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
[ 96, 62, 8, 25 ]
17
[ "96-62=34", "25-8=17", "34-17=17" ]
Current State: 17:[96, 62, 8, 25], Operations: [] Exploring Operation: 96-62=34, Resulting Numbers: [8, 25, 34] Generated Node #2: [8, 25, 34] from Operation: 96-62=34 Current State: 17:[8, 25, 34], Operations: ['96-62=34'] Exploring Operation: 25-8=17, Resulting Numbers: [34, 17] Generated Node #3: [34, 17] from Operation: 25-8=17 Current State: 17:[34, 17], Operations: ['96-62=34', '25-8=17'] Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[96, 62, 8, 25], Operations: [] Exploring Operation: 96-8=88, Resulting Numbers: [62, 25, 88] Generated Node #0,0: 17:[62, 25, 88] Operation: 96-8=88 Exploring Operation: 96-25=71, Resulting Numbers: [62, 8, 71] Generated Node #0,1: 17:[62, 8, 71] Operation: 96-25=71 Exploring Operation: 96/8=12, Resulting Numbers: [62, 25, 12] Generated Node #0,2: 17:[62, 25, 12] Operation: 96/8=12 Exploring Operation: 62-25=37, Resulting Numbers: [96, 8, 37] Generated Node #0,3: 17:[96, 8, 37] Operation: 62-25=37 Exploring Operation: 96-62=34, Resulting Numbers: [8, 25, 34] Generated Node #0,4: 17:[8, 25, 34] Operation: 96-62=34 Start Sub Search at level 1: Moving to Node #0,4 Current State: 17:[8, 25, 34], Operations: ['96-62=34'] Exploring Operation: 25-8=17, Resulting Numbers: [34, 17] Generated Node #0,4,0: 17:[34, 17] Operation: 25-8=17 Exploring Operation: 34-25=9, Resulting Numbers: [8, 9] Generated Node #0,4,1: 17:[8, 9] Operation: 34-25=9 Exploring Operation: 8+34=42, Resulting Numbers: [25, 42] Generated Node #0,4,2: 17:[25, 42] Operation: 8+34=42 Exploring Operation: 8+25=33, Resulting Numbers: [34, 33] Generated Node #0,4,3: 17:[34, 33] Operation: 8+25=33 Exploring Operation: 34-8=26, Resulting Numbers: [25, 26] Generated Node #0,4,4: 17:[25, 26] Operation: 34-8=26 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 17:[34, 17], Operations: ['96-62=34', '25-8=17'] Exploring Operation: 34+17=51, Resulting Numbers: [51] 51,17 unequal: No Solution Exploring Operation: 34*17=578, Resulting Numbers: [578] 578,17 unequal: No Solution Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[96, 62, 8, 25], Operations: [] Exploring Operation: 96-62=34, Resulting Numbers: [8, 25, 34] Generated Node #0,4: 17:[8, 25, 34] Operation: 96-62=34 Moving to Node #0,4 Current State: 17:[8, 25, 34], Operations: ['96-62=34'] Exploring Operation: 25-8=17, Resulting Numbers: [34, 17] Generated Node #0,4,0: 17:[34, 17] Operation: 25-8=17 Moving to Node #0,4,0 Current State: 17:[34, 17], Operations: ['96-62=34', '25-8=17'] Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 90, 42, 60, 57 ]
94
[ "90*60=5400", "5400-42=5358", "5358/57=94" ]
Current State: 94:[90, 42, 60, 57], Operations: [] Exploring Operation: 90*60=5400, Resulting Numbers: [42, 57, 5400] Generated Node #2: [42, 57, 5400] from Operation: 90*60=5400 Current State: 94:[42, 57, 5400], Operations: ['90*60=5400'] Exploring Operation: 5400-42=5358, Resulting Numbers: [57, 5358] Generated Node #3: [57, 5358] from Operation: 5400-42=5358 Current State: 94:[57, 5358], Operations: ['90*60=5400', '5400-42=5358'] Exploring Operation: 5358/57=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[90, 42, 60, 57], Operations: [] Exploring Operation: 60-42=18, Resulting Numbers: [90, 57, 18] Generated Node #0,0: 94:[90, 57, 18] Operation: 60-42=18 Exploring Operation: 42+57=99, Resulting Numbers: [90, 60, 99] Generated Node #0,1: 94:[90, 60, 99] Operation: 42+57=99 Exploring Operation: 60-57=3, Resulting Numbers: [90, 42, 3] Generated Node #0,2: 94:[90, 42, 3] Operation: 60-57=3 Exploring Operation: 42+60=102, Resulting Numbers: [90, 57, 102] Generated Node #0,3: 94:[90, 57, 102] Operation: 42+60=102 Exploring Operation: 90-42=48, Resulting Numbers: [60, 57, 48] Generated Node #0,4: 94:[60, 57, 48] Operation: 90-42=48 Moving to Node #0,2 Current State: 94:[90, 42, 3], Operations: ['60-57=3'] Exploring Operation: 90-3=87, Resulting Numbers: [42, 87] Generated Node #0,2,0: 94:[42, 87] Operation: 90-3=87 Exploring Operation: 42-3=39, Resulting Numbers: [90, 39] Generated Node #0,2,1: 94:[90, 39] Operation: 42-3=39 Exploring Operation: 42+3=45, Resulting Numbers: [90, 45] Generated Node #0,2,2: 94:[90, 45] Operation: 42+3=45 Exploring Operation: 90+3=93, Resulting Numbers: [42, 93] Generated Node #0,2,3: 94:[42, 93] Operation: 90+3=93 Exploring Operation: 90-42=48, Resulting Numbers: [3, 48] Generated Node #0,2,4: 94:[3, 48] Operation: 90-42=48 Moving to Node #0,3 Current State: 94:[90, 57, 102], Operations: ['42+60=102'] Exploring Operation: 102-57=45, Resulting Numbers: [90, 45] Generated Node #0,3,0: 94:[90, 45] Operation: 102-57=45 Exploring Operation: 90-57=33, Resulting Numbers: [102, 33] Generated Node #0,3,1: 94:[102, 33] Operation: 90-57=33 Exploring Operation: 102-90=12, Resulting Numbers: [57, 12] Generated Node #0,3,2: 94:[57, 12] Operation: 102-90=12 Exploring Operation: 90+57=147, Resulting Numbers: [102, 147] Generated Node #0,3,3: 94:[102, 147] Operation: 90+57=147 Exploring Operation: 57+102=159, Resulting Numbers: [90, 159] Generated Node #0,3,4: 94:[90, 159] Operation: 57+102=159 Moving to Node #0,1 Current State: 94:[90, 60, 99], Operations: ['42+57=99'] Exploring Operation: 90+60=150, Resulting Numbers: [99, 150] Generated Node #0,1,0: 94:[99, 150] Operation: 90+60=150 Exploring Operation: 99-90=9, Resulting Numbers: [60, 9] Generated Node #0,1,1: 94:[60, 9] Operation: 99-90=9 Exploring Operation: 90-60=30, Resulting Numbers: [99, 30] Generated Node #0,1,2: 94:[99, 30] Operation: 90-60=30 Exploring Operation: 60+99=159, Resulting Numbers: [90, 159] Generated Node #0,1,3: 94:[90, 159] Operation: 60+99=159 Exploring Operation: 99-60=39, Resulting Numbers: [90, 39] Generated Node #0,1,4: 94:[90, 39] Operation: 99-60=39 Moving to Node #0,4 Current State: 94:[60, 57, 48], Operations: ['90-42=48'] Exploring Operation: 57-48=9, Resulting Numbers: [60, 9] Generated Node #0,4,0: 94:[60, 9] Operation: 57-48=9 Exploring Operation: 60+57=117, Resulting Numbers: [48, 117] Generated Node #0,4,1: 94:[48, 117] Operation: 60+57=117 Exploring Operation: 60+48=108, Resulting Numbers: [57, 108] Generated Node #0,4,2: 94:[57, 108] Operation: 60+48=108 Exploring Operation: 60-48=12, Resulting Numbers: [57, 12] Generated Node #0,4,3: 94:[57, 12] Operation: 60-48=12 Exploring Operation: 60-57=3, Resulting Numbers: [48, 3] Generated Node #0,4,4: 94:[48, 3] Operation: 60-57=3 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 94:[48, 3], Operations: ['90-42=48', '60-57=3'] Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,94 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 48*3=144, Resulting Numbers: [144] 144,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 94:[60, 9], Operations: ['90-42=48', '57-48=9'] Exploring Operation: 60-9=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 60*9=540, Resulting Numbers: [540] 540,94 unequal: No Solution Exploring Operation: 60+9=69, Resulting Numbers: [69] 69,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 94:[57, 12], Operations: ['90-42=48', '60-48=12'] Exploring Operation: 57+12=69, Resulting Numbers: [69] 69,94 unequal: No Solution Exploring Operation: 57-12=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 57*12=684, Resulting Numbers: [684] 684,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 94:[48, 117], Operations: ['90-42=48', '60+57=117'] Exploring Operation: 48+117=165, Resulting Numbers: [165] 165,94 unequal: No Solution Exploring Operation: 48*117=5616, Resulting Numbers: [5616] 5616,94 unequal: No Solution Exploring Operation: 117-48=69, Resulting Numbers: [69] 69,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 94:[57, 108], Operations: ['90-42=48', '60+48=108'] Exploring Operation: 57*108=6156, Resulting Numbers: [6156] 6156,94 unequal: No Solution Exploring Operation: 108-57=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 57+108=165, Resulting Numbers: [165] 165,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 94:[90, 57, 18], Operations: ['60-42=18'] Exploring Operation: 57+18=75, Resulting Numbers: [90, 75] Generated Node #0,0,0: 94:[90, 75] Operation: 57+18=75 Exploring Operation: 57-18=39, Resulting Numbers: [90, 39] Generated Node #0,0,1: 94:[90, 39] Operation: 57-18=39 Exploring Operation: 90/18=5, Resulting Numbers: [57, 5] Generated Node #0,0,2: 94:[57, 5] Operation: 90/18=5 Exploring Operation: 90+18=108, Resulting Numbers: [57, 108] Generated Node #0,0,3: 94:[57, 108] Operation: 90+18=108 Exploring Operation: 90-57=33, Resulting Numbers: [18, 33] Generated Node #0,0,4: 94:[18, 33] Operation: 90-57=33 Moving to Node #0,2,4 Current State: 94:[3, 48], Operations: ['60-57=3', '90-42=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,94 unequal: No Solution Exploring Operation: 3*48=144, Resulting Numbers: [144] 144,94 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,94 unequal: No Solution Moving to Node #0,2,3 Current State: 94:[42, 93], Operations: ['60-57=3', '90+3=93'] Exploring Operation: 42+93=135, Resulting Numbers: [135] 135,94 unequal: No Solution Exploring Operation: 93-42=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 42*93=3906, Resulting Numbers: [3906] 3906,94 unequal: No Solution Moving to Node #0,3,0 Current State: 94:[90, 45], Operations: ['42+60=102', '102-57=45'] Exploring Operation: 90/45=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 90-45=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 90*45=4050, Resulting Numbers: [4050] 4050,94 unequal: No Solution Exploring Operation: 90+45=135, Resulting Numbers: [135] 135,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[90, 45], Operations: ['60-57=3', '42+3=45'] Exploring Operation: 90/45=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 90*45=4050, Resulting Numbers: [4050] 4050,94 unequal: No Solution Exploring Operation: 90+45=135, Resulting Numbers: [135] 135,94 unequal: No Solution Exploring Operation: 90-45=45, Resulting Numbers: [45] 45,94 unequal: No Solution Moving to Node #0,2,1 Current State: 94:[90, 39], Operations: ['60-57=3', '42-3=39'] Exploring Operation: 90-39=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 90*39=3510, Resulting Numbers: [3510] 3510,94 unequal: No Solution Exploring Operation: 90+39=129, Resulting Numbers: [129] 129,94 unequal: No Solution Moving to Node #0,1,4 Current State: 94:[90, 39], Operations: ['42+57=99', '99-60=39'] Exploring Operation: 90*39=3510, Resulting Numbers: [3510] 3510,94 unequal: No Solution Exploring Operation: 90+39=129, Resulting Numbers: [129] 129,94 unequal: No Solution Exploring Operation: 90-39=51, Resulting Numbers: [51] 51,94 unequal: No Solution Moving to Node #0,2,0 Current State: 94:[42, 87], Operations: ['60-57=3', '90-3=87'] Exploring Operation: 42*87=3654, Resulting Numbers: [3654] 3654,94 unequal: No Solution Exploring Operation: 87-42=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 42+87=129, Resulting Numbers: [129] 129,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[90, 39], Operations: ['60-42=18', '57-18=39'] Exploring Operation: 90-39=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 90*39=3510, Resulting Numbers: [3510] 3510,94 unequal: No Solution Exploring Operation: 90+39=129, Resulting Numbers: [129] 129,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[57, 5], Operations: ['60-42=18', '90/18=5'] Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,94 unequal: No Solution Exploring Operation: 57+5=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 57*5=285, Resulting Numbers: [285] 285,94 unequal: No Solution Moving to Node #0,3,2 Current State: 94:[57, 12], Operations: ['42+60=102', '102-90=12'] Exploring Operation: 57-12=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 57+12=69, Resulting Numbers: [69] 69,94 unequal: No Solution Exploring Operation: 57*12=684, Resulting Numbers: [684] 684,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[60, 9], Operations: ['42+57=99', '99-90=9'] Exploring Operation: 60-9=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 60*9=540, Resulting Numbers: [540] 540,94 unequal: No Solution Exploring Operation: 60+9=69, Resulting Numbers: [69] 69,94 unequal: No Solution Moving to Node #0,3,1 Current State: 94:[102, 33], Operations: ['42+60=102', '90-57=33'] Exploring Operation: 102*33=3366, Resulting Numbers: [3366] 3366,94 unequal: No Solution Exploring Operation: 102-33=69, Resulting Numbers: [69] 69,94 unequal: No Solution Exploring Operation: 102+33=135, Resulting Numbers: [135] 135,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[99, 30], Operations: ['42+57=99', '90-60=30'] Exploring Operation: 99*30=2970, Resulting Numbers: [2970] 2970,94 unequal: No Solution Exploring Operation: 99+30=129, Resulting Numbers: [129] 129,94 unequal: No Solution Exploring Operation: 99-30=69, Resulting Numbers: [69] 69,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[90, 75], Operations: ['60-42=18', '57+18=75'] Exploring Operation: 90*75=6750, Resulting Numbers: [6750] 6750,94 unequal: No Solution Exploring Operation: 90+75=165, Resulting Numbers: [165] 165,94 unequal: No Solution Exploring Operation: 90-75=15, Resulting Numbers: [15] 15,94 unequal: No Solution Moving to Node #0,0,3 Current State: 94:[57, 108], Operations: ['60-42=18', '90+18=108'] Exploring Operation: 57*108=6156, Resulting Numbers: [6156] 6156,94 unequal: No Solution Exploring Operation: 57+108=165, Resulting Numbers: [165] 165,94 unequal: No Solution Exploring Operation: 108-57=51, Resulting Numbers: [51] 51,94 unequal: No Solution Moving to Node #0,0,4 Current State: 94:[18, 33], Operations: ['60-42=18', '90-57=33'] Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,94 unequal: No Solution Exploring Operation: 18*33=594, Resulting Numbers: [594] 594,94 unequal: No Solution Moving to Node #0,3,3 Current State: 94:[102, 147], Operations: ['42+60=102', '90+57=147'] Exploring Operation: 102*147=14994, Resulting Numbers: [14994] 14994,94 unequal: No Solution Exploring Operation: 147-102=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 102+147=249, Resulting Numbers: [249] 249,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[99, 150], Operations: ['42+57=99', '90+60=150'] Exploring Operation: 99*150=14850, Resulting Numbers: [14850] 14850,94 unequal: No Solution Exploring Operation: 150-99=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 99+150=249, Resulting Numbers: [249] 249,94 unequal: No Solution Moving to Node #0,3,4 Current State: 94:[90, 159], Operations: ['42+60=102', '57+102=159'] Exploring Operation: 90*159=14310, Resulting Numbers: [14310] 14310,94 unequal: No Solution Exploring Operation: 159-90=69, Resulting Numbers: [69] 69,94 unequal: No Solution Exploring Operation: 90+159=249, Resulting Numbers: [249] 249,94 unequal: No Solution Moving to Node #0,1,3 Current State: 94:[90, 159], Operations: ['42+57=99', '60+99=159'] Exploring Operation: 90+159=249, Resulting Numbers: [249] 249,94 unequal: No Solution Exploring Operation: 159-90=69, Resulting Numbers: [69] 69,94 unequal: No Solution Exploring Operation: 90*159=14310, Resulting Numbers: [14310] 14310,94 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 20, 5, 8, 48 ]
68
[ "48-20=28", "5*8=40", "28+40=68" ]
Current State: 68:[20, 5, 8, 48], Operations: [] Exploring Operation: 48-20=28, Resulting Numbers: [5, 8, 28] Generated Node #2: [5, 8, 28] from Operation: 48-20=28 Current State: 68:[5, 8, 28], Operations: ['48-20=28'] Exploring Operation: 5*8=40, Resulting Numbers: [28, 40] Generated Node #3: [28, 40] from Operation: 5*8=40 Current State: 68:[28, 40], Operations: ['48-20=28', '5*8=40'] Exploring Operation: 28+40=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[20, 5, 8, 48], Operations: [] Exploring Operation: 20+48=68, Resulting Numbers: [5, 8, 68] Generated Node #0,0: 68:[5, 8, 68] Operation: 20+48=68 Exploring Operation: 48/8=6, Resulting Numbers: [20, 5, 6] Generated Node #0,1: 68:[20, 5, 6] Operation: 48/8=6 Exploring Operation: 48-8=40, Resulting Numbers: [20, 5, 40] Generated Node #0,2: 68:[20, 5, 40] Operation: 48-8=40 Moving to Node #0,0 Current State: 68:[5, 8, 68], Operations: ['20+48=68'] Exploring Operation: 8-5=3, Resulting Numbers: [68, 3] Generated Node #0,0,0: 68:[68, 3] Operation: 8-5=3 Exploring Operation: 5+8=13, Resulting Numbers: [68, 13] Generated Node #0,0,1: 68:[68, 13] Operation: 5+8=13 Exploring Operation: 5*8=40, Resulting Numbers: [68, 40] Generated Node #0,0,2: 68:[68, 40] Operation: 5*8=40 Moving to Node #0,1 Current State: 68:[20, 5, 6], Operations: ['48/8=6'] Exploring Operation: 20-6=14, Resulting Numbers: [5, 14] Generated Node #0,1,0: 68:[5, 14] Operation: 20-6=14 Exploring Operation: 20/5=4, Resulting Numbers: [6, 4] Generated Node #0,1,1: 68:[6, 4] Operation: 20/5=4 Exploring Operation: 20-5=15, Resulting Numbers: [6, 15] Generated Node #0,1,2: 68:[6, 15] Operation: 20-5=15 Moving to Node #0,2 Current State: 68:[20, 5, 40], Operations: ['48-8=40'] Exploring Operation: 40-20=20, Resulting Numbers: [5, 20] Generated Node #0,2,0: 68:[5, 20] Operation: 40-20=20 Exploring Operation: 40/20=2, Resulting Numbers: [5, 2] Generated Node #0,2,1: 68:[5, 2] Operation: 40/20=2 Exploring Operation: 40-5=35, Resulting Numbers: [20, 35] Generated Node #0,2,2: 68:[20, 35] Operation: 40-5=35 Moving to Node #0,0,0 Current State: 68:[68, 3], Operations: ['20+48=68', '8-5=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,68 unequal: No Solution Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,68 unequal: No Solution Exploring Operation: 68*3=204, Resulting Numbers: [204] 204,68 unequal: No Solution Moving to Node #0,2,1 Current State: 68:[5, 2], Operations: ['48-8=40', '40/20=2'] Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,68 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,68 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[6, 4], Operations: ['48/8=6', '20/5=4'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,68 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[6, 15], Operations: ['48/8=6', '20-5=15'] Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,68 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,68 unequal: No Solution Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,68 unequal: No Solution Moving to Node #0,2,2 Current State: 68:[20, 35], Operations: ['48-8=40', '40-5=35'] Exploring Operation: 20+35=55, Resulting Numbers: [55] 55,68 unequal: No Solution Exploring Operation: 20*35=700, Resulting Numbers: [700] 700,68 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[5, 14], Operations: ['48/8=6', '20-6=14'] Exploring Operation: 5*14=70, Resulting Numbers: [70] 70,68 unequal: No Solution Exploring Operation: 5+14=19, Resulting Numbers: [19] 19,68 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[68, 13], Operations: ['20+48=68', '5+8=13'] Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,68 unequal: No Solution Exploring Operation: 68+13=81, Resulting Numbers: [81] 81,68 unequal: No Solution Exploring Operation: 68*13=884, Resulting Numbers: [884] 884,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[5, 20], Operations: ['48-8=40', '40-20=20'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,68 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,68 unequal: No Solution Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[68, 40], Operations: ['20+48=68', '5*8=40'] Exploring Operation: 68-40=28, Resulting Numbers: [28] 28,68 unequal: No Solution Exploring Operation: 68*40=2720, Resulting Numbers: [2720] 2720,68 unequal: No Solution Exploring Operation: 68+40=108, Resulting Numbers: [108] 108,68 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 8, 2, 35, 71 ]
96
[ "8+2=10", "35+71=106", "106-10=96" ]
Current State: 96:[8, 2, 35, 71], Operations: [] Exploring Operation: 8+2=10, Resulting Numbers: [35, 71, 10] Generated Node #2: [35, 71, 10] from Operation: 8+2=10 Current State: 96:[35, 71, 10], Operations: ['8+2=10'] Exploring Operation: 35+71=106, Resulting Numbers: [10, 106] Generated Node #3: [10, 106] from Operation: 35+71=106 Current State: 96:[10, 106], Operations: ['8+2=10', '35+71=106'] Exploring Operation: 106-10=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[8, 2, 35, 71], Operations: [] Exploring Operation: 35+71=106, Resulting Numbers: [8, 2, 106] Generated Node #0,0: 96:[8, 2, 106] Operation: 35+71=106 Exploring Operation: 71-35=36, Resulting Numbers: [8, 2, 36] Generated Node #0,1: 96:[8, 2, 36] Operation: 71-35=36 Exploring Operation: 71-8=63, Resulting Numbers: [2, 35, 63] Generated Node #0,2: 96:[2, 35, 63] Operation: 71-8=63 Exploring Operation: 8+71=79, Resulting Numbers: [2, 35, 79] Generated Node #0,3: 96:[2, 35, 79] Operation: 8+71=79 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[8, 2, 36], Operations: ['71-35=36'] Exploring Operation: 8*2=16, Resulting Numbers: [36, 16] Generated Node #0,1,0: 96:[36, 16] Operation: 8*2=16 Exploring Operation: 36/2=18, Resulting Numbers: [8, 18] Generated Node #0,1,1: 96:[8, 18] Operation: 36/2=18 Exploring Operation: 36-2=34, Resulting Numbers: [8, 34] Generated Node #0,1,2: 96:[8, 34] Operation: 36-2=34 Exploring Operation: 8-2=6, Resulting Numbers: [36, 6] Generated Node #0,1,3: 96:[36, 6] Operation: 8-2=6 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[8, 18], Operations: ['71-35=36', '36/2=18'] Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,96 unequal: No Solution Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 96:[8, 34], Operations: ['71-35=36', '36-2=34'] Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,96 unequal: No Solution Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 8*34=272, Resulting Numbers: [272] 272,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[36, 16], Operations: ['71-35=36', '8*2=16'] Exploring Operation: 36*16=576, Resulting Numbers: [576] 576,96 unequal: No Solution Exploring Operation: 36-16=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 36+16=52, Resulting Numbers: [52] 52,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 96:[36, 6], Operations: ['71-35=36', '8-2=6'] Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,96 unequal: No Solution Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,96 unequal: No Solution Exploring Operation: 36*6=216, Resulting Numbers: [216] 216,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[8, 2, 106], Operations: ['35+71=106'] Exploring Operation: 8*2=16, Resulting Numbers: [106, 16] Generated Node #0,0,0: 96:[106, 16] Operation: 8*2=16 Exploring Operation: 106-2=104, Resulting Numbers: [8, 104] Generated Node #0,0,1: 96:[8, 104] Operation: 106-2=104 Exploring Operation: 106-8=98, Resulting Numbers: [2, 98] Generated Node #0,0,2: 96:[2, 98] Operation: 106-8=98 Exploring Operation: 106/2=53, Resulting Numbers: [8, 53] Generated Node #0,0,3: 96:[8, 53] Operation: 106/2=53 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 96:[2, 98], Operations: ['35+71=106', '106-8=98'] Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,96 unequal: No Solution Exploring Operation: 2*98=196, Resulting Numbers: [196] 196,96 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[8, 2, 35, 71], Operations: [] Exploring Operation: 35+71=106, Resulting Numbers: [8, 2, 106] Generated Node #0,0: 96:[8, 2, 106] Operation: 35+71=106 Moving to Node #0,0 Current State: 96:[8, 2, 106], Operations: ['35+71=106'] Exploring Operation: 106-8=98, Resulting Numbers: [2, 98] Generated Node #0,0,2: 96:[2, 98] Operation: 106-8=98 Moving to Node #0,0,2 Current State: 96:[2, 98], Operations: ['35+71=106', '106-8=98'] Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 55, 38, 57, 62 ]
98
[ "55+38=93", "62-57=5", "93+5=98" ]
Current State: 98:[55, 38, 57, 62], Operations: [] Exploring Operation: 55+38=93, Resulting Numbers: [57, 62, 93] Generated Node #2: [57, 62, 93] from Operation: 55+38=93 Current State: 98:[57, 62, 93], Operations: ['55+38=93'] Exploring Operation: 62-57=5, Resulting Numbers: [93, 5] Generated Node #3: [93, 5] from Operation: 62-57=5 Current State: 98:[93, 5], Operations: ['55+38=93', '62-57=5'] Exploring Operation: 93+5=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[55, 38, 57, 62], Operations: [] Exploring Operation: 62-57=5, Resulting Numbers: [55, 38, 5] Generated Node #0,0: 98:[55, 38, 5] Operation: 62-57=5 Exploring Operation: 38+57=95, Resulting Numbers: [55, 62, 95] Generated Node #0,1: 98:[55, 62, 95] Operation: 38+57=95 Exploring Operation: 55-38=17, Resulting Numbers: [57, 62, 17] Generated Node #0,2: 98:[57, 62, 17] Operation: 55-38=17 Exploring Operation: 38+62=100, Resulting Numbers: [55, 57, 100] Generated Node #0,3: 98:[55, 57, 100] Operation: 38+62=100 Exploring Operation: 62-55=7, Resulting Numbers: [38, 57, 7] Generated Node #0,4: 98:[38, 57, 7] Operation: 62-55=7 Start Sub Search at level 1: Moving to Node #0,3 Current State: 98:[55, 57, 100], Operations: ['38+62=100'] Exploring Operation: 100-57=43, Resulting Numbers: [55, 43] Generated Node #0,3,0: 98:[55, 43] Operation: 100-57=43 Exploring Operation: 57-55=2, Resulting Numbers: [100, 2] Generated Node #0,3,1: 98:[100, 2] Operation: 57-55=2 Exploring Operation: 55+57=112, Resulting Numbers: [100, 112] Generated Node #0,3,2: 98:[100, 112] Operation: 55+57=112 Exploring Operation: 55+100=155, Resulting Numbers: [57, 155] Generated Node #0,3,3: 98:[57, 155] Operation: 55+100=155 Exploring Operation: 100-55=45, Resulting Numbers: [57, 45] Generated Node #0,3,4: 98:[57, 45] Operation: 100-55=45 Moving to Node #0,3,1 Current State: 98:[100, 2], Operations: ['38+62=100', '57-55=2'] Exploring Operation: 100*2=200, Resulting Numbers: [200] 200,98 unequal: No Solution Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[55, 38, 57, 62], Operations: [] Exploring Operation: 38+62=100, Resulting Numbers: [55, 57, 100] Generated Node #0,3: 98:[55, 57, 100] Operation: 38+62=100 Moving to Node #0,3 Current State: 98:[55, 57, 100], Operations: ['38+62=100'] Exploring Operation: 57-55=2, Resulting Numbers: [100, 2] Generated Node #0,3,1: 98:[100, 2] Operation: 57-55=2 Moving to Node #0,3,1 Current State: 98:[100, 2], Operations: ['38+62=100', '57-55=2'] Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 21, 82, 83, 32 ]
54
[ "82-21=61", "83+32=115", "115-61=54" ]
Current State: 54:[21, 82, 83, 32], Operations: [] Exploring Operation: 82-21=61, Resulting Numbers: [83, 32, 61] Generated Node #2: [83, 32, 61] from Operation: 82-21=61 Current State: 54:[83, 32, 61], Operations: ['82-21=61'] Exploring Operation: 83+32=115, Resulting Numbers: [61, 115] Generated Node #3: [61, 115] from Operation: 83+32=115 Current State: 54:[61, 115], Operations: ['82-21=61', '83+32=115'] Exploring Operation: 115-61=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[21, 82, 83, 32], Operations: [] Exploring Operation: 83-32=51, Resulting Numbers: [21, 82, 51] Generated Node #0,0: 54:[21, 82, 51] Operation: 83-32=51 Exploring Operation: 83-82=1, Resulting Numbers: [21, 32, 1] Generated Node #0,1: 54:[21, 32, 1] Operation: 83-82=1 Moving to Node #0,1 Current State: 54:[21, 32, 1], Operations: ['83-82=1'] Exploring Operation: 32-21=11, Resulting Numbers: [1, 11] Generated Node #0,1,0: 54:[1, 11] Operation: 32-21=11 Exploring Operation: 21+32=53, Resulting Numbers: [1, 53] Generated Node #0,1,1: 54:[1, 53] Operation: 21+32=53 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 54:[1, 53], Operations: ['83-82=1', '21+32=53'] Exploring Operation: 1+53=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[21, 82, 83, 32], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [21, 32, 1] Generated Node #0,1: 54:[21, 32, 1] Operation: 83-82=1 Moving to Node #0,1 Current State: 54:[21, 32, 1], Operations: ['83-82=1'] Exploring Operation: 21+32=53, Resulting Numbers: [1, 53] Generated Node #0,1,1: 54:[1, 53] Operation: 21+32=53 Moving to Node #0,1,1 Current State: 54:[1, 53], Operations: ['83-82=1', '21+32=53'] Exploring Operation: 1+53=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 79, 56, 20, 24 ]
67
[ "79-56=23", "20+24=44", "23+44=67" ]
Current State: 67:[79, 56, 20, 24], Operations: [] Exploring Operation: 79-56=23, Resulting Numbers: [20, 24, 23] Generated Node #2: [20, 24, 23] from Operation: 79-56=23 Current State: 67:[20, 24, 23], Operations: ['79-56=23'] Exploring Operation: 20+24=44, Resulting Numbers: [23, 44] Generated Node #3: [23, 44] from Operation: 20+24=44 Current State: 67:[23, 44], Operations: ['79-56=23', '20+24=44'] Exploring Operation: 23+44=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[79, 56, 20, 24], Operations: [] Exploring Operation: 20+24=44, Resulting Numbers: [79, 56, 44] Generated Node #0,0: 67:[79, 56, 44] Operation: 20+24=44 Exploring Operation: 79-24=55, Resulting Numbers: [56, 20, 55] Generated Node #0,1: 67:[56, 20, 55] Operation: 79-24=55 Exploring Operation: 79-20=59, Resulting Numbers: [56, 24, 59] Generated Node #0,2: 67:[56, 24, 59] Operation: 79-20=59 Exploring Operation: 56+24=80, Resulting Numbers: [79, 20, 80] Generated Node #0,3: 67:[79, 20, 80] Operation: 56+24=80 Exploring Operation: 56+20=76, Resulting Numbers: [79, 24, 76] Generated Node #0,4: 67:[79, 24, 76] Operation: 56+20=76 Moving to Node #0,0 Current State: 67:[79, 56, 44], Operations: ['20+24=44'] Exploring Operation: 56-44=12, Resulting Numbers: [79, 12] Generated Node #0,0,0: 67:[79, 12] Operation: 56-44=12 Exploring Operation: 56+44=100, Resulting Numbers: [79, 100] Generated Node #0,0,1: 67:[79, 100] Operation: 56+44=100 Exploring Operation: 79-44=35, Resulting Numbers: [56, 35] Generated Node #0,0,2: 67:[56, 35] Operation: 79-44=35 Exploring Operation: 79+44=123, Resulting Numbers: [56, 123] Generated Node #0,0,3: 67:[56, 123] Operation: 79+44=123 Exploring Operation: 79-56=23, Resulting Numbers: [44, 23] Generated Node #0,0,4: 67:[44, 23] Operation: 79-56=23 Moving to Node #0,2 Current State: 67:[56, 24, 59], Operations: ['79-20=59'] Exploring Operation: 56-24=32, Resulting Numbers: [59, 32] Generated Node #0,2,0: 67:[59, 32] Operation: 56-24=32 Exploring Operation: 56+24=80, Resulting Numbers: [59, 80] Generated Node #0,2,1: 67:[59, 80] Operation: 56+24=80 Exploring Operation: 24+59=83, Resulting Numbers: [56, 83] Generated Node #0,2,2: 67:[56, 83] Operation: 24+59=83 Exploring Operation: 59-24=35, Resulting Numbers: [56, 35] Generated Node #0,2,3: 67:[56, 35] Operation: 59-24=35 Exploring Operation: 56+59=115, Resulting Numbers: [24, 115] Generated Node #0,2,4: 67:[24, 115] Operation: 56+59=115 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[59, 80], Operations: ['79-20=59', '56+24=80'] Exploring Operation: 59*80=4720, Resulting Numbers: [4720] 4720,67 unequal: No Solution Exploring Operation: 80-59=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 59+80=139, Resulting Numbers: [139] 139,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 67:[56, 83], Operations: ['79-20=59', '24+59=83'] Exploring Operation: 56*83=4648, Resulting Numbers: [4648] 4648,67 unequal: No Solution Exploring Operation: 56+83=139, Resulting Numbers: [139] 139,67 unequal: No Solution Exploring Operation: 83-56=27, Resulting Numbers: [27] 27,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[59, 32], Operations: ['79-20=59', '56-24=32'] Exploring Operation: 59*32=1888, Resulting Numbers: [1888] 1888,67 unequal: No Solution Exploring Operation: 59+32=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 59-32=27, Resulting Numbers: [27] 27,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 67:[56, 35], Operations: ['79-20=59', '59-24=35'] Exploring Operation: 56-35=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 56*35=1960, Resulting Numbers: [1960] 1960,67 unequal: No Solution Exploring Operation: 56+35=91, Resulting Numbers: [91] 91,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 67:[24, 115], Operations: ['79-20=59', '56+59=115'] Exploring Operation: 24*115=2760, Resulting Numbers: [2760] 2760,67 unequal: No Solution Exploring Operation: 115-24=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 24+115=139, Resulting Numbers: [139] 139,67 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: 67:[79, 24, 76], Operations: ['56+20=76'] Exploring Operation: 76-24=52, Resulting Numbers: [79, 52] Generated Node #0,4,0: 67:[79, 52] Operation: 76-24=52 Exploring Operation: 24+76=100, Resulting Numbers: [79, 100] Generated Node #0,4,1: 67:[79, 100] Operation: 24+76=100 Exploring Operation: 79+24=103, Resulting Numbers: [76, 103] Generated Node #0,4,2: 67:[76, 103] Operation: 79+24=103 Exploring Operation: 79-24=55, Resulting Numbers: [76, 55] Generated Node #0,4,3: 67:[76, 55] Operation: 79-24=55 Exploring Operation: 79-76=3, Resulting Numbers: [24, 3] Generated Node #0,4,4: 67:[24, 3] Operation: 79-76=3 Moving to Node #0,1 Current State: 67:[56, 20, 55], Operations: ['79-24=55'] Exploring Operation: 56-20=36, Resulting Numbers: [55, 36] Generated Node #0,1,0: 67:[55, 36] Operation: 56-20=36 Exploring Operation: 20+55=75, Resulting Numbers: [56, 75] Generated Node #0,1,1: 67:[56, 75] Operation: 20+55=75 Exploring Operation: 55-20=35, Resulting Numbers: [56, 35] Generated Node #0,1,2: 67:[56, 35] Operation: 55-20=35 Exploring Operation: 56+20=76, Resulting Numbers: [55, 76] Generated Node #0,1,3: 67:[55, 76] Operation: 56+20=76 Exploring Operation: 56+55=111, Resulting Numbers: [20, 111] Generated Node #0,1,4: 67:[20, 111] Operation: 56+55=111 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 67:[56, 75], Operations: ['79-24=55', '20+55=75'] Exploring Operation: 75-56=19, Resulting Numbers: [19] 19,67 unequal: No Solution Exploring Operation: 56*75=4200, Resulting Numbers: [4200] 4200,67 unequal: No Solution Exploring Operation: 56+75=131, Resulting Numbers: [131] 131,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 67:[55, 76], Operations: ['79-24=55', '56+20=76'] Exploring Operation: 76-55=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 55*76=4180, Resulting Numbers: [4180] 4180,67 unequal: No Solution Exploring Operation: 55+76=131, Resulting Numbers: [131] 131,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[55, 36], Operations: ['79-24=55', '56-20=36'] Exploring Operation: 55+36=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 55*36=1980, Resulting Numbers: [1980] 1980,67 unequal: No Solution Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 67:[56, 35], Operations: ['79-24=55', '55-20=35'] Exploring Operation: 56-35=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 56+35=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 56*35=1960, Resulting Numbers: [1960] 1960,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 67:[20, 111], Operations: ['79-24=55', '56+55=111'] Exploring Operation: 20+111=131, Resulting Numbers: [131] 131,67 unequal: No Solution Exploring Operation: 111-20=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 20*111=2220, Resulting Numbers: [2220] 2220,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 67:[79, 20, 80], Operations: ['56+24=80'] Exploring Operation: 80-20=60, Resulting Numbers: [79, 60] Generated Node #0,3,0: 67:[79, 60] Operation: 80-20=60 Exploring Operation: 79-20=59, Resulting Numbers: [80, 59] Generated Node #0,3,1: 67:[80, 59] Operation: 79-20=59 Exploring Operation: 20+80=100, Resulting Numbers: [79, 100] Generated Node #0,3,2: 67:[79, 100] Operation: 20+80=100 Exploring Operation: 79+20=99, Resulting Numbers: [80, 99] Generated Node #0,3,3: 67:[80, 99] Operation: 79+20=99 Exploring Operation: 80/20=4, Resulting Numbers: [79, 4] Generated Node #0,3,4: 67:[79, 4] Operation: 80/20=4 Moving to Node #0,3,0 Current State: 67:[79, 60], Operations: ['56+24=80', '80-20=60'] Exploring Operation: 79*60=4740, Resulting Numbers: [4740] 4740,67 unequal: No Solution Exploring Operation: 79+60=139, Resulting Numbers: [139] 139,67 unequal: No Solution Exploring Operation: 79-60=19, Resulting Numbers: [19] 19,67 unequal: No Solution Moving to Node #0,3,1 Current State: 67:[80, 59], Operations: ['56+24=80', '79-20=59'] Exploring Operation: 80*59=4720, Resulting Numbers: [4720] 4720,67 unequal: No Solution Exploring Operation: 80+59=139, Resulting Numbers: [139] 139,67 unequal: No Solution Exploring Operation: 80-59=21, Resulting Numbers: [21] 21,67 unequal: No Solution Moving to Node #0,4,3 Current State: 67:[76, 55], Operations: ['56+20=76', '79-24=55'] Exploring Operation: 76+55=131, Resulting Numbers: [131] 131,67 unequal: No Solution Exploring Operation: 76-55=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 76*55=4180, Resulting Numbers: [4180] 4180,67 unequal: No Solution Moving to Node #0,4,0 Current State: 67:[79, 52], Operations: ['56+20=76', '76-24=52'] Exploring Operation: 79+52=131, Resulting Numbers: [131] 131,67 unequal: No Solution Exploring Operation: 79*52=4108, Resulting Numbers: [4108] 4108,67 unequal: No Solution Exploring Operation: 79-52=27, Resulting Numbers: [27] 27,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[56, 35], Operations: ['20+24=44', '79-44=35'] Exploring Operation: 56+35=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 56-35=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 56*35=1960, Resulting Numbers: [1960] 1960,67 unequal: No Solution Moving to Node #0,3,2 Current State: 67:[79, 100], Operations: ['56+24=80', '20+80=100'] Exploring Operation: 79+100=179, Resulting Numbers: [179] 179,67 unequal: No Solution Exploring Operation: 100-79=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 79*100=7900, Resulting Numbers: [7900] 7900,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[79, 100], Operations: ['20+24=44', '56+44=100'] Exploring Operation: 79+100=179, Resulting Numbers: [179] 179,67 unequal: No Solution Exploring Operation: 100-79=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 79*100=7900, Resulting Numbers: [7900] 7900,67 unequal: No Solution Moving to Node #0,3,3 Current State: 67:[80, 99], Operations: ['56+24=80', '79+20=99'] Exploring Operation: 80+99=179, Resulting Numbers: [179] 179,67 unequal: No Solution Exploring Operation: 80*99=7920, Resulting Numbers: [7920] 7920,67 unequal: No Solution Exploring Operation: 99-80=19, Resulting Numbers: [19] 19,67 unequal: No Solution Moving to Node #0,4,1 Current State: 67:[79, 100], Operations: ['56+20=76', '24+76=100'] Exploring Operation: 79*100=7900, Resulting Numbers: [7900] 7900,67 unequal: No Solution Exploring Operation: 79+100=179, Resulting Numbers: [179] 179,67 unequal: No Solution Exploring Operation: 100-79=21, Resulting Numbers: [21] 21,67 unequal: No Solution Moving to Node #0,4,2 Current State: 67:[76, 103], Operations: ['56+20=76', '79+24=103'] Exploring Operation: 103-76=27, Resulting Numbers: [27] 27,67 unequal: No Solution Exploring Operation: 76+103=179, Resulting Numbers: [179] 179,67 unequal: No Solution Exploring Operation: 76*103=7828, Resulting Numbers: [7828] 7828,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[79, 12], Operations: ['20+24=44', '56-44=12'] Exploring Operation: 79*12=948, Resulting Numbers: [948] 948,67 unequal: No Solution Exploring Operation: 79+12=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 79-12=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[79, 56, 20, 24], Operations: [] Exploring Operation: 20+24=44, Resulting Numbers: [79, 56, 44] Generated Node #0,0: 67:[79, 56, 44] Operation: 20+24=44 Moving to Node #0,0 Current State: 67:[79, 56, 44], Operations: ['20+24=44'] Exploring Operation: 56-44=12, Resulting Numbers: [79, 12] Generated Node #0,0,0: 67:[79, 12] Operation: 56-44=12 Moving to Node #0,0,0 Current State: 67:[79, 12], Operations: ['20+24=44', '56-44=12'] Exploring Operation: 79-12=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
0.915799
hs_5
sum_heuristic
[ 72, 41, 40, 83 ]
74
[ "72-41=31", "83-40=43", "31+43=74" ]
Current State: 74:[72, 41, 40, 83], Operations: [] Exploring Operation: 72-41=31, Resulting Numbers: [40, 83, 31] Generated Node #2: [40, 83, 31] from Operation: 72-41=31 Current State: 74:[40, 83, 31], Operations: ['72-41=31'] Exploring Operation: 83-40=43, Resulting Numbers: [31, 43] Generated Node #3: [31, 43] from Operation: 83-40=43 Current State: 74:[31, 43], Operations: ['72-41=31', '83-40=43'] Exploring Operation: 31+43=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[72, 41, 40, 83], Operations: [] Exploring Operation: 41-40=1, Resulting Numbers: [72, 83, 1] Generated Node #0,0: 74:[72, 83, 1] Operation: 41-40=1 Exploring Operation: 83-41=42, Resulting Numbers: [72, 40, 42] Generated Node #0,1: 74:[72, 40, 42] Operation: 83-41=42 Exploring Operation: 83-40=43, Resulting Numbers: [72, 41, 43] Generated Node #0,2: 74:[72, 41, 43] Operation: 83-40=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[72, 40, 42], Operations: ['83-41=42'] Exploring Operation: 72-40=32, Resulting Numbers: [42, 32] Generated Node #0,1,0: 74:[42, 32] Operation: 72-40=32 Exploring Operation: 72-42=30, Resulting Numbers: [40, 30] Generated Node #0,1,1: 74:[40, 30] Operation: 72-42=30 Exploring Operation: 42-40=2, Resulting Numbers: [72, 2] Generated Node #0,1,2: 74:[72, 2] Operation: 42-40=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 74:[72, 2], Operations: ['83-41=42', '42-40=2'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,74 unequal: No Solution Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,74 unequal: No Solution Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[72, 41, 40, 83], Operations: [] Exploring Operation: 83-41=42, Resulting Numbers: [72, 40, 42] Generated Node #0,1: 74:[72, 40, 42] Operation: 83-41=42 Moving to Node #0,1 Current State: 74:[72, 40, 42], Operations: ['83-41=42'] Exploring Operation: 42-40=2, Resulting Numbers: [72, 2] Generated Node #0,1,2: 74:[72, 2] Operation: 42-40=2 Moving to Node #0,1,2 Current State: 74:[72, 2], Operations: ['83-41=42', '42-40=2'] Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 1, 96, 74, 34 ]
55
[ "96-1=95", "74-34=40", "95-40=55" ]
Current State: 55:[1, 96, 74, 34], Operations: [] Exploring Operation: 96-1=95, Resulting Numbers: [74, 34, 95] Generated Node #2: [74, 34, 95] from Operation: 96-1=95 Current State: 55:[74, 34, 95], Operations: ['96-1=95'] Exploring Operation: 74-34=40, Resulting Numbers: [95, 40] Generated Node #3: [95, 40] from Operation: 74-34=40 Current State: 55:[95, 40], Operations: ['96-1=95', '74-34=40'] Exploring Operation: 95-40=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[1, 96, 74, 34], Operations: [] Exploring Operation: 96-34=62, Resulting Numbers: [1, 74, 62] Generated Node #0,0: 55:[1, 74, 62] Operation: 96-34=62 Exploring Operation: 96-1=95, Resulting Numbers: [74, 34, 95] Generated Node #0,1: 55:[74, 34, 95] Operation: 96-1=95 Exploring Operation: 96-74=22, Resulting Numbers: [1, 34, 22] Generated Node #0,2: 55:[1, 34, 22] Operation: 96-74=22 Exploring Operation: 74-34=40, Resulting Numbers: [1, 96, 40] Generated Node #0,3: 55:[1, 96, 40] Operation: 74-34=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[1, 74, 62], Operations: ['96-34=62'] Exploring Operation: 74-62=12, Resulting Numbers: [1, 12] Generated Node #0,0,0: 55:[1, 12] Operation: 74-62=12 Exploring Operation: 62-1=61, Resulting Numbers: [74, 61] Generated Node #0,0,1: 55:[74, 61] Operation: 62-1=61 Exploring Operation: 1*74=74, Resulting Numbers: [62, 74] Generated Node #0,0,2: 55:[62, 74] Operation: 1*74=74 Exploring Operation: 74-1=73, Resulting Numbers: [62, 73] Generated Node #0,0,3: 55:[62, 73] Operation: 74-1=73 Moving to Node #0,0,0 Current State: 55:[1, 12], Operations: ['96-34=62', '74-62=12'] Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,55 unequal: No Solution Exploring Operation: 1+12=13, Resulting Numbers: [13] 13,55 unequal: No Solution Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,55 unequal: No Solution Moving to Node #0,0,3 Current State: 55:[62, 73], Operations: ['96-34=62', '74-1=73'] Exploring Operation: 73-62=11, Resulting Numbers: [11] 11,55 unequal: No Solution Exploring Operation: 62*73=4526, Resulting Numbers: [4526] 4526,55 unequal: No Solution Exploring Operation: 62+73=135, Resulting Numbers: [135] 135,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[74, 61], Operations: ['96-34=62', '62-1=61'] Exploring Operation: 74*61=4514, Resulting Numbers: [4514] 4514,55 unequal: No Solution Exploring Operation: 74+61=135, Resulting Numbers: [135] 135,55 unequal: No Solution Exploring Operation: 74-61=13, Resulting Numbers: [13] 13,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[62, 74], Operations: ['96-34=62', '1*74=74'] Exploring Operation: 74-62=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 62+74=136, Resulting Numbers: [136] 136,55 unequal: No Solution Exploring Operation: 62*74=4588, Resulting Numbers: [4588] 4588,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[1, 34, 22], Operations: ['96-74=22'] Exploring Operation: 34+22=56, Resulting Numbers: [1, 56] Generated Node #0,2,0: 55:[1, 56] Operation: 34+22=56 Exploring Operation: 1+34=35, Resulting Numbers: [22, 35] Generated Node #0,2,1: 55:[22, 35] Operation: 1+34=35 Exploring Operation: 34-22=12, Resulting Numbers: [1, 12] Generated Node #0,2,2: 55:[1, 12] Operation: 34-22=12 Exploring Operation: 22-1=21, Resulting Numbers: [34, 21] Generated Node #0,2,3: 55:[34, 21] Operation: 22-1=21 Moving to Node #0,2,0 Current State: 55:[1, 56], Operations: ['96-74=22', '34+22=56'] Exploring Operation: 1+56=57, Resulting Numbers: [57] 57,55 unequal: No Solution Exploring Operation: 1*56=56, Resulting Numbers: [56] 56,55 unequal: No Solution Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,55 unequal: No Solution Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[1, 96, 74, 34], Operations: [] Exploring Operation: 96-74=22, Resulting Numbers: [1, 34, 22] Generated Node #0,2: 55:[1, 34, 22] Operation: 96-74=22 Moving to Node #0,2 Current State: 55:[1, 34, 22], Operations: ['96-74=22'] Exploring Operation: 34+22=56, Resulting Numbers: [1, 56] Generated Node #0,2,0: 55:[1, 56] Operation: 34+22=56 Moving to Node #0,2,0 Current State: 55:[1, 56], Operations: ['96-74=22', '34+22=56'] Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
mult_heuristic
[ 59, 5, 73, 33 ]
42
[ "59+5=64", "73+33=106", "106-64=42" ]
Current State: 42:[59, 5, 73, 33], Operations: [] Exploring Operation: 59+5=64, Resulting Numbers: [73, 33, 64] Generated Node #2: [73, 33, 64] from Operation: 59+5=64 Current State: 42:[73, 33, 64], Operations: ['59+5=64'] Exploring Operation: 73+33=106, Resulting Numbers: [64, 106] Generated Node #3: [64, 106] from Operation: 73+33=106 Current State: 42:[64, 106], Operations: ['59+5=64', '73+33=106'] Exploring Operation: 106-64=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[59, 5, 73, 33], Operations: [] Exploring Operation: 59-33=26, Resulting Numbers: [5, 73, 26] Generated Node #0,0: 42:[5, 73, 26] Operation: 59-33=26 Exploring Operation: 73-33=40, Resulting Numbers: [59, 5, 40] Generated Node #0,1: 42:[59, 5, 40] Operation: 73-33=40 Exploring Operation: 73-59=14, Resulting Numbers: [5, 33, 14] Generated Node #0,2: 42:[5, 33, 14] Operation: 73-59=14 Moving to Node #0,2 Current State: 42:[5, 33, 14], Operations: ['73-59=14'] Exploring Operation: 33+14=47, Resulting Numbers: [5, 47] Generated Node #0,2,0: 42:[5, 47] Operation: 33+14=47 Exploring Operation: 33-14=19, Resulting Numbers: [5, 19] Generated Node #0,2,1: 42:[5, 19] Operation: 33-14=19 Exploring Operation: 5+33=38, Resulting Numbers: [14, 38] Generated Node #0,2,2: 42:[14, 38] Operation: 5+33=38 Moving to Node #0,1 Current State: 42:[59, 5, 40], Operations: ['73-33=40'] Exploring Operation: 59-40=19, Resulting Numbers: [5, 19] Generated Node #0,1,0: 42:[5, 19] Operation: 59-40=19 Exploring Operation: 40/5=8, Resulting Numbers: [59, 8] Generated Node #0,1,1: 42:[59, 8] Operation: 40/5=8 Exploring Operation: 59-5=54, Resulting Numbers: [40, 54] Generated Node #0,1,2: 42:[40, 54] Operation: 59-5=54 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 42:[5, 19], Operations: ['73-33=40', '59-40=19'] Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,42 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 42:[40, 54], Operations: ['73-33=40', '59-5=54'] Exploring Operation: 40+54=94, Resulting Numbers: [94] 94,42 unequal: No Solution Exploring Operation: 40*54=2160, Resulting Numbers: [2160] 2160,42 unequal: No Solution Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 42:[59, 8], Operations: ['73-33=40', '40/5=8'] Exploring Operation: 59+8=67, Resulting Numbers: [67] 67,42 unequal: No Solution Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,42 unequal: No Solution Exploring Operation: 59*8=472, Resulting Numbers: [472] 472,42 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: 42:[5, 73, 26], Operations: ['59-33=26'] Exploring Operation: 73-26=47, Resulting Numbers: [5, 47] Generated Node #0,0,0: 42:[5, 47] Operation: 73-26=47 Exploring Operation: 73-5=68, Resulting Numbers: [26, 68] Generated Node #0,0,1: 42:[26, 68] Operation: 73-5=68 Exploring Operation: 26-5=21, Resulting Numbers: [73, 21] Generated Node #0,0,2: 42:[73, 21] Operation: 26-5=21 Moving to Node #0,2,1 Current State: 42:[5, 19], Operations: ['73-59=14', '33-14=19'] Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,42 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,42 unequal: No Solution Moving to Node #0,2,2 Current State: 42:[14, 38], Operations: ['73-59=14', '5+33=38'] Exploring Operation: 14*38=532, Resulting Numbers: [532] 532,42 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 14+38=52, Resulting Numbers: [52] 52,42 unequal: No Solution Moving to Node #0,2,0 Current State: 42:[5, 47], Operations: ['73-59=14', '33+14=47'] Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,42 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[59, 5, 73, 33], Operations: [] Exploring Operation: 73-59=14, Resulting Numbers: [5, 33, 14] Generated Node #0,2: 42:[5, 33, 14] Operation: 73-59=14 Moving to Node #0,2 Current State: 42:[5, 33, 14], Operations: ['73-59=14'] Exploring Operation: 33+14=47, Resulting Numbers: [5, 47] Generated Node #0,2,0: 42:[5, 47] Operation: 33+14=47 Moving to Node #0,2,0 Current State: 42:[5, 47], Operations: ['73-59=14', '33+14=47'] Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
0.971354
hs_3
sum_heuristic
[ 54, 4, 20, 24 ]
66
[ "20/4=5", "24*5=120", "120-54=66" ]
Current State: 66:[54, 4, 20, 24], Operations: [] Exploring Operation: 20/4=5, Resulting Numbers: [54, 24, 5] Generated Node #2: [54, 24, 5] from Operation: 20/4=5 Current State: 66:[54, 24, 5], Operations: ['20/4=5'] Exploring Operation: 24*5=120, Resulting Numbers: [54, 120] Generated Node #3: [54, 120] from Operation: 24*5=120 Current State: 66:[54, 120], Operations: ['20/4=5', '24*5=120'] Exploring Operation: 120-54=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[54, 4, 20, 24], Operations: [] Exploring Operation: 54-20=34, Resulting Numbers: [4, 24, 34] Generated Node #0,0: 66:[4, 24, 34] Operation: 54-20=34 Exploring Operation: 54-24=30, Resulting Numbers: [4, 20, 30] Generated Node #0,1: 66:[4, 20, 30] Operation: 54-24=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[4, 24, 34], Operations: ['54-20=34'] Exploring Operation: 24/4=6, Resulting Numbers: [34, 6] Generated Node #0,0,0: 66:[34, 6] Operation: 24/4=6 Exploring Operation: 34-24=10, Resulting Numbers: [4, 10] Generated Node #0,0,1: 66:[4, 10] Operation: 34-24=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 66:[34, 6], Operations: ['54-20=34', '24/4=6'] Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,66 unequal: No Solution Exploring Operation: 34+6=40, Resulting Numbers: [40] 40,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 66:[4, 10], Operations: ['54-20=34', '34-24=10'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,66 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,66 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:[4, 20, 30], Operations: ['54-24=30'] Exploring Operation: 4+30=34, Resulting Numbers: [20, 34] Generated Node #0,1,0: 66:[20, 34] Operation: 4+30=34 Exploring Operation: 30-20=10, Resulting Numbers: [4, 10] Generated Node #0,1,1: 66:[4, 10] Operation: 30-20=10 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 66:[4, 10], Operations: ['54-24=30', '30-20=10'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,66 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,66 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 #0,1,0 Current State: 66:[20, 34], Operations: ['54-24=30', '4+30=34'] Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,66 unequal: No Solution Exploring Operation: 20+34=54, Resulting Numbers: [54] 54,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 6, 43, 24, 48 ]
90
[ "24-6=18", "48-43=5", "18*5=90" ]
Current State: 90:[6, 43, 24, 48], Operations: [] Exploring Operation: 24-6=18, Resulting Numbers: [43, 48, 18] Generated Node #2: [43, 48, 18] from Operation: 24-6=18 Current State: 90:[43, 48, 18], Operations: ['24-6=18'] Exploring Operation: 48-43=5, Resulting Numbers: [18, 5] Generated Node #3: [18, 5] from Operation: 48-43=5 Current State: 90:[18, 5], Operations: ['24-6=18', '48-43=5'] Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[6, 43, 24, 48], Operations: [] Exploring Operation: 48/24=2, Resulting Numbers: [6, 43, 2] Generated Node #0,0: 90:[6, 43, 2] Operation: 48/24=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[6, 43, 2], Operations: ['48/24=2'] Exploring Operation: 43+2=45, Resulting Numbers: [6, 45] Generated Node #0,0,0: 90:[6, 45] Operation: 43+2=45 Moving to Node #0,0,0 Current State: 90:[6, 45], Operations: ['48/24=2', '43+2=45'] Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,90 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
[ 85, 36, 13, 38 ]
24
[ "85-36=49", "38-13=25", "49-25=24" ]
