Operations: ['38-31=7'] Exploring Operation: 83-7=76, Resulting Numbers: [1, 76] Generated Node #0,1,0: 76:[1, 76] Operation: 83-7=76 Exploring Operation: 83-1=82, Resulting Numbers: [7, 82] Generated Node #0,1,1: 76:[7, 82] Operation: 83-1=82 Moving to Node #0,0 Current State: 76:[83, 38, 32], Operations: ['31+1=32'] Exploring Operation: 83-38=45, Resulting Numbers: [32, 45] Generated Node #0,0,0: 76:[32, 45] Operation: 83-38=45 Exploring Operation: 38-32=6, Resulting Numbers: [83, 6] Generated Node #0,0,1: 76:[83, 6] Operation: 38-32=6 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 76:[83, 6], Operations: ['31+1=32', '38-32=6'] Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,76 unequal: No Solution Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[32, 45], Operations: ['31+1=32', '83-38=45'] Exploring Operation: 45-32=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 32+45=77, Resulting Numbers: [77] 77,76 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: 76:[1, 76], Operations: ['38-31=7', '83-7=76'] Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[31, 83, 1, 38], Operations: [] Exploring Operation: 38-31=7, Resulting Numbers: [83, 1, 7] Generated Node #0,1: 76:[83, 1, 7] Operation: 38-31=7 Moving to Node #0,1 Current State: 76:[83, 1, 7], Operations: ['38-31=7'] Exploring Operation: 83-7=76, Resulting Numbers: [1, 76] Generated Node #0,1,0: 76:[1, 76] Operation: 83-7=76 Moving to Node #0,1,0 Current State: 76:[1, 76], Operations: ['38-31=7', '83-7=76'] Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 62, 92, 95, 57 ]
18
[ "92-62=30", "57*30=1710", "1710/95=18" ]
Current State: 18:[62, 92, 95, 57], Operations: [] Exploring Operation: 92-62=30, Resulting Numbers: [95, 57, 30] Generated Node #2: [95, 57, 30] from Operation: 92-62=30 Current State: 18:[95, 57, 30], Operations: ['92-62=30'] Exploring Operation: 57*30=1710, Resulting Numbers: [95, 1710] Generated Node #3: [95, 1710] from Operation: 57*30=1710 Current State: 18:[95, 1710], Operations: ['92-62=30', '57*30=1710'] Exploring Operation: 1710/95=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[62, 92, 95, 57], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [62, 57, 3] Generated Node #0,0: 18:[62, 57, 3] Operation: 95-92=3 Exploring Operation: 92-57=35, Resulting Numbers: [62, 95, 35] Generated Node #0,1: 18:[62, 95, 35] Operation: 92-57=35 Exploring Operation: 95-62=33, Resulting Numbers: [92, 57, 33] Generated Node #0,2: 18:[92, 57, 33] Operation: 95-62=33 Exploring Operation: 95-57=38, Resulting Numbers: [62, 92, 38] Generated Node #0,3: 18:[62, 92, 38] Operation: 95-57=38 Exploring Operation: 92-62=30, Resulting Numbers: [95, 57, 30] Generated Node #0,4: 18:[95, 57, 30] Operation: 92-62=30 Moving to Node #0,0 Current State: 18:[62, 57, 3], Operations: ['95-92=3'] Exploring Operation: 57-3=54, Resulting Numbers: [62, 54] Generated Node #0,0,0: 18:[62, 54] Operation: 57-3=54 Exploring Operation: 62+3=65, Resulting Numbers: [57, 65] Generated Node #0,0,1: 18:[57, 65] Operation: 62+3=65 Exploring Operation: 57/3=19, Resulting Numbers: [62, 19] Generated Node #0,0,2: 18:[62, 19] Operation: 57/3=19 Exploring Operation: 62-3=59, Resulting Numbers: [57, 59] Generated Node #0,0,3: 18:[57, 59] Operation: 62-3=59 Exploring Operation: 62-57=5, Resulting Numbers: [3, 5] Generated Node #0,0,4: 18:[3, 5] Operation: 62-57=5 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 18:[3, 5], Operations: ['95-92=3', '62-57=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,18 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,18 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 #0,0,2 Current State: 18:[62, 19], Operations: ['95-92=3', '57/3=19'] Exploring Operation: 62+19=81, Resulting Numbers: [81] 81,18 unequal: No Solution Exploring Operation: 62*19=1178, Resulting Numbers: [1178] 1178,18 unequal: No Solution Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,18 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 #0,0,0 Current State: 18:[62, 54], Operations: ['95-92=3', '57-3=54'] Exploring Operation: 62+54=116, Resulting Numbers: [116] 116,18 unequal: No Solution Exploring Operation: 62*54=3348, Resulting Numbers: [3348] 3348,18 unequal: No Solution Exploring Operation: 62-54=8, Resulting Numbers: [8] 8,18 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 #0,0,3 Current State: 18:[57, 59], Operations: ['95-92=3', '62-3=59'] Exploring Operation: 57*59=3363, Resulting Numbers: [3363] 3363,18 unequal: No Solution Exploring Operation: 59-57=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 57+59=116, Resulting Numbers: [116] 116,18 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:[57, 65], Operations: ['95-92=3', '62+3=65'] Exploring Operation: 57+65=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 65-57=8, Resulting Numbers: [8] 8,18 unequal: No Solution Exploring Operation: 57*65=3705, Resulting Numbers: [3705] 3705,18 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:[95, 57, 30], Operations: ['92-62=30'] Exploring Operation: 57-30=27, Resulting Numbers: [95, 27] Generated Node #0,4,0: 18:[95, 27] Operation: 57-30=27 Exploring Operation: 95-57=38, Resulting Numbers: [30, 38] Generated Node #0,4,1: 18:[30, 38] Operation: 95-57=38 Exploring Operation: 95+57=152, Resulting Numbers: [30, 152] Generated Node #0,4,2: 18:[30, 152] Operation: 95+57=152 Exploring Operation: 95-30=65, Resulting Numbers: [57, 65] Generated Node #0,4,3: 18:[57, 65] Operation: 95-30=65 Exploring Operation: 95+30=125, Resulting Numbers: [57, 125] Generated Node #0,4,4: 18:[57, 125] Operation: 95+30=125 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 18:[30, 38], Operations: ['92-62=30', '95-57=38'] Exploring Operation: 30+38=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 30*38=1140, Resulting Numbers: [1140] 1140,18 unequal: No Solution Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,18 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 #0,4,0 Current State: 18:[95, 27], Operations: ['92-62=30', '57-30=27'] Exploring Operation: 95*27=2565, Resulting Numbers: [2565] 2565,18 unequal: No Solution Exploring Operation: 95+27=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 95-27=68, Resulting Numbers: [68] 68,18 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 #0,4,3 Current State: 18:[57, 65], Operations: ['92-62=30', '95-30=65'] Exploring Operation: 65-57=8, Resulting Numbers: [8] 8,18 unequal: No Solution Exploring Operation: 57+65=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 57*65=3705, Resulting Numbers: [3705] 3705,18 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 #0,4,2 Current State: 18:[30, 152], Operations: ['92-62=30', '95+57=152'] Exploring Operation: 152-30=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 30*152=4560, Resulting Numbers: [4560] 4560,18 unequal: No Solution Exploring Operation: 30+152=182, Resulting Numbers: [182] 182,18 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 #0,4,4 Current State: 18:[57, 125], Operations: ['92-62=30', '95+30=125'] Exploring Operation: 57*125=7125, Resulting Numbers: [7125] 7125,18 unequal: No Solution Exploring Operation: 125-57=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 57+125=182, Resulting Numbers: [182] 182,18 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: 18:[92, 57, 33], Operations: ['95-62=33'] Exploring Operation: 57-33=24, Resulting Numbers: [92, 24] Generated Node #0,2,0: 18:[92, 24] Operation: 57-33=24 Exploring Operation: 92-33=59, Resulting Numbers: [57, 59] Generated Node #0,2,1: 18:[57, 59] Operation: 92-33=59 Exploring Operation: 92+33=125, Resulting Numbers: [57, 125] Generated Node #0,2,2: 18:[57, 125] Operation: 92+33=125 Exploring Operation: 92+57=149, Resulting Numbers: [33, 149] Generated Node #0,2,3: 18:[33, 149] Operation: 92+57=149 Exploring Operation: 92-57=35, Resulting Numbers: [33, 35] Generated Node #0,2,4: 18:[33, 35] Operation: 92-57=35 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 18:[33, 35], Operations: ['95-62=33', '92-57=35'] Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 33*35=1155, Resulting Numbers: [1155] 1155,18 unequal: No Solution Exploring Operation: 33+35=68, Resulting Numbers: [68] 68,18 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:[92, 24], Operations: ['95-62=33', '57-33=24'] Exploring Operation: 92-24=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 92+24=116, Resulting Numbers: [116] 116,18 unequal: No Solution Exploring Operation: 92*24=2208, Resulting Numbers: [2208] 2208,18 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:[57, 59], Operations: ['95-62=33', '92-33=59'] Exploring Operation: 57+59=116, Resulting Numbers: [116] 116,18 unequal: No Solution Exploring Operation: 57*59=3363, Resulting Numbers: [3363] 3363,18 unequal: No Solution Exploring Operation: 59-57=2, Resulting Numbers: [2] 2,18 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:[57, 125], Operations: ['95-62=33', '92+33=125'] Exploring Operation: 57*125=7125, Resulting Numbers: [7125] 7125,18 unequal: No Solution Exploring Operation: 57+125=182, Resulting Numbers: [182] 182,18 unequal: No Solution Exploring Operation: 125-57=68, Resulting Numbers: [68] 68,18 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:[33, 149], Operations: ['95-62=33', '92+57=149'] Exploring Operation: 33+149=182, Resulting Numbers: [182] 182,18 unequal: No Solution Exploring Operation: 33*149=4917, Resulting Numbers: [4917] 4917,18 unequal: No Solution Exploring Operation: 149-33=116, Resulting Numbers: [116] 116,18 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: 18:[62, 95, 35], Operations: ['92-57=35'] Exploring Operation: 95-35=60, Resulting Numbers: [62, 60] Generated Node #0,1,0: 18:[62, 60] Operation: 95-35=60 Exploring Operation: 95-62=33, Resulting Numbers: [35, 33] Generated Node #0,1,1: 18:[35, 33] Operation: 95-62=33 Exploring Operation: 62-35=27, Resulting Numbers: [95, 27] Generated Node #0,1,2: 18:[95, 27] Operation: 62-35=27 Exploring Operation: 62+35=97, Resulting Numbers: [95, 97] Generated Node #0,1,3: 18:[95, 97] Operation: 62+35=97 Exploring Operation: 62+95=157, Resulting Numbers: [35, 157] Generated Node #0,1,4: 18:[35, 157] Operation: 62+95=157 Moving to Node #0,3 Current State: 18:[62, 92, 38], Operations: ['95-57=38'] Exploring Operation: 92-62=30, Resulting Numbers: [38, 30] Generated Node #0,3,0: 18:[38, 30] Operation: 92-62=30 Exploring Operation: 62+38=100, Resulting Numbers: [92, 100] Generated Node #0,3,1: 18:[92, 100] Operation: 62+38=100 Exploring Operation: 62+92=154, Resulting Numbers: [38, 154] Generated Node #0,3,2: 18:[38, 154] Operation: 62+92=154 Exploring Operation: 92-38=54, Resulting Numbers: [62, 54] Generated Node #0,3,3: 18:[62, 54] Operation: 92-38=54 Exploring Operation: 62-38=24, Resulting Numbers: [92, 24] Generated Node #0,3,4: 18:[92, 24] Operation: 62-38=24 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 18:[38, 30], Operations: ['95-57=38', '92-62=30'] Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,18 unequal: No Solution Exploring Operation: 38*30=1140, Resulting Numbers: [1140] 1140,18 unequal: No Solution Exploring Operation: 38+30=68, Resulting Numbers: [68] 68,18 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 #0,3,3 Current State: 18:[62, 54], Operations: ['95-57=38', '92-38=54'] Exploring Operation: 62+54=116, Resulting Numbers: [116] 116,18 unequal: No Solution Exploring Operation: 62*54=3348, Resulting Numbers: [3348] 3348,18 unequal: No Solution Exploring Operation: 62-54=8, Resulting Numbers: [8] 8,18 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 #0,3,4 Current State: 18:[92, 24], Operations: ['95-57=38', '62-38=24'] Exploring Operation: 92+24=116, Resulting Numbers: [116] 116,18 unequal: No Solution Exploring Operation: 92-24=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 92*24=2208, Resulting Numbers: [2208] 2208,18 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 #0,3,1 Current State: 18:[92, 100], Operations: ['95-57=38', '62+38=100'] Exploring Operation: 100-92=8, Resulting Numbers: [8] 8,18 unequal: No Solution Exploring Operation: 92+100=192, Resulting Numbers: [192] 192,18 unequal: No Solution Exploring Operation: 92*100=9200, Resulting Numbers: [9200] 9200,18 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 #0,3,2 Current State: 18:[38, 154], Operations: ['95-57=38', '62+92=154'] Exploring Operation: 154-38=116, Resulting Numbers: [116] 116,18 unequal: No Solution Exploring Operation: 38+154=192, Resulting Numbers: [192] 192,18 unequal: No Solution Exploring Operation: 38*154=5852, Resulting Numbers: [5852] 5852,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 18:[35, 33], Operations: ['92-57=35', '95-62=33'] Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 35*33=1155, Resulting Numbers: [1155] 1155,18 unequal: No Solution Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[95, 27], Operations: ['92-57=35', '62-35=27'] Exploring Operation: 95-27=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 95*27=2565, Resulting Numbers: [2565] 2565,18 unequal: No Solution Exploring Operation: 95+27=122, Resulting Numbers: [122] 122,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[62, 60], Operations: ['92-57=35', '95-35=60'] Exploring Operation: 62+60=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 62*60=3720, Resulting Numbers: [3720] 3720,18 unequal: No Solution Moving to Node #0,1,3 Current State: 18:[95, 97], Operations: ['92-57=35', '62+35=97'] Exploring Operation: 97-95=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 95*97=9215, Resulting Numbers: [9215] 9215,18 unequal: No Solution Exploring Operation: 95+97=192, Resulting Numbers: [192] 192,18 unequal: No Solution Moving to Node #0,1,4 Current State: 18:[35, 157], Operations: ['92-57=35', '62+95=157'] Exploring Operation: 35*157=5495, Resulting Numbers: [5495] 5495,18 unequal: No Solution Exploring Operation: 157-35=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 35+157=192, Resulting Numbers: [192] 192,18 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 58, 19, 38, 66 ]
91
[ "38/19=2", "66/2=33", "58+33=91" ]
Current State: 91:[58, 19, 38, 66], Operations: [] Exploring Operation: 38/19=2, Resulting Numbers: [58, 66, 2] Generated Node #2: [58, 66, 2] from Operation: 38/19=2 Current State: 91:[58, 66, 2], Operations: ['38/19=2'] Exploring Operation: 66/2=33, Resulting Numbers: [58, 33] Generated Node #3: [58, 33] from Operation: 66/2=33 Current State: 91:[58, 33], Operations: ['38/19=2', '66/2=33'] Exploring Operation: 58+33=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[58, 19, 38, 66], Operations: [] Exploring Operation: 66-58=8, Resulting Numbers: [19, 38, 8] Generated Node #0,0: 91:[19, 38, 8] Operation: 66-58=8 Moving to Node #0,0 Current State: 91:[19, 38, 8], Operations: ['66-58=8'] Exploring Operation: 38/19=2, Resulting Numbers: [8, 2] Generated Node #0,0,0: 91:[8, 2] Operation: 38/19=2 Moving to Node #0,0,0 Current State: 91:[8, 2], Operations: ['66-58=8', '38/19=2'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,91 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 16, 20, 32, 23 ]
60
[ "20-16=4", "23*4=92", "92-32=60" ]
Current State: 60:[16, 20, 32, 23], Operations: [] Exploring Operation: 20-16=4, Resulting Numbers: [32, 23, 4] Generated Node #2: [32, 23, 4] from Operation: 20-16=4 Current State: 60:[32, 23, 4], Operations: ['20-16=4'] Exploring Operation: 23*4=92, Resulting Numbers: [32, 92] Generated Node #3: [32, 92] from Operation: 23*4=92 Current State: 60:[32, 92], Operations: ['20-16=4', '23*4=92'] Exploring Operation: 92-32=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[16, 20, 32, 23], Operations: [] Exploring Operation: 32/16=2, Resulting Numbers: [20, 23, 2] Generated Node #0,0: 60:[20, 23, 2] Operation: 32/16=2 Exploring Operation: 23-16=7, Resulting Numbers: [20, 32, 7] Generated Node #0,1: 60:[20, 32, 7] Operation: 23-16=7 Exploring Operation: 32-23=9, Resulting Numbers: [16, 20, 9] Generated Node #0,2: 60:[16, 20, 9] Operation: 32-23=9 Moving to Node #0,2 Current State: 60:[16, 20, 9], Operations: ['32-23=9'] Exploring Operation: 16-9=7, Resulting Numbers: [20, 7] Generated Node #0,2,0: 60:[20, 7] Operation: 16-9=7 Exploring Operation: 20+9=29, Resulting Numbers: [16, 29] Generated Node #0,2,1: 60:[16, 29] Operation: 20+9=29 Exploring Operation: 20-16=4, Resulting Numbers: [9, 4] Generated Node #0,2,2: 60:[9, 4] Operation: 20-16=4 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 60:[20, 7], Operations: ['32-23=9', '16-9=7'] Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,60 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,60 unequal: No Solution Exploring Operation: 20*7=140, Resulting Numbers: [140] 140,60 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 #0,2,2 Current State: 60:[9, 4], Operations: ['32-23=9', '20-16=4'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,60 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,60 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 #0,2,1 Current State: 60:[16, 29], Operations: ['32-23=9', '20+9=29'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,60 unequal: No Solution Exploring Operation: 16+29=45, Resulting Numbers: [45] 45,60 unequal: No Solution Exploring Operation: 16*29=464, Resulting Numbers: [464] 464,60 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: 60:[20, 23, 2], Operations: ['32/16=2'] Exploring Operation: 20/2=10, Resulting Numbers: [23, 10] Generated Node #0,0,0: 60:[23, 10] Operation: 20/2=10 Exploring Operation: 23-20=3, Resulting Numbers: [2, 3] Generated Node #0,0,1: 60:[2, 3] Operation: 23-20=3 Exploring Operation: 23-2=21, Resulting Numbers: [20, 21] Generated Node #0,0,2: 60:[20, 21] Operation: 23-2=21 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[2, 3], Operations: ['32/16=2', '23-20=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,60 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[20, 21], Operations: ['32/16=2', '23-2=21'] Exploring Operation: 20*21=420, Resulting Numbers: [420] 420,60 unequal: No Solution Exploring Operation: 20+21=41, Resulting Numbers: [41] 41,60 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,60 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 #0,0,0 Current State: 60:[23, 10], Operations: ['32/16=2', '20/2=10'] Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,60 unequal: No Solution Exploring Operation: 23*10=230, Resulting Numbers: [230] 230,60 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,60 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: 60:[20, 32, 7], Operations: ['23-16=7'] Exploring Operation: 20-7=13, Resulting Numbers: [32, 13] Generated Node #0,1,0: 60:[32, 13] Operation: 20-7=13 Exploring Operation: 32-20=12, Resulting Numbers: [7, 12] Generated Node #0,1,1: 60:[7, 12] Operation: 32-20=12 Exploring Operation: 20+7=27, Resulting Numbers: [32, 27] Generated Node #0,1,2: 60:[32, 27] Operation: 20+7=27 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[7, 12], Operations: ['23-16=7', '32-20=12'] Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,60 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 7+12=19, Resulting Numbers: [19] 19,60 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 #0,1,0 Current State: 60:[32, 13], Operations: ['23-16=7', '20-7=13'] Exploring Operation: 32+13=45, Resulting Numbers: [45] 45,60 unequal: No Solution Exploring Operation: 32-13=19, Resulting Numbers: [19] 19,60 unequal: No Solution Exploring Operation: 32*13=416, Resulting Numbers: [416] 416,60 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 #0,1,2 Current State: 60:[32, 27], Operations: ['23-16=7', '20+7=27'] Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,60 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
[ 44, 62, 4, 64 ]
67
[ "64-44=20", "20/4=5", "62+5=67" ]
Current State: 67:[44, 62, 4, 64], Operations: [] Exploring Operation: 64-44=20, Resulting Numbers: [62, 4, 20] Generated Node #2: [62, 4, 20] from Operation: 64-44=20 Current State: 67:[62, 4, 20], Operations: ['64-44=20'] Exploring Operation: 20/4=5, Resulting Numbers: [62, 5] Generated Node #3: [62, 5] from Operation: 20/4=5 Current State: 67:[62, 5], Operations: ['64-44=20', '20/4=5'] Exploring Operation: 62+5=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[44, 62, 4, 64], Operations: [] Exploring Operation: 44-4=40, Resulting Numbers: [62, 64, 40] Generated Node #0,0: 67:[62, 64, 40] Operation: 44-4=40 Exploring Operation: 44+4=48, Resulting Numbers: [62, 64, 48] Generated Node #0,1: 67:[62, 64, 48] Operation: 44+4=48 Exploring Operation: 62+4=66, Resulting Numbers: [44, 64, 66] Generated Node #0,2: 67:[44, 64, 66] Operation: 62+4=66 Exploring Operation: 4+64=68, Resulting Numbers: [44, 62, 68] Generated Node #0,3: 67:[44, 62, 68] Operation: 4+64=68 Moving to Node #0,1 Current State: 67:[62, 64, 48], Operations: ['44+4=48'] Exploring Operation: 64-48=16, Resulting Numbers: [62, 16] Generated Node #0,1,0: 67:[62, 16] Operation: 64-48=16 Exploring Operation: 62-48=14, Resulting Numbers: [64, 14] Generated Node #0,1,1: 67:[64, 14] Operation: 62-48=14 Exploring Operation: 62+48=110, Resulting Numbers: [64, 110] Generated Node #0,1,2: 67:[64, 110] Operation: 62+48=110 Exploring Operation: 64+48=112, Resulting Numbers: [62, 112] Generated Node #0,1,3: 67:[62, 112] Operation: 64+48=112 Moving to Node #0,2 Current State: 67:[44, 64, 66], Operations: ['62+4=66'] Exploring Operation: 64-44=20, Resulting Numbers: [66, 20] Generated Node #0,2,0: 67:[66, 20] Operation: 64-44=20 Exploring Operation: 66-44=22, Resulting Numbers: [64, 22] Generated Node #0,2,1: 67:[64, 22] Operation: 66-44=22 Exploring Operation: 44+66=110, Resulting Numbers: [64, 110] Generated Node #0,2,2: 67:[64, 110] Operation: 44+66=110 Exploring Operation: 44+64=108, Resulting Numbers: [66, 108] Generated Node #0,2,3: 67:[66, 108] Operation: 44+64=108 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 67:[66, 108], Operations: ['62+4=66', '44+64=108'] Exploring Operation: 66+108=174, Resulting Numbers: [174] 174,67 unequal: No Solution Exploring Operation: 66*108=7128, Resulting Numbers: [7128] 7128,67 unequal: No Solution Exploring Operation: 108-66=42, Resulting Numbers: [42] 42,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 67:[64, 110], Operations: ['62+4=66', '44+66=110'] Exploring Operation: 64*110=7040, Resulting Numbers: [7040] 7040,67 unequal: No Solution Exploring Operation: 110-64=46, Resulting Numbers: [46] 46,67 unequal: No Solution Exploring Operation: 64+110=174, Resulting Numbers: [174] 174,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[66, 20], Operations: ['62+4=66', '64-44=20'] Exploring Operation: 66+20=86, Resulting Numbers: [86] 86,67 unequal: No Solution Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,67 unequal: No Solution Exploring Operation: 66*20=1320, Resulting Numbers: [1320] 1320,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[64, 22], Operations: ['62+4=66', '66-44=22'] Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 64+22=86, Resulting Numbers: [86] 86,67 unequal: No Solution Exploring Operation: 64*22=1408, Resulting Numbers: [1408] 1408,67 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: 67:[44, 62, 68], Operations: ['4+64=68'] Exploring Operation: 68-44=24, Resulting Numbers: [62, 24] Generated Node #0,3,0: 67:[62, 24] Operation: 68-44=24 Exploring Operation: 44+62=106, Resulting Numbers: [68, 106] Generated Node #0,3,1: 67:[68, 106] Operation: 44+62=106 Exploring Operation: 44+68=112, Resulting Numbers: [62, 112] Generated Node #0,3,2: 67:[62, 112] Operation: 44+68=112 Exploring Operation: 62-44=18, Resulting Numbers: [68, 18] Generated Node #0,3,3: 67:[68, 18] Operation: 62-44=18 Moving to Node #0,0 Current State: 67:[62, 64, 40], Operations: ['44-4=40'] Exploring Operation: 64-40=24, Resulting Numbers: [62, 24] Generated Node #0,0,0: 67:[62, 24] Operation: 64-40=24 Exploring Operation: 62+40=102, Resulting Numbers: [64, 102] Generated Node #0,0,1: 67:[64, 102] Operation: 62+40=102 Exploring Operation: 62-40=22, Resulting Numbers: [64, 22] Generated Node #0,0,2: 67:[64, 22] Operation: 62-40=22 Exploring Operation: 64+40=104, Resulting Numbers: [62, 104] Generated Node #0,0,3: 67:[62, 104] Operation: 64+40=104 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[64, 102], Operations: ['44-4=40', '62+40=102'] Exploring Operation: 64+102=166, Resulting Numbers: [166] 166,67 unequal: No Solution Exploring Operation: 102-64=38, Resulting Numbers: [38] 38,67 unequal: No Solution Exploring Operation: 64*102=6528, Resulting Numbers: [6528] 6528,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 67:[62, 104], Operations: ['44-4=40', '64+40=104'] Exploring Operation: 104-62=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 62*104=6448, Resulting Numbers: [6448] 6448,67 unequal: No Solution Exploring Operation: 62+104=166, Resulting Numbers: [166] 166,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[62, 24], Operations: ['44-4=40', '64-40=24'] Exploring Operation: 62*24=1488, Resulting Numbers: [1488] 1488,67 unequal: No Solution Exploring Operation: 62+24=86, Resulting Numbers: [86] 86,67 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 67:[64, 22], Operations: ['44-4=40', '62-40=22'] Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 64+22=86, Resulting Numbers: [86] 86,67 unequal: No Solution Exploring Operation: 64*22=1408, Resulting Numbers: [1408] 1408,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 67:[68, 106], Operations: ['4+64=68', '44+62=106'] Exploring Operation: 106-68=38, Resulting Numbers: [38] 38,67 unequal: No Solution Exploring Operation: 68*106=7208, Resulting Numbers: [7208] 7208,67 unequal: No Solution Exploring Operation: 68+106=174, Resulting Numbers: [174] 174,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[64, 110], Operations: ['44+4=48', '62+48=110'] Exploring Operation: 64*110=7040, Resulting Numbers: [7040] 7040,67 unequal: No Solution Exploring Operation: 64+110=174, Resulting Numbers: [174] 174,67 unequal: No Solution Exploring Operation: 110-64=46, Resulting Numbers: [46] 46,67 unequal: No Solution Moving to Node #0,3,0 Current State: 67:[62, 24], Operations: ['4+64=68', '68-44=24'] Exploring Operation: 62*24=1488, Resulting Numbers: [1488] 1488,67 unequal: No Solution Exploring Operation: 62+24=86, Resulting Numbers: [86] 86,67 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,67 unequal: No Solution Moving to Node #0,3,2 Current State: 67:[62, 112], Operations: ['4+64=68', '44+68=112'] Exploring Operation: 112-62=50, Resulting Numbers: [50] 50,67 unequal: No Solution Exploring Operation: 62+112=174, Resulting Numbers: [174] 174,67 unequal: No Solution Exploring Operation: 62*112=6944, Resulting Numbers: [6944] 6944,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[62, 112], Operations: ['44+4=48', '64+48=112'] Exploring Operation: 62*112=6944, Resulting Numbers: [6944] 6944,67 unequal: No Solution Exploring Operation: 112-62=50, Resulting Numbers: [50] 50,67 unequal: No Solution Exploring Operation: 62+112=174, Resulting Numbers: [174] 174,67 unequal: No Solution Moving to Node #0,3,3 Current State: 67:[68, 18], Operations: ['4+64=68', '62-44=18'] Exploring Operation: 68*18=1224, Resulting Numbers: [1224] 1224,67 unequal: No Solution Exploring Operation: 68-18=50, Resulting Numbers: [50] 50,67 unequal: No Solution Exploring Operation: 68+18=86, Resulting Numbers: [86] 86,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[64, 14], Operations: ['44+4=48', '62-48=14'] Exploring Operation: 64-14=50, Resulting Numbers: [50] 50,67 unequal: No Solution Exploring Operation: 64+14=78, Resulting Numbers: [78] 78,67 unequal: No Solution Exploring Operation: 64*14=896, Resulting Numbers: [896] 896,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[62, 16], Operations: ['44+4=48', '64-48=16'] Exploring Operation: 62*16=992, Resulting Numbers: [992] 992,67 unequal: No Solution Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,67 unequal: No Solution Exploring Operation: 62+16=78, Resulting Numbers: [78] 78,67 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 15, 71, 70, 83 ]
73
[ "15+71=86", "83-70=13", "86-13=73" ]
Current State: 73:[15, 71, 70, 83], Operations: [] Exploring Operation: 15+71=86, Resulting Numbers: [70, 83, 86] Generated Node #2: [70, 83, 86] from Operation: 15+71=86 Current State: 73:[70, 83, 86], Operations: ['15+71=86'] Exploring Operation: 83-70=13, Resulting Numbers: [86, 13] Generated Node #3: [86, 13] from Operation: 83-70=13 Current State: 73:[86, 13], Operations: ['15+71=86', '83-70=13'] Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[15, 71, 70, 83], Operations: [] Exploring Operation: 83-15=68, Resulting Numbers: [71, 70, 68] Generated Node #0,0: 73:[71, 70, 68] Operation: 83-15=68 Exploring Operation: 15+70=85, Resulting Numbers: [71, 83, 85] Generated Node #0,1: 73:[71, 83, 85] Operation: 15+70=85 Moving to Node #0,0 Current State: 73:[71, 70, 68], Operations: ['83-15=68'] Exploring Operation: 70+68=138, Resulting Numbers: [71, 138] Generated Node #0,0,0: 73:[71, 138] Operation: 70+68=138 Exploring Operation: 71+68=139, Resulting Numbers: [70, 139] Generated Node #0,0,1: 73:[70, 139] Operation: 71+68=139 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[71, 138], Operations: ['83-15=68', '70+68=138'] Exploring Operation: 71+138=209, Resulting Numbers: [209] 209,73 unequal: No Solution Exploring Operation: 138-71=67, Resulting Numbers: [67] 67,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[70, 139], Operations: ['83-15=68', '71+68=139'] Exploring Operation: 139-70=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 70+139=209, Resulting Numbers: [209] 209,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 73:[71, 83, 85], Operations: ['15+70=85'] Exploring Operation: 85-71=14, Resulting Numbers: [83, 14] Generated Node #0,1,0: 73:[83, 14] Operation: 85-71=14 Exploring Operation: 83-71=12, Resulting Numbers: [85, 12] Generated Node #0,1,1: 73:[85, 12] Operation: 83-71=12 Moving to Node #0,1,0 Current State: 73:[83, 14], Operations: ['15+70=85', '85-71=14'] Exploring Operation: 83+14=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 83-14=69, Resulting Numbers: [69] 69,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[85, 12], Operations: ['15+70=85', '83-71=12'] Exploring Operation: 85+12=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[15, 71, 70, 83], Operations: [] Exploring Operation: 15+70=85, Resulting Numbers: [71, 83, 85] Generated Node #0,1: 73:[71, 83, 85] Operation: 15+70=85 Moving to Node #0,1 Current State: 73:[71, 83, 85], Operations: ['15+70=85'] Exploring Operation: 83-71=12, Resulting Numbers: [85, 12] Generated Node #0,1,1: 73:[85, 12] Operation: 83-71=12 Moving to Node #0,1,1 Current State: 73:[85, 12], Operations: ['15+70=85', '83-71=12'] Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
0.984375
hs_2
mult_heuristic
[ 64, 8, 15, 56 ]
33
[ "64/8=8", "56-15=41", "41-8=33" ]
Current State: 33:[64, 8, 15, 56], Operations: [] Exploring Operation: 64/8=8, Resulting Numbers: [15, 56, 8] Generated Node #2: [15, 56, 8] from Operation: 64/8=8 Current State: 33:[15, 56, 8], Operations: ['64/8=8'] Exploring Operation: 56-15=41, Resulting Numbers: [8, 41] Generated Node #3: [8, 41] from Operation: 56-15=41 Current State: 33:[8, 41], Operations: ['64/8=8', '56-15=41'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[64, 8, 15, 56], Operations: [] Exploring Operation: 64-56=8, Resulting Numbers: [8, 15, 8] Generated Node #0,0: 33:[8, 15, 8] Operation: 64-56=8 Moving to Node #0,0 Current State: 33:[8, 15, 8], Operations: ['64-56=8'] Exploring Operation: 8/8=1, Resulting Numbers: [15, 1] Generated Node #0,0,0: 33:[15, 1] Operation: 8/8=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[15, 1], Operations: ['64-56=8', '8/8=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 10, 21, 20, 62 ]
39
[ "20/10=2", "62-21=41", "41-2=39" ]
Current State: 39:[10, 21, 20, 62], Operations: [] Exploring Operation: 20/10=2, Resulting Numbers: [21, 62, 2] Generated Node #2: [21, 62, 2] from Operation: 20/10=2 Current State: 39:[21, 62, 2], Operations: ['20/10=2'] Exploring Operation: 62-21=41, Resulting Numbers: [2, 41] Generated Node #3: [2, 41] from Operation: 62-21=41 Current State: 39:[2, 41], Operations: ['20/10=2', '62-21=41'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[10, 21, 20, 62], Operations: [] Exploring Operation: 62-21=41, Resulting Numbers: [10, 20, 41] Generated Node #0,0: 39:[10, 20, 41] Operation: 62-21=41 Exploring Operation: 62-20=42, Resulting Numbers: [10, 21, 42] Generated Node #0,1: 39:[10, 21, 42] Operation: 62-20=42 Moving to Node #0,0 Current State: 39:[10, 20, 41], Operations: ['62-21=41'] Exploring Operation: 20-10=10, Resulting Numbers: [41, 10] Generated Node #0,0,0: 39:[41, 10] Operation: 20-10=10 Exploring Operation: 20/10=2, Resulting Numbers: [41, 2] Generated Node #0,0,1: 39:[41, 2] Operation: 20/10=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 39:[41, 2], Operations: ['62-21=41', '20/10=2'] Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,39 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[10, 21, 20, 62], Operations: [] Exploring Operation: 62-21=41, Resulting Numbers: [10, 20, 41] Generated Node #0,0: 39:[10, 20, 41] Operation: 62-21=41 Moving to Node #0,0 Current State: 39:[10, 20, 41], Operations: ['62-21=41'] Exploring Operation: 20/10=2, Resulting Numbers: [41, 2] Generated Node #0,0,1: 39:[41, 2] Operation: 20/10=2 Moving to Node #0,0,1 Current State: 39:[41, 2], Operations: ['62-21=41', '20/10=2'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 13, 54, 41, 32 ]
50
[ "54-13=41", "41-32=9", "41+9=50" ]
Current State: 50:[13, 54, 41, 32], Operations: [] Exploring Operation: 54-13=41, Resulting Numbers: [41, 32, 41] Generated Node #2: [41, 32, 41] from Operation: 54-13=41 Current State: 50:[41, 32, 41], Operations: ['54-13=41'] Exploring Operation: 41-32=9, Resulting Numbers: [9] 9,50 equal: Goal Reached Exploring Operation: 41+9=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[13, 54, 41, 32], Operations: [] Exploring Operation: 41-32=9, Resulting Numbers: [13, 54, 9] Generated Node #0,0: 50:[13, 54, 9] Operation: 41-32=9 Exploring Operation: 54-41=13, Resulting Numbers: [13, 32, 13] Generated Node #0,1: 50:[13, 32, 13] Operation: 54-41=13 Moving to Node #0,0 Current State: 50:[13, 54, 9], Operations: ['41-32=9'] Exploring Operation: 54/9=6, Resulting Numbers: [13, 6] Generated Node #0,0,0: 50:[13, 6] Operation: 54/9=6 Exploring Operation: 13-9=4, Resulting Numbers: [54, 4] Generated Node #0,0,1: 50:[54, 4] Operation: 13-9=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[13, 6], Operations: ['41-32=9', '54/9=6'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,50 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:[54, 4], Operations: ['41-32=9', '13-9=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[13, 54, 41, 32], Operations: [] Exploring Operation: 41-32=9, Resulting Numbers: [13, 54, 9] Generated Node #0,0: 50:[13, 54, 9] Operation: 41-32=9 Moving to Node #0,0 Current State: 50:[13, 54, 9], Operations: ['41-32=9'] Exploring Operation: 13-9=4, Resulting Numbers: [54, 4] Generated Node #0,0,1: 50:[54, 4] Operation: 13-9=4 Moving to Node #0,0,1 Current State: 50:[54, 4], Operations: ['41-32=9', '13-9=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 8, 72, 66, 64 ]
56
[ "66-64=2", "8*2=16", "72-16=56" ]
Current State: 56:[8, 72, 66, 64], Operations: [] Exploring Operation: 66-64=2, Resulting Numbers: [8, 72, 2] Generated Node #2: [8, 72, 2] from Operation: 66-64=2 Current State: 56:[8, 72, 2], Operations: ['66-64=2'] Exploring Operation: 8*2=16, Resulting Numbers: [72, 16] Generated Node #3: [72, 16] from Operation: 8*2=16 Current State: 56:[72, 16], Operations: ['66-64=2', '8*2=16'] Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[8, 72, 66, 64], Operations: [] Exploring Operation: 72-66=6, Resulting Numbers: [8, 64, 6] Generated Node #0,0: 56:[8, 64, 6] Operation: 72-66=6 Exploring Operation: 66-64=2, Resulting Numbers: [8, 72, 2] Generated Node #0,1: 56:[8, 72, 2] Operation: 66-64=2 Exploring Operation: 72/8=9, Resulting Numbers: [66, 64, 9] Generated Node #0,2: 56:[66, 64, 9] Operation: 72/8=9 Exploring Operation: 72-64=8, Resulting Numbers: [8, 66, 8] Generated Node #0,3: 56:[8, 66, 8] Operation: 72-64=8 Moving to Node #0,0 Current State: 56:[8, 64, 6], Operations: ['72-66=6'] Exploring Operation: 8+6=14, Resulting Numbers: [64, 14] Generated Node #0,0,0: 56:[64, 14] Operation: 8+6=14 Exploring Operation: 64-6=58, Resulting Numbers: [8, 58] Generated Node #0,0,1: 56:[8, 58] Operation: 64-6=58 Exploring Operation: 64/8=8, Resulting Numbers: [6, 8] Generated Node #0,0,2: 56:[6, 8] Operation: 64/8=8 Exploring Operation: 64-8=56, Resulting Numbers: [6, 56] Generated Node #0,0,3: 56:[6, 56] Operation: 64-8=56 Moving to Node #0,3 Current State: 56:[8, 66, 8], Operations: ['72-64=8'] Exploring Operation: 8/8=1, Resulting Numbers: [66, 1] Generated Node #0,3,0: 56:[66, 1] Operation: 8/8=1 Exploring Operation: 8+8=16, Resulting Numbers: [66, 16] Generated Node #0,3,1: 56:[66, 16] Operation: 8+8=16 Exploring Operation: 66-8=58, Resulting Numbers: [8, 58] Generated Node #0,3,2: 56:[8, 58] Operation: 66-8=58 Exploring Operation: 66-8=58, Resulting Numbers: [8, 58] Generated Node #0,3,3: 56:[8, 58] Operation: 66-8=58 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 56:[8, 58], Operations: ['72-64=8', '66-8=58'] Exploring Operation: 8+58=66, Resulting Numbers: [66] 66,56 unequal: No Solution Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,56 unequal: No Solution Exploring Operation: 8*58=464, Resulting Numbers: [464] 464,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 56:[8, 58], Operations: ['72-64=8', '66-8=58'] Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,56 unequal: No Solution Exploring Operation: 8+58=66, Resulting Numbers: [66] 66,56 unequal: No Solution Exploring Operation: 8*58=464, Resulting Numbers: [464] 464,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 56:[66, 1], Operations: ['72-64=8', '8/8=1'] Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,56 unequal: No Solution Exploring Operation: 66*1=66, Resulting Numbers: [66] 66,56 unequal: No Solution Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,56 unequal: No Solution Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 56:[66, 16], Operations: ['72-64=8', '8+8=16'] Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,56 unequal: No Solution Exploring Operation: 66*16=1056, Resulting Numbers: [1056] 1056,56 unequal: No Solution Exploring Operation: 66+16=82, Resulting Numbers: [82] 82,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 56:[8, 72, 2], Operations: ['66-64=2'] Exploring Operation: 72/8=9, Resulting Numbers: [2, 9] Generated Node #0,1,0: 56:[2, 9] Operation: 72/8=9 Exploring Operation: 72/2=36, Resulting Numbers: [8, 36] Generated Node #0,1,1: 56:[8, 36] Operation: 72/2=36 Exploring Operation: 72-2=70, Resulting Numbers: [8, 70] Generated Node #0,1,2: 56:[8, 70] Operation: 72-2=70 Exploring Operation: 72-8=64, Resulting Numbers: [2, 64] Generated Node #0,1,3: 56:[2, 64] Operation: 72-8=64 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 56:[2, 9], Operations: ['66-64=2', '72/8=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 56:[8, 36], Operations: ['66-64=2', '72/2=36'] Exploring Operation: 8*36=288, Resulting Numbers: [288] 288,56 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 8+36=44, Resulting Numbers: [44] 44,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 56:[2, 64], Operations: ['66-64=2', '72-8=64'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,56 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,56 unequal: No Solution Exploring Operation: 2*64=128, Resulting Numbers: [128] 128,56 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 56:[8, 70], Operations: ['66-64=2', '72-2=70'] Exploring Operation: 8*70=560, Resulting Numbers: [560] 560,56 unequal: No Solution Exploring Operation: 70-8=62, Resulting Numbers: [62] 62,56 unequal: No Solution Exploring Operation: 8+70=78, Resulting Numbers: [78] 78,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 56:[66, 64, 9], Operations: ['72/8=9'] Exploring Operation: 66+9=75, Resulting Numbers: [64, 75] Generated Node #0,2,0: 56:[64, 75] Operation: 66+9=75 Exploring Operation: 66-64=2, Resulting Numbers: [9, 2] Generated Node #0,2,1: 56:[9, 2] Operation: 66-64=2 Exploring Operation: 66-9=57, Resulting Numbers: [64, 57] Generated Node #0,2,2: 56:[64, 57] Operation: 66-9=57 Exploring Operation: 64-9=55, Resulting Numbers: [66, 55] Generated Node #0,2,3: 56:[66, 55] Operation: 64-9=55 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 56:[9, 2], Operations: ['72/8=9', '66-64=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,56 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,56 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 #0,2,2 Current State: 56:[64, 57], Operations: ['72/8=9', '66-9=57'] Exploring Operation: 64*57=3648, Resulting Numbers: [3648] 3648,56 unequal: No Solution Exploring Operation: 64-57=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 64+57=121, Resulting Numbers: [121] 121,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 56:[66, 55], Operations: ['72/8=9', '64-9=55'] Exploring Operation: 66*55=3630, Resulting Numbers: [3630] 3630,56 unequal: No Solution Exploring Operation: 66+55=121, Resulting Numbers: [121] 121,56 unequal: No Solution Exploring Operation: 66-55=11, Resulting Numbers: [11] 11,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 56:[64, 75], Operations: ['72/8=9', '66+9=75'] Exploring Operation: 64+75=139, Resulting Numbers: [139] 139,56 unequal: No Solution Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,56 unequal: No Solution Exploring Operation: 64*75=4800, Resulting Numbers: [4800] 4800,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 56:[6, 8], Operations: ['72-66=6', '64/8=8'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,56 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,56 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,56 unequal: No Solution Moving to Node #0,0,3 Current State: 56:[6, 56], Operations: ['72-66=6', '64-8=56'] Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,56 unequal: No Solution Exploring Operation: 6*56=336, Resulting Numbers: [336] 336,56 unequal: No Solution Exploring Operation: 6+56=62, Resulting Numbers: [62] 62,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[8, 58], Operations: ['72-66=6', '64-6=58'] Exploring Operation: 8*58=464, Resulting Numbers: [464] 464,56 unequal: No Solution Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,56 unequal: No Solution Exploring Operation: 8+58=66, Resulting Numbers: [66] 66,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[64, 14], Operations: ['72-66=6', '8+6=14'] Exploring Operation: 64*14=896, Resulting Numbers: [896] 896,56 unequal: No Solution Exploring Operation: 64+14=78, Resulting Numbers: [78] 78,56 unequal: No Solution Exploring Operation: 64-14=50, Resulting Numbers: [50] 50,56 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 27, 66, 45, 21 ]
89
[ "66*45=2970", "2970/27=110", "110-21=89" ]
Current State: 89:[27, 66, 45, 21], Operations: [] Exploring Operation: 66*45=2970, Resulting Numbers: [27, 21, 2970] Generated Node #2: [27, 21, 2970] from Operation: 66*45=2970 Current State: 89:[27, 21, 2970], Operations: ['66*45=2970'] Exploring Operation: 2970/27=110, Resulting Numbers: [21, 110] Generated Node #3: [21, 110] from Operation: 2970/27=110 Current State: 89:[21, 110], Operations: ['66*45=2970', '2970/27=110'] Exploring Operation: 110-21=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[27, 66, 45, 21], Operations: [] Exploring Operation: 27+45=72, Resulting Numbers: [66, 21, 72] Generated Node #0,0: 89:[66, 21, 72] Operation: 27+45=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[66, 21, 72], Operations: ['27+45=72'] Exploring Operation: 66+21=87, Resulting Numbers: [72, 87] Generated Node #0,0,0: 89:[72, 87] Operation: 66+21=87 Moving to Node #0,0,0 Current State: 89:[72, 87], Operations: ['27+45=72', '66+21=87'] Exploring Operation: 72+87=159, Resulting Numbers: [159] 159,89 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
[ 91, 48, 48, 60 ]
31
[ "91+48=139", "48+60=108", "139-108=31" ]
Current State: 31:[91, 48, 48, 60], Operations: [] Exploring Operation: 91+48=139, Resulting Numbers: [60, 139] Generated Node #2: [60, 139] from Operation: 91+48=139 Current State: 31:[60, 139], Operations: ['91+48=139'] Exploring Operation: 48+60=108, Resulting Numbers: [139, 108] Generated Node #3: [139, 108] from Operation: 48+60=108 Current State: 31:[139, 108], Operations: ['91+48=139', '48+60=108'] Exploring Operation: 139-108=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[91, 48, 48, 60], Operations: [] Exploring Operation: 91-60=31, Resulting Numbers: [48, 48, 31] Generated Node #0,0: 31:[48, 48, 31] Operation: 91-60=31 Exploring Operation: 91-48=43, Resulting Numbers: [48, 60, 43] Generated Node #0,1: 31:[48, 60, 43] Operation: 91-48=43 Exploring Operation: 91-48=43, Resulting Numbers: [48, 60, 43] Generated Node #0,2: 31:[48, 60, 43] Operation: 91-48=43 Exploring Operation: 60-48=12, Resulting Numbers: [91, 48, 12] Generated Node #0,3: 31:[91, 48, 12] Operation: 60-48=12 Exploring Operation: 60-48=12, Resulting Numbers: [91, 48, 12] Generated Node #0,4: 31:[91, 48, 12] Operation: 60-48=12 Moving to Node #0,0 Current State: 31:[48, 48, 31], Operations: ['91-60=31'] Exploring Operation: 48-48=0, Resulting Numbers: [31, 0] Generated Node #0,0,0: 31:[31, 0] Operation: 48-48=0 Exploring Operation: 48-31=17, Resulting Numbers: [48, 17] Generated Node #0,0,1: 31:[48, 17] Operation: 48-31=17 Exploring Operation: 48-31=17, Resulting Numbers: [48, 17] Generated Node #0,0,2: 31:[48, 17] Operation: 48-31=17 Exploring Operation: 48+48=96, Resulting Numbers: [31, 96] Generated Node #0,0,3: 31:[31, 96] Operation: 48+48=96 Exploring Operation: 48/48=1, Resulting Numbers: [31, 1] Generated Node #0,0,4: 31:[31, 1] Operation: 48/48=1 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 31:[31, 1], Operations: ['91-60=31', '48/48=1'] Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[91, 48, 48, 60], Operations: [] Exploring Operation: 91-60=31, Resulting Numbers: [48, 48, 31] Generated Node #0,0: 31:[48, 48, 31] Operation: 91-60=31 Moving to Node #0,0 Current State: 31:[48, 48, 31], Operations: ['91-60=31'] Exploring Operation: 48/48=1, Resulting Numbers: [31, 1] Generated Node #0,0,4: 31:[31, 1] Operation: 48/48=1 Moving to Node #0,0,4 Current State: 31:[31, 1], Operations: ['91-60=31', '48/48=1'] Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 33, 75, 24, 19 ]
47
[ "75-33=42", "24-19=5", "42+5=47" ]
Current State: 47:[33, 75, 24, 19], Operations: [] Exploring Operation: 75-33=42, Resulting Numbers: [24, 19, 42] Generated Node #2: [24, 19, 42] from Operation: 75-33=42 Current State: 47:[24, 19, 42], Operations: ['75-33=42'] Exploring Operation: 24-19=5, Resulting Numbers: [42, 5] Generated Node #3: [42, 5] from Operation: 24-19=5 Current State: 47:[42, 5], Operations: ['75-33=42', '24-19=5'] Exploring Operation: 42+5=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[33, 75, 24, 19], Operations: [] Exploring Operation: 75-33=42, Resulting Numbers: [24, 19, 42] Generated Node #0,0: 47:[24, 19, 42] Operation: 75-33=42 Exploring Operation: 33+19=52, Resulting Numbers: [75, 24, 52] Generated Node #0,1: 47:[75, 24, 52] Operation: 33+19=52 Exploring Operation: 75-19=56, Resulting Numbers: [33, 24, 56] Generated Node #0,2: 47:[33, 24, 56] Operation: 75-19=56 Exploring Operation: 24+19=43, Resulting Numbers: [33, 75, 43] Generated Node #0,3: 47:[33, 75, 43] Operation: 24+19=43 Exploring Operation: 75-24=51, Resulting Numbers: [33, 19, 51] Generated Node #0,4: 47:[33, 19, 51] Operation: 75-24=51 Moving to Node #0,2 Current State: 47:[33, 24, 56], Operations: ['75-19=56'] Exploring Operation: 56-24=32, Resulting Numbers: [33, 32] Generated Node #0,2,0: 47:[33, 32] Operation: 56-24=32 Exploring Operation: 56-33=23, Resulting Numbers: [24, 23] Generated Node #0,2,1: 47:[24, 23] Operation: 56-33=23 Exploring Operation: 33-24=9, Resulting Numbers: [56, 9] Generated Node #0,2,2: 47:[56, 9] Operation: 33-24=9 Exploring Operation: 33+24=57, Resulting Numbers: [56, 57] Generated Node #0,2,3: 47:[56, 57] Operation: 33+24=57 Exploring Operation: 24+56=80, Resulting Numbers: [33, 80] Generated Node #0,2,4: 47:[33, 80] Operation: 24+56=80 Moving to Node #0,4 Current State: 47:[33, 19, 51], Operations: ['75-24=51'] Exploring Operation: 33+19=52, Resulting Numbers: [51, 52] Generated Node #0,4,0: 47:[51, 52] Operation: 33+19=52 Exploring Operation: 51-33=18, Resulting Numbers: [19, 18] Generated Node #0,4,1: 47:[19, 18] Operation: 51-33=18 Exploring Operation: 19+51=70, Resulting Numbers: [33, 70] Generated Node #0,4,2: 47:[33, 70] Operation: 19+51=70 Exploring Operation: 33-19=14, Resulting Numbers: [51, 14] Generated Node #0,4,3: 47:[51, 14] Operation: 33-19=14 Exploring Operation: 51-19=32, Resulting Numbers: [33, 32] Generated Node #0,4,4: 47:[33, 32] Operation: 51-19=32 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 47:[51, 52], Operations: ['75-24=51', '33+19=52'] Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 51+52=103, Resulting Numbers: [103] 103,47 unequal: No Solution Exploring Operation: 51*52=2652, Resulting Numbers: [2652] 2652,47 unequal: No Solution No 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: 47:[33, 32], Operations: ['75-24=51', '51-19=32'] Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 33*32=1056, Resulting Numbers: [1056] 1056,47 unequal: No Solution Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,47 unequal: No Solution No 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: 47:[33, 70], Operations: ['75-24=51', '19+51=70'] Exploring Operation: 33*70=2310, Resulting Numbers: [2310] 2310,47 unequal: No Solution Exploring Operation: 70-33=37, Resulting Numbers: [37] 37,47 unequal: No Solution Exploring Operation: 33+70=103, Resulting Numbers: [103] 103,47 unequal: No Solution No 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: 47:[51, 14], Operations: ['75-24=51', '33-19=14'] Exploring Operation: 51*14=714, Resulting Numbers: [714] 714,47 unequal: No Solution Exploring Operation: 51+14=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,47 unequal: No Solution No 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: 47:[19, 18], Operations: ['75-24=51', '51-33=18'] Exploring Operation: 19*18=342, Resulting Numbers: [342] 342,47 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 19+18=37, Resulting Numbers: [37] 37,47 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: 47:[33, 75, 43], Operations: ['24+19=43'] Exploring Operation: 33+43=76, Resulting Numbers: [75, 76] Generated Node #0,3,0: 47:[75, 76] Operation: 33+43=76 Exploring Operation: 75-33=42, Resulting Numbers: [43, 42] Generated Node #0,3,1: 47:[43, 42] Operation: 75-33=42 Exploring Operation: 43-33=10, Resulting Numbers: [75, 10] Generated Node #0,3,2: 47:[75, 10] Operation: 43-33=10 Exploring Operation: 75-43=32, Resulting Numbers: [33, 32] Generated Node #0,3,3: 47:[33, 32] Operation: 75-43=32 Exploring Operation: 33+75=108, Resulting Numbers: [43, 108] Generated Node #0,3,4: 47:[43, 108] Operation: 33+75=108 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 47:[43, 42], Operations: ['24+19=43', '75-33=42'] Exploring Operation: 43+42=85, Resulting Numbers: [85] 85,47 unequal: No Solution Exploring Operation: 43*42=1806, Resulting Numbers: [1806] 1806,47 unequal: No Solution Exploring Operation: 43-42=1, Resulting Numbers: [1] 1,47 unequal: No Solution No 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: 47:[33, 32], Operations: ['24+19=43', '75-43=32'] Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 33*32=1056, Resulting Numbers: [1056] 1056,47 unequal: No Solution No 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: 47:[75, 76], Operations: ['24+19=43', '33+43=76'] Exploring Operation: 76-75=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 75*76=5700, Resulting Numbers: [5700] 5700,47 unequal: No Solution Exploring Operation: 75+76=151, Resulting Numbers: [151] 151,47 unequal: No Solution No 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: 47:[75, 10], Operations: ['24+19=43', '43-33=10'] Exploring Operation: 75+10=85, Resulting Numbers: [85] 85,47 unequal: No Solution Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 75*10=750, Resulting Numbers: [750] 750,47 unequal: No Solution No 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: 47:[43, 108], Operations: ['24+19=43', '33+75=108'] Exploring Operation: 43+108=151, Resulting Numbers: [151] 151,47 unequal: No Solution Exploring Operation: 43*108=4644, Resulting Numbers: [4644] 4644,47 unequal: No Solution Exploring Operation: 108-43=65, Resulting Numbers: [65] 65,47 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: 47:[24, 19, 42], Operations: ['75-33=42'] Exploring Operation: 19+42=61, Resulting Numbers: [24, 61] Generated Node #0,0,0: 47:[24, 61] Operation: 19+42=61 Exploring Operation: 24+19=43, Resulting Numbers: [42, 43] Generated Node #0,0,1: 47:[42, 43] Operation: 24+19=43 Exploring Operation: 42-19=23, Resulting Numbers: [24, 23] Generated Node #0,0,2: 47:[24, 23] Operation: 42-19=23 Exploring Operation: 24+42=66, Resulting Numbers: [19, 66] Generated Node #0,0,3: 47:[19, 66] Operation: 24+42=66 Exploring Operation: 24-19=5, Resulting Numbers: [42, 5] Generated Node #0,0,4: 47:[42, 5] Operation: 24-19=5 Moving to Node #0,1 Current State: 47:[75, 24, 52], Operations: ['33+19=52'] Exploring Operation: 24+52=76, Resulting Numbers: [75, 76] Generated Node #0,1,0: 47:[75, 76] Operation: 24+52=76 Exploring Operation: 75-52=23, Resulting Numbers: [24, 23] Generated Node #0,1,1: 47:[24, 23] Operation: 75-52=23 Exploring Operation: 75-24=51, Resulting Numbers: [52, 51] Generated Node #0,1,2: 47:[52, 51] Operation: 75-24=51 Exploring Operation: 75+24=99, Resulting Numbers: [52, 99] Generated Node #0,1,3: 47:[52, 99] Operation: 75+24=99 Exploring Operation: 52-24=28, Resulting Numbers: [75, 28] Generated Node #0,1,4: 47:[75, 28] Operation: 52-24=28 Moving to Node #0,0,1 Current State: 47:[42, 43], Operations: ['75-33=42', '24+19=43'] Exploring Operation: 42+43=85, Resulting Numbers: [85] 85,47 unequal: No Solution Exploring Operation: 42*43=1806, Resulting Numbers: [1806] 1806,47 unequal: No Solution Exploring Operation: 43-42=1, Resulting Numbers: [1] 1,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[52, 51], Operations: ['33+19=52', '75-24=51'] Exploring Operation: 52*51=2652, Resulting Numbers: [2652] 2652,47 unequal: No Solution Exploring Operation: 52+51=103, Resulting Numbers: [103] 103,47 unequal: No Solution Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,47 unequal: No Solution Moving to Node #0,2,3 Current State: 47:[56, 57], Operations: ['75-19=56', '33+24=57'] Exploring Operation: 56*57=3192, Resulting Numbers: [3192] 3192,47 unequal: No Solution Exploring Operation: 57-56=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 56+57=113, Resulting Numbers: [113] 113,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[33, 32], Operations: ['75-19=56', '56-24=32'] Exploring Operation: 33*32=1056, Resulting Numbers: [1056] 1056,47 unequal: No Solution Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[24, 61], Operations: ['75-33=42', '19+42=61'] Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,47 unequal: No Solution Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,47 unequal: No Solution Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[24, 23], Operations: ['75-19=56', '56-33=23'] Exploring Operation: 24*23=552, Resulting Numbers: [552] 552,47 unequal: No Solution Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 24+23=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[33, 75, 24, 19], Operations: [] Exploring Operation: 75-19=56, Resulting Numbers: [33, 24, 56] Generated Node #0,2: 47:[33, 24, 56] Operation: 75-19=56 Moving to Node #0,2 Current State: 47:[33, 24, 56], Operations: ['75-19=56'] Exploring Operation: 56-33=23, Resulting Numbers: [24, 23] Generated Node #0,2,1: 47:[24, 23] Operation: 56-33=23 Moving to Node #0,2,1 Current State: 47:[24, 23], Operations: ['75-19=56', '56-33=23'] Exploring Operation: 24+23=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
0.928819
hs_5
sum_heuristic
[ 17, 17, 2, 11 ]
79
[ "17+17=34", "2*34=68", "11+68=79" ]
Current State: 79:[17, 17, 2, 11], Operations: [] Exploring Operation: 17+17=34, Resulting Numbers: [2, 11, 34] Generated Node #2: [2, 11, 34] from Operation: 17+17=34 Current State: 79:[2, 11, 34], Operations: ['17+17=34'] Exploring Operation: 2*34=68, Resulting Numbers: [11, 68] Generated Node #3: [11, 68] from Operation: 2*34=68 Current State: 79:[11, 68], Operations: ['17+17=34', '2*34=68'] Exploring Operation: 11+68=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[17, 17, 2, 11], Operations: [] Exploring Operation: 17*2=34, Resulting Numbers: [17, 11, 34] Generated Node #0,0: 79:[17, 11, 34] Operation: 17*2=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[17, 11, 34], Operations: ['17*2=34'] Exploring Operation: 17+11=28, Resulting Numbers: [34, 28] Generated Node #0,0,0: 79:[34, 28] Operation: 17+11=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[34, 28], Operations: ['17*2=34', '17+11=28'] Exploring Operation: 34+28=62, Resulting Numbers: [62] 62,79 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 No solution found.
