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
[ 90, 64, 31, 25 ]
82
[ "90-64=26", "31+25=56", "26+56=82" ]
Current State: 82:[90, 64, 31, 25], Operations: [] Exploring Operation: 90-64=26, Resulting Numbers: [31, 25, 26] Generated Node #2: [31, 25, 26] from Operation: 90-64=26 Current State: 82:[31, 25, 26], Operations: ['90-64=26'] Exploring Operation: 31+25=56, Resulting Numbers: [26, 56] Generated Node #3: [26, 56] from Operation: 31+25=56 Current State: 82:[26, 56], Operations: ['90-64=26', '31+25=56'] Exploring Operation: 26+56=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[90, 64, 31, 25], Operations: [] Exploring Operation: 31-25=6, Resulting Numbers: [90, 64, 6] Generated Node #0,0: 82:[90, 64, 6] Operation: 31-25=6 Exploring Operation: 64-25=39, Resulting Numbers: [90, 31, 39] Generated Node #0,1: 82:[90, 31, 39] Operation: 64-25=39 Exploring Operation: 64+25=89, Resulting Numbers: [90, 31, 89] Generated Node #0,2: 82:[90, 31, 89] Operation: 64+25=89 Moving to Node #0,1 Current State: 82:[90, 31, 39], Operations: ['64-25=39'] Exploring Operation: 39-31=8, Resulting Numbers: [90, 8] Generated Node #0,1,0: 82:[90, 8] Operation: 39-31=8 Exploring Operation: 90-31=59, Resulting Numbers: [39, 59] Generated Node #0,1,1: 82:[39, 59] Operation: 90-31=59 Exploring Operation: 90-39=51, Resulting Numbers: [31, 51] Generated Node #0,1,2: 82:[31, 51] Operation: 90-39=51 Moving to Node #0,2 Current State: 82:[90, 31, 89], Operations: ['64+25=89'] Exploring Operation: 90-31=59, Resulting Numbers: [89, 59] Generated Node #0,2,0: 82:[89, 59] Operation: 90-31=59 Exploring Operation: 89-31=58, Resulting Numbers: [90, 58] Generated Node #0,2,1: 82:[90, 58] Operation: 89-31=58 Exploring Operation: 90-89=1, Resulting Numbers: [31, 1] Generated Node #0,2,2: 82:[31, 1] Operation: 90-89=1 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 82:[31, 1], Operations: ['64+25=89', '90-89=1'] Exploring Operation: 31+1=32, Resulting Numbers: [32] 32,82 unequal: No Solution Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,82 unequal: No Solution Exploring Operation: 31*1=31, Resulting Numbers: [31] 31,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 82:[89, 59], Operations: ['64+25=89', '90-31=59'] Exploring Operation: 89-59=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 89*59=5251, Resulting Numbers: [5251] 5251,82 unequal: No Solution Exploring Operation: 89+59=148, Resulting Numbers: [148] 148,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 82:[90, 58], Operations: ['64+25=89', '89-31=58'] Exploring Operation: 90+58=148, Resulting Numbers: [148] 148,82 unequal: No Solution Exploring Operation: 90*58=5220, Resulting Numbers: [5220] 5220,82 unequal: No Solution Exploring Operation: 90-58=32, Resulting Numbers: [32] 32,82 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: 82:[90, 64, 6], Operations: ['31-25=6'] Exploring Operation: 90-64=26, Resulting Numbers: [6, 26] Generated Node #0,0,0: 82:[6, 26] Operation: 90-64=26 Exploring Operation: 90-6=84, Resulting Numbers: [64, 84] Generated Node #0,0,1: 82:[64, 84] Operation: 90-6=84 Exploring Operation: 64+6=70, Resulting Numbers: [90, 70] Generated Node #0,0,2: 82:[90, 70] Operation: 64+6=70 Moving to Node #0,1,0 Current State: 82:[90, 8], Operations: ['64-25=39', '39-31=8'] Exploring Operation: 90*8=720, Resulting Numbers: [720] 720,82 unequal: No Solution Exploring Operation: 90+8=98, Resulting Numbers: [98] 98,82 unequal: No Solution Exploring Operation: 90-8=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[90, 64, 31, 25], Operations: [] Exploring Operation: 64-25=39, Resulting Numbers: [90, 31, 39] Generated Node #0,1: 82:[90, 31, 39] Operation: 64-25=39 Moving to Node #0,1 Current State: 82:[90, 31, 39], Operations: ['64-25=39'] Exploring Operation: 39-31=8, Resulting Numbers: [90, 8] Generated Node #0,1,0: 82:[90, 8] Operation: 39-31=8 Moving to Node #0,1,0 Current State: 82:[90, 8], Operations: ['64-25=39', '39-31=8'] Exploring Operation: 90-8=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.975694
hs_3
mult_heuristic
[ 51, 81, 20, 5 ]
34
[ "81-51=30", "20/5=4", "30+4=34" ]
Current State: 34:[51, 81, 20, 5], Operations: [] Exploring Operation: 81-51=30, Resulting Numbers: [20, 5, 30] Generated Node #2: [20, 5, 30] from Operation: 81-51=30 Current State: 34:[20, 5, 30], Operations: ['81-51=30'] Exploring Operation: 20/5=4, Resulting Numbers: [30, 4] Generated Node #3: [30, 4] from Operation: 20/5=4 Current State: 34:[30, 4], Operations: ['81-51=30', '20/5=4'] Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[51, 81, 20, 5], Operations: [] Exploring Operation: 51-20=31, Resulting Numbers: [81, 5, 31] Generated Node #0,0: 34:[81, 5, 31] Operation: 51-20=31 Exploring Operation: 81-20=61, Resulting Numbers: [51, 5, 61] Generated Node #0,1: 34:[51, 5, 61] Operation: 81-20=61 Exploring Operation: 81-51=30, Resulting Numbers: [20, 5, 30] Generated Node #0,2: 34:[20, 5, 30] Operation: 81-51=30 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[20, 5, 30], Operations: ['81-51=30'] Exploring Operation: 20-5=15, Resulting Numbers: [30, 15] Generated Node #0,2,0: 34:[30, 15] Operation: 20-5=15 Exploring Operation: 5+30=35, Resulting Numbers: [20, 35] Generated Node #0,2,1: 34:[20, 35] Operation: 5+30=35 Exploring Operation: 20/5=4, Resulting Numbers: [30, 4] Generated Node #0,2,2: 34:[30, 4] Operation: 20/5=4 Moving to Node #0,2,1 Current State: 34:[20, 35], Operations: ['81-51=30', '5+30=35'] Exploring Operation: 20*35=700, Resulting Numbers: [700] 700,34 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 20+35=55, Resulting Numbers: [55] 55,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[30, 15], Operations: ['81-51=30', '20-5=15'] Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 30+15=45, Resulting Numbers: [45] 45,34 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[30, 4], Operations: ['81-51=30', '20/5=4'] Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[51, 81, 20, 5], Operations: [] Exploring Operation: 81-51=30, Resulting Numbers: [20, 5, 30] Generated Node #0,2: 34:[20, 5, 30] Operation: 81-51=30 Moving to Node #0,2 Current State: 34:[20, 5, 30], Operations: ['81-51=30'] Exploring Operation: 20/5=4, Resulting Numbers: [30, 4] Generated Node #0,2,2: 34:[30, 4] Operation: 20/5=4 Moving to Node #0,2,2 Current State: 34:[30, 4], Operations: ['81-51=30', '20/5=4'] Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 63, 61, 92, 57 ]
87
[ "92*57=5244", "63+5244=5307", "5307/61=87" ]
Current State: 87:[63, 61, 92, 57], Operations: [] Exploring Operation: 92*57=5244, Resulting Numbers: [63, 61, 5244] Generated Node #2: [63, 61, 5244] from Operation: 92*57=5244 Current State: 87:[63, 61, 5244], Operations: ['92*57=5244'] Exploring Operation: 63+5244=5307, Resulting Numbers: [61, 5307] Generated Node #3: [61, 5307] from Operation: 63+5244=5307 Current State: 87:[61, 5307], Operations: ['92*57=5244', '63+5244=5307'] Exploring Operation: 5307/61=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[63, 61, 92, 57], Operations: [] Exploring Operation: 92-63=29, Resulting Numbers: [61, 57, 29] Generated Node #0,0: 87:[61, 57, 29] Operation: 92-63=29 Exploring Operation: 63-61=2, Resulting Numbers: [92, 57, 2] Generated Node #0,1: 87:[92, 57, 2] Operation: 63-61=2 Exploring Operation: 92-61=31, Resulting Numbers: [63, 57, 31] Generated Node #0,2: 87:[63, 57, 31] Operation: 92-61=31 Exploring Operation: 63-57=6, Resulting Numbers: [61, 92, 6] Generated Node #0,3: 87:[61, 92, 6] Operation: 63-57=6 Exploring Operation: 61-57=4, Resulting Numbers: [63, 92, 4] Generated Node #0,4: 87:[63, 92, 4] Operation: 61-57=4 Start Sub Search at level 1: Moving to Node #0,4 Current State: 87:[63, 92, 4], Operations: ['61-57=4'] Exploring Operation: 63+4=67, Resulting Numbers: [92, 67] Generated Node #0,4,0: 87:[92, 67] Operation: 63+4=67 Exploring Operation: 92-63=29, Resulting Numbers: [4, 29] Generated Node #0,4,1: 87:[4, 29] Operation: 92-63=29 Exploring Operation: 92/4=23, Resulting Numbers: [63, 23] Generated Node #0,4,2: 87:[63, 23] Operation: 92/4=23 Exploring Operation: 92-4=88, Resulting Numbers: [63, 88] Generated Node #0,4,3: 87:[63, 88] Operation: 92-4=88 Exploring Operation: 63-4=59, Resulting Numbers: [92, 59] Generated Node #0,4,4: 87:[92, 59] Operation: 63-4=59 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 87:[4, 29], Operations: ['61-57=4', '92-63=29'] Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,87 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,87 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 87:[92, 67], Operations: ['61-57=4', '63+4=67'] Exploring Operation: 92*67=6164, Resulting Numbers: [6164] 6164,87 unequal: No Solution Exploring Operation: 92+67=159, Resulting Numbers: [159] 159,87 unequal: No Solution Exploring Operation: 92-67=25, Resulting Numbers: [25] 25,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 87:[63, 88], Operations: ['61-57=4', '92-4=88'] Exploring Operation: 88-63=25, Resulting Numbers: [25] 25,87 unequal: No Solution Exploring Operation: 63+88=151, Resulting Numbers: [151] 151,87 unequal: No Solution Exploring Operation: 63*88=5544, Resulting Numbers: [5544] 5544,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 87:[63, 23], Operations: ['61-57=4', '92/4=23'] Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,87 unequal: No Solution Exploring Operation: 63*23=1449, Resulting Numbers: [1449] 1449,87 unequal: No Solution Exploring Operation: 63+23=86, Resulting Numbers: [86] 86,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 87:[92, 59], Operations: ['61-57=4', '63-4=59'] Exploring Operation: 92*59=5428, Resulting Numbers: [5428] 5428,87 unequal: No Solution Exploring Operation: 92-59=33, Resulting Numbers: [33] 33,87 unequal: No Solution Exploring Operation: 92+59=151, Resulting Numbers: [151] 151,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[92, 57, 2], Operations: ['63-61=2'] Exploring Operation: 92-2=90, Resulting Numbers: [57, 90] Generated Node #0,1,0: 87:[57, 90] Operation: 92-2=90 Exploring Operation: 57-2=55, Resulting Numbers: [92, 55] Generated Node #0,1,1: 87:[92, 55] Operation: 57-2=55 Exploring Operation: 57*2=114, Resulting Numbers: [92, 114] Generated Node #0,1,2: 87:[92, 114] Operation: 57*2=114 Exploring Operation: 92-57=35, Resulting Numbers: [2, 35] Generated Node #0,1,3: 87:[2, 35] Operation: 92-57=35 Exploring Operation: 57+2=59, Resulting Numbers: [92, 59] Generated Node #0,1,4: 87:[92, 59] Operation: 57+2=59 Moving to Node #0,1,3 Current State: 87:[2, 35], Operations: ['63-61=2', '92-57=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,87 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[92, 55], Operations: ['63-61=2', '57-2=55'] Exploring Operation: 92-55=37, Resulting Numbers: [37] 37,87 unequal: No Solution Exploring Operation: 92+55=147, Resulting Numbers: [147] 147,87 unequal: No Solution Exploring Operation: 92*55=5060, Resulting Numbers: [5060] 5060,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[57, 90], Operations: ['63-61=2', '92-2=90'] Exploring Operation: 90-57=33, Resulting Numbers: [33] 33,87 unequal: No Solution Exploring Operation: 57*90=5130, Resulting Numbers: [5130] 5130,87 unequal: No Solution Exploring Operation: 57+90=147, Resulting Numbers: [147] 147,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[92, 114], Operations: ['63-61=2', '57*2=114'] Exploring Operation: 114-92=22, Resulting Numbers: [22] 22,87 unequal: No Solution Exploring Operation: 92*114=10488, Resulting Numbers: [10488] 10488,87 unequal: No Solution Exploring Operation: 92+114=206, Resulting Numbers: [206] 206,87 unequal: No Solution Moving to Node #0,1,4 Current State: 87:[92, 59], Operations: ['63-61=2', '57+2=59'] Exploring Operation: 92+59=151, Resulting Numbers: [151] 151,87 unequal: No Solution Exploring Operation: 92*59=5428, Resulting Numbers: [5428] 5428,87 unequal: No Solution Exploring Operation: 92-59=33, Resulting Numbers: [33] 33,87 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 #0,3 Current State: 87:[61, 92, 6], Operations: ['63-57=6'] Exploring Operation: 61-6=55, Resulting Numbers: [92, 55] Generated Node #0,3,0: 87:[92, 55] Operation: 61-6=55 Exploring Operation: 92-6=86, Resulting Numbers: [61, 86] Generated Node #0,3,1: 87:[61, 86] Operation: 92-6=86 Exploring Operation: 92+6=98, Resulting Numbers: [61, 98] Generated Node #0,3,2: 87:[61, 98] Operation: 92+6=98 Exploring Operation: 92-61=31, Resulting Numbers: [6, 31] Generated Node #0,3,3: 87:[6, 31] Operation: 92-61=31 Exploring Operation: 61+6=67, Resulting Numbers: [92, 67] Generated Node #0,3,4: 87:[92, 67] Operation: 61+6=67 Moving to Node #0,3,3 Current State: 87:[6, 31], Operations: ['63-57=6', '92-61=31'] Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,87 unequal: No Solution Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,87 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,87 unequal: No Solution Moving to Node #0,3,4 Current State: 87:[92, 67], Operations: ['63-57=6', '61+6=67'] Exploring Operation: 92-67=25, Resulting Numbers: [25] 25,87 unequal: No Solution Exploring Operation: 92+67=159, Resulting Numbers: [159] 159,87 unequal: No Solution Exploring Operation: 92*67=6164, Resulting Numbers: [6164] 6164,87 unequal: No Solution Moving to Node #0,3,1 Current State: 87:[61, 86], Operations: ['63-57=6', '92-6=86'] Exploring Operation: 86-61=25, Resulting Numbers: [25] 25,87 unequal: No Solution Exploring Operation: 61+86=147, Resulting Numbers: [147] 147,87 unequal: No Solution Exploring Operation: 61*86=5246, Resulting Numbers: [5246] 5246,87 unequal: No Solution Moving to Node #0,3,0 Current State: 87:[92, 55], Operations: ['63-57=6', '61-6=55'] Exploring Operation: 92*55=5060, Resulting Numbers: [5060] 5060,87 unequal: No Solution Exploring Operation: 92+55=147, Resulting Numbers: [147] 147,87 unequal: No Solution Exploring Operation: 92-55=37, Resulting Numbers: [37] 37,87 unequal: No Solution Moving to Node #0,3,2 Current State: 87:[61, 98], Operations: ['63-57=6', '92+6=98'] Exploring Operation: 61+98=159, Resulting Numbers: [159] 159,87 unequal: No Solution Exploring Operation: 98-61=37, Resulting Numbers: [37] 37,87 unequal: No Solution Exploring Operation: 61*98=5978, Resulting Numbers: [5978] 5978,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[61, 57, 29], Operations: ['92-63=29'] Exploring Operation: 61+29=90, Resulting Numbers: [57, 90] Generated Node #0,0,0: 87:[57, 90] Operation: 61+29=90 Exploring Operation: 61-57=4, Resulting Numbers: [29, 4] Generated Node #0,0,1: 87:[29, 4] Operation: 61-57=4 Exploring Operation: 57+29=86, Resulting Numbers: [61, 86] Generated Node #0,0,2: 87:[61, 86] Operation: 57+29=86 Exploring Operation: 61+57=118, Resulting Numbers: [29, 118] Generated Node #0,0,3: 87:[29, 118] Operation: 61+57=118 Exploring Operation: 57-29=28, Resulting Numbers: [61, 28] Generated Node #0,0,4: 87:[61, 28] Operation: 57-29=28 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[29, 4], Operations: ['92-63=29', '61-57=4'] Exploring Operation: 29+4=33, Resulting Numbers: [33] 33,87 unequal: No Solution Exploring Operation: 29*4=116, Resulting Numbers: [116] 116,87 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 87:[61, 86], Operations: ['92-63=29', '57+29=86'] Exploring Operation: 61*86=5246, Resulting Numbers: [5246] 5246,87 unequal: No Solution Exploring Operation: 86-61=25, Resulting Numbers: [25] 25,87 unequal: No Solution Exploring Operation: 61+86=147, Resulting Numbers: [147] 147,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 87:[61, 28], Operations: ['92-63=29', '57-29=28'] Exploring Operation: 61+28=89, Resulting Numbers: [89] 89,87 unequal: No Solution Exploring Operation: 61*28=1708, Resulting Numbers: [1708] 1708,87 unequal: No Solution Exploring Operation: 61-28=33, Resulting Numbers: [33] 33,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[57, 90], Operations: ['92-63=29', '61+29=90'] Exploring Operation: 57+90=147, Resulting Numbers: [147] 147,87 unequal: No Solution Exploring Operation: 90-57=33, Resulting Numbers: [33] 33,87 unequal: No Solution Exploring Operation: 57*90=5130, Resulting Numbers: [5130] 5130,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 87:[29, 118], Operations: ['92-63=29', '61+57=118'] Exploring Operation: 118-29=89, Resulting Numbers: [89] 89,87 unequal: No Solution Exploring Operation: 29+118=147, Resulting Numbers: [147] 147,87 unequal: No Solution Exploring Operation: 29*118=3422, Resulting Numbers: [3422] 3422,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[63, 57, 31], Operations: ['92-61=31'] Exploring Operation: 57+31=88, Resulting Numbers: [63, 88] Generated Node #0,2,0: 87:[63, 88] Operation: 57+31=88 Exploring Operation: 57-31=26, Resulting Numbers: [63, 26] Generated Node #0,2,1: 87:[63, 26] Operation: 57-31=26 Exploring Operation: 63-57=6, Resulting Numbers: [31, 6] Generated Node #0,2,2: 87:[31, 6] Operation: 63-57=6 Exploring Operation: 63-31=32, Resulting Numbers: [57, 32] Generated Node #0,2,3: 87:[57, 32] Operation: 63-31=32 Exploring Operation: 63+57=120, Resulting Numbers: [31, 120] Generated Node #0,2,4: 87:[31, 120] Operation: 63+57=120 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 87:[31, 6], Operations: ['92-61=31', '63-57=6'] Exploring Operation: 31*6=186, Resulting Numbers: [186] 186,87 unequal: No Solution Exploring Operation: 31+6=37, Resulting Numbers: [37] 37,87 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 87:[63, 88], Operations: ['92-61=31', '57+31=88'] Exploring Operation: 63+88=151, Resulting Numbers: [151] 151,87 unequal: No Solution Exploring Operation: 88-63=25, Resulting Numbers: [25] 25,87 unequal: No Solution Exploring Operation: 63*88=5544, Resulting Numbers: [5544] 5544,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 87:[63, 26], Operations: ['92-61=31', '57-31=26'] Exploring Operation: 63+26=89, Resulting Numbers: [89] 89,87 unequal: No Solution Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,87 unequal: No Solution Exploring Operation: 63*26=1638, Resulting Numbers: [1638] 1638,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 87:[57, 32], Operations: ['92-61=31', '63-31=32'] Exploring Operation: 57*32=1824, Resulting Numbers: [1824] 1824,87 unequal: No Solution Exploring Operation: 57-32=25, Resulting Numbers: [25] 25,87 unequal: No Solution Exploring Operation: 57+32=89, Resulting Numbers: [89] 89,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 87:[31, 120], Operations: ['92-61=31', '63+57=120'] Exploring Operation: 31*120=3720, Resulting Numbers: [3720] 3720,87 unequal: No Solution Exploring Operation: 120-31=89, Resulting Numbers: [89] 89,87 unequal: No Solution Exploring Operation: 31+120=151, Resulting Numbers: [151] 151,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 15, 46, 23, 53 ]
91
[ "15+46=61", "53-23=30", "61+30=91" ]
Current State: 91:[15, 46, 23, 53], Operations: [] Exploring Operation: 15+46=61, Resulting Numbers: [23, 53, 61] Generated Node #2: [23, 53, 61] from Operation: 15+46=61 Current State: 91:[23, 53, 61], Operations: ['15+46=61'] Exploring Operation: 53-23=30, Resulting Numbers: [61, 30] Generated Node #3: [61, 30] from Operation: 53-23=30 Current State: 91:[61, 30], Operations: ['15+46=61', '53-23=30'] Exploring Operation: 61+30=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[15, 46, 23, 53], Operations: [] Exploring Operation: 53-46=7, Resulting Numbers: [15, 23, 7] Generated Node #0,0: 91:[15, 23, 7] Operation: 53-46=7 Moving to Node #0,0 Current State: 91:[15, 23, 7], Operations: ['53-46=7'] Exploring Operation: 23-15=8, Resulting Numbers: [7, 8] Generated Node #0,0,0: 91:[7, 8] Operation: 23-15=8 Moving to Node #0,0,0 Current State: 91:[7, 8], Operations: ['53-46=7', '23-15=8'] Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,91 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 21, 52, 18, 31 ]
86
[ "21+52=73", "31-18=13", "73+13=86" ]
Current State: 86:[21, 52, 18, 31], Operations: [] Exploring Operation: 21+52=73, Resulting Numbers: [18, 31, 73] Generated Node #2: [18, 31, 73] from Operation: 21+52=73 Current State: 86:[18, 31, 73], Operations: ['21+52=73'] Exploring Operation: 31-18=13, Resulting Numbers: [73, 13] Generated Node #3: [73, 13] from Operation: 31-18=13 Current State: 86:[73, 13], Operations: ['21+52=73', '31-18=13'] Exploring Operation: 73+13=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[21, 52, 18, 31], Operations: [] Exploring Operation: 18+31=49, Resulting Numbers: [21, 52, 49] Generated Node #0,0: 86:[21, 52, 49] Operation: 18+31=49 Exploring Operation: 21-18=3, Resulting Numbers: [52, 31, 3] Generated Node #0,1: 86:[52, 31, 3] Operation: 21-18=3 Exploring Operation: 21+18=39, Resulting Numbers: [52, 31, 39] Generated Node #0,2: 86:[52, 31, 39] Operation: 21+18=39 Exploring Operation: 21+31=52, Resulting Numbers: [52, 18, 52] Generated Node #0,3: 86:[52, 18, 52] Operation: 21+31=52 Exploring Operation: 31-21=10, Resulting Numbers: [52, 18, 10] Generated Node #0,4: 86:[52, 18, 10] Operation: 31-21=10 Moving to Node #0,1 Current State: 86:[52, 31, 3], Operations: ['21-18=3'] Exploring Operation: 31+3=34, Resulting Numbers: [52, 34] Generated Node #0,1,0: 86:[52, 34] Operation: 31+3=34 Exploring Operation: 52-3=49, Resulting Numbers: [31, 49] Generated Node #0,1,1: 86:[31, 49] Operation: 52-3=49 Exploring Operation: 31*3=93, Resulting Numbers: [52, 93] Generated Node #0,1,2: 86:[52, 93] Operation: 31*3=93 Exploring Operation: 52-31=21, Resulting Numbers: [3, 21] Generated Node #0,1,3: 86:[3, 21] Operation: 52-31=21 Exploring Operation: 52+31=83, Resulting Numbers: [3, 83] Generated Node #0,1,4: 86:[3, 83] Operation: 52+31=83 Moving to Node #0,2 Current State: 86:[52, 31, 39], Operations: ['21+18=39'] Exploring Operation: 52+31=83, Resulting Numbers: [39, 83] Generated Node #0,2,0: 86:[39, 83] Operation: 52+31=83 Exploring Operation: 52-39=13, Resulting Numbers: [31, 13] Generated Node #0,2,1: 86:[31, 13] Operation: 52-39=13 Exploring Operation: 52-31=21, Resulting Numbers: [39, 21] Generated Node #0,2,2: 86:[39, 21] Operation: 52-31=21 Exploring Operation: 39-31=8, Resulting Numbers: [52, 8] Generated Node #0,2,3: 86:[52, 8] Operation: 39-31=8 Exploring Operation: 52+39=91, Resulting Numbers: [31, 91] Generated Node #0,2,4: 86:[31, 91] Operation: 52+39=91 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 86:[39, 83], Operations: ['21+18=39', '52+31=83'] Exploring Operation: 39+83=122, Resulting Numbers: [122] 122,86 unequal: No Solution Exploring Operation: 83-39=44, Resulting Numbers: [44] 44,86 unequal: No Solution Exploring Operation: 39*83=3237, Resulting Numbers: [3237] 3237,86 unequal: No Solution No 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: 86:[52, 8], Operations: ['21+18=39', '39-31=8'] Exploring Operation: 52*8=416, Resulting Numbers: [416] 416,86 unequal: No Solution Exploring Operation: 52+8=60, Resulting Numbers: [60] 60,86 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 86:[31, 91], Operations: ['21+18=39', '52+39=91'] Exploring Operation: 31+91=122, Resulting Numbers: [122] 122,86 unequal: No Solution Exploring Operation: 91-31=60, Resulting Numbers: [60] 60,86 unequal: No Solution Exploring Operation: 31*91=2821, Resulting Numbers: [2821] 2821,86 unequal: No Solution No 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: 86:[31, 13], Operations: ['21+18=39', '52-39=13'] Exploring Operation: 31*13=403, Resulting Numbers: [403] 403,86 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,86 unequal: No Solution No 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: 86:[39, 21], Operations: ['21+18=39', '52-31=21'] Exploring Operation: 39+21=60, Resulting Numbers: [60] 60,86 unequal: No Solution Exploring Operation: 39*21=819, Resulting Numbers: [819] 819,86 unequal: No Solution Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,86 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: 86:[52, 18, 10], Operations: ['31-21=10'] Exploring Operation: 52-18=34, Resulting Numbers: [10, 34] Generated Node #0,4,0: 86:[10, 34] Operation: 52-18=34 Exploring Operation: 52+18=70, Resulting Numbers: [10, 70] Generated Node #0,4,1: 86:[10, 70] Operation: 52+18=70 Exploring Operation: 18+10=28, Resulting Numbers: [52, 28] Generated Node #0,4,2: 86:[52, 28] Operation: 18+10=28 Exploring Operation: 18-10=8, Resulting Numbers: [52, 8] Generated Node #0,4,3: 86:[52, 8] Operation: 18-10=8 Exploring Operation: 52-10=42, Resulting Numbers: [18, 42] Generated Node #0,4,4: 86:[18, 42] Operation: 52-10=42 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 86:[52, 8], Operations: ['31-21=10', '18-10=8'] Exploring Operation: 52+8=60, Resulting Numbers: [60] 60,86 unequal: No Solution Exploring Operation: 52*8=416, Resulting Numbers: [416] 416,86 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,86 unequal: No Solution No 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: 86:[10, 34], Operations: ['31-21=10', '52-18=34'] Exploring Operation: 10*34=340, Resulting Numbers: [340] 340,86 unequal: No Solution Exploring Operation: 10+34=44, Resulting Numbers: [44] 44,86 unequal: No Solution Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,86 unequal: No Solution No 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: 86:[18, 42], Operations: ['31-21=10', '52-10=42'] Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,86 unequal: No Solution Exploring Operation: 18+42=60, Resulting Numbers: [60] 60,86 unequal: No Solution Exploring Operation: 18*42=756, Resulting Numbers: [756] 756,86 unequal: No Solution No 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: 86:[10, 70], Operations: ['31-21=10', '52+18=70'] Exploring Operation: 10+70=80, Resulting Numbers: [80] 80,86 unequal: No Solution Exploring Operation: 70/10=7, Resulting Numbers: [7] 7,86 unequal: No Solution Exploring Operation: 70-10=60, Resulting Numbers: [60] 60,86 unequal: No Solution Exploring Operation: 10*70=700, Resulting Numbers: [700] 700,86 unequal: No Solution No 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: 86:[52, 28], Operations: ['31-21=10', '18+10=28'] Exploring Operation: 52*28=1456, Resulting Numbers: [1456] 1456,86 unequal: No Solution Exploring Operation: 52-28=24, Resulting Numbers: [24] 24,86 unequal: No Solution Exploring Operation: 52+28=80, Resulting Numbers: [80] 80,86 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: 86:[21, 52, 49], Operations: ['18+31=49'] Exploring Operation: 21+49=70, Resulting Numbers: [52, 70] Generated Node #0,0,0: 86:[52, 70] Operation: 21+49=70 Exploring Operation: 52-21=31, Resulting Numbers: [49, 31] Generated Node #0,0,1: 86:[49, 31] Operation: 52-21=31 Exploring Operation: 52-49=3, Resulting Numbers: [21, 3] Generated Node #0,0,2: 86:[21, 3] Operation: 52-49=3 Exploring Operation: 49-21=28, Resulting Numbers: [52, 28] Generated Node #0,0,3: 86:[52, 28] Operation: 49-21=28 Exploring Operation: 21+52=73, Resulting Numbers: [49, 73] Generated Node #0,0,4: 86:[49, 73] Operation: 21+52=73 Moving to Node #0,3 Current State: 86:[52, 18, 52], Operations: ['21+31=52'] Exploring Operation: 52+18=70, Resulting Numbers: [52, 70] Generated Node #0,3,0: 86:[52, 70] Operation: 52+18=70 Exploring Operation: 52-18=34, Resulting Numbers: [52, 34] Generated Node #0,3,1: 86:[52, 34] Operation: 52-18=34 Exploring Operation: 52/52=1, Resulting Numbers: [18, 1] Generated Node #0,3,2: 86:[18, 1] Operation: 52/52=1 Exploring Operation: 52-52=0, Resulting Numbers: [18, 0] Generated Node #0,3,3: 86:[18, 0] Operation: 52-52=0 Exploring Operation: 52-18=34, Resulting Numbers: [52, 34] Generated Node #0,3,4: 86:[52, 34] Operation: 52-18=34 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 86:[18, 1], Operations: ['21+31=52', '52/52=1'] Exploring Operation: 18+1=19, Resulting Numbers: [19] 19,86 unequal: No Solution Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,86 unequal: No Solution Exploring Operation: 18*1=18, Resulting Numbers: [18] 18,86 unequal: No Solution No 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: 86:[52, 34], Operations: ['21+31=52', '52-18=34'] Exploring Operation: 52*34=1768, Resulting Numbers: [1768] 1768,86 unequal: No Solution Exploring Operation: 52+34=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[21, 52, 18, 31], Operations: [] Exploring Operation: 21+31=52, Resulting Numbers: [52, 18, 52] Generated Node #0,3: 86:[52, 18, 52] Operation: 21+31=52 Moving to Node #0,3 Current State: 86:[52, 18, 52], Operations: ['21+31=52'] Exploring Operation: 52-18=34, Resulting Numbers: [52, 34] Generated Node #0,3,1: 86:[52, 34] Operation: 52-18=34 Moving to Node #0,3,1 Current State: 86:[52, 34], Operations: ['21+31=52', '52-18=34'] Exploring Operation: 52+34=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.938368
hs_5
mult_heuristic
[ 51, 77, 20, 41 ]
79
[ "51-41=10", "20/10=2", "77+2=79" ]
Current State: 79:[51, 77, 20, 41], Operations: [] Exploring Operation: 51-41=10, Resulting Numbers: [77, 20, 10] Generated Node #2: [77, 20, 10] from Operation: 51-41=10 Current State: 79:[77, 20, 10], Operations: ['51-41=10'] Exploring Operation: 20/10=2, Resulting Numbers: [77, 2] Generated Node #3: [77, 2] from Operation: 20/10=2 Current State: 79:[77, 2], Operations: ['51-41=10', '20/10=2'] Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[51, 77, 20, 41], Operations: [] Exploring Operation: 20+41=61, Resulting Numbers: [51, 77, 61] Generated Node #0,0: 79:[51, 77, 61] Operation: 20+41=61 Exploring Operation: 51+20=71, Resulting Numbers: [77, 41, 71] Generated Node #0,1: 79:[77, 41, 71] Operation: 51+20=71 Exploring Operation: 77+20=97, Resulting Numbers: [51, 41, 97] Generated Node #0,2: 79:[51, 41, 97] Operation: 77+20=97 Exploring Operation: 51+41=92, Resulting Numbers: [77, 20, 92] Generated Node #0,3: 79:[77, 20, 92] Operation: 51+41=92 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[51, 77, 61], Operations: ['20+41=61'] Exploring Operation: 61-51=10, Resulting Numbers: [77, 10] Generated Node #0,0,0: 79:[77, 10] Operation: 61-51=10 Exploring Operation: 51+77=128, Resulting Numbers: [61, 128] Generated Node #0,0,1: 79:[61, 128] Operation: 51+77=128 Exploring Operation: 51+61=112, Resulting Numbers: [77, 112] Generated Node #0,0,2: 79:[77, 112] Operation: 51+61=112 Exploring Operation: 77-51=26, Resulting Numbers: [61, 26] Generated Node #0,0,3: 79:[61, 26] Operation: 77-51=26 Moving to Node #0,0,2 Current State: 79:[77, 112], Operations: ['20+41=61', '51+61=112'] Exploring Operation: 112-77=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 77*112=8624, Resulting Numbers: [8624] 8624,79 unequal: No Solution Exploring Operation: 77+112=189, Resulting Numbers: [189] 189,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[61, 128], Operations: ['20+41=61', '51+77=128'] Exploring Operation: 61+128=189, Resulting Numbers: [189] 189,79 unequal: No Solution Exploring Operation: 128-61=67, Resulting Numbers: [67] 67,79 unequal: No Solution Exploring Operation: 61*128=7808, Resulting Numbers: [7808] 7808,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[61, 26], Operations: ['20+41=61', '77-51=26'] Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,79 unequal: No Solution Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,79 unequal: No Solution Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[77, 10], Operations: ['20+41=61', '61-51=10'] Exploring Operation: 77-10=67, Resulting Numbers: [67] 67,79 unequal: No Solution Exploring Operation: 77*10=770, Resulting Numbers: [770] 770,79 unequal: No Solution Exploring Operation: 77+10=87, Resulting Numbers: [87] 87,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[77, 41, 71], Operations: ['51+20=71'] Exploring Operation: 77-41=36, Resulting Numbers: [71, 36] Generated Node #0,1,0: 79:[71, 36] Operation: 77-41=36 Exploring Operation: 41+71=112, Resulting Numbers: [77, 112] Generated Node #0,1,1: 79:[77, 112] Operation: 41+71=112 Exploring Operation: 71-41=30, Resulting Numbers: [77, 30] Generated Node #0,1,2: 79:[77, 30] Operation: 71-41=30 Exploring Operation: 77+41=118, Resulting Numbers: [71, 118] Generated Node #0,1,3: 79:[71, 118] Operation: 77+41=118 Moving to Node #0,1,1 Current State: 79:[77, 112], Operations: ['51+20=71', '41+71=112'] Exploring Operation: 112-77=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 77+112=189, Resulting Numbers: [189] 189,79 unequal: No Solution Exploring Operation: 77*112=8624, Resulting Numbers: [8624] 8624,79 unequal: No Solution Moving to Node #0,1,3 Current State: 79:[71, 118], Operations: ['51+20=71', '77+41=118'] Exploring Operation: 71+118=189, Resulting Numbers: [189] 189,79 unequal: No Solution Exploring Operation: 118-71=47, Resulting Numbers: [47] 47,79 unequal: No Solution Exploring Operation: 71*118=8378, Resulting Numbers: [8378] 8378,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[77, 30], Operations: ['51+20=71', '71-41=30'] Exploring Operation: 77+30=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 77-30=47, Resulting Numbers: [47] 47,79 unequal: No Solution Exploring Operation: 77*30=2310, Resulting Numbers: [2310] 2310,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[71, 36], Operations: ['51+20=71', '77-41=36'] Exploring Operation: 71+36=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 71*36=2556, Resulting Numbers: [2556] 2556,79 unequal: No Solution Exploring Operation: 71-36=35, Resulting Numbers: [35] 35,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 79:[77, 20, 92], Operations: ['51+41=92'] Exploring Operation: 77+20=97, Resulting Numbers: [92, 97] Generated Node #0,3,0: 79:[92, 97] Operation: 77+20=97 Exploring Operation: 92-20=72, Resulting Numbers: [77, 72] Generated Node #0,3,1: 79:[77, 72] Operation: 92-20=72 Exploring Operation: 77-20=57, Resulting Numbers: [92, 57] Generated Node #0,3,2: 79:[92, 57] Operation: 77-20=57 Exploring Operation: 20+92=112, Resulting Numbers: [77, 112] Generated Node #0,3,3: 79:[77, 112] Operation: 20+92=112 Moving to Node #0,3,1 Current State: 79:[77, 72], Operations: ['51+41=92', '92-20=72'] Exploring Operation: 77+72=149, Resulting Numbers: [149] 149,79 unequal: No Solution Exploring Operation: 77*72=5544, Resulting Numbers: [5544] 5544,79 unequal: No Solution Exploring Operation: 77-72=5, Resulting Numbers: [5] 5,79 unequal: No Solution Moving to Node #0,3,0 Current State: 79:[92, 97], Operations: ['51+41=92', '77+20=97'] Exploring Operation: 97-92=5, Resulting Numbers: [5] 5,79 unequal: No Solution Exploring Operation: 92+97=189, Resulting Numbers: [189] 189,79 unequal: No Solution Exploring Operation: 92*97=8924, Resulting Numbers: [8924] 8924,79 unequal: No Solution Moving to Node #0,3,3 Current State: 79:[77, 112], Operations: ['51+41=92', '20+92=112'] Exploring Operation: 112-77=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 77*112=8624, Resulting Numbers: [8624] 8624,79 unequal: No Solution Exploring Operation: 77+112=189, Resulting Numbers: [189] 189,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[92, 57], Operations: ['51+41=92', '77-20=57'] Exploring Operation: 92+57=149, Resulting Numbers: [149] 149,79 unequal: No Solution Exploring Operation: 92-57=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 92*57=5244, Resulting Numbers: [5244] 5244,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[51, 41, 97], Operations: ['77+20=97'] Exploring Operation: 51+41=92, Resulting Numbers: [97, 92] Generated Node #0,2,0: 79:[97, 92] Operation: 51+41=92 Exploring Operation: 97-41=56, Resulting Numbers: [51, 56] Generated Node #0,2,1: 79:[51, 56] Operation: 97-41=56 Exploring Operation: 51-41=10, Resulting Numbers: [97, 10] Generated Node #0,2,2: 79:[97, 10] Operation: 51-41=10 Exploring Operation: 97-51=46, Resulting Numbers: [41, 46] Generated Node #0,2,3: 79:[41, 46] Operation: 97-51=46 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 79:[97, 92], Operations: ['77+20=97', '51+41=92'] Exploring Operation: 97-92=5, Resulting Numbers: [5] 5,79 unequal: No Solution Exploring Operation: 97+92=189, Resulting Numbers: [189] 189,79 unequal: No Solution Exploring Operation: 97*92=8924, Resulting Numbers: [8924] 8924,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 79:[51, 56], Operations: ['77+20=97', '97-41=56'] Exploring Operation: 51+56=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 56-51=5, Resulting Numbers: [5] 5,79 unequal: No Solution Exploring Operation: 51*56=2856, Resulting Numbers: [2856] 2856,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 79:[41, 46], Operations: ['77+20=97', '97-51=46'] Exploring Operation: 41*46=1886, Resulting Numbers: [1886] 1886,79 unequal: No Solution Exploring Operation: 41+46=87, Resulting Numbers: [87] 87,79 unequal: No Solution Exploring Operation: 46-41=5, Resulting Numbers: [5] 5,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 79:[97, 10], Operations: ['77+20=97', '51-41=10'] Exploring Operation: 97+10=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 97*10=970, Resulting Numbers: [970] 970,79 unequal: No Solution Exploring Operation: 97-10=87, Resulting Numbers: [87] 87,79 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_4
mult_heuristic
[ 55, 81, 27, 68 ]
68
[ "81-55=26", "27-26=1", "68*1=68" ]
Current State: 68:[55, 81, 27, 68], Operations: [] Exploring Operation: 81-55=26, Resulting Numbers: [27, 68, 26] Generated Node #2: [27, 68, 26] from Operation: 81-55=26 Current State: 68:[27, 68, 26], Operations: ['81-55=26'] Exploring Operation: 27-26=1, Resulting Numbers: [68, 1] Generated Node #3: [68, 1] from Operation: 27-26=1 Current State: 68:[68, 1], Operations: ['81-55=26', '27-26=1'] Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[55, 81, 27, 68], Operations: [] Exploring Operation: 55-27=28, Resulting Numbers: [81, 68, 28] Generated Node #0,0: 68:[81, 68, 28] Operation: 55-27=28 Exploring Operation: 81/27=3, Resulting Numbers: [55, 68, 3] Generated Node #0,1: 68:[55, 68, 3] Operation: 81/27=3 Exploring Operation: 81-55=26, Resulting Numbers: [27, 68, 26] Generated Node #0,2: 68:[27, 68, 26] Operation: 81-55=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[55, 68, 3], Operations: ['81/27=3'] Exploring Operation: 55-3=52, Resulting Numbers: [68, 52] Generated Node #0,1,0: 68:[68, 52] Operation: 55-3=52 Exploring Operation: 68-55=13, Resulting Numbers: [3, 13] Generated Node #0,1,1: 68:[3, 13] Operation: 68-55=13 Exploring Operation: 55+3=58, Resulting Numbers: [68, 58] Generated Node #0,1,2: 68:[68, 58] Operation: 55+3=58 Moving to Node #0,1,1 Current State: 68:[3, 13], Operations: ['81/27=3', '68-55=13'] Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,68 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,68 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[68, 58], Operations: ['81/27=3', '55+3=58'] Exploring Operation: 68*58=3944, Resulting Numbers: [3944] 3944,68 unequal: No Solution Exploring Operation: 68+58=126, Resulting Numbers: [126] 126,68 unequal: No Solution Exploring Operation: 68-58=10, Resulting Numbers: [10] 10,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[68, 52], Operations: ['81/27=3', '55-3=52'] Exploring Operation: 68*52=3536, Resulting Numbers: [3536] 3536,68 unequal: No Solution Exploring Operation: 68+52=120, Resulting Numbers: [120] 120,68 unequal: No Solution Exploring Operation: 68-52=16, Resulting Numbers: [16] 16,68 unequal: No Solution No 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: 68:[27, 68, 26], Operations: ['81-55=26'] Exploring Operation: 27-26=1, Resulting Numbers: [68, 1] Generated Node #0,2,0: 68:[68, 1] Operation: 27-26=1 Exploring Operation: 27+26=53, Resulting Numbers: [68, 53] Generated Node #0,2,1: 68:[68, 53] Operation: 27+26=53 Exploring Operation: 68-27=41, Resulting Numbers: [26, 41] Generated Node #0,2,2: 68:[26, 41] Operation: 68-27=41 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 68:[68, 1], Operations: ['81-55=26', '27-26=1'] Exploring Operation: 68+1=69, Resulting Numbers: [69] 69,68 unequal: No Solution Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[55, 81, 27, 68], Operations: [] Exploring Operation: 81-55=26, Resulting Numbers: [27, 68, 26] Generated Node #0,2: 68:[27, 68, 26] Operation: 81-55=26 Moving to Node #0,2 Current State: 68:[27, 68, 26], Operations: ['81-55=26'] Exploring Operation: 27-26=1, Resulting Numbers: [68, 1] Generated Node #0,2,0: 68:[68, 1] Operation: 27-26=1 Moving to Node #0,2,0 Current State: 68:[68, 1], Operations: ['81-55=26', '27-26=1'] Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 75, 3, 78, 77 ]
24
[ "75/3=25", "78-77=1", "25-1=24" ]
Current State: 24:[75, 3, 78, 77], Operations: [] Exploring Operation: 75/3=25, Resulting Numbers: [78, 77, 25] Generated Node #2: [78, 77, 25] from Operation: 75/3=25 Current State: 24:[78, 77, 25], Operations: ['75/3=25'] Exploring Operation: 78-77=1, Resulting Numbers: [25, 1] Generated Node #3: [25, 1] from Operation: 78-77=1 Current State: 24:[25, 1], Operations: ['75/3=25', '78-77=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[75, 3, 78, 77], Operations: [] Exploring Operation: 77-75=2, Resulting Numbers: [3, 78, 2] Generated Node #0,0: 24:[3, 78, 2] Operation: 77-75=2 Exploring Operation: 75/3=25, Resulting Numbers: [78, 77, 25] Generated Node #0,1: 24:[78, 77, 25] Operation: 75/3=25 Exploring Operation: 78-77=1, Resulting Numbers: [75, 3, 1] Generated Node #0,2: 24:[75, 3, 1] Operation: 78-77=1 Exploring Operation: 78-75=3, Resulting Numbers: [3, 77, 3] Generated Node #0,3: 24:[3, 77, 3] Operation: 78-75=3 Exploring Operation: 78/3=26, Resulting Numbers: [75, 77, 26] Generated Node #0,4: 24:[75, 77, 26] Operation: 78/3=26 Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[75, 3, 1], Operations: ['78-77=1'] Exploring Operation: 75/3=25, Resulting Numbers: [1, 25] Generated Node #0,2,0: 24:[1, 25] Operation: 75/3=25 Exploring Operation: 75/1=75, Resulting Numbers: [3, 75] Generated Node #0,2,1: 24:[3, 75] Operation: 75/1=75 Exploring Operation: 75-1=74, Resulting Numbers: [3, 74] Generated Node #0,2,2: 24:[3, 74] Operation: 75-1=74 Exploring Operation: 75-3=72, Resulting Numbers: [1, 72] Generated Node #0,2,3: 24:[1, 72] Operation: 75-3=72 Exploring Operation: 75*1=75, Resulting Numbers: [3, 75] Generated Node #0,2,4: 24:[3, 75] Operation: 75*1=75 Moving to Node #0,2,0 Current State: 24:[1, 25], Operations: ['78-77=1', '75/3=25'] Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,24 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[75, 3, 78, 77], Operations: [] Exploring Operation: 78-77=1, Resulting Numbers: [75, 3, 1] Generated Node #0,2: 24:[75, 3, 1] Operation: 78-77=1 Moving to Node #0,2 Current State: 24:[75, 3, 1], Operations: ['78-77=1'] Exploring Operation: 75/3=25, Resulting Numbers: [1, 25] Generated Node #0,2,0: 24:[1, 25] Operation: 75/3=25 Moving to Node #0,2,0 Current State: 24:[1, 25], Operations: ['78-77=1', '75/3=25'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 10, 39, 82, 46 ]
30
[ "82-39=43", "46-43=3", "10*3=30" ]
Current State: 30:[10, 39, 82, 46], Operations: [] Exploring Operation: 82-39=43, Resulting Numbers: [10, 46, 43] Generated Node #2: [10, 46, 43] from Operation: 82-39=43 Current State: 30:[10, 46, 43], Operations: ['82-39=43'] Exploring Operation: 46-43=3, Resulting Numbers: [10, 3] Generated Node #3: [10, 3] from Operation: 46-43=3 Current State: 30:[10, 3], Operations: ['82-39=43', '46-43=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[10, 39, 82, 46], Operations: [] Exploring Operation: 82-46=36, Resulting Numbers: [10, 39, 36] Generated Node #0,0: 30:[10, 39, 36] Operation: 82-46=36 Exploring Operation: 82-10=72, Resulting Numbers: [39, 46, 72] Generated Node #0,1: 30:[39, 46, 72] Operation: 82-10=72 Exploring Operation: 46-10=36, Resulting Numbers: [39, 82, 36] Generated Node #0,2: 30:[39, 82, 36] Operation: 46-10=36 Exploring Operation: 46-39=7, Resulting Numbers: [10, 82, 7] Generated Node #0,3: 30:[10, 82, 7] Operation: 46-39=7 Exploring Operation: 82-39=43, Resulting Numbers: [10, 46, 43] Generated Node #0,4: 30:[10, 46, 43] Operation: 82-39=43 Moving to Node #0,0 Current State: 30:[10, 39, 36], Operations: ['82-46=36'] Exploring Operation: 10+36=46, Resulting Numbers: [39, 46] Generated Node #0,0,0: 30:[39, 46] Operation: 10+36=46 Exploring Operation: 36-10=26, Resulting Numbers: [39, 26] Generated Node #0,0,1: 30:[39, 26] Operation: 36-10=26 Exploring Operation: 39-36=3, Resulting Numbers: [10, 3] Generated Node #0,0,2: 30:[10, 3] Operation: 39-36=3 Exploring Operation: 39-10=29, Resulting Numbers: [36, 29] Generated Node #0,0,3: 30:[36, 29] Operation: 39-10=29 Exploring Operation: 10+39=49, Resulting Numbers: [36, 49] Generated Node #0,0,4: 30:[36, 49] Operation: 10+39=49 Moving to Node #0,4 Current State: 30:[10, 46, 43], Operations: ['82-39=43'] Exploring Operation: 10+43=53, Resulting Numbers: [46, 53] Generated Node #0,4,0: 30:[46, 53] Operation: 10+43=53 Exploring Operation: 46-10=36, Resulting Numbers: [43, 36] Generated Node #0,4,1: 30:[43, 36] Operation: 46-10=36 Exploring Operation: 43-10=33, Resulting Numbers: [46, 33] Generated Node #0,4,2: 30:[46, 33] Operation: 43-10=33 Exploring Operation: 46-43=3, Resulting Numbers: [10, 3] Generated Node #0,4,3: 30:[10, 3] Operation: 46-43=3 Exploring Operation: 10+46=56, Resulting Numbers: [43, 56] Generated Node #0,4,4: 30:[43, 56] Operation: 10+46=56 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 30:[10, 3], Operations: ['82-39=43', '46-43=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[10, 39, 82, 46], Operations: [] Exploring Operation: 82-39=43, Resulting Numbers: [10, 46, 43] Generated Node #0,4: 30:[10, 46, 43] Operation: 82-39=43 Moving to Node #0,4 Current State: 30:[10, 46, 43], Operations: ['82-39=43'] Exploring Operation: 46-43=3, Resulting Numbers: [10, 3] Generated Node #0,4,3: 30:[10, 3] Operation: 46-43=3 Moving to Node #0,4,3 Current State: 30:[10, 3], Operations: ['82-39=43', '46-43=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 32, 85, 63, 18 ]
27
[ "32*63=2016", "2016/18=112", "112-85=27" ]
Current State: 27:[32, 85, 63, 18], Operations: [] Exploring Operation: 32*63=2016, Resulting Numbers: [85, 18, 2016] Generated Node #2: [85, 18, 2016] from Operation: 32*63=2016 Current State: 27:[85, 18, 2016], Operations: ['32*63=2016'] Exploring Operation: 2016/18=112, Resulting Numbers: [85, 112] Generated Node #3: [85, 112] from Operation: 2016/18=112 Current State: 27:[85, 112], Operations: ['32*63=2016', '2016/18=112'] Exploring Operation: 112-85=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[32, 85, 63, 18], Operations: [] Exploring Operation: 85-63=22, Resulting Numbers: [32, 18, 22] Generated Node #0,0: 27:[32, 18, 22] Operation: 85-63=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[32, 18, 22], Operations: ['85-63=22'] Exploring Operation: 22-18=4, Resulting Numbers: [32, 4] Generated Node #0,0,0: 27:[32, 4] Operation: 22-18=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[32, 4], Operations: ['85-63=22', '22-18=4'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 66, 18, 46, 61 ]
23
[ "66+18=84", "46+61=107", "107-84=23" ]