Current State: 24:[85, 36, 13, 38], Operations: [] Exploring Operation: 85-36=49, Resulting Numbers: [13, 38, 49] Generated Node #2: [13, 38, 49] from Operation: 85-36=49 Current State: 24:[13, 38, 49], Operations: ['85-36=49'] Exploring Operation: 38-13=25, Resulting Numbers: [49, 25] Generated Node #3: [49, 25] from Operation: 38-13=25 Current State: 24:[49, 25], Operations: ['85-36=49', '38-13=25'] Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[85, 36, 13, 38], Operations: [] Exploring Operation: 85-38=47, Resulting Numbers: [36, 13, 47] Generated Node #0,0: 24:[36, 13, 47] Operation: 85-38=47 Exploring Operation: 85-36=49, Resulting Numbers: [13, 38, 49] Generated Node #0,1: 24:[13, 38, 49] Operation: 85-36=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[36, 13, 47], Operations: ['85-38=47'] Exploring Operation: 47-36=11, Resulting Numbers: [13, 11] Generated Node #0,0,0: 24:[13, 11] Operation: 47-36=11 Exploring Operation: 47-13=34, Resulting Numbers: [36, 34] Generated Node #0,0,1: 24:[36, 34] Operation: 47-13=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[13, 11], Operations: ['85-38=47', '47-36=11'] Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[85, 36, 13, 38], Operations: [] Exploring Operation: 85-38=47, Resulting Numbers: [36, 13, 47] Generated Node #0,0: 24:[36, 13, 47] Operation: 85-38=47 Moving to Node #0,0 Current State: 24:[36, 13, 47], Operations: ['85-38=47'] Exploring Operation: 47-36=11, Resulting Numbers: [13, 11] Generated Node #0,0,0: 24:[13, 11] Operation: 47-36=11 Moving to Node #0,0,0 Current State: 24:[13, 11], Operations: ['85-38=47', '47-36=11'] Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 68, 19, 12, 83 ]
57
[ "68+12=80", "83-80=3", "19*3=57" ]
Current State: 57:[68, 19, 12, 83], Operations: [] Exploring Operation: 68+12=80, Resulting Numbers: [19, 83, 80] Generated Node #2: [19, 83, 80] from Operation: 68+12=80 Current State: 57:[19, 83, 80], Operations: ['68+12=80'] Exploring Operation: 83-80=3, Resulting Numbers: [19, 3] Generated Node #3: [19, 3] from Operation: 83-80=3 Current State: 57:[19, 3], Operations: ['68+12=80', '83-80=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[68, 19, 12, 83], Operations: [] Exploring Operation: 83-68=15, Resulting Numbers: [19, 12, 15] Generated Node #0,0: 57:[19, 12, 15] Operation: 83-68=15 Moving to Node #0,0 Current State: 57:[19, 12, 15], Operations: ['83-68=15'] Exploring Operation: 15-12=3, Resulting Numbers: [19, 3] Generated Node #0,0,0: 57:[19, 3] Operation: 15-12=3 Moving to Node #0,0,0 Current State: 57:[19, 3], Operations: ['83-68=15', '15-12=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[68, 19, 12, 83], Operations: [] Exploring Operation: 83-68=15, Resulting Numbers: [19, 12, 15] Generated Node #0,0: 57:[19, 12, 15] Operation: 83-68=15 Moving to Node #0,0 Current State: 57:[19, 12, 15], Operations: ['83-68=15'] Exploring Operation: 15-12=3, Resulting Numbers: [19, 3] Generated Node #0,0,0: 57:[19, 3] Operation: 15-12=3 Moving to Node #0,0,0 Current State: 57:[19, 3], Operations: ['83-68=15', '15-12=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 46, 93, 66, 70 ]
33
[ "93-70=23", "46/23=2", "66/2=33" ]
Current State: 33:[46, 93, 66, 70], Operations: [] Exploring Operation: 93-70=23, Resulting Numbers: [46, 66, 23] Generated Node #2: [46, 66, 23] from Operation: 93-70=23 Current State: 33:[46, 66, 23], Operations: ['93-70=23'] Exploring Operation: 46/23=2, Resulting Numbers: [66, 2] Generated Node #3: [66, 2] from Operation: 46/23=2 Current State: 33:[66, 2], Operations: ['93-70=23', '46/23=2'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[46, 93, 66, 70], Operations: [] Exploring Operation: 70-66=4, Resulting Numbers: [46, 93, 4] Generated Node #0,0: 33:[46, 93, 4] Operation: 70-66=4 Exploring Operation: 93-70=23, Resulting Numbers: [46, 66, 23] Generated Node #0,1: 33:[46, 66, 23] Operation: 93-70=23 Exploring Operation: 93-66=27, Resulting Numbers: [46, 70, 27] Generated Node #0,2: 33:[46, 70, 27] Operation: 93-66=27 Moving to Node #0,1 Current State: 33:[46, 66, 23], Operations: ['93-70=23'] Exploring Operation: 66-46=20, Resulting Numbers: [23, 20] Generated Node #0,1,0: 33:[23, 20] Operation: 66-46=20 Exploring Operation: 46/23=2, Resulting Numbers: [66, 2] Generated Node #0,1,1: 33:[66, 2] Operation: 46/23=2 Exploring Operation: 66-23=43, Resulting Numbers: [46, 43] Generated Node #0,1,2: 33:[46, 43] Operation: 66-23=43 Moving to Node #0,2 Current State: 33:[46, 70, 27], Operations: ['93-66=27'] Exploring Operation: 70-27=43, Resulting Numbers: [46, 43] Generated Node #0,2,0: 33:[46, 43] Operation: 70-27=43 Exploring Operation: 46-27=19, Resulting Numbers: [70, 19] Generated Node #0,2,1: 33:[70, 19] Operation: 46-27=19 Exploring Operation: 70-46=24, Resulting Numbers: [27, 24] Generated Node #0,2,2: 33:[27, 24] Operation: 70-46=24 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 33:[27, 24], Operations: ['93-66=27', '70-46=24'] Exploring Operation: 27*24=648, Resulting Numbers: [648] 648,33 unequal: No Solution Exploring Operation: 27+24=51, Resulting Numbers: [51] 51,33 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 33:[46, 43], Operations: ['93-66=27', '70-27=43'] Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,33 unequal: No Solution Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,33 unequal: No Solution Exploring Operation: 46*43=1978, Resulting Numbers: [1978] 1978,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 33:[70, 19], Operations: ['93-66=27', '46-27=19'] Exploring Operation: 70*19=1330, Resulting Numbers: [1330] 1330,33 unequal: No Solution Exploring Operation: 70+19=89, Resulting Numbers: [89] 89,33 unequal: No Solution Exploring Operation: 70-19=51, Resulting Numbers: [51] 51,33 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: 33:[46, 93, 4], Operations: ['70-66=4'] Exploring Operation: 46-4=42, Resulting Numbers: [93, 42] Generated Node #0,0,0: 33:[93, 42] Operation: 46-4=42 Exploring Operation: 93-4=89, Resulting Numbers: [46, 89] Generated Node #0,0,1: 33:[46, 89] Operation: 93-4=89 Exploring Operation: 93-46=47, Resulting Numbers: [4, 47] Generated Node #0,0,2: 33:[4, 47] Operation: 93-46=47 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 33:[4, 47], Operations: ['70-66=4', '93-46=47'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,33 unequal: No Solution Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,33 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[93, 42], Operations: ['70-66=4', '46-4=42'] Exploring Operation: 93+42=135, Resulting Numbers: [135] 135,33 unequal: No Solution Exploring Operation: 93*42=3906, Resulting Numbers: [3906] 3906,33 unequal: No Solution Exploring Operation: 93-42=51, Resulting Numbers: [51] 51,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 33:[46, 89], Operations: ['70-66=4', '93-4=89'] Exploring Operation: 89-46=43, Resulting Numbers: [43] 43,33 unequal: No Solution Exploring Operation: 46+89=135, Resulting Numbers: [135] 135,33 unequal: No Solution Exploring Operation: 46*89=4094, Resulting Numbers: [4094] 4094,33 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: 33:[23, 20], Operations: ['93-70=23', '66-46=20'] Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,33 unequal: No Solution Exploring Operation: 23*20=460, Resulting Numbers: [460] 460,33 unequal: No Solution Exploring Operation: 23+20=43, Resulting Numbers: [43] 43,33 unequal: No Solution Moving to Node #0,1,2 Current State: 33:[46, 43], Operations: ['93-70=23', '66-23=43'] Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,33 unequal: No Solution Exploring Operation: 46*43=1978, Resulting Numbers: [1978] 1978,33 unequal: No Solution Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,33 unequal: No Solution Moving to Node #0,1,1 Current State: 33:[66, 2], Operations: ['93-70=23', '46/23=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,33 unequal: No Solution Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,33 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[46, 93, 66, 70], Operations: [] Exploring Operation: 93-70=23, Resulting Numbers: [46, 66, 23] Generated Node #0,1: 33:[46, 66, 23] Operation: 93-70=23 Moving to Node #0,1 Current State: 33:[46, 66, 23], Operations: ['93-70=23'] Exploring Operation: 46/23=2, Resulting Numbers: [66, 2] Generated Node #0,1,1: 33:[66, 2] Operation: 46/23=2 Moving to Node #0,1,1 Current State: 33:[66, 2], Operations: ['93-70=23', '46/23=2'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
0.962674
hs_3
sum_heuristic
[ 8, 41, 57, 31 ]
30
[ "57+31=88", "88/8=11", "41-11=30" ]
Current State: 30:[8, 41, 57, 31], Operations: [] Exploring Operation: 57+31=88, Resulting Numbers: [8, 41, 88] Generated Node #2: [8, 41, 88] from Operation: 57+31=88 Current State: 30:[8, 41, 88], Operations: ['57+31=88'] Exploring Operation: 88/8=11, Resulting Numbers: [41, 11] Generated Node #3: [41, 11] from Operation: 88/8=11 Current State: 30:[41, 11], Operations: ['57+31=88', '88/8=11'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[8, 41, 57, 31], Operations: [] Exploring Operation: 41-31=10, Resulting Numbers: [8, 57, 10] Generated Node #0,0: 30:[8, 57, 10] Operation: 41-31=10 Exploring Operation: 41-8=33, Resulting Numbers: [57, 31, 33] Generated Node #0,1: 30:[57, 31, 33] Operation: 41-8=33 Exploring Operation: 57-41=16, Resulting Numbers: [8, 31, 16] Generated Node #0,2: 30:[8, 31, 16] Operation: 57-41=16 Exploring Operation: 57-31=26, Resulting Numbers: [8, 41, 26] Generated Node #0,3: 30:[8, 41, 26] Operation: 57-31=26 Exploring Operation: 57-8=49, Resulting Numbers: [41, 31, 49] Generated Node #0,4: 30:[41, 31, 49] Operation: 57-8=49 Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[8, 31, 16], Operations: ['57-41=16'] Exploring Operation: 8+16=24, Resulting Numbers: [31, 24] Generated Node #0,2,0: 30:[31, 24] Operation: 8+16=24 Exploring Operation: 16/8=2, Resulting Numbers: [31, 2] Generated Node #0,2,1: 30:[31, 2] Operation: 16/8=2 Exploring Operation: 31-8=23, Resulting Numbers: [16, 23] Generated Node #0,2,2: 30:[16, 23] Operation: 31-8=23 Exploring Operation: 16-8=8, Resulting Numbers: [31, 8] Generated Node #0,2,3: 30:[31, 8] Operation: 16-8=8 Exploring Operation: 31-16=15, Resulting Numbers: [8, 15] Generated Node #0,2,4: 30:[8, 15] Operation: 31-16=15 Moving to Node #0,2,1 Current State: 30:[31, 2], Operations: ['57-41=16', '16/8=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,30 unequal: No Solution Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,30 unequal: No Solution Moving to Node #0,2,4 Current State: 30:[8, 15], Operations: ['57-41=16', '31-16=15'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,30 unequal: No Solution Exploring Operation: 8*15=120, Resulting Numbers: [120] 120,30 unequal: No Solution Moving to Node #0,2,3 Current State: 30:[31, 8], Operations: ['57-41=16', '16-8=8'] Exploring Operation: 31+8=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 31*8=248, Resulting Numbers: [248] 248,30 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,30 unequal: No Solution Moving to Node #0,2,0 Current State: 30:[31, 24], Operations: ['57-41=16', '8+16=24'] Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,30 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,30 unequal: No Solution Moving to Node #0,2,2 Current State: 30:[16, 23], Operations: ['57-41=16', '31-8=23'] Exploring Operation: 16+23=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 16*23=368, Resulting Numbers: [368] 368,30 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 30:[8, 41, 26], Operations: ['57-31=26'] Exploring Operation: 8+41=49, Resulting Numbers: [26, 49] Generated Node #0,3,0: 30:[26, 49] Operation: 8+41=49 Exploring Operation: 41-26=15, Resulting Numbers: [8, 15] Generated Node #0,3,1: 30:[8, 15] Operation: 41-26=15 Exploring Operation: 26-8=18, Resulting Numbers: [41, 18] Generated Node #0,3,2: 30:[41, 18] Operation: 26-8=18 Exploring Operation: 41-8=33, Resulting Numbers: [26, 33] Generated Node #0,3,3: 30:[26, 33] Operation: 41-8=33 Exploring Operation: 8+26=34, Resulting Numbers: [41, 34] Generated Node #0,3,4: 30:[41, 34] Operation: 8+26=34 Moving to Node #0,3,1 Current State: 30:[8, 15], Operations: ['57-31=26', '41-26=15'] Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,30 unequal: No Solution Exploring Operation: 8*15=120, Resulting Numbers: [120] 120,30 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,30 unequal: No Solution Moving to Node #0,3,3 Current State: 30:[26, 33], Operations: ['57-31=26', '41-8=33'] Exploring Operation: 26+33=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 26*33=858, Resulting Numbers: [858] 858,30 unequal: No Solution Exploring Operation: 33-26=7, Resulting Numbers: [7] 7,30 unequal: No Solution Moving to Node #0,3,2 Current State: 30:[41, 18], Operations: ['57-31=26', '26-8=18'] Exploring Operation: 41*18=738, Resulting Numbers: [738] 738,30 unequal: No Solution Exploring Operation: 41+18=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 41-18=23, Resulting Numbers: [23] 23,30 unequal: No Solution Moving to Node #0,3,4 Current State: 30:[41, 34], Operations: ['57-31=26', '8+26=34'] Exploring Operation: 41*34=1394, Resulting Numbers: [1394] 1394,30 unequal: No Solution Exploring Operation: 41+34=75, Resulting Numbers: [75] 75,30 unequal: No Solution Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,30 unequal: No Solution Moving to Node #0,3,0 Current State: 30:[26, 49], Operations: ['57-31=26', '8+41=49'] Exploring Operation: 49-26=23, Resulting Numbers: [23] 23,30 unequal: No Solution Exploring Operation: 26+49=75, Resulting Numbers: [75] 75,30 unequal: No Solution Exploring Operation: 26*49=1274, Resulting Numbers: [1274] 1274,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[8, 57, 10], Operations: ['41-31=10'] Exploring Operation: 8+57=65, Resulting Numbers: [10, 65] Generated Node #0,0,0: 30:[10, 65] Operation: 8+57=65 Exploring Operation: 10-8=2, Resulting Numbers: [57, 2] Generated Node #0,0,1: 30:[57, 2] Operation: 10-8=2 Exploring Operation: 57-8=49, Resulting Numbers: [10, 49] Generated Node #0,0,2: 30:[10, 49] Operation: 57-8=49 Exploring Operation: 8+10=18, Resulting Numbers: [57, 18] Generated Node #0,0,3: 30:[57, 18] Operation: 8+10=18 Exploring Operation: 57-10=47, Resulting Numbers: [8, 47] Generated Node #0,0,4: 30:[8, 47] Operation: 57-10=47 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 30:[10, 49], Operations: ['41-31=10', '57-8=49'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 10*49=490, Resulting Numbers: [490] 490,30 unequal: No Solution No 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: 30:[8, 47], Operations: ['41-31=10', '57-10=47'] Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 8*47=376, Resulting Numbers: [376] 376,30 unequal: No Solution Exploring Operation: 8+47=55, Resulting Numbers: [55] 55,30 unequal: No Solution No 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: 30:[57, 2], Operations: ['41-31=10', '10-8=2'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,30 unequal: No Solution Exploring Operation: 57*2=114, Resulting Numbers: [114] 114,30 unequal: No Solution Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,30 unequal: No Solution No 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: 30:[57, 18], Operations: ['41-31=10', '8+10=18'] Exploring Operation: 57*18=1026, Resulting Numbers: [1026] 1026,30 unequal: No Solution Exploring Operation: 57+18=75, Resulting Numbers: [75] 75,30 unequal: No Solution Exploring Operation: 57-18=39, Resulting Numbers: [39] 39,30 unequal: No Solution No 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: 30:[10, 65], Operations: ['41-31=10', '8+57=65'] Exploring Operation: 65-10=55, Resulting Numbers: [55] 55,30 unequal: No Solution Exploring Operation: 10*65=650, Resulting Numbers: [650] 650,30 unequal: No Solution Exploring Operation: 10+65=75, Resulting Numbers: [75] 75,30 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: 30:[57, 31, 33], Operations: ['41-8=33'] Exploring Operation: 57-33=24, Resulting Numbers: [31, 24] Generated Node #0,1,0: 30:[31, 24] Operation: 57-33=24 Exploring Operation: 57-31=26, Resulting Numbers: [33, 26] Generated Node #0,1,1: 30:[33, 26] Operation: 57-31=26 Exploring Operation: 57+31=88, Resulting Numbers: [33, 88] Generated Node #0,1,2: 30:[33, 88] Operation: 57+31=88 Exploring Operation: 57+33=90, Resulting Numbers: [31, 90] Generated Node #0,1,3: 30:[31, 90] Operation: 57+33=90 Exploring Operation: 33-31=2, Resulting Numbers: [57, 2] Generated Node #0,1,4: 30:[57, 2] Operation: 33-31=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[31, 24], Operations: ['41-8=33', '57-33=24'] Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,30 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,30 unequal: No Solution No 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: 30:[33, 26], Operations: ['41-8=33', '57-31=26'] Exploring Operation: 33+26=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 33*26=858, Resulting Numbers: [858] 858,30 unequal: No Solution Exploring Operation: 33-26=7, Resulting Numbers: [7] 7,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 30:[57, 2], Operations: ['41-8=33', '33-31=2'] Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 57*2=114, Resulting Numbers: [114] 114,30 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,30 unequal: No Solution No 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: 30:[33, 88], Operations: ['41-8=33', '57+31=88'] Exploring Operation: 88-33=55, Resulting Numbers: [55] 55,30 unequal: No Solution Exploring Operation: 33*88=2904, Resulting Numbers: [2904] 2904,30 unequal: No Solution Exploring Operation: 33+88=121, Resulting Numbers: [121] 121,30 unequal: No Solution No 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: 30:[31, 90], Operations: ['41-8=33', '57+33=90'] Exploring Operation: 31+90=121, Resulting Numbers: [121] 121,30 unequal: No Solution Exploring Operation: 90-31=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 31*90=2790, Resulting Numbers: [2790] 2790,30 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: 30:[41, 31, 49], Operations: ['57-8=49'] Exploring Operation: 41-31=10, Resulting Numbers: [49, 10] Generated Node #0,4,0: 30:[49, 10] Operation: 41-31=10 Exploring Operation: 41+31=72, Resulting Numbers: [49, 72] Generated Node #0,4,1: 30:[49, 72] Operation: 41+31=72 Exploring Operation: 49-31=18, Resulting Numbers: [41, 18] Generated Node #0,4,2: 30:[41, 18] Operation: 49-31=18 Exploring Operation: 49-41=8, Resulting Numbers: [31, 8] Generated Node #0,4,3: 30:[31, 8] Operation: 49-41=8 Exploring Operation: 41+49=90, Resulting Numbers: [31, 90] Generated Node #0,4,4: 30:[31, 90] Operation: 41+49=90 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 30:[31, 8], Operations: ['57-8=49', '49-41=8'] Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,30 unequal: No Solution Exploring Operation: 31+8=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 31*8=248, Resulting Numbers: [248] 248,30 unequal: No Solution No 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: 30:[41, 18], Operations: ['57-8=49', '49-31=18'] Exploring Operation: 41+18=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 41-18=23, Resulting Numbers: [23] 23,30 unequal: No Solution Exploring Operation: 41*18=738, Resulting Numbers: [738] 738,30 unequal: No Solution No 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: 30:[49, 10], Operations: ['57-8=49', '41-31=10'] Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 49*10=490, Resulting Numbers: [490] 490,30 unequal: No Solution No 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: 30:[49, 72], Operations: ['57-8=49', '41+31=72'] Exploring Operation: 49+72=121, Resulting Numbers: [121] 121,30 unequal: No Solution Exploring Operation: 49*72=3528, Resulting Numbers: [3528] 3528,30 unequal: No Solution Exploring Operation: 72-49=23, Resulting Numbers: [23] 23,30 unequal: No Solution No 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: 30:[31, 90], Operations: ['57-8=49', '41+49=90'] Exploring Operation: 31+90=121, Resulting Numbers: [121] 121,30 unequal: No Solution Exploring Operation: 31*90=2790, Resulting Numbers: [2790] 2790,30 unequal: No Solution Exploring Operation: 90-31=59, Resulting Numbers: [59] 59,30 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
[ 5, 34, 93, 40 ]
73
[ "5*40=200", "34+93=127", "200-127=73" ]
Current State: 73:[5, 34, 93, 40], Operations: [] Exploring Operation: 5*40=200, Resulting Numbers: [34, 93, 200] Generated Node #2: [34, 93, 200] from Operation: 5*40=200 Current State: 73:[34, 93, 200], Operations: ['5*40=200'] Exploring Operation: 34+93=127, Resulting Numbers: [200, 127] Generated Node #3: [200, 127] from Operation: 34+93=127 Current State: 73:[200, 127], Operations: ['5*40=200', '34+93=127'] Exploring Operation: 200-127=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[5, 34, 93, 40], Operations: [] Exploring Operation: 34+40=74, Resulting Numbers: [5, 93, 74] Generated Node #0,0: 73:[5, 93, 74] Operation: 34+40=74 Exploring Operation: 93-5=88, Resulting Numbers: [34, 40, 88] Generated Node #0,1: 73:[34, 40, 88] Operation: 93-5=88 Exploring Operation: 5+34=39, Resulting Numbers: [93, 40, 39] Generated Node #0,2: 73:[93, 40, 39] Operation: 5+34=39 Exploring Operation: 5+40=45, Resulting Numbers: [34, 93, 45] Generated Node #0,3: 73:[34, 93, 45] Operation: 5+40=45 Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[34, 40, 88], Operations: ['93-5=88'] Exploring Operation: 40-34=6, Resulting Numbers: [88, 6] Generated Node #0,1,0: 73:[88, 6] Operation: 40-34=6 Exploring Operation: 34+40=74, Resulting Numbers: [88, 74] Generated Node #0,1,1: 73:[88, 74] Operation: 34+40=74 Exploring Operation: 88-40=48, Resulting Numbers: [34, 48] Generated Node #0,1,2: 73:[34, 48] Operation: 88-40=48 Exploring Operation: 88-34=54, Resulting Numbers: [40, 54] Generated Node #0,1,3: 73:[40, 54] Operation: 88-34=54 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[88, 74], Operations: ['93-5=88', '34+40=74'] Exploring Operation: 88*74=6512, Resulting Numbers: [6512] 6512,73 unequal: No Solution Exploring Operation: 88+74=162, Resulting Numbers: [162] 162,73 unequal: No Solution Exploring Operation: 88-74=14, Resulting Numbers: [14] 14,73 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 #0,1,3 Current State: 73:[40, 54], Operations: ['93-5=88', '88-34=54'] Exploring Operation: 40*54=2160, Resulting Numbers: [2160] 2160,73 unequal: No Solution Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,73 unequal: No Solution Exploring Operation: 40+54=94, Resulting Numbers: [94] 94,73 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 #0,1,2 Current State: 73:[34, 48], Operations: ['93-5=88', '88-40=48'] Exploring Operation: 34*48=1632, Resulting Numbers: [1632] 1632,73 unequal: No Solution Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,73 unequal: No Solution Exploring Operation: 34+48=82, Resulting Numbers: [82] 82,73 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 #0,1,0 Current State: 73:[88, 6], Operations: ['93-5=88', '40-34=6'] Exploring Operation: 88*6=528, Resulting Numbers: [528] 528,73 unequal: No Solution Exploring Operation: 88-6=82, Resulting Numbers: [82] 82,73 unequal: No Solution Exploring Operation: 88+6=94, Resulting Numbers: [94] 94,73 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 #0,2 Current State: 73:[93, 40, 39], Operations: ['5+34=39'] Exploring Operation: 93+39=132, Resulting Numbers: [40, 132] Generated Node #0,2,0: 73:[40, 132] Operation: 93+39=132 Exploring Operation: 93-40=53, Resulting Numbers: [39, 53] Generated Node #0,2,1: 73:[39, 53] Operation: 93-40=53 Exploring Operation: 93-39=54, Resulting Numbers: [40, 54] Generated Node #0,2,2: 73:[40, 54] Operation: 93-39=54 Exploring Operation: 40+39=79, Resulting Numbers: [93, 79] Generated Node #0,2,3: 73:[93, 79] Operation: 40+39=79 Moving to Node #0,2,3 Current State: 73:[93, 79], Operations: ['5+34=39', '40+39=79'] Exploring Operation: 93+79=172, Resulting Numbers: [172] 172,73 unequal: No Solution Exploring Operation: 93-79=14, Resulting Numbers: [14] 14,73 unequal: No Solution Exploring Operation: 93*79=7347, Resulting Numbers: [7347] 7347,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[40, 54], Operations: ['5+34=39', '93-39=54'] Exploring Operation: 40*54=2160, Resulting Numbers: [2160] 2160,73 unequal: No Solution Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,73 unequal: No Solution Exploring Operation: 40+54=94, Resulting Numbers: [94] 94,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[39, 53], Operations: ['5+34=39', '93-40=53'] Exploring Operation: 39+53=92, Resulting Numbers: [92] 92,73 unequal: No Solution Exploring Operation: 39*53=2067, Resulting Numbers: [2067] 2067,73 unequal: No Solution Exploring Operation: 53-39=14, Resulting Numbers: [14] 14,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[40, 132], Operations: ['5+34=39', '93+39=132'] Exploring Operation: 40+132=172, Resulting Numbers: [172] 172,73 unequal: No Solution Exploring Operation: 132-40=92, Resulting Numbers: [92] 92,73 unequal: No Solution Exploring Operation: 40*132=5280, Resulting Numbers: [5280] 5280,73 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:[34, 93, 45], Operations: ['5+40=45'] Exploring Operation: 93-34=59, Resulting Numbers: [45, 59] Generated Node #0,3,0: 73:[45, 59] Operation: 93-34=59 Exploring Operation: 93-45=48, Resulting Numbers: [34, 48] Generated Node #0,3,1: 73:[34, 48] Operation: 93-45=48 Exploring Operation: 34+45=79, Resulting Numbers: [93, 79] Generated Node #0,3,2: 73:[93, 79] Operation: 34+45=79 Exploring Operation: 34+93=127, Resulting Numbers: [45, 127] Generated Node #0,3,3: 73:[45, 127] Operation: 34+93=127 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 73:[93, 79], Operations: ['5+40=45', '34+45=79'] Exploring Operation: 93*79=7347, Resulting Numbers: [7347] 7347,73 unequal: No Solution Exploring Operation: 93+79=172, Resulting Numbers: [172] 172,73 unequal: No Solution Exploring Operation: 93-79=14, Resulting Numbers: [14] 14,73 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:[45, 59], Operations: ['5+40=45', '93-34=59'] Exploring Operation: 45*59=2655, Resulting Numbers: [2655] 2655,73 unequal: No Solution Exploring Operation: 45+59=104, Resulting Numbers: [104] 104,73 unequal: No Solution Exploring Operation: 59-45=14, Resulting Numbers: [14] 14,73 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 #0,3,1 Current State: 73:[34, 48], Operations: ['5+40=45', '93-45=48'] Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,73 unequal: No Solution Exploring Operation: 34+48=82, Resulting Numbers: [82] 82,73 unequal: No Solution Exploring Operation: 34*48=1632, Resulting Numbers: [1632] 1632,73 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:[45, 127], Operations: ['5+40=45', '34+93=127'] Exploring Operation: 45+127=172, Resulting Numbers: [172] 172,73 unequal: No Solution Exploring Operation: 127-45=82, Resulting Numbers: [82] 82,73 unequal: No Solution Exploring Operation: 45*127=5715, Resulting Numbers: [5715] 5715,73 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 #0,0 Current State: 73:[5, 93, 74], Operations: ['34+40=74'] Exploring Operation: 5+93=98, Resulting Numbers: [74, 98] Generated Node #0,0,0: 73:[74, 98] Operation: 5+93=98 Exploring Operation: 5+74=79, Resulting Numbers: [93, 79] Generated Node #0,0,1: 73:[93, 79] Operation: 5+74=79 Exploring Operation: 74-5=69, Resulting Numbers: [93, 69] Generated Node #0,0,2: 73:[93, 69] Operation: 74-5=69 Exploring Operation: 93-5=88, Resulting Numbers: [74, 88] Generated Node #0,0,3: 73:[74, 88] Operation: 93-5=88 Moving to Node #0,0,3 Current State: 73:[74, 88], Operations: ['34+40=74', '93-5=88'] Exploring Operation: 74*88=6512, Resulting Numbers: [6512] 6512,73 unequal: No Solution Exploring Operation: 74+88=162, Resulting Numbers: [162] 162,73 unequal: No Solution Exploring Operation: 88-74=14, Resulting Numbers: [14] 14,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[93, 69], Operations: ['34+40=74', '74-5=69'] Exploring Operation: 93+69=162, Resulting Numbers: [162] 162,73 unequal: No Solution Exploring Operation: 93-69=24, Resulting Numbers: [24] 24,73 unequal: No Solution Exploring Operation: 93*69=6417, Resulting Numbers: [6417] 6417,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[93, 79], Operations: ['34+40=74', '5+74=79'] Exploring Operation: 93+79=172, Resulting Numbers: [172] 172,73 unequal: No Solution Exploring Operation: 93-79=14, Resulting Numbers: [14] 14,73 unequal: No Solution Exploring Operation: 93*79=7347, Resulting Numbers: [7347] 7347,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[74, 98], Operations: ['34+40=74', '5+93=98'] Exploring Operation: 74+98=172, Resulting Numbers: [172] 172,73 unequal: No Solution Exploring Operation: 74*98=7252, Resulting Numbers: [7252] 7252,73 unequal: No Solution Exploring Operation: 98-74=24, Resulting Numbers: [24] 24,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 96, 97, 40, 2 ]
69
[ "96-40=56", "56/2=28", "97-28=69" ]
Current State: 69:[96, 97, 40, 2], Operations: [] Exploring Operation: 96-40=56, Resulting Numbers: [97, 2, 56] Generated Node #2: [97, 2, 56] from Operation: 96-40=56 Current State: 69:[97, 2, 56], Operations: ['96-40=56'] Exploring Operation: 56/2=28, Resulting Numbers: [97, 28] Generated Node #3: [97, 28] from Operation: 56/2=28 Current State: 69:[97, 28], Operations: ['96-40=56', '56/2=28'] Exploring Operation: 97-28=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[96, 97, 40, 2], Operations: [] Exploring Operation: 97-40=57, Resulting Numbers: [96, 2, 57] Generated Node #0,0: 69:[96, 2, 57] Operation: 97-40=57 Exploring Operation: 96-40=56, Resulting Numbers: [97, 2, 56] Generated Node #0,1: 69:[97, 2, 56] Operation: 96-40=56 Exploring Operation: 40/2=20, Resulting Numbers: [96, 97, 20] Generated Node #0,2: 69:[96, 97, 20] Operation: 40/2=20 Exploring Operation: 97-96=1, Resulting Numbers: [40, 2, 1] Generated Node #0,3: 69:[40, 2, 1] Operation: 97-96=1 Moving to Node #0,3 Current State: 69:[40, 2, 1], Operations: ['97-96=1'] Exploring Operation: 40/2=20, Resulting Numbers: [1, 20] Generated Node #0,3,0: 69:[1, 20] Operation: 40/2=20 Exploring Operation: 40*2=80, Resulting Numbers: [1, 80] Generated Node #0,3,1: 69:[1, 80] Operation: 40*2=80 Exploring Operation: 40-1=39, Resulting Numbers: [2, 39] Generated Node #0,3,2: 69:[2, 39] Operation: 40-1=39 Exploring Operation: 40-2=38, Resulting Numbers: [1, 38] Generated Node #0,3,3: 69:[1, 38] Operation: 40-2=38 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 69:[1, 20], Operations: ['97-96=1', '40/2=20'] Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,69 unequal: No Solution Exploring Operation: 1+20=21, Resulting Numbers: [21] 21,69 unequal: No Solution Exploring Operation: 1*20=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 69:[1, 80], Operations: ['97-96=1', '40*2=80'] Exploring Operation: 80/1=80, Resulting Numbers: [80] 80,69 unequal: No Solution Exploring Operation: 1+80=81, Resulting Numbers: [81] 81,69 unequal: No Solution Exploring Operation: 1*80=80, Resulting Numbers: [80] 80,69 unequal: No Solution Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 69:[2, 39], Operations: ['97-96=1', '40-1=39'] Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,69 unequal: No Solution Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,69 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 69:[1, 38], Operations: ['97-96=1', '40-2=38'] Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 1+38=39, Resulting Numbers: [39] 39,69 unequal: No Solution Exploring Operation: 1*38=38, Resulting Numbers: [38] 38,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 69:[96, 2, 57], Operations: ['97-40=57'] Exploring Operation: 96/2=48, Resulting Numbers: [57, 48] Generated Node #0,0,0: 69:[57, 48] Operation: 96/2=48 Exploring Operation: 96-57=39, Resulting Numbers: [2, 39] Generated Node #0,0,1: 69:[2, 39] Operation: 96-57=39 Exploring Operation: 96-2=94, Resulting Numbers: [57, 94] Generated Node #0,0,2: 69:[57, 94] Operation: 96-2=94 Exploring Operation: 2+57=59, Resulting Numbers: [96, 59] Generated Node #0,0,3: 69:[96, 59] Operation: 2+57=59 Moving to Node #0,1 Current State: 69:[97, 2, 56], Operations: ['96-40=56'] Exploring Operation: 56/2=28, Resulting Numbers: [97, 28] Generated Node #0,1,0: 69:[97, 28] Operation: 56/2=28 Exploring Operation: 97-56=41, Resulting Numbers: [2, 41] Generated Node #0,1,1: 69:[2, 41] Operation: 97-56=41 Exploring Operation: 97-2=95, Resulting Numbers: [56, 95] Generated Node #0,1,2: 69:[56, 95] Operation: 97-2=95 Exploring Operation: 2+56=58, Resulting Numbers: [97, 58] Generated Node #0,1,3: 69:[97, 58] Operation: 2+56=58 Moving to Node #0,2 Current State: 69:[96, 97, 20], Operations: ['40/2=20'] Exploring Operation: 97-96=1, Resulting Numbers: [20, 1] Generated Node #0,2,0: 69:[20, 1] Operation: 97-96=1 Exploring Operation: 96+20=116, Resulting Numbers: [97, 116] Generated Node #0,2,1: 69:[97, 116] Operation: 96+20=116 Exploring Operation: 96-20=76, Resulting Numbers: [97, 76] Generated Node #0,2,2: 69:[97, 76] Operation: 96-20=76 Exploring Operation: 97-20=77, Resulting Numbers: [96, 77] Generated Node #0,2,3: 69:[96, 77] Operation: 97-20=77 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 69:[20, 1], Operations: ['40/2=20', '97-96=1'] Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,69 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 69:[97, 76], Operations: ['40/2=20', '96-20=76'] Exploring Operation: 97-76=21, Resulting Numbers: [21] 21,69 unequal: No Solution Exploring Operation: 97*76=7372, Resulting Numbers: [7372] 7372,69 unequal: No Solution Exploring Operation: 97+76=173, Resulting Numbers: [173] 173,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 69:[96, 77], Operations: ['40/2=20', '97-20=77'] Exploring Operation: 96*77=7392, Resulting Numbers: [7392] 7392,69 unequal: No Solution Exploring Operation: 96+77=173, Resulting Numbers: [173] 173,69 unequal: No Solution Exploring Operation: 96-77=19, Resulting Numbers: [19] 19,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 69:[97, 116], Operations: ['40/2=20', '96+20=116'] Exploring Operation: 116-97=19, Resulting Numbers: [19] 19,69 unequal: No Solution Exploring Operation: 97*116=11252, Resulting Numbers: [11252] 11252,69 unequal: No Solution Exploring Operation: 97+116=213, Resulting Numbers: [213] 213,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 69:[2, 39], Operations: ['97-40=57', '96-57=39'] Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,69 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[2, 41], Operations: ['96-40=56', '97-56=41'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,69 unequal: No Solution Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,69 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,69 unequal: No Solution Moving to Node #0,1,0 Current State: 69:[97, 28], Operations: ['96-40=56', '56/2=28'] Exploring Operation: 97+28=125, Resulting Numbers: [125] 125,69 unequal: No Solution Exploring Operation: 97-28=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[96, 97, 40, 2], Operations: [] Exploring Operation: 96-40=56, Resulting Numbers: [97, 2, 56] Generated Node #0,1: 69:[97, 2, 56] Operation: 96-40=56 Moving to Node #0,1 Current State: 69:[97, 2, 56], Operations: ['96-40=56'] Exploring Operation: 56/2=28, Resulting Numbers: [97, 28] Generated Node #0,1,0: 69:[97, 28] Operation: 56/2=28 Moving to Node #0,1,0 Current State: 69:[97, 28], Operations: ['96-40=56', '56/2=28'] Exploring Operation: 97-28=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
0.947917
hs_4
sum_heuristic
[ 37, 89, 51, 36 ]
37
[ "89-37=52", "51-36=15", "52-15=37" ]
Current State: 37:[37, 89, 51, 36], Operations: [] Exploring Operation: 89-37=52, Resulting Numbers: [51, 36, 52] Generated Node #2: [51, 36, 52] from Operation: 89-37=52 Current State: 37:[51, 36, 52], Operations: ['89-37=52'] Exploring Operation: 51-36=15, Resulting Numbers: [52, 15] Generated Node #3: [52, 15] from Operation: 51-36=15 Current State: 37:[52, 15], Operations: ['89-37=52', '51-36=15'] Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[37, 89, 51, 36], Operations: [] Exploring Operation: 89-37=52, Resulting Numbers: [51, 36, 52] Generated Node #0,0: 37:[51, 36, 52] Operation: 89-37=52 Exploring Operation: 89-51=38, Resulting Numbers: [37, 36, 38] Generated Node #0,1: 37:[37, 36, 38] Operation: 89-51=38 Exploring Operation: 89-36=53, Resulting Numbers: [37, 51, 53] Generated Node #0,2: 37:[37, 51, 53] Operation: 89-36=53 Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[37, 36, 38], Operations: ['89-51=38'] Exploring Operation: 37+36=73, Resulting Numbers: [38, 73] Generated Node #0,1,0: 37:[38, 73] Operation: 37+36=73 Exploring Operation: 38-36=2, Resulting Numbers: [37, 2] Generated Node #0,1,1: 37:[37, 2] Operation: 38-36=2 Exploring Operation: 37-36=1, Resulting Numbers: [38, 1] Generated Node #0,1,2: 37:[38, 1] Operation: 37-36=1 Moving to Node #0,1,1 Current State: 37:[37, 2], Operations: ['89-51=38', '38-36=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,37 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,37 unequal: No Solution Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[38, 73], Operations: ['89-51=38', '37+36=73'] Exploring Operation: 38*73=2774, Resulting Numbers: [2774] 2774,37 unequal: No Solution Exploring Operation: 38+73=111, Resulting Numbers: [111] 111,37 unequal: No Solution Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[38, 1], Operations: ['89-51=38', '37-36=1'] Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[37, 89, 51, 36], Operations: [] Exploring Operation: 89-51=38, Resulting Numbers: [37, 36, 38] Generated Node #0,1: 37:[37, 36, 38] Operation: 89-51=38 Moving to Node #0,1 Current State: 37:[37, 36, 38], Operations: ['89-51=38'] Exploring Operation: 37-36=1, Resulting Numbers: [38, 1] Generated Node #0,1,2: 37:[38, 1] Operation: 37-36=1 Moving to Node #0,1,2 Current State: 37:[38, 1], Operations: ['89-51=38', '37-36=1'] Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 93, 50, 87, 15 ]
54
[ "93+87=180", "15*180=2700", "2700/50=54" ]
Current State: 54:[93, 50, 87, 15], Operations: [] Exploring Operation: 93+87=180, Resulting Numbers: [50, 15, 180] Generated Node #2: [50, 15, 180] from Operation: 93+87=180 Current State: 54:[50, 15, 180], Operations: ['93+87=180'] Exploring Operation: 15*180=2700, Resulting Numbers: [50, 2700] Generated Node #3: [50, 2700] from Operation: 15*180=2700 Current State: 54:[50, 2700], Operations: ['93+87=180', '15*180=2700'] Exploring Operation: 2700/50=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[93, 50, 87, 15], Operations: [] Exploring Operation: 93-87=6, Resulting Numbers: [50, 15, 6] Generated Node #0,0: 54:[50, 15, 6] Operation: 93-87=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[50, 15, 6], Operations: ['93-87=6'] Exploring Operation: 15-6=9, Resulting Numbers: [50, 9] Generated Node #0,0,0: 54:[50, 9] Operation: 15-6=9 Moving to Node #0,0,0 Current State: 54:[50, 9], Operations: ['93-87=6', '15-6=9'] Exploring Operation: 50+9=59, Resulting Numbers: [59] 59,54 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
[ 24, 44, 28, 29 ]
67
[ "24+44=68", "29-28=1", "68-1=67" ]
Current State: 67:[24, 44, 28, 29], Operations: [] Exploring Operation: 24+44=68, Resulting Numbers: [28, 29, 68] Generated Node #2: [28, 29, 68] from Operation: 24+44=68 Current State: 67:[28, 29, 68], Operations: ['24+44=68'] Exploring Operation: 29-28=1, Resulting Numbers: [68, 1] Generated Node #3: [68, 1] from Operation: 29-28=1 Current State: 67:[68, 1], Operations: ['24+44=68', '29-28=1'] Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[24, 44, 28, 29], Operations: [] Exploring Operation: 24+29=53, Resulting Numbers: [44, 28, 53] Generated Node #0,0: 67:[44, 28, 53] Operation: 24+29=53 Exploring Operation: 28+29=57, Resulting Numbers: [24, 44, 57] Generated Node #0,1: 67:[24, 44, 57] Operation: 28+29=57 Exploring Operation: 24+44=68, Resulting Numbers: [28, 29, 68] Generated Node #0,2: 67:[28, 29, 68] Operation: 24+44=68 Exploring Operation: 24+28=52, Resulting Numbers: [44, 29, 52] Generated Node #0,3: 67:[44, 29, 52] Operation: 24+28=52 Moving to Node #0,0 Current State: 67:[44, 28, 53], Operations: ['24+29=53'] Exploring Operation: 44+28=72, Resulting Numbers: [53, 72] Generated Node #0,0,0: 67:[53, 72] Operation: 44+28=72 Exploring Operation: 53-28=25, Resulting Numbers: [44, 25] Generated Node #0,0,1: 67:[44, 25] Operation: 53-28=25 Exploring Operation: 44-28=16, Resulting Numbers: [53, 16] Generated Node #0,0,2: 67:[53, 16] Operation: 44-28=16 Exploring Operation: 28+53=81, Resulting Numbers: [44, 81] Generated Node #0,0,3: 67:[44, 81] Operation: 28+53=81 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[53, 72], Operations: ['24+29=53', '44+28=72'] Exploring Operation: 72-53=19, Resulting Numbers: [19] 19,67 unequal: No Solution Exploring Operation: 53+72=125, Resulting Numbers: [125] 125,67 unequal: No Solution Exploring Operation: 53*72=3816, Resulting Numbers: [3816] 3816,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 67:[44, 81], Operations: ['24+29=53', '28+53=81'] Exploring Operation: 44+81=125, Resulting Numbers: [125] 125,67 unequal: No Solution Exploring Operation: 81-44=37, Resulting Numbers: [37] 37,67 unequal: No Solution Exploring Operation: 44*81=3564, Resulting Numbers: [3564] 3564,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[44, 25], Operations: ['24+29=53', '53-28=25'] Exploring Operation: 44*25=1100, Resulting Numbers: [1100] 1100,67 unequal: No Solution Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,67 unequal: No Solution Exploring Operation: 44+25=69, Resulting Numbers: [69] 69,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 67:[53, 16], Operations: ['24+29=53', '44-28=16'] Exploring Operation: 53*16=848, Resulting Numbers: [848] 848,67 unequal: No Solution Exploring Operation: 53+16=69, Resulting Numbers: [69] 69,67 unequal: No Solution Exploring Operation: 53-16=37, Resulting Numbers: [37] 37,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 67:[44, 29, 52], Operations: ['24+28=52'] Exploring Operation: 29+52=81, Resulting Numbers: [44, 81] Generated Node #0,3,0: 67:[44, 81] Operation: 29+52=81 Exploring Operation: 44-29=15, Resulting Numbers: [52, 15] Generated Node #0,3,1: 67:[52, 15] Operation: 44-29=15 Exploring Operation: 44+29=73, Resulting Numbers: [52, 73] Generated Node #0,3,2: 67:[52, 73] Operation: 44+29=73 Exploring Operation: 44+52=96, Resulting Numbers: [29, 96] Generated Node #0,3,3: 67:[29, 96] Operation: 44+52=96 Moving to Node #0,1 Current State: 67:[24, 44, 57], Operations: ['28+29=57'] Exploring Operation: 24+44=68, Resulting Numbers: [57, 68] Generated Node #0,1,0: 67:[57, 68] Operation: 24+44=68 Exploring Operation: 57-24=33, Resulting Numbers: [44, 33] Generated Node #0,1,1: 67:[44, 33] Operation: 57-24=33 Exploring Operation: 24+57=81, Resulting Numbers: [44, 81] Generated Node #0,1,2: 67:[44, 81] Operation: 24+57=81 Exploring Operation: 44-24=20, Resulting Numbers: [57, 20] Generated Node #0,1,3: 67:[57, 20] Operation: 44-24=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[57, 68], Operations: ['28+29=57', '24+44=68'] Exploring Operation: 57+68=125, Resulting Numbers: [125] 125,67 unequal: No Solution Exploring Operation: 68-57=11, Resulting Numbers: [11] 11,67 unequal: No Solution Exploring Operation: 57*68=3876, Resulting Numbers: [3876] 3876,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 67:[44, 81], Operations: ['28+29=57', '24+57=81'] Exploring Operation: 44*81=3564, Resulting Numbers: [3564] 3564,67 unequal: No Solution Exploring Operation: 44+81=125, Resulting Numbers: [125] 125,67 unequal: No Solution Exploring Operation: 81-44=37, Resulting Numbers: [37] 37,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 67:[44, 33], Operations: ['28+29=57', '57-24=33'] Exploring Operation: 44*33=1452, Resulting Numbers: [1452] 1452,67 unequal: No Solution Exploring Operation: 44+33=77, Resulting Numbers: [77] 77,67 unequal: No Solution Exploring Operation: 44-33=11, Resulting Numbers: [11] 11,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 67:[57, 20], Operations: ['28+29=57', '44-24=20'] Exploring Operation: 57*20=1140, Resulting Numbers: [1140] 1140,67 unequal: No Solution Exploring Operation: 57+20=77, Resulting Numbers: [77] 77,67 unequal: No Solution Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,67 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: 67:[28, 29, 68], Operations: ['24+44=68'] Exploring Operation: 68-28=40, Resulting Numbers: [29, 40] Generated Node #0,2,0: 67:[29, 40] Operation: 68-28=40 Exploring Operation: 28+29=57, Resulting Numbers: [68, 57] Generated Node #0,2,1: 67:[68, 57] Operation: 28+29=57 Exploring Operation: 29-28=1, Resulting Numbers: [68, 1] Generated Node #0,2,2: 67:[68, 1] Operation: 29-28=1 Exploring Operation: 28+68=96, Resulting Numbers: [29, 96] Generated Node #0,2,3: 67:[29, 96] Operation: 28+68=96 Moving to Node #0,2,1 Current State: 67:[68, 57], Operations: ['24+44=68', '28+29=57'] Exploring Operation: 68-57=11, Resulting Numbers: [11] 11,67 unequal: No Solution Exploring Operation: 68*57=3876, Resulting Numbers: [3876] 3876,67 unequal: No Solution Exploring Operation: 68+57=125, Resulting Numbers: [125] 125,67 unequal: No Solution Moving to Node #0,3,2 Current State: 67:[52, 73], Operations: ['24+28=52', '44+29=73'] Exploring Operation: 52*73=3796, Resulting Numbers: [3796] 3796,67 unequal: No Solution Exploring Operation: 52+73=125, Resulting Numbers: [125] 125,67 unequal: No Solution Exploring Operation: 73-52=21, Resulting Numbers: [21] 21,67 unequal: No Solution Moving to Node #0,3,0 Current State: 67:[44, 81], Operations: ['24+28=52', '29+52=81'] Exploring Operation: 44*81=3564, Resulting Numbers: [3564] 3564,67 unequal: No Solution Exploring Operation: 44+81=125, Resulting Numbers: [125] 125,67 unequal: No Solution Exploring Operation: 81-44=37, Resulting Numbers: [37] 37,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[29, 40], Operations: ['24+44=68', '68-28=40'] Exploring Operation: 40-29=11, Resulting Numbers: [11] 11,67 unequal: No Solution Exploring Operation: 29*40=1160, Resulting Numbers: [1160] 1160,67 unequal: No Solution Exploring Operation: 29+40=69, Resulting Numbers: [69] 69,67 unequal: No Solution Moving to Node #0,3,1 Current State: 67:[52, 15], Operations: ['24+28=52', '44-29=15'] Exploring Operation: 52*15=780, Resulting Numbers: [780] 780,67 unequal: No Solution Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,67 unequal: No Solution Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[24, 44, 28, 29], Operations: [] Exploring Operation: 24+28=52, Resulting Numbers: [44, 29, 52] Generated Node #0,3: 67:[44, 29, 52] Operation: 24+28=52 Moving to Node #0,3 Current State: 67:[44, 29, 52], Operations: ['24+28=52'] Exploring Operation: 44-29=15, Resulting Numbers: [52, 15] Generated Node #0,3,1: 67:[52, 15] Operation: 44-29=15 Moving to Node #0,3,1 Current State: 67:[52, 15], Operations: ['24+28=52', '44-29=15'] Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
0.945313
hs_4
sum_heuristic
[ 34, 42, 5, 68 ]
51
[ "68-5=63", "34*63=2142", "2142/42=51" ]
Current State: 51:[34, 42, 5, 68], Operations: [] Exploring Operation: 68-5=63, Resulting Numbers: [34, 42, 63] Generated Node #2: [34, 42, 63] from Operation: 68-5=63 Current State: 51:[34, 42, 63], Operations: ['68-5=63'] Exploring Operation: 34*63=2142, Resulting Numbers: [42, 2142] Generated Node #3: [42, 2142] from Operation: 34*63=2142 Current State: 51:[42, 2142], Operations: ['68-5=63', '34*63=2142'] Exploring Operation: 2142/42=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[34, 42, 5, 68], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [42, 5, 2] Generated Node #0,0: 51:[42, 5, 2] Operation: 68/34=2 Exploring Operation: 68-34=34, Resulting Numbers: [42, 5, 34] Generated Node #0,1: 51:[42, 5, 34] Operation: 68-34=34 Exploring Operation: 42-34=8, Resulting Numbers: [5, 68, 8] Generated Node #0,2: 51:[5, 68, 8] Operation: 42-34=8 Moving to Node #0,0 Current State: 51:[42, 5, 2], Operations: ['68/34=2'] Exploring Operation: 42/2=21, Resulting Numbers: [5, 21] Generated Node #0,0,0: 51:[5, 21] Operation: 42/2=21 Exploring Operation: 42+5=47, Resulting Numbers: [2, 47] Generated Node #0,0,1: 51:[2, 47] Operation: 42+5=47 Exploring Operation: 42+2=44, Resulting Numbers: [5, 44] Generated Node #0,0,2: 51:[5, 44] Operation: 42+2=44 Moving to Node #0,2 Current State: 51:[5, 68, 8], Operations: ['42-34=8'] Exploring Operation: 68-5=63, Resulting Numbers: [8, 63] Generated Node #0,2,0: 51:[8, 63] Operation: 68-5=63 Exploring Operation: 8-5=3, Resulting Numbers: [68, 3] Generated Node #0,2,1: 51:[68, 3] Operation: 8-5=3 Exploring Operation: 68-8=60, Resulting Numbers: [5, 60] Generated Node #0,2,2: 51:[5, 60] Operation: 68-8=60 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 51:[5, 60], Operations: ['42-34=8', '68-8=60'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,51 unequal: No Solution Exploring Operation: 5+60=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 51:[8, 63], Operations: ['42-34=8', '68-5=63'] Exploring Operation: 8*63=504, Resulting Numbers: [504] 504,51 unequal: No Solution Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 8+63=71, Resulting Numbers: [71] 71,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 51:[68, 3], Operations: ['42-34=8', '8-5=3'] Exploring Operation: 68*3=204, Resulting Numbers: [204] 204,51 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,51 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: 51:[42, 5, 34], Operations: ['68-34=34'] Exploring Operation: 5+34=39, Resulting Numbers: [42, 39] Generated Node #0,1,0: 51:[42, 39] Operation: 5+34=39 Exploring Operation: 42-34=8, Resulting Numbers: [5, 8] Generated Node #0,1,1: 51:[5, 8] Operation: 42-34=8 Exploring Operation: 42+5=47, Resulting Numbers: [34, 47] Generated Node #0,1,2: 51:[34, 47] Operation: 42+5=47 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 51:[5, 8], Operations: ['68-34=34', '42-34=8'] Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,51 unequal: No Solution Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,51 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 51:[42, 39], Operations: ['68-34=34', '5+34=39'] Exploring Operation: 42*39=1638, Resulting Numbers: [1638] 1638,51 unequal: No Solution Exploring Operation: 42+39=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 51:[34, 47], Operations: ['68-34=34', '42+5=47'] Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,51 unequal: No Solution Exploring Operation: 34+47=81, Resulting Numbers: [81] 81,51 unequal: No Solution Exploring Operation: 34*47=1598, Resulting Numbers: [1598] 1598,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 51:[2, 47], Operations: ['68/34=2', '42+5=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,51 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,51 unequal: No Solution Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[5, 21], Operations: ['68/34=2', '42/2=21'] Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,51 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[5, 44], Operations: ['68/34=2', '42+2=44'] Exploring Operation: 5*44=220, Resulting Numbers: [220] 220,51 unequal: No Solution Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,51 unequal: No Solution Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,51 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 92, 36, 46, 69 ]
18
[ "92+46=138", "36*69=2484", "2484/138=18" ]
Current State: 18:[92, 36, 46, 69], Operations: [] Exploring Operation: 92+46=138, Resulting Numbers: [36, 69, 138] Generated Node #2: [36, 69, 138] from Operation: 92+46=138 Current State: 18:[36, 69, 138], Operations: ['92+46=138'] Exploring Operation: 36*69=2484, Resulting Numbers: [138, 2484] Generated Node #3: [138, 2484] from Operation: 36*69=2484 Current State: 18:[138, 2484], Operations: ['92+46=138', '36*69=2484'] Exploring Operation: 2484/138=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[92, 36, 46, 69], Operations: [] Exploring Operation: 92/46=2, Resulting Numbers: [36, 69, 2] Generated Node #0,0: 18:[36, 69, 2] Operation: 92/46=2 Exploring Operation: 92-69=23, Resulting Numbers: [36, 46, 23] Generated Node #0,1: 18:[36, 46, 23] Operation: 92-69=23 Moving to Node #0,1 Current State: 18:[36, 46, 23], Operations: ['92-69=23'] Exploring Operation: 46-36=10, Resulting Numbers: [23, 10] Generated Node #0,1,0: 18:[23, 10] Operation: 46-36=10 Exploring Operation: 46/23=2, Resulting Numbers: [36, 2] Generated Node #0,1,1: 18:[36, 2] Operation: 46/23=2 Moving to Node #0,0 Current State: 18:[36, 69, 2], Operations: ['92/46=2'] Exploring Operation: 69-36=33, Resulting Numbers: [2, 33] Generated Node #0,0,0: 18:[2, 33] Operation: 69-36=33 Exploring Operation: 36/2=18, Resulting Numbers: [69, 18] Generated Node #0,0,1: 18:[69, 18] Operation: 36/2=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[2, 33], Operations: ['92/46=2', '69-36=33'] Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,18 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[69, 18], Operations: ['92/46=2', '36/2=18'] Exploring Operation: 69+18=87, Resulting Numbers: [87] 87,18 unequal: No Solution Exploring Operation: 69-18=51, Resulting Numbers: [51] 51,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 18:[23, 10], Operations: ['92-69=23', '46-36=10'] Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,18 unequal: No Solution Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[36, 2], Operations: ['92-69=23', '46/23=2'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[92, 36, 46, 69], Operations: [] Exploring Operation: 92-69=23, Resulting Numbers: [36, 46, 23] Generated Node #0,1: 18:[36, 46, 23] Operation: 92-69=23 Moving to Node #0,1 Current State: 18:[36, 46, 23], Operations: ['92-69=23'] Exploring Operation: 46/23=2, Resulting Numbers: [36, 2] Generated Node #0,1,1: 18:[36, 2] Operation: 46/23=2 Moving to Node #0,1,1 Current State: 18:[36, 2], Operations: ['92-69=23', '46/23=2'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.985243
hs_2
mult_heuristic
[ 63, 21, 99, 46 ]
79
[ "63/21=3", "99/3=33", "46+33=79" ]
Current State: 79:[63, 21, 99, 46], Operations: [] Exploring Operation: 63/21=3, Resulting Numbers: [99, 46, 3] Generated Node #2: [99, 46, 3] from Operation: 63/21=3 Current State: 79:[99, 46, 3], Operations: ['63/21=3'] Exploring Operation: 99/3=33, Resulting Numbers: [46, 33] Generated Node #3: [46, 33] from Operation: 99/3=33 Current State: 79:[46, 33], Operations: ['63/21=3', '99/3=33'] Exploring Operation: 46+33=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[63, 21, 99, 46], Operations: [] Exploring Operation: 21+46=67, Resulting Numbers: [63, 99, 67] Generated Node #0,0: 79:[63, 99, 67] Operation: 21+46=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[63, 99, 67], Operations: ['21+46=67'] Exploring Operation: 99-63=36, Resulting Numbers: [67, 36] Generated Node #0,0,0: 79:[67, 36] Operation: 99-63=36 Moving to Node #0,0,0 Current State: 79:[67, 36], Operations: ['21+46=67', '99-63=36'] Exploring Operation: 67+36=103, Resulting Numbers: [103] 103,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 3, 55, 80, 69 ]