0
hs_1
sum_heuristic
[ 89, 17, 10, 58 ]
58
[ "89+17=106", "58-10=48", "106-48=58" ]
Current State: 58:[89, 17, 10, 58], Operations: [] Exploring Operation: 89+17=106, Resulting Numbers: [10, 58, 106] Generated Node #2: [10, 58, 106] from Operation: 89+17=106 Current State: 58:[10, 58, 106], Operations: ['89+17=106'] Exploring Operation: 58-10=48, Resulting Numbers: [106, 48] Generated Node #3: [106, 48] from Operation: 58-10=48 Current State: 58:[106, 48], Operations: ['89+17=106', '58-10=48'] Exploring Operation: 106-48=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[89, 17, 10, 58], Operations: [] Exploring Operation: 89-17=72, Resulting Numbers: [10, 58, 72] Generated Node #0,0: 58:[10, 58, 72] Operation: 89-17=72 Exploring Operation: 89-10=79, Resulting Numbers: [17, 58, 79] Generated Node #0,1: 58:[17, 58, 79] Operation: 89-10=79 Exploring Operation: 89-58=31, Resulting Numbers: [17, 10, 31] Generated Node #0,2: 58:[17, 10, 31] Operation: 89-58=31 Moving to Node #0,0 Current State: 58:[10, 58, 72], Operations: ['89-17=72'] Exploring Operation: 10+58=68, Resulting Numbers: [72, 68] Generated Node #0,0,0: 58:[72, 68] Operation: 10+58=68 Exploring Operation: 72-10=62, Resulting Numbers: [58, 62] Generated Node #0,0,1: 58:[58, 62] Operation: 72-10=62 Exploring Operation: 72-58=14, Resulting Numbers: [10, 14] Generated Node #0,0,2: 58:[10, 14] Operation: 72-58=14 Moving to Node #0,2 Current State: 58:[17, 10, 31], Operations: ['89-58=31'] Exploring Operation: 17+10=27, Resulting Numbers: [31, 27] Generated Node #0,2,0: 58:[31, 27] Operation: 17+10=27 Exploring Operation: 17-10=7, Resulting Numbers: [31, 7] Generated Node #0,2,1: 58:[31, 7] Operation: 17-10=7 Exploring Operation: 17+31=48, Resulting Numbers: [10, 48] Generated Node #0,2,2: 58:[10, 48] Operation: 17+31=48 Moving to Node #0,1 Current State: 58:[17, 58, 79], Operations: ['89-10=79'] Exploring Operation: 58-17=41, Resulting Numbers: [79, 41] Generated Node #0,1,0: 58:[79, 41] Operation: 58-17=41 Exploring Operation: 79-58=21, Resulting Numbers: [17, 21] Generated Node #0,1,1: 58:[17, 21] Operation: 79-58=21 Exploring Operation: 79-17=62, Resulting Numbers: [58, 62] Generated Node #0,1,2: 58:[58, 62] Operation: 79-17=62 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 58:[58, 62], Operations: ['89-10=79', '79-17=62'] Exploring Operation: 58+62=120, Resulting Numbers: [120] 120,58 unequal: No Solution Exploring Operation: 58*62=3596, Resulting Numbers: [3596] 3596,58 unequal: No Solution Exploring Operation: 62-58=4, Resulting Numbers: [4] 4,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 58:[17, 21], Operations: ['89-10=79', '79-58=21'] Exploring Operation: 17+21=38, Resulting Numbers: [38] 38,58 unequal: No Solution Exploring Operation: 17*21=357, Resulting Numbers: [357] 357,58 unequal: No Solution Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,58 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 #0,1,0 Current State: 58:[79, 41], Operations: ['89-10=79', '58-17=41'] Exploring Operation: 79+41=120, Resulting Numbers: [120] 120,58 unequal: No Solution Exploring Operation: 79*41=3239, Resulting Numbers: [3239] 3239,58 unequal: No Solution Exploring Operation: 79-41=38, Resulting Numbers: [38] 38,58 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: 58:[58, 62], Operations: ['89-17=72', '72-10=62'] Exploring Operation: 58*62=3596, Resulting Numbers: [3596] 3596,58 unequal: No Solution Exploring Operation: 58+62=120, Resulting Numbers: [120] 120,58 unequal: No Solution Exploring Operation: 62-58=4, Resulting Numbers: [4] 4,58 unequal: No Solution Moving to Node #0,2,0 Current State: 58:[31, 27], Operations: ['89-58=31', '17+10=27'] Exploring Operation: 31*27=837, Resulting Numbers: [837] 837,58 unequal: No Solution Exploring Operation: 31+27=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[89, 17, 10, 58], Operations: [] Exploring Operation: 89-58=31, Resulting Numbers: [17, 10, 31] Generated Node #0,2: 58:[17, 10, 31] Operation: 89-58=31 Moving to Node #0,2 Current State: 58:[17, 10, 31], Operations: ['89-58=31'] Exploring Operation: 17+10=27, Resulting Numbers: [31, 27] Generated Node #0,2,0: 58:[31, 27] Operation: 17+10=27 Moving to Node #0,2,0 Current State: 58:[31, 27], Operations: ['89-58=31', '17+10=27'] Exploring Operation: 31+27=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
0.973958
hs_3
mult_heuristic
[ 45, 92, 95, 94 ]
79
[ "95-92=3", "45/3=15", "94-15=79" ]
Current State: 79:[45, 92, 95, 94], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [45, 94, 3] Generated Node #2: [45, 94, 3] from Operation: 95-92=3 Current State: 79:[45, 94, 3], Operations: ['95-92=3'] Exploring Operation: 45/3=15, Resulting Numbers: [94, 15] Generated Node #3: [94, 15] from Operation: 45/3=15 Current State: 79:[94, 15], Operations: ['95-92=3', '45/3=15'] Exploring Operation: 94-15=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[45, 92, 95, 94], Operations: [] Exploring Operation: 95-45=50, Resulting Numbers: [92, 94, 50] Generated Node #0,0: 79:[92, 94, 50] Operation: 95-45=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[92, 94, 50], Operations: ['95-45=50'] Exploring Operation: 94-50=44, Resulting Numbers: [92, 44] Generated Node #0,0,0: 79:[92, 44] Operation: 94-50=44 Moving to Node #0,0,0 Current State: 79:[92, 44], Operations: ['95-45=50', '94-50=44'] Exploring Operation: 92-44=48, Resulting Numbers: [48] 48,79 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
[ 10, 15, 25, 16 ]
34
[ "10+15=25", "25-16=9", "25+9=34" ]
Current State: 34:[10, 15, 25, 16], Operations: [] Exploring Operation: 10+15=25, Resulting Numbers: [25, 16, 25] Generated Node #2: [25, 16, 25] from Operation: 10+15=25 Current State: 34:[25, 16, 25], Operations: ['10+15=25'] Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,34 equal: Goal Reached Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[10, 15, 25, 16], Operations: [] Exploring Operation: 10+25=35, Resulting Numbers: [15, 16, 35] Generated Node #0,0: 34:[15, 16, 35] Operation: 10+25=35 Exploring Operation: 16-10=6, Resulting Numbers: [15, 25, 6] Generated Node #0,1: 34:[15, 25, 6] Operation: 16-10=6 Exploring Operation: 15-10=5, Resulting Numbers: [25, 16, 5] Generated Node #0,2: 34:[25, 16, 5] Operation: 15-10=5 Exploring Operation: 25-10=15, Resulting Numbers: [15, 16, 15] Generated Node #0,3: 34:[15, 16, 15] Operation: 25-10=15 Moving to Node #0,0 Current State: 34:[15, 16, 35], Operations: ['10+25=35'] Exploring Operation: 35-16=19, Resulting Numbers: [15, 19] Generated Node #0,0,0: 34:[15, 19] Operation: 35-16=19 Exploring Operation: 35-15=20, Resulting Numbers: [16, 20] Generated Node #0,0,1: 34:[16, 20] Operation: 35-15=20 Exploring Operation: 15+16=31, Resulting Numbers: [35, 31] Generated Node #0,0,2: 34:[35, 31] Operation: 15+16=31 Exploring Operation: 16-15=1, Resulting Numbers: [35, 1] Generated Node #0,0,3: 34:[35, 1] Operation: 16-15=1 Moving to Node #0,3 Current State: 34:[15, 16, 15], Operations: ['25-10=15'] Exploring Operation: 16-15=1, Resulting Numbers: [15, 1] Generated Node #0,3,0: 34:[15, 1] Operation: 16-15=1 Exploring Operation: 15/15=1, Resulting Numbers: [16, 1] Generated Node #0,3,1: 34:[16, 1] Operation: 15/15=1 Exploring Operation: 15-15=0, Resulting Numbers: [16, 0] Generated Node #0,3,2: 34:[16, 0] Operation: 15-15=0 Exploring Operation: 16-15=1, Resulting Numbers: [15, 1] Generated Node #0,3,3: 34:[15, 1] Operation: 16-15=1 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 34:[16, 1], Operations: ['25-10=15', '15/15=1'] Exploring Operation: 16+1=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 16*1=16, Resulting Numbers: [16] 16,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 34:[15, 1], Operations: ['25-10=15', '16-15=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,34 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 15+1=16, Resulting Numbers: [16] 16,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 34:[16, 0], Operations: ['25-10=15', '15-15=0'] Exploring Operation: 16-0=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 16*0=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 16+0=16, Resulting Numbers: [16] 16,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 34:[15, 1], Operations: ['25-10=15', '16-15=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,34 unequal: No Solution Exploring Operation: 15+1=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,34 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: 34:[25, 16, 5], Operations: ['15-10=5'] Exploring Operation: 25+16=41, Resulting Numbers: [5, 41] Generated Node #0,2,0: 34:[5, 41] Operation: 25+16=41 Exploring Operation: 25+5=30, Resulting Numbers: [16, 30] Generated Node #0,2,1: 34:[16, 30] Operation: 25+5=30 Exploring Operation: 25-5=20, Resulting Numbers: [16, 20] Generated Node #0,2,2: 34:[16, 20] Operation: 25-5=20 Exploring Operation: 25/5=5, Resulting Numbers: [16, 5] Generated Node #0,2,3: 34:[16, 5] Operation: 25/5=5 Moving to Node #0,1 Current State: 34:[15, 25, 6], Operations: ['16-10=6'] Exploring Operation: 25-6=19, Resulting Numbers: [15, 19] Generated Node #0,1,0: 34:[15, 19] Operation: 25-6=19 Exploring Operation: 25-15=10, Resulting Numbers: [6, 10] Generated Node #0,1,1: 34:[6, 10] Operation: 25-15=10 Exploring Operation: 25+6=31, Resulting Numbers: [15, 31] Generated Node #0,1,2: 34:[15, 31] Operation: 25+6=31 Exploring Operation: 15+25=40, Resulting Numbers: [6, 40] Generated Node #0,1,3: 34:[6, 40] Operation: 15+25=40 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 34:[15, 19], Operations: ['16-10=6', '25-6=19'] Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,34 unequal: No Solution Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[10, 15, 25, 16], Operations: [] Exploring Operation: 16-10=6, Resulting Numbers: [15, 25, 6] Generated Node #0,1: 34:[15, 25, 6] Operation: 16-10=6 Moving to Node #0,1 Current State: 34:[15, 25, 6], Operations: ['16-10=6'] Exploring Operation: 25-6=19, Resulting Numbers: [15, 19] Generated Node #0,1,0: 34:[15, 19] Operation: 25-6=19 Moving to Node #0,1,0 Current State: 34:[15, 19], Operations: ['16-10=6', '25-6=19'] Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_4
mult_heuristic
[ 78, 19, 85, 17 ]
14
[ "85-78=7", "19-17=2", "7*2=14" ]
Current State: 14:[78, 19, 85, 17], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [19, 17, 7] Generated Node #2: [19, 17, 7] from Operation: 85-78=7 Current State: 14:[19, 17, 7], Operations: ['85-78=7'] Exploring Operation: 19-17=2, Resulting Numbers: [7, 2] Generated Node #3: [7, 2] from Operation: 19-17=2 Current State: 14:[7, 2], Operations: ['85-78=7', '19-17=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[78, 19, 85, 17], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [19, 17, 7] Generated Node #0,0: 14:[19, 17, 7] Operation: 85-78=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[19, 17, 7], Operations: ['85-78=7'] Exploring Operation: 19-17=2, Resulting Numbers: [7, 2] Generated Node #0,0,0: 14:[7, 2] Operation: 19-17=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 14:[7, 2], Operations: ['85-78=7', '19-17=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[78, 19, 85, 17], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [19, 17, 7] Generated Node #0,0: 14:[19, 17, 7] Operation: 85-78=7 Moving to Node #0,0 Current State: 14:[19, 17, 7], Operations: ['85-78=7'] Exploring Operation: 19-17=2, Resulting Numbers: [7, 2] Generated Node #0,0,0: 14:[7, 2] Operation: 19-17=2 Moving to Node #0,0,0 Current State: 14:[7, 2], Operations: ['85-78=7', '19-17=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 27, 74, 7, 48 ]
16
[ "27*48=1296", "74+7=81", "1296/81=16" ]
Current State: 16:[27, 74, 7, 48], Operations: [] Exploring Operation: 27*48=1296, Resulting Numbers: [74, 7, 1296] Generated Node #2: [74, 7, 1296] from Operation: 27*48=1296 Current State: 16:[74, 7, 1296], Operations: ['27*48=1296'] Exploring Operation: 74+7=81, Resulting Numbers: [1296, 81] Generated Node #3: [1296, 81] from Operation: 74+7=81 Current State: 16:[1296, 81], Operations: ['27*48=1296', '74+7=81'] Exploring Operation: 1296/81=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[27, 74, 7, 48], Operations: [] Exploring Operation: 48-27=21, Resulting Numbers: [74, 7, 21] Generated Node #0,0: 16:[74, 7, 21] Operation: 48-27=21 Exploring Operation: 27-7=20, Resulting Numbers: [74, 48, 20] Generated Node #0,1: 16:[74, 48, 20] Operation: 27-7=20 Exploring Operation: 74-48=26, Resulting Numbers: [27, 7, 26] Generated Node #0,2: 16:[27, 7, 26] Operation: 74-48=26 Exploring Operation: 74-27=47, Resulting Numbers: [7, 48, 47] Generated Node #0,3: 16:[7, 48, 47] Operation: 74-27=47 Moving to Node #0,2 Current State: 16:[27, 7, 26], Operations: ['74-48=26'] Exploring Operation: 27-26=1, Resulting Numbers: [7, 1] Generated Node #0,2,0: 16:[7, 1] Operation: 27-26=1 Exploring Operation: 27+7=34, Resulting Numbers: [26, 34] Generated Node #0,2,1: 16:[26, 34] Operation: 27+7=34 Exploring Operation: 27-7=20, Resulting Numbers: [26, 20] Generated Node #0,2,2: 16:[26, 20] Operation: 27-7=20 Exploring Operation: 26-7=19, Resulting Numbers: [27, 19] Generated Node #0,2,3: 16:[27, 19] Operation: 26-7=19 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 16:[7, 1], Operations: ['74-48=26', '27-26=1'] Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,16 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,16 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:[26, 20], Operations: ['74-48=26', '27-7=20'] Exploring Operation: 26*20=520, Resulting Numbers: [520] 520,16 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,16 unequal: No Solution Exploring Operation: 26+20=46, Resulting Numbers: [46] 46,16 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 #0,2,3 Current State: 16:[27, 19], Operations: ['74-48=26', '26-7=19'] Exploring Operation: 27-19=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 27*19=513, Resulting Numbers: [513] 513,16 unequal: No Solution Exploring Operation: 27+19=46, Resulting Numbers: [46] 46,16 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:[26, 34], Operations: ['74-48=26', '27+7=34'] Exploring Operation: 26+34=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 26*34=884, Resulting Numbers: [884] 884,16 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:[7, 48, 47], Operations: ['74-27=47'] Exploring Operation: 7+48=55, Resulting Numbers: [47, 55] Generated Node #0,3,0: 16:[47, 55] Operation: 7+48=55 Exploring Operation: 48-7=41, Resulting Numbers: [47, 41] Generated Node #0,3,1: 16:[47, 41] Operation: 48-7=41 Exploring Operation: 47-7=40, Resulting Numbers: [48, 40] Generated Node #0,3,2: 16:[48, 40] Operation: 47-7=40 Exploring Operation: 48-47=1, Resulting Numbers: [7, 1] Generated Node #0,3,3: 16:[7, 1] Operation: 48-47=1 Moving to Node #0,0 Current State: 16:[74, 7, 21], Operations: ['48-27=21'] Exploring Operation: 21-7=14, Resulting Numbers: [74, 14] Generated Node #0,0,0: 16:[74, 14] Operation: 21-7=14 Exploring Operation: 74-7=67, Resulting Numbers: [21, 67] Generated Node #0,0,1: 16:[21, 67] Operation: 74-7=67 Exploring Operation: 74-21=53, Resulting Numbers: [7, 53] Generated Node #0,0,2: 16:[7, 53] Operation: 74-21=53 Exploring Operation: 21/7=3, Resulting Numbers: [74, 3] Generated Node #0,0,3: 16:[74, 3] Operation: 21/7=3 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[7, 53], Operations: ['48-27=21', '74-21=53'] Exploring Operation: 7*53=371, Resulting Numbers: [371] 371,16 unequal: No Solution Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,16 unequal: No Solution Exploring Operation: 7+53=60, Resulting Numbers: [60] 60,16 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:[21, 67], Operations: ['48-27=21', '74-7=67'] Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,16 unequal: No Solution Exploring Operation: 21+67=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 21*67=1407, Resulting Numbers: [1407] 1407,16 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:[74, 3], Operations: ['48-27=21', '21/7=3'] Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,16 unequal: No Solution Exploring Operation: 74+3=77, Resulting Numbers: [77] 77,16 unequal: No Solution Exploring Operation: 74*3=222, Resulting Numbers: [222] 222,16 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:[74, 14], Operations: ['48-27=21', '21-7=14'] Exploring Operation: 74-14=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 74+14=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 74*14=1036, Resulting Numbers: [1036] 1036,16 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:[74, 48, 20], Operations: ['27-7=20'] Exploring Operation: 48-20=28, Resulting Numbers: [74, 28] Generated Node #0,1,0: 16:[74, 28] Operation: 48-20=28 Exploring Operation: 74+48=122, Resulting Numbers: [20, 122] Generated Node #0,1,1: 16:[20, 122] Operation: 74+48=122 Exploring Operation: 74-20=54, Resulting Numbers: [48, 54] Generated Node #0,1,2: 16:[48, 54] Operation: 74-20=54 Exploring Operation: 74-48=26, Resulting Numbers: [20, 26] Generated Node #0,1,3: 16:[20, 26] Operation: 74-48=26 Moving to Node #0,3,3 Current State: 16:[7, 1], Operations: ['74-27=47', '48-47=1'] Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,16 unequal: No Solution Moving to Node #0,1,3 Current State: 16:[20, 26], Operations: ['27-7=20', '74-48=26'] Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,16 unequal: No Solution Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,16 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,16 unequal: No Solution Moving to Node #0,3,2 Current State: 16:[48, 40], Operations: ['74-27=47', '47-7=40'] Exploring Operation: 48*40=1920, Resulting Numbers: [1920] 1920,16 unequal: No Solution Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 48+40=88, Resulting Numbers: [88] 88,16 unequal: No Solution Moving to Node #0,3,1 Current State: 16:[47, 41], Operations: ['74-27=47', '48-7=41'] Exploring Operation: 47+41=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,16 unequal: No Solution Exploring Operation: 47*41=1927, Resulting Numbers: [1927] 1927,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[74, 28], Operations: ['27-7=20', '48-20=28'] Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,16 unequal: No Solution Exploring Operation: 74*28=2072, Resulting Numbers: [2072] 2072,16 unequal: No Solution Exploring Operation: 74+28=102, Resulting Numbers: [102] 102,16 unequal: No Solution Moving to Node #0,3,0 Current State: 16:[47, 55], Operations: ['74-27=47', '7+48=55'] Exploring Operation: 47+55=102, Resulting Numbers: [102] 102,16 unequal: No Solution Exploring Operation: 55-47=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 47*55=2585, Resulting Numbers: [2585] 2585,16 unequal: No Solution Moving to Node #0,1,2 Current State: 16:[48, 54], Operations: ['27-7=20', '74-20=54'] Exploring Operation: 48*54=2592, Resulting Numbers: [2592] 2592,16 unequal: No Solution Exploring Operation: 48+54=102, Resulting Numbers: [102] 102,16 unequal: No Solution Exploring Operation: 54-48=6, Resulting Numbers: [6] 6,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[20, 122], Operations: ['27-7=20', '74+48=122'] Exploring Operation: 20+122=142, Resulting Numbers: [142] 142,16 unequal: No Solution Exploring Operation: 20*122=2440, Resulting Numbers: [2440] 2440,16 unequal: No Solution Exploring Operation: 122-20=102, Resulting Numbers: [102] 102,16 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 68, 62, 36, 12 ]
33
[ "62*36=2232", "12+2232=2244", "2244/68=33" ]
Current State: 33:[68, 62, 36, 12], Operations: [] Exploring Operation: 62*36=2232, Resulting Numbers: [68, 12, 2232] Generated Node #2: [68, 12, 2232] from Operation: 62*36=2232 Current State: 33:[68, 12, 2232], Operations: ['62*36=2232'] Exploring Operation: 12+2232=2244, Resulting Numbers: [68, 2244] Generated Node #3: [68, 2244] from Operation: 12+2232=2244 Current State: 33:[68, 2244], Operations: ['62*36=2232', '12+2232=2244'] Exploring Operation: 2244/68=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[68, 62, 36, 12], Operations: [] Exploring Operation: 68-36=32, Resulting Numbers: [62, 12, 32] Generated Node #0,0: 33:[62, 12, 32] Operation: 68-36=32 Exploring Operation: 68-62=6, Resulting Numbers: [36, 12, 6] Generated Node #0,1: 33:[36, 12, 6] Operation: 68-62=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[36, 12, 6], Operations: ['68-62=6'] Exploring Operation: 36-6=30, Resulting Numbers: [12, 30] Generated Node #0,1,0: 33:[12, 30] Operation: 36-6=30 Exploring Operation: 36/12=3, Resulting Numbers: [6, 3] Generated Node #0,1,1: 33:[6, 3] Operation: 36/12=3 Moving to Node #0,1,1 Current State: 33:[6, 3], Operations: ['68-62=6', '36/12=3'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,33 unequal: No Solution Moving to Node #0,1,0 Current State: 33:[12, 30], Operations: ['68-62=6', '36-6=30'] Exploring Operation: 12+30=42, Resulting Numbers: [42] 42,33 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[62, 12, 32], Operations: ['68-36=32'] Exploring Operation: 62-12=50, Resulting Numbers: [32, 50] Generated Node #0,0,0: 33:[32, 50] Operation: 62-12=50 Exploring Operation: 62-32=30, Resulting Numbers: [12, 30] Generated Node #0,0,1: 33:[12, 30] Operation: 62-32=30 Moving to Node #0,0,1 Current State: 33:[12, 30], Operations: ['68-36=32', '62-32=30'] Exploring Operation: 12+30=42, Resulting Numbers: [42] 42,33 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,33 unequal: No Solution Moving to Node #0,0,0 Current State: 33:[32, 50], Operations: ['68-36=32', '62-12=50'] Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,33 unequal: No Solution Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,33 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
[ 29, 21, 66, 50 ]
17
[ "66+50=116", "116/29=4", "21-4=17" ]
Current State: 17:[29, 21, 66, 50], Operations: [] Exploring Operation: 66+50=116, Resulting Numbers: [29, 21, 116] Generated Node #2: [29, 21, 116] from Operation: 66+50=116 Current State: 17:[29, 21, 116], Operations: ['66+50=116'] Exploring Operation: 116/29=4, Resulting Numbers: [21, 4] Generated Node #3: [21, 4] from Operation: 116/29=4 Current State: 17:[21, 4], Operations: ['66+50=116', '116/29=4'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[29, 21, 66, 50], Operations: [] Exploring Operation: 50-29=21, Resulting Numbers: [21, 66, 21] Generated Node #0,0: 17:[21, 66, 21] Operation: 50-29=21 Exploring Operation: 66-50=16, Resulting Numbers: [29, 21, 16] Generated Node #0,1: 17:[29, 21, 16] Operation: 66-50=16 Exploring Operation: 66-21=45, Resulting Numbers: [29, 50, 45] Generated Node #0,2: 17:[29, 50, 45] Operation: 66-21=45 Exploring Operation: 66-29=37, Resulting Numbers: [21, 50, 37] Generated Node #0,3: 17:[21, 50, 37] Operation: 66-29=37 Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[29, 21, 16], Operations: ['66-50=16'] Exploring Operation: 21-16=5, Resulting Numbers: [29, 5] Generated Node #0,1,0: 17:[29, 5] Operation: 21-16=5 Exploring Operation: 29-16=13, Resulting Numbers: [21, 13] Generated Node #0,1,1: 17:[21, 13] Operation: 29-16=13 Exploring Operation: 29-21=8, Resulting Numbers: [16, 8] Generated Node #0,1,2: 17:[16, 8] Operation: 29-21=8 Exploring Operation: 29+16=45, Resulting Numbers: [21, 45] Generated Node #0,1,3: 17:[21, 45] Operation: 29+16=45 Moving to Node #0,1,1 Current State: 17:[21, 13], Operations: ['66-50=16', '29-16=13'] Exploring Operation: 21*13=273, Resulting Numbers: [273] 273,17 unequal: No Solution Exploring Operation: 21+13=34, Resulting Numbers: [34] 34,17 unequal: No Solution Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,17 unequal: No Solution Moving to Node #0,1,2 Current State: 17:[16, 8], Operations: ['66-50=16', '29-21=8'] Exploring Operation: 16+8=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 16*8=128, Resulting Numbers: [128] 128,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[29, 5], Operations: ['66-50=16', '21-16=5'] Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,17 unequal: No Solution Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,17 unequal: No Solution Moving to Node #0,1,3 Current State: 17:[21, 45], Operations: ['66-50=16', '29+16=45'] Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 21*45=945, Resulting Numbers: [945] 945,17 unequal: No Solution Exploring Operation: 21+45=66, Resulting Numbers: [66] 66,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[21, 66, 21], Operations: ['50-29=21'] Exploring Operation: 66-21=45, Resulting Numbers: [21, 45] Generated Node #0,0,0: 17:[21, 45] Operation: 66-21=45 Exploring Operation: 21/21=1, Resulting Numbers: [66, 1] Generated Node #0,0,1: 17:[66, 1] Operation: 21/21=1 Exploring Operation: 66-21=45, Resulting Numbers: [21, 45] Generated Node #0,0,2: 17:[21, 45] Operation: 66-21=45 Exploring Operation: 21-21=0, Resulting Numbers: [66, 0] Generated Node #0,0,3: 17:[66, 0] Operation: 21-21=0 Moving to Node #0,0,0 Current State: 17:[21, 45], Operations: ['50-29=21', '66-21=45'] Exploring Operation: 21+45=66, Resulting Numbers: [66] 66,17 unequal: No Solution Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 21*45=945, Resulting Numbers: [945] 945,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[21, 45], Operations: ['50-29=21', '66-21=45'] Exploring Operation: 21*45=945, Resulting Numbers: [945] 945,17 unequal: No Solution Exploring Operation: 21+45=66, Resulting Numbers: [66] 66,17 unequal: No Solution Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[66, 1], Operations: ['50-29=21', '21/21=1'] Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,17 unequal: No Solution Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,17 unequal: No Solution Exploring Operation: 66*1=66, Resulting Numbers: [66] 66,17 unequal: No Solution Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,17 unequal: No Solution Moving to Node #0,0,3 Current State: 17:[66, 0], Operations: ['50-29=21', '21-21=0'] Exploring Operation: 66-0=66, Resulting Numbers: [66] 66,17 unequal: No Solution Exploring Operation: 66*0=0, Resulting Numbers: [0] 0,17 unequal: No Solution Exploring Operation: 66+0=66, Resulting Numbers: [66] 66,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 17:[21, 50, 37], Operations: ['66-29=37'] Exploring Operation: 50-37=13, Resulting Numbers: [21, 13] Generated Node #0,3,0: 17:[21, 13] Operation: 50-37=13 Exploring Operation: 37-21=16, Resulting Numbers: [50, 16] Generated Node #0,3,1: 17:[50, 16] Operation: 37-21=16 Exploring Operation: 50-21=29, Resulting Numbers: [37, 29] Generated Node #0,3,2: 17:[37, 29] Operation: 50-21=29 Exploring Operation: 21+50=71, Resulting Numbers: [37, 71] Generated Node #0,3,3: 17:[37, 71] Operation: 21+50=71 Moving to Node #0,3,0 Current State: 17:[21, 13], Operations: ['66-29=37', '50-37=13'] Exploring Operation: 21*13=273, Resulting Numbers: [273] 273,17 unequal: No Solution Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 21+13=34, Resulting Numbers: [34] 34,17 unequal: No Solution Moving to Node #0,3,2 Current State: 17:[37, 29], Operations: ['66-29=37', '50-21=29'] Exploring Operation: 37-29=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 37+29=66, Resulting Numbers: [66] 66,17 unequal: No Solution Exploring Operation: 37*29=1073, Resulting Numbers: [1073] 1073,17 unequal: No Solution Moving to Node #0,3,1 Current State: 17:[50, 16], Operations: ['66-29=37', '37-21=16'] Exploring Operation: 50*16=800, Resulting Numbers: [800] 800,17 unequal: No Solution Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,17 unequal: No Solution Exploring Operation: 50+16=66, Resulting Numbers: [66] 66,17 unequal: No Solution Moving to Node #0,3,3 Current State: 17:[37, 71], Operations: ['66-29=37', '21+50=71'] Exploring Operation: 37*71=2627, Resulting Numbers: [2627] 2627,17 unequal: No Solution Exploring Operation: 37+71=108, Resulting Numbers: [108] 108,17 unequal: No Solution Exploring Operation: 71-37=34, Resulting Numbers: [34] 34,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[29, 50, 45], Operations: ['66-21=45'] Exploring Operation: 29+50=79, Resulting Numbers: [45, 79] Generated Node #0,2,0: 17:[45, 79] Operation: 29+50=79 Exploring Operation: 45-29=16, Resulting Numbers: [50, 16] Generated Node #0,2,1: 17:[50, 16] Operation: 45-29=16 Exploring Operation: 50-45=5, Resulting Numbers: [29, 5] Generated Node #0,2,2: 17:[29, 5] Operation: 50-45=5 Exploring Operation: 50-29=21, Resulting Numbers: [45, 21] Generated Node #0,2,3: 17:[45, 21] Operation: 50-29=21 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 17:[29, 5], Operations: ['66-21=45', '50-45=5'] Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,17 unequal: No Solution Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,17 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,17 unequal: No Solution No 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: 17:[45, 21], Operations: ['66-21=45', '50-29=21'] Exploring Operation: 45*21=945, Resulting Numbers: [945] 945,17 unequal: No Solution Exploring Operation: 45+21=66, Resulting Numbers: [66] 66,17 unequal: No Solution Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,17 unequal: No Solution No 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: 17:[50, 16], Operations: ['66-21=45', '45-29=16'] Exploring Operation: 50+16=66, Resulting Numbers: [66] 66,17 unequal: No Solution Exploring Operation: 50*16=800, Resulting Numbers: [800] 800,17 unequal: No Solution Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,17 unequal: No Solution No 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: 17:[45, 79], Operations: ['66-21=45', '29+50=79'] Exploring Operation: 45+79=124, Resulting Numbers: [124] 124,17 unequal: No Solution Exploring Operation: 45*79=3555, Resulting Numbers: [3555] 3555,17 unequal: No Solution Exploring Operation: 79-45=34, Resulting Numbers: [34] 34,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 52, 60, 5, 38 ]
35
[ "60-52=8", "5+38=43", "43-8=35" ]
Current State: 35:[52, 60, 5, 38], Operations: [] Exploring Operation: 60-52=8, Resulting Numbers: [5, 38, 8] Generated Node #2: [5, 38, 8] from Operation: 60-52=8 Current State: 35:[5, 38, 8], Operations: ['60-52=8'] Exploring Operation: 5+38=43, Resulting Numbers: [8, 43] Generated Node #3: [8, 43] from Operation: 5+38=43 Current State: 35:[8, 43], Operations: ['60-52=8', '5+38=43'] Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[52, 60, 5, 38], Operations: [] Exploring Operation: 60-52=8, Resulting Numbers: [5, 38, 8] Generated Node #0,0: 35:[5, 38, 8] Operation: 60-52=8 Exploring Operation: 60/5=12, Resulting Numbers: [52, 38, 12] Generated Node #0,1: 35:[52, 38, 12] Operation: 60/5=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[5, 38, 8], Operations: ['60-52=8'] Exploring Operation: 8-5=3, Resulting Numbers: [38, 3] Generated Node #0,0,0: 35:[38, 3] Operation: 8-5=3 Exploring Operation: 38-5=33, Resulting Numbers: [8, 33] Generated Node #0,0,1: 35:[8, 33] Operation: 38-5=33 Moving to Node #0,0,1 Current State: 35:[8, 33], Operations: ['60-52=8', '38-5=33'] Exploring Operation: 8+33=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[38, 3], Operations: ['60-52=8', '8-5=3'] Exploring Operation: 38+3=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[52, 60, 5, 38], Operations: [] Exploring Operation: 60-52=8, Resulting Numbers: [5, 38, 8] Generated Node #0,0: 35:[5, 38, 8] Operation: 60-52=8 Moving to Node #0,0 Current State: 35:[5, 38, 8], Operations: ['60-52=8'] Exploring Operation: 8-5=3, Resulting Numbers: [38, 3] Generated Node #0,0,0: 35:[38, 3] Operation: 8-5=3 Moving to Node #0,0,0 Current State: 35:[38, 3], Operations: ['60-52=8', '8-5=3'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 66, 58, 42, 99 ]
24
[ "58-42=16", "99*16=1584", "1584/66=24" ]
Current State: 24:[66, 58, 42, 99], Operations: [] Exploring Operation: 58-42=16, Resulting Numbers: [66, 99, 16] Generated Node #2: [66, 99, 16] from Operation: 58-42=16 Current State: 24:[66, 99, 16], Operations: ['58-42=16'] Exploring Operation: 99*16=1584, Resulting Numbers: [66, 1584] Generated Node #3: [66, 1584] from Operation: 99*16=1584 Current State: 24:[66, 1584], Operations: ['58-42=16', '99*16=1584'] Exploring Operation: 1584/66=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[66, 58, 42, 99], Operations: [] Exploring Operation: 66-58=8, Resulting Numbers: [42, 99, 8] Generated Node #0,0: 24:[42, 99, 8] Operation: 66-58=8 Exploring Operation: 99-66=33, Resulting Numbers: [58, 42, 33] Generated Node #0,1: 24:[58, 42, 33] Operation: 99-66=33 Exploring Operation: 99-58=41, Resulting Numbers: [66, 42, 41] Generated Node #0,2: 24:[66, 42, 41] Operation: 99-58=41 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[58, 42, 33], Operations: ['99-66=33'] Exploring Operation: 58-42=16, Resulting Numbers: [33, 16] Generated Node #0,1,0: 24:[33, 16] Operation: 58-42=16 Exploring Operation: 58-33=25, Resulting Numbers: [42, 25] Generated Node #0,1,1: 24:[42, 25] Operation: 58-33=25 Exploring Operation: 42-33=9, Resulting Numbers: [58, 9] Generated Node #0,1,2: 24:[58, 9] Operation: 42-33=9 Moving to Node #0,1,0 Current State: 24:[33, 16], Operations: ['99-66=33', '58-42=16'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 33*16=528, Resulting Numbers: [528] 528,24 unequal: No Solution Exploring Operation: 33+16=49, Resulting Numbers: [49] 49,24 unequal: No Solution Moving to Node #0,1,1 Current State: 24:[42, 25], Operations: ['99-66=33', '58-33=25'] Exploring Operation: 42*25=1050, Resulting Numbers: [1050] 1050,24 unequal: No Solution Exploring Operation: 42-25=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 42+25=67, Resulting Numbers: [67] 67,24 unequal: No Solution Moving to Node #0,1,2 Current State: 24:[58, 9], Operations: ['99-66=33', '42-33=9'] Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,24 unequal: No Solution Exploring Operation: 58*9=522, Resulting Numbers: [522] 522,24 unequal: No Solution Exploring Operation: 58+9=67, Resulting Numbers: [67] 67,24 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 #0,2 Current State: 24:[66, 42, 41], Operations: ['99-58=41'] Exploring Operation: 42-41=1, Resulting Numbers: [66, 1] Generated Node #0,2,0: 24:[66, 1] Operation: 42-41=1 Exploring Operation: 66-41=25, Resulting Numbers: [42, 25] Generated Node #0,2,1: 24:[42, 25] Operation: 66-41=25 Exploring Operation: 66-42=24, Resulting Numbers: [41, 24] Generated Node #0,2,2: 24:[41, 24] Operation: 66-42=24 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 24:[41, 24], Operations: ['99-58=41', '66-42=24'] Exploring Operation: 41+24=65, Resulting Numbers: [65] 65,24 unequal: No Solution Exploring Operation: 41*24=984, Resulting Numbers: [984] 984,24 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,24 unequal: No Solution No 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: 24:[42, 25], Operations: ['99-58=41', '66-41=25'] Exploring Operation: 42*25=1050, Resulting Numbers: [1050] 1050,24 unequal: No Solution Exploring Operation: 42-25=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 42+25=67, Resulting Numbers: [67] 67,24 unequal: No Solution No 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: 24:[66, 1], Operations: ['99-58=41', '42-41=1'] Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,24 unequal: No Solution Exploring Operation: 66*1=66, Resulting Numbers: [66] 66,24 unequal: No Solution Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[42, 99, 8], Operations: ['66-58=8'] Exploring Operation: 99-8=91, Resulting Numbers: [42, 91] Generated Node #0,0,0: 24:[42, 91] Operation: 99-8=91 Exploring Operation: 42-8=34, Resulting Numbers: [99, 34] Generated Node #0,0,1: 24:[99, 34] Operation: 42-8=34 Exploring Operation: 99-42=57, Resulting Numbers: [8, 57] Generated Node #0,0,2: 24:[8, 57] Operation: 99-42=57 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 24:[8, 57], Operations: ['66-58=8', '99-42=57'] Exploring Operation: 57-8=49, Resulting Numbers: [49] 49,24 unequal: No Solution Exploring Operation: 8*57=456, Resulting Numbers: [456] 456,24 unequal: No Solution Exploring Operation: 8+57=65, Resulting Numbers: [65] 65,24 unequal: No Solution No 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: 24:[42, 91], Operations: ['66-58=8', '99-8=91'] Exploring Operation: 42+91=133, Resulting Numbers: [133] 133,24 unequal: No Solution Exploring Operation: 91-42=49, Resulting Numbers: [49] 49,24 unequal: No Solution Exploring Operation: 42*91=3822, Resulting Numbers: [3822] 3822,24 unequal: No Solution No 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: 24:[99, 34], Operations: ['66-58=8', '42-8=34'] Exploring Operation: 99*34=3366, Resulting Numbers: [3366] 3366,24 unequal: No Solution Exploring Operation: 99+34=133, Resulting Numbers: [133] 133,24 unequal: No Solution Exploring Operation: 99-34=65, Resulting Numbers: [65] 65,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 29, 52, 57, 22 ]
56
[ "52-29=23", "57+22=79", "79-23=56" ]
Current State: 56:[29, 52, 57, 22], Operations: [] Exploring Operation: 52-29=23, Resulting Numbers: [57, 22, 23] Generated Node #2: [57, 22, 23] from Operation: 52-29=23 Current State: 56:[57, 22, 23], Operations: ['52-29=23'] Exploring Operation: 57+22=79, Resulting Numbers: [23, 79] Generated Node #3: [23, 79] from Operation: 57+22=79 Current State: 56:[23, 79], Operations: ['52-29=23', '57+22=79'] Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[29, 52, 57, 22], Operations: [] Exploring Operation: 57-29=28, Resulting Numbers: [52, 22, 28] Generated Node #0,0: 56:[52, 22, 28] Operation: 57-29=28 Exploring Operation: 29+22=51, Resulting Numbers: [52, 57, 51] Generated Node #0,1: 56:[52, 57, 51] Operation: 29+22=51 Exploring Operation: 52-22=30, Resulting Numbers: [29, 57, 30] Generated Node #0,2: 56:[29, 57, 30] Operation: 52-22=30 Exploring Operation: 29-22=7, Resulting Numbers: [52, 57, 7] Generated Node #0,3: 56:[52, 57, 7] Operation: 29-22=7 Exploring Operation: 57-52=5, Resulting Numbers: [29, 22, 5] Generated Node #0,4: 56:[29, 22, 5] Operation: 57-52=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[29, 57, 30], Operations: ['52-22=30'] Exploring Operation: 29+57=86, Resulting Numbers: [30, 86] Generated Node #0,2,0: 56:[30, 86] Operation: 29+57=86 Exploring Operation: 30-29=1, Resulting Numbers: [57, 1] Generated Node #0,2,1: 56:[57, 1] Operation: 30-29=1 Exploring Operation: 57-29=28, Resulting Numbers: [30, 28] Generated Node #0,2,2: 56:[30, 28] Operation: 57-29=28 Exploring Operation: 29+30=59, Resulting Numbers: [57, 59] Generated Node #0,2,3: 56:[57, 59] Operation: 29+30=59 Exploring Operation: 57-30=27, Resulting Numbers: [29, 27] Generated Node #0,2,4: 56:[29, 27] Operation: 57-30=27 Moving to Node #0,2,1 Current State: 56:[57, 1], Operations: ['52-22=30', '30-29=1'] Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,56 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[29, 52, 57, 22], Operations: [] Exploring Operation: 52-22=30, Resulting Numbers: [29, 57, 30] Generated Node #0,2: 56:[29, 57, 30] Operation: 52-22=30 Moving to Node #0,2 Current State: 56:[29, 57, 30], Operations: ['52-22=30'] Exploring Operation: 30-29=1, Resulting Numbers: [57, 1] Generated Node #0,2,1: 56:[57, 1] Operation: 30-29=1 Moving to Node #0,2,1 Current State: 56:[57, 1], Operations: ['52-22=30', '30-29=1'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 2, 83, 41, 47 ]
48
[ "2*41=82", "83+47=130", "130-82=48" ]
Current State: 48:[2, 83, 41, 47], Operations: [] Exploring Operation: 2*41=82, Resulting Numbers: [83, 47, 82] Generated Node #2: [83, 47, 82] from Operation: 2*41=82 Current State: 48:[83, 47, 82], Operations: ['2*41=82'] Exploring Operation: 83+47=130, Resulting Numbers: [82, 130] Generated Node #3: [82, 130] from Operation: 83+47=130 Current State: 48:[82, 130], Operations: ['2*41=82', '83+47=130'] Exploring Operation: 130-82=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[2, 83, 41, 47], Operations: [] Exploring Operation: 83-47=36, Resulting Numbers: [2, 41, 36] Generated Node #0,0: 48:[2, 41, 36] Operation: 83-47=36 Exploring Operation: 83-2=81, Resulting Numbers: [41, 47, 81] Generated Node #0,1: 48:[41, 47, 81] Operation: 83-2=81 Exploring Operation: 83-41=42, Resulting Numbers: [2, 47, 42] Generated Node #0,2: 48:[2, 47, 42] Operation: 83-41=42 Exploring Operation: 47-41=6, Resulting Numbers: [2, 83, 6] Generated Node #0,3: 48:[2, 83, 6] Operation: 47-41=6 Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[2, 47, 42], Operations: ['83-41=42'] Exploring Operation: 2+42=44, Resulting Numbers: [47, 44] Generated Node #0,2,0: 48:[47, 44] Operation: 2+42=44 Exploring Operation: 47-42=5, Resulting Numbers: [2, 5] Generated Node #0,2,1: 48:[2, 5] Operation: 47-42=5 Exploring Operation: 42/2=21, Resulting Numbers: [47, 21] Generated Node #0,2,2: 48:[47, 21] Operation: 42/2=21 Exploring Operation: 2+47=49, Resulting Numbers: [42, 49] Generated Node #0,2,3: 48:[42, 49] Operation: 2+47=49 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 48:[2, 5], Operations: ['83-41=42', '47-42=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,48 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,48 unequal: No Solution No 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: 48:[47, 21], Operations: ['83-41=42', '42/2=21'] Exploring Operation: 47+21=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 47*21=987, Resulting Numbers: [987] 987,48 unequal: No Solution Exploring Operation: 47-21=26, Resulting Numbers: [26] 26,48 unequal: No Solution No 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: 48:[47, 44], Operations: ['83-41=42', '2+42=44'] Exploring Operation: 47+44=91, Resulting Numbers: [91] 91,48 unequal: No Solution Exploring Operation: 47*44=2068, Resulting Numbers: [2068] 2068,48 unequal: No Solution Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,48 unequal: No Solution No 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: 48:[42, 49], Operations: ['83-41=42', '2+47=49'] Exploring Operation: 42*49=2058, Resulting Numbers: [2058] 2058,48 unequal: No Solution Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 42+49=91, Resulting Numbers: [91] 91,48 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: 48:[2, 41, 36], Operations: ['83-47=36'] Exploring Operation: 41-36=5, Resulting Numbers: [2, 5] Generated Node #0,0,0: 48:[2, 5] Operation: 41-36=5 Exploring Operation: 2+41=43, Resulting Numbers: [36, 43] Generated Node #0,0,1: 48:[36, 43] Operation: 2+41=43 Exploring Operation: 36/2=18, Resulting Numbers: [41, 18] Generated Node #0,0,2: 48:[41, 18] Operation: 36/2=18 Exploring Operation: 2+36=38, Resulting Numbers: [41, 38] Generated Node #0,0,3: 48:[41, 38] Operation: 2+36=38 Moving to Node #0,0,0 Current State: 48:[2, 5], Operations: ['83-47=36', '41-36=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,48 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,48 unequal: No Solution Moving to Node #0,0,2 Current State: 48:[41, 18], Operations: ['83-47=36', '36/2=18'] Exploring Operation: 41-18=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 41*18=738, Resulting Numbers: [738] 738,48 unequal: No Solution Exploring Operation: 41+18=59, Resulting Numbers: [59] 59,48 unequal: No Solution Moving to Node #0,0,3 Current State: 48:[41, 38], Operations: ['83-47=36', '2+36=38'] Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,48 unequal: No Solution Exploring Operation: 41+38=79, Resulting Numbers: [79] 79,48 unequal: No Solution Exploring Operation: 41*38=1558, Resulting Numbers: [1558] 1558,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[36, 43], Operations: ['83-47=36', '2+41=43'] Exploring Operation: 43-36=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 36+43=79, Resulting Numbers: [79] 79,48 unequal: No Solution Exploring Operation: 36*43=1548, Resulting Numbers: [1548] 1548,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 48:[2, 83, 6], Operations: ['47-41=6'] Exploring Operation: 2+6=8, Resulting Numbers: [83, 8] Generated Node #0,3,0: 48:[83, 8] Operation: 2+6=8 Exploring Operation: 83-2=81, Resulting Numbers: [6, 81] Generated Node #0,3,1: 48:[6, 81] Operation: 83-2=81 Exploring Operation: 83-6=77, Resulting Numbers: [2, 77] Generated Node #0,3,2: 48:[2, 77] Operation: 83-6=77 Exploring Operation: 2*6=12, Resulting Numbers: [83, 12] Generated Node #0,3,3: 48:[83, 12] Operation: 2*6=12 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 48:[2, 77], Operations: ['47-41=6', '83-6=77'] Exploring Operation: 2+77=79, Resulting Numbers: [79] 79,48 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 2*77=154, Resulting Numbers: [154] 154,48 unequal: No Solution No 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: 48:[6, 81], Operations: ['47-41=6', '83-2=81'] Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 6+81=87, Resulting Numbers: [87] 87,48 unequal: No Solution Exploring Operation: 6*81=486, Resulting Numbers: [486] 486,48 unequal: No Solution No 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: 48:[83, 8], Operations: ['47-41=6', '2+6=8'] Exploring Operation: 83*8=664, Resulting Numbers: [664] 664,48 unequal: No Solution Exploring Operation: 83+8=91, Resulting Numbers: [91] 91,48 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,48 unequal: No Solution No 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: 48:[83, 12], Operations: ['47-41=6', '2*6=12'] Exploring Operation: 83*12=996, Resulting Numbers: [996] 996,48 unequal: No Solution Exploring Operation: 83+12=95, Resulting Numbers: [95] 95,48 unequal: No Solution Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,48 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: 48:[41, 47, 81], Operations: ['83-2=81'] Exploring Operation: 41+47=88, Resulting Numbers: [81, 88] Generated Node #0,1,0: 48:[81, 88] Operation: 41+47=88 Exploring Operation: 47-41=6, Resulting Numbers: [81, 6] Generated Node #0,1,1: 48:[81, 6] Operation: 47-41=6 Exploring Operation: 81-47=34, Resulting Numbers: [41, 34] Generated Node #0,1,2: 48:[41, 34] Operation: 81-47=34 Exploring Operation: 81-41=40, Resulting Numbers: [47, 40] Generated Node #0,1,3: 48:[47, 40] Operation: 81-41=40 Moving to Node #0,1,3 Current State: 48:[47, 40], Operations: ['83-2=81', '81-41=40'] Exploring Operation: 47-40=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 47+40=87, Resulting Numbers: [87] 87,48 unequal: No Solution Exploring Operation: 47*40=1880, Resulting Numbers: [1880] 1880,48 unequal: No Solution Moving to Node #0,1,2 Current State: 48:[41, 34], Operations: ['83-2=81', '81-47=34'] Exploring Operation: 41+34=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 41*34=1394, Resulting Numbers: [1394] 1394,48 unequal: No Solution Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[81, 6], Operations: ['83-2=81', '47-41=6'] Exploring Operation: 81*6=486, Resulting Numbers: [486] 486,48 unequal: No Solution Exploring Operation: 81+6=87, Resulting Numbers: [87] 87,48 unequal: No Solution Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,48 unequal: No Solution Moving to Node #0,1,0 Current State: 48:[81, 88], Operations: ['83-2=81', '41+47=88'] Exploring Operation: 81+88=169, Resulting Numbers: [169] 169,48 unequal: No Solution Exploring Operation: 88-81=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 81*88=7128, Resulting Numbers: [7128] 7128,48 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