Current State: 23:[66, 18, 46, 61], Operations: [] Exploring Operation: 66+18=84, Resulting Numbers: [46, 61, 84] Generated Node #2: [46, 61, 84] from Operation: 66+18=84 Current State: 23:[46, 61, 84], Operations: ['66+18=84'] Exploring Operation: 46+61=107, Resulting Numbers: [84, 107] Generated Node #3: [84, 107] from Operation: 46+61=107 Current State: 23:[84, 107], Operations: ['66+18=84', '46+61=107'] Exploring Operation: 107-84=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[66, 18, 46, 61], Operations: [] Exploring Operation: 66-61=5, Resulting Numbers: [18, 46, 5] Generated Node #0,0: 23:[18, 46, 5] Operation: 66-61=5 Exploring Operation: 66-46=20, Resulting Numbers: [18, 61, 20] Generated Node #0,1: 23:[18, 61, 20] Operation: 66-46=20 Moving to Node #0,0 Current State: 23:[18, 46, 5], Operations: ['66-61=5'] Exploring Operation: 46-18=28, Resulting Numbers: [5, 28] Generated Node #0,0,0: 23:[5, 28] Operation: 46-18=28 Exploring Operation: 18+5=23, Resulting Numbers: [46, 23] Generated Node #0,0,1: 23:[46, 23] Operation: 18+5=23 Moving to Node #0,1 Current State: 23:[18, 61, 20], Operations: ['66-46=20'] Exploring Operation: 61-18=43, Resulting Numbers: [20, 43] Generated Node #0,1,0: 23:[20, 43] Operation: 61-18=43 Exploring Operation: 61-20=41, Resulting Numbers: [18, 41] Generated Node #0,1,1: 23:[18, 41] Operation: 61-20=41 Moving to Node #0,0,0 Current State: 23:[5, 28], Operations: ['66-61=5', '46-18=28'] Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,23 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[66, 18, 46, 61], Operations: [] Exploring Operation: 66-61=5, Resulting Numbers: [18, 46, 5] Generated Node #0,0: 23:[18, 46, 5] Operation: 66-61=5 Moving to Node #0,0 Current State: 23:[18, 46, 5], Operations: ['66-61=5'] Exploring Operation: 46-18=28, Resulting Numbers: [5, 28] Generated Node #0,0,0: 23:[5, 28] Operation: 46-18=28 Moving to Node #0,0,0 Current State: 23:[5, 28], Operations: ['66-61=5', '46-18=28'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.989583
hs_2
sum_heuristic
[ 81, 54, 21, 39 ]
90
[ "21+39=60", "81*60=4860", "4860/54=90" ]
Current State: 90:[81, 54, 21, 39], Operations: [] Exploring Operation: 21+39=60, Resulting Numbers: [81, 54, 60] Generated Node #2: [81, 54, 60] from Operation: 21+39=60 Current State: 90:[81, 54, 60], Operations: ['21+39=60'] Exploring Operation: 81*60=4860, Resulting Numbers: [54, 4860] Generated Node #3: [54, 4860] from Operation: 81*60=4860 Current State: 90:[54, 4860], Operations: ['21+39=60', '81*60=4860'] Exploring Operation: 4860/54=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[81, 54, 21, 39], Operations: [] Exploring Operation: 81-39=42, Resulting Numbers: [54, 21, 42] Generated Node #0,0: 90:[54, 21, 42] Operation: 81-39=42 Exploring Operation: 54-39=15, Resulting Numbers: [81, 21, 15] Generated Node #0,1: 90:[81, 21, 15] Operation: 54-39=15 Exploring Operation: 81-54=27, Resulting Numbers: [21, 39, 27] Generated Node #0,2: 90:[21, 39, 27] Operation: 81-54=27 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[81, 21, 15], Operations: ['54-39=15'] Exploring Operation: 81+15=96, Resulting Numbers: [21, 96] Generated Node #0,1,0: 90:[21, 96] Operation: 81+15=96 Exploring Operation: 81+21=102, Resulting Numbers: [15, 102] Generated Node #0,1,1: 90:[15, 102] Operation: 81+21=102 Exploring Operation: 21-15=6, Resulting Numbers: [81, 6] Generated Node #0,1,2: 90:[81, 6] Operation: 21-15=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[21, 96], Operations: ['54-39=15', '81+15=96'] Exploring Operation: 96-21=75, Resulting Numbers: [75] 75,90 unequal: No Solution Exploring Operation: 21*96=2016, Resulting Numbers: [2016] 2016,90 unequal: No Solution Exploring Operation: 21+96=117, Resulting Numbers: [117] 117,90 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:[81, 6], Operations: ['54-39=15', '21-15=6'] Exploring Operation: 81+6=87, Resulting Numbers: [87] 87,90 unequal: No Solution Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,90 unequal: No Solution Exploring Operation: 81*6=486, Resulting Numbers: [486] 486,90 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:[15, 102], Operations: ['54-39=15', '81+21=102'] Exploring Operation: 15+102=117, Resulting Numbers: [117] 117,90 unequal: No Solution Exploring Operation: 102-15=87, Resulting Numbers: [87] 87,90 unequal: No Solution Exploring Operation: 15*102=1530, Resulting Numbers: [1530] 1530,90 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:[21, 39, 27], Operations: ['81-54=27'] Exploring Operation: 39-21=18, Resulting Numbers: [27, 18] Generated Node #0,2,0: 90:[27, 18] Operation: 39-21=18 Exploring Operation: 27-21=6, Resulting Numbers: [39, 6] Generated Node #0,2,1: 90:[39, 6] Operation: 27-21=6 Exploring Operation: 39-27=12, Resulting Numbers: [21, 12] Generated Node #0,2,2: 90:[21, 12] Operation: 39-27=12 Moving to Node #0,2,0 Current State: 90:[27, 18], Operations: ['81-54=27', '39-21=18'] Exploring Operation: 27+18=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 27*18=486, Resulting Numbers: [486] 486,90 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[21, 12], Operations: ['81-54=27', '39-27=12'] Exploring Operation: 21*12=252, Resulting Numbers: [252] 252,90 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,90 unequal: No Solution Moving to Node #0,2,1 Current State: 90:[39, 6], Operations: ['81-54=27', '27-21=6'] Exploring Operation: 39+6=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 39*6=234, Resulting Numbers: [234] 234,90 unequal: No Solution Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[54, 21, 42], Operations: ['81-39=42'] Exploring Operation: 54-42=12, Resulting Numbers: [21, 12] Generated Node #0,0,0: 90:[21, 12] Operation: 54-42=12 Exploring Operation: 54+42=96, Resulting Numbers: [21, 96] Generated Node #0,0,1: 90:[21, 96] Operation: 54+42=96 Exploring Operation: 54-21=33, Resulting Numbers: [42, 33] Generated Node #0,0,2: 90:[42, 33] Operation: 54-21=33 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[21, 12], Operations: ['81-39=42', '54-42=12'] Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 21*12=252, Resulting Numbers: [252] 252,90 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 #0,0,2 Current State: 90:[42, 33], Operations: ['81-39=42', '54-21=33'] Exploring Operation: 42-33=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 42+33=75, Resulting Numbers: [75] 75,90 unequal: No Solution Exploring Operation: 42*33=1386, Resulting Numbers: [1386] 1386,90 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 #0,0,1 Current State: 90:[21, 96], Operations: ['81-39=42', '54+42=96'] Exploring Operation: 96-21=75, Resulting Numbers: [75] 75,90 unequal: No Solution Exploring Operation: 21+96=117, Resulting Numbers: [117] 117,90 unequal: No Solution Exploring Operation: 21*96=2016, Resulting Numbers: [2016] 2016,90 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_3
sum_heuristic
[ 47, 14, 83, 1 ]
51
[ "47-14=33", "83+1=84", "84-33=51" ]
Current State: 51:[47, 14, 83, 1], Operations: [] Exploring Operation: 47-14=33, Resulting Numbers: [83, 1, 33] Generated Node #2: [83, 1, 33] from Operation: 47-14=33 Current State: 51:[83, 1, 33], Operations: ['47-14=33'] Exploring Operation: 83+1=84, Resulting Numbers: [33, 84] Generated Node #3: [33, 84] from Operation: 83+1=84 Current State: 51:[33, 84], Operations: ['47-14=33', '83+1=84'] Exploring Operation: 84-33=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[47, 14, 83, 1], Operations: [] Exploring Operation: 83-47=36, Resulting Numbers: [14, 1, 36] Generated Node #0,0: 51:[14, 1, 36] Operation: 83-47=36 Moving to Node #0,0 Current State: 51:[14, 1, 36], Operations: ['83-47=36'] Exploring Operation: 14+36=50, Resulting Numbers: [1, 50] Generated Node #0,0,0: 51:[1, 50] Operation: 14+36=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[1, 50], Operations: ['83-47=36', '14+36=50'] Exploring Operation: 1+50=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[47, 14, 83, 1], Operations: [] Exploring Operation: 83-47=36, Resulting Numbers: [14, 1, 36] Generated Node #0,0: 51:[14, 1, 36] Operation: 83-47=36 Moving to Node #0,0 Current State: 51:[14, 1, 36], Operations: ['83-47=36'] Exploring Operation: 14+36=50, Resulting Numbers: [1, 50] Generated Node #0,0,0: 51:[1, 50] Operation: 14+36=50 Moving to Node #0,0,0 Current State: 51:[1, 50], Operations: ['83-47=36', '14+36=50'] Exploring Operation: 1+50=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 90, 19, 14, 6 ]
79
[ "90-19=71", "14-6=8", "71+8=79" ]
Current State: 79:[90, 19, 14, 6], Operations: [] Exploring Operation: 90-19=71, Resulting Numbers: [14, 6, 71] Generated Node #2: [14, 6, 71] from Operation: 90-19=71 Current State: 79:[14, 6, 71], Operations: ['90-19=71'] Exploring Operation: 14-6=8, Resulting Numbers: [71, 8] Generated Node #3: [71, 8] from Operation: 14-6=8 Current State: 79:[71, 8], Operations: ['90-19=71', '14-6=8'] Exploring Operation: 71+8=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[90, 19, 14, 6], Operations: [] Exploring Operation: 14*6=84, Resulting Numbers: [90, 19, 84] Generated Node #0,0: 79:[90, 19, 84] Operation: 14*6=84 Moving to Node #0,0 Current State: 79:[90, 19, 84], Operations: ['14*6=84'] Exploring Operation: 90-19=71, Resulting Numbers: [84, 71] Generated Node #0,0,0: 79:[84, 71] Operation: 90-19=71 Moving to Node #0,0,0 Current State: 79:[84, 71], Operations: ['14*6=84', '90-19=71'] Exploring Operation: 84-71=13, Resulting Numbers: [13] 13,79 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 9, 8, 84, 87 ]
15
[ "87-84=3", "8*3=24", "24-9=15" ]
Current State: 15:[9, 8, 84, 87], Operations: [] Exploring Operation: 87-84=3, Resulting Numbers: [9, 8, 3] Generated Node #2: [9, 8, 3] from Operation: 87-84=3 Current State: 15:[9, 8, 3], Operations: ['87-84=3'] Exploring Operation: 8*3=24, Resulting Numbers: [9, 24] Generated Node #3: [9, 24] from Operation: 8*3=24 Current State: 15:[9, 24], Operations: ['87-84=3', '8*3=24'] Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[9, 8, 84, 87], Operations: [] Exploring Operation: 87-9=78, Resulting Numbers: [8, 84, 78] Generated Node #0,0: 15:[8, 84, 78] Operation: 87-9=78 Exploring Operation: 87-84=3, Resulting Numbers: [9, 8, 3] Generated Node #0,1: 15:[9, 8, 3] Operation: 87-84=3 Exploring Operation: 87-8=79, Resulting Numbers: [9, 84, 79] Generated Node #0,2: 15:[9, 84, 79] Operation: 87-8=79 Exploring Operation: 84-9=75, Resulting Numbers: [8, 87, 75] Generated Node #0,3: 15:[8, 87, 75] Operation: 84-9=75 Exploring Operation: 84-8=76, Resulting Numbers: [9, 87, 76] Generated Node #0,4: 15:[9, 87, 76] Operation: 84-8=76 Moving to Node #0,1 Current State: 15:[9, 8, 3], Operations: ['87-84=3'] Exploring Operation: 9+8=17, Resulting Numbers: [3, 17] Generated Node #0,1,0: 15:[3, 17] Operation: 9+8=17 Exploring Operation: 9/3=3, Resulting Numbers: [8, 3] Generated Node #0,1,1: 15:[8, 3] Operation: 9/3=3 Exploring Operation: 8-3=5, Resulting Numbers: [9, 5] Generated Node #0,1,2: 15:[9, 5] Operation: 8-3=5 Exploring Operation: 9-8=1, Resulting Numbers: [3, 1] Generated Node #0,1,3: 15:[3, 1] Operation: 9-8=1 Exploring Operation: 9-3=6, Resulting Numbers: [8, 6] Generated Node #0,1,4: 15:[8, 6] Operation: 9-3=6 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 15:[3, 17], Operations: ['87-84=3', '9+8=17'] Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,15 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 15:[3, 1], Operations: ['87-84=3', '9-8=1'] Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 15:[8, 3], Operations: ['87-84=3', '9/3=3'] Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,15 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 15:[9, 5], Operations: ['87-84=3', '8-3=5'] Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,15 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 15:[8, 6], Operations: ['87-84=3', '9-3=6'] Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,15 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 15:[8, 87, 75], Operations: ['84-9=75'] Exploring Operation: 87-75=12, Resulting Numbers: [8, 12] Generated Node #0,3,0: 15:[8, 12] Operation: 87-75=12 Exploring Operation: 8+75=83, Resulting Numbers: [87, 83] Generated Node #0,3,1: 15:[87, 83] Operation: 8+75=83 Exploring Operation: 8+87=95, Resulting Numbers: [75, 95] Generated Node #0,3,2: 15:[75, 95] Operation: 8+87=95 Exploring Operation: 87-8=79, Resulting Numbers: [75, 79] Generated Node #0,3,3: 15:[75, 79] Operation: 87-8=79 Exploring Operation: 75-8=67, Resulting Numbers: [87, 67] Generated Node #0,3,4: 15:[87, 67] Operation: 75-8=67 Moving to Node #0,0 Current State: 15:[8, 84, 78], Operations: ['87-9=78'] Exploring Operation: 8+84=92, Resulting Numbers: [78, 92] Generated Node #0,0,0: 15:[78, 92] Operation: 8+84=92 Exploring Operation: 84-8=76, Resulting Numbers: [78, 76] Generated Node #0,0,1: 15:[78, 76] Operation: 84-8=76 Exploring Operation: 84-78=6, Resulting Numbers: [8, 6] Generated Node #0,0,2: 15:[8, 6] Operation: 84-78=6 Exploring Operation: 78-8=70, Resulting Numbers: [84, 70] Generated Node #0,0,3: 15:[84, 70] Operation: 78-8=70 Exploring Operation: 8+78=86, Resulting Numbers: [84, 86] Generated Node #0,0,4: 15:[84, 86] Operation: 8+78=86 Moving to Node #0,2 Current State: 15:[9, 84, 79], Operations: ['87-8=79'] Exploring Operation: 84-79=5, Resulting Numbers: [9, 5] Generated Node #0,2,0: 15:[9, 5] Operation: 84-79=5 Exploring Operation: 9+84=93, Resulting Numbers: [79, 93] Generated Node #0,2,1: 15:[79, 93] Operation: 9+84=93 Exploring Operation: 84-9=75, Resulting Numbers: [79, 75] Generated Node #0,2,2: 15:[79, 75] Operation: 84-9=75 Exploring Operation: 9+79=88, Resulting Numbers: [84, 88] Generated Node #0,2,3: 15:[84, 88] Operation: 9+79=88 Exploring Operation: 79-9=70, Resulting Numbers: [84, 70] Generated Node #0,2,4: 15:[84, 70] Operation: 79-9=70 Moving to Node #0,4 Current State: 15:[9, 87, 76], Operations: ['84-8=76'] Exploring Operation: 87-9=78, Resulting Numbers: [76, 78] Generated Node #0,4,0: 15:[76, 78] Operation: 87-9=78 Exploring Operation: 9+87=96, Resulting Numbers: [76, 96] Generated Node #0,4,1: 15:[76, 96] Operation: 9+87=96 Exploring Operation: 76-9=67, Resulting Numbers: [87, 67] Generated Node #0,4,2: 15:[87, 67] Operation: 76-9=67 Exploring Operation: 9+76=85, Resulting Numbers: [87, 85] Generated Node #0,4,3: 15:[87, 85] Operation: 9+76=85 Exploring Operation: 87-76=11, Resulting Numbers: [9, 11] Generated Node #0,4,4: 15:[9, 11] Operation: 87-76=11 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 15:[9, 11], Operations: ['84-8=76', '87-76=11'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 15:[76, 78], Operations: ['84-8=76', '87-9=78'] Exploring Operation: 76*78=5928, Resulting Numbers: [5928] 5928,15 unequal: No Solution Exploring Operation: 76+78=154, Resulting Numbers: [154] 154,15 unequal: No Solution Exploring Operation: 78-76=2, Resulting Numbers: [2] 2,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 15:[87, 67], Operations: ['84-8=76', '76-9=67'] Exploring Operation: 87*67=5829, Resulting Numbers: [5829] 5829,15 unequal: No Solution Exploring Operation: 87+67=154, Resulting Numbers: [154] 154,15 unequal: No Solution Exploring Operation: 87-67=20, Resulting Numbers: [20] 20,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 15:[76, 96], Operations: ['84-8=76', '9+87=96'] Exploring Operation: 76+96=172, Resulting Numbers: [172] 172,15 unequal: No Solution Exploring Operation: 96-76=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 76*96=7296, Resulting Numbers: [7296] 7296,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 15:[87, 85], Operations: ['84-8=76', '9+76=85'] Exploring Operation: 87*85=7395, Resulting Numbers: [7395] 7395,15 unequal: No Solution Exploring Operation: 87-85=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 87+85=172, Resulting Numbers: [172] 172,15 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: 15:[8, 6], Operations: ['87-9=78', '84-78=6'] Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,15 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,15 unequal: No Solution Moving to Node #0,2,0 Current State: 15:[9, 5], Operations: ['87-8=79', '84-79=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,15 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,15 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,15 unequal: No Solution Moving to Node #0,3,0 Current State: 15:[8, 12], Operations: ['84-9=75', '87-75=12'] Exploring Operation: 8+12=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 8*12=96, Resulting Numbers: [96] 96,15 unequal: No Solution Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[78, 76], Operations: ['87-9=78', '84-8=76'] Exploring Operation: 78+76=154, Resulting Numbers: [154] 154,15 unequal: No Solution Exploring Operation: 78-76=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 78*76=5928, Resulting Numbers: [5928] 5928,15 unequal: No Solution Moving to Node #0,3,4 Current State: 15:[87, 67], Operations: ['84-9=75', '75-8=67'] Exploring Operation: 87-67=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 87+67=154, Resulting Numbers: [154] 154,15 unequal: No Solution Exploring Operation: 87*67=5829, Resulting Numbers: [5829] 5829,15 unequal: No Solution Moving to Node #0,2,2 Current State: 15:[79, 75], Operations: ['87-8=79', '84-9=75'] Exploring Operation: 79+75=154, Resulting Numbers: [154] 154,15 unequal: No Solution Exploring Operation: 79-75=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 79*75=5925, Resulting Numbers: [5925] 5925,15 unequal: No Solution Moving to Node #0,2,4 Current State: 15:[84, 70], Operations: ['87-8=79', '79-9=70'] Exploring Operation: 84*70=5880, Resulting Numbers: [5880] 5880,15 unequal: No Solution Exploring Operation: 84+70=154, Resulting Numbers: [154] 154,15 unequal: No Solution Exploring Operation: 84-70=14, Resulting Numbers: [14] 14,15 unequal: No Solution Moving to Node #0,3,3 Current State: 15:[75, 79], Operations: ['84-9=75', '87-8=79'] Exploring Operation: 79-75=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 75*79=5925, Resulting Numbers: [5925] 5925,15 unequal: No Solution Exploring Operation: 75+79=154, Resulting Numbers: [154] 154,15 unequal: No Solution Moving to Node #0,0,3 Current State: 15:[84, 70], Operations: ['87-9=78', '78-8=70'] Exploring Operation: 84+70=154, Resulting Numbers: [154] 154,15 unequal: No Solution Exploring Operation: 84-70=14, Resulting Numbers: [14] 14,15 unequal: No Solution Exploring Operation: 84*70=5880, Resulting Numbers: [5880] 5880,15 unequal: No Solution Moving to Node #0,0,4 Current State: 15:[84, 86], Operations: ['87-9=78', '8+78=86'] Exploring Operation: 84+86=170, Resulting Numbers: [170] 170,15 unequal: No Solution Exploring Operation: 84*86=7224, Resulting Numbers: [7224] 7224,15 unequal: No Solution Exploring Operation: 86-84=2, Resulting Numbers: [2] 2,15 unequal: No Solution Moving to Node #0,3,2 Current State: 15:[75, 95], Operations: ['84-9=75', '8+87=95'] Exploring Operation: 95-75=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 75+95=170, Resulting Numbers: [170] 170,15 unequal: No Solution Exploring Operation: 75*95=7125, Resulting Numbers: [7125] 7125,15 unequal: No Solution Moving to Node #0,0,0 Current State: 15:[78, 92], Operations: ['87-9=78', '8+84=92'] Exploring Operation: 92-78=14, Resulting Numbers: [14] 14,15 unequal: No Solution Exploring Operation: 78*92=7176, Resulting Numbers: [7176] 7176,15 unequal: No Solution Exploring Operation: 78+92=170, Resulting Numbers: [170] 170,15 unequal: No Solution Moving to Node #0,3,1 Current State: 15:[87, 83], Operations: ['84-9=75', '8+75=83'] Exploring Operation: 87*83=7221, Resulting Numbers: [7221] 7221,15 unequal: No Solution Exploring Operation: 87+83=170, Resulting Numbers: [170] 170,15 unequal: No Solution Exploring Operation: 87-83=4, Resulting Numbers: [4] 4,15 unequal: No Solution Moving to Node #0,2,1 Current State: 15:[79, 93], Operations: ['87-8=79', '9+84=93'] Exploring Operation: 93-79=14, Resulting Numbers: [14] 14,15 unequal: No Solution Exploring Operation: 79*93=7347, Resulting Numbers: [7347] 7347,15 unequal: No Solution Exploring Operation: 79+93=172, Resulting Numbers: [172] 172,15 unequal: No Solution Moving to Node #0,2,3 Current State: 15:[84, 88], Operations: ['87-8=79', '9+79=88'] Exploring Operation: 88-84=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 84*88=7392, Resulting Numbers: [7392] 7392,15 unequal: No Solution Exploring Operation: 84+88=172, Resulting Numbers: [172] 172,15 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 5, 70, 62, 8 ]
32
[ "5*8=40", "70-62=8", "40-8=32" ]
Current State: 32:[5, 70, 62, 8], Operations: [] Exploring Operation: 5*8=40, Resulting Numbers: [70, 62, 40] Generated Node #2: [70, 62, 40] from Operation: 5*8=40 Current State: 32:[70, 62, 40], Operations: ['5*8=40'] Exploring Operation: 70-62=8, Resulting Numbers: [40, 8] Generated Node #3: [40, 8] from Operation: 70-62=8 Current State: 32:[40, 8], Operations: ['5*8=40', '70-62=8'] Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[5, 70, 62, 8], Operations: [] Exploring Operation: 70-62=8, Resulting Numbers: [5, 8, 8] Generated Node #0,0: 32:[5, 8, 8] Operation: 70-62=8 Moving to Node #0,0 Current State: 32:[5, 8, 8], Operations: ['70-62=8'] Exploring Operation: 8-5=3, Resulting Numbers: [8, 3] Generated Node #0,0,0: 32:[8, 3] Operation: 8-5=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[8, 3], Operations: ['70-62=8', '8-5=3'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,32 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
[ 66, 96, 56, 24 ]
82
[ "66+96=162", "56+24=80", "162-80=82" ]
Current State: 82:[66, 96, 56, 24], Operations: [] Exploring Operation: 66+96=162, Resulting Numbers: [56, 24, 162] Generated Node #2: [56, 24, 162] from Operation: 66+96=162 Current State: 82:[56, 24, 162], Operations: ['66+96=162'] Exploring Operation: 56+24=80, Resulting Numbers: [162, 80] Generated Node #3: [162, 80] from Operation: 56+24=80 Current State: 82:[162, 80], Operations: ['66+96=162', '56+24=80'] Exploring Operation: 162-80=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[66, 96, 56, 24], Operations: [] Exploring Operation: 56+24=80, Resulting Numbers: [66, 96, 80] Generated Node #0,0: 82:[66, 96, 80] Operation: 56+24=80 Exploring Operation: 66-24=42, Resulting Numbers: [96, 56, 42] Generated Node #0,1: 82:[96, 56, 42] Operation: 66-24=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[96, 56, 42], Operations: ['66-24=42'] Exploring Operation: 96-56=40, Resulting Numbers: [42, 40] Generated Node #0,1,0: 82:[42, 40] Operation: 96-56=40 Exploring Operation: 56-42=14, Resulting Numbers: [96, 14] Generated Node #0,1,1: 82:[96, 14] Operation: 56-42=14 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[42, 40], Operations: ['66-24=42', '96-56=40'] Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 42+40=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[66, 96, 56, 24], Operations: [] Exploring Operation: 66-24=42, Resulting Numbers: [96, 56, 42] Generated Node #0,1: 82:[96, 56, 42] Operation: 66-24=42 Moving to Node #0,1 Current State: 82:[96, 56, 42], Operations: ['66-24=42'] Exploring Operation: 96-56=40, Resulting Numbers: [42, 40] Generated Node #0,1,0: 82:[42, 40] Operation: 96-56=40 Moving to Node #0,1,0 Current State: 82:[42, 40], Operations: ['66-24=42', '96-56=40'] Exploring Operation: 42+40=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 8, 10, 21, 70 ]
11
[ "8*10=80", "21+70=91", "91-80=11" ]
Current State: 11:[8, 10, 21, 70], Operations: [] Exploring Operation: 8*10=80, Resulting Numbers: [21, 70, 80] Generated Node #2: [21, 70, 80] from Operation: 8*10=80 Current State: 11:[21, 70, 80], Operations: ['8*10=80'] Exploring Operation: 21+70=91, Resulting Numbers: [80, 91] Generated Node #3: [80, 91] from Operation: 21+70=91 Current State: 11:[80, 91], Operations: ['8*10=80', '21+70=91'] Exploring Operation: 91-80=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[8, 10, 21, 70], Operations: [] Exploring Operation: 21-8=13, Resulting Numbers: [10, 70, 13] Generated Node #0,0: 11:[10, 70, 13] Operation: 21-8=13 Exploring Operation: 70-8=62, Resulting Numbers: [10, 21, 62] Generated Node #0,1: 11:[10, 21, 62] Operation: 70-8=62 Exploring Operation: 70/10=7, Resulting Numbers: [8, 21, 7] Generated Node #0,2: 11:[8, 21, 7] Operation: 70/10=7 Exploring Operation: 70-21=49, Resulting Numbers: [8, 10, 49] Generated Node #0,3: 11:[8, 10, 49] Operation: 70-21=49 Moving to Node #0,2 Current State: 11:[8, 21, 7], Operations: ['70/10=7'] Exploring Operation: 21-7=14, Resulting Numbers: [8, 14] Generated Node #0,2,0: 11:[8, 14] Operation: 21-7=14 Exploring Operation: 21/7=3, Resulting Numbers: [8, 3] Generated Node #0,2,1: 11:[8, 3] Operation: 21/7=3 Exploring Operation: 8+7=15, Resulting Numbers: [21, 15] Generated Node #0,2,2: 11:[21, 15] Operation: 8+7=15 Exploring Operation: 21-8=13, Resulting Numbers: [7, 13] Generated Node #0,2,3: 11:[7, 13] Operation: 21-8=13 Moving to Node #0,3 Current State: 11:[8, 10, 49], Operations: ['70-21=49'] Exploring Operation: 49-10=39, Resulting Numbers: [8, 39] Generated Node #0,3,0: 11:[8, 39] Operation: 49-10=39 Exploring Operation: 49-8=41, Resulting Numbers: [10, 41] Generated Node #0,3,1: 11:[10, 41] Operation: 49-8=41 Exploring Operation: 8+10=18, Resulting Numbers: [49, 18] Generated Node #0,3,2: 11:[49, 18] Operation: 8+10=18 Exploring Operation: 10-8=2, Resulting Numbers: [49, 2] Generated Node #0,3,3: 11:[49, 2] Operation: 10-8=2 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 11:[8, 39], Operations: ['70-21=49', '49-10=39'] Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 8+39=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 8*39=312, Resulting Numbers: [312] 312,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 11:[10, 41], Operations: ['70-21=49', '49-8=41'] Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 10*41=410, Resulting Numbers: [410] 410,11 unequal: No Solution Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 11:[49, 18], Operations: ['70-21=49', '8+10=18'] Exploring Operation: 49*18=882, Resulting Numbers: [882] 882,11 unequal: No Solution Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 49+18=67, Resulting Numbers: [67] 67,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 11:[49, 2], Operations: ['70-21=49', '10-8=2'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,11 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,11 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: 11:[10, 21, 62], Operations: ['70-8=62'] Exploring Operation: 62-21=41, Resulting Numbers: [10, 41] Generated Node #0,1,0: 11:[10, 41] Operation: 62-21=41 Exploring Operation: 10+21=31, Resulting Numbers: [62, 31] Generated Node #0,1,1: 11:[62, 31] Operation: 10+21=31 Exploring Operation: 62-10=52, Resulting Numbers: [21, 52] Generated Node #0,1,2: 11:[21, 52] Operation: 62-10=52 Exploring Operation: 21-10=11, Resulting Numbers: [62, 11] Generated Node #0,1,3: 11:[62, 11] Operation: 21-10=11 Moving to Node #0,0 Current State: 11:[10, 70, 13], Operations: ['21-8=13'] Exploring Operation: 70-13=57, Resulting Numbers: [10, 57] Generated Node #0,0,0: 11:[10, 57] Operation: 70-13=57 Exploring Operation: 70/10=7, Resulting Numbers: [13, 7] Generated Node #0,0,1: 11:[13, 7] Operation: 70/10=7 Exploring Operation: 70-10=60, Resulting Numbers: [13, 60] Generated Node #0,0,2: 11:[13, 60] Operation: 70-10=60 Exploring Operation: 13-10=3, Resulting Numbers: [70, 3] Generated Node #0,0,3: 11:[70, 3] Operation: 13-10=3 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 11:[13, 7], Operations: ['21-8=13', '70/10=7'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,11 unequal: No Solution Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[10, 57], Operations: ['21-8=13', '70-13=57'] Exploring Operation: 57-10=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 10*57=570, Resulting Numbers: [570] 570,11 unequal: No Solution Exploring Operation: 10+57=67, Resulting Numbers: [67] 67,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 11:[13, 60], Operations: ['21-8=13', '70-10=60'] Exploring Operation: 13*60=780, Resulting Numbers: [780] 780,11 unequal: No Solution Exploring Operation: 13+60=73, Resulting Numbers: [73] 73,11 unequal: No Solution Exploring Operation: 60-13=47, Resulting Numbers: [47] 47,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 11:[70, 3], Operations: ['21-8=13', '13-10=3'] Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,11 unequal: No Solution Exploring Operation: 70+3=73, Resulting Numbers: [73] 73,11 unequal: No Solution Exploring Operation: 70*3=210, Resulting Numbers: [210] 210,11 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: 11:[8, 14], Operations: ['70/10=7', '21-7=14'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 8*14=112, Resulting Numbers: [112] 112,11 unequal: No Solution Exploring Operation: 8+14=22, Resulting Numbers: [22] 22,11 unequal: No Solution Moving to Node #0,2,3 Current State: 11:[7, 13], Operations: ['70/10=7', '21-8=13'] Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,11 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 7*13=91, Resulting Numbers: [91] 91,11 unequal: No Solution Moving to Node #0,2,1 Current State: 11:[8, 3], Operations: ['70/10=7', '21/7=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,11 unequal: No Solution Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[8, 10, 21, 70], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [8, 21, 7] Generated Node #0,2: 11:[8, 21, 7] Operation: 70/10=7 Moving to Node #0,2 Current State: 11:[8, 21, 7], Operations: ['70/10=7'] Exploring Operation: 21/7=3, Resulting Numbers: [8, 3] Generated Node #0,2,1: 11:[8, 3] Operation: 21/7=3 Moving to Node #0,2,1 Current State: 11:[8, 3], Operations: ['70/10=7', '21/7=3'] Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
0.950521
hs_4
mult_heuristic
[ 30, 27, 69, 35 ]
47
[ "30+27=57", "69+35=104", "104-57=47" ]
Current State: 47:[30, 27, 69, 35], Operations: [] Exploring Operation: 30+27=57, Resulting Numbers: [69, 35, 57] Generated Node #2: [69, 35, 57] from Operation: 30+27=57 Current State: 47:[69, 35, 57], Operations: ['30+27=57'] Exploring Operation: 69+35=104, Resulting Numbers: [57, 104] Generated Node #3: [57, 104] from Operation: 69+35=104 Current State: 47:[57, 104], Operations: ['30+27=57', '69+35=104'] Exploring Operation: 104-57=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[30, 27, 69, 35], Operations: [] Exploring Operation: 69-27=42, Resulting Numbers: [30, 35, 42] Generated Node #0,0: 47:[30, 35, 42] Operation: 69-27=42 Exploring Operation: 69-30=39, Resulting Numbers: [27, 35, 39] Generated Node #0,1: 47:[27, 35, 39] Operation: 69-30=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[30, 35, 42], Operations: ['69-27=42'] Exploring Operation: 30+42=72, Resulting Numbers: [35, 72] Generated Node #0,0,0: 47:[35, 72] Operation: 30+42=72 Exploring Operation: 30+35=65, Resulting Numbers: [42, 65] Generated Node #0,0,1: 47:[42, 65] Operation: 30+35=65 Moving to Node #0,0,1 Current State: 47:[42, 65], Operations: ['69-27=42', '30+35=65'] Exploring Operation: 65-42=23, Resulting Numbers: [23] 23,47 unequal: No Solution Exploring Operation: 42+65=107, Resulting Numbers: [107] 107,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[35, 72], Operations: ['69-27=42', '30+42=72'] Exploring Operation: 35+72=107, Resulting Numbers: [107] 107,47 unequal: No Solution Exploring Operation: 72-35=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 #0,1 Current State: 47:[27, 35, 39], Operations: ['69-30=39'] Exploring Operation: 27+35=62, Resulting Numbers: [39, 62] Generated Node #0,1,0: 47:[39, 62] Operation: 27+35=62 Exploring Operation: 27+39=66, Resulting Numbers: [35, 66] Generated Node #0,1,1: 47:[35, 66] Operation: 27+39=66 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 47:[39, 62], Operations: ['69-30=39', '27+35=62'] Exploring Operation: 39+62=101, Resulting Numbers: [101] 101,47 unequal: No Solution Exploring Operation: 62-39=23, Resulting Numbers: [23] 23,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 47:[35, 66], Operations: ['69-30=39', '27+39=66'] Exploring Operation: 35+66=101, Resulting Numbers: [101] 101,47 unequal: No Solution Exploring Operation: 66-35=31, Resulting Numbers: [31] 31,47 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_2
mult_heuristic
[ 4, 89, 11, 24 ]
98
[ "89-4=85", "24-11=13", "85+13=98" ]
Current State: 98:[4, 89, 11, 24], Operations: [] Exploring Operation: 89-4=85, Resulting Numbers: [11, 24, 85] Generated Node #2: [11, 24, 85] from Operation: 89-4=85 Current State: 98:[11, 24, 85], Operations: ['89-4=85'] Exploring Operation: 24-11=13, Resulting Numbers: [85, 13] Generated Node #3: [85, 13] from Operation: 24-11=13 Current State: 98:[85, 13], Operations: ['89-4=85', '24-11=13'] Exploring Operation: 85+13=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[4, 89, 11, 24], Operations: [] Exploring Operation: 89+11=100, Resulting Numbers: [4, 24, 100] Generated Node #0,0: 98:[4, 24, 100] Operation: 89+11=100 Exploring Operation: 4*24=96, Resulting Numbers: [89, 11, 96] Generated Node #0,1: 98:[89, 11, 96] Operation: 4*24=96 Exploring Operation: 24-11=13, Resulting Numbers: [4, 89, 13] Generated Node #0,2: 98:[4, 89, 13] Operation: 24-11=13 Exploring Operation: 24/4=6, Resulting Numbers: [89, 11, 6] Generated Node #0,3: 98:[89, 11, 6] Operation: 24/4=6 Exploring Operation: 4+89=93, Resulting Numbers: [11, 24, 93] Generated Node #0,4: 98:[11, 24, 93] Operation: 4+89=93 Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[4, 89, 13], Operations: ['24-11=13'] Exploring Operation: 13-4=9, Resulting Numbers: [89, 9] Generated Node #0,2,0: 98:[89, 9] Operation: 13-4=9 Exploring Operation: 4+13=17, Resulting Numbers: [89, 17] Generated Node #0,2,1: 98:[89, 17] Operation: 4+13=17 Exploring Operation: 4+89=93, Resulting Numbers: [13, 93] Generated Node #0,2,2: 98:[13, 93] Operation: 4+89=93 Exploring Operation: 4*13=52, Resulting Numbers: [89, 52] Generated Node #0,2,3: 98:[89, 52] Operation: 4*13=52 Exploring Operation: 89+13=102, Resulting Numbers: [4, 102] Generated Node #0,2,4: 98:[4, 102] Operation: 89+13=102 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 98:[13, 93], Operations: ['24-11=13', '4+89=93'] Exploring Operation: 93-13=80, Resulting Numbers: [80] 80,98 unequal: No Solution Exploring Operation: 13*93=1209, Resulting Numbers: [1209] 1209,98 unequal: No Solution Exploring Operation: 13+93=106, Resulting Numbers: [106] 106,98 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 #0,2,4 Current State: 98:[4, 102], Operations: ['24-11=13', '89+13=102'] Exploring Operation: 102-4=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[4, 89, 11, 24], Operations: [] Exploring Operation: 24-11=13, Resulting Numbers: [4, 89, 13] Generated Node #0,2: 98:[4, 89, 13] Operation: 24-11=13 Moving to Node #0,2 Current State: 98:[4, 89, 13], Operations: ['24-11=13'] Exploring Operation: 89+13=102, Resulting Numbers: [4, 102] Generated Node #0,2,4: 98:[4, 102] Operation: 89+13=102 Moving to Node #0,2,4 Current State: 98:[4, 102], Operations: ['24-11=13', '89+13=102'] Exploring Operation: 102-4=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 66, 17, 9, 56 ]
80
[ "66-56=10", "17-9=8", "10*8=80" ]
Current State: 80:[66, 17, 9, 56], Operations: [] Exploring Operation: 66-56=10, Resulting Numbers: [17, 9, 10] Generated Node #2: [17, 9, 10] from Operation: 66-56=10 Current State: 80:[17, 9, 10], Operations: ['66-56=10'] Exploring Operation: 17-9=8, Resulting Numbers: [10, 8] Generated Node #3: [10, 8] from Operation: 17-9=8 Current State: 80:[10, 8], Operations: ['66-56=10', '17-9=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[66, 17, 9, 56], Operations: [] Exploring Operation: 66-56=10, Resulting Numbers: [17, 9, 10] Generated Node #0,0: 80:[17, 9, 10] Operation: 66-56=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[17, 9, 10], Operations: ['66-56=10'] Exploring Operation: 17-9=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 80:[10, 8] Operation: 17-9=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[10, 8], Operations: ['66-56=10', '17-9=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[66, 17, 9, 56], Operations: [] Exploring Operation: 66-56=10, Resulting Numbers: [17, 9, 10] Generated Node #0,0: 80:[17, 9, 10] Operation: 66-56=10 Moving to Node #0,0 Current State: 80:[17, 9, 10], Operations: ['66-56=10'] Exploring Operation: 17-9=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 80:[10, 8] Operation: 17-9=8 Moving to Node #0,0,0 Current State: 80:[10, 8], Operations: ['66-56=10', '17-9=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 50, 25, 11, 38 ]
74
[ "50-25=25", "11+38=49", "25+49=74" ]
Current State: 74:[50, 25, 11, 38], Operations: [] Exploring Operation: 50-25=25, Resulting Numbers: [11, 38, 25] Generated Node #2: [11, 38, 25] from Operation: 50-25=25 Current State: 74:[11, 38, 25], Operations: ['50-25=25'] Exploring Operation: 11+38=49, Resulting Numbers: [25, 49] Generated Node #3: [25, 49] from Operation: 11+38=49 Current State: 74:[25, 49], Operations: ['50-25=25', '11+38=49'] Exploring Operation: 25+49=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[50, 25, 11, 38], Operations: [] Exploring Operation: 25+11=36, Resulting Numbers: [50, 38, 36] Generated Node #0,0: 74:[50, 38, 36] Operation: 25+11=36 Exploring Operation: 50-11=39, Resulting Numbers: [25, 38, 39] Generated Node #0,1: 74:[25, 38, 39] Operation: 50-11=39 Exploring Operation: 50/25=2, Resulting Numbers: [11, 38, 2] Generated Node #0,2: 74:[11, 38, 2] Operation: 50/25=2 Exploring Operation: 50+25=75, Resulting Numbers: [11, 38, 75] Generated Node #0,3: 74:[11, 38, 75] Operation: 50+25=75 Moving to Node #0,2 Current State: 74:[11, 38, 2], Operations: ['50/25=2'] Exploring Operation: 38*2=76, Resulting Numbers: [11, 76] Generated Node #0,2,0: 74:[11, 76] Operation: 38*2=76 Exploring Operation: 11-2=9, Resulting Numbers: [38, 9] Generated Node #0,2,1: 74:[38, 9] Operation: 11-2=9 Exploring Operation: 38-2=36, Resulting Numbers: [11, 36] Generated Node #0,2,2: 74:[11, 36] Operation: 38-2=36 Exploring Operation: 38-11=27, Resulting Numbers: [2, 27] Generated Node #0,2,3: 74:[2, 27] Operation: 38-11=27 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 74:[38, 9], Operations: ['50/25=2', '11-2=9'] Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,74 unequal: No Solution Exploring Operation: 38+9=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 38*9=342, Resulting Numbers: [342] 342,74 unequal: No Solution No 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: 74:[11, 36], Operations: ['50/25=2', '38-2=36'] Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 11*36=396, Resulting Numbers: [396] 396,74 unequal: No Solution Exploring Operation: 11+36=47, Resulting Numbers: [47] 47,74 unequal: No Solution No 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: 74:[2, 27], Operations: ['50/25=2', '38-11=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,74 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,74 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,74 unequal: No Solution No 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: 74:[11, 76], Operations: ['50/25=2', '38*2=76'] Exploring Operation: 11*76=836, Resulting Numbers: [836] 836,74 unequal: No Solution Exploring Operation: 11+76=87, Resulting Numbers: [87] 87,74 unequal: No Solution Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,74 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: 74:[11, 38, 75], Operations: ['50+25=75'] Exploring Operation: 11+38=49, Resulting Numbers: [75, 49] Generated Node #0,3,0: 74:[75, 49] Operation: 11+38=49 Exploring Operation: 38-11=27, Resulting Numbers: [75, 27] Generated Node #0,3,1: 74:[75, 27] Operation: 38-11=27 Exploring Operation: 75-38=37, Resulting Numbers: [11, 37] Generated Node #0,3,2: 74:[11, 37] Operation: 75-38=37 Exploring Operation: 75-11=64, Resulting Numbers: [38, 64] Generated Node #0,3,3: 74:[38, 64] Operation: 75-11=64 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 74:[11, 37], Operations: ['50+25=75', '75-38=37'] Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 11+37=48, Resulting Numbers: [48] 48,74 unequal: No Solution Exploring Operation: 11*37=407, Resulting Numbers: [407] 407,74 unequal: No Solution No 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: 74:[75, 27], Operations: ['50+25=75', '38-11=27'] Exploring Operation: 75+27=102, Resulting Numbers: [102] 102,74 unequal: No Solution Exploring Operation: 75-27=48, Resulting Numbers: [48] 48,74 unequal: No Solution Exploring Operation: 75*27=2025, Resulting Numbers: [2025] 2025,74 unequal: No Solution No 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: 74:[38, 64], Operations: ['50+25=75', '75-11=64'] Exploring Operation: 38*64=2432, Resulting Numbers: [2432] 2432,74 unequal: No Solution Exploring Operation: 64-38=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 38+64=102, Resulting Numbers: [102] 102,74 unequal: No Solution No 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: 74:[75, 49], Operations: ['50+25=75', '11+38=49'] Exploring Operation: 75*49=3675, Resulting Numbers: [3675] 3675,74 unequal: No Solution Exploring Operation: 75+49=124, Resulting Numbers: [124] 124,74 unequal: No Solution Exploring Operation: 75-49=26, Resulting Numbers: [26] 26,74 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: 74:[25, 38, 39], Operations: ['50-11=39'] Exploring Operation: 25+39=64, Resulting Numbers: [38, 64] Generated Node #0,1,0: 74:[38, 64] Operation: 25+39=64 Exploring Operation: 25+38=63, Resulting Numbers: [39, 63] Generated Node #0,1,1: 74:[39, 63] Operation: 25+38=63 Exploring Operation: 39-25=14, Resulting Numbers: [38, 14] Generated Node #0,1,2: 74:[38, 14] Operation: 39-25=14 Exploring Operation: 38-25=13, Resulting Numbers: [39, 13] Generated Node #0,1,3: 74:[39, 13] Operation: 38-25=13 Moving to Node #0,0 Current State: 74:[50, 38, 36], Operations: ['25+11=36'] Exploring Operation: 50-38=12, Resulting Numbers: [36, 12] Generated Node #0,0,0: 74:[36, 12] Operation: 50-38=12 Exploring Operation: 50-36=14, Resulting Numbers: [38, 14] Generated Node #0,0,1: 74:[38, 14] Operation: 50-36=14 Exploring Operation: 50+36=86, Resulting Numbers: [38, 86] Generated Node #0,0,2: 74:[38, 86] Operation: 50+36=86 Exploring Operation: 38+36=74, Resulting Numbers: [50, 74] Generated Node #0,0,3: 74:[50, 74] Operation: 38+36=74 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[36, 12], Operations: ['25+11=36', '50-38=12'] Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,74 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,74 unequal: No Solution Exploring Operation: 36+12=48, Resulting Numbers: [48] 48,74 unequal: No Solution Exploring Operation: 36*12=432, Resulting Numbers: [432] 432,74 unequal: No Solution No 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: 74:[38, 14], Operations: ['25+11=36', '50-36=14'] Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,74 unequal: No Solution Exploring Operation: 38*14=532, Resulting Numbers: [532] 532,74 unequal: No Solution Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,74 unequal: No Solution No 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: 74:[38, 86], Operations: ['25+11=36', '50+36=86'] Exploring Operation: 38*86=3268, Resulting Numbers: [3268] 3268,74 unequal: No Solution Exploring Operation: 38+86=124, Resulting Numbers: [124] 124,74 unequal: No Solution Exploring Operation: 86-38=48, Resulting Numbers: [48] 48,74 unequal: No Solution No 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: 74:[50, 74], Operations: ['25+11=36', '38+36=74'] Exploring Operation: 50+74=124, Resulting Numbers: [124] 124,74 unequal: No Solution Exploring Operation: 74-50=24, Resulting Numbers: [24] 24,74 unequal: No Solution Exploring Operation: 50*74=3700, Resulting Numbers: [3700] 3700,74 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: 74:[38, 64], Operations: ['50-11=39', '25+39=64'] Exploring Operation: 64-38=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 38*64=2432, Resulting Numbers: [2432] 2432,74 unequal: No Solution Exploring Operation: 38+64=102, Resulting Numbers: [102] 102,74 unequal: No Solution Moving to Node #0,1,2 Current State: 74:[38, 14], Operations: ['50-11=39', '39-25=14'] Exploring Operation: 38*14=532, Resulting Numbers: [532] 532,74 unequal: No Solution Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,74 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[39, 63], Operations: ['50-11=39', '25+38=63'] Exploring Operation: 39+63=102, Resulting Numbers: [102] 102,74 unequal: No Solution Exploring Operation: 63-39=24, Resulting Numbers: [24] 24,74 unequal: No Solution Exploring Operation: 39*63=2457, Resulting Numbers: [2457] 2457,74 unequal: No Solution Moving to Node #0,1,3 Current State: 74:[39, 13], Operations: ['50-11=39', '38-25=13'] Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,74 unequal: No Solution Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,74 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 39*13=507, Resulting Numbers: [507] 507,74 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 58, 20, 12, 32 ]
82
[ "58-20=38", "12+32=44", "38+44=82" ]
Current State: 82:[58, 20, 12, 32], Operations: [] Exploring Operation: 58-20=38, Resulting Numbers: [12, 32, 38] Generated Node #2: [12, 32, 38] from Operation: 58-20=38 Current State: 82:[12, 32, 38], Operations: ['58-20=38'] Exploring Operation: 12+32=44, Resulting Numbers: [38, 44] Generated Node #3: [38, 44] from Operation: 12+32=44 Current State: 82:[38, 44], Operations: ['58-20=38', '12+32=44'] Exploring Operation: 38+44=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[58, 20, 12, 32], Operations: [] Exploring Operation: 58-20=38, Resulting Numbers: [12, 32, 38] Generated Node #0,0: 82:[12, 32, 38] Operation: 58-20=38 Moving to Node #0,0 Current State: 82:[12, 32, 38], Operations: ['58-20=38'] Exploring Operation: 12+32=44, Resulting Numbers: [38, 44] Generated Node #0,0,0: 82:[38, 44] Operation: 12+32=44 Moving to Node #0,0,0 Current State: 82:[38, 44], Operations: ['58-20=38', '12+32=44'] Exploring Operation: 38+44=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[58, 20, 12, 32], Operations: [] Exploring Operation: 58-20=38, Resulting Numbers: [12, 32, 38] Generated Node #0,0: 82:[12, 32, 38] Operation: 58-20=38 Moving to Node #0,0 Current State: 82:[12, 32, 38], Operations: ['58-20=38'] Exploring Operation: 12+32=44, Resulting Numbers: [38, 44] Generated Node #0,0,0: 82:[38, 44] Operation: 12+32=44 Moving to Node #0,0,0 Current State: 82:[38, 44], Operations: ['58-20=38', '12+32=44'] Exploring Operation: 38+44=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 64, 33, 14, 73 ]
90
[ "64-33=31", "73-14=59", "31+59=90" ]