38
[ "69-55=14", "3*14=42", "80-42=38" ]
Current State: 38:[3, 55, 80, 69], Operations: [] Exploring Operation: 69-55=14, Resulting Numbers: [3, 80, 14] Generated Node #2: [3, 80, 14] from Operation: 69-55=14 Current State: 38:[3, 80, 14], Operations: ['69-55=14'] Exploring Operation: 3*14=42, Resulting Numbers: [80, 42] Generated Node #3: [80, 42] from Operation: 3*14=42 Current State: 38:[80, 42], Operations: ['69-55=14', '3*14=42'] Exploring Operation: 80-42=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[3, 55, 80, 69], Operations: [] Exploring Operation: 80-69=11, Resulting Numbers: [3, 55, 11] Generated Node #0,0: 38:[3, 55, 11] Operation: 80-69=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[3, 55, 11], Operations: ['80-69=11'] Exploring Operation: 55/11=5, Resulting Numbers: [3, 5] Generated Node #0,0,0: 38:[3, 5] Operation: 55/11=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 38:[3, 5], Operations: ['80-69=11', '55/11=5'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 34, 4, 39, 2 ]
95
[ "34*4=136", "39+2=41", "136-41=95" ]
Current State: 95:[34, 4, 39, 2], Operations: [] Exploring Operation: 34*4=136, Resulting Numbers: [39, 2, 136] Generated Node #2: [39, 2, 136] from Operation: 34*4=136 Current State: 95:[39, 2, 136], Operations: ['34*4=136'] Exploring Operation: 39+2=41, Resulting Numbers: [136, 41] Generated Node #3: [136, 41] from Operation: 39+2=41 Current State: 95:[136, 41], Operations: ['34*4=136', '39+2=41'] Exploring Operation: 136-41=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[34, 4, 39, 2], Operations: [] Exploring Operation: 34/2=17, Resulting Numbers: [4, 39, 17] Generated Node #0,0: 95:[4, 39, 17] Operation: 34/2=17 Exploring Operation: 34+39=73, Resulting Numbers: [4, 2, 73] Generated Node #0,1: 95:[4, 2, 73] Operation: 34+39=73 Exploring Operation: 39-34=5, Resulting Numbers: [4, 2, 5] Generated Node #0,2: 95:[4, 2, 5] Operation: 39-34=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 95:[4, 2, 5], Operations: ['39-34=5'] Exploring Operation: 4-2=2, Resulting Numbers: [5, 2] Generated Node #0,2,0: 95:[5, 2] Operation: 4-2=2 Exploring Operation: 4*2=8, Resulting Numbers: [5, 8] Generated Node #0,2,1: 95:[5, 8] Operation: 4*2=8 Exploring Operation: 4+2=6, Resulting Numbers: [5, 6] Generated Node #0,2,2: 95:[5, 6] Operation: 4+2=6 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 95:[5, 6], Operations: ['39-34=5', '4+2=6'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,95 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,95 unequal: No Solution Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 95:[5, 2], Operations: ['39-34=5', '4-2=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,95 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 95:[5, 8], Operations: ['39-34=5', '4*2=8'] Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,95 unequal: No Solution Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[4, 39, 17], Operations: ['34/2=17'] Exploring Operation: 4+17=21, Resulting Numbers: [39, 21] Generated Node #0,0,0: 95:[39, 21] Operation: 4+17=21 Exploring Operation: 39-17=22, Resulting Numbers: [4, 22] Generated Node #0,0,1: 95:[4, 22] Operation: 39-17=22 Exploring Operation: 39-4=35, Resulting Numbers: [17, 35] Generated Node #0,0,2: 95:[17, 35] Operation: 39-4=35 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 95:[4, 22], Operations: ['34/2=17', '39-17=22'] Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,95 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,95 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 95:[17, 35], Operations: ['34/2=17', '39-4=35'] Exploring Operation: 17*35=595, Resulting Numbers: [595] 595,95 unequal: No Solution Exploring Operation: 17+35=52, Resulting Numbers: [52] 52,95 unequal: No Solution Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 95:[39, 21], Operations: ['34/2=17', '4+17=21'] Exploring Operation: 39*21=819, Resulting Numbers: [819] 819,95 unequal: No Solution Exploring Operation: 39+21=60, Resulting Numbers: [60] 60,95 unequal: No Solution Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[4, 2, 73], Operations: ['34+39=73'] Exploring Operation: 4+73=77, Resulting Numbers: [2, 77] Generated Node #0,1,0: 95:[2, 77] Operation: 4+73=77 Exploring Operation: 2+73=75, Resulting Numbers: [4, 75] Generated Node #0,1,1: 95:[4, 75] Operation: 2+73=75 Exploring Operation: 4+2=6, Resulting Numbers: [73, 6] Generated Node #0,1,2: 95:[73, 6] Operation: 4+2=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 95:[2, 77], Operations: ['34+39=73', '4+73=77'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,95 unequal: No Solution Exploring Operation: 2+77=79, Resulting Numbers: [79] 79,95 unequal: No Solution Exploring Operation: 2*77=154, Resulting Numbers: [154] 154,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 95:[4, 75], Operations: ['34+39=73', '2+73=75'] Exploring Operation: 4+75=79, Resulting Numbers: [79] 79,95 unequal: No Solution Exploring Operation: 75-4=71, Resulting Numbers: [71] 71,95 unequal: No Solution Exploring Operation: 4*75=300, Resulting Numbers: [300] 300,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 95:[73, 6], Operations: ['34+39=73', '4+2=6'] Exploring Operation: 73*6=438, Resulting Numbers: [438] 438,95 unequal: No Solution Exploring Operation: 73-6=67, Resulting Numbers: [67] 67,95 unequal: No Solution Exploring Operation: 73+6=79, Resulting Numbers: [79] 79,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 43, 31, 29, 5 ]
19
[ "43-5=38", "31-29=2", "38/2=19" ]
Current State: 19:[43, 31, 29, 5], Operations: [] Exploring Operation: 43-5=38, Resulting Numbers: [31, 29, 38] Generated Node #2: [31, 29, 38] from Operation: 43-5=38 Current State: 19:[31, 29, 38], Operations: ['43-5=38'] Exploring Operation: 31-29=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 31-29=2 Current State: 19:[38, 2], Operations: ['43-5=38', '31-29=2'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[43, 31, 29, 5], Operations: [] Exploring Operation: 43-29=14, Resulting Numbers: [31, 5, 14] Generated Node #0,0: 19:[31, 5, 14] Operation: 43-29=14 Exploring Operation: 43-31=12, Resulting Numbers: [29, 5, 12] Generated Node #0,1: 19:[29, 5, 12] Operation: 43-31=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[31, 5, 14], Operations: ['43-29=14'] Exploring Operation: 5+14=19, Resulting Numbers: [31, 19] Generated Node #0,0,0: 19:[31, 19] Operation: 5+14=19 Exploring Operation: 31-5=26, Resulting Numbers: [14, 26] Generated Node #0,0,1: 19:[14, 26] Operation: 31-5=26 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[31, 19], Operations: ['43-29=14', '5+14=19'] Exploring Operation: 31+19=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 31-19=12, Resulting Numbers: [12] 12,19 unequal: No Solution No 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: 19:[14, 26], Operations: ['43-29=14', '31-5=26'] Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,19 unequal: No Solution Exploring Operation: 14+26=40, Resulting Numbers: [40] 40,19 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: 19:[29, 5, 12], Operations: ['43-31=12'] Exploring Operation: 5+12=17, Resulting Numbers: [29, 17] Generated Node #0,1,0: 19:[29, 17] Operation: 5+12=17 Exploring Operation: 29-5=24, Resulting Numbers: [12, 24] Generated Node #0,1,1: 19:[12, 24] Operation: 29-5=24 Moving to Node #0,1,0 Current State: 19:[29, 17], Operations: ['43-31=12', '5+12=17'] Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,19 unequal: No Solution Exploring Operation: 29+17=46, Resulting Numbers: [46] 46,19 unequal: No Solution Moving to Node #0,1,1 Current State: 19:[12, 24], Operations: ['43-31=12', '29-5=24'] Exploring Operation: 12+24=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,19 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
[ 84, 86, 92, 13 ]
81
[ "86-84=2", "92-13=79", "2+79=81" ]
Current State: 81:[84, 86, 92, 13], Operations: [] Exploring Operation: 86-84=2, Resulting Numbers: [92, 13, 2] Generated Node #2: [92, 13, 2] from Operation: 86-84=2 Current State: 81:[92, 13, 2], Operations: ['86-84=2'] Exploring Operation: 92-13=79, Resulting Numbers: [2, 79] Generated Node #3: [2, 79] from Operation: 92-13=79 Current State: 81:[2, 79], Operations: ['86-84=2', '92-13=79'] Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[84, 86, 92, 13], Operations: [] Exploring Operation: 92-86=6, Resulting Numbers: [84, 13, 6] Generated Node #0,0: 81:[84, 13, 6] Operation: 92-86=6 Exploring Operation: 92-84=8, Resulting Numbers: [86, 13, 8] Generated Node #0,1: 81:[86, 13, 8] Operation: 92-84=8 Moving to Node #0,0 Current State: 81:[84, 13, 6], Operations: ['92-86=6'] Exploring Operation: 13*6=78, Resulting Numbers: [84, 78] Generated Node #0,0,0: 81:[84, 78] Operation: 13*6=78 Exploring Operation: 13-6=7, Resulting Numbers: [84, 7] Generated Node #0,0,1: 81:[84, 7] Operation: 13-6=7 Moving to Node #0,1 Current State: 81:[86, 13, 8], Operations: ['92-84=8'] Exploring Operation: 86-8=78, Resulting Numbers: [13, 78] Generated Node #0,1,0: 81:[13, 78] Operation: 86-8=78 Exploring Operation: 13-8=5, Resulting Numbers: [86, 5] Generated Node #0,1,1: 81:[86, 5] Operation: 13-8=5 Moving to Node #0,0,1 Current State: 81:[84, 7], Operations: ['92-86=6', '13-6=7'] Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,81 unequal: No Solution Exploring Operation: 84-7=77, Resulting Numbers: [77] 77,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[84, 78], Operations: ['92-86=6', '13*6=78'] Exploring Operation: 84+78=162, Resulting Numbers: [162] 162,81 unequal: No Solution Exploring Operation: 84-78=6, Resulting Numbers: [6] 6,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[86, 5], Operations: ['92-84=8', '13-8=5'] Exploring Operation: 86+5=91, Resulting Numbers: [91] 91,81 unequal: No Solution Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[84, 86, 92, 13], Operations: [] Exploring Operation: 92-84=8, Resulting Numbers: [86, 13, 8] Generated Node #0,1: 81:[86, 13, 8] Operation: 92-84=8 Moving to Node #0,1 Current State: 81:[86, 13, 8], Operations: ['92-84=8'] Exploring Operation: 13-8=5, Resulting Numbers: [86, 5] Generated Node #0,1,1: 81:[86, 5] Operation: 13-8=5 Moving to Node #0,1,1 Current State: 81:[86, 5], Operations: ['92-84=8', '13-8=5'] Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 31, 51, 87, 51 ]
96
[ "31*87=2697", "51*51=2601", "2697-2601=96" ]
Current State: 96:[31, 51, 87, 51], Operations: [] Exploring Operation: 31*87=2697, Resulting Numbers: [51, 51, 2697] Generated Node #2: [51, 51, 2697] from Operation: 31*87=2697 Current State: 96:[51, 51, 2697], Operations: ['31*87=2697'] Exploring Operation: 51*51=2601, Resulting Numbers: [2697, 2601] Generated Node #3: [2697, 2601] from Operation: 51*51=2601 Current State: 96:[2697, 2601], Operations: ['31*87=2697', '51*51=2601'] Exploring Operation: 2697-2601=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[31, 51, 87, 51], Operations: [] Exploring Operation: 87-51=36, Resulting Numbers: [31, 51, 36] Generated Node #0,0: 96:[31, 51, 36] Operation: 87-51=36 Exploring Operation: 87-31=56, Resulting Numbers: [51, 51, 56] Generated Node #0,1: 96:[51, 51, 56] Operation: 87-31=56 Exploring Operation: 87-51=36, Resulting Numbers: [31, 51, 36] Generated Node #0,2: 96:[31, 51, 36] Operation: 87-51=36 Exploring Operation: 51-51=0, Resulting Numbers: [31, 87, 0] Generated Node #0,3: 96:[31, 87, 0] Operation: 51-51=0 Exploring Operation: 51/51=1, Resulting Numbers: [31, 87, 1] Generated Node #0,4: 96:[31, 87, 1] Operation: 51/51=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[31, 51, 36], Operations: ['87-51=36'] Exploring Operation: 36-31=5, Resulting Numbers: [51, 5] Generated Node #0,0,0: 96:[51, 5] Operation: 36-31=5 Exploring Operation: 51+36=87, Resulting Numbers: [31, 87] Generated Node #0,0,1: 96:[31, 87] Operation: 51+36=87 Exploring Operation: 51-36=15, Resulting Numbers: [31, 15] Generated Node #0,0,2: 96:[31, 15] Operation: 51-36=15 Exploring Operation: 51-31=20, Resulting Numbers: [36, 20] Generated Node #0,0,3: 96:[36, 20] Operation: 51-31=20 Exploring Operation: 31+51=82, Resulting Numbers: [36, 82] Generated Node #0,0,4: 96:[36, 82] Operation: 31+51=82 Moving to Node #0,0,2 Current State: 96:[31, 15], Operations: ['87-51=36', '51-36=15'] Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,96 unequal: No Solution Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[51, 5], Operations: ['87-51=36', '36-31=5'] Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[36, 20], Operations: ['87-51=36', '51-31=20'] Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,96 unequal: No Solution Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[31, 87], Operations: ['87-51=36', '51+36=87'] Exploring Operation: 87-31=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 31+87=118, Resulting Numbers: [118] 118,96 unequal: No Solution Exploring Operation: 31*87=2697, Resulting Numbers: [2697] 2697,96 unequal: No Solution Moving to Node #0,0,4 Current State: 96:[36, 82], Operations: ['87-51=36', '31+51=82'] Exploring Operation: 36*82=2952, Resulting Numbers: [2952] 2952,96 unequal: No Solution Exploring Operation: 36+82=118, Resulting Numbers: [118] 118,96 unequal: No Solution Exploring Operation: 82-36=46, Resulting Numbers: [46] 46,96 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 #0,2 Current State: 96:[31, 51, 36], Operations: ['87-51=36'] Exploring Operation: 31+51=82, Resulting Numbers: [36, 82] Generated Node #0,2,0: 96:[36, 82] Operation: 31+51=82 Exploring Operation: 51-31=20, Resulting Numbers: [36, 20] Generated Node #0,2,1: 96:[36, 20] Operation: 51-31=20 Exploring Operation: 51-36=15, Resulting Numbers: [31, 15] Generated Node #0,2,2: 96:[31, 15] Operation: 51-36=15 Exploring Operation: 36-31=5, Resulting Numbers: [51, 5] Generated Node #0,2,3: 96:[51, 5] Operation: 36-31=5 Exploring Operation: 51+36=87, Resulting Numbers: [31, 87] Generated Node #0,2,4: 96:[31, 87] Operation: 51+36=87 Moving to Node #0,2,2 Current State: 96:[31, 15], Operations: ['87-51=36', '51-36=15'] Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,96 unequal: No Solution Moving to Node #0,2,3 Current State: 96:[51, 5], Operations: ['87-51=36', '36-31=5'] Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,96 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[36, 20], Operations: ['87-51=36', '51-31=20'] Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,96 unequal: No Solution Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,96 unequal: No Solution Moving to Node #0,2,4 Current State: 96:[31, 87], Operations: ['87-51=36', '51+36=87'] Exploring Operation: 87-31=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 31*87=2697, Resulting Numbers: [2697] 2697,96 unequal: No Solution Exploring Operation: 31+87=118, Resulting Numbers: [118] 118,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[36, 82], Operations: ['87-51=36', '31+51=82'] Exploring Operation: 36*82=2952, Resulting Numbers: [2952] 2952,96 unequal: No Solution Exploring Operation: 36+82=118, Resulting Numbers: [118] 118,96 unequal: No Solution Exploring Operation: 82-36=46, Resulting Numbers: [46] 46,96 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 #0,4 Current State: 96:[31, 87, 1], Operations: ['51/51=1'] Exploring Operation: 31*1=31, Resulting Numbers: [87, 31] Generated Node #0,4,0: 96:[87, 31] Operation: 31*1=31 Exploring Operation: 87+1=88, Resulting Numbers: [31, 88] Generated Node #0,4,1: 96:[31, 88] Operation: 87+1=88 Exploring Operation: 31+1=32, Resulting Numbers: [87, 32] Generated Node #0,4,2: 96:[87, 32] Operation: 31+1=32 Exploring Operation: 87-31=56, Resulting Numbers: [1, 56] Generated Node #0,4,3: 96:[1, 56] Operation: 87-31=56 Exploring Operation: 31/1=31, Resulting Numbers: [87, 31] Generated Node #0,4,4: 96:[87, 31] Operation: 31/1=31 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 96:[31, 88], Operations: ['51/51=1', '87+1=88'] Exploring Operation: 31+88=119, Resulting Numbers: [119] 119,96 unequal: No Solution Exploring Operation: 88-31=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 31*88=2728, Resulting Numbers: [2728] 2728,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 96:[87, 32], Operations: ['51/51=1', '31+1=32'] Exploring Operation: 87*32=2784, Resulting Numbers: [2784] 2784,96 unequal: No Solution Exploring Operation: 87-32=55, Resulting Numbers: [55] 55,96 unequal: No Solution Exploring Operation: 87+32=119, Resulting Numbers: [119] 119,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 96:[1, 56], Operations: ['51/51=1', '87-31=56'] Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,96 unequal: No Solution Exploring Operation: 1*56=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 1+56=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 96:[87, 31], Operations: ['51/51=1', '31*1=31'] Exploring Operation: 87*31=2697, Resulting Numbers: [2697] 2697,96 unequal: No Solution Exploring Operation: 87+31=118, Resulting Numbers: [118] 118,96 unequal: No Solution Exploring Operation: 87-31=56, Resulting Numbers: [56] 56,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 96:[87, 31], Operations: ['51/51=1', '31/1=31'] Exploring Operation: 87+31=118, Resulting Numbers: [118] 118,96 unequal: No Solution Exploring Operation: 87*31=2697, Resulting Numbers: [2697] 2697,96 unequal: No Solution Exploring Operation: 87-31=56, Resulting Numbers: [56] 56,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 96:[31, 87, 0], Operations: ['51-51=0'] Exploring Operation: 31-0=31, Resulting Numbers: [87, 31] Generated Node #0,3,0: 96:[87, 31] Operation: 31-0=31 Exploring Operation: 31+0=31, Resulting Numbers: [87, 31] Generated Node #0,3,1: 96:[87, 31] Operation: 31+0=31 Exploring Operation: 87-31=56, Resulting Numbers: [0, 56] Generated Node #0,3,2: 96:[0, 56] Operation: 87-31=56 Exploring Operation: 87*0=0, Resulting Numbers: [31, 0] Generated Node #0,3,3: 96:[31, 0] Operation: 87*0=0 Exploring Operation: 87+0=87, Resulting Numbers: [31, 87] Generated Node #0,3,4: 96:[31, 87] Operation: 87+0=87 Moving to Node #0,3,3 Current State: 96:[31, 0], Operations: ['51-51=0', '87*0=0'] Exploring Operation: 31+0=31, Resulting Numbers: [31] 31,96 unequal: No Solution Exploring Operation: 31-0=31, Resulting Numbers: [31] 31,96 unequal: No Solution Exploring Operation: 31*0=0, Resulting Numbers: [0] 0,96 unequal: No Solution Moving to Node #0,3,1 Current State: 96:[87, 31], Operations: ['51-51=0', '31+0=31'] Exploring Operation: 87+31=118, Resulting Numbers: [118] 118,96 unequal: No Solution Exploring Operation: 87-31=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 87*31=2697, Resulting Numbers: [2697] 2697,96 unequal: No Solution Moving to Node #0,3,4 Current State: 96:[31, 87], Operations: ['51-51=0', '87+0=87'] Exploring Operation: 87-31=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 31+87=118, Resulting Numbers: [118] 118,96 unequal: No Solution Exploring Operation: 31*87=2697, Resulting Numbers: [2697] 2697,96 unequal: No Solution Moving to Node #0,3,0 Current State: 96:[87, 31], Operations: ['51-51=0', '31-0=31'] Exploring Operation: 87+31=118, Resulting Numbers: [118] 118,96 unequal: No Solution Exploring Operation: 87*31=2697, Resulting Numbers: [2697] 2697,96 unequal: No Solution Exploring Operation: 87-31=56, Resulting Numbers: [56] 56,96 unequal: No Solution Moving to Node #0,3,2 Current State: 96:[0, 56], Operations: ['51-51=0', '87-31=56'] Exploring Operation: 0*56=0, Resulting Numbers: [0] 0,96 unequal: No Solution Exploring Operation: 56-0=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 0+56=56, Resulting Numbers: [56] 56,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[51, 51, 56], Operations: ['87-31=56'] Exploring Operation: 51-51=0, Resulting Numbers: [56, 0] Generated Node #0,1,0: 96:[56, 0] Operation: 51-51=0 Exploring Operation: 51/51=1, Resulting Numbers: [56, 1] Generated Node #0,1,1: 96:[56, 1] Operation: 51/51=1 Exploring Operation: 56-51=5, Resulting Numbers: [51, 5] Generated Node #0,1,2: 96:[51, 5] Operation: 56-51=5 Exploring Operation: 56-51=5, Resulting Numbers: [51, 5] Generated Node #0,1,3: 96:[51, 5] Operation: 56-51=5 Exploring Operation: 51+51=102, Resulting Numbers: [56, 102] Generated Node #0,1,4: 96:[56, 102] Operation: 51+51=102 Moving to Node #0,1,2 Current State: 96:[51, 5], Operations: ['87-31=56', '56-51=5'] Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,96 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,96 unequal: No Solution Moving to Node #0,1,3 Current State: 96:[51, 5], Operations: ['87-31=56', '56-51=5'] Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[56, 1], Operations: ['87-31=56', '51/51=1'] Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[56, 0], Operations: ['87-31=56', '51-51=0'] Exploring Operation: 56*0=0, Resulting Numbers: [0] 0,96 unequal: No Solution Exploring Operation: 56-0=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 56+0=56, Resulting Numbers: [56] 56,96 unequal: No Solution Moving to Node #0,1,4 Current State: 96:[56, 102], Operations: ['87-31=56', '51+51=102'] Exploring Operation: 102-56=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 56+102=158, Resulting Numbers: [158] 158,96 unequal: No Solution Exploring Operation: 56*102=5712, Resulting Numbers: [5712] 5712,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 12, 32, 19, 35 ]
24
[ "12*32=384", "35-19=16", "384/16=24" ]
Current State: 24:[12, 32, 19, 35], Operations: [] Exploring Operation: 12*32=384, Resulting Numbers: [19, 35, 384] Generated Node #2: [19, 35, 384] from Operation: 12*32=384 Current State: 24:[19, 35, 384], Operations: ['12*32=384'] Exploring Operation: 35-19=16, Resulting Numbers: [384, 16] Generated Node #3: [384, 16] from Operation: 35-19=16 Current State: 24:[384, 16], Operations: ['12*32=384', '35-19=16'] Exploring Operation: 384/16=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[12, 32, 19, 35], Operations: [] Exploring Operation: 32-19=13, Resulting Numbers: [12, 35, 13] Generated Node #0,0: 24:[12, 35, 13] Operation: 32-19=13 Exploring Operation: 35-32=3, Resulting Numbers: [12, 19, 3] Generated Node #0,1: 24:[12, 19, 3] Operation: 35-32=3 Exploring Operation: 35-19=16, Resulting Numbers: [12, 32, 16] Generated Node #0,2: 24:[12, 32, 16] Operation: 35-19=16 Moving to Node #0,1 Current State: 24:[12, 19, 3], Operations: ['35-32=3'] Exploring Operation: 19-3=16, Resulting Numbers: [12, 16] Generated Node #0,1,0: 24:[12, 16] Operation: 19-3=16 Exploring Operation: 19+3=22, Resulting Numbers: [12, 22] Generated Node #0,1,1: 24:[12, 22] Operation: 19+3=22 Exploring Operation: 19-12=7, Resulting Numbers: [3, 7] Generated Node #0,1,2: 24:[3, 7] Operation: 19-12=7 Moving to Node #0,0 Current State: 24:[12, 35, 13], Operations: ['32-19=13'] Exploring Operation: 35-13=22, Resulting Numbers: [12, 22] Generated Node #0,0,0: 24:[12, 22] Operation: 35-13=22 Exploring Operation: 12+13=25, Resulting Numbers: [35, 25] Generated Node #0,0,1: 24:[35, 25] Operation: 12+13=25 Exploring Operation: 35-12=23, Resulting Numbers: [13, 23] Generated Node #0,0,2: 24:[13, 23] Operation: 35-12=23 Moving to Node #0,2 Current State: 24:[12, 32, 16], Operations: ['35-19=16'] Exploring Operation: 32-16=16, Resulting Numbers: [12, 16] Generated Node #0,2,0: 24:[12, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [12, 2] Generated Node #0,2,1: 24:[12, 2] Operation: 32/16=2 Exploring Operation: 32-12=20, Resulting Numbers: [16, 20] Generated Node #0,2,2: 24:[16, 20] Operation: 32-12=20 Moving to Node #0,2,1 Current State: 24:[12, 2], Operations: ['35-19=16', '32/16=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[12, 32, 19, 35], Operations: [] Exploring Operation: 35-19=16, Resulting Numbers: [12, 32, 16] Generated Node #0,2: 24:[12, 32, 16] Operation: 35-19=16 Moving to Node #0,2 Current State: 24:[12, 32, 16], Operations: ['35-19=16'] Exploring Operation: 32/16=2, Resulting Numbers: [12, 2] Generated Node #0,2,1: 24:[12, 2] Operation: 32/16=2 Moving to Node #0,2,1 Current State: 24:[12, 2], Operations: ['35-19=16', '32/16=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
0.985243
hs_3
sum_heuristic
[ 34, 17, 79, 46 ]
84
[ "34+17=51", "79-46=33", "51+33=84" ]
Current State: 84:[34, 17, 79, 46], Operations: [] Exploring Operation: 34+17=51, Resulting Numbers: [79, 46, 51] Generated Node #2: [79, 46, 51] from Operation: 34+17=51 Current State: 84:[79, 46, 51], Operations: ['34+17=51'] Exploring Operation: 79-46=33, Resulting Numbers: [51, 33] Generated Node #3: [51, 33] from Operation: 79-46=33 Current State: 84:[51, 33], Operations: ['34+17=51', '79-46=33'] Exploring Operation: 51+33=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[34, 17, 79, 46], Operations: [] Exploring Operation: 46-34=12, Resulting Numbers: [17, 79, 12] Generated Node #0,0: 84:[17, 79, 12] Operation: 46-34=12 Exploring Operation: 79-34=45, Resulting Numbers: [17, 46, 45] Generated Node #0,1: 84:[17, 46, 45] Operation: 79-34=45 Exploring Operation: 34/17=2, Resulting Numbers: [79, 46, 2] Generated Node #0,2: 84:[79, 46, 2] Operation: 34/17=2 Moving to Node #0,0 Current State: 84:[17, 79, 12], Operations: ['46-34=12'] Exploring Operation: 17-12=5, Resulting Numbers: [79, 5] Generated Node #0,0,0: 84:[79, 5] Operation: 17-12=5 Exploring Operation: 17+12=29, Resulting Numbers: [79, 29] Generated Node #0,0,1: 84:[79, 29] Operation: 17+12=29 Exploring Operation: 79+12=91, Resulting Numbers: [17, 91] Generated Node #0,0,2: 84:[17, 91] Operation: 79+12=91 Moving to Node #0,2 Current State: 84:[79, 46, 2], Operations: ['34/17=2'] Exploring Operation: 79-46=33, Resulting Numbers: [2, 33] Generated Node #0,2,0: 84:[2, 33] Operation: 79-46=33 Exploring Operation: 46-2=44, Resulting Numbers: [79, 44] Generated Node #0,2,1: 84:[79, 44] Operation: 46-2=44 Exploring Operation: 79+2=81, Resulting Numbers: [46, 81] Generated Node #0,2,2: 84:[46, 81] Operation: 79+2=81 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[2, 33], Operations: ['34/17=2', '79-46=33'] Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,84 unequal: No Solution Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,84 unequal: No Solution Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,84 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 #0,2,1 Current State: 84:[79, 44], Operations: ['34/17=2', '46-2=44'] Exploring Operation: 79+44=123, Resulting Numbers: [123] 123,84 unequal: No Solution Exploring Operation: 79-44=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 79*44=3476, Resulting Numbers: [3476] 3476,84 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 #0,2,2 Current State: 84:[46, 81], Operations: ['34/17=2', '79+2=81'] Exploring Operation: 46*81=3726, Resulting Numbers: [3726] 3726,84 unequal: No Solution Exploring Operation: 81-46=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 46+81=127, Resulting Numbers: [127] 127,84 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: 84:[17, 46, 45], Operations: ['79-34=45'] Exploring Operation: 46-45=1, Resulting Numbers: [17, 1] Generated Node #0,1,0: 84:[17, 1] Operation: 46-45=1 Exploring Operation: 45-17=28, Resulting Numbers: [46, 28] Generated Node #0,1,1: 84:[46, 28] Operation: 45-17=28 Exploring Operation: 46-17=29, Resulting Numbers: [45, 29] Generated Node #0,1,2: 84:[45, 29] Operation: 46-17=29 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 84:[17, 1], Operations: ['79-34=45', '46-45=1'] Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,84 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[46, 28], Operations: ['79-34=45', '45-17=28'] Exploring Operation: 46+28=74, Resulting Numbers: [74] 74,84 unequal: No Solution Exploring Operation: 46*28=1288, Resulting Numbers: [1288] 1288,84 unequal: No Solution Exploring Operation: 46-28=18, Resulting Numbers: [18] 18,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 84:[45, 29], Operations: ['79-34=45', '46-17=29'] Exploring Operation: 45+29=74, Resulting Numbers: [74] 74,84 unequal: No Solution Exploring Operation: 45*29=1305, Resulting Numbers: [1305] 1305,84 unequal: No Solution Exploring Operation: 45-29=16, Resulting Numbers: [16] 16,84 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: 84:[79, 5], Operations: ['46-34=12', '17-12=5'] Exploring Operation: 79+5=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[34, 17, 79, 46], Operations: [] Exploring Operation: 46-34=12, Resulting Numbers: [17, 79, 12] Generated Node #0,0: 84:[17, 79, 12] Operation: 46-34=12 Moving to Node #0,0 Current State: 84:[17, 79, 12], Operations: ['46-34=12'] Exploring Operation: 17-12=5, Resulting Numbers: [79, 5] Generated Node #0,0,0: 84:[79, 5] Operation: 17-12=5 Moving to Node #0,0,0 Current State: 84:[79, 5], Operations: ['46-34=12', '17-12=5'] Exploring Operation: 79+5=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.969618
hs_3
mult_heuristic
[ 62, 25, 34, 17 ]
20
[ "62-25=37", "34-17=17", "37-17=20" ]
Current State: 20:[62, 25, 34, 17], Operations: [] Exploring Operation: 62-25=37, Resulting Numbers: [34, 17, 37] Generated Node #2: [34, 17, 37] from Operation: 62-25=37 Current State: 20:[34, 17, 37], Operations: ['62-25=37'] Exploring Operation: 34-17=17, Resulting Numbers: [37, 17] Generated Node #3: [37, 17] from Operation: 34-17=17 Current State: 20:[37, 17], Operations: ['62-25=37', '34-17=17'] Exploring Operation: 37-17=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[62, 25, 34, 17], Operations: [] Exploring Operation: 62-25=37, Resulting Numbers: [34, 17, 37] Generated Node #0,0: 20:[34, 17, 37] Operation: 62-25=37 Exploring Operation: 62-34=28, Resulting Numbers: [25, 17, 28] Generated Node #0,1: 20:[25, 17, 28] Operation: 62-34=28 Exploring Operation: 62-17=45, Resulting Numbers: [25, 34, 45] Generated Node #0,2: 20:[25, 34, 45] Operation: 62-17=45 Moving to Node #0,1 Current State: 20:[25, 17, 28], Operations: ['62-34=28'] Exploring Operation: 28-25=3, Resulting Numbers: [17, 3] Generated Node #0,1,0: 20:[17, 3] Operation: 28-25=3 Exploring Operation: 25-17=8, Resulting Numbers: [28, 8] Generated Node #0,1,1: 20:[28, 8] Operation: 25-17=8 Exploring Operation: 28-17=11, Resulting Numbers: [25, 11] Generated Node #0,1,2: 20:[25, 11] Operation: 28-17=11 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 20:[17, 3], Operations: ['62-34=28', '28-25=3'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,20 unequal: No Solution Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,20 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[62, 25, 34, 17], Operations: [] Exploring Operation: 62-34=28, Resulting Numbers: [25, 17, 28] Generated Node #0,1: 20:[25, 17, 28] Operation: 62-34=28 Moving to Node #0,1 Current State: 20:[25, 17, 28], Operations: ['62-34=28'] Exploring Operation: 28-25=3, Resulting Numbers: [17, 3] Generated Node #0,1,0: 20:[17, 3] Operation: 28-25=3 Moving to Node #0,1,0 Current State: 20:[17, 3], Operations: ['62-34=28', '28-25=3'] Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 4, 18, 20, 41 ]
39
[ "4+18=22", "20+41=61", "61-22=39" ]
Current State: 39:[4, 18, 20, 41], Operations: [] Exploring Operation: 4+18=22, Resulting Numbers: [20, 41, 22] Generated Node #2: [20, 41, 22] from Operation: 4+18=22 Current State: 39:[20, 41, 22], Operations: ['4+18=22'] Exploring Operation: 20+41=61, Resulting Numbers: [22, 61] Generated Node #3: [22, 61] from Operation: 20+41=61 Current State: 39:[22, 61], Operations: ['4+18=22', '20+41=61'] Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[4, 18, 20, 41], Operations: [] Exploring Operation: 20-18=2, Resulting Numbers: [4, 41, 2] Generated Node #0,0: 39:[4, 41, 2] Operation: 20-18=2 Exploring Operation: 18+20=38, Resulting Numbers: [4, 41, 38] Generated Node #0,1: 39:[4, 41, 38] Operation: 18+20=38 Exploring Operation: 20/4=5, Resulting Numbers: [18, 41, 5] Generated Node #0,2: 39:[18, 41, 5] Operation: 20/4=5 Exploring Operation: 18-4=14, Resulting Numbers: [20, 41, 14] Generated Node #0,3: 39:[20, 41, 14] Operation: 18-4=14 Exploring Operation: 20-4=16, Resulting Numbers: [18, 41, 16] Generated Node #0,4: 39:[18, 41, 16] Operation: 20-4=16 Moving to Node #0,0 Current State: 39:[4, 41, 2], Operations: ['20-18=2'] Exploring Operation: 41-4=37, Resulting Numbers: [2, 37] Generated Node #0,0,0: 39:[2, 37] Operation: 41-4=37 Exploring Operation: 41-2=39, Resulting Numbers: [4, 39] Generated Node #0,0,1: 39:[4, 39] Operation: 41-2=39 Exploring Operation: 4/2=2, Resulting Numbers: [41, 2] Generated Node #0,0,2: 39:[41, 2] Operation: 4/2=2 Exploring Operation: 4+2=6, Resulting Numbers: [41, 6] Generated Node #0,0,3: 39:[41, 6] Operation: 4+2=6 Exploring Operation: 4-2=2, Resulting Numbers: [41, 2] Generated Node #0,0,4: 39:[41, 2] Operation: 4-2=2 Moving to Node #0,1 Current State: 39:[4, 41, 38], Operations: ['18+20=38'] Exploring Operation: 4+41=45, Resulting Numbers: [38, 45] Generated Node #0,1,0: 39:[38, 45] Operation: 4+41=45 Exploring Operation: 41-4=37, Resulting Numbers: [38, 37] Generated Node #0,1,1: 39:[38, 37] Operation: 41-4=37 Exploring Operation: 4+38=42, Resulting Numbers: [41, 42] Generated Node #0,1,2: 39:[41, 42] Operation: 4+38=42 Exploring Operation: 41-38=3, Resulting Numbers: [4, 3] Generated Node #0,1,3: 39:[4, 3] Operation: 41-38=3 Exploring Operation: 38-4=34, Resulting Numbers: [41, 34] Generated Node #0,1,4: 39:[41, 34] Operation: 38-4=34 Moving to Node #0,2 Current State: 39:[18, 41, 5], Operations: ['20/4=5'] Exploring Operation: 18+5=23, Resulting Numbers: [41, 23] Generated Node #0,2,0: 39:[41, 23] Operation: 18+5=23 Exploring Operation: 41+5=46, Resulting Numbers: [18, 46] Generated Node #0,2,1: 39:[18, 46] Operation: 41+5=46 Exploring Operation: 41-18=23, Resulting Numbers: [5, 23] Generated Node #0,2,2: 39:[5, 23] Operation: 41-18=23 Exploring Operation: 18-5=13, Resulting Numbers: [41, 13] Generated Node #0,2,3: 39:[41, 13] Operation: 18-5=13 Exploring Operation: 41-5=36, Resulting Numbers: [18, 36] Generated Node #0,2,4: 39:[18, 36] Operation: 41-5=36 Moving to Node #0,3 Current State: 39:[20, 41, 14], Operations: ['18-4=14'] Exploring Operation: 41-20=21, Resulting Numbers: [14, 21] Generated Node #0,3,0: 39:[14, 21] Operation: 41-20=21 Exploring Operation: 20+14=34, Resulting Numbers: [41, 34] Generated Node #0,3,1: 39:[41, 34] Operation: 20+14=34 Exploring Operation: 20+41=61, Resulting Numbers: [14, 61] Generated Node #0,3,2: 39:[14, 61] Operation: 20+41=61 Exploring Operation: 41-14=27, Resulting Numbers: [20, 27] Generated Node #0,3,3: 39:[20, 27] Operation: 41-14=27 Exploring Operation: 20-14=6, Resulting Numbers: [41, 6] Generated Node #0,3,4: 39:[41, 6] Operation: 20-14=6 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 39:[41, 6], Operations: ['18-4=14', '20-14=6'] Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 41*6=246, Resulting Numbers: [246] 246,39 unequal: No Solution Exploring Operation: 41+6=47, Resulting Numbers: [47] 47,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 39:[41, 34], Operations: ['18-4=14', '20+14=34'] Exploring Operation: 41+34=75, Resulting Numbers: [75] 75,39 unequal: No Solution Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 41*34=1394, Resulting Numbers: [1394] 1394,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 39:[14, 21], Operations: ['18-4=14', '41-20=21'] Exploring Operation: 14*21=294, Resulting Numbers: [294] 294,39 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 14+21=35, Resulting Numbers: [35] 35,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 39:[20, 27], Operations: ['18-4=14', '41-14=27'] Exploring Operation: 20*27=540, Resulting Numbers: [540] 540,39 unequal: No Solution Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 20+27=47, Resulting Numbers: [47] 47,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 39:[14, 61], Operations: ['18-4=14', '20+41=61'] Exploring Operation: 61-14=47, Resulting Numbers: [47] 47,39 unequal: No Solution Exploring Operation: 14*61=854, Resulting Numbers: [854] 854,39 unequal: No Solution Exploring Operation: 14+61=75, Resulting Numbers: [75] 75,39 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: 39:[18, 41, 16], Operations: ['20-4=16'] Exploring Operation: 18-16=2, Resulting Numbers: [41, 2] Generated Node #0,4,0: 39:[41, 2] Operation: 18-16=2 Exploring Operation: 41-16=25, Resulting Numbers: [18, 25] Generated Node #0,4,1: 39:[18, 25] Operation: 41-16=25 Exploring Operation: 18+16=34, Resulting Numbers: [41, 34] Generated Node #0,4,2: 39:[41, 34] Operation: 18+16=34 Exploring Operation: 41-18=23, Resulting Numbers: [16, 23] Generated Node #0,4,3: 39:[16, 23] Operation: 41-18=23 Exploring Operation: 18+41=59, Resulting Numbers: [16, 59] Generated Node #0,4,4: 39:[16, 59] Operation: 18+41=59 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 39:[41, 2], Operations: ['20-4=16', '18-16=2'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[4, 18, 20, 41], Operations: [] Exploring Operation: 20-4=16, Resulting Numbers: [18, 41, 16] Generated Node #0,4: 39:[18, 41, 16] Operation: 20-4=16 Moving to Node #0,4 Current State: 39:[18, 41, 16], Operations: ['20-4=16'] Exploring Operation: 18-16=2, Resulting Numbers: [41, 2] Generated Node #0,4,0: 39:[41, 2] Operation: 18-16=2 Moving to Node #0,4,0 Current State: 39:[41, 2], Operations: ['20-4=16', '18-16=2'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.956597
hs_5
mult_heuristic
[ 47, 56, 3, 79 ]
98
[ "47+79=126", "126/3=42", "56+42=98" ]
Current State: 98:[47, 56, 3, 79], Operations: [] Exploring Operation: 47+79=126, Resulting Numbers: [56, 3, 126] Generated Node #2: [56, 3, 126] from Operation: 47+79=126 Current State: 98:[56, 3, 126], Operations: ['47+79=126'] Exploring Operation: 126/3=42, Resulting Numbers: [56, 42] Generated Node #3: [56, 42] from Operation: 126/3=42 Current State: 98:[56, 42], Operations: ['47+79=126', '126/3=42'] Exploring Operation: 56+42=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[47, 56, 3, 79], Operations: [] Exploring Operation: 56-47=9, Resulting Numbers: [3, 79, 9] Generated Node #0,0: 98:[3, 79, 9] Operation: 56-47=9 Exploring Operation: 79-47=32, Resulting Numbers: [56, 3, 32] Generated Node #0,1: 98:[56, 3, 32] Operation: 79-47=32 Exploring Operation: 79-56=23, Resulting Numbers: [47, 3, 23] Generated Node #0,2: 98:[47, 3, 23] Operation: 79-56=23 Exploring Operation: 47+56=103, Resulting Numbers: [3, 79, 103] Generated Node #0,3: 98:[3, 79, 103] Operation: 47+56=103 Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[47, 3, 23], Operations: ['79-56=23'] Exploring Operation: 47-23=24, Resulting Numbers: [3, 24] Generated Node #0,2,0: 98:[3, 24] Operation: 47-23=24 Exploring Operation: 47-3=44, Resulting Numbers: [23, 44] Generated Node #0,2,1: 98:[23, 44] Operation: 47-3=44 Exploring Operation: 47+3=50, Resulting Numbers: [23, 50] Generated Node #0,2,2: 98:[23, 50] Operation: 47+3=50 Exploring Operation: 23-3=20, Resulting Numbers: [47, 20] Generated Node #0,2,3: 98:[47, 20] Operation: 23-3=20 Moving to Node #0,2,3 Current State: 98:[47, 20], Operations: ['79-56=23', '23-3=20'] Exploring Operation: 47+20=67, Resulting Numbers: [67] 67,98 unequal: No Solution Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,98 unequal: No Solution Exploring Operation: 47*20=940, Resulting Numbers: [940] 940,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[23, 50], Operations: ['79-56=23', '47+3=50'] Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,98 unequal: No Solution Exploring Operation: 23*50=1150, Resulting Numbers: [1150] 1150,98 unequal: No Solution Exploring Operation: 23+50=73, Resulting Numbers: [73] 73,98 unequal: No Solution Moving to Node #0,2,0 Current State: 98:[3, 24], Operations: ['79-56=23', '47-23=24'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,98 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,98 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[23, 44], Operations: ['79-56=23', '47-3=44'] Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 23*44=1012, Resulting Numbers: [1012] 1012,98 unequal: No Solution Exploring Operation: 23+44=67, Resulting Numbers: [67] 67,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[3, 79, 9], Operations: ['56-47=9'] Exploring Operation: 9-3=6, Resulting Numbers: [79, 6] Generated Node #0,0,0: 98:[79, 6] Operation: 9-3=6 Exploring Operation: 3+79=82, Resulting Numbers: [9, 82] Generated Node #0,0,1: 98:[9, 82] Operation: 3+79=82 Exploring Operation: 9/3=3, Resulting Numbers: [79, 3] Generated Node #0,0,2: 98:[79, 3] Operation: 9/3=3 Exploring Operation: 79+9=88, Resulting Numbers: [3, 88] Generated Node #0,0,3: 98:[3, 88] Operation: 79+9=88 Moving to Node #0,0,3 Current State: 98:[3, 88], Operations: ['56-47=9', '79+9=88'] Exploring Operation: 3+88=91, Resulting Numbers: [91] 91,98 unequal: No Solution Exploring Operation: 3*88=264, Resulting Numbers: [264] 264,98 unequal: No Solution Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[9, 82], Operations: ['56-47=9', '3+79=82'] Exploring Operation: 82-9=73, Resulting Numbers: [73] 73,98 unequal: No Solution Exploring Operation: 9+82=91, Resulting Numbers: [91] 91,98 unequal: No Solution Exploring Operation: 9*82=738, Resulting Numbers: [738] 738,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[79, 3], Operations: ['56-47=9', '9/3=3'] Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,98 unequal: No Solution Exploring Operation: 79*3=237, Resulting Numbers: [237] 237,98 unequal: No Solution Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[79, 6], Operations: ['56-47=9', '9-3=6'] Exploring Operation: 79*6=474, Resulting Numbers: [474] 474,98 unequal: No Solution Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,98 unequal: No Solution Exploring Operation: 79+6=85, Resulting Numbers: [85] 85,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[56, 3, 32], Operations: ['79-47=32'] Exploring Operation: 3*32=96, Resulting Numbers: [56, 96] Generated Node #0,1,0: 98:[56, 96] Operation: 3*32=96 Exploring Operation: 56+32=88, Resulting Numbers: [3, 88] Generated Node #0,1,1: 98:[3, 88] Operation: 56+32=88 Exploring Operation: 56-3=53, Resulting Numbers: [32, 53] Generated Node #0,1,2: 98:[32, 53] Operation: 56-3=53 Exploring Operation: 56-32=24, Resulting Numbers: [3, 24] Generated Node #0,1,3: 98:[3, 24] Operation: 56-32=24 Moving to Node #0,1,0 Current State: 98:[56, 96], Operations: ['79-47=32', '3*32=96'] Exploring Operation: 96-56=40, Resulting Numbers: [40] 40,98 unequal: No Solution Exploring Operation: 56*96=5376, Resulting Numbers: [5376] 5376,98 unequal: No Solution Exploring Operation: 56+96=152, Resulting Numbers: [152] 152,98 unequal: No Solution Moving to Node #0,1,3 Current State: 98:[3, 24], Operations: ['79-47=32', '56-32=24'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,98 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,98 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[3, 88], Operations: ['79-47=32', '56+32=88'] Exploring Operation: 3+88=91, Resulting Numbers: [91] 91,98 unequal: No Solution Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,98 unequal: No Solution Exploring Operation: 3*88=264, Resulting Numbers: [264] 264,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[32, 53], Operations: ['79-47=32', '56-3=53'] Exploring Operation: 32+53=85, Resulting Numbers: [85] 85,98 unequal: No Solution Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 32*53=1696, Resulting Numbers: [1696] 1696,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 98:[3, 79, 103], Operations: ['47+56=103'] Exploring Operation: 79-3=76, Resulting Numbers: [103, 76] Generated Node #0,3,0: 98:[103, 76] Operation: 79-3=76 Exploring Operation: 3+79=82, Resulting Numbers: [103, 82] Generated Node #0,3,1: 98:[103, 82] Operation: 3+79=82 Exploring Operation: 103-79=24, Resulting Numbers: [3, 24] Generated Node #0,3,2: 98:[3, 24] Operation: 103-79=24 Exploring Operation: 103-3=100, Resulting Numbers: [79, 100] Generated Node #0,3,3: 98:[79, 100] Operation: 103-3=100 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 98:[3, 24], Operations: ['47+56=103', '103-79=24'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,98 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,98 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 98:[103, 82], Operations: ['47+56=103', '3+79=82'] Exploring Operation: 103*82=8446, Resulting Numbers: [8446] 8446,98 unequal: No Solution Exploring Operation: 103+82=185, Resulting Numbers: [185] 185,98 unequal: No Solution Exploring Operation: 103-82=21, Resulting Numbers: [21] 21,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 98:[79, 100], Operations: ['47+56=103', '103-3=100'] Exploring Operation: 100-79=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 79+100=179, Resulting Numbers: [179] 179,98 unequal: No Solution Exploring Operation: 79*100=7900, Resulting Numbers: [7900] 7900,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 98:[103, 76], Operations: ['47+56=103', '79-3=76'] Exploring Operation: 103-76=27, Resulting Numbers: [27] 27,98 unequal: No Solution Exploring Operation: 103+76=179, Resulting Numbers: [179] 179,98 unequal: No Solution Exploring Operation: 103*76=7828, Resulting Numbers: [7828] 7828,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 73, 48, 26, 95 ]
91
[ "73+95=168", "26*168=4368", "4368/48=91" ]
Current State: 91:[73, 48, 26, 95], Operations: [] Exploring Operation: 73+95=168, Resulting Numbers: [48, 26, 168] Generated Node #2: [48, 26, 168] from Operation: 73+95=168 Current State: 91:[48, 26, 168], Operations: ['73+95=168'] Exploring Operation: 26*168=4368, Resulting Numbers: [48, 4368] Generated Node #3: [48, 4368] from Operation: 26*168=4368 Current State: 91:[48, 4368], Operations: ['73+95=168', '26*168=4368'] Exploring Operation: 4368/48=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[73, 48, 26, 95], Operations: [] Exploring Operation: 73-48=25, Resulting Numbers: [26, 95, 25] Generated Node #0,0: 91:[26, 95, 25] Operation: 73-48=25 Exploring Operation: 48-26=22, Resulting Numbers: [73, 95, 22] Generated Node #0,1: 91:[73, 95, 22] Operation: 48-26=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[26, 95, 25], Operations: ['73-48=25'] Exploring Operation: 26-25=1, Resulting Numbers: [95, 1] Generated Node #0,0,0: 91:[95, 1] Operation: 26-25=1 Exploring Operation: 95-26=69, Resulting Numbers: [25, 69] Generated Node #0,0,1: 91:[25, 69] Operation: 95-26=69 Moving to Node #0,0,0 Current State: 91:[95, 1], Operations: ['73-48=25', '26-25=1'] Exploring Operation: 95-1=94, Resulting Numbers: [94] 94,91 unequal: No Solution Exploring Operation: 95*1=95, Resulting Numbers: [95] 95,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[25, 69], Operations: ['73-48=25', '95-26=69'] Exploring Operation: 25+69=94, Resulting Numbers: [94] 94,91 unequal: No Solution Exploring Operation: 69-25=44, Resulting Numbers: [44] 44,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[73, 95, 22], Operations: ['48-26=22'] Exploring Operation: 73+22=95, Resulting Numbers: [95, 95] Generated Node #0,1,0: 91:[95, 95] Operation: 73+22=95 Exploring Operation: 95-73=22, Resulting Numbers: [22, 22] Generated Node #0,1,1: 91:[22, 22] Operation: 95-73=22 Moving to Node #0,1,0 Current State: 91:[95, 95], Operations: ['48-26=22', '73+22=95'] Exploring Operation: 95/95=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 95-95=0, Resulting Numbers: [0] 0,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[22, 22], Operations: ['48-26=22', '95-73=22'] Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,91 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
[ 11, 64, 84, 29 ]
69
[ "84-29=55", "55/11=5", "64+5=69" ]
Current State: 69:[11, 64, 84, 29], Operations: [] Exploring Operation: 84-29=55, Resulting Numbers: [11, 64, 55] Generated Node #2: [11, 64, 55] from Operation: 84-29=55 Current State: 69:[11, 64, 55], Operations: ['84-29=55'] Exploring Operation: 55/11=5, Resulting Numbers: [64, 5] Generated Node #3: [64, 5] from Operation: 55/11=5 Current State: 69:[64, 5], Operations: ['84-29=55', '55/11=5'] Exploring Operation: 64+5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[11, 64, 84, 29], Operations: [] Exploring Operation: 84-11=73, Resulting Numbers: [64, 29, 73] Generated Node #0,0: 69:[64, 29, 73] Operation: 84-11=73 Moving to Node #0,0 Current State: 69:[64, 29, 73], Operations: ['84-11=73'] Exploring Operation: 73-64=9, Resulting Numbers: [29, 9] Generated Node #0,0,0: 69:[29, 9] Operation: 73-64=9 Moving to Node #0,0,0 Current State: 69:[29, 9], Operations: ['84-11=73', '73-64=9'] Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,69 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 60, 72, 54, 45 ]
35
[ "60*72=4320", "4320/54=80", "80-45=35" ]
Current State: 35:[60, 72, 54, 45], Operations: [] Exploring Operation: 60*72=4320, Resulting Numbers: [54, 45, 4320] Generated Node #2: [54, 45, 4320] from Operation: 60*72=4320 Current State: 35:[54, 45, 4320], Operations: ['60*72=4320'] Exploring Operation: 4320/54=80, Resulting Numbers: [45, 80] Generated Node #3: [45, 80] from Operation: 4320/54=80 Current State: 35:[45, 80], Operations: ['60*72=4320', '4320/54=80'] Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[60, 72, 54, 45], Operations: [] Exploring Operation: 72-60=12, Resulting Numbers: [54, 45, 12] Generated Node #0,0: 35:[54, 45, 12] Operation: 72-60=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[54, 45, 12], Operations: ['72-60=12'] Exploring Operation: 54-45=9, Resulting Numbers: [12, 9] Generated Node #0,0,0: 35:[12, 9] Operation: 54-45=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[12, 9], Operations: ['72-60=12', '54-45=9'] Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 27, 37, 6, 66 ]
59
[ "27*6=162", "37+66=103", "162-103=59" ]
Current State: 59:[27, 37, 6, 66], Operations: [] Exploring Operation: 27*6=162, Resulting Numbers: [37, 66, 162] Generated Node #2: [37, 66, 162] from Operation: 27*6=162 Current State: 59:[37, 66, 162], Operations: ['27*6=162'] Exploring Operation: 37+66=103, Resulting Numbers: [162, 103] Generated Node #3: [162, 103] from Operation: 37+66=103 Current State: 59:[162, 103], Operations: ['27*6=162', '37+66=103'] Exploring Operation: 162-103=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[27, 37, 6, 66], Operations: [] Exploring Operation: 37+6=43, Resulting Numbers: [27, 66, 43] Generated Node #0,0: 59:[27, 66, 43] Operation: 37+6=43 Exploring Operation: 27+6=33, Resulting Numbers: [37, 66, 33] Generated Node #0,1: 59:[37, 66, 33] Operation: 27+6=33 Exploring Operation: 66-6=60, Resulting Numbers: [27, 37, 60] Generated Node #0,2: 59:[27, 37, 60] Operation: 66-6=60 Moving to Node #0,0 Current State: 59:[27, 66, 43], Operations: ['37+6=43'] Exploring Operation: 27+43=70, Resulting Numbers: [66, 70] Generated Node #0,0,0: 59:[66, 70] Operation: 27+43=70 Exploring Operation: 27+66=93, Resulting Numbers: [43, 93] Generated Node #0,0,1: 59:[43, 93] Operation: 27+66=93 Exploring Operation: 66-27=39, Resulting Numbers: [43, 39] Generated Node #0,0,2: 59:[43, 39] Operation: 66-27=39 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[66, 70], Operations: ['37+6=43', '27+43=70'] Exploring Operation: 66*70=4620, Resulting Numbers: [4620] 4620,59 unequal: No Solution Exploring Operation: 70-66=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 66+70=136, Resulting Numbers: [136] 136,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 59:[43, 39], Operations: ['37+6=43', '66-27=39'] Exploring Operation: 43+39=82, Resulting Numbers: [82] 82,59 unequal: No Solution Exploring Operation: 43-39=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 43*39=1677, Resulting Numbers: [1677] 1677,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[43, 93], Operations: ['37+6=43', '27+66=93'] Exploring Operation: 43*93=3999, Resulting Numbers: [3999] 3999,59 unequal: No Solution Exploring Operation: 43+93=136, Resulting Numbers: [136] 136,59 unequal: No Solution Exploring Operation: 93-43=50, Resulting Numbers: [50] 50,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 59:[37, 66, 33], Operations: ['27+6=33'] Exploring Operation: 37+33=70, Resulting Numbers: [66, 70] Generated Node #0,1,0: 59:[66, 70] Operation: 37+33=70 Exploring Operation: 66-37=29, Resulting Numbers: [33, 29] Generated Node #0,1,1: 59:[33, 29] Operation: 66-37=29 Exploring Operation: 66-33=33, Resulting Numbers: [37, 33] Generated Node #0,1,2: 59:[37, 33] Operation: 66-33=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[66, 70], Operations: ['27+6=33', '37+33=70'] Exploring Operation: 66*70=4620, Resulting Numbers: [4620] 4620,59 unequal: No Solution Exploring Operation: 66+70=136, Resulting Numbers: [136] 136,59 unequal: No Solution Exploring Operation: 70-66=4, Resulting Numbers: [4] 4,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[37, 33], Operations: ['27+6=33', '66-33=33'] Exploring Operation: 37*33=1221, Resulting Numbers: [1221] 1221,59 unequal: No Solution Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 37+33=70, Resulting Numbers: [70] 70,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[33, 29], Operations: ['27+6=33', '66-37=29'] Exploring Operation: 33*29=957, Resulting Numbers: [957] 957,59 unequal: No Solution Exploring Operation: 33-29=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 33+29=62, Resulting Numbers: [62] 62,59 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: 59:[27, 37, 60], Operations: ['66-6=60'] Exploring Operation: 60-27=33, Resulting Numbers: [37, 33] Generated Node #0,2,0: 59:[37, 33] Operation: 60-27=33 Exploring Operation: 37-27=10, Resulting Numbers: [60, 10] Generated Node #0,2,1: 59:[60, 10] Operation: 37-27=10 Exploring Operation: 27+37=64, Resulting Numbers: [60, 64] Generated Node #0,2,2: 59:[60, 64] Operation: 27+37=64 Moving to Node #0,2,2 Current State: 59:[60, 64], Operations: ['66-6=60', '27+37=64'] Exploring Operation: 60*64=3840, Resulting Numbers: [3840] 3840,59 unequal: No Solution Exploring Operation: 60+64=124, Resulting Numbers: [124] 124,59 unequal: No Solution Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[37, 33], Operations: ['66-6=60', '60-27=33'] Exploring Operation: 37*33=1221, Resulting Numbers: [1221] 1221,59 unequal: No Solution Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 37+33=70, Resulting Numbers: [70] 70,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[60, 10], Operations: ['66-6=60', '37-27=10'] Exploring Operation: 60+10=70, Resulting Numbers: [70] 70,59 unequal: No Solution Exploring Operation: 60/10=6, Resulting Numbers: [6] 6,59 unequal: No Solution Exploring Operation: 60-10=50, Resulting Numbers: [50] 50,59 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 51, 28, 3, 25 ]