[ 53, 38, 91, 85 ]
84
[ "53+38=91", "91/91=1", "85-1=84" ]
Current State: 84:[53, 38, 91, 85], Operations: [] Exploring Operation: 53+38=91, Resulting Numbers: [91, 85, 91] Generated Node #2: [91, 85, 91] from Operation: 53+38=91 Current State: 84:[91, 85, 91], Operations: ['53+38=91'] Exploring Operation: 91/91=1, Resulting Numbers: [85, 1] Generated Node #3: [85, 1] from Operation: 91/91=1 Current State: 84:[85, 1], Operations: ['53+38=91', '91/91=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[53, 38, 91, 85], Operations: [] Exploring Operation: 53-38=15, Resulting Numbers: [91, 85, 15] Generated Node #0,0: 84:[91, 85, 15] Operation: 53-38=15 Exploring Operation: 53+38=91, Resulting Numbers: [91, 85, 91] Generated Node #0,1: 84:[91, 85, 91] Operation: 53+38=91 Exploring Operation: 91-53=38, Resulting Numbers: [38, 85, 38] Generated Node #0,2: 84:[38, 85, 38] Operation: 91-53=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[91, 85, 15], Operations: ['53-38=15'] Exploring Operation: 91-15=76, Resulting Numbers: [85, 76] Generated Node #0,0,0: 84:[85, 76] Operation: 91-15=76 Exploring Operation: 85-15=70, Resulting Numbers: [91, 70] Generated Node #0,0,1: 84:[91, 70] Operation: 85-15=70 Exploring Operation: 91-85=6, Resulting Numbers: [15, 6] Generated Node #0,0,2: 84:[15, 6] Operation: 91-85=6 Moving to Node #0,0,2 Current State: 84:[15, 6], Operations: ['53-38=15', '91-85=6'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,84 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[85, 76], Operations: ['53-38=15', '91-15=76'] Exploring Operation: 85-76=9, Resulting Numbers: [9] 9,84 unequal: No Solution Exploring Operation: 85*76=6460, Resulting Numbers: [6460] 6460,84 unequal: No Solution Exploring Operation: 85+76=161, Resulting Numbers: [161] 161,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[91, 70], Operations: ['53-38=15', '85-15=70'] Exploring Operation: 91+70=161, Resulting Numbers: [161] 161,84 unequal: No Solution Exploring Operation: 91-70=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 91*70=6370, Resulting Numbers: [6370] 6370,84 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 #0,2 Current State: 84:[38, 85, 38], Operations: ['91-53=38'] Exploring Operation: 38/38=1, Resulting Numbers: [85, 1] Generated Node #0,2,0: 84:[85, 1] Operation: 38/38=1 Exploring Operation: 85-38=47, Resulting Numbers: [38, 47] Generated Node #0,2,1: 84:[38, 47] Operation: 85-38=47 Exploring Operation: 38-38=0, Resulting Numbers: [85, 0] Generated Node #0,2,2: 84:[85, 0] Operation: 38-38=0 Moving to Node #0,2,0 Current State: 84:[85, 1], Operations: ['91-53=38', '38/38=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[53, 38, 91, 85], Operations: [] Exploring Operation: 91-53=38, Resulting Numbers: [38, 85, 38] Generated Node #0,2: 84:[38, 85, 38] Operation: 91-53=38 Moving to Node #0,2 Current State: 84:[38, 85, 38], Operations: ['91-53=38'] Exploring Operation: 38/38=1, Resulting Numbers: [85, 1] Generated Node #0,2,0: 84:[85, 1] Operation: 38/38=1 Moving to Node #0,2,0 Current State: 84:[85, 1], Operations: ['91-53=38', '38/38=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 28, 68, 78, 19 ]
99
[ "68-28=40", "78-19=59", "40+59=99" ]
Current State: 99:[28, 68, 78, 19], Operations: [] Exploring Operation: 68-28=40, Resulting Numbers: [78, 19, 40] Generated Node #2: [78, 19, 40] from Operation: 68-28=40 Current State: 99:[78, 19, 40], Operations: ['68-28=40'] Exploring Operation: 78-19=59, Resulting Numbers: [40, 59] Generated Node #3: [40, 59] from Operation: 78-19=59 Current State: 99:[40, 59], Operations: ['68-28=40', '78-19=59'] Exploring Operation: 40+59=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[28, 68, 78, 19], Operations: [] Exploring Operation: 78-68=10, Resulting Numbers: [28, 19, 10] Generated Node #0,0: 99:[28, 19, 10] Operation: 78-68=10 Exploring Operation: 68+19=87, Resulting Numbers: [28, 78, 87] Generated Node #0,1: 99:[28, 78, 87] Operation: 68+19=87 Exploring Operation: 28+68=96, Resulting Numbers: [78, 19, 96] Generated Node #0,2: 99:[78, 19, 96] Operation: 28+68=96 Exploring Operation: 68-28=40, Resulting Numbers: [78, 19, 40] Generated Node #0,3: 99:[78, 19, 40] Operation: 68-28=40 Exploring Operation: 78+19=97, Resulting Numbers: [28, 68, 97] Generated Node #0,4: 99:[28, 68, 97] Operation: 78+19=97 Moving to Node #0,0 Current State: 99:[28, 19, 10], Operations: ['78-68=10'] Exploring Operation: 28-19=9, Resulting Numbers: [10, 9] Generated Node #0,0,0: 99:[10, 9] Operation: 28-19=9 Exploring Operation: 19-10=9, Resulting Numbers: [28, 9] Generated Node #0,0,1: 99:[28, 9] Operation: 19-10=9 Exploring Operation: 28+10=38, Resulting Numbers: [19, 38] Generated Node #0,0,2: 99:[19, 38] Operation: 28+10=38 Exploring Operation: 19+10=29, Resulting Numbers: [28, 29] Generated Node #0,0,3: 99:[28, 29] Operation: 19+10=29 Exploring Operation: 28+19=47, Resulting Numbers: [10, 47] Generated Node #0,0,4: 99:[10, 47] Operation: 28+19=47 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[10, 9], Operations: ['78-68=10', '28-19=9'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,99 unequal: No Solution Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[28, 9], Operations: ['78-68=10', '19-10=9'] Exploring Operation: 28+9=37, Resulting Numbers: [37] 37,99 unequal: No Solution Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,99 unequal: No Solution Exploring Operation: 28*9=252, Resulting Numbers: [252] 252,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 99:[28, 29], Operations: ['78-68=10', '19+10=29'] Exploring Operation: 28*29=812, Resulting Numbers: [812] 812,99 unequal: No Solution Exploring Operation: 28+29=57, Resulting Numbers: [57] 57,99 unequal: No Solution Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 99:[19, 38], Operations: ['78-68=10', '28+10=38'] Exploring Operation: 19*38=722, Resulting Numbers: [722] 722,99 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,99 unequal: No Solution Exploring Operation: 19+38=57, Resulting Numbers: [57] 57,99 unequal: No Solution Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 99:[10, 47], Operations: ['78-68=10', '28+19=47'] Exploring Operation: 10*47=470, Resulting Numbers: [470] 470,99 unequal: No Solution Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,99 unequal: No Solution Exploring Operation: 10+47=57, Resulting Numbers: [57] 57,99 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: 99:[78, 19, 96], Operations: ['28+68=96'] Exploring Operation: 78+19=97, Resulting Numbers: [96, 97] Generated Node #0,2,0: 99:[96, 97] Operation: 78+19=97 Exploring Operation: 19+96=115, Resulting Numbers: [78, 115] Generated Node #0,2,1: 99:[78, 115] Operation: 19+96=115 Exploring Operation: 96-19=77, Resulting Numbers: [78, 77] Generated Node #0,2,2: 99:[78, 77] Operation: 96-19=77 Exploring Operation: 78-19=59, Resulting Numbers: [96, 59] Generated Node #0,2,3: 99:[96, 59] Operation: 78-19=59 Exploring Operation: 96-78=18, Resulting Numbers: [19, 18] Generated Node #0,2,4: 99:[19, 18] Operation: 96-78=18 Moving to Node #0,3 Current State: 99:[78, 19, 40], Operations: ['68-28=40'] Exploring Operation: 78+19=97, Resulting Numbers: [40, 97] Generated Node #0,3,0: 99:[40, 97] Operation: 78+19=97 Exploring Operation: 78+40=118, Resulting Numbers: [19, 118] Generated Node #0,3,1: 99:[19, 118] Operation: 78+40=118 Exploring Operation: 78-40=38, Resulting Numbers: [19, 38] Generated Node #0,3,2: 99:[19, 38] Operation: 78-40=38 Exploring Operation: 40-19=21, Resulting Numbers: [78, 21] Generated Node #0,3,3: 99:[78, 21] Operation: 40-19=21 Exploring Operation: 78-19=59, Resulting Numbers: [40, 59] Generated Node #0,3,4: 99:[40, 59] Operation: 78-19=59 Moving to Node #0,1 Current State: 99:[28, 78, 87], Operations: ['68+19=87'] Exploring Operation: 78-28=50, Resulting Numbers: [87, 50] Generated Node #0,1,0: 99:[87, 50] Operation: 78-28=50 Exploring Operation: 87-28=59, Resulting Numbers: [78, 59] Generated Node #0,1,1: 99:[78, 59] Operation: 87-28=59 Exploring Operation: 28+78=106, Resulting Numbers: [87, 106] Generated Node #0,1,2: 99:[87, 106] Operation: 28+78=106 Exploring Operation: 28+87=115, Resulting Numbers: [78, 115] Generated Node #0,1,3: 99:[78, 115] Operation: 28+87=115 Exploring Operation: 87-78=9, Resulting Numbers: [28, 9] Generated Node #0,1,4: 99:[28, 9] Operation: 87-78=9 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 99:[28, 9], Operations: ['68+19=87', '87-78=9'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,99 unequal: No Solution Exploring Operation: 28+9=37, Resulting Numbers: [37] 37,99 unequal: No Solution Exploring Operation: 28*9=252, Resulting Numbers: [252] 252,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 99:[87, 106], Operations: ['68+19=87', '28+78=106'] Exploring Operation: 106-87=19, Resulting Numbers: [19] 19,99 unequal: No Solution Exploring Operation: 87+106=193, Resulting Numbers: [193] 193,99 unequal: No Solution Exploring Operation: 87*106=9222, Resulting Numbers: [9222] 9222,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[87, 50], Operations: ['68+19=87', '78-28=50'] Exploring Operation: 87+50=137, Resulting Numbers: [137] 137,99 unequal: No Solution Exploring Operation: 87-50=37, Resulting Numbers: [37] 37,99 unequal: No Solution Exploring Operation: 87*50=4350, Resulting Numbers: [4350] 4350,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 99:[78, 115], Operations: ['68+19=87', '28+87=115'] Exploring Operation: 78+115=193, Resulting Numbers: [193] 193,99 unequal: No Solution Exploring Operation: 115-78=37, Resulting Numbers: [37] 37,99 unequal: No Solution Exploring Operation: 78*115=8970, Resulting Numbers: [8970] 8970,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[78, 59], Operations: ['68+19=87', '87-28=59'] Exploring Operation: 78-59=19, Resulting Numbers: [19] 19,99 unequal: No Solution Exploring Operation: 78+59=137, Resulting Numbers: [137] 137,99 unequal: No Solution Exploring Operation: 78*59=4602, Resulting Numbers: [4602] 4602,99 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: 99:[28, 68, 97], Operations: ['78+19=97'] Exploring Operation: 97-68=29, Resulting Numbers: [28, 29] Generated Node #0,4,0: 99:[28, 29] Operation: 97-68=29 Exploring Operation: 28+97=125, Resulting Numbers: [68, 125] Generated Node #0,4,1: 99:[68, 125] Operation: 28+97=125 Exploring Operation: 97-28=69, Resulting Numbers: [68, 69] Generated Node #0,4,2: 99:[68, 69] Operation: 97-28=69 Exploring Operation: 68-28=40, Resulting Numbers: [97, 40] Generated Node #0,4,3: 99:[97, 40] Operation: 68-28=40 Exploring Operation: 28+68=96, Resulting Numbers: [97, 96] Generated Node #0,4,4: 99:[97, 96] Operation: 28+68=96 Moving to Node #0,2,0 Current State: 99:[96, 97], Operations: ['28+68=96', '78+19=97'] Exploring Operation: 96*97=9312, Resulting Numbers: [9312] 9312,99 unequal: No Solution Exploring Operation: 96+97=193, Resulting Numbers: [193] 193,99 unequal: No Solution Exploring Operation: 97-96=1, Resulting Numbers: [1] 1,99 unequal: No Solution Moving to Node #0,4,4 Current State: 99:[97, 96], Operations: ['78+19=97', '28+68=96'] Exploring Operation: 97-96=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 97*96=9312, Resulting Numbers: [9312] 9312,99 unequal: No Solution Exploring Operation: 97+96=193, Resulting Numbers: [193] 193,99 unequal: No Solution Moving to Node #0,3,0 Current State: 99:[40, 97], Operations: ['68-28=40', '78+19=97'] Exploring Operation: 97-40=57, Resulting Numbers: [57] 57,99 unequal: No Solution Exploring Operation: 40+97=137, Resulting Numbers: [137] 137,99 unequal: No Solution Exploring Operation: 40*97=3880, Resulting Numbers: [3880] 3880,99 unequal: No Solution Moving to Node #0,4,0 Current State: 99:[28, 29], Operations: ['78+19=97', '97-68=29'] Exploring Operation: 28+29=57, Resulting Numbers: [57] 57,99 unequal: No Solution Exploring Operation: 28*29=812, Resulting Numbers: [812] 812,99 unequal: No Solution Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,99 unequal: No Solution Moving to Node #0,4,3 Current State: 99:[97, 40], Operations: ['78+19=97', '68-28=40'] Exploring Operation: 97+40=137, Resulting Numbers: [137] 137,99 unequal: No Solution Exploring Operation: 97*40=3880, Resulting Numbers: [3880] 3880,99 unequal: No Solution Exploring Operation: 97-40=57, Resulting Numbers: [57] 57,99 unequal: No Solution Moving to Node #0,3,2 Current State: 99:[19, 38], Operations: ['68-28=40', '78-40=38'] Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,99 unequal: No Solution Exploring Operation: 19+38=57, Resulting Numbers: [57] 57,99 unequal: No Solution Exploring Operation: 19*38=722, Resulting Numbers: [722] 722,99 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,99 unequal: No Solution Moving to Node #0,2,4 Current State: 99:[19, 18], Operations: ['28+68=96', '96-78=18'] Exploring Operation: 19+18=37, Resulting Numbers: [37] 37,99 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 19*18=342, Resulting Numbers: [342] 342,99 unequal: No Solution Moving to Node #0,3,1 Current State: 99:[19, 118], Operations: ['68-28=40', '78+40=118'] Exploring Operation: 19+118=137, Resulting Numbers: [137] 137,99 unequal: No Solution Exploring Operation: 19*118=2242, Resulting Numbers: [2242] 2242,99 unequal: No Solution Exploring Operation: 118-19=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[28, 68, 78, 19], Operations: [] Exploring Operation: 68-28=40, Resulting Numbers: [78, 19, 40] Generated Node #0,3: 99:[78, 19, 40] Operation: 68-28=40 Moving to Node #0,3 Current State: 99:[78, 19, 40], Operations: ['68-28=40'] Exploring Operation: 78+40=118, Resulting Numbers: [19, 118] Generated Node #0,3,1: 99:[19, 118] Operation: 78+40=118 Moving to Node #0,3,1 Current State: 99:[19, 118], Operations: ['68-28=40', '78+40=118'] Exploring Operation: 118-19=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
0.921875
hs_5
mult_heuristic
[ 63, 32, 13, 11 ]
94
[ "13-11=2", "63*2=126", "126-32=94" ]
Current State: 94:[63, 32, 13, 11], Operations: [] Exploring Operation: 13-11=2, Resulting Numbers: [63, 32, 2] Generated Node #2: [63, 32, 2] from Operation: 13-11=2 Current State: 94:[63, 32, 2], Operations: ['13-11=2'] Exploring Operation: 63*2=126, Resulting Numbers: [32, 126] Generated Node #3: [32, 126] from Operation: 63*2=126 Current State: 94:[32, 126], Operations: ['13-11=2', '63*2=126'] Exploring Operation: 126-32=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[63, 32, 13, 11], Operations: [] Exploring Operation: 32+13=45, Resulting Numbers: [63, 11, 45] Generated Node #0,0: 94:[63, 11, 45] Operation: 32+13=45 Exploring Operation: 63+32=95, Resulting Numbers: [13, 11, 95] Generated Node #0,1: 94:[13, 11, 95] Operation: 63+32=95 Exploring Operation: 63-13=50, Resulting Numbers: [32, 11, 50] Generated Node #0,2: 94:[32, 11, 50] Operation: 63-13=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[13, 11, 95], Operations: ['63+32=95'] Exploring Operation: 95-11=84, Resulting Numbers: [13, 84] Generated Node #0,1,0: 94:[13, 84] Operation: 95-11=84 Exploring Operation: 13-11=2, Resulting Numbers: [95, 2] Generated Node #0,1,1: 94:[95, 2] Operation: 13-11=2 Exploring Operation: 95-13=82, Resulting Numbers: [11, 82] Generated Node #0,1,2: 94:[11, 82] Operation: 95-13=82 Moving to Node #0,1,1 Current State: 94:[95, 2], Operations: ['63+32=95', '13-11=2'] Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,94 unequal: No Solution Exploring Operation: 95*2=190, Resulting Numbers: [190] 190,94 unequal: No Solution Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[13, 84], Operations: ['63+32=95', '95-11=84'] Exploring Operation: 13*84=1092, Resulting Numbers: [1092] 1092,94 unequal: No Solution Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,94 unequal: No Solution Exploring Operation: 13+84=97, Resulting Numbers: [97] 97,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[11, 82], Operations: ['63+32=95', '95-13=82'] Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,94 unequal: No Solution Exploring Operation: 11+82=93, Resulting Numbers: [93] 93,94 unequal: No Solution Exploring Operation: 11*82=902, Resulting Numbers: [902] 902,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[63, 11, 45], Operations: ['32+13=45'] Exploring Operation: 63-11=52, Resulting Numbers: [45, 52] Generated Node #0,0,0: 94:[45, 52] Operation: 63-11=52 Exploring Operation: 63+45=108, Resulting Numbers: [11, 108] Generated Node #0,0,1: 94:[11, 108] Operation: 63+45=108 Exploring Operation: 63+11=74, Resulting Numbers: [45, 74] Generated Node #0,0,2: 94:[45, 74] Operation: 63+11=74 Moving to Node #0,0,0 Current State: 94:[45, 52], Operations: ['32+13=45', '63-11=52'] Exploring Operation: 45+52=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 45*52=2340, Resulting Numbers: [2340] 2340,94 unequal: No Solution Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[45, 74], Operations: ['32+13=45', '63+11=74'] Exploring Operation: 45+74=119, Resulting Numbers: [119] 119,94 unequal: No Solution Exploring Operation: 45*74=3330, Resulting Numbers: [3330] 3330,94 unequal: No Solution Exploring Operation: 74-45=29, Resulting Numbers: [29] 29,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[11, 108], Operations: ['32+13=45', '63+45=108'] Exploring Operation: 11+108=119, Resulting Numbers: [119] 119,94 unequal: No Solution Exploring Operation: 108-11=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 11*108=1188, Resulting Numbers: [1188] 1188,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[32, 11, 50], Operations: ['63-13=50'] Exploring Operation: 32+50=82, Resulting Numbers: [11, 82] Generated Node #0,2,0: 94:[11, 82] Operation: 32+50=82 Exploring Operation: 32-11=21, Resulting Numbers: [50, 21] Generated Node #0,2,1: 94:[50, 21] Operation: 32-11=21 Exploring Operation: 32+11=43, Resulting Numbers: [50, 43] Generated Node #0,2,2: 94:[50, 43] Operation: 32+11=43 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 94:[50, 43], Operations: ['63-13=50', '32+11=43'] Exploring Operation: 50+43=93, Resulting Numbers: [93] 93,94 unequal: No Solution Exploring Operation: 50*43=2150, Resulting Numbers: [2150] 2150,94 unequal: No Solution Exploring Operation: 50-43=7, Resulting Numbers: [7] 7,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 94:[11, 82], Operations: ['63-13=50', '32+50=82'] Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,94 unequal: No Solution Exploring Operation: 11*82=902, Resulting Numbers: [902] 902,94 unequal: No Solution Exploring Operation: 11+82=93, Resulting Numbers: [93] 93,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 94:[50, 21], Operations: ['63-13=50', '32-11=21'] Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,94 unequal: No Solution Exploring Operation: 50*21=1050, Resulting Numbers: [1050] 1050,94 unequal: No Solution Exploring Operation: 50+21=71, Resulting Numbers: [71] 71,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 70, 6, 8, 60 ]
60
[ "70*6=420", "8*60=480", "480-420=60" ]
Current State: 60:[70, 6, 8, 60], Operations: [] Exploring Operation: 70*6=420, Resulting Numbers: [8, 60, 420] Generated Node #2: [8, 60, 420] from Operation: 70*6=420 Current State: 60:[8, 60, 420], Operations: ['70*6=420'] Exploring Operation: 8*60=480, Resulting Numbers: [420, 480] Generated Node #3: [420, 480] from Operation: 8*60=480 Current State: 60:[420, 480], Operations: ['70*6=420', '8*60=480'] Exploring Operation: 480-420=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[70, 6, 8, 60], Operations: [] Exploring Operation: 70-8=62, Resulting Numbers: [6, 60, 62] Generated Node #0,0: 60:[6, 60, 62] Operation: 70-8=62 Exploring Operation: 70-60=10, Resulting Numbers: [6, 8, 10] Generated Node #0,1: 60:[6, 8, 10] Operation: 70-60=10 Exploring Operation: 70-6=64, Resulting Numbers: [8, 60, 64] Generated Node #0,2: 60:[8, 60, 64] Operation: 70-6=64 Moving to Node #0,0 Current State: 60:[6, 60, 62], Operations: ['70-8=62'] Exploring Operation: 62-6=56, Resulting Numbers: [60, 56] Generated Node #0,0,0: 60:[60, 56] Operation: 62-6=56 Exploring Operation: 60/6=10, Resulting Numbers: [62, 10] Generated Node #0,0,1: 60:[62, 10] Operation: 60/6=10 Exploring Operation: 62-60=2, Resulting Numbers: [6, 2] Generated Node #0,0,2: 60:[6, 2] Operation: 62-60=2 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[6, 2], Operations: ['70-8=62', '62-60=2'] Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[62, 10], Operations: ['70-8=62', '60/6=10'] Exploring Operation: 62+10=72, Resulting Numbers: [72] 72,60 unequal: No Solution Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,60 unequal: No Solution Exploring Operation: 62*10=620, Resulting Numbers: [620] 620,60 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 #0,0,0 Current State: 60:[60, 56], Operations: ['70-8=62', '62-6=56'] Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 60*56=3360, Resulting Numbers: [3360] 3360,60 unequal: No Solution Exploring Operation: 60+56=116, Resulting Numbers: [116] 116,60 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: 60:[6, 8, 10], Operations: ['70-60=10'] Exploring Operation: 8-6=2, Resulting Numbers: [10, 2] Generated Node #0,1,0: 60:[10, 2] Operation: 8-6=2 Exploring Operation: 6+8=14, Resulting Numbers: [10, 14] Generated Node #0,1,1: 60:[10, 14] Operation: 6+8=14 Exploring Operation: 10-8=2, Resulting Numbers: [6, 2] Generated Node #0,1,2: 60:[6, 2] Operation: 10-8=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[10, 2], Operations: ['70-60=10', '8-6=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,60 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,60 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 #0,1,2 Current State: 60:[6, 2], Operations: ['70-60=10', '10-8=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,60 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 #0,1,1 Current State: 60:[10, 14], Operations: ['70-60=10', '6+8=14'] Exploring Operation: 10*14=140, Resulting Numbers: [140] 140,60 unequal: No Solution Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,60 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,60 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: 60:[8, 60, 64], Operations: ['70-6=64'] Exploring Operation: 64/8=8, Resulting Numbers: [60, 8] Generated Node #0,2,0: 60:[60, 8] Operation: 64/8=8 Exploring Operation: 64-60=4, Resulting Numbers: [8, 4] Generated Node #0,2,1: 60:[8, 4] Operation: 64-60=4 Exploring Operation: 64-8=56, Resulting Numbers: [60, 56] Generated Node #0,2,2: 60:[60, 56] Operation: 64-8=56 Moving to Node #0,2,0 Current State: 60:[60, 8], Operations: ['70-6=64', '64/8=8'] Exploring Operation: 60*8=480, Resulting Numbers: [480] 480,60 unequal: No Solution Exploring Operation: 60-8=52, Resulting Numbers: [52] 52,60 unequal: No Solution Exploring Operation: 60+8=68, Resulting Numbers: [68] 68,60 unequal: No Solution Moving to Node #0,2,1 Current State: 60:[8, 4], Operations: ['70-6=64', '64-60=4'] Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,60 unequal: No Solution Moving to Node #0,2,2 Current State: 60:[60, 56], Operations: ['70-6=64', '64-8=56'] Exploring Operation: 60+56=116, Resulting Numbers: [116] 116,60 unequal: No Solution Exploring Operation: 60*56=3360, Resulting Numbers: [3360] 3360,60 unequal: No Solution Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,60 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 58, 52, 56, 36 ]
14
[ "58-52=6", "56-36=20", "20-6=14" ]
Current State: 14:[58, 52, 56, 36], Operations: [] Exploring Operation: 58-52=6, Resulting Numbers: [56, 36, 6] Generated Node #2: [56, 36, 6] from Operation: 58-52=6 Current State: 14:[56, 36, 6], Operations: ['58-52=6'] Exploring Operation: 56-36=20, Resulting Numbers: [6, 20] Generated Node #3: [6, 20] from Operation: 56-36=20 Current State: 14:[6, 20], Operations: ['58-52=6', '56-36=20'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[58, 52, 56, 36], Operations: [] Exploring Operation: 56-52=4, Resulting Numbers: [58, 36, 4] Generated Node #0,0: 14:[58, 36, 4] Operation: 56-52=4 Exploring Operation: 58-52=6, Resulting Numbers: [56, 36, 6] Generated Node #0,1: 14:[56, 36, 6] Operation: 58-52=6 Exploring Operation: 58-56=2, Resulting Numbers: [52, 36, 2] Generated Node #0,2: 14:[52, 36, 2] Operation: 58-56=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[52, 36, 2], Operations: ['58-56=2'] Exploring Operation: 52/2=26, Resulting Numbers: [36, 26] Generated Node #0,2,0: 14:[36, 26] Operation: 52/2=26 Exploring Operation: 52-36=16, Resulting Numbers: [2, 16] Generated Node #0,2,1: 14:[2, 16] Operation: 52-36=16 Exploring Operation: 36/2=18, Resulting Numbers: [52, 18] Generated Node #0,2,2: 14:[52, 18] Operation: 36/2=18 Moving to Node #0,2,1 Current State: 14:[2, 16], Operations: ['58-56=2', '52-36=16'] Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[58, 52, 56, 36], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [52, 36, 2] Generated Node #0,2: 14:[52, 36, 2] Operation: 58-56=2 Moving to Node #0,2 Current State: 14:[52, 36, 2], Operations: ['58-56=2'] Exploring Operation: 52-36=16, Resulting Numbers: [2, 16] Generated Node #0,2,1: 14:[2, 16] Operation: 52-36=16 Moving to Node #0,2,1 Current State: 14:[2, 16], Operations: ['58-56=2', '52-36=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 99, 13, 46, 89 ]
49
[ "99-13=86", "46+89=135", "135-86=49" ]
Current State: 49:[99, 13, 46, 89], Operations: [] Exploring Operation: 99-13=86, Resulting Numbers: [46, 89, 86] Generated Node #2: [46, 89, 86] from Operation: 99-13=86 Current State: 49:[46, 89, 86], Operations: ['99-13=86'] Exploring Operation: 46+89=135, Resulting Numbers: [86, 135] Generated Node #3: [86, 135] from Operation: 46+89=135 Current State: 49:[86, 135], Operations: ['99-13=86', '46+89=135'] Exploring Operation: 135-86=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[99, 13, 46, 89], Operations: [] Exploring Operation: 99-89=10, Resulting Numbers: [13, 46, 10] Generated Node #0,0: 49:[13, 46, 10] Operation: 99-89=10 Exploring Operation: 99-46=53, Resulting Numbers: [13, 89, 53] Generated Node #0,1: 49:[13, 89, 53] Operation: 99-46=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[13, 46, 10], Operations: ['99-89=10'] Exploring Operation: 13+46=59, Resulting Numbers: [10, 59] Generated Node #0,0,0: 49:[10, 59] Operation: 13+46=59 Exploring Operation: 13-10=3, Resulting Numbers: [46, 3] Generated Node #0,0,1: 49:[46, 3] Operation: 13-10=3 Moving to Node #0,0,1 Current State: 49:[46, 3], Operations: ['99-89=10', '13-10=3'] Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,49 unequal: No Solution Exploring Operation: 46+3=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[99, 13, 46, 89], Operations: [] Exploring Operation: 99-89=10, Resulting Numbers: [13, 46, 10] Generated Node #0,0: 49:[13, 46, 10] Operation: 99-89=10 Moving to Node #0,0 Current State: 49:[13, 46, 10], Operations: ['99-89=10'] Exploring Operation: 13-10=3, Resulting Numbers: [46, 3] Generated Node #0,0,1: 49:[46, 3] Operation: 13-10=3 Moving to Node #0,0,1 Current State: 49:[46, 3], Operations: ['99-89=10', '13-10=3'] Exploring Operation: 46+3=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 31, 97, 60, 32 ]
37
[ "32-31=1", "97-60=37", "1*37=37" ]
Current State: 37:[31, 97, 60, 32], Operations: [] Exploring Operation: 32-31=1, Resulting Numbers: [97, 60, 1] Generated Node #2: [97, 60, 1] from Operation: 32-31=1 Current State: 37:[97, 60, 1], Operations: ['32-31=1'] Exploring Operation: 97-60=37, Resulting Numbers: [1, 37] Generated Node #3: [1, 37] from Operation: 97-60=37 Current State: 37:[1, 37], Operations: ['32-31=1', '97-60=37'] Exploring Operation: 1*37=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[31, 97, 60, 32], Operations: [] Exploring Operation: 97-60=37, Resulting Numbers: [31, 32, 37] Generated Node #0,0: 37:[31, 32, 37] Operation: 97-60=37 Exploring Operation: 97-31=66, Resulting Numbers: [60, 32, 66] Generated Node #0,1: 37:[60, 32, 66] Operation: 97-31=66 Exploring Operation: 97-32=65, Resulting Numbers: [31, 60, 65] Generated Node #0,2: 37:[31, 60, 65] Operation: 97-32=65 Exploring Operation: 60-31=29, Resulting Numbers: [97, 32, 29] Generated Node #0,3: 37:[97, 32, 29] Operation: 60-31=29 Moving to Node #0,0 Current State: 37:[31, 32, 37], Operations: ['97-60=37'] Exploring Operation: 32-31=1, Resulting Numbers: [37, 1] Generated Node #0,0,0: 37:[37, 1] Operation: 32-31=1 Exploring Operation: 31+32=63, Resulting Numbers: [37, 63] Generated Node #0,0,1: 37:[37, 63] Operation: 31+32=63 Exploring Operation: 31+37=68, Resulting Numbers: [32, 68] Generated Node #0,0,2: 37:[32, 68] Operation: 31+37=68 Exploring Operation: 37-31=6, Resulting Numbers: [32, 6] Generated Node #0,0,3: 37:[32, 6] Operation: 37-31=6 Moving to Node #0,2 Current State: 37:[31, 60, 65], Operations: ['97-32=65'] Exploring Operation: 65-60=5, Resulting Numbers: [31, 5] Generated Node #0,2,0: 37:[31, 5] Operation: 65-60=5 Exploring Operation: 65-31=34, Resulting Numbers: [60, 34] Generated Node #0,2,1: 37:[60, 34] Operation: 65-31=34 Exploring Operation: 31+60=91, Resulting Numbers: [65, 91] Generated Node #0,2,2: 37:[65, 91] Operation: 31+60=91 Exploring Operation: 60-31=29, Resulting Numbers: [65, 29] Generated Node #0,2,3: 37:[65, 29] Operation: 60-31=29 Moving to Node #0,1 Current State: 37:[60, 32, 66], Operations: ['97-31=66'] Exploring Operation: 60+32=92, Resulting Numbers: [66, 92] Generated Node #0,1,0: 37:[66, 92] Operation: 60+32=92 Exploring Operation: 60-32=28, Resulting Numbers: [66, 28] Generated Node #0,1,1: 37:[66, 28] Operation: 60-32=28 Exploring Operation: 66-32=34, Resulting Numbers: [60, 34] Generated Node #0,1,2: 37:[60, 34] Operation: 66-32=34 Exploring Operation: 66-60=6, Resulting Numbers: [32, 6] Generated Node #0,1,3: 37:[32, 6] Operation: 66-60=6 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 37:[60, 34], Operations: ['97-31=66', '66-32=34'] Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 60+34=94, Resulting Numbers: [94] 94,37 unequal: No Solution Exploring Operation: 60*34=2040, Resulting Numbers: [2040] 2040,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 37:[32, 6], Operations: ['97-31=66', '66-60=6'] Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 37:[66, 28], Operations: ['97-31=66', '60-32=28'] Exploring Operation: 66*28=1848, Resulting Numbers: [1848] 1848,37 unequal: No Solution Exploring Operation: 66+28=94, Resulting Numbers: [94] 94,37 unequal: No Solution Exploring Operation: 66-28=38, Resulting Numbers: [38] 38,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[66, 92], Operations: ['97-31=66', '60+32=92'] Exploring Operation: 66*92=6072, Resulting Numbers: [6072] 6072,37 unequal: No Solution Exploring Operation: 66+92=158, Resulting Numbers: [158] 158,37 unequal: No Solution Exploring Operation: 92-66=26, Resulting Numbers: [26] 26,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 37:[97, 32, 29], Operations: ['60-31=29'] Exploring Operation: 97-32=65, Resulting Numbers: [29, 65] Generated Node #0,3,0: 37:[29, 65] Operation: 97-32=65 Exploring Operation: 32+29=61, Resulting Numbers: [97, 61] Generated Node #0,3,1: 37:[97, 61] Operation: 32+29=61 Exploring Operation: 97+29=126, Resulting Numbers: [32, 126] Generated Node #0,3,2: 37:[32, 126] Operation: 97+29=126 Exploring Operation: 97-29=68, Resulting Numbers: [32, 68] Generated Node #0,3,3: 37:[32, 68] Operation: 97-29=68 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 37:[29, 65], Operations: ['60-31=29', '97-32=65'] Exploring Operation: 29+65=94, Resulting Numbers: [94] 94,37 unequal: No Solution Exploring Operation: 65-29=36, Resulting Numbers: [36] 36,37 unequal: No Solution Exploring Operation: 29*65=1885, Resulting Numbers: [1885] 1885,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 37:[32, 68], Operations: ['60-31=29', '97-29=68'] Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,37 unequal: No Solution Exploring Operation: 32*68=2176, Resulting Numbers: [2176] 2176,37 unequal: No Solution Exploring Operation: 32+68=100, Resulting Numbers: [100] 100,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 37:[97, 61], Operations: ['60-31=29', '32+29=61'] Exploring Operation: 97+61=158, Resulting Numbers: [158] 158,37 unequal: No Solution Exploring Operation: 97-61=36, Resulting Numbers: [36] 36,37 unequal: No Solution Exploring Operation: 97*61=5917, Resulting Numbers: [5917] 5917,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 37:[32, 126], Operations: ['60-31=29', '97+29=126'] Exploring Operation: 126-32=94, Resulting Numbers: [94] 94,37 unequal: No Solution Exploring Operation: 32*126=4032, Resulting Numbers: [4032] 4032,37 unequal: No Solution Exploring Operation: 32+126=158, Resulting Numbers: [158] 158,37 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: 37:[37, 63], Operations: ['97-60=37', '31+32=63'] Exploring Operation: 37+63=100, Resulting Numbers: [100] 100,37 unequal: No Solution Exploring Operation: 37*63=2331, Resulting Numbers: [2331] 2331,37 unequal: No Solution Exploring Operation: 63-37=26, Resulting Numbers: [26] 26,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[60, 34], Operations: ['97-32=65', '65-31=34'] Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 60*34=2040, Resulting Numbers: [2040] 2040,37 unequal: No Solution Exploring Operation: 60+34=94, Resulting Numbers: [94] 94,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[32, 68], Operations: ['97-60=37', '31+37=68'] Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,37 unequal: No Solution Exploring Operation: 32+68=100, Resulting Numbers: [100] 100,37 unequal: No Solution Exploring Operation: 32*68=2176, Resulting Numbers: [2176] 2176,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[65, 29], Operations: ['97-32=65', '60-31=29'] Exploring Operation: 65+29=94, Resulting Numbers: [94] 94,37 unequal: No Solution Exploring Operation: 65*29=1885, Resulting Numbers: [1885] 1885,37 unequal: No Solution Exploring Operation: 65-29=36, Resulting Numbers: [36] 36,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[37, 1], Operations: ['97-60=37', '32-31=1'] Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[31, 97, 60, 32], Operations: [] Exploring Operation: 97-60=37, Resulting Numbers: [31, 32, 37] Generated Node #0,0: 37:[31, 32, 37] Operation: 97-60=37 Moving to Node #0,0 Current State: 37:[31, 32, 37], Operations: ['97-60=37'] Exploring Operation: 32-31=1, Resulting Numbers: [37, 1] Generated Node #0,0,0: 37:[37, 1] Operation: 32-31=1 Moving to Node #0,0,0 Current State: 37:[37, 1], Operations: ['97-60=37', '32-31=1'] Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
0.947049
hs_4
sum_heuristic
[ 8, 2, 82, 26 ]
63
[ "82-8=74", "74/2=37", "26+37=63" ]
Current State: 63:[8, 2, 82, 26], Operations: [] Exploring Operation: 82-8=74, Resulting Numbers: [2, 26, 74] Generated Node #2: [2, 26, 74] from Operation: 82-8=74 Current State: 63:[2, 26, 74], Operations: ['82-8=74'] Exploring Operation: 74/2=37, Resulting Numbers: [26, 37] Generated Node #3: [26, 37] from Operation: 74/2=37 Current State: 63:[26, 37], Operations: ['82-8=74', '74/2=37'] Exploring Operation: 26+37=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[8, 2, 82, 26], Operations: [] Exploring Operation: 82-8=74, Resulting Numbers: [2, 26, 74] Generated Node #0,0: 63:[2, 26, 74] Operation: 82-8=74 Exploring Operation: 26-8=18, Resulting Numbers: [2, 82, 18] Generated Node #0,1: 63:[2, 82, 18] Operation: 26-8=18 Exploring Operation: 82-26=56, Resulting Numbers: [8, 2, 56] Generated Node #0,2: 63:[8, 2, 56] Operation: 82-26=56 Start Sub Search at level 1: Moving to Node #0,2 Current State: 63:[8, 2, 56], Operations: ['82-26=56'] Exploring Operation: 8+56=64, Resulting Numbers: [2, 64] Generated Node #0,2,0: 63:[2, 64] Operation: 8+56=64 Exploring Operation: 56/8=7, Resulting Numbers: [2, 7] Generated Node #0,2,1: 63:[2, 7] Operation: 56/8=7 Exploring Operation: 2+56=58, Resulting Numbers: [8, 58] Generated Node #0,2,2: 63:[8, 58] Operation: 2+56=58 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 63:[2, 7], Operations: ['82-26=56', '56/8=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,63 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,63 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 63:[2, 64], Operations: ['82-26=56', '8+56=64'] Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,63 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,63 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 63:[8, 58], Operations: ['82-26=56', '2+56=58'] Exploring Operation: 8+58=66, Resulting Numbers: [66] 66,63 unequal: No Solution Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,63 unequal: No Solution Exploring Operation: 8*58=464, Resulting Numbers: [464] 464,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[2, 26, 74], Operations: ['82-8=74'] Exploring Operation: 26-2=24, Resulting Numbers: [74, 24] Generated Node #0,0,0: 63:[74, 24] Operation: 26-2=24 Exploring Operation: 74-2=72, Resulting Numbers: [26, 72] Generated Node #0,0,1: 63:[26, 72] Operation: 74-2=72 Exploring Operation: 26/2=13, Resulting Numbers: [74, 13] Generated Node #0,0,2: 63:[74, 13] Operation: 26/2=13 Moving to Node #0,0,0 Current State: 63:[74, 24], Operations: ['82-8=74', '26-2=24'] Exploring Operation: 74*24=1776, Resulting Numbers: [1776] 1776,63 unequal: No Solution Exploring Operation: 74-24=50, Resulting Numbers: [50] 50,63 unequal: No Solution Exploring Operation: 74+24=98, Resulting Numbers: [98] 98,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[26, 72], Operations: ['82-8=74', '74-2=72'] Exploring Operation: 26+72=98, Resulting Numbers: [98] 98,63 unequal: No Solution Exploring Operation: 26*72=1872, Resulting Numbers: [1872] 1872,63 unequal: No Solution Exploring Operation: 72-26=46, Resulting Numbers: [46] 46,63 unequal: No Solution Moving to Node #0,0,2 Current State: 63:[74, 13], Operations: ['82-8=74', '26/2=13'] Exploring Operation: 74+13=87, Resulting Numbers: [87] 87,63 unequal: No Solution Exploring Operation: 74*13=962, Resulting Numbers: [962] 962,63 unequal: No Solution Exploring Operation: 74-13=61, Resulting Numbers: [61] 61,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[2, 82, 18], Operations: ['26-8=18'] Exploring Operation: 82-18=64, Resulting Numbers: [2, 64] Generated Node #0,1,0: 63:[2, 64] Operation: 82-18=64 Exploring Operation: 18/2=9, Resulting Numbers: [82, 9] Generated Node #0,1,1: 63:[82, 9] Operation: 18/2=9 Exploring Operation: 82-2=80, Resulting Numbers: [18, 80] Generated Node #0,1,2: 63:[18, 80] Operation: 82-2=80 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 63:[2, 64], Operations: ['26-8=18', '82-18=64'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,63 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 63:[82, 9], Operations: ['26-8=18', '18/2=9'] Exploring Operation: 82-9=73, Resulting Numbers: [73] 73,63 unequal: No Solution Exploring Operation: 82*9=738, Resulting Numbers: [738] 738,63 unequal: No Solution Exploring Operation: 82+9=91, Resulting Numbers: [91] 91,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 63:[18, 80], Operations: ['26-8=18', '82-2=80'] Exploring Operation: 18+80=98, Resulting Numbers: [98] 98,63 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 18*80=1440, Resulting Numbers: [1440] 1440,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 77, 91, 91, 52 ]
33
[ "91-52=39", "77*39=3003", "3003/91=33" ]