Current State: 90:[64, 33, 14, 73], Operations: [] Exploring Operation: 64-33=31, Resulting Numbers: [14, 73, 31] Generated Node #2: [14, 73, 31] from Operation: 64-33=31 Current State: 90:[14, 73, 31], Operations: ['64-33=31'] Exploring Operation: 73-14=59, Resulting Numbers: [31, 59] Generated Node #3: [31, 59] from Operation: 73-14=59 Current State: 90:[31, 59], Operations: ['64-33=31', '73-14=59'] Exploring Operation: 31+59=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[64, 33, 14, 73], Operations: [] Exploring Operation: 64+33=97, Resulting Numbers: [14, 73, 97] Generated Node #0,0: 90:[14, 73, 97] Operation: 64+33=97 Exploring Operation: 64-33=31, Resulting Numbers: [14, 73, 31] Generated Node #0,1: 90:[14, 73, 31] Operation: 64-33=31 Exploring Operation: 73-64=9, Resulting Numbers: [33, 14, 9] Generated Node #0,2: 90:[33, 14, 9] Operation: 73-64=9 Moving to Node #0,2 Current State: 90:[33, 14, 9], Operations: ['73-64=9'] Exploring Operation: 33+14=47, Resulting Numbers: [9, 47] Generated Node #0,2,0: 90:[9, 47] Operation: 33+14=47 Exploring Operation: 33-14=19, Resulting Numbers: [9, 19] Generated Node #0,2,1: 90:[9, 19] Operation: 33-14=19 Exploring Operation: 14-9=5, Resulting Numbers: [33, 5] Generated Node #0,2,2: 90:[33, 5] Operation: 14-9=5 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 90:[9, 19], Operations: ['73-64=9', '33-14=19'] Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 9*19=171, Resulting Numbers: [171] 171,90 unequal: No Solution Exploring Operation: 9+19=28, Resulting Numbers: [28] 28,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 90:[9, 47], Operations: ['73-64=9', '33+14=47'] Exploring Operation: 9+47=56, Resulting Numbers: [56] 56,90 unequal: No Solution Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,90 unequal: No Solution Exploring Operation: 9*47=423, Resulting Numbers: [423] 423,90 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 #0,2,2 Current State: 90:[33, 5], Operations: ['73-64=9', '14-9=5'] Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,90 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,90 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 90:[14, 73, 31], Operations: ['64-33=31'] Exploring Operation: 14+73=87, Resulting Numbers: [31, 87] Generated Node #0,1,0: 90:[31, 87] Operation: 14+73=87 Exploring Operation: 73-31=42, Resulting Numbers: [14, 42] Generated Node #0,1,1: 90:[14, 42] Operation: 73-31=42 Exploring Operation: 73-14=59, Resulting Numbers: [31, 59] Generated Node #0,1,2: 90:[31, 59] Operation: 73-14=59 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[31, 87], Operations: ['64-33=31', '14+73=87'] Exploring Operation: 31*87=2697, Resulting Numbers: [2697] 2697,90 unequal: No Solution Exploring Operation: 31+87=118, Resulting Numbers: [118] 118,90 unequal: No Solution Exploring Operation: 87-31=56, Resulting Numbers: [56] 56,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[14, 42], Operations: ['64-33=31', '73-31=42'] Exploring Operation: 42-14=28, Resulting Numbers: [28] 28,90 unequal: No Solution Exploring Operation: 14+42=56, Resulting Numbers: [56] 56,90 unequal: No Solution Exploring Operation: 42/14=3, Resulting Numbers: [3] 3,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 90:[31, 59], Operations: ['64-33=31', '73-14=59'] Exploring Operation: 31+59=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[64, 33, 14, 73], Operations: [] Exploring Operation: 64-33=31, Resulting Numbers: [14, 73, 31] Generated Node #0,1: 90:[14, 73, 31] Operation: 64-33=31 Moving to Node #0,1 Current State: 90:[14, 73, 31], Operations: ['64-33=31'] Exploring Operation: 73-14=59, Resulting Numbers: [31, 59] Generated Node #0,1,2: 90:[31, 59] Operation: 73-14=59 Moving to Node #0,1,2 Current State: 90:[31, 59], Operations: ['64-33=31', '73-14=59'] Exploring Operation: 31+59=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
mult_heuristic
[ 64, 98, 35, 10 ]
36
[ "98*10=980", "980/35=28", "64-28=36" ]
Current State: 36:[64, 98, 35, 10], Operations: [] Exploring Operation: 98*10=980, Resulting Numbers: [64, 35, 980] Generated Node #2: [64, 35, 980] from Operation: 98*10=980 Current State: 36:[64, 35, 980], Operations: ['98*10=980'] Exploring Operation: 980/35=28, Resulting Numbers: [64, 28] Generated Node #3: [64, 28] from Operation: 980/35=28 Current State: 36:[64, 28], Operations: ['98*10=980', '980/35=28'] Exploring Operation: 64-28=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[64, 98, 35, 10], Operations: [] Exploring Operation: 64-35=29, Resulting Numbers: [98, 10, 29] Generated Node #0,0: 36:[98, 10, 29] Operation: 64-35=29 Exploring Operation: 98-35=63, Resulting Numbers: [64, 10, 63] Generated Node #0,1: 36:[64, 10, 63] Operation: 98-35=63 Exploring Operation: 98-64=34, Resulting Numbers: [35, 10, 34] Generated Node #0,2: 36:[35, 10, 34] Operation: 98-64=34 Exploring Operation: 64-10=54, Resulting Numbers: [98, 35, 54] Generated Node #0,3: 36:[98, 35, 54] Operation: 64-10=54 Exploring Operation: 98-10=88, Resulting Numbers: [64, 35, 88] Generated Node #0,4: 36:[64, 35, 88] Operation: 98-10=88 Moving to Node #0,2 Current State: 36:[35, 10, 34], Operations: ['98-64=34'] Exploring Operation: 35-10=25, Resulting Numbers: [34, 25] Generated Node #0,2,0: 36:[34, 25] Operation: 35-10=25 Exploring Operation: 35-34=1, Resulting Numbers: [10, 1] Generated Node #0,2,1: 36:[10, 1] Operation: 35-34=1 Exploring Operation: 10+34=44, Resulting Numbers: [35, 44] Generated Node #0,2,2: 36:[35, 44] Operation: 10+34=44 Exploring Operation: 35+10=45, Resulting Numbers: [34, 45] Generated Node #0,2,3: 36:[34, 45] Operation: 35+10=45 Exploring Operation: 34-10=24, Resulting Numbers: [35, 24] Generated Node #0,2,4: 36:[35, 24] Operation: 34-10=24 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 36:[10, 1], Operations: ['98-64=34', '35-34=1'] Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,36 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 #0,2,4 Current State: 36:[35, 24], Operations: ['98-64=34', '34-10=24'] Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 35*24=840, Resulting Numbers: [840] 840,36 unequal: No Solution Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,36 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:[34, 25], Operations: ['98-64=34', '35-10=25'] Exploring Operation: 34+25=59, Resulting Numbers: [59] 59,36 unequal: No Solution Exploring Operation: 34*25=850, Resulting Numbers: [850] 850,36 unequal: No Solution Exploring Operation: 34-25=9, Resulting Numbers: [9] 9,36 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:[35, 44], Operations: ['98-64=34', '10+34=44'] Exploring Operation: 35*44=1540, Resulting Numbers: [1540] 1540,36 unequal: No Solution Exploring Operation: 35+44=79, Resulting Numbers: [79] 79,36 unequal: No Solution Exploring Operation: 44-35=9, Resulting Numbers: [9] 9,36 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:[34, 45], Operations: ['98-64=34', '35+10=45'] Exploring Operation: 34+45=79, Resulting Numbers: [79] 79,36 unequal: No Solution Exploring Operation: 34*45=1530, Resulting Numbers: [1530] 1530,36 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,36 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:[64, 10, 63], Operations: ['98-35=63'] Exploring Operation: 64-63=1, Resulting Numbers: [10, 1] Generated Node #0,1,0: 36:[10, 1] Operation: 64-63=1 Exploring Operation: 63-10=53, Resulting Numbers: [64, 53] Generated Node #0,1,1: 36:[64, 53] Operation: 63-10=53 Exploring Operation: 64+10=74, Resulting Numbers: [63, 74] Generated Node #0,1,2: 36:[63, 74] Operation: 64+10=74 Exploring Operation: 64-10=54, Resulting Numbers: [63, 54] Generated Node #0,1,3: 36:[63, 54] Operation: 64-10=54 Exploring Operation: 10+63=73, Resulting Numbers: [64, 73] Generated Node #0,1,4: 36:[64, 73] Operation: 10+63=73 Moving to Node #0,0 Current State: 36:[98, 10, 29], Operations: ['64-35=29'] Exploring Operation: 29-10=19, Resulting Numbers: [98, 19] Generated Node #0,0,0: 36:[98, 19] Operation: 29-10=19 Exploring Operation: 98+10=108, Resulting Numbers: [29, 108] Generated Node #0,0,1: 36:[29, 108] Operation: 98+10=108 Exploring Operation: 98-10=88, Resulting Numbers: [29, 88] Generated Node #0,0,2: 36:[29, 88] Operation: 98-10=88 Exploring Operation: 98-29=69, Resulting Numbers: [10, 69] Generated Node #0,0,3: 36:[10, 69] Operation: 98-29=69 Exploring Operation: 10+29=39, Resulting Numbers: [98, 39] Generated Node #0,0,4: 36:[98, 39] Operation: 10+29=39 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 36:[10, 69], Operations: ['64-35=29', '98-29=69'] Exploring Operation: 10*69=690, Resulting Numbers: [690] 690,36 unequal: No Solution Exploring Operation: 10+69=79, Resulting Numbers: [79] 79,36 unequal: No Solution Exploring Operation: 69-10=59, Resulting Numbers: [59] 59,36 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:[29, 88], Operations: ['64-35=29', '98-10=88'] Exploring Operation: 29*88=2552, Resulting Numbers: [2552] 2552,36 unequal: No Solution Exploring Operation: 29+88=117, Resulting Numbers: [117] 117,36 unequal: No Solution Exploring Operation: 88-29=59, Resulting Numbers: [59] 59,36 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:[98, 19], Operations: ['64-35=29', '29-10=19'] Exploring Operation: 98+19=117, Resulting Numbers: [117] 117,36 unequal: No Solution Exploring Operation: 98*19=1862, Resulting Numbers: [1862] 1862,36 unequal: No Solution Exploring Operation: 98-19=79, Resulting Numbers: [79] 79,36 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 #0,0,4 Current State: 36:[98, 39], Operations: ['64-35=29', '10+29=39'] Exploring Operation: 98*39=3822, Resulting Numbers: [3822] 3822,36 unequal: No Solution Exploring Operation: 98+39=137, Resulting Numbers: [137] 137,36 unequal: No Solution Exploring Operation: 98-39=59, Resulting Numbers: [59] 59,36 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 #0,0,1 Current State: 36:[29, 108], Operations: ['64-35=29', '98+10=108'] Exploring Operation: 29*108=3132, Resulting Numbers: [3132] 3132,36 unequal: No Solution Exploring Operation: 29+108=137, Resulting Numbers: [137] 137,36 unequal: No Solution Exploring Operation: 108-29=79, Resulting Numbers: [79] 79,36 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:[98, 35, 54], Operations: ['64-10=54'] Exploring Operation: 98-54=44, Resulting Numbers: [35, 44] Generated Node #0,3,0: 36:[35, 44] Operation: 98-54=44 Exploring Operation: 98+35=133, Resulting Numbers: [54, 133] Generated Node #0,3,1: 36:[54, 133] Operation: 98+35=133 Exploring Operation: 98-35=63, Resulting Numbers: [54, 63] Generated Node #0,3,2: 36:[54, 63] Operation: 98-35=63 Exploring Operation: 54-35=19, Resulting Numbers: [98, 19] Generated Node #0,3,3: 36:[98, 19] Operation: 54-35=19 Exploring Operation: 35+54=89, Resulting Numbers: [98, 89] Generated Node #0,3,4: 36:[98, 89] Operation: 35+54=89 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 36:[35, 44], Operations: ['64-10=54', '98-54=44'] Exploring Operation: 44-35=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 35+44=79, Resulting Numbers: [79] 79,36 unequal: No Solution Exploring Operation: 35*44=1540, Resulting Numbers: [1540] 1540,36 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:[54, 63], Operations: ['64-10=54', '98-35=63'] Exploring Operation: 54+63=117, Resulting Numbers: [117] 117,36 unequal: No Solution Exploring Operation: 54*63=3402, Resulting Numbers: [3402] 3402,36 unequal: No Solution Exploring Operation: 63-54=9, Resulting Numbers: [9] 9,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 36:[98, 19], Operations: ['64-10=54', '54-35=19'] Exploring Operation: 98*19=1862, Resulting Numbers: [1862] 1862,36 unequal: No Solution Exploring Operation: 98+19=117, Resulting Numbers: [117] 117,36 unequal: No Solution Exploring Operation: 98-19=79, Resulting Numbers: [79] 79,36 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:[54, 133], Operations: ['64-10=54', '98+35=133'] Exploring Operation: 133-54=79, Resulting Numbers: [79] 79,36 unequal: No Solution Exploring Operation: 54*133=7182, Resulting Numbers: [7182] 7182,36 unequal: No Solution Exploring Operation: 54+133=187, Resulting Numbers: [187] 187,36 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 #0,3,4 Current State: 36:[98, 89], Operations: ['64-10=54', '35+54=89'] Exploring Operation: 98-89=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 98+89=187, Resulting Numbers: [187] 187,36 unequal: No Solution Exploring Operation: 98*89=8722, Resulting Numbers: [8722] 8722,36 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: 36:[64, 35, 88], Operations: ['98-10=88'] Exploring Operation: 88-35=53, Resulting Numbers: [64, 53] Generated Node #0,4,0: 36:[64, 53] Operation: 88-35=53 Exploring Operation: 64+35=99, Resulting Numbers: [88, 99] Generated Node #0,4,1: 36:[88, 99] Operation: 64+35=99 Exploring Operation: 35+88=123, Resulting Numbers: [64, 123] Generated Node #0,4,2: 36:[64, 123] Operation: 35+88=123 Exploring Operation: 88-64=24, Resulting Numbers: [35, 24] Generated Node #0,4,3: 36:[35, 24] Operation: 88-64=24 Exploring Operation: 64-35=29, Resulting Numbers: [88, 29] Generated Node #0,4,4: 36:[88, 29] Operation: 64-35=29 Moving to Node #0,1,0 Current State: 36:[10, 1], Operations: ['98-35=63', '64-63=1'] Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,36 unequal: No Solution Moving to Node #0,4,3 Current State: 36:[35, 24], Operations: ['98-10=88', '88-64=24'] Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,36 unequal: No Solution Exploring Operation: 35*24=840, Resulting Numbers: [840] 840,36 unequal: No Solution Moving to Node #0,4,0 Current State: 36:[64, 53], Operations: ['98-10=88', '88-35=53'] Exploring Operation: 64*53=3392, Resulting Numbers: [3392] 3392,36 unequal: No Solution Exploring Operation: 64-53=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 64+53=117, Resulting Numbers: [117] 117,36 unequal: No Solution Moving to Node #0,1,3 Current State: 36:[63, 54], Operations: ['98-35=63', '64-10=54'] Exploring Operation: 63-54=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 63+54=117, Resulting Numbers: [117] 117,36 unequal: No Solution Exploring Operation: 63*54=3402, Resulting Numbers: [3402] 3402,36 unequal: No Solution Moving to Node #0,1,1 Current State: 36:[64, 53], Operations: ['98-35=63', '63-10=53'] Exploring Operation: 64+53=117, Resulting Numbers: [117] 117,36 unequal: No Solution Exploring Operation: 64-53=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 64*53=3392, Resulting Numbers: [3392] 3392,36 unequal: No Solution Moving to Node #0,4,4 Current State: 36:[88, 29], Operations: ['98-10=88', '64-35=29'] Exploring Operation: 88+29=117, Resulting Numbers: [117] 117,36 unequal: No Solution Exploring Operation: 88*29=2552, Resulting Numbers: [2552] 2552,36 unequal: No Solution Exploring Operation: 88-29=59, Resulting Numbers: [59] 59,36 unequal: No Solution Moving to Node #0,1,2 Current State: 36:[63, 74], Operations: ['98-35=63', '64+10=74'] Exploring Operation: 74-63=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 63*74=4662, Resulting Numbers: [4662] 4662,36 unequal: No Solution Exploring Operation: 63+74=137, Resulting Numbers: [137] 137,36 unequal: No Solution Moving to Node #0,1,4 Current State: 36:[64, 73], Operations: ['98-35=63', '10+63=73'] Exploring Operation: 73-64=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 64*73=4672, Resulting Numbers: [4672] 4672,36 unequal: No Solution Exploring Operation: 64+73=137, Resulting Numbers: [137] 137,36 unequal: No Solution Moving to Node #0,4,2 Current State: 36:[64, 123], Operations: ['98-10=88', '35+88=123'] Exploring Operation: 64+123=187, Resulting Numbers: [187] 187,36 unequal: No Solution Exploring Operation: 64*123=7872, Resulting Numbers: [7872] 7872,36 unequal: No Solution Exploring Operation: 123-64=59, Resulting Numbers: [59] 59,36 unequal: No Solution Moving to Node #0,4,1 Current State: 36:[88, 99], Operations: ['98-10=88', '64+35=99'] Exploring Operation: 88+99=187, Resulting Numbers: [187] 187,36 unequal: No Solution Exploring Operation: 88*99=8712, Resulting Numbers: [8712] 8712,36 unequal: No Solution Exploring Operation: 99-88=11, Resulting Numbers: [11] 11,36 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 83, 50, 1, 83 ]
50
[ "83+50=133", "1*83=83", "133-83=50" ]
Current State: 50:[83, 50, 1, 83], Operations: [] Exploring Operation: 83+50=133, Resulting Numbers: [1, 133] Generated Node #2: [1, 133] from Operation: 83+50=133 Current State: 50:[1, 133], Operations: ['83+50=133'] Exploring Operation: 1*83=83, Resulting Numbers: [133, 83] Generated Node #3: [133, 83] from Operation: 1*83=83 Current State: 50:[133, 83], Operations: ['83+50=133', '1*83=83'] Exploring Operation: 133-83=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[83, 50, 1, 83], Operations: [] Exploring Operation: 83-50=33, Resulting Numbers: [1, 83, 33] Generated Node #0,0: 50:[1, 83, 33] Operation: 83-50=33 Exploring Operation: 83-1=82, Resulting Numbers: [50, 83, 82] Generated Node #0,1: 50:[50, 83, 82] Operation: 83-1=82 Exploring Operation: 83/83=1, Resulting Numbers: [50, 1, 1] Generated Node #0,2: 50:[50, 1, 1] Operation: 83/83=1 Exploring Operation: 83-50=33, Resulting Numbers: [83, 1, 33] Generated Node #0,3: 50:[83, 1, 33] Operation: 83-50=33 Exploring Operation: 83-83=0, Resulting Numbers: [50, 1, 0] Generated Node #0,4: 50:[50, 1, 0] Operation: 83-83=0 Moving to Node #0,2 Current State: 50:[50, 1, 1], Operations: ['83/83=1'] Exploring Operation: 50/1=50, Resulting Numbers: [1, 50] Generated Node #0,2,0: 50:[1, 50] Operation: 50/1=50 Exploring Operation: 50/1=50, Resulting Numbers: [1, 50] Generated Node #0,2,1: 50:[1, 50] Operation: 50/1=50 Exploring Operation: 50*1=50, Resulting Numbers: [1, 50] Generated Node #0,2,2: 50:[1, 50] Operation: 50*1=50 Exploring Operation: 1+1=2, Resulting Numbers: [50, 2] Generated Node #0,2,3: 50:[50, 2] Operation: 1+1=2 Exploring Operation: 50*1=50, Resulting Numbers: [1, 50] Generated Node #0,2,4: 50:[1, 50] Operation: 50*1=50 Moving to Node #0,4 Current State: 50:[50, 1, 0], Operations: ['83-83=0'] Exploring Operation: 50-0=50, Resulting Numbers: [1, 50] Generated Node #0,4,0: 50:[1, 50] Operation: 50-0=50 Exploring Operation: 50*1=50, Resulting Numbers: [0, 50] Generated Node #0,4,1: 50:[0, 50] Operation: 50*1=50 Exploring Operation: 1-0=1, Resulting Numbers: [50, 1] Generated Node #0,4,2: 50:[50, 1] Operation: 1-0=1 Exploring Operation: 1+0=1, Resulting Numbers: [50, 1] Generated Node #0,4,3: 50:[50, 1] Operation: 1+0=1 Exploring Operation: 50+0=50, Resulting Numbers: [1, 50] Generated Node #0,4,4: 50:[1, 50] Operation: 50+0=50 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 50:[1, 50], Operations: ['83-83=0', '50-0=50'] Exploring Operation: 1+50=51, Resulting Numbers: [51] 51,50 unequal: No Solution Exploring Operation: 1*50=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[83, 50, 1, 83], Operations: [] Exploring Operation: 83-83=0, Resulting Numbers: [50, 1, 0] Generated Node #0,4: 50:[50, 1, 0] Operation: 83-83=0 Moving to Node #0,4 Current State: 50:[50, 1, 0], Operations: ['83-83=0'] Exploring Operation: 50-0=50, Resulting Numbers: [1, 50] Generated Node #0,4,0: 50:[1, 50] Operation: 50-0=50 Moving to Node #0,4,0 Current State: 50:[1, 50], Operations: ['83-83=0', '50-0=50'] Exploring Operation: 1*50=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 35, 7, 44, 69 ]
71
[ "35+7=42", "44+69=113", "113-42=71" ]
Current State: 71:[35, 7, 44, 69], Operations: [] Exploring Operation: 35+7=42, Resulting Numbers: [44, 69, 42] Generated Node #2: [44, 69, 42] from Operation: 35+7=42 Current State: 71:[44, 69, 42], Operations: ['35+7=42'] Exploring Operation: 44+69=113, Resulting Numbers: [42, 113] Generated Node #3: [42, 113] from Operation: 44+69=113 Current State: 71:[42, 113], Operations: ['35+7=42', '44+69=113'] Exploring Operation: 113-42=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[35, 7, 44, 69], Operations: [] Exploring Operation: 35+7=42, Resulting Numbers: [44, 69, 42] Generated Node #0,0: 71:[44, 69, 42] Operation: 35+7=42 Exploring Operation: 7+44=51, Resulting Numbers: [35, 69, 51] Generated Node #0,1: 71:[35, 69, 51] Operation: 7+44=51 Moving to Node #0,0 Current State: 71:[44, 69, 42], Operations: ['35+7=42'] Exploring Operation: 69+42=111, Resulting Numbers: [44, 111] Generated Node #0,0,0: 71:[44, 111] Operation: 69+42=111 Exploring Operation: 44+42=86, Resulting Numbers: [69, 86] Generated Node #0,0,1: 71:[69, 86] Operation: 44+42=86 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 71:[69, 86], Operations: ['35+7=42', '44+42=86'] Exploring Operation: 86-69=17, Resulting Numbers: [17] 17,71 unequal: No Solution Exploring Operation: 69+86=155, Resulting Numbers: [155] 155,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[44, 111], Operations: ['35+7=42', '69+42=111'] Exploring Operation: 111-44=67, Resulting Numbers: [67] 67,71 unequal: No Solution Exploring Operation: 44+111=155, Resulting Numbers: [155] 155,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 71:[35, 69, 51], Operations: ['7+44=51'] Exploring Operation: 35+69=104, Resulting Numbers: [51, 104] Generated Node #0,1,0: 71:[51, 104] Operation: 35+69=104 Exploring Operation: 35+51=86, Resulting Numbers: [69, 86] Generated Node #0,1,1: 71:[69, 86] Operation: 35+51=86 Moving to Node #0,1,1 Current State: 71:[69, 86], Operations: ['7+44=51', '35+51=86'] Exploring Operation: 86-69=17, Resulting Numbers: [17] 17,71 unequal: No Solution Exploring Operation: 69+86=155, Resulting Numbers: [155] 155,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[51, 104], Operations: ['7+44=51', '35+69=104'] Exploring Operation: 104-51=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 51+104=155, Resulting Numbers: [155] 155,71 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 18, 66, 75, 4 ]
25
[ "18+4=22", "66/22=3", "75/3=25" ]
Current State: 25:[18, 66, 75, 4], Operations: [] Exploring Operation: 18+4=22, Resulting Numbers: [66, 75, 22] Generated Node #2: [66, 75, 22] from Operation: 18+4=22 Current State: 25:[66, 75, 22], Operations: ['18+4=22'] Exploring Operation: 66/22=3, Resulting Numbers: [75, 3] Generated Node #3: [75, 3] from Operation: 66/22=3 Current State: 25:[75, 3], Operations: ['18+4=22', '66/22=3'] Exploring Operation: 75/3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[18, 66, 75, 4], Operations: [] Exploring Operation: 66-18=48, Resulting Numbers: [75, 4, 48] Generated Node #0,0: 25:[75, 4, 48] Operation: 66-18=48 Exploring Operation: 75-18=57, Resulting Numbers: [66, 4, 57] Generated Node #0,1: 25:[66, 4, 57] Operation: 75-18=57 Exploring Operation: 75-66=9, Resulting Numbers: [18, 4, 9] Generated Node #0,2: 25:[18, 4, 9] Operation: 75-66=9 Exploring Operation: 18+4=22, Resulting Numbers: [66, 75, 22] Generated Node #0,3: 25:[66, 75, 22] Operation: 18+4=22 Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[18, 4, 9], Operations: ['75-66=9'] Exploring Operation: 18/9=2, Resulting Numbers: [4, 2] Generated Node #0,2,0: 25:[4, 2] Operation: 18/9=2 Exploring Operation: 18+9=27, Resulting Numbers: [4, 27] Generated Node #0,2,1: 25:[4, 27] Operation: 18+9=27 Exploring Operation: 18-9=9, Resulting Numbers: [4, 9] Generated Node #0,2,2: 25:[4, 9] Operation: 18-9=9 Exploring Operation: 18+4=22, Resulting Numbers: [9, 22] Generated Node #0,2,3: 25:[9, 22] Operation: 18+4=22 Moving to Node #0,2,1 Current State: 25:[4, 27], Operations: ['75-66=9', '18+9=27'] Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,25 unequal: No Solution Exploring Operation: 4*27=108, Resulting Numbers: [108] 108,25 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,25 unequal: No Solution Moving to Node #0,2,0 Current State: 25:[4, 2], Operations: ['75-66=9', '18/9=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,25 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,25 unequal: No Solution Moving to Node #0,2,2 Current State: 25:[4, 9], Operations: ['75-66=9', '18-9=9'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,25 unequal: No Solution Moving to Node #0,2,3 Current State: 25:[9, 22], Operations: ['75-66=9', '18+4=22'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,25 unequal: No Solution Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[75, 4, 48], Operations: ['66-18=48'] Exploring Operation: 75-4=71, Resulting Numbers: [48, 71] Generated Node #0,0,0: 25:[48, 71] Operation: 75-4=71 Exploring Operation: 48/4=12, Resulting Numbers: [75, 12] Generated Node #0,0,1: 25:[75, 12] Operation: 48/4=12 Exploring Operation: 75-48=27, Resulting Numbers: [4, 27] Generated Node #0,0,2: 25:[4, 27] Operation: 75-48=27 Exploring Operation: 48-4=44, Resulting Numbers: [75, 44] Generated Node #0,0,3: 25:[75, 44] Operation: 48-4=44 Moving to Node #0,0,2 Current State: 25:[4, 27], Operations: ['66-18=48', '75-48=27'] Exploring Operation: 4*27=108, Resulting Numbers: [108] 108,25 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,25 unequal: No Solution Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[75, 12], Operations: ['66-18=48', '48/4=12'] Exploring Operation: 75*12=900, Resulting Numbers: [900] 900,25 unequal: No Solution Exploring Operation: 75+12=87, Resulting Numbers: [87] 87,25 unequal: No Solution Exploring Operation: 75-12=63, Resulting Numbers: [63] 63,25 unequal: No Solution Moving to Node #0,0,3 Current State: 25:[75, 44], Operations: ['66-18=48', '48-4=44'] Exploring Operation: 75+44=119, Resulting Numbers: [119] 119,25 unequal: No Solution Exploring Operation: 75-44=31, Resulting Numbers: [31] 31,25 unequal: No Solution Exploring Operation: 75*44=3300, Resulting Numbers: [3300] 3300,25 unequal: No Solution Moving to Node #0,0,0 Current State: 25:[48, 71], Operations: ['66-18=48', '75-4=71'] Exploring Operation: 71-48=23, Resulting Numbers: [23] 23,25 unequal: No Solution Exploring Operation: 48*71=3408, Resulting Numbers: [3408] 3408,25 unequal: No Solution Exploring Operation: 48+71=119, Resulting Numbers: [119] 119,25 unequal: No Solution No 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:[66, 4, 57], Operations: ['75-18=57'] Exploring Operation: 66-57=9, Resulting Numbers: [4, 9] Generated Node #0,1,0: 25:[4, 9] Operation: 66-57=9 Exploring Operation: 66+4=70, Resulting Numbers: [57, 70] Generated Node #0,1,1: 25:[57, 70] Operation: 66+4=70 Exploring Operation: 57-4=53, Resulting Numbers: [66, 53] Generated Node #0,1,2: 25:[66, 53] Operation: 57-4=53 Exploring Operation: 66-4=62, Resulting Numbers: [57, 62] Generated Node #0,1,3: 25:[57, 62] Operation: 66-4=62 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[4, 9], Operations: ['75-18=57', '66-57=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,25 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:[66, 53], Operations: ['75-18=57', '57-4=53'] Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 66*53=3498, Resulting Numbers: [3498] 3498,25 unequal: No Solution Exploring Operation: 66+53=119, Resulting Numbers: [119] 119,25 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 #0,1,3 Current State: 25:[57, 62], Operations: ['75-18=57', '66-4=62'] Exploring Operation: 62-57=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 57+62=119, Resulting Numbers: [119] 119,25 unequal: No Solution Exploring Operation: 57*62=3534, Resulting Numbers: [3534] 3534,25 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:[57, 70], Operations: ['75-18=57', '66+4=70'] Exploring Operation: 57*70=3990, Resulting Numbers: [3990] 3990,25 unequal: No Solution Exploring Operation: 70-57=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 57+70=127, Resulting Numbers: [127] 127,25 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 #0,3 Current State: 25:[66, 75, 22], Operations: ['18+4=22'] Exploring Operation: 75-66=9, Resulting Numbers: [22, 9] Generated Node #0,3,0: 25:[22, 9] Operation: 75-66=9 Exploring Operation: 66/22=3, Resulting Numbers: [75, 3] Generated Node #0,3,1: 25:[75, 3] Operation: 66/22=3 Exploring Operation: 75-22=53, Resulting Numbers: [66, 53] Generated Node #0,3,2: 25:[66, 53] Operation: 75-22=53 Exploring Operation: 66-22=44, Resulting Numbers: [75, 44] Generated Node #0,3,3: 25:[75, 44] Operation: 66-22=44 Moving to Node #0,3,0 Current State: 25:[22, 9], Operations: ['18+4=22', '75-66=9'] Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,25 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,25 unequal: No Solution Moving to Node #0,3,1 Current State: 25:[75, 3], Operations: ['18+4=22', '66/22=3'] Exploring Operation: 75*3=225, Resulting Numbers: [225] 225,25 unequal: No Solution Exploring Operation: 75-3=72, Resulting Numbers: [72] 72,25 unequal: No Solution Exploring Operation: 75/3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[18, 66, 75, 4], Operations: [] Exploring Operation: 18+4=22, Resulting Numbers: [66, 75, 22] Generated Node #0,3: 25:[66, 75, 22] Operation: 18+4=22 Moving to Node #0,3 Current State: 25:[66, 75, 22], Operations: ['18+4=22'] Exploring Operation: 66/22=3, Resulting Numbers: [75, 3] Generated Node #0,3,1: 25:[75, 3] Operation: 66/22=3 Moving to Node #0,3,1 Current State: 25:[75, 3], Operations: ['18+4=22', '66/22=3'] Exploring Operation: 75/3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.94184
hs_4
mult_heuristic
[ 95, 3, 16, 41 ]
73
[ "95+3=98", "41-16=25", "98-25=73" ]
Current State: 73:[95, 3, 16, 41], Operations: [] Exploring Operation: 95+3=98, Resulting Numbers: [16, 41, 98] Generated Node #2: [16, 41, 98] from Operation: 95+3=98 Current State: 73:[16, 41, 98], Operations: ['95+3=98'] Exploring Operation: 41-16=25, Resulting Numbers: [98, 25] Generated Node #3: [98, 25] from Operation: 41-16=25 Current State: 73:[98, 25], Operations: ['95+3=98', '41-16=25'] Exploring Operation: 98-25=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[95, 3, 16, 41], Operations: [] Exploring Operation: 3*16=48, Resulting Numbers: [95, 41, 48] Generated Node #0,0: 73:[95, 41, 48] Operation: 3*16=48 Exploring Operation: 95-3=92, Resulting Numbers: [16, 41, 92] Generated Node #0,1: 73:[16, 41, 92] Operation: 95-3=92 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[95, 41, 48], Operations: ['3*16=48'] Exploring Operation: 41+48=89, Resulting Numbers: [95, 89] Generated Node #0,0,0: 73:[95, 89] Operation: 41+48=89 Exploring Operation: 95-41=54, Resulting Numbers: [48, 54] Generated Node #0,0,1: 73:[48, 54] Operation: 95-41=54 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[95, 89], Operations: ['3*16=48', '41+48=89'] Exploring Operation: 95+89=184, Resulting Numbers: [184] 184,73 unequal: No Solution Exploring Operation: 95-89=6, Resulting Numbers: [6] 6,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[48, 54], Operations: ['3*16=48', '95-41=54'] Exploring Operation: 54-48=6, Resulting Numbers: [6] 6,73 unequal: No Solution Exploring Operation: 48+54=102, Resulting Numbers: [102] 102,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[16, 41, 92], Operations: ['95-3=92'] Exploring Operation: 92-16=76, Resulting Numbers: [41, 76] Generated Node #0,1,0: 73:[41, 76] Operation: 92-16=76 Exploring Operation: 16+41=57, Resulting Numbers: [92, 57] Generated Node #0,1,1: 73:[92, 57] Operation: 16+41=57 Moving to Node #0,1,0 Current State: 73:[41, 76], Operations: ['95-3=92', '92-16=76'] Exploring Operation: 76-41=35, Resulting Numbers: [35] 35,73 unequal: No Solution Exploring Operation: 41+76=117, Resulting Numbers: [117] 117,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[92, 57], Operations: ['95-3=92', '16+41=57'] Exploring Operation: 92-57=35, Resulting Numbers: [35] 35,73 unequal: No Solution Exploring Operation: 92+57=149, Resulting Numbers: [149] 149,73 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
[ 26, 72, 91, 16 ]
61
[ "72-26=46", "91+16=107", "107-46=61" ]
Current State: 61:[26, 72, 91, 16], Operations: [] Exploring Operation: 72-26=46, Resulting Numbers: [91, 16, 46] Generated Node #2: [91, 16, 46] from Operation: 72-26=46 Current State: 61:[91, 16, 46], Operations: ['72-26=46'] Exploring Operation: 91+16=107, Resulting Numbers: [46, 107] Generated Node #3: [46, 107] from Operation: 91+16=107 Current State: 61:[46, 107], Operations: ['72-26=46', '91+16=107'] Exploring Operation: 107-46=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[26, 72, 91, 16], Operations: [] Exploring Operation: 26+16=42, Resulting Numbers: [72, 91, 42] Generated Node #0,0: 61:[72, 91, 42] Operation: 26+16=42 Exploring Operation: 91-16=75, Resulting Numbers: [26, 72, 75] Generated Node #0,1: 61:[26, 72, 75] Operation: 91-16=75 Exploring Operation: 72-26=46, Resulting Numbers: [91, 16, 46] Generated Node #0,2: 61:[91, 16, 46] Operation: 72-26=46 Exploring Operation: 91-26=65, Resulting Numbers: [72, 16, 65] Generated Node #0,3: 61:[72, 16, 65] Operation: 91-26=65 Exploring Operation: 72-16=56, Resulting Numbers: [26, 91, 56] Generated Node #0,4: 61:[26, 91, 56] Operation: 72-16=56 Moving to Node #0,0 Current State: 61:[72, 91, 42], Operations: ['26+16=42'] Exploring Operation: 72+42=114, Resulting Numbers: [91, 114] Generated Node #0,0,0: 61:[91, 114] Operation: 72+42=114 Exploring Operation: 72-42=30, Resulting Numbers: [91, 30] Generated Node #0,0,1: 61:[91, 30] Operation: 72-42=30 Exploring Operation: 91+42=133, Resulting Numbers: [72, 133] Generated Node #0,0,2: 61:[72, 133] Operation: 91+42=133 Exploring Operation: 91-42=49, Resulting Numbers: [72, 49] Generated Node #0,0,3: 61:[72, 49] Operation: 91-42=49 Exploring Operation: 91-72=19, Resulting Numbers: [42, 19] Generated Node #0,0,4: 61:[42, 19] Operation: 91-72=19 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 61:[72, 49], Operations: ['26+16=42', '91-42=49'] Exploring Operation: 72+49=121, Resulting Numbers: [121] 121,61 unequal: No Solution Exploring Operation: 72*49=3528, Resulting Numbers: [3528] 3528,61 unequal: No Solution Exploring Operation: 72-49=23, Resulting Numbers: [23] 23,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[91, 30], Operations: ['26+16=42', '72-42=30'] Exploring Operation: 91*30=2730, Resulting Numbers: [2730] 2730,61 unequal: No Solution Exploring Operation: 91-30=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[26, 72, 91, 16], Operations: [] Exploring Operation: 26+16=42, Resulting Numbers: [72, 91, 42] Generated Node #0,0: 61:[72, 91, 42] Operation: 26+16=42 Moving to Node #0,0 Current State: 61:[72, 91, 42], Operations: ['26+16=42'] Exploring Operation: 72-42=30, Resulting Numbers: [91, 30] Generated Node #0,0,1: 61:[91, 30] Operation: 72-42=30 Moving to Node #0,0,1 Current State: 61:[91, 30], Operations: ['26+16=42', '72-42=30'] Exploring Operation: 91-30=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 38, 72, 62, 93 ]
31
[ "62-38=24", "72/24=3", "93/3=31" ]
Current State: 31:[38, 72, 62, 93], Operations: [] Exploring Operation: 62-38=24, Resulting Numbers: [72, 93, 24] Generated Node #2: [72, 93, 24] from Operation: 62-38=24 Current State: 31:[72, 93, 24], Operations: ['62-38=24'] Exploring Operation: 72/24=3, Resulting Numbers: [93, 3] Generated Node #3: [93, 3] from Operation: 72/24=3 Current State: 31:[93, 3], Operations: ['62-38=24', '72/24=3'] Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[38, 72, 62, 93], Operations: [] Exploring Operation: 72-62=10, Resulting Numbers: [38, 93, 10] Generated Node #0,0: 31:[38, 93, 10] Operation: 72-62=10 Exploring Operation: 93-72=21, Resulting Numbers: [38, 62, 21] Generated Node #0,1: 31:[38, 62, 21] Operation: 93-72=21 Exploring Operation: 93-62=31, Resulting Numbers: [38, 72, 31] Generated Node #0,2: 31:[38, 72, 31] Operation: 93-62=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[38, 62, 21], Operations: ['93-72=21'] Exploring Operation: 38-21=17, Resulting Numbers: [62, 17] Generated Node #0,1,0: 31:[62, 17] Operation: 38-21=17 Exploring Operation: 62-21=41, Resulting Numbers: [38, 41] Generated Node #0,1,1: 31:[38, 41] Operation: 62-21=41 Exploring Operation: 62-38=24, Resulting Numbers: [21, 24] Generated Node #0,1,2: 31:[21, 24] Operation: 62-38=24 Moving to Node #0,1,1 Current State: 31:[38, 41], Operations: ['93-72=21', '62-21=41'] Exploring Operation: 38+41=79, Resulting Numbers: [79] 79,31 unequal: No Solution Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 38*41=1558, Resulting Numbers: [1558] 1558,31 unequal: No Solution Moving to Node #0,1,2 Current State: 31:[21, 24], Operations: ['93-72=21', '62-38=24'] Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 21*24=504, Resulting Numbers: [504] 504,31 unequal: No Solution Exploring Operation: 21+24=45, Resulting Numbers: [45] 45,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[62, 17], Operations: ['93-72=21', '38-21=17'] Exploring Operation: 62+17=79, Resulting Numbers: [79] 79,31 unequal: No Solution Exploring Operation: 62-17=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 62*17=1054, Resulting Numbers: [1054] 1054,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 31:[38, 72, 31], Operations: ['93-62=31'] Exploring Operation: 72-38=34, Resulting Numbers: [31, 34] Generated Node #0,2,0: 31:[31, 34] Operation: 72-38=34 Exploring Operation: 72-31=41, Resulting Numbers: [38, 41] Generated Node #0,2,1: 31:[38, 41] Operation: 72-31=41 Exploring Operation: 38-31=7, Resulting Numbers: [72, 7] Generated Node #0,2,2: 31:[72, 7] Operation: 38-31=7 Moving to Node #0,2,0 Current State: 31:[31, 34], Operations: ['93-62=31', '72-38=34'] Exploring Operation: 31*34=1054, Resulting Numbers: [1054] 1054,31 unequal: No Solution Exploring Operation: 31+34=65, Resulting Numbers: [65] 65,31 unequal: No Solution Exploring Operation: 34-31=3, Resulting Numbers: [3] 3,31 unequal: No Solution Moving to Node #0,2,1 Current State: 31:[38, 41], Operations: ['93-62=31', '72-31=41'] Exploring Operation: 38*41=1558, Resulting Numbers: [1558] 1558,31 unequal: No Solution Exploring Operation: 38+41=79, Resulting Numbers: [79] 79,31 unequal: No Solution Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[72, 7], Operations: ['93-62=31', '38-31=7'] Exploring Operation: 72+7=79, Resulting Numbers: [79] 79,31 unequal: No Solution Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,31 unequal: No Solution Exploring Operation: 72*7=504, Resulting Numbers: [504] 504,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[38, 93, 10], Operations: ['72-62=10'] Exploring Operation: 93-10=83, Resulting Numbers: [38, 83] Generated Node #0,0,0: 31:[38, 83] Operation: 93-10=83 Exploring Operation: 38-10=28, Resulting Numbers: [93, 28] Generated Node #0,0,1: 31:[93, 28] Operation: 38-10=28 Exploring Operation: 93-38=55, Resulting Numbers: [10, 55] Generated Node #0,0,2: 31:[10, 55] Operation: 93-38=55 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 31:[10, 55], Operations: ['72-62=10', '93-38=55'] Exploring Operation: 55-10=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 10+55=65, Resulting Numbers: [65] 65,31 unequal: No Solution Exploring Operation: 10*55=550, Resulting Numbers: [550] 550,31 unequal: No Solution No 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: 31:[38, 83], Operations: ['72-62=10', '93-10=83'] Exploring Operation: 83-38=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 38*83=3154, Resulting Numbers: [3154] 3154,31 unequal: No Solution Exploring Operation: 38+83=121, Resulting Numbers: [121] 121,31 unequal: No Solution No 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: 31:[93, 28], Operations: ['72-62=10', '38-10=28'] Exploring Operation: 93+28=121, Resulting Numbers: [121] 121,31 unequal: No Solution Exploring Operation: 93*28=2604, Resulting Numbers: [2604] 2604,31 unequal: No Solution Exploring Operation: 93-28=65, Resulting Numbers: [65] 65,31 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_3
mult_heuristic
[ 49, 20, 99, 9 ]
32
[ "49+99=148", "20*9=180", "180-148=32" ]
Current State: 32:[49, 20, 99, 9], Operations: [] Exploring Operation: 49+99=148, Resulting Numbers: [20, 9, 148] Generated Node #2: [20, 9, 148] from Operation: 49+99=148 Current State: 32:[20, 9, 148], Operations: ['49+99=148'] Exploring Operation: 20*9=180, Resulting Numbers: [148, 180] Generated Node #3: [148, 180] from Operation: 20*9=180 Current State: 32:[148, 180], Operations: ['49+99=148', '20*9=180'] Exploring Operation: 180-148=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[49, 20, 99, 9], Operations: [] Exploring Operation: 99-49=50, Resulting Numbers: [20, 9, 50] Generated Node #0,0: 32:[20, 9, 50] Operation: 99-49=50 Exploring Operation: 99-20=79, Resulting Numbers: [49, 9, 79] Generated Node #0,1: 32:[49, 9, 79] Operation: 99-20=79 Exploring Operation: 99/9=11, Resulting Numbers: [49, 20, 11] Generated Node #0,2: 32:[49, 20, 11] Operation: 99/9=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[20, 9, 50], Operations: ['99-49=50'] Exploring Operation: 50-9=41, Resulting Numbers: [20, 41] Generated Node #0,0,0: 32:[20, 41] Operation: 50-9=41 Exploring Operation: 20+9=29, Resulting Numbers: [50, 29] Generated Node #0,0,1: 32:[50, 29] Operation: 20+9=29 Exploring Operation: 50-20=30, Resulting Numbers: [9, 30] Generated Node #0,0,2: 32:[9, 30] Operation: 50-20=30 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 32:[9, 30], Operations: ['99-49=50', '50-20=30'] Exploring Operation: 9+30=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,32 unequal: No Solution Exploring Operation: 9*30=270, Resulting Numbers: [270] 270,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[20, 41], Operations: ['99-49=50', '50-9=41'] Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,32 unequal: No Solution Exploring Operation: 20+41=61, Resulting Numbers: [61] 61,32 unequal: No Solution Exploring Operation: 20*41=820, Resulting Numbers: [820] 820,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 32:[50, 29], Operations: ['99-49=50', '20+9=29'] Exploring Operation: 50*29=1450, Resulting Numbers: [1450] 1450,32 unequal: No Solution Exploring Operation: 50-29=21, Resulting Numbers: [21] 21,32 unequal: No Solution Exploring Operation: 50+29=79, Resulting Numbers: [79] 79,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[49, 20, 11], Operations: ['99/9=11'] Exploring Operation: 49-20=29, Resulting Numbers: [11, 29] Generated Node #0,2,0: 32:[11, 29] Operation: 49-20=29 Exploring Operation: 49-11=38, Resulting Numbers: [20, 38] Generated Node #0,2,1: 32:[20, 38] Operation: 49-11=38 Exploring Operation: 20+11=31, Resulting Numbers: [49, 31] Generated Node #0,2,2: 32:[49, 31] Operation: 20+11=31 Moving to Node #0,2,0 Current State: 32:[11, 29], Operations: ['99/9=11', '49-20=29'] Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 11+29=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 11*29=319, Resulting Numbers: [319] 319,32 unequal: No Solution Moving to Node #0,2,1 Current State: 32:[20, 38], Operations: ['99/9=11', '49-11=38'] Exploring Operation: 20*38=760, Resulting Numbers: [760] 760,32 unequal: No Solution Exploring Operation: 38-20=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 20+38=58, Resulting Numbers: [58] 58,32 unequal: No Solution Moving to Node #0,2,2 Current State: 32:[49, 31], Operations: ['99/9=11', '20+11=31'] Exploring Operation: 49-31=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 49+31=80, Resulting Numbers: [80] 80,32 unequal: No Solution Exploring Operation: 49*31=1519, Resulting Numbers: [1519] 1519,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[49, 9, 79], Operations: ['99-20=79'] Exploring Operation: 79-49=30, Resulting Numbers: [9, 30] Generated Node #0,1,0: 32:[9, 30] Operation: 79-49=30 Exploring Operation: 79-9=70, Resulting Numbers: [49, 70] Generated Node #0,1,1: 32:[49, 70] Operation: 79-9=70 Exploring Operation: 49-9=40, Resulting Numbers: [79, 40] Generated Node #0,1,2: 32:[79, 40] Operation: 49-9=40 Moving to Node #0,1,0 Current State: 32:[9, 30], Operations: ['99-20=79', '79-49=30'] Exploring Operation: 9*30=270, Resulting Numbers: [270] 270,32 unequal: No Solution Exploring Operation: 9+30=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,32 unequal: No Solution Moving to Node #0,1,1 Current State: 32:[49, 70], Operations: ['99-20=79', '79-9=70'] Exploring Operation: 70-49=21, Resulting Numbers: [21] 21,32 unequal: No Solution Exploring Operation: 49*70=3430, Resulting Numbers: [3430] 3430,32 unequal: No Solution Exploring Operation: 49+70=119, Resulting Numbers: [119] 119,32 unequal: No Solution Moving to Node #0,1,2 Current State: 32:[79, 40], Operations: ['99-20=79', '49-9=40'] Exploring Operation: 79-40=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 79*40=3160, Resulting Numbers: [3160] 3160,32 unequal: No Solution Exploring Operation: 79+40=119, Resulting Numbers: [119] 119,32 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
[ 12, 3, 50, 5 ]
77
[ "12+50=62", "3*5=15", "62+15=77" ]
Current State: 77:[12, 3, 50, 5], Operations: [] Exploring Operation: 12+50=62, Resulting Numbers: [3, 5, 62] Generated Node #2: [3, 5, 62] from Operation: 12+50=62 Current State: 77:[3, 5, 62], Operations: ['12+50=62'] Exploring Operation: 3*5=15, Resulting Numbers: [62, 15] Generated Node #3: [62, 15] from Operation: 3*5=15 Current State: 77:[62, 15], Operations: ['12+50=62', '3*5=15'] Exploring Operation: 62+15=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[12, 3, 50, 5], Operations: [] Exploring Operation: 50/5=10, Resulting Numbers: [12, 3, 10] Generated Node #0,0: 77:[12, 3, 10] Operation: 50/5=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[12, 3, 10], Operations: ['50/5=10'] Exploring Operation: 10-3=7, Resulting Numbers: [12, 7] Generated Node #0,0,0: 77:[12, 7] Operation: 10-3=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[12, 7], Operations: ['50/5=10', '10-3=7'] Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,77 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
[ 11, 45, 2, 63 ]
38
[ "11-2=9", "63/9=7", "45-7=38" ]
Current State: 38:[11, 45, 2, 63], Operations: [] Exploring Operation: 11-2=9, Resulting Numbers: [45, 63, 9] Generated Node #2: [45, 63, 9] from Operation: 11-2=9 Current State: 38:[45, 63, 9], Operations: ['11-2=9'] Exploring Operation: 63/9=7, Resulting Numbers: [45, 7] Generated Node #3: [45, 7] from Operation: 63/9=7 Current State: 38:[45, 7], Operations: ['11-2=9', '63/9=7'] Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[11, 45, 2, 63], Operations: [] Exploring Operation: 63-45=18, Resulting Numbers: [11, 2, 18] Generated Node #0,0: 38:[11, 2, 18] Operation: 63-45=18 Moving to Node #0,0 Current State: 38:[11, 2, 18], Operations: ['63-45=18'] Exploring Operation: 11*2=22, Resulting Numbers: [18, 22] Generated Node #0,0,0: 38:[18, 22] Operation: 11*2=22 Moving to Node #0,0,0 Current State: 38:[18, 22], Operations: ['63-45=18', '11*2=22'] Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,38 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 46, 14, 16, 36 ]
13
[ "16-14=2", "46/2=23", "36-23=13" ]
Current State: 13:[46, 14, 16, 36], Operations: [] Exploring Operation: 16-14=2, Resulting Numbers: [46, 36, 2] Generated Node #2: [46, 36, 2] from Operation: 16-14=2 Current State: 13:[46, 36, 2], Operations: ['16-14=2'] Exploring Operation: 46/2=23, Resulting Numbers: [36, 23] Generated Node #3: [36, 23] from Operation: 46/2=23 Current State: 13:[36, 23], Operations: ['16-14=2', '46/2=23'] Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[46, 14, 16, 36], Operations: [] Exploring Operation: 46-16=30, Resulting Numbers: [14, 36, 30] Generated Node #0,0: 13:[14, 36, 30] Operation: 46-16=30 Exploring Operation: 46-36=10, Resulting Numbers: [14, 16, 10] Generated Node #0,1: 13:[14, 16, 10] Operation: 46-36=10 Exploring Operation: 36-16=20, Resulting Numbers: [46, 14, 20] Generated Node #0,2: 13:[46, 14, 20] Operation: 36-16=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[14, 16, 10], Operations: ['46-36=10'] Exploring Operation: 16-10=6, Resulting Numbers: [14, 6] Generated Node #0,1,0: 13:[14, 6] Operation: 16-10=6 Exploring Operation: 16-14=2, Resulting Numbers: [10, 2] Generated Node #0,1,1: 13:[10, 2] Operation: 16-14=2 Exploring Operation: 14-10=4, Resulting Numbers: [16, 4] Generated Node #0,1,2: 13:[16, 4] Operation: 14-10=4 Moving to Node #0,1,0 Current State: 13:[14, 6], Operations: ['46-36=10', '16-10=6'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 14*6=84, Resulting Numbers: [84] 84,13 unequal: No Solution Moving to Node #0,1,2 Current State: 13:[16, 4], Operations: ['46-36=10', '14-10=4'] Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,13 unequal: No Solution Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[10, 2], Operations: ['46-36=10', '16-14=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,13 unequal: No Solution No 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: 13:[14, 36, 30], Operations: ['46-16=30'] Exploring Operation: 30-14=16, Resulting Numbers: [36, 16] Generated Node #0,0,0: 13:[36, 16] Operation: 30-14=16 Exploring Operation: 36-14=22, Resulting Numbers: [30, 22] Generated Node #0,0,1: 13:[30, 22] Operation: 36-14=22 Exploring Operation: 36-30=6, Resulting Numbers: [14, 6] Generated Node #0,0,2: 13:[14, 6] Operation: 36-30=6 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 13:[14, 6], Operations: ['46-16=30', '36-30=6'] Exploring Operation: 14*6=84, Resulting Numbers: [84] 84,13 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,13 unequal: No Solution No 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: 13:[36, 16], Operations: ['46-16=30', '30-14=16'] Exploring Operation: 36+16=52, Resulting Numbers: [52] 52,13 unequal: No Solution Exploring Operation: 36*16=576, Resulting Numbers: [576] 576,13 unequal: No Solution Exploring Operation: 36-16=20, Resulting Numbers: [20] 20,13 unequal: No Solution No 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: 13:[30, 22], Operations: ['46-16=30', '36-14=22'] Exploring Operation: 30*22=660, Resulting Numbers: [660] 660,13 unequal: No Solution Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,13 unequal: No Solution Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,13 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: 13:[46, 14, 20], Operations: ['36-16=20'] Exploring Operation: 46-20=26, Resulting Numbers: [14, 26] Generated Node #0,2,0: 13:[14, 26] Operation: 46-20=26 Exploring Operation: 46-14=32, Resulting Numbers: [20, 32] Generated Node #0,2,1: 13:[20, 32] Operation: 46-14=32 Exploring Operation: 20-14=6, Resulting Numbers: [46, 6] Generated Node #0,2,2: 13:[46, 6] Operation: 20-14=6 Moving to Node #0,2,0 Current State: 13:[14, 26], Operations: ['36-16=20', '46-20=26'] Exploring Operation: 14*26=364, Resulting Numbers: [364] 364,13 unequal: No Solution Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,13 unequal: No Solution Exploring Operation: 14+26=40, Resulting Numbers: [40] 40,13 unequal: No Solution Moving to Node #0,2,1 Current State: 13:[20, 32], Operations: ['36-16=20', '46-14=32'] Exploring Operation: 20+32=52, Resulting Numbers: [52] 52,13 unequal: No Solution Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,13 unequal: No Solution Exploring Operation: 20*32=640, Resulting Numbers: [640] 640,13 unequal: No Solution Moving to Node #0,2,2 Current State: 13:[46, 6], Operations: ['36-16=20', '20-14=6'] Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 46*6=276, Resulting Numbers: [276] 276,13 unequal: No Solution Exploring Operation: 46+6=52, Resulting Numbers: [52] 52,13 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