57
[ "51+28=79", "25-3=22", "79-22=57" ]
Current State: 57:[51, 28, 3, 25], Operations: [] Exploring Operation: 51+28=79, Resulting Numbers: [3, 25, 79] Generated Node #2: [3, 25, 79] from Operation: 51+28=79 Current State: 57:[3, 25, 79], Operations: ['51+28=79'] Exploring Operation: 25-3=22, Resulting Numbers: [79, 22] Generated Node #3: [79, 22] from Operation: 25-3=22 Current State: 57:[79, 22], Operations: ['51+28=79', '25-3=22'] Exploring Operation: 79-22=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[51, 28, 3, 25], Operations: [] Exploring Operation: 28-25=3, Resulting Numbers: [51, 3, 3] Generated Node #0,0: 57:[51, 3, 3] Operation: 28-25=3 Moving to Node #0,0 Current State: 57:[51, 3, 3], Operations: ['28-25=3'] Exploring Operation: 51/3=17, Resulting Numbers: [3, 17] Generated Node #0,0,0: 57:[3, 17] Operation: 51/3=17 Moving to Node #0,0,0 Current State: 57:[3, 17], Operations: ['28-25=3', '51/3=17'] Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,57 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 61, 44, 17, 17 ]
61
[ "17-17=0", "44*0=0", "61+0=61" ]
Current State: 61:[61, 44, 17, 17], Operations: [] Exploring Operation: 17-17=0, Resulting Numbers: [61, 44, 0] Generated Node #2: [61, 44, 0] from Operation: 17-17=0 Current State: 61:[61, 44, 0], Operations: ['17-17=0'] Exploring Operation: 44*0=0, Resulting Numbers: [61, 0] Generated Node #3: [61, 0] from Operation: 44*0=0 Current State: 61:[61, 0], Operations: ['17-17=0', '44*0=0'] Exploring Operation: 61+0=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[61, 44, 17, 17], Operations: [] Exploring Operation: 17+17=34, Resulting Numbers: [61, 44, 34] Generated Node #0,0: 61:[61, 44, 34] Operation: 17+17=34 Exploring Operation: 44+17=61, Resulting Numbers: [61, 17, 61] Generated Node #0,1: 61:[61, 17, 61] Operation: 44+17=61 Exploring Operation: 44+17=61, Resulting Numbers: [61, 17, 61] Generated Node #0,2: 61:[61, 17, 61] Operation: 44+17=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[61, 44, 34], Operations: ['17+17=34'] Exploring Operation: 61-34=27, Resulting Numbers: [44, 27] Generated Node #0,0,0: 61:[44, 27] Operation: 61-34=27 Exploring Operation: 61+34=95, Resulting Numbers: [44, 95] Generated Node #0,0,1: 61:[44, 95] Operation: 61+34=95 Exploring Operation: 44+34=78, Resulting Numbers: [61, 78] Generated Node #0,0,2: 61:[61, 78] Operation: 44+34=78 Moving to Node #0,0,2 Current State: 61:[61, 78], Operations: ['17+17=34', '44+34=78'] Exploring Operation: 61*78=4758, Resulting Numbers: [4758] 4758,61 unequal: No Solution Exploring Operation: 78-61=17, Resulting Numbers: [17] 17,61 unequal: No Solution Exploring Operation: 61+78=139, Resulting Numbers: [139] 139,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[44, 27], Operations: ['17+17=34', '61-34=27'] Exploring Operation: 44*27=1188, Resulting Numbers: [1188] 1188,61 unequal: No Solution Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,61 unequal: No Solution Exploring Operation: 44+27=71, Resulting Numbers: [71] 71,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[44, 95], Operations: ['17+17=34', '61+34=95'] Exploring Operation: 95-44=51, Resulting Numbers: [51] 51,61 unequal: No Solution Exploring Operation: 44+95=139, Resulting Numbers: [139] 139,61 unequal: No Solution Exploring Operation: 44*95=4180, Resulting Numbers: [4180] 4180,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[61, 17, 61], Operations: ['44+17=61'] Exploring Operation: 61+17=78, Resulting Numbers: [61, 78] Generated Node #0,1,0: 61:[61, 78] Operation: 61+17=78 Exploring Operation: 61-17=44, Resulting Numbers: [61, 44] Generated Node #0,1,1: 61:[61, 44] Operation: 61-17=44 Exploring Operation: 17+61=78, Resulting Numbers: [61, 78] Generated Node #0,1,2: 61:[61, 78] Operation: 17+61=78 Moving to Node #0,1,0 Current State: 61:[61, 78], Operations: ['44+17=61', '61+17=78'] Exploring Operation: 61+78=139, Resulting Numbers: [139] 139,61 unequal: No Solution Exploring Operation: 61*78=4758, Resulting Numbers: [4758] 4758,61 unequal: No Solution Exploring Operation: 78-61=17, Resulting Numbers: [17] 17,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[61, 44], Operations: ['44+17=61', '61-17=44'] Exploring Operation: 61+44=105, Resulting Numbers: [105] 105,61 unequal: No Solution Exploring Operation: 61*44=2684, Resulting Numbers: [2684] 2684,61 unequal: No Solution Exploring Operation: 61-44=17, Resulting Numbers: [17] 17,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[61, 78], Operations: ['44+17=61', '17+61=78'] Exploring Operation: 61+78=139, Resulting Numbers: [139] 139,61 unequal: No Solution Exploring Operation: 78-61=17, Resulting Numbers: [17] 17,61 unequal: No Solution Exploring Operation: 61*78=4758, Resulting Numbers: [4758] 4758,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[61, 17, 61], Operations: ['44+17=61'] Exploring Operation: 17+61=78, Resulting Numbers: [61, 78] Generated Node #0,2,0: 61:[61, 78] Operation: 17+61=78 Exploring Operation: 61-17=44, Resulting Numbers: [61, 44] Generated Node #0,2,1: 61:[61, 44] Operation: 61-17=44 Exploring Operation: 61+17=78, Resulting Numbers: [61, 78] Generated Node #0,2,2: 61:[61, 78] Operation: 61+17=78 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 61:[61, 78], Operations: ['44+17=61', '17+61=78'] Exploring Operation: 61+78=139, Resulting Numbers: [139] 139,61 unequal: No Solution Exploring Operation: 61*78=4758, Resulting Numbers: [4758] 4758,61 unequal: No Solution Exploring Operation: 78-61=17, Resulting Numbers: [17] 17,61 unequal: No Solution No 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: 61:[61, 44], Operations: ['44+17=61', '61-17=44'] Exploring Operation: 61-44=17, Resulting Numbers: [17] 17,61 unequal: No Solution Exploring Operation: 61+44=105, Resulting Numbers: [105] 105,61 unequal: No Solution Exploring Operation: 61*44=2684, Resulting Numbers: [2684] 2684,61 unequal: No Solution No 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: 61:[61, 78], Operations: ['44+17=61', '61+17=78'] Exploring Operation: 61*78=4758, Resulting Numbers: [4758] 4758,61 unequal: No Solution Exploring Operation: 78-61=17, Resulting Numbers: [17] 17,61 unequal: No Solution Exploring Operation: 61+78=139, Resulting Numbers: [139] 139,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 73, 77, 83, 8 ]
79
[ "77-73=4", "83-8=75", "4+75=79" ]
Current State: 79:[73, 77, 83, 8], Operations: [] Exploring Operation: 77-73=4, Resulting Numbers: [83, 8, 4] Generated Node #2: [83, 8, 4] from Operation: 77-73=4 Current State: 79:[83, 8, 4], Operations: ['77-73=4'] Exploring Operation: 83-8=75, Resulting Numbers: [4, 75] Generated Node #3: [4, 75] from Operation: 83-8=75 Current State: 79:[4, 75], Operations: ['77-73=4', '83-8=75'] Exploring Operation: 4+75=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[73, 77, 83, 8], Operations: [] Exploring Operation: 77+8=85, Resulting Numbers: [73, 83, 85] Generated Node #0,0: 79:[73, 83, 85] Operation: 77+8=85 Exploring Operation: 73+8=81, Resulting Numbers: [77, 83, 81] Generated Node #0,1: 79:[77, 83, 81] Operation: 73+8=81 Exploring Operation: 83-8=75, Resulting Numbers: [73, 77, 75] Generated Node #0,2: 79:[73, 77, 75] Operation: 83-8=75 Exploring Operation: 73-8=65, Resulting Numbers: [77, 83, 65] Generated Node #0,3: 79:[77, 83, 65] Operation: 73-8=65 Moving to Node #0,1 Current State: 79:[77, 83, 81], Operations: ['73+8=81'] Exploring Operation: 77+83=160, Resulting Numbers: [81, 160] Generated Node #0,1,0: 79:[81, 160] Operation: 77+83=160 Exploring Operation: 83-81=2, Resulting Numbers: [77, 2] Generated Node #0,1,1: 79:[77, 2] Operation: 83-81=2 Exploring Operation: 81-77=4, Resulting Numbers: [83, 4] Generated Node #0,1,2: 79:[83, 4] Operation: 81-77=4 Exploring Operation: 83-77=6, Resulting Numbers: [81, 6] Generated Node #0,1,3: 79:[81, 6] Operation: 83-77=6 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 79:[81, 6], Operations: ['73+8=81', '83-77=6'] Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,79 unequal: No Solution Exploring Operation: 81*6=486, Resulting Numbers: [486] 486,79 unequal: No Solution Exploring Operation: 81+6=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 #0,1,1 Current State: 79:[77, 2], Operations: ['73+8=81', '83-81=2'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,79 unequal: No Solution Exploring Operation: 77*2=154, Resulting Numbers: [154] 154,79 unequal: No Solution Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[73, 77, 83, 8], Operations: [] Exploring Operation: 73+8=81, Resulting Numbers: [77, 83, 81] Generated Node #0,1: 79:[77, 83, 81] Operation: 73+8=81 Moving to Node #0,1 Current State: 79:[77, 83, 81], Operations: ['73+8=81'] Exploring Operation: 83-81=2, Resulting Numbers: [77, 2] Generated Node #0,1,1: 79:[77, 2] Operation: 83-81=2 Moving to Node #0,1,1 Current State: 79:[77, 2], Operations: ['73+8=81', '83-81=2'] Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 15, 19, 8, 10 ]
21
[ "15-10=5", "8*5=40", "40-19=21" ]
Current State: 21:[15, 19, 8, 10], Operations: [] Exploring Operation: 15-10=5, Resulting Numbers: [19, 8, 5] Generated Node #2: [19, 8, 5] from Operation: 15-10=5 Current State: 21:[19, 8, 5], Operations: ['15-10=5'] Exploring Operation: 8*5=40, Resulting Numbers: [19, 40] Generated Node #3: [19, 40] from Operation: 8*5=40 Current State: 21:[19, 40], Operations: ['15-10=5', '8*5=40'] Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[15, 19, 8, 10], Operations: [] Exploring Operation: 15-10=5, Resulting Numbers: [19, 8, 5] Generated Node #0,0: 21:[19, 8, 5] Operation: 15-10=5 Exploring Operation: 19-15=4, Resulting Numbers: [8, 10, 4] Generated Node #0,1: 21:[8, 10, 4] Operation: 19-15=4 Exploring Operation: 15-8=7, Resulting Numbers: [19, 10, 7] Generated Node #0,2: 21:[19, 10, 7] Operation: 15-8=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[19, 8, 5], Operations: ['15-10=5'] Exploring Operation: 8-5=3, Resulting Numbers: [19, 3] Generated Node #0,0,0: 21:[19, 3] Operation: 8-5=3 Exploring Operation: 19-8=11, Resulting Numbers: [5, 11] Generated Node #0,0,1: 21:[5, 11] Operation: 19-8=11 Exploring Operation: 19+5=24, Resulting Numbers: [8, 24] Generated Node #0,0,2: 21:[8, 24] Operation: 19+5=24 Moving to Node #0,0,0 Current State: 21:[19, 3], Operations: ['15-10=5', '8-5=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,21 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,21 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,21 unequal: No Solution Moving to Node #0,0,2 Current State: 21:[8, 24], Operations: ['15-10=5', '19+5=24'] Exploring Operation: 8+24=32, Resulting Numbers: [32] 32,21 unequal: No Solution Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[5, 11], Operations: ['15-10=5', '19-8=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,21 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[8, 10, 4], Operations: ['19-15=4'] Exploring Operation: 10-4=6, Resulting Numbers: [8, 6] Generated Node #0,1,0: 21:[8, 6] Operation: 10-4=6 Exploring Operation: 10-8=2, Resulting Numbers: [4, 2] Generated Node #0,1,1: 21:[4, 2] Operation: 10-8=2 Exploring Operation: 8+10=18, Resulting Numbers: [4, 18] Generated Node #0,1,2: 21:[4, 18] Operation: 8+10=18 Moving to Node #0,1,0 Current State: 21:[8, 6], Operations: ['19-15=4', '10-4=6'] Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[4, 2], Operations: ['19-15=4', '10-8=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[4, 18], Operations: ['19-15=4', '8+10=18'] Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,21 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,21 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[19, 10, 7], Operations: ['15-8=7'] Exploring Operation: 19-10=9, Resulting Numbers: [7, 9] Generated Node #0,2,0: 21:[7, 9] Operation: 19-10=9 Exploring Operation: 10-7=3, Resulting Numbers: [19, 3] Generated Node #0,2,1: 21:[19, 3] Operation: 10-7=3 Exploring Operation: 10+7=17, Resulting Numbers: [19, 17] Generated Node #0,2,2: 21:[19, 17] Operation: 10+7=17 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 21:[7, 9], Operations: ['15-8=7', '19-10=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,21 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,21 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 21:[19, 3], Operations: ['15-8=7', '10-7=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,21 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,21 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 21:[19, 17], Operations: ['15-8=7', '10+7=17'] Exploring Operation: 19-17=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 19+17=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 19*17=323, Resulting Numbers: [323] 323,21 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 No solution found.
0
hs_3
sum_heuristic
[ 20, 92, 51, 67 ]
23
[ "20+51=71", "71-67=4", "92/4=23" ]
Current State: 23:[20, 92, 51, 67], Operations: [] Exploring Operation: 20+51=71, Resulting Numbers: [92, 67, 71] Generated Node #2: [92, 67, 71] from Operation: 20+51=71 Current State: 23:[92, 67, 71], Operations: ['20+51=71'] Exploring Operation: 71-67=4, Resulting Numbers: [92, 4] Generated Node #3: [92, 4] from Operation: 71-67=4 Current State: 23:[92, 4], Operations: ['20+51=71', '71-67=4'] Exploring Operation: 92/4=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[20, 92, 51, 67], Operations: [] Exploring Operation: 67-51=16, Resulting Numbers: [20, 92, 16] Generated Node #0,0: 23:[20, 92, 16] Operation: 67-51=16 Exploring Operation: 92-67=25, Resulting Numbers: [20, 51, 25] Generated Node #0,1: 23:[20, 51, 25] Operation: 92-67=25 Exploring Operation: 92-51=41, Resulting Numbers: [20, 67, 41] Generated Node #0,2: 23:[20, 67, 41] Operation: 92-51=41 Moving to Node #0,1 Current State: 23:[20, 51, 25], Operations: ['92-67=25'] Exploring Operation: 25-20=5, Resulting Numbers: [51, 5] Generated Node #0,1,0: 23:[51, 5] Operation: 25-20=5 Exploring Operation: 51-20=31, Resulting Numbers: [25, 31] Generated Node #0,1,1: 23:[25, 31] Operation: 51-20=31 Exploring Operation: 51-25=26, Resulting Numbers: [20, 26] Generated Node #0,1,2: 23:[20, 26] Operation: 51-25=26 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 23:[20, 26], Operations: ['92-67=25', '51-25=26'] Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[25, 31], Operations: ['92-67=25', '51-20=31'] Exploring Operation: 25*31=775, Resulting Numbers: [775] 775,23 unequal: No Solution Exploring Operation: 25+31=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[51, 5], Operations: ['92-67=25', '25-20=5'] Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,23 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,23 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: 23:[20, 67, 41], Operations: ['92-51=41'] Exploring Operation: 67-41=26, Resulting Numbers: [20, 26] Generated Node #0,2,0: 23:[20, 26] Operation: 67-41=26 Exploring Operation: 67-20=47, Resulting Numbers: [41, 47] Generated Node #0,2,1: 23:[41, 47] Operation: 67-20=47 Exploring Operation: 41-20=21, Resulting Numbers: [67, 21] Generated Node #0,2,2: 23:[67, 21] Operation: 41-20=21 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 23:[20, 26], Operations: ['92-51=41', '67-41=26'] Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[41, 47], Operations: ['92-51=41', '67-20=47'] Exploring Operation: 41*47=1927, Resulting Numbers: [1927] 1927,23 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 41+47=88, Resulting Numbers: [88] 88,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 23:[67, 21], Operations: ['92-51=41', '41-20=21'] Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 67*21=1407, Resulting Numbers: [1407] 1407,23 unequal: No Solution Exploring Operation: 67+21=88, Resulting Numbers: [88] 88,23 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: 23:[20, 92, 16], Operations: ['67-51=16'] Exploring Operation: 92-16=76, Resulting Numbers: [20, 76] Generated Node #0,0,0: 23:[20, 76] Operation: 92-16=76 Exploring Operation: 92-20=72, Resulting Numbers: [16, 72] Generated Node #0,0,1: 23:[16, 72] Operation: 92-20=72 Exploring Operation: 20+16=36, Resulting Numbers: [92, 36] Generated Node #0,0,2: 23:[92, 36] Operation: 20+16=36 Moving to Node #0,0,0 Current State: 23:[20, 76], Operations: ['67-51=16', '92-16=76'] Exploring Operation: 20+76=96, Resulting Numbers: [96] 96,23 unequal: No Solution Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 20*76=1520, Resulting Numbers: [1520] 1520,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[16, 72], Operations: ['67-51=16', '92-20=72'] Exploring Operation: 16*72=1152, Resulting Numbers: [1152] 1152,23 unequal: No Solution Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 16+72=88, Resulting Numbers: [88] 88,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[92, 36], Operations: ['67-51=16', '20+16=36'] Exploring Operation: 92+36=128, Resulting Numbers: [128] 128,23 unequal: No Solution Exploring Operation: 92*36=3312, Resulting Numbers: [3312] 3312,23 unequal: No Solution Exploring Operation: 92-36=56, Resulting Numbers: [56] 56,23 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 9, 48, 13, 85 ]
59
[ "48-9=39", "13+85=98", "98-39=59" ]
Current State: 59:[9, 48, 13, 85], Operations: [] Exploring Operation: 48-9=39, Resulting Numbers: [13, 85, 39] Generated Node #2: [13, 85, 39] from Operation: 48-9=39 Current State: 59:[13, 85, 39], Operations: ['48-9=39'] Exploring Operation: 13+85=98, Resulting Numbers: [39, 98] Generated Node #3: [39, 98] from Operation: 13+85=98 Current State: 59:[39, 98], Operations: ['48-9=39', '13+85=98'] Exploring Operation: 98-39=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[9, 48, 13, 85], Operations: [] Exploring Operation: 9+48=57, Resulting Numbers: [13, 85, 57] Generated Node #0,0: 59:[13, 85, 57] Operation: 9+48=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[13, 85, 57], Operations: ['9+48=57'] Exploring Operation: 85-13=72, Resulting Numbers: [57, 72] Generated Node #0,0,0: 59:[57, 72] Operation: 85-13=72 Moving to Node #0,0,0 Current State: 59:[57, 72], Operations: ['9+48=57', '85-13=72'] Exploring Operation: 72-57=15, Resulting Numbers: [15] 15,59 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
[ 39, 77, 9, 59 ]
88
[ "77-39=38", "59-9=50", "38+50=88" ]
Current State: 88:[39, 77, 9, 59], Operations: [] Exploring Operation: 77-39=38, Resulting Numbers: [9, 59, 38] Generated Node #2: [9, 59, 38] from Operation: 77-39=38 Current State: 88:[9, 59, 38], Operations: ['77-39=38'] Exploring Operation: 59-9=50, Resulting Numbers: [38, 50] Generated Node #3: [38, 50] from Operation: 59-9=50 Current State: 88:[38, 50], Operations: ['77-39=38', '59-9=50'] Exploring Operation: 38+50=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[39, 77, 9, 59], Operations: [] Exploring Operation: 59-39=20, Resulting Numbers: [77, 9, 20] Generated Node #0,0: 88:[77, 9, 20] Operation: 59-39=20 Exploring Operation: 39+59=98, Resulting Numbers: [77, 9, 98] Generated Node #0,1: 88:[77, 9, 98] Operation: 39+59=98 Exploring Operation: 77-59=18, Resulting Numbers: [39, 9, 18] Generated Node #0,2: 88:[39, 9, 18] Operation: 77-59=18 Exploring Operation: 77-39=38, Resulting Numbers: [9, 59, 38] Generated Node #0,3: 88:[9, 59, 38] Operation: 77-39=38 Exploring Operation: 77+9=86, Resulting Numbers: [39, 59, 86] Generated Node #0,4: 88:[39, 59, 86] Operation: 77+9=86 Moving to Node #0,2 Current State: 88:[39, 9, 18], Operations: ['77-59=18'] Exploring Operation: 18/9=2, Resulting Numbers: [39, 2] Generated Node #0,2,0: 88:[39, 2] Operation: 18/9=2 Exploring Operation: 9+18=27, Resulting Numbers: [39, 27] Generated Node #0,2,1: 88:[39, 27] Operation: 9+18=27 Exploring Operation: 39-18=21, Resulting Numbers: [9, 21] Generated Node #0,2,2: 88:[9, 21] Operation: 39-18=21 Exploring Operation: 39+9=48, Resulting Numbers: [18, 48] Generated Node #0,2,3: 88:[18, 48] Operation: 39+9=48 Exploring Operation: 18-9=9, Resulting Numbers: [39, 9] Generated Node #0,2,4: 88:[39, 9] Operation: 18-9=9 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 88:[9, 21], Operations: ['77-59=18', '39-18=21'] Exploring Operation: 9*21=189, Resulting Numbers: [189] 189,88 unequal: No Solution Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,88 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 88:[39, 2], Operations: ['77-59=18', '18/9=2'] Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,88 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 88:[39, 9], Operations: ['77-59=18', '18-9=9'] Exploring Operation: 39*9=351, Resulting Numbers: [351] 351,88 unequal: No Solution Exploring Operation: 39-9=30, Resulting Numbers: [30] 30,88 unequal: No Solution Exploring Operation: 39+9=48, Resulting Numbers: [48] 48,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 88:[18, 48], Operations: ['77-59=18', '39+9=48'] Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,88 unequal: No Solution Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,88 unequal: No Solution Exploring Operation: 18+48=66, Resulting Numbers: [66] 66,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 88:[39, 27], Operations: ['77-59=18', '9+18=27'] Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,88 unequal: No Solution Exploring Operation: 39*27=1053, Resulting Numbers: [1053] 1053,88 unequal: No Solution Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,88 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: 88:[77, 9, 20], Operations: ['59-39=20'] Exploring Operation: 77+9=86, Resulting Numbers: [20, 86] Generated Node #0,0,0: 88:[20, 86] Operation: 77+9=86 Exploring Operation: 9+20=29, Resulting Numbers: [77, 29] Generated Node #0,0,1: 88:[77, 29] Operation: 9+20=29 Exploring Operation: 20-9=11, Resulting Numbers: [77, 11] Generated Node #0,0,2: 88:[77, 11] Operation: 20-9=11 Exploring Operation: 77+20=97, Resulting Numbers: [9, 97] Generated Node #0,0,3: 88:[9, 97] Operation: 77+20=97 Exploring Operation: 77-20=57, Resulting Numbers: [9, 57] Generated Node #0,0,4: 88:[9, 57] Operation: 77-20=57 Moving to Node #0,1 Current State: 88:[77, 9, 98], Operations: ['39+59=98'] Exploring Operation: 98-77=21, Resulting Numbers: [9, 21] Generated Node #0,1,0: 88:[9, 21] Operation: 98-77=21 Exploring Operation: 9+98=107, Resulting Numbers: [77, 107] Generated Node #0,1,1: 88:[77, 107] Operation: 9+98=107 Exploring Operation: 77+9=86, Resulting Numbers: [98, 86] Generated Node #0,1,2: 88:[98, 86] Operation: 77+9=86 Exploring Operation: 98-9=89, Resulting Numbers: [77, 89] Generated Node #0,1,3: 88:[77, 89] Operation: 98-9=89 Exploring Operation: 77-9=68, Resulting Numbers: [98, 68] Generated Node #0,1,4: 88:[98, 68] Operation: 77-9=68 Moving to Node #0,3 Current State: 88:[9, 59, 38], Operations: ['77-39=38'] Exploring Operation: 59-9=50, Resulting Numbers: [38, 50] Generated Node #0,3,0: 88:[38, 50] Operation: 59-9=50 Exploring Operation: 59-38=21, Resulting Numbers: [9, 21] Generated Node #0,3,1: 88:[9, 21] Operation: 59-38=21 Exploring Operation: 59+38=97, Resulting Numbers: [9, 97] Generated Node #0,3,2: 88:[9, 97] Operation: 59+38=97 Exploring Operation: 9+38=47, Resulting Numbers: [59, 47] Generated Node #0,3,3: 88:[59, 47] Operation: 9+38=47 Exploring Operation: 38-9=29, Resulting Numbers: [59, 29] Generated Node #0,3,4: 88:[59, 29] Operation: 38-9=29 Moving to Node #0,4 Current State: 88:[39, 59, 86], Operations: ['77+9=86'] Exploring Operation: 86-59=27, Resulting Numbers: [39, 27] Generated Node #0,4,0: 88:[39, 27] Operation: 86-59=27 Exploring Operation: 86-39=47, Resulting Numbers: [59, 47] Generated Node #0,4,1: 88:[59, 47] Operation: 86-39=47 Exploring Operation: 59-39=20, Resulting Numbers: [86, 20] Generated Node #0,4,2: 88:[86, 20] Operation: 59-39=20 Exploring Operation: 39+86=125, Resulting Numbers: [59, 125] Generated Node #0,4,3: 88:[59, 125] Operation: 39+86=125 Exploring Operation: 39+59=98, Resulting Numbers: [86, 98] Generated Node #0,4,4: 88:[86, 98] Operation: 39+59=98 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 88:[86, 20], Operations: ['77+9=86', '59-39=20'] Exploring Operation: 86-20=66, Resulting Numbers: [66] 66,88 unequal: No Solution Exploring Operation: 86+20=106, Resulting Numbers: [106] 106,88 unequal: No Solution Exploring Operation: 86*20=1720, Resulting Numbers: [1720] 1720,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 88:[39, 27], Operations: ['77+9=86', '86-59=27'] Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,88 unequal: No Solution Exploring Operation: 39*27=1053, Resulting Numbers: [1053] 1053,88 unequal: No Solution Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 88:[86, 98], Operations: ['77+9=86', '39+59=98'] Exploring Operation: 86+98=184, Resulting Numbers: [184] 184,88 unequal: No Solution Exploring Operation: 86*98=8428, Resulting Numbers: [8428] 8428,88 unequal: No Solution Exploring Operation: 98-86=12, Resulting Numbers: [12] 12,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 88:[59, 47], Operations: ['77+9=86', '86-39=47'] Exploring Operation: 59*47=2773, Resulting Numbers: [2773] 2773,88 unequal: No Solution Exploring Operation: 59+47=106, Resulting Numbers: [106] 106,88 unequal: No Solution Exploring Operation: 59-47=12, Resulting Numbers: [12] 12,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 88:[59, 125], Operations: ['77+9=86', '39+86=125'] Exploring Operation: 59*125=7375, Resulting Numbers: [7375] 7375,88 unequal: No Solution Exploring Operation: 125-59=66, Resulting Numbers: [66] 66,88 unequal: No Solution Exploring Operation: 59+125=184, Resulting Numbers: [184] 184,88 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: 88:[9, 21], Operations: ['39+59=98', '98-77=21'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 9*21=189, Resulting Numbers: [189] 189,88 unequal: No Solution Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,88 unequal: No Solution Moving to Node #0,3,1 Current State: 88:[9, 21], Operations: ['77-39=38', '59-38=21'] Exploring Operation: 9*21=189, Resulting Numbers: [189] 189,88 unequal: No Solution Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,88 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[20, 86], Operations: ['59-39=20', '77+9=86'] Exploring Operation: 20*86=1720, Resulting Numbers: [1720] 1720,88 unequal: No Solution Exploring Operation: 20+86=106, Resulting Numbers: [106] 106,88 unequal: No Solution Exploring Operation: 86-20=66, Resulting Numbers: [66] 66,88 unequal: No Solution Moving to Node #0,3,2 Current State: 88:[9, 97], Operations: ['77-39=38', '59+38=97'] Exploring Operation: 9+97=106, Resulting Numbers: [106] 106,88 unequal: No Solution Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[39, 77, 9, 59], Operations: [] Exploring Operation: 77-39=38, Resulting Numbers: [9, 59, 38] Generated Node #0,3: 88:[9, 59, 38] Operation: 77-39=38 Moving to Node #0,3 Current State: 88:[9, 59, 38], Operations: ['77-39=38'] Exploring Operation: 59+38=97, Resulting Numbers: [9, 97] Generated Node #0,3,2: 88:[9, 97] Operation: 59+38=97 Moving to Node #0,3,2 Current State: 88:[9, 97], Operations: ['77-39=38', '59+38=97'] Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.934896
hs_5
sum_heuristic
[ 32, 32, 3, 22 ]
39
[ "32+32=64", "3+22=25", "64-25=39" ]
Current State: 39:[32, 32, 3, 22], Operations: [] Exploring Operation: 32+32=64, Resulting Numbers: [3, 22, 64] Generated Node #2: [3, 22, 64] from Operation: 32+32=64 Current State: 39:[3, 22, 64], Operations: ['32+32=64'] Exploring Operation: 3+22=25, Resulting Numbers: [64, 25] Generated Node #3: [64, 25] from Operation: 3+22=25 Current State: 39:[64, 25], Operations: ['32+32=64', '3+22=25'] Exploring Operation: 64-25=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[32, 32, 3, 22], Operations: [] Exploring Operation: 32-22=10, Resulting Numbers: [32, 3, 10] Generated Node #0,0: 39:[32, 3, 10] Operation: 32-22=10 Exploring Operation: 32-32=0, Resulting Numbers: [3, 22, 0] Generated Node #0,1: 39:[3, 22, 0] Operation: 32-32=0 Exploring Operation: 32-22=10, Resulting Numbers: [32, 3, 10] Generated Node #0,2: 39:[32, 3, 10] Operation: 32-22=10 Exploring Operation: 32/32=1, Resulting Numbers: [3, 22, 1] Generated Node #0,3: 39:[3, 22, 1] Operation: 32/32=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[32, 3, 10], Operations: ['32-22=10'] Exploring Operation: 32-10=22, Resulting Numbers: [3, 22] Generated Node #0,0,0: 39:[3, 22] Operation: 32-10=22 Exploring Operation: 3+10=13, Resulting Numbers: [32, 13] Generated Node #0,0,1: 39:[32, 13] Operation: 3+10=13 Exploring Operation: 32+3=35, Resulting Numbers: [10, 35] Generated Node #0,0,2: 39:[10, 35] Operation: 32+3=35 Exploring Operation: 32+10=42, Resulting Numbers: [3, 42] Generated Node #0,0,3: 39:[3, 42] Operation: 32+10=42 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 39:[3, 42], Operations: ['32-22=10', '32+10=42'] Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,39 unequal: No Solution Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,39 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[32, 32, 3, 22], Operations: [] Exploring Operation: 32-22=10, Resulting Numbers: [32, 3, 10] Generated Node #0,0: 39:[32, 3, 10] Operation: 32-22=10 Moving to Node #0,0 Current State: 39:[32, 3, 10], Operations: ['32-22=10'] Exploring Operation: 32+10=42, Resulting Numbers: [3, 42] Generated Node #0,0,3: 39:[3, 42] Operation: 32+10=42 Moving to Node #0,0,3 Current State: 39:[3, 42], Operations: ['32-22=10', '32+10=42'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 78, 42, 11, 13 ]
81
[ "13-11=2", "78/2=39", "42+39=81" ]
Current State: 81:[78, 42, 11, 13], Operations: [] Exploring Operation: 13-11=2, Resulting Numbers: [78, 42, 2] Generated Node #2: [78, 42, 2] from Operation: 13-11=2 Current State: 81:[78, 42, 2], Operations: ['13-11=2'] Exploring Operation: 78/2=39, Resulting Numbers: [42, 39] Generated Node #3: [42, 39] from Operation: 78/2=39 Current State: 81:[42, 39], Operations: ['13-11=2', '78/2=39'] Exploring Operation: 42+39=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[78, 42, 11, 13], Operations: [] Exploring Operation: 42-13=29, Resulting Numbers: [78, 11, 29] Generated Node #0,0: 81:[78, 11, 29] Operation: 42-13=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[78, 11, 29], Operations: ['42-13=29'] Exploring Operation: 78+11=89, Resulting Numbers: [29, 89] Generated Node #0,0,0: 81:[29, 89] Operation: 78+11=89 Moving to Node #0,0,0 Current State: 81:[29, 89], Operations: ['42-13=29', '78+11=89'] Exploring Operation: 89-29=60, Resulting Numbers: [60] 60,81 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
[ 52, 86, 70, 1 ]
35
[ "86-52=34", "70-1=69", "69-34=35" ]
Current State: 35:[52, 86, 70, 1], Operations: [] Exploring Operation: 86-52=34, Resulting Numbers: [70, 1, 34] Generated Node #2: [70, 1, 34] from Operation: 86-52=34 Current State: 35:[70, 1, 34], Operations: ['86-52=34'] Exploring Operation: 70-1=69, Resulting Numbers: [34, 69] Generated Node #3: [34, 69] from Operation: 70-1=69 Current State: 35:[34, 69], Operations: ['86-52=34', '70-1=69'] Exploring Operation: 69-34=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[52, 86, 70, 1], Operations: [] Exploring Operation: 70-52=18, Resulting Numbers: [86, 1, 18] Generated Node #0,0: 35:[86, 1, 18] Operation: 70-52=18 Exploring Operation: 52-1=51, Resulting Numbers: [86, 70, 51] Generated Node #0,1: 35:[86, 70, 51] Operation: 52-1=51 Exploring Operation: 86-52=34, Resulting Numbers: [70, 1, 34] Generated Node #0,2: 35:[70, 1, 34] Operation: 86-52=34 Exploring Operation: 86-70=16, Resulting Numbers: [52, 1, 16] Generated Node #0,3: 35:[52, 1, 16] Operation: 86-70=16 Moving to Node #0,3 Current State: 35:[52, 1, 16], Operations: ['86-70=16'] Exploring Operation: 52-16=36, Resulting Numbers: [1, 36] Generated Node #0,3,0: 35:[1, 36] Operation: 52-16=36 Exploring Operation: 52*1=52, Resulting Numbers: [16, 52] Generated Node #0,3,1: 35:[16, 52] Operation: 52*1=52 Exploring Operation: 16-1=15, Resulting Numbers: [52, 15] Generated Node #0,3,2: 35:[52, 15] Operation: 16-1=15 Exploring Operation: 52-1=51, Resulting Numbers: [16, 51] Generated Node #0,3,3: 35:[16, 51] Operation: 52-1=51 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 35:[1, 36], Operations: ['86-70=16', '52-16=36'] Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,35 unequal: No Solution Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[52, 86, 70, 1], Operations: [] Exploring Operation: 86-70=16, Resulting Numbers: [52, 1, 16] Generated Node #0,3: 35:[52, 1, 16] Operation: 86-70=16 Moving to Node #0,3 Current State: 35:[52, 1, 16], Operations: ['86-70=16'] Exploring Operation: 52-16=36, Resulting Numbers: [1, 36] Generated Node #0,3,0: 35:[1, 36] Operation: 52-16=36 Moving to Node #0,3,0 Current State: 35:[1, 36], Operations: ['86-70=16', '52-16=36'] Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 23, 93, 89, 50 ]
23
[ "23+93=116", "89+50=139", "139-116=23" ]
Current State: 23:[23, 93, 89, 50], Operations: [] Exploring Operation: 23+93=116, Resulting Numbers: [89, 50, 116] Generated Node #2: [89, 50, 116] from Operation: 23+93=116 Current State: 23:[89, 50, 116], Operations: ['23+93=116'] Exploring Operation: 89+50=139, Resulting Numbers: [116, 139] Generated Node #3: [116, 139] from Operation: 89+50=139 Current State: 23:[116, 139], Operations: ['23+93=116', '89+50=139'] Exploring Operation: 139-116=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[23, 93, 89, 50], Operations: [] Exploring Operation: 89-50=39, Resulting Numbers: [23, 93, 39] Generated Node #0,0: 23:[23, 93, 39] Operation: 89-50=39 Exploring Operation: 93-23=70, Resulting Numbers: [89, 50, 70] Generated Node #0,1: 23:[89, 50, 70] Operation: 93-23=70 Exploring Operation: 93-50=43, Resulting Numbers: [23, 89, 43] Generated Node #0,2: 23:[23, 89, 43] Operation: 93-50=43 Exploring Operation: 93-89=4, Resulting Numbers: [23, 50, 4] Generated Node #0,3: 23:[23, 50, 4] Operation: 93-89=4 Moving to Node #0,3 Current State: 23:[23, 50, 4], Operations: ['93-89=4'] Exploring Operation: 50-23=27, Resulting Numbers: [4, 27] Generated Node #0,3,0: 23:[4, 27] Operation: 50-23=27 Exploring Operation: 23+4=27, Resulting Numbers: [50, 27] Generated Node #0,3,1: 23:[50, 27] Operation: 23+4=27 Exploring Operation: 23-4=19, Resulting Numbers: [50, 19] Generated Node #0,3,2: 23:[50, 19] Operation: 23-4=19 Exploring Operation: 50-4=46, Resulting Numbers: [23, 46] Generated Node #0,3,3: 23:[23, 46] Operation: 50-4=46 Moving to Node #0,2 Current State: 23:[23, 89, 43], Operations: ['93-50=43'] Exploring Operation: 89-23=66, Resulting Numbers: [43, 66] Generated Node #0,2,0: 23:[43, 66] Operation: 89-23=66 Exploring Operation: 43-23=20, Resulting Numbers: [89, 20] Generated Node #0,2,1: 23:[89, 20] Operation: 43-23=20 Exploring Operation: 23+89=112, Resulting Numbers: [43, 112] Generated Node #0,2,2: 23:[43, 112] Operation: 23+89=112 Exploring Operation: 89-43=46, Resulting Numbers: [23, 46] Generated Node #0,2,3: 23:[23, 46] Operation: 89-43=46 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 23:[23, 46], Operations: ['93-50=43', '89-43=46'] Exploring Operation: 23+46=69, Resulting Numbers: [69] 69,23 unequal: No Solution Exploring Operation: 46/23=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[23, 93, 89, 50], Operations: [] Exploring Operation: 93-50=43, Resulting Numbers: [23, 89, 43] Generated Node #0,2: 23:[23, 89, 43] Operation: 93-50=43 Moving to Node #0,2 Current State: 23:[23, 89, 43], Operations: ['93-50=43'] Exploring Operation: 89-43=46, Resulting Numbers: [23, 46] Generated Node #0,2,3: 23:[23, 46] Operation: 89-43=46 Moving to Node #0,2,3 Current State: 23:[23, 46], Operations: ['93-50=43', '89-43=46'] Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 93, 35, 10, 62 ]
76
[ "93+35=128", "62-10=52", "128-52=76" ]
Current State: 76:[93, 35, 10, 62], Operations: [] Exploring Operation: 93+35=128, Resulting Numbers: [10, 62, 128] Generated Node #2: [10, 62, 128] from Operation: 93+35=128 Current State: 76:[10, 62, 128], Operations: ['93+35=128'] Exploring Operation: 62-10=52, Resulting Numbers: [128, 52] Generated Node #3: [128, 52] from Operation: 62-10=52 Current State: 76:[128, 52], Operations: ['93+35=128', '62-10=52'] Exploring Operation: 128-52=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[93, 35, 10, 62], Operations: [] Exploring Operation: 93-10=83, Resulting Numbers: [35, 62, 83] Generated Node #0,0: 76:[35, 62, 83] Operation: 93-10=83 Exploring Operation: 62-10=52, Resulting Numbers: [93, 35, 52] Generated Node #0,1: 76:[93, 35, 52] Operation: 62-10=52 Exploring Operation: 93-62=31, Resulting Numbers: [35, 10, 31] Generated Node #0,2: 76:[35, 10, 31] Operation: 93-62=31 Exploring Operation: 10+62=72, Resulting Numbers: [93, 35, 72] Generated Node #0,3: 76:[93, 35, 72] Operation: 10+62=72 Exploring Operation: 62-35=27, Resulting Numbers: [93, 10, 27] Generated Node #0,4: 76:[93, 10, 27] Operation: 62-35=27 Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[35, 10, 31], Operations: ['93-62=31'] Exploring Operation: 31-10=21, Resulting Numbers: [35, 21] Generated Node #0,2,0: 76:[35, 21] Operation: 31-10=21 Exploring Operation: 10+31=41, Resulting Numbers: [35, 41] Generated Node #0,2,1: 76:[35, 41] Operation: 10+31=41 Exploring Operation: 35-31=4, Resulting Numbers: [10, 4] Generated Node #0,2,2: 76:[10, 4] Operation: 35-31=4 Exploring Operation: 35+10=45, Resulting Numbers: [31, 45] Generated Node #0,2,3: 76:[31, 45] Operation: 35+10=45 Exploring Operation: 35-10=25, Resulting Numbers: [31, 25] Generated Node #0,2,4: 76:[31, 25] Operation: 35-10=25 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 76:[35, 21], Operations: ['93-62=31', '31-10=21'] Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 35*21=735, Resulting Numbers: [735] 735,76 unequal: No Solution Exploring Operation: 35+21=56, Resulting Numbers: [56] 56,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 76:[35, 41], Operations: ['93-62=31', '10+31=41'] Exploring Operation: 35+41=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[93, 35, 10, 62], Operations: [] Exploring Operation: 93-62=31, Resulting Numbers: [35, 10, 31] Generated Node #0,2: 76:[35, 10, 31] Operation: 93-62=31 Moving to Node #0,2 Current State: 76:[35, 10, 31], Operations: ['93-62=31'] Exploring Operation: 10+31=41, Resulting Numbers: [35, 41] Generated Node #0,2,1: 76:[35, 41] Operation: 10+31=41 Moving to Node #0,2,1 Current State: 76:[35, 41], Operations: ['93-62=31', '10+31=41'] Exploring Operation: 35+41=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 18, 75, 42, 72 ]
87
[ "75-18=57", "72-42=30", "57+30=87" ]
Current State: 87:[18, 75, 42, 72], Operations: [] Exploring Operation: 75-18=57, Resulting Numbers: [42, 72, 57] Generated Node #2: [42, 72, 57] from Operation: 75-18=57 Current State: 87:[42, 72, 57], Operations: ['75-18=57'] Exploring Operation: 72-42=30, Resulting Numbers: [57, 30] Generated Node #3: [57, 30] from Operation: 72-42=30 Current State: 87:[57, 30], Operations: ['75-18=57', '72-42=30'] Exploring Operation: 57+30=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[18, 75, 42, 72], Operations: [] Exploring Operation: 72-42=30, Resulting Numbers: [18, 75, 30] Generated Node #0,0: 87:[18, 75, 30] Operation: 72-42=30 Exploring Operation: 18+72=90, Resulting Numbers: [75, 42, 90] Generated Node #0,1: 87:[75, 42, 90] Operation: 18+72=90 Exploring Operation: 72/18=4, Resulting Numbers: [75, 42, 4] Generated Node #0,2: 87:[75, 42, 4] Operation: 72/18=4 Exploring Operation: 75-72=3, Resulting Numbers: [18, 42, 3] Generated Node #0,3: 87:[18, 42, 3] Operation: 75-72=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[18, 75, 30], Operations: ['72-42=30'] Exploring Operation: 75-30=45, Resulting Numbers: [18, 45] Generated Node #0,0,0: 87:[18, 45] Operation: 75-30=45 Exploring Operation: 75-18=57, Resulting Numbers: [30, 57] Generated Node #0,0,1: 87:[30, 57] Operation: 75-18=57 Exploring Operation: 30-18=12, Resulting Numbers: [75, 12] Generated Node #0,0,2: 87:[75, 12] Operation: 30-18=12 Exploring Operation: 18+75=93, Resulting Numbers: [30, 93] Generated Node #0,0,3: 87:[30, 93] Operation: 18+75=93 Moving to Node #0,0,3 Current State: 87:[30, 93], Operations: ['72-42=30', '18+75=93'] Exploring Operation: 93-30=63, Resulting Numbers: [63] 63,87 unequal: No Solution Exploring Operation: 30*93=2790, Resulting Numbers: [2790] 2790,87 unequal: No Solution Exploring Operation: 30+93=123, Resulting Numbers: [123] 123,87 unequal: No Solution Moving to Node #0,0,2 Current State: 87:[75, 12], Operations: ['72-42=30', '30-18=12'] Exploring Operation: 75*12=900, Resulting Numbers: [900] 900,87 unequal: No Solution Exploring Operation: 75+12=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[18, 75, 42, 72], Operations: [] Exploring Operation: 72-42=30, Resulting Numbers: [18, 75, 30] Generated Node #0,0: 87:[18, 75, 30] Operation: 72-42=30 Moving to Node #0,0 Current State: 87:[18, 75, 30], Operations: ['72-42=30'] Exploring Operation: 30-18=12, Resulting Numbers: [75, 12] Generated Node #0,0,2: 87:[75, 12] Operation: 30-18=12 Moving to Node #0,0,2 Current State: 87:[75, 12], Operations: ['72-42=30', '30-18=12'] Exploring Operation: 75+12=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 47, 41, 55, 32 ]
29
[ "47-41=6", "55-32=23", "6+23=29" ]
Current State: 29:[47, 41, 55, 32], Operations: [] Exploring Operation: 47-41=6, Resulting Numbers: [55, 32, 6] Generated Node #2: [55, 32, 6] from Operation: 47-41=6 Current State: 29:[55, 32, 6], Operations: ['47-41=6'] Exploring Operation: 55-32=23, Resulting Numbers: [6, 23] Generated Node #3: [6, 23] from Operation: 55-32=23 Current State: 29:[6, 23], Operations: ['47-41=6', '55-32=23'] Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[47, 41, 55, 32], Operations: [] Exploring Operation: 47-41=6, Resulting Numbers: [55, 32, 6] Generated Node #0,0: 29:[55, 32, 6] Operation: 47-41=6 Exploring Operation: 55-41=14, Resulting Numbers: [47, 32, 14] Generated Node #0,1: 29:[47, 32, 14] Operation: 55-41=14 Exploring Operation: 55-47=8, Resulting Numbers: [41, 32, 8] Generated Node #0,2: 29:[41, 32, 8] Operation: 55-47=8 Exploring Operation: 55-32=23, Resulting Numbers: [47, 41, 23] Generated Node #0,3: 29:[47, 41, 23] Operation: 55-32=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[47, 32, 14], Operations: ['55-41=14'] Exploring Operation: 32-14=18, Resulting Numbers: [47, 18] Generated Node #0,1,0: 29:[47, 18] Operation: 32-14=18 Exploring Operation: 47+14=61, Resulting Numbers: [32, 61] Generated Node #0,1,1: 29:[32, 61] Operation: 47+14=61 Exploring Operation: 47-14=33, Resulting Numbers: [32, 33] Generated Node #0,1,2: 29:[32, 33] Operation: 47-14=33 Exploring Operation: 47-32=15, Resulting Numbers: [14, 15] Generated Node #0,1,3: 29:[14, 15] Operation: 47-32=15 Moving to Node #0,1,2 Current State: 29:[32, 33], Operations: ['55-41=14', '47-14=33'] Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 32+33=65, Resulting Numbers: [65] 65,29 unequal: No Solution Exploring Operation: 32*33=1056, Resulting Numbers: [1056] 1056,29 unequal: No Solution Moving to Node #0,1,3 Current State: 29:[14, 15], Operations: ['55-41=14', '47-32=15'] Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[47, 41, 55, 32], Operations: [] Exploring Operation: 55-41=14, Resulting Numbers: [47, 32, 14] Generated Node #0,1: 29:[47, 32, 14] Operation: 55-41=14 Moving to Node #0,1 Current State: 29:[47, 32, 14], Operations: ['55-41=14'] Exploring Operation: 47-32=15, Resulting Numbers: [14, 15] Generated Node #0,1,3: 29:[14, 15] Operation: 47-32=15 Moving to Node #0,1,3 Current State: 29:[14, 15], Operations: ['55-41=14', '47-32=15'] Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 23, 68, 60, 7 ]
70
[ "23+7=30", "60/30=2", "68+2=70" ]
Current State: 70:[23, 68, 60, 7], Operations: [] Exploring Operation: 23+7=30, Resulting Numbers: [68, 60, 30] Generated Node #2: [68, 60, 30] from Operation: 23+7=30 Current State: 70:[68, 60, 30], Operations: ['23+7=30'] Exploring Operation: 60/30=2, Resulting Numbers: [68, 2] Generated Node #3: [68, 2] from Operation: 60/30=2 Current State: 70:[68, 2], Operations: ['23+7=30', '60/30=2'] Exploring Operation: 68+2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[23, 68, 60, 7], Operations: [] Exploring Operation: 60-23=37, Resulting Numbers: [68, 7, 37] Generated Node #0,0: 70:[68, 7, 37] Operation: 60-23=37 Exploring Operation: 68-60=8, Resulting Numbers: [23, 7, 8] Generated Node #0,1: 70:[23, 7, 8] Operation: 68-60=8 Exploring Operation: 23-7=16, Resulting Numbers: [68, 60, 16] Generated Node #0,2: 70:[68, 60, 16] Operation: 23-7=16 Exploring Operation: 60+7=67, Resulting Numbers: [23, 68, 67] Generated Node #0,3: 70:[23, 68, 67] Operation: 60+7=67 Moving to Node #0,0 Current State: 70:[68, 7, 37], Operations: ['60-23=37'] Exploring Operation: 68+7=75, Resulting Numbers: [37, 75] Generated Node #0,0,0: 70:[37, 75] Operation: 68+7=75 Exploring Operation: 68-37=31, Resulting Numbers: [7, 31] Generated Node #0,0,1: 70:[7, 31] Operation: 68-37=31 Exploring Operation: 68-7=61, Resulting Numbers: [37, 61] Generated Node #0,0,2: 70:[37, 61] Operation: 68-7=61 Exploring Operation: 37-7=30, Resulting Numbers: [68, 30] Generated Node #0,0,3: 70:[68, 30] Operation: 37-7=30 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 70:[7, 31], Operations: ['60-23=37', '68-37=31'] Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 7+31=38, Resulting Numbers: [38] 38,70 unequal: No Solution Exploring Operation: 7*31=217, Resulting Numbers: [217] 217,70 unequal: No Solution No 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: 70:[37, 75], Operations: ['60-23=37', '68+7=75'] Exploring Operation: 37*75=2775, Resulting Numbers: [2775] 2775,70 unequal: No Solution Exploring Operation: 37+75=112, Resulting Numbers: [112] 112,70 unequal: No Solution Exploring Operation: 75-37=38, Resulting Numbers: [38] 38,70 unequal: No Solution No 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: 70:[68, 30], Operations: ['60-23=37', '37-7=30'] Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,70 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,70 unequal: No Solution Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,70 unequal: No Solution No 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: 70:[37, 61], Operations: ['60-23=37', '68-7=61'] Exploring Operation: 61-37=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 37*61=2257, Resulting Numbers: [2257] 2257,70 unequal: No Solution Exploring Operation: 37+61=98, Resulting Numbers: [98] 98,70 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: 70:[23, 7, 8], Operations: ['68-60=8'] Exploring Operation: 23-8=15, Resulting Numbers: [7, 15] Generated Node #0,1,0: 70:[7, 15] Operation: 23-8=15 Exploring Operation: 23+7=30, Resulting Numbers: [8, 30] Generated Node #0,1,1: 70:[8, 30] Operation: 23+7=30 Exploring Operation: 23-7=16, Resulting Numbers: [8, 16] Generated Node #0,1,2: 70:[8, 16] Operation: 23-7=16 Exploring Operation: 23+8=31, Resulting Numbers: [7, 31] Generated Node #0,1,3: 70:[7, 31] Operation: 23+8=31 Moving to Node #0,3 Current State: 70:[23, 68, 67], Operations: ['60+7=67'] Exploring Operation: 23+67=90, Resulting Numbers: [68, 90] Generated Node #0,3,0: 70:[68, 90] Operation: 23+67=90 Exploring Operation: 67-23=44, Resulting Numbers: [68, 44] Generated Node #0,3,1: 70:[68, 44] Operation: 67-23=44 Exploring Operation: 68-23=45, Resulting Numbers: [67, 45] Generated Node #0,3,2: 70:[67, 45] Operation: 68-23=45 Exploring Operation: 68-67=1, Resulting Numbers: [23, 1] Generated Node #0,3,3: 70:[23, 1] Operation: 68-67=1 Moving to Node #0,2 Current State: 70:[68, 60, 16], Operations: ['23-7=16'] Exploring Operation: 60+16=76, Resulting Numbers: [68, 76] Generated Node #0,2,0: 70:[68, 76] Operation: 60+16=76 Exploring Operation: 68-60=8, Resulting Numbers: [16, 8] Generated Node #0,2,1: 70:[16, 8] Operation: 68-60=8 Exploring Operation: 68+16=84, Resulting Numbers: [60, 84] Generated Node #0,2,2: 70:[60, 84] Operation: 68+16=84 Exploring Operation: 60-16=44, Resulting Numbers: [68, 44] Generated Node #0,2,3: 70:[68, 44] Operation: 60-16=44 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 70:[16, 8], Operations: ['23-7=16', '68-60=8'] Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 16+8=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 16*8=128, Resulting Numbers: [128] 128,70 unequal: No Solution No 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: 70:[68, 76], Operations: ['23-7=16', '60+16=76'] Exploring Operation: 76-68=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 68+76=144, Resulting Numbers: [144] 144,70 unequal: No Solution Exploring Operation: 68*76=5168, Resulting Numbers: [5168] 5168,70 unequal: No Solution No 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: 70:[68, 44], Operations: ['23-7=16', '60-16=44'] Exploring Operation: 68+44=112, Resulting Numbers: [112] 112,70 unequal: No Solution Exploring Operation: 68*44=2992, Resulting Numbers: [2992] 2992,70 unequal: No Solution Exploring Operation: 68-44=24, Resulting Numbers: [24] 24,70 unequal: No Solution No 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: 70:[60, 84], Operations: ['23-7=16', '68+16=84'] Exploring Operation: 60+84=144, Resulting Numbers: [144] 144,70 unequal: No Solution Exploring Operation: 60*84=5040, Resulting Numbers: [5040] 5040,70 unequal: No Solution Exploring Operation: 84-60=24, Resulting Numbers: [24] 24,70 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: 70:[7, 15], Operations: ['68-60=8', '23-8=15'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,70 unequal: No Solution Exploring Operation: 7*15=105, Resulting Numbers: [105] 105,70 unequal: No Solution Moving to Node #0,1,2 Current State: 70:[8, 16], Operations: ['68-60=8', '23-7=16'] Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 8+16=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 8*16=128, Resulting Numbers: [128] 128,70 unequal: No Solution Moving to Node #0,1,3 Current State: 70:[7, 31], Operations: ['68-60=8', '23+8=31'] Exploring Operation: 7+31=38, Resulting Numbers: [38] 38,70 unequal: No Solution Exploring Operation: 7*31=217, Resulting Numbers: [217] 217,70 unequal: No Solution Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[8, 30], Operations: ['68-60=8', '23+7=30'] Exploring Operation: 8*30=240, Resulting Numbers: [240] 240,70 unequal: No Solution Exploring Operation: 8+30=38, Resulting Numbers: [38] 38,70 unequal: No Solution Exploring Operation: 30-8=22, Resulting Numbers: [22] 22,70 unequal: No Solution Moving to Node #0,3,3 Current State: 70:[23, 1], Operations: ['60+7=67', '68-67=1'] Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,70 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,70 unequal: No Solution Moving to Node #0,3,1 Current State: 70:[68, 44], Operations: ['60+7=67', '67-23=44'] Exploring Operation: 68+44=112, Resulting Numbers: [112] 112,70 unequal: No Solution Exploring Operation: 68-44=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 68*44=2992, Resulting Numbers: [2992] 2992,70 unequal: No Solution Moving to Node #0,3,2 Current State: 70:[67, 45], Operations: ['60+7=67', '68-23=45'] Exploring Operation: 67-45=22, Resulting Numbers: [22] 22,70 unequal: No Solution Exploring Operation: 67+45=112, Resulting Numbers: [112] 112,70 unequal: No Solution Exploring Operation: 67*45=3015, Resulting Numbers: [3015] 3015,70 unequal: No Solution Moving to Node #0,3,0 Current State: 70:[68, 90], Operations: ['60+7=67', '23+67=90'] Exploring Operation: 68+90=158, Resulting Numbers: [158] 158,70 unequal: No Solution Exploring Operation: 90-68=22, Resulting Numbers: [22] 22,70 unequal: No Solution Exploring Operation: 68*90=6120, Resulting Numbers: [6120] 6120,70 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 2, 17, 29, 18 ]
81
[ "2*17=34", "29+18=47", "34+47=81" ]
Current State: 81:[2, 17, 29, 18], Operations: [] Exploring Operation: 2*17=34, Resulting Numbers: [29, 18, 34] Generated Node #2: [29, 18, 34] from Operation: 2*17=34 Current State: 81:[29, 18, 34], Operations: ['2*17=34'] Exploring Operation: 29+18=47, Resulting Numbers: [34, 47] Generated Node #3: [34, 47] from Operation: 29+18=47 Current State: 81:[34, 47], Operations: ['2*17=34', '29+18=47'] Exploring Operation: 34+47=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[2, 17, 29, 18], Operations: [] Exploring Operation: 18-17=1, Resulting Numbers: [2, 29, 1] Generated Node #0,0: 81:[2, 29, 1] Operation: 18-17=1 Exploring Operation: 18/2=9, Resulting Numbers: [17, 29, 9] Generated Node #0,1: 81:[17, 29, 9] Operation: 18/2=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[2, 29, 1], Operations: ['18-17=1'] Exploring Operation: 2+1=3, Resulting Numbers: [29, 3] Generated Node #0,0,0: 81:[29, 3] Operation: 2+1=3 Exploring Operation: 29-2=27, Resulting Numbers: [1, 27] Generated Node #0,0,1: 81:[1, 27] Operation: 29-2=27 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[29, 3], Operations: ['18-17=1', '2+1=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,81 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,81 unequal: No Solution No 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:[1, 27], Operations: ['18-17=1', '29-2=27'] Exploring Operation: 1*27=27, Resulting Numbers: [27] 27,81 unequal: No Solution Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,81 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 #0,1 Current State: 81:[17, 29, 9], Operations: ['18/2=9'] Exploring Operation: 29-17=12, Resulting Numbers: [9, 12] Generated Node #0,1,0: 81:[9, 12] Operation: 29-17=12 Exploring Operation: 17+9=26, Resulting Numbers: [29, 26] Generated Node #0,1,1: 81:[29, 26] Operation: 17+9=26 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 81:[9, 12], Operations: ['18/2=9', '29-17=12'] Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,81 unequal: No Solution Exploring Operation: 9+12=21, Resulting Numbers: [21] 21,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 81:[29, 26], Operations: ['18/2=9', '17+9=26'] Exploring Operation: 29+26=55, Resulting Numbers: [55] 55,81 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,81 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 No solution found.