Current State: 33:[77, 91, 91, 52], Operations: [] Exploring Operation: 91-52=39, Resulting Numbers: [77, 39] Generated Node #2: [77, 39] from Operation: 91-52=39 Current State: 33:[77, 39], Operations: ['91-52=39'] Exploring Operation: 77*39=3003, Resulting Numbers: [3003] 3003,33 equal: Goal Reached Exploring Operation: 3003/91=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[77, 91, 91, 52], Operations: [] Exploring Operation: 91/91=1, Resulting Numbers: [77, 52, 1] Generated Node #0,0: 33:[77, 52, 1] Operation: 91/91=1 Moving to Node #0,0 Current State: 33:[77, 52, 1], Operations: ['91/91=1'] Exploring Operation: 77-52=25, Resulting Numbers: [1, 25] Generated Node #0,0,0: 33:[1, 25] Operation: 77-52=25 Moving to Node #0,0,0 Current State: 33:[1, 25], Operations: ['91/91=1', '77-52=25'] Exploring Operation: 1+25=26, Resulting Numbers: [26] 26,33 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 17, 20, 20, 16 ]
33
[ "17+20=37", "20-16=4", "37-4=33" ]
Current State: 33:[17, 20, 20, 16], Operations: [] Exploring Operation: 17+20=37, Resulting Numbers: [16, 37] Generated Node #2: [16, 37] from Operation: 17+20=37 Current State: 33:[16, 37], Operations: ['17+20=37'] Exploring Operation: 20-16=4, Resulting Numbers: [37, 4] Generated Node #3: [37, 4] from Operation: 20-16=4 Current State: 33:[37, 4], Operations: ['17+20=37', '20-16=4'] Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[17, 20, 20, 16], Operations: [] Exploring Operation: 20-17=3, Resulting Numbers: [20, 16, 3] Generated Node #0,0: 33:[20, 16, 3] Operation: 20-17=3 Exploring Operation: 20/20=1, Resulting Numbers: [17, 16, 1] Generated Node #0,1: 33:[17, 16, 1] Operation: 20/20=1 Exploring Operation: 20-17=3, Resulting Numbers: [20, 16, 3] Generated Node #0,2: 33:[20, 16, 3] Operation: 20-17=3 Moving to Node #0,1 Current State: 33:[17, 16, 1], Operations: ['20/20=1'] Exploring Operation: 17-16=1, Resulting Numbers: [1, 1] Generated Node #0,1,0: 33:[1, 1] Operation: 17-16=1 Exploring Operation: 17-1=16, Resulting Numbers: [16, 16] Generated Node #0,1,1: 33:[16, 16] Operation: 17-1=16 Exploring Operation: 17+16=33, Resulting Numbers: [1, 33] Generated Node #0,1,2: 33:[1, 33] Operation: 17+16=33 Moving to Node #0,0 Current State: 33:[20, 16, 3], Operations: ['20-17=3'] Exploring Operation: 20-16=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 33:[3, 4] Operation: 20-16=4 Exploring Operation: 20-3=17, Resulting Numbers: [16, 17] Generated Node #0,0,1: 33:[16, 17] Operation: 20-3=17 Exploring Operation: 20+16=36, Resulting Numbers: [3, 36] Generated Node #0,0,2: 33:[3, 36] Operation: 20+16=36 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[3, 4], Operations: ['20-17=3', '20-16=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,33 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 33:[3, 36], Operations: ['20-17=3', '20+16=36'] Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,33 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[17, 20, 20, 16], Operations: [] Exploring Operation: 20-17=3, Resulting Numbers: [20, 16, 3] Generated Node #0,0: 33:[20, 16, 3] Operation: 20-17=3 Moving to Node #0,0 Current State: 33:[20, 16, 3], Operations: ['20-17=3'] Exploring Operation: 20+16=36, Resulting Numbers: [3, 36] Generated Node #0,0,2: 33:[3, 36] Operation: 20+16=36 Moving to Node #0,0,2 Current State: 33:[3, 36], Operations: ['20-17=3', '20+16=36'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 59, 70, 38, 56 ]
36
[ "59-56=3", "70+38=108", "108/3=36" ]
Current State: 36:[59, 70, 38, 56], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [70, 38, 3] Generated Node #2: [70, 38, 3] from Operation: 59-56=3 Current State: 36:[70, 38, 3], Operations: ['59-56=3'] Exploring Operation: 70+38=108, Resulting Numbers: [3, 108] Generated Node #3: [3, 108] from Operation: 70+38=108 Current State: 36:[3, 108], Operations: ['59-56=3', '70+38=108'] Exploring Operation: 108/3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[59, 70, 38, 56], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [70, 38, 3] Generated Node #0,0: 36:[70, 38, 3] Operation: 59-56=3 Exploring Operation: 70-38=32, Resulting Numbers: [59, 56, 32] Generated Node #0,1: 36:[59, 56, 32] Operation: 70-38=32 Exploring Operation: 70-59=11, Resulting Numbers: [38, 56, 11] Generated Node #0,2: 36:[38, 56, 11] Operation: 70-59=11 Exploring Operation: 70-56=14, Resulting Numbers: [59, 38, 14] Generated Node #0,3: 36:[59, 38, 14] Operation: 70-56=14 Moving to Node #0,2 Current State: 36:[38, 56, 11], Operations: ['70-59=11'] Exploring Operation: 56-11=45, Resulting Numbers: [38, 45] Generated Node #0,2,0: 36:[38, 45] Operation: 56-11=45 Exploring Operation: 56-38=18, Resulting Numbers: [11, 18] Generated Node #0,2,1: 36:[11, 18] Operation: 56-38=18 Exploring Operation: 38+11=49, Resulting Numbers: [56, 49] Generated Node #0,2,2: 36:[56, 49] Operation: 38+11=49 Exploring Operation: 38-11=27, Resulting Numbers: [56, 27] Generated Node #0,2,3: 36:[56, 27] Operation: 38-11=27 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 36:[11, 18], Operations: ['70-59=11', '56-38=18'] Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 11+18=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 11*18=198, Resulting Numbers: [198] 198,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 36:[38, 45], Operations: ['70-59=11', '56-11=45'] Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,36 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 38*45=1710, Resulting Numbers: [1710] 1710,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 36:[56, 27], Operations: ['70-59=11', '38-11=27'] Exploring Operation: 56-27=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 56+27=83, Resulting Numbers: [83] 83,36 unequal: No Solution Exploring Operation: 56*27=1512, Resulting Numbers: [1512] 1512,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 36:[56, 49], Operations: ['70-59=11', '38+11=49'] Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 56+49=105, Resulting Numbers: [105] 105,36 unequal: No Solution Exploring Operation: 56*49=2744, Resulting Numbers: [2744] 2744,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 36:[59, 38, 14], Operations: ['70-56=14'] Exploring Operation: 59+14=73, Resulting Numbers: [38, 73] Generated Node #0,3,0: 36:[38, 73] Operation: 59+14=73 Exploring Operation: 59-14=45, Resulting Numbers: [38, 45] Generated Node #0,3,1: 36:[38, 45] Operation: 59-14=45 Exploring Operation: 38-14=24, Resulting Numbers: [59, 24] Generated Node #0,3,2: 36:[59, 24] Operation: 38-14=24 Exploring Operation: 59-38=21, Resulting Numbers: [14, 21] Generated Node #0,3,3: 36:[14, 21] Operation: 59-38=21 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 36:[14, 21], Operations: ['70-56=14', '59-38=21'] Exploring Operation: 14+21=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 14*21=294, Resulting Numbers: [294] 294,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 36:[38, 45], Operations: ['70-56=14', '59-14=45'] Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,36 unequal: No Solution Exploring Operation: 38*45=1710, Resulting Numbers: [1710] 1710,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 36:[59, 24], Operations: ['70-56=14', '38-14=24'] Exploring Operation: 59*24=1416, Resulting Numbers: [1416] 1416,36 unequal: No Solution Exploring Operation: 59-24=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 59+24=83, Resulting Numbers: [83] 83,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 36:[38, 73], Operations: ['70-56=14', '59+14=73'] Exploring Operation: 38+73=111, Resulting Numbers: [111] 111,36 unequal: No Solution Exploring Operation: 38*73=2774, Resulting Numbers: [2774] 2774,36 unequal: No Solution Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 36:[70, 38, 3], Operations: ['59-56=3'] Exploring Operation: 70-3=67, Resulting Numbers: [38, 67] Generated Node #0,0,0: 36:[38, 67] Operation: 70-3=67 Exploring Operation: 70-38=32, Resulting Numbers: [3, 32] Generated Node #0,0,1: 36:[3, 32] Operation: 70-38=32 Exploring Operation: 70+3=73, Resulting Numbers: [38, 73] Generated Node #0,0,2: 36:[38, 73] Operation: 70+3=73 Exploring Operation: 38-3=35, Resulting Numbers: [70, 35] Generated Node #0,0,3: 36:[70, 35] Operation: 38-3=35 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[3, 32], Operations: ['59-56=3', '70-38=32'] Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,36 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[38, 67], Operations: ['59-56=3', '70-3=67'] Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 38*67=2546, Resulting Numbers: [2546] 2546,36 unequal: No Solution Exploring Operation: 38+67=105, Resulting Numbers: [105] 105,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 36:[70, 35], Operations: ['59-56=3', '38-3=35'] Exploring Operation: 70-35=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 70+35=105, Resulting Numbers: [105] 105,36 unequal: No Solution Exploring Operation: 70*35=2450, Resulting Numbers: [2450] 2450,36 unequal: No Solution Exploring Operation: 70/35=2, Resulting Numbers: [2] 2,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 36:[38, 73], Operations: ['59-56=3', '70+3=73'] Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 38+73=111, Resulting Numbers: [111] 111,36 unequal: No Solution Exploring Operation: 38*73=2774, Resulting Numbers: [2774] 2774,36 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: 36:[59, 56, 32], Operations: ['70-38=32'] Exploring Operation: 59+32=91, Resulting Numbers: [56, 91] Generated Node #0,1,0: 36:[56, 91] Operation: 59+32=91 Exploring Operation: 56-32=24, Resulting Numbers: [59, 24] Generated Node #0,1,1: 36:[59, 24] Operation: 56-32=24 Exploring Operation: 59-56=3, Resulting Numbers: [32, 3] Generated Node #0,1,2: 36:[32, 3] Operation: 59-56=3 Exploring Operation: 59-32=27, Resulting Numbers: [56, 27] Generated Node #0,1,3: 36:[56, 27] Operation: 59-32=27 Moving to Node #0,1,2 Current State: 36:[32, 3], Operations: ['70-38=32', '59-56=3'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 32*3=96, Resulting Numbers: [96] 96,36 unequal: No Solution Moving to Node #0,1,3 Current State: 36:[56, 27], Operations: ['70-38=32', '59-32=27'] Exploring Operation: 56+27=83, Resulting Numbers: [83] 83,36 unequal: No Solution Exploring Operation: 56*27=1512, Resulting Numbers: [1512] 1512,36 unequal: No Solution Exploring Operation: 56-27=29, Resulting Numbers: [29] 29,36 unequal: No Solution Moving to Node #0,1,1 Current State: 36:[59, 24], Operations: ['70-38=32', '56-32=24'] Exploring Operation: 59*24=1416, Resulting Numbers: [1416] 1416,36 unequal: No Solution Exploring Operation: 59-24=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 59+24=83, Resulting Numbers: [83] 83,36 unequal: No Solution Moving to Node #0,1,0 Current State: 36:[56, 91], Operations: ['70-38=32', '59+32=91'] Exploring Operation: 56+91=147, Resulting Numbers: [147] 147,36 unequal: No Solution Exploring Operation: 91-56=35, Resulting Numbers: [35] 35,36 unequal: No Solution Exploring Operation: 56*91=5096, Resulting Numbers: [5096] 5096,36 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 7, 64, 50, 32 ]
39
[ "64-7=57", "50-32=18", "57-18=39" ]
Current State: 39:[7, 64, 50, 32], Operations: [] Exploring Operation: 64-7=57, Resulting Numbers: [50, 32, 57] Generated Node #2: [50, 32, 57] from Operation: 64-7=57 Current State: 39:[50, 32, 57], Operations: ['64-7=57'] Exploring Operation: 50-32=18, Resulting Numbers: [57, 18] Generated Node #3: [57, 18] from Operation: 50-32=18 Current State: 39:[57, 18], Operations: ['64-7=57', '50-32=18'] Exploring Operation: 57-18=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[7, 64, 50, 32], Operations: [] Exploring Operation: 64-50=14, Resulting Numbers: [7, 32, 14] Generated Node #0,0: 39:[7, 32, 14] Operation: 64-50=14 Exploring Operation: 64-32=32, Resulting Numbers: [7, 50, 32] Generated Node #0,1: 39:[7, 50, 32] Operation: 64-32=32 Exploring Operation: 50-32=18, Resulting Numbers: [7, 64, 18] Generated Node #0,2: 39:[7, 64, 18] Operation: 50-32=18 Exploring Operation: 64/32=2, Resulting Numbers: [7, 50, 2] Generated Node #0,3: 39:[7, 50, 2] Operation: 64/32=2 Moving to Node #0,0 Current State: 39:[7, 32, 14], Operations: ['64-50=14'] Exploring Operation: 14/7=2, Resulting Numbers: [32, 2] Generated Node #0,0,0: 39:[32, 2] Operation: 14/7=2 Exploring Operation: 7+32=39, Resulting Numbers: [14, 39] Generated Node #0,0,1: 39:[14, 39] Operation: 7+32=39 Exploring Operation: 32-14=18, Resulting Numbers: [7, 18] Generated Node #0,0,2: 39:[7, 18] Operation: 32-14=18 Exploring Operation: 14-7=7, Resulting Numbers: [32, 7] Generated Node #0,0,3: 39:[32, 7] Operation: 14-7=7 Moving to Node #0,3 Current State: 39:[7, 50, 2], Operations: ['64/32=2'] Exploring Operation: 7*2=14, Resulting Numbers: [50, 14] Generated Node #0,3,0: 39:[50, 14] Operation: 7*2=14 Exploring Operation: 50-7=43, Resulting Numbers: [2, 43] Generated Node #0,3,1: 39:[2, 43] Operation: 50-7=43 Exploring Operation: 7-2=5, Resulting Numbers: [50, 5] Generated Node #0,3,2: 39:[50, 5] Operation: 7-2=5 Exploring Operation: 50-2=48, Resulting Numbers: [7, 48] Generated Node #0,3,3: 39:[7, 48] Operation: 50-2=48 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 39:[2, 43], Operations: ['64/32=2', '50-7=43'] Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,39 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,39 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 #0,3,0 Current State: 39:[50, 14], Operations: ['64/32=2', '7*2=14'] Exploring Operation: 50-14=36, Resulting Numbers: [36] 36,39 unequal: No Solution Exploring Operation: 50*14=700, Resulting Numbers: [700] 700,39 unequal: No Solution Exploring Operation: 50+14=64, Resulting Numbers: [64] 64,39 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 #0,3,2 Current State: 39:[50, 5], Operations: ['64/32=2', '7-2=5'] Exploring Operation: 50+5=55, Resulting Numbers: [55] 55,39 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,39 unequal: No Solution Exploring Operation: 50*5=250, Resulting Numbers: [250] 250,39 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 #0,3,3 Current State: 39:[7, 48], Operations: ['64/32=2', '50-2=48'] Exploring Operation: 7+48=55, Resulting Numbers: [55] 55,39 unequal: No Solution Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 7*48=336, Resulting Numbers: [336] 336,39 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:[7, 50, 32], Operations: ['64-32=32'] Exploring Operation: 50-32=18, Resulting Numbers: [7, 18] Generated Node #0,1,0: 39:[7, 18] Operation: 50-32=18 Exploring Operation: 32-7=25, Resulting Numbers: [50, 25] Generated Node #0,1,1: 39:[50, 25] Operation: 32-7=25 Exploring Operation: 7+32=39, Resulting Numbers: [50, 39] Generated Node #0,1,2: 39:[50, 39] Operation: 7+32=39 Exploring Operation: 50-7=43, Resulting Numbers: [32, 43] Generated Node #0,1,3: 39:[32, 43] Operation: 50-7=43 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[7, 18], Operations: ['64-32=32', '50-32=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,39 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,39 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 #0,1,2 Current State: 39:[50, 39], Operations: ['64-32=32', '7+32=39'] Exploring Operation: 50-39=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 50*39=1950, Resulting Numbers: [1950] 1950,39 unequal: No Solution Exploring Operation: 50+39=89, Resulting Numbers: [89] 89,39 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 #0,1,3 Current State: 39:[32, 43], Operations: ['64-32=32', '50-7=43'] Exploring Operation: 32*43=1376, Resulting Numbers: [1376] 1376,39 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 32+43=75, Resulting Numbers: [75] 75,39 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:[50, 25], Operations: ['64-32=32', '32-7=25'] Exploring Operation: 50+25=75, Resulting Numbers: [75] 75,39 unequal: No Solution Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 50*25=1250, Resulting Numbers: [1250] 1250,39 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: 39:[7, 64, 18], Operations: ['50-32=18'] Exploring Operation: 7+64=71, Resulting Numbers: [18, 71] Generated Node #0,2,0: 39:[18, 71] Operation: 7+64=71 Exploring Operation: 18-7=11, Resulting Numbers: [64, 11] Generated Node #0,2,1: 39:[64, 11] Operation: 18-7=11 Exploring Operation: 64-7=57, Resulting Numbers: [18, 57] Generated Node #0,2,2: 39:[18, 57] Operation: 64-7=57 Exploring Operation: 64-18=46, Resulting Numbers: [7, 46] Generated Node #0,2,3: 39:[7, 46] Operation: 64-18=46 Moving to Node #0,0,1 Current State: 39:[14, 39], Operations: ['64-50=14', '7+32=39'] Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 14+39=53, Resulting Numbers: [53] 53,39 unequal: No Solution Exploring Operation: 14*39=546, Resulting Numbers: [546] 546,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[32, 2], Operations: ['64-50=14', '14/7=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,39 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,39 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[7, 18], Operations: ['64-50=14', '32-14=18'] Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,39 unequal: No Solution Moving to Node #0,2,3 Current State: 39:[7, 46], Operations: ['50-32=18', '64-18=46'] Exploring Operation: 7*46=322, Resulting Numbers: [322] 322,39 unequal: No Solution Exploring Operation: 7+46=53, Resulting Numbers: [53] 53,39 unequal: No Solution Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[7, 64, 50, 32], Operations: [] Exploring Operation: 50-32=18, Resulting Numbers: [7, 64, 18] Generated Node #0,2: 39:[7, 64, 18] Operation: 50-32=18 Moving to Node #0,2 Current State: 39:[7, 64, 18], Operations: ['50-32=18'] Exploring Operation: 64-18=46, Resulting Numbers: [7, 46] Generated Node #0,2,3: 39:[7, 46] Operation: 64-18=46 Moving to Node #0,2,3 Current State: 39:[7, 46], Operations: ['50-32=18', '64-18=46'] Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
0.945313
hs_4
mult_heuristic
[ 5, 80, 15, 50 ]
81
[ "80/5=16", "15+50=65", "16+65=81" ]
Current State: 81:[5, 80, 15, 50], Operations: [] Exploring Operation: 80/5=16, Resulting Numbers: [15, 50, 16] Generated Node #2: [15, 50, 16] from Operation: 80/5=16 Current State: 81:[15, 50, 16], Operations: ['80/5=16'] Exploring Operation: 15+50=65, Resulting Numbers: [16, 65] Generated Node #3: [16, 65] from Operation: 15+50=65 Current State: 81:[16, 65], Operations: ['80/5=16', '15+50=65'] Exploring Operation: 16+65=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[5, 80, 15, 50], Operations: [] Exploring Operation: 80-50=30, Resulting Numbers: [5, 15, 30] Generated Node #0,0: 81:[5, 15, 30] Operation: 80-50=30 Exploring Operation: 50/5=10, Resulting Numbers: [80, 15, 10] Generated Node #0,1: 81:[80, 15, 10] Operation: 50/5=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[80, 15, 10], Operations: ['50/5=10'] Exploring Operation: 15+10=25, Resulting Numbers: [80, 25] Generated Node #0,1,0: 81:[80, 25] Operation: 15+10=25 Exploring Operation: 15-10=5, Resulting Numbers: [80, 5] Generated Node #0,1,1: 81:[80, 5] Operation: 15-10=5 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 81:[80, 25], Operations: ['50/5=10', '15+10=25'] Exploring Operation: 80+25=105, Resulting Numbers: [105] 105,81 unequal: No Solution Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 81:[80, 5], Operations: ['50/5=10', '15-10=5'] Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[5, 15, 30], Operations: ['80-50=30'] Exploring Operation: 15/5=3, Resulting Numbers: [30, 3] Generated Node #0,0,0: 81:[30, 3] Operation: 15/5=3 Exploring Operation: 30/15=2, Resulting Numbers: [5, 2] Generated Node #0,0,1: 81:[5, 2] Operation: 30/15=2 Moving to Node #0,0,0 Current State: 81:[30, 3], Operations: ['80-50=30', '15/5=3'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,81 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[5, 2], Operations: ['80-50=30', '30/15=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,81 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,81 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
[ 56, 50, 72, 45 ]
24
[ "50*72=3600", "3600/45=80", "80-56=24" ]
Current State: 24:[56, 50, 72, 45], Operations: [] Exploring Operation: 50*72=3600, Resulting Numbers: [56, 45, 3600] Generated Node #2: [56, 45, 3600] from Operation: 50*72=3600 Current State: 24:[56, 45, 3600], Operations: ['50*72=3600'] Exploring Operation: 3600/45=80, Resulting Numbers: [56, 80] Generated Node #3: [56, 80] from Operation: 3600/45=80 Current State: 24:[56, 80], Operations: ['50*72=3600', '3600/45=80'] Exploring Operation: 80-56=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[56, 50, 72, 45], Operations: [] Exploring Operation: 72-56=16, Resulting Numbers: [50, 45, 16] Generated Node #0,0: 24:[50, 45, 16] Operation: 72-56=16 Exploring Operation: 72-50=22, Resulting Numbers: [56, 45, 22] Generated Node #0,1: 24:[56, 45, 22] Operation: 72-50=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[50, 45, 16], Operations: ['72-56=16'] Exploring Operation: 50-16=34, Resulting Numbers: [45, 34] Generated Node #0,0,0: 24:[45, 34] Operation: 50-16=34 Exploring Operation: 50-45=5, Resulting Numbers: [16, 5] Generated Node #0,0,1: 24:[16, 5] Operation: 50-45=5 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 24:[16, 5], Operations: ['72-56=16', '50-45=5'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,24 unequal: No Solution No 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: 24:[45, 34], Operations: ['72-56=16', '50-16=34'] Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 45+34=79, Resulting Numbers: [79] 79,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[56, 45, 22], Operations: ['72-50=22'] Exploring Operation: 56-22=34, Resulting Numbers: [45, 34] Generated Node #0,1,0: 24:[45, 34] Operation: 56-22=34 Exploring Operation: 56-45=11, Resulting Numbers: [22, 11] Generated Node #0,1,1: 24:[22, 11] Operation: 56-45=11 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 24:[22, 11], Operations: ['72-50=22', '56-45=11'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,24 unequal: No Solution No 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: 24:[45, 34], Operations: ['72-50=22', '56-22=34'] Exploring Operation: 45+34=79, Resulting Numbers: [79] 79,24 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 68, 82, 85, 99 ]
35
[ "85-82=3", "99/3=33", "68-33=35" ]
Current State: 35:[68, 82, 85, 99], Operations: [] Exploring Operation: 85-82=3, Resulting Numbers: [68, 99, 3] Generated Node #2: [68, 99, 3] from Operation: 85-82=3 Current State: 35:[68, 99, 3], Operations: ['85-82=3'] Exploring Operation: 99/3=33, Resulting Numbers: [68, 33] Generated Node #3: [68, 33] from Operation: 99/3=33 Current State: 35:[68, 33], Operations: ['85-82=3', '99/3=33'] Exploring Operation: 68-33=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[68, 82, 85, 99], Operations: [] Exploring Operation: 99-85=14, Resulting Numbers: [68, 82, 14] Generated Node #0,0: 35:[68, 82, 14] Operation: 99-85=14 Exploring Operation: 99-82=17, Resulting Numbers: [68, 85, 17] Generated Node #0,1: 35:[68, 85, 17] Operation: 99-82=17 Exploring Operation: 99-68=31, Resulting Numbers: [82, 85, 31] Generated Node #0,2: 35:[82, 85, 31] Operation: 99-68=31 Exploring Operation: 85-82=3, Resulting Numbers: [68, 99, 3] Generated Node #0,3: 35:[68, 99, 3] Operation: 85-82=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[68, 82, 14], Operations: ['99-85=14'] Exploring Operation: 68+14=82, Resulting Numbers: [82, 82] Generated Node #0,0,0: 35:[82, 82] Operation: 68+14=82 Exploring Operation: 68-14=54, Resulting Numbers: [82, 54] Generated Node #0,0,1: 35:[82, 54] Operation: 68-14=54 Exploring Operation: 82-68=14, Resulting Numbers: [14, 14] Generated Node #0,0,2: 35:[14, 14] Operation: 82-68=14 Exploring Operation: 82-14=68, Resulting Numbers: [68, 68] Generated Node #0,0,3: 35:[68, 68] Operation: 82-14=68 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 35:[14, 14], Operations: ['99-85=14', '82-68=14'] Exploring Operation: 14-14=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 14*14=196, Resulting Numbers: [196] 196,35 unequal: No Solution Exploring Operation: 14/14=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 14+14=28, Resulting Numbers: [28] 28,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 35:[82, 54], Operations: ['99-85=14', '68-14=54'] Exploring Operation: 82+54=136, Resulting Numbers: [136] 136,35 unequal: No Solution Exploring Operation: 82*54=4428, Resulting Numbers: [4428] 4428,35 unequal: No Solution Exploring Operation: 82-54=28, Resulting Numbers: [28] 28,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 35:[68, 68], Operations: ['99-85=14', '82-14=68'] Exploring Operation: 68*68=4624, Resulting Numbers: [4624] 4624,35 unequal: No Solution Exploring Operation: 68/68=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 68+68=136, Resulting Numbers: [136] 136,35 unequal: No Solution Exploring Operation: 68-68=0, Resulting Numbers: [0] 0,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[82, 82], Operations: ['99-85=14', '68+14=82'] Exploring Operation: 82+82=164, Resulting Numbers: [164] 164,35 unequal: No Solution Exploring Operation: 82/82=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 82-82=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 82*82=6724, Resulting Numbers: [6724] 6724,35 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:[68, 85, 17], Operations: ['99-82=17'] Exploring Operation: 68/17=4, Resulting Numbers: [85, 4] Generated Node #0,1,0: 35:[85, 4] Operation: 68/17=4 Exploring Operation: 85-68=17, Resulting Numbers: [17, 17] Generated Node #0,1,1: 35:[17, 17] Operation: 85-68=17 Exploring Operation: 85/17=5, Resulting Numbers: [68, 5] Generated Node #0,1,2: 35:[68, 5] Operation: 85/17=5 Exploring Operation: 68-17=51, Resulting Numbers: [85, 51] Generated Node #0,1,3: 35:[85, 51] Operation: 68-17=51 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 35:[17, 17], Operations: ['99-82=17', '85-68=17'] Exploring Operation: 17/17=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 17-17=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 17+17=34, Resulting Numbers: [34] 34,35 unequal: No Solution Exploring Operation: 17*17=289, Resulting Numbers: [289] 289,35 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 #0,1,2 Current State: 35:[68, 5], Operations: ['99-82=17', '85/17=5'] Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,35 unequal: No Solution Exploring Operation: 68+5=73, Resulting Numbers: [73] 73,35 unequal: No Solution Exploring Operation: 68*5=340, Resulting Numbers: [340] 340,35 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 #0,1,0 Current State: 35:[85, 4], Operations: ['99-82=17', '68/17=4'] Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,35 unequal: No Solution Exploring Operation: 85+4=89, Resulting Numbers: [89] 89,35 unequal: No Solution Exploring Operation: 85*4=340, Resulting Numbers: [340] 340,35 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 #0,1,3 Current State: 35:[85, 51], Operations: ['99-82=17', '68-17=51'] Exploring Operation: 85+51=136, Resulting Numbers: [136] 136,35 unequal: No Solution Exploring Operation: 85*51=4335, Resulting Numbers: [4335] 4335,35 unequal: No Solution Exploring Operation: 85-51=34, Resulting Numbers: [34] 34,35 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 #0,3 Current State: 35:[68, 99, 3], Operations: ['85-82=3'] Exploring Operation: 68-3=65, Resulting Numbers: [99, 65] Generated Node #0,3,0: 35:[99, 65] Operation: 68-3=65 Exploring Operation: 99-3=96, Resulting Numbers: [68, 96] Generated Node #0,3,1: 35:[68, 96] Operation: 99-3=96 Exploring Operation: 99-68=31, Resulting Numbers: [3, 31] Generated Node #0,3,2: 35:[3, 31] Operation: 99-68=31 Exploring Operation: 99/3=33, Resulting Numbers: [68, 33] Generated Node #0,3,3: 35:[68, 33] Operation: 99/3=33 Moving to Node #0,3,2 Current State: 35:[3, 31], Operations: ['85-82=3', '99-68=31'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,35 unequal: No Solution Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,35 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,35 unequal: No Solution Moving to Node #0,3,3 Current State: 35:[68, 33], Operations: ['85-82=3', '99/3=33'] Exploring Operation: 68-33=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[68, 82, 85, 99], Operations: [] Exploring Operation: 85-82=3, Resulting Numbers: [68, 99, 3] Generated Node #0,3: 35:[68, 99, 3] Operation: 85-82=3 Moving to Node #0,3 Current State: 35:[68, 99, 3], Operations: ['85-82=3'] Exploring Operation: 99/3=33, Resulting Numbers: [68, 33] Generated Node #0,3,3: 35:[68, 33] Operation: 99/3=33 Moving to Node #0,3,3 Current State: 35:[68, 33], Operations: ['85-82=3', '99/3=33'] Exploring Operation: 68-33=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.954861
hs_4
mult_heuristic
[ 4, 89, 87, 70 ]
64
[ "4+89=93", "87+70=157", "157-93=64" ]
Current State: 64:[4, 89, 87, 70], Operations: [] Exploring Operation: 4+89=93, Resulting Numbers: [87, 70, 93] Generated Node #2: [87, 70, 93] from Operation: 4+89=93 Current State: 64:[87, 70, 93], Operations: ['4+89=93'] Exploring Operation: 87+70=157, Resulting Numbers: [93, 157] Generated Node #3: [93, 157] from Operation: 87+70=157 Current State: 64:[93, 157], Operations: ['4+89=93', '87+70=157'] Exploring Operation: 157-93=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[4, 89, 87, 70], Operations: [] Exploring Operation: 89-70=19, Resulting Numbers: [4, 87, 19] Generated Node #0,0: 64:[4, 87, 19] Operation: 89-70=19 Exploring Operation: 89-87=2, Resulting Numbers: [4, 70, 2] Generated Node #0,1: 64:[4, 70, 2] Operation: 89-87=2 Exploring Operation: 87-4=83, Resulting Numbers: [89, 70, 83] Generated Node #0,2: 64:[89, 70, 83] Operation: 87-4=83 Exploring Operation: 87-70=17, Resulting Numbers: [4, 89, 17] Generated Node #0,3: 64:[4, 89, 17] Operation: 87-70=17 Exploring Operation: 89-4=85, Resulting Numbers: [87, 70, 85] Generated Node #0,4: 64:[87, 70, 85] Operation: 89-4=85 Moving to Node #0,1 Current State: 64:[4, 70, 2], Operations: ['89-87=2'] Exploring Operation: 70/2=35, Resulting Numbers: [4, 35] Generated Node #0,1,0: 64:[4, 35] Operation: 70/2=35 Exploring Operation: 4*2=8, Resulting Numbers: [70, 8] Generated Node #0,1,1: 64:[70, 8] Operation: 4*2=8 Exploring Operation: 70-4=66, Resulting Numbers: [2, 66] Generated Node #0,1,2: 64:[2, 66] Operation: 70-4=66 Exploring Operation: 4-2=2, Resulting Numbers: [70, 2] Generated Node #0,1,3: 64:[70, 2] Operation: 4-2=2 Exploring Operation: 70-2=68, Resulting Numbers: [4, 68] Generated Node #0,1,4: 64:[4, 68] Operation: 70-2=68 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 64:[2, 66], Operations: ['89-87=2', '70-4=66'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[4, 89, 87, 70], Operations: [] Exploring Operation: 89-87=2, Resulting Numbers: [4, 70, 2] Generated Node #0,1: 64:[4, 70, 2] Operation: 89-87=2 Moving to Node #0,1 Current State: 64:[4, 70, 2], Operations: ['89-87=2'] Exploring Operation: 70-4=66, Resulting Numbers: [2, 66] Generated Node #0,1,2: 64:[2, 66] Operation: 70-4=66 Moving to Node #0,1,2 Current State: 64:[2, 66], Operations: ['89-87=2', '70-4=66'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 2, 27, 25, 64 ]
76
[ "2*64=128", "27+25=52", "128-52=76" ]
Current State: 76:[2, 27, 25, 64], Operations: [] Exploring Operation: 2*64=128, Resulting Numbers: [27, 25, 128] Generated Node #2: [27, 25, 128] from Operation: 2*64=128 Current State: 76:[27, 25, 128], Operations: ['2*64=128'] Exploring Operation: 27+25=52, Resulting Numbers: [128, 52] Generated Node #3: [128, 52] from Operation: 27+25=52 Current State: 76:[128, 52], Operations: ['2*64=128', '27+25=52'] Exploring Operation: 128-52=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[2, 27, 25, 64], Operations: [] Exploring Operation: 64/2=32, Resulting Numbers: [27, 25, 32] Generated Node #0,0: 76:[27, 25, 32] Operation: 64/2=32 Exploring Operation: 64-25=39, Resulting Numbers: [2, 27, 39] Generated Node #0,1: 76:[2, 27, 39] Operation: 64-25=39 Exploring Operation: 64-27=37, Resulting Numbers: [2, 25, 37] Generated Node #0,2: 76:[2, 25, 37] Operation: 64-27=37 Exploring Operation: 27-25=2, Resulting Numbers: [2, 64, 2] Generated Node #0,3: 76:[2, 64, 2] Operation: 27-25=2 Exploring Operation: 27+64=91, Resulting Numbers: [2, 25, 91] Generated Node #0,4: 76:[2, 25, 91] Operation: 27+64=91 Moving to Node #0,2 Current State: 76:[2, 25, 37], Operations: ['64-27=37'] Exploring Operation: 37-25=12, Resulting Numbers: [2, 12] Generated Node #0,2,0: 76:[2, 12] Operation: 37-25=12 Exploring Operation: 2+25=27, Resulting Numbers: [37, 27] Generated Node #0,2,1: 76:[37, 27] Operation: 2+25=27 Exploring Operation: 2*37=74, Resulting Numbers: [25, 74] Generated Node #0,2,2: 76:[25, 74] Operation: 2*37=74 Exploring Operation: 2+37=39, Resulting Numbers: [25, 39] Generated Node #0,2,3: 76:[25, 39] Operation: 2+37=39 Exploring Operation: 25-2=23, Resulting Numbers: [37, 23] Generated Node #0,2,4: 76:[37, 23] Operation: 25-2=23 Moving to Node #0,1 Current State: 76:[2, 27, 39], Operations: ['64-25=39'] Exploring Operation: 2+27=29, Resulting Numbers: [39, 29] Generated Node #0,1,0: 76:[39, 29] Operation: 2+27=29 Exploring Operation: 39-2=37, Resulting Numbers: [27, 37] Generated Node #0,1,1: 76:[27, 37] Operation: 39-2=37 Exploring Operation: 39-27=12, Resulting Numbers: [2, 12] Generated Node #0,1,2: 76:[2, 12] Operation: 39-27=12 Exploring Operation: 27-2=25, Resulting Numbers: [39, 25] Generated Node #0,1,3: 76:[39, 25] Operation: 27-2=25 Exploring Operation: 2*39=78, Resulting Numbers: [27, 78] Generated Node #0,1,4: 76:[27, 78] Operation: 2*39=78 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 76:[2, 12], Operations: ['64-25=39', '39-27=12'] Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 76:[39, 25], Operations: ['64-25=39', '27-2=25'] Exploring Operation: 39*25=975, Resulting Numbers: [975] 975,76 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 39+25=64, Resulting Numbers: [64] 64,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 76:[27, 37], Operations: ['64-25=39', '39-2=37'] Exploring Operation: 27*37=999, Resulting Numbers: [999] 999,76 unequal: No Solution Exploring Operation: 27+37=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 76:[39, 29], Operations: ['64-25=39', '2+27=29'] Exploring Operation: 39+29=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 39-29=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 39*29=1131, Resulting Numbers: [1131] 1131,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 76:[27, 78], Operations: ['64-25=39', '2*39=78'] Exploring Operation: 27*78=2106, Resulting Numbers: [2106] 2106,76 unequal: No Solution Exploring Operation: 78-27=51, Resulting Numbers: [51] 51,76 unequal: No Solution Exploring Operation: 27+78=105, Resulting Numbers: [105] 105,76 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: 76:[2, 64, 2], Operations: ['27-25=2'] Exploring Operation: 64/2=32, Resulting Numbers: [2, 32] Generated Node #0,3,0: 76:[2, 32] Operation: 64/2=32 Exploring Operation: 64+2=66, Resulting Numbers: [2, 66] Generated Node #0,3,1: 76:[2, 66] Operation: 64+2=66 Exploring Operation: 2+64=66, Resulting Numbers: [2, 66] Generated Node #0,3,2: 76:[2, 66] Operation: 2+64=66 Exploring Operation: 2+2=4, Resulting Numbers: [64, 4] Generated Node #0,3,3: 76:[64, 4] Operation: 2+2=4 Exploring Operation: 64/2=32, Resulting Numbers: [2, 32] Generated Node #0,3,4: 76:[2, 32] Operation: 64/2=32 Moving to Node #0,0 Current State: 76:[27, 25, 32], Operations: ['64/2=32'] Exploring Operation: 27+32=59, Resulting Numbers: [25, 59] Generated Node #0,0,0: 76:[25, 59] Operation: 27+32=59 Exploring Operation: 27-25=2, Resulting Numbers: [32, 2] Generated Node #0,0,1: 76:[32, 2] Operation: 27-25=2 Exploring Operation: 32-27=5, Resulting Numbers: [25, 5] Generated Node #0,0,2: 76:[25, 5] Operation: 32-27=5 Exploring Operation: 27+25=52, Resulting Numbers: [32, 52] Generated Node #0,0,3: 76:[32, 52] Operation: 27+25=52 Exploring Operation: 32-25=7, Resulting Numbers: [27, 7] Generated Node #0,0,4: 76:[27, 7] Operation: 32-25=7 Moving to Node #0,4 Current State: 76:[2, 25, 91], Operations: ['27+64=91'] Exploring Operation: 2+91=93, Resulting Numbers: [25, 93] Generated Node #0,4,0: 76:[25, 93] Operation: 2+91=93 Exploring Operation: 91-25=66, Resulting Numbers: [2, 66] Generated Node #0,4,1: 76:[2, 66] Operation: 91-25=66 Exploring Operation: 25-2=23, Resulting Numbers: [91, 23] Generated Node #0,4,2: 76:[91, 23] Operation: 25-2=23 Exploring Operation: 91-2=89, Resulting Numbers: [25, 89] Generated Node #0,4,3: 76:[25, 89] Operation: 91-2=89 Exploring Operation: 2+25=27, Resulting Numbers: [91, 27] Generated Node #0,4,4: 76:[91, 27] Operation: 2+25=27 Moving to Node #0,2,4 Current State: 76:[37, 23], Operations: ['64-27=37', '25-2=23'] Exploring Operation: 37*23=851, Resulting Numbers: [851] 851,76 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 37+23=60, Resulting Numbers: [60] 60,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[2, 32], Operations: ['27-25=2', '64/2=32'] Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,76 unequal: No Solution Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,76 unequal: No Solution Moving to Node #0,3,4 Current State: 76:[2, 32], Operations: ['27-25=2', '64/2=32'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,76 unequal: No Solution Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,76 unequal: No Solution Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[32, 2], Operations: ['64/2=32', '27-25=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,76 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,76 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,76 unequal: No Solution Moving to Node #0,2,3 Current State: 76:[25, 39], Operations: ['64-27=37', '2+37=39'] Exploring Operation: 25*39=975, Resulting Numbers: [975] 975,76 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 25+39=64, Resulting Numbers: [64] 64,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[25, 5], Operations: ['64/2=32', '32-27=5'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,76 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,76 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[2, 12], Operations: ['64-27=37', '37-25=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,76 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[25, 74], Operations: ['64-27=37', '2*37=74'] Exploring Operation: 25+74=99, Resulting Numbers: [99] 99,76 unequal: No Solution Exploring Operation: 74-25=49, Resulting Numbers: [49] 49,76 unequal: No Solution Exploring Operation: 25*74=1850, Resulting Numbers: [1850] 1850,76 unequal: No Solution Moving to Node #0,2,1 Current State: 76:[37, 27], Operations: ['64-27=37', '2+25=27'] Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 37*27=999, Resulting Numbers: [999] 999,76 unequal: No Solution Moving to Node #0,4,1 Current State: 76:[2, 66], Operations: ['27+64=91', '91-25=66'] Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 2*66=132, Resulting Numbers: [132] 132,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[2, 66], Operations: ['27-25=2', '2+64=66'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 2*66=132, Resulting Numbers: [132] 132,76 unequal: No Solution Moving to Node #0,3,1 Current State: 76:[2, 66], Operations: ['27-25=2', '64+2=66'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 2*66=132, Resulting Numbers: [132] 132,76 unequal: No Solution Moving to Node #0,0,4 Current State: 76:[27, 7], Operations: ['64/2=32', '32-25=7'] Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,76 unequal: No Solution Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[64, 4], Operations: ['27-25=2', '2+2=4'] Exploring Operation: 64*4=256, Resulting Numbers: [256] 256,76 unequal: No Solution Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,76 unequal: No Solution Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,76 unequal: No Solution Moving to Node #0,4,2 Current State: 76:[91, 23], Operations: ['27+64=91', '25-2=23'] Exploring Operation: 91+23=114, Resulting Numbers: [114] 114,76 unequal: No Solution Exploring Operation: 91-23=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 91*23=2093, Resulting Numbers: [2093] 2093,76 unequal: No Solution Moving to Node #0,4,3 Current State: 76:[25, 89], Operations: ['27+64=91', '91-2=89'] Exploring Operation: 25+89=114, Resulting Numbers: [114] 114,76 unequal: No Solution Exploring Operation: 25*89=2225, Resulting Numbers: [2225] 2225,76 unequal: No Solution Exploring Operation: 89-25=64, Resulting Numbers: [64] 64,76 unequal: No Solution Moving to Node #0,0,3 Current State: 76:[32, 52], Operations: ['64/2=32', '27+25=52'] Exploring Operation: 32+52=84, Resulting Numbers: [84] 84,76 unequal: No Solution Exploring Operation: 32*52=1664, Resulting Numbers: [1664] 1664,76 unequal: No Solution Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,76 unequal: No Solution Moving to Node #0,4,0 Current State: 76:[25, 93], Operations: ['27+64=91', '2+91=93'] Exploring Operation: 25+93=118, Resulting Numbers: [118] 118,76 unequal: No Solution Exploring Operation: 93-25=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 25*93=2325, Resulting Numbers: [2325] 2325,76 unequal: No Solution Moving to Node #0,4,4 Current State: 76:[91, 27], Operations: ['27+64=91', '2+25=27'] Exploring Operation: 91-27=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 91+27=118, Resulting Numbers: [118] 118,76 unequal: No Solution Exploring Operation: 91*27=2457, Resulting Numbers: [2457] 2457,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[25, 59], Operations: ['64/2=32', '27+32=59'] Exploring Operation: 25+59=84, Resulting Numbers: [84] 84,76 unequal: No Solution Exploring Operation: 25*59=1475, Resulting Numbers: [1475] 1475,76 unequal: No Solution Exploring Operation: 59-25=34, Resulting Numbers: [34] 34,76 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 32, 97, 80, 36 ]
68
[ "36-32=4", "97-80=17", "4*17=68" ]
Current State: 68:[32, 97, 80, 36], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [97, 80, 4] Generated Node #2: [97, 80, 4] from Operation: 36-32=4 Current State: 68:[97, 80, 4], Operations: ['36-32=4'] Exploring Operation: 97-80=17, Resulting Numbers: [4, 17] Generated Node #3: [4, 17] from Operation: 97-80=17 Current State: 68:[4, 17], Operations: ['36-32=4', '97-80=17'] Exploring Operation: 4*17=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[32, 97, 80, 36], Operations: [] Exploring Operation: 97-36=61, Resulting Numbers: [32, 80, 61] Generated Node #0,0: 68:[32, 80, 61] Operation: 97-36=61 Exploring Operation: 97-80=17, Resulting Numbers: [32, 36, 17] Generated Node #0,1: 68:[32, 36, 17] Operation: 97-80=17 Exploring Operation: 97-32=65, Resulting Numbers: [80, 36, 65] Generated Node #0,2: 68:[80, 36, 65] Operation: 97-32=65 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[32, 36, 17], Operations: ['97-80=17'] Exploring Operation: 32+36=68, Resulting Numbers: [17, 68] Generated Node #0,1,0: 68:[17, 68] Operation: 32+36=68 Exploring Operation: 36-32=4, Resulting Numbers: [17, 4] Generated Node #0,1,1: 68:[17, 4] Operation: 36-32=4 Exploring Operation: 32-17=15, Resulting Numbers: [36, 15] Generated Node #0,1,2: 68:[36, 15] Operation: 32-17=15 Moving to Node #0,1,0 Current State: 68:[17, 68], Operations: ['97-80=17', '32+36=68'] Exploring Operation: 17+68=85, Resulting Numbers: [85] 85,68 unequal: No Solution Exploring Operation: 68-17=51, Resulting Numbers: [51] 51,68 unequal: No Solution Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[17, 4], Operations: ['97-80=17', '36-32=4'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[32, 97, 80, 36], Operations: [] Exploring Operation: 97-80=17, Resulting Numbers: [32, 36, 17] Generated Node #0,1: 68:[32, 36, 17] Operation: 97-80=17 Moving to Node #0,1 Current State: 68:[32, 36, 17], Operations: ['97-80=17'] Exploring Operation: 36-32=4, Resulting Numbers: [17, 4] Generated Node #0,1,1: 68:[17, 4] Operation: 36-32=4 Moving to Node #0,1,1 Current State: 68:[17, 4], Operations: ['97-80=17', '36-32=4'] Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 6, 8, 36, 43 ]