[ 77, 24, 3, 32 ]
72
[ "77+24=101", "32-3=29", "101-29=72" ]
Current State: 72:[77, 24, 3, 32], Operations: [] Exploring Operation: 77+24=101, Resulting Numbers: [3, 32, 101] Generated Node #2: [3, 32, 101] from Operation: 77+24=101 Current State: 72:[3, 32, 101], Operations: ['77+24=101'] Exploring Operation: 32-3=29, Resulting Numbers: [101, 29] Generated Node #3: [101, 29] from Operation: 32-3=29 Current State: 72:[101, 29], Operations: ['77+24=101', '32-3=29'] Exploring Operation: 101-29=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[77, 24, 3, 32], Operations: [] Exploring Operation: 77-3=74, Resulting Numbers: [24, 32, 74] Generated Node #0,0: 72:[24, 32, 74] Operation: 77-3=74 Exploring Operation: 77-32=45, Resulting Numbers: [24, 3, 45] Generated Node #0,1: 72:[24, 3, 45] Operation: 77-32=45 Exploring Operation: 3+32=35, Resulting Numbers: [77, 24, 35] Generated Node #0,2: 72:[77, 24, 35] Operation: 3+32=35 Exploring Operation: 32-24=8, Resulting Numbers: [77, 3, 8] Generated Node #0,3: 72:[77, 3, 8] Operation: 32-24=8 Exploring Operation: 24*3=72, Resulting Numbers: [77, 32, 72] Generated Node #0,4: 72:[77, 32, 72] Operation: 24*3=72 Moving to Node #0,3 Current State: 72:[77, 3, 8], Operations: ['32-24=8'] Exploring Operation: 3*8=24, Resulting Numbers: [77, 24] Generated Node #0,3,0: 72:[77, 24] Operation: 3*8=24 Exploring Operation: 8-3=5, Resulting Numbers: [77, 5] Generated Node #0,3,1: 72:[77, 5] Operation: 8-3=5 Exploring Operation: 3+8=11, Resulting Numbers: [77, 11] Generated Node #0,3,2: 72:[77, 11] Operation: 3+8=11 Exploring Operation: 77-3=74, Resulting Numbers: [8, 74] Generated Node #0,3,3: 72:[8, 74] Operation: 77-3=74 Exploring Operation: 77-8=69, Resulting Numbers: [3, 69] Generated Node #0,3,4: 72:[3, 69] Operation: 77-8=69 Moving to Node #0,2 Current State: 72:[77, 24, 35], Operations: ['3+32=35'] Exploring Operation: 24+35=59, Resulting Numbers: [77, 59] Generated Node #0,2,0: 72:[77, 59] Operation: 24+35=59 Exploring Operation: 77-24=53, Resulting Numbers: [35, 53] Generated Node #0,2,1: 72:[35, 53] Operation: 77-24=53 Exploring Operation: 77+24=101, Resulting Numbers: [35, 101] Generated Node #0,2,2: 72:[35, 101] Operation: 77+24=101 Exploring Operation: 77-35=42, Resulting Numbers: [24, 42] Generated Node #0,2,3: 72:[24, 42] Operation: 77-35=42 Exploring Operation: 35-24=11, Resulting Numbers: [77, 11] Generated Node #0,2,4: 72:[77, 11] Operation: 35-24=11 Moving to Node #0,0 Current State: 72:[24, 32, 74], Operations: ['77-3=74'] Exploring Operation: 24+74=98, Resulting Numbers: [32, 98] Generated Node #0,0,0: 72:[32, 98] Operation: 24+74=98 Exploring Operation: 74-24=50, Resulting Numbers: [32, 50] Generated Node #0,0,1: 72:[32, 50] Operation: 74-24=50 Exploring Operation: 74-32=42, Resulting Numbers: [24, 42] Generated Node #0,0,2: 72:[24, 42] Operation: 74-32=42 Exploring Operation: 24+32=56, Resulting Numbers: [74, 56] Generated Node #0,0,3: 72:[74, 56] Operation: 24+32=56 Exploring Operation: 32-24=8, Resulting Numbers: [74, 8] Generated Node #0,0,4: 72:[74, 8] Operation: 32-24=8 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 72:[74, 8], Operations: ['77-3=74', '32-24=8'] Exploring Operation: 74+8=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,72 unequal: No Solution Exploring Operation: 74*8=592, Resulting Numbers: [592] 592,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 72:[24, 42], Operations: ['77-3=74', '74-32=42'] Exploring Operation: 24*42=1008, Resulting Numbers: [1008] 1008,72 unequal: No Solution Exploring Operation: 24+42=66, Resulting Numbers: [66] 66,72 unequal: No Solution Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[32, 50], Operations: ['77-3=74', '74-24=50'] Exploring Operation: 32*50=1600, Resulting Numbers: [1600] 1600,72 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 72:[74, 56], Operations: ['77-3=74', '24+32=56'] Exploring Operation: 74+56=130, Resulting Numbers: [130] 130,72 unequal: No Solution Exploring Operation: 74*56=4144, Resulting Numbers: [4144] 4144,72 unequal: No Solution Exploring Operation: 74-56=18, Resulting Numbers: [18] 18,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[32, 98], Operations: ['77-3=74', '24+74=98'] Exploring Operation: 32*98=3136, Resulting Numbers: [3136] 3136,72 unequal: No Solution Exploring Operation: 32+98=130, Resulting Numbers: [130] 130,72 unequal: No Solution Exploring Operation: 98-32=66, Resulting Numbers: [66] 66,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 72:[24, 3, 45], Operations: ['77-32=45'] Exploring Operation: 24+45=69, Resulting Numbers: [3, 69] Generated Node #0,1,0: 72:[3, 69] Operation: 24+45=69 Exploring Operation: 45/3=15, Resulting Numbers: [24, 15] Generated Node #0,1,1: 72:[24, 15] Operation: 45/3=15 Exploring Operation: 24*3=72, Resulting Numbers: [45, 72] Generated Node #0,1,2: 72:[45, 72] Operation: 24*3=72 Exploring Operation: 45-24=21, Resulting Numbers: [3, 21] Generated Node #0,1,3: 72:[3, 21] Operation: 45-24=21 Exploring Operation: 45-3=42, Resulting Numbers: [24, 42] Generated Node #0,1,4: 72:[24, 42] Operation: 45-3=42 Moving to Node #0,4 Current State: 72:[77, 32, 72], Operations: ['24*3=72'] Exploring Operation: 77+32=109, Resulting Numbers: [72, 109] Generated Node #0,4,0: 72:[72, 109] Operation: 77+32=109 Exploring Operation: 32+72=104, Resulting Numbers: [77, 104] Generated Node #0,4,1: 72:[77, 104] Operation: 32+72=104 Exploring Operation: 77-32=45, Resulting Numbers: [72, 45] Generated Node #0,4,2: 72:[72, 45] Operation: 77-32=45 Exploring Operation: 72-32=40, Resulting Numbers: [77, 40] Generated Node #0,4,3: 72:[77, 40] Operation: 72-32=40 Exploring Operation: 77-72=5, Resulting Numbers: [32, 5] Generated Node #0,4,4: 72:[32, 5] Operation: 77-72=5 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 72:[32, 5], Operations: ['24*3=72', '77-72=5'] Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 72:[72, 45], Operations: ['24*3=72', '77-32=45'] Exploring Operation: 72-45=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 72+45=117, Resulting Numbers: [117] 117,72 unequal: No Solution Exploring Operation: 72*45=3240, Resulting Numbers: [3240] 3240,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 72:[77, 40], Operations: ['24*3=72', '72-32=40'] Exploring Operation: 77-40=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 77*40=3080, Resulting Numbers: [3080] 3080,72 unequal: No Solution Exploring Operation: 77+40=117, Resulting Numbers: [117] 117,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 72:[72, 109], Operations: ['24*3=72', '77+32=109'] Exploring Operation: 72+109=181, Resulting Numbers: [181] 181,72 unequal: No Solution Exploring Operation: 109-72=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 72*109=7848, Resulting Numbers: [7848] 7848,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 72:[77, 104], Operations: ['24*3=72', '32+72=104'] Exploring Operation: 104-77=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 77+104=181, Resulting Numbers: [181] 181,72 unequal: No Solution Exploring Operation: 77*104=8008, Resulting Numbers: [8008] 8008,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,3 Current State: 72:[8, 74], Operations: ['32-24=8', '77-3=74'] Exploring Operation: 8+74=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,72 unequal: No Solution Exploring Operation: 8*74=592, Resulting Numbers: [592] 592,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[24, 15], Operations: ['77-32=45', '45/3=15'] Exploring Operation: 24*15=360, Resulting Numbers: [360] 360,72 unequal: No Solution Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,72 unequal: No Solution Moving to Node #0,1,3 Current State: 72:[3, 21], Operations: ['77-32=45', '45-24=21'] Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,72 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 3*21=63, Resulting Numbers: [63] 63,72 unequal: No Solution Moving to Node #0,3,4 Current State: 72:[3, 69], Operations: ['32-24=8', '77-8=69'] Exploring Operation: 3*69=207, Resulting Numbers: [207] 207,72 unequal: No Solution Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 3+69=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[77, 24, 3, 32], Operations: [] Exploring Operation: 32-24=8, Resulting Numbers: [77, 3, 8] Generated Node #0,3: 72:[77, 3, 8] Operation: 32-24=8 Moving to Node #0,3 Current State: 72:[77, 3, 8], Operations: ['32-24=8'] Exploring Operation: 77-8=69, Resulting Numbers: [3, 69] Generated Node #0,3,4: 72:[3, 69] Operation: 77-8=69 Moving to Node #0,3,4 Current State: 72:[3, 69], Operations: ['32-24=8', '77-8=69'] Exploring Operation: 3+69=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.93316
hs_5
mult_heuristic
[ 71, 10, 96, 9 ]
88
[ "71+9=80", "80/10=8", "96-8=88" ]
Current State: 88:[71, 10, 96, 9], Operations: [] Exploring Operation: 71+9=80, Resulting Numbers: [10, 96, 80] Generated Node #2: [10, 96, 80] from Operation: 71+9=80 Current State: 88:[10, 96, 80], Operations: ['71+9=80'] Exploring Operation: 80/10=8, Resulting Numbers: [96, 8] Generated Node #3: [96, 8] from Operation: 80/10=8 Current State: 88:[96, 8], Operations: ['71+9=80', '80/10=8'] Exploring Operation: 96-8=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[71, 10, 96, 9], Operations: [] Exploring Operation: 96-71=25, Resulting Numbers: [10, 9, 25] Generated Node #0,0: 88:[10, 9, 25] Operation: 96-71=25 Moving to Node #0,0 Current State: 88:[10, 9, 25], Operations: ['96-71=25'] Exploring Operation: 10-9=1, Resulting Numbers: [25, 1] Generated Node #0,0,0: 88:[25, 1] Operation: 10-9=1 Moving to Node #0,0,0 Current State: 88:[25, 1], Operations: ['96-71=25', '10-9=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,88 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 91, 57, 14, 4 ]
16
[ "91-57=34", "14+4=18", "34-18=16" ]
Current State: 16:[91, 57, 14, 4], Operations: [] Exploring Operation: 91-57=34, Resulting Numbers: [14, 4, 34] Generated Node #2: [14, 4, 34] from Operation: 91-57=34 Current State: 16:[14, 4, 34], Operations: ['91-57=34'] Exploring Operation: 14+4=18, Resulting Numbers: [34, 18] Generated Node #3: [34, 18] from Operation: 14+4=18 Current State: 16:[34, 18], Operations: ['91-57=34', '14+4=18'] Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[91, 57, 14, 4], Operations: [] Exploring Operation: 91-57=34, Resulting Numbers: [14, 4, 34] Generated Node #0,0: 16:[14, 4, 34] Operation: 91-57=34 Exploring Operation: 91-14=77, Resulting Numbers: [57, 4, 77] Generated Node #0,1: 16:[57, 4, 77] Operation: 91-14=77 Exploring Operation: 57-14=43, Resulting Numbers: [91, 4, 43] Generated Node #0,2: 16:[91, 4, 43] Operation: 57-14=43 Moving to Node #0,0 Current State: 16:[14, 4, 34], Operations: ['91-57=34'] Exploring Operation: 14+4=18, Resulting Numbers: [34, 18] Generated Node #0,0,0: 16:[34, 18] Operation: 14+4=18 Exploring Operation: 34-4=30, Resulting Numbers: [14, 30] Generated Node #0,0,1: 16:[14, 30] Operation: 34-4=30 Exploring Operation: 34-14=20, Resulting Numbers: [4, 20] Generated Node #0,0,2: 16:[4, 20] Operation: 34-14=20 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[4, 20], Operations: ['91-57=34', '34-14=20'] Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,16 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[91, 57, 14, 4], Operations: [] Exploring Operation: 91-57=34, Resulting Numbers: [14, 4, 34] Generated Node #0,0: 16:[14, 4, 34] Operation: 91-57=34 Moving to Node #0,0 Current State: 16:[14, 4, 34], Operations: ['91-57=34'] Exploring Operation: 34-14=20, Resulting Numbers: [4, 20] Generated Node #0,0,2: 16:[4, 20] Operation: 34-14=20 Moving to Node #0,0,2 Current State: 16:[4, 20], Operations: ['91-57=34', '34-14=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 66, 73, 57, 61 ]
28
[ "73-66=7", "61-57=4", "7*4=28" ]
Current State: 28:[66, 73, 57, 61], Operations: [] Exploring Operation: 73-66=7, Resulting Numbers: [57, 61, 7] Generated Node #2: [57, 61, 7] from Operation: 73-66=7 Current State: 28:[57, 61, 7], Operations: ['73-66=7'] Exploring Operation: 61-57=4, Resulting Numbers: [7, 4] Generated Node #3: [7, 4] from Operation: 61-57=4 Current State: 28:[7, 4], Operations: ['73-66=7', '61-57=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[66, 73, 57, 61], Operations: [] Exploring Operation: 73-66=7, Resulting Numbers: [57, 61, 7] Generated Node #0,0: 28:[57, 61, 7] Operation: 73-66=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[57, 61, 7], Operations: ['73-66=7'] Exploring Operation: 61-57=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 28:[7, 4] Operation: 61-57=4 Moving to Node #0,0,0 Current State: 28:[7, 4], Operations: ['73-66=7', '61-57=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[66, 73, 57, 61], Operations: [] Exploring Operation: 73-66=7, Resulting Numbers: [57, 61, 7] Generated Node #0,0: 28:[57, 61, 7] Operation: 73-66=7 Moving to Node #0,0 Current State: 28:[57, 61, 7], Operations: ['73-66=7'] Exploring Operation: 61-57=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 28:[7, 4] Operation: 61-57=4 Moving to Node #0,0,0 Current State: 28:[7, 4], Operations: ['73-66=7', '61-57=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 66, 22, 21, 20 ]
89
[ "66+22=88", "21-20=1", "88+1=89" ]
Current State: 89:[66, 22, 21, 20], Operations: [] Exploring Operation: 66+22=88, Resulting Numbers: [21, 20, 88] Generated Node #2: [21, 20, 88] from Operation: 66+22=88 Current State: 89:[21, 20, 88], Operations: ['66+22=88'] Exploring Operation: 21-20=1, Resulting Numbers: [88, 1] Generated Node #3: [88, 1] from Operation: 21-20=1 Current State: 89:[88, 1], Operations: ['66+22=88', '21-20=1'] Exploring Operation: 88+1=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[66, 22, 21, 20], Operations: [] Exploring Operation: 66+22=88, Resulting Numbers: [21, 20, 88] Generated Node #0,0: 89:[21, 20, 88] Operation: 66+22=88 Exploring Operation: 22+21=43, Resulting Numbers: [66, 20, 43] Generated Node #0,1: 89:[66, 20, 43] Operation: 22+21=43 Exploring Operation: 66+20=86, Resulting Numbers: [22, 21, 86] Generated Node #0,2: 89:[22, 21, 86] Operation: 66+20=86 Exploring Operation: 22+20=42, Resulting Numbers: [66, 21, 42] Generated Node #0,3: 89:[66, 21, 42] Operation: 22+20=42 Exploring Operation: 66+21=87, Resulting Numbers: [22, 20, 87] Generated Node #0,4: 89:[22, 20, 87] Operation: 66+21=87 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[21, 20, 88], Operations: ['66+22=88'] Exploring Operation: 20+88=108, Resulting Numbers: [21, 108] Generated Node #0,0,0: 89:[21, 108] Operation: 20+88=108 Exploring Operation: 21+88=109, Resulting Numbers: [20, 109] Generated Node #0,0,1: 89:[20, 109] Operation: 21+88=109 Exploring Operation: 21+20=41, Resulting Numbers: [88, 41] Generated Node #0,0,2: 89:[88, 41] Operation: 21+20=41 Exploring Operation: 88-20=68, Resulting Numbers: [21, 68] Generated Node #0,0,3: 89:[21, 68] Operation: 88-20=68 Exploring Operation: 21-20=1, Resulting Numbers: [88, 1] Generated Node #0,0,4: 89:[88, 1] Operation: 21-20=1 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[88, 41], Operations: ['66+22=88', '21+20=41'] Exploring Operation: 88-41=47, Resulting Numbers: [47] 47,89 unequal: No Solution Exploring Operation: 88*41=3608, Resulting Numbers: [3608] 3608,89 unequal: No Solution Exploring Operation: 88+41=129, Resulting Numbers: [129] 129,89 unequal: No Solution No 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: 89:[21, 108], Operations: ['66+22=88', '20+88=108'] Exploring Operation: 21*108=2268, Resulting Numbers: [2268] 2268,89 unequal: No Solution Exploring Operation: 108-21=87, Resulting Numbers: [87] 87,89 unequal: No Solution Exploring Operation: 21+108=129, Resulting Numbers: [129] 129,89 unequal: No Solution No 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: 89:[20, 109], Operations: ['66+22=88', '21+88=109'] Exploring Operation: 109-20=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[66, 22, 21, 20], Operations: [] Exploring Operation: 66+22=88, Resulting Numbers: [21, 20, 88] Generated Node #0,0: 89:[21, 20, 88] Operation: 66+22=88 Moving to Node #0,0 Current State: 89:[21, 20, 88], Operations: ['66+22=88'] Exploring Operation: 21+88=109, Resulting Numbers: [20, 109] Generated Node #0,0,1: 89:[20, 109] Operation: 21+88=109 Moving to Node #0,0,1 Current State: 89:[20, 109], Operations: ['66+22=88', '21+88=109'] Exploring Operation: 109-20=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 65, 61, 95, 24 ]
10
[ "65*24=1560", "61+95=156", "1560/156=10" ]
Current State: 10:[65, 61, 95, 24], Operations: [] Exploring Operation: 65*24=1560, Resulting Numbers: [61, 95, 1560] Generated Node #2: [61, 95, 1560] from Operation: 65*24=1560 Current State: 10:[61, 95, 1560], Operations: ['65*24=1560'] Exploring Operation: 61+95=156, Resulting Numbers: [1560, 156] Generated Node #3: [1560, 156] from Operation: 61+95=156 Current State: 10:[1560, 156], Operations: ['65*24=1560', '61+95=156'] Exploring Operation: 1560/156=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[65, 61, 95, 24], Operations: [] Exploring Operation: 95-65=30, Resulting Numbers: [61, 24, 30] Generated Node #0,0: 10:[61, 24, 30] Operation: 95-65=30 Exploring Operation: 95-61=34, Resulting Numbers: [65, 24, 34] Generated Node #0,1: 10:[65, 24, 34] Operation: 95-61=34 Exploring Operation: 65-61=4, Resulting Numbers: [95, 24, 4] Generated Node #0,2: 10:[95, 24, 4] Operation: 65-61=4 Moving to Node #0,0 Current State: 10:[61, 24, 30], Operations: ['95-65=30'] Exploring Operation: 61-30=31, Resulting Numbers: [24, 31] Generated Node #0,0,0: 10:[24, 31] Operation: 61-30=31 Exploring Operation: 30-24=6, Resulting Numbers: [61, 6] Generated Node #0,0,1: 10:[61, 6] Operation: 30-24=6 Exploring Operation: 61-24=37, Resulting Numbers: [30, 37] Generated Node #0,0,2: 10:[30, 37] Operation: 61-24=37 Moving to Node #0,1 Current State: 10:[65, 24, 34], Operations: ['95-61=34'] Exploring Operation: 65-24=41, Resulting Numbers: [34, 41] Generated Node #0,1,0: 10:[34, 41] Operation: 65-24=41 Exploring Operation: 65-34=31, Resulting Numbers: [24, 31] Generated Node #0,1,1: 10:[24, 31] Operation: 65-34=31 Exploring Operation: 34-24=10, Resulting Numbers: [65, 10] Generated Node #0,1,2: 10:[65, 10] Operation: 34-24=10 Moving to Node #0,2 Current State: 10:[95, 24, 4], Operations: ['65-61=4'] Exploring Operation: 24/4=6, Resulting Numbers: [95, 6] Generated Node #0,2,0: 10:[95, 6] Operation: 24/4=6 Exploring Operation: 95-4=91, Resulting Numbers: [24, 91] Generated Node #0,2,1: 10:[24, 91] Operation: 95-4=91 Exploring Operation: 95-24=71, Resulting Numbers: [4, 71] Generated Node #0,2,2: 10:[4, 71] Operation: 95-24=71 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 10:[4, 71], Operations: ['65-61=4', '95-24=71'] Exploring Operation: 4+71=75, Resulting Numbers: [75] 75,10 unequal: No Solution Exploring Operation: 4*71=284, Resulting Numbers: [284] 284,10 unequal: No Solution Exploring Operation: 71-4=67, Resulting Numbers: [67] 67,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 10:[95, 6], Operations: ['65-61=4', '24/4=6'] Exploring Operation: 95-6=89, Resulting Numbers: [89] 89,10 unequal: No Solution Exploring Operation: 95*6=570, Resulting Numbers: [570] 570,10 unequal: No Solution Exploring Operation: 95+6=101, Resulting Numbers: [101] 101,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 10:[24, 91], Operations: ['65-61=4', '95-4=91'] Exploring Operation: 24*91=2184, Resulting Numbers: [2184] 2184,10 unequal: No Solution Exploring Operation: 24+91=115, Resulting Numbers: [115] 115,10 unequal: No Solution Exploring Operation: 91-24=67, Resulting Numbers: [67] 67,10 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: 10:[24, 31], Operations: ['95-65=30', '61-30=31'] Exploring Operation: 24+31=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 24*31=744, Resulting Numbers: [744] 744,10 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,10 unequal: No Solution Moving to Node #0,1,1 Current State: 10:[24, 31], Operations: ['95-61=34', '65-34=31'] Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,10 unequal: No Solution Exploring Operation: 24+31=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 24*31=744, Resulting Numbers: [744] 744,10 unequal: No Solution Moving to Node #0,0,2 Current State: 10:[30, 37], Operations: ['95-65=30', '61-24=37'] Exploring Operation: 37-30=7, Resulting Numbers: [7] 7,10 unequal: No Solution Exploring Operation: 30*37=1110, Resulting Numbers: [1110] 1110,10 unequal: No Solution Exploring Operation: 30+37=67, Resulting Numbers: [67] 67,10 unequal: No Solution Moving to Node #0,0,1 Current State: 10:[61, 6], Operations: ['95-65=30', '30-24=6'] Exploring Operation: 61+6=67, Resulting Numbers: [67] 67,10 unequal: No Solution Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 61*6=366, Resulting Numbers: [366] 366,10 unequal: No Solution Moving to Node #0,1,2 Current State: 10:[65, 10], Operations: ['95-61=34', '34-24=10'] Exploring Operation: 65-10=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 65*10=650, Resulting Numbers: [650] 650,10 unequal: No Solution Exploring Operation: 65+10=75, Resulting Numbers: [75] 75,10 unequal: No Solution Moving to Node #0,1,0 Current State: 10:[34, 41], Operations: ['95-61=34', '65-24=41'] Exploring Operation: 34*41=1394, Resulting Numbers: [1394] 1394,10 unequal: No Solution Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,10 unequal: No Solution Exploring Operation: 34+41=75, Resulting Numbers: [75] 75,10 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 62, 15, 3, 51 ]
94
[ "62+15=77", "51/3=17", "77+17=94" ]
Current State: 94:[62, 15, 3, 51], Operations: [] Exploring Operation: 62+15=77, Resulting Numbers: [3, 51, 77] Generated Node #2: [3, 51, 77] from Operation: 62+15=77 Current State: 94:[3, 51, 77], Operations: ['62+15=77'] Exploring Operation: 51/3=17, Resulting Numbers: [77, 17] Generated Node #3: [77, 17] from Operation: 51/3=17 Current State: 94:[77, 17], Operations: ['62+15=77', '51/3=17'] Exploring Operation: 77+17=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[62, 15, 3, 51], Operations: [] Exploring Operation: 62-15=47, Resulting Numbers: [3, 51, 47] Generated Node #0,0: 94:[3, 51, 47] Operation: 62-15=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[3, 51, 47], Operations: ['62-15=47'] Exploring Operation: 51-3=48, Resulting Numbers: [47, 48] Generated Node #0,0,0: 94:[47, 48] Operation: 51-3=48 Moving to Node #0,0,0 Current State: 94:[47, 48], Operations: ['62-15=47', '51-3=48'] Exploring Operation: 47+48=95, Resulting Numbers: [95] 95,94 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
[ 83, 49, 34, 5 ]
73
[ "83-49=34", "34+5=39", "34+39=73" ]
Current State: 73:[83, 49, 34, 5], Operations: [] Exploring Operation: 83-49=34, Resulting Numbers: [34, 5, 34] Generated Node #2: [34, 5, 34] from Operation: 83-49=34 Current State: 73:[34, 5, 34], Operations: ['83-49=34'] Exploring Operation: 34+5=39, Resulting Numbers: [39] 39,73 equal: Goal Reached Exploring Operation: 34+39=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[83, 49, 34, 5], Operations: [] Exploring Operation: 83-5=78, Resulting Numbers: [49, 34, 78] Generated Node #0,0: 73:[49, 34, 78] Operation: 83-5=78 Exploring Operation: 49-5=44, Resulting Numbers: [83, 34, 44] Generated Node #0,1: 73:[83, 34, 44] Operation: 49-5=44 Exploring Operation: 83+5=88, Resulting Numbers: [49, 34, 88] Generated Node #0,2: 73:[49, 34, 88] Operation: 83+5=88 Exploring Operation: 49+5=54, Resulting Numbers: [83, 34, 54] Generated Node #0,3: 73:[83, 34, 54] Operation: 49+5=54 Exploring Operation: 34+5=39, Resulting Numbers: [83, 49, 39] Generated Node #0,4: 73:[83, 49, 39] Operation: 34+5=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[49, 34, 78], Operations: ['83-5=78'] Exploring Operation: 78-34=44, Resulting Numbers: [49, 44] Generated Node #0,0,0: 73:[49, 44] Operation: 78-34=44 Exploring Operation: 49-34=15, Resulting Numbers: [78, 15] Generated Node #0,0,1: 73:[78, 15] Operation: 49-34=15 Exploring Operation: 34+78=112, Resulting Numbers: [49, 112] Generated Node #0,0,2: 73:[49, 112] Operation: 34+78=112 Exploring Operation: 78-49=29, Resulting Numbers: [34, 29] Generated Node #0,0,3: 73:[34, 29] Operation: 78-49=29 Exploring Operation: 49+34=83, Resulting Numbers: [78, 83] Generated Node #0,0,4: 73:[78, 83] Operation: 49+34=83 Moving to Node #0,0,4 Current State: 73:[78, 83], Operations: ['83-5=78', '49+34=83'] Exploring Operation: 78*83=6474, Resulting Numbers: [6474] 6474,73 unequal: No Solution Exploring Operation: 78+83=161, Resulting Numbers: [161] 161,73 unequal: No Solution Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[49, 44], Operations: ['83-5=78', '78-34=44'] Exploring Operation: 49*44=2156, Resulting Numbers: [2156] 2156,73 unequal: No Solution Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,73 unequal: No Solution Exploring Operation: 49+44=93, Resulting Numbers: [93] 93,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[78, 15], Operations: ['83-5=78', '49-34=15'] Exploring Operation: 78*15=1170, Resulting Numbers: [1170] 1170,73 unequal: No Solution Exploring Operation: 78+15=93, Resulting Numbers: [93] 93,73 unequal: No Solution Exploring Operation: 78-15=63, Resulting Numbers: [63] 63,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[49, 112], Operations: ['83-5=78', '34+78=112'] Exploring Operation: 49+112=161, Resulting Numbers: [161] 161,73 unequal: No Solution Exploring Operation: 49*112=5488, Resulting Numbers: [5488] 5488,73 unequal: No Solution Exploring Operation: 112-49=63, Resulting Numbers: [63] 63,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[34, 29], Operations: ['83-5=78', '78-49=29'] Exploring Operation: 34*29=986, Resulting Numbers: [986] 986,73 unequal: No Solution Exploring Operation: 34+29=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 73:[83, 34, 54], Operations: ['49+5=54'] Exploring Operation: 83-34=49, Resulting Numbers: [54, 49] Generated Node #0,3,0: 73:[54, 49] Operation: 83-34=49 Exploring Operation: 34+54=88, Resulting Numbers: [83, 88] Generated Node #0,3,1: 73:[83, 88] Operation: 34+54=88 Exploring Operation: 83+34=117, Resulting Numbers: [54, 117] Generated Node #0,3,2: 73:[54, 117] Operation: 83+34=117 Exploring Operation: 54-34=20, Resulting Numbers: [83, 20] Generated Node #0,3,3: 73:[83, 20] Operation: 54-34=20 Exploring Operation: 83-54=29, Resulting Numbers: [34, 29] Generated Node #0,3,4: 73:[34, 29] Operation: 83-54=29 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 73:[83, 88], Operations: ['49+5=54', '34+54=88'] Exploring Operation: 88-83=5, Resulting Numbers: [5] 5,73 unequal: No Solution Exploring Operation: 83*88=7304, Resulting Numbers: [7304] 7304,73 unequal: No Solution Exploring Operation: 83+88=171, Resulting Numbers: [171] 171,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 73:[54, 49], Operations: ['49+5=54', '83-34=49'] Exploring Operation: 54+49=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 54*49=2646, Resulting Numbers: [2646] 2646,73 unequal: No Solution Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 73:[54, 117], Operations: ['49+5=54', '83+34=117'] Exploring Operation: 54*117=6318, Resulting Numbers: [6318] 6318,73 unequal: No Solution Exploring Operation: 54+117=171, Resulting Numbers: [171] 171,73 unequal: No Solution Exploring Operation: 117-54=63, Resulting Numbers: [63] 63,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 73:[83, 20], Operations: ['49+5=54', '54-34=20'] Exploring Operation: 83*20=1660, Resulting Numbers: [1660] 1660,73 unequal: No Solution Exploring Operation: 83-20=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 83+20=103, Resulting Numbers: [103] 103,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 73:[34, 29], Operations: ['49+5=54', '83-54=29'] Exploring Operation: 34+29=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,73 unequal: No Solution Exploring Operation: 34*29=986, Resulting Numbers: [986] 986,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 73:[83, 49, 39], Operations: ['34+5=39'] Exploring Operation: 83-39=44, Resulting Numbers: [49, 44] Generated Node #0,4,0: 73:[49, 44] Operation: 83-39=44 Exploring Operation: 49-39=10, Resulting Numbers: [83, 10] Generated Node #0,4,1: 73:[83, 10] Operation: 49-39=10 Exploring Operation: 83-49=34, Resulting Numbers: [39, 34] Generated Node #0,4,2: 73:[39, 34] Operation: 83-49=34 Exploring Operation: 49+39=88, Resulting Numbers: [83, 88] Generated Node #0,4,3: 73:[83, 88] Operation: 49+39=88 Exploring Operation: 83+39=122, Resulting Numbers: [49, 122] Generated Node #0,4,4: 73:[49, 122] Operation: 83+39=122 Moving to Node #0,4,3 Current State: 73:[83, 88], Operations: ['34+5=39', '49+39=88'] Exploring Operation: 83+88=171, Resulting Numbers: [171] 171,73 unequal: No Solution Exploring Operation: 88-83=5, Resulting Numbers: [5] 5,73 unequal: No Solution Exploring Operation: 83*88=7304, Resulting Numbers: [7304] 7304,73 unequal: No Solution Moving to Node #0,4,0 Current State: 73:[49, 44], Operations: ['34+5=39', '83-39=44'] Exploring Operation: 49+44=93, Resulting Numbers: [93] 93,73 unequal: No Solution Exploring Operation: 49*44=2156, Resulting Numbers: [2156] 2156,73 unequal: No Solution Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,73 unequal: No Solution Moving to Node #0,4,1 Current State: 73:[83, 10], Operations: ['34+5=39', '49-39=10'] Exploring Operation: 83+10=93, Resulting Numbers: [93] 93,73 unequal: No Solution Exploring Operation: 83*10=830, Resulting Numbers: [830] 830,73 unequal: No Solution Exploring Operation: 83-10=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[83, 49, 34, 5], Operations: [] Exploring Operation: 34+5=39, Resulting Numbers: [83, 49, 39] Generated Node #0,4: 73:[83, 49, 39] Operation: 34+5=39 Moving to Node #0,4 Current State: 73:[83, 49, 39], Operations: ['34+5=39'] Exploring Operation: 49-39=10, Resulting Numbers: [83, 10] Generated Node #0,4,1: 73:[83, 10] Operation: 49-39=10 Moving to Node #0,4,1 Current State: 73:[83, 10], Operations: ['34+5=39', '49-39=10'] Exploring Operation: 83-10=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.945313
hs_5
mult_heuristic
[ 25, 71, 88, 54 ]
27
[ "88+54=142", "142/71=2", "25+2=27" ]
Current State: 27:[25, 71, 88, 54], Operations: [] Exploring Operation: 88+54=142, Resulting Numbers: [25, 71, 142] Generated Node #2: [25, 71, 142] from Operation: 88+54=142 Current State: 27:[25, 71, 142], Operations: ['88+54=142'] Exploring Operation: 142/71=2, Resulting Numbers: [25, 2] Generated Node #3: [25, 2] from Operation: 142/71=2 Current State: 27:[25, 2], Operations: ['88+54=142', '142/71=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[25, 71, 88, 54], Operations: [] Exploring Operation: 88-71=17, Resulting Numbers: [25, 54, 17] Generated Node #0,0: 27:[25, 54, 17] Operation: 88-71=17 Exploring Operation: 71-54=17, Resulting Numbers: [25, 88, 17] Generated Node #0,1: 27:[25, 88, 17] Operation: 71-54=17 Exploring Operation: 88-54=34, Resulting Numbers: [25, 71, 34] Generated Node #0,2: 27:[25, 71, 34] Operation: 88-54=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[25, 54, 17], Operations: ['88-71=17'] Exploring Operation: 54-25=29, Resulting Numbers: [17, 29] Generated Node #0,0,0: 27:[17, 29] Operation: 54-25=29 Exploring Operation: 54-17=37, Resulting Numbers: [25, 37] Generated Node #0,0,1: 27:[25, 37] Operation: 54-17=37 Exploring Operation: 25-17=8, Resulting Numbers: [54, 8] Generated Node #0,0,2: 27:[54, 8] Operation: 25-17=8 Moving to Node #0,0,0 Current State: 27:[17, 29], Operations: ['88-71=17', '54-25=29'] Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 17+29=46, Resulting Numbers: [46] 46,27 unequal: No Solution Exploring Operation: 17*29=493, Resulting Numbers: [493] 493,27 unequal: No Solution Moving to Node #0,0,1 Current State: 27:[25, 37], Operations: ['88-71=17', '54-17=37'] Exploring Operation: 25*37=925, Resulting Numbers: [925] 925,27 unequal: No Solution Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,27 unequal: No Solution Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[54, 8], Operations: ['88-71=17', '25-17=8'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,27 unequal: No Solution Exploring Operation: 54*8=432, Resulting Numbers: [432] 432,27 unequal: No Solution Exploring Operation: 54+8=62, Resulting Numbers: [62] 62,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[25, 71, 34], Operations: ['88-54=34'] Exploring Operation: 71-34=37, Resulting Numbers: [25, 37] Generated Node #0,2,0: 27:[25, 37] Operation: 71-34=37 Exploring Operation: 71-25=46, Resulting Numbers: [34, 46] Generated Node #0,2,1: 27:[34, 46] Operation: 71-25=46 Exploring Operation: 34-25=9, Resulting Numbers: [71, 9] Generated Node #0,2,2: 27:[71, 9] Operation: 34-25=9 Moving to Node #0,2,0 Current State: 27:[25, 37], Operations: ['88-54=34', '71-34=37'] Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,27 unequal: No Solution Exploring Operation: 25*37=925, Resulting Numbers: [925] 925,27 unequal: No Solution Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,27 unequal: No Solution Moving to Node #0,2,1 Current State: 27:[34, 46], Operations: ['88-54=34', '71-25=46'] Exploring Operation: 34*46=1564, Resulting Numbers: [1564] 1564,27 unequal: No Solution Exploring Operation: 46-34=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 34+46=80, Resulting Numbers: [80] 80,27 unequal: No Solution Moving to Node #0,2,2 Current State: 27:[71, 9], Operations: ['88-54=34', '34-25=9'] Exploring Operation: 71*9=639, Resulting Numbers: [639] 639,27 unequal: No Solution Exploring Operation: 71+9=80, Resulting Numbers: [80] 80,27 unequal: No Solution Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[25, 88, 17], Operations: ['71-54=17'] Exploring Operation: 88-17=71, Resulting Numbers: [25, 71] Generated Node #0,1,0: 27:[25, 71] Operation: 88-17=71 Exploring Operation: 25-17=8, Resulting Numbers: [88, 8] Generated Node #0,1,1: 27:[88, 8] Operation: 25-17=8 Exploring Operation: 88-25=63, Resulting Numbers: [17, 63] Generated Node #0,1,2: 27:[17, 63] Operation: 88-25=63 Moving to Node #0,1,2 Current State: 27:[17, 63], Operations: ['71-54=17', '88-25=63'] Exploring Operation: 17*63=1071, Resulting Numbers: [1071] 1071,27 unequal: No Solution Exploring Operation: 63-17=46, Resulting Numbers: [46] 46,27 unequal: No Solution Exploring Operation: 17+63=80, Resulting Numbers: [80] 80,27 unequal: No Solution Moving to Node #0,1,0 Current State: 27:[25, 71], Operations: ['71-54=17', '88-17=71'] Exploring Operation: 25*71=1775, Resulting Numbers: [1775] 1775,27 unequal: No Solution Exploring Operation: 71-25=46, Resulting Numbers: [46] 46,27 unequal: No Solution Exploring Operation: 25+71=96, Resulting Numbers: [96] 96,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[88, 8], Operations: ['71-54=17', '25-17=8'] Exploring Operation: 88/8=11, Resulting Numbers: [11] 11,27 unequal: No Solution Exploring Operation: 88-8=80, Resulting Numbers: [80] 80,27 unequal: No Solution Exploring Operation: 88+8=96, Resulting Numbers: [96] 96,27 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
[ 54, 35, 90, 29 ]
24
[ "54+90=144", "35-29=6", "144/6=24" ]
Current State: 24:[54, 35, 90, 29], Operations: [] Exploring Operation: 54+90=144, Resulting Numbers: [35, 29, 144] Generated Node #2: [35, 29, 144] from Operation: 54+90=144 Current State: 24:[35, 29, 144], Operations: ['54+90=144'] Exploring Operation: 35-29=6, Resulting Numbers: [144, 6] Generated Node #3: [144, 6] from Operation: 35-29=6 Current State: 24:[144, 6], Operations: ['54+90=144', '35-29=6'] Exploring Operation: 144/6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[54, 35, 90, 29], Operations: [] Exploring Operation: 90-54=36, Resulting Numbers: [35, 29, 36] Generated Node #0,0: 24:[35, 29, 36] Operation: 90-54=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[35, 29, 36], Operations: ['90-54=36'] Exploring Operation: 36-35=1, Resulting Numbers: [29, 1] Generated Node #0,0,0: 24:[29, 1] Operation: 36-35=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[29, 1], Operations: ['90-54=36', '36-35=1'] Exploring Operation: 29-1=28, Resulting Numbers: [28] 28,24 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_1
mult_heuristic
[ 93, 27, 41, 56 ]
81
[ "93-27=66", "56-41=15", "66+15=81" ]
Current State: 81:[93, 27, 41, 56], Operations: [] Exploring Operation: 93-27=66, Resulting Numbers: [41, 56, 66] Generated Node #2: [41, 56, 66] from Operation: 93-27=66 Current State: 81:[41, 56, 66], Operations: ['93-27=66'] Exploring Operation: 56-41=15, Resulting Numbers: [66, 15] Generated Node #3: [66, 15] from Operation: 56-41=15 Current State: 81:[66, 15], Operations: ['93-27=66', '56-41=15'] Exploring Operation: 66+15=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[93, 27, 41, 56], Operations: [] Exploring Operation: 56-41=15, Resulting Numbers: [93, 27, 15] Generated Node #0,0: 81:[93, 27, 15] Operation: 56-41=15 Exploring Operation: 27+56=83, Resulting Numbers: [93, 41, 83] Generated Node #0,1: 81:[93, 41, 83] Operation: 27+56=83 Exploring Operation: 93-56=37, Resulting Numbers: [27, 41, 37] Generated Node #0,2: 81:[27, 41, 37] Operation: 93-56=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[93, 27, 15], Operations: ['56-41=15'] Exploring Operation: 93-15=78, Resulting Numbers: [27, 78] Generated Node #0,0,0: 81:[27, 78] Operation: 93-15=78 Exploring Operation: 27-15=12, Resulting Numbers: [93, 12] Generated Node #0,0,1: 81:[93, 12] Operation: 27-15=12 Exploring Operation: 93-27=66, Resulting Numbers: [15, 66] Generated Node #0,0,2: 81:[15, 66] Operation: 93-27=66 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[27, 78], Operations: ['56-41=15', '93-15=78'] Exploring Operation: 27+78=105, Resulting Numbers: [105] 105,81 unequal: No Solution Exploring Operation: 27*78=2106, Resulting Numbers: [2106] 2106,81 unequal: No Solution Exploring Operation: 78-27=51, Resulting Numbers: [51] 51,81 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 #0,0,1 Current State: 81:[93, 12], Operations: ['56-41=15', '27-15=12'] Exploring Operation: 93-12=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[93, 27, 41, 56], Operations: [] Exploring Operation: 56-41=15, Resulting Numbers: [93, 27, 15] Generated Node #0,0: 81:[93, 27, 15] Operation: 56-41=15 Moving to Node #0,0 Current State: 81:[93, 27, 15], Operations: ['56-41=15'] Exploring Operation: 27-15=12, Resulting Numbers: [93, 12] Generated Node #0,0,1: 81:[93, 12] Operation: 27-15=12 Moving to Node #0,0,1 Current State: 81:[93, 12], Operations: ['56-41=15', '27-15=12'] Exploring Operation: 93-12=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 93, 44, 2, 39 ]
83
[ "44-39=5", "2*5=10", "93-10=83" ]
Current State: 83:[93, 44, 2, 39], Operations: [] Exploring Operation: 44-39=5, Resulting Numbers: [93, 2, 5] Generated Node #2: [93, 2, 5] from Operation: 44-39=5 Current State: 83:[93, 2, 5], Operations: ['44-39=5'] Exploring Operation: 2*5=10, Resulting Numbers: [93, 10] Generated Node #3: [93, 10] from Operation: 2*5=10 Current State: 83:[93, 10], Operations: ['44-39=5', '2*5=10'] Exploring Operation: 93-10=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[93, 44, 2, 39], Operations: [] Exploring Operation: 44*2=88, Resulting Numbers: [93, 39, 88] Generated Node #0,0: 83:[93, 39, 88] Operation: 44*2=88 Exploring Operation: 44+2=46, Resulting Numbers: [93, 39, 46] Generated Node #0,1: 83:[93, 39, 46] Operation: 44+2=46 Exploring Operation: 93-2=91, Resulting Numbers: [44, 39, 91] Generated Node #0,2: 83:[44, 39, 91] Operation: 93-2=91 Exploring Operation: 2*39=78, Resulting Numbers: [93, 44, 78] Generated Node #0,3: 83:[93, 44, 78] Operation: 2*39=78 Start Sub Search at level 1: Moving to Node #0,3 Current State: 83:[93, 44, 78], Operations: ['2*39=78'] Exploring Operation: 44+78=122, Resulting Numbers: [93, 122] Generated Node #0,3,0: 83:[93, 122] Operation: 44+78=122 Exploring Operation: 93+44=137, Resulting Numbers: [78, 137] Generated Node #0,3,1: 83:[78, 137] Operation: 93+44=137 Exploring Operation: 93-44=49, Resulting Numbers: [78, 49] Generated Node #0,3,2: 83:[78, 49] Operation: 93-44=49 Exploring Operation: 78-44=34, Resulting Numbers: [93, 34] Generated Node #0,3,3: 83:[93, 34] Operation: 78-44=34 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 83:[78, 49], Operations: ['2*39=78', '93-44=49'] Exploring Operation: 78+49=127, Resulting Numbers: [127] 127,83 unequal: No Solution Exploring Operation: 78*49=3822, Resulting Numbers: [3822] 3822,83 unequal: No Solution Exploring Operation: 78-49=29, Resulting Numbers: [29] 29,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 83:[93, 122], Operations: ['2*39=78', '44+78=122'] Exploring Operation: 122-93=29, Resulting Numbers: [29] 29,83 unequal: No Solution Exploring Operation: 93*122=11346, Resulting Numbers: [11346] 11346,83 unequal: No Solution Exploring Operation: 93+122=215, Resulting Numbers: [215] 215,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 83:[78, 137], Operations: ['2*39=78', '93+44=137'] Exploring Operation: 78*137=10686, Resulting Numbers: [10686] 10686,83 unequal: No Solution Exploring Operation: 78+137=215, Resulting Numbers: [215] 215,83 unequal: No Solution Exploring Operation: 137-78=59, Resulting Numbers: [59] 59,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 83:[93, 34], Operations: ['2*39=78', '78-44=34'] Exploring Operation: 93-34=59, Resulting Numbers: [59] 59,83 unequal: No Solution Exploring Operation: 93+34=127, Resulting Numbers: [127] 127,83 unequal: No Solution Exploring Operation: 93*34=3162, Resulting Numbers: [3162] 3162,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[93, 39, 88], Operations: ['44*2=88'] Exploring Operation: 88-39=49, Resulting Numbers: [93, 49] Generated Node #0,0,0: 83:[93, 49] Operation: 88-39=49 Exploring Operation: 93+39=132, Resulting Numbers: [88, 132] Generated Node #0,0,1: 83:[88, 132] Operation: 93+39=132 Exploring Operation: 93-39=54, Resulting Numbers: [88, 54] Generated Node #0,0,2: 83:[88, 54] Operation: 93-39=54 Exploring Operation: 39+88=127, Resulting Numbers: [93, 127] Generated Node #0,0,3: 83:[93, 127] Operation: 39+88=127 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 83:[88, 54], Operations: ['44*2=88', '93-39=54'] Exploring Operation: 88*54=4752, Resulting Numbers: [4752] 4752,83 unequal: No Solution Exploring Operation: 88-54=34, Resulting Numbers: [34] 34,83 unequal: No Solution Exploring Operation: 88+54=142, Resulting Numbers: [142] 142,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[93, 49], Operations: ['44*2=88', '88-39=49'] Exploring Operation: 93+49=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 93*49=4557, Resulting Numbers: [4557] 4557,83 unequal: No Solution Exploring Operation: 93-49=44, Resulting Numbers: [44] 44,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[88, 132], Operations: ['44*2=88', '93+39=132'] Exploring Operation: 88*132=11616, Resulting Numbers: [11616] 11616,83 unequal: No Solution Exploring Operation: 88+132=220, Resulting Numbers: [220] 220,83 unequal: No Solution Exploring Operation: 132-88=44, Resulting Numbers: [44] 44,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 83:[93, 127], Operations: ['44*2=88', '39+88=127'] Exploring Operation: 93+127=220, Resulting Numbers: [220] 220,83 unequal: No Solution Exploring Operation: 127-93=34, Resulting Numbers: [34] 34,83 unequal: No Solution Exploring Operation: 93*127=11811, Resulting Numbers: [11811] 11811,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[93, 39, 46], Operations: ['44+2=46'] Exploring Operation: 93-39=54, Resulting Numbers: [46, 54] Generated Node #0,1,0: 83:[46, 54] Operation: 93-39=54 Exploring Operation: 93+39=132, Resulting Numbers: [46, 132] Generated Node #0,1,1: 83:[46, 132] Operation: 93+39=132 Exploring Operation: 93-46=47, Resulting Numbers: [39, 47] Generated Node #0,1,2: 83:[39, 47] Operation: 93-46=47 Exploring Operation: 39+46=85, Resulting Numbers: [93, 85] Generated Node #0,1,3: 83:[93, 85] Operation: 39+46=85 Moving to Node #0,1,3 Current State: 83:[93, 85], Operations: ['44+2=46', '39+46=85'] Exploring Operation: 93*85=7905, Resulting Numbers: [7905] 7905,83 unequal: No Solution Exploring Operation: 93-85=8, Resulting Numbers: [8] 8,83 unequal: No Solution Exploring Operation: 93+85=178, Resulting Numbers: [178] 178,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[46, 54], Operations: ['44+2=46', '93-39=54'] Exploring Operation: 46*54=2484, Resulting Numbers: [2484] 2484,83 unequal: No Solution Exploring Operation: 46+54=100, Resulting Numbers: [100] 100,83 unequal: No Solution Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[39, 47], Operations: ['44+2=46', '93-46=47'] Exploring Operation: 39*47=1833, Resulting Numbers: [1833] 1833,83 unequal: No Solution Exploring Operation: 39+47=86, Resulting Numbers: [86] 86,83 unequal: No Solution Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[46, 132], Operations: ['44+2=46', '93+39=132'] Exploring Operation: 46*132=6072, Resulting Numbers: [6072] 6072,83 unequal: No Solution Exploring Operation: 46+132=178, Resulting Numbers: [178] 178,83 unequal: No Solution Exploring Operation: 132-46=86, Resulting Numbers: [86] 86,83 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 Current State: 83:[44, 39, 91], Operations: ['93-2=91'] Exploring Operation: 44+39=83, Resulting Numbers: [91, 83] Generated Node #0,2,0: 83:[91, 83] Operation: 44+39=83 Exploring Operation: 91-44=47, Resulting Numbers: [39, 47] Generated Node #0,2,1: 83:[39, 47] Operation: 91-44=47 Exploring Operation: 44-39=5, Resulting Numbers: [91, 5] Generated Node #0,2,2: 83:[91, 5] Operation: 44-39=5 Exploring Operation: 91-39=52, Resulting Numbers: [44, 52] Generated Node #0,2,3: 83:[44, 52] Operation: 91-39=52 Moving to Node #0,2,0 Current State: 83:[91, 83], Operations: ['93-2=91', '44+39=83'] Exploring Operation: 91+83=174, Resulting Numbers: [174] 174,83 unequal: No Solution Exploring Operation: 91*83=7553, Resulting Numbers: [7553] 7553,83 unequal: No Solution Exploring Operation: 91-83=8, Resulting Numbers: [8] 8,83 unequal: No Solution Moving to Node #0,2,3 Current State: 83:[44, 52], Operations: ['93-2=91', '91-39=52'] Exploring Operation: 52-44=8, Resulting Numbers: [8] 8,83 unequal: No Solution Exploring Operation: 44*52=2288, Resulting Numbers: [2288] 2288,83 unequal: No Solution Exploring Operation: 44+52=96, Resulting Numbers: [96] 96,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[39, 47], Operations: ['93-2=91', '91-44=47'] Exploring Operation: 39*47=1833, Resulting Numbers: [1833] 1833,83 unequal: No Solution Exploring Operation: 39+47=86, Resulting Numbers: [86] 86,83 unequal: No Solution Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[91, 5], Operations: ['93-2=91', '44-39=5'] Exploring Operation: 91+5=96, Resulting Numbers: [96] 96,83 unequal: No Solution Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,83 unequal: No Solution Exploring Operation: 91*5=455, Resulting Numbers: [455] 455,83 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