0
hs_2
sum_heuristic
[ 11, 58, 52, 33 ]
99
[ "58-52=6", "11*6=66", "33+66=99" ]
Current State: 99:[11, 58, 52, 33], Operations: [] Exploring Operation: 58-52=6, Resulting Numbers: [11, 33, 6] Generated Node #2: [11, 33, 6] from Operation: 58-52=6 Current State: 99:[11, 33, 6], Operations: ['58-52=6'] Exploring Operation: 11*6=66, Resulting Numbers: [33, 66] Generated Node #3: [33, 66] from Operation: 11*6=66 Current State: 99:[33, 66], Operations: ['58-52=6', '11*6=66'] Exploring Operation: 33+66=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[11, 58, 52, 33], Operations: [] Exploring Operation: 58-52=6, Resulting Numbers: [11, 33, 6] Generated Node #0,0: 99:[11, 33, 6] Operation: 58-52=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[11, 33, 6], Operations: ['58-52=6'] Exploring Operation: 11-6=5, Resulting Numbers: [33, 5] Generated Node #0,0,0: 99:[33, 5] Operation: 11-6=5 Moving to Node #0,0,0 Current State: 99:[33, 5], Operations: ['58-52=6', '11-6=5'] Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 17, 2, 20, 56 ]
62
[ "20-17=3", "2*3=6", "56+6=62" ]
Current State: 62:[17, 2, 20, 56], Operations: [] Exploring Operation: 20-17=3, Resulting Numbers: [2, 56, 3] Generated Node #2: [2, 56, 3] from Operation: 20-17=3 Current State: 62:[2, 56, 3], Operations: ['20-17=3'] Exploring Operation: 2*3=6, Resulting Numbers: [56, 6] Generated Node #3: [56, 6] from Operation: 2*3=6 Current State: 62:[56, 6], Operations: ['20-17=3', '2*3=6'] Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[17, 2, 20, 56], Operations: [] Exploring Operation: 56-20=36, Resulting Numbers: [17, 2, 36] Generated Node #0,0: 62:[17, 2, 36] Operation: 56-20=36 Exploring Operation: 17*2=34, Resulting Numbers: [20, 56, 34] Generated Node #0,1: 62:[20, 56, 34] Operation: 17*2=34 Exploring Operation: 17+20=37, Resulting Numbers: [2, 56, 37] Generated Node #0,2: 62:[2, 56, 37] Operation: 17+20=37 Exploring Operation: 56-17=39, Resulting Numbers: [2, 20, 39] Generated Node #0,3: 62:[2, 20, 39] Operation: 56-17=39 Exploring Operation: 20-17=3, Resulting Numbers: [2, 56, 3] Generated Node #0,4: 62:[2, 56, 3] Operation: 20-17=3 Start Sub Search at level 1: Moving to Node #0,4 Current State: 62:[2, 56, 3], Operations: ['20-17=3'] Exploring Operation: 56-2=54, Resulting Numbers: [3, 54] Generated Node #0,4,0: 62:[3, 54] Operation: 56-2=54 Exploring Operation: 56+3=59, Resulting Numbers: [2, 59] Generated Node #0,4,1: 62:[2, 59] Operation: 56+3=59 Exploring Operation: 56/2=28, Resulting Numbers: [3, 28] Generated Node #0,4,2: 62:[3, 28] Operation: 56/2=28 Exploring Operation: 2+56=58, Resulting Numbers: [3, 58] Generated Node #0,4,3: 62:[3, 58] Operation: 2+56=58 Exploring Operation: 3-2=1, Resulting Numbers: [56, 1] Generated Node #0,4,4: 62:[56, 1] Operation: 3-2=1 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 62:[2, 59], Operations: ['20-17=3', '56+3=59'] Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,62 unequal: No Solution Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,62 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 62:[3, 28], Operations: ['20-17=3', '56/2=28'] Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,62 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 62:[3, 58], Operations: ['20-17=3', '2+56=58'] Exploring Operation: 3*58=174, Resulting Numbers: [174] 174,62 unequal: No Solution Exploring Operation: 3+58=61, Resulting Numbers: [61] 61,62 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 62:[56, 1], Operations: ['20-17=3', '3-2=1'] Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,62 unequal: No Solution Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,62 unequal: No Solution Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,62 unequal: No Solution Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 62:[3, 54], Operations: ['20-17=3', '56-2=54'] Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,62 unequal: No Solution Exploring Operation: 3+54=57, Resulting Numbers: [57] 57,62 unequal: No Solution Exploring Operation: 3*54=162, Resulting Numbers: [162] 162,62 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[2, 56, 37], Operations: ['17+20=37'] Exploring Operation: 56-37=19, Resulting Numbers: [2, 19] Generated Node #0,2,0: 62:[2, 19] Operation: 56-37=19 Exploring Operation: 2+56=58, Resulting Numbers: [37, 58] Generated Node #0,2,1: 62:[37, 58] Operation: 2+56=58 Exploring Operation: 56-2=54, Resulting Numbers: [37, 54] Generated Node #0,2,2: 62:[37, 54] Operation: 56-2=54 Exploring Operation: 56/2=28, Resulting Numbers: [37, 28] Generated Node #0,2,3: 62:[37, 28] Operation: 56/2=28 Exploring Operation: 37-2=35, Resulting Numbers: [56, 35] Generated Node #0,2,4: 62:[56, 35] Operation: 37-2=35 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 62:[37, 28], Operations: ['17+20=37', '56/2=28'] Exploring Operation: 37*28=1036, Resulting Numbers: [1036] 1036,62 unequal: No Solution Exploring Operation: 37-28=9, Resulting Numbers: [9] 9,62 unequal: No Solution Exploring Operation: 37+28=65, Resulting Numbers: [65] 65,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 62:[37, 58], Operations: ['17+20=37', '2+56=58'] Exploring Operation: 58-37=21, Resulting Numbers: [21] 21,62 unequal: No Solution Exploring Operation: 37*58=2146, Resulting Numbers: [2146] 2146,62 unequal: No Solution Exploring Operation: 37+58=95, Resulting Numbers: [95] 95,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 62:[56, 35], Operations: ['17+20=37', '37-2=35'] Exploring Operation: 56-35=21, Resulting Numbers: [21] 21,62 unequal: No Solution Exploring Operation: 56*35=1960, Resulting Numbers: [1960] 1960,62 unequal: No Solution Exploring Operation: 56+35=91, Resulting Numbers: [91] 91,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 62:[2, 19], Operations: ['17+20=37', '56-37=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,62 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 62:[37, 54], Operations: ['17+20=37', '56-2=54'] Exploring Operation: 37*54=1998, Resulting Numbers: [1998] 1998,62 unequal: No Solution Exploring Operation: 54-37=17, Resulting Numbers: [17] 17,62 unequal: No Solution Exploring Operation: 37+54=91, Resulting Numbers: [91] 91,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[17, 2, 36], Operations: ['56-20=36'] Exploring Operation: 17+36=53, Resulting Numbers: [2, 53] Generated Node #0,0,0: 62:[2, 53] Operation: 17+36=53 Exploring Operation: 36-2=34, Resulting Numbers: [17, 34] Generated Node #0,0,1: 62:[17, 34] Operation: 36-2=34 Exploring Operation: 17*2=34, Resulting Numbers: [36, 34] Generated Node #0,0,2: 62:[36, 34] Operation: 17*2=34 Exploring Operation: 36-17=19, Resulting Numbers: [2, 19] Generated Node #0,0,3: 62:[2, 19] Operation: 36-17=19 Exploring Operation: 17+2=19, Resulting Numbers: [36, 19] Generated Node #0,0,4: 62:[36, 19] Operation: 17+2=19 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 62:[36, 34], Operations: ['56-20=36', '17*2=34'] Exploring Operation: 36+34=70, Resulting Numbers: [70] 70,62 unequal: No Solution Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 36*34=1224, Resulting Numbers: [1224] 1224,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[2, 53], Operations: ['56-20=36', '17+36=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,62 unequal: No Solution Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,62 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 62:[2, 19], Operations: ['56-20=36', '36-17=19'] Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,62 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 62:[17, 34], Operations: ['56-20=36', '36-2=34'] Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,62 unequal: No Solution Exploring Operation: 17*34=578, Resulting Numbers: [578] 578,62 unequal: No Solution Exploring Operation: 17+34=51, Resulting Numbers: [51] 51,62 unequal: No Solution Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 62:[36, 19], Operations: ['56-20=36', '17+2=19'] Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,62 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,62 unequal: No Solution Exploring Operation: 36*19=684, Resulting Numbers: [684] 684,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 62:[2, 20, 39], Operations: ['56-17=39'] Exploring Operation: 20/2=10, Resulting Numbers: [39, 10] Generated Node #0,3,0: 62:[39, 10] Operation: 20/2=10 Exploring Operation: 20+39=59, Resulting Numbers: [2, 59] Generated Node #0,3,1: 62:[2, 59] Operation: 20+39=59 Exploring Operation: 2+20=22, Resulting Numbers: [39, 22] Generated Node #0,3,2: 62:[39, 22] Operation: 2+20=22 Exploring Operation: 39-20=19, Resulting Numbers: [2, 19] Generated Node #0,3,3: 62:[2, 19] Operation: 39-20=19 Exploring Operation: 2*20=40, Resulting Numbers: [39, 40] Generated Node #0,3,4: 62:[39, 40] Operation: 2*20=40 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 62:[2, 59], Operations: ['56-17=39', '20+39=59'] Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,62 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,62 unequal: No Solution Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 62:[2, 19], Operations: ['56-17=39', '39-20=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,62 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 62:[39, 10], Operations: ['56-17=39', '20/2=10'] Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 39+10=49, Resulting Numbers: [49] 49,62 unequal: No Solution Exploring Operation: 39*10=390, Resulting Numbers: [390] 390,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 62:[39, 22], Operations: ['56-17=39', '2+20=22'] Exploring Operation: 39+22=61, Resulting Numbers: [61] 61,62 unequal: No Solution Exploring Operation: 39-22=17, Resulting Numbers: [17] 17,62 unequal: No Solution Exploring Operation: 39*22=858, Resulting Numbers: [858] 858,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 62:[39, 40], Operations: ['56-17=39', '2*20=40'] Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,62 unequal: No Solution Exploring Operation: 39+40=79, Resulting Numbers: [79] 79,62 unequal: No Solution Exploring Operation: 39*40=1560, Resulting Numbers: [1560] 1560,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[20, 56, 34], Operations: ['17*2=34'] Exploring Operation: 56-34=22, Resulting Numbers: [20, 22] Generated Node #0,1,0: 62:[20, 22] Operation: 56-34=22 Exploring Operation: 34-20=14, Resulting Numbers: [56, 14] Generated Node #0,1,1: 62:[56, 14] Operation: 34-20=14 Exploring Operation: 56-20=36, Resulting Numbers: [34, 36] Generated Node #0,1,2: 62:[34, 36] Operation: 56-20=36 Exploring Operation: 20+56=76, Resulting Numbers: [34, 76] Generated Node #0,1,3: 62:[34, 76] Operation: 20+56=76 Exploring Operation: 20+34=54, Resulting Numbers: [56, 54] Generated Node #0,1,4: 62:[56, 54] Operation: 20+34=54 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 62:[34, 36], Operations: ['17*2=34', '56-20=36'] Exploring Operation: 34+36=70, Resulting Numbers: [70] 70,62 unequal: No Solution Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 34*36=1224, Resulting Numbers: [1224] 1224,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 62:[56, 54], Operations: ['17*2=34', '20+34=54'] Exploring Operation: 56*54=3024, Resulting Numbers: [3024] 3024,62 unequal: No Solution Exploring Operation: 56-54=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 56+54=110, Resulting Numbers: [110] 110,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 62:[34, 76], Operations: ['17*2=34', '20+56=76'] Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 34+76=110, Resulting Numbers: [110] 110,62 unequal: No Solution Exploring Operation: 34*76=2584, Resulting Numbers: [2584] 2584,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 62:[56, 14], Operations: ['17*2=34', '34-20=14'] Exploring Operation: 56+14=70, Resulting Numbers: [70] 70,62 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,62 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 56*14=784, Resulting Numbers: [784] 784,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 62:[20, 22], Operations: ['17*2=34', '56-34=22'] Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 20*22=440, Resulting Numbers: [440] 440,62 unequal: No Solution Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 15, 96, 68, 26 ]
39
[ "96-15=81", "68-26=42", "81-42=39" ]
Current State: 39:[15, 96, 68, 26], Operations: [] Exploring Operation: 96-15=81, Resulting Numbers: [68, 26, 81] Generated Node #2: [68, 26, 81] from Operation: 96-15=81 Current State: 39:[68, 26, 81], Operations: ['96-15=81'] Exploring Operation: 68-26=42, Resulting Numbers: [81, 42] Generated Node #3: [81, 42] from Operation: 68-26=42 Current State: 39:[81, 42], Operations: ['96-15=81', '68-26=42'] Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[15, 96, 68, 26], Operations: [] Exploring Operation: 96-26=70, Resulting Numbers: [15, 68, 70] Generated Node #0,0: 39:[15, 68, 70] Operation: 96-26=70 Exploring Operation: 96-68=28, Resulting Numbers: [15, 26, 28] Generated Node #0,1: 39:[15, 26, 28] Operation: 96-68=28 Exploring Operation: 96-15=81, Resulting Numbers: [68, 26, 81] Generated Node #0,2: 39:[68, 26, 81] Operation: 96-15=81 Exploring Operation: 68-26=42, Resulting Numbers: [15, 96, 42] Generated Node #0,3: 39:[15, 96, 42] Operation: 68-26=42 Moving to Node #0,1 Current State: 39:[15, 26, 28], Operations: ['96-68=28'] Exploring Operation: 28-26=2, Resulting Numbers: [15, 2] Generated Node #0,1,0: 39:[15, 2] Operation: 28-26=2 Exploring Operation: 28-15=13, Resulting Numbers: [26, 13] Generated Node #0,1,1: 39:[26, 13] Operation: 28-15=13 Exploring Operation: 15+26=41, Resulting Numbers: [28, 41] Generated Node #0,1,2: 39:[28, 41] Operation: 15+26=41 Exploring Operation: 26-15=11, Resulting Numbers: [28, 11] Generated Node #0,1,3: 39:[28, 11] Operation: 26-15=11 Moving to Node #0,3 Current State: 39:[15, 96, 42], Operations: ['68-26=42'] Exploring Operation: 96-42=54, Resulting Numbers: [15, 54] Generated Node #0,3,0: 39:[15, 54] Operation: 96-42=54 Exploring Operation: 42-15=27, Resulting Numbers: [96, 27] Generated Node #0,3,1: 39:[96, 27] Operation: 42-15=27 Exploring Operation: 96-15=81, Resulting Numbers: [42, 81] Generated Node #0,3,2: 39:[42, 81] Operation: 96-15=81 Exploring Operation: 15+96=111, Resulting Numbers: [42, 111] Generated Node #0,3,3: 39:[42, 111] Operation: 15+96=111 Moving to Node #0,0 Current State: 39:[15, 68, 70], Operations: ['96-26=70'] Exploring Operation: 70-15=55, Resulting Numbers: [68, 55] Generated Node #0,0,0: 39:[68, 55] Operation: 70-15=55 Exploring Operation: 68-15=53, Resulting Numbers: [70, 53] Generated Node #0,0,1: 39:[70, 53] Operation: 68-15=53 Exploring Operation: 70-68=2, Resulting Numbers: [15, 2] Generated Node #0,0,2: 39:[15, 2] Operation: 70-68=2 Exploring Operation: 15+68=83, Resulting Numbers: [70, 83] Generated Node #0,0,3: 39:[70, 83] Operation: 15+68=83 Moving to Node #0,2 Current State: 39:[68, 26, 81], Operations: ['96-15=81'] Exploring Operation: 68-26=42, Resulting Numbers: [81, 42] Generated Node #0,2,0: 39:[81, 42] Operation: 68-26=42 Exploring Operation: 68+26=94, Resulting Numbers: [81, 94] Generated Node #0,2,1: 39:[81, 94] Operation: 68+26=94 Exploring Operation: 81-26=55, Resulting Numbers: [68, 55] Generated Node #0,2,2: 39:[68, 55] Operation: 81-26=55 Exploring Operation: 81-68=13, Resulting Numbers: [26, 13] Generated Node #0,2,3: 39:[26, 13] Operation: 81-68=13 Moving to Node #0,1,0 Current State: 39:[15, 2], Operations: ['96-68=28', '28-26=2'] Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,39 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[15, 2], Operations: ['96-26=70', '70-68=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,39 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,39 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[28, 41], Operations: ['96-68=28', '15+26=41'] Exploring Operation: 28+41=69, Resulting Numbers: [69] 69,39 unequal: No Solution Exploring Operation: 28*41=1148, Resulting Numbers: [1148] 1148,39 unequal: No Solution Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,39 unequal: No Solution Moving to Node #0,2,3 Current State: 39:[26, 13], Operations: ['96-15=81', '81-68=13'] Exploring Operation: 26*13=338, Resulting Numbers: [338] 338,39 unequal: No Solution Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 26+13=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[15, 96, 68, 26], Operations: [] Exploring Operation: 96-15=81, Resulting Numbers: [68, 26, 81] Generated Node #0,2: 39:[68, 26, 81] Operation: 96-15=81 Moving to Node #0,2 Current State: 39:[68, 26, 81], Operations: ['96-15=81'] Exploring Operation: 81-68=13, Resulting Numbers: [26, 13] Generated Node #0,2,3: 39:[26, 13] Operation: 81-68=13 Moving to Node #0,2,3 Current State: 39:[26, 13], Operations: ['96-15=81', '81-68=13'] Exploring Operation: 26+13=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
0.967882
hs_4
mult_heuristic
[ 18, 15, 50, 14 ]
12
[ "18-15=3", "50-14=36", "36/3=12" ]
Current State: 12:[18, 15, 50, 14], Operations: [] Exploring Operation: 18-15=3, Resulting Numbers: [50, 14, 3] Generated Node #2: [50, 14, 3] from Operation: 18-15=3 Current State: 12:[50, 14, 3], Operations: ['18-15=3'] Exploring Operation: 50-14=36, Resulting Numbers: [3, 36] Generated Node #3: [3, 36] from Operation: 50-14=36 Current State: 12:[3, 36], Operations: ['18-15=3', '50-14=36'] Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[18, 15, 50, 14], Operations: [] Exploring Operation: 50-15=35, Resulting Numbers: [18, 14, 35] Generated Node #0,0: 12:[18, 14, 35] Operation: 50-15=35 Exploring Operation: 50-18=32, Resulting Numbers: [15, 14, 32] Generated Node #0,1: 12:[15, 14, 32] Operation: 50-18=32 Exploring Operation: 18-15=3, Resulting Numbers: [50, 14, 3] Generated Node #0,2: 12:[50, 14, 3] Operation: 18-15=3 Exploring Operation: 50-14=36, Resulting Numbers: [18, 15, 36] Generated Node #0,3: 12:[18, 15, 36] Operation: 50-14=36 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[15, 14, 32], Operations: ['50-18=32'] Exploring Operation: 15+14=29, Resulting Numbers: [32, 29] Generated Node #0,1,0: 12:[32, 29] Operation: 15+14=29 Exploring Operation: 32-15=17, Resulting Numbers: [14, 17] Generated Node #0,1,1: 12:[14, 17] Operation: 32-15=17 Exploring Operation: 32-14=18, Resulting Numbers: [15, 18] Generated Node #0,1,2: 12:[15, 18] Operation: 32-14=18 Exploring Operation: 15-14=1, Resulting Numbers: [32, 1] Generated Node #0,1,3: 12:[32, 1] Operation: 15-14=1 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 12:[14, 17], Operations: ['50-18=32', '32-15=17'] Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 14*17=238, Resulting Numbers: [238] 238,12 unequal: No Solution Exploring Operation: 14+17=31, Resulting Numbers: [31] 31,12 unequal: No Solution No 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: 12:[15, 18], Operations: ['50-18=32', '32-14=18'] Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,12 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,12 unequal: No Solution No 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: 12:[32, 1], Operations: ['50-18=32', '15-14=1'] Exploring Operation: 32*1=32, Resulting Numbers: [32] 32,12 unequal: No Solution Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,12 unequal: No Solution Exploring Operation: 32/1=32, Resulting Numbers: [32] 32,12 unequal: No Solution No 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: 12:[32, 29], Operations: ['50-18=32', '15+14=29'] Exploring Operation: 32*29=928, Resulting Numbers: [928] 928,12 unequal: No Solution Exploring Operation: 32-29=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 32+29=61, Resulting Numbers: [61] 61,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[18, 14, 35], Operations: ['50-15=35'] Exploring Operation: 35-18=17, Resulting Numbers: [14, 17] Generated Node #0,0,0: 12:[14, 17] Operation: 35-18=17 Exploring Operation: 18+14=32, Resulting Numbers: [35, 32] Generated Node #0,0,1: 12:[35, 32] Operation: 18+14=32 Exploring Operation: 35-14=21, Resulting Numbers: [18, 21] Generated Node #0,0,2: 12:[18, 21] Operation: 35-14=21 Exploring Operation: 18-14=4, Resulting Numbers: [35, 4] Generated Node #0,0,3: 12:[35, 4] Operation: 18-14=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[14, 17], Operations: ['50-15=35', '35-18=17'] Exploring Operation: 14*17=238, Resulting Numbers: [238] 238,12 unequal: No Solution Exploring Operation: 14+17=31, Resulting Numbers: [31] 31,12 unequal: No Solution Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,12 unequal: No Solution No 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: 12:[18, 21], Operations: ['50-15=35', '35-14=21'] Exploring Operation: 18*21=378, Resulting Numbers: [378] 378,12 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 18+21=39, Resulting Numbers: [39] 39,12 unequal: No Solution No 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: 12:[35, 4], Operations: ['50-15=35', '18-14=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 35*4=140, Resulting Numbers: [140] 140,12 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,12 unequal: No Solution No 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: 12:[35, 32], Operations: ['50-15=35', '18+14=32'] Exploring Operation: 35*32=1120, Resulting Numbers: [1120] 1120,12 unequal: No Solution Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 35+32=67, Resulting Numbers: [67] 67,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[18, 15, 36], Operations: ['50-14=36'] Exploring Operation: 36-18=18, Resulting Numbers: [15, 18] Generated Node #0,3,0: 12:[15, 18] Operation: 36-18=18 Exploring Operation: 36-15=21, Resulting Numbers: [18, 21] Generated Node #0,3,1: 12:[18, 21] Operation: 36-15=21 Exploring Operation: 36/18=2, Resulting Numbers: [15, 2] Generated Node #0,3,2: 12:[15, 2] Operation: 36/18=2 Exploring Operation: 18-15=3, Resulting Numbers: [36, 3] Generated Node #0,3,3: 12:[36, 3] Operation: 18-15=3 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 12:[15, 2], Operations: ['50-14=36', '36/18=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,12 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,12 unequal: No Solution No 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: 12:[15, 18], Operations: ['50-14=36', '36-18=18'] Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,12 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,12 unequal: No Solution No 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: 12:[18, 21], Operations: ['50-14=36', '36-15=21'] Exploring Operation: 18*21=378, Resulting Numbers: [378] 378,12 unequal: No Solution Exploring Operation: 18+21=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,12 unequal: No Solution No 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: 12:[36, 3], Operations: ['50-14=36', '18-15=3'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 36*3=108, Resulting Numbers: [108] 108,12 unequal: No Solution Exploring Operation: 36+3=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[18, 15, 50, 14], Operations: [] Exploring Operation: 50-14=36, Resulting Numbers: [18, 15, 36] Generated Node #0,3: 12:[18, 15, 36] Operation: 50-14=36 Moving to Node #0,3 Current State: 12:[18, 15, 36], Operations: ['50-14=36'] Exploring Operation: 18-15=3, Resulting Numbers: [36, 3] Generated Node #0,3,3: 12:[36, 3] Operation: 18-15=3 Moving to Node #0,3,3 Current State: 12:[36, 3], Operations: ['50-14=36', '18-15=3'] Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.949653
hs_4
sum_heuristic
[ 64, 88, 81, 77 ]
28
[ "88-64=24", "81-77=4", "24+4=28" ]
Current State: 28:[64, 88, 81, 77], Operations: [] Exploring Operation: 88-64=24, Resulting Numbers: [81, 77, 24] Generated Node #2: [81, 77, 24] from Operation: 88-64=24 Current State: 28:[81, 77, 24], Operations: ['88-64=24'] Exploring Operation: 81-77=4, Resulting Numbers: [24, 4] Generated Node #3: [24, 4] from Operation: 81-77=4 Current State: 28:[24, 4], Operations: ['88-64=24', '81-77=4'] Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[64, 88, 81, 77], Operations: [] Exploring Operation: 88-81=7, Resulting Numbers: [64, 77, 7] Generated Node #0,0: 28:[64, 77, 7] Operation: 88-81=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[64, 77, 7], Operations: ['88-81=7'] Exploring Operation: 77-64=13, Resulting Numbers: [7, 13] Generated Node #0,0,0: 28:[7, 13] Operation: 77-64=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[7, 13], Operations: ['88-81=7', '77-64=13'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,28 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
sum_heuristic
[ 88, 93, 35, 58 ]
98
[ "93-88=5", "35+58=93", "5+93=98" ]
Current State: 98:[88, 93, 35, 58], Operations: [] Exploring Operation: 93-88=5, Resulting Numbers: [35, 58, 5] Generated Node #2: [35, 58, 5] from Operation: 93-88=5 Current State: 98:[35, 58, 5], Operations: ['93-88=5'] Exploring Operation: 35+58=93, Resulting Numbers: [5, 93] Generated Node #3: [5, 93] from Operation: 35+58=93 Current State: 98:[5, 93], Operations: ['93-88=5', '35+58=93'] Exploring Operation: 5+93=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[88, 93, 35, 58], Operations: [] Exploring Operation: 88-35=53, Resulting Numbers: [93, 58, 53] Generated Node #0,0: 98:[93, 58, 53] Operation: 88-35=53 Exploring Operation: 35+58=93, Resulting Numbers: [88, 93, 93] Generated Node #0,1: 98:[88, 93, 93] Operation: 35+58=93 Exploring Operation: 58-35=23, Resulting Numbers: [88, 93, 23] Generated Node #0,2: 98:[88, 93, 23] Operation: 58-35=23 Moving to Node #0,0 Current State: 98:[93, 58, 53], Operations: ['88-35=53'] Exploring Operation: 58-53=5, Resulting Numbers: [93, 5] Generated Node #0,0,0: 98:[93, 5] Operation: 58-53=5 Exploring Operation: 93-58=35, Resulting Numbers: [53, 35] Generated Node #0,0,1: 98:[53, 35] Operation: 93-58=35 Exploring Operation: 93-53=40, Resulting Numbers: [58, 40] Generated Node #0,0,2: 98:[58, 40] Operation: 93-53=40 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[93, 5], Operations: ['88-35=53', '58-53=5'] Exploring Operation: 93+5=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[88, 93, 35, 58], Operations: [] Exploring Operation: 88-35=53, Resulting Numbers: [93, 58, 53] Generated Node #0,0: 98:[93, 58, 53] Operation: 88-35=53 Moving to Node #0,0 Current State: 98:[93, 58, 53], Operations: ['88-35=53'] Exploring Operation: 58-53=5, Resulting Numbers: [93, 5] Generated Node #0,0,0: 98:[93, 5] Operation: 58-53=5 Moving to Node #0,0,0 Current State: 98:[93, 5], Operations: ['88-35=53', '58-53=5'] Exploring Operation: 93+5=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 55, 90, 1, 84 ]
49
[ "90-55=35", "1*84=84", "84-35=49" ]
Current State: 49:[55, 90, 1, 84], Operations: [] Exploring Operation: 90-55=35, Resulting Numbers: [1, 84, 35] Generated Node #2: [1, 84, 35] from Operation: 90-55=35 Current State: 49:[1, 84, 35], Operations: ['90-55=35'] Exploring Operation: 1*84=84, Resulting Numbers: [35, 84] Generated Node #3: [35, 84] from Operation: 1*84=84 Current State: 49:[35, 84], Operations: ['90-55=35', '1*84=84'] Exploring Operation: 84-35=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[55, 90, 1, 84], Operations: [] Exploring Operation: 90-84=6, Resulting Numbers: [55, 1, 6] Generated Node #0,0: 49:[55, 1, 6] Operation: 90-84=6 Exploring Operation: 84-55=29, Resulting Numbers: [90, 1, 29] Generated Node #0,1: 49:[90, 1, 29] Operation: 84-55=29 Exploring Operation: 55-1=54, Resulting Numbers: [90, 84, 54] Generated Node #0,2: 49:[90, 84, 54] Operation: 55-1=54 Exploring Operation: 90-55=35, Resulting Numbers: [1, 84, 35] Generated Node #0,3: 49:[1, 84, 35] Operation: 90-55=35 Exploring Operation: 90-1=89, Resulting Numbers: [55, 84, 89] Generated Node #0,4: 49:[55, 84, 89] Operation: 90-1=89 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[55, 1, 6], Operations: ['90-84=6'] Exploring Operation: 55-6=49, Resulting Numbers: [1, 49] Generated Node #0,0,0: 49:[1, 49] Operation: 55-6=49 Exploring Operation: 55/1=55, Resulting Numbers: [6, 55] Generated Node #0,0,1: 49:[6, 55] Operation: 55/1=55 Exploring Operation: 1+6=7, Resulting Numbers: [55, 7] Generated Node #0,0,2: 49:[55, 7] Operation: 1+6=7 Exploring Operation: 55*1=55, Resulting Numbers: [6, 55] Generated Node #0,0,3: 49:[6, 55] Operation: 55*1=55 Exploring Operation: 55-1=54, Resulting Numbers: [6, 54] Generated Node #0,0,4: 49:[6, 54] Operation: 55-1=54 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[1, 49], Operations: ['90-84=6', '55-6=49'] Exploring Operation: 1+49=50, Resulting Numbers: [50] 50,49 unequal: No Solution Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[55, 90, 1, 84], Operations: [] Exploring Operation: 90-84=6, Resulting Numbers: [55, 1, 6] Generated Node #0,0: 49:[55, 1, 6] Operation: 90-84=6 Moving to Node #0,0 Current State: 49:[55, 1, 6], Operations: ['90-84=6'] Exploring Operation: 55-6=49, Resulting Numbers: [1, 49] Generated Node #0,0,0: 49:[1, 49] Operation: 55-6=49 Moving to Node #0,0,0 Current State: 49:[1, 49], Operations: ['90-84=6', '55-6=49'] Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 34, 42, 4, 14 ]
77
[ "34*14=476", "476/4=119", "119-42=77" ]
Current State: 77:[34, 42, 4, 14], Operations: [] Exploring Operation: 34*14=476, Resulting Numbers: [42, 4, 476] Generated Node #2: [42, 4, 476] from Operation: 34*14=476 Current State: 77:[42, 4, 476], Operations: ['34*14=476'] Exploring Operation: 476/4=119, Resulting Numbers: [42, 119] Generated Node #3: [42, 119] from Operation: 476/4=119 Current State: 77:[42, 119], Operations: ['34*14=476', '476/4=119'] Exploring Operation: 119-42=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[34, 42, 4, 14], Operations: [] Exploring Operation: 42/14=3, Resulting Numbers: [34, 4, 3] Generated Node #0,0: 77:[34, 4, 3] Operation: 42/14=3 Exploring Operation: 34-14=20, Resulting Numbers: [42, 4, 20] Generated Node #0,1: 77:[42, 4, 20] Operation: 34-14=20 Exploring Operation: 34+42=76, Resulting Numbers: [4, 14, 76] Generated Node #0,2: 77:[4, 14, 76] Operation: 34+42=76 Exploring Operation: 42-14=28, Resulting Numbers: [34, 4, 28] Generated Node #0,3: 77:[34, 4, 28] Operation: 42-14=28 Exploring Operation: 42-34=8, Resulting Numbers: [4, 14, 8] Generated Node #0,4: 77:[4, 14, 8] Operation: 42-34=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[4, 14, 76], Operations: ['34+42=76'] Exploring Operation: 14-4=10, Resulting Numbers: [76, 10] Generated Node #0,2,0: 77:[76, 10] Operation: 14-4=10 Exploring Operation: 76-4=72, Resulting Numbers: [14, 72] Generated Node #0,2,1: 77:[14, 72] Operation: 76-4=72 Exploring Operation: 4+76=80, Resulting Numbers: [14, 80] Generated Node #0,2,2: 77:[14, 80] Operation: 4+76=80 Exploring Operation: 4+14=18, Resulting Numbers: [76, 18] Generated Node #0,2,3: 77:[76, 18] Operation: 4+14=18 Exploring Operation: 76/4=19, Resulting Numbers: [14, 19] Generated Node #0,2,4: 77:[14, 19] Operation: 76/4=19 Moving to Node #0,2,0 Current State: 77:[76, 10], Operations: ['34+42=76', '14-4=10'] Exploring Operation: 76-10=66, Resulting Numbers: [66] 66,77 unequal: No Solution Exploring Operation: 76+10=86, Resulting Numbers: [86] 86,77 unequal: No Solution Exploring Operation: 76*10=760, Resulting Numbers: [760] 760,77 unequal: No Solution Moving to Node #0,2,2 Current State: 77:[14, 80], Operations: ['34+42=76', '4+76=80'] Exploring Operation: 14+80=94, Resulting Numbers: [94] 94,77 unequal: No Solution Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,77 unequal: No Solution Exploring Operation: 14*80=1120, Resulting Numbers: [1120] 1120,77 unequal: No Solution Moving to Node #0,2,1 Current State: 77:[14, 72], Operations: ['34+42=76', '76-4=72'] Exploring Operation: 14+72=86, Resulting Numbers: [86] 86,77 unequal: No Solution Exploring Operation: 72-14=58, Resulting Numbers: [58] 58,77 unequal: No Solution Exploring Operation: 14*72=1008, Resulting Numbers: [1008] 1008,77 unequal: No Solution Moving to Node #0,2,3 Current State: 77:[76, 18], Operations: ['34+42=76', '4+14=18'] Exploring Operation: 76-18=58, Resulting Numbers: [58] 58,77 unequal: No Solution Exploring Operation: 76+18=94, Resulting Numbers: [94] 94,77 unequal: No Solution Exploring Operation: 76*18=1368, Resulting Numbers: [1368] 1368,77 unequal: No Solution Moving to Node #0,2,4 Current State: 77:[14, 19], Operations: ['34+42=76', '76/4=19'] Exploring Operation: 14+19=33, Resulting Numbers: [33] 33,77 unequal: No Solution Exploring Operation: 19-14=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 14*19=266, Resulting Numbers: [266] 266,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 77:[4, 14, 8], Operations: ['42-34=8'] Exploring Operation: 14-8=6, Resulting Numbers: [4, 6] Generated Node #0,4,0: 77:[4, 6] Operation: 14-8=6 Exploring Operation: 14-4=10, Resulting Numbers: [8, 10] Generated Node #0,4,1: 77:[8, 10] Operation: 14-4=10 Exploring Operation: 8-4=4, Resulting Numbers: [14, 4] Generated Node #0,4,2: 77:[14, 4] Operation: 8-4=4 Exploring Operation: 4+8=12, Resulting Numbers: [14, 12] Generated Node #0,4,3: 77:[14, 12] Operation: 4+8=12 Exploring Operation: 4+14=18, Resulting Numbers: [8, 18] Generated Node #0,4,4: 77:[8, 18] Operation: 4+14=18 Moving to Node #0,4,1 Current State: 77:[8, 10], Operations: ['42-34=8', '14-4=10'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,77 unequal: No Solution Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,77 unequal: No Solution Moving to Node #0,4,3 Current State: 77:[14, 12], Operations: ['42-34=8', '4+8=12'] Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,77 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,77 unequal: No Solution Moving to Node #0,4,0 Current State: 77:[4, 6], Operations: ['42-34=8', '14-8=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,77 unequal: No Solution Moving to Node #0,4,2 Current State: 77:[14, 4], Operations: ['42-34=8', '8-4=4'] Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,77 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,77 unequal: No Solution Moving to Node #0,4,4 Current State: 77:[8, 18], Operations: ['42-34=8', '4+14=18'] Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,77 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[34, 4, 3], Operations: ['42/14=3'] Exploring Operation: 34-3=31, Resulting Numbers: [4, 31] Generated Node #0,0,0: 77:[4, 31] Operation: 34-3=31 Exploring Operation: 34-4=30, Resulting Numbers: [3, 30] Generated Node #0,0,1: 77:[3, 30] Operation: 34-4=30 Exploring Operation: 4*3=12, Resulting Numbers: [34, 12] Generated Node #0,0,2: 77:[34, 12] Operation: 4*3=12 Exploring Operation: 4+3=7, Resulting Numbers: [34, 7] Generated Node #0,0,3: 77:[34, 7] Operation: 4+3=7 Exploring Operation: 34*3=102, Resulting Numbers: [4, 102] Generated Node #0,0,4: 77:[4, 102] Operation: 34*3=102 Moving to Node #0,0,0 Current State: 77:[4, 31], Operations: ['42/14=3', '34-3=31'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,77 unequal: No Solution Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,77 unequal: No Solution Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,77 unequal: No Solution Moving to Node #0,0,3 Current State: 77:[34, 7], Operations: ['42/14=3', '4+3=7'] Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,77 unequal: No Solution Exploring Operation: 34*7=238, Resulting Numbers: [238] 238,77 unequal: No Solution Exploring Operation: 34+7=41, Resulting Numbers: [41] 41,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[3, 30], Operations: ['42/14=3', '34-4=30'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,77 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,77 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[34, 12], Operations: ['42/14=3', '4*3=12'] Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 34+12=46, Resulting Numbers: [46] 46,77 unequal: No Solution Exploring Operation: 34*12=408, Resulting Numbers: [408] 408,77 unequal: No Solution Moving to Node #0,0,4 Current State: 77:[4, 102], Operations: ['42/14=3', '34*3=102'] Exploring Operation: 102-4=98, Resulting Numbers: [98] 98,77 unequal: No Solution Exploring Operation: 4+102=106, Resulting Numbers: [106] 106,77 unequal: No Solution Exploring Operation: 4*102=408, Resulting Numbers: [408] 408,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[42, 4, 20], Operations: ['34-14=20'] Exploring Operation: 42-20=22, Resulting Numbers: [4, 22] Generated Node #0,1,0: 77:[4, 22] Operation: 42-20=22 Exploring Operation: 20/4=5, Resulting Numbers: [42, 5] Generated Node #0,1,1: 77:[42, 5] Operation: 20/4=5 Exploring Operation: 42+20=62, Resulting Numbers: [4, 62] Generated Node #0,1,2: 77:[4, 62] Operation: 42+20=62 Exploring Operation: 4*20=80, Resulting Numbers: [42, 80] Generated Node #0,1,3: 77:[42, 80] Operation: 4*20=80 Exploring Operation: 42-4=38, Resulting Numbers: [20, 38] Generated Node #0,1,4: 77:[20, 38] Operation: 42-4=38 Moving to Node #0,1,0 Current State: 77:[4, 22], Operations: ['34-14=20', '42-20=22'] Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,77 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,77 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,77 unequal: No Solution Moving to Node #0,1,2 Current State: 77:[4, 62], Operations: ['34-14=20', '42+20=62'] Exploring Operation: 4*62=248, Resulting Numbers: [248] 248,77 unequal: No Solution Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,77 unequal: No Solution Exploring Operation: 4+62=66, Resulting Numbers: [66] 66,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[42, 5], Operations: ['34-14=20', '20/4=5'] Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,77 unequal: No Solution Exploring Operation: 42+5=47, Resulting Numbers: [47] 47,77 unequal: No Solution Exploring Operation: 42*5=210, Resulting Numbers: [210] 210,77 unequal: No Solution Moving to Node #0,1,3 Current State: 77:[42, 80], Operations: ['34-14=20', '4*20=80'] Exploring Operation: 42+80=122, Resulting Numbers: [122] 122,77 unequal: No Solution Exploring Operation: 80-42=38, Resulting Numbers: [38] 38,77 unequal: No Solution Exploring Operation: 42*80=3360, Resulting Numbers: [3360] 3360,77 unequal: No Solution Moving to Node #0,1,4 Current State: 77:[20, 38], Operations: ['34-14=20', '42-4=38'] Exploring Operation: 20*38=760, Resulting Numbers: [760] 760,77 unequal: No Solution Exploring Operation: 38-20=18, Resulting Numbers: [18] 18,77 unequal: No Solution Exploring Operation: 20+38=58, Resulting Numbers: [58] 58,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[34, 4, 28], Operations: ['42-14=28'] Exploring Operation: 28/4=7, Resulting Numbers: [34, 7] Generated Node #0,3,0: 77:[34, 7] Operation: 28/4=7 Exploring Operation: 34-28=6, Resulting Numbers: [4, 6] Generated Node #0,3,1: 77:[4, 6] Operation: 34-28=6 Exploring Operation: 34+28=62, Resulting Numbers: [4, 62] Generated Node #0,3,2: 77:[4, 62] Operation: 34+28=62 Exploring Operation: 34-4=30, Resulting Numbers: [28, 30] Generated Node #0,3,3: 77:[28, 30] Operation: 34-4=30 Exploring Operation: 28-4=24, Resulting Numbers: [34, 24] Generated Node #0,3,4: 77:[34, 24] Operation: 28-4=24 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 77:[4, 6], Operations: ['42-14=28', '34-28=6'] Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,77 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,77 unequal: No Solution No 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: 77:[4, 62], Operations: ['42-14=28', '34+28=62'] Exploring Operation: 4+62=66, Resulting Numbers: [66] 66,77 unequal: No Solution Exploring Operation: 4*62=248, Resulting Numbers: [248] 248,77 unequal: No Solution Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,77 unequal: No Solution No 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: 77:[34, 7], Operations: ['42-14=28', '28/4=7'] Exploring Operation: 34*7=238, Resulting Numbers: [238] 238,77 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,77 unequal: No Solution Exploring Operation: 34+7=41, Resulting Numbers: [41] 41,77 unequal: No Solution No 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: 77:[28, 30], Operations: ['42-14=28', '34-4=30'] Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,77 unequal: No Solution Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 28*30=840, Resulting Numbers: [840] 840,77 unequal: No Solution No 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: 77:[34, 24], Operations: ['42-14=28', '28-4=24'] Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,77 unequal: No Solution Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,77 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_5
mult_heuristic
[ 24, 37, 20, 91 ]
21
[ "20+91=111", "111/37=3", "24-3=21" ]
Current State: 21:[24, 37, 20, 91], Operations: [] Exploring Operation: 20+91=111, Resulting Numbers: [24, 37, 111] Generated Node #2: [24, 37, 111] from Operation: 20+91=111 Current State: 21:[24, 37, 111], Operations: ['20+91=111'] Exploring Operation: 111/37=3, Resulting Numbers: [24, 3] Generated Node #3: [24, 3] from Operation: 111/37=3 Current State: 21:[24, 3], Operations: ['20+91=111', '111/37=3'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[24, 37, 20, 91], Operations: [] Exploring Operation: 37-24=13, Resulting Numbers: [20, 91, 13] Generated Node #0,0: 21:[20, 91, 13] Operation: 37-24=13 Exploring Operation: 91-24=67, Resulting Numbers: [37, 20, 67] Generated Node #0,1: 21:[37, 20, 67] Operation: 91-24=67 Exploring Operation: 91-37=54, Resulting Numbers: [24, 20, 54] Generated Node #0,2: 21:[24, 20, 54] Operation: 91-37=54 Exploring Operation: 91-20=71, Resulting Numbers: [24, 37, 71] Generated Node #0,3: 21:[24, 37, 71] Operation: 91-20=71 Moving to Node #0,2 Current State: 21:[24, 20, 54], Operations: ['91-37=54'] Exploring Operation: 24+20=44, Resulting Numbers: [54, 44] Generated Node #0,2,0: 21:[54, 44] Operation: 24+20=44 Exploring Operation: 54-24=30, Resulting Numbers: [20, 30] Generated Node #0,2,1: 21:[20, 30] Operation: 54-24=30 Exploring Operation: 24-20=4, Resulting Numbers: [54, 4] Generated Node #0,2,2: 21:[54, 4] Operation: 24-20=4 Exploring Operation: 54-20=34, Resulting Numbers: [24, 34] Generated Node #0,2,3: 21:[24, 34] Operation: 54-20=34 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 21:[20, 30], Operations: ['91-37=54', '54-24=30'] Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,21 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 21:[24, 34], Operations: ['91-37=54', '54-20=34'] Exploring Operation: 24*34=816, Resulting Numbers: [816] 816,21 unequal: No Solution Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 24+34=58, Resulting Numbers: [58] 58,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 21:[54, 4], Operations: ['91-37=54', '24-20=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 54*4=216, Resulting Numbers: [216] 216,21 unequal: No Solution Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 21:[54, 44], Operations: ['91-37=54', '24+20=44'] Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 54+44=98, Resulting Numbers: [98] 98,21 unequal: No Solution Exploring Operation: 54*44=2376, Resulting Numbers: [2376] 2376,21 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: 21:[37, 20, 67], Operations: ['91-24=67'] Exploring Operation: 37-20=17, Resulting Numbers: [67, 17] Generated Node #0,1,0: 21:[67, 17] Operation: 37-20=17 Exploring Operation: 67-20=47, Resulting Numbers: [37, 47] Generated Node #0,1,1: 21:[37, 47] Operation: 67-20=47 Exploring Operation: 37+20=57, Resulting Numbers: [67, 57] Generated Node #0,1,2: 21:[67, 57] Operation: 37+20=57 Exploring Operation: 67-37=30, Resulting Numbers: [20, 30] Generated Node #0,1,3: 21:[20, 30] Operation: 67-37=30 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 21:[20, 30], Operations: ['91-24=67', '67-37=30'] Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,21 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 21:[37, 47], Operations: ['91-24=67', '67-20=47'] Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 37+47=84, Resulting Numbers: [84] 84,21 unequal: No Solution Exploring Operation: 37*47=1739, Resulting Numbers: [1739] 1739,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 21:[67, 17], Operations: ['91-24=67', '37-20=17'] Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 67+17=84, Resulting Numbers: [84] 84,21 unequal: No Solution Exploring Operation: 67*17=1139, Resulting Numbers: [1139] 1139,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 21:[67, 57], Operations: ['91-24=67', '37+20=57'] Exploring Operation: 67+57=124, Resulting Numbers: [124] 124,21 unequal: No Solution Exploring Operation: 67*57=3819, Resulting Numbers: [3819] 3819,21 unequal: No Solution Exploring Operation: 67-57=10, Resulting Numbers: [10] 10,21 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: 21:[24, 37, 71], Operations: ['91-20=71'] Exploring Operation: 37-24=13, Resulting Numbers: [71, 13] Generated Node #0,3,0: 21:[71, 13] Operation: 37-24=13 Exploring Operation: 71-37=34, Resulting Numbers: [24, 34] Generated Node #0,3,1: 21:[24, 34] Operation: 71-37=34 Exploring Operation: 71-24=47, Resulting Numbers: [37, 47] Generated Node #0,3,2: 21:[37, 47] Operation: 71-24=47 Exploring Operation: 24+37=61, Resulting Numbers: [71, 61] Generated Node #0,3,3: 21:[71, 61] Operation: 24+37=61 Moving to Node #0,0 Current State: 21:[20, 91, 13], Operations: ['37-24=13'] Exploring Operation: 91/13=7, Resulting Numbers: [20, 7] Generated Node #0,0,0: 21:[20, 7] Operation: 91/13=7 Exploring Operation: 20-13=7, Resulting Numbers: [91, 7] Generated Node #0,0,1: 21:[91, 7] Operation: 20-13=7 Exploring Operation: 91-20=71, Resulting Numbers: [13, 71] Generated Node #0,0,2: 21:[13, 71] Operation: 91-20=71 Exploring Operation: 91-13=78, Resulting Numbers: [20, 78] Generated Node #0,0,3: 21:[20, 78] Operation: 91-13=78 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[20, 7], Operations: ['37-24=13', '91/13=7'] Exploring Operation: 20*7=140, Resulting Numbers: [140] 140,21 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,21 unequal: No Solution Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 21:[13, 71], Operations: ['37-24=13', '91-20=71'] Exploring Operation: 13+71=84, Resulting Numbers: [84] 84,21 unequal: No Solution Exploring Operation: 71-13=58, Resulting Numbers: [58] 58,21 unequal: No Solution Exploring Operation: 13*71=923, Resulting Numbers: [923] 923,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 21:[20, 78], Operations: ['37-24=13', '91-13=78'] Exploring Operation: 20*78=1560, Resulting Numbers: [1560] 1560,21 unequal: No Solution Exploring Operation: 78-20=58, Resulting Numbers: [58] 58,21 unequal: No Solution Exploring Operation: 20+78=98, Resulting Numbers: [98] 98,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[91, 7], Operations: ['37-24=13', '20-13=7'] Exploring Operation: 91+7=98, Resulting Numbers: [98] 98,21 unequal: No Solution Exploring Operation: 91*7=637, Resulting Numbers: [637] 637,21 unequal: No Solution Exploring Operation: 91/7=13, Resulting Numbers: [13] 13,21 unequal: No Solution Exploring Operation: 91-7=84, Resulting Numbers: [84] 84,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 21:[24, 34], Operations: ['91-20=71', '71-37=34'] Exploring Operation: 24*34=816, Resulting Numbers: [816] 816,21 unequal: No Solution Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 24+34=58, Resulting Numbers: [58] 58,21 unequal: No Solution Moving to Node #0,3,2 Current State: 21:[37, 47], Operations: ['91-20=71', '71-24=47'] Exploring Operation: 37*47=1739, Resulting Numbers: [1739] 1739,21 unequal: No Solution Exploring Operation: 37+47=84, Resulting Numbers: [84] 84,21 unequal: No Solution Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,21 unequal: No Solution Moving to Node #0,3,0 Current State: 21:[71, 13], Operations: ['91-20=71', '37-24=13'] Exploring Operation: 71*13=923, Resulting Numbers: [923] 923,21 unequal: No Solution Exploring Operation: 71-13=58, Resulting Numbers: [58] 58,21 unequal: No Solution Exploring Operation: 71+13=84, Resulting Numbers: [84] 84,21 unequal: No Solution Moving to Node #0,3,3 Current State: 21:[71, 61], Operations: ['91-20=71', '24+37=61'] Exploring Operation: 71*61=4331, Resulting Numbers: [4331] 4331,21 unequal: No Solution Exploring Operation: 71-61=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 71+61=132, Resulting Numbers: [132] 132,21 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 44, 34, 12, 16 ]
68
[ "44-12=32", "34*32=1088", "1088/16=68" ]