90
[ "36-8=28", "43-28=15", "6*15=90" ]
Current State: 90:[6, 8, 36, 43], Operations: [] Exploring Operation: 36-8=28, Resulting Numbers: [6, 43, 28] Generated Node #2: [6, 43, 28] from Operation: 36-8=28 Current State: 90:[6, 43, 28], Operations: ['36-8=28'] Exploring Operation: 43-28=15, Resulting Numbers: [6, 15] Generated Node #3: [6, 15] from Operation: 43-28=15 Current State: 90:[6, 15], Operations: ['36-8=28', '43-28=15'] Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[6, 8, 36, 43], Operations: [] Exploring Operation: 43-36=7, Resulting Numbers: [6, 8, 7] Generated Node #0,0: 90:[6, 8, 7] Operation: 43-36=7 Exploring Operation: 36-6=30, Resulting Numbers: [8, 43, 30] Generated Node #0,1: 90:[8, 43, 30] Operation: 36-6=30 Exploring Operation: 36/6=6, Resulting Numbers: [8, 43, 6] Generated Node #0,2: 90:[8, 43, 6] Operation: 36/6=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[6, 8, 7], Operations: ['43-36=7'] Exploring Operation: 8-7=1, Resulting Numbers: [6, 1] Generated Node #0,0,0: 90:[6, 1] Operation: 8-7=1 Exploring Operation: 8+7=15, Resulting Numbers: [6, 15] Generated Node #0,0,1: 90:[6, 15] Operation: 8+7=15 Exploring Operation: 8-6=2, Resulting Numbers: [7, 2] Generated Node #0,0,2: 90:[7, 2] Operation: 8-6=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 90:[6, 15], Operations: ['43-36=7', '8+7=15'] Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[6, 8, 36, 43], Operations: [] Exploring Operation: 43-36=7, Resulting Numbers: [6, 8, 7] Generated Node #0,0: 90:[6, 8, 7] Operation: 43-36=7 Moving to Node #0,0 Current State: 90:[6, 8, 7], Operations: ['43-36=7'] Exploring Operation: 8+7=15, Resulting Numbers: [6, 15] Generated Node #0,0,1: 90:[6, 15] Operation: 8+7=15 Moving to Node #0,0,1 Current State: 90:[6, 15], Operations: ['43-36=7', '8+7=15'] Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 6, 58, 68, 16 ]
32
[ "58-6=52", "68+16=84", "84-52=32" ]
Current State: 32:[6, 58, 68, 16], Operations: [] Exploring Operation: 58-6=52, Resulting Numbers: [68, 16, 52] Generated Node #2: [68, 16, 52] from Operation: 58-6=52 Current State: 32:[68, 16, 52], Operations: ['58-6=52'] Exploring Operation: 68+16=84, Resulting Numbers: [52, 84] Generated Node #3: [52, 84] from Operation: 68+16=84 Current State: 32:[52, 84], Operations: ['58-6=52', '68+16=84'] Exploring Operation: 84-52=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[6, 58, 68, 16], Operations: [] Exploring Operation: 58-16=42, Resulting Numbers: [6, 68, 42] Generated Node #0,0: 32:[6, 68, 42] Operation: 58-16=42 Exploring Operation: 68-58=10, Resulting Numbers: [6, 16, 10] Generated Node #0,1: 32:[6, 16, 10] Operation: 68-58=10 Moving to Node #0,1 Current State: 32:[6, 16, 10], Operations: ['68-58=10'] Exploring Operation: 10-6=4, Resulting Numbers: [16, 4] Generated Node #0,1,0: 32:[16, 4] Operation: 10-6=4 Exploring Operation: 6+10=16, Resulting Numbers: [16, 16] Generated Node #0,1,1: 32:[16, 16] Operation: 6+10=16 Moving to Node #0,0 Current State: 32:[6, 68, 42], Operations: ['58-16=42'] Exploring Operation: 42/6=7, Resulting Numbers: [68, 7] Generated Node #0,0,0: 32:[68, 7] Operation: 42/6=7 Exploring Operation: 68-42=26, Resulting Numbers: [6, 26] Generated Node #0,0,1: 32:[6, 26] Operation: 68-42=26 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[6, 26], Operations: ['58-16=42', '68-42=26'] Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[6, 58, 68, 16], Operations: [] Exploring Operation: 58-16=42, Resulting Numbers: [6, 68, 42] Generated Node #0,0: 32:[6, 68, 42] Operation: 58-16=42 Moving to Node #0,0 Current State: 32:[6, 68, 42], Operations: ['58-16=42'] Exploring Operation: 68-42=26, Resulting Numbers: [6, 26] Generated Node #0,0,1: 32:[6, 26] Operation: 68-42=26 Moving to Node #0,0,1 Current State: 32:[6, 26], Operations: ['58-16=42', '68-42=26'] Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 99, 27, 17, 37 ]
35
[ "99+37=136", "136/17=8", "27+8=35" ]
Current State: 35:[99, 27, 17, 37], Operations: [] Exploring Operation: 99+37=136, Resulting Numbers: [27, 17, 136] Generated Node #2: [27, 17, 136] from Operation: 99+37=136 Current State: 35:[27, 17, 136], Operations: ['99+37=136'] Exploring Operation: 136/17=8, Resulting Numbers: [27, 8] Generated Node #3: [27, 8] from Operation: 136/17=8 Current State: 35:[27, 8], Operations: ['99+37=136', '136/17=8'] Exploring Operation: 27+8=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[99, 27, 17, 37], Operations: [] Exploring Operation: 99-37=62, Resulting Numbers: [27, 17, 62] Generated Node #0,0: 35:[27, 17, 62] Operation: 99-37=62 Exploring Operation: 99-27=72, Resulting Numbers: [17, 37, 72] Generated Node #0,1: 35:[17, 37, 72] Operation: 99-27=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[27, 17, 62], Operations: ['99-37=62'] Exploring Operation: 62-27=35, Resulting Numbers: [17, 35] Generated Node #0,0,0: 35:[17, 35] Operation: 62-27=35 Exploring Operation: 62-17=45, Resulting Numbers: [27, 45] Generated Node #0,0,1: 35:[27, 45] Operation: 62-17=45 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[17, 35], Operations: ['99-37=62', '62-27=35'] Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,35 unequal: No Solution Exploring Operation: 17+35=52, Resulting Numbers: [52] 52,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 35:[27, 45], Operations: ['99-37=62', '62-17=45'] Exploring Operation: 27+45=72, Resulting Numbers: [72] 72,35 unequal: No Solution Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,35 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:[17, 37, 72], Operations: ['99-27=72'] Exploring Operation: 72-17=55, Resulting Numbers: [37, 55] Generated Node #0,1,0: 35:[37, 55] Operation: 72-17=55 Exploring Operation: 72-37=35, Resulting Numbers: [17, 35] Generated Node #0,1,1: 35:[17, 35] Operation: 72-37=35 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 35:[17, 35], Operations: ['99-27=72', '72-37=35'] Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,35 unequal: No Solution Exploring Operation: 17+35=52, Resulting Numbers: [52] 52,35 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 #0,1,0 Current State: 35:[37, 55], Operations: ['99-27=72', '72-17=55'] Exploring Operation: 37+55=92, Resulting Numbers: [92] 92,35 unequal: No Solution Exploring Operation: 55-37=18, Resulting Numbers: [18] 18,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 92, 12, 93, 72 ]
61
[ "92+12=104", "93+72=165", "165-104=61" ]
Current State: 61:[92, 12, 93, 72], Operations: [] Exploring Operation: 92+12=104, Resulting Numbers: [93, 72, 104] Generated Node #2: [93, 72, 104] from Operation: 92+12=104 Current State: 61:[93, 72, 104], Operations: ['92+12=104'] Exploring Operation: 93+72=165, Resulting Numbers: [104, 165] Generated Node #3: [104, 165] from Operation: 93+72=165 Current State: 61:[104, 165], Operations: ['92+12=104', '93+72=165'] Exploring Operation: 165-104=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[92, 12, 93, 72], Operations: [] Exploring Operation: 92+12=104, Resulting Numbers: [93, 72, 104] Generated Node #0,0: 61:[93, 72, 104] Operation: 92+12=104 Exploring Operation: 93-12=81, Resulting Numbers: [92, 72, 81] Generated Node #0,1: 61:[92, 72, 81] Operation: 93-12=81 Exploring Operation: 12+93=105, Resulting Numbers: [92, 72, 105] Generated Node #0,2: 61:[92, 72, 105] Operation: 12+93=105 Exploring Operation: 72-12=60, Resulting Numbers: [92, 93, 60] Generated Node #0,3: 61:[92, 93, 60] Operation: 72-12=60 Exploring Operation: 92-12=80, Resulting Numbers: [93, 72, 80] Generated Node #0,4: 61:[93, 72, 80] Operation: 92-12=80 Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[92, 72, 81], Operations: ['93-12=81'] Exploring Operation: 81-72=9, Resulting Numbers: [92, 9] Generated Node #0,1,0: 61:[92, 9] Operation: 81-72=9 Exploring Operation: 92-81=11, Resulting Numbers: [72, 11] Generated Node #0,1,1: 61:[72, 11] Operation: 92-81=11 Exploring Operation: 92+72=164, Resulting Numbers: [81, 164] Generated Node #0,1,2: 61:[81, 164] Operation: 92+72=164 Exploring Operation: 92-72=20, Resulting Numbers: [81, 20] Generated Node #0,1,3: 61:[81, 20] Operation: 92-72=20 Exploring Operation: 92+81=173, Resulting Numbers: [72, 173] Generated Node #0,1,4: 61:[72, 173] Operation: 92+81=173 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[72, 11], Operations: ['93-12=81', '92-81=11'] Exploring Operation: 72-11=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[92, 12, 93, 72], Operations: [] Exploring Operation: 93-12=81, Resulting Numbers: [92, 72, 81] Generated Node #0,1: 61:[92, 72, 81] Operation: 93-12=81 Moving to Node #0,1 Current State: 61:[92, 72, 81], Operations: ['93-12=81'] Exploring Operation: 92-81=11, Resulting Numbers: [72, 11] Generated Node #0,1,1: 61:[72, 11] Operation: 92-81=11 Moving to Node #0,1,1 Current State: 61:[72, 11], Operations: ['93-12=81', '92-81=11'] Exploring Operation: 72-11=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 11, 9, 48, 69 ]
51
[ "11*48=528", "528-69=459", "459/9=51" ]
Current State: 51:[11, 9, 48, 69], Operations: [] Exploring Operation: 11*48=528, Resulting Numbers: [9, 69, 528] Generated Node #2: [9, 69, 528] from Operation: 11*48=528 Current State: 51:[9, 69, 528], Operations: ['11*48=528'] Exploring Operation: 528-69=459, Resulting Numbers: [9, 459] Generated Node #3: [9, 459] from Operation: 528-69=459 Current State: 51:[9, 459], Operations: ['11*48=528', '528-69=459'] Exploring Operation: 459/9=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[11, 9, 48, 69], Operations: [] Exploring Operation: 11+9=20, Resulting Numbers: [48, 69, 20] Generated Node #0,0: 51:[48, 69, 20] Operation: 11+9=20 Exploring Operation: 69-11=58, Resulting Numbers: [9, 48, 58] Generated Node #0,1: 51:[9, 48, 58] Operation: 69-11=58 Exploring Operation: 11-9=2, Resulting Numbers: [48, 69, 2] Generated Node #0,2: 51:[48, 69, 2] Operation: 11-9=2 Exploring Operation: 69-48=21, Resulting Numbers: [11, 9, 21] Generated Node #0,3: 51:[11, 9, 21] Operation: 69-48=21 Exploring Operation: 69-9=60, Resulting Numbers: [11, 48, 60] Generated Node #0,4: 51:[11, 48, 60] Operation: 69-9=60 Moving to Node #0,1 Current State: 51:[9, 48, 58], Operations: ['69-11=58'] Exploring Operation: 58-9=49, Resulting Numbers: [48, 49] Generated Node #0,1,0: 51:[48, 49] Operation: 58-9=49 Exploring Operation: 48-9=39, Resulting Numbers: [58, 39] Generated Node #0,1,1: 51:[58, 39] Operation: 48-9=39 Exploring Operation: 9+58=67, Resulting Numbers: [48, 67] Generated Node #0,1,2: 51:[48, 67] Operation: 9+58=67 Exploring Operation: 58-48=10, Resulting Numbers: [9, 10] Generated Node #0,1,3: 51:[9, 10] Operation: 58-48=10 Exploring Operation: 9+48=57, Resulting Numbers: [58, 57] Generated Node #0,1,4: 51:[58, 57] Operation: 9+48=57 Moving to Node #0,3 Current State: 51:[11, 9, 21], Operations: ['69-48=21'] Exploring Operation: 11-9=2, Resulting Numbers: [21, 2] Generated Node #0,3,0: 51:[21, 2] Operation: 11-9=2 Exploring Operation: 9+21=30, Resulting Numbers: [11, 30] Generated Node #0,3,1: 51:[11, 30] Operation: 9+21=30 Exploring Operation: 11+9=20, Resulting Numbers: [21, 20] Generated Node #0,3,2: 51:[21, 20] Operation: 11+9=20 Exploring Operation: 21-9=12, Resulting Numbers: [11, 12] Generated Node #0,3,3: 51:[11, 12] Operation: 21-9=12 Exploring Operation: 21-11=10, Resulting Numbers: [9, 10] Generated Node #0,3,4: 51:[9, 10] Operation: 21-11=10 Moving to Node #0,4 Current State: 51:[11, 48, 60], Operations: ['69-9=60'] Exploring Operation: 60-11=49, Resulting Numbers: [48, 49] Generated Node #0,4,0: 51:[48, 49] Operation: 60-11=49 Exploring Operation: 48-11=37, Resulting Numbers: [60, 37] Generated Node #0,4,1: 51:[60, 37] Operation: 48-11=37 Exploring Operation: 60-48=12, Resulting Numbers: [11, 12] Generated Node #0,4,2: 51:[11, 12] Operation: 60-48=12 Exploring Operation: 11+60=71, Resulting Numbers: [48, 71] Generated Node #0,4,3: 51:[48, 71] Operation: 11+60=71 Exploring Operation: 11+48=59, Resulting Numbers: [60, 59] Generated Node #0,4,4: 51:[60, 59] Operation: 11+48=59 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 51:[48, 49], Operations: ['69-9=60', '60-11=49'] Exploring Operation: 48+49=97, Resulting Numbers: [97] 97,51 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 48*49=2352, Resulting Numbers: [2352] 2352,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 51:[11, 12], Operations: ['69-9=60', '60-48=12'] Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 11*12=132, Resulting Numbers: [132] 132,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 51:[60, 59], Operations: ['69-9=60', '11+48=59'] Exploring Operation: 60*59=3540, Resulting Numbers: [3540] 3540,51 unequal: No Solution Exploring Operation: 60+59=119, Resulting Numbers: [119] 119,51 unequal: No Solution Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 51:[60, 37], Operations: ['69-9=60', '48-11=37'] Exploring Operation: 60-37=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 60+37=97, Resulting Numbers: [97] 97,51 unequal: No Solution Exploring Operation: 60*37=2220, Resulting Numbers: [2220] 2220,51 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 #0,4,3 Current State: 51:[48, 71], Operations: ['69-9=60', '11+60=71'] Exploring Operation: 71-48=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 48*71=3408, Resulting Numbers: [3408] 3408,51 unequal: No Solution Exploring Operation: 48+71=119, Resulting Numbers: [119] 119,51 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: 51:[48, 69, 2], Operations: ['11-9=2'] Exploring Operation: 69-48=21, Resulting Numbers: [2, 21] Generated Node #0,2,0: 51:[2, 21] Operation: 69-48=21 Exploring Operation: 69+2=71, Resulting Numbers: [48, 71] Generated Node #0,2,1: 51:[48, 71] Operation: 69+2=71 Exploring Operation: 69-2=67, Resulting Numbers: [48, 67] Generated Node #0,2,2: 51:[48, 67] Operation: 69-2=67 Exploring Operation: 48+2=50, Resulting Numbers: [69, 50] Generated Node #0,2,3: 51:[69, 50] Operation: 48+2=50 Exploring Operation: 48-2=46, Resulting Numbers: [69, 46] Generated Node #0,2,4: 51:[69, 46] Operation: 48-2=46 Moving to Node #0,0 Current State: 51:[48, 69, 20], Operations: ['11+9=20'] Exploring Operation: 69+20=89, Resulting Numbers: [48, 89] Generated Node #0,0,0: 51:[48, 89] Operation: 69+20=89 Exploring Operation: 48-20=28, Resulting Numbers: [69, 28] Generated Node #0,0,1: 51:[69, 28] Operation: 48-20=28 Exploring Operation: 48+20=68, Resulting Numbers: [69, 68] Generated Node #0,0,2: 51:[69, 68] Operation: 48+20=68 Exploring Operation: 69-20=49, Resulting Numbers: [48, 49] Generated Node #0,0,3: 51:[48, 49] Operation: 69-20=49 Exploring Operation: 69-48=21, Resulting Numbers: [20, 21] Generated Node #0,0,4: 51:[20, 21] Operation: 69-48=21 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 51:[48, 49], Operations: ['11+9=20', '69-20=49'] Exploring Operation: 48*49=2352, Resulting Numbers: [2352] 2352,51 unequal: No Solution Exploring Operation: 48+49=97, Resulting Numbers: [97] 97,51 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,51 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 #0,0,4 Current State: 51:[20, 21], Operations: ['11+9=20', '69-48=21'] Exploring Operation: 20+21=41, Resulting Numbers: [41] 41,51 unequal: No Solution Exploring Operation: 20*21=420, Resulting Numbers: [420] 420,51 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,51 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 #0,0,1 Current State: 51:[69, 28], Operations: ['11+9=20', '48-20=28'] Exploring Operation: 69+28=97, Resulting Numbers: [97] 97,51 unequal: No Solution Exploring Operation: 69*28=1932, Resulting Numbers: [1932] 1932,51 unequal: No Solution Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,51 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 #0,0,2 Current State: 51:[69, 68], Operations: ['11+9=20', '48+20=68'] Exploring Operation: 69-68=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 69*68=4692, Resulting Numbers: [4692] 4692,51 unequal: No Solution Exploring Operation: 69+68=137, Resulting Numbers: [137] 137,51 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 #0,0,0 Current State: 51:[48, 89], Operations: ['11+9=20', '69+20=89'] Exploring Operation: 48+89=137, Resulting Numbers: [137] 137,51 unequal: No Solution Exploring Operation: 48*89=4272, Resulting Numbers: [4272] 4272,51 unequal: No Solution Exploring Operation: 89-48=41, Resulting Numbers: [41] 41,51 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: 51:[48, 49], Operations: ['69-11=58', '58-9=49'] Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 48+49=97, Resulting Numbers: [97] 97,51 unequal: No Solution Exploring Operation: 48*49=2352, Resulting Numbers: [2352] 2352,51 unequal: No Solution Moving to Node #0,3,0 Current State: 51:[21, 2], Operations: ['69-48=21', '11-9=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,51 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,51 unequal: No Solution Moving to Node #0,2,0 Current State: 51:[2, 21], Operations: ['11-9=2', '69-48=21'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,51 unequal: No Solution Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,51 unequal: No Solution Moving to Node #0,3,2 Current State: 51:[21, 20], Operations: ['69-48=21', '11+9=20'] Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 21*20=420, Resulting Numbers: [420] 420,51 unequal: No Solution Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,51 unequal: No Solution Moving to Node #0,3,3 Current State: 51:[11, 12], Operations: ['69-48=21', '21-9=12'] Exploring Operation: 11*12=132, Resulting Numbers: [132] 132,51 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,51 unequal: No Solution Moving to Node #0,1,4 Current State: 51:[58, 57], Operations: ['69-11=58', '9+48=57'] Exploring Operation: 58*57=3306, Resulting Numbers: [3306] 3306,51 unequal: No Solution Exploring Operation: 58+57=115, Resulting Numbers: [115] 115,51 unequal: No Solution Exploring Operation: 58-57=1, Resulting Numbers: [1] 1,51 unequal: No Solution Moving to Node #0,1,3 Current State: 51:[9, 10], Operations: ['69-11=58', '58-48=10'] Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,51 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,51 unequal: No Solution Moving to Node #0,3,4 Current State: 51:[9, 10], Operations: ['69-48=21', '21-11=10'] Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,51 unequal: No Solution Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[48, 67], Operations: ['11-9=2', '69-2=67'] Exploring Operation: 48*67=3216, Resulting Numbers: [3216] 3216,51 unequal: No Solution Exploring Operation: 48+67=115, Resulting Numbers: [115] 115,51 unequal: No Solution Exploring Operation: 67-48=19, Resulting Numbers: [19] 19,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[58, 39], Operations: ['69-11=58', '48-9=39'] Exploring Operation: 58*39=2262, Resulting Numbers: [2262] 2262,51 unequal: No Solution Exploring Operation: 58+39=97, Resulting Numbers: [97] 97,51 unequal: No Solution Exploring Operation: 58-39=19, Resulting Numbers: [19] 19,51 unequal: No Solution Moving to Node #0,1,2 Current State: 51:[48, 67], Operations: ['69-11=58', '9+58=67'] Exploring Operation: 48*67=3216, Resulting Numbers: [3216] 3216,51 unequal: No Solution Exploring Operation: 48+67=115, Resulting Numbers: [115] 115,51 unequal: No Solution Exploring Operation: 67-48=19, Resulting Numbers: [19] 19,51 unequal: No Solution Moving to Node #0,3,1 Current State: 51:[11, 30], Operations: ['69-48=21', '9+21=30'] Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 11+30=41, Resulting Numbers: [41] 41,51 unequal: No Solution Exploring Operation: 11*30=330, Resulting Numbers: [330] 330,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[69, 50], Operations: ['11-9=2', '48+2=50'] Exploring Operation: 69*50=3450, Resulting Numbers: [3450] 3450,51 unequal: No Solution Exploring Operation: 69+50=119, Resulting Numbers: [119] 119,51 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[48, 71], Operations: ['11-9=2', '69+2=71'] Exploring Operation: 48*71=3408, Resulting Numbers: [3408] 3408,51 unequal: No Solution Exploring Operation: 71-48=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 48+71=119, Resulting Numbers: [119] 119,51 unequal: No Solution Moving to Node #0,2,4 Current State: 51:[69, 46], Operations: ['11-9=2', '48-2=46'] Exploring Operation: 69-46=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 69*46=3174, Resulting Numbers: [3174] 3174,51 unequal: No Solution Exploring Operation: 69+46=115, Resulting Numbers: [115] 115,51 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 58, 24, 65, 46 ]
29
[ "58+24=82", "65+46=111", "111-82=29" ]
Current State: 29:[58, 24, 65, 46], Operations: [] Exploring Operation: 58+24=82, Resulting Numbers: [65, 46, 82] Generated Node #2: [65, 46, 82] from Operation: 58+24=82 Current State: 29:[65, 46, 82], Operations: ['58+24=82'] Exploring Operation: 65+46=111, Resulting Numbers: [82, 111] Generated Node #3: [82, 111] from Operation: 65+46=111 Current State: 29:[82, 111], Operations: ['58+24=82', '65+46=111'] Exploring Operation: 111-82=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[58, 24, 65, 46], Operations: [] Exploring Operation: 65-46=19, Resulting Numbers: [58, 24, 19] Generated Node #0,0: 29:[58, 24, 19] Operation: 65-46=19 Exploring Operation: 58-24=34, Resulting Numbers: [65, 46, 34] Generated Node #0,1: 29:[65, 46, 34] Operation: 58-24=34 Exploring Operation: 65-58=7, Resulting Numbers: [24, 46, 7] Generated Node #0,2: 29:[24, 46, 7] Operation: 65-58=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[58, 24, 19], Operations: ['65-46=19'] Exploring Operation: 24+19=43, Resulting Numbers: [58, 43] Generated Node #0,0,0: 29:[58, 43] Operation: 24+19=43 Exploring Operation: 58-24=34, Resulting Numbers: [19, 34] Generated Node #0,0,1: 29:[19, 34] Operation: 58-24=34 Exploring Operation: 58-19=39, Resulting Numbers: [24, 39] Generated Node #0,0,2: 29:[24, 39] Operation: 58-19=39 Moving to Node #0,0,1 Current State: 29:[19, 34], Operations: ['65-46=19', '58-24=34'] Exploring Operation: 34-19=15, Resulting Numbers: [15] 15,29 unequal: No Solution Exploring Operation: 19*34=646, Resulting Numbers: [646] 646,29 unequal: No Solution Exploring Operation: 19+34=53, Resulting Numbers: [53] 53,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[24, 39], Operations: ['65-46=19', '58-19=39'] Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,29 unequal: No Solution Exploring Operation: 24+39=63, Resulting Numbers: [63] 63,29 unequal: No Solution Exploring Operation: 24*39=936, Resulting Numbers: [936] 936,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[58, 43], Operations: ['65-46=19', '24+19=43'] Exploring Operation: 58+43=101, Resulting Numbers: [101] 101,29 unequal: No Solution Exploring Operation: 58-43=15, Resulting Numbers: [15] 15,29 unequal: No Solution Exploring Operation: 58*43=2494, Resulting Numbers: [2494] 2494,29 unequal: No Solution No 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: 29:[24, 46, 7], Operations: ['65-58=7'] Exploring Operation: 46-7=39, Resulting Numbers: [24, 39] Generated Node #0,2,0: 29:[24, 39] Operation: 46-7=39 Exploring Operation: 46-24=22, Resulting Numbers: [7, 22] Generated Node #0,2,1: 29:[7, 22] Operation: 46-24=22 Exploring Operation: 24+7=31, Resulting Numbers: [46, 31] Generated Node #0,2,2: 29:[46, 31] Operation: 24+7=31 Moving to Node #0,2,0 Current State: 29:[24, 39], Operations: ['65-58=7', '46-7=39'] Exploring Operation: 24*39=936, Resulting Numbers: [936] 936,29 unequal: No Solution Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,29 unequal: No Solution Exploring Operation: 24+39=63, Resulting Numbers: [63] 63,29 unequal: No Solution Moving to Node #0,2,2 Current State: 29:[46, 31], Operations: ['65-58=7', '24+7=31'] Exploring Operation: 46+31=77, Resulting Numbers: [77] 77,29 unequal: No Solution Exploring Operation: 46*31=1426, Resulting Numbers: [1426] 1426,29 unequal: No Solution Exploring Operation: 46-31=15, Resulting Numbers: [15] 15,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[7, 22], Operations: ['65-58=7', '46-24=22'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,29 unequal: No Solution Exploring Operation: 7*22=154, Resulting Numbers: [154] 154,29 unequal: No Solution Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[58, 24, 65, 46], Operations: [] Exploring Operation: 65-58=7, Resulting Numbers: [24, 46, 7] Generated Node #0,2: 29:[24, 46, 7] Operation: 65-58=7 Moving to Node #0,2 Current State: 29:[24, 46, 7], Operations: ['65-58=7'] Exploring Operation: 46-24=22, Resulting Numbers: [7, 22] Generated Node #0,2,1: 29:[7, 22] Operation: 46-24=22 Moving to Node #0,2,1 Current State: 29:[7, 22], Operations: ['65-58=7', '46-24=22'] Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_3
mult_heuristic
[ 12, 63, 15, 57 ]
62
[ "12+63=75", "75/15=5", "57+5=62" ]
Current State: 62:[12, 63, 15, 57], Operations: [] Exploring Operation: 12+63=75, Resulting Numbers: [15, 57, 75] Generated Node #2: [15, 57, 75] from Operation: 12+63=75 Current State: 62:[15, 57, 75], Operations: ['12+63=75'] Exploring Operation: 75/15=5, Resulting Numbers: [57, 5] Generated Node #3: [57, 5] from Operation: 75/15=5 Current State: 62:[57, 5], Operations: ['12+63=75', '75/15=5'] Exploring Operation: 57+5=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[12, 63, 15, 57], Operations: [] Exploring Operation: 12+15=27, Resulting Numbers: [63, 57, 27] Generated Node #0,0: 62:[63, 57, 27] Operation: 12+15=27 Exploring Operation: 15-12=3, Resulting Numbers: [63, 57, 3] Generated Node #0,1: 62:[63, 57, 3] Operation: 15-12=3 Exploring Operation: 12+57=69, Resulting Numbers: [63, 15, 69] Generated Node #0,2: 62:[63, 15, 69] Operation: 12+57=69 Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[63, 57, 3], Operations: ['15-12=3'] Exploring Operation: 57+3=60, Resulting Numbers: [63, 60] Generated Node #0,1,0: 62:[63, 60] Operation: 57+3=60 Exploring Operation: 63-57=6, Resulting Numbers: [3, 6] Generated Node #0,1,1: 62:[3, 6] Operation: 63-57=6 Exploring Operation: 63-3=60, Resulting Numbers: [57, 60] Generated Node #0,1,2: 62:[57, 60] Operation: 63-3=60 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 62:[63, 60], Operations: ['15-12=3', '57+3=60'] Exploring Operation: 63*60=3780, Resulting Numbers: [3780] 3780,62 unequal: No Solution Exploring Operation: 63+60=123, Resulting Numbers: [123] 123,62 unequal: No Solution Exploring Operation: 63-60=3, Resulting Numbers: [3] 3,62 unequal: No Solution No 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: 62:[3, 6], Operations: ['15-12=3', '63-57=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,62 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,62 unequal: No Solution No 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: 62:[57, 60], Operations: ['15-12=3', '63-3=60'] Exploring Operation: 57*60=3420, Resulting Numbers: [3420] 3420,62 unequal: No Solution Exploring Operation: 60-57=3, Resulting Numbers: [3] 3,62 unequal: No Solution Exploring Operation: 57+60=117, Resulting Numbers: [117] 117,62 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: 62:[63, 57, 27], Operations: ['12+15=27'] Exploring Operation: 63-57=6, Resulting Numbers: [27, 6] Generated Node #0,0,0: 62:[27, 6] Operation: 63-57=6 Exploring Operation: 63-27=36, Resulting Numbers: [57, 36] Generated Node #0,0,1: 62:[57, 36] Operation: 63-27=36 Exploring Operation: 57-27=30, Resulting Numbers: [63, 30] Generated Node #0,0,2: 62:[63, 30] Operation: 57-27=30 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 62:[63, 30], Operations: ['12+15=27', '57-27=30'] Exploring Operation: 63*30=1890, Resulting Numbers: [1890] 1890,62 unequal: No Solution Exploring Operation: 63+30=93, Resulting Numbers: [93] 93,62 unequal: No Solution Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,62 unequal: No Solution No 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: 62:[27, 6], Operations: ['12+15=27', '63-57=6'] Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,62 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,62 unequal: No Solution Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,62 unequal: No Solution No 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: 62:[57, 36], Operations: ['12+15=27', '63-27=36'] Exploring Operation: 57+36=93, Resulting Numbers: [93] 93,62 unequal: No Solution Exploring Operation: 57-36=21, Resulting Numbers: [21] 21,62 unequal: No Solution Exploring Operation: 57*36=2052, Resulting Numbers: [2052] 2052,62 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: 62:[63, 15, 69], Operations: ['12+57=69'] Exploring Operation: 63-15=48, Resulting Numbers: [69, 48] Generated Node #0,2,0: 62:[69, 48] Operation: 63-15=48 Exploring Operation: 69-63=6, Resulting Numbers: [15, 6] Generated Node #0,2,1: 62:[15, 6] Operation: 69-63=6 Exploring Operation: 69-15=54, Resulting Numbers: [63, 54] Generated Node #0,2,2: 62:[63, 54] Operation: 69-15=54 Moving to Node #0,2,2 Current State: 62:[63, 54], Operations: ['12+57=69', '69-15=54'] Exploring Operation: 63+54=117, Resulting Numbers: [117] 117,62 unequal: No Solution Exploring Operation: 63*54=3402, Resulting Numbers: [3402] 3402,62 unequal: No Solution Exploring Operation: 63-54=9, Resulting Numbers: [9] 9,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[15, 6], Operations: ['12+57=69', '69-63=6'] Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,62 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,62 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[69, 48], Operations: ['12+57=69', '63-15=48'] Exploring Operation: 69-48=21, Resulting Numbers: [21] 21,62 unequal: No Solution Exploring Operation: 69*48=3312, Resulting Numbers: [3312] 3312,62 unequal: No Solution Exploring Operation: 69+48=117, Resulting Numbers: [117] 117,62 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
[ 2, 14, 89, 24 ]
85
[ "2*14=28", "89+24=113", "113-28=85" ]
Current State: 85:[2, 14, 89, 24], Operations: [] Exploring Operation: 2*14=28, Resulting Numbers: [89, 24, 28] Generated Node #2: [89, 24, 28] from Operation: 2*14=28 Current State: 85:[89, 24, 28], Operations: ['2*14=28'] Exploring Operation: 89+24=113, Resulting Numbers: [28, 113] Generated Node #3: [28, 113] from Operation: 89+24=113 Current State: 85:[28, 113], Operations: ['2*14=28', '89+24=113'] Exploring Operation: 113-28=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[2, 14, 89, 24], Operations: [] Exploring Operation: 2+14=16, Resulting Numbers: [89, 24, 16] Generated Node #0,0: 85:[89, 24, 16] Operation: 2+14=16 Moving to Node #0,0 Current State: 85:[89, 24, 16], Operations: ['2+14=16'] Exploring Operation: 24-16=8, Resulting Numbers: [89, 8] Generated Node #0,0,0: 85:[89, 8] Operation: 24-16=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[89, 8], Operations: ['2+14=16', '24-16=8'] Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 26, 4, 66, 50 ]
90
[ "66-50=16", "4*16=64", "26+64=90" ]
Current State: 90:[26, 4, 66, 50], Operations: [] Exploring Operation: 66-50=16, Resulting Numbers: [26, 4, 16] Generated Node #2: [26, 4, 16] from Operation: 66-50=16 Current State: 90:[26, 4, 16], Operations: ['66-50=16'] Exploring Operation: 4*16=64, Resulting Numbers: [26, 64] Generated Node #3: [26, 64] from Operation: 4*16=64 Current State: 90:[26, 64], Operations: ['66-50=16', '4*16=64'] Exploring Operation: 26+64=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[26, 4, 66, 50], Operations: [] Exploring Operation: 66-50=16, Resulting Numbers: [26, 4, 16] Generated Node #0,0: 90:[26, 4, 16] Operation: 66-50=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[26, 4, 16], Operations: ['66-50=16'] Exploring Operation: 26+4=30, Resulting Numbers: [16, 30] Generated Node #0,0,0: 90:[16, 30] Operation: 26+4=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[16, 30], Operations: ['66-50=16', '26+4=30'] Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 60, 65, 57, 37 ]
62
[ "57-37=20", "60/20=3", "65-3=62" ]
Current State: 62:[60, 65, 57, 37], Operations: [] Exploring Operation: 57-37=20, Resulting Numbers: [60, 65, 20] Generated Node #2: [60, 65, 20] from Operation: 57-37=20 Current State: 62:[60, 65, 20], Operations: ['57-37=20'] Exploring Operation: 60/20=3, Resulting Numbers: [65, 3] Generated Node #3: [65, 3] from Operation: 60/20=3 Current State: 62:[65, 3], Operations: ['57-37=20', '60/20=3'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[60, 65, 57, 37], Operations: [] Exploring Operation: 65-37=28, Resulting Numbers: [60, 57, 28] Generated Node #0,0: 62:[60, 57, 28] Operation: 65-37=28 Exploring Operation: 60-57=3, Resulting Numbers: [65, 37, 3] Generated Node #0,1: 62:[65, 37, 3] Operation: 60-57=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[60, 57, 28], Operations: ['65-37=28'] Exploring Operation: 57-28=29, Resulting Numbers: [60, 29] Generated Node #0,0,0: 62:[60, 29] Operation: 57-28=29 Exploring Operation: 60-57=3, Resulting Numbers: [28, 3] Generated Node #0,0,1: 62:[28, 3] Operation: 60-57=3 Moving to Node #0,0,0 Current State: 62:[60, 29], Operations: ['65-37=28', '57-28=29'] Exploring Operation: 60+29=89, Resulting Numbers: [89] 89,62 unequal: No Solution Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,62 unequal: No Solution Moving to Node #0,0,1 Current State: 62:[28, 3], Operations: ['65-37=28', '60-57=3'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[65, 37, 3], Operations: ['60-57=3'] Exploring Operation: 65-3=62, Resulting Numbers: [37, 62] Generated Node #0,1,0: 62:[37, 62] Operation: 65-3=62 Exploring Operation: 65-37=28, Resulting Numbers: [3, 28] Generated Node #0,1,1: 62:[3, 28] Operation: 65-37=28 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 62:[3, 28], Operations: ['60-57=3', '65-37=28'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,62 unequal: No Solution No 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: 62:[37, 62], Operations: ['60-57=3', '65-3=62'] Exploring Operation: 62-37=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 37+62=99, Resulting Numbers: [99] 99,62 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
[ 93, 45, 47, 34 ]
34
[ "93-45=48", "48-47=1", "34*1=34" ]
Current State: 34:[93, 45, 47, 34], Operations: [] Exploring Operation: 93-45=48, Resulting Numbers: [47, 34, 48] Generated Node #2: [47, 34, 48] from Operation: 93-45=48 Current State: 34:[47, 34, 48], Operations: ['93-45=48'] Exploring Operation: 48-47=1, Resulting Numbers: [34, 1] Generated Node #3: [34, 1] from Operation: 48-47=1 Current State: 34:[34, 1], Operations: ['93-45=48', '48-47=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[93, 45, 47, 34], Operations: [] Exploring Operation: 93-45=48, Resulting Numbers: [47, 34, 48] Generated Node #0,0: 34:[47, 34, 48] Operation: 93-45=48 Exploring Operation: 93-47=46, Resulting Numbers: [45, 34, 46] Generated Node #0,1: 34:[45, 34, 46] Operation: 93-47=46 Moving to Node #0,1 Current State: 34:[45, 34, 46], Operations: ['93-47=46'] Exploring Operation: 46-45=1, Resulting Numbers: [34, 1] Generated Node #0,1,0: 34:[34, 1] Operation: 46-45=1 Exploring Operation: 46-34=12, Resulting Numbers: [45, 12] Generated Node #0,1,1: 34:[45, 12] Operation: 46-34=12 Moving to Node #0,0 Current State: 34:[47, 34, 48], Operations: ['93-45=48'] Exploring Operation: 48-34=14, Resulting Numbers: [47, 14] Generated Node #0,0,0: 34:[47, 14] Operation: 48-34=14 Exploring Operation: 48-47=1, Resulting Numbers: [34, 1] Generated Node #0,0,1: 34:[34, 1] Operation: 48-47=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 34:[34, 1], Operations: ['93-45=48', '48-47=1'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[93, 45, 47, 34], Operations: [] Exploring Operation: 93-45=48, Resulting Numbers: [47, 34, 48] Generated Node #0,0: 34:[47, 34, 48] Operation: 93-45=48 Moving to Node #0,0 Current State: 34:[47, 34, 48], Operations: ['93-45=48'] Exploring Operation: 48-47=1, Resulting Numbers: [34, 1] Generated Node #0,0,1: 34:[34, 1] Operation: 48-47=1 Moving to Node #0,0,1 Current State: 34:[34, 1], Operations: ['93-45=48', '48-47=1'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 35, 20, 5, 78 ]
80
[ "35+5=40", "40/20=2", "78+2=80" ]
Current State: 80:[35, 20, 5, 78], Operations: [] Exploring Operation: 35+5=40, Resulting Numbers: [20, 78, 40] Generated Node #2: [20, 78, 40] from Operation: 35+5=40 Current State: 80:[20, 78, 40], Operations: ['35+5=40'] Exploring Operation: 40/20=2, Resulting Numbers: [78, 2] Generated Node #3: [78, 2] from Operation: 40/20=2 Current State: 80:[78, 2], Operations: ['35+5=40', '40/20=2'] Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[35, 20, 5, 78], Operations: [] Exploring Operation: 35+5=40, Resulting Numbers: [20, 78, 40] Generated Node #0,0: 80:[20, 78, 40] Operation: 35+5=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[20, 78, 40], Operations: ['35+5=40'] Exploring Operation: 40-20=20, Resulting Numbers: [78, 20] Generated Node #0,0,0: 80:[78, 20] Operation: 40-20=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[78, 20], Operations: ['35+5=40', '40-20=20'] Exploring Operation: 78+20=98, Resulting Numbers: [98] 98,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 64, 5, 38, 67 ]
23
[ "67-64=3", "5*3=15", "38-15=23" ]
Current State: 23:[64, 5, 38, 67], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [5, 38, 3] Generated Node #2: [5, 38, 3] from Operation: 67-64=3 Current State: 23:[5, 38, 3], Operations: ['67-64=3'] Exploring Operation: 5*3=15, Resulting Numbers: [38, 15] Generated Node #3: [38, 15] from Operation: 5*3=15 Current State: 23:[38, 15], Operations: ['67-64=3', '5*3=15'] Exploring Operation: 38-15=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[64, 5, 38, 67], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [5, 38, 3] Generated Node #0,0: 23:[5, 38, 3] Operation: 67-64=3 Exploring Operation: 64-38=26, Resulting Numbers: [5, 67, 26] Generated Node #0,1: 23:[5, 67, 26] Operation: 64-38=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[5, 38, 3], Operations: ['67-64=3'] Exploring Operation: 38-5=33, Resulting Numbers: [3, 33] Generated Node #0,0,0: 23:[3, 33] Operation: 38-5=33 Exploring Operation: 5*3=15, Resulting Numbers: [38, 15] Generated Node #0,0,1: 23:[38, 15] Operation: 5*3=15 Moving to Node #0,0,1 Current State: 23:[38, 15], Operations: ['67-64=3', '5*3=15'] Exploring Operation: 38-15=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[64, 5, 38, 67], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [5, 38, 3] Generated Node #0,0: 23:[5, 38, 3] Operation: 67-64=3 Moving to Node #0,0 Current State: 23:[5, 38, 3], Operations: ['67-64=3'] Exploring Operation: 5*3=15, Resulting Numbers: [38, 15] Generated Node #0,0,1: 23:[38, 15] Operation: 5*3=15 Moving to Node #0,0,1 Current State: 23:[38, 15], Operations: ['67-64=3', '5*3=15'] Exploring Operation: 38-15=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 85, 11, 64, 16 ]
10
[ "85+11=96", "64+96=160", "160/16=10" ]
Current State: 10:[85, 11, 64, 16], Operations: [] Exploring Operation: 85+11=96, Resulting Numbers: [64, 16, 96] Generated Node #2: [64, 16, 96] from Operation: 85+11=96 Current State: 10:[64, 16, 96], Operations: ['85+11=96'] Exploring Operation: 64+96=160, Resulting Numbers: [16, 160] Generated Node #3: [16, 160] from Operation: 64+96=160 Current State: 10:[16, 160], Operations: ['85+11=96', '64+96=160'] Exploring Operation: 160/16=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[85, 11, 64, 16], Operations: [] Exploring Operation: 64/16=4, Resulting Numbers: [85, 11, 4] Generated Node #0,0: 10:[85, 11, 4] Operation: 64/16=4 Exploring Operation: 85-16=69, Resulting Numbers: [11, 64, 69] Generated Node #0,1: 10:[11, 64, 69] Operation: 85-16=69 Exploring Operation: 85-64=21, Resulting Numbers: [11, 16, 21] Generated Node #0,2: 10:[11, 16, 21] Operation: 85-64=21 Moving to Node #0,2 Current State: 10:[11, 16, 21], Operations: ['85-64=21'] Exploring Operation: 21-16=5, Resulting Numbers: [11, 5] Generated Node #0,2,0: 10:[11, 5] Operation: 21-16=5 Exploring Operation: 16-11=5, Resulting Numbers: [21, 5] Generated Node #0,2,1: 10:[21, 5] Operation: 16-11=5 Exploring Operation: 21-11=10, Resulting Numbers: [16, 10] Generated Node #0,2,2: 10:[16, 10] Operation: 21-11=10 Moving to Node #0,0 Current State: 10:[85, 11, 4], Operations: ['64/16=4'] Exploring Operation: 85-11=74, Resulting Numbers: [4, 74] Generated Node #0,0,0: 10:[4, 74] Operation: 85-11=74 Exploring Operation: 85-4=81, Resulting Numbers: [11, 81] Generated Node #0,0,1: 10:[11, 81] Operation: 85-4=81 Exploring Operation: 11-4=7, Resulting Numbers: [85, 7] Generated Node #0,0,2: 10:[85, 7] Operation: 11-4=7 Moving to Node #0,1 Current State: 10:[11, 64, 69], Operations: ['85-16=69'] Exploring Operation: 64-11=53, Resulting Numbers: [69, 53] Generated Node #0,1,0: 10:[69, 53] Operation: 64-11=53 Exploring Operation: 69-11=58, Resulting Numbers: [64, 58] Generated Node #0,1,1: 10:[64, 58] Operation: 69-11=58 Exploring Operation: 69-64=5, Resulting Numbers: [11, 5] Generated Node #0,1,2: 10:[11, 5] Operation: 69-64=5 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 10:[11, 5], Operations: ['85-16=69', '69-64=5'] Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,10 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 10:[69, 53], Operations: ['85-16=69', '64-11=53'] Exploring Operation: 69*53=3657, Resulting Numbers: [3657] 3657,10 unequal: No Solution Exploring Operation: 69+53=122, Resulting Numbers: [122] 122,10 unequal: No Solution Exploring Operation: 69-53=16, Resulting Numbers: [16] 16,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 10:[64, 58], Operations: ['85-16=69', '69-11=58'] Exploring Operation: 64*58=3712, Resulting Numbers: [3712] 3712,10 unequal: No Solution Exploring Operation: 64-58=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 64+58=122, Resulting Numbers: [122] 122,10 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: 10:[11, 5], Operations: ['85-64=21', '21-16=5'] Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,10 unequal: No Solution Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,10 unequal: No Solution Moving to Node #0,2,2 Current State: 10:[16, 10], Operations: ['85-64=21', '21-11=10'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,10 unequal: No Solution Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,10 unequal: No Solution Moving to Node #0,2,1 Current State: 10:[21, 5], Operations: ['85-64=21', '16-11=5'] Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,10 unequal: No Solution Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,10 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,10 unequal: No Solution Moving to Node #0,0,0 Current State: 10:[4, 74], Operations: ['64/16=4', '85-11=74'] Exploring Operation: 4+74=78, Resulting Numbers: [78] 78,10 unequal: No Solution Exploring Operation: 4*74=296, Resulting Numbers: [296] 296,10 unequal: No Solution Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,10 unequal: No Solution Moving to Node #0,0,1 Current State: 10:[11, 81], Operations: ['64/16=4', '85-4=81'] Exploring Operation: 11*81=891, Resulting Numbers: [891] 891,10 unequal: No Solution Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,10 unequal: No Solution Exploring Operation: 11+81=92, Resulting Numbers: [92] 92,10 unequal: No Solution Moving to Node #0,0,2 Current State: 10:[85, 7], Operations: ['64/16=4', '11-4=7'] Exploring Operation: 85-7=78, Resulting Numbers: [78] 78,10 unequal: No Solution Exploring Operation: 85*7=595, Resulting Numbers: [595] 595,10 unequal: No Solution Exploring Operation: 85+7=92, Resulting Numbers: [92] 92,10 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 12, 42, 23, 34 ]