[ 44, 81, 84, 83 ]
86
[ "83-81=2", "84/2=42", "44+42=86" ]
Current State: 86:[44, 81, 84, 83], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [44, 84, 2] Generated Node #2: [44, 84, 2] from Operation: 83-81=2 Current State: 86:[44, 84, 2], Operations: ['83-81=2'] Exploring Operation: 84/2=42, Resulting Numbers: [44, 42] Generated Node #3: [44, 42] from Operation: 84/2=42 Current State: 86:[44, 42], Operations: ['83-81=2', '84/2=42'] Exploring Operation: 44+42=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[44, 81, 84, 83], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [44, 83, 3] Generated Node #0,0: 86:[44, 83, 3] Operation: 84-81=3 Exploring Operation: 84-83=1, Resulting Numbers: [44, 81, 1] Generated Node #0,1: 86:[44, 81, 1] Operation: 84-83=1 Exploring Operation: 83-81=2, Resulting Numbers: [44, 84, 2] Generated Node #0,2: 86:[44, 84, 2] Operation: 83-81=2 Moving to Node #0,2 Current State: 86:[44, 84, 2], Operations: ['83-81=2'] Exploring Operation: 84-44=40, Resulting Numbers: [2, 40] Generated Node #0,2,0: 86:[2, 40] Operation: 84-44=40 Exploring Operation: 84+2=86, Resulting Numbers: [44, 86] Generated Node #0,2,1: 86:[44, 86] Operation: 84+2=86 Exploring Operation: 84/2=42, Resulting Numbers: [44, 42] Generated Node #0,2,2: 86:[44, 42] Operation: 84/2=42 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 86:[44, 86], Operations: ['83-81=2', '84+2=86'] Exploring Operation: 44+86=130, Resulting Numbers: [130] 130,86 unequal: No Solution Exploring Operation: 86-44=42, Resulting Numbers: [42] 42,86 unequal: No Solution Exploring Operation: 44*86=3784, Resulting Numbers: [3784] 3784,86 unequal: No Solution No 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: 86:[44, 42], Operations: ['83-81=2', '84/2=42'] Exploring Operation: 44+42=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[44, 81, 84, 83], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [44, 84, 2] Generated Node #0,2: 86:[44, 84, 2] Operation: 83-81=2 Moving to Node #0,2 Current State: 86:[44, 84, 2], Operations: ['83-81=2'] Exploring Operation: 84/2=42, Resulting Numbers: [44, 42] Generated Node #0,2,2: 86:[44, 42] Operation: 84/2=42 Moving to Node #0,2,2 Current State: 86:[44, 42], Operations: ['83-81=2', '84/2=42'] Exploring Operation: 44+42=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 24, 3, 45, 30 ]
36
[ "24-3=21", "45-30=15", "21+15=36" ]
Current State: 36:[24, 3, 45, 30], Operations: [] Exploring Operation: 24-3=21, Resulting Numbers: [45, 30, 21] Generated Node #2: [45, 30, 21] from Operation: 24-3=21 Current State: 36:[45, 30, 21], Operations: ['24-3=21'] Exploring Operation: 45-30=15, Resulting Numbers: [21, 15] Generated Node #3: [21, 15] from Operation: 45-30=15 Current State: 36:[21, 15], Operations: ['24-3=21', '45-30=15'] Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[24, 3, 45, 30], Operations: [] Exploring Operation: 45-24=21, Resulting Numbers: [3, 30, 21] Generated Node #0,0: 36:[3, 30, 21] Operation: 45-24=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[3, 30, 21], Operations: ['45-24=21'] Exploring Operation: 30-21=9, Resulting Numbers: [3, 9] Generated Node #0,0,0: 36:[3, 9] Operation: 30-21=9 Moving to Node #0,0,0 Current State: 36:[3, 9], Operations: ['45-24=21', '30-21=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 5, 3, 21, 13 ]
68
[ "5-3=2", "21+13=34", "2*34=68" ]
Current State: 68:[5, 3, 21, 13], Operations: [] Exploring Operation: 5-3=2, Resulting Numbers: [21, 13, 2] Generated Node #2: [21, 13, 2] from Operation: 5-3=2 Current State: 68:[21, 13, 2], Operations: ['5-3=2'] Exploring Operation: 21+13=34, Resulting Numbers: [2, 34] Generated Node #3: [2, 34] from Operation: 21+13=34 Current State: 68:[2, 34], Operations: ['5-3=2', '21+13=34'] Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[5, 3, 21, 13], Operations: [] Exploring Operation: 21-3=18, Resulting Numbers: [5, 13, 18] Generated Node #0,0: 68:[5, 13, 18] Operation: 21-3=18 Exploring Operation: 5+13=18, Resulting Numbers: [3, 21, 18] Generated Node #0,1: 68:[3, 21, 18] Operation: 5+13=18 Exploring Operation: 3+13=16, Resulting Numbers: [5, 21, 16] Generated Node #0,2: 68:[5, 21, 16] Operation: 3+13=16 Exploring Operation: 21+13=34, Resulting Numbers: [5, 3, 34] Generated Node #0,3: 68:[5, 3, 34] Operation: 21+13=34 Exploring Operation: 21-5=16, Resulting Numbers: [3, 13, 16] Generated Node #0,4: 68:[3, 13, 16] Operation: 21-5=16 Moving to Node #0,3 Current State: 68:[5, 3, 34], Operations: ['21+13=34'] Exploring Operation: 5-3=2, Resulting Numbers: [34, 2] Generated Node #0,3,0: 68:[34, 2] Operation: 5-3=2 Exploring Operation: 5*3=15, Resulting Numbers: [34, 15] Generated Node #0,3,1: 68:[34, 15] Operation: 5*3=15 Exploring Operation: 34-3=31, Resulting Numbers: [5, 31] Generated Node #0,3,2: 68:[5, 31] Operation: 34-3=31 Exploring Operation: 3+34=37, Resulting Numbers: [5, 37] Generated Node #0,3,3: 68:[5, 37] Operation: 3+34=37 Exploring Operation: 5+3=8, Resulting Numbers: [34, 8] Generated Node #0,3,4: 68:[34, 8] Operation: 5+3=8 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 68:[34, 2], Operations: ['21+13=34', '5-3=2'] Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[5, 3, 21, 13], Operations: [] Exploring Operation: 21+13=34, Resulting Numbers: [5, 3, 34] Generated Node #0,3: 68:[5, 3, 34] Operation: 21+13=34 Moving to Node #0,3 Current State: 68:[5, 3, 34], Operations: ['21+13=34'] Exploring Operation: 5-3=2, Resulting Numbers: [34, 2] Generated Node #0,3,0: 68:[34, 2] Operation: 5-3=2 Moving to Node #0,3,0 Current State: 68:[34, 2], Operations: ['21+13=34', '5-3=2'] Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 71, 71, 54, 38 ]
92
[ "71-71=0", "54+38=92", "0+92=92" ]
Current State: 92:[71, 71, 54, 38], Operations: [] Exploring Operation: 71-71=0, Resulting Numbers: [54, 38, 0] Generated Node #2: [54, 38, 0] from Operation: 71-71=0 Current State: 92:[54, 38, 0], Operations: ['71-71=0'] Exploring Operation: 54+38=92, Resulting Numbers: [0, 92] Generated Node #3: [0, 92] from Operation: 54+38=92 Current State: 92:[0, 92], Operations: ['71-71=0', '54+38=92'] Exploring Operation: 0+92=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[71, 71, 54, 38], Operations: [] Exploring Operation: 71-54=17, Resulting Numbers: [71, 38, 17] Generated Node #0,0: 92:[71, 38, 17] Operation: 71-54=17 Exploring Operation: 71-71=0, Resulting Numbers: [54, 38, 0] Generated Node #0,1: 92:[54, 38, 0] Operation: 71-71=0 Exploring Operation: 71/71=1, Resulting Numbers: [54, 38, 1] Generated Node #0,2: 92:[54, 38, 1] Operation: 71/71=1 Exploring Operation: 71-54=17, Resulting Numbers: [71, 38, 17] Generated Node #0,3: 92:[71, 38, 17] Operation: 71-54=17 Moving to Node #0,2 Current State: 92:[54, 38, 1], Operations: ['71/71=1'] Exploring Operation: 38+1=39, Resulting Numbers: [54, 39] Generated Node #0,2,0: 92:[54, 39] Operation: 38+1=39 Exploring Operation: 54+38=92, Resulting Numbers: [1, 92] Generated Node #0,2,1: 92:[1, 92] Operation: 54+38=92 Exploring Operation: 54-1=53, Resulting Numbers: [38, 53] Generated Node #0,2,2: 92:[38, 53] Operation: 54-1=53 Exploring Operation: 54-38=16, Resulting Numbers: [1, 16] Generated Node #0,2,3: 92:[1, 16] Operation: 54-38=16 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 92:[1, 92], Operations: ['71/71=1', '54+38=92'] Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[71, 71, 54, 38], Operations: [] Exploring Operation: 71/71=1, Resulting Numbers: [54, 38, 1] Generated Node #0,2: 92:[54, 38, 1] Operation: 71/71=1 Moving to Node #0,2 Current State: 92:[54, 38, 1], Operations: ['71/71=1'] Exploring Operation: 54+38=92, Resulting Numbers: [1, 92] Generated Node #0,2,1: 92:[1, 92] Operation: 54+38=92 Moving to Node #0,2,1 Current State: 92:[1, 92], Operations: ['71/71=1', '54+38=92'] Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 39, 7, 9, 8 ]
31
[ "39-7=32", "9-8=1", "32-1=31" ]
Current State: 31:[39, 7, 9, 8], Operations: [] Exploring Operation: 39-7=32, Resulting Numbers: [9, 8, 32] Generated Node #2: [9, 8, 32] from Operation: 39-7=32 Current State: 31:[9, 8, 32], Operations: ['39-7=32'] Exploring Operation: 9-8=1, Resulting Numbers: [32, 1] Generated Node #3: [32, 1] from Operation: 9-8=1 Current State: 31:[32, 1], Operations: ['39-7=32', '9-8=1'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[39, 7, 9, 8], Operations: [] Exploring Operation: 39-7=32, Resulting Numbers: [9, 8, 32] Generated Node #0,0: 31:[9, 8, 32] Operation: 39-7=32 Exploring Operation: 7+9=16, Resulting Numbers: [39, 8, 16] Generated Node #0,1: 31:[39, 8, 16] Operation: 7+9=16 Exploring Operation: 7+8=15, Resulting Numbers: [39, 9, 15] Generated Node #0,2: 31:[39, 9, 15] Operation: 7+8=15 Exploring Operation: 39-8=31, Resulting Numbers: [7, 9, 31] Generated Node #0,3: 31:[7, 9, 31] Operation: 39-8=31 Moving to Node #0,0 Current State: 31:[9, 8, 32], Operations: ['39-7=32'] Exploring Operation: 9+8=17, Resulting Numbers: [32, 17] Generated Node #0,0,0: 31:[32, 17] Operation: 9+8=17 Exploring Operation: 32-8=24, Resulting Numbers: [9, 24] Generated Node #0,0,1: 31:[9, 24] Operation: 32-8=24 Exploring Operation: 32-9=23, Resulting Numbers: [8, 23] Generated Node #0,0,2: 31:[8, 23] Operation: 32-9=23 Exploring Operation: 9-8=1, Resulting Numbers: [32, 1] Generated Node #0,0,3: 31:[32, 1] Operation: 9-8=1 Moving to Node #0,2 Current State: 31:[39, 9, 15], Operations: ['7+8=15'] Exploring Operation: 39-9=30, Resulting Numbers: [15, 30] Generated Node #0,2,0: 31:[15, 30] Operation: 39-9=30 Exploring Operation: 39+9=48, Resulting Numbers: [15, 48] Generated Node #0,2,1: 31:[15, 48] Operation: 39+9=48 Exploring Operation: 9+15=24, Resulting Numbers: [39, 24] Generated Node #0,2,2: 31:[39, 24] Operation: 9+15=24 Exploring Operation: 39-15=24, Resulting Numbers: [9, 24] Generated Node #0,2,3: 31:[9, 24] Operation: 39-15=24 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 31:[39, 24], Operations: ['7+8=15', '9+15=24'] Exploring Operation: 39*24=936, Resulting Numbers: [936] 936,31 unequal: No Solution Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 39+24=63, Resulting Numbers: [63] 63,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[15, 30], Operations: ['7+8=15', '39-9=30'] Exploring Operation: 15*30=450, Resulting Numbers: [450] 450,31 unequal: No Solution Exploring Operation: 15+30=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 31:[9, 24], Operations: ['7+8=15', '39-15=24'] Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,31 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 31:[15, 48], Operations: ['7+8=15', '39+9=48'] Exploring Operation: 15*48=720, Resulting Numbers: [720] 720,31 unequal: No Solution Exploring Operation: 15+48=63, Resulting Numbers: [63] 63,31 unequal: No Solution Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,31 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: 31:[39, 8, 16], Operations: ['7+9=16'] Exploring Operation: 39-8=31, Resulting Numbers: [16, 31] Generated Node #0,1,0: 31:[16, 31] Operation: 39-8=31 Exploring Operation: 39-16=23, Resulting Numbers: [8, 23] Generated Node #0,1,1: 31:[8, 23] Operation: 39-16=23 Exploring Operation: 8+16=24, Resulting Numbers: [39, 24] Generated Node #0,1,2: 31:[39, 24] Operation: 8+16=24 Exploring Operation: 39+8=47, Resulting Numbers: [16, 47] Generated Node #0,1,3: 31:[16, 47] Operation: 39+8=47 Moving to Node #0,3 Current State: 31:[7, 9, 31], Operations: ['39-8=31'] Exploring Operation: 7+31=38, Resulting Numbers: [9, 38] Generated Node #0,3,0: 31:[9, 38] Operation: 7+31=38 Exploring Operation: 9-7=2, Resulting Numbers: [31, 2] Generated Node #0,3,1: 31:[31, 2] Operation: 9-7=2 Exploring Operation: 31-7=24, Resulting Numbers: [9, 24] Generated Node #0,3,2: 31:[9, 24] Operation: 31-7=24 Exploring Operation: 7+9=16, Resulting Numbers: [31, 16] Generated Node #0,3,3: 31:[31, 16] Operation: 7+9=16 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 31:[31, 16], Operations: ['39-8=31', '7+9=16'] Exploring Operation: 31+16=47, Resulting Numbers: [47] 47,31 unequal: No Solution Exploring Operation: 31-16=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 31*16=496, Resulting Numbers: [496] 496,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 31:[9, 38], Operations: ['39-8=31', '7+31=38'] Exploring Operation: 9+38=47, Resulting Numbers: [47] 47,31 unequal: No Solution Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,31 unequal: No Solution Exploring Operation: 9*38=342, Resulting Numbers: [342] 342,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 31:[31, 2], Operations: ['39-8=31', '9-7=2'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,31 unequal: No Solution Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,31 unequal: No Solution Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 31:[9, 24], Operations: ['39-8=31', '31-7=24'] Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,31 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,31 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: 31:[32, 17], Operations: ['39-7=32', '9+8=17'] Exploring Operation: 32*17=544, Resulting Numbers: [544] 544,31 unequal: No Solution Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 32+17=49, Resulting Numbers: [49] 49,31 unequal: No Solution Moving to Node #0,1,2 Current State: 31:[39, 24], Operations: ['7+9=16', '8+16=24'] Exploring Operation: 39+24=63, Resulting Numbers: [63] 63,31 unequal: No Solution Exploring Operation: 39*24=936, Resulting Numbers: [936] 936,31 unequal: No Solution Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[16, 31], Operations: ['7+9=16', '39-8=31'] Exploring Operation: 16+31=47, Resulting Numbers: [47] 47,31 unequal: No Solution Exploring Operation: 16*31=496, Resulting Numbers: [496] 496,31 unequal: No Solution Exploring Operation: 31-16=15, Resulting Numbers: [15] 15,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[9, 24], Operations: ['39-7=32', '32-8=24'] Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,31 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[8, 23], Operations: ['7+9=16', '39-16=23'] Exploring Operation: 8+23=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[39, 7, 9, 8], Operations: [] Exploring Operation: 7+9=16, Resulting Numbers: [39, 8, 16] Generated Node #0,1: 31:[39, 8, 16] Operation: 7+9=16 Moving to Node #0,1 Current State: 31:[39, 8, 16], Operations: ['7+9=16'] Exploring Operation: 39-16=23, Resulting Numbers: [8, 23] Generated Node #0,1,1: 31:[8, 23] Operation: 39-16=23 Moving to Node #0,1,1 Current State: 31:[8, 23], Operations: ['7+9=16', '39-16=23'] Exploring Operation: 8+23=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
0.946181
hs_4
mult_heuristic
[ 99, 39, 15, 47 ]
43
[ "99-39=60", "60/15=4", "47-4=43" ]
Current State: 43:[99, 39, 15, 47], Operations: [] Exploring Operation: 99-39=60, Resulting Numbers: [15, 47, 60] Generated Node #2: [15, 47, 60] from Operation: 99-39=60 Current State: 43:[15, 47, 60], Operations: ['99-39=60'] Exploring Operation: 60/15=4, Resulting Numbers: [47, 4] Generated Node #3: [47, 4] from Operation: 60/15=4 Current State: 43:[47, 4], Operations: ['99-39=60', '60/15=4'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[99, 39, 15, 47], Operations: [] Exploring Operation: 99-47=52, Resulting Numbers: [39, 15, 52] Generated Node #0,0: 43:[39, 15, 52] Operation: 99-47=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[39, 15, 52], Operations: ['99-47=52'] Exploring Operation: 52-15=37, Resulting Numbers: [39, 37] Generated Node #0,0,0: 43:[39, 37] Operation: 52-15=37 Moving to Node #0,0,0 Current State: 43:[39, 37], Operations: ['99-47=52', '52-15=37'] Exploring Operation: 39+37=76, Resulting Numbers: [76] 76,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 67, 22, 1, 69 ]
21
[ "67+22=89", "69-1=68", "89-68=21" ]
Current State: 21:[67, 22, 1, 69], Operations: [] Exploring Operation: 67+22=89, Resulting Numbers: [1, 69, 89] Generated Node #2: [1, 69, 89] from Operation: 67+22=89 Current State: 21:[1, 69, 89], Operations: ['67+22=89'] Exploring Operation: 69-1=68, Resulting Numbers: [89, 68] Generated Node #3: [89, 68] from Operation: 69-1=68 Current State: 21:[89, 68], Operations: ['67+22=89', '69-1=68'] Exploring Operation: 89-68=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[67, 22, 1, 69], Operations: [] Exploring Operation: 69-22=47, Resulting Numbers: [67, 1, 47] Generated Node #0,0: 21:[67, 1, 47] Operation: 69-22=47 Exploring Operation: 69-67=2, Resulting Numbers: [22, 1, 2] Generated Node #0,1: 21:[22, 1, 2] Operation: 69-67=2 Exploring Operation: 67-22=45, Resulting Numbers: [1, 69, 45] Generated Node #0,2: 21:[1, 69, 45] Operation: 67-22=45 Exploring Operation: 67-1=66, Resulting Numbers: [22, 69, 66] Generated Node #0,3: 21:[22, 69, 66] Operation: 67-1=66 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[22, 1, 2], Operations: ['69-67=2'] Exploring Operation: 22/1=22, Resulting Numbers: [2, 22] Generated Node #0,1,0: 21:[2, 22] Operation: 22/1=22 Exploring Operation: 1+2=3, Resulting Numbers: [22, 3] Generated Node #0,1,1: 21:[22, 3] Operation: 1+2=3 Exploring Operation: 22*1=22, Resulting Numbers: [2, 22] Generated Node #0,1,2: 21:[2, 22] Operation: 22*1=22 Exploring Operation: 22-1=21, Resulting Numbers: [2, 21] Generated Node #0,1,3: 21:[2, 21] Operation: 22-1=21 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 21:[22, 3], Operations: ['69-67=2', '1+2=3'] Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,21 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 21:[2, 21], Operations: ['69-67=2', '22-1=21'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,21 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 21:[2, 22], Operations: ['69-67=2', '22/1=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,21 unequal: No Solution Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,21 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,21 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 21:[2, 22], Operations: ['69-67=2', '22*1=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,21 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,21 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[67, 1, 47], Operations: ['69-22=47'] Exploring Operation: 67-1=66, Resulting Numbers: [47, 66] Generated Node #0,0,0: 21:[47, 66] Operation: 67-1=66 Exploring Operation: 47-1=46, Resulting Numbers: [67, 46] Generated Node #0,0,1: 21:[67, 46] Operation: 47-1=46 Exploring Operation: 67*1=67, Resulting Numbers: [47, 67] Generated Node #0,0,2: 21:[47, 67] Operation: 67*1=67 Exploring Operation: 67-47=20, Resulting Numbers: [1, 20] Generated Node #0,0,3: 21:[1, 20] Operation: 67-47=20 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 21:[1, 20], Operations: ['69-22=47', '67-47=20'] Exploring Operation: 1+20=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[67, 22, 1, 69], Operations: [] Exploring Operation: 69-22=47, Resulting Numbers: [67, 1, 47] Generated Node #0,0: 21:[67, 1, 47] Operation: 69-22=47 Moving to Node #0,0 Current State: 21:[67, 1, 47], Operations: ['69-22=47'] Exploring Operation: 67-47=20, Resulting Numbers: [1, 20] Generated Node #0,0,3: 21:[1, 20] Operation: 67-47=20 Moving to Node #0,0,3 Current State: 21:[1, 20], Operations: ['69-22=47', '67-47=20'] Exploring Operation: 1+20=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 3, 23, 15, 45 ]
34
[ "3+23=26", "15+45=60", "60-26=34" ]
Current State: 34:[3, 23, 15, 45], Operations: [] Exploring Operation: 3+23=26, Resulting Numbers: [15, 45, 26] Generated Node #2: [15, 45, 26] from Operation: 3+23=26 Current State: 34:[15, 45, 26], Operations: ['3+23=26'] Exploring Operation: 15+45=60, Resulting Numbers: [26, 60] Generated Node #3: [26, 60] from Operation: 15+45=60 Current State: 34:[26, 60], Operations: ['3+23=26', '15+45=60'] Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[3, 23, 15, 45], Operations: [] Exploring Operation: 45-23=22, Resulting Numbers: [3, 15, 22] Generated Node #0,0: 34:[3, 15, 22] Operation: 45-23=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[3, 15, 22], Operations: ['45-23=22'] Exploring Operation: 22-3=19, Resulting Numbers: [15, 19] Generated Node #0,0,0: 34:[15, 19] Operation: 22-3=19 Moving to Node #0,0,0 Current State: 34:[15, 19], Operations: ['45-23=22', '22-3=19'] Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[3, 23, 15, 45], Operations: [] Exploring Operation: 45-23=22, Resulting Numbers: [3, 15, 22] Generated Node #0,0: 34:[3, 15, 22] Operation: 45-23=22 Moving to Node #0,0 Current State: 34:[3, 15, 22], Operations: ['45-23=22'] Exploring Operation: 22-3=19, Resulting Numbers: [15, 19] Generated Node #0,0,0: 34:[15, 19] Operation: 22-3=19 Moving to Node #0,0,0 Current State: 34:[15, 19], Operations: ['45-23=22', '22-3=19'] Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 92, 3, 33, 48 ]
14
[ "92+3=95", "33+48=81", "95-81=14" ]
Current State: 14:[92, 3, 33, 48], Operations: [] Exploring Operation: 92+3=95, Resulting Numbers: [33, 48, 95] Generated Node #2: [33, 48, 95] from Operation: 92+3=95 Current State: 14:[33, 48, 95], Operations: ['92+3=95'] Exploring Operation: 33+48=81, Resulting Numbers: [95, 81] Generated Node #3: [95, 81] from Operation: 33+48=81 Current State: 14:[95, 81], Operations: ['92+3=95', '33+48=81'] Exploring Operation: 95-81=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[92, 3, 33, 48], Operations: [] Exploring Operation: 92-33=59, Resulting Numbers: [3, 48, 59] Generated Node #0,0: 14:[3, 48, 59] Operation: 92-33=59 Exploring Operation: 48-33=15, Resulting Numbers: [92, 3, 15] Generated Node #0,1: 14:[92, 3, 15] Operation: 48-33=15 Exploring Operation: 92-48=44, Resulting Numbers: [3, 33, 44] Generated Node #0,2: 14:[3, 33, 44] Operation: 92-48=44 Moving to Node #0,2 Current State: 14:[3, 33, 44], Operations: ['92-48=44'] Exploring Operation: 33-3=30, Resulting Numbers: [44, 30] Generated Node #0,2,0: 14:[44, 30] Operation: 33-3=30 Exploring Operation: 44-33=11, Resulting Numbers: [3, 11] Generated Node #0,2,1: 14:[3, 11] Operation: 44-33=11 Exploring Operation: 33/3=11, Resulting Numbers: [44, 11] Generated Node #0,2,2: 14:[44, 11] Operation: 33/3=11 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 14:[3, 11], Operations: ['92-48=44', '44-33=11'] Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,14 unequal: No Solution Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[92, 3, 33, 48], Operations: [] Exploring Operation: 92-48=44, Resulting Numbers: [3, 33, 44] Generated Node #0,2: 14:[3, 33, 44] Operation: 92-48=44 Moving to Node #0,2 Current State: 14:[3, 33, 44], Operations: ['92-48=44'] Exploring Operation: 44-33=11, Resulting Numbers: [3, 11] Generated Node #0,2,1: 14:[3, 11] Operation: 44-33=11 Moving to Node #0,2,1 Current State: 14:[3, 11], Operations: ['92-48=44', '44-33=11'] Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 26, 56, 70, 88 ]
48
[ "56-26=30", "88-70=18", "30+18=48" ]
Current State: 48:[26, 56, 70, 88], Operations: [] Exploring Operation: 56-26=30, Resulting Numbers: [70, 88, 30] Generated Node #2: [70, 88, 30] from Operation: 56-26=30 Current State: 48:[70, 88, 30], Operations: ['56-26=30'] Exploring Operation: 88-70=18, Resulting Numbers: [30, 18] Generated Node #3: [30, 18] from Operation: 88-70=18 Current State: 48:[30, 18], Operations: ['56-26=30', '88-70=18'] Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[26, 56, 70, 88], Operations: [] Exploring Operation: 88-70=18, Resulting Numbers: [26, 56, 18] Generated Node #0,0: 48:[26, 56, 18] Operation: 88-70=18 Exploring Operation: 88-26=62, Resulting Numbers: [56, 70, 62] Generated Node #0,1: 48:[56, 70, 62] Operation: 88-26=62 Exploring Operation: 88-56=32, Resulting Numbers: [26, 70, 32] Generated Node #0,2: 48:[26, 70, 32] Operation: 88-56=32 Exploring Operation: 70-56=14, Resulting Numbers: [26, 88, 14] Generated Node #0,3: 48:[26, 88, 14] Operation: 70-56=14 Moving to Node #0,0 Current State: 48:[26, 56, 18], Operations: ['88-70=18'] Exploring Operation: 56-26=30, Resulting Numbers: [18, 30] Generated Node #0,0,0: 48:[18, 30] Operation: 56-26=30 Exploring Operation: 26+18=44, Resulting Numbers: [56, 44] Generated Node #0,0,1: 48:[56, 44] Operation: 26+18=44 Exploring Operation: 26-18=8, Resulting Numbers: [56, 8] Generated Node #0,0,2: 48:[56, 8] Operation: 26-18=8 Exploring Operation: 56-18=38, Resulting Numbers: [26, 38] Generated Node #0,0,3: 48:[26, 38] Operation: 56-18=38 Moving to Node #0,2 Current State: 48:[26, 70, 32], Operations: ['88-56=32'] Exploring Operation: 32-26=6, Resulting Numbers: [70, 6] Generated Node #0,2,0: 48:[70, 6] Operation: 32-26=6 Exploring Operation: 70-26=44, Resulting Numbers: [32, 44] Generated Node #0,2,1: 48:[32, 44] Operation: 70-26=44 Exploring Operation: 70-32=38, Resulting Numbers: [26, 38] Generated Node #0,2,2: 48:[26, 38] Operation: 70-32=38 Exploring Operation: 26+32=58, Resulting Numbers: [70, 58] Generated Node #0,2,3: 48:[70, 58] Operation: 26+32=58 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 48:[32, 44], Operations: ['88-56=32', '70-26=44'] Exploring Operation: 32*44=1408, Resulting Numbers: [1408] 1408,48 unequal: No Solution Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,48 unequal: No Solution Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 48:[26, 38], Operations: ['88-56=32', '70-32=38'] Exploring Operation: 26*38=988, Resulting Numbers: [988] 988,48 unequal: No Solution Exploring Operation: 38-26=12, Resulting Numbers: [12] 12,48 unequal: No Solution Exploring Operation: 26+38=64, Resulting Numbers: [64] 64,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 48:[70, 6], Operations: ['88-56=32', '32-26=6'] Exploring Operation: 70+6=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 70*6=420, Resulting Numbers: [420] 420,48 unequal: No Solution Exploring Operation: 70-6=64, Resulting Numbers: [64] 64,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 48:[70, 58], Operations: ['88-56=32', '26+32=58'] Exploring Operation: 70*58=4060, Resulting Numbers: [4060] 4060,48 unequal: No Solution Exploring Operation: 70+58=128, Resulting Numbers: [128] 128,48 unequal: No Solution Exploring Operation: 70-58=12, Resulting Numbers: [12] 12,48 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: 48:[26, 88, 14], Operations: ['70-56=14'] Exploring Operation: 26-14=12, Resulting Numbers: [88, 12] Generated Node #0,3,0: 48:[88, 12] Operation: 26-14=12 Exploring Operation: 88-14=74, Resulting Numbers: [26, 74] Generated Node #0,3,1: 48:[26, 74] Operation: 88-14=74 Exploring Operation: 26+14=40, Resulting Numbers: [88, 40] Generated Node #0,3,2: 48:[88, 40] Operation: 26+14=40 Exploring Operation: 88-26=62, Resulting Numbers: [14, 62] Generated Node #0,3,3: 48:[14, 62] Operation: 88-26=62 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 48:[14, 62], Operations: ['70-56=14', '88-26=62'] Exploring Operation: 14*62=868, Resulting Numbers: [868] 868,48 unequal: No Solution Exploring Operation: 62-14=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[26, 56, 70, 88], Operations: [] Exploring Operation: 70-56=14, Resulting Numbers: [26, 88, 14] Generated Node #0,3: 48:[26, 88, 14] Operation: 70-56=14 Moving to Node #0,3 Current State: 48:[26, 88, 14], Operations: ['70-56=14'] Exploring Operation: 88-26=62, Resulting Numbers: [14, 62] Generated Node #0,3,3: 48:[14, 62] Operation: 88-26=62 Moving to Node #0,3,3 Current State: 48:[14, 62], Operations: ['70-56=14', '88-26=62'] Exploring Operation: 62-14=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
sum_heuristic
[ 12, 55, 57, 59 ]
35
[ "57-55=2", "12*2=24", "59-24=35" ]
Current State: 35:[12, 55, 57, 59], Operations: [] Exploring Operation: 57-55=2, Resulting Numbers: [12, 59, 2] Generated Node #2: [12, 59, 2] from Operation: 57-55=2 Current State: 35:[12, 59, 2], Operations: ['57-55=2'] Exploring Operation: 12*2=24, Resulting Numbers: [59, 24] Generated Node #3: [59, 24] from Operation: 12*2=24 Current State: 35:[59, 24], Operations: ['57-55=2', '12*2=24'] Exploring Operation: 59-24=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[12, 55, 57, 59], Operations: [] Exploring Operation: 55-12=43, Resulting Numbers: [57, 59, 43] Generated Node #0,0: 35:[57, 59, 43] Operation: 55-12=43 Exploring Operation: 57-55=2, Resulting Numbers: [12, 59, 2] Generated Node #0,1: 35:[12, 59, 2] Operation: 57-55=2 Exploring Operation: 57-12=45, Resulting Numbers: [55, 59, 45] Generated Node #0,2: 35:[55, 59, 45] Operation: 57-12=45 Exploring Operation: 59-57=2, Resulting Numbers: [12, 55, 2] Generated Node #0,3: 35:[12, 55, 2] Operation: 59-57=2 Exploring Operation: 59-55=4, Resulting Numbers: [12, 57, 4] Generated Node #0,4: 35:[12, 57, 4] Operation: 59-55=4 Moving to Node #0,3 Current State: 35:[12, 55, 2], Operations: ['59-57=2'] Exploring Operation: 12-2=10, Resulting Numbers: [55, 10] Generated Node #0,3,0: 35:[55, 10] Operation: 12-2=10 Exploring Operation: 55-2=53, Resulting Numbers: [12, 53] Generated Node #0,3,1: 35:[12, 53] Operation: 55-2=53 Exploring Operation: 55-12=43, Resulting Numbers: [2, 43] Generated Node #0,3,2: 35:[2, 43] Operation: 55-12=43 Exploring Operation: 12+2=14, Resulting Numbers: [55, 14] Generated Node #0,3,3: 35:[55, 14] Operation: 12+2=14 Exploring Operation: 12/2=6, Resulting Numbers: [55, 6] Generated Node #0,3,4: 35:[55, 6] Operation: 12/2=6 Moving to Node #0,4 Current State: 35:[12, 57, 4], Operations: ['59-55=4'] Exploring Operation: 12/4=3, Resulting Numbers: [57, 3] Generated Node #0,4,0: 35:[57, 3] Operation: 12/4=3 Exploring Operation: 12-4=8, Resulting Numbers: [57, 8] Generated Node #0,4,1: 35:[57, 8] Operation: 12-4=8 Exploring Operation: 12+4=16, Resulting Numbers: [57, 16] Generated Node #0,4,2: 35:[57, 16] Operation: 12+4=16 Exploring Operation: 57-4=53, Resulting Numbers: [12, 53] Generated Node #0,4,3: 35:[12, 53] Operation: 57-4=53 Exploring Operation: 57-12=45, Resulting Numbers: [4, 45] Generated Node #0,4,4: 35:[4, 45] Operation: 57-12=45 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 35:[4, 45], Operations: ['59-55=4', '57-12=45'] Exploring Operation: 4+45=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 4*45=180, Resulting Numbers: [180] 180,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 35:[57, 8], Operations: ['59-55=4', '12-4=8'] Exploring Operation: 57-8=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 57+8=65, Resulting Numbers: [65] 65,35 unequal: No Solution Exploring Operation: 57*8=456, Resulting Numbers: [456] 456,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 35:[12, 53], Operations: ['59-55=4', '57-4=53'] Exploring Operation: 12+53=65, Resulting Numbers: [65] 65,35 unequal: No Solution Exploring Operation: 12*53=636, Resulting Numbers: [636] 636,35 unequal: No Solution Exploring Operation: 53-12=41, Resulting Numbers: [41] 41,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 35:[57, 3], Operations: ['59-55=4', '12/4=3'] Exploring Operation: 57+3=60, Resulting Numbers: [60] 60,35 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,35 unequal: No Solution Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,35 unequal: No Solution Exploring Operation: 57*3=171, Resulting Numbers: [171] 171,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 35:[57, 16], Operations: ['59-55=4', '12+4=16'] Exploring Operation: 57+16=73, Resulting Numbers: [73] 73,35 unequal: No Solution Exploring Operation: 57*16=912, Resulting Numbers: [912] 912,35 unequal: No Solution Exploring Operation: 57-16=41, Resulting Numbers: [41] 41,35 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: 35:[12, 59, 2], Operations: ['57-55=2'] Exploring Operation: 12-2=10, Resulting Numbers: [59, 10] Generated Node #0,1,0: 35:[59, 10] Operation: 12-2=10 Exploring Operation: 59-12=47, Resulting Numbers: [2, 47] Generated Node #0,1,1: 35:[2, 47] Operation: 59-12=47 Exploring Operation: 12/2=6, Resulting Numbers: [59, 6] Generated Node #0,1,2: 35:[59, 6] Operation: 12/2=6 Exploring Operation: 12+2=14, Resulting Numbers: [59, 14] Generated Node #0,1,3: 35:[59, 14] Operation: 12+2=14 Exploring Operation: 59-2=57, Resulting Numbers: [12, 57] Generated Node #0,1,4: 35:[12, 57] Operation: 59-2=57 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[2, 47], Operations: ['57-55=2', '59-12=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,35 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 35:[59, 6], Operations: ['57-55=2', '12/2=6'] Exploring Operation: 59*6=354, Resulting Numbers: [354] 354,35 unequal: No Solution Exploring Operation: 59+6=65, Resulting Numbers: [65] 65,35 unequal: No Solution Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[59, 10], Operations: ['57-55=2', '12-2=10'] Exploring Operation: 59-10=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 59*10=590, Resulting Numbers: [590] 590,35 unequal: No Solution Exploring Operation: 59+10=69, Resulting Numbers: [69] 69,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 35:[12, 57], Operations: ['57-55=2', '59-2=57'] Exploring Operation: 12+57=69, Resulting Numbers: [69] 69,35 unequal: No Solution Exploring Operation: 57-12=45, Resulting Numbers: [45] 45,35 unequal: No Solution Exploring Operation: 12*57=684, Resulting Numbers: [684] 684,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 35:[59, 14], Operations: ['57-55=2', '12+2=14'] Exploring Operation: 59-14=45, Resulting Numbers: [45] 45,35 unequal: No Solution Exploring Operation: 59*14=826, Resulting Numbers: [826] 826,35 unequal: No Solution Exploring Operation: 59+14=73, Resulting Numbers: [73] 73,35 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: 35:[57, 59, 43], Operations: ['55-12=43'] Exploring Operation: 57+43=100, Resulting Numbers: [59, 100] Generated Node #0,0,0: 35:[59, 100] Operation: 57+43=100 Exploring Operation: 57+59=116, Resulting Numbers: [43, 116] Generated Node #0,0,1: 35:[43, 116] Operation: 57+59=116 Exploring Operation: 59-57=2, Resulting Numbers: [43, 2] Generated Node #0,0,2: 35:[43, 2] Operation: 59-57=2 Exploring Operation: 59-43=16, Resulting Numbers: [57, 16] Generated Node #0,0,3: 35:[57, 16] Operation: 59-43=16 Exploring Operation: 57-43=14, Resulting Numbers: [59, 14] Generated Node #0,0,4: 35:[59, 14] Operation: 57-43=14 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 35:[43, 2], Operations: ['55-12=43', '59-57=2'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 43*2=86, Resulting Numbers: [86] 86,35 unequal: No Solution Exploring Operation: 43+2=45, Resulting Numbers: [45] 45,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 35:[57, 16], Operations: ['55-12=43', '59-43=16'] Exploring Operation: 57+16=73, Resulting Numbers: [73] 73,35 unequal: No Solution Exploring Operation: 57*16=912, Resulting Numbers: [912] 912,35 unequal: No Solution Exploring Operation: 57-16=41, Resulting Numbers: [41] 41,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 35:[59, 14], Operations: ['55-12=43', '57-43=14'] Exploring Operation: 59+14=73, Resulting Numbers: [73] 73,35 unequal: No Solution Exploring Operation: 59-14=45, Resulting Numbers: [45] 45,35 unequal: No Solution Exploring Operation: 59*14=826, Resulting Numbers: [826] 826,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[59, 100], Operations: ['55-12=43', '57+43=100'] Exploring Operation: 59*100=5900, Resulting Numbers: [5900] 5900,35 unequal: No Solution Exploring Operation: 59+100=159, Resulting Numbers: [159] 159,35 unequal: No Solution Exploring Operation: 100-59=41, Resulting Numbers: [41] 41,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 35:[43, 116], Operations: ['55-12=43', '57+59=116'] Exploring Operation: 43+116=159, Resulting Numbers: [159] 159,35 unequal: No Solution Exploring Operation: 43*116=4988, Resulting Numbers: [4988] 4988,35 unequal: No Solution Exploring Operation: 116-43=73, Resulting Numbers: [73] 73,35 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: 35:[55, 59, 45], Operations: ['57-12=45'] Exploring Operation: 55+45=100, Resulting Numbers: [59, 100] Generated Node #0,2,0: 35:[59, 100] Operation: 55+45=100 Exploring Operation: 55-45=10, Resulting Numbers: [59, 10] Generated Node #0,2,1: 35:[59, 10] Operation: 55-45=10 Exploring Operation: 59-45=14, Resulting Numbers: [55, 14] Generated Node #0,2,2: 35:[55, 14] Operation: 59-45=14 Exploring Operation: 55+59=114, Resulting Numbers: [45, 114] Generated Node #0,2,3: 35:[45, 114] Operation: 55+59=114 Exploring Operation: 59-55=4, Resulting Numbers: [45, 4] Generated Node #0,2,4: 35:[45, 4] Operation: 59-55=4 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 35:[45, 4], Operations: ['57-12=45', '59-55=4'] Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,35 unequal: No Solution Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 35:[59, 10], Operations: ['57-12=45', '55-45=10'] Exploring Operation: 59-10=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 59+10=69, Resulting Numbers: [69] 69,35 unequal: No Solution Exploring Operation: 59*10=590, Resulting Numbers: [590] 590,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 35:[55, 14], Operations: ['57-12=45', '59-45=14'] Exploring Operation: 55*14=770, Resulting Numbers: [770] 770,35 unequal: No Solution Exploring Operation: 55+14=69, Resulting Numbers: [69] 69,35 unequal: No Solution Exploring Operation: 55-14=41, Resulting Numbers: [41] 41,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 35:[59, 100], Operations: ['57-12=45', '55+45=100'] Exploring Operation: 100-59=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 59*100=5900, Resulting Numbers: [5900] 5900,35 unequal: No Solution Exploring Operation: 59+100=159, Resulting Numbers: [159] 159,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 35:[45, 114], Operations: ['57-12=45', '55+59=114'] Exploring Operation: 45*114=5130, Resulting Numbers: [5130] 5130,35 unequal: No Solution Exploring Operation: 45+114=159, Resulting Numbers: [159] 159,35 unequal: No Solution Exploring Operation: 114-45=69, Resulting Numbers: [69] 69,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 35:[2, 43], Operations: ['59-57=2', '55-12=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,35 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,35 unequal: No Solution Moving to Node #0,3,4 Current State: 35:[55, 6], Operations: ['59-57=2', '12/2=6'] Exploring Operation: 55-6=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 55+6=61, Resulting Numbers: [61] 61,35 unequal: No Solution Exploring Operation: 55*6=330, Resulting Numbers: [330] 330,35 unequal: No Solution Moving to Node #0,3,0 Current State: 35:[55, 10], Operations: ['59-57=2', '12-2=10'] Exploring Operation: 55*10=550, Resulting Numbers: [550] 550,35 unequal: No Solution Exploring Operation: 55-10=45, Resulting Numbers: [45] 45,35 unequal: No Solution Exploring Operation: 55+10=65, Resulting Numbers: [65] 65,35 unequal: No Solution Moving to Node #0,3,1 Current State: 35:[12, 53], Operations: ['59-57=2', '55-2=53'] Exploring Operation: 12*53=636, Resulting Numbers: [636] 636,35 unequal: No Solution Exploring Operation: 12+53=65, Resulting Numbers: [65] 65,35 unequal: No Solution Exploring Operation: 53-12=41, Resulting Numbers: [41] 41,35 unequal: No Solution Moving to Node #0,3,3 Current State: 35:[55, 14], Operations: ['59-57=2', '12+2=14'] Exploring Operation: 55*14=770, Resulting Numbers: [770] 770,35 unequal: No Solution Exploring Operation: 55-14=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 55+14=69, Resulting Numbers: [69] 69,35 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 5, 57, 69, 78 ]
95
[ "57-5=52", "69+78=147", "147-52=95" ]
Current State: 95:[5, 57, 69, 78], Operations: [] Exploring Operation: 57-5=52, Resulting Numbers: [69, 78, 52] Generated Node #2: [69, 78, 52] from Operation: 57-5=52 Current State: 95:[69, 78, 52], Operations: ['57-5=52'] Exploring Operation: 69+78=147, Resulting Numbers: [52, 147] Generated Node #3: [52, 147] from Operation: 69+78=147 Current State: 95:[52, 147], Operations: ['57-5=52', '69+78=147'] Exploring Operation: 147-52=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[5, 57, 69, 78], Operations: [] Exploring Operation: 78-57=21, Resulting Numbers: [5, 69, 21] Generated Node #0,0: 95:[5, 69, 21] Operation: 78-57=21 Exploring Operation: 69-57=12, Resulting Numbers: [5, 78, 12] Generated Node #0,1: 95:[5, 78, 12] Operation: 69-57=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[5, 78, 12], Operations: ['69-57=12'] Exploring Operation: 5+78=83, Resulting Numbers: [12, 83] Generated Node #0,1,0: 95:[12, 83] Operation: 5+78=83 Exploring Operation: 78+12=90, Resulting Numbers: [5, 90] Generated Node #0,1,1: 95:[5, 90] Operation: 78+12=90 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 95:[5, 90], Operations: ['69-57=12', '78+12=90'] Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,95 unequal: No Solution Exploring Operation: 5+90=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[5, 57, 69, 78], Operations: [] Exploring Operation: 69-57=12, Resulting Numbers: [5, 78, 12] Generated Node #0,1: 95:[5, 78, 12] Operation: 69-57=12 Moving to Node #0,1 Current State: 95:[5, 78, 12], Operations: ['69-57=12'] Exploring Operation: 78+12=90, Resulting Numbers: [5, 90] Generated Node #0,1,1: 95:[5, 90] Operation: 78+12=90 Moving to Node #0,1,1 Current State: 95:[5, 90], Operations: ['69-57=12', '78+12=90'] Exploring Operation: 5+90=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 2, 58, 40, 43 ]
58
[ "2+40=42", "43-42=1", "58*1=58" ]
Current State: 58:[2, 58, 40, 43], Operations: [] Exploring Operation: 2+40=42, Resulting Numbers: [58, 43, 42] Generated Node #2: [58, 43, 42] from Operation: 2+40=42 Current State: 58:[58, 43, 42], Operations: ['2+40=42'] Exploring Operation: 43-42=1, Resulting Numbers: [58, 1] Generated Node #3: [58, 1] from Operation: 43-42=1 Current State: 58:[58, 1], Operations: ['2+40=42', '43-42=1'] Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[2, 58, 40, 43], Operations: [] Exploring Operation: 40-2=38, Resulting Numbers: [58, 43, 38] Generated Node #0,0: 58:[58, 43, 38] Operation: 40-2=38 Exploring Operation: 43-40=3, Resulting Numbers: [2, 58, 3] Generated Node #0,1: 58:[2, 58, 3] Operation: 43-40=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[2, 58, 3], Operations: ['43-40=3'] Exploring Operation: 58/2=29, Resulting Numbers: [3, 29] Generated Node #0,1,0: 58:[3, 29] Operation: 58/2=29 Exploring Operation: 3-2=1, Resulting Numbers: [58, 1] Generated Node #0,1,1: 58:[58, 1] Operation: 3-2=1 Moving to Node #0,1,0 Current State: 58:[3, 29], Operations: ['43-40=3', '58/2=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,58 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[58, 1], Operations: ['43-40=3', '3-2=1'] Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[2, 58, 40, 43], Operations: [] Exploring Operation: 43-40=3, Resulting Numbers: [2, 58, 3] Generated Node #0,1: 58:[2, 58, 3] Operation: 43-40=3 Moving to Node #0,1 Current State: 58:[2, 58, 3], Operations: ['43-40=3'] Exploring Operation: 3-2=1, Resulting Numbers: [58, 1] Generated Node #0,1,1: 58:[58, 1] Operation: 3-2=1 Moving to Node #0,1,1 Current State: 58:[58, 1], Operations: ['43-40=3', '3-2=1'] Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 74, 28, 7, 11 ]
19
[ "74-11=63", "63/7=9", "28-9=19" ]