Current State: 68:[44, 34, 12, 16], Operations: [] Exploring Operation: 44-12=32, Resulting Numbers: [34, 16, 32] Generated Node #2: [34, 16, 32] from Operation: 44-12=32 Current State: 68:[34, 16, 32], Operations: ['44-12=32'] Exploring Operation: 34*32=1088, Resulting Numbers: [16, 1088] Generated Node #3: [16, 1088] from Operation: 34*32=1088 Current State: 68:[16, 1088], Operations: ['44-12=32', '34*32=1088'] Exploring Operation: 1088/16=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[44, 34, 12, 16], Operations: [] Exploring Operation: 44-12=32, Resulting Numbers: [34, 16, 32] Generated Node #0,0: 68:[34, 16, 32] Operation: 44-12=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[34, 16, 32], Operations: ['44-12=32'] Exploring Operation: 32/16=2, Resulting Numbers: [34, 2] Generated Node #0,0,0: 68:[34, 2] Operation: 32/16=2 Moving to Node #0,0,0 Current State: 68:[34, 2], Operations: ['44-12=32', '32/16=2'] Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[44, 34, 12, 16], Operations: [] Exploring Operation: 44-12=32, Resulting Numbers: [34, 16, 32] Generated Node #0,0: 68:[34, 16, 32] Operation: 44-12=32 Moving to Node #0,0 Current State: 68:[34, 16, 32], Operations: ['44-12=32'] Exploring Operation: 32/16=2, Resulting Numbers: [34, 2] Generated Node #0,0,0: 68:[34, 2] Operation: 32/16=2 Moving to Node #0,0,0 Current State: 68:[34, 2], Operations: ['44-12=32', '32/16=2'] Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 58, 55, 49, 53 ]
34
[ "58-55=3", "49+53=102", "102/3=34" ]
Current State: 34:[58, 55, 49, 53], Operations: [] Exploring Operation: 58-55=3, Resulting Numbers: [49, 53, 3] Generated Node #2: [49, 53, 3] from Operation: 58-55=3 Current State: 34:[49, 53, 3], Operations: ['58-55=3'] Exploring Operation: 49+53=102, Resulting Numbers: [3, 102] Generated Node #3: [3, 102] from Operation: 49+53=102 Current State: 34:[3, 102], Operations: ['58-55=3', '49+53=102'] Exploring Operation: 102/3=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[58, 55, 49, 53], Operations: [] Exploring Operation: 58-53=5, Resulting Numbers: [55, 49, 5] Generated Node #0,0: 34:[55, 49, 5] Operation: 58-53=5 Exploring Operation: 58-55=3, Resulting Numbers: [49, 53, 3] Generated Node #0,1: 34:[49, 53, 3] Operation: 58-55=3 Exploring Operation: 58-49=9, Resulting Numbers: [55, 53, 9] Generated Node #0,2: 34:[55, 53, 9] Operation: 58-49=9 Exploring Operation: 55-53=2, Resulting Numbers: [58, 49, 2] Generated Node #0,3: 34:[58, 49, 2] Operation: 55-53=2 Exploring Operation: 55-49=6, Resulting Numbers: [58, 53, 6] Generated Node #0,4: 34:[58, 53, 6] Operation: 55-49=6 Moving to Node #0,1 Current State: 34:[49, 53, 3], Operations: ['58-55=3'] Exploring Operation: 53+3=56, Resulting Numbers: [49, 56] Generated Node #0,1,0: 34:[49, 56] Operation: 53+3=56 Exploring Operation: 53-3=50, Resulting Numbers: [49, 50] Generated Node #0,1,1: 34:[49, 50] Operation: 53-3=50 Exploring Operation: 49-3=46, Resulting Numbers: [53, 46] Generated Node #0,1,2: 34:[53, 46] Operation: 49-3=46 Exploring Operation: 53-49=4, Resulting Numbers: [3, 4] Generated Node #0,1,3: 34:[3, 4] Operation: 53-49=4 Exploring Operation: 49+3=52, Resulting Numbers: [53, 52] Generated Node #0,1,4: 34:[53, 52] Operation: 49+3=52 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 34:[3, 4], Operations: ['58-55=3', '53-49=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 34:[49, 50], Operations: ['58-55=3', '53-3=50'] Exploring Operation: 49+50=99, Resulting Numbers: [99] 99,34 unequal: No Solution Exploring Operation: 49*50=2450, Resulting Numbers: [2450] 2450,34 unequal: No Solution Exploring Operation: 50-49=1, Resulting Numbers: [1] 1,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 34:[53, 46], Operations: ['58-55=3', '49-3=46'] Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 53+46=99, Resulting Numbers: [99] 99,34 unequal: No Solution Exploring Operation: 53*46=2438, Resulting Numbers: [2438] 2438,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 34:[49, 56], Operations: ['58-55=3', '53+3=56'] Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,34 unequal: No Solution Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,34 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 34:[53, 52], Operations: ['58-55=3', '49+3=52'] Exploring Operation: 53+52=105, Resulting Numbers: [105] 105,34 unequal: No Solution Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 53*52=2756, Resulting Numbers: [2756] 2756,34 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: 34:[58, 49, 2], Operations: ['55-53=2'] Exploring Operation: 58+2=60, Resulting Numbers: [49, 60] Generated Node #0,3,0: 34:[49, 60] Operation: 58+2=60 Exploring Operation: 49-2=47, Resulting Numbers: [58, 47] Generated Node #0,3,1: 34:[58, 47] Operation: 49-2=47 Exploring Operation: 58-2=56, Resulting Numbers: [49, 56] Generated Node #0,3,2: 34:[49, 56] Operation: 58-2=56 Exploring Operation: 58/2=29, Resulting Numbers: [49, 29] Generated Node #0,3,3: 34:[49, 29] Operation: 58/2=29 Exploring Operation: 58-49=9, Resulting Numbers: [2, 9] Generated Node #0,3,4: 34:[2, 9] Operation: 58-49=9 Moving to Node #0,0 Current State: 34:[55, 49, 5], Operations: ['58-53=5'] Exploring Operation: 55-49=6, Resulting Numbers: [5, 6] Generated Node #0,0,0: 34:[5, 6] Operation: 55-49=6 Exploring Operation: 49-5=44, Resulting Numbers: [55, 44] Generated Node #0,0,1: 34:[55, 44] Operation: 49-5=44 Exploring Operation: 55+5=60, Resulting Numbers: [49, 60] Generated Node #0,0,2: 34:[49, 60] Operation: 55+5=60 Exploring Operation: 55/5=11, Resulting Numbers: [49, 11] Generated Node #0,0,3: 34:[49, 11] Operation: 55/5=11 Exploring Operation: 55-5=50, Resulting Numbers: [49, 50] Generated Node #0,0,4: 34:[49, 50] Operation: 55-5=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 34:[5, 6], Operations: ['58-53=5', '55-49=6'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 34:[49, 11], Operations: ['58-53=5', '55/5=11'] Exploring Operation: 49*11=539, Resulting Numbers: [539] 539,34 unequal: No Solution Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,34 unequal: No Solution Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 34:[55, 44], Operations: ['58-53=5', '49-5=44'] Exploring Operation: 55+44=99, Resulting Numbers: [99] 99,34 unequal: No Solution Exploring Operation: 55*44=2420, Resulting Numbers: [2420] 2420,34 unequal: No Solution Exploring Operation: 55-44=11, Resulting Numbers: [11] 11,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 34:[49, 50], Operations: ['58-53=5', '55-5=50'] Exploring Operation: 49*50=2450, Resulting Numbers: [2450] 2450,34 unequal: No Solution Exploring Operation: 50-49=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 49+50=99, Resulting Numbers: [99] 99,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 34:[49, 60], Operations: ['58-53=5', '55+5=60'] Exploring Operation: 49*60=2940, Resulting Numbers: [2940] 2940,34 unequal: No Solution Exploring Operation: 49+60=109, Resulting Numbers: [109] 109,34 unequal: No Solution Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 34:[55, 53, 9], Operations: ['58-49=9'] Exploring Operation: 53-9=44, Resulting Numbers: [55, 44] Generated Node #0,2,0: 34:[55, 44] Operation: 53-9=44 Exploring Operation: 53+9=62, Resulting Numbers: [55, 62] Generated Node #0,2,1: 34:[55, 62] Operation: 53+9=62 Exploring Operation: 55+9=64, Resulting Numbers: [53, 64] Generated Node #0,2,2: 34:[53, 64] Operation: 55+9=64 Exploring Operation: 55-53=2, Resulting Numbers: [9, 2] Generated Node #0,2,3: 34:[9, 2] Operation: 55-53=2 Exploring Operation: 55-9=46, Resulting Numbers: [53, 46] Generated Node #0,2,4: 34:[53, 46] Operation: 55-9=46 Moving to Node #0,4 Current State: 34:[58, 53, 6], Operations: ['55-49=6'] Exploring Operation: 53+6=59, Resulting Numbers: [58, 59] Generated Node #0,4,0: 34:[58, 59] Operation: 53+6=59 Exploring Operation: 58+6=64, Resulting Numbers: [53, 64] Generated Node #0,4,1: 34:[53, 64] Operation: 58+6=64 Exploring Operation: 58-53=5, Resulting Numbers: [6, 5] Generated Node #0,4,2: 34:[6, 5] Operation: 58-53=5 Exploring Operation: 53-6=47, Resulting Numbers: [58, 47] Generated Node #0,4,3: 34:[58, 47] Operation: 53-6=47 Exploring Operation: 58-6=52, Resulting Numbers: [53, 52] Generated Node #0,4,4: 34:[53, 52] Operation: 58-6=52 Moving to Node #0,3,4 Current State: 34:[2, 9], Operations: ['55-53=2', '58-49=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,34 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,34 unequal: No Solution Moving to Node #0,2,3 Current State: 34:[9, 2], Operations: ['58-49=9', '55-53=2'] Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,34 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,34 unequal: No Solution Moving to Node #0,4,2 Current State: 34:[6, 5], Operations: ['55-49=6', '58-53=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,34 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,34 unequal: No Solution Moving to Node #0,3,3 Current State: 34:[49, 29], Operations: ['55-53=2', '58/2=29'] Exploring Operation: 49+29=78, Resulting Numbers: [78] 78,34 unequal: No Solution Exploring Operation: 49*29=1421, Resulting Numbers: [1421] 1421,34 unequal: No Solution Exploring Operation: 49-29=20, Resulting Numbers: [20] 20,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[55, 44], Operations: ['58-49=9', '53-9=44'] Exploring Operation: 55+44=99, Resulting Numbers: [99] 99,34 unequal: No Solution Exploring Operation: 55-44=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 55*44=2420, Resulting Numbers: [2420] 2420,34 unequal: No Solution Moving to Node #0,2,4 Current State: 34:[53, 46], Operations: ['58-49=9', '55-9=46'] Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 53*46=2438, Resulting Numbers: [2438] 2438,34 unequal: No Solution Exploring Operation: 53+46=99, Resulting Numbers: [99] 99,34 unequal: No Solution Moving to Node #0,3,1 Current State: 34:[58, 47], Operations: ['55-53=2', '49-2=47'] Exploring Operation: 58*47=2726, Resulting Numbers: [2726] 2726,34 unequal: No Solution Exploring Operation: 58-47=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 58+47=105, Resulting Numbers: [105] 105,34 unequal: No Solution Moving to Node #0,4,3 Current State: 34:[58, 47], Operations: ['55-49=6', '53-6=47'] Exploring Operation: 58+47=105, Resulting Numbers: [105] 105,34 unequal: No Solution Exploring Operation: 58*47=2726, Resulting Numbers: [2726] 2726,34 unequal: No Solution Exploring Operation: 58-47=11, Resulting Numbers: [11] 11,34 unequal: No Solution Moving to Node #0,3,2 Current State: 34:[49, 56], Operations: ['55-53=2', '58-2=56'] Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,34 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,34 unequal: No Solution Moving to Node #0,4,4 Current State: 34:[53, 52], Operations: ['55-49=6', '58-6=52'] Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 53*52=2756, Resulting Numbers: [2756] 2756,34 unequal: No Solution Exploring Operation: 53+52=105, Resulting Numbers: [105] 105,34 unequal: No Solution Moving to Node #0,3,0 Current State: 34:[49, 60], Operations: ['55-53=2', '58+2=60'] Exploring Operation: 49+60=109, Resulting Numbers: [109] 109,34 unequal: No Solution Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 49*60=2940, Resulting Numbers: [2940] 2940,34 unequal: No Solution Moving to Node #0,4,0 Current State: 34:[58, 59], Operations: ['55-49=6', '53+6=59'] Exploring Operation: 58*59=3422, Resulting Numbers: [3422] 3422,34 unequal: No Solution Exploring Operation: 58+59=117, Resulting Numbers: [117] 117,34 unequal: No Solution Exploring Operation: 59-58=1, Resulting Numbers: [1] 1,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[53, 64], Operations: ['58-49=9', '55+9=64'] Exploring Operation: 64-53=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 53+64=117, Resulting Numbers: [117] 117,34 unequal: No Solution Exploring Operation: 53*64=3392, Resulting Numbers: [3392] 3392,34 unequal: No Solution Moving to Node #0,2,1 Current State: 34:[55, 62], Operations: ['58-49=9', '53+9=62'] Exploring Operation: 55+62=117, Resulting Numbers: [117] 117,34 unequal: No Solution Exploring Operation: 62-55=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 55*62=3410, Resulting Numbers: [3410] 3410,34 unequal: No Solution Moving to Node #0,4,1 Current State: 34:[53, 64], Operations: ['55-49=6', '58+6=64'] Exploring Operation: 53+64=117, Resulting Numbers: [117] 117,34 unequal: No Solution Exploring Operation: 64-53=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 53*64=3392, Resulting Numbers: [3392] 3392,34 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 18, 20, 70, 78 ]
10
[ "20-18=2", "78-70=8", "2+8=10" ]
Current State: 10:[18, 20, 70, 78], Operations: [] Exploring Operation: 20-18=2, Resulting Numbers: [70, 78, 2] Generated Node #2: [70, 78, 2] from Operation: 20-18=2 Current State: 10:[70, 78, 2], Operations: ['20-18=2'] Exploring Operation: 78-70=8, Resulting Numbers: [2, 8] Generated Node #3: [2, 8] from Operation: 78-70=8 Current State: 10:[2, 8], Operations: ['20-18=2', '78-70=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[18, 20, 70, 78], Operations: [] Exploring Operation: 78-70=8, Resulting Numbers: [18, 20, 8] Generated Node #0,0: 10:[18, 20, 8] Operation: 78-70=8 Moving to Node #0,0 Current State: 10:[18, 20, 8], Operations: ['78-70=8'] Exploring Operation: 20-18=2, Resulting Numbers: [8, 2] Generated Node #0,0,0: 10:[8, 2] Operation: 20-18=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[8, 2], Operations: ['78-70=8', '20-18=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[18, 20, 70, 78], Operations: [] Exploring Operation: 78-70=8, Resulting Numbers: [18, 20, 8] Generated Node #0,0: 10:[18, 20, 8] Operation: 78-70=8 Moving to Node #0,0 Current State: 10:[18, 20, 8], Operations: ['78-70=8'] Exploring Operation: 20-18=2, Resulting Numbers: [8, 2] Generated Node #0,0,0: 10:[8, 2] Operation: 20-18=2 Moving to Node #0,0,0 Current State: 10:[8, 2], Operations: ['78-70=8', '20-18=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 83, 14, 89, 76 ]
82
[ "83-14=69", "89-76=13", "69+13=82" ]
Current State: 82:[83, 14, 89, 76], Operations: [] Exploring Operation: 83-14=69, Resulting Numbers: [89, 76, 69] Generated Node #2: [89, 76, 69] from Operation: 83-14=69 Current State: 82:[89, 76, 69], Operations: ['83-14=69'] Exploring Operation: 89-76=13, Resulting Numbers: [69, 13] Generated Node #3: [69, 13] from Operation: 89-76=13 Current State: 82:[69, 13], Operations: ['83-14=69', '89-76=13'] Exploring Operation: 69+13=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[83, 14, 89, 76], Operations: [] Exploring Operation: 14+76=90, Resulting Numbers: [83, 89, 90] Generated Node #0,0: 82:[83, 89, 90] Operation: 14+76=90 Exploring Operation: 89-14=75, Resulting Numbers: [83, 76, 75] Generated Node #0,1: 82:[83, 76, 75] Operation: 89-14=75 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[83, 76, 75], Operations: ['89-14=75'] Exploring Operation: 76-75=1, Resulting Numbers: [83, 1] Generated Node #0,1,0: 82:[83, 1] Operation: 76-75=1 Exploring Operation: 83-76=7, Resulting Numbers: [75, 7] Generated Node #0,1,1: 82:[75, 7] Operation: 83-76=7 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[83, 1], Operations: ['89-14=75', '76-75=1'] Exploring Operation: 83*1=83, Resulting Numbers: [83] 83,82 unequal: No Solution Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[83, 14, 89, 76], Operations: [] Exploring Operation: 89-14=75, Resulting Numbers: [83, 76, 75] Generated Node #0,1: 82:[83, 76, 75] Operation: 89-14=75 Moving to Node #0,1 Current State: 82:[83, 76, 75], Operations: ['89-14=75'] Exploring Operation: 76-75=1, Resulting Numbers: [83, 1] Generated Node #0,1,0: 82:[83, 1] Operation: 76-75=1 Moving to Node #0,1,0 Current State: 82:[83, 1], Operations: ['89-14=75', '76-75=1'] Exploring Operation: 83-1=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
sum_heuristic
[ 57, 84, 26, 74 ]
93
[ "57+84=141", "74-26=48", "141-48=93" ]
Current State: 93:[57, 84, 26, 74], Operations: [] Exploring Operation: 57+84=141, Resulting Numbers: [26, 74, 141] Generated Node #2: [26, 74, 141] from Operation: 57+84=141 Current State: 93:[26, 74, 141], Operations: ['57+84=141'] Exploring Operation: 74-26=48, Resulting Numbers: [141, 48] Generated Node #3: [141, 48] from Operation: 74-26=48 Current State: 93:[141, 48], Operations: ['57+84=141', '74-26=48'] Exploring Operation: 141-48=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[57, 84, 26, 74], Operations: [] Exploring Operation: 57-26=31, Resulting Numbers: [84, 74, 31] Generated Node #0,0: 93:[84, 74, 31] Operation: 57-26=31 Exploring Operation: 84-57=27, Resulting Numbers: [26, 74, 27] Generated Node #0,1: 93:[26, 74, 27] Operation: 84-57=27 Exploring Operation: 57+26=83, Resulting Numbers: [84, 74, 83] Generated Node #0,2: 93:[84, 74, 83] Operation: 57+26=83 Exploring Operation: 84-74=10, Resulting Numbers: [57, 26, 10] Generated Node #0,3: 93:[57, 26, 10] Operation: 84-74=10 Exploring Operation: 74-57=17, Resulting Numbers: [84, 26, 17] Generated Node #0,4: 93:[84, 26, 17] Operation: 74-57=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[84, 74, 31], Operations: ['57-26=31'] Exploring Operation: 84-31=53, Resulting Numbers: [74, 53] Generated Node #0,0,0: 93:[74, 53] Operation: 84-31=53 Exploring Operation: 84+31=115, Resulting Numbers: [74, 115] Generated Node #0,0,1: 93:[74, 115] Operation: 84+31=115 Exploring Operation: 84-74=10, Resulting Numbers: [31, 10] Generated Node #0,0,2: 93:[31, 10] Operation: 84-74=10 Exploring Operation: 74-31=43, Resulting Numbers: [84, 43] Generated Node #0,0,3: 93:[84, 43] Operation: 74-31=43 Exploring Operation: 74+31=105, Resulting Numbers: [84, 105] Generated Node #0,0,4: 93:[84, 105] Operation: 74+31=105 Moving to Node #0,0,2 Current State: 93:[31, 10], Operations: ['57-26=31', '84-74=10'] Exploring Operation: 31+10=41, Resulting Numbers: [41] 41,93 unequal: No Solution Exploring Operation: 31*10=310, Resulting Numbers: [310] 310,93 unequal: No Solution Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,93 unequal: No Solution Moving to Node #0,0,4 Current State: 93:[84, 105], Operations: ['57-26=31', '74+31=105'] Exploring Operation: 105-84=21, Resulting Numbers: [21] 21,93 unequal: No Solution Exploring Operation: 84+105=189, Resulting Numbers: [189] 189,93 unequal: No Solution Exploring Operation: 84*105=8820, Resulting Numbers: [8820] 8820,93 unequal: No Solution Moving to Node #0,0,3 Current State: 93:[84, 43], Operations: ['57-26=31', '74-31=43'] Exploring Operation: 84+43=127, Resulting Numbers: [127] 127,93 unequal: No Solution Exploring Operation: 84*43=3612, Resulting Numbers: [3612] 3612,93 unequal: No Solution Exploring Operation: 84-43=41, Resulting Numbers: [41] 41,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[74, 53], Operations: ['57-26=31', '84-31=53'] Exploring Operation: 74+53=127, Resulting Numbers: [127] 127,93 unequal: No Solution Exploring Operation: 74*53=3922, Resulting Numbers: [3922] 3922,93 unequal: No Solution Exploring Operation: 74-53=21, Resulting Numbers: [21] 21,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[74, 115], Operations: ['57-26=31', '84+31=115'] Exploring Operation: 74*115=8510, Resulting Numbers: [8510] 8510,93 unequal: No Solution Exploring Operation: 115-74=41, Resulting Numbers: [41] 41,93 unequal: No Solution Exploring Operation: 74+115=189, Resulting Numbers: [189] 189,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[26, 74, 27], Operations: ['84-57=27'] Exploring Operation: 74+27=101, Resulting Numbers: [26, 101] Generated Node #0,1,0: 93:[26, 101] Operation: 74+27=101 Exploring Operation: 26+74=100, Resulting Numbers: [27, 100] Generated Node #0,1,1: 93:[27, 100] Operation: 26+74=100 Exploring Operation: 74-27=47, Resulting Numbers: [26, 47] Generated Node #0,1,2: 93:[26, 47] Operation: 74-27=47 Exploring Operation: 74-26=48, Resulting Numbers: [27, 48] Generated Node #0,1,3: 93:[27, 48] Operation: 74-26=48 Exploring Operation: 27-26=1, Resulting Numbers: [74, 1] Generated Node #0,1,4: 93:[74, 1] Operation: 27-26=1 Moving to Node #0,1,1 Current State: 93:[27, 100], Operations: ['84-57=27', '26+74=100'] Exploring Operation: 100-27=73, Resulting Numbers: [73] 73,93 unequal: No Solution Exploring Operation: 27*100=2700, Resulting Numbers: [2700] 2700,93 unequal: No Solution Exploring Operation: 27+100=127, Resulting Numbers: [127] 127,93 unequal: No Solution Moving to Node #0,1,0 Current State: 93:[26, 101], Operations: ['84-57=27', '74+27=101'] Exploring Operation: 101-26=75, Resulting Numbers: [75] 75,93 unequal: No Solution Exploring Operation: 26+101=127, Resulting Numbers: [127] 127,93 unequal: No Solution Exploring Operation: 26*101=2626, Resulting Numbers: [2626] 2626,93 unequal: No Solution Moving to Node #0,1,2 Current State: 93:[26, 47], Operations: ['84-57=27', '74-27=47'] Exploring Operation: 26+47=73, Resulting Numbers: [73] 73,93 unequal: No Solution Exploring Operation: 47-26=21, Resulting Numbers: [21] 21,93 unequal: No Solution Exploring Operation: 26*47=1222, Resulting Numbers: [1222] 1222,93 unequal: No Solution Moving to Node #0,1,3 Current State: 93:[27, 48], Operations: ['84-57=27', '74-26=48'] Exploring Operation: 27*48=1296, Resulting Numbers: [1296] 1296,93 unequal: No Solution Exploring Operation: 27+48=75, Resulting Numbers: [75] 75,93 unequal: No Solution Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,93 unequal: No Solution Moving to Node #0,1,4 Current State: 93:[74, 1], Operations: ['84-57=27', '27-26=1'] Exploring Operation: 74/1=74, Resulting Numbers: [74] 74,93 unequal: No Solution Exploring Operation: 74-1=73, Resulting Numbers: [73] 73,93 unequal: No Solution Exploring Operation: 74+1=75, Resulting Numbers: [75] 75,93 unequal: No Solution Exploring Operation: 74*1=74, Resulting Numbers: [74] 74,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 93:[84, 26, 17], Operations: ['74-57=17'] Exploring Operation: 26-17=9, Resulting Numbers: [84, 9] Generated Node #0,4,0: 93:[84, 9] Operation: 26-17=9 Exploring Operation: 84-17=67, Resulting Numbers: [26, 67] Generated Node #0,4,1: 93:[26, 67] Operation: 84-17=67 Exploring Operation: 84+17=101, Resulting Numbers: [26, 101] Generated Node #0,4,2: 93:[26, 101] Operation: 84+17=101 Exploring Operation: 84+26=110, Resulting Numbers: [17, 110] Generated Node #0,4,3: 93:[17, 110] Operation: 84+26=110 Exploring Operation: 26+17=43, Resulting Numbers: [84, 43] Generated Node #0,4,4: 93:[84, 43] Operation: 26+17=43 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 93:[26, 101], Operations: ['74-57=17', '84+17=101'] Exploring Operation: 26*101=2626, Resulting Numbers: [2626] 2626,93 unequal: No Solution Exploring Operation: 26+101=127, Resulting Numbers: [127] 127,93 unequal: No Solution Exploring Operation: 101-26=75, Resulting Numbers: [75] 75,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 93:[84, 9], Operations: ['74-57=17', '26-17=9'] Exploring Operation: 84+9=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[57, 84, 26, 74], Operations: [] Exploring Operation: 74-57=17, Resulting Numbers: [84, 26, 17] Generated Node #0,4: 93:[84, 26, 17] Operation: 74-57=17 Moving to Node #0,4 Current State: 93:[84, 26, 17], Operations: ['74-57=17'] Exploring Operation: 26-17=9, Resulting Numbers: [84, 9] Generated Node #0,4,0: 93:[84, 9] Operation: 26-17=9 Moving to Node #0,4,0 Current State: 93:[84, 9], Operations: ['74-57=17', '26-17=9'] Exploring Operation: 84+9=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.948785
hs_5
mult_heuristic
[ 2, 31, 44, 63 ]
28
[ "63-31=32", "32/2=16", "44-16=28" ]
Current State: 28:[2, 31, 44, 63], Operations: [] Exploring Operation: 63-31=32, Resulting Numbers: [2, 44, 32] Generated Node #2: [2, 44, 32] from Operation: 63-31=32 Current State: 28:[2, 44, 32], Operations: ['63-31=32'] Exploring Operation: 32/2=16, Resulting Numbers: [44, 16] Generated Node #3: [44, 16] from Operation: 32/2=16 Current State: 28:[44, 16], Operations: ['63-31=32', '32/2=16'] Exploring Operation: 44-16=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[2, 31, 44, 63], Operations: [] Exploring Operation: 63-31=32, Resulting Numbers: [2, 44, 32] Generated Node #0,0: 28:[2, 44, 32] Operation: 63-31=32 Exploring Operation: 63-44=19, Resulting Numbers: [2, 31, 19] Generated Node #0,1: 28:[2, 31, 19] Operation: 63-44=19 Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[2, 31, 19], Operations: ['63-44=19'] Exploring Operation: 31-2=29, Resulting Numbers: [19, 29] Generated Node #0,1,0: 28:[19, 29] Operation: 31-2=29 Exploring Operation: 31-19=12, Resulting Numbers: [2, 12] Generated Node #0,1,1: 28:[2, 12] Operation: 31-19=12 Moving to Node #0,1,1 Current State: 28:[2, 12], Operations: ['63-44=19', '31-19=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[19, 29], Operations: ['63-44=19', '31-2=29'] Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,28 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[2, 44, 32], Operations: ['63-31=32'] Exploring Operation: 44-32=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 28:[2, 12] Operation: 44-32=12 Exploring Operation: 44/2=22, Resulting Numbers: [32, 22] Generated Node #0,0,1: 28:[32, 22] Operation: 44/2=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[2, 12], Operations: ['63-31=32', '44-32=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,28 unequal: No Solution No 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: 28:[32, 22], Operations: ['63-31=32', '44/2=22'] Exploring Operation: 32+22=54, Resulting Numbers: [54] 54,28 unequal: No Solution Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,28 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_2
sum_heuristic
[ 56, 43, 2, 46 ]
48
[ "56-46=10", "10/2=5", "43+5=48" ]
Current State: 48:[56, 43, 2, 46], Operations: [] Exploring Operation: 56-46=10, Resulting Numbers: [43, 2, 10] Generated Node #2: [43, 2, 10] from Operation: 56-46=10 Current State: 48:[43, 2, 10], Operations: ['56-46=10'] Exploring Operation: 10/2=5, Resulting Numbers: [43, 5] Generated Node #3: [43, 5] from Operation: 10/2=5 Current State: 48:[43, 5], Operations: ['56-46=10', '10/2=5'] Exploring Operation: 43+5=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[56, 43, 2, 46], Operations: [] Exploring Operation: 56-43=13, Resulting Numbers: [2, 46, 13] Generated Node #0,0: 48:[2, 46, 13] Operation: 56-43=13 Exploring Operation: 56-46=10, Resulting Numbers: [43, 2, 10] Generated Node #0,1: 48:[43, 2, 10] Operation: 56-46=10 Moving to Node #0,0 Current State: 48:[2, 46, 13], Operations: ['56-43=13'] Exploring Operation: 46/2=23, Resulting Numbers: [13, 23] Generated Node #0,0,0: 48:[13, 23] Operation: 46/2=23 Exploring Operation: 2+46=48, Resulting Numbers: [13, 48] Generated Node #0,0,1: 48:[13, 48] Operation: 2+46=48 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 48:[13, 48], Operations: ['56-43=13', '2+46=48'] Exploring Operation: 13+48=61, Resulting Numbers: [61] 61,48 unequal: No Solution Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,48 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 #0,0,0 Current State: 48:[13, 23], Operations: ['56-43=13', '46/2=23'] Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 13+23=36, Resulting Numbers: [36] 36,48 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: 48:[43, 2, 10], Operations: ['56-46=10'] Exploring Operation: 43+2=45, Resulting Numbers: [10, 45] Generated Node #0,1,0: 48:[10, 45] Operation: 43+2=45 Exploring Operation: 43+10=53, Resulting Numbers: [2, 53] Generated Node #0,1,1: 48:[2, 53] Operation: 43+10=53 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[10, 45], Operations: ['56-46=10', '43+2=45'] Exploring Operation: 10+45=55, Resulting Numbers: [55] 55,48 unequal: No Solution Exploring Operation: 45-10=35, Resulting Numbers: [35] 35,48 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 #0,1,1 Current State: 48:[2, 53], Operations: ['56-46=10', '43+10=53'] Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,48 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,48 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
[ 37, 29, 85, 67 ]
84
[ "37+29=66", "85-67=18", "66+18=84" ]
Current State: 84:[37, 29, 85, 67], Operations: [] Exploring Operation: 37+29=66, Resulting Numbers: [85, 67, 66] Generated Node #2: [85, 67, 66] from Operation: 37+29=66 Current State: 84:[85, 67, 66], Operations: ['37+29=66'] Exploring Operation: 85-67=18, Resulting Numbers: [66, 18] Generated Node #3: [66, 18] from Operation: 85-67=18 Current State: 84:[66, 18], Operations: ['37+29=66', '85-67=18'] Exploring Operation: 66+18=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[37, 29, 85, 67], Operations: [] Exploring Operation: 67-37=30, Resulting Numbers: [29, 85, 30] Generated Node #0,0: 84:[29, 85, 30] Operation: 67-37=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[29, 85, 30], Operations: ['67-37=30'] Exploring Operation: 30-29=1, Resulting Numbers: [85, 1] Generated Node #0,0,0: 84:[85, 1] Operation: 30-29=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 84:[85, 1], Operations: ['67-37=30', '30-29=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[37, 29, 85, 67], Operations: [] Exploring Operation: 67-37=30, Resulting Numbers: [29, 85, 30] Generated Node #0,0: 84:[29, 85, 30] Operation: 67-37=30 Moving to Node #0,0 Current State: 84:[29, 85, 30], Operations: ['67-37=30'] Exploring Operation: 30-29=1, Resulting Numbers: [85, 1] Generated Node #0,0,0: 84:[85, 1] Operation: 30-29=1 Moving to Node #0,0,0 Current State: 84:[85, 1], Operations: ['67-37=30', '30-29=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 98, 24, 60, 77 ]
91
[ "98-24=74", "77-60=17", "74+17=91" ]
Current State: 91:[98, 24, 60, 77], Operations: [] Exploring Operation: 98-24=74, Resulting Numbers: [60, 77, 74] Generated Node #2: [60, 77, 74] from Operation: 98-24=74 Current State: 91:[60, 77, 74], Operations: ['98-24=74'] Exploring Operation: 77-60=17, Resulting Numbers: [74, 17] Generated Node #3: [74, 17] from Operation: 77-60=17 Current State: 91:[74, 17], Operations: ['98-24=74', '77-60=17'] Exploring Operation: 74+17=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[98, 24, 60, 77], Operations: [] Exploring Operation: 77-60=17, Resulting Numbers: [98, 24, 17] Generated Node #0,0: 91:[98, 24, 17] Operation: 77-60=17 Exploring Operation: 60-24=36, Resulting Numbers: [98, 77, 36] Generated Node #0,1: 91:[98, 77, 36] Operation: 60-24=36 Exploring Operation: 24+77=101, Resulting Numbers: [98, 60, 101] Generated Node #0,2: 91:[98, 60, 101] Operation: 24+77=101 Exploring Operation: 24+60=84, Resulting Numbers: [98, 77, 84] Generated Node #0,3: 91:[98, 77, 84] Operation: 24+60=84 Moving to Node #0,0 Current State: 91:[98, 24, 17], Operations: ['77-60=17'] Exploring Operation: 98-24=74, Resulting Numbers: [17, 74] Generated Node #0,0,0: 91:[17, 74] Operation: 98-24=74 Exploring Operation: 98-17=81, Resulting Numbers: [24, 81] Generated Node #0,0,1: 91:[24, 81] Operation: 98-17=81 Exploring Operation: 98+24=122, Resulting Numbers: [17, 122] Generated Node #0,0,2: 91:[17, 122] Operation: 98+24=122 Exploring Operation: 24-17=7, Resulting Numbers: [98, 7] Generated Node #0,0,3: 91:[98, 7] Operation: 24-17=7 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 91:[98, 7], Operations: ['77-60=17', '24-17=7'] Exploring Operation: 98/7=14, Resulting Numbers: [14] 14,91 unequal: No Solution Exploring Operation: 98-7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[98, 24, 60, 77], Operations: [] Exploring Operation: 77-60=17, Resulting Numbers: [98, 24, 17] Generated Node #0,0: 91:[98, 24, 17] Operation: 77-60=17 Moving to Node #0,0 Current State: 91:[98, 24, 17], Operations: ['77-60=17'] Exploring Operation: 24-17=7, Resulting Numbers: [98, 7] Generated Node #0,0,3: 91:[98, 7] Operation: 24-17=7 Moving to Node #0,0,3 Current State: 91:[98, 7], Operations: ['77-60=17', '24-17=7'] Exploring Operation: 98-7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 40, 43, 25, 9 ]
84
[ "43-40=3", "25*3=75", "9+75=84" ]
Current State: 84:[40, 43, 25, 9], Operations: [] Exploring Operation: 43-40=3, Resulting Numbers: [25, 9, 3] Generated Node #2: [25, 9, 3] from Operation: 43-40=3 Current State: 84:[25, 9, 3], Operations: ['43-40=3'] Exploring Operation: 25*3=75, Resulting Numbers: [9, 75] Generated Node #3: [9, 75] from Operation: 25*3=75 Current State: 84:[9, 75], Operations: ['43-40=3', '25*3=75'] Exploring Operation: 9+75=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[40, 43, 25, 9], Operations: [] Exploring Operation: 40-9=31, Resulting Numbers: [43, 25, 31] Generated Node #0,0: 84:[43, 25, 31] Operation: 40-9=31 Exploring Operation: 25-9=16, Resulting Numbers: [40, 43, 16] Generated Node #0,1: 84:[40, 43, 16] Operation: 25-9=16 Exploring Operation: 40+43=83, Resulting Numbers: [25, 9, 83] Generated Node #0,2: 84:[25, 9, 83] Operation: 40+43=83 Exploring Operation: 43-40=3, Resulting Numbers: [25, 9, 3] Generated Node #0,3: 84:[25, 9, 3] Operation: 43-40=3 Exploring Operation: 40-25=15, Resulting Numbers: [43, 9, 15] Generated Node #0,4: 84:[43, 9, 15] Operation: 40-25=15 Moving to Node #0,4 Current State: 84:[43, 9, 15], Operations: ['40-25=15'] Exploring Operation: 43-9=34, Resulting Numbers: [15, 34] Generated Node #0,4,0: 84:[15, 34] Operation: 43-9=34 Exploring Operation: 43+9=52, Resulting Numbers: [15, 52] Generated Node #0,4,1: 84:[15, 52] Operation: 43+9=52 Exploring Operation: 15-9=6, Resulting Numbers: [43, 6] Generated Node #0,4,2: 84:[43, 6] Operation: 15-9=6 Exploring Operation: 9+15=24, Resulting Numbers: [43, 24] Generated Node #0,4,3: 84:[43, 24] Operation: 9+15=24 Exploring Operation: 43-15=28, Resulting Numbers: [9, 28] Generated Node #0,4,4: 84:[9, 28] Operation: 43-15=28 Moving to Node #0,3 Current State: 84:[25, 9, 3], Operations: ['43-40=3'] Exploring Operation: 9+3=12, Resulting Numbers: [25, 12] Generated Node #0,3,0: 84:[25, 12] Operation: 9+3=12 Exploring Operation: 25-3=22, Resulting Numbers: [9, 22] Generated Node #0,3,1: 84:[9, 22] Operation: 25-3=22 Exploring Operation: 9-3=6, Resulting Numbers: [25, 6] Generated Node #0,3,2: 84:[25, 6] Operation: 9-3=6 Exploring Operation: 25+3=28, Resulting Numbers: [9, 28] Generated Node #0,3,3: 84:[9, 28] Operation: 25+3=28 Exploring Operation: 25-9=16, Resulting Numbers: [3, 16] Generated Node #0,3,4: 84:[3, 16] Operation: 25-9=16 Moving to Node #0,1 Current State: 84:[40, 43, 16], Operations: ['25-9=16'] Exploring Operation: 43-40=3, Resulting Numbers: [16, 3] Generated Node #0,1,0: 84:[16, 3] Operation: 43-40=3 Exploring Operation: 43-16=27, Resulting Numbers: [40, 27] Generated Node #0,1,1: 84:[40, 27] Operation: 43-16=27 Exploring Operation: 40-16=24, Resulting Numbers: [43, 24] Generated Node #0,1,2: 84:[43, 24] Operation: 40-16=24 Exploring Operation: 40+43=83, Resulting Numbers: [16, 83] Generated Node #0,1,3: 84:[16, 83] Operation: 40+43=83 Exploring Operation: 40+16=56, Resulting Numbers: [43, 56] Generated Node #0,1,4: 84:[43, 56] Operation: 40+16=56 Moving to Node #0,2 Current State: 84:[25, 9, 83], Operations: ['40+43=83'] Exploring Operation: 9+83=92, Resulting Numbers: [25, 92] Generated Node #0,2,0: 84:[25, 92] Operation: 9+83=92 Exploring Operation: 83-25=58, Resulting Numbers: [9, 58] Generated Node #0,2,1: 84:[9, 58] Operation: 83-25=58 Exploring Operation: 25-9=16, Resulting Numbers: [83, 16] Generated Node #0,2,2: 84:[83, 16] Operation: 25-9=16 Exploring Operation: 83-9=74, Resulting Numbers: [25, 74] Generated Node #0,2,3: 84:[25, 74] Operation: 83-9=74 Exploring Operation: 25+9=34, Resulting Numbers: [83, 34] Generated Node #0,2,4: 84:[83, 34] Operation: 25+9=34 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 84:[83, 16], Operations: ['40+43=83', '25-9=16'] Exploring Operation: 83*16=1328, Resulting Numbers: [1328] 1328,84 unequal: No Solution Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 83+16=99, Resulting Numbers: [99] 99,84 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 #0,2,4 Current State: 84:[83, 34], Operations: ['40+43=83', '25+9=34'] Exploring Operation: 83-34=49, Resulting Numbers: [49] 49,84 unequal: No Solution Exploring Operation: 83*34=2822, Resulting Numbers: [2822] 2822,84 unequal: No Solution Exploring Operation: 83+34=117, Resulting Numbers: [117] 117,84 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 #0,2,0 Current State: 84:[25, 92], Operations: ['40+43=83', '9+83=92'] Exploring Operation: 25*92=2300, Resulting Numbers: [2300] 2300,84 unequal: No Solution Exploring Operation: 92-25=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 25+92=117, Resulting Numbers: [117] 117,84 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 #0,2,3 Current State: 84:[25, 74], Operations: ['40+43=83', '83-9=74'] Exploring Operation: 25*74=1850, Resulting Numbers: [1850] 1850,84 unequal: No Solution Exploring Operation: 25+74=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 74-25=49, Resulting Numbers: [49] 49,84 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 #0,2,1 Current State: 84:[9, 58], Operations: ['40+43=83', '83-25=58'] Exploring Operation: 9+58=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 9*58=522, Resulting Numbers: [522] 522,84 unequal: No Solution Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,84 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: 84:[43, 25, 31], Operations: ['40-9=31'] Exploring Operation: 43-25=18, Resulting Numbers: [31, 18] Generated Node #0,0,0: 84:[31, 18] Operation: 43-25=18 Exploring Operation: 31-25=6, Resulting Numbers: [43, 6] Generated Node #0,0,1: 84:[43, 6] Operation: 31-25=6 Exploring Operation: 25+31=56, Resulting Numbers: [43, 56] Generated Node #0,0,2: 84:[43, 56] Operation: 25+31=56 Exploring Operation: 43-31=12, Resulting Numbers: [25, 12] Generated Node #0,0,3: 84:[25, 12] Operation: 43-31=12 Exploring Operation: 43+31=74, Resulting Numbers: [25, 74] Generated Node #0,0,4: 84:[25, 74] Operation: 43+31=74 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[43, 6], Operations: ['40-9=31', '31-25=6'] Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,84 unequal: No Solution Exploring Operation: 43*6=258, Resulting Numbers: [258] 258,84 unequal: No Solution Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,84 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 #0,0,3 Current State: 84:[25, 12], Operations: ['40-9=31', '43-31=12'] Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,84 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,84 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,84 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 #0,0,0 Current State: 84:[31, 18], Operations: ['40-9=31', '43-25=18'] Exploring Operation: 31+18=49, Resulting Numbers: [49] 49,84 unequal: No Solution Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 31*18=558, Resulting Numbers: [558] 558,84 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 #0,0,4 Current State: 84:[25, 74], Operations: ['40-9=31', '43+31=74'] Exploring Operation: 25*74=1850, Resulting Numbers: [1850] 1850,84 unequal: No Solution Exploring Operation: 25+74=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 74-25=49, Resulting Numbers: [49] 49,84 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 #0,0,2 Current State: 84:[43, 56], Operations: ['40-9=31', '25+31=56'] Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 43*56=2408, Resulting Numbers: [2408] 2408,84 unequal: No Solution Exploring Operation: 43+56=99, Resulting Numbers: [99] 99,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,2 Current State: 84:[43, 6], Operations: ['40-25=15', '15-9=6'] Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,84 unequal: No Solution Exploring Operation: 43*6=258, Resulting Numbers: [258] 258,84 unequal: No Solution Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[9, 28], Operations: ['43-40=3', '25+3=28'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,84 unequal: No Solution Exploring Operation: 9*28=252, Resulting Numbers: [252] 252,84 unequal: No Solution Moving to Node #0,3,4 Current State: 84:[3, 16], Operations: ['43-40=3', '25-9=16'] Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,84 unequal: No Solution Moving to Node #0,4,4 Current State: 84:[9, 28], Operations: ['40-25=15', '43-15=28'] Exploring Operation: 9*28=252, Resulting Numbers: [252] 252,84 unequal: No Solution Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[16, 3], Operations: ['25-9=16', '43-40=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[40, 27], Operations: ['25-9=16', '43-16=27'] Exploring Operation: 40+27=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 40*27=1080, Resulting Numbers: [1080] 1080,84 unequal: No Solution Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[16, 83], Operations: ['25-9=16', '40+43=83'] Exploring Operation: 16*83=1328, Resulting Numbers: [1328] 1328,84 unequal: No Solution Exploring Operation: 16+83=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,84 unequal: No Solution Moving to Node #0,3,2 Current State: 84:[25, 6], Operations: ['43-40=3', '9-3=6'] Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,84 unequal: No Solution Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,84 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,84 unequal: No Solution Moving to Node #0,3,0 Current State: 84:[25, 12], Operations: ['43-40=3', '9+3=12'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,84 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,84 unequal: No Solution Moving to Node #0,3,1 Current State: 84:[9, 22], Operations: ['43-40=3', '25-3=22'] Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,84 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,84 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[43, 24], Operations: ['25-9=16', '40-16=24'] Exploring Operation: 43*24=1032, Resulting Numbers: [1032] 1032,84 unequal: No Solution Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,84 unequal: No Solution Moving to Node #0,4,3 Current State: 84:[43, 24], Operations: ['40-25=15', '9+15=24'] Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 43*24=1032, Resulting Numbers: [1032] 1032,84 unequal: No Solution Moving to Node #0,4,0 Current State: 84:[15, 34], Operations: ['40-25=15', '43-9=34'] Exploring Operation: 15*34=510, Resulting Numbers: [510] 510,84 unequal: No Solution Exploring Operation: 15+34=49, Resulting Numbers: [49] 49,84 unequal: No Solution Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,84 unequal: No Solution Moving to Node #0,4,1 Current State: 84:[15, 52], Operations: ['40-25=15', '43+9=52'] Exploring Operation: 15+52=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,84 unequal: No Solution Exploring Operation: 15*52=780, Resulting Numbers: [780] 780,84 unequal: No Solution Moving to Node #0,1,4 Current State: 84:[43, 56], Operations: ['25-9=16', '40+16=56'] Exploring Operation: 43*56=2408, Resulting Numbers: [2408] 2408,84 unequal: No Solution Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 43+56=99, Resulting Numbers: [99] 99,84 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 4, 53, 5, 7 ]
61
[ "53-4=49", "5+7=12", "49+12=61" ]
Current State: 61:[4, 53, 5, 7], Operations: [] Exploring Operation: 53-4=49, Resulting Numbers: [5, 7, 49] Generated Node #2: [5, 7, 49] from Operation: 53-4=49 Current State: 61:[5, 7, 49], Operations: ['53-4=49'] Exploring Operation: 5+7=12, Resulting Numbers: [49, 12] Generated Node #3: [49, 12] from Operation: 5+7=12 Current State: 61:[49, 12], Operations: ['53-4=49', '5+7=12'] Exploring Operation: 49+12=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[4, 53, 5, 7], Operations: [] Exploring Operation: 4*7=28, Resulting Numbers: [53, 5, 28] Generated Node #0,0: 61:[53, 5, 28] Operation: 4*7=28 Exploring Operation: 5*7=35, Resulting Numbers: [4, 53, 35] Generated Node #0,1: 61:[4, 53, 35] Operation: 5*7=35 Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[4, 53, 35], Operations: ['5*7=35'] Exploring Operation: 4+35=39, Resulting Numbers: [53, 39] Generated Node #0,1,0: 61:[53, 39] Operation: 4+35=39 Exploring Operation: 4+53=57, Resulting Numbers: [35, 57] Generated Node #0,1,1: 61:[35, 57] Operation: 4+53=57 Moving to Node #0,1,0 Current State: 61:[53, 39], Operations: ['5*7=35', '4+35=39'] Exploring Operation: 53-39=14, Resulting Numbers: [14] 14,61 unequal: No Solution Exploring Operation: 53+39=92, Resulting Numbers: [92] 92,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[35, 57], Operations: ['5*7=35', '4+53=57'] Exploring Operation: 35+57=92, Resulting Numbers: [92] 92,61 unequal: No Solution Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,61 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 Current State: 61:[53, 5, 28], Operations: ['4*7=28'] Exploring Operation: 53+5=58, Resulting Numbers: [28, 58] Generated Node #0,0,0: 61:[28, 58] Operation: 53+5=58 Exploring Operation: 5+28=33, Resulting Numbers: [53, 33] Generated Node #0,0,1: 61:[53, 33] Operation: 5+28=33 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[28, 58], Operations: ['4*7=28', '53+5=58'] Exploring Operation: 58-28=30, Resulting Numbers: [30] 30,61 unequal: No Solution Exploring Operation: 28+58=86, Resulting Numbers: [86] 86,61 unequal: No Solution No 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: 61:[53, 33], Operations: ['4*7=28', '5+28=33'] Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,61 unequal: No Solution Exploring Operation: 53+33=86, Resulting Numbers: [86] 86,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 34, 1, 96, 22 ]
83
[ "34+1=35", "96+22=118", "118-35=83" ]
Current State: 83:[34, 1, 96, 22], Operations: [] Exploring Operation: 34+1=35, Resulting Numbers: [96, 22, 35] Generated Node #2: [96, 22, 35] from Operation: 34+1=35 Current State: 83:[96, 22, 35], Operations: ['34+1=35'] Exploring Operation: 96+22=118, Resulting Numbers: [35, 118] Generated Node #3: [35, 118] from Operation: 96+22=118 Current State: 83:[35, 118], Operations: ['34+1=35', '96+22=118'] Exploring Operation: 118-35=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[34, 1, 96, 22], Operations: [] Exploring Operation: 96-1=95, Resulting Numbers: [34, 22, 95] Generated Node #0,0: 83:[34, 22, 95] Operation: 96-1=95 Exploring Operation: 34+1=35, Resulting Numbers: [96, 22, 35] Generated Node #0,1: 83:[96, 22, 35] Operation: 34+1=35 Exploring Operation: 1+22=23, Resulting Numbers: [34, 96, 23] Generated Node #0,2: 83:[34, 96, 23] Operation: 1+22=23 Exploring Operation: 34+22=56, Resulting Numbers: [1, 96, 56] Generated Node #0,3: 83:[1, 96, 56] Operation: 34+22=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[34, 22, 95], Operations: ['96-1=95'] Exploring Operation: 95-22=73, Resulting Numbers: [34, 73] Generated Node #0,0,0: 83:[34, 73] Operation: 95-22=73 Exploring Operation: 34-22=12, Resulting Numbers: [95, 12] Generated Node #0,0,1: 83:[95, 12] Operation: 34-22=12 Exploring Operation: 95-34=61, Resulting Numbers: [22, 61] Generated Node #0,0,2: 83:[22, 61] Operation: 95-34=61 Exploring Operation: 34+22=56, Resulting Numbers: [95, 56] Generated Node #0,0,3: 83:[95, 56] Operation: 34+22=56 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 83:[95, 56], Operations: ['96-1=95', '34+22=56'] Exploring Operation: 95+56=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 95*56=5320, Resulting Numbers: [5320] 5320,83 unequal: No Solution Exploring Operation: 95-56=39, Resulting Numbers: [39] 39,83 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:[34, 73], Operations: ['96-1=95', '95-22=73'] Exploring Operation: 34+73=107, Resulting Numbers: [107] 107,83 unequal: No Solution Exploring Operation: 73-34=39, Resulting Numbers: [39] 39,83 unequal: No Solution Exploring Operation: 34*73=2482, Resulting Numbers: [2482] 2482,83 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:[95, 12], Operations: ['96-1=95', '34-22=12'] Exploring Operation: 95-12=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[34, 1, 96, 22], Operations: [] Exploring Operation: 96-1=95, Resulting Numbers: [34, 22, 95] Generated Node #0,0: 83:[34, 22, 95] Operation: 96-1=95 Moving to Node #0,0 Current State: 83:[34, 22, 95], Operations: ['96-1=95'] Exploring Operation: 34-22=12, Resulting Numbers: [95, 12] Generated Node #0,0,1: 83:[95, 12] Operation: 34-22=12 Moving to Node #0,0,1 Current State: 83:[95, 12], Operations: ['96-1=95', '34-22=12'] Exploring Operation: 95-12=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 87, 79, 85, 14 ]
67
[ "87+79=166", "85+14=99", "166-99=67" ]
Current State: 67:[87, 79, 85, 14], Operations: [] Exploring Operation: 87+79=166, Resulting Numbers: [85, 14, 166] Generated Node #2: [85, 14, 166] from Operation: 87+79=166 Current State: 67:[85, 14, 166], Operations: ['87+79=166'] Exploring Operation: 85+14=99, Resulting Numbers: [166, 99] Generated Node #3: [166, 99] from Operation: 85+14=99 Current State: 67:[166, 99], Operations: ['87+79=166', '85+14=99'] Exploring Operation: 166-99=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[87, 79, 85, 14], Operations: [] Exploring Operation: 85-14=71, Resulting Numbers: [87, 79, 71] Generated Node #0,0: 67:[87, 79, 71] Operation: 85-14=71 Exploring Operation: 87+14=101, Resulting Numbers: [79, 85, 101] Generated Node #0,1: 67:[79, 85, 101] Operation: 87+14=101 Exploring Operation: 87-14=73, Resulting Numbers: [79, 85, 73] Generated Node #0,2: 67:[79, 85, 73] Operation: 87-14=73 Exploring Operation: 79-14=65, Resulting Numbers: [87, 85, 65] Generated Node #0,3: 67:[87, 85, 65] Operation: 79-14=65 Moving to Node #0,0 Current State: 67:[87, 79, 71], Operations: ['85-14=71'] Exploring Operation: 87+79=166, Resulting Numbers: [71, 166] Generated Node #0,0,0: 67:[71, 166] Operation: 87+79=166 Exploring Operation: 87-71=16, Resulting Numbers: [79, 16] Generated Node #0,0,1: 67:[79, 16] Operation: 87-71=16 Exploring Operation: 87-79=8, Resulting Numbers: [71, 8] Generated Node #0,0,2: 67:[71, 8] Operation: 87-79=8 Exploring Operation: 79-71=8, Resulting Numbers: [87, 8] Generated Node #0,0,3: 67:[87, 8] Operation: 79-71=8 Moving to Node #0,2 Current State: 67:[79, 85, 73], Operations: ['87-14=73'] Exploring Operation: 85-79=6, Resulting Numbers: [73, 6] Generated Node #0,2,0: 67:[73, 6] Operation: 85-79=6 Exploring Operation: 79-73=6, Resulting Numbers: [85, 6] Generated Node #0,2,1: 67:[85, 6] Operation: 79-73=6 Exploring Operation: 85-73=12, Resulting Numbers: [79, 12] Generated Node #0,2,2: 67:[79, 12] Operation: 85-73=12 Exploring Operation: 79+85=164, Resulting Numbers: [73, 164] Generated Node #0,2,3: 67:[73, 164] Operation: 79+85=164 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[73, 6], Operations: ['87-14=73', '85-79=6'] Exploring Operation: 73*6=438, Resulting Numbers: [438] 438,67 unequal: No Solution Exploring Operation: 73-6=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[87, 79, 85, 14], Operations: [] Exploring Operation: 87-14=73, Resulting Numbers: [79, 85, 73] Generated Node #0,2: 67:[79, 85, 73] Operation: 87-14=73 Moving to Node #0,2 Current State: 67:[79, 85, 73], Operations: ['87-14=73'] Exploring Operation: 85-79=6, Resulting Numbers: [73, 6] Generated Node #0,2,0: 67:[73, 6] Operation: 85-79=6 Moving to Node #0,2,0 Current State: 67:[73, 6], Operations: ['87-14=73', '85-79=6'] Exploring Operation: 73-6=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 38, 45, 42, 70 ]
84
[ "45*70=3150", "42+3150=3192", "3192/38=84" ]
Current State: 84:[38, 45, 42, 70], Operations: [] Exploring Operation: 45*70=3150, Resulting Numbers: [38, 42, 3150] Generated Node #2: [38, 42, 3150] from Operation: 45*70=3150 Current State: 84:[38, 42, 3150], Operations: ['45*70=3150'] Exploring Operation: 42+3150=3192, Resulting Numbers: [38, 3192] Generated Node #3: [38, 3192] from Operation: 42+3150=3192 Current State: 84:[38, 3192], Operations: ['45*70=3150', '42+3150=3192'] Exploring Operation: 3192/38=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[38, 45, 42, 70], Operations: [] Exploring Operation: 70-38=32, Resulting Numbers: [45, 42, 32] Generated Node #0,0: 84:[45, 42, 32] Operation: 70-38=32 Exploring Operation: 70-45=25, Resulting Numbers: [38, 42, 25] Generated Node #0,1: 84:[38, 42, 25] Operation: 70-45=25 Moving to Node #0,0 Current State: 84:[45, 42, 32], Operations: ['70-38=32'] Exploring Operation: 45-42=3, Resulting Numbers: [32, 3] Generated Node #0,0,0: 84:[32, 3] Operation: 45-42=3 Exploring Operation: 45-32=13, Resulting Numbers: [42, 13] Generated Node #0,0,1: 84:[42, 13] Operation: 45-32=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[42, 13], Operations: ['70-38=32', '45-32=13'] Exploring Operation: 42-13=29, Resulting Numbers: [29] 29,84 unequal: No Solution Exploring Operation: 42+13=55, Resulting Numbers: [55] 55,84 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 #0,0,0 Current State: 84:[32, 3], Operations: ['70-38=32', '45-42=3'] Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,84 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: 84:[38, 42, 25], Operations: ['70-45=25'] Exploring Operation: 38-25=13, Resulting Numbers: [42, 13] Generated Node #0,1,0: 84:[42, 13] Operation: 38-25=13 Exploring Operation: 42-38=4, Resulting Numbers: [25, 4] Generated Node #0,1,1: 84:[25, 4] Operation: 42-38=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 84:[42, 13], Operations: ['70-45=25', '38-25=13'] Exploring Operation: 42-13=29, Resulting Numbers: [29] 29,84 unequal: No Solution Exploring Operation: 42+13=55, Resulting Numbers: [55] 55,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[25, 4], Operations: ['70-45=25', '42-38=4'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,84 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
[ 36, 62, 40, 82 ]
80
[ "40-36=4", "82-62=20", "4*20=80" ]
Current State: 80:[36, 62, 40, 82], Operations: [] Exploring Operation: 40-36=4, Resulting Numbers: [62, 82, 4] Generated Node #2: [62, 82, 4] from Operation: 40-36=4 Current State: 80:[62, 82, 4], Operations: ['40-36=4'] Exploring Operation: 82-62=20, Resulting Numbers: [4, 20] Generated Node #3: [4, 20] from Operation: 82-62=20 Current State: 80:[4, 20], Operations: ['40-36=4', '82-62=20'] Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[36, 62, 40, 82], Operations: [] Exploring Operation: 82-62=20, Resulting Numbers: [36, 40, 20] Generated Node #0,0: 80:[36, 40, 20] Operation: 82-62=20 Moving to Node #0,0 Current State: 80:[36, 40, 20], Operations: ['82-62=20'] Exploring Operation: 40-36=4, Resulting Numbers: [20, 4] Generated Node #0,0,0: 80:[20, 4] Operation: 40-36=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[20, 4], Operations: ['82-62=20', '40-36=4'] Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[36, 62, 40, 82], Operations: [] Exploring Operation: 82-62=20, Resulting Numbers: [36, 40, 20] Generated Node #0,0: 80:[36, 40, 20] Operation: 82-62=20 Moving to Node #0,0 Current State: 80:[36, 40, 20], Operations: ['82-62=20'] Exploring Operation: 40-36=4, Resulting Numbers: [20, 4] Generated Node #0,0,0: 80:[20, 4] Operation: 40-36=4 Moving to Node #0,0,0 Current State: 80:[20, 4], Operations: ['82-62=20', '40-36=4'] Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 68, 1, 23, 57 ]
54
[ "68+1=69", "69/23=3", "57-3=54" ]
Current State: 54:[68, 1, 23, 57], Operations: [] Exploring Operation: 68+1=69, Resulting Numbers: [23, 57, 69] Generated Node #2: [23, 57, 69] from Operation: 68+1=69 Current State: 54:[23, 57, 69], Operations: ['68+1=69'] Exploring Operation: 69/23=3, Resulting Numbers: [57, 3] Generated Node #3: [57, 3] from Operation: 69/23=3 Current State: 54:[57, 3], Operations: ['68+1=69', '69/23=3'] Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[68, 1, 23, 57], Operations: [] Exploring Operation: 68-23=45, Resulting Numbers: [1, 57, 45] Generated Node #0,0: 54:[1, 57, 45] Operation: 68-23=45 Exploring Operation: 68-57=11, Resulting Numbers: [1, 23, 11] Generated Node #0,1: 54:[1, 23, 11] Operation: 68-57=11 Moving to Node #0,1 Current State: 54:[1, 23, 11], Operations: ['68-57=11'] Exploring Operation: 1+23=24, Resulting Numbers: [11, 24] Generated Node #0,1,0: 54:[11, 24] Operation: 1+23=24 Exploring Operation: 23-11=12, Resulting Numbers: [1, 12] Generated Node #0,1,1: 54:[1, 12] Operation: 23-11=12 Moving to Node #0,0 Current State: 54:[1, 57, 45], Operations: ['68-23=45'] Exploring Operation: 57-1=56, Resulting Numbers: [45, 56] Generated Node #0,0,0: 54:[45, 56] Operation: 57-1=56 Exploring Operation: 57-45=12, Resulting Numbers: [1, 12] Generated Node #0,0,1: 54:[1, 12] Operation: 57-45=12 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[1, 12], Operations: ['68-23=45', '57-45=12'] Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[45, 56], Operations: ['68-23=45', '57-1=56'] Exploring Operation: 56-45=11, Resulting Numbers: [11] 11,54 unequal: No Solution Exploring Operation: 45+56=101, Resulting Numbers: [101] 101,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 54:[1, 12], Operations: ['68-57=11', '23-11=12'] Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[11, 24], Operations: ['68-57=11', '1+23=24'] Exploring Operation: 24-11=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 11+24=35, Resulting Numbers: [35] 35,54 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 13, 56, 96, 16 ]
49
[ "56-13=43", "96/16=6", "43+6=49" ]
Current State: 49:[13, 56, 96, 16], Operations: [] Exploring Operation: 56-13=43, Resulting Numbers: [96, 16, 43] Generated Node #2: [96, 16, 43] from Operation: 56-13=43 Current State: 49:[96, 16, 43], Operations: ['56-13=43'] Exploring Operation: 96/16=6, Resulting Numbers: [43, 6] Generated Node #3: [43, 6] from Operation: 96/16=6 Current State: 49:[43, 6], Operations: ['56-13=43', '96/16=6'] Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[13, 56, 96, 16], Operations: [] Exploring Operation: 96/16=6, Resulting Numbers: [13, 56, 6] Generated Node #0,0: 49:[13, 56, 6] Operation: 96/16=6 Exploring Operation: 96-56=40, Resulting Numbers: [13, 16, 40] Generated Node #0,1: 49:[13, 16, 40] Operation: 96-56=40 Moving to Node #0,0 Current State: 49:[13, 56, 6], Operations: ['96/16=6'] Exploring Operation: 56-13=43, Resulting Numbers: [6, 43] Generated Node #0,0,0: 49:[6, 43] Operation: 56-13=43 Exploring Operation: 13-6=7, Resulting Numbers: [56, 7] Generated Node #0,0,1: 49:[56, 7] Operation: 13-6=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 49:[6, 43], Operations: ['96/16=6', '56-13=43'] Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 6+43=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[13, 56, 96, 16], Operations: [] Exploring Operation: 96/16=6, Resulting Numbers: [13, 56, 6] Generated Node #0,0: 49:[13, 56, 6] Operation: 96/16=6 Moving to Node #0,0 Current State: 49:[13, 56, 6], Operations: ['96/16=6'] Exploring Operation: 56-13=43, Resulting Numbers: [6, 43] Generated Node #0,0,0: 49:[6, 43] Operation: 56-13=43 Moving to Node #0,0,0 Current State: 49:[6, 43], Operations: ['96/16=6', '56-13=43'] Exploring Operation: 6+43=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 88, 3, 38, 61 ]
33
[ "88-38=50", "61-50=11", "3*11=33" ]
Current State: 33:[88, 3, 38, 61], Operations: [] Exploring Operation: 88-38=50, Resulting Numbers: [3, 61, 50] Generated Node #2: [3, 61, 50] from Operation: 88-38=50 Current State: 33:[3, 61, 50], Operations: ['88-38=50'] Exploring Operation: 61-50=11, Resulting Numbers: [3, 11] Generated Node #3: [3, 11] from Operation: 61-50=11 Current State: 33:[3, 11], Operations: ['88-38=50', '61-50=11'] Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[88, 3, 38, 61], Operations: [] Exploring Operation: 88-38=50, Resulting Numbers: [3, 61, 50] Generated Node #0,0: 33:[3, 61, 50] Operation: 88-38=50 Exploring Operation: 88-61=27, Resulting Numbers: [3, 38, 27] Generated Node #0,1: 33:[3, 38, 27] Operation: 88-61=27 Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[3, 38, 27], Operations: ['88-61=27'] Exploring Operation: 38-27=11, Resulting Numbers: [3, 11] Generated Node #0,1,0: 33:[3, 11] Operation: 38-27=11 Exploring Operation: 27/3=9, Resulting Numbers: [38, 9] Generated Node #0,1,1: 33:[38, 9] Operation: 27/3=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 33:[3, 11], Operations: ['88-61=27', '38-27=11'] Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[88, 3, 38, 61], Operations: [] Exploring Operation: 88-61=27, Resulting Numbers: [3, 38, 27] Generated Node #0,1: 33:[3, 38, 27] Operation: 88-61=27 Moving to Node #0,1 Current State: 33:[3, 38, 27], Operations: ['88-61=27'] Exploring Operation: 38-27=11, Resulting Numbers: [3, 11] Generated Node #0,1,0: 33:[3, 11] Operation: 38-27=11 Moving to Node #0,1,0 Current State: 33:[3, 11], Operations: ['88-61=27', '38-27=11'] Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 13, 75, 37, 82 ]
54
[ "82-75=7", "13*7=91", "91-37=54" ]
Current State: 54:[13, 75, 37, 82], Operations: [] Exploring Operation: 82-75=7, Resulting Numbers: [13, 37, 7] Generated Node #2: [13, 37, 7] from Operation: 82-75=7 Current State: 54:[13, 37, 7], Operations: ['82-75=7'] Exploring Operation: 13*7=91, Resulting Numbers: [37, 91] Generated Node #3: [37, 91] from Operation: 13*7=91 Current State: 54:[37, 91], Operations: ['82-75=7', '13*7=91'] Exploring Operation: 91-37=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[13, 75, 37, 82], Operations: [] Exploring Operation: 82-37=45, Resulting Numbers: [13, 75, 45] Generated Node #0,0: 54:[13, 75, 45] Operation: 82-37=45 Exploring Operation: 75-13=62, Resulting Numbers: [37, 82, 62] Generated Node #0,1: 54:[37, 82, 62] Operation: 75-13=62 Exploring Operation: 82-75=7, Resulting Numbers: [13, 37, 7] Generated Node #0,2: 54:[13, 37, 7] Operation: 82-75=7 Exploring Operation: 82-13=69, Resulting Numbers: [75, 37, 69] Generated Node #0,3: 54:[75, 37, 69] Operation: 82-13=69 Exploring Operation: 75-37=38, Resulting Numbers: [13, 82, 38] Generated Node #0,4: 54:[13, 82, 38] Operation: 75-37=38 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[13, 37, 7], Operations: ['82-75=7'] Exploring Operation: 13+7=20, Resulting Numbers: [37, 20] Generated Node #0,2,0: 54:[37, 20] Operation: 13+7=20 Exploring Operation: 37-13=24, Resulting Numbers: [7, 24] Generated Node #0,2,1: 54:[7, 24] Operation: 37-13=24 Exploring Operation: 13+37=50, Resulting Numbers: [7, 50] Generated Node #0,2,2: 54:[7, 50] Operation: 13+37=50 Exploring Operation: 37-7=30, Resulting Numbers: [13, 30] Generated Node #0,2,3: 54:[13, 30] Operation: 37-7=30 Exploring Operation: 13-7=6, Resulting Numbers: [37, 6] Generated Node #0,2,4: 54:[37, 6] Operation: 13-7=6 Moving to Node #0,2,1 Current State: 54:[7, 24], Operations: ['82-75=7', '37-13=24'] Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 7*24=168, Resulting Numbers: [168] 168,54 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,54 unequal: No Solution Moving to Node #0,2,2 Current State: 54:[7, 50], Operations: ['82-75=7', '13+37=50'] Exploring Operation: 7*50=350, Resulting Numbers: [350] 350,54 unequal: No Solution Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,54 unequal: No Solution Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,54 unequal: No Solution Moving to Node #0,2,3 Current State: 54:[13, 30], Operations: ['82-75=7', '37-7=30'] Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,54 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,54 unequal: No Solution Moving to Node #0,2,4 Current State: 54:[37, 6], Operations: ['82-75=7', '13-7=6'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 37*6=222, Resulting Numbers: [222] 222,54 unequal: No Solution Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[37, 20], Operations: ['82-75=7', '13+7=20'] Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 37*20=740, Resulting Numbers: [740] 740,54 unequal: No Solution Exploring Operation: 37+20=57, Resulting Numbers: [57] 57,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[13, 75, 45], Operations: ['82-37=45'] Exploring Operation: 45-13=32, Resulting Numbers: [75, 32] Generated Node #0,0,0: 54:[75, 32] Operation: 45-13=32 Exploring Operation: 75-45=30, Resulting Numbers: [13, 30] Generated Node #0,0,1: 54:[13, 30] Operation: 75-45=30 Exploring Operation: 13+75=88, Resulting Numbers: [45, 88] Generated Node #0,0,2: 54:[45, 88] Operation: 13+75=88 Exploring Operation: 75-13=62, Resulting Numbers: [45, 62] Generated Node #0,0,3: 54:[45, 62] Operation: 75-13=62 Exploring Operation: 13+45=58, Resulting Numbers: [75, 58] Generated Node #0,0,4: 54:[75, 58] Operation: 13+45=58 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 54:[13, 30], Operations: ['82-37=45', '75-45=30'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,54 unequal: No Solution Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 54:[45, 62], Operations: ['82-37=45', '75-13=62'] Exploring Operation: 45+62=107, Resulting Numbers: [107] 107,54 unequal: No Solution Exploring Operation: 62-45=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 45*62=2790, Resulting Numbers: [2790] 2790,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 54:[75, 58], Operations: ['82-37=45', '13+45=58'] Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 75*58=4350, Resulting Numbers: [4350] 4350,54 unequal: No Solution Exploring Operation: 75+58=133, Resulting Numbers: [133] 133,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[75, 32], Operations: ['82-37=45', '45-13=32'] Exploring Operation: 75-32=43, Resulting Numbers: [43] 43,54 unequal: No Solution Exploring Operation: 75*32=2400, Resulting Numbers: [2400] 2400,54 unequal: No Solution Exploring Operation: 75+32=107, Resulting Numbers: [107] 107,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 54:[45, 88], Operations: ['82-37=45', '13+75=88'] Exploring Operation: 88-45=43, Resulting Numbers: [43] 43,54 unequal: No Solution Exploring Operation: 45*88=3960, Resulting Numbers: [3960] 3960,54 unequal: No Solution Exploring Operation: 45+88=133, Resulting Numbers: [133] 133,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 54:[13, 82, 38], Operations: ['75-37=38'] Exploring Operation: 13+38=51, Resulting Numbers: [82, 51] Generated Node #0,4,0: 54:[82, 51] Operation: 13+38=51 Exploring Operation: 82-38=44, Resulting Numbers: [13, 44] Generated Node #0,4,1: 54:[13, 44] Operation: 82-38=44 Exploring Operation: 82-13=69, Resulting Numbers: [38, 69] Generated Node #0,4,2: 54:[38, 69] Operation: 82-13=69 Exploring Operation: 38-13=25, Resulting Numbers: [82, 25] Generated Node #0,4,3: 54:[82, 25] Operation: 38-13=25 Exploring Operation: 13+82=95, Resulting Numbers: [38, 95] Generated Node #0,4,4: 54:[38, 95] Operation: 13+82=95 Moving to Node #0,4,1 Current State: 54:[13, 44], Operations: ['75-37=38', '82-38=44'] Exploring Operation: 13*44=572, Resulting Numbers: [572] 572,54 unequal: No Solution Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 13+44=57, Resulting Numbers: [57] 57,54 unequal: No Solution Moving to Node #0,4,2 Current State: 54:[38, 69], Operations: ['75-37=38', '82-13=69'] Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 38+69=107, Resulting Numbers: [107] 107,54 unequal: No Solution Exploring Operation: 38*69=2622, Resulting Numbers: [2622] 2622,54 unequal: No Solution Moving to Node #0,4,3 Current State: 54:[82, 25], Operations: ['75-37=38', '38-13=25'] Exploring Operation: 82-25=57, Resulting Numbers: [57] 57,54 unequal: No Solution Exploring Operation: 82*25=2050, Resulting Numbers: [2050] 2050,54 unequal: No Solution Exploring Operation: 82+25=107, Resulting Numbers: [107] 107,54 unequal: No Solution Moving to Node #0,4,0 Current State: 54:[82, 51], Operations: ['75-37=38', '13+38=51'] Exploring Operation: 82*51=4182, Resulting Numbers: [4182] 4182,54 unequal: No Solution Exploring Operation: 82+51=133, Resulting Numbers: [133] 133,54 unequal: No Solution Exploring Operation: 82-51=31, Resulting Numbers: [31] 31,54 unequal: No Solution Moving to Node #0,4,4 Current State: 54:[38, 95], Operations: ['75-37=38', '13+82=95'] Exploring Operation: 38*95=3610, Resulting Numbers: [3610] 3610,54 unequal: No Solution Exploring Operation: 95-38=57, Resulting Numbers: [57] 57,54 unequal: No Solution Exploring Operation: 38+95=133, Resulting Numbers: [133] 133,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[37, 82, 62], Operations: ['75-13=62'] Exploring Operation: 62-37=25, Resulting Numbers: [82, 25] Generated Node #0,1,0: 54:[82, 25] Operation: 62-37=25 Exploring Operation: 37+62=99, Resulting Numbers: [82, 99] Generated Node #0,1,1: 54:[82, 99] Operation: 37+62=99 Exploring Operation: 82-62=20, Resulting Numbers: [37, 20] Generated Node #0,1,2: 54:[37, 20] Operation: 82-62=20 Exploring Operation: 37+82=119, Resulting Numbers: [62, 119] Generated Node #0,1,3: 54:[62, 119] Operation: 37+82=119 Exploring Operation: 82-37=45, Resulting Numbers: [62, 45] Generated Node #0,1,4: 54:[62, 45] Operation: 82-37=45 Moving to Node #0,1,2 Current State: 54:[37, 20], Operations: ['75-13=62', '82-62=20'] Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 37*20=740, Resulting Numbers: [740] 740,54 unequal: No Solution Exploring Operation: 37+20=57, Resulting Numbers: [57] 57,54 unequal: No Solution Moving to Node #0,1,4 Current State: 54:[62, 45], Operations: ['75-13=62', '82-37=45'] Exploring Operation: 62+45=107, Resulting Numbers: [107] 107,54 unequal: No Solution Exploring Operation: 62*45=2790, Resulting Numbers: [2790] 2790,54 unequal: No Solution Exploring Operation: 62-45=17, Resulting Numbers: [17] 17,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[82, 25], Operations: ['75-13=62', '62-37=25'] Exploring Operation: 82-25=57, Resulting Numbers: [57] 57,54 unequal: No Solution Exploring Operation: 82*25=2050, Resulting Numbers: [2050] 2050,54 unequal: No Solution Exploring Operation: 82+25=107, Resulting Numbers: [107] 107,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[82, 99], Operations: ['75-13=62', '37+62=99'] Exploring Operation: 82+99=181, Resulting Numbers: [181] 181,54 unequal: No Solution Exploring Operation: 99-82=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 82*99=8118, Resulting Numbers: [8118] 8118,54 unequal: No Solution Moving to Node #0,1,3 Current State: 54:[62, 119], Operations: ['75-13=62', '37+82=119'] Exploring Operation: 119-62=57, Resulting Numbers: [57] 57,54 unequal: No Solution Exploring Operation: 62+119=181, Resulting Numbers: [181] 181,54 unequal: No Solution Exploring Operation: 62*119=7378, Resulting Numbers: [7378] 7378,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 54:[75, 37, 69], Operations: ['82-13=69'] Exploring Operation: 69-37=32, Resulting Numbers: [75, 32] Generated Node #0,3,0: 54:[75, 32] Operation: 69-37=32 Exploring Operation: 75-37=38, Resulting Numbers: [69, 38] Generated Node #0,3,1: 54:[69, 38] Operation: 75-37=38 Exploring Operation: 37+69=106, Resulting Numbers: [75, 106] Generated Node #0,3,2: 54:[75, 106] Operation: 37+69=106 Exploring Operation: 75-69=6, Resulting Numbers: [37, 6] Generated Node #0,3,3: 54:[37, 6] Operation: 75-69=6 Exploring Operation: 75+37=112, Resulting Numbers: [69, 112] Generated Node #0,3,4: 54:[69, 112] Operation: 75+37=112 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 54:[37, 6], Operations: ['82-13=69', '75-69=6'] Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,54 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 37*6=222, Resulting Numbers: [222] 222,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 54:[75, 32], Operations: ['82-13=69', '69-37=32'] Exploring Operation: 75+32=107, Resulting Numbers: [107] 107,54 unequal: No Solution Exploring Operation: 75-32=43, Resulting Numbers: [43] 43,54 unequal: No Solution Exploring Operation: 75*32=2400, Resulting Numbers: [2400] 2400,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 54:[69, 38], Operations: ['82-13=69', '75-37=38'] Exploring Operation: 69+38=107, Resulting Numbers: [107] 107,54 unequal: No Solution Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 69*38=2622, Resulting Numbers: [2622] 2622,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 54:[75, 106], Operations: ['82-13=69', '37+69=106'] Exploring Operation: 75+106=181, Resulting Numbers: [181] 181,54 unequal: No Solution Exploring Operation: 106-75=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 75*106=7950, Resulting Numbers: [7950] 7950,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 54:[69, 112], Operations: ['82-13=69', '75+37=112'] Exploring Operation: 112-69=43, Resulting Numbers: [43] 43,54 unequal: No Solution Exploring Operation: 69*112=7728, Resulting Numbers: [7728] 7728,54 unequal: No Solution Exploring Operation: 69+112=181, Resulting Numbers: [181] 181,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 25, 93, 55, 41 ]
75
[ "93-55=38", "41-38=3", "25*3=75" ]
Current State: 75:[25, 93, 55, 41], Operations: [] Exploring Operation: 93-55=38, Resulting Numbers: [25, 41, 38] Generated Node #2: [25, 41, 38] from Operation: 93-55=38 Current State: 75:[25, 41, 38], Operations: ['93-55=38'] Exploring Operation: 41-38=3, Resulting Numbers: [25, 3] Generated Node #3: [25, 3] from Operation: 41-38=3 Current State: 75:[25, 3], Operations: ['93-55=38', '41-38=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[25, 93, 55, 41], Operations: [] Exploring Operation: 55-41=14, Resulting Numbers: [25, 93, 14] Generated Node #0,0: 75:[25, 93, 14] Operation: 55-41=14 Exploring Operation: 93-55=38, Resulting Numbers: [25, 41, 38] Generated Node #0,1: 75:[25, 41, 38] Operation: 93-55=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[25, 93, 14], Operations: ['55-41=14'] Exploring Operation: 93-25=68, Resulting Numbers: [14, 68] Generated Node #0,0,0: 75:[14, 68] Operation: 93-25=68 Exploring Operation: 93-14=79, Resulting Numbers: [25, 79] Generated Node #0,0,1: 75:[25, 79] Operation: 93-14=79 Moving to Node #0,0,1 Current State: 75:[25, 79], Operations: ['55-41=14', '93-14=79'] Exploring Operation: 79-25=54, Resulting Numbers: [54] 54,75 unequal: No Solution Exploring Operation: 25+79=104, Resulting Numbers: [104] 104,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[14, 68], Operations: ['55-41=14', '93-25=68'] Exploring Operation: 14+68=82, Resulting Numbers: [82] 82,75 unequal: No Solution Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[25, 41, 38], Operations: ['93-55=38'] Exploring Operation: 41+38=79, Resulting Numbers: [25, 79] Generated Node #0,1,0: 75:[25, 79] Operation: 41+38=79 Exploring Operation: 41-38=3, Resulting Numbers: [25, 3] Generated Node #0,1,1: 75:[25, 3] Operation: 41-38=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[25, 3], Operations: ['93-55=38', '41-38=3'] Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[25, 93, 55, 41], Operations: [] Exploring Operation: 93-55=38, Resulting Numbers: [25, 41, 38] Generated Node #0,1: 75:[25, 41, 38] Operation: 93-55=38 Moving to Node #0,1 Current State: 75:[25, 41, 38], Operations: ['93-55=38'] Exploring Operation: 41-38=3, Resulting Numbers: [25, 3] Generated Node #0,1,1: 75:[25, 3] Operation: 41-38=3 Moving to Node #0,1,1 Current State: 75:[25, 3], Operations: ['93-55=38', '41-38=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 4, 77, 28, 95 ]
44
[ "95-77=18", "4*18=72", "72-28=44" ]
Current State: 44:[4, 77, 28, 95], Operations: [] Exploring Operation: 95-77=18, Resulting Numbers: [4, 28, 18] Generated Node #2: [4, 28, 18] from Operation: 95-77=18 Current State: 44:[4, 28, 18], Operations: ['95-77=18'] Exploring Operation: 4*18=72, Resulting Numbers: [28, 72] Generated Node #3: [28, 72] from Operation: 4*18=72 Current State: 44:[28, 72], Operations: ['95-77=18', '4*18=72'] Exploring Operation: 72-28=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[4, 77, 28, 95], Operations: [] Exploring Operation: 95-77=18, Resulting Numbers: [4, 28, 18] Generated Node #0,0: 44:[4, 28, 18] Operation: 95-77=18 Moving to Node #0,0 Current State: 44:[4, 28, 18], Operations: ['95-77=18'] Exploring Operation: 28-18=10, Resulting Numbers: [4, 10] Generated Node #0,0,0: 44:[4, 10] Operation: 28-18=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[4, 10], Operations: ['95-77=18', '28-18=10'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,44 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
[ 54, 16, 18, 79 ]
52
[ "18-16=2", "54/2=27", "79-27=52" ]
Current State: 52:[54, 16, 18, 79], Operations: [] Exploring Operation: 18-16=2, Resulting Numbers: [54, 79, 2] Generated Node #2: [54, 79, 2] from Operation: 18-16=2 Current State: 52:[54, 79, 2], Operations: ['18-16=2'] Exploring Operation: 54/2=27, Resulting Numbers: [79, 27] Generated Node #3: [79, 27] from Operation: 54/2=27 Current State: 52:[79, 27], Operations: ['18-16=2', '54/2=27'] Exploring Operation: 79-27=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[54, 16, 18, 79], Operations: [] Exploring Operation: 79-16=63, Resulting Numbers: [54, 18, 63] Generated Node #0,0: 52:[54, 18, 63] Operation: 79-16=63 Exploring Operation: 79-18=61, Resulting Numbers: [54, 16, 61] Generated Node #0,1: 52:[54, 16, 61] Operation: 79-18=61 Exploring Operation: 79-54=25, Resulting Numbers: [16, 18, 25] Generated Node #0,2: 52:[16, 18, 25] Operation: 79-54=25 Exploring Operation: 18-16=2, Resulting Numbers: [54, 79, 2] Generated Node #0,3: 52:[54, 79, 2] Operation: 18-16=2 Moving to Node #0,2 Current State: 52:[16, 18, 25], Operations: ['79-54=25'] Exploring Operation: 25-18=7, Resulting Numbers: [16, 7] Generated Node #0,2,0: 52:[16, 7] Operation: 25-18=7 Exploring Operation: 18-16=2, Resulting Numbers: [25, 2] Generated Node #0,2,1: 52:[25, 2] Operation: 18-16=2 Exploring Operation: 25-16=9, Resulting Numbers: [18, 9] Generated Node #0,2,2: 52:[18, 9] Operation: 25-16=9 Exploring Operation: 16+18=34, Resulting Numbers: [25, 34] Generated Node #0,2,3: 52:[25, 34] Operation: 16+18=34 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 52:[25, 2], Operations: ['79-54=25', '18-16=2'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,52 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 52:[16, 7], Operations: ['79-54=25', '25-18=7'] Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,52 unequal: No Solution Exploring Operation: 16*7=112, Resulting Numbers: [112] 112,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 52:[18, 9], Operations: ['79-54=25', '25-16=9'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,52 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 18*9=162, Resulting Numbers: [162] 162,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 52:[25, 34], Operations: ['79-54=25', '16+18=34'] Exploring Operation: 34-25=9, Resulting Numbers: [9] 9,52 unequal: No Solution Exploring Operation: 25+34=59, Resulting Numbers: [59] 59,52 unequal: No Solution Exploring Operation: 25*34=850, Resulting Numbers: [850] 850,52 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: 52:[54, 16, 61], Operations: ['79-18=61'] Exploring Operation: 61-16=45, Resulting Numbers: [54, 45] Generated Node #0,1,0: 52:[54, 45] Operation: 61-16=45 Exploring Operation: 54-16=38, Resulting Numbers: [61, 38] Generated Node #0,1,1: 52:[61, 38] Operation: 54-16=38 Exploring Operation: 61-54=7, Resulting Numbers: [16, 7] Generated Node #0,1,2: 52:[16, 7] Operation: 61-54=7 Exploring Operation: 54+16=70, Resulting Numbers: [61, 70] Generated Node #0,1,3: 52:[61, 70] Operation: 54+16=70 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 52:[16, 7], Operations: ['79-18=61', '61-54=7'] Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,52 unequal: No Solution Exploring Operation: 16*7=112, Resulting Numbers: [112] 112,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 52:[54, 45], Operations: ['79-18=61', '61-16=45'] Exploring Operation: 54+45=99, Resulting Numbers: [99] 99,52 unequal: No Solution Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,52 unequal: No Solution Exploring Operation: 54*45=2430, Resulting Numbers: [2430] 2430,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 52:[61, 38], Operations: ['79-18=61', '54-16=38'] Exploring Operation: 61-38=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 61+38=99, Resulting Numbers: [99] 99,52 unequal: No Solution Exploring Operation: 61*38=2318, Resulting Numbers: [2318] 2318,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 52:[61, 70], Operations: ['79-18=61', '54+16=70'] Exploring Operation: 61*70=4270, Resulting Numbers: [4270] 4270,52 unequal: No Solution Exploring Operation: 61+70=131, Resulting Numbers: [131] 131,52 unequal: No Solution Exploring Operation: 70-61=9, Resulting Numbers: [9] 9,52 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: 52:[54, 18, 63], Operations: ['79-16=63'] Exploring Operation: 54-18=36, Resulting Numbers: [63, 36] Generated Node #0,0,0: 52:[63, 36] Operation: 54-18=36 Exploring Operation: 63-18=45, Resulting Numbers: [54, 45] Generated Node #0,0,1: 52:[54, 45] Operation: 63-18=45 Exploring Operation: 63-54=9, Resulting Numbers: [18, 9] Generated Node #0,0,2: 52:[18, 9] Operation: 63-54=9 Exploring Operation: 54/18=3, Resulting Numbers: [63, 3] Generated Node #0,0,3: 52:[63, 3] Operation: 54/18=3 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 52:[54, 45], Operations: ['79-16=63', '63-18=45'] Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,52 unequal: No Solution Exploring Operation: 54+45=99, Resulting Numbers: [99] 99,52 unequal: No Solution Exploring Operation: 54*45=2430, Resulting Numbers: [2430] 2430,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 52:[18, 9], Operations: ['79-16=63', '63-54=9'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,52 unequal: No Solution Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 18*9=162, Resulting Numbers: [162] 162,52 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 52:[63, 3], Operations: ['79-16=63', '54/18=3'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,52 unequal: No Solution Exploring Operation: 63*3=189, Resulting Numbers: [189] 189,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[63, 36], Operations: ['79-16=63', '54-18=36'] Exploring Operation: 63+36=99, Resulting Numbers: [99] 99,52 unequal: No Solution Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 63*36=2268, Resulting Numbers: [2268] 2268,52 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: 52:[54, 79, 2], Operations: ['18-16=2'] Exploring Operation: 54-2=52, Resulting Numbers: [79, 52] Generated Node #0,3,0: 52:[79, 52] Operation: 54-2=52 Exploring Operation: 79-2=77, Resulting Numbers: [54, 77] Generated Node #0,3,1: 52:[54, 77] Operation: 79-2=77 Exploring Operation: 54/2=27, Resulting Numbers: [79, 27] Generated Node #0,3,2: 52:[79, 27] Operation: 54/2=27 Exploring Operation: 79-54=25, Resulting Numbers: [2, 25] Generated Node #0,3,3: 52:[2, 25] Operation: 79-54=25 Moving to Node #0,3,3 Current State: 52:[2, 25], Operations: ['18-16=2', '79-54=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,52 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,52 unequal: No Solution Moving to Node #0,3,1 Current State: 52:[54, 77], Operations: ['18-16=2', '79-2=77'] Exploring Operation: 54+77=131, Resulting Numbers: [131] 131,52 unequal: No Solution Exploring Operation: 77-54=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 54*77=4158, Resulting Numbers: [4158] 4158,52 unequal: No Solution Moving to Node #0,3,0 Current State: 52:[79, 52], Operations: ['18-16=2', '54-2=52'] Exploring Operation: 79+52=131, Resulting Numbers: [131] 131,52 unequal: No Solution Exploring Operation: 79*52=4108, Resulting Numbers: [4108] 4108,52 unequal: No Solution Exploring Operation: 79-52=27, Resulting Numbers: [27] 27,52 unequal: No Solution Moving to Node #0,3,2 Current State: 52:[79, 27], Operations: ['18-16=2', '54/2=27'] Exploring Operation: 79+27=106, Resulting Numbers: [106] 106,52 unequal: No Solution Exploring Operation: 79*27=2133, Resulting Numbers: [2133] 2133,52 unequal: No Solution Exploring Operation: 79-27=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[54, 16, 18, 79], Operations: [] Exploring Operation: 18-16=2, Resulting Numbers: [54, 79, 2] Generated Node #0,3: 52:[54, 79, 2] Operation: 18-16=2 Moving to Node #0,3 Current State: 52:[54, 79, 2], Operations: ['18-16=2'] Exploring Operation: 54/2=27, Resulting Numbers: [79, 27] Generated Node #0,3,2: 52:[79, 27] Operation: 54/2=27 Moving to Node #0,3,2 Current State: 52:[79, 27], Operations: ['18-16=2', '54/2=27'] Exploring Operation: 79-27=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
0.934896
hs_4
sum_heuristic
[ 88, 38, 2, 33 ]
74
[ "88-33=55", "38/2=19", "55+19=74" ]
Current State: 74:[88, 38, 2, 33], Operations: [] Exploring Operation: 88-33=55, Resulting Numbers: [38, 2, 55] Generated Node #2: [38, 2, 55] from Operation: 88-33=55 Current State: 74:[38, 2, 55], Operations: ['88-33=55'] Exploring Operation: 38/2=19, Resulting Numbers: [55, 19] Generated Node #3: [55, 19] from Operation: 38/2=19 Current State: 74:[55, 19], Operations: ['88-33=55', '38/2=19'] Exploring Operation: 55+19=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[88, 38, 2, 33], Operations: [] Exploring Operation: 88-38=50, Resulting Numbers: [2, 33, 50] Generated Node #0,0: 74:[2, 33, 50] Operation: 88-38=50 Exploring Operation: 88-2=86, Resulting Numbers: [38, 33, 86] Generated Node #0,1: 74:[38, 33, 86] Operation: 88-2=86 Exploring Operation: 88/2=44, Resulting Numbers: [38, 33, 44] Generated Node #0,2: 74:[38, 33, 44] Operation: 88/2=44 Moving to Node #0,2 Current State: 74:[38, 33, 44], Operations: ['88/2=44'] Exploring Operation: 38+33=71, Resulting Numbers: [44, 71] Generated Node #0,2,0: 74:[44, 71] Operation: 38+33=71 Exploring Operation: 44-38=6, Resulting Numbers: [33, 6] Generated Node #0,2,1: 74:[33, 6] Operation: 44-38=6 Exploring Operation: 33+44=77, Resulting Numbers: [38, 77] Generated Node #0,2,2: 74:[38, 77] Operation: 33+44=77 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 74:[38, 77], Operations: ['88/2=44', '33+44=77'] Exploring Operation: 38*77=2926, Resulting Numbers: [2926] 2926,74 unequal: No Solution Exploring Operation: 77-38=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 38+77=115, Resulting Numbers: [115] 115,74 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 #0,2,1 Current State: 74:[33, 6], Operations: ['88/2=44', '44-38=6'] Exploring Operation: 33+6=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 33*6=198, Resulting Numbers: [198] 198,74 unequal: No Solution Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,74 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:[44, 71], Operations: ['88/2=44', '38+33=71'] Exploring Operation: 44*71=3124, Resulting Numbers: [3124] 3124,74 unequal: No Solution Exploring Operation: 44+71=115, Resulting Numbers: [115] 115,74 unequal: No Solution Exploring Operation: 71-44=27, Resulting Numbers: [27] 27,74 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: 74:[2, 33, 50], Operations: ['88-38=50'] Exploring Operation: 33+50=83, Resulting Numbers: [2, 83] Generated Node #0,0,0: 74:[2, 83] Operation: 33+50=83 Exploring Operation: 2+33=35, Resulting Numbers: [50, 35] Generated Node #0,0,1: 74:[50, 35] Operation: 2+33=35 Exploring Operation: 50-2=48, Resulting Numbers: [33, 48] Generated Node #0,0,2: 74:[33, 48] Operation: 50-2=48 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[2, 83], Operations: ['88-38=50', '33+50=83'] Exploring Operation: 2+83=85, Resulting Numbers: [85] 85,74 unequal: No Solution Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,74 unequal: No Solution Exploring Operation: 2*83=166, Resulting Numbers: [166] 166,74 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:[50, 35], Operations: ['88-38=50', '2+33=35'] Exploring Operation: 50*35=1750, Resulting Numbers: [1750] 1750,74 unequal: No Solution Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,74 unequal: No Solution Exploring Operation: 50+35=85, Resulting Numbers: [85] 85,74 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:[33, 48], Operations: ['88-38=50', '50-2=48'] Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,74 unequal: No Solution Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,74 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,74 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:[38, 33, 86], Operations: ['88-2=86'] Exploring Operation: 38-33=5, Resulting Numbers: [86, 5] Generated Node #0,1,0: 74:[86, 5] Operation: 38-33=5 Exploring Operation: 38+33=71, Resulting Numbers: [86, 71] Generated Node #0,1,1: 74:[86, 71] Operation: 38+33=71 Exploring Operation: 86-38=48, Resulting Numbers: [33, 48] Generated Node #0,1,2: 74:[33, 48] Operation: 86-38=48 Moving to Node #0,1,0 Current State: 74:[86, 5], Operations: ['88-2=86', '38-33=5'] Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,74 unequal: No Solution Exploring Operation: 86*5=430, Resulting Numbers: [430] 430,74 unequal: No Solution Exploring Operation: 86+5=91, Resulting Numbers: [91] 91,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[86, 71], Operations: ['88-2=86', '38+33=71'] Exploring Operation: 86-71=15, Resulting Numbers: [15] 15,74 unequal: No Solution Exploring Operation: 86+71=157, Resulting Numbers: [157] 157,74 unequal: No Solution Exploring Operation: 86*71=6106, Resulting Numbers: [6106] 6106,74 unequal: No Solution Moving to Node #0,1,2 Current State: 74:[33, 48], Operations: ['88-2=86', '86-38=48'] Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,74 unequal: No Solution Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,74 unequal: No Solution Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,74 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 24, 52, 18, 32 ]
71
[ "52*18=936", "936/24=39", "32+39=71" ]
Current State: 71:[24, 52, 18, 32], Operations: [] Exploring Operation: 52*18=936, Resulting Numbers: [24, 32, 936] Generated Node #2: [24, 32, 936] from Operation: 52*18=936 Current State: 71:[24, 32, 936], Operations: ['52*18=936'] Exploring Operation: 936/24=39, Resulting Numbers: [32, 39] Generated Node #3: [32, 39] from Operation: 936/24=39 Current State: 71:[32, 39], Operations: ['52*18=936', '936/24=39'] Exploring Operation: 32+39=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[24, 52, 18, 32], Operations: [] Exploring Operation: 24+32=56, Resulting Numbers: [52, 18, 56] Generated Node #0,0: 71:[52, 18, 56] Operation: 24+32=56 Exploring Operation: 24+18=42, Resulting Numbers: [52, 32, 42] Generated Node #0,1: 71:[52, 32, 42] Operation: 24+18=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[52, 18, 56], Operations: ['24+32=56'] Exploring Operation: 18+56=74, Resulting Numbers: [52, 74] Generated Node #0,0,0: 71:[52, 74] Operation: 18+56=74 Exploring Operation: 52+18=70, Resulting Numbers: [56, 70] Generated Node #0,0,1: 71:[56, 70] Operation: 52+18=70 Moving to Node #0,0,1 Current State: 71:[56, 70], Operations: ['24+32=56', '52+18=70'] Exploring Operation: 70-56=14, Resulting Numbers: [14] 14,71 unequal: No Solution Exploring Operation: 56+70=126, Resulting Numbers: [126] 126,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[52, 74], Operations: ['24+32=56', '18+56=74'] Exploring Operation: 74-52=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 52+74=126, Resulting Numbers: [126] 126,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[52, 32, 42], Operations: ['24+18=42'] Exploring Operation: 32+42=74, Resulting Numbers: [52, 74] Generated Node #0,1,0: 71:[52, 74] Operation: 32+42=74 Exploring Operation: 52+32=84, Resulting Numbers: [42, 84] Generated Node #0,1,1: 71:[42, 84] Operation: 52+32=84 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 71:[52, 74], Operations: ['24+18=42', '32+42=74'] Exploring Operation: 74-52=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 52+74=126, Resulting Numbers: [126] 126,71 unequal: No Solution No 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: 71:[42, 84], Operations: ['24+18=42', '52+32=84'] Exploring Operation: 42+84=126, Resulting Numbers: [126] 126,71 unequal: No Solution Exploring Operation: 84-42=42, Resulting Numbers: [42] 42,71 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
[ 83, 87, 17, 14 ]
82
[ "87-83=4", "17*4=68", "14+68=82" ]
Current State: 82:[83, 87, 17, 14], Operations: [] Exploring Operation: 87-83=4, Resulting Numbers: [17, 14, 4] Generated Node #2: [17, 14, 4] from Operation: 87-83=4 Current State: 82:[17, 14, 4], Operations: ['87-83=4'] Exploring Operation: 17*4=68, Resulting Numbers: [14, 68] Generated Node #3: [14, 68] from Operation: 17*4=68 Current State: 82:[14, 68], Operations: ['87-83=4', '17*4=68'] Exploring Operation: 14+68=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[83, 87, 17, 14], Operations: [] Exploring Operation: 17-14=3, Resulting Numbers: [83, 87, 3] Generated Node #0,0: 82:[83, 87, 3] Operation: 17-14=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[83, 87, 3], Operations: ['17-14=3'] Exploring Operation: 87-83=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 82:[3, 4] Operation: 87-83=4 Moving to Node #0,0,0 Current State: 82:[3, 4], Operations: ['17-14=3', '87-83=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 33, 70, 69, 40 ]
73
[ "33+40=73", "70-69=1", "73*1=73" ]
Current State: 73:[33, 70, 69, 40], Operations: [] Exploring Operation: 33+40=73, Resulting Numbers: [70, 69, 73] Generated Node #2: [70, 69, 73] from Operation: 33+40=73 Current State: 73:[70, 69, 73], Operations: ['33+40=73'] Exploring Operation: 70-69=1, Resulting Numbers: [73, 1] Generated Node #3: [73, 1] from Operation: 70-69=1 Current State: 73:[73, 1], Operations: ['33+40=73', '70-69=1'] Exploring Operation: 73*1=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[33, 70, 69, 40], Operations: [] Exploring Operation: 33+40=73, Resulting Numbers: [70, 69, 73] Generated Node #0,0: 73:[70, 69, 73] Operation: 33+40=73 Moving to Node #0,0 Current State: 73:[70, 69, 73], Operations: ['33+40=73'] Exploring Operation: 70+69=139, Resulting Numbers: [73, 139] Generated Node #0,0,0: 73:[73, 139] Operation: 70+69=139 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[73, 139], Operations: ['33+40=73', '70+69=139'] Exploring Operation: 139-73=66, Resulting Numbers: [66] 66,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 5, 98, 80, 78 ]
55
[ "5+98=103", "80+78=158", "158-103=55" ]
Current State: 55:[5, 98, 80, 78], Operations: [] Exploring Operation: 5+98=103, Resulting Numbers: [80, 78, 103] Generated Node #2: [80, 78, 103] from Operation: 5+98=103 Current State: 55:[80, 78, 103], Operations: ['5+98=103'] Exploring Operation: 80+78=158, Resulting Numbers: [103, 158] Generated Node #3: [103, 158] from Operation: 80+78=158 Current State: 55:[103, 158], Operations: ['5+98=103', '80+78=158'] Exploring Operation: 158-103=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[5, 98, 80, 78], Operations: [] Exploring Operation: 80/5=16, Resulting Numbers: [98, 78, 16] Generated Node #0,0: 55:[98, 78, 16] Operation: 80/5=16 Exploring Operation: 80-78=2, Resulting Numbers: [5, 98, 2] Generated Node #0,1: 55:[5, 98, 2] Operation: 80-78=2 Exploring Operation: 98-80=18, Resulting Numbers: [5, 78, 18] Generated Node #0,2: 55:[5, 78, 18] Operation: 98-80=18 Exploring Operation: 98-78=20, Resulting Numbers: [5, 80, 20] Generated Node #0,3: 55:[5, 80, 20] Operation: 98-78=20 Moving to Node #0,2 Current State: 55:[5, 78, 18], Operations: ['98-80=18'] Exploring Operation: 78-5=73, Resulting Numbers: [18, 73] Generated Node #0,2,0: 55:[18, 73] Operation: 78-5=73 Exploring Operation: 5+78=83, Resulting Numbers: [18, 83] Generated Node #0,2,1: 55:[18, 83] Operation: 5+78=83 Exploring Operation: 78-18=60, Resulting Numbers: [5, 60] Generated Node #0,2,2: 55:[5, 60] Operation: 78-18=60 Exploring Operation: 18-5=13, Resulting Numbers: [78, 13] Generated Node #0,2,3: 55:[78, 13] Operation: 18-5=13 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 55:[5, 60], Operations: ['98-80=18', '78-18=60'] Exploring Operation: 5*60=300, Resulting Numbers: [300] 300,55 unequal: No Solution Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[5, 98, 80, 78], Operations: [] Exploring Operation: 98-80=18, Resulting Numbers: [5, 78, 18] Generated Node #0,2: 55:[5, 78, 18] Operation: 98-80=18 Moving to Node #0,2 Current State: 55:[5, 78, 18], Operations: ['98-80=18'] Exploring Operation: 78-18=60, Resulting Numbers: [5, 60] Generated Node #0,2,2: 55:[5, 60] Operation: 78-18=60 Moving to Node #0,2,2 Current State: 55:[5, 60], Operations: ['98-80=18', '78-18=60'] Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 35, 13, 21, 17 ]
25
[ "35+17=52", "52/13=4", "21+4=25" ]