87
[ "42-12=30", "23+34=57", "30+57=87" ]
Current State: 87:[12, 42, 23, 34], Operations: [] Exploring Operation: 42-12=30, Resulting Numbers: [23, 34, 30] Generated Node #2: [23, 34, 30] from Operation: 42-12=30 Current State: 87:[23, 34, 30], Operations: ['42-12=30'] Exploring Operation: 23+34=57, Resulting Numbers: [30, 57] Generated Node #3: [30, 57] from Operation: 23+34=57 Current State: 87:[30, 57], Operations: ['42-12=30', '23+34=57'] Exploring Operation: 30+57=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[12, 42, 23, 34], Operations: [] Exploring Operation: 12+23=35, Resulting Numbers: [42, 34, 35] Generated Node #0,0: 87:[42, 34, 35] Operation: 12+23=35 Exploring Operation: 42-12=30, Resulting Numbers: [23, 34, 30] Generated Node #0,1: 87:[23, 34, 30] Operation: 42-12=30 Exploring Operation: 42-34=8, Resulting Numbers: [12, 23, 8] Generated Node #0,2: 87:[12, 23, 8] Operation: 42-34=8 Moving to Node #0,1 Current State: 87:[23, 34, 30], Operations: ['42-12=30'] Exploring Operation: 30-23=7, Resulting Numbers: [34, 7] Generated Node #0,1,0: 87:[34, 7] Operation: 30-23=7 Exploring Operation: 34-30=4, Resulting Numbers: [23, 4] Generated Node #0,1,1: 87:[23, 4] Operation: 34-30=4 Exploring Operation: 34-23=11, Resulting Numbers: [30, 11] Generated Node #0,1,2: 87:[30, 11] Operation: 34-23=11 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 87:[23, 4], Operations: ['42-12=30', '34-30=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,87 unequal: No Solution Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,87 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 87:[34, 7], Operations: ['42-12=30', '30-23=7'] Exploring Operation: 34+7=41, Resulting Numbers: [41] 41,87 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,87 unequal: No Solution Exploring Operation: 34*7=238, Resulting Numbers: [238] 238,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 87:[30, 11], Operations: ['42-12=30', '34-23=11'] Exploring Operation: 30+11=41, Resulting Numbers: [41] 41,87 unequal: No Solution Exploring Operation: 30*11=330, Resulting Numbers: [330] 330,87 unequal: No Solution Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,87 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: 87:[12, 23, 8], Operations: ['42-34=8'] Exploring Operation: 12-8=4, Resulting Numbers: [23, 4] Generated Node #0,2,0: 87:[23, 4] Operation: 12-8=4 Exploring Operation: 12+23=35, Resulting Numbers: [8, 35] Generated Node #0,2,1: 87:[8, 35] Operation: 12+23=35 Exploring Operation: 23+8=31, Resulting Numbers: [12, 31] Generated Node #0,2,2: 87:[12, 31] Operation: 23+8=31 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 87:[23, 4], Operations: ['42-34=8', '12-8=4'] Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,87 unequal: No Solution Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,87 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,87 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:[8, 35], Operations: ['42-34=8', '12+23=35'] Exploring Operation: 8*35=280, Resulting Numbers: [280] 280,87 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,87 unequal: No Solution Exploring Operation: 8+35=43, Resulting Numbers: [43] 43,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 87:[12, 31], Operations: ['42-34=8', '23+8=31'] Exploring Operation: 12+31=43, Resulting Numbers: [43] 43,87 unequal: No Solution Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,87 unequal: No Solution Exploring Operation: 12*31=372, Resulting Numbers: [372] 372,87 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:[42, 34, 35], Operations: ['12+23=35'] Exploring Operation: 42+35=77, Resulting Numbers: [34, 77] Generated Node #0,0,0: 87:[34, 77] Operation: 42+35=77 Exploring Operation: 42-34=8, Resulting Numbers: [35, 8] Generated Node #0,0,1: 87:[35, 8] Operation: 42-34=8 Exploring Operation: 42-35=7, Resulting Numbers: [34, 7] Generated Node #0,0,2: 87:[34, 7] Operation: 42-35=7 Moving to Node #0,0,2 Current State: 87:[34, 7], Operations: ['12+23=35', '42-35=7'] Exploring Operation: 34*7=238, Resulting Numbers: [238] 238,87 unequal: No Solution Exploring Operation: 34+7=41, Resulting Numbers: [41] 41,87 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,87 unequal: No Solution Moving to Node #0,0,1 Current State: 87:[35, 8], Operations: ['12+23=35', '42-34=8'] Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,87 unequal: No Solution Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,87 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[34, 77], Operations: ['12+23=35', '42+35=77'] Exploring Operation: 34*77=2618, Resulting Numbers: [2618] 2618,87 unequal: No Solution Exploring Operation: 34+77=111, Resulting Numbers: [111] 111,87 unequal: No Solution Exploring Operation: 77-34=43, Resulting Numbers: [43] 43,87 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 93, 39, 15, 73 ]
52
[ "93-73=20", "39*20=780", "780/15=52" ]
Current State: 52:[93, 39, 15, 73], Operations: [] Exploring Operation: 93-73=20, Resulting Numbers: [39, 15, 20] Generated Node #2: [39, 15, 20] from Operation: 93-73=20 Current State: 52:[39, 15, 20], Operations: ['93-73=20'] Exploring Operation: 39*20=780, Resulting Numbers: [15, 780] Generated Node #3: [15, 780] from Operation: 39*20=780 Current State: 52:[15, 780], Operations: ['93-73=20', '39*20=780'] Exploring Operation: 780/15=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[93, 39, 15, 73], Operations: [] Exploring Operation: 93-39=54, Resulting Numbers: [15, 73, 54] Generated Node #0,0: 52:[15, 73, 54] Operation: 93-39=54 Exploring Operation: 73-39=34, Resulting Numbers: [93, 15, 34] Generated Node #0,1: 52:[93, 15, 34] Operation: 73-39=34 Exploring Operation: 93-73=20, Resulting Numbers: [39, 15, 20] Generated Node #0,2: 52:[39, 15, 20] Operation: 93-73=20 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[39, 15, 20], Operations: ['93-73=20'] Exploring Operation: 39-15=24, Resulting Numbers: [20, 24] Generated Node #0,2,0: 52:[20, 24] Operation: 39-15=24 Exploring Operation: 39-20=19, Resulting Numbers: [15, 19] Generated Node #0,2,1: 52:[15, 19] Operation: 39-20=19 Exploring Operation: 39+15=54, Resulting Numbers: [20, 54] Generated Node #0,2,2: 52:[20, 54] Operation: 39+15=54 Moving to Node #0,2,0 Current State: 52:[20, 24], Operations: ['93-73=20', '39-15=24'] Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,52 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,52 unequal: No Solution Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,52 unequal: No Solution Moving to Node #0,2,1 Current State: 52:[15, 19], Operations: ['93-73=20', '39-20=19'] Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,52 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,52 unequal: No Solution Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,52 unequal: No Solution Moving to Node #0,2,2 Current State: 52:[20, 54], Operations: ['93-73=20', '39+15=54'] Exploring Operation: 20*54=1080, Resulting Numbers: [1080] 1080,52 unequal: No Solution Exploring Operation: 20+54=74, Resulting Numbers: [74] 74,52 unequal: No Solution Exploring Operation: 54-20=34, Resulting Numbers: [34] 34,52 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 #0,0 Current State: 52:[15, 73, 54], Operations: ['93-39=54'] Exploring Operation: 54-15=39, Resulting Numbers: [73, 39] Generated Node #0,0,0: 52:[73, 39] Operation: 54-15=39 Exploring Operation: 73-54=19, Resulting Numbers: [15, 19] Generated Node #0,0,1: 52:[15, 19] Operation: 73-54=19 Exploring Operation: 73-15=58, Resulting Numbers: [54, 58] Generated Node #0,0,2: 52:[54, 58] Operation: 73-15=58 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[15, 19], Operations: ['93-39=54', '73-54=19'] Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,52 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,52 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 #0,0,2 Current State: 52:[54, 58], Operations: ['93-39=54', '73-15=58'] Exploring Operation: 54+58=112, Resulting Numbers: [112] 112,52 unequal: No Solution Exploring Operation: 58-54=4, Resulting Numbers: [4] 4,52 unequal: No Solution Exploring Operation: 54*58=3132, Resulting Numbers: [3132] 3132,52 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 #0,0,0 Current State: 52:[73, 39], Operations: ['93-39=54', '54-15=39'] Exploring Operation: 73*39=2847, Resulting Numbers: [2847] 2847,52 unequal: No Solution Exploring Operation: 73-39=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 73+39=112, Resulting Numbers: [112] 112,52 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:[93, 15, 34], Operations: ['73-39=34'] Exploring Operation: 15+34=49, Resulting Numbers: [93, 49] Generated Node #0,1,0: 52:[93, 49] Operation: 15+34=49 Exploring Operation: 93-34=59, Resulting Numbers: [15, 59] Generated Node #0,1,1: 52:[15, 59] Operation: 93-34=59 Exploring Operation: 93-15=78, Resulting Numbers: [34, 78] Generated Node #0,1,2: 52:[34, 78] Operation: 93-15=78 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[15, 59], Operations: ['73-39=34', '93-34=59'] Exploring Operation: 15*59=885, Resulting Numbers: [885] 885,52 unequal: No Solution Exploring Operation: 59-15=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 15+59=74, Resulting Numbers: [74] 74,52 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 #0,1,2 Current State: 52:[34, 78], Operations: ['73-39=34', '93-15=78'] Exploring Operation: 78-34=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 34*78=2652, Resulting Numbers: [2652] 2652,52 unequal: No Solution Exploring Operation: 34+78=112, Resulting Numbers: [112] 112,52 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 #0,1,0 Current State: 52:[93, 49], Operations: ['73-39=34', '15+34=49'] Exploring Operation: 93-49=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 93+49=142, Resulting Numbers: [142] 142,52 unequal: No Solution Exploring Operation: 93*49=4557, Resulting Numbers: [4557] 4557,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 5, 52, 17, 13 ]
98
[ "17+13=30", "5*30=150", "150-52=98" ]
Current State: 98:[5, 52, 17, 13], Operations: [] Exploring Operation: 17+13=30, Resulting Numbers: [5, 52, 30] Generated Node #2: [5, 52, 30] from Operation: 17+13=30 Current State: 98:[5, 52, 30], Operations: ['17+13=30'] Exploring Operation: 5*30=150, Resulting Numbers: [52, 150] Generated Node #3: [52, 150] from Operation: 5*30=150 Current State: 98:[52, 150], Operations: ['17+13=30', '5*30=150'] Exploring Operation: 150-52=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[5, 52, 17, 13], Operations: [] Exploring Operation: 52-5=47, Resulting Numbers: [17, 13, 47] Generated Node #0,0: 98:[17, 13, 47] Operation: 52-5=47 Exploring Operation: 13-5=8, Resulting Numbers: [52, 17, 8] Generated Node #0,1: 98:[52, 17, 8] Operation: 13-5=8 Exploring Operation: 17-5=12, Resulting Numbers: [52, 13, 12] Generated Node #0,2: 98:[52, 13, 12] Operation: 17-5=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[17, 13, 47], Operations: ['52-5=47'] Exploring Operation: 17-13=4, Resulting Numbers: [47, 4] Generated Node #0,0,0: 98:[47, 4] Operation: 17-13=4 Exploring Operation: 17+47=64, Resulting Numbers: [13, 64] Generated Node #0,0,1: 98:[13, 64] Operation: 17+47=64 Exploring Operation: 13+47=60, Resulting Numbers: [17, 60] Generated Node #0,0,2: 98:[17, 60] Operation: 13+47=60 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[47, 4], Operations: ['52-5=47', '17-13=4'] Exploring Operation: 47+4=51, Resulting Numbers: [51] 51,98 unequal: No Solution Exploring Operation: 47*4=188, Resulting Numbers: [188] 188,98 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 98:[17, 60], Operations: ['52-5=47', '13+47=60'] Exploring Operation: 17*60=1020, Resulting Numbers: [1020] 1020,98 unequal: No Solution Exploring Operation: 17+60=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 60-17=43, Resulting Numbers: [43] 43,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 98:[13, 64], Operations: ['52-5=47', '17+47=64'] Exploring Operation: 13*64=832, Resulting Numbers: [832] 832,98 unequal: No Solution Exploring Operation: 64-13=51, Resulting Numbers: [51] 51,98 unequal: No Solution Exploring Operation: 13+64=77, Resulting Numbers: [77] 77,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[52, 13, 12], Operations: ['17-5=12'] Exploring Operation: 13-12=1, Resulting Numbers: [52, 1] Generated Node #0,2,0: 98:[52, 1] Operation: 13-12=1 Exploring Operation: 52/13=4, Resulting Numbers: [12, 4] Generated Node #0,2,1: 98:[12, 4] Operation: 52/13=4 Exploring Operation: 52-12=40, Resulting Numbers: [13, 40] Generated Node #0,2,2: 98:[13, 40] Operation: 52-12=40 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 98:[52, 1], Operations: ['17-5=12', '13-12=1'] Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,98 unequal: No Solution Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,98 unequal: No Solution Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 98:[12, 4], Operations: ['17-5=12', '52/13=4'] Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,98 unequal: No Solution Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 98:[13, 40], Operations: ['17-5=12', '52-12=40'] Exploring Operation: 13+40=53, Resulting Numbers: [53] 53,98 unequal: No Solution Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,98 unequal: No Solution Exploring Operation: 13*40=520, Resulting Numbers: [520] 520,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[52, 17, 8], Operations: ['13-5=8'] Exploring Operation: 17-8=9, Resulting Numbers: [52, 9] Generated Node #0,1,0: 98:[52, 9] Operation: 17-8=9 Exploring Operation: 52+8=60, Resulting Numbers: [17, 60] Generated Node #0,1,1: 98:[17, 60] Operation: 52+8=60 Exploring Operation: 52-8=44, Resulting Numbers: [17, 44] Generated Node #0,1,2: 98:[17, 44] Operation: 52-8=44 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 98:[52, 9], Operations: ['13-5=8', '17-8=9'] Exploring Operation: 52*9=468, Resulting Numbers: [468] 468,98 unequal: No Solution Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,98 unequal: No Solution Exploring Operation: 52+9=61, Resulting Numbers: [61] 61,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 98:[17, 44], Operations: ['13-5=8', '52-8=44'] Exploring Operation: 17*44=748, Resulting Numbers: [748] 748,98 unequal: No Solution Exploring Operation: 17+44=61, Resulting Numbers: [61] 61,98 unequal: No Solution Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 98:[17, 60], Operations: ['13-5=8', '52+8=60'] Exploring Operation: 17+60=77, Resulting Numbers: [77] 77,98 unequal: No Solution Exploring Operation: 60-17=43, Resulting Numbers: [43] 43,98 unequal: No Solution Exploring Operation: 17*60=1020, Resulting Numbers: [1020] 1020,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 48, 83, 62, 28 ]
81
[ "62-48=14", "28/14=2", "83-2=81" ]
Current State: 81:[48, 83, 62, 28], Operations: [] Exploring Operation: 62-48=14, Resulting Numbers: [83, 28, 14] Generated Node #2: [83, 28, 14] from Operation: 62-48=14 Current State: 81:[83, 28, 14], Operations: ['62-48=14'] Exploring Operation: 28/14=2, Resulting Numbers: [83, 2] Generated Node #3: [83, 2] from Operation: 28/14=2 Current State: 81:[83, 2], Operations: ['62-48=14', '28/14=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[48, 83, 62, 28], Operations: [] Exploring Operation: 48-28=20, Resulting Numbers: [83, 62, 20] Generated Node #0,0: 81:[83, 62, 20] Operation: 48-28=20 Exploring Operation: 62-48=14, Resulting Numbers: [83, 28, 14] Generated Node #0,1: 81:[83, 28, 14] Operation: 62-48=14 Exploring Operation: 83-48=35, Resulting Numbers: [62, 28, 35] Generated Node #0,2: 81:[62, 28, 35] Operation: 83-48=35 Exploring Operation: 48+28=76, Resulting Numbers: [83, 62, 76] Generated Node #0,3: 81:[83, 62, 76] Operation: 48+28=76 Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[83, 28, 14], Operations: ['62-48=14'] Exploring Operation: 83+14=97, Resulting Numbers: [28, 97] Generated Node #0,1,0: 81:[28, 97] Operation: 83+14=97 Exploring Operation: 83-14=69, Resulting Numbers: [28, 69] Generated Node #0,1,1: 81:[28, 69] Operation: 83-14=69 Exploring Operation: 28/14=2, Resulting Numbers: [83, 2] Generated Node #0,1,2: 81:[83, 2] Operation: 28/14=2 Exploring Operation: 28-14=14, Resulting Numbers: [83, 14] Generated Node #0,1,3: 81:[83, 14] Operation: 28-14=14 Moving to Node #0,1,2 Current State: 81:[83, 2], Operations: ['62-48=14', '28/14=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[48, 83, 62, 28], Operations: [] Exploring Operation: 62-48=14, Resulting Numbers: [83, 28, 14] Generated Node #0,1: 81:[83, 28, 14] Operation: 62-48=14 Moving to Node #0,1 Current State: 81:[83, 28, 14], Operations: ['62-48=14'] Exploring Operation: 28/14=2, Resulting Numbers: [83, 2] Generated Node #0,1,2: 81:[83, 2] Operation: 28/14=2 Moving to Node #0,1,2 Current State: 81:[83, 2], Operations: ['62-48=14', '28/14=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 93, 40, 48, 51 ]
96
[ "93-40=53", "53-51=2", "48*2=96" ]
Current State: 96:[93, 40, 48, 51], Operations: [] Exploring Operation: 93-40=53, Resulting Numbers: [48, 51, 53] Generated Node #2: [48, 51, 53] from Operation: 93-40=53 Current State: 96:[48, 51, 53], Operations: ['93-40=53'] Exploring Operation: 53-51=2, Resulting Numbers: [48, 2] Generated Node #3: [48, 2] from Operation: 53-51=2 Current State: 96:[48, 2], Operations: ['93-40=53', '53-51=2'] Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[93, 40, 48, 51], Operations: [] Exploring Operation: 48-40=8, Resulting Numbers: [93, 51, 8] Generated Node #0,0: 96:[93, 51, 8] Operation: 48-40=8 Exploring Operation: 93-40=53, Resulting Numbers: [48, 51, 53] Generated Node #0,1: 96:[48, 51, 53] Operation: 93-40=53 Exploring Operation: 51-40=11, Resulting Numbers: [93, 48, 11] Generated Node #0,2: 96:[93, 48, 11] Operation: 51-40=11 Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[93, 48, 11], Operations: ['51-40=11'] Exploring Operation: 93+11=104, Resulting Numbers: [48, 104] Generated Node #0,2,0: 96:[48, 104] Operation: 93+11=104 Exploring Operation: 93-48=45, Resulting Numbers: [11, 45] Generated Node #0,2,1: 96:[11, 45] Operation: 93-48=45 Exploring Operation: 48-11=37, Resulting Numbers: [93, 37] Generated Node #0,2,2: 96:[93, 37] Operation: 48-11=37 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 96:[11, 45], Operations: ['51-40=11', '93-48=45'] Exploring Operation: 11*45=495, Resulting Numbers: [495] 495,96 unequal: No Solution Exploring Operation: 11+45=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 96:[48, 104], Operations: ['51-40=11', '93+11=104'] Exploring Operation: 48*104=4992, Resulting Numbers: [4992] 4992,96 unequal: No Solution Exploring Operation: 104-48=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 48+104=152, Resulting Numbers: [152] 152,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 96:[93, 37], Operations: ['51-40=11', '48-11=37'] Exploring Operation: 93*37=3441, Resulting Numbers: [3441] 3441,96 unequal: No Solution Exploring Operation: 93-37=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 93+37=130, Resulting Numbers: [130] 130,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[93, 51, 8], Operations: ['48-40=8'] Exploring Operation: 93-51=42, Resulting Numbers: [8, 42] Generated Node #0,0,0: 96:[8, 42] Operation: 93-51=42 Exploring Operation: 93+8=101, Resulting Numbers: [51, 101] Generated Node #0,0,1: 96:[51, 101] Operation: 93+8=101 Exploring Operation: 51-8=43, Resulting Numbers: [93, 43] Generated Node #0,0,2: 96:[93, 43] Operation: 51-8=43 Moving to Node #0,0,0 Current State: 96:[8, 42], Operations: ['48-40=8', '93-51=42'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,96 unequal: No Solution Exploring Operation: 8*42=336, Resulting Numbers: [336] 336,96 unequal: No Solution Exploring Operation: 8+42=50, Resulting Numbers: [50] 50,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[51, 101], Operations: ['48-40=8', '93+8=101'] Exploring Operation: 51+101=152, Resulting Numbers: [152] 152,96 unequal: No Solution Exploring Operation: 51*101=5151, Resulting Numbers: [5151] 5151,96 unequal: No Solution Exploring Operation: 101-51=50, Resulting Numbers: [50] 50,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[93, 43], Operations: ['48-40=8', '51-8=43'] Exploring Operation: 93*43=3999, Resulting Numbers: [3999] 3999,96 unequal: No Solution Exploring Operation: 93-43=50, Resulting Numbers: [50] 50,96 unequal: No Solution Exploring Operation: 93+43=136, Resulting Numbers: [136] 136,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[48, 51, 53], Operations: ['93-40=53'] Exploring Operation: 53-51=2, Resulting Numbers: [48, 2] Generated Node #0,1,0: 96:[48, 2] Operation: 53-51=2 Exploring Operation: 51-48=3, Resulting Numbers: [53, 3] Generated Node #0,1,1: 96:[53, 3] Operation: 51-48=3 Exploring Operation: 53-48=5, Resulting Numbers: [51, 5] Generated Node #0,1,2: 96:[51, 5] Operation: 53-48=5 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[48, 2], Operations: ['93-40=53', '53-51=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,96 unequal: No Solution Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[93, 40, 48, 51], Operations: [] Exploring Operation: 93-40=53, Resulting Numbers: [48, 51, 53] Generated Node #0,1: 96:[48, 51, 53] Operation: 93-40=53 Moving to Node #0,1 Current State: 96:[48, 51, 53], Operations: ['93-40=53'] Exploring Operation: 53-51=2, Resulting Numbers: [48, 2] Generated Node #0,1,0: 96:[48, 2] Operation: 53-51=2 Moving to Node #0,1,0 Current State: 96:[48, 2], Operations: ['93-40=53', '53-51=2'] Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
sum_heuristic
[ 60, 20, 66, 61 ]
83
[ "60/20=3", "66/3=22", "61+22=83" ]
Current State: 83:[60, 20, 66, 61], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [66, 61, 3] Generated Node #2: [66, 61, 3] from Operation: 60/20=3 Current State: 83:[66, 61, 3], Operations: ['60/20=3'] Exploring Operation: 66/3=22, Resulting Numbers: [61, 22] Generated Node #3: [61, 22] from Operation: 66/3=22 Current State: 83:[61, 22], Operations: ['60/20=3', '66/3=22'] Exploring Operation: 61+22=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[60, 20, 66, 61], Operations: [] Exploring Operation: 60+20=80, Resulting Numbers: [66, 61, 80] Generated Node #0,0: 83:[66, 61, 80] Operation: 60+20=80 Exploring Operation: 20+61=81, Resulting Numbers: [60, 66, 81] Generated Node #0,1: 83:[60, 66, 81] Operation: 20+61=81 Exploring Operation: 20+66=86, Resulting Numbers: [60, 61, 86] Generated Node #0,2: 83:[60, 61, 86] Operation: 20+66=86 Moving to Node #0,0 Current State: 83:[66, 61, 80], Operations: ['60+20=80'] Exploring Operation: 66+61=127, Resulting Numbers: [80, 127] Generated Node #0,0,0: 83:[80, 127] Operation: 66+61=127 Exploring Operation: 61+80=141, Resulting Numbers: [66, 141] Generated Node #0,0,1: 83:[66, 141] Operation: 61+80=141 Exploring Operation: 66-61=5, Resulting Numbers: [80, 5] Generated Node #0,0,2: 83:[80, 5] Operation: 66-61=5 Moving to Node #0,1 Current State: 83:[60, 66, 81], Operations: ['20+61=81'] Exploring Operation: 60+66=126, Resulting Numbers: [81, 126] Generated Node #0,1,0: 83:[81, 126] Operation: 60+66=126 Exploring Operation: 66-60=6, Resulting Numbers: [81, 6] Generated Node #0,1,1: 83:[81, 6] Operation: 66-60=6 Exploring Operation: 60+81=141, Resulting Numbers: [66, 141] Generated Node #0,1,2: 83:[66, 141] Operation: 60+81=141 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 83:[81, 126], Operations: ['20+61=81', '60+66=126'] Exploring Operation: 126-81=45, Resulting Numbers: [45] 45,83 unequal: No Solution Exploring Operation: 81*126=10206, Resulting Numbers: [10206] 10206,83 unequal: No Solution Exploring Operation: 81+126=207, Resulting Numbers: [207] 207,83 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 #0,1,2 Current State: 83:[66, 141], Operations: ['20+61=81', '60+81=141'] Exploring Operation: 141-66=75, Resulting Numbers: [75] 75,83 unequal: No Solution Exploring Operation: 66+141=207, Resulting Numbers: [207] 207,83 unequal: No Solution Exploring Operation: 66*141=9306, Resulting Numbers: [9306] 9306,83 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:[81, 6], Operations: ['20+61=81', '66-60=6'] Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,83 unequal: No Solution Exploring Operation: 81*6=486, Resulting Numbers: [486] 486,83 unequal: No Solution Exploring Operation: 81+6=87, Resulting Numbers: [87] 87,83 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: 83:[60, 61, 86], Operations: ['20+66=86'] Exploring Operation: 60+61=121, Resulting Numbers: [86, 121] Generated Node #0,2,0: 83:[86, 121] Operation: 60+61=121 Exploring Operation: 86-60=26, Resulting Numbers: [61, 26] Generated Node #0,2,1: 83:[61, 26] Operation: 86-60=26 Exploring Operation: 86-61=25, Resulting Numbers: [60, 25] Generated Node #0,2,2: 83:[60, 25] Operation: 86-61=25 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 83:[86, 121], Operations: ['20+66=86', '60+61=121'] Exploring Operation: 121-86=35, Resulting Numbers: [35] 35,83 unequal: No Solution Exploring Operation: 86+121=207, Resulting Numbers: [207] 207,83 unequal: No Solution Exploring Operation: 86*121=10406, Resulting Numbers: [10406] 10406,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 83:[61, 26], Operations: ['20+66=86', '86-60=26'] Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,83 unequal: No Solution Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 83:[60, 25], Operations: ['20+66=86', '86-61=25'] Exploring Operation: 60+25=85, Resulting Numbers: [85] 85,83 unequal: No Solution Exploring Operation: 60*25=1500, Resulting Numbers: [1500] 1500,83 unequal: No Solution Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,83 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: 83:[80, 127], Operations: ['60+20=80', '66+61=127'] Exploring Operation: 127-80=47, Resulting Numbers: [47] 47,83 unequal: No Solution Exploring Operation: 80*127=10160, Resulting Numbers: [10160] 10160,83 unequal: No Solution Exploring Operation: 80+127=207, Resulting Numbers: [207] 207,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[66, 141], Operations: ['60+20=80', '61+80=141'] Exploring Operation: 141-66=75, Resulting Numbers: [75] 75,83 unequal: No Solution Exploring Operation: 66+141=207, Resulting Numbers: [207] 207,83 unequal: No Solution Exploring Operation: 66*141=9306, Resulting Numbers: [9306] 9306,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[80, 5], Operations: ['60+20=80', '66-61=5'] Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,83 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,83 unequal: No Solution Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,83 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 7, 12, 13, 7 ]
90
[ "7*12=84", "13-7=6", "84+6=90" ]
Current State: 90:[7, 12, 13, 7], Operations: [] Exploring Operation: 7*12=84, Resulting Numbers: [13, 84] Generated Node #2: [13, 84] from Operation: 7*12=84 Current State: 90:[13, 84], Operations: ['7*12=84'] Exploring Operation: 13-7=6, Resulting Numbers: [84, 6] Generated Node #3: [84, 6] from Operation: 13-7=6 Current State: 90:[84, 6], Operations: ['7*12=84', '13-7=6'] Exploring Operation: 84+6=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[7, 12, 13, 7], Operations: [] Exploring Operation: 13-7=6, Resulting Numbers: [12, 7, 6] Generated Node #0,0: 90:[12, 7, 6] Operation: 13-7=6 Exploring Operation: 12-7=5, Resulting Numbers: [7, 13, 5] Generated Node #0,1: 90:[7, 13, 5] Operation: 12-7=5 Exploring Operation: 13-7=6, Resulting Numbers: [7, 12, 6] Generated Node #0,2: 90:[7, 12, 6] Operation: 13-7=6 Exploring Operation: 13-12=1, Resulting Numbers: [7, 7, 1] Generated Node #0,3: 90:[7, 7, 1] Operation: 13-12=1 Exploring Operation: 12-7=5, Resulting Numbers: [13, 7, 5] Generated Node #0,4: 90:[13, 7, 5] Operation: 12-7=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[12, 7, 6], Operations: ['13-7=6'] Exploring Operation: 12/6=2, Resulting Numbers: [7, 2] Generated Node #0,0,0: 90:[7, 2] Operation: 12/6=2 Exploring Operation: 12+6=18, Resulting Numbers: [7, 18] Generated Node #0,0,1: 90:[7, 18] Operation: 12+6=18 Exploring Operation: 12-7=5, Resulting Numbers: [6, 5] Generated Node #0,0,2: 90:[6, 5] Operation: 12-7=5 Exploring Operation: 12-6=6, Resulting Numbers: [7, 6] Generated Node #0,0,3: 90:[7, 6] Operation: 12-6=6 Exploring Operation: 12+7=19, Resulting Numbers: [6, 19] Generated Node #0,0,4: 90:[6, 19] Operation: 12+7=19 Moving to Node #0,0,2 Current State: 90:[6, 5], Operations: ['13-7=6', '12-7=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,90 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[7, 18], Operations: ['13-7=6', '12+6=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,90 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,90 unequal: No Solution Moving to Node #0,0,4 Current State: 90:[6, 19], Operations: ['13-7=6', '12+7=19'] Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,90 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[7, 2], Operations: ['13-7=6', '12/6=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,90 unequal: No Solution Moving to Node #0,0,3 Current State: 90:[7, 6], Operations: ['13-7=6', '12-6=6'] Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,90 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,90 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 Current State: 90:[7, 13, 5], Operations: ['12-7=5'] Exploring Operation: 13-7=6, Resulting Numbers: [5, 6] Generated Node #0,1,0: 90:[5, 6] Operation: 13-7=6 Exploring Operation: 7*13=91, Resulting Numbers: [5, 91] Generated Node #0,1,1: 90:[5, 91] Operation: 7*13=91 Exploring Operation: 7-5=2, Resulting Numbers: [13, 2] Generated Node #0,1,2: 90:[13, 2] Operation: 7-5=2 Exploring Operation: 13+5=18, Resulting Numbers: [7, 18] Generated Node #0,1,3: 90:[7, 18] Operation: 13+5=18 Exploring Operation: 7+13=20, Resulting Numbers: [5, 20] Generated Node #0,1,4: 90:[5, 20] Operation: 7+13=20 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[5, 6], Operations: ['12-7=5', '13-7=6'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,90 unequal: No Solution Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[5, 91], Operations: ['12-7=5', '7*13=91'] Exploring Operation: 5*91=455, Resulting Numbers: [455] 455,90 unequal: No Solution Exploring Operation: 5+91=96, Resulting Numbers: [96] 96,90 unequal: No Solution Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 90:[7, 18], Operations: ['12-7=5', '13+5=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,90 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,90 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 90:[13, 2], Operations: ['12-7=5', '7-5=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,90 unequal: No Solution Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 90:[5, 20], Operations: ['12-7=5', '7+13=20'] Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,90 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,90 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[7, 12, 6], Operations: ['13-7=6'] Exploring Operation: 7+12=19, Resulting Numbers: [6, 19] Generated Node #0,2,0: 90:[6, 19] Operation: 7+12=19 Exploring Operation: 12+6=18, Resulting Numbers: [7, 18] Generated Node #0,2,1: 90:[7, 18] Operation: 12+6=18 Exploring Operation: 12-6=6, Resulting Numbers: [7, 6] Generated Node #0,2,2: 90:[7, 6] Operation: 12-6=6 Exploring Operation: 12-7=5, Resulting Numbers: [6, 5] Generated Node #0,2,3: 90:[6, 5] Operation: 12-7=5 Exploring Operation: 12/6=2, Resulting Numbers: [7, 2] Generated Node #0,2,4: 90:[7, 2] Operation: 12/6=2 Moving to Node #0,2,3 Current State: 90:[6, 5], Operations: ['13-7=6', '12-7=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,90 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,90 unequal: No Solution Moving to Node #0,2,1 Current State: 90:[7, 18], Operations: ['13-7=6', '12+6=18'] Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,90 unequal: No Solution Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,90 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,90 unequal: No Solution Moving to Node #0,2,4 Current State: 90:[7, 2], Operations: ['13-7=6', '12/6=2'] Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,90 unequal: No Solution Moving to Node #0,2,0 Current State: 90:[6, 19], Operations: ['13-7=6', '7+12=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,90 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[7, 6], Operations: ['13-7=6', '12-6=6'] Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,90 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 #0,3 Current State: 90:[7, 7, 1], Operations: ['13-12=1'] Exploring Operation: 7/7=1, Resulting Numbers: [1, 1] Generated Node #0,3,0: 90:[1, 1] Operation: 7/7=1 Exploring Operation: 7-1=6, Resulting Numbers: [7, 6] Generated Node #0,3,1: 90:[7, 6] Operation: 7-1=6 Exploring Operation: 7+7=14, Resulting Numbers: [1, 14] Generated Node #0,3,2: 90:[1, 14] Operation: 7+7=14 Exploring Operation: 7+1=8, Resulting Numbers: [7, 8] Generated Node #0,3,3: 90:[7, 8] Operation: 7+1=8 Exploring Operation: 7-1=6, Resulting Numbers: [7, 6] Generated Node #0,3,4: 90:[7, 6] Operation: 7-1=6 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 90:[7, 6], Operations: ['13-12=1', '7-1=6'] Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,90 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 90:[7, 6], Operations: ['13-12=1', '7-1=6'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,90 unequal: No Solution Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 90:[1, 1], Operations: ['13-12=1', '7/7=1'] Exploring Operation: 1/1=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 1*1=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 1+1=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 1-1=0, Resulting Numbers: [0] 0,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 90:[1, 14], Operations: ['13-12=1', '7+7=14'] Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 90:[7, 8], Operations: ['13-12=1', '7+1=8'] Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,90 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 90:[13, 7, 5], Operations: ['12-7=5'] Exploring Operation: 13*7=91, Resulting Numbers: [5, 91] Generated Node #0,4,0: 90:[5, 91] Operation: 13*7=91 Exploring Operation: 13-7=6, Resulting Numbers: [5, 6] Generated Node #0,4,1: 90:[5, 6] Operation: 13-7=6 Exploring Operation: 13+7=20, Resulting Numbers: [5, 20] Generated Node #0,4,2: 90:[5, 20] Operation: 13+7=20 Exploring Operation: 13+5=18, Resulting Numbers: [7, 18] Generated Node #0,4,3: 90:[7, 18] Operation: 13+5=18 Exploring Operation: 13-5=8, Resulting Numbers: [7, 8] Generated Node #0,4,4: 90:[7, 8] Operation: 13-5=8 Moving to Node #0,4,1 Current State: 90:[5, 6], Operations: ['12-7=5', '13-7=6'] Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,90 unequal: No Solution Moving to Node #0,4,3 Current State: 90:[7, 18], Operations: ['12-7=5', '13+5=18'] Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,90 unequal: No Solution Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,90 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,90 unequal: No Solution Moving to Node #0,4,0 Current State: 90:[5, 91], Operations: ['12-7=5', '13*7=91'] Exploring Operation: 5*91=455, Resulting Numbers: [455] 455,90 unequal: No Solution Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,90 unequal: No Solution Exploring Operation: 5+91=96, Resulting Numbers: [96] 96,90 unequal: No Solution Moving to Node #0,4,2 Current State: 90:[5, 20], Operations: ['12-7=5', '13+7=20'] Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,90 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,90 unequal: No Solution Moving to Node #0,4,4 Current State: 90:[7, 8], Operations: ['12-7=5', '13-5=8'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,90 unequal: No Solution Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 47, 30, 48, 7 ]
25
[ "47-7=40", "30*40=1200", "1200/48=25" ]
Current State: 25:[47, 30, 48, 7], Operations: [] Exploring Operation: 47-7=40, Resulting Numbers: [30, 48, 40] Generated Node #2: [30, 48, 40] from Operation: 47-7=40 Current State: 25:[30, 48, 40], Operations: ['47-7=40'] Exploring Operation: 30*40=1200, Resulting Numbers: [48, 1200] Generated Node #3: [48, 1200] from Operation: 30*40=1200 Current State: 25:[48, 1200], Operations: ['47-7=40', '30*40=1200'] Exploring Operation: 1200/48=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[47, 30, 48, 7], Operations: [] Exploring Operation: 48-47=1, Resulting Numbers: [30, 7, 1] Generated Node #0,0: 25:[30, 7, 1] Operation: 48-47=1 Exploring Operation: 48-30=18, Resulting Numbers: [47, 7, 18] Generated Node #0,1: 25:[47, 7, 18] Operation: 48-30=18 Exploring Operation: 47-30=17, Resulting Numbers: [48, 7, 17] Generated Node #0,2: 25:[48, 7, 17] Operation: 47-30=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[30, 7, 1], Operations: ['48-47=1'] Exploring Operation: 30-7=23, Resulting Numbers: [1, 23] Generated Node #0,0,0: 25:[1, 23] Operation: 30-7=23 Exploring Operation: 7-1=6, Resulting Numbers: [30, 6] Generated Node #0,0,1: 25:[30, 6] Operation: 7-1=6 Exploring Operation: 30-1=29, Resulting Numbers: [7, 29] Generated Node #0,0,2: 25:[7, 29] Operation: 30-1=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[1, 23], Operations: ['48-47=1', '30-7=23'] Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 1*23=23, Resulting Numbers: [23] 23,25 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,25 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:[30, 6], Operations: ['48-47=1', '7-1=6'] Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 30+6=36, Resulting Numbers: [36] 36,25 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 #0,0,2 Current State: 25:[7, 29], Operations: ['48-47=1', '30-1=29'] Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,25 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,25 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,25 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 #0,1 Current State: 25:[47, 7, 18], Operations: ['48-30=18'] Exploring Operation: 47-18=29, Resulting Numbers: [7, 29] Generated Node #0,1,0: 25:[7, 29] Operation: 47-18=29 Exploring Operation: 7+18=25, Resulting Numbers: [47, 25] Generated Node #0,1,1: 25:[47, 25] Operation: 7+18=25 Exploring Operation: 47-7=40, Resulting Numbers: [18, 40] Generated Node #0,1,2: 25:[18, 40] Operation: 47-7=40 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[7, 29], Operations: ['48-30=18', '47-18=29'] Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,25 unequal: No Solution Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,25 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,25 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:[47, 25], Operations: ['48-30=18', '7+18=25'] Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,25 unequal: No Solution Exploring Operation: 47+25=72, Resulting Numbers: [72] 72,25 unequal: No Solution Exploring Operation: 47*25=1175, Resulting Numbers: [1175] 1175,25 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 #0,1,2 Current State: 25:[18, 40], Operations: ['48-30=18', '47-7=40'] Exploring Operation: 18+40=58, Resulting Numbers: [58] 58,25 unequal: No Solution Exploring Operation: 18*40=720, Resulting Numbers: [720] 720,25 unequal: No Solution Exploring Operation: 40-18=22, Resulting Numbers: [22] 22,25 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 #0,2 Current State: 25:[48, 7, 17], Operations: ['47-30=17'] Exploring Operation: 48-7=41, Resulting Numbers: [17, 41] Generated Node #0,2,0: 25:[17, 41] Operation: 48-7=41 Exploring Operation: 48-17=31, Resulting Numbers: [7, 31] Generated Node #0,2,1: 25:[7, 31] Operation: 48-17=31 Exploring Operation: 7+17=24, Resulting Numbers: [48, 24] Generated Node #0,2,2: 25:[48, 24] Operation: 7+17=24 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 25:[7, 31], Operations: ['47-30=17', '48-17=31'] Exploring Operation: 7+31=38, Resulting Numbers: [38] 38,25 unequal: No Solution Exploring Operation: 7*31=217, Resulting Numbers: [217] 217,25 unequal: No Solution Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,25 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 #0,2,0 Current State: 25:[17, 41], Operations: ['47-30=17', '48-7=41'] Exploring Operation: 41-17=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 17+41=58, Resulting Numbers: [58] 58,25 unequal: No Solution Exploring Operation: 17*41=697, Resulting Numbers: [697] 697,25 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 #0,2,2 Current State: 25:[48, 24], Operations: ['47-30=17', '7+17=24'] Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 48+24=72, Resulting Numbers: [72] 72,25 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_3
mult_heuristic
[ 42, 9, 91, 90 ]
52
[ "42+9=51", "91-90=1", "51+1=52" ]
Current State: 52:[42, 9, 91, 90], Operations: [] Exploring Operation: 42+9=51, Resulting Numbers: [91, 90, 51] Generated Node #2: [91, 90, 51] from Operation: 42+9=51 Current State: 52:[91, 90, 51], Operations: ['42+9=51'] Exploring Operation: 91-90=1, Resulting Numbers: [51, 1] Generated Node #3: [51, 1] from Operation: 91-90=1 Current State: 52:[51, 1], Operations: ['42+9=51', '91-90=1'] Exploring Operation: 51+1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[42, 9, 91, 90], Operations: [] Exploring Operation: 90-42=48, Resulting Numbers: [9, 91, 48] Generated Node #0,0: 52:[9, 91, 48] Operation: 90-42=48 Exploring Operation: 91-42=49, Resulting Numbers: [9, 90, 49] Generated Node #0,1: 52:[9, 90, 49] Operation: 91-42=49 Exploring Operation: 91-90=1, Resulting Numbers: [42, 9, 1] Generated Node #0,2: 52:[42, 9, 1] Operation: 91-90=1 Exploring Operation: 90/9=10, Resulting Numbers: [42, 91, 10] Generated Node #0,3: 52:[42, 91, 10] Operation: 90/9=10 Exploring Operation: 42+9=51, Resulting Numbers: [91, 90, 51] Generated Node #0,4: 52:[91, 90, 51] Operation: 42+9=51 Moving to Node #0,2 Current State: 52:[42, 9, 1], Operations: ['91-90=1'] Exploring Operation: 42+1=43, Resulting Numbers: [9, 43] Generated Node #0,2,0: 52:[9, 43] Operation: 42+1=43 Exploring Operation: 42*1=42, Resulting Numbers: [9, 42] Generated Node #0,2,1: 52:[9, 42] Operation: 42*1=42 Exploring Operation: 9+1=10, Resulting Numbers: [42, 10] Generated Node #0,2,2: 52:[42, 10] Operation: 9+1=10 Exploring Operation: 42+9=51, Resulting Numbers: [1, 51] Generated Node #0,2,3: 52:[1, 51] Operation: 42+9=51 Exploring Operation: 42-9=33, Resulting Numbers: [1, 33] Generated Node #0,2,4: 52:[1, 33] Operation: 42-9=33 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 52:[1, 51], Operations: ['91-90=1', '42+9=51'] Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,52 unequal: No Solution Exploring Operation: 1+51=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[42, 9, 91, 90], Operations: [] Exploring Operation: 91-90=1, Resulting Numbers: [42, 9, 1] Generated Node #0,2: 52:[42, 9, 1] Operation: 91-90=1 Moving to Node #0,2 Current State: 52:[42, 9, 1], Operations: ['91-90=1'] Exploring Operation: 42+9=51, Resulting Numbers: [1, 51] Generated Node #0,2,3: 52:[1, 51] Operation: 42+9=51 Moving to Node #0,2,3 Current State: 52:[1, 51], Operations: ['91-90=1', '42+9=51'] Exploring Operation: 1+51=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 90, 96, 50, 75 ]
36
[ "90*50=4500", "4500/75=60", "96-60=36" ]
Current State: 36:[90, 96, 50, 75], Operations: [] Exploring Operation: 90*50=4500, Resulting Numbers: [96, 75, 4500] Generated Node #2: [96, 75, 4500] from Operation: 90*50=4500 Current State: 36:[96, 75, 4500], Operations: ['90*50=4500'] Exploring Operation: 4500/75=60, Resulting Numbers: [96, 60] Generated Node #3: [96, 60] from Operation: 4500/75=60 Current State: 36:[96, 60], Operations: ['90*50=4500', '4500/75=60'] Exploring Operation: 96-60=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[90, 96, 50, 75], Operations: [] Exploring Operation: 96-75=21, Resulting Numbers: [90, 50, 21] Generated Node #0,0: 36:[90, 50, 21] Operation: 96-75=21 Exploring Operation: 96-90=6, Resulting Numbers: [50, 75, 6] Generated Node #0,1: 36:[50, 75, 6] Operation: 96-90=6 Exploring Operation: 90-75=15, Resulting Numbers: [96, 50, 15] Generated Node #0,2: 36:[96, 50, 15] Operation: 90-75=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[50, 75, 6], Operations: ['96-90=6'] Exploring Operation: 75-50=25, Resulting Numbers: [6, 25] Generated Node #0,1,0: 36:[6, 25] Operation: 75-50=25 Exploring Operation: 75-6=69, Resulting Numbers: [50, 69] Generated Node #0,1,1: 36:[50, 69] Operation: 75-6=69 Exploring Operation: 50-6=44, Resulting Numbers: [75, 44] Generated Node #0,1,2: 36:[75, 44] Operation: 50-6=44 Moving to Node #0,1,0 Current State: 36:[6, 25], Operations: ['96-90=6', '75-50=25'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,36 unequal: No Solution Exploring Operation: 6*25=150, Resulting Numbers: [150] 150,36 unequal: No Solution Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,36 unequal: No Solution Moving to Node #0,1,1 Current State: 36:[50, 69], Operations: ['96-90=6', '75-6=69'] Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,36 unequal: No Solution Exploring Operation: 50+69=119, Resulting Numbers: [119] 119,36 unequal: No Solution Exploring Operation: 50*69=3450, Resulting Numbers: [3450] 3450,36 unequal: No Solution Moving to Node #0,1,2 Current State: 36:[75, 44], Operations: ['96-90=6', '50-6=44'] Exploring Operation: 75*44=3300, Resulting Numbers: [3300] 3300,36 unequal: No Solution Exploring Operation: 75+44=119, Resulting Numbers: [119] 119,36 unequal: No Solution Exploring Operation: 75-44=31, Resulting Numbers: [31] 31,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[90, 50, 21], Operations: ['96-75=21'] Exploring Operation: 50-21=29, Resulting Numbers: [90, 29] Generated Node #0,0,0: 36:[90, 29] Operation: 50-21=29 Exploring Operation: 90-21=69, Resulting Numbers: [50, 69] Generated Node #0,0,1: 36:[50, 69] Operation: 90-21=69 Exploring Operation: 90-50=40, Resulting Numbers: [21, 40] Generated Node #0,0,2: 36:[21, 40] Operation: 90-50=40 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 36:[21, 40], Operations: ['96-75=21', '90-50=40'] Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,36 unequal: No Solution Exploring Operation: 21*40=840, Resulting Numbers: [840] 840,36 unequal: No Solution Exploring Operation: 21+40=61, Resulting Numbers: [61] 61,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 36:[50, 69], Operations: ['96-75=21', '90-21=69'] Exploring Operation: 50*69=3450, Resulting Numbers: [3450] 3450,36 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,36 unequal: No Solution Exploring Operation: 50+69=119, Resulting Numbers: [119] 119,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[90, 29], Operations: ['96-75=21', '50-21=29'] Exploring Operation: 90+29=119, Resulting Numbers: [119] 119,36 unequal: No Solution Exploring Operation: 90*29=2610, Resulting Numbers: [2610] 2610,36 unequal: No Solution Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 36:[96, 50, 15], Operations: ['90-75=15'] Exploring Operation: 96-15=81, Resulting Numbers: [50, 81] Generated Node #0,2,0: 36:[50, 81] Operation: 96-15=81 Exploring Operation: 50-15=35, Resulting Numbers: [96, 35] Generated Node #0,2,1: 36:[96, 35] Operation: 50-15=35 Exploring Operation: 96-50=46, Resulting Numbers: [15, 46] Generated Node #0,2,2: 36:[15, 46] Operation: 96-50=46 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 36:[15, 46], Operations: ['90-75=15', '96-50=46'] Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,36 unequal: No Solution Exploring Operation: 15+46=61, Resulting Numbers: [61] 61,36 unequal: No Solution Exploring Operation: 15*46=690, Resulting Numbers: [690] 690,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 36:[50, 81], Operations: ['90-75=15', '96-15=81'] Exploring Operation: 50*81=4050, Resulting Numbers: [4050] 4050,36 unequal: No Solution Exploring Operation: 50+81=131, Resulting Numbers: [131] 131,36 unequal: No Solution Exploring Operation: 81-50=31, Resulting Numbers: [31] 31,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 36:[96, 35], Operations: ['90-75=15', '50-15=35'] Exploring Operation: 96+35=131, Resulting Numbers: [131] 131,36 unequal: No Solution Exploring Operation: 96*35=3360, Resulting Numbers: [3360] 3360,36 unequal: No Solution Exploring Operation: 96-35=61, Resulting Numbers: [61] 61,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 55, 64, 43, 98 ]
22
[ "55+64=119", "43+98=141", "141-119=22" ]
Current State: 22:[55, 64, 43, 98], Operations: [] Exploring Operation: 55+64=119, Resulting Numbers: [43, 98, 119] Generated Node #2: [43, 98, 119] from Operation: 55+64=119 Current State: 22:[43, 98, 119], Operations: ['55+64=119'] Exploring Operation: 43+98=141, Resulting Numbers: [119, 141] Generated Node #3: [119, 141] from Operation: 43+98=141 Current State: 22:[119, 141], Operations: ['55+64=119', '43+98=141'] Exploring Operation: 141-119=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[55, 64, 43, 98], Operations: [] Exploring Operation: 98-64=34, Resulting Numbers: [55, 43, 34] Generated Node #0,0: 22:[55, 43, 34] Operation: 98-64=34 Exploring Operation: 98-55=43, Resulting Numbers: [64, 43, 43] Generated Node #0,1: 22:[64, 43, 43] Operation: 98-55=43 Moving to Node #0,0 Current State: 22:[55, 43, 34], Operations: ['98-64=34'] Exploring Operation: 55-43=12, Resulting Numbers: [34, 12] Generated Node #0,0,0: 22:[34, 12] Operation: 55-43=12 Exploring Operation: 55-34=21, Resulting Numbers: [43, 21] Generated Node #0,0,1: 22:[43, 21] Operation: 55-34=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[34, 12], Operations: ['98-64=34', '55-43=12'] Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[55, 64, 43, 98], Operations: [] Exploring Operation: 98-64=34, Resulting Numbers: [55, 43, 34] Generated Node #0,0: 22:[55, 43, 34] Operation: 98-64=34 Moving to Node #0,0 Current State: 22:[55, 43, 34], Operations: ['98-64=34'] Exploring Operation: 55-43=12, Resulting Numbers: [34, 12] Generated Node #0,0,0: 22:[34, 12] Operation: 55-43=12 Moving to Node #0,0,0 Current State: 22:[34, 12], Operations: ['98-64=34', '55-43=12'] Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 42, 35, 49, 95 ]
91
[ "49*95=4655", "4655/35=133", "133-42=91" ]
Current State: 91:[42, 35, 49, 95], Operations: [] Exploring Operation: 49*95=4655, Resulting Numbers: [42, 35, 4655] Generated Node #2: [42, 35, 4655] from Operation: 49*95=4655 Current State: 91:[42, 35, 4655], Operations: ['49*95=4655'] Exploring Operation: 4655/35=133, Resulting Numbers: [42, 133] Generated Node #3: [42, 133] from Operation: 4655/35=133 Current State: 91:[42, 133], Operations: ['49*95=4655', '4655/35=133'] Exploring Operation: 133-42=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[42, 35, 49, 95], Operations: [] Exploring Operation: 42+49=91, Resulting Numbers: [35, 95, 91] Generated Node #0,0: 91:[35, 95, 91] Operation: 42+49=91 Exploring Operation: 49-42=7, Resulting Numbers: [35, 95, 7] Generated Node #0,1: 91:[35, 95, 7] Operation: 49-42=7 Moving to Node #0,0 Current State: 91:[35, 95, 91], Operations: ['42+49=91'] Exploring Operation: 95-91=4, Resulting Numbers: [35, 4] Generated Node #0,0,0: 91:[35, 4] Operation: 95-91=4 Exploring Operation: 95-35=60, Resulting Numbers: [91, 60] Generated Node #0,0,1: 91:[91, 60] Operation: 95-35=60 Moving to Node #0,1 Current State: 91:[35, 95, 7], Operations: ['49-42=7'] Exploring Operation: 35-7=28, Resulting Numbers: [95, 28] Generated Node #0,1,0: 91:[95, 28] Operation: 35-7=28 Exploring Operation: 35/7=5, Resulting Numbers: [95, 5] Generated Node #0,1,1: 91:[95, 5] Operation: 35/7=5 Moving to Node #0,1,1 Current State: 91:[95, 5], Operations: ['49-42=7', '35/7=5'] Exploring Operation: 95-5=90, Resulting Numbers: [90] 90,91 unequal: No Solution Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,91 unequal: No Solution Moving to Node #0,1,0 Current State: 91:[95, 28], Operations: ['49-42=7', '35-7=28'] Exploring Operation: 95-28=67, Resulting Numbers: [67] 67,91 unequal: No Solution Exploring Operation: 95+28=123, Resulting Numbers: [123] 123,91 unequal: No Solution Moving to Node #0,0,0 Current State: 91:[35, 4], Operations: ['42+49=91', '95-91=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,91 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[91, 60], Operations: ['42+49=91', '95-35=60'] Exploring Operation: 91-60=31, Resulting Numbers: [31] 31,91 unequal: No Solution Exploring Operation: 91+60=151, Resulting Numbers: [151] 151,91 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 8, 66, 3, 1 ]
91
[ "8*3=24", "66+1=67", "24+67=91" ]
Current State: 91:[8, 66, 3, 1], Operations: [] Exploring Operation: 8*3=24, Resulting Numbers: [66, 1, 24] Generated Node #2: [66, 1, 24] from Operation: 8*3=24 Current State: 91:[66, 1, 24], Operations: ['8*3=24'] Exploring Operation: 66+1=67, Resulting Numbers: [24, 67] Generated Node #3: [24, 67] from Operation: 66+1=67 Current State: 91:[24, 67], Operations: ['8*3=24', '66+1=67'] Exploring Operation: 24+67=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[8, 66, 3, 1], Operations: [] Exploring Operation: 66/3=22, Resulting Numbers: [8, 1, 22] Generated Node #0,0: 91:[8, 1, 22] Operation: 66/3=22 Moving to Node #0,0 Current State: 91:[8, 1, 22], Operations: ['66/3=22'] Exploring Operation: 22-8=14, Resulting Numbers: [1, 14] Generated Node #0,0,0: 91:[1, 14] Operation: 22-8=14 Moving to Node #0,0,0 Current State: 91:[1, 14], Operations: ['66/3=22', '22-8=14'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,91 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 6, 21, 81, 33 ]
24
[ "33-6=27", "81/27=3", "21+3=24" ]
Current State: 24:[6, 21, 81, 33], Operations: [] Exploring Operation: 33-6=27, Resulting Numbers: [21, 81, 27] Generated Node #2: [21, 81, 27] from Operation: 33-6=27 Current State: 24:[21, 81, 27], Operations: ['33-6=27'] Exploring Operation: 81/27=3, Resulting Numbers: [21, 3] Generated Node #3: [21, 3] from Operation: 81/27=3 Current State: 24:[21, 3], Operations: ['33-6=27', '81/27=3'] Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[6, 21, 81, 33], Operations: [] Exploring Operation: 81-33=48, Resulting Numbers: [6, 21, 48] Generated Node #0,0: 24:[6, 21, 48] Operation: 81-33=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[6, 21, 48], Operations: ['81-33=48'] Exploring Operation: 48/6=8, Resulting Numbers: [21, 8] Generated Node #0,0,0: 24:[21, 8] Operation: 48/6=8 Moving to Node #0,0,0 Current State: 24:[21, 8], Operations: ['81-33=48', '48/6=8'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,24 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
[ 35, 15, 41, 1 ]
75
[ "41-35=6", "6-1=5", "15*5=75" ]
Current State: 75:[35, 15, 41, 1], Operations: [] Exploring Operation: 41-35=6, Resulting Numbers: [15, 1, 6] Generated Node #2: [15, 1, 6] from Operation: 41-35=6 Current State: 75:[15, 1, 6], Operations: ['41-35=6'] Exploring Operation: 6-1=5, Resulting Numbers: [15, 5] Generated Node #3: [15, 5] from Operation: 6-1=5 Current State: 75:[15, 5], Operations: ['41-35=6', '6-1=5'] Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[35, 15, 41, 1], Operations: [] Exploring Operation: 41-35=6, Resulting Numbers: [15, 1, 6] Generated Node #0,0: 75:[15, 1, 6] Operation: 41-35=6 Exploring Operation: 35+41=76, Resulting Numbers: [15, 1, 76] Generated Node #0,1: 75:[15, 1, 76] Operation: 35+41=76 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[15, 1, 6], Operations: ['41-35=6'] Exploring Operation: 6-1=5, Resulting Numbers: [15, 5] Generated Node #0,0,0: 75:[15, 5] Operation: 6-1=5 Exploring Operation: 15*1=15, Resulting Numbers: [6, 15] Generated Node #0,0,1: 75:[6, 15] Operation: 15*1=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[15, 5], Operations: ['41-35=6', '6-1=5'] Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[35, 15, 41, 1], Operations: [] Exploring Operation: 41-35=6, Resulting Numbers: [15, 1, 6] Generated Node #0,0: 75:[15, 1, 6] Operation: 41-35=6 Moving to Node #0,0 Current State: 75:[15, 1, 6], Operations: ['41-35=6'] Exploring Operation: 6-1=5, Resulting Numbers: [15, 5] Generated Node #0,0,0: 75:[15, 5] Operation: 6-1=5 Moving to Node #0,0,0 Current State: 75:[15, 5], Operations: ['41-35=6', '6-1=5'] Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 13, 87, 53, 76 ]
29
[ "13+87=100", "53+76=129", "129-100=29" ]
Current State: 29:[13, 87, 53, 76], Operations: [] Exploring Operation: 13+87=100, Resulting Numbers: [53, 76, 100] Generated Node #2: [53, 76, 100] from Operation: 13+87=100 Current State: 29:[53, 76, 100], Operations: ['13+87=100'] Exploring Operation: 53+76=129, Resulting Numbers: [100, 129] Generated Node #3: [100, 129] from Operation: 53+76=129 Current State: 29:[100, 129], Operations: ['13+87=100', '53+76=129'] Exploring Operation: 129-100=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[13, 87, 53, 76], Operations: [] Exploring Operation: 87-76=11, Resulting Numbers: [13, 53, 11] Generated Node #0,0: 29:[13, 53, 11] Operation: 87-76=11 Exploring Operation: 87-53=34, Resulting Numbers: [13, 76, 34] Generated Node #0,1: 29:[13, 76, 34] Operation: 87-53=34 Exploring Operation: 76-53=23, Resulting Numbers: [13, 87, 23] Generated Node #0,2: 29:[13, 87, 23] Operation: 76-53=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[13, 53, 11], Operations: ['87-76=11'] Exploring Operation: 53-13=40, Resulting Numbers: [11, 40] Generated Node #0,0,0: 29:[11, 40] Operation: 53-13=40 Exploring Operation: 13+11=24, Resulting Numbers: [53, 24] Generated Node #0,0,1: 29:[53, 24] Operation: 13+11=24 Exploring Operation: 53-11=42, Resulting Numbers: [13, 42] Generated Node #0,0,2: 29:[13, 42] Operation: 53-11=42 Moving to Node #0,0,0 Current State: 29:[11, 40], Operations: ['87-76=11', '53-13=40'] Exploring Operation: 11*40=440, Resulting Numbers: [440] 440,29 unequal: No Solution Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[13, 87, 53, 76], Operations: [] Exploring Operation: 87-76=11, Resulting Numbers: [13, 53, 11] Generated Node #0,0: 29:[13, 53, 11] Operation: 87-76=11 Moving to Node #0,0 Current State: 29:[13, 53, 11], Operations: ['87-76=11'] Exploring Operation: 53-13=40, Resulting Numbers: [11, 40] Generated Node #0,0,0: 29:[11, 40] Operation: 53-13=40 Moving to Node #0,0,0 Current State: 29:[11, 40], Operations: ['87-76=11', '53-13=40'] Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 80, 3, 39, 88 ]
50
[ "80-3=77", "39+88=127", "127-77=50" ]
Current State: 50:[80, 3, 39, 88], Operations: [] Exploring Operation: 80-3=77, Resulting Numbers: [39, 88, 77] Generated Node #2: [39, 88, 77] from Operation: 80-3=77 Current State: 50:[39, 88, 77], Operations: ['80-3=77'] Exploring Operation: 39+88=127, Resulting Numbers: [77, 127] Generated Node #3: [77, 127] from Operation: 39+88=127 Current State: 50:[77, 127], Operations: ['80-3=77', '39+88=127'] Exploring Operation: 127-77=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[80, 3, 39, 88], Operations: [] Exploring Operation: 88-39=49, Resulting Numbers: [80, 3, 49] Generated Node #0,0: 50:[80, 3, 49] Operation: 88-39=49 Exploring Operation: 88-80=8, Resulting Numbers: [3, 39, 8] Generated Node #0,1: 50:[3, 39, 8] Operation: 88-80=8 Exploring Operation: 80-39=41, Resulting Numbers: [3, 88, 41] Generated Node #0,2: 50:[3, 88, 41] Operation: 80-39=41 Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[3, 39, 8], Operations: ['88-80=8'] Exploring Operation: 39-8=31, Resulting Numbers: [3, 31] Generated Node #0,1,0: 50:[3, 31] Operation: 39-8=31 Exploring Operation: 39+8=47, Resulting Numbers: [3, 47] Generated Node #0,1,1: 50:[3, 47] Operation: 39+8=47 Exploring Operation: 39/3=13, Resulting Numbers: [8, 13] Generated Node #0,1,2: 50:[8, 13] Operation: 39/3=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 50:[3, 47], Operations: ['88-80=8', '39+8=47'] Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,50 unequal: No Solution Exploring Operation: 3*47=141, Resulting Numbers: [141] 141,50 unequal: No Solution Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[80, 3, 39, 88], Operations: [] Exploring Operation: 88-80=8, Resulting Numbers: [3, 39, 8] Generated Node #0,1: 50:[3, 39, 8] Operation: 88-80=8 Moving to Node #0,1 Current State: 50:[3, 39, 8], Operations: ['88-80=8'] Exploring Operation: 39+8=47, Resulting Numbers: [3, 47] Generated Node #0,1,1: 50:[3, 47] Operation: 39+8=47 Moving to Node #0,1,1 Current State: 50:[3, 47], Operations: ['88-80=8', '39+8=47'] Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 96, 84, 26, 28 ]
66
[ "96-84=12", "26+28=54", "12+54=66" ]
Current State: 66:[96, 84, 26, 28], Operations: [] Exploring Operation: 96-84=12, Resulting Numbers: [26, 28, 12] Generated Node #2: [26, 28, 12] from Operation: 96-84=12 Current State: 66:[26, 28, 12], Operations: ['96-84=12'] Exploring Operation: 26+28=54, Resulting Numbers: [12, 54] Generated Node #3: [12, 54] from Operation: 26+28=54 Current State: 66:[12, 54], Operations: ['96-84=12', '26+28=54'] Exploring Operation: 12+54=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[96, 84, 26, 28], Operations: [] Exploring Operation: 96-28=68, Resulting Numbers: [84, 26, 68] Generated Node #0,0: 66:[84, 26, 68] Operation: 96-28=68 Exploring Operation: 96-84=12, Resulting Numbers: [26, 28, 12] Generated Node #0,1: 66:[26, 28, 12] Operation: 96-84=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[26, 28, 12], Operations: ['96-84=12'] Exploring Operation: 28-26=2, Resulting Numbers: [12, 2] Generated Node #0,1,0: 66:[12, 2] Operation: 28-26=2 Exploring Operation: 26-12=14, Resulting Numbers: [28, 14] Generated Node #0,1,1: 66:[28, 14] Operation: 26-12=14 Moving to Node #0,1,0 Current State: 66:[12, 2], Operations: ['96-84=12', '28-26=2'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,66 unequal: No Solution Moving to Node #0,1,1 Current State: 66:[28, 14], Operations: ['96-84=12', '26-12=14'] Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,66 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[84, 26, 68], Operations: ['96-28=68'] Exploring Operation: 84-68=16, Resulting Numbers: [26, 16] Generated Node #0,0,0: 66:[26, 16] Operation: 84-68=16 Exploring Operation: 84-26=58, Resulting Numbers: [68, 58] Generated Node #0,0,1: 66:[68, 58] Operation: 84-26=58 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 66:[26, 16], Operations: ['96-28=68', '84-68=16'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 26+16=42, Resulting Numbers: [42] 42,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 66:[68, 58], Operations: ['96-28=68', '84-26=58'] Exploring Operation: 68+58=126, Resulting Numbers: [126] 126,66 unequal: No Solution Exploring Operation: 68-58=10, Resulting Numbers: [10] 10,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 76, 82, 3, 63 ]
83
[ "76*3=228", "82+63=145", "228-145=83" ]
Current State: 83:[76, 82, 3, 63], Operations: [] Exploring Operation: 76*3=228, Resulting Numbers: [82, 63, 228] Generated Node #2: [82, 63, 228] from Operation: 76*3=228 Current State: 83:[82, 63, 228], Operations: ['76*3=228'] Exploring Operation: 82+63=145, Resulting Numbers: [228, 145] Generated Node #3: [228, 145] from Operation: 82+63=145 Current State: 83:[228, 145], Operations: ['76*3=228', '82+63=145'] Exploring Operation: 228-145=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[76, 82, 3, 63], Operations: [] Exploring Operation: 3+63=66, Resulting Numbers: [76, 82, 66] Generated Node #0,0: 83:[76, 82, 66] Operation: 3+63=66 Exploring Operation: 76+3=79, Resulting Numbers: [82, 63, 79] Generated Node #0,1: 83:[82, 63, 79] Operation: 76+3=79 Exploring Operation: 82+3=85, Resulting Numbers: [76, 63, 85] Generated Node #0,2: 83:[76, 63, 85] Operation: 82+3=85 Moving to Node #0,0 Current State: 83:[76, 82, 66], Operations: ['3+63=66'] Exploring Operation: 76-66=10, Resulting Numbers: [82, 10] Generated Node #0,0,0: 83:[82, 10] Operation: 76-66=10 Exploring Operation: 82+66=148, Resulting Numbers: [76, 148] Generated Node #0,0,1: 83:[76, 148] Operation: 82+66=148 Exploring Operation: 76+66=142, Resulting Numbers: [82, 142] Generated Node #0,0,2: 83:[82, 142] Operation: 76+66=142 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[82, 142], Operations: ['3+63=66', '76+66=142'] Exploring Operation: 142-82=60, Resulting Numbers: [60] 60,83 unequal: No Solution Exploring Operation: 82+142=224, Resulting Numbers: [224] 224,83 unequal: No Solution Exploring Operation: 82*142=11644, Resulting Numbers: [11644] 11644,83 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:[76, 148], Operations: ['3+63=66', '82+66=148'] Exploring Operation: 76+148=224, Resulting Numbers: [224] 224,83 unequal: No Solution Exploring Operation: 76*148=11248, Resulting Numbers: [11248] 11248,83 unequal: No Solution Exploring Operation: 148-76=72, Resulting Numbers: [72] 72,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[82, 10], Operations: ['3+63=66', '76-66=10'] Exploring Operation: 82+10=92, Resulting Numbers: [92] 92,83 unequal: No Solution Exploring Operation: 82*10=820, Resulting Numbers: [820] 820,83 unequal: No Solution Exploring Operation: 82-10=72, Resulting Numbers: [72] 72,83 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:[82, 63, 79], Operations: ['76+3=79'] Exploring Operation: 63+79=142, Resulting Numbers: [82, 142] Generated Node #0,1,0: 83:[82, 142] Operation: 63+79=142 Exploring Operation: 82+63=145, Resulting Numbers: [79, 145] Generated Node #0,1,1: 83:[79, 145] Operation: 82+63=145 Exploring Operation: 82-63=19, Resulting Numbers: [79, 19] Generated Node #0,1,2: 83:[79, 19] Operation: 82-63=19 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 83:[82, 142], Operations: ['76+3=79', '63+79=142'] Exploring Operation: 82+142=224, Resulting Numbers: [224] 224,83 unequal: No Solution Exploring Operation: 142-82=60, Resulting Numbers: [60] 60,83 unequal: No Solution Exploring Operation: 82*142=11644, Resulting Numbers: [11644] 11644,83 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:[79, 145], Operations: ['76+3=79', '82+63=145'] Exploring Operation: 145-79=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 79*145=11455, Resulting Numbers: [11455] 11455,83 unequal: No Solution Exploring Operation: 79+145=224, Resulting Numbers: [224] 224,83 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 #0,1,2 Current State: 83:[79, 19], Operations: ['76+3=79', '82-63=19'] Exploring Operation: 79-19=60, Resulting Numbers: [60] 60,83 unequal: No Solution Exploring Operation: 79*19=1501, Resulting Numbers: [1501] 1501,83 unequal: No Solution Exploring Operation: 79+19=98, Resulting Numbers: [98] 98,83 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: 83:[76, 63, 85], Operations: ['82+3=85'] Exploring Operation: 85-63=22, Resulting Numbers: [76, 22] Generated Node #0,2,0: 83:[76, 22] Operation: 85-63=22 Exploring Operation: 76-63=13, Resulting Numbers: [85, 13] Generated Node #0,2,1: 83:[85, 13] Operation: 76-63=13 Exploring Operation: 76+63=139, Resulting Numbers: [85, 139] Generated Node #0,2,2: 83:[85, 139] Operation: 76+63=139 Moving to Node #0,2,2 Current State: 83:[85, 139], Operations: ['82+3=85', '76+63=139'] Exploring Operation: 85+139=224, Resulting Numbers: [224] 224,83 unequal: No Solution Exploring Operation: 139-85=54, Resulting Numbers: [54] 54,83 unequal: No Solution Exploring Operation: 85*139=11815, Resulting Numbers: [11815] 11815,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[76, 22], Operations: ['82+3=85', '85-63=22'] Exploring Operation: 76-22=54, Resulting Numbers: [54] 54,83 unequal: No Solution Exploring Operation: 76*22=1672, Resulting Numbers: [1672] 1672,83 unequal: No Solution Exploring Operation: 76+22=98, Resulting Numbers: [98] 98,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[85, 13], Operations: ['82+3=85', '76-63=13'] Exploring Operation: 85*13=1105, Resulting Numbers: [1105] 1105,83 unequal: No Solution Exploring Operation: 85-13=72, Resulting Numbers: [72] 72,83 unequal: No Solution Exploring Operation: 85+13=98, Resulting Numbers: [98] 98,83 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 31, 7, 89, 63 ]
65
[ "31*7=217", "89+63=152", "217-152=65" ]
Current State: 65:[31, 7, 89, 63], Operations: [] Exploring Operation: 31*7=217, Resulting Numbers: [89, 63, 217] Generated Node #2: [89, 63, 217] from Operation: 31*7=217 Current State: 65:[89, 63, 217], Operations: ['31*7=217'] Exploring Operation: 89+63=152, Resulting Numbers: [217, 152] Generated Node #3: [217, 152] from Operation: 89+63=152 Current State: 65:[217, 152], Operations: ['31*7=217', '89+63=152'] Exploring Operation: 217-152=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[31, 7, 89, 63], Operations: [] Exploring Operation: 89-31=58, Resulting Numbers: [7, 63, 58] Generated Node #0,0: 65:[7, 63, 58] Operation: 89-31=58 Moving to Node #0,0 Current State: 65:[7, 63, 58], Operations: ['89-31=58'] Exploring Operation: 7+58=65, Resulting Numbers: [63, 65] Generated Node #0,0,0: 65:[63, 65] Operation: 7+58=65 Moving to Node #0,0,0 Current State: 65:[63, 65], Operations: ['89-31=58', '7+58=65'] Exploring Operation: 65-63=2, Resulting Numbers: [2] 2,65 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 95, 31, 93, 35 ]
57
[ "95-35=60", "93/31=3", "60-3=57" ]
Current State: 57:[95, 31, 93, 35], Operations: [] Exploring Operation: 95-35=60, Resulting Numbers: [31, 93, 60] Generated Node #2: [31, 93, 60] from Operation: 95-35=60 Current State: 57:[31, 93, 60], Operations: ['95-35=60'] Exploring Operation: 93/31=3, Resulting Numbers: [60, 3] Generated Node #3: [60, 3] from Operation: 93/31=3 Current State: 57:[60, 3], Operations: ['95-35=60', '93/31=3'] Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[95, 31, 93, 35], Operations: [] Exploring Operation: 93/31=3, Resulting Numbers: [95, 35, 3] Generated Node #0,0: 57:[95, 35, 3] Operation: 93/31=3 Exploring Operation: 95-35=60, Resulting Numbers: [31, 93, 60] Generated Node #0,1: 57:[31, 93, 60] Operation: 95-35=60 Exploring Operation: 95-93=2, Resulting Numbers: [31, 35, 2] Generated Node #0,2: 57:[31, 35, 2] Operation: 95-93=2 Exploring Operation: 93-35=58, Resulting Numbers: [95, 31, 58] Generated Node #0,3: 57:[95, 31, 58] Operation: 93-35=58 Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[31, 35, 2], Operations: ['95-93=2'] Exploring Operation: 35*2=70, Resulting Numbers: [31, 70] Generated Node #0,2,0: 57:[31, 70] Operation: 35*2=70 Exploring Operation: 31*2=62, Resulting Numbers: [35, 62] Generated Node #0,2,1: 57:[35, 62] Operation: 31*2=62 Exploring Operation: 35-31=4, Resulting Numbers: [2, 4] Generated Node #0,2,2: 57:[2, 4] Operation: 35-31=4 Exploring Operation: 31+35=66, Resulting Numbers: [2, 66] Generated Node #0,2,3: 57:[2, 66] Operation: 31+35=66 Moving to Node #0,2,2 Current State: 57:[2, 4], Operations: ['95-93=2', '35-31=4'] Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,57 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,57 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,57 unequal: No Solution Moving to Node #0,2,3 Current State: 57:[2, 66], Operations: ['95-93=2', '31+35=66'] Exploring Operation: 2*66=132, Resulting Numbers: [132] 132,57 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,57 unequal: No Solution Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,57 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[35, 62], Operations: ['95-93=2', '31*2=62'] Exploring Operation: 62-35=27, Resulting Numbers: [27] 27,57 unequal: No Solution Exploring Operation: 35+62=97, Resulting Numbers: [97] 97,57 unequal: No Solution Exploring Operation: 35*62=2170, Resulting Numbers: [2170] 2170,57 unequal: No Solution Moving to Node #0,2,0 Current State: 57:[31, 70], Operations: ['95-93=2', '35*2=70'] Exploring Operation: 31*70=2170, Resulting Numbers: [2170] 2170,57 unequal: No Solution Exploring Operation: 31+70=101, Resulting Numbers: [101] 101,57 unequal: No Solution Exploring Operation: 70-31=39, Resulting Numbers: [39] 39,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[31, 93, 60], Operations: ['95-35=60'] Exploring Operation: 93/31=3, Resulting Numbers: [60, 3] Generated Node #0,1,0: 57:[60, 3] Operation: 93/31=3 Exploring Operation: 60-31=29, Resulting Numbers: [93, 29] Generated Node #0,1,1: 57:[93, 29] Operation: 60-31=29 Exploring Operation: 93-60=33, Resulting Numbers: [31, 33] Generated Node #0,1,2: 57:[31, 33] Operation: 93-60=33 Exploring Operation: 93-31=62, Resulting Numbers: [60, 62] Generated Node #0,1,3: 57:[60, 62] Operation: 93-31=62 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 57:[60, 3], Operations: ['95-35=60', '93/31=3'] Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,57 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 60*3=180, Resulting Numbers: [180] 180,57 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[95, 31, 93, 35], Operations: [] Exploring Operation: 95-35=60, Resulting Numbers: [31, 93, 60] Generated Node #0,1: 57:[31, 93, 60] Operation: 95-35=60 Moving to Node #0,1 Current State: 57:[31, 93, 60], Operations: ['95-35=60'] Exploring Operation: 93/31=3, Resulting Numbers: [60, 3] Generated Node #0,1,0: 57:[60, 3] Operation: 93/31=3 Moving to Node #0,1,0 Current State: 57:[60, 3], Operations: ['95-35=60', '93/31=3'] Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.970486
hs_4
sum_heuristic
[ 55, 55, 5, 38 ]
77
[ "55+55=110", "38-5=33", "110-33=77" ]
Current State: 77:[55, 55, 5, 38], Operations: [] Exploring Operation: 55+55=110, Resulting Numbers: [5, 38, 110] Generated Node #2: [5, 38, 110] from Operation: 55+55=110 Current State: 77:[5, 38, 110], Operations: ['55+55=110'] Exploring Operation: 38-5=33, Resulting Numbers: [110, 33] Generated Node #3: [110, 33] from Operation: 38-5=33 Current State: 77:[110, 33], Operations: ['55+55=110', '38-5=33'] Exploring Operation: 110-33=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[55, 55, 5, 38], Operations: [] Exploring Operation: 55/55=1, Resulting Numbers: [5, 38, 1] Generated Node #0,0: 77:[5, 38, 1] Operation: 55/55=1 Exploring Operation: 55-38=17, Resulting Numbers: [55, 5, 17] Generated Node #0,1: 77:[55, 5, 17] Operation: 55-38=17 Exploring Operation: 55-55=0, Resulting Numbers: [5, 38, 0] Generated Node #0,2: 77:[5, 38, 0] Operation: 55-55=0 Exploring Operation: 55-38=17, Resulting Numbers: [55, 5, 17] Generated Node #0,3: 77:[55, 5, 17] Operation: 55-38=17 Moving to Node #0,1 Current State: 77:[55, 5, 17], Operations: ['55-38=17'] Exploring Operation: 17-5=12, Resulting Numbers: [55, 12] Generated Node #0,1,0: 77:[55, 12] Operation: 17-5=12 Exploring Operation: 55/5=11, Resulting Numbers: [17, 11] Generated Node #0,1,1: 77:[17, 11] Operation: 55/5=11 Exploring Operation: 55+17=72, Resulting Numbers: [5, 72] Generated Node #0,1,2: 77:[5, 72] Operation: 55+17=72 Exploring Operation: 55+5=60, Resulting Numbers: [17, 60] Generated Node #0,1,3: 77:[17, 60] Operation: 55+5=60 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 77:[17, 11], Operations: ['55-38=17', '55/5=11'] Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,77 unequal: No Solution Exploring Operation: 17*11=187, Resulting Numbers: [187] 187,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 77:[5, 72], Operations: ['55-38=17', '55+17=72'] Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,77 unequal: No Solution Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[55, 55, 5, 38], Operations: [] Exploring Operation: 55-38=17, Resulting Numbers: [55, 5, 17] Generated Node #0,1: 77:[55, 5, 17] Operation: 55-38=17 Moving to Node #0,1 Current State: 77:[55, 5, 17], Operations: ['55-38=17'] Exploring Operation: 55+17=72, Resulting Numbers: [5, 72] Generated Node #0,1,2: 77:[5, 72] Operation: 55+17=72 Moving to Node #0,1,2 Current State: 77:[5, 72], Operations: ['55-38=17', '55+17=72'] Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 7, 58, 36, 18 ]
16
[ "36-7=29", "58/29=2", "18-2=16" ]
Current State: 16:[7, 58, 36, 18], Operations: [] Exploring Operation: 36-7=29, Resulting Numbers: [58, 18, 29] Generated Node #2: [58, 18, 29] from Operation: 36-7=29 Current State: 16:[58, 18, 29], Operations: ['36-7=29'] Exploring Operation: 58/29=2, Resulting Numbers: [18, 2] Generated Node #3: [18, 2] from Operation: 58/29=2 Current State: 16:[18, 2], Operations: ['36-7=29', '58/29=2'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[7, 58, 36, 18], Operations: [] Exploring Operation: 36-18=18, Resulting Numbers: [7, 58, 18] Generated Node #0,0: 16:[7, 58, 18] Operation: 36-18=18 Exploring Operation: 36/18=2, Resulting Numbers: [7, 58, 2] Generated Node #0,1: 16:[7, 58, 2] Operation: 36/18=2 Exploring Operation: 58-18=40, Resulting Numbers: [7, 36, 40] Generated Node #0,2: 16:[7, 36, 40] Operation: 58-18=40 Exploring Operation: 58-36=22, Resulting Numbers: [7, 18, 22] Generated Node #0,3: 16:[7, 18, 22] Operation: 58-36=22 Start Sub Search at level 1: Moving to Node #0,3 Current State: 16:[7, 18, 22], Operations: ['58-36=22'] Exploring Operation: 22-18=4, Resulting Numbers: [7, 4] Generated Node #0,3,0: 16:[7, 4] Operation: 22-18=4 Exploring Operation: 18-7=11, Resulting Numbers: [22, 11] Generated Node #0,3,1: 16:[22, 11] Operation: 18-7=11 Exploring Operation: 22-7=15, Resulting Numbers: [18, 15] Generated Node #0,3,2: 16:[18, 15] Operation: 22-7=15 Exploring Operation: 7+18=25, Resulting Numbers: [22, 25] Generated Node #0,3,3: 16:[22, 25] Operation: 7+18=25 Moving to Node #0,3,0 Current State: 16:[7, 4], Operations: ['58-36=22', '22-18=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,16 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,16 unequal: No Solution Moving to Node #0,3,2 Current State: 16:[18, 15], Operations: ['58-36=22', '22-7=15'] Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,16 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,16 unequal: No Solution Moving to Node #0,3,1 Current State: 16:[22, 11], Operations: ['58-36=22', '18-7=11'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,16 unequal: No Solution Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 22*11=242, Resulting Numbers: [242] 242,16 unequal: No Solution Moving to Node #0,3,3 Current State: 16:[22, 25], Operations: ['58-36=22', '7+18=25'] Exploring Operation: 22+25=47, Resulting Numbers: [47] 47,16 unequal: No Solution Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 22*25=550, Resulting Numbers: [550] 550,16 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 #0,1 Current State: 16:[7, 58, 2], Operations: ['36/18=2'] Exploring Operation: 58/2=29, Resulting Numbers: [7, 29] Generated Node #0,1,0: 16:[7, 29] Operation: 58/2=29 Exploring Operation: 58-7=51, Resulting Numbers: [2, 51] Generated Node #0,1,1: 16:[2, 51] Operation: 58-7=51 Exploring Operation: 58-2=56, Resulting Numbers: [7, 56] Generated Node #0,1,2: 16:[7, 56] Operation: 58-2=56 Exploring Operation: 7+2=9, Resulting Numbers: [58, 9] Generated Node #0,1,3: 16:[58, 9] Operation: 7+2=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[7, 29], Operations: ['36/18=2', '58/2=29'] Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,16 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,16 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,16 unequal: No Solution No 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: 16:[2, 51], Operations: ['36/18=2', '58-7=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,16 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,16 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,16 unequal: No Solution No 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: 16:[7, 56], Operations: ['36/18=2', '58-2=56'] Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 7+56=63, Resulting Numbers: [63] 63,16 unequal: No Solution Exploring Operation: 7*56=392, Resulting Numbers: [392] 392,16 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,16 unequal: No Solution No 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: 16:[58, 9], Operations: ['36/18=2', '7+2=9'] Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,16 unequal: No Solution Exploring Operation: 58*9=522, Resulting Numbers: [522] 522,16 unequal: No Solution Exploring Operation: 58+9=67, Resulting Numbers: [67] 67,16 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: 16:[7, 58, 18], Operations: ['36-18=18'] Exploring Operation: 58-18=40, Resulting Numbers: [7, 40] Generated Node #0,0,0: 16:[7, 40] Operation: 58-18=40 Exploring Operation: 58-7=51, Resulting Numbers: [18, 51] Generated Node #0,0,1: 16:[18, 51] Operation: 58-7=51 Exploring Operation: 7+58=65, Resulting Numbers: [18, 65] Generated Node #0,0,2: 16:[18, 65] Operation: 7+58=65 Exploring Operation: 18-7=11, Resulting Numbers: [58, 11] Generated Node #0,0,3: 16:[58, 11] Operation: 18-7=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 16:[7, 40], Operations: ['36-18=18', '58-18=40'] Exploring Operation: 7+40=47, Resulting Numbers: [47] 47,16 unequal: No Solution Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,16 unequal: No Solution Exploring Operation: 7*40=280, Resulting Numbers: [280] 280,16 unequal: No Solution No 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: 16:[18, 51], Operations: ['36-18=18', '58-7=51'] Exploring Operation: 18+51=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 18*51=918, Resulting Numbers: [918] 918,16 unequal: No Solution Exploring Operation: 51-18=33, Resulting Numbers: [33] 33,16 unequal: No Solution No 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: 16:[58, 11], Operations: ['36-18=18', '18-7=11'] Exploring Operation: 58+11=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,16 unequal: No Solution Exploring Operation: 58*11=638, Resulting Numbers: [638] 638,16 unequal: No Solution No 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: 16:[18, 65], Operations: ['36-18=18', '7+58=65'] Exploring Operation: 18*65=1170, Resulting Numbers: [1170] 1170,16 unequal: No Solution Exploring Operation: 65-18=47, Resulting Numbers: [47] 47,16 unequal: No Solution Exploring Operation: 18+65=83, Resulting Numbers: [83] 83,16 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: 16:[7, 36, 40], Operations: ['58-18=40'] Exploring Operation: 7+36=43, Resulting Numbers: [40, 43] Generated Node #0,2,0: 16:[40, 43] Operation: 7+36=43 Exploring Operation: 40-36=4, Resulting Numbers: [7, 4] Generated Node #0,2,1: 16:[7, 4] Operation: 40-36=4 Exploring Operation: 40-7=33, Resulting Numbers: [36, 33] Generated Node #0,2,2: 16:[36, 33] Operation: 40-7=33 Exploring Operation: 36-7=29, Resulting Numbers: [40, 29] Generated Node #0,2,3: 16:[40, 29] Operation: 36-7=29 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 16:[7, 4], Operations: ['58-18=40', '40-36=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,16 unequal: No Solution No 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: 16:[36, 33], Operations: ['58-18=40', '40-7=33'] Exploring Operation: 36+33=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 36-33=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 36*33=1188, Resulting Numbers: [1188] 1188,16 unequal: No Solution No 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: 16:[40, 29], Operations: ['58-18=40', '36-7=29'] Exploring Operation: 40-29=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 40*29=1160, Resulting Numbers: [1160] 1160,16 unequal: No Solution Exploring Operation: 40+29=69, Resulting Numbers: [69] 69,16 unequal: No Solution No 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: 16:[40, 43], Operations: ['58-18=40', '7+36=43'] Exploring Operation: 40+43=83, Resulting Numbers: [83] 83,16 unequal: No Solution Exploring Operation: 40*43=1720, Resulting Numbers: [1720] 1720,16 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 6, 12, 3, 41 ]
81
[ "41-12=29", "3*29=87", "87-6=81" ]
Current State: 81:[6, 12, 3, 41], Operations: [] Exploring Operation: 41-12=29, Resulting Numbers: [6, 3, 29] Generated Node #2: [6, 3, 29] from Operation: 41-12=29 Current State: 81:[6, 3, 29], Operations: ['41-12=29'] Exploring Operation: 3*29=87, Resulting Numbers: [6, 87] Generated Node #3: [6, 87] from Operation: 3*29=87 Current State: 81:[6, 87], Operations: ['41-12=29', '3*29=87'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[6, 12, 3, 41], Operations: [] Exploring Operation: 6+3=9, Resulting Numbers: [12, 41, 9] Generated Node #0,0: 81:[12, 41, 9] Operation: 6+3=9 Exploring Operation: 41-6=35, Resulting Numbers: [12, 3, 35] Generated Node #0,1: 81:[12, 3, 35] Operation: 41-6=35 Exploring Operation: 41-12=29, Resulting Numbers: [6, 3, 29] Generated Node #0,2: 81:[6, 3, 29] Operation: 41-12=29 Exploring Operation: 12-6=6, Resulting Numbers: [3, 41, 6] Generated Node #0,3: 81:[3, 41, 6] Operation: 12-6=6 Exploring Operation: 12/6=2, Resulting Numbers: [3, 41, 2] Generated Node #0,4: 81:[3, 41, 2] Operation: 12/6=2 Moving to Node #0,2 Current State: 81:[6, 3, 29], Operations: ['41-12=29'] Exploring Operation: 6-3=3, Resulting Numbers: [29, 3] Generated Node #0,2,0: 81:[29, 3] Operation: 6-3=3 Exploring Operation: 29-6=23, Resulting Numbers: [3, 23] Generated Node #0,2,1: 81:[3, 23] Operation: 29-6=23 Exploring Operation: 6+3=9, Resulting Numbers: [29, 9] Generated Node #0,2,2: 81:[29, 9] Operation: 6+3=9 Exploring Operation: 6/3=2, Resulting Numbers: [29, 2] Generated Node #0,2,3: 81:[29, 2] Operation: 6/3=2 Exploring Operation: 29-3=26, Resulting Numbers: [6, 26] Generated Node #0,2,4: 81:[6, 26] Operation: 29-3=26 Moving to Node #0,1 Current State: 81:[12, 3, 35], Operations: ['41-6=35'] Exploring Operation: 12-3=9, Resulting Numbers: [35, 9] Generated Node #0,1,0: 81:[35, 9] Operation: 12-3=9 Exploring Operation: 35-3=32, Resulting Numbers: [12, 32] Generated Node #0,1,1: 81:[12, 32] Operation: 35-3=32 Exploring Operation: 12+3=15, Resulting Numbers: [35, 15] Generated Node #0,1,2: 81:[35, 15] Operation: 12+3=15 Exploring Operation: 12/3=4, Resulting Numbers: [35, 4] Generated Node #0,1,3: 81:[35, 4] Operation: 12/3=4 Exploring Operation: 35-12=23, Resulting Numbers: [3, 23] Generated Node #0,1,4: 81:[3, 23] Operation: 35-12=23 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 81:[3, 23], Operations: ['41-6=35', '35-12=23'] Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,81 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,81 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 #0,1,0 Current State: 81:[35, 9], Operations: ['41-6=35', '12-3=9'] Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,81 unequal: No Solution Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,81 unequal: No Solution Exploring Operation: 35*9=315, Resulting Numbers: [315] 315,81 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 #0,1,1 Current State: 81:[12, 32], Operations: ['41-6=35', '35-3=32'] Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 12+32=44, Resulting Numbers: [44] 44,81 unequal: No Solution Exploring Operation: 12*32=384, Resulting Numbers: [384] 384,81 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 #0,1,3 Current State: 81:[35, 4], Operations: ['41-6=35', '12/3=4'] Exploring Operation: 35*4=140, Resulting Numbers: [140] 140,81 unequal: No Solution Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,81 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 #0,1,2 Current State: 81:[35, 15], Operations: ['41-6=35', '12+3=15'] Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 35+15=50, Resulting Numbers: [50] 50,81 unequal: No Solution Exploring Operation: 35*15=525, Resulting Numbers: [525] 525,81 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: 81:[3, 41, 2], Operations: ['12/6=2'] Exploring Operation: 41*2=82, Resulting Numbers: [3, 82] Generated Node #0,4,0: 81:[3, 82] Operation: 41*2=82 Exploring Operation: 41-2=39, Resulting Numbers: [3, 39] Generated Node #0,4,1: 81:[3, 39] Operation: 41-2=39 Exploring Operation: 3-2=1, Resulting Numbers: [41, 1] Generated Node #0,4,2: 81:[41, 1] Operation: 3-2=1 Exploring Operation: 41-3=38, Resulting Numbers: [2, 38] Generated Node #0,4,3: 81:[2, 38] Operation: 41-3=38 Exploring Operation: 3+2=5, Resulting Numbers: [41, 5] Generated Node #0,4,4: 81:[41, 5] Operation: 3+2=5 Moving to Node #0,0 Current State: 81:[12, 41, 9], Operations: ['6+3=9'] Exploring Operation: 41-12=29, Resulting Numbers: [9, 29] Generated Node #0,0,0: 81:[9, 29] Operation: 41-12=29 Exploring Operation: 12-9=3, Resulting Numbers: [41, 3] Generated Node #0,0,1: 81:[41, 3] Operation: 12-9=3 Exploring Operation: 41-9=32, Resulting Numbers: [12, 32] Generated Node #0,0,2: 81:[12, 32] Operation: 41-9=32 Exploring Operation: 12+9=21, Resulting Numbers: [41, 21] Generated Node #0,0,3: 81:[41, 21] Operation: 12+9=21 Exploring Operation: 12+41=53, Resulting Numbers: [9, 53] Generated Node #0,0,4: 81:[9, 53] Operation: 12+41=53 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[9, 29], Operations: ['6+3=9', '41-12=29'] Exploring Operation: 9*29=261, Resulting Numbers: [261] 261,81 unequal: No Solution 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 No 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: 81:[12, 32], Operations: ['6+3=9', '41-9=32'] Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 12+32=44, Resulting Numbers: [44] 44,81 unequal: No Solution Exploring Operation: 12*32=384, Resulting Numbers: [384] 384,81 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 #0,0,1 Current State: 81:[41, 3], Operations: ['6+3=9', '12-9=3'] Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,81 unequal: No Solution Exploring Operation: 41*3=123, Resulting Numbers: [123] 123,81 unequal: No Solution Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,81 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 #0,0,3 Current State: 81:[41, 21], Operations: ['6+3=9', '12+9=21'] Exploring Operation: 41+21=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 41-21=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 41*21=861, Resulting Numbers: [861] 861,81 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 #0,0,4 Current State: 81:[9, 53], Operations: ['6+3=9', '12+41=53'] Exploring Operation: 53-9=44, Resulting Numbers: [44] 44,81 unequal: No Solution Exploring Operation: 9*53=477, Resulting Numbers: [477] 477,81 unequal: No Solution Exploring Operation: 9+53=62, Resulting Numbers: [62] 62,81 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: 81:[3, 41, 6], Operations: ['12-6=6'] Exploring Operation: 41-3=38, Resulting Numbers: [6, 38] Generated Node #0,3,0: 81:[6, 38] Operation: 41-3=38 Exploring Operation: 41-6=35, Resulting Numbers: [3, 35] Generated Node #0,3,1: 81:[3, 35] Operation: 41-6=35 Exploring Operation: 3+6=9, Resulting Numbers: [41, 9] Generated Node #0,3,2: 81:[41, 9] Operation: 3+6=9 Exploring Operation: 6-3=3, Resulting Numbers: [41, 3] Generated Node #0,3,3: 81:[41, 3] Operation: 6-3=3 Exploring Operation: 6/3=2, Resulting Numbers: [41, 2] Generated Node #0,3,4: 81:[41, 2] Operation: 6/3=2 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 81:[3, 35], Operations: ['12-6=6', '41-6=35'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,81 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,81 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,81 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 #0,3,0 Current State: 81:[6, 38], Operations: ['12-6=6', '41-3=38'] Exploring Operation: 6*38=228, Resulting Numbers: [228] 228,81 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,81 unequal: No Solution Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,81 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 #0,3,2 Current State: 81:[41, 9], Operations: ['12-6=6', '3+6=9'] Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,81 unequal: No Solution Exploring Operation: 41*9=369, Resulting Numbers: [369] 369,81 unequal: No Solution Exploring Operation: 41+9=50, Resulting Numbers: [50] 50,81 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 #0,3,3 Current State: 81:[41, 3], Operations: ['12-6=6', '6-3=3'] Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,81 unequal: No Solution Exploring Operation: 41*3=123, Resulting Numbers: [123] 123,81 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,81 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 #0,3,4 Current State: 81:[41, 2], Operations: ['12-6=6', '6/3=2'] Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,81 unequal: No Solution Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,81 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,81 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: 81:[3, 82], Operations: ['12/6=2', '41*2=82'] Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,81 unequal: No Solution Exploring Operation: 3+82=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 3*82=246, Resulting Numbers: [246] 246,81 unequal: No Solution Moving to Node #0,2,0 Current State: 81:[29, 3], Operations: ['41-12=29', '6-3=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,81 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,81 unequal: No Solution Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,81 unequal: No Solution Moving to Node #0,2,2 Current State: 81:[29, 9], Operations: ['41-12=29', '6+3=9'] Exploring Operation: 29+9=38, Resulting Numbers: [38] 38,81 unequal: No Solution Exploring Operation: 29*9=261, Resulting Numbers: [261] 261,81 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,81 unequal: No Solution Moving to Node #0,2,3 Current State: 81:[29, 2], Operations: ['41-12=29', '6/3=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,81 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,81 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,81 unequal: No Solution Moving to Node #0,2,4 Current State: 81:[6, 26], Operations: ['41-12=29', '29-3=26'] Exploring Operation: 6*26=156, Resulting Numbers: [156] 156,81 unequal: No Solution Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,81 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,81 unequal: No Solution Moving to Node #0,2,1 Current State: 81:[3, 23], Operations: ['41-12=29', '29-6=23'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,81 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,81 unequal: No Solution Moving to Node #0,4,1 Current State: 81:[3, 39], Operations: ['12/6=2', '41-2=39'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,81 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,81 unequal: No Solution Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,81 unequal: No Solution Exploring Operation: 3*39=117, Resulting Numbers: [117] 117,81 unequal: No Solution Moving to Node #0,4,3 Current State: 81:[2, 38], Operations: ['12/6=2', '41-3=38'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,81 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,81 unequal: No Solution Exploring Operation: 2+38=40, Resulting Numbers: [40] 40,81 unequal: No Solution Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,81 unequal: No Solution Moving to Node #0,4,4 Current State: 81:[41, 5], Operations: ['12/6=2', '3+2=5'] Exploring Operation: 41+5=46, Resulting Numbers: [46] 46,81 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,81 unequal: No Solution Exploring Operation: 41*5=205, Resulting Numbers: [205] 205,81 unequal: No Solution Moving to Node #0,4,2 Current State: 81:[41, 1], Operations: ['12/6=2', '3-2=1'] Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,81 unequal: No Solution Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,81 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,81 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,81 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 72, 67, 93, 20 ]
97
[ "72-67=5", "20/5=4", "93+4=97" ]
Current State: 97:[72, 67, 93, 20], Operations: [] Exploring Operation: 72-67=5, Resulting Numbers: [93, 20, 5] Generated Node #2: [93, 20, 5] from Operation: 72-67=5 Current State: 97:[93, 20, 5], Operations: ['72-67=5'] Exploring Operation: 20/5=4, Resulting Numbers: [93, 4] Generated Node #3: [93, 4] from Operation: 20/5=4 Current State: 97:[93, 4], Operations: ['72-67=5', '20/5=4'] Exploring Operation: 93+4=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[72, 67, 93, 20], Operations: [] Exploring Operation: 72+20=92, Resulting Numbers: [67, 93, 92] Generated Node #0,0: 97:[67, 93, 92] Operation: 72+20=92 Exploring Operation: 93+20=113, Resulting Numbers: [72, 67, 113] Generated Node #0,1: 97:[72, 67, 113] Operation: 93+20=113 Exploring Operation: 67+20=87, Resulting Numbers: [72, 93, 87] Generated Node #0,2: 97:[72, 93, 87] Operation: 67+20=87 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[67, 93, 92], Operations: ['72+20=92'] Exploring Operation: 67+92=159, Resulting Numbers: [93, 159] Generated Node #0,0,0: 97:[93, 159] Operation: 67+92=159 Exploring Operation: 93-67=26, Resulting Numbers: [92, 26] Generated Node #0,0,1: 97:[92, 26] Operation: 93-67=26 Exploring Operation: 67+93=160, Resulting Numbers: [92, 160] Generated Node #0,0,2: 97:[92, 160] Operation: 67+93=160 Moving to Node #0,0,0 Current State: 97:[93, 159], Operations: ['72+20=92', '67+92=159'] Exploring Operation: 93+159=252, Resulting Numbers: [252] 252,97 unequal: No Solution Exploring Operation: 159-93=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 93*159=14787, Resulting Numbers: [14787] 14787,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[92, 160], Operations: ['72+20=92', '67+93=160'] Exploring Operation: 92*160=14720, Resulting Numbers: [14720] 14720,97 unequal: No Solution Exploring Operation: 92+160=252, Resulting Numbers: [252] 252,97 unequal: No Solution Exploring Operation: 160-92=68, Resulting Numbers: [68] 68,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[92, 26], Operations: ['72+20=92', '93-67=26'] Exploring Operation: 92-26=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 92*26=2392, Resulting Numbers: [2392] 2392,97 unequal: No Solution Exploring Operation: 92+26=118, Resulting Numbers: [118] 118,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[72, 93, 87], Operations: ['67+20=87'] Exploring Operation: 72+87=159, Resulting Numbers: [93, 159] Generated Node #0,2,0: 97:[93, 159] Operation: 72+87=159 Exploring Operation: 72+93=165, Resulting Numbers: [87, 165] Generated Node #0,2,1: 97:[87, 165] Operation: 72+93=165 Exploring Operation: 93-72=21, Resulting Numbers: [87, 21] Generated Node #0,2,2: 97:[87, 21] Operation: 93-72=21 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 97:[93, 159], Operations: ['67+20=87', '72+87=159'] Exploring Operation: 93*159=14787, Resulting Numbers: [14787] 14787,97 unequal: No Solution Exploring Operation: 159-93=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 93+159=252, Resulting Numbers: [252] 252,97 unequal: No Solution No 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: 97:[87, 165], Operations: ['67+20=87', '72+93=165'] Exploring Operation: 87+165=252, Resulting Numbers: [252] 252,97 unequal: No Solution Exploring Operation: 87*165=14355, Resulting Numbers: [14355] 14355,97 unequal: No Solution Exploring Operation: 165-87=78, Resulting Numbers: [78] 78,97 unequal: No Solution No 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: 97:[87, 21], Operations: ['67+20=87', '93-72=21'] Exploring Operation: 87*21=1827, Resulting Numbers: [1827] 1827,97 unequal: No Solution Exploring Operation: 87-21=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 87+21=108, Resulting Numbers: [108] 108,97 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: 97:[72, 67, 113], Operations: ['93+20=113'] Exploring Operation: 113-72=41, Resulting Numbers: [67, 41] Generated Node #0,1,0: 97:[67, 41] Operation: 113-72=41 Exploring Operation: 72+67=139, Resulting Numbers: [113, 139] Generated Node #0,1,1: 97:[113, 139] Operation: 72+67=139 Exploring Operation: 113-67=46, Resulting Numbers: [72, 46] Generated Node #0,1,2: 97:[72, 46] Operation: 113-67=46 Moving to Node #0,1,1 Current State: 97:[113, 139], Operations: ['93+20=113', '72+67=139'] Exploring Operation: 139-113=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 113*139=15707, Resulting Numbers: [15707] 15707,97 unequal: No Solution Exploring Operation: 113+139=252, Resulting Numbers: [252] 252,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[72, 46], Operations: ['93+20=113', '113-67=46'] Exploring Operation: 72-46=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 72*46=3312, Resulting Numbers: [3312] 3312,97 unequal: No Solution Exploring Operation: 72+46=118, Resulting Numbers: [118] 118,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[67, 41], Operations: ['93+20=113', '113-72=41'] Exploring Operation: 67*41=2747, Resulting Numbers: [2747] 2747,97 unequal: No Solution Exploring Operation: 67+41=108, Resulting Numbers: [108] 108,97 unequal: No Solution Exploring Operation: 67-41=26, Resulting Numbers: [26] 26,97 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
[ 4, 21, 64, 62 ]
23
[ "4+21=25", "64-62=2", "25-2=23" ]
Current State: 23:[4, 21, 64, 62], Operations: [] Exploring Operation: 4+21=25, Resulting Numbers: [64, 62, 25] Generated Node #2: [64, 62, 25] from Operation: 4+21=25 Current State: 23:[64, 62, 25], Operations: ['4+21=25'] Exploring Operation: 64-62=2, Resulting Numbers: [25, 2] Generated Node #3: [25, 2] from Operation: 64-62=2 Current State: 23:[25, 2], Operations: ['4+21=25', '64-62=2'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[4, 21, 64, 62], Operations: [] Exploring Operation: 64/4=16, Resulting Numbers: [21, 62, 16] Generated Node #0,0: 23:[21, 62, 16] Operation: 64/4=16 Exploring Operation: 64-62=2, Resulting Numbers: [4, 21, 2] Generated Node #0,1: 23:[4, 21, 2] Operation: 64-62=2 Moving to Node #0,1 Current State: 23:[4, 21, 2], Operations: ['64-62=2'] Exploring Operation: 4+2=6, Resulting Numbers: [21, 6] Generated Node #0,1,0: 23:[21, 6] Operation: 4+2=6 Exploring Operation: 4*2=8, Resulting Numbers: [21, 8] Generated Node #0,1,1: 23:[21, 8] Operation: 4*2=8 Moving to Node #0,0 Current State: 23:[21, 62, 16], Operations: ['64/4=16'] Exploring Operation: 62-16=46, Resulting Numbers: [21, 46] Generated Node #0,0,0: 23:[21, 46] Operation: 62-16=46 Exploring Operation: 62-21=41, Resulting Numbers: [16, 41] Generated Node #0,0,1: 23:[16, 41] Operation: 62-21=41 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 23:[21, 46], Operations: ['64/4=16', '62-16=46'] Exploring Operation: 21+46=67, Resulting Numbers: [67] 67,23 unequal: No Solution Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 23:[16, 41], Operations: ['64/4=16', '62-21=41'] Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,23 unequal: No Solution Exploring Operation: 16+41=57, Resulting Numbers: [57] 57,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 23:[21, 8], Operations: ['64-62=2', '4*2=8'] Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,23 unequal: No Solution Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[21, 6], Operations: ['64-62=2', '4+2=6'] Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 21+6=27, Resulting Numbers: [27] 27,23 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 94, 8, 15, 30 ]
100
[ "94+8=102", "30/15=2", "102-2=100" ]
Current State: 100:[94, 8, 15, 30], Operations: [] Exploring Operation: 94+8=102, Resulting Numbers: [15, 30, 102] Generated Node #2: [15, 30, 102] from Operation: 94+8=102 Current State: 100:[15, 30, 102], Operations: ['94+8=102'] Exploring Operation: 30/15=2, Resulting Numbers: [102, 2] Generated Node #3: [102, 2] from Operation: 30/15=2 Current State: 100:[102, 2], Operations: ['94+8=102', '30/15=2'] Exploring Operation: 102-2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[94, 8, 15, 30], Operations: [] Exploring Operation: 8+15=23, Resulting Numbers: [94, 30, 23] Generated Node #0,0: 100:[94, 30, 23] Operation: 8+15=23 Exploring Operation: 30-8=22, Resulting Numbers: [94, 15, 22] Generated Node #0,1: 100:[94, 15, 22] Operation: 30-8=22 Exploring Operation: 15-8=7, Resulting Numbers: [94, 30, 7] Generated Node #0,2: 100:[94, 30, 7] Operation: 15-8=7 Exploring Operation: 94+8=102, Resulting Numbers: [15, 30, 102] Generated Node #0,3: 100:[15, 30, 102] Operation: 94+8=102 Exploring Operation: 30/15=2, Resulting Numbers: [94, 8, 2] Generated Node #0,4: 100:[94, 8, 2] Operation: 30/15=2 Start Sub Search at level 1: Moving to Node #0,4 Current State: 100:[94, 8, 2], Operations: ['30/15=2'] Exploring Operation: 8/2=4, Resulting Numbers: [94, 4] Generated Node #0,4,0: 100:[94, 4] Operation: 8/2=4 Exploring Operation: 8+2=10, Resulting Numbers: [94, 10] Generated Node #0,4,1: 100:[94, 10] Operation: 8+2=10 Exploring Operation: 94+8=102, Resulting Numbers: [2, 102] Generated Node #0,4,2: 100:[2, 102] Operation: 94+8=102 Exploring Operation: 94+2=96, Resulting Numbers: [8, 96] Generated Node #0,4,3: 100:[8, 96] Operation: 94+2=96 Exploring Operation: 94/2=47, Resulting Numbers: [8, 47] Generated Node #0,4,4: 100:[8, 47] Operation: 94/2=47 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 100:[2, 102], Operations: ['30/15=2', '94+8=102'] Exploring Operation: 102-2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[94, 8, 15, 30], Operations: [] Exploring Operation: 30/15=2, Resulting Numbers: [94, 8, 2] Generated Node #0,4: 100:[94, 8, 2] Operation: 30/15=2 Moving to Node #0,4 Current State: 100:[94, 8, 2], Operations: ['30/15=2'] Exploring Operation: 94+8=102, Resulting Numbers: [2, 102] Generated Node #0,4,2: 100:[2, 102] Operation: 94+8=102 Moving to Node #0,4,2 Current State: 100:[2, 102], Operations: ['30/15=2', '94+8=102'] Exploring Operation: 102-2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 35, 55, 18, 46 ]
62
[ "35+55=90", "46-18=28", "90-28=62" ]
Current State: 62:[35, 55, 18, 46], Operations: [] Exploring Operation: 35+55=90, Resulting Numbers: [18, 46, 90] Generated Node #2: [18, 46, 90] from Operation: 35+55=90 Current State: 62:[18, 46, 90], Operations: ['35+55=90'] Exploring Operation: 46-18=28, Resulting Numbers: [90, 28] Generated Node #3: [90, 28] from Operation: 46-18=28 Current State: 62:[90, 28], Operations: ['35+55=90', '46-18=28'] Exploring Operation: 90-28=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[35, 55, 18, 46], Operations: [] Exploring Operation: 18+46=64, Resulting Numbers: [35, 55, 64] Generated Node #0,0: 62:[35, 55, 64] Operation: 18+46=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[35, 55, 64], Operations: ['18+46=64'] Exploring Operation: 64-35=29, Resulting Numbers: [55, 29] Generated Node #0,0,0: 62:[55, 29] Operation: 64-35=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[55, 29], Operations: ['18+46=64', '64-35=29'] Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,62 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
[ 64, 36, 55, 48 ]
82
[ "36*48=1728", "1728/64=27", "55+27=82" ]
Current State: 82:[64, 36, 55, 48], Operations: [] Exploring Operation: 36*48=1728, Resulting Numbers: [64, 55, 1728] Generated Node #2: [64, 55, 1728] from Operation: 36*48=1728 Current State: 82:[64, 55, 1728], Operations: ['36*48=1728'] Exploring Operation: 1728/64=27, Resulting Numbers: [55, 27] Generated Node #3: [55, 27] from Operation: 1728/64=27 Current State: 82:[55, 27], Operations: ['36*48=1728', '1728/64=27'] Exploring Operation: 55+27=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[64, 36, 55, 48], Operations: [] Exploring Operation: 64-55=9, Resulting Numbers: [36, 48, 9] Generated Node #0,0: 82:[36, 48, 9] Operation: 64-55=9 Exploring Operation: 55-48=7, Resulting Numbers: [64, 36, 7] Generated Node #0,1: 82:[64, 36, 7] Operation: 55-48=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[36, 48, 9], Operations: ['64-55=9'] Exploring Operation: 48-9=39, Resulting Numbers: [36, 39] Generated Node #0,0,0: 82:[36, 39] Operation: 48-9=39 Exploring Operation: 36+48=84, Resulting Numbers: [9, 84] Generated Node #0,0,1: 82:[9, 84] Operation: 36+48=84 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[36, 39], Operations: ['64-55=9', '48-9=39'] Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 36+39=75, Resulting Numbers: [75] 75,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[9, 84], Operations: ['64-55=9', '36+48=84'] Exploring Operation: 9+84=93, Resulting Numbers: [93] 93,82 unequal: No Solution Exploring Operation: 84-9=75, Resulting Numbers: [75] 75,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[64, 36, 7], Operations: ['55-48=7'] Exploring Operation: 64+7=71, Resulting Numbers: [36, 71] Generated Node #0,1,0: 82:[36, 71] Operation: 64+7=71 Exploring Operation: 64-36=28, Resulting Numbers: [7, 28] Generated Node #0,1,1: 82:[7, 28] Operation: 64-36=28 Moving to Node #0,1,0 Current State: 82:[36, 71], Operations: ['55-48=7', '64+7=71'] Exploring Operation: 71-36=35, Resulting Numbers: [35] 35,82 unequal: No Solution Exploring Operation: 36+71=107, Resulting Numbers: [107] 107,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[7, 28], Operations: ['55-48=7', '64-36=28'] Exploring Operation: 7+28=35, Resulting Numbers: [35] 35,82 unequal: No Solution Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 38, 85, 97, 96 ]
30
[ "97-85=12", "96/12=8", "38-8=30" ]
Current State: 30:[38, 85, 97, 96], Operations: [] Exploring Operation: 97-85=12, Resulting Numbers: [38, 96, 12] Generated Node #2: [38, 96, 12] from Operation: 97-85=12 Current State: 30:[38, 96, 12], Operations: ['97-85=12'] Exploring Operation: 96/12=8, Resulting Numbers: [38, 8] Generated Node #3: [38, 8] from Operation: 96/12=8 Current State: 30:[38, 8], Operations: ['97-85=12', '96/12=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[38, 85, 97, 96], Operations: [] Exploring Operation: 97-96=1, Resulting Numbers: [38, 85, 1] Generated Node #0,0: 30:[38, 85, 1] Operation: 97-96=1 Exploring Operation: 97-85=12, Resulting Numbers: [38, 96, 12] Generated Node #0,1: 30:[38, 96, 12] Operation: 97-85=12 Exploring Operation: 85-38=47, Resulting Numbers: [97, 96, 47] Generated Node #0,2: 30:[97, 96, 47] Operation: 85-38=47 Exploring Operation: 96-85=11, Resulting Numbers: [38, 97, 11] Generated Node #0,3: 30:[38, 97, 11] Operation: 96-85=11 Moving to Node #0,0 Current State: 30:[38, 85, 1], Operations: ['97-96=1'] Exploring Operation: 85-1=84, Resulting Numbers: [38, 84] Generated Node #0,0,0: 30:[38, 84] Operation: 85-1=84 Exploring Operation: 85-38=47, Resulting Numbers: [1, 47] Generated Node #0,0,1: 30:[1, 47] Operation: 85-38=47 Exploring Operation: 38*1=38, Resulting Numbers: [85, 38] Generated Node #0,0,2: 30:[85, 38] Operation: 38*1=38 Exploring Operation: 38-1=37, Resulting Numbers: [85, 37] Generated Node #0,0,3: 30:[85, 37] Operation: 38-1=37 Moving to Node #0,3 Current State: 30:[38, 97, 11], Operations: ['96-85=11'] Exploring Operation: 38+11=49, Resulting Numbers: [97, 49] Generated Node #0,3,0: 30:[97, 49] Operation: 38+11=49 Exploring Operation: 97-11=86, Resulting Numbers: [38, 86] Generated Node #0,3,1: 30:[38, 86] Operation: 97-11=86 Exploring Operation: 97-38=59, Resulting Numbers: [11, 59] Generated Node #0,3,2: 30:[11, 59] Operation: 97-38=59 Exploring Operation: 38-11=27, Resulting Numbers: [97, 27] Generated Node #0,3,3: 30:[97, 27] Operation: 38-11=27 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 30:[11, 59], Operations: ['96-85=11', '97-38=59'] Exploring Operation: 11*59=649, Resulting Numbers: [649] 649,30 unequal: No Solution Exploring Operation: 11+59=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,30 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 #0,3,1 Current State: 30:[38, 86], Operations: ['96-85=11', '97-11=86'] Exploring Operation: 38*86=3268, Resulting Numbers: [3268] 3268,30 unequal: No Solution Exploring Operation: 38+86=124, Resulting Numbers: [124] 124,30 unequal: No Solution Exploring Operation: 86-38=48, Resulting Numbers: [48] 48,30 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 #0,3,3 Current State: 30:[97, 27], Operations: ['96-85=11', '38-11=27'] Exploring Operation: 97-27=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 97*27=2619, Resulting Numbers: [2619] 2619,30 unequal: No Solution Exploring Operation: 97+27=124, Resulting Numbers: [124] 124,30 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 #0,3,0 Current State: 30:[97, 49], Operations: ['96-85=11', '38+11=49'] Exploring Operation: 97-49=48, Resulting Numbers: [48] 48,30 unequal: No Solution Exploring Operation: 97*49=4753, Resulting Numbers: [4753] 4753,30 unequal: No Solution Exploring Operation: 97+49=146, Resulting Numbers: [146] 146,30 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: 30:[38, 96, 12], Operations: ['97-85=12'] Exploring Operation: 96-12=84, Resulting Numbers: [38, 84] Generated Node #0,1,0: 30:[38, 84] Operation: 96-12=84 Exploring Operation: 96-38=58, Resulting Numbers: [12, 58] Generated Node #0,1,1: 30:[12, 58] Operation: 96-38=58 Exploring Operation: 96/12=8, Resulting Numbers: [38, 8] Generated Node #0,1,2: 30:[38, 8] Operation: 96/12=8 Exploring Operation: 38-12=26, Resulting Numbers: [96, 26] Generated Node #0,1,3: 30:[96, 26] Operation: 38-12=26 Moving to Node #0,2 Current State: 30:[97, 96, 47], Operations: ['85-38=47'] Exploring Operation: 97-47=50, Resulting Numbers: [96, 50] Generated Node #0,2,0: 30:[96, 50] Operation: 97-47=50 Exploring Operation: 96-47=49, Resulting Numbers: [97, 49] Generated Node #0,2,1: 30:[97, 49] Operation: 96-47=49 Exploring Operation: 97+96=193, Resulting Numbers: [47, 193] Generated Node #0,2,2: 30:[47, 193] Operation: 97+96=193 Exploring Operation: 97-96=1, Resulting Numbers: [47, 1] Generated Node #0,2,3: 30:[47, 1] Operation: 97-96=1 Moving to Node #0,1,2 Current State: 30:[38, 8], Operations: ['97-85=12', '96/12=8'] Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,30 unequal: No Solution Exploring Operation: 38*8=304, Resulting Numbers: [304] 304,30 unequal: No Solution Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[38, 85, 97, 96], Operations: [] Exploring Operation: 97-85=12, Resulting Numbers: [38, 96, 12] Generated Node #0,1: 30:[38, 96, 12] Operation: 97-85=12 Moving to Node #0,1 Current State: 30:[38, 96, 12], Operations: ['97-85=12'] Exploring Operation: 96/12=8, Resulting Numbers: [38, 8] Generated Node #0,1,2: 30:[38, 8] Operation: 96/12=8 Moving to Node #0,1,2 Current State: 30:[38, 8], Operations: ['97-85=12', '96/12=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
0.966146
hs_4
sum_heuristic
[ 51, 21, 75, 75 ]
73
[ "51+21=72", "75/75=1", "72+1=73" ]
Current State: 73:[51, 21, 75, 75], Operations: [] Exploring Operation: 51+21=72, Resulting Numbers: [75, 75, 72] Generated Node #2: [75, 75, 72] from Operation: 51+21=72 Current State: 73:[75, 75, 72], Operations: ['51+21=72'] Exploring Operation: 75/75=1, Resulting Numbers: [72, 1] Generated Node #3: [72, 1] from Operation: 75/75=1 Current State: 73:[72, 1], Operations: ['51+21=72', '75/75=1'] Exploring Operation: 72+1=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[51, 21, 75, 75], Operations: [] Exploring Operation: 75-21=54, Resulting Numbers: [51, 75, 54] Generated Node #0,0: 73:[51, 75, 54] Operation: 75-21=54 Exploring Operation: 51+21=72, Resulting Numbers: [75, 75, 72] Generated Node #0,1: 73:[75, 75, 72] Operation: 51+21=72 Moving to Node #0,1 Current State: 73:[75, 75, 72], Operations: ['51+21=72'] Exploring Operation: 75-72=3, Resulting Numbers: [75, 3] Generated Node #0,1,0: 73:[75, 3] Operation: 75-72=3 Exploring Operation: 75-72=3, Resulting Numbers: [75, 3] Generated Node #0,1,1: 73:[75, 3] Operation: 75-72=3 Moving to Node #0,0 Current State: 73:[51, 75, 54], Operations: ['75-21=54'] Exploring Operation: 75-51=24, Resulting Numbers: [54, 24] Generated Node #0,0,0: 73:[54, 24] Operation: 75-51=24 Exploring Operation: 51+54=105, Resulting Numbers: [75, 105] Generated Node #0,0,1: 73:[75, 105] Operation: 51+54=105 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[75, 105], Operations: ['75-21=54', '51+54=105'] Exploring Operation: 75+105=180, Resulting Numbers: [180] 180,73 unequal: No Solution Exploring Operation: 105-75=30, Resulting Numbers: [30] 30,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[54, 24], Operations: ['75-21=54', '75-51=24'] Exploring Operation: 54+24=78, Resulting Numbers: [78] 78,73 unequal: No Solution Exploring Operation: 54-24=30, Resulting Numbers: [30] 30,73 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: 73:[75, 3], Operations: ['51+21=72', '75-72=3'] Exploring Operation: 75+3=78, Resulting Numbers: [78] 78,73 unequal: No Solution Exploring Operation: 75-3=72, Resulting Numbers: [72] 72,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[75, 3], Operations: ['51+21=72', '75-72=3'] Exploring Operation: 75-3=72, Resulting Numbers: [72] 72,73 unequal: No Solution Exploring Operation: 75+3=78, Resulting Numbers: [78] 78,73 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 58, 72, 81, 48 ]
97
[ "58+72=130", "81-48=33", "130-33=97" ]
Current State: 97:[58, 72, 81, 48], Operations: [] Exploring Operation: 58+72=130, Resulting Numbers: [81, 48, 130] Generated Node #2: [81, 48, 130] from Operation: 58+72=130 Current State: 97:[81, 48, 130], Operations: ['58+72=130'] Exploring Operation: 81-48=33, Resulting Numbers: [130, 33] Generated Node #3: [130, 33] from Operation: 81-48=33 Current State: 97:[130, 33], Operations: ['58+72=130', '81-48=33'] Exploring Operation: 130-33=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[58, 72, 81, 48], Operations: [] Exploring Operation: 58+48=106, Resulting Numbers: [72, 81, 106] Generated Node #0,0: 97:[72, 81, 106] Operation: 58+48=106 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[72, 81, 106], Operations: ['58+48=106'] Exploring Operation: 72+81=153, Resulting Numbers: [106, 153] Generated Node #0,0,0: 97:[106, 153] Operation: 72+81=153 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[106, 153], Operations: ['58+48=106', '72+81=153'] Exploring Operation: 153-106=47, Resulting Numbers: [47] 47,97 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
[ 56, 64, 54, 67 ]
21
[ "64-56=8", "67-54=13", "8+13=21" ]
Current State: 21:[56, 64, 54, 67], Operations: [] Exploring Operation: 64-56=8, Resulting Numbers: [54, 67, 8] Generated Node #2: [54, 67, 8] from Operation: 64-56=8 Current State: 21:[54, 67, 8], Operations: ['64-56=8'] Exploring Operation: 67-54=13, Resulting Numbers: [8, 13] Generated Node #3: [8, 13] from Operation: 67-54=13 Current State: 21:[8, 13], Operations: ['64-56=8', '67-54=13'] Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[56, 64, 54, 67], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [56, 54, 3] Generated Node #0,0: 21:[56, 54, 3] Operation: 67-64=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[56, 54, 3], Operations: ['67-64=3'] Exploring Operation: 56-54=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 21:[3, 2] Operation: 56-54=2 Moving to Node #0,0,0 Current State: 21:[3, 2], Operations: ['67-64=3', '56-54=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,21 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
[ 65, 85, 2, 37 ]
31
[ "85-37=48", "2*48=96", "96-65=31" ]
Current State: 31:[65, 85, 2, 37], Operations: [] Exploring Operation: 85-37=48, Resulting Numbers: [65, 2, 48] Generated Node #2: [65, 2, 48] from Operation: 85-37=48 Current State: 31:[65, 2, 48], Operations: ['85-37=48'] Exploring Operation: 2*48=96, Resulting Numbers: [65, 96] Generated Node #3: [65, 96] from Operation: 2*48=96 Current State: 31:[65, 96], Operations: ['85-37=48', '2*48=96'] Exploring Operation: 96-65=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[65, 85, 2, 37], Operations: [] Exploring Operation: 85-65=20, Resulting Numbers: [2, 37, 20] Generated Node #0,0: 31:[2, 37, 20] Operation: 85-65=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[2, 37, 20], Operations: ['85-65=20'] Exploring Operation: 37-2=35, Resulting Numbers: [20, 35] Generated Node #0,0,0: 31:[20, 35] Operation: 37-2=35 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[20, 35], Operations: ['85-65=20', '37-2=35'] Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 44, 50, 7, 59 ]
88
[ "50+7=57", "59-57=2", "44*2=88" ]
Current State: 88:[44, 50, 7, 59], Operations: [] Exploring Operation: 50+7=57, Resulting Numbers: [44, 59, 57] Generated Node #2: [44, 59, 57] from Operation: 50+7=57 Current State: 88:[44, 59, 57], Operations: ['50+7=57'] Exploring Operation: 59-57=2, Resulting Numbers: [44, 2] Generated Node #3: [44, 2] from Operation: 59-57=2 Current State: 88:[44, 2], Operations: ['50+7=57', '59-57=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[44, 50, 7, 59], Operations: [] Exploring Operation: 50-7=43, Resulting Numbers: [44, 59, 43] Generated Node #0,0: 88:[44, 59, 43] Operation: 50-7=43 Exploring Operation: 59-44=15, Resulting Numbers: [50, 7, 15] Generated Node #0,1: 88:[50, 7, 15] Operation: 59-44=15 Exploring Operation: 59-50=9, Resulting Numbers: [44, 7, 9] Generated Node #0,2: 88:[44, 7, 9] Operation: 59-50=9 Exploring Operation: 59-7=52, Resulting Numbers: [44, 50, 52] Generated Node #0,3: 88:[44, 50, 52] Operation: 59-7=52 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[44, 7, 9], Operations: ['59-50=9'] Exploring Operation: 44-7=37, Resulting Numbers: [9, 37] Generated Node #0,2,0: 88:[9, 37] Operation: 44-7=37 Exploring Operation: 9-7=2, Resulting Numbers: [44, 2] Generated Node #0,2,1: 88:[44, 2] Operation: 9-7=2 Exploring Operation: 7+9=16, Resulting Numbers: [44, 16] Generated Node #0,2,2: 88:[44, 16] Operation: 7+9=16 Exploring Operation: 44+7=51, Resulting Numbers: [9, 51] Generated Node #0,2,3: 88:[9, 51] Operation: 44+7=51 Moving to Node #0,2,1 Current State: 88:[44, 2], Operations: ['59-50=9', '9-7=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[44, 50, 7, 59], Operations: [] Exploring Operation: 59-50=9, Resulting Numbers: [44, 7, 9] Generated Node #0,2: 88:[44, 7, 9] Operation: 59-50=9 Moving to Node #0,2 Current State: 88:[44, 7, 9], Operations: ['59-50=9'] Exploring Operation: 9-7=2, Resulting Numbers: [44, 2] Generated Node #0,2,1: 88:[44, 2] Operation: 9-7=2 Moving to Node #0,2,1 Current State: 88:[44, 2], Operations: ['59-50=9', '9-7=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 92, 14, 55, 63 ]
98
[ "92+14=106", "63-55=8", "106-8=98" ]
Current State: 98:[92, 14, 55, 63], Operations: [] Exploring Operation: 92+14=106, Resulting Numbers: [55, 63, 106] Generated Node #2: [55, 63, 106] from Operation: 92+14=106 Current State: 98:[55, 63, 106], Operations: ['92+14=106'] Exploring Operation: 63-55=8, Resulting Numbers: [106, 8] Generated Node #3: [106, 8] from Operation: 63-55=8 Current State: 98:[106, 8], Operations: ['92+14=106', '63-55=8'] Exploring Operation: 106-8=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[92, 14, 55, 63], Operations: [] Exploring Operation: 63-55=8, Resulting Numbers: [92, 14, 8] Generated Node #0,0: 98:[92, 14, 8] Operation: 63-55=8 Exploring Operation: 63-14=49, Resulting Numbers: [92, 55, 49] Generated Node #0,1: 98:[92, 55, 49] Operation: 63-14=49 Exploring Operation: 92-55=37, Resulting Numbers: [14, 63, 37] Generated Node #0,2: 98:[14, 63, 37] Operation: 92-55=37 Exploring Operation: 92-63=29, Resulting Numbers: [14, 55, 29] Generated Node #0,3: 98:[14, 55, 29] Operation: 92-63=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[92, 14, 8], Operations: ['63-55=8'] Exploring Operation: 92+8=100, Resulting Numbers: [14, 100] Generated Node #0,0,0: 98:[14, 100] Operation: 92+8=100 Exploring Operation: 92-8=84, Resulting Numbers: [14, 84] Generated Node #0,0,1: 98:[14, 84] Operation: 92-8=84 Exploring Operation: 14-8=6, Resulting Numbers: [92, 6] Generated Node #0,0,2: 98:[92, 6] Operation: 14-8=6 Exploring Operation: 92+14=106, Resulting Numbers: [8, 106] Generated Node #0,0,3: 98:[8, 106] Operation: 92+14=106 Moving to Node #0,0,0 Current State: 98:[14, 100], Operations: ['63-55=8', '92+8=100'] Exploring Operation: 14*100=1400, Resulting Numbers: [1400] 1400,98 unequal: No Solution Exploring Operation: 14+100=114, Resulting Numbers: [114] 114,98 unequal: No Solution Exploring Operation: 100-14=86, Resulting Numbers: [86] 86,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[92, 6], Operations: ['63-55=8', '14-8=6'] Exploring Operation: 92-6=86, Resulting Numbers: [86] 86,98 unequal: No Solution Exploring Operation: 92+6=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[92, 14, 55, 63], Operations: [] Exploring Operation: 63-55=8, Resulting Numbers: [92, 14, 8] Generated Node #0,0: 98:[92, 14, 8] Operation: 63-55=8 Moving to Node #0,0 Current State: 98:[92, 14, 8], Operations: ['63-55=8'] Exploring Operation: 14-8=6, Resulting Numbers: [92, 6] Generated Node #0,0,2: 98:[92, 6] Operation: 14-8=6 Moving to Node #0,0,2 Current State: 98:[92, 6], Operations: ['63-55=8', '14-8=6'] Exploring Operation: 92+6=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 42, 47, 45, 50 ]
10
[ "47-42=5", "50-45=5", "5+5=10" ]
Current State: 10:[42, 47, 45, 50], Operations: [] Exploring Operation: 47-42=5, Resulting Numbers: [45, 50, 5] Generated Node #2: [45, 50, 5] from Operation: 47-42=5 Current State: 10:[45, 50, 5], Operations: ['47-42=5'] Exploring Operation: 50-45=5, Resulting Numbers: [5, 5] Generated Node #3: [5, 5] from Operation: 50-45=5 Current State: 10:[5, 5], Operations: ['47-42=5', '50-45=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[42, 47, 45, 50], Operations: [] Exploring Operation: 50-47=3, Resulting Numbers: [42, 45, 3] Generated Node #0,0: 10:[42, 45, 3] Operation: 50-47=3 Exploring Operation: 50-45=5, Resulting Numbers: [42, 47, 5] Generated Node #0,1: 10:[42, 47, 5] Operation: 50-45=5 Moving to Node #0,0 Current State: 10:[42, 45, 3], Operations: ['50-47=3'] Exploring Operation: 45-42=3, Resulting Numbers: [3, 3] Generated Node #0,0,0: 10:[3, 3] Operation: 45-42=3 Exploring Operation: 45/3=15, Resulting Numbers: [42, 15] Generated Node #0,0,1: 10:[42, 15] Operation: 45/3=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[3, 3], Operations: ['50-47=3', '45-42=3'] Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,10 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 #0,0,1 Current State: 10:[42, 15], Operations: ['50-47=3', '45/3=15'] Exploring Operation: 42+15=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,10 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: 10:[42, 47, 5], Operations: ['50-45=5'] Exploring Operation: 42-5=37, Resulting Numbers: [47, 37] Generated Node #0,1,0: 10:[47, 37] Operation: 42-5=37 Exploring Operation: 47-42=5, Resulting Numbers: [5, 5] Generated Node #0,1,1: 10:[5, 5] Operation: 47-42=5 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 10:[5, 5], Operations: ['50-45=5', '47-42=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[42, 47, 45, 50], Operations: [] Exploring Operation: 50-45=5, Resulting Numbers: [42, 47, 5] Generated Node #0,1: 10:[42, 47, 5] Operation: 50-45=5 Moving to Node #0,1 Current State: 10:[42, 47, 5], Operations: ['50-45=5'] Exploring Operation: 47-42=5, Resulting Numbers: [5, 5] Generated Node #0,1,1: 10:[5, 5] Operation: 47-42=5 Moving to Node #0,1,1 Current State: 10:[5, 5], Operations: ['50-45=5', '47-42=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 2, 50, 72, 28 ]
16
[ "72-50=22", "2*22=44", "44-28=16" ]
Current State: 16:[2, 50, 72, 28], Operations: [] Exploring Operation: 72-50=22, Resulting Numbers: [2, 28, 22] Generated Node #2: [2, 28, 22] from Operation: 72-50=22 Current State: 16:[2, 28, 22], Operations: ['72-50=22'] Exploring Operation: 2*22=44, Resulting Numbers: [28, 44] Generated Node #3: [28, 44] from Operation: 2*22=44 Current State: 16:[28, 44], Operations: ['72-50=22', '2*22=44'] Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[2, 50, 72, 28], Operations: [] Exploring Operation: 50-28=22, Resulting Numbers: [2, 72, 22] Generated Node #0,0: 16:[2, 72, 22] Operation: 50-28=22 Exploring Operation: 72-50=22, Resulting Numbers: [2, 28, 22] Generated Node #0,1: 16:[2, 28, 22] Operation: 72-50=22 Moving to Node #0,1 Current State: 16:[2, 28, 22], Operations: ['72-50=22'] Exploring Operation: 28/2=14, Resulting Numbers: [22, 14] Generated Node #0,1,0: 16:[22, 14] Operation: 28/2=14 Exploring Operation: 28-22=6, Resulting Numbers: [2, 6] Generated Node #0,1,1: 16:[2, 6] Operation: 28-22=6 Moving to Node #0,0 Current State: 16:[2, 72, 22], Operations: ['50-28=22'] Exploring Operation: 72/2=36, Resulting Numbers: [22, 36] Generated Node #0,0,0: 16:[22, 36] Operation: 72/2=36 Exploring Operation: 72-22=50, Resulting Numbers: [2, 50] Generated Node #0,0,1: 16:[2, 50] Operation: 72-22=50 Moving to Node #0,1,1 Current State: 16:[2, 6], Operations: ['72-50=22', '28-22=6'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,16 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[22, 14], Operations: ['72-50=22', '28/2=14'] Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 22+14=36, Resulting Numbers: [36] 36,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[22, 36], Operations: ['50-28=22', '72/2=36'] Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,16 unequal: No Solution Exploring Operation: 22+36=58, Resulting Numbers: [58] 58,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[2, 50], Operations: ['50-28=22', '72-22=50'] Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,16 unequal: No Solution No solution found.
0
hs_2
sum_heuristic