Current State: 19:[74, 28, 7, 11], Operations: [] Exploring Operation: 74-11=63, Resulting Numbers: [28, 7, 63] Generated Node #2: [28, 7, 63] from Operation: 74-11=63 Current State: 19:[28, 7, 63], Operations: ['74-11=63'] Exploring Operation: 63/7=9, Resulting Numbers: [28, 9] Generated Node #3: [28, 9] from Operation: 63/7=9 Current State: 19:[28, 9], Operations: ['74-11=63', '63/7=9'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[74, 28, 7, 11], Operations: [] Exploring Operation: 74-28=46, Resulting Numbers: [7, 11, 46] Generated Node #0,0: 19:[7, 11, 46] Operation: 74-28=46 Exploring Operation: 7+11=18, Resulting Numbers: [74, 28, 18] Generated Node #0,1: 19:[74, 28, 18] Operation: 7+11=18 Exploring Operation: 74-7=67, Resulting Numbers: [28, 11, 67] Generated Node #0,2: 19:[28, 11, 67] Operation: 74-7=67 Exploring Operation: 28-7=21, Resulting Numbers: [74, 11, 21] Generated Node #0,3: 19:[74, 11, 21] Operation: 28-7=21 Exploring Operation: 74-11=63, Resulting Numbers: [28, 7, 63] Generated Node #0,4: 19:[28, 7, 63] Operation: 74-11=63 Moving to Node #0,0 Current State: 19:[7, 11, 46], Operations: ['74-28=46'] Exploring Operation: 7+11=18, Resulting Numbers: [46, 18] Generated Node #0,0,0: 19:[46, 18] Operation: 7+11=18 Exploring Operation: 46-11=35, Resulting Numbers: [7, 35] Generated Node #0,0,1: 19:[7, 35] Operation: 46-11=35 Exploring Operation: 7+46=53, Resulting Numbers: [11, 53] Generated Node #0,0,2: 19:[11, 53] Operation: 7+46=53 Exploring Operation: 11-7=4, Resulting Numbers: [46, 4] Generated Node #0,0,3: 19:[46, 4] Operation: 11-7=4 Exploring Operation: 46-7=39, Resulting Numbers: [11, 39] Generated Node #0,0,4: 19:[11, 39] Operation: 46-7=39 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[46, 18], Operations: ['74-28=46', '7+11=18'] Exploring Operation: 46*18=828, Resulting Numbers: [828] 828,19 unequal: No Solution Exploring Operation: 46-18=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 46+18=64, Resulting Numbers: [64] 64,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 19:[7, 35], Operations: ['74-28=46', '46-11=35'] Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,19 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,19 unequal: No Solution Exploring Operation: 7*35=245, Resulting Numbers: [245] 245,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 19:[11, 39], Operations: ['74-28=46', '46-7=39'] Exploring Operation: 11*39=429, Resulting Numbers: [429] 429,19 unequal: No Solution Exploring Operation: 11+39=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 19:[11, 53], Operations: ['74-28=46', '7+46=53'] Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,19 unequal: No Solution Exploring Operation: 11+53=64, Resulting Numbers: [64] 64,19 unequal: No Solution Exploring Operation: 11*53=583, Resulting Numbers: [583] 583,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 19:[46, 4], Operations: ['74-28=46', '11-7=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,19 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,19 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: 19:[28, 11, 67], Operations: ['74-7=67'] Exploring Operation: 11+67=78, Resulting Numbers: [28, 78] Generated Node #0,2,0: 19:[28, 78] Operation: 11+67=78 Exploring Operation: 67-28=39, Resulting Numbers: [11, 39] Generated Node #0,2,1: 19:[11, 39] Operation: 67-28=39 Exploring Operation: 67-11=56, Resulting Numbers: [28, 56] Generated Node #0,2,2: 19:[28, 56] Operation: 67-11=56 Exploring Operation: 28-11=17, Resulting Numbers: [67, 17] Generated Node #0,2,3: 19:[67, 17] Operation: 28-11=17 Exploring Operation: 28+11=39, Resulting Numbers: [67, 39] Generated Node #0,2,4: 19:[67, 39] Operation: 28+11=39 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 19:[11, 39], Operations: ['74-7=67', '67-28=39'] Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 11+39=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 11*39=429, Resulting Numbers: [429] 429,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 19:[28, 56], Operations: ['74-7=67', '67-11=56'] Exploring Operation: 56-28=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 56/28=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 28*56=1568, Resulting Numbers: [1568] 1568,19 unequal: No Solution Exploring Operation: 28+56=84, Resulting Numbers: [84] 84,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 19:[67, 17], Operations: ['74-7=67', '28-11=17'] Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 67*17=1139, Resulting Numbers: [1139] 1139,19 unequal: No Solution Exploring Operation: 67+17=84, Resulting Numbers: [84] 84,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 19:[28, 78], Operations: ['74-7=67', '11+67=78'] Exploring Operation: 28*78=2184, Resulting Numbers: [2184] 2184,19 unequal: No Solution Exploring Operation: 28+78=106, Resulting Numbers: [106] 106,19 unequal: No Solution Exploring Operation: 78-28=50, Resulting Numbers: [50] 50,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 19:[67, 39], Operations: ['74-7=67', '28+11=39'] Exploring Operation: 67*39=2613, Resulting Numbers: [2613] 2613,19 unequal: No Solution Exploring Operation: 67+39=106, Resulting Numbers: [106] 106,19 unequal: No Solution Exploring Operation: 67-39=28, Resulting Numbers: [28] 28,19 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: 19:[28, 7, 63], Operations: ['74-11=63'] Exploring Operation: 63/7=9, Resulting Numbers: [28, 9] Generated Node #0,4,0: 19:[28, 9] Operation: 63/7=9 Exploring Operation: 28/7=4, Resulting Numbers: [63, 4] Generated Node #0,4,1: 19:[63, 4] Operation: 28/7=4 Exploring Operation: 63-7=56, Resulting Numbers: [28, 56] Generated Node #0,4,2: 19:[28, 56] Operation: 63-7=56 Exploring Operation: 28-7=21, Resulting Numbers: [63, 21] Generated Node #0,4,3: 19:[63, 21] Operation: 28-7=21 Exploring Operation: 63-28=35, Resulting Numbers: [7, 35] Generated Node #0,4,4: 19:[7, 35] Operation: 63-28=35 Moving to Node #0,1 Current State: 19:[74, 28, 18], Operations: ['7+11=18'] Exploring Operation: 74-18=56, Resulting Numbers: [28, 56] Generated Node #0,1,0: 19:[28, 56] Operation: 74-18=56 Exploring Operation: 74-28=46, Resulting Numbers: [18, 46] Generated Node #0,1,1: 19:[18, 46] Operation: 74-28=46 Exploring Operation: 74+18=92, Resulting Numbers: [28, 92] Generated Node #0,1,2: 19:[28, 92] Operation: 74+18=92 Exploring Operation: 28+18=46, Resulting Numbers: [74, 46] Generated Node #0,1,3: 19:[74, 46] Operation: 28+18=46 Exploring Operation: 28-18=10, Resulting Numbers: [74, 10] Generated Node #0,1,4: 19:[74, 10] Operation: 28-18=10 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 19:[18, 46], Operations: ['7+11=18', '74-28=46'] Exploring Operation: 18*46=828, Resulting Numbers: [828] 828,19 unequal: No Solution Exploring Operation: 18+46=64, Resulting Numbers: [64] 64,19 unequal: No Solution Exploring Operation: 46-18=28, Resulting Numbers: [28] 28,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 19:[28, 56], Operations: ['7+11=18', '74-18=56'] Exploring Operation: 56/28=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 28+56=84, Resulting Numbers: [84] 84,19 unequal: No Solution Exploring Operation: 28*56=1568, Resulting Numbers: [1568] 1568,19 unequal: No Solution Exploring Operation: 56-28=28, Resulting Numbers: [28] 28,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 19:[74, 10], Operations: ['7+11=18', '28-18=10'] Exploring Operation: 74*10=740, Resulting Numbers: [740] 740,19 unequal: No Solution Exploring Operation: 74-10=64, Resulting Numbers: [64] 64,19 unequal: No Solution Exploring Operation: 74+10=84, Resulting Numbers: [84] 84,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 19:[28, 92], Operations: ['7+11=18', '74+18=92'] Exploring Operation: 28+92=120, Resulting Numbers: [120] 120,19 unequal: No Solution Exploring Operation: 28*92=2576, Resulting Numbers: [2576] 2576,19 unequal: No Solution Exploring Operation: 92-28=64, Resulting Numbers: [64] 64,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 19:[74, 46], Operations: ['7+11=18', '28+18=46'] Exploring Operation: 74-46=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 74+46=120, Resulting Numbers: [120] 120,19 unequal: No Solution Exploring Operation: 74*46=3404, Resulting Numbers: [3404] 3404,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 19:[74, 11, 21], Operations: ['28-7=21'] Exploring Operation: 21-11=10, Resulting Numbers: [74, 10] Generated Node #0,3,0: 19:[74, 10] Operation: 21-11=10 Exploring Operation: 74-21=53, Resulting Numbers: [11, 53] Generated Node #0,3,1: 19:[11, 53] Operation: 74-21=53 Exploring Operation: 11+21=32, Resulting Numbers: [74, 32] Generated Node #0,3,2: 19:[74, 32] Operation: 11+21=32 Exploring Operation: 74+11=85, Resulting Numbers: [21, 85] Generated Node #0,3,3: 19:[21, 85] Operation: 74+11=85 Exploring Operation: 74-11=63, Resulting Numbers: [21, 63] Generated Node #0,3,4: 19:[21, 63] Operation: 74-11=63 Moving to Node #0,4,0 Current State: 19:[28, 9], Operations: ['74-11=63', '63/7=9'] Exploring Operation: 28*9=252, Resulting Numbers: [252] 252,19 unequal: No Solution Exploring Operation: 28+9=37, Resulting Numbers: [37] 37,19 unequal: No Solution Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[74, 28, 7, 11], Operations: [] Exploring Operation: 74-11=63, Resulting Numbers: [28, 7, 63] Generated Node #0,4: 19:[28, 7, 63] Operation: 74-11=63 Moving to Node #0,4 Current State: 19:[28, 7, 63], Operations: ['74-11=63'] Exploring Operation: 63/7=9, Resulting Numbers: [28, 9] Generated Node #0,4,0: 19:[28, 9] Operation: 63/7=9 Moving to Node #0,4,0 Current State: 19:[28, 9], Operations: ['74-11=63', '63/7=9'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
0.926215
hs_5
mult_heuristic
[ 17, 20, 22, 50 ]
84
[ "20-17=3", "50-22=28", "3*28=84" ]
Current State: 84:[17, 20, 22, 50], Operations: [] Exploring Operation: 20-17=3, Resulting Numbers: [22, 50, 3] Generated Node #2: [22, 50, 3] from Operation: 20-17=3 Current State: 84:[22, 50, 3], Operations: ['20-17=3'] Exploring Operation: 50-22=28, Resulting Numbers: [3, 28] Generated Node #3: [3, 28] from Operation: 50-22=28 Current State: 84:[3, 28], Operations: ['20-17=3', '50-22=28'] Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[17, 20, 22, 50], Operations: [] Exploring Operation: 50-22=28, Resulting Numbers: [17, 20, 28] Generated Node #0,0: 84:[17, 20, 28] Operation: 50-22=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[17, 20, 28], Operations: ['50-22=28'] Exploring Operation: 20-17=3, Resulting Numbers: [28, 3] Generated Node #0,0,0: 84:[28, 3] Operation: 20-17=3 Moving to Node #0,0,0 Current State: 84:[28, 3], Operations: ['50-22=28', '20-17=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[17, 20, 22, 50], Operations: [] Exploring Operation: 50-22=28, Resulting Numbers: [17, 20, 28] Generated Node #0,0: 84:[17, 20, 28] Operation: 50-22=28 Moving to Node #0,0 Current State: 84:[17, 20, 28], Operations: ['50-22=28'] Exploring Operation: 20-17=3, Resulting Numbers: [28, 3] Generated Node #0,0,0: 84:[28, 3] Operation: 20-17=3 Moving to Node #0,0,0 Current State: 84:[28, 3], Operations: ['50-22=28', '20-17=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 42, 40, 3, 19 ]
13
[ "42-40=2", "3*2=6", "19-6=13" ]
Current State: 13:[42, 40, 3, 19], Operations: [] Exploring Operation: 42-40=2, Resulting Numbers: [3, 19, 2] Generated Node #2: [3, 19, 2] from Operation: 42-40=2 Current State: 13:[3, 19, 2], Operations: ['42-40=2'] Exploring Operation: 3*2=6, Resulting Numbers: [19, 6] Generated Node #3: [19, 6] from Operation: 3*2=6 Current State: 13:[19, 6], Operations: ['42-40=2', '3*2=6'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[42, 40, 3, 19], Operations: [] Exploring Operation: 42-19=23, Resulting Numbers: [40, 3, 23] Generated Node #0,0: 13:[40, 3, 23] Operation: 42-19=23 Exploring Operation: 40-19=21, Resulting Numbers: [42, 3, 21] Generated Node #0,1: 13:[42, 3, 21] Operation: 40-19=21 Exploring Operation: 42-40=2, Resulting Numbers: [3, 19, 2] Generated Node #0,2: 13:[3, 19, 2] Operation: 42-40=2 Exploring Operation: 42/3=14, Resulting Numbers: [40, 19, 14] Generated Node #0,3: 13:[40, 19, 14] Operation: 42/3=14 Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[3, 19, 2], Operations: ['42-40=2'] Exploring Operation: 19-2=17, Resulting Numbers: [3, 17] Generated Node #0,2,0: 13:[3, 17] Operation: 19-2=17 Exploring Operation: 3*2=6, Resulting Numbers: [19, 6] Generated Node #0,2,1: 13:[19, 6] Operation: 3*2=6 Exploring Operation: 3+2=5, Resulting Numbers: [19, 5] Generated Node #0,2,2: 13:[19, 5] Operation: 3+2=5 Exploring Operation: 19-3=16, Resulting Numbers: [2, 16] Generated Node #0,2,3: 13:[2, 16] Operation: 19-3=16 Moving to Node #0,2,1 Current State: 13:[19, 6], Operations: ['42-40=2', '3*2=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,13 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,13 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[42, 40, 3, 19], Operations: [] Exploring Operation: 42-40=2, Resulting Numbers: [3, 19, 2] Generated Node #0,2: 13:[3, 19, 2] Operation: 42-40=2 Moving to Node #0,2 Current State: 13:[3, 19, 2], Operations: ['42-40=2'] Exploring Operation: 3*2=6, Resulting Numbers: [19, 6] Generated Node #0,2,1: 13:[19, 6] Operation: 3*2=6 Moving to Node #0,2,1 Current State: 13:[19, 6], Operations: ['42-40=2', '3*2=6'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 56, 27, 90, 78 ]
84
[ "27+90=117", "56*117=6552", "6552/78=84" ]
Current State: 84:[56, 27, 90, 78], Operations: [] Exploring Operation: 27+90=117, Resulting Numbers: [56, 78, 117] Generated Node #2: [56, 78, 117] from Operation: 27+90=117 Current State: 84:[56, 78, 117], Operations: ['27+90=117'] Exploring Operation: 56*117=6552, Resulting Numbers: [78, 6552] Generated Node #3: [78, 6552] from Operation: 56*117=6552 Current State: 84:[78, 6552], Operations: ['27+90=117', '56*117=6552'] Exploring Operation: 6552/78=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[56, 27, 90, 78], Operations: [] Exploring Operation: 90-78=12, Resulting Numbers: [56, 27, 12] Generated Node #0,0: 84:[56, 27, 12] Operation: 90-78=12 Exploring Operation: 78-56=22, Resulting Numbers: [27, 90, 22] Generated Node #0,1: 84:[27, 90, 22] Operation: 78-56=22 Exploring Operation: 90-56=34, Resulting Numbers: [27, 78, 34] Generated Node #0,2: 84:[27, 78, 34] Operation: 90-56=34 Exploring Operation: 56+27=83, Resulting Numbers: [90, 78, 83] Generated Node #0,3: 84:[90, 78, 83] Operation: 56+27=83 Exploring Operation: 56-27=29, Resulting Numbers: [90, 78, 29] Generated Node #0,4: 84:[90, 78, 29] Operation: 56-27=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[27, 90, 22], Operations: ['78-56=22'] Exploring Operation: 27+22=49, Resulting Numbers: [90, 49] Generated Node #0,1,0: 84:[90, 49] Operation: 27+22=49 Exploring Operation: 90-27=63, Resulting Numbers: [22, 63] Generated Node #0,1,1: 84:[22, 63] Operation: 90-27=63 Exploring Operation: 90+22=112, Resulting Numbers: [27, 112] Generated Node #0,1,2: 84:[27, 112] Operation: 90+22=112 Exploring Operation: 90-22=68, Resulting Numbers: [27, 68] Generated Node #0,1,3: 84:[27, 68] Operation: 90-22=68 Exploring Operation: 27-22=5, Resulting Numbers: [90, 5] Generated Node #0,1,4: 84:[90, 5] Operation: 27-22=5 Moving to Node #0,1,4 Current State: 84:[90, 5], Operations: ['78-56=22', '27-22=5'] Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,84 unequal: No Solution Exploring Operation: 90*5=450, Resulting Numbers: [450] 450,84 unequal: No Solution Exploring Operation: 90-5=85, Resulting Numbers: [85] 85,84 unequal: No Solution Exploring Operation: 90+5=95, Resulting Numbers: [95] 95,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[90, 49], Operations: ['78-56=22', '27+22=49'] Exploring Operation: 90*49=4410, Resulting Numbers: [4410] 4410,84 unequal: No Solution Exploring Operation: 90+49=139, Resulting Numbers: [139] 139,84 unequal: No Solution Exploring Operation: 90-49=41, Resulting Numbers: [41] 41,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[27, 68], Operations: ['78-56=22', '90-22=68'] Exploring Operation: 27+68=95, Resulting Numbers: [95] 95,84 unequal: No Solution Exploring Operation: 68-27=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 27*68=1836, Resulting Numbers: [1836] 1836,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[22, 63], Operations: ['78-56=22', '90-27=63'] Exploring Operation: 22+63=85, Resulting Numbers: [85] 85,84 unequal: No Solution Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 22*63=1386, Resulting Numbers: [1386] 1386,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[27, 112], Operations: ['78-56=22', '90+22=112'] Exploring Operation: 27*112=3024, Resulting Numbers: [3024] 3024,84 unequal: No Solution Exploring Operation: 112-27=85, Resulting Numbers: [85] 85,84 unequal: No Solution Exploring Operation: 27+112=139, Resulting Numbers: [139] 139,84 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:[27, 78, 34], Operations: ['90-56=34'] Exploring Operation: 27+34=61, Resulting Numbers: [78, 61] Generated Node #0,2,0: 84:[78, 61] Operation: 27+34=61 Exploring Operation: 27+78=105, Resulting Numbers: [34, 105] Generated Node #0,2,1: 84:[34, 105] Operation: 27+78=105 Exploring Operation: 78-27=51, Resulting Numbers: [34, 51] Generated Node #0,2,2: 84:[34, 51] Operation: 78-27=51 Exploring Operation: 78-34=44, Resulting Numbers: [27, 44] Generated Node #0,2,3: 84:[27, 44] Operation: 78-34=44 Exploring Operation: 34-27=7, Resulting Numbers: [78, 7] Generated Node #0,2,4: 84:[78, 7] Operation: 34-27=7 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 84:[27, 44], Operations: ['90-56=34', '78-34=44'] Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 27*44=1188, Resulting Numbers: [1188] 1188,84 unequal: No Solution Exploring Operation: 27+44=71, Resulting Numbers: [71] 71,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 84:[78, 7], Operations: ['90-56=34', '34-27=7'] Exploring Operation: 78-7=71, Resulting Numbers: [71] 71,84 unequal: No Solution Exploring Operation: 78*7=546, Resulting Numbers: [546] 546,84 unequal: No Solution Exploring Operation: 78+7=85, Resulting Numbers: [85] 85,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 84:[34, 51], Operations: ['90-56=34', '78-27=51'] Exploring Operation: 34*51=1734, Resulting Numbers: [1734] 1734,84 unequal: No Solution Exploring Operation: 51-34=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 34+51=85, Resulting Numbers: [85] 85,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 84:[78, 61], Operations: ['90-56=34', '27+34=61'] Exploring Operation: 78-61=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 78+61=139, Resulting Numbers: [139] 139,84 unequal: No Solution Exploring Operation: 78*61=4758, Resulting Numbers: [4758] 4758,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 84:[34, 105], Operations: ['90-56=34', '27+78=105'] Exploring Operation: 34+105=139, Resulting Numbers: [139] 139,84 unequal: No Solution Exploring Operation: 34*105=3570, Resulting Numbers: [3570] 3570,84 unequal: No Solution Exploring Operation: 105-34=71, Resulting Numbers: [71] 71,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 84:[90, 78, 83], Operations: ['56+27=83'] Exploring Operation: 90-78=12, Resulting Numbers: [83, 12] Generated Node #0,3,0: 84:[83, 12] Operation: 90-78=12 Exploring Operation: 78+83=161, Resulting Numbers: [90, 161] Generated Node #0,3,1: 84:[90, 161] Operation: 78+83=161 Exploring Operation: 90-83=7, Resulting Numbers: [78, 7] Generated Node #0,3,2: 84:[78, 7] Operation: 90-83=7 Exploring Operation: 83-78=5, Resulting Numbers: [90, 5] Generated Node #0,3,3: 84:[90, 5] Operation: 83-78=5 Exploring Operation: 90+78=168, Resulting Numbers: [83, 168] Generated Node #0,3,4: 84:[83, 168] Operation: 90+78=168 Moving to Node #0,3,0 Current State: 84:[83, 12], Operations: ['56+27=83', '90-78=12'] Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,84 unequal: No Solution Exploring Operation: 83+12=95, Resulting Numbers: [95] 95,84 unequal: No Solution Exploring Operation: 83*12=996, Resulting Numbers: [996] 996,84 unequal: No Solution Moving to Node #0,3,2 Current State: 84:[78, 7], Operations: ['56+27=83', '90-83=7'] Exploring Operation: 78-7=71, Resulting Numbers: [71] 71,84 unequal: No Solution Exploring Operation: 78*7=546, Resulting Numbers: [546] 546,84 unequal: No Solution Exploring Operation: 78+7=85, Resulting Numbers: [85] 85,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[90, 5], Operations: ['56+27=83', '83-78=5'] Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,84 unequal: No Solution Exploring Operation: 90*5=450, Resulting Numbers: [450] 450,84 unequal: No Solution Exploring Operation: 90+5=95, Resulting Numbers: [95] 95,84 unequal: No Solution Exploring Operation: 90-5=85, Resulting Numbers: [85] 85,84 unequal: No Solution Moving to Node #0,3,1 Current State: 84:[90, 161], Operations: ['56+27=83', '78+83=161'] Exploring Operation: 90*161=14490, Resulting Numbers: [14490] 14490,84 unequal: No Solution Exploring Operation: 161-90=71, Resulting Numbers: [71] 71,84 unequal: No Solution Exploring Operation: 90+161=251, Resulting Numbers: [251] 251,84 unequal: No Solution Moving to Node #0,3,4 Current State: 84:[83, 168], Operations: ['56+27=83', '90+78=168'] Exploring Operation: 83*168=13944, Resulting Numbers: [13944] 13944,84 unequal: No Solution Exploring Operation: 83+168=251, Resulting Numbers: [251] 251,84 unequal: No Solution Exploring Operation: 168-83=85, Resulting Numbers: [85] 85,84 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 #0,4 Current State: 84:[90, 78, 29], Operations: ['56-27=29'] Exploring Operation: 78-29=49, Resulting Numbers: [90, 49] Generated Node #0,4,0: 84:[90, 49] Operation: 78-29=49 Exploring Operation: 90+29=119, Resulting Numbers: [78, 119] Generated Node #0,4,1: 84:[78, 119] Operation: 90+29=119 Exploring Operation: 90-29=61, Resulting Numbers: [78, 61] Generated Node #0,4,2: 84:[78, 61] Operation: 90-29=61 Exploring Operation: 78+29=107, Resulting Numbers: [90, 107] Generated Node #0,4,3: 84:[90, 107] Operation: 78+29=107 Exploring Operation: 90-78=12, Resulting Numbers: [29, 12] Generated Node #0,4,4: 84:[29, 12] Operation: 90-78=12 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 84:[29, 12], Operations: ['56-27=29', '90-78=12'] Exploring Operation: 29*12=348, Resulting Numbers: [348] 348,84 unequal: No Solution Exploring Operation: 29+12=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 84:[90, 49], Operations: ['56-27=29', '78-29=49'] Exploring Operation: 90-49=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 90+49=139, Resulting Numbers: [139] 139,84 unequal: No Solution Exploring Operation: 90*49=4410, Resulting Numbers: [4410] 4410,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 84:[78, 61], Operations: ['56-27=29', '90-29=61'] Exploring Operation: 78+61=139, Resulting Numbers: [139] 139,84 unequal: No Solution Exploring Operation: 78*61=4758, Resulting Numbers: [4758] 4758,84 unequal: No Solution Exploring Operation: 78-61=17, Resulting Numbers: [17] 17,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 84:[90, 107], Operations: ['56-27=29', '78+29=107'] Exploring Operation: 107-90=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 90+107=197, Resulting Numbers: [197] 197,84 unequal: No Solution Exploring Operation: 90*107=9630, Resulting Numbers: [9630] 9630,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 84:[78, 119], Operations: ['56-27=29', '90+29=119'] Exploring Operation: 78*119=9282, Resulting Numbers: [9282] 9282,84 unequal: No Solution Exploring Operation: 119-78=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 78+119=197, Resulting Numbers: [197] 197,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[56, 27, 12], Operations: ['90-78=12'] Exploring Operation: 56-12=44, Resulting Numbers: [27, 44] Generated Node #0,0,0: 84:[27, 44] Operation: 56-12=44 Exploring Operation: 56-27=29, Resulting Numbers: [12, 29] Generated Node #0,0,1: 84:[12, 29] Operation: 56-27=29 Exploring Operation: 56+12=68, Resulting Numbers: [27, 68] Generated Node #0,0,2: 84:[27, 68] Operation: 56+12=68 Exploring Operation: 56+27=83, Resulting Numbers: [12, 83] Generated Node #0,0,3: 84:[12, 83] Operation: 56+27=83 Exploring Operation: 27-12=15, Resulting Numbers: [56, 15] Generated Node #0,0,4: 84:[56, 15] Operation: 27-12=15 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 84:[12, 29], Operations: ['90-78=12', '56-27=29'] Exploring Operation: 12*29=348, Resulting Numbers: [348] 348,84 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 12+29=41, Resulting Numbers: [41] 41,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 84:[12, 83], Operations: ['90-78=12', '56+27=83'] Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,84 unequal: No Solution Exploring Operation: 12*83=996, Resulting Numbers: [996] 996,84 unequal: No Solution Exploring Operation: 12+83=95, Resulting Numbers: [95] 95,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 84:[27, 44], Operations: ['90-78=12', '56-12=44'] Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 27+44=71, Resulting Numbers: [71] 71,84 unequal: No Solution Exploring Operation: 27*44=1188, Resulting Numbers: [1188] 1188,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 84:[56, 15], Operations: ['90-78=12', '27-12=15'] Exploring Operation: 56*15=840, Resulting Numbers: [840] 840,84 unequal: No Solution Exploring Operation: 56-15=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 56+15=71, Resulting Numbers: [71] 71,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 84:[27, 68], Operations: ['90-78=12', '56+12=68'] Exploring Operation: 68-27=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 27+68=95, Resulting Numbers: [95] 95,84 unequal: No Solution Exploring Operation: 27*68=1836, Resulting Numbers: [1836] 1836,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 62, 3, 56, 69 ]
37
[ "62+69=131", "3*56=168", "168-131=37" ]
Current State: 37:[62, 3, 56, 69], Operations: [] Exploring Operation: 62+69=131, Resulting Numbers: [3, 56, 131] Generated Node #2: [3, 56, 131] from Operation: 62+69=131 Current State: 37:[3, 56, 131], Operations: ['62+69=131'] Exploring Operation: 3*56=168, Resulting Numbers: [131, 168] Generated Node #3: [131, 168] from Operation: 3*56=168 Current State: 37:[131, 168], Operations: ['62+69=131', '3*56=168'] Exploring Operation: 168-131=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[62, 3, 56, 69], Operations: [] Exploring Operation: 62-3=59, Resulting Numbers: [56, 69, 59] Generated Node #0,0: 37:[56, 69, 59] Operation: 62-3=59 Exploring Operation: 69/3=23, Resulting Numbers: [62, 56, 23] Generated Node #0,1: 37:[62, 56, 23] Operation: 69/3=23 Moving to Node #0,1 Current State: 37:[62, 56, 23], Operations: ['69/3=23'] Exploring Operation: 62-23=39, Resulting Numbers: [56, 39] Generated Node #0,1,0: 37:[56, 39] Operation: 62-23=39 Exploring Operation: 56-23=33, Resulting Numbers: [62, 33] Generated Node #0,1,1: 37:[62, 33] Operation: 56-23=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[56, 39], Operations: ['69/3=23', '62-23=39'] Exploring Operation: 56+39=95, Resulting Numbers: [95] 95,37 unequal: No Solution Exploring Operation: 56-39=17, Resulting Numbers: [17] 17,37 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:[62, 33], Operations: ['69/3=23', '56-23=33'] Exploring Operation: 62+33=95, Resulting Numbers: [95] 95,37 unequal: No Solution Exploring Operation: 62-33=29, Resulting Numbers: [29] 29,37 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: 37:[56, 69, 59], Operations: ['62-3=59'] Exploring Operation: 69-59=10, Resulting Numbers: [56, 10] Generated Node #0,0,0: 37:[56, 10] Operation: 69-59=10 Exploring Operation: 69-56=13, Resulting Numbers: [59, 13] Generated Node #0,0,1: 37:[59, 13] Operation: 69-56=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[56, 10], Operations: ['62-3=59', '69-59=10'] Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,37 unequal: No Solution Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,37 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 #0,0,1 Current State: 37:[59, 13], Operations: ['62-3=59', '69-56=13'] Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,37 unequal: No Solution Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,37 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
[ 33, 48, 16, 36 ]
96
[ "36-33=3", "48-16=32", "3*32=96" ]
Current State: 96:[33, 48, 16, 36], Operations: [] Exploring Operation: 36-33=3, Resulting Numbers: [48, 16, 3] Generated Node #2: [48, 16, 3] from Operation: 36-33=3 Current State: 96:[48, 16, 3], Operations: ['36-33=3'] Exploring Operation: 48-16=32, Resulting Numbers: [3, 32] Generated Node #3: [3, 32] from Operation: 48-16=32 Current State: 96:[3, 32], Operations: ['36-33=3', '48-16=32'] Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[33, 48, 16, 36], Operations: [] Exploring Operation: 36-33=3, Resulting Numbers: [48, 16, 3] Generated Node #0,0: 96:[48, 16, 3] Operation: 36-33=3 Exploring Operation: 48-33=15, Resulting Numbers: [16, 36, 15] Generated Node #0,1: 96:[16, 36, 15] Operation: 48-33=15 Exploring Operation: 48-36=12, Resulting Numbers: [33, 16, 12] Generated Node #0,2: 96:[33, 16, 12] Operation: 48-36=12 Exploring Operation: 33+16=49, Resulting Numbers: [48, 36, 49] Generated Node #0,3: 96:[48, 36, 49] Operation: 33+16=49 Moving to Node #0,0 Current State: 96:[48, 16, 3], Operations: ['36-33=3'] Exploring Operation: 48/3=16, Resulting Numbers: [16, 16] Generated Node #0,0,0: 96:[16, 16] Operation: 48/3=16 Exploring Operation: 48-16=32, Resulting Numbers: [3, 32] Generated Node #0,0,1: 96:[3, 32] Operation: 48-16=32 Exploring Operation: 16*3=48, Resulting Numbers: [48, 48] Generated Node #0,0,2: 96:[48, 48] Operation: 16*3=48 Exploring Operation: 48/16=3, Resulting Numbers: [3, 3] Generated Node #0,0,3: 96:[3, 3] Operation: 48/16=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[16, 16], Operations: ['36-33=3', '48/3=16'] Exploring Operation: 16/16=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 16*16=256, Resulting Numbers: [256] 256,96 unequal: No Solution Exploring Operation: 16-16=0, Resulting Numbers: [0] 0,96 unequal: No Solution Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 96:[3, 32], Operations: ['36-33=3', '48-16=32'] Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,96 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,96 unequal: No Solution Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[33, 48, 16, 36], Operations: [] Exploring Operation: 36-33=3, Resulting Numbers: [48, 16, 3] Generated Node #0,0: 96:[48, 16, 3] Operation: 36-33=3 Moving to Node #0,0 Current State: 96:[48, 16, 3], Operations: ['36-33=3'] Exploring Operation: 48-16=32, Resulting Numbers: [3, 32] Generated Node #0,0,1: 96:[3, 32] Operation: 48-16=32 Moving to Node #0,0,1 Current State: 96:[3, 32], Operations: ['36-33=3', '48-16=32'] Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 33, 84, 66, 75 ]
11
[ "33+66=99", "84-75=9", "99/9=11" ]
Current State: 11:[33, 84, 66, 75], Operations: [] Exploring Operation: 33+66=99, Resulting Numbers: [84, 75, 99] Generated Node #2: [84, 75, 99] from Operation: 33+66=99 Current State: 11:[84, 75, 99], Operations: ['33+66=99'] Exploring Operation: 84-75=9, Resulting Numbers: [99, 9] Generated Node #3: [99, 9] from Operation: 84-75=9 Current State: 11:[99, 9], Operations: ['33+66=99', '84-75=9'] Exploring Operation: 99/9=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[33, 84, 66, 75], Operations: [] Exploring Operation: 66/33=2, Resulting Numbers: [84, 75, 2] Generated Node #0,0: 11:[84, 75, 2] Operation: 66/33=2 Exploring Operation: 84-66=18, Resulting Numbers: [33, 75, 18] Generated Node #0,1: 11:[33, 75, 18] Operation: 84-66=18 Exploring Operation: 84-75=9, Resulting Numbers: [33, 66, 9] Generated Node #0,2: 11:[33, 66, 9] Operation: 84-75=9 Exploring Operation: 75-66=9, Resulting Numbers: [33, 84, 9] Generated Node #0,3: 11:[33, 84, 9] Operation: 75-66=9 Exploring Operation: 84-33=51, Resulting Numbers: [66, 75, 51] Generated Node #0,4: 11:[66, 75, 51] Operation: 84-33=51 Moving to Node #0,2 Current State: 11:[33, 66, 9], Operations: ['84-75=9'] Exploring Operation: 66-33=33, Resulting Numbers: [9, 33] Generated Node #0,2,0: 11:[9, 33] Operation: 66-33=33 Exploring Operation: 66-9=57, Resulting Numbers: [33, 57] Generated Node #0,2,1: 11:[33, 57] Operation: 66-9=57 Exploring Operation: 66/33=2, Resulting Numbers: [9, 2] Generated Node #0,2,2: 11:[9, 2] Operation: 66/33=2 Exploring Operation: 33+9=42, Resulting Numbers: [66, 42] Generated Node #0,2,3: 11:[66, 42] Operation: 33+9=42 Exploring Operation: 33-9=24, Resulting Numbers: [66, 24] Generated Node #0,2,4: 11:[66, 24] Operation: 33-9=24 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 11:[9, 2], Operations: ['84-75=9', '66/33=2'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[33, 84, 66, 75], Operations: [] Exploring Operation: 84-75=9, Resulting Numbers: [33, 66, 9] Generated Node #0,2: 11:[33, 66, 9] Operation: 84-75=9 Moving to Node #0,2 Current State: 11:[33, 66, 9], Operations: ['84-75=9'] Exploring Operation: 66/33=2, Resulting Numbers: [9, 2] Generated Node #0,2,2: 11:[9, 2] Operation: 66/33=2 Moving to Node #0,2,2 Current State: 11:[9, 2], Operations: ['84-75=9', '66/33=2'] Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 80, 62, 98, 68 ]
66
[ "62+98=160", "160/80=2", "68-2=66" ]
Current State: 66:[80, 62, 98, 68], Operations: [] Exploring Operation: 62+98=160, Resulting Numbers: [80, 68, 160] Generated Node #2: [80, 68, 160] from Operation: 62+98=160 Current State: 66:[80, 68, 160], Operations: ['62+98=160'] Exploring Operation: 160/80=2, Resulting Numbers: [68, 2] Generated Node #3: [68, 2] from Operation: 160/80=2 Current State: 66:[68, 2], Operations: ['62+98=160', '160/80=2'] Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[80, 62, 98, 68], Operations: [] Exploring Operation: 98-80=18, Resulting Numbers: [62, 68, 18] Generated Node #0,0: 66:[62, 68, 18] Operation: 98-80=18 Exploring Operation: 98-68=30, Resulting Numbers: [80, 62, 30] Generated Node #0,1: 66:[80, 62, 30] Operation: 98-68=30 Exploring Operation: 98-62=36, Resulting Numbers: [80, 68, 36] Generated Node #0,2: 66:[80, 68, 36] Operation: 98-62=36 Exploring Operation: 80-62=18, Resulting Numbers: [98, 68, 18] Generated Node #0,3: 66:[98, 68, 18] Operation: 80-62=18 Exploring Operation: 80-68=12, Resulting Numbers: [62, 98, 12] Generated Node #0,4: 66:[62, 98, 12] Operation: 80-68=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[62, 68, 18], Operations: ['98-80=18'] Exploring Operation: 68+18=86, Resulting Numbers: [62, 86] Generated Node #0,0,0: 66:[62, 86] Operation: 68+18=86 Exploring Operation: 68-62=6, Resulting Numbers: [18, 6] Generated Node #0,0,1: 66:[18, 6] Operation: 68-62=6 Exploring Operation: 62-18=44, Resulting Numbers: [68, 44] Generated Node #0,0,2: 66:[68, 44] Operation: 62-18=44 Exploring Operation: 68-18=50, Resulting Numbers: [62, 50] Generated Node #0,0,3: 66:[62, 50] Operation: 68-18=50 Exploring Operation: 62+18=80, Resulting Numbers: [68, 80] Generated Node #0,0,4: 66:[68, 80] Operation: 62+18=80 Moving to Node #0,0,1 Current State: 66:[18, 6], Operations: ['98-80=18', '68-62=6'] Exploring Operation: 18+6=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 18*6=108, Resulting Numbers: [108] 108,66 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,66 unequal: No Solution Moving to Node #0,0,2 Current State: 66:[68, 44], Operations: ['98-80=18', '62-18=44'] Exploring Operation: 68+44=112, Resulting Numbers: [112] 112,66 unequal: No Solution Exploring Operation: 68*44=2992, Resulting Numbers: [2992] 2992,66 unequal: No Solution Exploring Operation: 68-44=24, Resulting Numbers: [24] 24,66 unequal: No Solution Moving to Node #0,0,4 Current State: 66:[68, 80], Operations: ['98-80=18', '62+18=80'] Exploring Operation: 68*80=5440, Resulting Numbers: [5440] 5440,66 unequal: No Solution Exploring Operation: 68+80=148, Resulting Numbers: [148] 148,66 unequal: No Solution Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,66 unequal: No Solution Moving to Node #0,0,3 Current State: 66:[62, 50], Operations: ['98-80=18', '68-18=50'] Exploring Operation: 62-50=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 62*50=3100, Resulting Numbers: [3100] 3100,66 unequal: No Solution Exploring Operation: 62+50=112, Resulting Numbers: [112] 112,66 unequal: No Solution Moving to Node #0,0,0 Current State: 66:[62, 86], Operations: ['98-80=18', '68+18=86'] Exploring Operation: 86-62=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 62*86=5332, Resulting Numbers: [5332] 5332,66 unequal: No Solution Exploring Operation: 62+86=148, Resulting Numbers: [148] 148,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 66:[80, 68, 36], Operations: ['98-62=36'] Exploring Operation: 68+36=104, Resulting Numbers: [80, 104] Generated Node #0,2,0: 66:[80, 104] Operation: 68+36=104 Exploring Operation: 80-68=12, Resulting Numbers: [36, 12] Generated Node #0,2,1: 66:[36, 12] Operation: 80-68=12 Exploring Operation: 68-36=32, Resulting Numbers: [80, 32] Generated Node #0,2,2: 66:[80, 32] Operation: 68-36=32 Exploring Operation: 80-36=44, Resulting Numbers: [68, 44] Generated Node #0,2,3: 66:[68, 44] Operation: 80-36=44 Exploring Operation: 80+36=116, Resulting Numbers: [68, 116] Generated Node #0,2,4: 66:[68, 116] Operation: 80+36=116 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 66:[36, 12], Operations: ['98-62=36', '80-68=12'] Exploring Operation: 36*12=432, Resulting Numbers: [432] 432,66 unequal: No Solution Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,66 unequal: No Solution Exploring Operation: 36+12=48, Resulting Numbers: [48] 48,66 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 #0,2,3 Current State: 66:[68, 44], Operations: ['98-62=36', '80-36=44'] Exploring Operation: 68*44=2992, Resulting Numbers: [2992] 2992,66 unequal: No Solution Exploring Operation: 68-44=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 68+44=112, Resulting Numbers: [112] 112,66 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 #0,2,2 Current State: 66:[80, 32], Operations: ['98-62=36', '68-36=32'] Exploring Operation: 80+32=112, Resulting Numbers: [112] 112,66 unequal: No Solution Exploring Operation: 80*32=2560, Resulting Numbers: [2560] 2560,66 unequal: No Solution Exploring Operation: 80-32=48, Resulting Numbers: [48] 48,66 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 #0,2,0 Current State: 66:[80, 104], Operations: ['98-62=36', '68+36=104'] Exploring Operation: 104-80=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 80*104=8320, Resulting Numbers: [8320] 8320,66 unequal: No Solution Exploring Operation: 80+104=184, Resulting Numbers: [184] 184,66 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 #0,2,4 Current State: 66:[68, 116], Operations: ['98-62=36', '80+36=116'] Exploring Operation: 116-68=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 68+116=184, Resulting Numbers: [184] 184,66 unequal: No Solution Exploring Operation: 68*116=7888, Resulting Numbers: [7888] 7888,66 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[80, 62, 30], Operations: ['98-68=30'] Exploring Operation: 62+30=92, Resulting Numbers: [80, 92] Generated Node #0,1,0: 66:[80, 92] Operation: 62+30=92 Exploring Operation: 62-30=32, Resulting Numbers: [80, 32] Generated Node #0,1,1: 66:[80, 32] Operation: 62-30=32 Exploring Operation: 80-30=50, Resulting Numbers: [62, 50] Generated Node #0,1,2: 66:[62, 50] Operation: 80-30=50 Exploring Operation: 80-62=18, Resulting Numbers: [30, 18] Generated Node #0,1,3: 66:[30, 18] Operation: 80-62=18 Exploring Operation: 80+30=110, Resulting Numbers: [62, 110] Generated Node #0,1,4: 66:[62, 110] Operation: 80+30=110 Moving to Node #0,1,3 Current State: 66:[30, 18], Operations: ['98-68=30', '80-62=18'] Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 30*18=540, Resulting Numbers: [540] 540,66 unequal: No Solution Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,66 unequal: No Solution Moving to Node #0,1,1 Current State: 66:[80, 32], Operations: ['98-68=30', '62-30=32'] Exploring Operation: 80*32=2560, Resulting Numbers: [2560] 2560,66 unequal: No Solution Exploring Operation: 80+32=112, Resulting Numbers: [112] 112,66 unequal: No Solution Exploring Operation: 80-32=48, Resulting Numbers: [48] 48,66 unequal: No Solution Moving to Node #0,1,2 Current State: 66:[62, 50], Operations: ['98-68=30', '80-30=50'] Exploring Operation: 62-50=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 62*50=3100, Resulting Numbers: [3100] 3100,66 unequal: No Solution Exploring Operation: 62+50=112, Resulting Numbers: [112] 112,66 unequal: No Solution Moving to Node #0,1,0 Current State: 66:[80, 92], Operations: ['98-68=30', '62+30=92'] Exploring Operation: 80*92=7360, Resulting Numbers: [7360] 7360,66 unequal: No Solution Exploring Operation: 92-80=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 80+92=172, Resulting Numbers: [172] 172,66 unequal: No Solution Moving to Node #0,1,4 Current State: 66:[62, 110], Operations: ['98-68=30', '80+30=110'] Exploring Operation: 110-62=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 62+110=172, Resulting Numbers: [172] 172,66 unequal: No Solution Exploring Operation: 62*110=6820, Resulting Numbers: [6820] 6820,66 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 #0,4 Current State: 66:[62, 98, 12], Operations: ['80-68=12'] Exploring Operation: 62-12=50, Resulting Numbers: [98, 50] Generated Node #0,4,0: 66:[98, 50] Operation: 62-12=50 Exploring Operation: 62+12=74, Resulting Numbers: [98, 74] Generated Node #0,4,1: 66:[98, 74] Operation: 62+12=74 Exploring Operation: 98+12=110, Resulting Numbers: [62, 110] Generated Node #0,4,2: 66:[62, 110] Operation: 98+12=110 Exploring Operation: 98-12=86, Resulting Numbers: [62, 86] Generated Node #0,4,3: 66:[62, 86] Operation: 98-12=86 Exploring Operation: 98-62=36, Resulting Numbers: [12, 36] Generated Node #0,4,4: 66:[12, 36] Operation: 98-62=36 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 66:[12, 36], Operations: ['80-68=12', '98-62=36'] Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,66 unequal: No Solution Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 12+36=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 12*36=432, Resulting Numbers: [432] 432,66 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 #0,4,3 Current State: 66:[62, 86], Operations: ['80-68=12', '98-12=86'] Exploring Operation: 62+86=148, Resulting Numbers: [148] 148,66 unequal: No Solution Exploring Operation: 62*86=5332, Resulting Numbers: [5332] 5332,66 unequal: No Solution Exploring Operation: 86-62=24, Resulting Numbers: [24] 24,66 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 #0,4,1 Current State: 66:[98, 74], Operations: ['80-68=12', '62+12=74'] Exploring Operation: 98-74=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 98+74=172, Resulting Numbers: [172] 172,66 unequal: No Solution Exploring Operation: 98*74=7252, Resulting Numbers: [7252] 7252,66 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 #0,4,0 Current State: 66:[98, 50], Operations: ['80-68=12', '62-12=50'] Exploring Operation: 98-50=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 98+50=148, Resulting Numbers: [148] 148,66 unequal: No Solution Exploring Operation: 98*50=4900, Resulting Numbers: [4900] 4900,66 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 #0,4,2 Current State: 66:[62, 110], Operations: ['80-68=12', '98+12=110'] Exploring Operation: 62*110=6820, Resulting Numbers: [6820] 6820,66 unequal: No Solution Exploring Operation: 110-62=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 62+110=172, Resulting Numbers: [172] 172,66 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 Start Sub Search at level 1: Moving to Node #0,3 Current State: 66:[98, 68, 18], Operations: ['80-62=18'] Exploring Operation: 98+18=116, Resulting Numbers: [68, 116] Generated Node #0,3,0: 66:[68, 116] Operation: 98+18=116 Exploring Operation: 98-18=80, Resulting Numbers: [68, 80] Generated Node #0,3,1: 66:[68, 80] Operation: 98-18=80 Exploring Operation: 68-18=50, Resulting Numbers: [98, 50] Generated Node #0,3,2: 66:[98, 50] Operation: 68-18=50 Exploring Operation: 98-68=30, Resulting Numbers: [18, 30] Generated Node #0,3,3: 66:[18, 30] Operation: 98-68=30 Exploring Operation: 68+18=86, Resulting Numbers: [98, 86] Generated Node #0,3,4: 66:[98, 86] Operation: 68+18=86 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 66:[18, 30], Operations: ['80-62=18', '98-68=30'] Exploring Operation: 18+30=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 18*30=540, Resulting Numbers: [540] 540,66 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 #0,3,1 Current State: 66:[68, 80], Operations: ['80-62=18', '98-18=80'] Exploring Operation: 68+80=148, Resulting Numbers: [148] 148,66 unequal: No Solution Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 68*80=5440, Resulting Numbers: [5440] 5440,66 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 #0,3,2 Current State: 66:[98, 50], Operations: ['80-62=18', '68-18=50'] Exploring Operation: 98*50=4900, Resulting Numbers: [4900] 4900,66 unequal: No Solution Exploring Operation: 98+50=148, Resulting Numbers: [148] 148,66 unequal: No Solution Exploring Operation: 98-50=48, Resulting Numbers: [48] 48,66 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 #0,3,0 Current State: 66:[68, 116], Operations: ['80-62=18', '98+18=116'] Exploring Operation: 68*116=7888, Resulting Numbers: [7888] 7888,66 unequal: No Solution Exploring Operation: 116-68=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 68+116=184, Resulting Numbers: [184] 184,66 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 #0,3,4 Current State: 66:[98, 86], Operations: ['80-62=18', '68+18=86'] Exploring Operation: 98+86=184, Resulting Numbers: [184] 184,66 unequal: No Solution Exploring Operation: 98*86=8428, Resulting Numbers: [8428] 8428,66 unequal: No Solution Exploring Operation: 98-86=12, Resulting Numbers: [12] 12,66 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_5
mult_heuristic
[ 65, 6, 5, 20 ]
25
[ "20-5=15", "6*15=90", "90-65=25" ]
Current State: 25:[65, 6, 5, 20], Operations: [] Exploring Operation: 20-5=15, Resulting Numbers: [65, 6, 15] Generated Node #2: [65, 6, 15] from Operation: 20-5=15 Current State: 25:[65, 6, 15], Operations: ['20-5=15'] Exploring Operation: 6*15=90, Resulting Numbers: [65, 90] Generated Node #3: [65, 90] from Operation: 6*15=90 Current State: 25:[65, 90], Operations: ['20-5=15', '6*15=90'] Exploring Operation: 90-65=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[65, 6, 5, 20], Operations: [] Exploring Operation: 65/5=13, Resulting Numbers: [6, 20, 13] Generated Node #0,0: 25:[6, 20, 13] Operation: 65/5=13 Moving to Node #0,0 Current State: 25:[6, 20, 13], Operations: ['65/5=13'] Exploring Operation: 20-13=7, Resulting Numbers: [6, 7] Generated Node #0,0,0: 25:[6, 7] Operation: 20-13=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[6, 7], Operations: ['65/5=13', '20-13=7'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 63, 30, 8, 67 ]
26
[ "63-30=33", "67-8=59", "59-33=26" ]
Current State: 26:[63, 30, 8, 67], Operations: [] Exploring Operation: 63-30=33, Resulting Numbers: [8, 67, 33] Generated Node #2: [8, 67, 33] from Operation: 63-30=33 Current State: 26:[8, 67, 33], Operations: ['63-30=33'] Exploring Operation: 67-8=59, Resulting Numbers: [33, 59] Generated Node #3: [33, 59] from Operation: 67-8=59 Current State: 26:[33, 59], Operations: ['63-30=33', '67-8=59'] Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[63, 30, 8, 67], Operations: [] Exploring Operation: 67-63=4, Resulting Numbers: [30, 8, 4] Generated Node #0,0: 26:[30, 8, 4] Operation: 67-63=4 Exploring Operation: 63-30=33, Resulting Numbers: [8, 67, 33] Generated Node #0,1: 26:[8, 67, 33] Operation: 63-30=33 Exploring Operation: 63-8=55, Resulting Numbers: [30, 67, 55] Generated Node #0,2: 26:[30, 67, 55] Operation: 63-8=55 Exploring Operation: 67-30=37, Resulting Numbers: [63, 8, 37] Generated Node #0,3: 26:[63, 8, 37] Operation: 67-30=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[30, 8, 4], Operations: ['67-63=4'] Exploring Operation: 8+4=12, Resulting Numbers: [30, 12] Generated Node #0,0,0: 26:[30, 12] Operation: 8+4=12 Exploring Operation: 8/4=2, Resulting Numbers: [30, 2] Generated Node #0,0,1: 26:[30, 2] Operation: 8/4=2 Exploring Operation: 30-4=26, Resulting Numbers: [8, 26] Generated Node #0,0,2: 26:[8, 26] Operation: 30-4=26 Exploring Operation: 30-8=22, Resulting Numbers: [4, 22] Generated Node #0,0,3: 26:[4, 22] Operation: 30-8=22 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 26:[30, 2], Operations: ['67-63=4', '8/4=2'] Exploring Operation: 30*2=60, Resulting Numbers: [60] 60,26 unequal: No Solution Exploring Operation: 30+2=32, Resulting Numbers: [32] 32,26 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,26 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,26 unequal: No Solution No 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: 26:[30, 12], Operations: ['67-63=4', '8+4=12'] Exploring Operation: 30+12=42, Resulting Numbers: [42] 42,26 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 30*12=360, Resulting Numbers: [360] 360,26 unequal: No Solution No 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: 26:[8, 26], Operations: ['67-63=4', '30-4=26'] Exploring Operation: 8+26=34, Resulting Numbers: [34] 34,26 unequal: No Solution Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 8*26=208, Resulting Numbers: [208] 208,26 unequal: No Solution No 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: 26:[4, 22], Operations: ['67-63=4', '30-8=22'] Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,26 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[63, 30, 8, 67], Operations: [] Exploring Operation: 67-63=4, Resulting Numbers: [30, 8, 4] Generated Node #0,0: 26:[30, 8, 4] Operation: 67-63=4 Moving to Node #0,0 Current State: 26:[30, 8, 4], Operations: ['67-63=4'] Exploring Operation: 30-8=22, Resulting Numbers: [4, 22] Generated Node #0,0,3: 26:[4, 22] Operation: 30-8=22 Moving to Node #0,0,3 Current State: 26:[4, 22], Operations: ['67-63=4', '30-8=22'] Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_4
mult_heuristic
[ 10, 40, 9, 14 ]
16
[ "40+14=54", "54/9=6", "10+6=16" ]