Current State: 25:[35, 13, 21, 17], Operations: [] Exploring Operation: 35+17=52, Resulting Numbers: [13, 21, 52] Generated Node #2: [13, 21, 52] from Operation: 35+17=52 Current State: 25:[13, 21, 52], Operations: ['35+17=52'] Exploring Operation: 52/13=4, Resulting Numbers: [21, 4] Generated Node #3: [21, 4] from Operation: 52/13=4 Current State: 25:[21, 4], Operations: ['35+17=52', '52/13=4'] Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[35, 13, 21, 17], Operations: [] Exploring Operation: 35-13=22, Resulting Numbers: [21, 17, 22] Generated Node #0,0: 25:[21, 17, 22] Operation: 35-13=22 Exploring Operation: 17-13=4, Resulting Numbers: [35, 21, 4] Generated Node #0,1: 25:[35, 21, 4] Operation: 17-13=4 Exploring Operation: 35-17=18, Resulting Numbers: [13, 21, 18] Generated Node #0,2: 25:[13, 21, 18] Operation: 35-17=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[21, 17, 22], Operations: ['35-13=22'] Exploring Operation: 22-17=5, Resulting Numbers: [21, 5] Generated Node #0,0,0: 25:[21, 5] Operation: 22-17=5 Exploring Operation: 21-17=4, Resulting Numbers: [22, 4] Generated Node #0,0,1: 25:[22, 4] Operation: 21-17=4 Exploring Operation: 22-21=1, Resulting Numbers: [17, 1] Generated Node #0,0,2: 25:[17, 1] Operation: 22-21=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[21, 5], Operations: ['35-13=22', '22-17=5'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 25:[22, 4], Operations: ['35-13=22', '21-17=4'] Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 25:[17, 1], Operations: ['35-13=22', '22-21=1'] Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[35, 21, 4], Operations: ['17-13=4'] Exploring Operation: 35-4=31, Resulting Numbers: [21, 31] Generated Node #0,1,0: 25:[21, 31] Operation: 35-4=31 Exploring Operation: 21+4=25, Resulting Numbers: [35, 25] Generated Node #0,1,1: 25:[35, 25] Operation: 21+4=25 Exploring Operation: 35-21=14, Resulting Numbers: [4, 14] Generated Node #0,1,2: 25:[4, 14] Operation: 35-21=14 Moving to Node #0,1,0 Current State: 25:[21, 31], Operations: ['17-13=4', '35-4=31'] Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,25 unequal: No Solution Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,25 unequal: No Solution Moving to Node #0,1,1 Current State: 25:[35, 25], Operations: ['17-13=4', '21+4=25'] Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,25 unequal: No Solution Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,25 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,25 unequal: No Solution Moving to Node #0,1,2 Current State: 25:[4, 14], Operations: ['17-13=4', '35-21=14'] Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,25 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,25 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 #0,2 Current State: 25:[13, 21, 18], Operations: ['35-17=18'] Exploring Operation: 21-13=8, Resulting Numbers: [18, 8] Generated Node #0,2,0: 25:[18, 8] Operation: 21-13=8 Exploring Operation: 18-13=5, Resulting Numbers: [21, 5] Generated Node #0,2,1: 25:[21, 5] Operation: 18-13=5 Exploring Operation: 13+18=31, Resulting Numbers: [21, 31] Generated Node #0,2,2: 25:[21, 31] Operation: 13+18=31 Moving to Node #0,2,1 Current State: 25:[21, 5], Operations: ['35-17=18', '18-13=5'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,25 unequal: No Solution Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,25 unequal: No Solution Moving to Node #0,2,0 Current State: 25:[18, 8], Operations: ['35-17=18', '21-13=8'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,25 unequal: No Solution Moving to Node #0,2,2 Current State: 25:[21, 31], Operations: ['35-17=18', '13+18=31'] Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,25 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,25 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
[ 81, 55, 66, 70 ]
71
[ "81-70=11", "55/11=5", "66+5=71" ]
Current State: 71:[81, 55, 66, 70], Operations: [] Exploring Operation: 81-70=11, Resulting Numbers: [55, 66, 11] Generated Node #2: [55, 66, 11] from Operation: 81-70=11 Current State: 71:[55, 66, 11], Operations: ['81-70=11'] Exploring Operation: 55/11=5, Resulting Numbers: [66, 5] Generated Node #3: [66, 5] from Operation: 55/11=5 Current State: 71:[66, 5], Operations: ['81-70=11', '55/11=5'] Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[81, 55, 66, 70], Operations: [] Exploring Operation: 55+66=121, Resulting Numbers: [81, 70, 121] Generated Node #0,0: 71:[81, 70, 121] Operation: 55+66=121 Exploring Operation: 81-55=26, Resulting Numbers: [66, 70, 26] Generated Node #0,1: 71:[66, 70, 26] Operation: 81-55=26 Exploring Operation: 55+70=125, Resulting Numbers: [81, 66, 125] Generated Node #0,2: 71:[81, 66, 125] Operation: 55+70=125 Exploring Operation: 81+55=136, Resulting Numbers: [66, 70, 136] Generated Node #0,3: 71:[66, 70, 136] Operation: 81+55=136 Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[66, 70, 26], Operations: ['81-55=26'] Exploring Operation: 70+26=96, Resulting Numbers: [66, 96] Generated Node #0,1,0: 71:[66, 96] Operation: 70+26=96 Exploring Operation: 66-26=40, Resulting Numbers: [70, 40] Generated Node #0,1,1: 71:[70, 40] Operation: 66-26=40 Exploring Operation: 70-26=44, Resulting Numbers: [66, 44] Generated Node #0,1,2: 71:[66, 44] Operation: 70-26=44 Exploring Operation: 66+26=92, Resulting Numbers: [70, 92] Generated Node #0,1,3: 71:[70, 92] Operation: 66+26=92 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 71:[70, 92], Operations: ['81-55=26', '66+26=92'] Exploring Operation: 70*92=6440, Resulting Numbers: [6440] 6440,71 unequal: No Solution Exploring Operation: 92-70=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 70+92=162, Resulting Numbers: [162] 162,71 unequal: No Solution No 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: 71:[66, 96], Operations: ['81-55=26', '70+26=96'] Exploring Operation: 96-66=30, Resulting Numbers: [30] 30,71 unequal: No Solution Exploring Operation: 66+96=162, Resulting Numbers: [162] 162,71 unequal: No Solution Exploring Operation: 66*96=6336, Resulting Numbers: [6336] 6336,71 unequal: No Solution No 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: 71:[70, 40], Operations: ['81-55=26', '66-26=40'] Exploring Operation: 70+40=110, Resulting Numbers: [110] 110,71 unequal: No Solution Exploring Operation: 70*40=2800, Resulting Numbers: [2800] 2800,71 unequal: No Solution Exploring Operation: 70-40=30, Resulting Numbers: [30] 30,71 unequal: No Solution No 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: 71:[66, 44], Operations: ['81-55=26', '70-26=44'] Exploring Operation: 66*44=2904, Resulting Numbers: [2904] 2904,71 unequal: No Solution Exploring Operation: 66+44=110, Resulting Numbers: [110] 110,71 unequal: No Solution Exploring Operation: 66-44=22, Resulting Numbers: [22] 22,71 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: 71:[81, 70, 121], Operations: ['55+66=121'] Exploring Operation: 81+70=151, Resulting Numbers: [121, 151] Generated Node #0,0,0: 71:[121, 151] Operation: 81+70=151 Exploring Operation: 121-81=40, Resulting Numbers: [70, 40] Generated Node #0,0,1: 71:[70, 40] Operation: 121-81=40 Exploring Operation: 81-70=11, Resulting Numbers: [121, 11] Generated Node #0,0,2: 71:[121, 11] Operation: 81-70=11 Exploring Operation: 121-70=51, Resulting Numbers: [81, 51] Generated Node #0,0,3: 71:[81, 51] Operation: 121-70=51 Moving to Node #0,0,3 Current State: 71:[81, 51], Operations: ['55+66=121', '121-70=51'] Exploring Operation: 81+51=132, Resulting Numbers: [132] 132,71 unequal: No Solution Exploring Operation: 81*51=4131, Resulting Numbers: [4131] 4131,71 unequal: No Solution Exploring Operation: 81-51=30, Resulting Numbers: [30] 30,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[70, 40], Operations: ['55+66=121', '121-81=40'] Exploring Operation: 70-40=30, Resulting Numbers: [30] 30,71 unequal: No Solution Exploring Operation: 70*40=2800, Resulting Numbers: [2800] 2800,71 unequal: No Solution Exploring Operation: 70+40=110, Resulting Numbers: [110] 110,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[121, 11], Operations: ['55+66=121', '81-70=11'] Exploring Operation: 121-11=110, Resulting Numbers: [110] 110,71 unequal: No Solution Exploring Operation: 121/11=11, Resulting Numbers: [11] 11,71 unequal: No Solution Exploring Operation: 121+11=132, Resulting Numbers: [132] 132,71 unequal: No Solution Exploring Operation: 121*11=1331, Resulting Numbers: [1331] 1331,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[121, 151], Operations: ['55+66=121', '81+70=151'] Exploring Operation: 151-121=30, Resulting Numbers: [30] 30,71 unequal: No Solution Exploring Operation: 121*151=18271, Resulting Numbers: [18271] 18271,71 unequal: No Solution Exploring Operation: 121+151=272, Resulting Numbers: [272] 272,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[81, 66, 125], Operations: ['55+70=125'] Exploring Operation: 81-66=15, Resulting Numbers: [125, 15] Generated Node #0,2,0: 71:[125, 15] Operation: 81-66=15 Exploring Operation: 125-66=59, Resulting Numbers: [81, 59] Generated Node #0,2,1: 71:[81, 59] Operation: 125-66=59 Exploring Operation: 81+66=147, Resulting Numbers: [125, 147] Generated Node #0,2,2: 71:[125, 147] Operation: 81+66=147 Exploring Operation: 125-81=44, Resulting Numbers: [66, 44] Generated Node #0,2,3: 71:[66, 44] Operation: 125-81=44 Moving to Node #0,2,1 Current State: 71:[81, 59], Operations: ['55+70=125', '125-66=59'] Exploring Operation: 81-59=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 81*59=4779, Resulting Numbers: [4779] 4779,71 unequal: No Solution Exploring Operation: 81+59=140, Resulting Numbers: [140] 140,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[66, 44], Operations: ['55+70=125', '125-81=44'] Exploring Operation: 66-44=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 66+44=110, Resulting Numbers: [110] 110,71 unequal: No Solution Exploring Operation: 66*44=2904, Resulting Numbers: [2904] 2904,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[125, 15], Operations: ['55+70=125', '81-66=15'] Exploring Operation: 125+15=140, Resulting Numbers: [140] 140,71 unequal: No Solution Exploring Operation: 125-15=110, Resulting Numbers: [110] 110,71 unequal: No Solution Exploring Operation: 125*15=1875, Resulting Numbers: [1875] 1875,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[125, 147], Operations: ['55+70=125', '81+66=147'] Exploring Operation: 125*147=18375, Resulting Numbers: [18375] 18375,71 unequal: No Solution Exploring Operation: 125+147=272, Resulting Numbers: [272] 272,71 unequal: No Solution Exploring Operation: 147-125=22, Resulting Numbers: [22] 22,71 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 #0,3 Current State: 71:[66, 70, 136], Operations: ['81+55=136'] Exploring Operation: 136-66=70, Resulting Numbers: [70, 70] Generated Node #0,3,0: 71:[70, 70] Operation: 136-66=70 Exploring Operation: 70-66=4, Resulting Numbers: [136, 4] Generated Node #0,3,1: 71:[136, 4] Operation: 70-66=4 Exploring Operation: 66+70=136, Resulting Numbers: [136, 136] Generated Node #0,3,2: 71:[136, 136] Operation: 66+70=136 Exploring Operation: 136-70=66, Resulting Numbers: [66, 66] Generated Node #0,3,3: 71:[66, 66] Operation: 136-70=66 Moving to Node #0,3,0 Current State: 71:[70, 70], Operations: ['81+55=136', '136-66=70'] Exploring Operation: 70/70=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 70*70=4900, Resulting Numbers: [4900] 4900,71 unequal: No Solution Exploring Operation: 70+70=140, Resulting Numbers: [140] 140,71 unequal: No Solution Exploring Operation: 70-70=0, Resulting Numbers: [0] 0,71 unequal: No Solution Moving to Node #0,3,3 Current State: 71:[66, 66], Operations: ['81+55=136', '136-70=66'] Exploring Operation: 66+66=132, Resulting Numbers: [132] 132,71 unequal: No Solution Exploring Operation: 66-66=0, Resulting Numbers: [0] 0,71 unequal: No Solution Exploring Operation: 66/66=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 66*66=4356, Resulting Numbers: [4356] 4356,71 unequal: No Solution Moving to Node #0,3,2 Current State: 71:[136, 136], Operations: ['81+55=136', '66+70=136'] Exploring Operation: 136*136=18496, Resulting Numbers: [18496] 18496,71 unequal: No Solution Exploring Operation: 136+136=272, Resulting Numbers: [272] 272,71 unequal: No Solution Exploring Operation: 136/136=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 136-136=0, Resulting Numbers: [0] 0,71 unequal: No Solution Moving to Node #0,3,1 Current State: 71:[136, 4], Operations: ['81+55=136', '70-66=4'] Exploring Operation: 136+4=140, Resulting Numbers: [140] 140,71 unequal: No Solution Exploring Operation: 136*4=544, Resulting Numbers: [544] 544,71 unequal: No Solution Exploring Operation: 136-4=132, Resulting Numbers: [132] 132,71 unequal: No Solution Exploring Operation: 136/4=34, Resulting Numbers: [34] 34,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 10, 68, 22, 9 ]
62
[ "22-9=13", "10*13=130", "130-68=62" ]
Current State: 62:[10, 68, 22, 9], Operations: [] Exploring Operation: 22-9=13, Resulting Numbers: [10, 68, 13] Generated Node #2: [10, 68, 13] from Operation: 22-9=13 Current State: 62:[10, 68, 13], Operations: ['22-9=13'] Exploring Operation: 10*13=130, Resulting Numbers: [68, 130] Generated Node #3: [68, 130] from Operation: 10*13=130 Current State: 62:[68, 130], Operations: ['22-9=13', '10*13=130'] Exploring Operation: 130-68=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[10, 68, 22, 9], Operations: [] Exploring Operation: 10+22=32, Resulting Numbers: [68, 9, 32] Generated Node #0,0: 62:[68, 9, 32] Operation: 10+22=32 Exploring Operation: 68-10=58, Resulting Numbers: [22, 9, 58] Generated Node #0,1: 62:[22, 9, 58] Operation: 68-10=58 Exploring Operation: 10-9=1, Resulting Numbers: [68, 22, 1] Generated Node #0,2: 62:[68, 22, 1] Operation: 10-9=1 Exploring Operation: 22+9=31, Resulting Numbers: [10, 68, 31] Generated Node #0,3: 62:[10, 68, 31] Operation: 22+9=31 Moving to Node #0,0 Current State: 62:[68, 9, 32], Operations: ['10+22=32'] Exploring Operation: 68-32=36, Resulting Numbers: [9, 36] Generated Node #0,0,0: 62:[9, 36] Operation: 68-32=36 Exploring Operation: 32-9=23, Resulting Numbers: [68, 23] Generated Node #0,0,1: 62:[68, 23] Operation: 32-9=23 Exploring Operation: 68-9=59, Resulting Numbers: [32, 59] Generated Node #0,0,2: 62:[32, 59] Operation: 68-9=59 Exploring Operation: 68+9=77, Resulting Numbers: [32, 77] Generated Node #0,0,3: 62:[32, 77] Operation: 68+9=77 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 62:[32, 59], Operations: ['10+22=32', '68-9=59'] Exploring Operation: 32*59=1888, Resulting Numbers: [1888] 1888,62 unequal: No Solution Exploring Operation: 32+59=91, Resulting Numbers: [91] 91,62 unequal: No Solution Exploring Operation: 59-32=27, Resulting Numbers: [27] 27,62 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:[9, 36], Operations: ['10+22=32', '68-32=36'] Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,62 unequal: No Solution Exploring Operation: 9*36=324, Resulting Numbers: [324] 324,62 unequal: No Solution Exploring Operation: 9+36=45, Resulting Numbers: [45] 45,62 unequal: No Solution Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 62:[68, 23], Operations: ['10+22=32', '32-9=23'] Exploring Operation: 68-23=45, Resulting Numbers: [45] 45,62 unequal: No Solution Exploring Operation: 68*23=1564, Resulting Numbers: [1564] 1564,62 unequal: No Solution Exploring Operation: 68+23=91, Resulting Numbers: [91] 91,62 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 #0,0,3 Current State: 62:[32, 77], Operations: ['10+22=32', '68+9=77'] Exploring Operation: 77-32=45, Resulting Numbers: [45] 45,62 unequal: No Solution Exploring Operation: 32*77=2464, Resulting Numbers: [2464] 2464,62 unequal: No Solution Exploring Operation: 32+77=109, Resulting Numbers: [109] 109,62 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: 62:[10, 68, 31], Operations: ['22+9=31'] Exploring Operation: 68-31=37, Resulting Numbers: [10, 37] Generated Node #0,3,0: 62:[10, 37] Operation: 68-31=37 Exploring Operation: 10+68=78, Resulting Numbers: [31, 78] Generated Node #0,3,1: 62:[31, 78] Operation: 10+68=78 Exploring Operation: 10+31=41, Resulting Numbers: [68, 41] Generated Node #0,3,2: 62:[68, 41] Operation: 10+31=41 Exploring Operation: 68-10=58, Resulting Numbers: [31, 58] Generated Node #0,3,3: 62:[31, 58] Operation: 68-10=58 Moving to Node #0,2 Current State: 62:[68, 22, 1], Operations: ['10-9=1'] Exploring Operation: 68/1=68, Resulting Numbers: [22, 68] Generated Node #0,2,0: 62:[22, 68] Operation: 68/1=68 Exploring Operation: 68-1=67, Resulting Numbers: [22, 67] Generated Node #0,2,1: 62:[22, 67] Operation: 68-1=67 Exploring Operation: 22+1=23, Resulting Numbers: [68, 23] Generated Node #0,2,2: 62:[68, 23] Operation: 22+1=23 Exploring Operation: 68*1=68, Resulting Numbers: [22, 68] Generated Node #0,2,3: 62:[22, 68] Operation: 68*1=68 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 62:[22, 67], Operations: ['10-9=1', '68-1=67'] Exploring Operation: 67-22=45, Resulting Numbers: [45] 45,62 unequal: No Solution Exploring Operation: 22*67=1474, Resulting Numbers: [1474] 1474,62 unequal: No Solution Exploring Operation: 22+67=89, Resulting Numbers: [89] 89,62 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 #0,2,2 Current State: 62:[68, 23], Operations: ['10-9=1', '22+1=23'] Exploring Operation: 68+23=91, Resulting Numbers: [91] 91,62 unequal: No Solution Exploring Operation: 68*23=1564, Resulting Numbers: [1564] 1564,62 unequal: No Solution Exploring Operation: 68-23=45, Resulting Numbers: [45] 45,62 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 #0,2,0 Current State: 62:[22, 68], Operations: ['10-9=1', '68/1=68'] Exploring Operation: 68-22=46, Resulting Numbers: [46] 46,62 unequal: No Solution Exploring Operation: 22*68=1496, Resulting Numbers: [1496] 1496,62 unequal: No Solution Exploring Operation: 22+68=90, Resulting Numbers: [90] 90,62 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 #0,2,3 Current State: 62:[22, 68], Operations: ['10-9=1', '68*1=68'] Exploring Operation: 22*68=1496, Resulting Numbers: [1496] 1496,62 unequal: No Solution Exploring Operation: 22+68=90, Resulting Numbers: [90] 90,62 unequal: No Solution Exploring Operation: 68-22=46, Resulting Numbers: [46] 46,62 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:[22, 9, 58], Operations: ['68-10=58'] Exploring Operation: 22-9=13, Resulting Numbers: [58, 13] Generated Node #0,1,0: 62:[58, 13] Operation: 22-9=13 Exploring Operation: 22+9=31, Resulting Numbers: [58, 31] Generated Node #0,1,1: 62:[58, 31] Operation: 22+9=31 Exploring Operation: 58-22=36, Resulting Numbers: [9, 36] Generated Node #0,1,2: 62:[9, 36] Operation: 58-22=36 Exploring Operation: 9+58=67, Resulting Numbers: [22, 67] Generated Node #0,1,3: 62:[22, 67] Operation: 9+58=67 Moving to Node #0,3,3 Current State: 62:[31, 58], Operations: ['22+9=31', '68-10=58'] Exploring Operation: 58-31=27, Resulting Numbers: [27] 27,62 unequal: No Solution Exploring Operation: 31*58=1798, Resulting Numbers: [1798] 1798,62 unequal: No Solution Exploring Operation: 31+58=89, Resulting Numbers: [89] 89,62 unequal: No Solution Moving to Node #0,1,1 Current State: 62:[58, 31], Operations: ['68-10=58', '22+9=31'] Exploring Operation: 58+31=89, Resulting Numbers: [89] 89,62 unequal: No Solution Exploring Operation: 58-31=27, Resulting Numbers: [27] 27,62 unequal: No Solution Exploring Operation: 58*31=1798, Resulting Numbers: [1798] 1798,62 unequal: No Solution Moving to Node #0,1,2 Current State: 62:[9, 36], Operations: ['68-10=58', '58-22=36'] Exploring Operation: 9*36=324, Resulting Numbers: [324] 324,62 unequal: No Solution Exploring Operation: 9+36=45, Resulting Numbers: [45] 45,62 unequal: No Solution Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,62 unequal: No Solution Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,62 unequal: No Solution Moving to Node #0,1,3 Current State: 62:[22, 67], Operations: ['68-10=58', '9+58=67'] Exploring Operation: 22+67=89, Resulting Numbers: [89] 89,62 unequal: No Solution Exploring Operation: 67-22=45, Resulting Numbers: [45] 45,62 unequal: No Solution Exploring Operation: 22*67=1474, Resulting Numbers: [1474] 1474,62 unequal: No Solution Moving to Node #0,3,0 Current State: 62:[10, 37], Operations: ['22+9=31', '68-31=37'] Exploring Operation: 37-10=27, Resulting Numbers: [27] 27,62 unequal: No Solution Exploring Operation: 10*37=370, Resulting Numbers: [370] 370,62 unequal: No Solution Exploring Operation: 10+37=47, Resulting Numbers: [47] 47,62 unequal: No Solution Moving to Node #0,1,0 Current State: 62:[58, 13], Operations: ['68-10=58', '22-9=13'] Exploring Operation: 58*13=754, Resulting Numbers: [754] 754,62 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,62 unequal: No Solution Exploring Operation: 58+13=71, Resulting Numbers: [71] 71,62 unequal: No Solution Moving to Node #0,3,2 Current State: 62:[68, 41], Operations: ['22+9=31', '10+31=41'] Exploring Operation: 68-41=27, Resulting Numbers: [27] 27,62 unequal: No Solution Exploring Operation: 68+41=109, Resulting Numbers: [109] 109,62 unequal: No Solution Exploring Operation: 68*41=2788, Resulting Numbers: [2788] 2788,62 unequal: No Solution Moving to Node #0,3,1 Current State: 62:[31, 78], Operations: ['22+9=31', '10+68=78'] Exploring Operation: 31+78=109, Resulting Numbers: [109] 109,62 unequal: No Solution Exploring Operation: 78-31=47, Resulting Numbers: [47] 47,62 unequal: No Solution Exploring Operation: 31*78=2418, Resulting Numbers: [2418] 2418,62 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 54, 88, 43, 32 ]
46
[ "43-32=11", "88/11=8", "54-8=46" ]
Current State: 46:[54, 88, 43, 32], Operations: [] Exploring Operation: 43-32=11, Resulting Numbers: [54, 88, 11] Generated Node #2: [54, 88, 11] from Operation: 43-32=11 Current State: 46:[54, 88, 11], Operations: ['43-32=11'] Exploring Operation: 88/11=8, Resulting Numbers: [54, 8] Generated Node #3: [54, 8] from Operation: 88/11=8 Current State: 46:[54, 8], Operations: ['43-32=11', '88/11=8'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[54, 88, 43, 32], Operations: [] Exploring Operation: 54-32=22, Resulting Numbers: [88, 43, 22] Generated Node #0,0: 46:[88, 43, 22] Operation: 54-32=22 Exploring Operation: 88-32=56, Resulting Numbers: [54, 43, 56] Generated Node #0,1: 46:[54, 43, 56] Operation: 88-32=56 Exploring Operation: 88-54=34, Resulting Numbers: [43, 32, 34] Generated Node #0,2: 46:[43, 32, 34] Operation: 88-54=34 Exploring Operation: 43-32=11, Resulting Numbers: [54, 88, 11] Generated Node #0,3: 46:[54, 88, 11] Operation: 43-32=11 Exploring Operation: 88-43=45, Resulting Numbers: [54, 32, 45] Generated Node #0,4: 46:[54, 32, 45] Operation: 88-43=45 Moving to Node #0,4 Current State: 46:[54, 32, 45], Operations: ['88-43=45'] Exploring Operation: 54-45=9, Resulting Numbers: [32, 9] Generated Node #0,4,0: 46:[32, 9] Operation: 54-45=9 Exploring Operation: 32+45=77, Resulting Numbers: [54, 77] Generated Node #0,4,1: 46:[54, 77] Operation: 32+45=77 Exploring Operation: 45-32=13, Resulting Numbers: [54, 13] Generated Node #0,4,2: 46:[54, 13] Operation: 45-32=13 Exploring Operation: 54+32=86, Resulting Numbers: [45, 86] Generated Node #0,4,3: 46:[45, 86] Operation: 54+32=86 Exploring Operation: 54-32=22, Resulting Numbers: [45, 22] Generated Node #0,4,4: 46:[45, 22] Operation: 54-32=22 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 46:[45, 22], Operations: ['88-43=45', '54-32=22'] Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 45+22=67, Resulting Numbers: [67] 67,46 unequal: No Solution Exploring Operation: 45*22=990, Resulting Numbers: [990] 990,46 unequal: No Solution No 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: 46:[32, 9], Operations: ['88-43=45', '54-45=9'] Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 32*9=288, Resulting Numbers: [288] 288,46 unequal: No Solution Exploring Operation: 32+9=41, Resulting Numbers: [41] 41,46 unequal: No Solution No 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: 46:[54, 13], Operations: ['88-43=45', '45-32=13'] Exploring Operation: 54+13=67, Resulting Numbers: [67] 67,46 unequal: No Solution Exploring Operation: 54*13=702, Resulting Numbers: [702] 702,46 unequal: No Solution Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,46 unequal: No Solution No 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: 46:[54, 77], Operations: ['88-43=45', '32+45=77'] Exploring Operation: 77-54=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 54*77=4158, Resulting Numbers: [4158] 4158,46 unequal: No Solution Exploring Operation: 54+77=131, Resulting Numbers: [131] 131,46 unequal: No Solution No 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: 46:[45, 86], Operations: ['88-43=45', '54+32=86'] Exploring Operation: 45*86=3870, Resulting Numbers: [3870] 3870,46 unequal: No Solution Exploring Operation: 86-45=41, Resulting Numbers: [41] 41,46 unequal: No Solution Exploring Operation: 45+86=131, Resulting Numbers: [131] 131,46 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: 46:[54, 43, 56], Operations: ['88-32=56'] Exploring Operation: 43+56=99, Resulting Numbers: [54, 99] Generated Node #0,1,0: 46:[54, 99] Operation: 43+56=99 Exploring Operation: 54-43=11, Resulting Numbers: [56, 11] Generated Node #0,1,1: 46:[56, 11] Operation: 54-43=11 Exploring Operation: 54+43=97, Resulting Numbers: [56, 97] Generated Node #0,1,2: 46:[56, 97] Operation: 54+43=97 Exploring Operation: 56-54=2, Resulting Numbers: [43, 2] Generated Node #0,1,3: 46:[43, 2] Operation: 56-54=2 Exploring Operation: 56-43=13, Resulting Numbers: [54, 13] Generated Node #0,1,4: 46:[54, 13] Operation: 56-43=13 Moving to Node #0,2 Current State: 46:[43, 32, 34], Operations: ['88-54=34'] Exploring Operation: 34-32=2, Resulting Numbers: [43, 2] Generated Node #0,2,0: 46:[43, 2] Operation: 34-32=2 Exploring Operation: 32+34=66, Resulting Numbers: [43, 66] Generated Node #0,2,1: 46:[43, 66] Operation: 32+34=66 Exploring Operation: 43+32=75, Resulting Numbers: [34, 75] Generated Node #0,2,2: 46:[34, 75] Operation: 43+32=75 Exploring Operation: 43-34=9, Resulting Numbers: [32, 9] Generated Node #0,2,3: 46:[32, 9] Operation: 43-34=9 Exploring Operation: 43-32=11, Resulting Numbers: [34, 11] Generated Node #0,2,4: 46:[34, 11] Operation: 43-32=11 Moving to Node #0,0 Current State: 46:[88, 43, 22], Operations: ['54-32=22'] Exploring Operation: 88-22=66, Resulting Numbers: [43, 66] Generated Node #0,0,0: 46:[43, 66] Operation: 88-22=66 Exploring Operation: 88-43=45, Resulting Numbers: [22, 45] Generated Node #0,0,1: 46:[22, 45] Operation: 88-43=45 Exploring Operation: 43-22=21, Resulting Numbers: [88, 21] Generated Node #0,0,2: 46:[88, 21] Operation: 43-22=21 Exploring Operation: 43+22=65, Resulting Numbers: [88, 65] Generated Node #0,0,3: 46:[88, 65] Operation: 43+22=65 Exploring Operation: 88/22=4, Resulting Numbers: [43, 4] Generated Node #0,0,4: 46:[43, 4] Operation: 88/22=4 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 46:[22, 45], Operations: ['54-32=22', '88-43=45'] Exploring Operation: 22+45=67, Resulting Numbers: [67] 67,46 unequal: No Solution Exploring Operation: 22*45=990, Resulting Numbers: [990] 990,46 unequal: No Solution Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,46 unequal: No Solution No 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: 46:[43, 4], Operations: ['54-32=22', '88/22=4'] Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,46 unequal: No Solution Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,46 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,46 unequal: No Solution No 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: 46:[43, 66], Operations: ['54-32=22', '88-22=66'] Exploring Operation: 43*66=2838, Resulting Numbers: [2838] 2838,46 unequal: No Solution Exploring Operation: 43+66=109, Resulting Numbers: [109] 109,46 unequal: No Solution Exploring Operation: 66-43=23, Resulting Numbers: [23] 23,46 unequal: No Solution No 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: 46:[88, 21], Operations: ['54-32=22', '43-22=21'] Exploring Operation: 88+21=109, Resulting Numbers: [109] 109,46 unequal: No Solution Exploring Operation: 88*21=1848, Resulting Numbers: [1848] 1848,46 unequal: No Solution Exploring Operation: 88-21=67, Resulting Numbers: [67] 67,46 unequal: No Solution No 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: 46:[88, 65], Operations: ['54-32=22', '43+22=65'] Exploring Operation: 88*65=5720, Resulting Numbers: [5720] 5720,46 unequal: No Solution Exploring Operation: 88-65=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 88+65=153, Resulting Numbers: [153] 153,46 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: 46:[54, 88, 11], Operations: ['43-32=11'] Exploring Operation: 54+11=65, Resulting Numbers: [88, 65] Generated Node #0,3,0: 46:[88, 65] Operation: 54+11=65 Exploring Operation: 88-54=34, Resulting Numbers: [11, 34] Generated Node #0,3,1: 46:[11, 34] Operation: 88-54=34 Exploring Operation: 88/11=8, Resulting Numbers: [54, 8] Generated Node #0,3,2: 46:[54, 8] Operation: 88/11=8 Exploring Operation: 88-11=77, Resulting Numbers: [54, 77] Generated Node #0,3,3: 46:[54, 77] Operation: 88-11=77 Exploring Operation: 54-11=43, Resulting Numbers: [88, 43] Generated Node #0,3,4: 46:[88, 43] Operation: 54-11=43 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 46:[54, 8], Operations: ['43-32=11', '88/11=8'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[54, 88, 43, 32], Operations: [] Exploring Operation: 43-32=11, Resulting Numbers: [54, 88, 11] Generated Node #0,3: 46:[54, 88, 11] Operation: 43-32=11 Moving to Node #0,3 Current State: 46:[54, 88, 11], Operations: ['43-32=11'] Exploring Operation: 88/11=8, Resulting Numbers: [54, 8] Generated Node #0,3,2: 46:[54, 8] Operation: 88/11=8 Moving to Node #0,3,2 Current State: 46:[54, 8], Operations: ['43-32=11', '88/11=8'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.943576
hs_5
sum_heuristic
[ 13, 43, 92, 2 ]
74
[ "13+43=56", "92+56=148", "148/2=74" ]
Current State: 74:[13, 43, 92, 2], Operations: [] Exploring Operation: 13+43=56, Resulting Numbers: [92, 2, 56] Generated Node #2: [92, 2, 56] from Operation: 13+43=56 Current State: 74:[92, 2, 56], Operations: ['13+43=56'] Exploring Operation: 92+56=148, Resulting Numbers: [2, 148] Generated Node #3: [2, 148] from Operation: 92+56=148 Current State: 74:[2, 148], Operations: ['13+43=56', '92+56=148'] Exploring Operation: 148/2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[13, 43, 92, 2], Operations: [] Exploring Operation: 92-43=49, Resulting Numbers: [13, 2, 49] Generated Node #0,0: 74:[13, 2, 49] Operation: 92-43=49 Exploring Operation: 92/2=46, Resulting Numbers: [13, 43, 46] Generated Node #0,1: 74:[13, 43, 46] Operation: 92/2=46 Exploring Operation: 43-13=30, Resulting Numbers: [92, 2, 30] Generated Node #0,2: 74:[92, 2, 30] Operation: 43-13=30 Exploring Operation: 92-13=79, Resulting Numbers: [43, 2, 79] Generated Node #0,3: 74:[43, 2, 79] Operation: 92-13=79 Start Sub Search at level 1: Moving to Node #0,3 Current State: 74:[43, 2, 79], Operations: ['92-13=79'] Exploring Operation: 79-2=77, Resulting Numbers: [43, 77] Generated Node #0,3,0: 74:[43, 77] Operation: 79-2=77 Exploring Operation: 43+2=45, Resulting Numbers: [79, 45] Generated Node #0,3,1: 74:[79, 45] Operation: 43+2=45 Exploring Operation: 43-2=41, Resulting Numbers: [79, 41] Generated Node #0,3,2: 74:[79, 41] Operation: 43-2=41 Exploring Operation: 79-43=36, Resulting Numbers: [2, 36] Generated Node #0,3,3: 74:[2, 36] Operation: 79-43=36 Moving to Node #0,3,3 Current State: 74:[2, 36], Operations: ['92-13=79', '79-43=36'] Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,74 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,74 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,74 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,74 unequal: No Solution Moving to Node #0,3,2 Current State: 74:[79, 41], Operations: ['92-13=79', '43-2=41'] Exploring Operation: 79+41=120, Resulting Numbers: [120] 120,74 unequal: No Solution Exploring Operation: 79-41=38, Resulting Numbers: [38] 38,74 unequal: No Solution Exploring Operation: 79*41=3239, Resulting Numbers: [3239] 3239,74 unequal: No Solution Moving to Node #0,3,0 Current State: 74:[43, 77], Operations: ['92-13=79', '79-2=77'] Exploring Operation: 43+77=120, Resulting Numbers: [120] 120,74 unequal: No Solution Exploring Operation: 77-43=34, Resulting Numbers: [34] 34,74 unequal: No Solution Exploring Operation: 43*77=3311, Resulting Numbers: [3311] 3311,74 unequal: No Solution Moving to Node #0,3,1 Current State: 74:[79, 45], Operations: ['92-13=79', '43+2=45'] Exploring Operation: 79-45=34, Resulting Numbers: [34] 34,74 unequal: No Solution Exploring Operation: 79+45=124, Resulting Numbers: [124] 124,74 unequal: No Solution Exploring Operation: 79*45=3555, Resulting Numbers: [3555] 3555,74 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 Current State: 74:[13, 2, 49], Operations: ['92-43=49'] Exploring Operation: 13-2=11, Resulting Numbers: [49, 11] Generated Node #0,0,0: 74:[49, 11] Operation: 13-2=11 Exploring Operation: 49-13=36, Resulting Numbers: [2, 36] Generated Node #0,0,1: 74:[2, 36] Operation: 49-13=36 Exploring Operation: 13+49=62, Resulting Numbers: [2, 62] Generated Node #0,0,2: 74:[2, 62] Operation: 13+49=62 Exploring Operation: 49-2=47, Resulting Numbers: [13, 47] Generated Node #0,0,3: 74:[13, 47] Operation: 49-2=47 Moving to Node #0,0,1 Current State: 74:[2, 36], Operations: ['92-43=49', '49-13=36'] Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,74 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,74 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,74 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,74 unequal: No Solution Moving to Node #0,0,2 Current State: 74:[2, 62], Operations: ['92-43=49', '13+49=62'] Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,74 unequal: No Solution Exploring Operation: 2*62=124, Resulting Numbers: [124] 124,74 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,74 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,74 unequal: No Solution Moving to Node #0,0,3 Current State: 74:[13, 47], Operations: ['92-43=49', '49-2=47'] Exploring Operation: 13*47=611, Resulting Numbers: [611] 611,74 unequal: No Solution Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,74 unequal: No Solution Exploring Operation: 13+47=60, Resulting Numbers: [60] 60,74 unequal: No Solution Moving to Node #0,0,0 Current State: 74:[49, 11], Operations: ['92-43=49', '13-2=11'] Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,74 unequal: No Solution Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,74 unequal: No Solution Exploring Operation: 49*11=539, Resulting Numbers: [539] 539,74 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 Current State: 74:[92, 2, 30], Operations: ['43-13=30'] Exploring Operation: 92-2=90, Resulting Numbers: [30, 90] Generated Node #0,2,0: 74:[30, 90] Operation: 92-2=90 Exploring Operation: 2+30=32, Resulting Numbers: [92, 32] Generated Node #0,2,1: 74:[92, 32] Operation: 2+30=32 Exploring Operation: 92-30=62, Resulting Numbers: [2, 62] Generated Node #0,2,2: 74:[2, 62] Operation: 92-30=62 Exploring Operation: 92/2=46, Resulting Numbers: [30, 46] Generated Node #0,2,3: 74:[30, 46] Operation: 92/2=46 Moving to Node #0,2,2 Current State: 74:[2, 62], Operations: ['43-13=30', '92-30=62'] Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,74 unequal: No Solution Exploring Operation: 2*62=124, Resulting Numbers: [124] 124,74 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,74 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,74 unequal: No Solution Moving to Node #0,2,3 Current State: 74:[30, 46], Operations: ['43-13=30', '92/2=46'] Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,74 unequal: No Solution Exploring Operation: 30+46=76, Resulting Numbers: [76] 76,74 unequal: No Solution Exploring Operation: 30*46=1380, Resulting Numbers: [1380] 1380,74 unequal: No Solution Moving to Node #0,2,1 Current State: 74:[92, 32], Operations: ['43-13=30', '2+30=32'] Exploring Operation: 92+32=124, Resulting Numbers: [124] 124,74 unequal: No Solution Exploring Operation: 92*32=2944, Resulting Numbers: [2944] 2944,74 unequal: No Solution Exploring Operation: 92-32=60, Resulting Numbers: [60] 60,74 unequal: No Solution Moving to Node #0,2,0 Current State: 74:[30, 90], Operations: ['43-13=30', '92-2=90'] Exploring Operation: 90/30=3, Resulting Numbers: [3] 3,74 unequal: No Solution Exploring Operation: 90-30=60, Resulting Numbers: [60] 60,74 unequal: No Solution Exploring Operation: 30*90=2700, Resulting Numbers: [2700] 2700,74 unequal: No Solution Exploring Operation: 30+90=120, Resulting Numbers: [120] 120,74 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 #0,1 Current State: 74:[13, 43, 46], Operations: ['92/2=46'] Exploring Operation: 43-13=30, Resulting Numbers: [46, 30] Generated Node #0,1,0: 74:[46, 30] Operation: 43-13=30 Exploring Operation: 46-43=3, Resulting Numbers: [13, 3] Generated Node #0,1,1: 74:[13, 3] Operation: 46-43=3 Exploring Operation: 46-13=33, Resulting Numbers: [43, 33] Generated Node #0,1,2: 74:[43, 33] Operation: 46-13=33 Exploring Operation: 13+46=59, Resulting Numbers: [43, 59] Generated Node #0,1,3: 74:[43, 59] Operation: 13+46=59 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 74:[43, 33], Operations: ['92/2=46', '46-13=33'] Exploring Operation: 43+33=76, Resulting Numbers: [76] 76,74 unequal: No Solution Exploring Operation: 43-33=10, Resulting Numbers: [10] 10,74 unequal: No Solution Exploring Operation: 43*33=1419, Resulting Numbers: [1419] 1419,74 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:[13, 3], Operations: ['92/2=46', '46-43=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,74 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,74 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 #0,1,0 Current State: 74:[46, 30], Operations: ['92/2=46', '43-13=30'] Exploring Operation: 46*30=1380, Resulting Numbers: [1380] 1380,74 unequal: No Solution Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,74 unequal: No Solution Exploring Operation: 46+30=76, Resulting Numbers: [76] 76,74 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 #0,1,3 Current State: 74:[43, 59], Operations: ['92/2=46', '13+46=59'] Exploring Operation: 59-43=16, Resulting Numbers: [16] 16,74 unequal: No Solution Exploring Operation: 43*59=2537, Resulting Numbers: [2537] 2537,74 unequal: No Solution Exploring Operation: 43+59=102, Resulting Numbers: [102] 102,74 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_4
mult_heuristic
[ 93, 78, 80, 54 ]
48
[ "93-80=13", "78/13=6", "54-6=48" ]
Current State: 48:[93, 78, 80, 54], Operations: [] Exploring Operation: 93-80=13, Resulting Numbers: [78, 54, 13] Generated Node #2: [78, 54, 13] from Operation: 93-80=13 Current State: 48:[78, 54, 13], Operations: ['93-80=13'] Exploring Operation: 78/13=6, Resulting Numbers: [54, 6] Generated Node #3: [54, 6] from Operation: 78/13=6 Current State: 48:[54, 6], Operations: ['93-80=13', '78/13=6'] Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[93, 78, 80, 54], Operations: [] Exploring Operation: 93-80=13, Resulting Numbers: [78, 54, 13] Generated Node #0,0: 48:[78, 54, 13] Operation: 93-80=13 Moving to Node #0,0 Current State: 48:[78, 54, 13], Operations: ['93-80=13'] Exploring Operation: 78-54=24, Resulting Numbers: [13, 24] Generated Node #0,0,0: 48:[13, 24] Operation: 78-54=24 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[13, 24], Operations: ['93-80=13', '78-54=24'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,48 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, 34, 3, 40 ]
89
[ "5*3=15", "34+40=74", "15+74=89" ]
Current State: 89:[5, 34, 3, 40], Operations: [] Exploring Operation: 5*3=15, Resulting Numbers: [34, 40, 15] Generated Node #2: [34, 40, 15] from Operation: 5*3=15 Current State: 89:[34, 40, 15], Operations: ['5*3=15'] Exploring Operation: 34+40=74, Resulting Numbers: [15, 74] Generated Node #3: [15, 74] from Operation: 34+40=74 Current State: 89:[15, 74], Operations: ['5*3=15', '34+40=74'] Exploring Operation: 15+74=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[5, 34, 3, 40], Operations: [] Exploring Operation: 5*3=15, Resulting Numbers: [34, 40, 15] Generated Node #0,0: 89:[34, 40, 15] Operation: 5*3=15 Exploring Operation: 5+34=39, Resulting Numbers: [3, 40, 39] Generated Node #0,1: 89:[3, 40, 39] Operation: 5+34=39 Exploring Operation: 3*40=120, Resulting Numbers: [5, 34, 120] Generated Node #0,2: 89:[5, 34, 120] Operation: 3*40=120 Exploring Operation: 34*3=102, Resulting Numbers: [5, 40, 102] Generated Node #0,3: 89:[5, 40, 102] Operation: 34*3=102 Start Sub Search at level 1: Moving to Node #0,3 Current State: 89:[5, 40, 102], Operations: ['34*3=102'] Exploring Operation: 40-5=35, Resulting Numbers: [102, 35] Generated Node #0,3,0: 89:[102, 35] Operation: 40-5=35 Exploring Operation: 5+102=107, Resulting Numbers: [40, 107] Generated Node #0,3,1: 89:[40, 107] Operation: 5+102=107 Exploring Operation: 5+40=45, Resulting Numbers: [102, 45] Generated Node #0,3,2: 89:[102, 45] Operation: 5+40=45 Exploring Operation: 102-5=97, Resulting Numbers: [40, 97] Generated Node #0,3,3: 89:[40, 97] Operation: 102-5=97 Moving to Node #0,3,2 Current State: 89:[102, 45], Operations: ['34*3=102', '5+40=45'] Exploring Operation: 102-45=57, Resulting Numbers: [57] 57,89 unequal: No Solution Exploring Operation: 102+45=147, Resulting Numbers: [147] 147,89 unequal: No Solution Exploring Operation: 102*45=4590, Resulting Numbers: [4590] 4590,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[40, 97], Operations: ['34*3=102', '102-5=97'] Exploring Operation: 40*97=3880, Resulting Numbers: [3880] 3880,89 unequal: No Solution Exploring Operation: 97-40=57, Resulting Numbers: [57] 57,89 unequal: No Solution Exploring Operation: 40+97=137, Resulting Numbers: [137] 137,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[40, 107], Operations: ['34*3=102', '5+102=107'] Exploring Operation: 40+107=147, Resulting Numbers: [147] 147,89 unequal: No Solution Exploring Operation: 107-40=67, Resulting Numbers: [67] 67,89 unequal: No Solution Exploring Operation: 40*107=4280, Resulting Numbers: [4280] 4280,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[102, 35], Operations: ['34*3=102', '40-5=35'] Exploring Operation: 102*35=3570, Resulting Numbers: [3570] 3570,89 unequal: No Solution Exploring Operation: 102+35=137, Resulting Numbers: [137] 137,89 unequal: No Solution Exploring Operation: 102-35=67, Resulting Numbers: [67] 67,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[5, 34, 120], Operations: ['3*40=120'] Exploring Operation: 120-5=115, Resulting Numbers: [34, 115] Generated Node #0,2,0: 89:[34, 115] Operation: 120-5=115 Exploring Operation: 5+34=39, Resulting Numbers: [120, 39] Generated Node #0,2,1: 89:[120, 39] Operation: 5+34=39 Exploring Operation: 120-34=86, Resulting Numbers: [5, 86] Generated Node #0,2,2: 89:[5, 86] Operation: 120-34=86 Exploring Operation: 34-5=29, Resulting Numbers: [120, 29] Generated Node #0,2,3: 89:[120, 29] Operation: 34-5=29 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 89:[34, 115], Operations: ['3*40=120', '120-5=115'] Exploring Operation: 115-34=81, Resulting Numbers: [81] 81,89 unequal: No Solution Exploring Operation: 34+115=149, Resulting Numbers: [149] 149,89 unequal: No Solution Exploring Operation: 34*115=3910, Resulting Numbers: [3910] 3910,89 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 #0,2,1 Current State: 89:[120, 39], Operations: ['3*40=120', '5+34=39'] Exploring Operation: 120*39=4680, Resulting Numbers: [4680] 4680,89 unequal: No Solution Exploring Operation: 120-39=81, Resulting Numbers: [81] 81,89 unequal: No Solution Exploring Operation: 120+39=159, Resulting Numbers: [159] 159,89 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 #0,2,2 Current State: 89:[5, 86], Operations: ['3*40=120', '120-34=86'] Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,89 unequal: No Solution Exploring Operation: 5+86=91, Resulting Numbers: [91] 91,89 unequal: No Solution Exploring Operation: 5*86=430, Resulting Numbers: [430] 430,89 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 #0,2,3 Current State: 89:[120, 29], Operations: ['3*40=120', '34-5=29'] Exploring Operation: 120-29=91, Resulting Numbers: [91] 91,89 unequal: No Solution Exploring Operation: 120*29=3480, Resulting Numbers: [3480] 3480,89 unequal: No Solution Exploring Operation: 120+29=149, Resulting Numbers: [149] 149,89 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: 89:[34, 40, 15], Operations: ['5*3=15'] Exploring Operation: 40+15=55, Resulting Numbers: [34, 55] Generated Node #0,0,0: 89:[34, 55] Operation: 40+15=55 Exploring Operation: 34+15=49, Resulting Numbers: [40, 49] Generated Node #0,0,1: 89:[40, 49] Operation: 34+15=49 Exploring Operation: 34-15=19, Resulting Numbers: [40, 19] Generated Node #0,0,2: 89:[40, 19] Operation: 34-15=19 Exploring Operation: 34+40=74, Resulting Numbers: [15, 74] Generated Node #0,0,3: 89:[15, 74] Operation: 34+40=74 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[34, 55], Operations: ['5*3=15', '40+15=55'] Exploring Operation: 34+55=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[5, 34, 3, 40], Operations: [] Exploring Operation: 5*3=15, Resulting Numbers: [34, 40, 15] Generated Node #0,0: 89:[34, 40, 15] Operation: 5*3=15 Moving to Node #0,0 Current State: 89:[34, 40, 15], Operations: ['5*3=15'] Exploring Operation: 40+15=55, Resulting Numbers: [34, 55] Generated Node #0,0,0: 89:[34, 55] Operation: 40+15=55 Moving to Node #0,0,0 Current State: 89:[34, 55], Operations: ['5*3=15', '40+15=55'] Exploring Operation: 34+55=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.960938
hs_4
sum_heuristic
[ 8, 8, 93, 73 ]
20
[ "8-8=0", "93-73=20", "0+20=20" ]
Current State: 20:[8, 8, 93, 73], Operations: [] Exploring Operation: 8-8=0, Resulting Numbers: [93, 73, 0] Generated Node #2: [93, 73, 0] from Operation: 8-8=0 Current State: 20:[93, 73, 0], Operations: ['8-8=0'] Exploring Operation: 93-73=20, Resulting Numbers: [0, 20] Generated Node #3: [0, 20] from Operation: 93-73=20 Current State: 20:[0, 20], Operations: ['8-8=0', '93-73=20'] Exploring Operation: 0+20=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[8, 8, 93, 73], Operations: [] Exploring Operation: 93-73=20, Resulting Numbers: [8, 8, 20] Generated Node #0,0: 20:[8, 8, 20] Operation: 93-73=20 Exploring Operation: 93-8=85, Resulting Numbers: [8, 73, 85] Generated Node #0,1: 20:[8, 73, 85] Operation: 93-8=85 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[8, 8, 20], Operations: ['93-73=20'] Exploring Operation: 8-8=0, Resulting Numbers: [20, 0] Generated Node #0,0,0: 20:[20, 0] Operation: 8-8=0 Exploring Operation: 8/8=1, Resulting Numbers: [20, 1] Generated Node #0,0,1: 20:[20, 1] Operation: 8/8=1 Moving to Node #0,0,1 Current State: 20:[20, 1], Operations: ['93-73=20', '8/8=1'] Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[8, 8, 93, 73], Operations: [] Exploring Operation: 93-73=20, Resulting Numbers: [8, 8, 20] Generated Node #0,0: 20:[8, 8, 20] Operation: 93-73=20 Moving to Node #0,0 Current State: 20:[8, 8, 20], Operations: ['93-73=20'] Exploring Operation: 8/8=1, Resulting Numbers: [20, 1] Generated Node #0,0,1: 20:[20, 1] Operation: 8/8=1 Moving to Node #0,0,1 Current State: 20:[20, 1], Operations: ['93-73=20', '8/8=1'] Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 36, 40, 69, 81 ]
16
[ "40-36=4", "81-69=12", "4+12=16" ]
Current State: 16:[36, 40, 69, 81], Operations: [] Exploring Operation: 40-36=4, Resulting Numbers: [69, 81, 4] Generated Node #2: [69, 81, 4] from Operation: 40-36=4 Current State: 16:[69, 81, 4], Operations: ['40-36=4'] Exploring Operation: 81-69=12, Resulting Numbers: [4, 12] Generated Node #3: [4, 12] from Operation: 81-69=12 Current State: 16:[4, 12], Operations: ['40-36=4', '81-69=12'] Exploring Operation: 4+12=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[36, 40, 69, 81], Operations: [] Exploring Operation: 81-69=12, Resulting Numbers: [36, 40, 12] Generated Node #0,0: 16:[36, 40, 12] Operation: 81-69=12 Exploring Operation: 69-40=29, Resulting Numbers: [36, 81, 29] Generated Node #0,1: 16:[36, 81, 29] Operation: 69-40=29 Moving to Node #0,0 Current State: 16:[36, 40, 12], Operations: ['81-69=12'] Exploring Operation: 36/12=3, Resulting Numbers: [40, 3] Generated Node #0,0,0: 16:[40, 3] Operation: 36/12=3 Exploring Operation: 40-36=4, Resulting Numbers: [12, 4] Generated Node #0,0,1: 16:[12, 4] Operation: 40-36=4 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[12, 4], Operations: ['81-69=12', '40-36=4'] Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[36, 40, 69, 81], Operations: [] Exploring Operation: 81-69=12, Resulting Numbers: [36, 40, 12] Generated Node #0,0: 16:[36, 40, 12] Operation: 81-69=12 Moving to Node #0,0 Current State: 16:[36, 40, 12], Operations: ['81-69=12'] Exploring Operation: 40-36=4, Resulting Numbers: [12, 4] Generated Node #0,0,1: 16:[12, 4] Operation: 40-36=4 Moving to Node #0,0,1 Current State: 16:[12, 4], Operations: ['81-69=12', '40-36=4'] Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 58, 31, 25, 21 ]
68
[ "31-25=6", "21*6=126", "126-58=68" ]
Current State: 68:[58, 31, 25, 21], Operations: [] Exploring Operation: 31-25=6, Resulting Numbers: [58, 21, 6] Generated Node #2: [58, 21, 6] from Operation: 31-25=6 Current State: 68:[58, 21, 6], Operations: ['31-25=6'] Exploring Operation: 21*6=126, Resulting Numbers: [58, 126] Generated Node #3: [58, 126] from Operation: 21*6=126 Current State: 68:[58, 126], Operations: ['31-25=6', '21*6=126'] Exploring Operation: 126-58=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[58, 31, 25, 21], Operations: [] Exploring Operation: 58-25=33, Resulting Numbers: [31, 21, 33] Generated Node #0,0: 68:[31, 21, 33] Operation: 58-25=33 Moving to Node #0,0 Current State: 68:[31, 21, 33], Operations: ['58-25=33'] Exploring Operation: 33-31=2, Resulting Numbers: [21, 2] Generated Node #0,0,0: 68:[21, 2] Operation: 33-31=2 Moving to Node #0,0,0 Current State: 68:[21, 2], Operations: ['58-25=33', '33-31=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,68 unequal: No Solution No solution found.
0
hs_1
mult_heuristic