Current State: 16:[10, 40, 9, 14], Operations: [] Exploring Operation: 40+14=54, Resulting Numbers: [10, 9, 54] Generated Node #2: [10, 9, 54] from Operation: 40+14=54 Current State: 16:[10, 9, 54], Operations: ['40+14=54'] Exploring Operation: 54/9=6, Resulting Numbers: [10, 6] Generated Node #3: [10, 6] from Operation: 54/9=6 Current State: 16:[10, 6], Operations: ['40+14=54', '54/9=6'] Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[10, 40, 9, 14], Operations: [] Exploring Operation: 40-9=31, Resulting Numbers: [10, 14, 31] Generated Node #0,0: 16:[10, 14, 31] Operation: 40-9=31 Exploring Operation: 14-10=4, Resulting Numbers: [40, 9, 4] Generated Node #0,1: 16:[40, 9, 4] Operation: 14-10=4 Exploring Operation: 40/10=4, Resulting Numbers: [9, 14, 4] Generated Node #0,2: 16:[9, 14, 4] Operation: 40/10=4 Exploring Operation: 40-14=26, Resulting Numbers: [10, 9, 26] Generated Node #0,3: 16:[10, 9, 26] Operation: 40-14=26 Exploring Operation: 40-10=30, Resulting Numbers: [9, 14, 30] Generated Node #0,4: 16:[9, 14, 30] Operation: 40-10=30 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[9, 14, 4], Operations: ['40/10=4'] Exploring Operation: 9-4=5, Resulting Numbers: [14, 5] Generated Node #0,2,0: 16:[14, 5] Operation: 9-4=5 Exploring Operation: 14+4=18, Resulting Numbers: [9, 18] Generated Node #0,2,1: 16:[9, 18] Operation: 14+4=18 Exploring Operation: 9+4=13, Resulting Numbers: [14, 13] Generated Node #0,2,2: 16:[14, 13] Operation: 9+4=13 Exploring Operation: 14-9=5, Resulting Numbers: [4, 5] Generated Node #0,2,3: 16:[4, 5] Operation: 14-9=5 Exploring Operation: 14-4=10, Resulting Numbers: [9, 10] Generated Node #0,2,4: 16:[9, 10] Operation: 14-4=10 Moving to Node #0,2,3 Current State: 16:[4, 5], Operations: ['40/10=4', '14-9=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,16 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[9, 18], Operations: ['40/10=4', '14+4=18'] Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 9*18=162, Resulting Numbers: [162] 162,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[14, 5], Operations: ['40/10=4', '9-4=5'] Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,16 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,16 unequal: No Solution Moving to Node #0,2,4 Current State: 16:[9, 10], Operations: ['40/10=4', '14-4=10'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,16 unequal: No Solution Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,16 unequal: No Solution Moving to Node #0,2,2 Current State: 16:[14, 13], Operations: ['40/10=4', '9+4=13'] Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 16:[10, 9, 26], Operations: ['40-14=26'] Exploring Operation: 10+9=19, Resulting Numbers: [26, 19] Generated Node #0,3,0: 16:[26, 19] Operation: 10+9=19 Exploring Operation: 26-9=17, Resulting Numbers: [10, 17] Generated Node #0,3,1: 16:[10, 17] Operation: 26-9=17 Exploring Operation: 26-10=16, Resulting Numbers: [9, 16] Generated Node #0,3,2: 16:[9, 16] Operation: 26-10=16 Exploring Operation: 10+26=36, Resulting Numbers: [9, 36] Generated Node #0,3,3: 16:[9, 36] Operation: 10+26=36 Exploring Operation: 10-9=1, Resulting Numbers: [26, 1] Generated Node #0,3,4: 16:[26, 1] Operation: 10-9=1 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 16:[9, 16], Operations: ['40-14=26', '26-10=16'] Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,16 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 #0,3,1 Current State: 16:[10, 17], Operations: ['40-14=26', '26-9=17'] Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 10+17=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 10*17=170, Resulting Numbers: [170] 170,16 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 #0,3,4 Current State: 16:[26, 1], Operations: ['40-14=26', '10-9=1'] Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 26+1=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 26*1=26, Resulting Numbers: [26] 26,16 unequal: No Solution Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,16 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 #0,3,0 Current State: 16:[26, 19], Operations: ['40-14=26', '10+9=19'] Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,16 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,16 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 #0,3,3 Current State: 16:[9, 36], Operations: ['40-14=26', '10+26=36'] Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,16 unequal: No Solution Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 9*36=324, Resulting Numbers: [324] 324,16 unequal: No Solution Exploring Operation: 9+36=45, Resulting Numbers: [45] 45,16 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 #0,4 Current State: 16:[9, 14, 30], Operations: ['40-10=30'] Exploring Operation: 9+14=23, Resulting Numbers: [30, 23] Generated Node #0,4,0: 16:[30, 23] Operation: 9+14=23 Exploring Operation: 9+30=39, Resulting Numbers: [14, 39] Generated Node #0,4,1: 16:[14, 39] Operation: 9+30=39 Exploring Operation: 14-9=5, Resulting Numbers: [30, 5] Generated Node #0,4,2: 16:[30, 5] Operation: 14-9=5 Exploring Operation: 30-14=16, Resulting Numbers: [9, 16] Generated Node #0,4,3: 16:[9, 16] Operation: 30-14=16 Exploring Operation: 30-9=21, Resulting Numbers: [14, 21] Generated Node #0,4,4: 16:[14, 21] Operation: 30-9=21 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 16:[9, 16], Operations: ['40-10=30', '30-14=16'] Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,16 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,16 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 #0,4,4 Current State: 16:[14, 21], Operations: ['40-10=30', '30-9=21'] Exploring Operation: 14*21=294, Resulting Numbers: [294] 294,16 unequal: No Solution Exploring Operation: 14+21=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,16 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 #0,4,2 Current State: 16:[30, 5], Operations: ['40-10=30', '14-9=5'] Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 30*5=150, Resulting Numbers: [150] 150,16 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,16 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 #0,4,0 Current State: 16:[30, 23], Operations: ['40-10=30', '9+14=23'] Exploring Operation: 30+23=53, Resulting Numbers: [53] 53,16 unequal: No Solution Exploring Operation: 30*23=690, Resulting Numbers: [690] 690,16 unequal: No Solution Exploring Operation: 30-23=7, Resulting Numbers: [7] 7,16 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 #0,4,1 Current State: 16:[14, 39], Operations: ['40-10=30', '9+30=39'] Exploring Operation: 14+39=53, Resulting Numbers: [53] 53,16 unequal: No Solution Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 14*39=546, Resulting Numbers: [546] 546,16 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:[10, 14, 31], Operations: ['40-9=31'] Exploring Operation: 31-14=17, Resulting Numbers: [10, 17] Generated Node #0,0,0: 16:[10, 17] Operation: 31-14=17 Exploring Operation: 14-10=4, Resulting Numbers: [31, 4] Generated Node #0,0,1: 16:[31, 4] Operation: 14-10=4 Exploring Operation: 10+31=41, Resulting Numbers: [14, 41] Generated Node #0,0,2: 16:[14, 41] Operation: 10+31=41 Exploring Operation: 10+14=24, Resulting Numbers: [31, 24] Generated Node #0,0,3: 16:[31, 24] Operation: 10+14=24 Exploring Operation: 31-10=21, Resulting Numbers: [14, 21] Generated Node #0,0,4: 16:[14, 21] Operation: 31-10=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 16:[10, 17], Operations: ['40-9=31', '31-14=17'] Exploring Operation: 10+17=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 10*17=170, Resulting Numbers: [170] 170,16 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,16 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 #0,0,4 Current State: 16:[14, 21], Operations: ['40-9=31', '31-10=21'] Exploring Operation: 14*21=294, Resulting Numbers: [294] 294,16 unequal: No Solution Exploring Operation: 14+21=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,16 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:[31, 4], Operations: ['40-9=31', '14-10=4'] Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,16 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,16 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:[31, 24], Operations: ['40-9=31', '10+14=24'] Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,16 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,16 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:[14, 41], Operations: ['40-9=31', '10+31=41'] Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 14+41=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 14*41=574, Resulting Numbers: [574] 574,16 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 #0,1 Current State: 16:[40, 9, 4], Operations: ['14-10=4'] Exploring Operation: 9-4=5, Resulting Numbers: [40, 5] Generated Node #0,1,0: 16:[40, 5] Operation: 9-4=5 Exploring Operation: 9+4=13, Resulting Numbers: [40, 13] Generated Node #0,1,1: 16:[40, 13] Operation: 9+4=13 Exploring Operation: 40-9=31, Resulting Numbers: [4, 31] Generated Node #0,1,2: 16:[4, 31] Operation: 40-9=31 Exploring Operation: 40-4=36, Resulting Numbers: [9, 36] Generated Node #0,1,3: 16:[9, 36] Operation: 40-4=36 Exploring Operation: 40/4=10, Resulting Numbers: [9, 10] Generated Node #0,1,4: 16:[9, 10] Operation: 40/4=10 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 16:[9, 10], Operations: ['14-10=4', '40/4=10'] Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,16 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,16 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:[4, 31], Operations: ['14-10=4', '40-9=31'] Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,16 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,16 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:[9, 36], Operations: ['14-10=4', '40-4=36'] Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,16 unequal: No Solution Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 9+36=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 9*36=324, Resulting Numbers: [324] 324,16 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 #0,1,0 Current State: 16:[40, 5], Operations: ['14-10=4', '9-4=5'] Exploring Operation: 40*5=200, Resulting Numbers: [200] 200,16 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 40+5=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,16 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:[40, 13], Operations: ['14-10=4', '9+4=13'] Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 40+13=53, Resulting Numbers: [53] 53,16 unequal: No Solution Exploring Operation: 40*13=520, Resulting Numbers: [520] 520,16 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_5
mult_heuristic
[ 30, 40, 45, 77 ]
80
[ "30+45=75", "77-75=2", "40*2=80" ]
Current State: 80:[30, 40, 45, 77], Operations: [] Exploring Operation: 30+45=75, Resulting Numbers: [40, 77, 75] Generated Node #2: [40, 77, 75] from Operation: 30+45=75 Current State: 80:[40, 77, 75], Operations: ['30+45=75'] Exploring Operation: 77-75=2, Resulting Numbers: [40, 2] Generated Node #3: [40, 2] from Operation: 77-75=2 Current State: 80:[40, 2], Operations: ['30+45=75', '77-75=2'] Exploring Operation: 40*2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[30, 40, 45, 77], Operations: [] Exploring Operation: 45-30=15, Resulting Numbers: [40, 77, 15] Generated Node #0,0: 80:[40, 77, 15] Operation: 45-30=15 Exploring Operation: 30+45=75, Resulting Numbers: [40, 77, 75] Generated Node #0,1: 80:[40, 77, 75] Operation: 30+45=75 Exploring Operation: 40-30=10, Resulting Numbers: [45, 77, 10] Generated Node #0,2: 80:[45, 77, 10] Operation: 40-30=10 Exploring Operation: 77-30=47, Resulting Numbers: [40, 45, 47] Generated Node #0,3: 80:[40, 45, 47] Operation: 77-30=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[40, 77, 15], Operations: ['45-30=15'] Exploring Operation: 77-40=37, Resulting Numbers: [15, 37] Generated Node #0,0,0: 80:[15, 37] Operation: 77-40=37 Exploring Operation: 40+15=55, Resulting Numbers: [77, 55] Generated Node #0,0,1: 80:[77, 55] Operation: 40+15=55 Exploring Operation: 40-15=25, Resulting Numbers: [77, 25] Generated Node #0,0,2: 80:[77, 25] Operation: 40-15=25 Exploring Operation: 77+15=92, Resulting Numbers: [40, 92] Generated Node #0,0,3: 80:[40, 92] Operation: 77+15=92 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[15, 37], Operations: ['45-30=15', '77-40=37'] Exploring Operation: 15+37=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,80 unequal: No Solution Exploring Operation: 15*37=555, Resulting Numbers: [555] 555,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 80:[77, 25], Operations: ['45-30=15', '40-15=25'] Exploring Operation: 77*25=1925, Resulting Numbers: [1925] 1925,80 unequal: No Solution Exploring Operation: 77-25=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 77+25=102, Resulting Numbers: [102] 102,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 80:[40, 92], Operations: ['45-30=15', '77+15=92'] Exploring Operation: 40*92=3680, Resulting Numbers: [3680] 3680,80 unequal: No Solution Exploring Operation: 92-40=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 40+92=132, Resulting Numbers: [132] 132,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 80:[77, 55], Operations: ['45-30=15', '40+15=55'] Exploring Operation: 77-55=22, Resulting Numbers: [22] 22,80 unequal: No Solution Exploring Operation: 77+55=132, Resulting Numbers: [132] 132,80 unequal: No Solution Exploring Operation: 77*55=4235, Resulting Numbers: [4235] 4235,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[40, 77, 75], Operations: ['30+45=75'] Exploring Operation: 75-40=35, Resulting Numbers: [77, 35] Generated Node #0,1,0: 80:[77, 35] Operation: 75-40=35 Exploring Operation: 40+75=115, Resulting Numbers: [77, 115] Generated Node #0,1,1: 80:[77, 115] Operation: 40+75=115 Exploring Operation: 77-75=2, Resulting Numbers: [40, 2] Generated Node #0,1,2: 80:[40, 2] Operation: 77-75=2 Exploring Operation: 77-40=37, Resulting Numbers: [75, 37] Generated Node #0,1,3: 80:[75, 37] Operation: 77-40=37 Moving to Node #0,1,2 Current State: 80:[40, 2], Operations: ['30+45=75', '77-75=2'] Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,80 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,80 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 40*2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[30, 40, 45, 77], Operations: [] Exploring Operation: 30+45=75, Resulting Numbers: [40, 77, 75] Generated Node #0,1: 80:[40, 77, 75] Operation: 30+45=75 Moving to Node #0,1 Current State: 80:[40, 77, 75], Operations: ['30+45=75'] Exploring Operation: 77-75=2, Resulting Numbers: [40, 2] Generated Node #0,1,2: 80:[40, 2] Operation: 77-75=2 Moving to Node #0,1,2 Current State: 80:[40, 2], Operations: ['30+45=75', '77-75=2'] Exploring Operation: 40*2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 18, 67, 69, 91 ]
92
[ "91-67=24", "69*24=1656", "1656/18=92" ]
Current State: 92:[18, 67, 69, 91], Operations: [] Exploring Operation: 91-67=24, Resulting Numbers: [18, 69, 24] Generated Node #2: [18, 69, 24] from Operation: 91-67=24 Current State: 92:[18, 69, 24], Operations: ['91-67=24'] Exploring Operation: 69*24=1656, Resulting Numbers: [18, 1656] Generated Node #3: [18, 1656] from Operation: 69*24=1656 Current State: 92:[18, 1656], Operations: ['91-67=24', '69*24=1656'] Exploring Operation: 1656/18=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[18, 67, 69, 91], Operations: [] Exploring Operation: 67-18=49, Resulting Numbers: [69, 91, 49] Generated Node #0,0: 92:[69, 91, 49] Operation: 67-18=49 Exploring Operation: 69-67=2, Resulting Numbers: [18, 91, 2] Generated Node #0,1: 92:[18, 91, 2] Operation: 69-67=2 Moving to Node #0,1 Current State: 92:[18, 91, 2], Operations: ['69-67=2'] Exploring Operation: 18/2=9, Resulting Numbers: [91, 9] Generated Node #0,1,0: 92:[91, 9] Operation: 18/2=9 Exploring Operation: 18+2=20, Resulting Numbers: [91, 20] Generated Node #0,1,1: 92:[91, 20] Operation: 18+2=20 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[91, 20], Operations: ['69-67=2', '18+2=20'] Exploring Operation: 91-20=71, Resulting Numbers: [71] 71,92 unequal: No Solution Exploring Operation: 91+20=111, Resulting Numbers: [111] 111,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[91, 9], Operations: ['69-67=2', '18/2=9'] Exploring Operation: 91+9=100, Resulting Numbers: [100] 100,92 unequal: No Solution Exploring Operation: 91-9=82, Resulting Numbers: [82] 82,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 92:[69, 91, 49], Operations: ['67-18=49'] Exploring Operation: 69-49=20, Resulting Numbers: [91, 20] Generated Node #0,0,0: 92:[91, 20] Operation: 69-49=20 Exploring Operation: 91-69=22, Resulting Numbers: [49, 22] Generated Node #0,0,1: 92:[49, 22] Operation: 91-69=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[91, 20], Operations: ['67-18=49', '69-49=20'] Exploring Operation: 91+20=111, Resulting Numbers: [111] 111,92 unequal: No Solution Exploring Operation: 91-20=71, Resulting Numbers: [71] 71,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[49, 22], Operations: ['67-18=49', '91-69=22'] Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 49+22=71, Resulting Numbers: [71] 71,92 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
[ 32, 92, 43, 51 ]
96
[ "51-43=8", "32/8=4", "92+4=96" ]
Current State: 96:[32, 92, 43, 51], Operations: [] Exploring Operation: 51-43=8, Resulting Numbers: [32, 92, 8] Generated Node #2: [32, 92, 8] from Operation: 51-43=8 Current State: 96:[32, 92, 8], Operations: ['51-43=8'] Exploring Operation: 32/8=4, Resulting Numbers: [92, 4] Generated Node #3: [92, 4] from Operation: 32/8=4 Current State: 96:[92, 4], Operations: ['51-43=8', '32/8=4'] Exploring Operation: 92+4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[32, 92, 43, 51], Operations: [] Exploring Operation: 51-43=8, Resulting Numbers: [32, 92, 8] Generated Node #0,0: 96:[32, 92, 8] Operation: 51-43=8 Exploring Operation: 92-43=49, Resulting Numbers: [32, 51, 49] Generated Node #0,1: 96:[32, 51, 49] Operation: 92-43=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[32, 92, 8], Operations: ['51-43=8'] Exploring Operation: 32/8=4, Resulting Numbers: [92, 4] Generated Node #0,0,0: 96:[92, 4] Operation: 32/8=4 Exploring Operation: 32-8=24, Resulting Numbers: [92, 24] Generated Node #0,0,1: 96:[92, 24] Operation: 32-8=24 Moving to Node #0,0,0 Current State: 96:[92, 4], Operations: ['51-43=8', '32/8=4'] Exploring Operation: 92+4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[32, 92, 43, 51], Operations: [] Exploring Operation: 51-43=8, Resulting Numbers: [32, 92, 8] Generated Node #0,0: 96:[32, 92, 8] Operation: 51-43=8 Moving to Node #0,0 Current State: 96:[32, 92, 8], Operations: ['51-43=8'] Exploring Operation: 32/8=4, Resulting Numbers: [92, 4] Generated Node #0,0,0: 96:[92, 4] Operation: 32/8=4 Moving to Node #0,0,0 Current State: 96:[92, 4], Operations: ['51-43=8', '32/8=4'] Exploring Operation: 92+4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 54, 12, 7, 99 ]
93
[ "54-12=42", "42/7=6", "99-6=93" ]
Current State: 93:[54, 12, 7, 99], Operations: [] Exploring Operation: 54-12=42, Resulting Numbers: [7, 99, 42] Generated Node #2: [7, 99, 42] from Operation: 54-12=42 Current State: 93:[7, 99, 42], Operations: ['54-12=42'] Exploring Operation: 42/7=6, Resulting Numbers: [99, 6] Generated Node #3: [99, 6] from Operation: 42/7=6 Current State: 93:[99, 6], Operations: ['54-12=42', '42/7=6'] Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[54, 12, 7, 99], Operations: [] Exploring Operation: 54-12=42, Resulting Numbers: [7, 99, 42] Generated Node #0,0: 93:[7, 99, 42] Operation: 54-12=42 Exploring Operation: 99-54=45, Resulting Numbers: [12, 7, 45] Generated Node #0,1: 93:[12, 7, 45] Operation: 99-54=45 Exploring Operation: 99-12=87, Resulting Numbers: [54, 7, 87] Generated Node #0,2: 93:[54, 7, 87] Operation: 99-12=87 Exploring Operation: 54-7=47, Resulting Numbers: [12, 99, 47] Generated Node #0,3: 93:[12, 99, 47] Operation: 54-7=47 Exploring Operation: 12-7=5, Resulting Numbers: [54, 99, 5] Generated Node #0,4: 93:[54, 99, 5] Operation: 12-7=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[7, 99, 42], Operations: ['54-12=42'] Exploring Operation: 7+99=106, Resulting Numbers: [42, 106] Generated Node #0,0,0: 93:[42, 106] Operation: 7+99=106 Exploring Operation: 7+42=49, Resulting Numbers: [99, 49] Generated Node #0,0,1: 93:[99, 49] Operation: 7+42=49 Exploring Operation: 42-7=35, Resulting Numbers: [99, 35] Generated Node #0,0,2: 93:[99, 35] Operation: 42-7=35 Exploring Operation: 42/7=6, Resulting Numbers: [99, 6] Generated Node #0,0,3: 93:[99, 6] Operation: 42/7=6 Exploring Operation: 99-7=92, Resulting Numbers: [42, 92] Generated Node #0,0,4: 93:[42, 92] Operation: 99-7=92 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 93:[99, 6], Operations: ['54-12=42', '42/7=6'] Exploring Operation: 99*6=594, Resulting Numbers: [594] 594,93 unequal: No Solution Exploring Operation: 99+6=105, Resulting Numbers: [105] 105,93 unequal: No Solution Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[54, 12, 7, 99], Operations: [] Exploring Operation: 54-12=42, Resulting Numbers: [7, 99, 42] Generated Node #0,0: 93:[7, 99, 42] Operation: 54-12=42 Moving to Node #0,0 Current State: 93:[7, 99, 42], Operations: ['54-12=42'] Exploring Operation: 42/7=6, Resulting Numbers: [99, 6] Generated Node #0,0,3: 93:[99, 6] Operation: 42/7=6 Moving to Node #0,0,3 Current State: 93:[99, 6], Operations: ['54-12=42', '42/7=6'] Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 3, 30, 9, 5 ]
40
[ "30/3=10", "9-5=4", "10*4=40" ]
Current State: 40:[3, 30, 9, 5], Operations: [] Exploring Operation: 30/3=10, Resulting Numbers: [9, 5, 10] Generated Node #2: [9, 5, 10] from Operation: 30/3=10 Current State: 40:[9, 5, 10], Operations: ['30/3=10'] Exploring Operation: 9-5=4, Resulting Numbers: [10, 4] Generated Node #3: [10, 4] from Operation: 9-5=4 Current State: 40:[10, 4], Operations: ['30/3=10', '9-5=4'] Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[3, 30, 9, 5], Operations: [] Exploring Operation: 30/3=10, Resulting Numbers: [9, 5, 10] Generated Node #0,0: 40:[9, 5, 10] Operation: 30/3=10 Exploring Operation: 30+9=39, Resulting Numbers: [3, 5, 39] Generated Node #0,1: 40:[3, 5, 39] Operation: 30+9=39 Moving to Node #0,0 Current State: 40:[9, 5, 10], Operations: ['30/3=10'] Exploring Operation: 9-5=4, Resulting Numbers: [10, 4] Generated Node #0,0,0: 40:[10, 4] Operation: 9-5=4 Exploring Operation: 9+10=19, Resulting Numbers: [5, 19] Generated Node #0,0,1: 40:[5, 19] Operation: 9+10=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[10, 4], Operations: ['30/3=10', '9-5=4'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[3, 30, 9, 5], Operations: [] Exploring Operation: 30/3=10, Resulting Numbers: [9, 5, 10] Generated Node #0,0: 40:[9, 5, 10] Operation: 30/3=10 Moving to Node #0,0 Current State: 40:[9, 5, 10], Operations: ['30/3=10'] Exploring Operation: 9-5=4, Resulting Numbers: [10, 4] Generated Node #0,0,0: 40:[10, 4] Operation: 9-5=4 Moving to Node #0,0,0 Current State: 40:[10, 4], Operations: ['30/3=10', '9-5=4'] Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 51, 62, 21, 52 ]
62
[ "62-51=11", "21+52=73", "73-11=62" ]
Current State: 62:[51, 62, 21, 52], Operations: [] Exploring Operation: 62-51=11, Resulting Numbers: [21, 52, 11] Generated Node #2: [21, 52, 11] from Operation: 62-51=11 Current State: 62:[21, 52, 11], Operations: ['62-51=11'] Exploring Operation: 21+52=73, Resulting Numbers: [11, 73] Generated Node #3: [11, 73] from Operation: 21+52=73 Current State: 62:[11, 73], Operations: ['62-51=11', '21+52=73'] Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[51, 62, 21, 52], Operations: [] Exploring Operation: 52-21=31, Resulting Numbers: [51, 62, 31] Generated Node #0,0: 62:[51, 62, 31] Operation: 52-21=31 Exploring Operation: 51-21=30, Resulting Numbers: [62, 52, 30] Generated Node #0,1: 62:[62, 52, 30] Operation: 51-21=30 Exploring Operation: 52-51=1, Resulting Numbers: [62, 21, 1] Generated Node #0,2: 62:[62, 21, 1] Operation: 52-51=1 Moving to Node #0,0 Current State: 62:[51, 62, 31], Operations: ['52-21=31'] Exploring Operation: 62-31=31, Resulting Numbers: [51, 31] Generated Node #0,0,0: 62:[51, 31] Operation: 62-31=31 Exploring Operation: 62-51=11, Resulting Numbers: [31, 11] Generated Node #0,0,1: 62:[31, 11] Operation: 62-51=11 Exploring Operation: 51-31=20, Resulting Numbers: [62, 20] Generated Node #0,0,2: 62:[62, 20] Operation: 51-31=20 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 62:[31, 11], Operations: ['52-21=31', '62-51=11'] Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,62 unequal: No Solution Exploring Operation: 31*11=341, Resulting Numbers: [341] 341,62 unequal: No Solution Exploring Operation: 31+11=42, Resulting Numbers: [42] 42,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[51, 31], Operations: ['52-21=31', '62-31=31'] Exploring Operation: 51*31=1581, Resulting Numbers: [1581] 1581,62 unequal: No Solution Exploring Operation: 51-31=20, Resulting Numbers: [20] 20,62 unequal: No Solution Exploring Operation: 51+31=82, Resulting Numbers: [82] 82,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 62:[62, 20], Operations: ['52-21=31', '51-31=20'] Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 62*20=1240, Resulting Numbers: [1240] 1240,62 unequal: No Solution Exploring Operation: 62+20=82, Resulting Numbers: [82] 82,62 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: 62:[62, 52, 30], Operations: ['51-21=30'] Exploring Operation: 52-30=22, Resulting Numbers: [62, 22] Generated Node #0,1,0: 62:[62, 22] Operation: 52-30=22 Exploring Operation: 62-52=10, Resulting Numbers: [30, 10] Generated Node #0,1,1: 62:[30, 10] Operation: 62-52=10 Exploring Operation: 62-30=32, Resulting Numbers: [52, 32] Generated Node #0,1,2: 62:[52, 32] Operation: 62-30=32 Moving to Node #0,2 Current State: 62:[62, 21, 1], Operations: ['52-51=1'] Exploring Operation: 62/1=62, Resulting Numbers: [21, 62] Generated Node #0,2,0: 62:[21, 62] Operation: 62/1=62 Exploring Operation: 62*1=62, Resulting Numbers: [21, 62] Generated Node #0,2,1: 62:[21, 62] Operation: 62*1=62 Exploring Operation: 21+1=22, Resulting Numbers: [62, 22] Generated Node #0,2,2: 62:[62, 22] Operation: 21+1=22 Moving to Node #0,1,0 Current State: 62:[62, 22], Operations: ['51-21=30', '52-30=22'] Exploring Operation: 62*22=1364, Resulting Numbers: [1364] 1364,62 unequal: No Solution Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,62 unequal: No Solution Exploring Operation: 62+22=84, Resulting Numbers: [84] 84,62 unequal: No Solution Moving to Node #0,1,1 Current State: 62:[30, 10], Operations: ['51-21=30', '62-52=10'] Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,62 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,62 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[62, 22], Operations: ['52-51=1', '21+1=22'] Exploring Operation: 62+22=84, Resulting Numbers: [84] 84,62 unequal: No Solution Exploring Operation: 62*22=1364, Resulting Numbers: [1364] 1364,62 unequal: No Solution Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[21, 62], Operations: ['52-51=1', '62*1=62'] Exploring Operation: 21*62=1302, Resulting Numbers: [1302] 1302,62 unequal: No Solution Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,62 unequal: No Solution Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[21, 62], Operations: ['52-51=1', '62/1=62'] Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,62 unequal: No Solution Exploring Operation: 21*62=1302, Resulting Numbers: [1302] 1302,62 unequal: No Solution Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,62 unequal: No Solution Moving to Node #0,1,2 Current State: 62:[52, 32], Operations: ['51-21=30', '62-30=32'] Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,62 unequal: No Solution Exploring Operation: 52+32=84, Resulting Numbers: [84] 84,62 unequal: No Solution Exploring Operation: 52*32=1664, Resulting Numbers: [1664] 1664,62 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 2, 79, 27, 87 ]
56
[ "79+87=166", "166/2=83", "83-27=56" ]
Current State: 56:[2, 79, 27, 87], Operations: [] Exploring Operation: 79+87=166, Resulting Numbers: [2, 27, 166] Generated Node #2: [2, 27, 166] from Operation: 79+87=166 Current State: 56:[2, 27, 166], Operations: ['79+87=166'] Exploring Operation: 166/2=83, Resulting Numbers: [27, 83] Generated Node #3: [27, 83] from Operation: 166/2=83 Current State: 56:[27, 83], Operations: ['79+87=166', '166/2=83'] Exploring Operation: 83-27=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[2, 79, 27, 87], Operations: [] Exploring Operation: 87-27=60, Resulting Numbers: [2, 79, 60] Generated Node #0,0: 56:[2, 79, 60] Operation: 87-27=60 Exploring Operation: 79-27=52, Resulting Numbers: [2, 87, 52] Generated Node #0,1: 56:[2, 87, 52] Operation: 79-27=52 Exploring Operation: 87-79=8, Resulting Numbers: [2, 27, 8] Generated Node #0,2: 56:[2, 27, 8] Operation: 87-79=8 Moving to Node #0,2 Current State: 56:[2, 27, 8], Operations: ['87-79=8'] Exploring Operation: 2*27=54, Resulting Numbers: [8, 54] Generated Node #0,2,0: 56:[8, 54] Operation: 2*27=54 Exploring Operation: 8/2=4, Resulting Numbers: [27, 4] Generated Node #0,2,1: 56:[27, 4] Operation: 8/2=4 Exploring Operation: 2+27=29, Resulting Numbers: [8, 29] Generated Node #0,2,2: 56:[8, 29] Operation: 2+27=29 Moving to Node #0,0 Current State: 56:[2, 79, 60], Operations: ['87-27=60'] Exploring Operation: 60-2=58, Resulting Numbers: [79, 58] Generated Node #0,0,0: 56:[79, 58] Operation: 60-2=58 Exploring Operation: 79-60=19, Resulting Numbers: [2, 19] Generated Node #0,0,1: 56:[2, 19] Operation: 79-60=19 Exploring Operation: 79-2=77, Resulting Numbers: [60, 77] Generated Node #0,0,2: 56:[60, 77] Operation: 79-2=77 Moving to Node #0,1 Current State: 56:[2, 87, 52], Operations: ['79-27=52'] Exploring Operation: 87-2=85, Resulting Numbers: [52, 85] Generated Node #0,1,0: 56:[52, 85] Operation: 87-2=85 Exploring Operation: 87-52=35, Resulting Numbers: [2, 35] Generated Node #0,1,1: 56:[2, 35] Operation: 87-52=35 Exploring Operation: 2+52=54, Resulting Numbers: [87, 54] Generated Node #0,1,2: 56:[87, 54] Operation: 2+52=54 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 56:[2, 35], Operations: ['79-27=52', '87-52=35'] Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,56 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,56 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 56:[52, 85], Operations: ['79-27=52', '87-2=85'] Exploring Operation: 85-52=33, Resulting Numbers: [33] 33,56 unequal: No Solution Exploring Operation: 52+85=137, Resulting Numbers: [137] 137,56 unequal: No Solution Exploring Operation: 52*85=4420, Resulting Numbers: [4420] 4420,56 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:[87, 54], Operations: ['79-27=52', '2+52=54'] Exploring Operation: 87*54=4698, Resulting Numbers: [4698] 4698,56 unequal: No Solution Exploring Operation: 87-54=33, Resulting Numbers: [33] 33,56 unequal: No Solution Exploring Operation: 87+54=141, Resulting Numbers: [141] 141,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 56:[27, 4], Operations: ['87-79=8', '8/2=4'] Exploring Operation: 27+4=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,56 unequal: No Solution Exploring Operation: 27*4=108, Resulting Numbers: [108] 108,56 unequal: No Solution Moving to Node #0,2,2 Current State: 56:[8, 29], Operations: ['87-79=8', '2+27=29'] Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,56 unequal: No Solution Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,56 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,56 unequal: No Solution Moving to Node #0,2,0 Current State: 56:[8, 54], Operations: ['87-79=8', '2*27=54'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,56 unequal: No Solution Exploring Operation: 8*54=432, Resulting Numbers: [432] 432,56 unequal: No Solution Exploring Operation: 8+54=62, Resulting Numbers: [62] 62,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[2, 19], Operations: ['87-27=60', '79-60=19'] Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,56 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,56 unequal: No Solution Moving to Node #0,0,2 Current State: 56:[60, 77], Operations: ['87-27=60', '79-2=77'] Exploring Operation: 60*77=4620, Resulting Numbers: [4620] 4620,56 unequal: No Solution Exploring Operation: 60+77=137, Resulting Numbers: [137] 137,56 unequal: No Solution Exploring Operation: 77-60=17, Resulting Numbers: [17] 17,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[79, 58], Operations: ['87-27=60', '60-2=58'] Exploring Operation: 79-58=21, Resulting Numbers: [21] 21,56 unequal: No Solution Exploring Operation: 79*58=4582, Resulting Numbers: [4582] 4582,56 unequal: No Solution Exploring Operation: 79+58=137, Resulting Numbers: [137] 137,56 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 2, 90, 41, 35 ]
30
[ "2*90=180", "41-35=6", "180/6=30" ]
Current State: 30:[2, 90, 41, 35], Operations: [] Exploring Operation: 2*90=180, Resulting Numbers: [41, 35, 180] Generated Node #2: [41, 35, 180] from Operation: 2*90=180 Current State: 30:[41, 35, 180], Operations: ['2*90=180'] Exploring Operation: 41-35=6, Resulting Numbers: [180, 6] Generated Node #3: [180, 6] from Operation: 41-35=6 Current State: 30:[180, 6], Operations: ['2*90=180', '41-35=6'] Exploring Operation: 180/6=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[2, 90, 41, 35], Operations: [] Exploring Operation: 90-41=49, Resulting Numbers: [2, 35, 49] Generated Node #0,0: 30:[2, 35, 49] Operation: 90-41=49 Exploring Operation: 90-35=55, Resulting Numbers: [2, 41, 55] Generated Node #0,1: 30:[2, 41, 55] Operation: 90-35=55 Exploring Operation: 90/2=45, Resulting Numbers: [41, 35, 45] Generated Node #0,2: 30:[41, 35, 45] Operation: 90/2=45 Moving to Node #0,0 Current State: 30:[2, 35, 49], Operations: ['90-41=49'] Exploring Operation: 49-35=14, Resulting Numbers: [2, 14] Generated Node #0,0,0: 30:[2, 14] Operation: 49-35=14 Exploring Operation: 49-2=47, Resulting Numbers: [35, 47] Generated Node #0,0,1: 30:[35, 47] Operation: 49-2=47 Exploring Operation: 35-2=33, Resulting Numbers: [49, 33] Generated Node #0,0,2: 30:[49, 33] Operation: 35-2=33 Moving to Node #0,2 Current State: 30:[41, 35, 45], Operations: ['90/2=45'] Exploring Operation: 45-35=10, Resulting Numbers: [41, 10] Generated Node #0,2,0: 30:[41, 10] Operation: 45-35=10 Exploring Operation: 45-41=4, Resulting Numbers: [35, 4] Generated Node #0,2,1: 30:[35, 4] Operation: 45-41=4 Exploring Operation: 41-35=6, Resulting Numbers: [45, 6] Generated Node #0,2,2: 30:[45, 6] Operation: 41-35=6 Moving to Node #0,1 Current State: 30:[2, 41, 55], Operations: ['90-35=55'] Exploring Operation: 55-41=14, Resulting Numbers: [2, 14] Generated Node #0,1,0: 30:[2, 14] Operation: 55-41=14 Exploring Operation: 41-2=39, Resulting Numbers: [55, 39] Generated Node #0,1,1: 30:[55, 39] Operation: 41-2=39 Exploring Operation: 55-2=53, Resulting Numbers: [41, 53] Generated Node #0,1,2: 30:[41, 53] Operation: 55-2=53 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 30:[2, 14], Operations: ['90-35=55', '55-41=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,30 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,30 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 #0,1,1 Current State: 30:[55, 39], Operations: ['90-35=55', '41-2=39'] Exploring Operation: 55*39=2145, Resulting Numbers: [2145] 2145,30 unequal: No Solution Exploring Operation: 55-39=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 55+39=94, Resulting Numbers: [94] 94,30 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 #0,1,2 Current State: 30:[41, 53], Operations: ['90-35=55', '55-2=53'] Exploring Operation: 41+53=94, Resulting Numbers: [94] 94,30 unequal: No Solution Exploring Operation: 41*53=2173, Resulting Numbers: [2173] 2173,30 unequal: No Solution Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,30 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: 30:[2, 14], Operations: ['90-41=49', '49-35=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,30 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,30 unequal: No Solution Moving to Node #0,2,1 Current State: 30:[35, 4], Operations: ['90/2=45', '45-41=4'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,30 unequal: No Solution Exploring Operation: 35*4=140, Resulting Numbers: [140] 140,30 unequal: No Solution Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,30 unequal: No Solution Moving to Node #0,2,0 Current State: 30:[41, 10], Operations: ['90/2=45', '45-35=10'] Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,30 unequal: No Solution Exploring Operation: 41+10=51, Resulting Numbers: [51] 51,30 unequal: No Solution Exploring Operation: 41*10=410, Resulting Numbers: [410] 410,30 unequal: No Solution Moving to Node #0,2,2 Current State: 30:[45, 6], Operations: ['90/2=45', '41-35=6'] Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,30 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,30 unequal: No Solution Moving to Node #0,0,1 Current State: 30:[35, 47], Operations: ['90-41=49', '49-2=47'] Exploring Operation: 35+47=82, Resulting Numbers: [82] 82,30 unequal: No Solution Exploring Operation: 47-35=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 35*47=1645, Resulting Numbers: [1645] 1645,30 unequal: No Solution Moving to Node #0,0,2 Current State: 30:[49, 33], Operations: ['90-41=49', '35-2=33'] Exploring Operation: 49-33=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 49*33=1617, Resulting Numbers: [1617] 1617,30 unequal: No Solution Exploring Operation: 49+33=82, Resulting Numbers: [82] 82,30 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 55, 71, 33, 3 ]
31
[ "55+71=126", "126-33=93", "93/3=31" ]
Current State: 31:[55, 71, 33, 3], Operations: [] Exploring Operation: 55+71=126, Resulting Numbers: [33, 3, 126] Generated Node #2: [33, 3, 126] from Operation: 55+71=126 Current State: 31:[33, 3, 126], Operations: ['55+71=126'] Exploring Operation: 126-33=93, Resulting Numbers: [3, 93] Generated Node #3: [3, 93] from Operation: 126-33=93 Current State: 31:[3, 93], Operations: ['55+71=126', '126-33=93'] Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[55, 71, 33, 3], Operations: [] Exploring Operation: 71-55=16, Resulting Numbers: [33, 3, 16] Generated Node #0,0: 31:[33, 3, 16] Operation: 71-55=16 Exploring Operation: 71-33=38, Resulting Numbers: [55, 3, 38] Generated Node #0,1: 31:[55, 3, 38] Operation: 71-33=38 Moving to Node #0,0 Current State: 31:[33, 3, 16], Operations: ['71-55=16'] Exploring Operation: 33-3=30, Resulting Numbers: [16, 30] Generated Node #0,0,0: 31:[16, 30] Operation: 33-3=30 Exploring Operation: 3+16=19, Resulting Numbers: [33, 19] Generated Node #0,0,1: 31:[33, 19] Operation: 3+16=19 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[33, 19], Operations: ['71-55=16', '3+16=19'] Exploring Operation: 33-19=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 33+19=52, Resulting Numbers: [52] 52,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[16, 30], Operations: ['71-55=16', '33-3=30'] Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,31 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: 31:[55, 3, 38], Operations: ['71-33=38'] Exploring Operation: 38-3=35, Resulting Numbers: [55, 35] Generated Node #0,1,0: 31:[55, 35] Operation: 38-3=35 Exploring Operation: 55-3=52, Resulting Numbers: [38, 52] Generated Node #0,1,1: 31:[38, 52] Operation: 55-3=52 Moving to Node #0,1,0 Current State: 31:[55, 35], Operations: ['71-33=38', '38-3=35'] Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 55+35=90, Resulting Numbers: [90] 90,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[38, 52], Operations: ['71-33=38', '55-3=52'] Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 38+52=90, Resulting Numbers: [90] 90,31 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 53, 4, 2, 60 ]
83
[ "4-2=2", "60/2=30", "53+30=83" ]
Current State: 83:[53, 4, 2, 60], Operations: [] Exploring Operation: 4-2=2, Resulting Numbers: [53, 60, 2] Generated Node #2: [53, 60, 2] from Operation: 4-2=2 Current State: 83:[53, 60, 2], Operations: ['4-2=2'] Exploring Operation: 60/2=30, Resulting Numbers: [53, 30] Generated Node #3: [53, 30] from Operation: 60/2=30 Current State: 83:[53, 30], Operations: ['4-2=2', '60/2=30'] Exploring Operation: 53+30=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[53, 4, 2, 60], Operations: [] Exploring Operation: 53*2=106, Resulting Numbers: [4, 60, 106] Generated Node #0,0: 83:[4, 60, 106] Operation: 53*2=106 Exploring Operation: 4*2=8, Resulting Numbers: [53, 60, 8] Generated Node #0,1: 83:[53, 60, 8] Operation: 4*2=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[4, 60, 106], Operations: ['53*2=106'] Exploring Operation: 106-4=102, Resulting Numbers: [60, 102] Generated Node #0,0,0: 83:[60, 102] Operation: 106-4=102 Exploring Operation: 4+60=64, Resulting Numbers: [106, 64] Generated Node #0,0,1: 83:[106, 64] Operation: 4+60=64 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[60, 102], Operations: ['53*2=106', '106-4=102'] Exploring Operation: 60+102=162, Resulting Numbers: [162] 162,83 unequal: No Solution Exploring Operation: 102-60=42, Resulting Numbers: [42] 42,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[106, 64], Operations: ['53*2=106', '4+60=64'] Exploring Operation: 106-64=42, Resulting Numbers: [42] 42,83 unequal: No Solution Exploring Operation: 106+64=170, Resulting Numbers: [170] 170,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[53, 60, 8], Operations: ['4*2=8'] Exploring Operation: 53+8=61, Resulting Numbers: [60, 61] Generated Node #0,1,0: 83:[60, 61] Operation: 53+8=61 Exploring Operation: 60+8=68, Resulting Numbers: [53, 68] Generated Node #0,1,1: 83:[53, 68] Operation: 60+8=68 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[60, 61], Operations: ['4*2=8', '53+8=61'] Exploring Operation: 60+61=121, Resulting Numbers: [121] 121,83 unequal: No Solution Exploring Operation: 61-60=1, Resulting Numbers: [1] 1,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[53, 68], Operations: ['4*2=8', '60+8=68'] Exploring Operation: 53+68=121, Resulting Numbers: [121] 121,83 unequal: No Solution Exploring Operation: 68-53=15, Resulting Numbers: [15] 15,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 91, 27, 23, 41 ]
76
[ "91*23=2093", "2093-41=2052", "2052/27=76" ]
Current State: 76:[91, 27, 23, 41], Operations: [] Exploring Operation: 91*23=2093, Resulting Numbers: [27, 41, 2093] Generated Node #2: [27, 41, 2093] from Operation: 91*23=2093 Current State: 76:[27, 41, 2093], Operations: ['91*23=2093'] Exploring Operation: 2093-41=2052, Resulting Numbers: [27, 2052] Generated Node #3: [27, 2052] from Operation: 2093-41=2052 Current State: 76:[27, 2052], Operations: ['91*23=2093', '2093-41=2052'] Exploring Operation: 2052/27=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[91, 27, 23, 41], Operations: [] Exploring Operation: 27-23=4, Resulting Numbers: [91, 41, 4] Generated Node #0,0: 76:[91, 41, 4] Operation: 27-23=4 Moving to Node #0,0 Current State: 76:[91, 41, 4], Operations: ['27-23=4'] Exploring Operation: 91-41=50, Resulting Numbers: [4, 50] Generated Node #0,0,0: 76:[4, 50] Operation: 91-41=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[4, 50], Operations: ['27-23=4', '91-41=50'] Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,76 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
[ 12, 60, 79, 86 ]
79
[ "12+60=72", "86-79=7", "72+7=79" ]
Current State: 79:[12, 60, 79, 86], Operations: [] Exploring Operation: 12+60=72, Resulting Numbers: [79, 86, 72] Generated Node #2: [79, 86, 72] from Operation: 12+60=72 Current State: 79:[79, 86, 72], Operations: ['12+60=72'] Exploring Operation: 86-79=7, Resulting Numbers: [72, 7] Generated Node #3: [72, 7] from Operation: 86-79=7 Current State: 79:[72, 7], Operations: ['12+60=72', '86-79=7'] Exploring Operation: 72+7=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[12, 60, 79, 86], Operations: [] Exploring Operation: 12+60=72, Resulting Numbers: [79, 86, 72] Generated Node #0,0: 79:[79, 86, 72] Operation: 12+60=72 Moving to Node #0,0 Current State: 79:[79, 86, 72], Operations: ['12+60=72'] Exploring Operation: 86-72=14, Resulting Numbers: [79, 14] Generated Node #0,0,0: 79:[79, 14] Operation: 86-72=14 Moving to Node #0,0,0 Current State: 79:[79, 14], Operations: ['12+60=72', '86-72=14'] Exploring Operation: 79+14=93, Resulting Numbers: [93] 93,79 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 18, 9, 1, 25 ]
23
[ "18/9=2", "1*25=25", "25-2=23" ]
Current State: 23:[18, 9, 1, 25], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [1, 25, 2] Generated Node #2: [1, 25, 2] from Operation: 18/9=2 Current State: 23:[1, 25, 2], Operations: ['18/9=2'] Exploring Operation: 1*25=25, Resulting Numbers: [2, 25] Generated Node #3: [2, 25] from Operation: 1*25=25 Current State: 23:[2, 25], Operations: ['18/9=2', '1*25=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[18, 9, 1, 25], Operations: [] Exploring Operation: 18+1=19, Resulting Numbers: [9, 25, 19] Generated Node #0,0: 23:[9, 25, 19] Operation: 18+1=19 Exploring Operation: 9+1=10, Resulting Numbers: [18, 25, 10] Generated Node #0,1: 23:[18, 25, 10] Operation: 9+1=10 Exploring Operation: 25-1=24, Resulting Numbers: [18, 9, 24] Generated Node #0,2: 23:[18, 9, 24] Operation: 25-1=24 Exploring Operation: 18*1=18, Resulting Numbers: [9, 25, 18] Generated Node #0,3: 23:[9, 25, 18] Operation: 18*1=18 Moving to Node #0,0 Current State: 23:[9, 25, 19], Operations: ['18+1=19'] Exploring Operation: 9+19=28, Resulting Numbers: [25, 28] Generated Node #0,0,0: 23:[25, 28] Operation: 9+19=28 Exploring Operation: 25-9=16, Resulting Numbers: [19, 16] Generated Node #0,0,1: 23:[19, 16] Operation: 25-9=16 Exploring Operation: 9+25=34, Resulting Numbers: [19, 34] Generated Node #0,0,2: 23:[19, 34] Operation: 9+25=34 Exploring Operation: 19-9=10, Resulting Numbers: [25, 10] Generated Node #0,0,3: 23:[25, 10] Operation: 19-9=10 Moving to Node #0,2 Current State: 23:[18, 9, 24], Operations: ['25-1=24'] Exploring Operation: 18-9=9, Resulting Numbers: [24, 9] Generated Node #0,2,0: 23:[24, 9] Operation: 18-9=9 Exploring Operation: 24-9=15, Resulting Numbers: [18, 15] Generated Node #0,2,1: 23:[18, 15] Operation: 24-9=15 Exploring Operation: 18+9=27, Resulting Numbers: [24, 27] Generated Node #0,2,2: 23:[24, 27] Operation: 18+9=27 Exploring Operation: 9+24=33, Resulting Numbers: [18, 33] Generated Node #0,2,3: 23:[18, 33] Operation: 9+24=33 Moving to Node #0,1 Current State: 23:[18, 25, 10], Operations: ['9+1=10'] Exploring Operation: 18+10=28, Resulting Numbers: [25, 28] Generated Node #0,1,0: 23:[25, 28] Operation: 18+10=28 Exploring Operation: 18-10=8, Resulting Numbers: [25, 8] Generated Node #0,1,1: 23:[25, 8] Operation: 18-10=8 Exploring Operation: 25+10=35, Resulting Numbers: [18, 35] Generated Node #0,1,2: 23:[18, 35] Operation: 25+10=35 Exploring Operation: 25-10=15, Resulting Numbers: [18, 15] Generated Node #0,1,3: 23:[18, 15] Operation: 25-10=15 Moving to Node #0,3 Current State: 23:[9, 25, 18], Operations: ['18*1=18'] Exploring Operation: 25-9=16, Resulting Numbers: [18, 16] Generated Node #0,3,0: 23:[18, 16] Operation: 25-9=16 Exploring Operation: 9+18=27, Resulting Numbers: [25, 27] Generated Node #0,3,1: 23:[25, 27] Operation: 9+18=27 Exploring Operation: 18-9=9, Resulting Numbers: [25, 9] Generated Node #0,3,2: 23:[25, 9] Operation: 18-9=9 Exploring Operation: 9+25=34, Resulting Numbers: [18, 34] Generated Node #0,3,3: 23:[18, 34] Operation: 9+25=34 Moving to Node #0,2,2 Current State: 23:[24, 27], Operations: ['25-1=24', '18+9=27'] Exploring Operation: 24*27=648, Resulting Numbers: [648] 648,23 unequal: No Solution Exploring Operation: 24+27=51, Resulting Numbers: [51] 51,23 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,23 unequal: No Solution Moving to Node #0,3,1 Current State: 23:[25, 27], Operations: ['18*1=18', '9+18=27'] Exploring Operation: 25*27=675, Resulting Numbers: [675] 675,23 unequal: No Solution Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 25+27=52, Resulting Numbers: [52] 52,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[25, 28], Operations: ['18+1=19', '9+19=28'] Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 25+28=53, Resulting Numbers: [53] 53,23 unequal: No Solution Exploring Operation: 25*28=700, Resulting Numbers: [700] 700,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[25, 28], Operations: ['9+1=10', '18+10=28'] Exploring Operation: 25*28=700, Resulting Numbers: [700] 700,23 unequal: No Solution Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 25+28=53, Resulting Numbers: [53] 53,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[19, 16], Operations: ['18+1=19', '25-9=16'] Exploring Operation: 19*16=304, Resulting Numbers: [304] 304,23 unequal: No Solution Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 19+16=35, Resulting Numbers: [35] 35,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[18, 16], Operations: ['18*1=18', '25-9=16'] Exploring Operation: 18*16=288, Resulting Numbers: [288] 288,23 unequal: No Solution Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[18, 15], Operations: ['25-1=24', '24-9=15'] Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,23 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,23 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,23 unequal: No Solution Moving to Node #0,1,3 Current State: 23:[18, 15], Operations: ['9+1=10', '25-10=15'] Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,23 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,23 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[24, 9], Operations: ['25-1=24', '18-9=9'] Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 24+9=33, Resulting Numbers: [33] 33,23 unequal: No Solution Exploring Operation: 24*9=216, Resulting Numbers: [216] 216,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[19, 34], Operations: ['18+1=19', '9+25=34'] Exploring Operation: 34-19=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 19+34=53, Resulting Numbers: [53] 53,23 unequal: No Solution Exploring Operation: 19*34=646, Resulting Numbers: [646] 646,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[25, 10], Operations: ['18+1=19', '19-9=10'] Exploring Operation: 25*10=250, Resulting Numbers: [250] 250,23 unequal: No Solution Exploring Operation: 25+10=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[18, 33], Operations: ['25-1=24', '9+24=33'] Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 18*33=594, Resulting Numbers: [594] 594,23 unequal: No Solution Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,23 unequal: No Solution Moving to Node #0,3,2 Current State: 23:[25, 9], Operations: ['18*1=18', '18-9=9'] Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,23 unequal: No Solution Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[18, 34], Operations: ['18*1=18', '9+25=34'] Exploring Operation: 18*34=612, Resulting Numbers: [612] 612,23 unequal: No Solution Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 18+34=52, Resulting Numbers: [52] 52,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[25, 8], Operations: ['9+1=10', '18-10=8'] Exploring Operation: 25*8=200, Resulting Numbers: [200] 200,23 unequal: No Solution Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,23 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[18, 35], Operations: ['9+1=10', '25+10=35'] Exploring Operation: 18*35=630, Resulting Numbers: [630] 630,23 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,23 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 72, 45, 2, 92 ]
37
[ "72+92=164", "164/2=82", "82-45=37" ]
Current State: 37:[72, 45, 2, 92], Operations: [] Exploring Operation: 72+92=164, Resulting Numbers: [45, 2, 164] Generated Node #2: [45, 2, 164] from Operation: 72+92=164 Current State: 37:[45, 2, 164], Operations: ['72+92=164'] Exploring Operation: 164/2=82, Resulting Numbers: [45, 82] Generated Node #3: [45, 82] from Operation: 164/2=82 Current State: 37:[45, 82], Operations: ['72+92=164', '164/2=82'] Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[72, 45, 2, 92], Operations: [] Exploring Operation: 92-72=20, Resulting Numbers: [45, 2, 20] Generated Node #0,0: 37:[45, 2, 20] Operation: 92-72=20 Exploring Operation: 92/2=46, Resulting Numbers: [72, 45, 46] Generated Node #0,1: 37:[72, 45, 46] Operation: 92/2=46 Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[72, 45, 46], Operations: ['92/2=46'] Exploring Operation: 72-45=27, Resulting Numbers: [46, 27] Generated Node #0,1,0: 37:[46, 27] Operation: 72-45=27 Exploring Operation: 72-46=26, Resulting Numbers: [45, 26] Generated Node #0,1,1: 37:[45, 26] Operation: 72-46=26 Moving to Node #0,1,0 Current State: 37:[46, 27], Operations: ['92/2=46', '72-45=27'] Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,37 unequal: No Solution Exploring Operation: 46+27=73, Resulting Numbers: [73] 73,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[45, 26], Operations: ['92/2=46', '72-46=26'] Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,37 unequal: No Solution Exploring Operation: 45+26=71, Resulting Numbers: [71] 71,37 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 #0,0 Current State: 37:[45, 2, 20], Operations: ['92-72=20'] Exploring Operation: 45-2=43, Resulting Numbers: [20, 43] Generated Node #0,0,0: 37:[20, 43] Operation: 45-2=43 Exploring Operation: 2*20=40, Resulting Numbers: [45, 40] Generated Node #0,0,1: 37:[45, 40] Operation: 2*20=40 Moving to Node #0,0,1 Current State: 37:[45, 40], Operations: ['92-72=20', '2*20=40'] Exploring Operation: 45+40=85, Resulting Numbers: [85] 85,37 unequal: No Solution Exploring Operation: 45-40=5, Resulting Numbers: [5] 5,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[20, 43], Operations: ['92-72=20', '45-2=43'] Exploring Operation: 20+43=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,37 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
[ 72, 95, 52, 92 ]
97
[ "52+92=144", "144/72=2", "95+2=97" ]
Current State: 97:[72, 95, 52, 92], Operations: [] Exploring Operation: 52+92=144, Resulting Numbers: [72, 95, 144] Generated Node #2: [72, 95, 144] from Operation: 52+92=144 Current State: 97:[72, 95, 144], Operations: ['52+92=144'] Exploring Operation: 144/72=2, Resulting Numbers: [95, 2] Generated Node #3: [95, 2] from Operation: 144/72=2 Current State: 97:[95, 2], Operations: ['52+92=144', '144/72=2'] Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[72, 95, 52, 92], Operations: [] Exploring Operation: 72+52=124, Resulting Numbers: [95, 92, 124] Generated Node #0,0: 97:[95, 92, 124] Operation: 72+52=124 Exploring Operation: 95+52=147, Resulting Numbers: [72, 92, 147] Generated Node #0,1: 97:[72, 92, 147] Operation: 95+52=147 Exploring Operation: 52+92=144, Resulting Numbers: [72, 95, 144] Generated Node #0,2: 97:[72, 95, 144] Operation: 52+92=144 Exploring Operation: 72-52=20, Resulting Numbers: [95, 92, 20] Generated Node #0,3: 97:[95, 92, 20] Operation: 72-52=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[95, 92, 124], Operations: ['72+52=124'] Exploring Operation: 95+92=187, Resulting Numbers: [124, 187] Generated Node #0,0,0: 97:[124, 187] Operation: 95+92=187 Exploring Operation: 95-92=3, Resulting Numbers: [124, 3] Generated Node #0,0,1: 97:[124, 3] Operation: 95-92=3 Exploring Operation: 124-95=29, Resulting Numbers: [92, 29] Generated Node #0,0,2: 97:[92, 29] Operation: 124-95=29 Exploring Operation: 124-92=32, Resulting Numbers: [95, 32] Generated Node #0,0,3: 97:[95, 32] Operation: 124-92=32 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 97:[95, 32], Operations: ['72+52=124', '124-92=32'] Exploring Operation: 95+32=127, Resulting Numbers: [127] 127,97 unequal: No Solution Exploring Operation: 95*32=3040, Resulting Numbers: [3040] 3040,97 unequal: No Solution Exploring Operation: 95-32=63, Resulting Numbers: [63] 63,97 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 #0,0,2 Current State: 97:[92, 29], Operations: ['72+52=124', '124-95=29'] Exploring Operation: 92+29=121, Resulting Numbers: [121] 121,97 unequal: No Solution Exploring Operation: 92-29=63, Resulting Numbers: [63] 63,97 unequal: No Solution Exploring Operation: 92*29=2668, Resulting Numbers: [2668] 2668,97 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 #0,0,0 Current State: 97:[124, 187], Operations: ['72+52=124', '95+92=187'] Exploring Operation: 124+187=311, Resulting Numbers: [311] 311,97 unequal: No Solution Exploring Operation: 187-124=63, Resulting Numbers: [63] 63,97 unequal: No Solution Exploring Operation: 124*187=23188, Resulting Numbers: [23188] 23188,97 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 #0,0,1 Current State: 97:[124, 3], Operations: ['72+52=124', '95-92=3'] Exploring Operation: 124*3=372, Resulting Numbers: [372] 372,97 unequal: No Solution Exploring Operation: 124+3=127, Resulting Numbers: [127] 127,97 unequal: No Solution Exploring Operation: 124-3=121, Resulting Numbers: [121] 121,97 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 #0,2 Current State: 97:[72, 95, 144], Operations: ['52+92=144'] Exploring Operation: 144/72=2, Resulting Numbers: [95, 2] Generated Node #0,2,0: 97:[95, 2] Operation: 144/72=2 Exploring Operation: 144-95=49, Resulting Numbers: [72, 49] Generated Node #0,2,1: 97:[72, 49] Operation: 144-95=49 Exploring Operation: 144-72=72, Resulting Numbers: [95, 72] Generated Node #0,2,2: 97:[95, 72] Operation: 144-72=72 Exploring Operation: 72+95=167, Resulting Numbers: [144, 167] Generated Node #0,2,3: 97:[144, 167] Operation: 72+95=167 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 97:[95, 72], Operations: ['52+92=144', '144-72=72'] Exploring Operation: 95*72=6840, Resulting Numbers: [6840] 6840,97 unequal: No Solution Exploring Operation: 95-72=23, Resulting Numbers: [23] 23,97 unequal: No Solution Exploring Operation: 95+72=167, Resulting Numbers: [167] 167,97 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:[72, 49], Operations: ['52+92=144', '144-95=49'] Exploring Operation: 72*49=3528, Resulting Numbers: [3528] 3528,97 unequal: No Solution Exploring Operation: 72-49=23, Resulting Numbers: [23] 23,97 unequal: No Solution Exploring Operation: 72+49=121, Resulting Numbers: [121] 121,97 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 #0,2,0 Current State: 97:[95, 2], Operations: ['52+92=144', '144/72=2'] Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,97 unequal: No Solution Exploring Operation: 95*2=190, Resulting Numbers: [190] 190,97 unequal: No Solution Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[72, 95, 52, 92], Operations: [] Exploring Operation: 52+92=144, Resulting Numbers: [72, 95, 144] Generated Node #0,2: 97:[72, 95, 144] Operation: 52+92=144 Moving to Node #0,2 Current State: 97:[72, 95, 144], Operations: ['52+92=144'] Exploring Operation: 144/72=2, Resulting Numbers: [95, 2] Generated Node #0,2,0: 97:[95, 2] Operation: 144/72=2 Moving to Node #0,2,0 Current State: 97:[95, 2], Operations: ['52+92=144', '144/72=2'] Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_4
mult_heuristic
[ 5, 12, 27, 80 ]
19
[ "27-12=15", "80+15=95", "95/5=19" ]
Current State: 19:[5, 12, 27, 80], Operations: [] Exploring Operation: 27-12=15, Resulting Numbers: [5, 80, 15] Generated Node #2: [5, 80, 15] from Operation: 27-12=15 Current State: 19:[5, 80, 15], Operations: ['27-12=15'] Exploring Operation: 80+15=95, Resulting Numbers: [5, 95] Generated Node #3: [5, 95] from Operation: 80+15=95 Current State: 19:[5, 95], Operations: ['27-12=15', '80+15=95'] Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[5, 12, 27, 80], Operations: [] Exploring Operation: 80/5=16, Resulting Numbers: [12, 27, 16] Generated Node #0,0: 19:[12, 27, 16] Operation: 80/5=16 Moving to Node #0,0 Current State: 19:[12, 27, 16], Operations: ['80/5=16'] Exploring Operation: 27-12=15, Resulting Numbers: [16, 15] Generated Node #0,0,0: 19:[16, 15] Operation: 27-12=15 Moving to Node #0,0,0 Current State: 19:[16, 15], Operations: ['80/5=16', '27-12=15'] Exploring Operation: 16+15=31, Resulting Numbers: [31] 31,19 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 53, 62, 94, 10 ]
93
[ "62-53=9", "94-10=84", "9+84=93" ]
Current State: 93:[53, 62, 94, 10], Operations: [] Exploring Operation: 62-53=9, Resulting Numbers: [94, 10, 9] Generated Node #2: [94, 10, 9] from Operation: 62-53=9 Current State: 93:[94, 10, 9], Operations: ['62-53=9'] Exploring Operation: 94-10=84, Resulting Numbers: [9, 84] Generated Node #3: [9, 84] from Operation: 94-10=84 Current State: 93:[9, 84], Operations: ['62-53=9', '94-10=84'] Exploring Operation: 9+84=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[53, 62, 94, 10], Operations: [] Exploring Operation: 94-62=32, Resulting Numbers: [53, 10, 32] Generated Node #0,0: 93:[53, 10, 32] Operation: 94-62=32 Exploring Operation: 53-10=43, Resulting Numbers: [62, 94, 43] Generated Node #0,1: 93:[62, 94, 43] Operation: 53-10=43 Exploring Operation: 53+62=115, Resulting Numbers: [94, 10, 115] Generated Node #0,2: 93:[94, 10, 115] Operation: 53+62=115 Exploring Operation: 62-53=9, Resulting Numbers: [94, 10, 9] Generated Node #0,3: 93:[94, 10, 9] Operation: 62-53=9 Moving to Node #0,3 Current State: 93:[94, 10, 9], Operations: ['62-53=9'] Exploring Operation: 10+9=19, Resulting Numbers: [94, 19] Generated Node #0,3,0: 93:[94, 19] Operation: 10+9=19 Exploring Operation: 10*9=90, Resulting Numbers: [94, 90] Generated Node #0,3,1: 93:[94, 90] Operation: 10*9=90 Exploring Operation: 94-10=84, Resulting Numbers: [9, 84] Generated Node #0,3,2: 93:[9, 84] Operation: 94-10=84 Exploring Operation: 10-9=1, Resulting Numbers: [94, 1] Generated Node #0,3,3: 93:[94, 1] Operation: 10-9=1 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 93:[94, 1], Operations: ['62-53=9', '10-9=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[53, 62, 94, 10], Operations: [] Exploring Operation: 62-53=9, Resulting Numbers: [94, 10, 9] Generated Node #0,3: 93:[94, 10, 9] Operation: 62-53=9 Moving to Node #0,3 Current State: 93:[94, 10, 9], Operations: ['62-53=9'] Exploring Operation: 10-9=1, Resulting Numbers: [94, 1] Generated Node #0,3,3: 93:[94, 1] Operation: 10-9=1 Moving to Node #0,3,3 Current State: 93:[94, 1], Operations: ['62-53=9', '10-9=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 34, 2, 85, 82 ]
87
[ "34/2=17", "85/17=5", "82+5=87" ]
Current State: 87:[34, 2, 85, 82], Operations: [] Exploring Operation: 34/2=17, Resulting Numbers: [85, 82, 17] Generated Node #2: [85, 82, 17] from Operation: 34/2=17 Current State: 87:[85, 82, 17], Operations: ['34/2=17'] Exploring Operation: 85/17=5, Resulting Numbers: [82, 5] Generated Node #3: [82, 5] from Operation: 85/17=5 Current State: 87:[82, 5], Operations: ['34/2=17', '85/17=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[34, 2, 85, 82], Operations: [] Exploring Operation: 85-82=3, Resulting Numbers: [34, 2, 3] Generated Node #0,0: 87:[34, 2, 3] Operation: 85-82=3 Exploring Operation: 34-2=32, Resulting Numbers: [85, 82, 32] Generated Node #0,1: 87:[85, 82, 32] Operation: 34-2=32 Moving to Node #0,0 Current State: 87:[34, 2, 3], Operations: ['85-82=3'] Exploring Operation: 34-3=31, Resulting Numbers: [2, 31] Generated Node #0,0,0: 87:[2, 31] Operation: 34-3=31 Exploring Operation: 34-2=32, Resulting Numbers: [3, 32] Generated Node #0,0,1: 87:[3, 32] Operation: 34-2=32 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[2, 31], Operations: ['85-82=3', '34-3=31'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,87 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 87:[3, 32], Operations: ['85-82=3', '34-2=32'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,87 unequal: No Solution Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 87:[85, 82, 32], Operations: ['34-2=32'] Exploring Operation: 85-82=3, Resulting Numbers: [32, 3] Generated Node #0,1,0: 87:[32, 3] Operation: 85-82=3 Exploring Operation: 82-32=50, Resulting Numbers: [85, 50] Generated Node #0,1,1: 87:[85, 50] Operation: 82-32=50 Moving to Node #0,1,0 Current State: 87:[32, 3], Operations: ['34-2=32', '85-82=3'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,87 unequal: No Solution Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[85, 50], Operations: ['34-2=32', '82-32=50'] Exploring Operation: 85-50=35, Resulting Numbers: [35] 35,87 unequal: No Solution Exploring Operation: 85+50=135, Resulting Numbers: [135] 135,87 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 37, 78, 40, 71 ]
11
[ "37+40=77", "78-71=7", "77/7=11" ]
Current State: 11:[37, 78, 40, 71], Operations: [] Exploring Operation: 37+40=77, Resulting Numbers: [78, 71, 77] Generated Node #2: [78, 71, 77] from Operation: 37+40=77 Current State: 11:[78, 71, 77], Operations: ['37+40=77'] Exploring Operation: 78-71=7, Resulting Numbers: [77, 7] Generated Node #3: [77, 7] from Operation: 78-71=7 Current State: 11:[77, 7], Operations: ['37+40=77', '78-71=7'] Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[37, 78, 40, 71], Operations: [] Exploring Operation: 78-71=7, Resulting Numbers: [37, 40, 7] Generated Node #0,0: 11:[37, 40, 7] Operation: 78-71=7 Exploring Operation: 78-40=38, Resulting Numbers: [37, 71, 38] Generated Node #0,1: 11:[37, 71, 38] Operation: 78-40=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[37, 40, 7], Operations: ['78-71=7'] Exploring Operation: 40-37=3, Resulting Numbers: [7, 3] Generated Node #0,0,0: 11:[7, 3] Operation: 40-37=3 Exploring Operation: 37-7=30, Resulting Numbers: [40, 30] Generated Node #0,0,1: 11:[40, 30] Operation: 37-7=30 Moving to Node #0,0,0 Current State: 11:[7, 3], Operations: ['78-71=7', '40-37=3'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[40, 30], Operations: ['78-71=7', '37-7=30'] Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,11 unequal: No Solution Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[37, 71, 38], Operations: ['78-40=38'] Exploring Operation: 71-38=33, Resulting Numbers: [37, 33] Generated Node #0,1,0: 11:[37, 33] Operation: 71-38=33 Exploring Operation: 71-37=34, Resulting Numbers: [38, 34] Generated Node #0,1,1: 11:[38, 34] Operation: 71-37=34 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 11:[37, 33], Operations: ['78-40=38', '71-38=33'] Exploring Operation: 37+33=70, Resulting Numbers: [70] 70,11 unequal: No Solution Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 11:[38, 34], Operations: ['78-40=38', '71-37=34'] Exploring Operation: 38+34=72, Resulting Numbers: [72] 72,11 unequal: No Solution Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 59, 70, 56, 51 ]
96
[ "70-59=11", "56+51=107", "107-11=96" ]
Current State: 96:[59, 70, 56, 51], Operations: [] Exploring Operation: 70-59=11, Resulting Numbers: [56, 51, 11] Generated Node #2: [56, 51, 11] from Operation: 70-59=11 Current State: 96:[56, 51, 11], Operations: ['70-59=11'] Exploring Operation: 56+51=107, Resulting Numbers: [11, 107] Generated Node #3: [11, 107] from Operation: 56+51=107 Current State: 96:[11, 107], Operations: ['70-59=11', '56+51=107'] Exploring Operation: 107-11=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[59, 70, 56, 51], Operations: [] Exploring Operation: 70-59=11, Resulting Numbers: [56, 51, 11] Generated Node #0,0: 96:[56, 51, 11] Operation: 70-59=11 Moving to Node #0,0 Current State: 96:[56, 51, 11], Operations: ['70-59=11'] Exploring Operation: 56-51=5, Resulting Numbers: [11, 5] Generated Node #0,0,0: 96:[11, 5] Operation: 56-51=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[11, 5], Operations: ['70-59=11', '56-51=5'] Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,96 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
[ 36, 28, 21, 77 ]
91
[ "36-28=8", "21*8=168", "168-77=91" ]
Current State: 91:[36, 28, 21, 77], Operations: [] Exploring Operation: 36-28=8, Resulting Numbers: [21, 77, 8] Generated Node #2: [21, 77, 8] from Operation: 36-28=8 Current State: 91:[21, 77, 8], Operations: ['36-28=8'] Exploring Operation: 21*8=168, Resulting Numbers: [77, 168] Generated Node #3: [77, 168] from Operation: 21*8=168 Current State: 91:[77, 168], Operations: ['36-28=8', '21*8=168'] Exploring Operation: 168-77=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[36, 28, 21, 77], Operations: [] Exploring Operation: 36-28=8, Resulting Numbers: [21, 77, 8] Generated Node #0,0: 91:[21, 77, 8] Operation: 36-28=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[21, 77, 8], Operations: ['36-28=8'] Exploring Operation: 21+77=98, Resulting Numbers: [8, 98] Generated Node #0,0,0: 91:[8, 98] Operation: 21+77=98 Moving to Node #0,0,0 Current State: 91:[8, 98], Operations: ['36-28=8', '21+77=98'] Exploring Operation: 98-8=90, Resulting Numbers: [90] 90,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 41, 87, 35, 28 ]
81
[ "41-35=6", "28*6=168", "168-87=81" ]
Current State: 81:[41, 87, 35, 28], Operations: [] Exploring Operation: 41-35=6, Resulting Numbers: [87, 28, 6] Generated Node #2: [87, 28, 6] from Operation: 41-35=6 Current State: 81:[87, 28, 6], Operations: ['41-35=6'] Exploring Operation: 28*6=168, Resulting Numbers: [87, 168] Generated Node #3: [87, 168] from Operation: 28*6=168 Current State: 81:[87, 168], Operations: ['41-35=6', '28*6=168'] Exploring Operation: 168-87=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[41, 87, 35, 28], Operations: [] Exploring Operation: 41+28=69, Resulting Numbers: [87, 35, 69] Generated Node #0,0: 81:[87, 35, 69] Operation: 41+28=69 Exploring Operation: 41-35=6, Resulting Numbers: [87, 28, 6] Generated Node #0,1: 81:[87, 28, 6] Operation: 41-35=6 Exploring Operation: 41-28=13, Resulting Numbers: [87, 35, 13] Generated Node #0,2: 81:[87, 35, 13] Operation: 41-28=13 Exploring Operation: 41+35=76, Resulting Numbers: [87, 28, 76] Generated Node #0,3: 81:[87, 28, 76] Operation: 41+35=76 Exploring Operation: 35-28=7, Resulting Numbers: [41, 87, 7] Generated Node #0,4: 81:[41, 87, 7] Operation: 35-28=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[87, 28, 6], Operations: ['41-35=6'] Exploring Operation: 87+6=93, Resulting Numbers: [28, 93] Generated Node #0,1,0: 81:[28, 93] Operation: 87+6=93 Exploring Operation: 28-6=22, Resulting Numbers: [87, 22] Generated Node #0,1,1: 81:[87, 22] Operation: 28-6=22 Exploring Operation: 87-6=81, Resulting Numbers: [28, 81] Generated Node #0,1,2: 81:[28, 81] Operation: 87-6=81 Exploring Operation: 87-28=59, Resulting Numbers: [6, 59] Generated Node #0,1,3: 81:[6, 59] Operation: 87-28=59 Exploring Operation: 28+6=34, Resulting Numbers: [87, 34] Generated Node #0,1,4: 81:[87, 34] Operation: 28+6=34 Moving to Node #0,1,2 Current State: 81:[28, 81], Operations: ['41-35=6', '87-6=81'] Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 28*81=2268, Resulting Numbers: [2268] 2268,81 unequal: No Solution Exploring Operation: 28+81=109, Resulting Numbers: [109] 109,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[87, 22], Operations: ['41-35=6', '28-6=22'] Exploring Operation: 87+22=109, Resulting Numbers: [109] 109,81 unequal: No Solution Exploring Operation: 87*22=1914, Resulting Numbers: [1914] 1914,81 unequal: No Solution Exploring Operation: 87-22=65, Resulting Numbers: [65] 65,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[28, 93], Operations: ['41-35=6', '87+6=93'] Exploring Operation: 93-28=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 28+93=121, Resulting Numbers: [121] 121,81 unequal: No Solution Exploring Operation: 28*93=2604, Resulting Numbers: [2604] 2604,81 unequal: No Solution Moving to Node #0,1,4 Current State: 81:[87, 34], Operations: ['41-35=6', '28+6=34'] Exploring Operation: 87*34=2958, Resulting Numbers: [2958] 2958,81 unequal: No Solution Exploring Operation: 87-34=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 87+34=121, Resulting Numbers: [121] 121,81 unequal: No Solution Moving to Node #0,1,3 Current State: 81:[6, 59], Operations: ['41-35=6', '87-28=59'] Exploring Operation: 6+59=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 6*59=354, Resulting Numbers: [354] 354,81 unequal: No Solution Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,81 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 Current State: 81:[87, 28, 76], Operations: ['41+35=76'] Exploring Operation: 76-28=48, Resulting Numbers: [87, 48] Generated Node #0,3,0: 81:[87, 48] Operation: 76-28=48 Exploring Operation: 87-28=59, Resulting Numbers: [76, 59] Generated Node #0,3,1: 81:[76, 59] Operation: 87-28=59 Exploring Operation: 28+76=104, Resulting Numbers: [87, 104] Generated Node #0,3,2: 81:[87, 104] Operation: 28+76=104 Exploring Operation: 87-76=11, Resulting Numbers: [28, 11] Generated Node #0,3,3: 81:[28, 11] Operation: 87-76=11 Exploring Operation: 87+28=115, Resulting Numbers: [76, 115] Generated Node #0,3,4: 81:[76, 115] Operation: 87+28=115 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 81:[28, 11], Operations: ['41+35=76', '87-76=11'] Exploring Operation: 28+11=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,81 unequal: No Solution Exploring Operation: 28*11=308, Resulting Numbers: [308] 308,81 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 #0,3,0 Current State: 81:[87, 48], Operations: ['41+35=76', '76-28=48'] Exploring Operation: 87*48=4176, Resulting Numbers: [4176] 4176,81 unequal: No Solution Exploring Operation: 87+48=135, Resulting Numbers: [135] 135,81 unequal: No Solution Exploring Operation: 87-48=39, Resulting Numbers: [39] 39,81 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 #0,3,1 Current State: 81:[76, 59], Operations: ['41+35=76', '87-28=59'] Exploring Operation: 76*59=4484, Resulting Numbers: [4484] 4484,81 unequal: No Solution Exploring Operation: 76-59=17, Resulting Numbers: [17] 17,81 unequal: No Solution Exploring Operation: 76+59=135, Resulting Numbers: [135] 135,81 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 #0,3,2 Current State: 81:[87, 104], Operations: ['41+35=76', '28+76=104'] Exploring Operation: 104-87=17, Resulting Numbers: [17] 17,81 unequal: No Solution Exploring Operation: 87+104=191, Resulting Numbers: [191] 191,81 unequal: No Solution Exploring Operation: 87*104=9048, Resulting Numbers: [9048] 9048,81 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 #0,3,4 Current State: 81:[76, 115], Operations: ['41+35=76', '87+28=115'] Exploring Operation: 76*115=8740, Resulting Numbers: [8740] 8740,81 unequal: No Solution Exploring Operation: 76+115=191, Resulting Numbers: [191] 191,81 unequal: No Solution Exploring Operation: 115-76=39, Resulting Numbers: [39] 39,81 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 #0,2 Current State: 81:[87, 35, 13], Operations: ['41-28=13'] Exploring Operation: 35+13=48, Resulting Numbers: [87, 48] Generated Node #0,2,0: 81:[87, 48] Operation: 35+13=48 Exploring Operation: 35-13=22, Resulting Numbers: [87, 22] Generated Node #0,2,1: 81:[87, 22] Operation: 35-13=22 Exploring Operation: 87-13=74, Resulting Numbers: [35, 74] Generated Node #0,2,2: 81:[35, 74] Operation: 87-13=74 Exploring Operation: 87+13=100, Resulting Numbers: [35, 100] Generated Node #0,2,3: 81:[35, 100] Operation: 87+13=100 Exploring Operation: 87-35=52, Resulting Numbers: [13, 52] Generated Node #0,2,4: 81:[13, 52] Operation: 87-35=52 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 81:[87, 22], Operations: ['41-28=13', '35-13=22'] Exploring Operation: 87*22=1914, Resulting Numbers: [1914] 1914,81 unequal: No Solution Exploring Operation: 87-22=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 87+22=109, Resulting Numbers: [109] 109,81 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 #0,2,2 Current State: 81:[35, 74], Operations: ['41-28=13', '87-13=74'] Exploring Operation: 35*74=2590, Resulting Numbers: [2590] 2590,81 unequal: No Solution Exploring Operation: 35+74=109, Resulting Numbers: [109] 109,81 unequal: No Solution Exploring Operation: 74-35=39, Resulting Numbers: [39] 39,81 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 #0,2,0 Current State: 81:[87, 48], Operations: ['41-28=13', '35+13=48'] Exploring Operation: 87-48=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 87*48=4176, Resulting Numbers: [4176] 4176,81 unequal: No Solution Exploring Operation: 87+48=135, Resulting Numbers: [135] 135,81 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 #0,2,3 Current State: 81:[35, 100], Operations: ['41-28=13', '87+13=100'] Exploring Operation: 100-35=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 35*100=3500, Resulting Numbers: [3500] 3500,81 unequal: No Solution Exploring Operation: 35+100=135, Resulting Numbers: [135] 135,81 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 #0,2,4 Current State: 81:[13, 52], Operations: ['41-28=13', '87-35=52'] Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,81 unequal: No Solution Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 13*52=676, Resulting Numbers: [676] 676,81 unequal: No Solution Exploring Operation: 13+52=65, Resulting Numbers: [65] 65,81 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 #0,4 Current State: 81:[41, 87, 7], Operations: ['35-28=7'] Exploring Operation: 87-41=46, Resulting Numbers: [7, 46] Generated Node #0,4,0: 81:[7, 46] Operation: 87-41=46 Exploring Operation: 87-7=80, Resulting Numbers: [41, 80] Generated Node #0,4,1: 81:[41, 80] Operation: 87-7=80 Exploring Operation: 41+7=48, Resulting Numbers: [87, 48] Generated Node #0,4,2: 81:[87, 48] Operation: 41+7=48 Exploring Operation: 87+7=94, Resulting Numbers: [41, 94] Generated Node #0,4,3: 81:[41, 94] Operation: 87+7=94 Exploring Operation: 41-7=34, Resulting Numbers: [87, 34] Generated Node #0,4,4: 81:[87, 34] Operation: 41-7=34 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 81:[87, 34], Operations: ['35-28=7', '41-7=34'] Exploring Operation: 87*34=2958, Resulting Numbers: [2958] 2958,81 unequal: No Solution Exploring Operation: 87-34=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 87+34=121, Resulting Numbers: [121] 121,81 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 #0,4,1 Current State: 81:[41, 80], Operations: ['35-28=7', '87-7=80'] Exploring Operation: 41+80=121, Resulting Numbers: [121] 121,81 unequal: No Solution Exploring Operation: 80-41=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 41*80=3280, Resulting Numbers: [3280] 3280,81 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 #0,4,0 Current State: 81:[7, 46], Operations: ['35-28=7', '87-41=46'] Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 7*46=322, Resulting Numbers: [322] 322,81 unequal: No Solution Exploring Operation: 7+46=53, Resulting Numbers: [53] 53,81 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 #0,4,2 Current State: 81:[87, 48], Operations: ['35-28=7', '41+7=48'] Exploring Operation: 87+48=135, Resulting Numbers: [135] 135,81 unequal: No Solution Exploring Operation: 87*48=4176, Resulting Numbers: [4176] 4176,81 unequal: No Solution Exploring Operation: 87-48=39, Resulting Numbers: [39] 39,81 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 #0,4,3 Current State: 81:[41, 94], Operations: ['35-28=7', '87+7=94'] Exploring Operation: 41*94=3854, Resulting Numbers: [3854] 3854,81 unequal: No Solution Exploring Operation: 94-41=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 41+94=135, Resulting Numbers: [135] 135,81 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:[87, 35, 69], Operations: ['41+28=69'] Exploring Operation: 87+35=122, Resulting Numbers: [69, 122] Generated Node #0,0,0: 81:[69, 122] Operation: 87+35=122 Exploring Operation: 87-35=52, Resulting Numbers: [69, 52] Generated Node #0,0,1: 81:[69, 52] Operation: 87-35=52 Exploring Operation: 69-35=34, Resulting Numbers: [87, 34] Generated Node #0,0,2: 81:[87, 34] Operation: 69-35=34 Exploring Operation: 87-69=18, Resulting Numbers: [35, 18] Generated Node #0,0,3: 81:[35, 18] Operation: 87-69=18 Exploring Operation: 35+69=104, Resulting Numbers: [87, 104] Generated Node #0,0,4: 81:[87, 104] Operation: 35+69=104 Moving to Node #0,0,2 Current State: 81:[87, 34], Operations: ['41+28=69', '69-35=34'] Exploring Operation: 87-34=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 87+34=121, Resulting Numbers: [121] 121,81 unequal: No Solution Exploring Operation: 87*34=2958, Resulting Numbers: [2958] 2958,81 unequal: No Solution Moving to Node #0,0,3 Current State: 81:[35, 18], Operations: ['41+28=69', '87-69=18'] Exploring Operation: 35+18=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,81 unequal: No Solution Exploring Operation: 35*18=630, Resulting Numbers: [630] 630,81 unequal: No Solution Moving to Node #0,0,4 Current State: 81:[87, 104], Operations: ['41+28=69', '35+69=104'] Exploring Operation: 87+104=191, Resulting Numbers: [191] 191,81 unequal: No Solution Exploring Operation: 87*104=9048, Resulting Numbers: [9048] 9048,81 unequal: No Solution Exploring Operation: 104-87=17, Resulting Numbers: [17] 17,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[69, 52], Operations: ['41+28=69', '87-35=52'] Exploring Operation: 69-52=17, Resulting Numbers: [17] 17,81 unequal: No Solution Exploring Operation: 69*52=3588, Resulting Numbers: [3588] 3588,81 unequal: No Solution Exploring Operation: 69+52=121, Resulting Numbers: [121] 121,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[69, 122], Operations: ['41+28=69', '87+35=122'] Exploring Operation: 122-69=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 69+122=191, Resulting Numbers: [191] 191,81 unequal: No Solution Exploring Operation: 69*122=8418, Resulting Numbers: [8418] 8418,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 48, 96, 82, 75 ]
13
[ "48+96=144", "82+75=157", "157-144=13" ]
Current State: 13:[48, 96, 82, 75], Operations: [] Exploring Operation: 48+96=144, Resulting Numbers: [82, 75, 144] Generated Node #2: [82, 75, 144] from Operation: 48+96=144 Current State: 13:[82, 75, 144], Operations: ['48+96=144'] Exploring Operation: 82+75=157, Resulting Numbers: [144, 157] Generated Node #3: [144, 157] from Operation: 82+75=157 Current State: 13:[144, 157], Operations: ['48+96=144', '82+75=157'] Exploring Operation: 157-144=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[48, 96, 82, 75], Operations: [] Exploring Operation: 96-82=14, Resulting Numbers: [48, 75, 14] Generated Node #0,0: 13:[48, 75, 14] Operation: 96-82=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[48, 75, 14], Operations: ['96-82=14'] Exploring Operation: 75-48=27, Resulting Numbers: [14, 27] Generated Node #0,0,0: 13:[14, 27] Operation: 75-48=27 Moving to Node #0,0,0 Current State: 13:[14, 27], Operations: ['96-82=14', '75-48=27'] Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[48, 96, 82, 75], Operations: [] Exploring Operation: 96-82=14, Resulting Numbers: [48, 75, 14] Generated Node #0,0: 13:[48, 75, 14] Operation: 96-82=14 Moving to Node #0,0 Current State: 13:[48, 75, 14], Operations: ['96-82=14'] Exploring Operation: 75-48=27, Resulting Numbers: [14, 27] Generated Node #0,0,0: 13:[14, 27] Operation: 75-48=27 Moving to Node #0,0,0 Current State: 13:[14, 27], Operations: ['96-82=14', '75-48=27'] Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 79, 13, 35, 73 ]
54
[ "79+13=92", "73-35=38", "92-38=54" ]
Current State: 54:[79, 13, 35, 73], Operations: [] Exploring Operation: 79+13=92, Resulting Numbers: [35, 73, 92] Generated Node #2: [35, 73, 92] from Operation: 79+13=92 Current State: 54:[35, 73, 92], Operations: ['79+13=92'] Exploring Operation: 73-35=38, Resulting Numbers: [92, 38] Generated Node #3: [92, 38] from Operation: 73-35=38 Current State: 54:[92, 38], Operations: ['79+13=92', '73-35=38'] Exploring Operation: 92-38=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[79, 13, 35, 73], Operations: [] Exploring Operation: 79-73=6, Resulting Numbers: [13, 35, 6] Generated Node #0,0: 54:[13, 35, 6] Operation: 79-73=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[13, 35, 6], Operations: ['79-73=6'] Exploring Operation: 35-13=22, Resulting Numbers: [6, 22] Generated Node #0,0,0: 54:[6, 22] Operation: 35-13=22 Moving to Node #0,0,0 Current State: 54:[6, 22], Operations: ['79-73=6', '35-13=22'] Exploring Operation: 6+22=28, Resulting Numbers: [28] 28,54 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
[ 29, 79, 86, 78 ]
57
[ "86-29=57", "79-78=1", "57*1=57" ]
Current State: 57:[29, 79, 86, 78], Operations: [] Exploring Operation: 86-29=57, Resulting Numbers: [79, 78, 57] Generated Node #2: [79, 78, 57] from Operation: 86-29=57 Current State: 57:[79, 78, 57], Operations: ['86-29=57'] Exploring Operation: 79-78=1, Resulting Numbers: [57, 1] Generated Node #3: [57, 1] from Operation: 79-78=1 Current State: 57:[57, 1], Operations: ['86-29=57', '79-78=1'] Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[29, 79, 86, 78], Operations: [] Exploring Operation: 86-29=57, Resulting Numbers: [79, 78, 57] Generated Node #0,0: 57:[79, 78, 57] Operation: 86-29=57 Exploring Operation: 79-78=1, Resulting Numbers: [29, 86, 1] Generated Node #0,1: 57:[29, 86, 1] Operation: 79-78=1 Exploring Operation: 86-79=7, Resulting Numbers: [29, 78, 7] Generated Node #0,2: 57:[29, 78, 7] Operation: 86-79=7 Exploring Operation: 86-78=8, Resulting Numbers: [29, 79, 8] Generated Node #0,3: 57:[29, 79, 8] Operation: 86-78=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[29, 78, 7], Operations: ['86-79=7'] Exploring Operation: 29+7=36, Resulting Numbers: [78, 36] Generated Node #0,2,0: 57:[78, 36] Operation: 29+7=36 Exploring Operation: 78-29=49, Resulting Numbers: [7, 49] Generated Node #0,2,1: 57:[7, 49] Operation: 78-29=49 Exploring Operation: 29-7=22, Resulting Numbers: [78, 22] Generated Node #0,2,2: 57:[78, 22] Operation: 29-7=22 Exploring Operation: 78-7=71, Resulting Numbers: [29, 71] Generated Node #0,2,3: 57:[29, 71] Operation: 78-7=71 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 57:[7, 49], Operations: ['86-79=7', '78-29=49'] Exploring Operation: 7*49=343, Resulting Numbers: [343] 343,57 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,57 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,57 unequal: No Solution Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,57 unequal: No Solution No 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: 57:[78, 22], Operations: ['86-79=7', '29-7=22'] Exploring Operation: 78-22=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 78*22=1716, Resulting Numbers: [1716] 1716,57 unequal: No Solution Exploring Operation: 78+22=100, Resulting Numbers: [100] 100,57 unequal: No Solution No 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: 57:[29, 71], Operations: ['86-79=7', '78-7=71'] Exploring Operation: 29*71=2059, Resulting Numbers: [2059] 2059,57 unequal: No Solution Exploring Operation: 29+71=100, Resulting Numbers: [100] 100,57 unequal: No Solution Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,57 unequal: No Solution No 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: 57:[78, 36], Operations: ['86-79=7', '29+7=36'] Exploring Operation: 78*36=2808, Resulting Numbers: [2808] 2808,57 unequal: No Solution Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,57 unequal: No Solution Exploring Operation: 78+36=114, Resulting Numbers: [114] 114,57 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: 57:[29, 79, 8], Operations: ['86-78=8'] Exploring Operation: 29-8=21, Resulting Numbers: [79, 21] Generated Node #0,3,0: 57:[79, 21] Operation: 29-8=21 Exploring Operation: 29+8=37, Resulting Numbers: [79, 37] Generated Node #0,3,1: 57:[79, 37] Operation: 29+8=37 Exploring Operation: 79-29=50, Resulting Numbers: [8, 50] Generated Node #0,3,2: 57:[8, 50] Operation: 79-29=50 Exploring Operation: 79-8=71, Resulting Numbers: [29, 71] Generated Node #0,3,3: 57:[29, 71] Operation: 79-8=71 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 57:[8, 50], Operations: ['86-78=8', '79-29=50'] Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,57 unequal: No Solution Exploring Operation: 8*50=400, Resulting Numbers: [400] 400,57 unequal: No Solution Exploring Operation: 8+50=58, Resulting Numbers: [58] 58,57 unequal: No Solution No 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: 57:[79, 21], Operations: ['86-78=8', '29-8=21'] Exploring Operation: 79*21=1659, Resulting Numbers: [1659] 1659,57 unequal: No Solution Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,57 unequal: No Solution Exploring Operation: 79+21=100, Resulting Numbers: [100] 100,57 unequal: No Solution No 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: 57:[29, 71], Operations: ['86-78=8', '79-8=71'] Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,57 unequal: No Solution Exploring Operation: 29*71=2059, Resulting Numbers: [2059] 2059,57 unequal: No Solution Exploring Operation: 29+71=100, Resulting Numbers: [100] 100,57 unequal: No Solution No 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: 57:[79, 37], Operations: ['86-78=8', '29+8=37'] Exploring Operation: 79+37=116, Resulting Numbers: [116] 116,57 unequal: No Solution Exploring Operation: 79-37=42, Resulting Numbers: [42] 42,57 unequal: No Solution Exploring Operation: 79*37=2923, Resulting Numbers: [2923] 2923,57 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: 57:[29, 86, 1], Operations: ['79-78=1'] Exploring Operation: 29*1=29, Resulting Numbers: [86, 29] Generated Node #0,1,0: 57:[86, 29] Operation: 29*1=29 Exploring Operation: 86-29=57, Resulting Numbers: [1, 57] Generated Node #0,1,1: 57:[1, 57] Operation: 86-29=57 Exploring Operation: 86-1=85, Resulting Numbers: [29, 85] Generated Node #0,1,2: 57:[29, 85] Operation: 86-1=85 Exploring Operation: 29-1=28, Resulting Numbers: [86, 28] Generated Node #0,1,3: 57:[86, 28] Operation: 29-1=28 Moving to Node #0,1,1 Current State: 57:[1, 57], Operations: ['79-78=1', '86-29=57'] Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[29, 79, 86, 78], Operations: [] Exploring Operation: 79-78=1, Resulting Numbers: [29, 86, 1] Generated Node #0,1: 57:[29, 86, 1] Operation: 79-78=1 Moving to Node #0,1 Current State: 57:[29, 86, 1], Operations: ['79-78=1'] Exploring Operation: 86-29=57, Resulting Numbers: [1, 57] Generated Node #0,1,1: 57:[1, 57] Operation: 86-29=57 Moving to Node #0,1,1 Current State: 57:[1, 57], Operations: ['79-78=1', '86-29=57'] Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.960069
hs_4
mult_heuristic
[ 56, 8, 17, 23 ]
28
[ "8+17=25", "25-23=2", "56/2=28" ]
Current State: 28:[56, 8, 17, 23], Operations: [] Exploring Operation: 8+17=25, Resulting Numbers: [56, 23, 25] Generated Node #2: [56, 23, 25] from Operation: 8+17=25 Current State: 28:[56, 23, 25], Operations: ['8+17=25'] Exploring Operation: 25-23=2, Resulting Numbers: [56, 2] Generated Node #3: [56, 2] from Operation: 25-23=2 Current State: 28:[56, 2], Operations: ['8+17=25', '25-23=2'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[56, 8, 17, 23], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [17, 23, 7] Generated Node #0,0: 28:[17, 23, 7] Operation: 56/8=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[17, 23, 7], Operations: ['56/8=7'] Exploring Operation: 23-17=6, Resulting Numbers: [7, 6] Generated Node #0,0,0: 28:[7, 6] Operation: 23-17=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[7, 6], Operations: ['56/8=7', '23-17=6'] Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,28 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
[ 87, 7, 26, 6 ]
74
[ "87+7=94", "26-6=20", "94-20=74" ]
Current State: 74:[87, 7, 26, 6], Operations: [] Exploring Operation: 87+7=94, Resulting Numbers: [26, 6, 94] Generated Node #2: [26, 6, 94] from Operation: 87+7=94 Current State: 74:[26, 6, 94], Operations: ['87+7=94'] Exploring Operation: 26-6=20, Resulting Numbers: [94, 20] Generated Node #3: [94, 20] from Operation: 26-6=20 Current State: 74:[94, 20], Operations: ['87+7=94', '26-6=20'] Exploring Operation: 94-20=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[87, 7, 26, 6], Operations: [] Exploring Operation: 7+26=33, Resulting Numbers: [87, 6, 33] Generated Node #0,0: 74:[87, 6, 33] Operation: 7+26=33 Exploring Operation: 87-7=80, Resulting Numbers: [26, 6, 80] Generated Node #0,1: 74:[26, 6, 80] Operation: 87-7=80 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[87, 6, 33], Operations: ['7+26=33'] Exploring Operation: 6+33=39, Resulting Numbers: [87, 39] Generated Node #0,0,0: 74:[87, 39] Operation: 6+33=39 Exploring Operation: 87-6=81, Resulting Numbers: [33, 81] Generated Node #0,0,1: 74:[33, 81] Operation: 87-6=81 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 74:[33, 81], Operations: ['7+26=33', '87-6=81'] Exploring Operation: 81-33=48, Resulting Numbers: [48] 48,74 unequal: No Solution Exploring Operation: 33+81=114, Resulting Numbers: [114] 114,74 unequal: No Solution No 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: 74:[87, 39], Operations: ['7+26=33', '6+33=39'] Exploring Operation: 87+39=126, Resulting Numbers: [126] 126,74 unequal: No Solution Exploring Operation: 87-39=48, Resulting Numbers: [48] 48,74 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: 74:[26, 6, 80], Operations: ['87-7=80'] Exploring Operation: 80-6=74, Resulting Numbers: [26, 74] Generated Node #0,1,0: 74:[26, 74] Operation: 80-6=74 Exploring Operation: 26+6=32, Resulting Numbers: [80, 32] Generated Node #0,1,1: 74:[80, 32] Operation: 26+6=32 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 74:[26, 74], Operations: ['87-7=80', '80-6=74'] Exploring Operation: 26+74=100, Resulting Numbers: [100] 100,74 unequal: No Solution Exploring Operation: 74-26=48, Resulting Numbers: [48] 48,74 unequal: No Solution No 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: 74:[80, 32], Operations: ['87-7=80', '26+6=32'] Exploring Operation: 80-32=48, Resulting Numbers: [48] 48,74 unequal: No Solution Exploring Operation: 80+32=112, Resulting Numbers: [112] 112,74 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
[ 29, 23, 33, 49 ]
30
[ "29+23=52", "33+49=82", "82-52=30" ]
Current State: 30:[29, 23, 33, 49], Operations: [] Exploring Operation: 29+23=52, Resulting Numbers: [33, 49, 52] Generated Node #2: [33, 49, 52] from Operation: 29+23=52 Current State: 30:[33, 49, 52], Operations: ['29+23=52'] Exploring Operation: 33+49=82, Resulting Numbers: [52, 82] Generated Node #3: [52, 82] from Operation: 33+49=82 Current State: 30:[52, 82], Operations: ['29+23=52', '33+49=82'] Exploring Operation: 82-52=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[29, 23, 33, 49], Operations: [] Exploring Operation: 49-23=26, Resulting Numbers: [29, 33, 26] Generated Node #0,0: 30:[29, 33, 26] Operation: 49-23=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[29, 33, 26], Operations: ['49-23=26'] Exploring Operation: 33-26=7, Resulting Numbers: [29, 7] Generated Node #0,0,0: 30:[29, 7] Operation: 33-26=7 Moving to Node #0,0,0 Current State: 30:[29, 7], Operations: ['49-23=26', '33-26=7'] Exploring Operation: 29+7=36, Resulting Numbers: [36] 36,30 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
[ 8, 3, 70, 83 ]
47
[ "83-70=13", "3*13=39", "8+39=47" ]
Current State: 47:[8, 3, 70, 83], Operations: [] Exploring Operation: 83-70=13, Resulting Numbers: [8, 3, 13] Generated Node #2: [8, 3, 13] from Operation: 83-70=13 Current State: 47:[8, 3, 13], Operations: ['83-70=13'] Exploring Operation: 3*13=39, Resulting Numbers: [8, 39] Generated Node #3: [8, 39] from Operation: 3*13=39 Current State: 47:[8, 39], Operations: ['83-70=13', '3*13=39'] Exploring Operation: 8+39=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[8, 3, 70, 83], Operations: [] Exploring Operation: 8*3=24, Resulting Numbers: [70, 83, 24] Generated Node #0,0: 47:[70, 83, 24] Operation: 8*3=24 Moving to Node #0,0 Current State: 47:[70, 83, 24], Operations: ['8*3=24'] Exploring Operation: 83-24=59, Resulting Numbers: [70, 59] Generated Node #0,0,0: 47:[70, 59] Operation: 83-24=59 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[70, 59], Operations: ['8*3=24', '83-24=59'] Exploring Operation: 70-59=11, Resulting Numbers: [11] 11,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic