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
[ 13, 9, 21, 75 ]
58
[ "13-9=4", "75-21=54", "4+54=58" ]
Current State: 58:[13, 9, 21, 75], Operations: [] Exploring Operation: 13-9=4, Resulting Numbers: [21, 75, 4] Generated Node #2: [21, 75, 4] from Operation: 13-9=4 Current State: 58:[21, 75, 4], Operations: ['13-9=4'] Exploring Operation: 75-21=54, Resulting Numbers: [4, 54] Generated Node #3: [4, 54] from Operation: 75-21=54 Current State: 58:[4, 54], Operations: ['13-9=4', '75-21=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[13, 9, 21, 75], Operations: [] Exploring Operation: 13-9=4, Resulting Numbers: [21, 75, 4] Generated Node #0,0: 58:[21, 75, 4] Operation: 13-9=4 Exploring Operation: 75-13=62, Resulting Numbers: [9, 21, 62] Generated Node #0,1: 58:[9, 21, 62] Operation: 75-13=62 Exploring Operation: 75-21=54, Resulting Numbers: [13, 9, 54] Generated Node #0,2: 58:[13, 9, 54] Operation: 75-21=54 Moving to Node #0,1 Current State: 58:[9, 21, 62], Operations: ['75-13=62'] Exploring Operation: 21-9=12, Resulting Numbers: [62, 12] Generated Node #0,1,0: 58:[62, 12] Operation: 21-9=12 Exploring Operation: 62-9=53, Resulting Numbers: [21, 53] Generated Node #0,1,1: 58:[21, 53] Operation: 62-9=53 Exploring Operation: 9+21=30, Resulting Numbers: [62, 30] Generated Node #0,1,2: 58:[62, 30] Operation: 9+21=30 Moving to Node #0,2 Current State: 58:[13, 9, 54], Operations: ['75-21=54'] Exploring Operation: 54/9=6, Resulting Numbers: [13, 6] Generated Node #0,2,0: 58:[13, 6] Operation: 54/9=6 Exploring Operation: 13+9=22, Resulting Numbers: [54, 22] Generated Node #0,2,1: 58:[54, 22] Operation: 13+9=22 Exploring Operation: 13-9=4, Resulting Numbers: [54, 4] Generated Node #0,2,2: 58:[54, 4] Operation: 13-9=4 Moving to Node #0,0 Current State: 58:[21, 75, 4], Operations: ['13-9=4'] Exploring Operation: 75-4=71, Resulting Numbers: [21, 71] Generated Node #0,0,0: 58:[21, 71] Operation: 75-4=71 Exploring Operation: 75-21=54, Resulting Numbers: [4, 54] Generated Node #0,0,1: 58:[4, 54] Operation: 75-21=54 Exploring Operation: 21+4=25, Resulting Numbers: [75, 25] Generated Node #0,0,2: 58:[75, 25] Operation: 21+4=25 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 58:[4, 54], Operations: ['13-9=4', '75-21=54'] Exploring Operation: 4*54=216, Resulting Numbers: [216] 216,58 unequal: No Solution Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[13, 9, 21, 75], Operations: [] Exploring Operation: 13-9=4, Resulting Numbers: [21, 75, 4] Generated Node #0,0: 58:[21, 75, 4] Operation: 13-9=4 Moving to Node #0,0 Current State: 58:[21, 75, 4], Operations: ['13-9=4'] Exploring Operation: 75-21=54, Resulting Numbers: [4, 54] Generated Node #0,0,1: 58:[4, 54] Operation: 75-21=54 Moving to Node #0,0,1 Current State: 58:[4, 54], Operations: ['13-9=4', '75-21=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 76, 29, 48, 80 ]
73
[ "76+29=105", "80-48=32", "105-32=73" ]
Current State: 73:[76, 29, 48, 80], Operations: [] Exploring Operation: 76+29=105, Resulting Numbers: [48, 80, 105] Generated Node #2: [48, 80, 105] from Operation: 76+29=105 Current State: 73:[48, 80, 105], Operations: ['76+29=105'] Exploring Operation: 80-48=32, Resulting Numbers: [105, 32] Generated Node #3: [105, 32] from Operation: 80-48=32 Current State: 73:[105, 32], Operations: ['76+29=105', '80-48=32'] Exploring Operation: 105-32=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[76, 29, 48, 80], Operations: [] Exploring Operation: 48-29=19, Resulting Numbers: [76, 80, 19] Generated Node #0,0: 73:[76, 80, 19] Operation: 48-29=19 Exploring Operation: 76-29=47, Resulting Numbers: [48, 80, 47] Generated Node #0,1: 73:[48, 80, 47] Operation: 76-29=47 Exploring Operation: 29+48=77, Resulting Numbers: [76, 80, 77] Generated Node #0,2: 73:[76, 80, 77] Operation: 29+48=77 Exploring Operation: 80-29=51, Resulting Numbers: [76, 48, 51] Generated Node #0,3: 73:[76, 48, 51] Operation: 80-29=51 Exploring Operation: 76+29=105, Resulting Numbers: [48, 80, 105] Generated Node #0,4: 73:[48, 80, 105] Operation: 76+29=105 Moving to Node #0,2 Current State: 73:[76, 80, 77], Operations: ['29+48=77'] Exploring Operation: 80-76=4, Resulting Numbers: [77, 4] Generated Node #0,2,0: 73:[77, 4] Operation: 80-76=4 Exploring Operation: 77-76=1, Resulting Numbers: [80, 1] Generated Node #0,2,1: 73:[80, 1] Operation: 77-76=1 Exploring Operation: 76+77=153, Resulting Numbers: [80, 153] Generated Node #0,2,2: 73:[80, 153] Operation: 76+77=153 Exploring Operation: 76+80=156, Resulting Numbers: [77, 156] Generated Node #0,2,3: 73:[77, 156] Operation: 76+80=156 Exploring Operation: 80-77=3, Resulting Numbers: [76, 3] Generated Node #0,2,4: 73:[76, 3] Operation: 80-77=3 Moving to Node #0,3 Current State: 73:[76, 48, 51], Operations: ['80-29=51'] Exploring Operation: 76-48=28, Resulting Numbers: [51, 28] Generated Node #0,3,0: 73:[51, 28] Operation: 76-48=28 Exploring Operation: 76-51=25, Resulting Numbers: [48, 25] Generated Node #0,3,1: 73:[48, 25] Operation: 76-51=25 Exploring Operation: 48+51=99, Resulting Numbers: [76, 99] Generated Node #0,3,2: 73:[76, 99] Operation: 48+51=99 Exploring Operation: 51-48=3, Resulting Numbers: [76, 3] Generated Node #0,3,3: 73:[76, 3] Operation: 51-48=3 Exploring Operation: 76+48=124, Resulting Numbers: [51, 124] Generated Node #0,3,4: 73:[51, 124] Operation: 76+48=124 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 73:[76, 99], Operations: ['80-29=51', '48+51=99'] Exploring Operation: 76*99=7524, Resulting Numbers: [7524] 7524,73 unequal: No Solution Exploring Operation: 76+99=175, Resulting Numbers: [175] 175,73 unequal: No Solution Exploring Operation: 99-76=23, Resulting Numbers: [23] 23,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 73:[51, 28], Operations: ['80-29=51', '76-48=28'] Exploring Operation: 51-28=23, Resulting Numbers: [23] 23,73 unequal: No Solution Exploring Operation: 51+28=79, Resulting Numbers: [79] 79,73 unequal: No Solution Exploring Operation: 51*28=1428, Resulting Numbers: [1428] 1428,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 73:[48, 25], Operations: ['80-29=51', '76-51=25'] Exploring Operation: 48+25=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[76, 29, 48, 80], Operations: [] Exploring Operation: 80-29=51, Resulting Numbers: [76, 48, 51] Generated Node #0,3: 73:[76, 48, 51] Operation: 80-29=51 Moving to Node #0,3 Current State: 73:[76, 48, 51], Operations: ['80-29=51'] Exploring Operation: 76-51=25, Resulting Numbers: [48, 25] Generated Node #0,3,1: 73:[48, 25] Operation: 76-51=25 Moving to Node #0,3,1 Current State: 73:[48, 25], Operations: ['80-29=51', '76-51=25'] Exploring Operation: 48+25=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
mult_heuristic
[ 32, 12, 64, 48 ]
82
[ "12*48=576", "576/32=18", "64+18=82" ]
Current State: 82:[32, 12, 64, 48], Operations: [] Exploring Operation: 12*48=576, Resulting Numbers: [32, 64, 576] Generated Node #2: [32, 64, 576] from Operation: 12*48=576 Current State: 82:[32, 64, 576], Operations: ['12*48=576'] Exploring Operation: 576/32=18, Resulting Numbers: [64, 18] Generated Node #3: [64, 18] from Operation: 576/32=18 Current State: 82:[64, 18], Operations: ['12*48=576', '576/32=18'] Exploring Operation: 64+18=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[32, 12, 64, 48], Operations: [] Exploring Operation: 64/32=2, Resulting Numbers: [12, 48, 2] Generated Node #0,0: 82:[12, 48, 2] Operation: 64/32=2 Exploring Operation: 64-12=52, Resulting Numbers: [32, 48, 52] Generated Node #0,1: 82:[32, 48, 52] Operation: 64-12=52 Exploring Operation: 64-32=32, Resulting Numbers: [12, 48, 32] Generated Node #0,2: 82:[12, 48, 32] Operation: 64-32=32 Exploring Operation: 12+64=76, Resulting Numbers: [32, 48, 76] Generated Node #0,3: 82:[32, 48, 76] Operation: 12+64=76 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[12, 48, 2], Operations: ['64/32=2'] Exploring Operation: 12-2=10, Resulting Numbers: [48, 10] Generated Node #0,0,0: 82:[48, 10] Operation: 12-2=10 Exploring Operation: 48/12=4, Resulting Numbers: [2, 4] Generated Node #0,0,1: 82:[2, 4] Operation: 48/12=4 Exploring Operation: 12/2=6, Resulting Numbers: [48, 6] Generated Node #0,0,2: 82:[48, 6] Operation: 12/2=6 Exploring Operation: 48-12=36, Resulting Numbers: [2, 36] Generated Node #0,0,3: 82:[2, 36] Operation: 48-12=36 Moving to Node #0,0,1 Current State: 82:[2, 4], Operations: ['64/32=2', '48/12=4'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,82 unequal: No Solution Moving to Node #0,0,3 Current State: 82:[2, 36], Operations: ['64/32=2', '48-12=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,82 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,82 unequal: No Solution Moving to Node #0,0,2 Current State: 82:[48, 6], Operations: ['64/32=2', '12/2=6'] Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,82 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 48*6=288, Resulting Numbers: [288] 288,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[48, 10], Operations: ['64/32=2', '12-2=10'] Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,82 unequal: No Solution Exploring Operation: 48+10=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 48*10=480, Resulting Numbers: [480] 480,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[32, 48, 76], Operations: ['12+64=76'] Exploring Operation: 76-48=28, Resulting Numbers: [32, 28] Generated Node #0,3,0: 82:[32, 28] Operation: 76-48=28 Exploring Operation: 32+48=80, Resulting Numbers: [76, 80] Generated Node #0,3,1: 82:[76, 80] Operation: 32+48=80 Exploring Operation: 48-32=16, Resulting Numbers: [76, 16] Generated Node #0,3,2: 82:[76, 16] Operation: 48-32=16 Exploring Operation: 76-32=44, Resulting Numbers: [48, 44] Generated Node #0,3,3: 82:[48, 44] Operation: 76-32=44 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 82:[76, 80], Operations: ['12+64=76', '32+48=80'] Exploring Operation: 80-76=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 76+80=156, Resulting Numbers: [156] 156,82 unequal: No Solution Exploring Operation: 76*80=6080, Resulting Numbers: [6080] 6080,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 82:[48, 44], Operations: ['12+64=76', '76-32=44'] Exploring Operation: 48*44=2112, Resulting Numbers: [2112] 2112,82 unequal: No Solution Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 82:[76, 16], Operations: ['12+64=76', '48-32=16'] Exploring Operation: 76-16=60, Resulting Numbers: [60] 60,82 unequal: No Solution Exploring Operation: 76*16=1216, Resulting Numbers: [1216] 1216,82 unequal: No Solution Exploring Operation: 76+16=92, Resulting Numbers: [92] 92,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 82:[32, 28], Operations: ['12+64=76', '76-48=28'] Exploring Operation: 32+28=60, Resulting Numbers: [60] 60,82 unequal: No Solution Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 32*28=896, Resulting Numbers: [896] 896,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[12, 48, 32], Operations: ['64-32=32'] Exploring Operation: 48-12=36, Resulting Numbers: [32, 36] Generated Node #0,2,0: 82:[32, 36] Operation: 48-12=36 Exploring Operation: 12+32=44, Resulting Numbers: [48, 44] Generated Node #0,2,1: 82:[48, 44] Operation: 12+32=44 Exploring Operation: 48/12=4, Resulting Numbers: [32, 4] Generated Node #0,2,2: 82:[32, 4] Operation: 48/12=4 Exploring Operation: 48+32=80, Resulting Numbers: [12, 80] Generated Node #0,2,3: 82:[12, 80] Operation: 48+32=80 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[48, 44], Operations: ['64-32=32', '12+32=44'] Exploring Operation: 48*44=2112, Resulting Numbers: [2112] 2112,82 unequal: No Solution Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,82 unequal: No Solution Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 82:[32, 4], Operations: ['64-32=32', '48/12=4'] Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 32*4=128, Resulting Numbers: [128] 128,82 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 82:[12, 80], Operations: ['64-32=32', '48+32=80'] Exploring Operation: 12*80=960, Resulting Numbers: [960] 960,82 unequal: No Solution Exploring Operation: 80-12=68, Resulting Numbers: [68] 68,82 unequal: No Solution Exploring Operation: 12+80=92, Resulting Numbers: [92] 92,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[32, 36], Operations: ['64-32=32', '48-12=36'] Exploring Operation: 36-32=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 32*36=1152, Resulting Numbers: [1152] 1152,82 unequal: No Solution Exploring Operation: 32+36=68, Resulting Numbers: [68] 68,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[32, 48, 52], Operations: ['64-12=52'] Exploring Operation: 32+48=80, Resulting Numbers: [52, 80] Generated Node #0,1,0: 82:[52, 80] Operation: 32+48=80 Exploring Operation: 48-32=16, Resulting Numbers: [52, 16] Generated Node #0,1,1: 82:[52, 16] Operation: 48-32=16 Exploring Operation: 52-48=4, Resulting Numbers: [32, 4] Generated Node #0,1,2: 82:[32, 4] Operation: 52-48=4 Exploring Operation: 32+52=84, Resulting Numbers: [48, 84] Generated Node #0,1,3: 82:[48, 84] Operation: 32+52=84 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 82:[48, 84], Operations: ['64-12=52', '32+52=84'] Exploring Operation: 48*84=4032, Resulting Numbers: [4032] 4032,82 unequal: No Solution Exploring Operation: 48+84=132, Resulting Numbers: [132] 132,82 unequal: No Solution Exploring Operation: 84-48=36, Resulting Numbers: [36] 36,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 82:[32, 4], Operations: ['64-12=52', '52-48=4'] Exploring Operation: 32*4=128, Resulting Numbers: [128] 128,82 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[52, 80], Operations: ['64-12=52', '32+48=80'] Exploring Operation: 52*80=4160, Resulting Numbers: [4160] 4160,82 unequal: No Solution Exploring Operation: 52+80=132, Resulting Numbers: [132] 132,82 unequal: No Solution Exploring Operation: 80-52=28, Resulting Numbers: [28] 28,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[52, 16], Operations: ['64-12=52', '48-32=16'] Exploring Operation: 52*16=832, Resulting Numbers: [832] 832,82 unequal: No Solution Exploring Operation: 52-16=36, Resulting Numbers: [36] 36,82 unequal: No Solution Exploring Operation: 52+16=68, Resulting Numbers: [68] 68,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 5, 8, 47, 77 ]
17
[ "5+8=13", "77-47=30", "30-13=17" ]
Current State: 17:[5, 8, 47, 77], Operations: [] Exploring Operation: 5+8=13, Resulting Numbers: [47, 77, 13] Generated Node #2: [47, 77, 13] from Operation: 5+8=13 Current State: 17:[47, 77, 13], Operations: ['5+8=13'] Exploring Operation: 77-47=30, Resulting Numbers: [13, 30] Generated Node #3: [13, 30] from Operation: 77-47=30 Current State: 17:[13, 30], Operations: ['5+8=13', '77-47=30'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[5, 8, 47, 77], Operations: [] Exploring Operation: 77-47=30, Resulting Numbers: [5, 8, 30] Generated Node #0,0: 17:[5, 8, 30] Operation: 77-47=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[5, 8, 30], Operations: ['77-47=30'] Exploring Operation: 5+8=13, Resulting Numbers: [30, 13] Generated Node #0,0,0: 17:[30, 13] Operation: 5+8=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[30, 13], Operations: ['77-47=30', '5+8=13'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[5, 8, 47, 77], Operations: [] Exploring Operation: 77-47=30, Resulting Numbers: [5, 8, 30] Generated Node #0,0: 17:[5, 8, 30] Operation: 77-47=30 Moving to Node #0,0 Current State: 17:[5, 8, 30], Operations: ['77-47=30'] Exploring Operation: 5+8=13, Resulting Numbers: [30, 13] Generated Node #0,0,0: 17:[30, 13] Operation: 5+8=13 Moving to Node #0,0,0 Current State: 17:[30, 13], Operations: ['77-47=30', '5+8=13'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 8, 45, 75, 20 ]
42
[ "8+45=53", "75+20=95", "95-53=42" ]
Current State: 42:[8, 45, 75, 20], Operations: [] Exploring Operation: 8+45=53, Resulting Numbers: [75, 20, 53] Generated Node #2: [75, 20, 53] from Operation: 8+45=53 Current State: 42:[75, 20, 53], Operations: ['8+45=53'] Exploring Operation: 75+20=95, Resulting Numbers: [53, 95] Generated Node #3: [53, 95] from Operation: 75+20=95 Current State: 42:[53, 95], Operations: ['8+45=53', '75+20=95'] Exploring Operation: 95-53=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[8, 45, 75, 20], Operations: [] Exploring Operation: 75-45=30, Resulting Numbers: [8, 20, 30] Generated Node #0,0: 42:[8, 20, 30] Operation: 75-45=30 Exploring Operation: 75-20=55, Resulting Numbers: [8, 45, 55] Generated Node #0,1: 42:[8, 45, 55] Operation: 75-20=55 Moving to Node #0,0 Current State: 42:[8, 20, 30], Operations: ['75-45=30'] Exploring Operation: 30-8=22, Resulting Numbers: [20, 22] Generated Node #0,0,0: 42:[20, 22] Operation: 30-8=22 Exploring Operation: 30-20=10, Resulting Numbers: [8, 10] Generated Node #0,0,1: 42:[8, 10] Operation: 30-20=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[20, 22], Operations: ['75-45=30', '30-8=22'] Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[8, 45, 75, 20], Operations: [] Exploring Operation: 75-45=30, Resulting Numbers: [8, 20, 30] Generated Node #0,0: 42:[8, 20, 30] Operation: 75-45=30 Moving to Node #0,0 Current State: 42:[8, 20, 30], Operations: ['75-45=30'] Exploring Operation: 30-8=22, Resulting Numbers: [20, 22] Generated Node #0,0,0: 42:[20, 22] Operation: 30-8=22 Moving to Node #0,0,0 Current State: 42:[20, 22], Operations: ['75-45=30', '30-8=22'] Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 8, 14, 40, 27 ]
46
[ "40/8=5", "14+27=41", "5+41=46" ]
Current State: 46:[8, 14, 40, 27], Operations: [] Exploring Operation: 40/8=5, Resulting Numbers: [14, 27, 5] Generated Node #2: [14, 27, 5] from Operation: 40/8=5 Current State: 46:[14, 27, 5], Operations: ['40/8=5'] Exploring Operation: 14+27=41, Resulting Numbers: [5, 41] Generated Node #3: [5, 41] from Operation: 14+27=41 Current State: 46:[5, 41], Operations: ['40/8=5', '14+27=41'] Exploring Operation: 5+41=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[8, 14, 40, 27], Operations: [] Exploring Operation: 40-14=26, Resulting Numbers: [8, 27, 26] Generated Node #0,0: 46:[8, 27, 26] Operation: 40-14=26 Exploring Operation: 8+14=22, Resulting Numbers: [40, 27, 22] Generated Node #0,1: 46:[40, 27, 22] Operation: 8+14=22 Exploring Operation: 14-8=6, Resulting Numbers: [40, 27, 6] Generated Node #0,2: 46:[40, 27, 6] Operation: 14-8=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[40, 27, 22], Operations: ['8+14=22'] Exploring Operation: 40-22=18, Resulting Numbers: [27, 18] Generated Node #0,1,0: 46:[27, 18] Operation: 40-22=18 Exploring Operation: 27+22=49, Resulting Numbers: [40, 49] Generated Node #0,1,1: 46:[40, 49] Operation: 27+22=49 Exploring Operation: 27-22=5, Resulting Numbers: [40, 5] Generated Node #0,1,2: 46:[40, 5] Operation: 27-22=5 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[27, 18], Operations: ['8+14=22', '40-22=18'] Exploring Operation: 27*18=486, Resulting Numbers: [486] 486,46 unequal: No Solution Exploring Operation: 27+18=45, Resulting Numbers: [45] 45,46 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,46 unequal: No Solution No 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: 46:[40, 49], Operations: ['8+14=22', '27+22=49'] Exploring Operation: 49-40=9, Resulting Numbers: [9] 9,46 unequal: No Solution Exploring Operation: 40+49=89, Resulting Numbers: [89] 89,46 unequal: No Solution Exploring Operation: 40*49=1960, Resulting Numbers: [1960] 1960,46 unequal: No Solution No 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: 46:[40, 5], Operations: ['8+14=22', '27-22=5'] Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,46 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,46 unequal: No Solution Exploring Operation: 40+5=45, Resulting Numbers: [45] 45,46 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: 46:[8, 27, 26], Operations: ['40-14=26'] Exploring Operation: 27-26=1, Resulting Numbers: [8, 1] Generated Node #0,0,0: 46:[8, 1] Operation: 27-26=1 Exploring Operation: 26-8=18, Resulting Numbers: [27, 18] Generated Node #0,0,1: 46:[27, 18] Operation: 26-8=18 Exploring Operation: 27-8=19, Resulting Numbers: [26, 19] Generated Node #0,0,2: 46:[26, 19] Operation: 27-8=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[8, 1], Operations: ['40-14=26', '27-26=1'] Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,46 unequal: No Solution Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,46 unequal: No Solution No 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: 46:[26, 19], Operations: ['40-14=26', '27-8=19'] Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,46 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,46 unequal: No Solution No 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: 46:[27, 18], Operations: ['40-14=26', '26-8=18'] Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,46 unequal: No Solution Exploring Operation: 27+18=45, Resulting Numbers: [45] 45,46 unequal: No Solution Exploring Operation: 27*18=486, Resulting Numbers: [486] 486,46 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: 46:[40, 27, 6], Operations: ['14-8=6'] Exploring Operation: 40+6=46, Resulting Numbers: [27, 46] Generated Node #0,2,0: 46:[27, 46] Operation: 40+6=46 Exploring Operation: 27-6=21, Resulting Numbers: [40, 21] Generated Node #0,2,1: 46:[40, 21] Operation: 27-6=21 Exploring Operation: 40-27=13, Resulting Numbers: [6, 13] Generated Node #0,2,2: 46:[6, 13] Operation: 40-27=13 Moving to Node #0,2,0 Current State: 46:[27, 46], Operations: ['14-8=6', '40+6=46'] Exploring Operation: 27*46=1242, Resulting Numbers: [1242] 1242,46 unequal: No Solution Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 27+46=73, Resulting Numbers: [73] 73,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[40, 21], Operations: ['14-8=6', '27-6=21'] Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 40*21=840, Resulting Numbers: [840] 840,46 unequal: No Solution Exploring Operation: 40+21=61, Resulting Numbers: [61] 61,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[6, 13], Operations: ['14-8=6', '40-27=13'] Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,46 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 71, 8, 20, 68 ]
25
[ "71*8=568", "568-68=500", "500/20=25" ]
Current State: 25:[71, 8, 20, 68], Operations: [] Exploring Operation: 71*8=568, Resulting Numbers: [20, 68, 568] Generated Node #2: [20, 68, 568] from Operation: 71*8=568 Current State: 25:[20, 68, 568], Operations: ['71*8=568'] Exploring Operation: 568-68=500, Resulting Numbers: [20, 500] Generated Node #3: [20, 500] from Operation: 568-68=500 Current State: 25:[20, 500], Operations: ['71*8=568', '568-68=500'] Exploring Operation: 500/20=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[71, 8, 20, 68], Operations: [] Exploring Operation: 68-8=60, Resulting Numbers: [71, 20, 60] Generated Node #0,0: 25:[71, 20, 60] Operation: 68-8=60 Exploring Operation: 71-20=51, Resulting Numbers: [8, 68, 51] Generated Node #0,1: 25:[8, 68, 51] Operation: 71-20=51 Exploring Operation: 68-20=48, Resulting Numbers: [71, 8, 48] Generated Node #0,2: 25:[71, 8, 48] Operation: 68-20=48 Exploring Operation: 71-68=3, Resulting Numbers: [8, 20, 3] Generated Node #0,3: 25:[8, 20, 3] Operation: 71-68=3 Exploring Operation: 71-8=63, Resulting Numbers: [20, 68, 63] Generated Node #0,4: 25:[20, 68, 63] Operation: 71-8=63 Start Sub Search at level 1: Moving to Node #0,3 Current State: 25:[8, 20, 3], Operations: ['71-68=3'] Exploring Operation: 8+20=28, Resulting Numbers: [3, 28] Generated Node #0,3,0: 25:[3, 28] Operation: 8+20=28 Exploring Operation: 20+3=23, Resulting Numbers: [8, 23] Generated Node #0,3,1: 25:[8, 23] Operation: 20+3=23 Exploring Operation: 8-3=5, Resulting Numbers: [20, 5] Generated Node #0,3,2: 25:[20, 5] Operation: 8-3=5 Exploring Operation: 8*3=24, Resulting Numbers: [20, 24] Generated Node #0,3,3: 25:[20, 24] Operation: 8*3=24 Exploring Operation: 20-8=12, Resulting Numbers: [3, 12] Generated Node #0,3,4: 25:[3, 12] Operation: 20-8=12 Moving to Node #0,3,0 Current State: 25:[3, 28], Operations: ['71-68=3', '8+20=28'] Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,25 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[71, 8, 20, 68], Operations: [] Exploring Operation: 71-68=3, Resulting Numbers: [8, 20, 3] Generated Node #0,3: 25:[8, 20, 3] Operation: 71-68=3 Moving to Node #0,3 Current State: 25:[8, 20, 3], Operations: ['71-68=3'] Exploring Operation: 8+20=28, Resulting Numbers: [3, 28] Generated Node #0,3,0: 25:[3, 28] Operation: 8+20=28 Moving to Node #0,3,0 Current State: 25:[3, 28], Operations: ['71-68=3', '8+20=28'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 14, 33, 43, 15 ]
66
[ "43-15=28", "28/14=2", "33*2=66" ]
Current State: 66:[14, 33, 43, 15], Operations: [] Exploring Operation: 43-15=28, Resulting Numbers: [14, 33, 28] Generated Node #2: [14, 33, 28] from Operation: 43-15=28 Current State: 66:[14, 33, 28], Operations: ['43-15=28'] Exploring Operation: 28/14=2, Resulting Numbers: [33, 2] Generated Node #3: [33, 2] from Operation: 28/14=2 Current State: 66:[33, 2], Operations: ['43-15=28', '28/14=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[14, 33, 43, 15], Operations: [] Exploring Operation: 43-15=28, Resulting Numbers: [14, 33, 28] Generated Node #0,0: 66:[14, 33, 28] Operation: 43-15=28 Exploring Operation: 43-14=29, Resulting Numbers: [33, 15, 29] Generated Node #0,1: 66:[33, 15, 29] Operation: 43-14=29 Exploring Operation: 43+15=58, Resulting Numbers: [14, 33, 58] Generated Node #0,2: 66:[14, 33, 58] Operation: 43+15=58 Exploring Operation: 43-33=10, Resulting Numbers: [14, 15, 10] Generated Node #0,3: 66:[14, 15, 10] Operation: 43-33=10 Exploring Operation: 15-14=1, Resulting Numbers: [33, 43, 1] Generated Node #0,4: 66:[33, 43, 1] Operation: 15-14=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[14, 33, 28], Operations: ['43-15=28'] Exploring Operation: 33-14=19, Resulting Numbers: [28, 19] Generated Node #0,0,0: 66:[28, 19] Operation: 33-14=19 Exploring Operation: 33-28=5, Resulting Numbers: [14, 5] Generated Node #0,0,1: 66:[14, 5] Operation: 33-28=5 Exploring Operation: 28-14=14, Resulting Numbers: [33, 14] Generated Node #0,0,2: 66:[33, 14] Operation: 28-14=14 Exploring Operation: 33+28=61, Resulting Numbers: [14, 61] Generated Node #0,0,3: 66:[14, 61] Operation: 33+28=61 Exploring Operation: 28/14=2, Resulting Numbers: [33, 2] Generated Node #0,0,4: 66:[33, 2] Operation: 28/14=2 Moving to Node #0,0,4 Current State: 66:[33, 2], Operations: ['43-15=28', '28/14=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[14, 33, 43, 15], Operations: [] Exploring Operation: 43-15=28, Resulting Numbers: [14, 33, 28] Generated Node #0,0: 66:[14, 33, 28] Operation: 43-15=28 Moving to Node #0,0 Current State: 66:[14, 33, 28], Operations: ['43-15=28'] Exploring Operation: 28/14=2, Resulting Numbers: [33, 2] Generated Node #0,0,4: 66:[33, 2] Operation: 28/14=2 Moving to Node #0,0,4 Current State: 66:[33, 2], Operations: ['43-15=28', '28/14=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 9, 21, 78, 23 ]
71
[ "9+21=30", "78+23=101", "101-30=71" ]
Current State: 71:[9, 21, 78, 23], Operations: [] Exploring Operation: 9+21=30, Resulting Numbers: [78, 23, 30] Generated Node #2: [78, 23, 30] from Operation: 9+21=30 Current State: 71:[78, 23, 30], Operations: ['9+21=30'] Exploring Operation: 78+23=101, Resulting Numbers: [30, 101] Generated Node #3: [30, 101] from Operation: 78+23=101 Current State: 71:[30, 101], Operations: ['9+21=30', '78+23=101'] Exploring Operation: 101-30=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[9, 21, 78, 23], Operations: [] Exploring Operation: 21+23=44, Resulting Numbers: [9, 78, 44] Generated Node #0,0: 71:[9, 78, 44] Operation: 21+23=44 Exploring Operation: 78-9=69, Resulting Numbers: [21, 23, 69] Generated Node #0,1: 71:[21, 23, 69] Operation: 78-9=69 Exploring Operation: 9+23=32, Resulting Numbers: [21, 78, 32] Generated Node #0,2: 71:[21, 78, 32] Operation: 9+23=32 Exploring Operation: 9+21=30, Resulting Numbers: [78, 23, 30] Generated Node #0,3: 71:[78, 23, 30] Operation: 9+21=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[9, 78, 44], Operations: ['21+23=44'] Exploring Operation: 9+78=87, Resulting Numbers: [44, 87] Generated Node #0,0,0: 71:[44, 87] Operation: 9+78=87 Exploring Operation: 44-9=35, Resulting Numbers: [78, 35] Generated Node #0,0,1: 71:[78, 35] Operation: 44-9=35 Exploring Operation: 78-9=69, Resulting Numbers: [44, 69] Generated Node #0,0,2: 71:[44, 69] Operation: 78-9=69 Exploring Operation: 9+44=53, Resulting Numbers: [78, 53] Generated Node #0,0,3: 71:[78, 53] Operation: 9+44=53 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 71:[78, 53], Operations: ['21+23=44', '9+44=53'] Exploring Operation: 78*53=4134, Resulting Numbers: [4134] 4134,71 unequal: No Solution Exploring Operation: 78-53=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 78+53=131, Resulting Numbers: [131] 131,71 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 #0,0,2 Current State: 71:[44, 69], Operations: ['21+23=44', '78-9=69'] Exploring Operation: 69-44=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 44+69=113, Resulting Numbers: [113] 113,71 unequal: No Solution Exploring Operation: 44*69=3036, Resulting Numbers: [3036] 3036,71 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 #0,0,0 Current State: 71:[44, 87], Operations: ['21+23=44', '9+78=87'] Exploring Operation: 87-44=43, Resulting Numbers: [43] 43,71 unequal: No Solution Exploring Operation: 44*87=3828, Resulting Numbers: [3828] 3828,71 unequal: No Solution Exploring Operation: 44+87=131, Resulting Numbers: [131] 131,71 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 #0,0,1 Current State: 71:[78, 35], Operations: ['21+23=44', '44-9=35'] Exploring Operation: 78-35=43, Resulting Numbers: [43] 43,71 unequal: No Solution Exploring Operation: 78+35=113, Resulting Numbers: [113] 113,71 unequal: No Solution Exploring Operation: 78*35=2730, Resulting Numbers: [2730] 2730,71 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 #0,2 Current State: 71:[21, 78, 32], Operations: ['9+23=32'] Exploring Operation: 21+78=99, Resulting Numbers: [32, 99] Generated Node #0,2,0: 71:[32, 99] Operation: 21+78=99 Exploring Operation: 21+32=53, Resulting Numbers: [78, 53] Generated Node #0,2,1: 71:[78, 53] Operation: 21+32=53 Exploring Operation: 32-21=11, Resulting Numbers: [78, 11] Generated Node #0,2,2: 71:[78, 11] Operation: 32-21=11 Exploring Operation: 78-21=57, Resulting Numbers: [32, 57] Generated Node #0,2,3: 71:[32, 57] Operation: 78-21=57 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 71:[78, 53], Operations: ['9+23=32', '21+32=53'] Exploring Operation: 78+53=131, Resulting Numbers: [131] 131,71 unequal: No Solution Exploring Operation: 78*53=4134, Resulting Numbers: [4134] 4134,71 unequal: No Solution Exploring Operation: 78-53=25, Resulting Numbers: [25] 25,71 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 #0,2,3 Current State: 71:[32, 57], Operations: ['9+23=32', '78-21=57'] Exploring Operation: 57-32=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 32+57=89, Resulting Numbers: [89] 89,71 unequal: No Solution Exploring Operation: 32*57=1824, Resulting Numbers: [1824] 1824,71 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 #0,2,0 Current State: 71:[32, 99], Operations: ['9+23=32', '21+78=99'] Exploring Operation: 32*99=3168, Resulting Numbers: [3168] 3168,71 unequal: No Solution Exploring Operation: 99-32=67, Resulting Numbers: [67] 67,71 unequal: No Solution Exploring Operation: 32+99=131, Resulting Numbers: [131] 131,71 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 #0,2,2 Current State: 71:[78, 11], Operations: ['9+23=32', '32-21=11'] Exploring Operation: 78*11=858, Resulting Numbers: [858] 858,71 unequal: No Solution Exploring Operation: 78-11=67, Resulting Numbers: [67] 67,71 unequal: No Solution Exploring Operation: 78+11=89, Resulting Numbers: [89] 89,71 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 #0,3 Current State: 71:[78, 23, 30], Operations: ['9+21=30'] Exploring Operation: 23+30=53, Resulting Numbers: [78, 53] Generated Node #0,3,0: 71:[78, 53] Operation: 23+30=53 Exploring Operation: 78-30=48, Resulting Numbers: [23, 48] Generated Node #0,3,1: 71:[23, 48] Operation: 78-30=48 Exploring Operation: 78-23=55, Resulting Numbers: [30, 55] Generated Node #0,3,2: 71:[30, 55] Operation: 78-23=55 Exploring Operation: 78+23=101, Resulting Numbers: [30, 101] Generated Node #0,3,3: 71:[30, 101] Operation: 78+23=101 Moving to Node #0,3,0 Current State: 71:[78, 53], Operations: ['9+21=30', '23+30=53'] Exploring Operation: 78-53=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 78+53=131, Resulting Numbers: [131] 131,71 unequal: No Solution Exploring Operation: 78*53=4134, Resulting Numbers: [4134] 4134,71 unequal: No Solution Moving to Node #0,3,2 Current State: 71:[30, 55], Operations: ['9+21=30', '78-23=55'] Exploring Operation: 30*55=1650, Resulting Numbers: [1650] 1650,71 unequal: No Solution Exploring Operation: 30+55=85, Resulting Numbers: [85] 85,71 unequal: No Solution Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,71 unequal: No Solution Moving to Node #0,3,3 Current State: 71:[30, 101], Operations: ['9+21=30', '78+23=101'] Exploring Operation: 30+101=131, Resulting Numbers: [131] 131,71 unequal: No Solution Exploring Operation: 30*101=3030, Resulting Numbers: [3030] 3030,71 unequal: No Solution Exploring Operation: 101-30=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[9, 21, 78, 23], Operations: [] Exploring Operation: 9+21=30, Resulting Numbers: [78, 23, 30] Generated Node #0,3: 71:[78, 23, 30] Operation: 9+21=30 Moving to Node #0,3 Current State: 71:[78, 23, 30], Operations: ['9+21=30'] Exploring Operation: 78+23=101, Resulting Numbers: [30, 101] Generated Node #0,3,3: 71:[30, 101] Operation: 78+23=101 Moving to Node #0,3,3 Current State: 71:[30, 101], Operations: ['9+21=30', '78+23=101'] Exploring Operation: 101-30=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.953993
hs_4
mult_heuristic
[ 36, 66, 5, 51 ]
56
[ "36+66=102", "51-5=46", "102-46=56" ]
Current State: 56:[36, 66, 5, 51], Operations: [] Exploring Operation: 36+66=102, Resulting Numbers: [5, 51, 102] Generated Node #2: [5, 51, 102] from Operation: 36+66=102 Current State: 56:[5, 51, 102], Operations: ['36+66=102'] Exploring Operation: 51-5=46, Resulting Numbers: [102, 46] Generated Node #3: [102, 46] from Operation: 51-5=46 Current State: 56:[102, 46], Operations: ['36+66=102', '51-5=46'] Exploring Operation: 102-46=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[36, 66, 5, 51], Operations: [] Exploring Operation: 36-5=31, Resulting Numbers: [66, 51, 31] Generated Node #0,0: 56:[66, 51, 31] Operation: 36-5=31 Exploring Operation: 51-36=15, Resulting Numbers: [66, 5, 15] Generated Node #0,1: 56:[66, 5, 15] Operation: 51-36=15 Exploring Operation: 66-51=15, Resulting Numbers: [36, 5, 15] Generated Node #0,2: 56:[36, 5, 15] Operation: 66-51=15 Exploring Operation: 66-36=30, Resulting Numbers: [5, 51, 30] Generated Node #0,3: 56:[5, 51, 30] Operation: 66-36=30 Moving to Node #0,3 Current State: 56:[5, 51, 30], Operations: ['66-36=30'] Exploring Operation: 30/5=6, Resulting Numbers: [51, 6] Generated Node #0,3,0: 56:[51, 6] Operation: 30/5=6 Exploring Operation: 30-5=25, Resulting Numbers: [51, 25] Generated Node #0,3,1: 56:[51, 25] Operation: 30-5=25 Exploring Operation: 51-30=21, Resulting Numbers: [5, 21] Generated Node #0,3,2: 56:[5, 21] Operation: 51-30=21 Exploring Operation: 5+51=56, Resulting Numbers: [30, 56] Generated Node #0,3,3: 56:[30, 56] Operation: 5+51=56 Moving to Node #0,2 Current State: 56:[36, 5, 15], Operations: ['66-51=15'] Exploring Operation: 36-5=31, Resulting Numbers: [15, 31] Generated Node #0,2,0: 56:[15, 31] Operation: 36-5=31 Exploring Operation: 36+15=51, Resulting Numbers: [5, 51] Generated Node #0,2,1: 56:[5, 51] Operation: 36+15=51 Exploring Operation: 15/5=3, Resulting Numbers: [36, 3] Generated Node #0,2,2: 56:[36, 3] Operation: 15/5=3 Exploring Operation: 36-15=21, Resulting Numbers: [5, 21] Generated Node #0,2,3: 56:[5, 21] Operation: 36-15=21 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 56:[15, 31], Operations: ['66-51=15', '36-5=31'] Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,56 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,56 unequal: No Solution Exploring Operation: 15*31=465, Resulting Numbers: [465] 465,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 56:[5, 51], Operations: ['66-51=15', '36+15=51'] Exploring Operation: 5*51=255, Resulting Numbers: [255] 255,56 unequal: No Solution Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[36, 66, 5, 51], Operations: [] Exploring Operation: 66-51=15, Resulting Numbers: [36, 5, 15] Generated Node #0,2: 56:[36, 5, 15] Operation: 66-51=15 Moving to Node #0,2 Current State: 56:[36, 5, 15], Operations: ['66-51=15'] Exploring Operation: 36+15=51, Resulting Numbers: [5, 51] Generated Node #0,2,1: 56:[5, 51] Operation: 36+15=51 Moving to Node #0,2,1 Current State: 56:[5, 51], Operations: ['66-51=15', '36+15=51'] Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 56, 73, 87, 28 ]
58
[ "87-73=14", "28/14=2", "56+2=58" ]
Current State: 58:[56, 73, 87, 28], Operations: [] Exploring Operation: 87-73=14, Resulting Numbers: [56, 28, 14] Generated Node #2: [56, 28, 14] from Operation: 87-73=14 Current State: 58:[56, 28, 14], Operations: ['87-73=14'] Exploring Operation: 28/14=2, Resulting Numbers: [56, 2] Generated Node #3: [56, 2] from Operation: 28/14=2 Current State: 58:[56, 2], Operations: ['87-73=14', '28/14=2'] Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[56, 73, 87, 28], Operations: [] Exploring Operation: 56/28=2, Resulting Numbers: [73, 87, 2] Generated Node #0,0: 58:[73, 87, 2] Operation: 56/28=2 Exploring Operation: 87-56=31, Resulting Numbers: [73, 28, 31] Generated Node #0,1: 58:[73, 28, 31] Operation: 87-56=31 Exploring Operation: 87-73=14, Resulting Numbers: [56, 28, 14] Generated Node #0,2: 58:[56, 28, 14] Operation: 87-73=14 Exploring Operation: 73-56=17, Resulting Numbers: [87, 28, 17] Generated Node #0,3: 58:[87, 28, 17] Operation: 73-56=17 Exploring Operation: 87-28=59, Resulting Numbers: [56, 73, 59] Generated Node #0,4: 58:[56, 73, 59] Operation: 87-28=59 Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[56, 28, 14], Operations: ['87-73=14'] Exploring Operation: 28/14=2, Resulting Numbers: [56, 2] Generated Node #0,2,0: 58:[56, 2] Operation: 28/14=2 Exploring Operation: 56+14=70, Resulting Numbers: [28, 70] Generated Node #0,2,1: 58:[28, 70] Operation: 56+14=70 Exploring Operation: 56/28=2, Resulting Numbers: [14, 2] Generated Node #0,2,2: 58:[14, 2] Operation: 56/28=2 Exploring Operation: 56/14=4, Resulting Numbers: [28, 4] Generated Node #0,2,3: 58:[28, 4] Operation: 56/14=4 Exploring Operation: 56-28=28, Resulting Numbers: [14, 28] Generated Node #0,2,4: 58:[14, 28] Operation: 56-28=28 Moving to Node #0,2,0 Current State: 58:[56, 2], Operations: ['87-73=14', '28/14=2'] Exploring Operation: 56*2=112, Resulting Numbers: [112] 112,58 unequal: No Solution Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[56, 73, 87, 28], Operations: [] Exploring Operation: 87-73=14, Resulting Numbers: [56, 28, 14] Generated Node #0,2: 58:[56, 28, 14] Operation: 87-73=14 Moving to Node #0,2 Current State: 58:[56, 28, 14], Operations: ['87-73=14'] Exploring Operation: 28/14=2, Resulting Numbers: [56, 2] Generated Node #0,2,0: 58:[56, 2] Operation: 28/14=2 Moving to Node #0,2,0 Current State: 58:[56, 2], Operations: ['87-73=14', '28/14=2'] Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 86, 11, 6, 61 ]
98
[ "11+61=72", "72/6=12", "86+12=98" ]
Current State: 98:[86, 11, 6, 61], Operations: [] Exploring Operation: 11+61=72, Resulting Numbers: [86, 6, 72] Generated Node #2: [86, 6, 72] from Operation: 11+61=72 Current State: 98:[86, 6, 72], Operations: ['11+61=72'] Exploring Operation: 72/6=12, Resulting Numbers: [86, 12] Generated Node #3: [86, 12] from Operation: 72/6=12 Current State: 98:[86, 12], Operations: ['11+61=72', '72/6=12'] Exploring Operation: 86+12=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[86, 11, 6, 61], Operations: [] Exploring Operation: 86+6=92, Resulting Numbers: [11, 61, 92] Generated Node #0,0: 98:[11, 61, 92] Operation: 86+6=92 Exploring Operation: 61-6=55, Resulting Numbers: [86, 11, 55] Generated Node #0,1: 98:[86, 11, 55] Operation: 61-6=55 Exploring Operation: 86+11=97, Resulting Numbers: [6, 61, 97] Generated Node #0,2: 98:[6, 61, 97] Operation: 86+11=97 Exploring Operation: 61-11=50, Resulting Numbers: [86, 6, 50] Generated Node #0,3: 98:[86, 6, 50] Operation: 61-11=50 Exploring Operation: 86-61=25, Resulting Numbers: [11, 6, 25] Generated Node #0,4: 98:[11, 6, 25] Operation: 86-61=25 Moving to Node #0,2 Current State: 98:[6, 61, 97], Operations: ['86+11=97'] Exploring Operation: 6+61=67, Resulting Numbers: [97, 67] Generated Node #0,2,0: 98:[97, 67] Operation: 6+61=67 Exploring Operation: 61-6=55, Resulting Numbers: [97, 55] Generated Node #0,2,1: 98:[97, 55] Operation: 61-6=55 Exploring Operation: 6+97=103, Resulting Numbers: [61, 103] Generated Node #0,2,2: 98:[61, 103] Operation: 6+97=103 Exploring Operation: 97-6=91, Resulting Numbers: [61, 91] Generated Node #0,2,3: 98:[61, 91] Operation: 97-6=91 Exploring Operation: 97-61=36, Resulting Numbers: [6, 36] Generated Node #0,2,4: 98:[6, 36] Operation: 97-61=36 Moving to Node #0,3 Current State: 98:[86, 6, 50], Operations: ['61-11=50'] Exploring Operation: 86-6=80, Resulting Numbers: [50, 80] Generated Node #0,3,0: 98:[50, 80] Operation: 86-6=80 Exploring Operation: 86+6=92, Resulting Numbers: [50, 92] Generated Node #0,3,1: 98:[50, 92] Operation: 86+6=92 Exploring Operation: 6+50=56, Resulting Numbers: [86, 56] Generated Node #0,3,2: 98:[86, 56] Operation: 6+50=56 Exploring Operation: 86-50=36, Resulting Numbers: [6, 36] Generated Node #0,3,3: 98:[6, 36] Operation: 86-50=36 Exploring Operation: 50-6=44, Resulting Numbers: [86, 44] Generated Node #0,3,4: 98:[86, 44] Operation: 50-6=44 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 98:[50, 92], Operations: ['61-11=50', '86+6=92'] Exploring Operation: 92-50=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 50*92=4600, Resulting Numbers: [4600] 4600,98 unequal: No Solution Exploring Operation: 50+92=142, Resulting Numbers: [142] 142,98 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 #0,3,3 Current State: 98:[6, 36], Operations: ['61-11=50', '86-50=36'] Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,98 unequal: No Solution Exploring Operation: 6+36=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 6*36=216, Resulting Numbers: [216] 216,98 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,98 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 #0,3,4 Current State: 98:[86, 44], Operations: ['61-11=50', '50-6=44'] Exploring Operation: 86*44=3784, Resulting Numbers: [3784] 3784,98 unequal: No Solution Exploring Operation: 86-44=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 86+44=130, Resulting Numbers: [130] 130,98 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 #0,3,0 Current State: 98:[50, 80], Operations: ['61-11=50', '86-6=80'] Exploring Operation: 50*80=4000, Resulting Numbers: [4000] 4000,98 unequal: No Solution Exploring Operation: 50+80=130, Resulting Numbers: [130] 130,98 unequal: No Solution Exploring Operation: 80-50=30, Resulting Numbers: [30] 30,98 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 #0,3,2 Current State: 98:[86, 56], Operations: ['61-11=50', '6+50=56'] Exploring Operation: 86-56=30, Resulting Numbers: [30] 30,98 unequal: No Solution Exploring Operation: 86*56=4816, Resulting Numbers: [4816] 4816,98 unequal: No Solution Exploring Operation: 86+56=142, Resulting Numbers: [142] 142,98 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: 98:[11, 6, 25], Operations: ['86-61=25'] Exploring Operation: 11+25=36, Resulting Numbers: [6, 36] Generated Node #0,4,0: 98:[6, 36] Operation: 11+25=36 Exploring Operation: 25-6=19, Resulting Numbers: [11, 19] Generated Node #0,4,1: 98:[11, 19] Operation: 25-6=19 Exploring Operation: 11-6=5, Resulting Numbers: [25, 5] Generated Node #0,4,2: 98:[25, 5] Operation: 11-6=5 Exploring Operation: 11+6=17, Resulting Numbers: [25, 17] Generated Node #0,4,3: 98:[25, 17] Operation: 11+6=17 Exploring Operation: 25-11=14, Resulting Numbers: [6, 14] Generated Node #0,4,4: 98:[6, 14] Operation: 25-11=14 Moving to Node #0,0 Current State: 98:[11, 61, 92], Operations: ['86+6=92'] Exploring Operation: 61-11=50, Resulting Numbers: [92, 50] Generated Node #0,0,0: 98:[92, 50] Operation: 61-11=50 Exploring Operation: 11+61=72, Resulting Numbers: [92, 72] Generated Node #0,0,1: 98:[92, 72] Operation: 11+61=72 Exploring Operation: 11+92=103, Resulting Numbers: [61, 103] Generated Node #0,0,2: 98:[61, 103] Operation: 11+92=103 Exploring Operation: 92-11=81, Resulting Numbers: [61, 81] Generated Node #0,0,3: 98:[61, 81] Operation: 92-11=81 Exploring Operation: 92-61=31, Resulting Numbers: [11, 31] Generated Node #0,0,4: 98:[11, 31] Operation: 92-61=31 Moving to Node #0,1 Current State: 98:[86, 11, 55], Operations: ['61-6=55'] Exploring Operation: 55-11=44, Resulting Numbers: [86, 44] Generated Node #0,1,0: 98:[86, 44] Operation: 55-11=44 Exploring Operation: 55/11=5, Resulting Numbers: [86, 5] Generated Node #0,1,1: 98:[86, 5] Operation: 55/11=5 Exploring Operation: 86-55=31, Resulting Numbers: [11, 31] Generated Node #0,1,2: 98:[11, 31] Operation: 86-55=31 Exploring Operation: 86+11=97, Resulting Numbers: [55, 97] Generated Node #0,1,3: 98:[55, 97] Operation: 86+11=97 Exploring Operation: 86-11=75, Resulting Numbers: [55, 75] Generated Node #0,1,4: 98:[55, 75] Operation: 86-11=75 Moving to Node #0,4,4 Current State: 98:[6, 14], Operations: ['86-61=25', '25-11=14'] Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,98 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,98 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[97, 55], Operations: ['86+11=97', '61-6=55'] Exploring Operation: 97*55=5335, Resulting Numbers: [5335] 5335,98 unequal: No Solution Exploring Operation: 97-55=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 97+55=152, Resulting Numbers: [152] 152,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[92, 50], Operations: ['86+6=92', '61-11=50'] Exploring Operation: 92+50=142, Resulting Numbers: [142] 142,98 unequal: No Solution Exploring Operation: 92-50=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 92*50=4600, Resulting Numbers: [4600] 4600,98 unequal: No Solution Moving to Node #0,1,3 Current State: 98:[55, 97], Operations: ['61-6=55', '86+11=97'] Exploring Operation: 55*97=5335, Resulting Numbers: [5335] 5335,98 unequal: No Solution Exploring Operation: 55+97=152, Resulting Numbers: [152] 152,98 unequal: No Solution Exploring Operation: 97-55=42, Resulting Numbers: [42] 42,98 unequal: No Solution Moving to Node #0,4,1 Current State: 98:[11, 19], Operations: ['86-61=25', '25-6=19'] Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,98 unequal: No Solution Exploring Operation: 11*19=209, Resulting Numbers: [209] 209,98 unequal: No Solution Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,98 unequal: No Solution Moving to Node #0,4,2 Current State: 98:[25, 5], Operations: ['86-61=25', '11-6=5'] Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,98 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,98 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,98 unequal: No Solution Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[86, 5], Operations: ['61-6=55', '55/11=5'] Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,98 unequal: No Solution Exploring Operation: 86*5=430, Resulting Numbers: [430] 430,98 unequal: No Solution Exploring Operation: 86+5=91, Resulting Numbers: [91] 91,98 unequal: No Solution Moving to Node #0,4,3 Current State: 98:[25, 17], Operations: ['86-61=25', '11+6=17'] Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,98 unequal: No Solution Exploring Operation: 25*17=425, Resulting Numbers: [425] 425,98 unequal: No Solution Exploring Operation: 25+17=42, Resulting Numbers: [42] 42,98 unequal: No Solution Moving to Node #0,4,0 Current State: 98:[6, 36], Operations: ['86-61=25', '11+25=36'] Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,98 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,98 unequal: No Solution Exploring Operation: 6+36=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 6*36=216, Resulting Numbers: [216] 216,98 unequal: No Solution Moving to Node #0,2,4 Current State: 98:[6, 36], Operations: ['86+11=97', '97-61=36'] Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,98 unequal: No Solution Exploring Operation: 6*36=216, Resulting Numbers: [216] 216,98 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,98 unequal: No Solution Exploring Operation: 6+36=42, Resulting Numbers: [42] 42,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[61, 103], Operations: ['86+11=97', '6+97=103'] Exploring Operation: 61*103=6283, Resulting Numbers: [6283] 6283,98 unequal: No Solution Exploring Operation: 61+103=164, Resulting Numbers: [164] 164,98 unequal: No Solution Exploring Operation: 103-61=42, Resulting Numbers: [42] 42,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[61, 103], Operations: ['86+6=92', '11+92=103'] Exploring Operation: 103-61=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 61*103=6283, Resulting Numbers: [6283] 6283,98 unequal: No Solution Exploring Operation: 61+103=164, Resulting Numbers: [164] 164,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[86, 44], Operations: ['61-6=55', '55-11=44'] Exploring Operation: 86*44=3784, Resulting Numbers: [3784] 3784,98 unequal: No Solution Exploring Operation: 86-44=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 86+44=130, Resulting Numbers: [130] 130,98 unequal: No Solution Moving to Node #0,2,0 Current State: 98:[97, 67], Operations: ['86+11=97', '6+61=67'] Exploring Operation: 97-67=30, Resulting Numbers: [30] 30,98 unequal: No Solution Exploring Operation: 97+67=164, Resulting Numbers: [164] 164,98 unequal: No Solution Exploring Operation: 97*67=6499, Resulting Numbers: [6499] 6499,98 unequal: No Solution Moving to Node #0,2,3 Current State: 98:[61, 91], Operations: ['86+11=97', '97-6=91'] Exploring Operation: 61+91=152, Resulting Numbers: [152] 152,98 unequal: No Solution Exploring Operation: 91-61=30, Resulting Numbers: [30] 30,98 unequal: No Solution Exploring Operation: 61*91=5551, Resulting Numbers: [5551] 5551,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[11, 31], Operations: ['61-6=55', '86-55=31'] Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 11*31=341, Resulting Numbers: [341] 341,98 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,98 unequal: No Solution Moving to Node #0,0,4 Current State: 98:[11, 31], Operations: ['86+6=92', '92-61=31'] Exploring Operation: 11*31=341, Resulting Numbers: [341] 341,98 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,98 unequal: No Solution Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[92, 72], Operations: ['86+6=92', '11+61=72'] Exploring Operation: 92*72=6624, Resulting Numbers: [6624] 6624,98 unequal: No Solution Exploring Operation: 92-72=20, Resulting Numbers: [20] 20,98 unequal: No Solution Exploring Operation: 92+72=164, Resulting Numbers: [164] 164,98 unequal: No Solution Moving to Node #0,0,3 Current State: 98:[61, 81], Operations: ['86+6=92', '92-11=81'] Exploring Operation: 61*81=4941, Resulting Numbers: [4941] 4941,98 unequal: No Solution Exploring Operation: 61+81=142, Resulting Numbers: [142] 142,98 unequal: No Solution Exploring Operation: 81-61=20, Resulting Numbers: [20] 20,98 unequal: No Solution Moving to Node #0,1,4 Current State: 98:[55, 75], Operations: ['61-6=55', '86-11=75'] Exploring Operation: 55*75=4125, Resulting Numbers: [4125] 4125,98 unequal: No Solution Exploring Operation: 55+75=130, Resulting Numbers: [130] 130,98 unequal: No Solution Exploring Operation: 75-55=20, Resulting Numbers: [20] 20,98 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 50, 31, 15, 25 ]
18
[ "50/25=2", "31-15=16", "2+16=18" ]
Current State: 18:[50, 31, 15, 25], Operations: [] Exploring Operation: 50/25=2, Resulting Numbers: [31, 15, 2] Generated Node #2: [31, 15, 2] from Operation: 50/25=2 Current State: 18:[31, 15, 2], Operations: ['50/25=2'] Exploring Operation: 31-15=16, Resulting Numbers: [2, 16] Generated Node #3: [2, 16] from Operation: 31-15=16 Current State: 18:[2, 16], Operations: ['50/25=2', '31-15=16'] Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[50, 31, 15, 25], Operations: [] Exploring Operation: 50-31=19, Resulting Numbers: [15, 25, 19] Generated Node #0,0: 18:[15, 25, 19] Operation: 50-31=19 Moving to Node #0,0 Current State: 18:[15, 25, 19], Operations: ['50-31=19'] Exploring Operation: 25-15=10, Resulting Numbers: [19, 10] Generated Node #0,0,0: 18:[19, 10] Operation: 25-15=10 Moving to Node #0,0,0 Current State: 18:[19, 10], Operations: ['50-31=19', '25-15=10'] Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,18 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 84, 75, 53, 53 ]
50
[ "84+75=159", "159/53=3", "53-3=50" ]
Current State: 50:[84, 75, 53, 53], Operations: [] Exploring Operation: 84+75=159, Resulting Numbers: [53, 53, 159] Generated Node #2: [53, 53, 159] from Operation: 84+75=159 Current State: 50:[53, 53, 159], Operations: ['84+75=159'] Exploring Operation: 159/53=3, Resulting Numbers: [3] 3,50 equal: Goal Reached Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[84, 75, 53, 53], Operations: [] Exploring Operation: 84-75=9, Resulting Numbers: [53, 53, 9] Generated Node #0,0: 50:[53, 53, 9] Operation: 84-75=9 Moving to Node #0,0 Current State: 50:[53, 53, 9], Operations: ['84-75=9'] Exploring Operation: 53/53=1, Resulting Numbers: [9, 1] Generated Node #0,0,0: 50:[9, 1] Operation: 53/53=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[9, 1], Operations: ['84-75=9', '53/53=1'] Exploring Operation: 9+1=10, Resulting Numbers: [10] 10,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 11, 24, 6, 82 ]
89
[ "24-11=13", "82-6=76", "13+76=89" ]
Current State: 89:[11, 24, 6, 82], Operations: [] Exploring Operation: 24-11=13, Resulting Numbers: [6, 82, 13] Generated Node #2: [6, 82, 13] from Operation: 24-11=13 Current State: 89:[6, 82, 13], Operations: ['24-11=13'] Exploring Operation: 82-6=76, Resulting Numbers: [13, 76] Generated Node #3: [13, 76] from Operation: 82-6=76 Current State: 89:[13, 76], Operations: ['24-11=13', '82-6=76'] Exploring Operation: 13+76=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[11, 24, 6, 82], Operations: [] Exploring Operation: 11+6=17, Resulting Numbers: [24, 82, 17] Generated Node #0,0: 89:[24, 82, 17] Operation: 11+6=17 Exploring Operation: 11+24=35, Resulting Numbers: [6, 82, 35] Generated Node #0,1: 89:[6, 82, 35] Operation: 11+24=35 Exploring Operation: 24*6=144, Resulting Numbers: [11, 82, 144] Generated Node #0,2: 89:[11, 82, 144] Operation: 24*6=144 Exploring Operation: 11*6=66, Resulting Numbers: [24, 82, 66] Generated Node #0,3: 89:[24, 82, 66] Operation: 11*6=66 Exploring Operation: 24+6=30, Resulting Numbers: [11, 82, 30] Generated Node #0,4: 89:[11, 82, 30] Operation: 24+6=30 Start Sub Search at level 1: Moving to Node #0,3 Current State: 89:[24, 82, 66], Operations: ['11*6=66'] Exploring Operation: 24+66=90, Resulting Numbers: [82, 90] Generated Node #0,3,0: 89:[82, 90] Operation: 24+66=90 Exploring Operation: 82+66=148, Resulting Numbers: [24, 148] Generated Node #0,3,1: 89:[24, 148] Operation: 82+66=148 Exploring Operation: 82-24=58, Resulting Numbers: [66, 58] Generated Node #0,3,2: 89:[66, 58] Operation: 82-24=58 Exploring Operation: 66-24=42, Resulting Numbers: [82, 42] Generated Node #0,3,3: 89:[82, 42] Operation: 66-24=42 Exploring Operation: 24+82=106, Resulting Numbers: [66, 106] Generated Node #0,3,4: 89:[66, 106] Operation: 24+82=106 Moving to Node #0,3,0 Current State: 89:[82, 90], Operations: ['11*6=66', '24+66=90'] Exploring Operation: 82*90=7380, Resulting Numbers: [7380] 7380,89 unequal: No Solution Exploring Operation: 82+90=172, Resulting Numbers: [172] 172,89 unequal: No Solution Exploring Operation: 90-82=8, Resulting Numbers: [8] 8,89 unequal: No Solution Moving to Node #0,3,4 Current State: 89:[66, 106], Operations: ['11*6=66', '24+82=106'] Exploring Operation: 106-66=40, Resulting Numbers: [40] 40,89 unequal: No Solution Exploring Operation: 66*106=6996, Resulting Numbers: [6996] 6996,89 unequal: No Solution Exploring Operation: 66+106=172, Resulting Numbers: [172] 172,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[66, 58], Operations: ['11*6=66', '82-24=58'] Exploring Operation: 66*58=3828, Resulting Numbers: [3828] 3828,89 unequal: No Solution Exploring Operation: 66+58=124, Resulting Numbers: [124] 124,89 unequal: No Solution Exploring Operation: 66-58=8, Resulting Numbers: [8] 8,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[82, 42], Operations: ['11*6=66', '66-24=42'] Exploring Operation: 82+42=124, Resulting Numbers: [124] 124,89 unequal: No Solution Exploring Operation: 82*42=3444, Resulting Numbers: [3444] 3444,89 unequal: No Solution Exploring Operation: 82-42=40, Resulting Numbers: [40] 40,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[24, 148], Operations: ['11*6=66', '82+66=148'] Exploring Operation: 148-24=124, Resulting Numbers: [124] 124,89 unequal: No Solution Exploring Operation: 24*148=3552, Resulting Numbers: [3552] 3552,89 unequal: No Solution Exploring Operation: 24+148=172, Resulting Numbers: [172] 172,89 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:[11, 82, 144], Operations: ['24*6=144'] Exploring Operation: 82-11=71, Resulting Numbers: [144, 71] Generated Node #0,2,0: 89:[144, 71] Operation: 82-11=71 Exploring Operation: 144-82=62, Resulting Numbers: [11, 62] Generated Node #0,2,1: 89:[11, 62] Operation: 144-82=62 Exploring Operation: 144-11=133, Resulting Numbers: [82, 133] Generated Node #0,2,2: 89:[82, 133] Operation: 144-11=133 Exploring Operation: 11+82=93, Resulting Numbers: [144, 93] Generated Node #0,2,3: 89:[144, 93] Operation: 11+82=93 Exploring Operation: 11+144=155, Resulting Numbers: [82, 155] Generated Node #0,2,4: 89:[82, 155] Operation: 11+144=155 Moving to Node #0,2,2 Current State: 89:[82, 133], Operations: ['24*6=144', '144-11=133'] Exploring Operation: 133-82=51, Resulting Numbers: [51] 51,89 unequal: No Solution Exploring Operation: 82*133=10906, Resulting Numbers: [10906] 10906,89 unequal: No Solution Exploring Operation: 82+133=215, Resulting Numbers: [215] 215,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[144, 93], Operations: ['24*6=144', '11+82=93'] Exploring Operation: 144-93=51, Resulting Numbers: [51] 51,89 unequal: No Solution Exploring Operation: 144*93=13392, Resulting Numbers: [13392] 13392,89 unequal: No Solution Exploring Operation: 144+93=237, Resulting Numbers: [237] 237,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[144, 71], Operations: ['24*6=144', '82-11=71'] Exploring Operation: 144*71=10224, Resulting Numbers: [10224] 10224,89 unequal: No Solution Exploring Operation: 144-71=73, Resulting Numbers: [73] 73,89 unequal: No Solution Exploring Operation: 144+71=215, Resulting Numbers: [215] 215,89 unequal: No Solution Moving to Node #0,2,4 Current State: 89:[82, 155], Operations: ['24*6=144', '11+144=155'] Exploring Operation: 155-82=73, Resulting Numbers: [73] 73,89 unequal: No Solution Exploring Operation: 82*155=12710, Resulting Numbers: [12710] 12710,89 unequal: No Solution Exploring Operation: 82+155=237, Resulting Numbers: [237] 237,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[11, 62], Operations: ['24*6=144', '144-82=62'] Exploring Operation: 11+62=73, Resulting Numbers: [73] 73,89 unequal: No Solution Exploring Operation: 62-11=51, Resulting Numbers: [51] 51,89 unequal: No Solution Exploring Operation: 11*62=682, Resulting Numbers: [682] 682,89 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 #0,0 Current State: 89:[24, 82, 17], Operations: ['11+6=17'] Exploring Operation: 24+17=41, Resulting Numbers: [82, 41] Generated Node #0,0,0: 89:[82, 41] Operation: 24+17=41 Exploring Operation: 24-17=7, Resulting Numbers: [82, 7] Generated Node #0,0,1: 89:[82, 7] Operation: 24-17=7 Exploring Operation: 24+82=106, Resulting Numbers: [17, 106] Generated Node #0,0,2: 89:[17, 106] Operation: 24+82=106 Exploring Operation: 82-17=65, Resulting Numbers: [24, 65] Generated Node #0,0,3: 89:[24, 65] Operation: 82-17=65 Exploring Operation: 82+17=99, Resulting Numbers: [24, 99] Generated Node #0,0,4: 89:[24, 99] Operation: 82+17=99 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[82, 41], Operations: ['11+6=17', '24+17=41'] Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,89 unequal: No Solution Exploring Operation: 82*41=3362, Resulting Numbers: [3362] 3362,89 unequal: No Solution Exploring Operation: 82+41=123, Resulting Numbers: [123] 123,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 89:[24, 99], Operations: ['11+6=17', '82+17=99'] Exploring Operation: 99-24=75, Resulting Numbers: [75] 75,89 unequal: No Solution Exploring Operation: 24*99=2376, Resulting Numbers: [2376] 2376,89 unequal: No Solution Exploring Operation: 24+99=123, Resulting Numbers: [123] 123,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[82, 7], Operations: ['11+6=17', '24-17=7'] Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,89 unequal: No Solution Exploring Operation: 82*7=574, Resulting Numbers: [574] 574,89 unequal: No Solution Exploring Operation: 82+7=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[11, 24, 6, 82], Operations: [] Exploring Operation: 11+6=17, Resulting Numbers: [24, 82, 17] Generated Node #0,0: 89:[24, 82, 17] Operation: 11+6=17 Moving to Node #0,0 Current State: 89:[24, 82, 17], Operations: ['11+6=17'] Exploring Operation: 24-17=7, Resulting Numbers: [82, 7] Generated Node #0,0,1: 89:[82, 7] Operation: 24-17=7 Moving to Node #0,0,1 Current State: 89:[82, 7], Operations: ['11+6=17', '24-17=7'] Exploring Operation: 82+7=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.944444
hs_5
sum_heuristic
[ 19, 75, 3, 90 ]
78
[ "75-19=56", "3*56=168", "168-90=78" ]
Current State: 78:[19, 75, 3, 90], Operations: [] Exploring Operation: 75-19=56, Resulting Numbers: [3, 90, 56] Generated Node #2: [3, 90, 56] from Operation: 75-19=56 Current State: 78:[3, 90, 56], Operations: ['75-19=56'] Exploring Operation: 3*56=168, Resulting Numbers: [90, 168] Generated Node #3: [90, 168] from Operation: 3*56=168 Current State: 78:[90, 168], Operations: ['75-19=56', '3*56=168'] Exploring Operation: 168-90=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[19, 75, 3, 90], Operations: [] Exploring Operation: 90-19=71, Resulting Numbers: [75, 3, 71] Generated Node #0,0: 78:[75, 3, 71] Operation: 90-19=71 Exploring Operation: 90-75=15, Resulting Numbers: [19, 3, 15] Generated Node #0,1: 78:[19, 3, 15] Operation: 90-75=15 Moving to Node #0,1 Current State: 78:[19, 3, 15], Operations: ['90-75=15'] Exploring Operation: 19-15=4, Resulting Numbers: [3, 4] Generated Node #0,1,0: 78:[3, 4] Operation: 19-15=4 Exploring Operation: 19-3=16, Resulting Numbers: [15, 16] Generated Node #0,1,1: 78:[15, 16] Operation: 19-3=16 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[3, 4], Operations: ['90-75=15', '19-15=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,78 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,78 unequal: No Solution No 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: 78:[15, 16], Operations: ['90-75=15', '19-3=16'] Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,78 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: 78:[75, 3, 71], Operations: ['90-19=71'] Exploring Operation: 75-71=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 78:[3, 4] Operation: 75-71=4 Exploring Operation: 75+3=78, Resulting Numbers: [71, 78] Generated Node #0,0,1: 78:[71, 78] Operation: 75+3=78 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[3, 4], Operations: ['90-19=71', '75-71=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,78 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,78 unequal: No Solution No 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: 78:[71, 78], Operations: ['90-19=71', '75+3=78'] Exploring Operation: 78-71=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 71+78=149, Resulting Numbers: [149] 149,78 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
[ 21, 13, 56, 91 ]
53
[ "21*13=273", "273/91=3", "56-3=53" ]
Current State: 53:[21, 13, 56, 91], Operations: [] Exploring Operation: 21*13=273, Resulting Numbers: [56, 91, 273] Generated Node #2: [56, 91, 273] from Operation: 21*13=273 Current State: 53:[56, 91, 273], Operations: ['21*13=273'] Exploring Operation: 273/91=3, Resulting Numbers: [56, 3] Generated Node #3: [56, 3] from Operation: 273/91=3 Current State: 53:[56, 3], Operations: ['21*13=273', '273/91=3'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[21, 13, 56, 91], Operations: [] Exploring Operation: 91-13=78, Resulting Numbers: [21, 56, 78] Generated Node #0,0: 53:[21, 56, 78] Operation: 91-13=78 Exploring Operation: 91-21=70, Resulting Numbers: [13, 56, 70] Generated Node #0,1: 53:[13, 56, 70] Operation: 91-21=70 Exploring Operation: 21+13=34, Resulting Numbers: [56, 91, 34] Generated Node #0,2: 53:[56, 91, 34] Operation: 21+13=34 Moving to Node #0,0 Current State: 53:[21, 56, 78], Operations: ['91-13=78'] Exploring Operation: 56-21=35, Resulting Numbers: [78, 35] Generated Node #0,0,0: 53:[78, 35] Operation: 56-21=35 Exploring Operation: 21+56=77, Resulting Numbers: [78, 77] Generated Node #0,0,1: 53:[78, 77] Operation: 21+56=77 Exploring Operation: 78-21=57, Resulting Numbers: [56, 57] Generated Node #0,0,2: 53:[56, 57] Operation: 78-21=57 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 53:[56, 57], Operations: ['91-13=78', '78-21=57'] Exploring Operation: 56*57=3192, Resulting Numbers: [3192] 3192,53 unequal: No Solution Exploring Operation: 56+57=113, Resulting Numbers: [113] 113,53 unequal: No Solution Exploring Operation: 57-56=1, Resulting Numbers: [1] 1,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[78, 35], Operations: ['91-13=78', '56-21=35'] Exploring Operation: 78+35=113, Resulting Numbers: [113] 113,53 unequal: No Solution Exploring Operation: 78-35=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 78*35=2730, Resulting Numbers: [2730] 2730,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[78, 77], Operations: ['91-13=78', '21+56=77'] Exploring Operation: 78-77=1, Resulting Numbers: [1] 1,53 unequal: No Solution Exploring Operation: 78*77=6006, Resulting Numbers: [6006] 6006,53 unequal: No Solution Exploring Operation: 78+77=155, Resulting Numbers: [155] 155,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 53:[13, 56, 70], Operations: ['91-21=70'] Exploring Operation: 70-13=57, Resulting Numbers: [56, 57] Generated Node #0,1,0: 53:[56, 57] Operation: 70-13=57 Exploring Operation: 56-13=43, Resulting Numbers: [70, 43] Generated Node #0,1,1: 53:[70, 43] Operation: 56-13=43 Exploring Operation: 13+56=69, Resulting Numbers: [70, 69] Generated Node #0,1,2: 53:[70, 69] Operation: 13+56=69 Moving to Node #0,2 Current State: 53:[56, 91, 34], Operations: ['21+13=34'] Exploring Operation: 56-34=22, Resulting Numbers: [91, 22] Generated Node #0,2,0: 53:[91, 22] Operation: 56-34=22 Exploring Operation: 91-56=35, Resulting Numbers: [34, 35] Generated Node #0,2,1: 53:[34, 35] Operation: 91-56=35 Exploring Operation: 91-34=57, Resulting Numbers: [56, 57] Generated Node #0,2,2: 53:[56, 57] Operation: 91-34=57 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 53:[56, 57], Operations: ['21+13=34', '91-34=57'] Exploring Operation: 56+57=113, Resulting Numbers: [113] 113,53 unequal: No Solution Exploring Operation: 57-56=1, Resulting Numbers: [1] 1,53 unequal: No Solution Exploring Operation: 56*57=3192, Resulting Numbers: [3192] 3192,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 53:[34, 35], Operations: ['21+13=34', '91-56=35'] Exploring Operation: 34*35=1190, Resulting Numbers: [1190] 1190,53 unequal: No Solution Exploring Operation: 34+35=69, Resulting Numbers: [69] 69,53 unequal: No Solution Exploring Operation: 35-34=1, Resulting Numbers: [1] 1,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 53:[91, 22], Operations: ['21+13=34', '56-34=22'] Exploring Operation: 91*22=2002, Resulting Numbers: [2002] 2002,53 unequal: No Solution Exploring Operation: 91-22=69, Resulting Numbers: [69] 69,53 unequal: No Solution Exploring Operation: 91+22=113, Resulting Numbers: [113] 113,53 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: 53:[56, 57], Operations: ['91-21=70', '70-13=57'] Exploring Operation: 56*57=3192, Resulting Numbers: [3192] 3192,53 unequal: No Solution Exploring Operation: 57-56=1, Resulting Numbers: [1] 1,53 unequal: No Solution Exploring Operation: 56+57=113, Resulting Numbers: [113] 113,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[70, 43], Operations: ['91-21=70', '56-13=43'] Exploring Operation: 70*43=3010, Resulting Numbers: [3010] 3010,53 unequal: No Solution Exploring Operation: 70+43=113, Resulting Numbers: [113] 113,53 unequal: No Solution Exploring Operation: 70-43=27, Resulting Numbers: [27] 27,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[70, 69], Operations: ['91-21=70', '13+56=69'] Exploring Operation: 70+69=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 70*69=4830, Resulting Numbers: [4830] 4830,53 unequal: No Solution Exploring Operation: 70-69=1, Resulting Numbers: [1] 1,53 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 29, 52, 37, 36 ]
22
[ "52-29=23", "37-36=1", "23-1=22" ]
Current State: 22:[29, 52, 37, 36], Operations: [] Exploring Operation: 52-29=23, Resulting Numbers: [37, 36, 23] Generated Node #2: [37, 36, 23] from Operation: 52-29=23 Current State: 22:[37, 36, 23], Operations: ['52-29=23'] Exploring Operation: 37-36=1, Resulting Numbers: [23, 1] Generated Node #3: [23, 1] from Operation: 37-36=1 Current State: 22:[23, 1], Operations: ['52-29=23', '37-36=1'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[29, 52, 37, 36], Operations: [] Exploring Operation: 52-36=16, Resulting Numbers: [29, 37, 16] Generated Node #0,0: 22:[29, 37, 16] Operation: 52-36=16 Exploring Operation: 37-29=8, Resulting Numbers: [52, 36, 8] Generated Node #0,1: 22:[52, 36, 8] Operation: 37-29=8 Exploring Operation: 37-36=1, Resulting Numbers: [29, 52, 1] Generated Node #0,2: 22:[29, 52, 1] Operation: 37-36=1 Exploring Operation: 52-37=15, Resulting Numbers: [29, 36, 15] Generated Node #0,3: 22:[29, 36, 15] Operation: 52-37=15 Exploring Operation: 52-29=23, Resulting Numbers: [37, 36, 23] Generated Node #0,4: 22:[37, 36, 23] Operation: 52-29=23 Moving to Node #0,3 Current State: 22:[29, 36, 15], Operations: ['52-37=15'] Exploring Operation: 29-15=14, Resulting Numbers: [36, 14] Generated Node #0,3,0: 22:[36, 14] Operation: 29-15=14 Exploring Operation: 29+15=44, Resulting Numbers: [36, 44] Generated Node #0,3,1: 22:[36, 44] Operation: 29+15=44 Exploring Operation: 36-29=7, Resulting Numbers: [15, 7] Generated Node #0,3,2: 22:[15, 7] Operation: 36-29=7 Exploring Operation: 36-15=21, Resulting Numbers: [29, 21] Generated Node #0,3,3: 22:[29, 21] Operation: 36-15=21 Exploring Operation: 36+15=51, Resulting Numbers: [29, 51] Generated Node #0,3,4: 22:[29, 51] Operation: 36+15=51 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 22:[15, 7], Operations: ['52-37=15', '36-29=7'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,22 unequal: No Solution Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[29, 52, 37, 36], Operations: [] Exploring Operation: 52-37=15, Resulting Numbers: [29, 36, 15] Generated Node #0,3: 22:[29, 36, 15] Operation: 52-37=15 Moving to Node #0,3 Current State: 22:[29, 36, 15], Operations: ['52-37=15'] Exploring Operation: 36-29=7, Resulting Numbers: [15, 7] Generated Node #0,3,2: 22:[15, 7] Operation: 36-29=7 Moving to Node #0,3,2 Current State: 22:[15, 7], Operations: ['52-37=15', '36-29=7'] Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 73, 18, 64, 76 ]
85
[ "73-18=55", "64+76=140", "140-55=85" ]
Current State: 85:[73, 18, 64, 76], Operations: [] Exploring Operation: 73-18=55, Resulting Numbers: [64, 76, 55] Generated Node #2: [64, 76, 55] from Operation: 73-18=55 Current State: 85:[64, 76, 55], Operations: ['73-18=55'] Exploring Operation: 64+76=140, Resulting Numbers: [55, 140] Generated Node #3: [55, 140] from Operation: 64+76=140 Current State: 85:[55, 140], Operations: ['73-18=55', '64+76=140'] Exploring Operation: 140-55=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[73, 18, 64, 76], Operations: [] Exploring Operation: 73-64=9, Resulting Numbers: [18, 76, 9] Generated Node #0,0: 85:[18, 76, 9] Operation: 73-64=9 Exploring Operation: 18+64=82, Resulting Numbers: [73, 76, 82] Generated Node #0,1: 85:[73, 76, 82] Operation: 18+64=82 Exploring Operation: 76-73=3, Resulting Numbers: [18, 64, 3] Generated Node #0,2: 85:[18, 64, 3] Operation: 76-73=3 Exploring Operation: 76-64=12, Resulting Numbers: [73, 18, 12] Generated Node #0,3: 85:[73, 18, 12] Operation: 76-64=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[18, 76, 9], Operations: ['73-64=9'] Exploring Operation: 18+76=94, Resulting Numbers: [9, 94] Generated Node #0,0,0: 85:[9, 94] Operation: 18+76=94 Exploring Operation: 18/9=2, Resulting Numbers: [76, 2] Generated Node #0,0,1: 85:[76, 2] Operation: 18/9=2 Exploring Operation: 18-9=9, Resulting Numbers: [76, 9] Generated Node #0,0,2: 85:[76, 9] Operation: 18-9=9 Exploring Operation: 76+9=85, Resulting Numbers: [18, 85] Generated Node #0,0,3: 85:[18, 85] Operation: 76+9=85 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 85:[18, 85], Operations: ['73-64=9', '76+9=85'] Exploring Operation: 18*85=1530, Resulting Numbers: [1530] 1530,85 unequal: No Solution Exploring Operation: 18+85=103, Resulting Numbers: [103] 103,85 unequal: No Solution Exploring Operation: 85-18=67, Resulting Numbers: [67] 67,85 unequal: No Solution No 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: 85:[76, 2], Operations: ['73-64=9', '18/9=2'] Exploring Operation: 76*2=152, Resulting Numbers: [152] 152,85 unequal: No Solution Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,85 unequal: No Solution Exploring Operation: 76+2=78, Resulting Numbers: [78] 78,85 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,85 unequal: No Solution No 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: 85:[9, 94], Operations: ['73-64=9', '18+76=94'] Exploring Operation: 9*94=846, Resulting Numbers: [846] 846,85 unequal: No Solution Exploring Operation: 9+94=103, Resulting Numbers: [103] 103,85 unequal: No Solution Exploring Operation: 94-9=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[73, 18, 64, 76], Operations: [] Exploring Operation: 73-64=9, Resulting Numbers: [18, 76, 9] Generated Node #0,0: 85:[18, 76, 9] Operation: 73-64=9 Moving to Node #0,0 Current State: 85:[18, 76, 9], Operations: ['73-64=9'] Exploring Operation: 18+76=94, Resulting Numbers: [9, 94] Generated Node #0,0,0: 85:[9, 94] Operation: 18+76=94 Moving to Node #0,0,0 Current State: 85:[9, 94], Operations: ['73-64=9', '18+76=94'] Exploring Operation: 94-9=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_4
mult_heuristic
[ 76, 39, 46, 81 ]
80
[ "76+39=115", "81-46=35", "115-35=80" ]
Current State: 80:[76, 39, 46, 81], Operations: [] Exploring Operation: 76+39=115, Resulting Numbers: [46, 81, 115] Generated Node #2: [46, 81, 115] from Operation: 76+39=115 Current State: 80:[46, 81, 115], Operations: ['76+39=115'] Exploring Operation: 81-46=35, Resulting Numbers: [115, 35] Generated Node #3: [115, 35] from Operation: 81-46=35 Current State: 80:[115, 35], Operations: ['76+39=115', '81-46=35'] Exploring Operation: 115-35=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[76, 39, 46, 81], Operations: [] Exploring Operation: 76-39=37, Resulting Numbers: [46, 81, 37] Generated Node #0,0: 80:[46, 81, 37] Operation: 76-39=37 Exploring Operation: 46-39=7, Resulting Numbers: [76, 81, 7] Generated Node #0,1: 80:[76, 81, 7] Operation: 46-39=7 Exploring Operation: 81-76=5, Resulting Numbers: [39, 46, 5] Generated Node #0,2: 80:[39, 46, 5] Operation: 81-76=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[76, 81, 7], Operations: ['46-39=7'] Exploring Operation: 76+7=83, Resulting Numbers: [81, 83] Generated Node #0,1,0: 80:[81, 83] Operation: 76+7=83 Exploring Operation: 81-7=74, Resulting Numbers: [76, 74] Generated Node #0,1,1: 80:[76, 74] Operation: 81-7=74 Exploring Operation: 81-76=5, Resulting Numbers: [7, 5] Generated Node #0,1,2: 80:[7, 5] Operation: 81-76=5 Moving to Node #0,1,2 Current State: 80:[7, 5], Operations: ['46-39=7', '81-76=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,80 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[81, 83], Operations: ['46-39=7', '76+7=83'] Exploring Operation: 81*83=6723, Resulting Numbers: [6723] 6723,80 unequal: No Solution Exploring Operation: 81+83=164, Resulting Numbers: [164] 164,80 unequal: No Solution Exploring Operation: 83-81=2, Resulting Numbers: [2] 2,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[76, 74], Operations: ['46-39=7', '81-7=74'] Exploring Operation: 76-74=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 76+74=150, Resulting Numbers: [150] 150,80 unequal: No Solution Exploring Operation: 76*74=5624, Resulting Numbers: [5624] 5624,80 unequal: No Solution No 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: 80:[39, 46, 5], Operations: ['81-76=5'] Exploring Operation: 39+46=85, Resulting Numbers: [5, 85] Generated Node #0,2,0: 80:[5, 85] Operation: 39+46=85 Exploring Operation: 46-39=7, Resulting Numbers: [5, 7] Generated Node #0,2,1: 80:[5, 7] Operation: 46-39=7 Exploring Operation: 46-5=41, Resulting Numbers: [39, 41] Generated Node #0,2,2: 80:[39, 41] Operation: 46-5=41 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 80:[5, 7], Operations: ['81-76=5', '46-39=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,80 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 80:[39, 41], Operations: ['81-76=5', '46-5=41'] Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 39+41=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[76, 39, 46, 81], Operations: [] Exploring Operation: 81-76=5, Resulting Numbers: [39, 46, 5] Generated Node #0,2: 80:[39, 46, 5] Operation: 81-76=5 Moving to Node #0,2 Current State: 80:[39, 46, 5], Operations: ['81-76=5'] Exploring Operation: 46-5=41, Resulting Numbers: [39, 41] Generated Node #0,2,2: 80:[39, 41] Operation: 46-5=41 Moving to Node #0,2,2 Current State: 80:[39, 41], Operations: ['81-76=5', '46-5=41'] Exploring Operation: 39+41=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.976563
hs_3
mult_heuristic
[ 92, 75, 92, 23 ]
86
[ "92-75=17", "92-23=69", "17+69=86" ]
Current State: 86:[92, 75, 92, 23], Operations: [] Exploring Operation: 92-75=17, Resulting Numbers: [23, 17] Generated Node #2: [23, 17] from Operation: 92-75=17 Current State: 86:[23, 17], Operations: ['92-75=17'] Exploring Operation: 92-23=69, Resulting Numbers: [17, 69] Generated Node #3: [17, 69] from Operation: 92-23=69 Current State: 86:[17, 69], Operations: ['92-75=17', '92-23=69'] Exploring Operation: 17+69=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[92, 75, 92, 23], Operations: [] Exploring Operation: 75+23=98, Resulting Numbers: [92, 92, 98] Generated Node #0,0: 86:[92, 92, 98] Operation: 75+23=98 Exploring Operation: 75-23=52, Resulting Numbers: [92, 92, 52] Generated Node #0,1: 86:[92, 92, 52] Operation: 75-23=52 Exploring Operation: 92/23=4, Resulting Numbers: [75, 92, 4] Generated Node #0,2: 86:[75, 92, 4] Operation: 92/23=4 Exploring Operation: 92/23=4, Resulting Numbers: [92, 75, 4] Generated Node #0,3: 86:[92, 75, 4] Operation: 92/23=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[75, 92, 4], Operations: ['92/23=4'] Exploring Operation: 75-4=71, Resulting Numbers: [92, 71] Generated Node #0,2,0: 86:[92, 71] Operation: 75-4=71 Exploring Operation: 92-4=88, Resulting Numbers: [75, 88] Generated Node #0,2,1: 86:[75, 88] Operation: 92-4=88 Exploring Operation: 92-75=17, Resulting Numbers: [4, 17] Generated Node #0,2,2: 86:[4, 17] Operation: 92-75=17 Exploring Operation: 75+4=79, Resulting Numbers: [92, 79] Generated Node #0,2,3: 86:[92, 79] Operation: 75+4=79 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 86:[75, 88], Operations: ['92/23=4', '92-4=88'] Exploring Operation: 88-75=13, Resulting Numbers: [13] 13,86 unequal: No Solution Exploring Operation: 75*88=6600, Resulting Numbers: [6600] 6600,86 unequal: No Solution Exploring Operation: 75+88=163, Resulting Numbers: [163] 163,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 86:[92, 79], Operations: ['92/23=4', '75+4=79'] Exploring Operation: 92-79=13, Resulting Numbers: [13] 13,86 unequal: No Solution Exploring Operation: 92*79=7268, Resulting Numbers: [7268] 7268,86 unequal: No Solution Exploring Operation: 92+79=171, Resulting Numbers: [171] 171,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 86:[4, 17], Operations: ['92/23=4', '92-75=17'] Exploring Operation: 4+17=21, Resulting Numbers: [21] 21,86 unequal: No Solution Exploring Operation: 4*17=68, Resulting Numbers: [68] 68,86 unequal: No Solution Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 86:[92, 71], Operations: ['92/23=4', '75-4=71'] Exploring Operation: 92*71=6532, Resulting Numbers: [6532] 6532,86 unequal: No Solution Exploring Operation: 92-71=21, Resulting Numbers: [21] 21,86 unequal: No Solution Exploring Operation: 92+71=163, Resulting Numbers: [163] 163,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[92, 75, 4], Operations: ['92/23=4'] Exploring Operation: 75+4=79, Resulting Numbers: [92, 79] Generated Node #0,3,0: 86:[92, 79] Operation: 75+4=79 Exploring Operation: 92-4=88, Resulting Numbers: [75, 88] Generated Node #0,3,1: 86:[75, 88] Operation: 92-4=88 Exploring Operation: 92-75=17, Resulting Numbers: [4, 17] Generated Node #0,3,2: 86:[4, 17] Operation: 92-75=17 Exploring Operation: 92+4=96, Resulting Numbers: [75, 96] Generated Node #0,3,3: 86:[75, 96] Operation: 92+4=96 Moving to Node #0,3,0 Current State: 86:[92, 79], Operations: ['92/23=4', '75+4=79'] Exploring Operation: 92+79=171, Resulting Numbers: [171] 171,86 unequal: No Solution Exploring Operation: 92-79=13, Resulting Numbers: [13] 13,86 unequal: No Solution Exploring Operation: 92*79=7268, Resulting Numbers: [7268] 7268,86 unequal: No Solution Moving to Node #0,3,1 Current State: 86:[75, 88], Operations: ['92/23=4', '92-4=88'] Exploring Operation: 75*88=6600, Resulting Numbers: [6600] 6600,86 unequal: No Solution Exploring Operation: 75+88=163, Resulting Numbers: [163] 163,86 unequal: No Solution Exploring Operation: 88-75=13, Resulting Numbers: [13] 13,86 unequal: No Solution Moving to Node #0,3,2 Current State: 86:[4, 17], Operations: ['92/23=4', '92-75=17'] Exploring Operation: 4*17=68, Resulting Numbers: [68] 68,86 unequal: No Solution Exploring Operation: 4+17=21, Resulting Numbers: [21] 21,86 unequal: No Solution Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,86 unequal: No Solution Moving to Node #0,3,3 Current State: 86:[75, 96], Operations: ['92/23=4', '92+4=96'] Exploring Operation: 96-75=21, Resulting Numbers: [21] 21,86 unequal: No Solution Exploring Operation: 75*96=7200, Resulting Numbers: [7200] 7200,86 unequal: No Solution Exploring Operation: 75+96=171, Resulting Numbers: [171] 171,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[92, 92, 52], Operations: ['75-23=52'] Exploring Operation: 92-52=40, Resulting Numbers: [92, 40] Generated Node #0,1,0: 86:[92, 40] Operation: 92-52=40 Exploring Operation: 92-52=40, Resulting Numbers: [92, 40] Generated Node #0,1,1: 86:[92, 40] Operation: 92-52=40 Exploring Operation: 92-92=0, Resulting Numbers: [52, 0] Generated Node #0,1,2: 86:[52, 0] Operation: 92-92=0 Exploring Operation: 92/92=1, Resulting Numbers: [52, 1] Generated Node #0,1,3: 86:[52, 1] Operation: 92/92=1 Moving to Node #0,1,0 Current State: 86:[92, 40], Operations: ['75-23=52', '92-52=40'] Exploring Operation: 92-40=52, Resulting Numbers: [52] 52,86 unequal: No Solution Exploring Operation: 92+40=132, Resulting Numbers: [132] 132,86 unequal: No Solution Exploring Operation: 92*40=3680, Resulting Numbers: [3680] 3680,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[92, 40], Operations: ['75-23=52', '92-52=40'] Exploring Operation: 92*40=3680, Resulting Numbers: [3680] 3680,86 unequal: No Solution Exploring Operation: 92-40=52, Resulting Numbers: [52] 52,86 unequal: No Solution Exploring Operation: 92+40=132, Resulting Numbers: [132] 132,86 unequal: No Solution Moving to Node #0,1,3 Current State: 86:[52, 1], Operations: ['75-23=52', '92/92=1'] Exploring Operation: 52+1=53, Resulting Numbers: [53] 53,86 unequal: No Solution Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,86 unequal: No Solution Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,86 unequal: No Solution Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,86 unequal: No Solution Moving to Node #0,1,2 Current State: 86:[52, 0], Operations: ['75-23=52', '92-92=0'] Exploring Operation: 52-0=52, Resulting Numbers: [52] 52,86 unequal: No Solution Exploring Operation: 52*0=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 52+0=52, Resulting Numbers: [52] 52,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[92, 92, 98], Operations: ['75+23=98'] Exploring Operation: 98-92=6, Resulting Numbers: [92, 6] Generated Node #0,0,0: 86:[92, 6] Operation: 98-92=6 Exploring Operation: 98-92=6, Resulting Numbers: [92, 6] Generated Node #0,0,1: 86:[92, 6] Operation: 98-92=6 Exploring Operation: 92/92=1, Resulting Numbers: [98, 1] Generated Node #0,0,2: 86:[98, 1] Operation: 92/92=1 Exploring Operation: 92-92=0, Resulting Numbers: [98, 0] Generated Node #0,0,3: 86:[98, 0] Operation: 92-92=0 Moving to Node #0,0,0 Current State: 86:[92, 6], Operations: ['75+23=98', '98-92=6'] Exploring Operation: 92-6=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[92, 75, 92, 23], Operations: [] Exploring Operation: 75+23=98, Resulting Numbers: [92, 92, 98] Generated Node #0,0: 86:[92, 92, 98] Operation: 75+23=98 Moving to Node #0,0 Current State: 86:[92, 92, 98], Operations: ['75+23=98'] Exploring Operation: 98-92=6, Resulting Numbers: [92, 6] Generated Node #0,0,0: 86:[92, 6] Operation: 98-92=6 Moving to Node #0,0,0 Current State: 86:[92, 6], Operations: ['75+23=98', '98-92=6'] Exploring Operation: 92-6=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.946181
hs_4
mult_heuristic
[ 2, 10, 40, 16 ]
17
[ "10+40=50", "50-16=34", "34/2=17" ]
Current State: 17:[2, 10, 40, 16], Operations: [] Exploring Operation: 10+40=50, Resulting Numbers: [2, 16, 50] Generated Node #2: [2, 16, 50] from Operation: 10+40=50 Current State: 17:[2, 16, 50], Operations: ['10+40=50'] Exploring Operation: 50-16=34, Resulting Numbers: [2, 34] Generated Node #3: [2, 34] from Operation: 50-16=34 Current State: 17:[2, 34], Operations: ['10+40=50', '50-16=34'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[2, 10, 40, 16], Operations: [] Exploring Operation: 40-2=38, Resulting Numbers: [10, 16, 38] Generated Node #0,0: 17:[10, 16, 38] Operation: 40-2=38 Exploring Operation: 2*10=20, Resulting Numbers: [40, 16, 20] Generated Node #0,1: 17:[40, 16, 20] Operation: 2*10=20 Exploring Operation: 40/2=20, Resulting Numbers: [10, 16, 20] Generated Node #0,2: 17:[10, 16, 20] Operation: 40/2=20 Exploring Operation: 2+10=12, Resulting Numbers: [40, 16, 12] Generated Node #0,3: 17:[40, 16, 12] Operation: 2+10=12 Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[10, 16, 20], Operations: ['40/2=20'] Exploring Operation: 20-10=10, Resulting Numbers: [16, 10] Generated Node #0,2,0: 17:[16, 10] Operation: 20-10=10 Exploring Operation: 10+20=30, Resulting Numbers: [16, 30] Generated Node #0,2,1: 17:[16, 30] Operation: 10+20=30 Exploring Operation: 10+16=26, Resulting Numbers: [20, 26] Generated Node #0,2,2: 17:[20, 26] Operation: 10+16=26 Exploring Operation: 16-10=6, Resulting Numbers: [20, 6] Generated Node #0,2,3: 17:[20, 6] Operation: 16-10=6 Moving to Node #0,2,0 Current State: 17:[16, 10], Operations: ['40/2=20', '20-10=10'] Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,17 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[20, 26], Operations: ['40/2=20', '10+16=26'] Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,17 unequal: No Solution Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,17 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,17 unequal: No Solution Moving to Node #0,2,3 Current State: 17:[20, 6], Operations: ['40/2=20', '16-10=6'] Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,17 unequal: No Solution Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,17 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[16, 30], Operations: ['40/2=20', '10+20=30'] Exploring Operation: 16*30=480, Resulting Numbers: [480] 480,17 unequal: No Solution Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,17 unequal: No Solution Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[40, 16, 20], Operations: ['2*10=20'] Exploring Operation: 40-16=24, Resulting Numbers: [20, 24] Generated Node #0,1,0: 17:[20, 24] Operation: 40-16=24 Exploring Operation: 20-16=4, Resulting Numbers: [40, 4] Generated Node #0,1,1: 17:[40, 4] Operation: 20-16=4 Exploring Operation: 40-20=20, Resulting Numbers: [16, 20] Generated Node #0,1,2: 17:[16, 20] Operation: 40-20=20 Exploring Operation: 40/20=2, Resulting Numbers: [16, 2] Generated Node #0,1,3: 17:[16, 2] Operation: 40/20=2 Moving to Node #0,1,2 Current State: 17:[16, 20], Operations: ['2*10=20', '40-20=20'] Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 16+20=36, Resulting Numbers: [36] 36,17 unequal: No Solution Exploring Operation: 16*20=320, Resulting Numbers: [320] 320,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[20, 24], Operations: ['2*10=20', '40-16=24'] Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,17 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,17 unequal: No Solution Moving to Node #0,1,3 Current State: 17:[16, 2], Operations: ['2*10=20', '40/20=2'] Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,17 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,17 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[40, 4], Operations: ['2*10=20', '20-16=4'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,17 unequal: No Solution Exploring Operation: 40+4=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 40*4=160, Resulting Numbers: [160] 160,17 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[10, 16, 38], Operations: ['40-2=38'] Exploring Operation: 10+16=26, Resulting Numbers: [38, 26] Generated Node #0,0,0: 17:[38, 26] Operation: 10+16=26 Exploring Operation: 16-10=6, Resulting Numbers: [38, 6] Generated Node #0,0,1: 17:[38, 6] Operation: 16-10=6 Exploring Operation: 38-10=28, Resulting Numbers: [16, 28] Generated Node #0,0,2: 17:[16, 28] Operation: 38-10=28 Exploring Operation: 38-16=22, Resulting Numbers: [10, 22] Generated Node #0,0,3: 17:[10, 22] Operation: 38-16=22 Moving to Node #0,0,2 Current State: 17:[16, 28], Operations: ['40-2=38', '38-10=28'] Exploring Operation: 16+28=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 16*28=448, Resulting Numbers: [448] 448,17 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,17 unequal: No Solution Moving to Node #0,0,3 Current State: 17:[10, 22], Operations: ['40-2=38', '38-16=22'] Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 10*22=220, Resulting Numbers: [220] 220,17 unequal: No Solution Exploring Operation: 10+22=32, Resulting Numbers: [32] 32,17 unequal: No Solution Moving to Node #0,0,0 Current State: 17:[38, 26], Operations: ['40-2=38', '10+16=26'] Exploring Operation: 38*26=988, Resulting Numbers: [988] 988,17 unequal: No Solution Exploring Operation: 38+26=64, Resulting Numbers: [64] 64,17 unequal: No Solution Exploring Operation: 38-26=12, Resulting Numbers: [12] 12,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[38, 6], Operations: ['40-2=38', '16-10=6'] Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,17 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,17 unequal: No Solution Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 17:[40, 16, 12], Operations: ['2+10=12'] Exploring Operation: 40-12=28, Resulting Numbers: [16, 28] Generated Node #0,3,0: 17:[16, 28] Operation: 40-12=28 Exploring Operation: 16+12=28, Resulting Numbers: [40, 28] Generated Node #0,3,1: 17:[40, 28] Operation: 16+12=28 Exploring Operation: 40-16=24, Resulting Numbers: [12, 24] Generated Node #0,3,2: 17:[12, 24] Operation: 40-16=24 Exploring Operation: 40+12=52, Resulting Numbers: [16, 52] Generated Node #0,3,3: 17:[16, 52] Operation: 40+12=52 Moving to Node #0,3,0 Current State: 17:[16, 28], Operations: ['2+10=12', '40-12=28'] Exploring Operation: 16+28=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 16*28=448, Resulting Numbers: [448] 448,17 unequal: No Solution Moving to Node #0,3,2 Current State: 17:[12, 24], Operations: ['2+10=12', '40-16=24'] Exploring Operation: 12*24=288, Resulting Numbers: [288] 288,17 unequal: No Solution Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 12+24=36, Resulting Numbers: [36] 36,17 unequal: No Solution Moving to Node #0,3,1 Current State: 17:[40, 28], Operations: ['2+10=12', '16+12=28'] Exploring Operation: 40+28=68, Resulting Numbers: [68] 68,17 unequal: No Solution Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 40*28=1120, Resulting Numbers: [1120] 1120,17 unequal: No Solution Moving to Node #0,3,3 Current State: 17:[16, 52], Operations: ['2+10=12', '40+12=52'] Exploring Operation: 16+52=68, Resulting Numbers: [68] 68,17 unequal: No Solution Exploring Operation: 16*52=832, Resulting Numbers: [832] 832,17 unequal: No Solution Exploring Operation: 52-16=36, Resulting Numbers: [36] 36,17 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
[ 8, 72, 91, 71 ]
82
[ "8+72=80", "91+71=162", "162-80=82" ]
Current State: 82:[8, 72, 91, 71], Operations: [] Exploring Operation: 8+72=80, Resulting Numbers: [91, 71, 80] Generated Node #2: [91, 71, 80] from Operation: 8+72=80 Current State: 82:[91, 71, 80], Operations: ['8+72=80'] Exploring Operation: 91+71=162, Resulting Numbers: [80, 162] Generated Node #3: [80, 162] from Operation: 91+71=162 Current State: 82:[80, 162], Operations: ['8+72=80', '91+71=162'] Exploring Operation: 162-80=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[8, 72, 91, 71], Operations: [] Exploring Operation: 72-71=1, Resulting Numbers: [8, 91, 1] Generated Node #0,0: 82:[8, 91, 1] Operation: 72-71=1 Exploring Operation: 91-8=83, Resulting Numbers: [72, 71, 83] Generated Node #0,1: 82:[72, 71, 83] Operation: 91-8=83 Exploring Operation: 8+71=79, Resulting Numbers: [72, 91, 79] Generated Node #0,2: 82:[72, 91, 79] Operation: 8+71=79 Exploring Operation: 8+72=80, Resulting Numbers: [91, 71, 80] Generated Node #0,3: 82:[91, 71, 80] Operation: 8+72=80 Moving to Node #0,0 Current State: 82:[8, 91, 1], Operations: ['72-71=1'] Exploring Operation: 8-1=7, Resulting Numbers: [91, 7] Generated Node #0,0,0: 82:[91, 7] Operation: 8-1=7 Exploring Operation: 91-8=83, Resulting Numbers: [1, 83] Generated Node #0,0,1: 82:[1, 83] Operation: 91-8=83 Exploring Operation: 8*1=8, Resulting Numbers: [91, 8] Generated Node #0,0,2: 82:[91, 8] Operation: 8*1=8 Exploring Operation: 91-1=90, Resulting Numbers: [8, 90] Generated Node #0,0,3: 82:[8, 90] Operation: 91-1=90 Moving to Node #0,2 Current State: 82:[72, 91, 79], Operations: ['8+71=79'] Exploring Operation: 79-72=7, Resulting Numbers: [91, 7] Generated Node #0,2,0: 82:[91, 7] Operation: 79-72=7 Exploring Operation: 72+79=151, Resulting Numbers: [91, 151] Generated Node #0,2,1: 82:[91, 151] Operation: 72+79=151 Exploring Operation: 91-79=12, Resulting Numbers: [72, 12] Generated Node #0,2,2: 82:[72, 12] Operation: 91-79=12 Exploring Operation: 91-72=19, Resulting Numbers: [79, 19] Generated Node #0,2,3: 82:[79, 19] Operation: 91-72=19 Moving to Node #0,1 Current State: 82:[72, 71, 83], Operations: ['91-8=83'] Exploring Operation: 83-72=11, Resulting Numbers: [71, 11] Generated Node #0,1,0: 82:[71, 11] Operation: 83-72=11 Exploring Operation: 72+71=143, Resulting Numbers: [83, 143] Generated Node #0,1,1: 82:[83, 143] Operation: 72+71=143 Exploring Operation: 83-71=12, Resulting Numbers: [72, 12] Generated Node #0,1,2: 82:[72, 12] Operation: 83-71=12 Exploring Operation: 72-71=1, Resulting Numbers: [83, 1] Generated Node #0,1,3: 82:[83, 1] Operation: 72-71=1 Moving to Node #0,3 Current State: 82:[91, 71, 80], Operations: ['8+72=80'] Exploring Operation: 91-71=20, Resulting Numbers: [80, 20] Generated Node #0,3,0: 82:[80, 20] Operation: 91-71=20 Exploring Operation: 71+80=151, Resulting Numbers: [91, 151] Generated Node #0,3,1: 82:[91, 151] Operation: 71+80=151 Exploring Operation: 91-80=11, Resulting Numbers: [71, 11] Generated Node #0,3,2: 82:[71, 11] Operation: 91-80=11 Exploring Operation: 80-71=9, Resulting Numbers: [91, 9] Generated Node #0,3,3: 82:[91, 9] Operation: 80-71=9 Moving to Node #0,0,1 Current State: 82:[1, 83], Operations: ['72-71=1', '91-8=83'] Exploring Operation: 83/1=83, Resulting Numbers: [83] 83,82 unequal: No Solution Exploring Operation: 1+83=84, Resulting Numbers: [84] 84,82 unequal: No Solution Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[8, 72, 91, 71], Operations: [] Exploring Operation: 72-71=1, Resulting Numbers: [8, 91, 1] Generated Node #0,0: 82:[8, 91, 1] Operation: 72-71=1 Moving to Node #0,0 Current State: 82:[8, 91, 1], Operations: ['72-71=1'] Exploring Operation: 91-8=83, Resulting Numbers: [1, 83] Generated Node #0,0,1: 82:[1, 83] Operation: 91-8=83 Moving to Node #0,0,1 Current State: 82:[1, 83], Operations: ['72-71=1', '91-8=83'] Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.976563
hs_4
mult_heuristic
[ 39, 13, 59, 75 ]
48
[ "39/13=3", "75-59=16", "3*16=48" ]
Current State: 48:[39, 13, 59, 75], Operations: [] Exploring Operation: 39/13=3, Resulting Numbers: [59, 75, 3] Generated Node #2: [59, 75, 3] from Operation: 39/13=3 Current State: 48:[59, 75, 3], Operations: ['39/13=3'] Exploring Operation: 75-59=16, Resulting Numbers: [3, 16] Generated Node #3: [3, 16] from Operation: 75-59=16 Current State: 48:[3, 16], Operations: ['39/13=3', '75-59=16'] Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[39, 13, 59, 75], Operations: [] Exploring Operation: 75-59=16, Resulting Numbers: [39, 13, 16] Generated Node #0,0: 48:[39, 13, 16] Operation: 75-59=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[39, 13, 16], Operations: ['75-59=16'] Exploring Operation: 39/13=3, Resulting Numbers: [16, 3] Generated Node #0,0,0: 48:[16, 3] Operation: 39/13=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[16, 3], Operations: ['75-59=16', '39/13=3'] Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[39, 13, 59, 75], Operations: [] Exploring Operation: 75-59=16, Resulting Numbers: [39, 13, 16] Generated Node #0,0: 48:[39, 13, 16] Operation: 75-59=16 Moving to Node #0,0 Current State: 48:[39, 13, 16], Operations: ['75-59=16'] Exploring Operation: 39/13=3, Resulting Numbers: [16, 3] Generated Node #0,0,0: 48:[16, 3] Operation: 39/13=3 Moving to Node #0,0,0 Current State: 48:[16, 3], Operations: ['75-59=16', '39/13=3'] Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 56, 68, 68, 17 ]
38
[ "56-17=39", "68/68=1", "39-1=38" ]
Current State: 38:[56, 68, 68, 17], Operations: [] Exploring Operation: 56-17=39, Resulting Numbers: [68, 68, 39] Generated Node #2: [68, 68, 39] from Operation: 56-17=39 Current State: 38:[68, 68, 39], Operations: ['56-17=39'] Exploring Operation: 68/68=1, Resulting Numbers: [39, 1] Generated Node #3: [39, 1] from Operation: 68/68=1 Current State: 38:[39, 1], Operations: ['56-17=39', '68/68=1'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[56, 68, 68, 17], Operations: [] Exploring Operation: 68-56=12, Resulting Numbers: [68, 17, 12] Generated Node #0,0: 38:[68, 17, 12] Operation: 68-56=12 Exploring Operation: 68-56=12, Resulting Numbers: [68, 17, 12] Generated Node #0,1: 38:[68, 17, 12] Operation: 68-56=12 Exploring Operation: 68/68=1, Resulting Numbers: [56, 17, 1] Generated Node #0,2: 38:[56, 17, 1] Operation: 68/68=1 Exploring Operation: 68-68=0, Resulting Numbers: [56, 17, 0] Generated Node #0,3: 38:[56, 17, 0] Operation: 68-68=0 Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[56, 17, 1], Operations: ['68/68=1'] Exploring Operation: 56-17=39, Resulting Numbers: [1, 39] Generated Node #0,2,0: 38:[1, 39] Operation: 56-17=39 Exploring Operation: 56*1=56, Resulting Numbers: [17, 56] Generated Node #0,2,1: 38:[17, 56] Operation: 56*1=56 Exploring Operation: 56-1=55, Resulting Numbers: [17, 55] Generated Node #0,2,2: 38:[17, 55] Operation: 56-1=55 Exploring Operation: 17+1=18, Resulting Numbers: [56, 18] Generated Node #0,2,3: 38:[56, 18] Operation: 17+1=18 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 38:[1, 39], Operations: ['68/68=1', '56-17=39'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,38 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[56, 68, 68, 17], Operations: [] Exploring Operation: 68/68=1, Resulting Numbers: [56, 17, 1] Generated Node #0,2: 38:[56, 17, 1] Operation: 68/68=1 Moving to Node #0,2 Current State: 38:[56, 17, 1], Operations: ['68/68=1'] Exploring Operation: 56-17=39, Resulting Numbers: [1, 39] Generated Node #0,2,0: 38:[1, 39] Operation: 56-17=39 Moving to Node #0,2,0 Current State: 38:[1, 39], Operations: ['68/68=1', '56-17=39'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 79, 5, 36, 61 ]
40
[ "79+61=140", "5*36=180", "180-140=40" ]
Current State: 40:[79, 5, 36, 61], Operations: [] Exploring Operation: 79+61=140, Resulting Numbers: [5, 36, 140] Generated Node #2: [5, 36, 140] from Operation: 79+61=140 Current State: 40:[5, 36, 140], Operations: ['79+61=140'] Exploring Operation: 5*36=180, Resulting Numbers: [140, 180] Generated Node #3: [140, 180] from Operation: 5*36=180 Current State: 40:[140, 180], Operations: ['79+61=140', '5*36=180'] Exploring Operation: 180-140=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[79, 5, 36, 61], Operations: [] Exploring Operation: 79-36=43, Resulting Numbers: [5, 61, 43] Generated Node #0,0: 40:[5, 61, 43] Operation: 79-36=43 Exploring Operation: 61-36=25, Resulting Numbers: [79, 5, 25] Generated Node #0,1: 40:[79, 5, 25] Operation: 61-36=25 Exploring Operation: 79-61=18, Resulting Numbers: [5, 36, 18] Generated Node #0,2: 40:[5, 36, 18] Operation: 79-61=18 Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[5, 36, 18], Operations: ['79-61=18'] Exploring Operation: 36/18=2, Resulting Numbers: [5, 2] Generated Node #0,2,0: 40:[5, 2] Operation: 36/18=2 Exploring Operation: 5+36=41, Resulting Numbers: [18, 41] Generated Node #0,2,1: 40:[18, 41] Operation: 5+36=41 Exploring Operation: 36-18=18, Resulting Numbers: [5, 18] Generated Node #0,2,2: 40:[5, 18] Operation: 36-18=18 Moving to Node #0,2,0 Current State: 40:[5, 2], Operations: ['79-61=18', '36/18=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,40 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,40 unequal: No Solution Moving to Node #0,2,2 Current State: 40:[5, 18], Operations: ['79-61=18', '36-18=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,40 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,40 unequal: No Solution Moving to Node #0,2,1 Current State: 40:[18, 41], Operations: ['79-61=18', '5+36=41'] Exploring Operation: 41-18=23, Resulting Numbers: [23] 23,40 unequal: No Solution Exploring Operation: 18+41=59, Resulting Numbers: [59] 59,40 unequal: No Solution Exploring Operation: 18*41=738, Resulting Numbers: [738] 738,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[5, 61, 43], Operations: ['79-36=43'] Exploring Operation: 61-5=56, Resulting Numbers: [43, 56] Generated Node #0,0,0: 40:[43, 56] Operation: 61-5=56 Exploring Operation: 43-5=38, Resulting Numbers: [61, 38] Generated Node #0,0,1: 40:[61, 38] Operation: 43-5=38 Exploring Operation: 61-43=18, Resulting Numbers: [5, 18] Generated Node #0,0,2: 40:[5, 18] Operation: 61-43=18 Moving to Node #0,0,2 Current State: 40:[5, 18], Operations: ['79-36=43', '61-43=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,40 unequal: No Solution Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,40 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,40 unequal: No Solution Moving to Node #0,0,0 Current State: 40:[43, 56], Operations: ['79-36=43', '61-5=56'] Exploring Operation: 43*56=2408, Resulting Numbers: [2408] 2408,40 unequal: No Solution Exploring Operation: 43+56=99, Resulting Numbers: [99] 99,40 unequal: No Solution Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[61, 38], Operations: ['79-36=43', '43-5=38'] Exploring Operation: 61-38=23, Resulting Numbers: [23] 23,40 unequal: No Solution Exploring Operation: 61+38=99, Resulting Numbers: [99] 99,40 unequal: No Solution Exploring Operation: 61*38=2318, Resulting Numbers: [2318] 2318,40 unequal: No Solution No 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: 40:[79, 5, 25], Operations: ['61-36=25'] Exploring Operation: 79-25=54, Resulting Numbers: [5, 54] Generated Node #0,1,0: 40:[5, 54] Operation: 79-25=54 Exploring Operation: 25-5=20, Resulting Numbers: [79, 20] Generated Node #0,1,1: 40:[79, 20] Operation: 25-5=20 Exploring Operation: 79-5=74, Resulting Numbers: [25, 74] Generated Node #0,1,2: 40:[25, 74] Operation: 79-5=74 Moving to Node #0,1,0 Current State: 40:[5, 54], Operations: ['61-36=25', '79-25=54'] Exploring Operation: 5*54=270, Resulting Numbers: [270] 270,40 unequal: No Solution Exploring Operation: 5+54=59, Resulting Numbers: [59] 59,40 unequal: No Solution Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,40 unequal: No Solution Moving to Node #0,1,1 Current State: 40:[79, 20], Operations: ['61-36=25', '25-5=20'] Exploring Operation: 79*20=1580, Resulting Numbers: [1580] 1580,40 unequal: No Solution Exploring Operation: 79+20=99, Resulting Numbers: [99] 99,40 unequal: No Solution Exploring Operation: 79-20=59, Resulting Numbers: [59] 59,40 unequal: No Solution Moving to Node #0,1,2 Current State: 40:[25, 74], Operations: ['61-36=25', '79-5=74'] Exploring Operation: 25+74=99, Resulting Numbers: [99] 99,40 unequal: No Solution Exploring Operation: 74-25=49, Resulting Numbers: [49] 49,40 unequal: No Solution Exploring Operation: 25*74=1850, Resulting Numbers: [1850] 1850,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 17, 39, 52, 13 ]
15
[ "39-13=26", "52/26=2", "17-2=15" ]
Current State: 15:[17, 39, 52, 13], Operations: [] Exploring Operation: 39-13=26, Resulting Numbers: [17, 52, 26] Generated Node #2: [17, 52, 26] from Operation: 39-13=26 Current State: 15:[17, 52, 26], Operations: ['39-13=26'] Exploring Operation: 52/26=2, Resulting Numbers: [17, 2] Generated Node #3: [17, 2] from Operation: 52/26=2 Current State: 15:[17, 2], Operations: ['39-13=26', '52/26=2'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[17, 39, 52, 13], Operations: [] Exploring Operation: 52-39=13, Resulting Numbers: [17, 13, 13] Generated Node #0,0: 15:[17, 13, 13] Operation: 52-39=13 Exploring Operation: 52/13=4, Resulting Numbers: [17, 39, 4] Generated Node #0,1: 15:[17, 39, 4] Operation: 52/13=4 Exploring Operation: 39/13=3, Resulting Numbers: [17, 52, 3] Generated Node #0,2: 15:[17, 52, 3] Operation: 39/13=3 Moving to Node #0,0 Current State: 15:[17, 13, 13], Operations: ['52-39=13'] Exploring Operation: 17-13=4, Resulting Numbers: [13, 4] Generated Node #0,0,0: 15:[13, 4] Operation: 17-13=4 Exploring Operation: 13/13=1, Resulting Numbers: [17, 1] Generated Node #0,0,1: 15:[17, 1] Operation: 13/13=1 Exploring Operation: 17-13=4, Resulting Numbers: [13, 4] Generated Node #0,0,2: 15:[13, 4] Operation: 17-13=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[13, 4], Operations: ['52-39=13', '17-13=4'] Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,15 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 15:[13, 4], Operations: ['52-39=13', '17-13=4'] Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,15 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 15:[17, 1], Operations: ['52-39=13', '13/13=1'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,15 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 15:[17, 39, 4], Operations: ['52/13=4'] Exploring Operation: 39-17=22, Resulting Numbers: [4, 22] Generated Node #0,1,0: 15:[4, 22] Operation: 39-17=22 Exploring Operation: 17-4=13, Resulting Numbers: [39, 13] Generated Node #0,1,1: 15:[39, 13] Operation: 17-4=13 Exploring Operation: 39-4=35, Resulting Numbers: [17, 35] Generated Node #0,1,2: 15:[17, 35] Operation: 39-4=35 Moving to Node #0,2 Current State: 15:[17, 52, 3], Operations: ['39/13=3'] Exploring Operation: 17-3=14, Resulting Numbers: [52, 14] Generated Node #0,2,0: 15:[52, 14] Operation: 17-3=14 Exploring Operation: 52-3=49, Resulting Numbers: [17, 49] Generated Node #0,2,1: 15:[17, 49] Operation: 52-3=49 Exploring Operation: 52-17=35, Resulting Numbers: [3, 35] Generated Node #0,2,2: 15:[3, 35] Operation: 52-17=35 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 15:[3, 35], Operations: ['39/13=3', '52-17=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,15 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 15:[17, 49], Operations: ['39/13=3', '52-3=49'] Exploring Operation: 17*49=833, Resulting Numbers: [833] 833,15 unequal: No Solution Exploring Operation: 49-17=32, Resulting Numbers: [32] 32,15 unequal: No Solution Exploring Operation: 17+49=66, Resulting Numbers: [66] 66,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 15:[52, 14], Operations: ['39/13=3', '17-3=14'] Exploring Operation: 52+14=66, Resulting Numbers: [66] 66,15 unequal: No Solution Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 52*14=728, Resulting Numbers: [728] 728,15 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: 15:[4, 22], Operations: ['52/13=4', '39-17=22'] Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,15 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,15 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[17, 35], Operations: ['52/13=4', '39-4=35'] Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 17+35=52, Resulting Numbers: [52] 52,15 unequal: No Solution Exploring Operation: 17*35=595, Resulting Numbers: [595] 595,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[39, 13], Operations: ['52/13=4', '17-4=13'] Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,15 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,15 unequal: No Solution Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,15 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 81, 73, 30, 62 ]
84
[ "81-73=8", "30+62=92", "92-8=84" ]
Current State: 84:[81, 73, 30, 62], Operations: [] Exploring Operation: 81-73=8, Resulting Numbers: [30, 62, 8] Generated Node #2: [30, 62, 8] from Operation: 81-73=8 Current State: 84:[30, 62, 8], Operations: ['81-73=8'] Exploring Operation: 30+62=92, Resulting Numbers: [8, 92] Generated Node #3: [8, 92] from Operation: 30+62=92 Current State: 84:[8, 92], Operations: ['81-73=8', '30+62=92'] Exploring Operation: 92-8=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[81, 73, 30, 62], Operations: [] Exploring Operation: 73-62=11, Resulting Numbers: [81, 30, 11] Generated Node #0,0: 84:[81, 30, 11] Operation: 73-62=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[81, 30, 11], Operations: ['73-62=11'] Exploring Operation: 30+11=41, Resulting Numbers: [81, 41] Generated Node #0,0,0: 84:[81, 41] Operation: 30+11=41 Moving to Node #0,0,0 Current State: 84:[81, 41], Operations: ['73-62=11', '30+11=41'] Exploring Operation: 81-41=40, Resulting Numbers: [40] 40,84 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
[ 81, 28, 7, 75 ]
28
[ "81-7=74", "75-74=1", "28*1=28" ]
Current State: 28:[81, 28, 7, 75], Operations: [] Exploring Operation: 81-7=74, Resulting Numbers: [28, 75, 74] Generated Node #2: [28, 75, 74] from Operation: 81-7=74 Current State: 28:[28, 75, 74], Operations: ['81-7=74'] Exploring Operation: 75-74=1, Resulting Numbers: [28, 1] Generated Node #3: [28, 1] from Operation: 75-74=1 Current State: 28:[28, 1], Operations: ['81-7=74', '75-74=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[81, 28, 7, 75], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [28, 7, 6] Generated Node #0,0: 28:[28, 7, 6] Operation: 81-75=6 Exploring Operation: 81-28=53, Resulting Numbers: [7, 75, 53] Generated Node #0,1: 28:[7, 75, 53] Operation: 81-28=53 Exploring Operation: 75-28=47, Resulting Numbers: [81, 7, 47] Generated Node #0,2: 28:[81, 7, 47] Operation: 75-28=47 Exploring Operation: 75-7=68, Resulting Numbers: [81, 28, 68] Generated Node #0,3: 28:[81, 28, 68] Operation: 75-7=68 Exploring Operation: 81-7=74, Resulting Numbers: [28, 75, 74] Generated Node #0,4: 28:[28, 75, 74] Operation: 81-7=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[28, 7, 6], Operations: ['81-75=6'] Exploring Operation: 28/7=4, Resulting Numbers: [6, 4] Generated Node #0,0,0: 28:[6, 4] Operation: 28/7=4 Exploring Operation: 7-6=1, Resulting Numbers: [28, 1] Generated Node #0,0,1: 28:[28, 1] Operation: 7-6=1 Exploring Operation: 28+6=34, Resulting Numbers: [7, 34] Generated Node #0,0,2: 28:[7, 34] Operation: 28+6=34 Exploring Operation: 28-6=22, Resulting Numbers: [7, 22] Generated Node #0,0,3: 28:[7, 22] Operation: 28-6=22 Exploring Operation: 7+6=13, Resulting Numbers: [28, 13] Generated Node #0,0,4: 28:[28, 13] Operation: 7+6=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[6, 4], Operations: ['81-75=6', '28/7=4'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,28 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,28 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:[28, 1], Operations: ['81-75=6', '7-6=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[81, 28, 7, 75], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [28, 7, 6] Generated Node #0,0: 28:[28, 7, 6] Operation: 81-75=6 Moving to Node #0,0 Current State: 28:[28, 7, 6], Operations: ['81-75=6'] Exploring Operation: 7-6=1, Resulting Numbers: [28, 1] Generated Node #0,0,1: 28:[28, 1] Operation: 7-6=1 Moving to Node #0,0,1 Current State: 28:[28, 1], Operations: ['81-75=6', '7-6=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 35, 87, 16, 7 ]
99
[ "35+87=122", "16+7=23", "122-23=99" ]
Current State: 99:[35, 87, 16, 7], Operations: [] Exploring Operation: 35+87=122, Resulting Numbers: [16, 7, 122] Generated Node #2: [16, 7, 122] from Operation: 35+87=122 Current State: 99:[16, 7, 122], Operations: ['35+87=122'] Exploring Operation: 16+7=23, Resulting Numbers: [122, 23] Generated Node #3: [122, 23] from Operation: 16+7=23 Current State: 99:[122, 23], Operations: ['35+87=122', '16+7=23'] Exploring Operation: 122-23=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[35, 87, 16, 7], Operations: [] Exploring Operation: 35/7=5, Resulting Numbers: [87, 16, 5] Generated Node #0,0: 99:[87, 16, 5] Operation: 35/7=5 Exploring Operation: 87+7=94, Resulting Numbers: [35, 16, 94] Generated Node #0,1: 99:[35, 16, 94] Operation: 87+7=94 Exploring Operation: 16-7=9, Resulting Numbers: [35, 87, 9] Generated Node #0,2: 99:[35, 87, 9] Operation: 16-7=9 Exploring Operation: 87+16=103, Resulting Numbers: [35, 7, 103] Generated Node #0,3: 99:[35, 7, 103] Operation: 87+16=103 Start Sub Search at level 1: Moving to Node #0,3 Current State: 99:[35, 7, 103], Operations: ['87+16=103'] Exploring Operation: 35/7=5, Resulting Numbers: [103, 5] Generated Node #0,3,0: 99:[103, 5] Operation: 35/7=5 Exploring Operation: 35-7=28, Resulting Numbers: [103, 28] Generated Node #0,3,1: 99:[103, 28] Operation: 35-7=28 Exploring Operation: 35+7=42, Resulting Numbers: [103, 42] Generated Node #0,3,2: 99:[103, 42] Operation: 35+7=42 Exploring Operation: 103-7=96, Resulting Numbers: [35, 96] Generated Node #0,3,3: 99:[35, 96] Operation: 103-7=96 Moving to Node #0,3,3 Current State: 99:[35, 96], Operations: ['87+16=103', '103-7=96'] Exploring Operation: 35+96=131, Resulting Numbers: [131] 131,99 unequal: No Solution Exploring Operation: 35*96=3360, Resulting Numbers: [3360] 3360,99 unequal: No Solution Exploring Operation: 96-35=61, Resulting Numbers: [61] 61,99 unequal: No Solution Moving to Node #0,3,0 Current State: 99:[103, 5], Operations: ['87+16=103', '35/7=5'] Exploring Operation: 103-5=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 103*5=515, Resulting Numbers: [515] 515,99 unequal: No Solution Exploring Operation: 103+5=108, Resulting Numbers: [108] 108,99 unequal: No Solution Moving to Node #0,3,1 Current State: 99:[103, 28], Operations: ['87+16=103', '35-7=28'] Exploring Operation: 103-28=75, Resulting Numbers: [75] 75,99 unequal: No Solution Exploring Operation: 103*28=2884, Resulting Numbers: [2884] 2884,99 unequal: No Solution Exploring Operation: 103+28=131, Resulting Numbers: [131] 131,99 unequal: No Solution Moving to Node #0,3,2 Current State: 99:[103, 42], Operations: ['87+16=103', '35+7=42'] Exploring Operation: 103+42=145, Resulting Numbers: [145] 145,99 unequal: No Solution Exploring Operation: 103-42=61, Resulting Numbers: [61] 61,99 unequal: No Solution Exploring Operation: 103*42=4326, Resulting Numbers: [4326] 4326,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[35, 16, 94], Operations: ['87+7=94'] Exploring Operation: 94-16=78, Resulting Numbers: [35, 78] Generated Node #0,1,0: 99:[35, 78] Operation: 94-16=78 Exploring Operation: 16+94=110, Resulting Numbers: [35, 110] Generated Node #0,1,1: 99:[35, 110] Operation: 16+94=110 Exploring Operation: 35+16=51, Resulting Numbers: [94, 51] Generated Node #0,1,2: 99:[94, 51] Operation: 35+16=51 Exploring Operation: 35-16=19, Resulting Numbers: [94, 19] Generated Node #0,1,3: 99:[94, 19] Operation: 35-16=19 Moving to Node #0,1,1 Current State: 99:[35, 110], Operations: ['87+7=94', '16+94=110'] Exploring Operation: 35*110=3850, Resulting Numbers: [3850] 3850,99 unequal: No Solution Exploring Operation: 110-35=75, Resulting Numbers: [75] 75,99 unequal: No Solution Exploring Operation: 35+110=145, Resulting Numbers: [145] 145,99 unequal: No Solution Moving to Node #0,1,3 Current State: 99:[94, 19], Operations: ['87+7=94', '35-16=19'] Exploring Operation: 94+19=113, Resulting Numbers: [113] 113,99 unequal: No Solution Exploring Operation: 94*19=1786, Resulting Numbers: [1786] 1786,99 unequal: No Solution Exploring Operation: 94-19=75, Resulting Numbers: [75] 75,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[94, 51], Operations: ['87+7=94', '35+16=51'] Exploring Operation: 94+51=145, Resulting Numbers: [145] 145,99 unequal: No Solution Exploring Operation: 94*51=4794, Resulting Numbers: [4794] 4794,99 unequal: No Solution Exploring Operation: 94-51=43, Resulting Numbers: [43] 43,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[35, 78], Operations: ['87+7=94', '94-16=78'] Exploring Operation: 35+78=113, Resulting Numbers: [113] 113,99 unequal: No Solution Exploring Operation: 35*78=2730, Resulting Numbers: [2730] 2730,99 unequal: No Solution Exploring Operation: 78-35=43, Resulting Numbers: [43] 43,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[35, 87, 9], Operations: ['16-7=9'] Exploring Operation: 35-9=26, Resulting Numbers: [87, 26] Generated Node #0,2,0: 99:[87, 26] Operation: 35-9=26 Exploring Operation: 87-35=52, Resulting Numbers: [9, 52] Generated Node #0,2,1: 99:[9, 52] Operation: 87-35=52 Exploring Operation: 35+87=122, Resulting Numbers: [9, 122] Generated Node #0,2,2: 99:[9, 122] Operation: 35+87=122 Exploring Operation: 87+9=96, Resulting Numbers: [35, 96] Generated Node #0,2,3: 99:[35, 96] Operation: 87+9=96 Moving to Node #0,2,3 Current State: 99:[35, 96], Operations: ['16-7=9', '87+9=96'] Exploring Operation: 35*96=3360, Resulting Numbers: [3360] 3360,99 unequal: No Solution Exploring Operation: 96-35=61, Resulting Numbers: [61] 61,99 unequal: No Solution Exploring Operation: 35+96=131, Resulting Numbers: [131] 131,99 unequal: No Solution Moving to Node #0,2,1 Current State: 99:[9, 52], Operations: ['16-7=9', '87-35=52'] Exploring Operation: 9+52=61, Resulting Numbers: [61] 61,99 unequal: No Solution Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,99 unequal: No Solution Exploring Operation: 9*52=468, Resulting Numbers: [468] 468,99 unequal: No Solution Moving to Node #0,2,0 Current State: 99:[87, 26], Operations: ['16-7=9', '35-9=26'] Exploring Operation: 87-26=61, Resulting Numbers: [61] 61,99 unequal: No Solution Exploring Operation: 87*26=2262, Resulting Numbers: [2262] 2262,99 unequal: No Solution Exploring Operation: 87+26=113, Resulting Numbers: [113] 113,99 unequal: No Solution Moving to Node #0,2,2 Current State: 99:[9, 122], Operations: ['16-7=9', '35+87=122'] Exploring Operation: 9+122=131, Resulting Numbers: [131] 131,99 unequal: No Solution Exploring Operation: 9*122=1098, Resulting Numbers: [1098] 1098,99 unequal: No Solution Exploring Operation: 122-9=113, Resulting Numbers: [113] 113,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[87, 16, 5], Operations: ['35/7=5'] Exploring Operation: 87+5=92, Resulting Numbers: [16, 92] Generated Node #0,0,0: 99:[16, 92] Operation: 87+5=92 Exploring Operation: 87+16=103, Resulting Numbers: [5, 103] Generated Node #0,0,1: 99:[5, 103] Operation: 87+16=103 Exploring Operation: 16-5=11, Resulting Numbers: [87, 11] Generated Node #0,0,2: 99:[87, 11] Operation: 16-5=11 Exploring Operation: 87-5=82, Resulting Numbers: [16, 82] Generated Node #0,0,3: 99:[16, 82] Operation: 87-5=82 Moving to Node #0,0,1 Current State: 99:[5, 103], Operations: ['35/7=5', '87+16=103'] Exploring Operation: 103-5=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 5+103=108, Resulting Numbers: [108] 108,99 unequal: No Solution Exploring Operation: 5*103=515, Resulting Numbers: [515] 515,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[87, 11], Operations: ['35/7=5', '16-5=11'] Exploring Operation: 87-11=76, Resulting Numbers: [76] 76,99 unequal: No Solution Exploring Operation: 87+11=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 87*11=957, Resulting Numbers: [957] 957,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[16, 92], Operations: ['35/7=5', '87+5=92'] Exploring Operation: 92-16=76, Resulting Numbers: [76] 76,99 unequal: No Solution Exploring Operation: 16*92=1472, Resulting Numbers: [1472] 1472,99 unequal: No Solution Exploring Operation: 16+92=108, Resulting Numbers: [108] 108,99 unequal: No Solution Moving to Node #0,0,3 Current State: 99:[16, 82], Operations: ['35/7=5', '87-5=82'] Exploring Operation: 16*82=1312, Resulting Numbers: [1312] 1312,99 unequal: No Solution Exploring Operation: 16+82=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 82-16=66, Resulting Numbers: [66] 66,99 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
[ 58, 81, 37, 63 ]
77
[ "81-58=23", "37+63=100", "100-23=77" ]
Current State: 77:[58, 81, 37, 63], Operations: [] Exploring Operation: 81-58=23, Resulting Numbers: [37, 63, 23] Generated Node #2: [37, 63, 23] from Operation: 81-58=23 Current State: 77:[37, 63, 23], Operations: ['81-58=23'] Exploring Operation: 37+63=100, Resulting Numbers: [23, 100] Generated Node #3: [23, 100] from Operation: 37+63=100 Current State: 77:[23, 100], Operations: ['81-58=23', '37+63=100'] Exploring Operation: 100-23=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[58, 81, 37, 63], Operations: [] Exploring Operation: 58-37=21, Resulting Numbers: [81, 63, 21] Generated Node #0,0: 77:[81, 63, 21] Operation: 58-37=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[81, 63, 21], Operations: ['58-37=21'] Exploring Operation: 63/21=3, Resulting Numbers: [81, 3] Generated Node #0,0,0: 77:[81, 3] Operation: 63/21=3 Moving to Node #0,0,0 Current State: 77:[81, 3], Operations: ['58-37=21', '63/21=3'] Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,77 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
[ 21, 68, 9, 18 ]
56
[ "68-21=47", "18-9=9", "47+9=56" ]
Current State: 56:[21, 68, 9, 18], Operations: [] Exploring Operation: 68-21=47, Resulting Numbers: [9, 18, 47] Generated Node #2: [9, 18, 47] from Operation: 68-21=47 Current State: 56:[9, 18, 47], Operations: ['68-21=47'] Exploring Operation: 18-9=9, Resulting Numbers: [47, 9] Generated Node #3: [47, 9] from Operation: 18-9=9 Current State: 56:[47, 9], Operations: ['68-21=47', '18-9=9'] Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[21, 68, 9, 18], Operations: [] Exploring Operation: 68-21=47, Resulting Numbers: [9, 18, 47] Generated Node #0,0: 56:[9, 18, 47] Operation: 68-21=47 Exploring Operation: 68-9=59, Resulting Numbers: [21, 18, 59] Generated Node #0,1: 56:[21, 18, 59] Operation: 68-9=59 Exploring Operation: 21+9=30, Resulting Numbers: [68, 18, 30] Generated Node #0,2: 56:[68, 18, 30] Operation: 21+9=30 Exploring Operation: 68-18=50, Resulting Numbers: [21, 9, 50] Generated Node #0,3: 56:[21, 9, 50] Operation: 68-18=50 Exploring Operation: 21-18=3, Resulting Numbers: [68, 9, 3] Generated Node #0,4: 56:[68, 9, 3] Operation: 21-18=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[9, 18, 47], Operations: ['68-21=47'] Exploring Operation: 18-9=9, Resulting Numbers: [47, 9] Generated Node #0,0,0: 56:[47, 9] Operation: 18-9=9 Exploring Operation: 18/9=2, Resulting Numbers: [47, 2] Generated Node #0,0,1: 56:[47, 2] Operation: 18/9=2 Exploring Operation: 9+18=27, Resulting Numbers: [47, 27] Generated Node #0,0,2: 56:[47, 27] Operation: 9+18=27 Exploring Operation: 47-18=29, Resulting Numbers: [9, 29] Generated Node #0,0,3: 56:[9, 29] Operation: 47-18=29 Exploring Operation: 9+47=56, Resulting Numbers: [18, 56] Generated Node #0,0,4: 56:[18, 56] Operation: 9+47=56 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 56:[9, 29], Operations: ['68-21=47', '47-18=29'] Exploring Operation: 9*29=261, Resulting Numbers: [261] 261,56 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 56:[18, 56], Operations: ['68-21=47', '9+47=56'] Exploring Operation: 18+56=74, Resulting Numbers: [74] 74,56 unequal: No Solution Exploring Operation: 56-18=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 18*56=1008, Resulting Numbers: [1008] 1008,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 56:[47, 2], Operations: ['68-21=47', '18/9=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,56 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,56 unequal: No Solution Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[47, 9], Operations: ['68-21=47', '18-9=9'] Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[21, 68, 9, 18], Operations: [] Exploring Operation: 68-21=47, Resulting Numbers: [9, 18, 47] Generated Node #0,0: 56:[9, 18, 47] Operation: 68-21=47 Moving to Node #0,0 Current State: 56:[9, 18, 47], Operations: ['68-21=47'] Exploring Operation: 18-9=9, Resulting Numbers: [47, 9] Generated Node #0,0,0: 56:[47, 9] Operation: 18-9=9 Moving to Node #0,0,0 Current State: 56:[47, 9], Operations: ['68-21=47', '18-9=9'] Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_5
mult_heuristic
[ 90, 30, 28, 20 ]
96
[ "90*28=2520", "2520/20=126", "126-30=96" ]
Current State: 96:[90, 30, 28, 20], Operations: [] Exploring Operation: 90*28=2520, Resulting Numbers: [30, 20, 2520] Generated Node #2: [30, 20, 2520] from Operation: 90*28=2520 Current State: 96:[30, 20, 2520], Operations: ['90*28=2520'] Exploring Operation: 2520/20=126, Resulting Numbers: [30, 126] Generated Node #3: [30, 126] from Operation: 2520/20=126 Current State: 96:[30, 126], Operations: ['90*28=2520', '2520/20=126'] Exploring Operation: 126-30=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[90, 30, 28, 20], Operations: [] Exploring Operation: 90/30=3, Resulting Numbers: [28, 20, 3] Generated Node #0,0: 96:[28, 20, 3] Operation: 90/30=3 Exploring Operation: 28+20=48, Resulting Numbers: [90, 30, 48] Generated Node #0,1: 96:[90, 30, 48] Operation: 28+20=48 Exploring Operation: 30-28=2, Resulting Numbers: [90, 20, 2] Generated Node #0,2: 96:[90, 20, 2] Operation: 30-28=2 Exploring Operation: 28-20=8, Resulting Numbers: [90, 30, 8] Generated Node #0,3: 96:[90, 30, 8] Operation: 28-20=8 Exploring Operation: 30+20=50, Resulting Numbers: [90, 28, 50] Generated Node #0,4: 96:[90, 28, 50] Operation: 30+20=50 Moving to Node #0,0 Current State: 96:[28, 20, 3], Operations: ['90/30=3'] Exploring Operation: 28+3=31, Resulting Numbers: [20, 31] Generated Node #0,0,0: 96:[20, 31] Operation: 28+3=31 Exploring Operation: 28-20=8, Resulting Numbers: [3, 8] Generated Node #0,0,1: 96:[3, 8] Operation: 28-20=8 Exploring Operation: 20+3=23, Resulting Numbers: [28, 23] Generated Node #0,0,2: 96:[28, 23] Operation: 20+3=23 Exploring Operation: 28-3=25, Resulting Numbers: [20, 25] Generated Node #0,0,3: 96:[20, 25] Operation: 28-3=25 Exploring Operation: 28+20=48, Resulting Numbers: [3, 48] Generated Node #0,0,4: 96:[3, 48] Operation: 28+20=48 Moving to Node #0,3 Current State: 96:[90, 30, 8], Operations: ['28-20=8'] Exploring Operation: 30+8=38, Resulting Numbers: [90, 38] Generated Node #0,3,0: 96:[90, 38] Operation: 30+8=38 Exploring Operation: 90-30=60, Resulting Numbers: [8, 60] Generated Node #0,3,1: 96:[8, 60] Operation: 90-30=60 Exploring Operation: 90+8=98, Resulting Numbers: [30, 98] Generated Node #0,3,2: 96:[30, 98] Operation: 90+8=98 Exploring Operation: 30-8=22, Resulting Numbers: [90, 22] Generated Node #0,3,3: 96:[90, 22] Operation: 30-8=22 Exploring Operation: 90/30=3, Resulting Numbers: [8, 3] Generated Node #0,3,4: 96:[8, 3] Operation: 90/30=3 Moving to Node #0,1 Current State: 96:[90, 30, 48], Operations: ['28+20=48'] Exploring Operation: 90-48=42, Resulting Numbers: [30, 42] Generated Node #0,1,0: 96:[30, 42] Operation: 90-48=42 Exploring Operation: 90-30=60, Resulting Numbers: [48, 60] Generated Node #0,1,1: 96:[48, 60] Operation: 90-30=60 Exploring Operation: 90+30=120, Resulting Numbers: [48, 120] Generated Node #0,1,2: 96:[48, 120] Operation: 90+30=120 Exploring Operation: 90/30=3, Resulting Numbers: [48, 3] Generated Node #0,1,3: 96:[48, 3] Operation: 90/30=3 Exploring Operation: 48-30=18, Resulting Numbers: [90, 18] Generated Node #0,1,4: 96:[90, 18] Operation: 48-30=18 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 96:[48, 3], Operations: ['28+20=48', '90/30=3'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,96 unequal: No Solution Exploring Operation: 48*3=144, Resulting Numbers: [144] 144,96 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,96 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 #0,1,0 Current State: 96:[30, 42], Operations: ['28+20=48', '90-48=42'] Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 30*42=1260, Resulting Numbers: [1260] 1260,96 unequal: No Solution Exploring Operation: 30+42=72, Resulting Numbers: [72] 72,96 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 #0,1,4 Current State: 96:[90, 18], Operations: ['28+20=48', '48-30=18'] Exploring Operation: 90+18=108, Resulting Numbers: [108] 108,96 unequal: No Solution Exploring Operation: 90*18=1620, Resulting Numbers: [1620] 1620,96 unequal: No Solution Exploring Operation: 90-18=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 90/18=5, Resulting Numbers: [5] 5,96 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 #0,1,1 Current State: 96:[48, 60], Operations: ['28+20=48', '90-30=60'] Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,96 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,96 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 #0,1,2 Current State: 96:[48, 120], Operations: ['28+20=48', '90+30=120'] Exploring Operation: 48+120=168, Resulting Numbers: [168] 168,96 unequal: No Solution Exploring Operation: 120-48=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 48*120=5760, Resulting Numbers: [5760] 5760,96 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: 96:[90, 20, 2], Operations: ['30-28=2'] Exploring Operation: 90+2=92, Resulting Numbers: [20, 92] Generated Node #0,2,0: 96:[20, 92] Operation: 90+2=92 Exploring Operation: 20-2=18, Resulting Numbers: [90, 18] Generated Node #0,2,1: 96:[90, 18] Operation: 20-2=18 Exploring Operation: 20+2=22, Resulting Numbers: [90, 22] Generated Node #0,2,2: 96:[90, 22] Operation: 20+2=22 Exploring Operation: 20/2=10, Resulting Numbers: [90, 10] Generated Node #0,2,3: 96:[90, 10] Operation: 20/2=10 Exploring Operation: 90/2=45, Resulting Numbers: [20, 45] Generated Node #0,2,4: 96:[20, 45] Operation: 90/2=45 Moving to Node #0,4 Current State: 96:[90, 28, 50], Operations: ['30+20=50'] Exploring Operation: 90-50=40, Resulting Numbers: [28, 40] Generated Node #0,4,0: 96:[28, 40] Operation: 90-50=40 Exploring Operation: 28+50=78, Resulting Numbers: [90, 78] Generated Node #0,4,1: 96:[90, 78] Operation: 28+50=78 Exploring Operation: 90-28=62, Resulting Numbers: [50, 62] Generated Node #0,4,2: 96:[50, 62] Operation: 90-28=62 Exploring Operation: 90+28=118, Resulting Numbers: [50, 118] Generated Node #0,4,3: 96:[50, 118] Operation: 90+28=118 Exploring Operation: 50-28=22, Resulting Numbers: [90, 22] Generated Node #0,4,4: 96:[90, 22] Operation: 50-28=22 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 96:[90, 22], Operations: ['30+20=50', '50-28=22'] Exploring Operation: 90*22=1980, Resulting Numbers: [1980] 1980,96 unequal: No Solution Exploring Operation: 90-22=68, Resulting Numbers: [68] 68,96 unequal: No Solution Exploring Operation: 90+22=112, Resulting Numbers: [112] 112,96 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 #0,4,0 Current State: 96:[28, 40], Operations: ['30+20=50', '90-50=40'] Exploring Operation: 28+40=68, Resulting Numbers: [68] 68,96 unequal: No Solution Exploring Operation: 28*40=1120, Resulting Numbers: [1120] 1120,96 unequal: No Solution Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,96 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 #0,4,2 Current State: 96:[50, 62], Operations: ['30+20=50', '90-28=62'] Exploring Operation: 50+62=112, Resulting Numbers: [112] 112,96 unequal: No Solution Exploring Operation: 62-50=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 50*62=3100, Resulting Numbers: [3100] 3100,96 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 #0,4,1 Current State: 96:[90, 78], Operations: ['30+20=50', '28+50=78'] Exploring Operation: 90*78=7020, Resulting Numbers: [7020] 7020,96 unequal: No Solution Exploring Operation: 90-78=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 90+78=168, Resulting Numbers: [168] 168,96 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 #0,4,3 Current State: 96:[50, 118], Operations: ['30+20=50', '90+28=118'] Exploring Operation: 50+118=168, Resulting Numbers: [168] 168,96 unequal: No Solution Exploring Operation: 118-50=68, Resulting Numbers: [68] 68,96 unequal: No Solution Exploring Operation: 50*118=5900, Resulting Numbers: [5900] 5900,96 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: 96:[3, 8], Operations: ['90/30=3', '28-20=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,96 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,96 unequal: No Solution Moving to Node #0,3,4 Current State: 96:[8, 3], Operations: ['28-20=8', '90/30=3'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,96 unequal: No Solution Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,96 unequal: No Solution Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,96 unequal: No Solution Moving to Node #0,0,4 Current State: 96:[3, 48], Operations: ['90/30=3', '28+20=48'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,96 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 3*48=144, Resulting Numbers: [144] 144,96 unequal: No Solution Moving to Node #0,3,2 Current State: 96:[30, 98], Operations: ['28-20=8', '90+8=98'] Exploring Operation: 30+98=128, Resulting Numbers: [128] 128,96 unequal: No Solution Exploring Operation: 98-30=68, Resulting Numbers: [68] 68,96 unequal: No Solution Exploring Operation: 30*98=2940, Resulting Numbers: [2940] 2940,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[20, 31], Operations: ['90/30=3', '28+3=31'] Exploring Operation: 20*31=620, Resulting Numbers: [620] 620,96 unequal: No Solution Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,96 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[20, 25], Operations: ['90/30=3', '28-3=25'] Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,96 unequal: No Solution Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[28, 23], Operations: ['90/30=3', '20+3=23'] Exploring Operation: 28+23=51, Resulting Numbers: [51] 51,96 unequal: No Solution Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,96 unequal: No Solution Exploring Operation: 28*23=644, Resulting Numbers: [644] 644,96 unequal: No Solution Moving to Node #0,2,4 Current State: 96:[20, 45], Operations: ['30-28=2', '90/2=45'] Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,96 unequal: No Solution Exploring Operation: 20*45=900, Resulting Numbers: [900] 900,96 unequal: No Solution Exploring Operation: 20+45=65, Resulting Numbers: [65] 65,96 unequal: No Solution Moving to Node #0,2,2 Current State: 96:[90, 22], Operations: ['30-28=2', '20+2=22'] Exploring Operation: 90*22=1980, Resulting Numbers: [1980] 1980,96 unequal: No Solution Exploring Operation: 90-22=68, Resulting Numbers: [68] 68,96 unequal: No Solution Exploring Operation: 90+22=112, Resulting Numbers: [112] 112,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[90, 18], Operations: ['30-28=2', '20-2=18'] Exploring Operation: 90-18=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 90*18=1620, Resulting Numbers: [1620] 1620,96 unequal: No Solution Exploring Operation: 90/18=5, Resulting Numbers: [5] 5,96 unequal: No Solution Exploring Operation: 90+18=108, Resulting Numbers: [108] 108,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[20, 92], Operations: ['30-28=2', '90+2=92'] Exploring Operation: 20+92=112, Resulting Numbers: [112] 112,96 unequal: No Solution Exploring Operation: 20*92=1840, Resulting Numbers: [1840] 1840,96 unequal: No Solution Exploring Operation: 92-20=72, Resulting Numbers: [72] 72,96 unequal: No Solution Moving to Node #0,3,3 Current State: 96:[90, 22], Operations: ['28-20=8', '30-8=22'] Exploring Operation: 90*22=1980, Resulting Numbers: [1980] 1980,96 unequal: No Solution Exploring Operation: 90+22=112, Resulting Numbers: [112] 112,96 unequal: No Solution Exploring Operation: 90-22=68, Resulting Numbers: [68] 68,96 unequal: No Solution Moving to Node #0,2,3 Current State: 96:[90, 10], Operations: ['30-28=2', '20/2=10'] Exploring Operation: 90/10=9, Resulting Numbers: [9] 9,96 unequal: No Solution Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,96 unequal: No Solution Exploring Operation: 90*10=900, Resulting Numbers: [900] 900,96 unequal: No Solution Exploring Operation: 90+10=100, Resulting Numbers: [100] 100,96 unequal: No Solution Moving to Node #0,3,1 Current State: 96:[8, 60], Operations: ['28-20=8', '90-30=60'] Exploring Operation: 8+60=68, Resulting Numbers: [68] 68,96 unequal: No Solution Exploring Operation: 8*60=480, Resulting Numbers: [480] 480,96 unequal: No Solution Exploring Operation: 60-8=52, Resulting Numbers: [52] 52,96 unequal: No Solution Moving to Node #0,3,0 Current State: 96:[90, 38], Operations: ['28-20=8', '30+8=38'] Exploring Operation: 90*38=3420, Resulting Numbers: [3420] 3420,96 unequal: No Solution Exploring Operation: 90-38=52, Resulting Numbers: [52] 52,96 unequal: No Solution Exploring Operation: 90+38=128, Resulting Numbers: [128] 128,96 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 7, 96, 2, 88 ]
90
[ "96-7=89", "2*89=178", "178-88=90" ]
Current State: 90:[7, 96, 2, 88], Operations: [] Exploring Operation: 96-7=89, Resulting Numbers: [2, 88, 89] Generated Node #2: [2, 88, 89] from Operation: 96-7=89 Current State: 90:[2, 88, 89], Operations: ['96-7=89'] Exploring Operation: 2*89=178, Resulting Numbers: [88, 178] Generated Node #3: [88, 178] from Operation: 2*89=178 Current State: 90:[88, 178], Operations: ['96-7=89', '2*89=178'] Exploring Operation: 178-88=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[7, 96, 2, 88], Operations: [] Exploring Operation: 96/2=48, Resulting Numbers: [7, 88, 48] Generated Node #0,0: 90:[7, 88, 48] Operation: 96/2=48 Exploring Operation: 96-7=89, Resulting Numbers: [2, 88, 89] Generated Node #0,1: 90:[2, 88, 89] Operation: 96-7=89 Exploring Operation: 96-2=94, Resulting Numbers: [7, 88, 94] Generated Node #0,2: 90:[7, 88, 94] Operation: 96-2=94 Exploring Operation: 96-88=8, Resulting Numbers: [7, 2, 8] Generated Node #0,3: 90:[7, 2, 8] Operation: 96-88=8 Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[7, 2, 8], Operations: ['96-88=8'] Exploring Operation: 7+2=9, Resulting Numbers: [8, 9] Generated Node #0,3,0: 90:[8, 9] Operation: 7+2=9 Exploring Operation: 7-2=5, Resulting Numbers: [8, 5] Generated Node #0,3,1: 90:[8, 5] Operation: 7-2=5 Exploring Operation: 7+8=15, Resulting Numbers: [2, 15] Generated Node #0,3,2: 90:[2, 15] Operation: 7+8=15 Exploring Operation: 8-7=1, Resulting Numbers: [2, 1] Generated Node #0,3,3: 90:[2, 1] Operation: 8-7=1 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 90:[2, 15], Operations: ['96-88=8', '7+8=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,90 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 90:[8, 9], Operations: ['96-88=8', '7+2=9'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,90 unequal: No Solution Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 90:[8, 5], Operations: ['96-88=8', '7-2=5'] Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,90 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 90:[2, 1], Operations: ['96-88=8', '8-7=1'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[2, 88, 89], Operations: ['96-7=89'] Exploring Operation: 2+88=90, Resulting Numbers: [89, 90] Generated Node #0,1,0: 90:[89, 90] Operation: 2+88=90 Exploring Operation: 2+89=91, Resulting Numbers: [88, 91] Generated Node #0,1,1: 90:[88, 91] Operation: 2+89=91 Exploring Operation: 89-88=1, Resulting Numbers: [2, 1] Generated Node #0,1,2: 90:[2, 1] Operation: 89-88=1 Exploring Operation: 88/2=44, Resulting Numbers: [89, 44] Generated Node #0,1,3: 90:[89, 44] Operation: 88/2=44 Moving to Node #0,1,0 Current State: 90:[89, 90], Operations: ['96-7=89', '2+88=90'] Exploring Operation: 89*90=8010, Resulting Numbers: [8010] 8010,90 unequal: No Solution Exploring Operation: 89+90=179, Resulting Numbers: [179] 179,90 unequal: No Solution Exploring Operation: 90-89=1, Resulting Numbers: [1] 1,90 unequal: No Solution Moving to Node #0,1,2 Current State: 90:[2, 1], Operations: ['96-7=89', '89-88=1'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,90 unequal: No Solution Moving to Node #0,1,3 Current State: 90:[89, 44], Operations: ['96-7=89', '88/2=44'] Exploring Operation: 89-44=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 89+44=133, Resulting Numbers: [133] 133,90 unequal: No Solution Exploring Operation: 89*44=3916, Resulting Numbers: [3916] 3916,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[88, 91], Operations: ['96-7=89', '2+89=91'] Exploring Operation: 91-88=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 88*91=8008, Resulting Numbers: [8008] 8008,90 unequal: No Solution Exploring Operation: 88+91=179, Resulting Numbers: [179] 179,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[7, 88, 48], Operations: ['96/2=48'] Exploring Operation: 7+88=95, Resulting Numbers: [48, 95] Generated Node #0,0,0: 90:[48, 95] Operation: 7+88=95 Exploring Operation: 88-7=81, Resulting Numbers: [48, 81] Generated Node #0,0,1: 90:[48, 81] Operation: 88-7=81 Exploring Operation: 88-48=40, Resulting Numbers: [7, 40] Generated Node #0,0,2: 90:[7, 40] Operation: 88-48=40 Exploring Operation: 48-7=41, Resulting Numbers: [88, 41] Generated Node #0,0,3: 90:[88, 41] Operation: 48-7=41 Moving to Node #0,0,2 Current State: 90:[7, 40], Operations: ['96/2=48', '88-48=40'] Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 7*40=280, Resulting Numbers: [280] 280,90 unequal: No Solution Exploring Operation: 7+40=47, Resulting Numbers: [47] 47,90 unequal: No Solution Moving to Node #0,0,3 Current State: 90:[88, 41], Operations: ['96/2=48', '48-7=41'] Exploring Operation: 88-41=47, Resulting Numbers: [47] 47,90 unequal: No Solution Exploring Operation: 88+41=129, Resulting Numbers: [129] 129,90 unequal: No Solution Exploring Operation: 88*41=3608, Resulting Numbers: [3608] 3608,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[48, 95], Operations: ['96/2=48', '7+88=95'] Exploring Operation: 95-48=47, Resulting Numbers: [47] 47,90 unequal: No Solution Exploring Operation: 48+95=143, Resulting Numbers: [143] 143,90 unequal: No Solution Exploring Operation: 48*95=4560, Resulting Numbers: [4560] 4560,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[48, 81], Operations: ['96/2=48', '88-7=81'] Exploring Operation: 48+81=129, Resulting Numbers: [129] 129,90 unequal: No Solution Exploring Operation: 48*81=3888, Resulting Numbers: [3888] 3888,90 unequal: No Solution Exploring Operation: 81-48=33, Resulting Numbers: [33] 33,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[7, 88, 94], Operations: ['96-2=94'] Exploring Operation: 94-7=87, Resulting Numbers: [88, 87] Generated Node #0,2,0: 90:[88, 87] Operation: 94-7=87 Exploring Operation: 88-7=81, Resulting Numbers: [94, 81] Generated Node #0,2,1: 90:[94, 81] Operation: 88-7=81 Exploring Operation: 7+88=95, Resulting Numbers: [94, 95] Generated Node #0,2,2: 90:[94, 95] Operation: 7+88=95 Exploring Operation: 94-88=6, Resulting Numbers: [7, 6] Generated Node #0,2,3: 90:[7, 6] Operation: 94-88=6 Moving to Node #0,2,3 Current State: 90:[7, 6], Operations: ['96-2=94', '94-88=6'] Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,90 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,90 unequal: No Solution Moving to Node #0,2,0 Current State: 90:[88, 87], Operations: ['96-2=94', '94-7=87'] Exploring Operation: 88*87=7656, Resulting Numbers: [7656] 7656,90 unequal: No Solution Exploring Operation: 88+87=175, Resulting Numbers: [175] 175,90 unequal: No Solution Exploring Operation: 88-87=1, Resulting Numbers: [1] 1,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[94, 95], Operations: ['96-2=94', '7+88=95'] Exploring Operation: 94*95=8930, Resulting Numbers: [8930] 8930,90 unequal: No Solution Exploring Operation: 95-94=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 94+95=189, Resulting Numbers: [189] 189,90 unequal: No Solution Moving to Node #0,2,1 Current State: 90:[94, 81], Operations: ['96-2=94', '88-7=81'] Exploring Operation: 94*81=7614, Resulting Numbers: [7614] 7614,90 unequal: No Solution Exploring Operation: 94-81=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 94+81=175, Resulting Numbers: [175] 175,90 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
[ 5, 31, 29, 15 ]
80
[ "5+31=36", "29+15=44", "36+44=80" ]
Current State: 80:[5, 31, 29, 15], Operations: [] Exploring Operation: 5+31=36, Resulting Numbers: [29, 15, 36] Generated Node #2: [29, 15, 36] from Operation: 5+31=36 Current State: 80:[29, 15, 36], Operations: ['5+31=36'] Exploring Operation: 29+15=44, Resulting Numbers: [36, 44] Generated Node #3: [36, 44] from Operation: 29+15=44 Current State: 80:[36, 44], Operations: ['5+31=36', '29+15=44'] Exploring Operation: 36+44=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[5, 31, 29, 15], Operations: [] Exploring Operation: 31-29=2, Resulting Numbers: [5, 15, 2] Generated Node #0,0: 80:[5, 15, 2] Operation: 31-29=2 Moving to Node #0,0 Current State: 80:[5, 15, 2], Operations: ['31-29=2'] Exploring Operation: 5+15=20, Resulting Numbers: [2, 20] Generated Node #0,0,0: 80:[2, 20] Operation: 5+15=20 Moving to Node #0,0,0 Current State: 80:[2, 20], Operations: ['31-29=2', '5+15=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,80 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 52, 5, 9, 65 ]
13
[ "52*5=260", "260/65=4", "9+4=13" ]
Current State: 13:[52, 5, 9, 65], Operations: [] Exploring Operation: 52*5=260, Resulting Numbers: [9, 65, 260] Generated Node #2: [9, 65, 260] from Operation: 52*5=260 Current State: 13:[9, 65, 260], Operations: ['52*5=260'] Exploring Operation: 260/65=4, Resulting Numbers: [9, 4] Generated Node #3: [9, 4] from Operation: 260/65=4 Current State: 13:[9, 4], Operations: ['52*5=260', '260/65=4'] Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[52, 5, 9, 65], Operations: [] Exploring Operation: 65/5=13, Resulting Numbers: [52, 9, 13] Generated Node #0,0: 13:[52, 9, 13] Operation: 65/5=13 Exploring Operation: 65-52=13, Resulting Numbers: [5, 9, 13] Generated Node #0,1: 13:[5, 9, 13] Operation: 65-52=13 Exploring Operation: 52-5=47, Resulting Numbers: [9, 65, 47] Generated Node #0,2: 13:[9, 65, 47] Operation: 52-5=47 Moving to Node #0,1 Current State: 13:[5, 9, 13], Operations: ['65-52=13'] Exploring Operation: 5+9=14, Resulting Numbers: [13, 14] Generated Node #0,1,0: 13:[13, 14] Operation: 5+9=14 Exploring Operation: 5+13=18, Resulting Numbers: [9, 18] Generated Node #0,1,1: 13:[9, 18] Operation: 5+13=18 Exploring Operation: 9-5=4, Resulting Numbers: [13, 4] Generated Node #0,1,2: 13:[13, 4] Operation: 9-5=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 13:[13, 14], Operations: ['65-52=13', '5+9=14'] Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,13 unequal: No Solution Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,13 unequal: No Solution Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 13:[9, 18], Operations: ['65-52=13', '5+13=18'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,13 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 13:[13, 4], Operations: ['65-52=13', '9-5=4'] Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,13 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,13 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: 13:[52, 9, 13], Operations: ['65/5=13'] Exploring Operation: 52/13=4, Resulting Numbers: [9, 4] Generated Node #0,0,0: 13:[9, 4] Operation: 52/13=4 Exploring Operation: 52-9=43, Resulting Numbers: [13, 43] Generated Node #0,0,1: 13:[13, 43] Operation: 52-9=43 Exploring Operation: 52-13=39, Resulting Numbers: [9, 39] Generated Node #0,0,2: 13:[9, 39] Operation: 52-13=39 Moving to Node #0,2 Current State: 13:[9, 65, 47], Operations: ['52-5=47'] Exploring Operation: 65-9=56, Resulting Numbers: [47, 56] Generated Node #0,2,0: 13:[47, 56] Operation: 65-9=56 Exploring Operation: 47-9=38, Resulting Numbers: [65, 38] Generated Node #0,2,1: 13:[65, 38] Operation: 47-9=38 Exploring Operation: 65-47=18, Resulting Numbers: [9, 18] Generated Node #0,2,2: 13:[9, 18] Operation: 65-47=18 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 13:[9, 18], Operations: ['52-5=47', '65-47=18'] Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,13 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 13:[47, 56], Operations: ['52-5=47', '65-9=56'] Exploring Operation: 47*56=2632, Resulting Numbers: [2632] 2632,13 unequal: No Solution Exploring Operation: 56-47=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 47+56=103, Resulting Numbers: [103] 103,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 13:[65, 38], Operations: ['52-5=47', '47-9=38'] Exploring Operation: 65-38=27, Resulting Numbers: [27] 27,13 unequal: No Solution Exploring Operation: 65+38=103, Resulting Numbers: [103] 103,13 unequal: No Solution Exploring Operation: 65*38=2470, Resulting Numbers: [2470] 2470,13 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: 13:[9, 4], Operations: ['65/5=13', '52/13=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,13 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[52, 5, 9, 65], Operations: [] Exploring Operation: 65/5=13, Resulting Numbers: [52, 9, 13] Generated Node #0,0: 13:[52, 9, 13] Operation: 65/5=13 Moving to Node #0,0 Current State: 13:[52, 9, 13], Operations: ['65/5=13'] Exploring Operation: 52/13=4, Resulting Numbers: [9, 4] Generated Node #0,0,0: 13:[9, 4] Operation: 52/13=4 Moving to Node #0,0,0 Current State: 13:[9, 4], Operations: ['65/5=13', '52/13=4'] Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
0.967882
hs_3
sum_heuristic
[ 56, 44, 6, 45 ]
24
[ "56-45=11", "44*6=264", "264/11=24" ]
Current State: 24:[56, 44, 6, 45], Operations: [] Exploring Operation: 56-45=11, Resulting Numbers: [44, 6, 11] Generated Node #2: [44, 6, 11] from Operation: 56-45=11 Current State: 24:[44, 6, 11], Operations: ['56-45=11'] Exploring Operation: 44*6=264, Resulting Numbers: [11, 264] Generated Node #3: [11, 264] from Operation: 44*6=264 Current State: 24:[11, 264], Operations: ['56-45=11', '44*6=264'] Exploring Operation: 264/11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[56, 44, 6, 45], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [56, 6, 1] Generated Node #0,0: 24:[56, 6, 1] Operation: 45-44=1 Exploring Operation: 56-45=11, Resulting Numbers: [44, 6, 11] Generated Node #0,1: 24:[44, 6, 11] Operation: 56-45=11 Exploring Operation: 56-44=12, Resulting Numbers: [6, 45, 12] Generated Node #0,2: 24:[6, 45, 12] Operation: 56-44=12 Exploring Operation: 56-6=50, Resulting Numbers: [44, 45, 50] Generated Node #0,3: 24:[44, 45, 50] Operation: 56-6=50 Moving to Node #0,1 Current State: 24:[44, 6, 11], Operations: ['56-45=11'] Exploring Operation: 44-6=38, Resulting Numbers: [11, 38] Generated Node #0,1,0: 24:[11, 38] Operation: 44-6=38 Exploring Operation: 44-11=33, Resulting Numbers: [6, 33] Generated Node #0,1,1: 24:[6, 33] Operation: 44-11=33 Exploring Operation: 11-6=5, Resulting Numbers: [44, 5] Generated Node #0,1,2: 24:[44, 5] Operation: 11-6=5 Exploring Operation: 44/11=4, Resulting Numbers: [6, 4] Generated Node #0,1,3: 24:[6, 4] Operation: 44/11=4 Moving to Node #0,2 Current State: 24:[6, 45, 12], Operations: ['56-44=12'] Exploring Operation: 45-12=33, Resulting Numbers: [6, 33] Generated Node #0,2,0: 24:[6, 33] Operation: 45-12=33 Exploring Operation: 45-6=39, Resulting Numbers: [12, 39] Generated Node #0,2,1: 24:[12, 39] Operation: 45-6=39 Exploring Operation: 12/6=2, Resulting Numbers: [45, 2] Generated Node #0,2,2: 24:[45, 2] Operation: 12/6=2 Exploring Operation: 12-6=6, Resulting Numbers: [45, 6] Generated Node #0,2,3: 24:[45, 6] Operation: 12-6=6 Moving to Node #0,0 Current State: 24:[56, 6, 1], Operations: ['45-44=1'] Exploring Operation: 56-1=55, Resulting Numbers: [6, 55] Generated Node #0,0,0: 24:[6, 55] Operation: 56-1=55 Exploring Operation: 56*1=56, Resulting Numbers: [6, 56] Generated Node #0,0,1: 24:[6, 56] Operation: 56*1=56 Exploring Operation: 56-6=50, Resulting Numbers: [1, 50] Generated Node #0,0,2: 24:[1, 50] Operation: 56-6=50 Exploring Operation: 56/1=56, Resulting Numbers: [6, 56] Generated Node #0,0,3: 24:[6, 56] Operation: 56/1=56 Moving to Node #0,3 Current State: 24:[44, 45, 50], Operations: ['56-6=50'] Exploring Operation: 50-44=6, Resulting Numbers: [45, 6] Generated Node #0,3,0: 24:[45, 6] Operation: 50-44=6 Exploring Operation: 45-44=1, Resulting Numbers: [50, 1] Generated Node #0,3,1: 24:[50, 1] Operation: 45-44=1 Exploring Operation: 44+45=89, Resulting Numbers: [50, 89] Generated Node #0,3,2: 24:[50, 89] Operation: 44+45=89 Exploring Operation: 50-45=5, Resulting Numbers: [44, 5] Generated Node #0,3,3: 24:[44, 5] Operation: 50-45=5 Moving to Node #0,1,3 Current State: 24:[6, 4], Operations: ['56-45=11', '44/11=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,24 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[56, 44, 6, 45], Operations: [] Exploring Operation: 56-45=11, Resulting Numbers: [44, 6, 11] Generated Node #0,1: 24:[44, 6, 11] Operation: 56-45=11 Moving to Node #0,1 Current State: 24:[44, 6, 11], Operations: ['56-45=11'] Exploring Operation: 44/11=4, Resulting Numbers: [6, 4] Generated Node #0,1,3: 24:[6, 4] Operation: 44/11=4 Moving to Node #0,1,3 Current State: 24:[6, 4], Operations: ['56-45=11', '44/11=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
0.977431
hs_4
sum_heuristic
[ 6, 3, 39, 50 ]
35
[ "6+39=45", "45/3=15", "50-15=35" ]
Current State: 35:[6, 3, 39, 50], Operations: [] Exploring Operation: 6+39=45, Resulting Numbers: [3, 50, 45] Generated Node #2: [3, 50, 45] from Operation: 6+39=45 Current State: 35:[3, 50, 45], Operations: ['6+39=45'] Exploring Operation: 45/3=15, Resulting Numbers: [50, 15] Generated Node #3: [50, 15] from Operation: 45/3=15 Current State: 35:[50, 15], Operations: ['6+39=45', '45/3=15'] Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[6, 3, 39, 50], Operations: [] Exploring Operation: 50-6=44, Resulting Numbers: [3, 39, 44] Generated Node #0,0: 35:[3, 39, 44] Operation: 50-6=44 Exploring Operation: 39-3=36, Resulting Numbers: [6, 50, 36] Generated Node #0,1: 35:[6, 50, 36] Operation: 39-3=36 Exploring Operation: 50-39=11, Resulting Numbers: [6, 3, 11] Generated Node #0,2: 35:[6, 3, 11] Operation: 50-39=11 Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[6, 3, 11], Operations: ['50-39=11'] Exploring Operation: 3*11=33, Resulting Numbers: [6, 33] Generated Node #0,2,0: 35:[6, 33] Operation: 3*11=33 Exploring Operation: 11-6=5, Resulting Numbers: [3, 5] Generated Node #0,2,1: 35:[3, 5] Operation: 11-6=5 Exploring Operation: 11-3=8, Resulting Numbers: [6, 8] Generated Node #0,2,2: 35:[6, 8] Operation: 11-3=8 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 35:[3, 5], Operations: ['50-39=11', '11-6=5'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,35 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 35:[6, 8], Operations: ['50-39=11', '11-3=8'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 35:[6, 33], Operations: ['50-39=11', '3*11=33'] Exploring Operation: 6+33=39, Resulting Numbers: [39] 39,35 unequal: No Solution Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 6*33=198, Resulting Numbers: [198] 198,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[3, 39, 44], Operations: ['50-6=44'] Exploring Operation: 39-3=36, Resulting Numbers: [44, 36] Generated Node #0,0,0: 35:[44, 36] Operation: 39-3=36 Exploring Operation: 44-3=41, Resulting Numbers: [39, 41] Generated Node #0,0,1: 35:[39, 41] Operation: 44-3=41 Exploring Operation: 44-39=5, Resulting Numbers: [3, 5] Generated Node #0,0,2: 35:[3, 5] Operation: 44-39=5 Moving to Node #0,0,2 Current State: 35:[3, 5], Operations: ['50-6=44', '44-39=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,35 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[44, 36], Operations: ['50-6=44', '39-3=36'] Exploring Operation: 44+36=80, Resulting Numbers: [80] 80,35 unequal: No Solution Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 44*36=1584, Resulting Numbers: [1584] 1584,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[39, 41], Operations: ['50-6=44', '44-3=41'] Exploring Operation: 39+41=80, Resulting Numbers: [80] 80,35 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 39*41=1599, Resulting Numbers: [1599] 1599,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[6, 50, 36], Operations: ['39-3=36'] Exploring Operation: 50-36=14, Resulting Numbers: [6, 14] Generated Node #0,1,0: 35:[6, 14] Operation: 50-36=14 Exploring Operation: 36/6=6, Resulting Numbers: [50, 6] Generated Node #0,1,1: 35:[50, 6] Operation: 36/6=6 Exploring Operation: 50-6=44, Resulting Numbers: [36, 44] Generated Node #0,1,2: 35:[36, 44] Operation: 50-6=44 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 35:[6, 14], Operations: ['39-3=36', '50-36=14'] Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,35 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,35 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 35:[36, 44], Operations: ['39-3=36', '50-6=44'] Exploring Operation: 36*44=1584, Resulting Numbers: [1584] 1584,35 unequal: No Solution Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 36+44=80, Resulting Numbers: [80] 80,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 35:[50, 6], Operations: ['39-3=36', '36/6=6'] Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 50+6=56, Resulting Numbers: [56] 56,35 unequal: No Solution Exploring Operation: 50*6=300, Resulting Numbers: [300] 300,35 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_3
mult_heuristic
[ 51, 48, 81, 25 ]
59
[ "51-48=3", "81-25=56", "3+56=59" ]
Current State: 59:[51, 48, 81, 25], Operations: [] Exploring Operation: 51-48=3, Resulting Numbers: [81, 25, 3] Generated Node #2: [81, 25, 3] from Operation: 51-48=3 Current State: 59:[81, 25, 3], Operations: ['51-48=3'] Exploring Operation: 81-25=56, Resulting Numbers: [3, 56] Generated Node #3: [3, 56] from Operation: 81-25=56 Current State: 59:[3, 56], Operations: ['51-48=3', '81-25=56'] Exploring Operation: 3+56=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[51, 48, 81, 25], Operations: [] Exploring Operation: 81-25=56, Resulting Numbers: [51, 48, 56] Generated Node #0,0: 59:[51, 48, 56] Operation: 81-25=56 Exploring Operation: 48+25=73, Resulting Numbers: [51, 81, 73] Generated Node #0,1: 59:[51, 81, 73] Operation: 48+25=73 Moving to Node #0,0 Current State: 59:[51, 48, 56], Operations: ['81-25=56'] Exploring Operation: 48+56=104, Resulting Numbers: [51, 104] Generated Node #0,0,0: 59:[51, 104] Operation: 48+56=104 Exploring Operation: 51+48=99, Resulting Numbers: [56, 99] Generated Node #0,0,1: 59:[56, 99] Operation: 51+48=99 Moving to Node #0,1 Current State: 59:[51, 81, 73], Operations: ['48+25=73'] Exploring Operation: 73-51=22, Resulting Numbers: [81, 22] Generated Node #0,1,0: 59:[81, 22] Operation: 73-51=22 Exploring Operation: 81-51=30, Resulting Numbers: [73, 30] Generated Node #0,1,1: 59:[73, 30] Operation: 81-51=30 Moving to Node #0,0,1 Current State: 59:[56, 99], Operations: ['81-25=56', '51+48=99'] Exploring Operation: 99-56=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 56+99=155, Resulting Numbers: [155] 155,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[73, 30], Operations: ['48+25=73', '81-51=30'] Exploring Operation: 73+30=103, Resulting Numbers: [103] 103,59 unequal: No Solution Exploring Operation: 73-30=43, Resulting Numbers: [43] 43,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[51, 104], Operations: ['81-25=56', '48+56=104'] Exploring Operation: 104-51=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 51+104=155, Resulting Numbers: [155] 155,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[81, 22], Operations: ['48+25=73', '73-51=22'] Exploring Operation: 81+22=103, Resulting Numbers: [103] 103,59 unequal: No Solution Exploring Operation: 81-22=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[51, 48, 81, 25], Operations: [] Exploring Operation: 48+25=73, Resulting Numbers: [51, 81, 73] Generated Node #0,1: 59:[51, 81, 73] Operation: 48+25=73 Moving to Node #0,1 Current State: 59:[51, 81, 73], Operations: ['48+25=73'] Exploring Operation: 73-51=22, Resulting Numbers: [81, 22] Generated Node #0,1,0: 59:[81, 22] Operation: 73-51=22 Moving to Node #0,1,0 Current State: 59:[81, 22], Operations: ['48+25=73', '73-51=22'] Exploring Operation: 81-22=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
0.984375
hs_2
mult_heuristic
[ 31, 17, 9, 73 ]
78
[ "31-17=14", "73-9=64", "14+64=78" ]
Current State: 78:[31, 17, 9, 73], Operations: [] Exploring Operation: 31-17=14, Resulting Numbers: [9, 73, 14] Generated Node #2: [9, 73, 14] from Operation: 31-17=14 Current State: 78:[9, 73, 14], Operations: ['31-17=14'] Exploring Operation: 73-9=64, Resulting Numbers: [14, 64] Generated Node #3: [14, 64] from Operation: 73-9=64 Current State: 78:[14, 64], Operations: ['31-17=14', '73-9=64'] Exploring Operation: 14+64=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[31, 17, 9, 73], Operations: [] Exploring Operation: 31-17=14, Resulting Numbers: [9, 73, 14] Generated Node #0,0: 78:[9, 73, 14] Operation: 31-17=14 Exploring Operation: 31+9=40, Resulting Numbers: [17, 73, 40] Generated Node #0,1: 78:[17, 73, 40] Operation: 31+9=40 Moving to Node #0,0 Current State: 78:[9, 73, 14], Operations: ['31-17=14'] Exploring Operation: 14-9=5, Resulting Numbers: [73, 5] Generated Node #0,0,0: 78:[73, 5] Operation: 14-9=5 Exploring Operation: 9+73=82, Resulting Numbers: [14, 82] Generated Node #0,0,1: 78:[14, 82] Operation: 9+73=82 Moving to Node #0,1 Current State: 78:[17, 73, 40], Operations: ['31+9=40'] Exploring Operation: 40-17=23, Resulting Numbers: [73, 23] Generated Node #0,1,0: 78:[73, 23] Operation: 40-17=23 Exploring Operation: 73-40=33, Resulting Numbers: [17, 33] Generated Node #0,1,1: 78:[17, 33] Operation: 73-40=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[73, 23], Operations: ['31+9=40', '40-17=23'] Exploring Operation: 73+23=96, Resulting Numbers: [96] 96,78 unequal: No Solution Exploring Operation: 73-23=50, Resulting Numbers: [50] 50,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[17, 33], Operations: ['31+9=40', '73-40=33'] Exploring Operation: 17+33=50, Resulting Numbers: [50] 50,78 unequal: No Solution Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,78 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: 78:[14, 82], Operations: ['31-17=14', '9+73=82'] Exploring Operation: 82-14=68, Resulting Numbers: [68] 68,78 unequal: No Solution Exploring Operation: 14+82=96, Resulting Numbers: [96] 96,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[73, 5], Operations: ['31-17=14', '14-9=5'] Exploring Operation: 73+5=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[31, 17, 9, 73], Operations: [] Exploring Operation: 31-17=14, Resulting Numbers: [9, 73, 14] Generated Node #0,0: 78:[9, 73, 14] Operation: 31-17=14 Moving to Node #0,0 Current State: 78:[9, 73, 14], Operations: ['31-17=14'] Exploring Operation: 14-9=5, Resulting Numbers: [73, 5] Generated Node #0,0,0: 78:[73, 5] Operation: 14-9=5 Moving to Node #0,0,0 Current State: 78:[73, 5], Operations: ['31-17=14', '14-9=5'] Exploring Operation: 73+5=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
0.985243
hs_2
mult_heuristic
[ 88, 64, 38, 35 ]
79
[ "88+64=152", "38+35=73", "152-73=79" ]
Current State: 79:[88, 64, 38, 35], Operations: [] Exploring Operation: 88+64=152, Resulting Numbers: [38, 35, 152] Generated Node #2: [38, 35, 152] from Operation: 88+64=152 Current State: 79:[38, 35, 152], Operations: ['88+64=152'] Exploring Operation: 38+35=73, Resulting Numbers: [152, 73] Generated Node #3: [152, 73] from Operation: 38+35=73 Current State: 79:[152, 73], Operations: ['88+64=152', '38+35=73'] Exploring Operation: 152-73=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[88, 64, 38, 35], Operations: [] Exploring Operation: 64+38=102, Resulting Numbers: [88, 35, 102] Generated Node #0,0: 79:[88, 35, 102] Operation: 64+38=102 Exploring Operation: 88-38=50, Resulting Numbers: [64, 35, 50] Generated Node #0,1: 79:[64, 35, 50] Operation: 88-38=50 Exploring Operation: 88-35=53, Resulting Numbers: [64, 38, 53] Generated Node #0,2: 79:[64, 38, 53] Operation: 88-35=53 Exploring Operation: 64+35=99, Resulting Numbers: [88, 38, 99] Generated Node #0,3: 79:[88, 38, 99] Operation: 64+35=99 Exploring Operation: 38+35=73, Resulting Numbers: [88, 64, 73] Generated Node #0,4: 79:[88, 64, 73] Operation: 38+35=73 Start Sub Search at level 1: Moving to Node #0,4 Current State: 79:[88, 64, 73], Operations: ['38+35=73'] Exploring Operation: 88+64=152, Resulting Numbers: [73, 152] Generated Node #0,4,0: 79:[73, 152] Operation: 88+64=152 Exploring Operation: 88-64=24, Resulting Numbers: [73, 24] Generated Node #0,4,1: 79:[73, 24] Operation: 88-64=24 Exploring Operation: 88-73=15, Resulting Numbers: [64, 15] Generated Node #0,4,2: 79:[64, 15] Operation: 88-73=15 Exploring Operation: 64+73=137, Resulting Numbers: [88, 137] Generated Node #0,4,3: 79:[88, 137] Operation: 64+73=137 Exploring Operation: 73-64=9, Resulting Numbers: [88, 9] Generated Node #0,4,4: 79:[88, 9] Operation: 73-64=9 Moving to Node #0,4,1 Current State: 79:[73, 24], Operations: ['38+35=73', '88-64=24'] Exploring Operation: 73+24=97, Resulting Numbers: [97] 97,79 unequal: No Solution Exploring Operation: 73*24=1752, Resulting Numbers: [1752] 1752,79 unequal: No Solution Exploring Operation: 73-24=49, Resulting Numbers: [49] 49,79 unequal: No Solution Moving to Node #0,4,3 Current State: 79:[88, 137], Operations: ['38+35=73', '64+73=137'] Exploring Operation: 88+137=225, Resulting Numbers: [225] 225,79 unequal: No Solution Exploring Operation: 88*137=12056, Resulting Numbers: [12056] 12056,79 unequal: No Solution Exploring Operation: 137-88=49, Resulting Numbers: [49] 49,79 unequal: No Solution Moving to Node #0,4,0 Current State: 79:[73, 152], Operations: ['38+35=73', '88+64=152'] Exploring Operation: 73*152=11096, Resulting Numbers: [11096] 11096,79 unequal: No Solution Exploring Operation: 73+152=225, Resulting Numbers: [225] 225,79 unequal: No Solution Exploring Operation: 152-73=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[88, 64, 38, 35], Operations: [] Exploring Operation: 38+35=73, Resulting Numbers: [88, 64, 73] Generated Node #0,4: 79:[88, 64, 73] Operation: 38+35=73 Moving to Node #0,4 Current State: 79:[88, 64, 73], Operations: ['38+35=73'] Exploring Operation: 88+64=152, Resulting Numbers: [73, 152] Generated Node #0,4,0: 79:[73, 152] Operation: 88+64=152 Moving to Node #0,4,0 Current State: 79:[73, 152], Operations: ['38+35=73', '88+64=152'] Exploring Operation: 152-73=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 22, 88, 83, 89 ]
21
[ "88-83=5", "22*5=110", "110-89=21" ]
Current State: 21:[22, 88, 83, 89], Operations: [] Exploring Operation: 88-83=5, Resulting Numbers: [22, 89, 5] Generated Node #2: [22, 89, 5] from Operation: 88-83=5 Current State: 21:[22, 89, 5], Operations: ['88-83=5'] Exploring Operation: 22*5=110, Resulting Numbers: [89, 110] Generated Node #3: [89, 110] from Operation: 22*5=110 Current State: 21:[89, 110], Operations: ['88-83=5', '22*5=110'] Exploring Operation: 110-89=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[22, 88, 83, 89], Operations: [] Exploring Operation: 89-88=1, Resulting Numbers: [22, 83, 1] Generated Node #0,0: 21:[22, 83, 1] Operation: 89-88=1 Moving to Node #0,0 Current State: 21:[22, 83, 1], Operations: ['89-88=1'] Exploring Operation: 83-22=61, Resulting Numbers: [1, 61] Generated Node #0,0,0: 21:[1, 61] Operation: 83-22=61 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[1, 61], Operations: ['89-88=1', '83-22=61'] Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 46, 35, 47, 41 ]
23
[ "46*41=1886", "35+47=82", "1886/82=23" ]
Current State: 23:[46, 35, 47, 41], Operations: [] Exploring Operation: 46*41=1886, Resulting Numbers: [35, 47, 1886] Generated Node #2: [35, 47, 1886] from Operation: 46*41=1886 Current State: 23:[35, 47, 1886], Operations: ['46*41=1886'] Exploring Operation: 35+47=82, Resulting Numbers: [1886, 82] Generated Node #3: [1886, 82] from Operation: 35+47=82 Current State: 23:[1886, 82], Operations: ['46*41=1886', '35+47=82'] Exploring Operation: 1886/82=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[46, 35, 47, 41], Operations: [] Exploring Operation: 47-46=1, Resulting Numbers: [35, 41, 1] Generated Node #0,0: 23:[35, 41, 1] Operation: 47-46=1 Moving to Node #0,0 Current State: 23:[35, 41, 1], Operations: ['47-46=1'] Exploring Operation: 35-1=34, Resulting Numbers: [41, 34] Generated Node #0,0,0: 23:[41, 34] Operation: 35-1=34 Moving to Node #0,0,0 Current State: 23:[41, 34], Operations: ['47-46=1', '35-1=34'] Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,23 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 23, 43, 3, 25 ]
31
[ "43-25=18", "3*18=54", "54-23=31" ]
Current State: 31:[23, 43, 3, 25], Operations: [] Exploring Operation: 43-25=18, Resulting Numbers: [23, 3, 18] Generated Node #2: [23, 3, 18] from Operation: 43-25=18 Current State: 31:[23, 3, 18], Operations: ['43-25=18'] Exploring Operation: 3*18=54, Resulting Numbers: [23, 54] Generated Node #3: [23, 54] from Operation: 3*18=54 Current State: 31:[23, 54], Operations: ['43-25=18', '3*18=54'] Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[23, 43, 3, 25], Operations: [] Exploring Operation: 23+3=26, Resulting Numbers: [43, 25, 26] Generated Node #0,0: 31:[43, 25, 26] Operation: 23+3=26 Exploring Operation: 43-3=40, Resulting Numbers: [23, 25, 40] Generated Node #0,1: 31:[23, 25, 40] Operation: 43-3=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[43, 25, 26], Operations: ['23+3=26'] Exploring Operation: 43-25=18, Resulting Numbers: [26, 18] Generated Node #0,0,0: 31:[26, 18] Operation: 43-25=18 Exploring Operation: 43-26=17, Resulting Numbers: [25, 17] Generated Node #0,0,1: 31:[25, 17] Operation: 43-26=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[26, 18], Operations: ['23+3=26', '43-25=18'] Exploring Operation: 26-18=8, Resulting Numbers: [8] 8,31 unequal: No Solution Exploring Operation: 26+18=44, Resulting Numbers: [44] 44,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 31:[25, 17], Operations: ['23+3=26', '43-26=17'] Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,31 unequal: No Solution Exploring Operation: 25+17=42, Resulting Numbers: [42] 42,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[23, 25, 40], Operations: ['43-3=40'] Exploring Operation: 40-25=15, Resulting Numbers: [23, 15] Generated Node #0,1,0: 31:[23, 15] Operation: 40-25=15 Exploring Operation: 40-23=17, Resulting Numbers: [25, 17] Generated Node #0,1,1: 31:[25, 17] Operation: 40-23=17 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 31:[25, 17], Operations: ['43-3=40', '40-23=17'] Exploring Operation: 25+17=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 31:[23, 15], Operations: ['43-3=40', '40-25=15'] Exploring Operation: 23+15=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 95, 54, 80, 40 ]
82
[ "95-54=41", "80/40=2", "41*2=82" ]
Current State: 82:[95, 54, 80, 40], Operations: [] Exploring Operation: 95-54=41, Resulting Numbers: [80, 40, 41] Generated Node #2: [80, 40, 41] from Operation: 95-54=41 Current State: 82:[80, 40, 41], Operations: ['95-54=41'] Exploring Operation: 80/40=2, Resulting Numbers: [41, 2] Generated Node #3: [41, 2] from Operation: 80/40=2 Current State: 82:[41, 2], Operations: ['95-54=41', '80/40=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[95, 54, 80, 40], Operations: [] Exploring Operation: 95-54=41, Resulting Numbers: [80, 40, 41] Generated Node #0,0: 82:[80, 40, 41] Operation: 95-54=41 Exploring Operation: 95-80=15, Resulting Numbers: [54, 40, 15] Generated Node #0,1: 82:[54, 40, 15] Operation: 95-80=15 Exploring Operation: 80/40=2, Resulting Numbers: [95, 54, 2] Generated Node #0,2: 82:[95, 54, 2] Operation: 80/40=2 Exploring Operation: 54+40=94, Resulting Numbers: [95, 80, 94] Generated Node #0,3: 82:[95, 80, 94] Operation: 54+40=94 Moving to Node #0,0 Current State: 82:[80, 40, 41], Operations: ['95-54=41'] Exploring Operation: 80/40=2, Resulting Numbers: [41, 2] Generated Node #0,0,0: 82:[41, 2] Operation: 80/40=2 Exploring Operation: 80-41=39, Resulting Numbers: [40, 39] Generated Node #0,0,1: 82:[40, 39] Operation: 80-41=39 Exploring Operation: 40+41=81, Resulting Numbers: [80, 81] Generated Node #0,0,2: 82:[80, 81] Operation: 40+41=81 Exploring Operation: 80-40=40, Resulting Numbers: [41, 40] Generated Node #0,0,3: 82:[41, 40] Operation: 80-40=40 Moving to Node #0,2 Current State: 82:[95, 54, 2], Operations: ['80/40=2'] Exploring Operation: 54-2=52, Resulting Numbers: [95, 52] Generated Node #0,2,0: 82:[95, 52] Operation: 54-2=52 Exploring Operation: 54/2=27, Resulting Numbers: [95, 27] Generated Node #0,2,1: 82:[95, 27] Operation: 54/2=27 Exploring Operation: 95-2=93, Resulting Numbers: [54, 93] Generated Node #0,2,2: 82:[54, 93] Operation: 95-2=93 Exploring Operation: 95-54=41, Resulting Numbers: [2, 41] Generated Node #0,2,3: 82:[2, 41] Operation: 95-54=41 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 82:[2, 41], Operations: ['80/40=2', '95-54=41'] Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,82 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[95, 54, 80, 40], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [95, 54, 2] Generated Node #0,2: 82:[95, 54, 2] Operation: 80/40=2 Moving to Node #0,2 Current State: 82:[95, 54, 2], Operations: ['80/40=2'] Exploring Operation: 95-54=41, Resulting Numbers: [2, 41] Generated Node #0,2,3: 82:[2, 41] Operation: 95-54=41 Moving to Node #0,2,3 Current State: 82:[2, 41], Operations: ['80/40=2', '95-54=41'] Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 24, 73, 18, 63 ]
16
[ "24+73=97", "18+63=81", "97-81=16" ]
Current State: 16:[24, 73, 18, 63], Operations: [] Exploring Operation: 24+73=97, Resulting Numbers: [18, 63, 97] Generated Node #2: [18, 63, 97] from Operation: 24+73=97 Current State: 16:[18, 63, 97], Operations: ['24+73=97'] Exploring Operation: 18+63=81, Resulting Numbers: [97, 81] Generated Node #3: [97, 81] from Operation: 18+63=81 Current State: 16:[97, 81], Operations: ['24+73=97', '18+63=81'] Exploring Operation: 97-81=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[24, 73, 18, 63], Operations: [] Exploring Operation: 73-63=10, Resulting Numbers: [24, 18, 10] Generated Node #0,0: 16:[24, 18, 10] Operation: 73-63=10 Moving to Node #0,0 Current State: 16:[24, 18, 10], Operations: ['73-63=10'] Exploring Operation: 24-18=6, Resulting Numbers: [10, 6] Generated Node #0,0,0: 16:[10, 6] Operation: 24-18=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[10, 6], Operations: ['73-63=10', '24-18=6'] Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[24, 73, 18, 63], Operations: [] Exploring Operation: 73-63=10, Resulting Numbers: [24, 18, 10] Generated Node #0,0: 16:[24, 18, 10] Operation: 73-63=10 Moving to Node #0,0 Current State: 16:[24, 18, 10], Operations: ['73-63=10'] Exploring Operation: 24-18=6, Resulting Numbers: [10, 6] Generated Node #0,0,0: 16:[10, 6] Operation: 24-18=6 Moving to Node #0,0,0 Current State: 16:[10, 6], Operations: ['73-63=10', '24-18=6'] Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 32, 29, 16, 6 ]
33
[ "32/16=2", "29+6=35", "35-2=33" ]
Current State: 33:[32, 29, 16, 6], Operations: [] Exploring Operation: 32/16=2, Resulting Numbers: [29, 6, 2] Generated Node #2: [29, 6, 2] from Operation: 32/16=2 Current State: 33:[29, 6, 2], Operations: ['32/16=2'] Exploring Operation: 29+6=35, Resulting Numbers: [2, 35] Generated Node #3: [2, 35] from Operation: 29+6=35 Current State: 33:[2, 35], Operations: ['32/16=2', '29+6=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[32, 29, 16, 6], Operations: [] Exploring Operation: 29-16=13, Resulting Numbers: [32, 6, 13] Generated Node #0,0: 33:[32, 6, 13] Operation: 29-16=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[32, 6, 13], Operations: ['29-16=13'] Exploring Operation: 13-6=7, Resulting Numbers: [32, 7] Generated Node #0,0,0: 33:[32, 7] Operation: 13-6=7 Moving to Node #0,0,0 Current State: 33:[32, 7], Operations: ['29-16=13', '13-6=7'] Exploring Operation: 32+7=39, Resulting Numbers: [39] 39,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 32, 51, 67, 58 ]
56
[ "67-51=16", "32/16=2", "58-2=56" ]
Current State: 56:[32, 51, 67, 58], Operations: [] Exploring Operation: 67-51=16, Resulting Numbers: [32, 58, 16] Generated Node #2: [32, 58, 16] from Operation: 67-51=16 Current State: 56:[32, 58, 16], Operations: ['67-51=16'] Exploring Operation: 32/16=2, Resulting Numbers: [58, 2] Generated Node #3: [58, 2] from Operation: 32/16=2 Current State: 56:[58, 2], Operations: ['67-51=16', '32/16=2'] Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[32, 51, 67, 58], Operations: [] Exploring Operation: 51-32=19, Resulting Numbers: [67, 58, 19] Generated Node #0,0: 56:[67, 58, 19] Operation: 51-32=19 Exploring Operation: 58-51=7, Resulting Numbers: [32, 67, 7] Generated Node #0,1: 56:[32, 67, 7] Operation: 58-51=7 Exploring Operation: 67-58=9, Resulting Numbers: [32, 51, 9] Generated Node #0,2: 56:[32, 51, 9] Operation: 67-58=9 Exploring Operation: 67-32=35, Resulting Numbers: [51, 58, 35] Generated Node #0,3: 56:[51, 58, 35] Operation: 67-32=35 Exploring Operation: 67-51=16, Resulting Numbers: [32, 58, 16] Generated Node #0,4: 56:[32, 58, 16] Operation: 67-51=16 Start Sub Search at level 1: Moving to Node #0,4 Current State: 56:[32, 58, 16], Operations: ['67-51=16'] Exploring Operation: 32-16=16, Resulting Numbers: [58, 16] Generated Node #0,4,0: 56:[58, 16] Operation: 32-16=16 Exploring Operation: 58-16=42, Resulting Numbers: [32, 42] Generated Node #0,4,1: 56:[32, 42] Operation: 58-16=42 Exploring Operation: 58-32=26, Resulting Numbers: [16, 26] Generated Node #0,4,2: 56:[16, 26] Operation: 58-32=26 Exploring Operation: 32+16=48, Resulting Numbers: [58, 48] Generated Node #0,4,3: 56:[58, 48] Operation: 32+16=48 Exploring Operation: 32/16=2, Resulting Numbers: [58, 2] Generated Node #0,4,4: 56:[58, 2] Operation: 32/16=2 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 56:[58, 2], Operations: ['67-51=16', '32/16=2'] Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,56 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[32, 51, 67, 58], Operations: [] Exploring Operation: 67-51=16, Resulting Numbers: [32, 58, 16] Generated Node #0,4: 56:[32, 58, 16] Operation: 67-51=16 Moving to Node #0,4 Current State: 56:[32, 58, 16], Operations: ['67-51=16'] Exploring Operation: 32/16=2, Resulting Numbers: [58, 2] Generated Node #0,4,4: 56:[58, 2] Operation: 32/16=2 Moving to Node #0,4,4 Current State: 56:[58, 2], Operations: ['67-51=16', '32/16=2'] Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 54, 85, 4, 51 ]
84
[ "54+85=139", "4+51=55", "139-55=84" ]
Current State: 84:[54, 85, 4, 51], Operations: [] Exploring Operation: 54+85=139, Resulting Numbers: [4, 51, 139] Generated Node #2: [4, 51, 139] from Operation: 54+85=139 Current State: 84:[4, 51, 139], Operations: ['54+85=139'] Exploring Operation: 4+51=55, Resulting Numbers: [139, 55] Generated Node #3: [139, 55] from Operation: 4+51=55 Current State: 84:[139, 55], Operations: ['54+85=139', '4+51=55'] Exploring Operation: 139-55=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[54, 85, 4, 51], Operations: [] Exploring Operation: 85-54=31, Resulting Numbers: [4, 51, 31] Generated Node #0,0: 84:[4, 51, 31] Operation: 85-54=31 Exploring Operation: 54-51=3, Resulting Numbers: [85, 4, 3] Generated Node #0,1: 84:[85, 4, 3] Operation: 54-51=3 Moving to Node #0,1 Current State: 84:[85, 4, 3], Operations: ['54-51=3'] Exploring Operation: 4*3=12, Resulting Numbers: [85, 12] Generated Node #0,1,0: 84:[85, 12] Operation: 4*3=12 Exploring Operation: 4+3=7, Resulting Numbers: [85, 7] Generated Node #0,1,1: 84:[85, 7] Operation: 4+3=7 Moving to Node #0,0 Current State: 84:[4, 51, 31], Operations: ['85-54=31'] Exploring Operation: 51+31=82, Resulting Numbers: [4, 82] Generated Node #0,0,0: 84:[4, 82] Operation: 51+31=82 Exploring Operation: 51-31=20, Resulting Numbers: [4, 20] Generated Node #0,0,1: 84:[4, 20] Operation: 51-31=20 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[4, 20], Operations: ['85-54=31', '51-31=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,84 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:[4, 82], Operations: ['85-54=31', '51+31=82'] Exploring Operation: 4+82=86, Resulting Numbers: [86] 86,84 unequal: No Solution Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,84 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: 84:[85, 12], Operations: ['54-51=3', '4*3=12'] Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,84 unequal: No Solution Exploring Operation: 85+12=97, Resulting Numbers: [97] 97,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[85, 7], Operations: ['54-51=3', '4+3=7'] Exploring Operation: 85+7=92, Resulting Numbers: [92] 92,84 unequal: No Solution Exploring Operation: 85-7=78, Resulting Numbers: [78] 78,84 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 97, 19, 80, 80 ]
44
[ "97+19=116", "80+80=160", "160-116=44" ]
Current State: 44:[97, 19, 80, 80], Operations: [] Exploring Operation: 97+19=116, Resulting Numbers: [80, 80, 116] Generated Node #2: [80, 80, 116] from Operation: 97+19=116 Current State: 44:[80, 80, 116], Operations: ['97+19=116'] Exploring Operation: 80+80=160, Resulting Numbers: [116, 160] Generated Node #3: [116, 160] from Operation: 80+80=160 Current State: 44:[116, 160], Operations: ['97+19=116', '80+80=160'] Exploring Operation: 160-116=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[97, 19, 80, 80], Operations: [] Exploring Operation: 97-80=17, Resulting Numbers: [19, 80, 17] Generated Node #0,0: 44:[19, 80, 17] Operation: 97-80=17 Exploring Operation: 97-80=17, Resulting Numbers: [19, 80, 17] Generated Node #0,1: 44:[19, 80, 17] Operation: 97-80=17 Exploring Operation: 80/80=1, Resulting Numbers: [97, 19, 1] Generated Node #0,2: 44:[97, 19, 1] Operation: 80/80=1 Exploring Operation: 80-80=0, Resulting Numbers: [97, 19, 0] Generated Node #0,3: 44:[97, 19, 0] Operation: 80-80=0 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[19, 80, 17], Operations: ['97-80=17'] Exploring Operation: 19-17=2, Resulting Numbers: [80, 2] Generated Node #0,0,0: 44:[80, 2] Operation: 19-17=2 Exploring Operation: 80-17=63, Resulting Numbers: [19, 63] Generated Node #0,0,1: 44:[19, 63] Operation: 80-17=63 Exploring Operation: 19+17=36, Resulting Numbers: [80, 36] Generated Node #0,0,2: 44:[80, 36] Operation: 19+17=36 Exploring Operation: 80-19=61, Resulting Numbers: [17, 61] Generated Node #0,0,3: 44:[17, 61] Operation: 80-19=61 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 44:[19, 63], Operations: ['97-80=17', '80-17=63'] Exploring Operation: 63-19=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[97, 19, 80, 80], Operations: [] Exploring Operation: 97-80=17, Resulting Numbers: [19, 80, 17] Generated Node #0,0: 44:[19, 80, 17] Operation: 97-80=17 Moving to Node #0,0 Current State: 44:[19, 80, 17], Operations: ['97-80=17'] Exploring Operation: 80-17=63, Resulting Numbers: [19, 63] Generated Node #0,0,1: 44:[19, 63] Operation: 80-17=63 Moving to Node #0,0,1 Current State: 44:[19, 63], Operations: ['97-80=17', '80-17=63'] Exploring Operation: 63-19=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 17, 73, 25, 68 ]
52
[ "68/17=4", "73-25=48", "4+48=52" ]
Current State: 52:[17, 73, 25, 68], Operations: [] Exploring Operation: 68/17=4, Resulting Numbers: [73, 25, 4] Generated Node #2: [73, 25, 4] from Operation: 68/17=4 Current State: 52:[73, 25, 4], Operations: ['68/17=4'] Exploring Operation: 73-25=48, Resulting Numbers: [4, 48] Generated Node #3: [4, 48] from Operation: 73-25=48 Current State: 52:[4, 48], Operations: ['68/17=4', '73-25=48'] Exploring Operation: 4+48=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[17, 73, 25, 68], Operations: [] Exploring Operation: 68-17=51, Resulting Numbers: [73, 25, 51] Generated Node #0,0: 52:[73, 25, 51] Operation: 68-17=51 Exploring Operation: 73-68=5, Resulting Numbers: [17, 25, 5] Generated Node #0,1: 52:[17, 25, 5] Operation: 73-68=5 Exploring Operation: 68/17=4, Resulting Numbers: [73, 25, 4] Generated Node #0,2: 52:[73, 25, 4] Operation: 68/17=4 Exploring Operation: 73-17=56, Resulting Numbers: [25, 68, 56] Generated Node #0,3: 52:[25, 68, 56] Operation: 73-17=56 Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[17, 25, 5], Operations: ['73-68=5'] Exploring Operation: 17-5=12, Resulting Numbers: [25, 12] Generated Node #0,1,0: 52:[25, 12] Operation: 17-5=12 Exploring Operation: 25-17=8, Resulting Numbers: [5, 8] Generated Node #0,1,1: 52:[5, 8] Operation: 25-17=8 Exploring Operation: 17+5=22, Resulting Numbers: [25, 22] Generated Node #0,1,2: 52:[25, 22] Operation: 17+5=22 Exploring Operation: 25/5=5, Resulting Numbers: [17, 5] Generated Node #0,1,3: 52:[17, 5] Operation: 25/5=5 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[25, 12], Operations: ['73-68=5', '17-5=12'] Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,52 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,52 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[5, 8], Operations: ['73-68=5', '25-17=8'] Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,52 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,52 unequal: No Solution Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[25, 22], Operations: ['73-68=5', '17+5=22'] Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,52 unequal: No Solution Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 25*22=550, Resulting Numbers: [550] 550,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 52:[17, 5], Operations: ['73-68=5', '25/5=5'] Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,52 unequal: No Solution Exploring Operation: 17*5=85, Resulting Numbers: [85] 85,52 unequal: No Solution Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[25, 68, 56], Operations: ['73-17=56'] Exploring Operation: 68-56=12, Resulting Numbers: [25, 12] Generated Node #0,3,0: 52:[25, 12] Operation: 68-56=12 Exploring Operation: 68-25=43, Resulting Numbers: [56, 43] Generated Node #0,3,1: 52:[56, 43] Operation: 68-25=43 Exploring Operation: 25+68=93, Resulting Numbers: [56, 93] Generated Node #0,3,2: 52:[56, 93] Operation: 25+68=93 Exploring Operation: 56-25=31, Resulting Numbers: [68, 31] Generated Node #0,3,3: 52:[68, 31] Operation: 56-25=31 Moving to Node #0,3,0 Current State: 52:[25, 12], Operations: ['73-17=56', '68-56=12'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,52 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,52 unequal: No Solution Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,52 unequal: No Solution Moving to Node #0,3,1 Current State: 52:[56, 43], Operations: ['73-17=56', '68-25=43'] Exploring Operation: 56+43=99, Resulting Numbers: [99] 99,52 unequal: No Solution Exploring Operation: 56*43=2408, Resulting Numbers: [2408] 2408,52 unequal: No Solution Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,52 unequal: No Solution Moving to Node #0,3,3 Current State: 52:[68, 31], Operations: ['73-17=56', '56-25=31'] Exploring Operation: 68*31=2108, Resulting Numbers: [2108] 2108,52 unequal: No Solution Exploring Operation: 68+31=99, Resulting Numbers: [99] 99,52 unequal: No Solution Exploring Operation: 68-31=37, Resulting Numbers: [37] 37,52 unequal: No Solution Moving to Node #0,3,2 Current State: 52:[56, 93], Operations: ['73-17=56', '25+68=93'] Exploring Operation: 56+93=149, Resulting Numbers: [149] 149,52 unequal: No Solution Exploring Operation: 93-56=37, Resulting Numbers: [37] 37,52 unequal: No Solution Exploring Operation: 56*93=5208, Resulting Numbers: [5208] 5208,52 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 Current State: 52:[73, 25, 4], Operations: ['68/17=4'] Exploring Operation: 25+4=29, Resulting Numbers: [73, 29] Generated Node #0,2,0: 52:[73, 29] Operation: 25+4=29 Exploring Operation: 73+4=77, Resulting Numbers: [25, 77] Generated Node #0,2,1: 52:[25, 77] Operation: 73+4=77 Exploring Operation: 73-4=69, Resulting Numbers: [25, 69] Generated Node #0,2,2: 52:[25, 69] Operation: 73-4=69 Exploring Operation: 73-25=48, Resulting Numbers: [4, 48] Generated Node #0,2,3: 52:[4, 48] Operation: 73-25=48 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 52:[4, 48], Operations: ['68/17=4', '73-25=48'] Exploring Operation: 48/4=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 4+48=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[17, 73, 25, 68], Operations: [] Exploring Operation: 68/17=4, Resulting Numbers: [73, 25, 4] Generated Node #0,2: 52:[73, 25, 4] Operation: 68/17=4 Moving to Node #0,2 Current State: 52:[73, 25, 4], Operations: ['68/17=4'] Exploring Operation: 73-25=48, Resulting Numbers: [4, 48] Generated Node #0,2,3: 52:[4, 48] Operation: 73-25=48 Moving to Node #0,2,3 Current State: 52:[4, 48], Operations: ['68/17=4', '73-25=48'] Exploring Operation: 4+48=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.960069
hs_4
sum_heuristic
[ 59, 33, 84, 20 ]
38
[ "59-33=26", "84-20=64", "64-26=38" ]
Current State: 38:[59, 33, 84, 20], Operations: [] Exploring Operation: 59-33=26, Resulting Numbers: [84, 20, 26] Generated Node #2: [84, 20, 26] from Operation: 59-33=26 Current State: 38:[84, 20, 26], Operations: ['59-33=26'] Exploring Operation: 84-20=64, Resulting Numbers: [26, 64] Generated Node #3: [26, 64] from Operation: 84-20=64 Current State: 38:[26, 64], Operations: ['59-33=26', '84-20=64'] Exploring Operation: 64-26=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[59, 33, 84, 20], Operations: [] Exploring Operation: 59-20=39, Resulting Numbers: [33, 84, 39] Generated Node #0,0: 38:[33, 84, 39] Operation: 59-20=39 Exploring Operation: 84-33=51, Resulting Numbers: [59, 20, 51] Generated Node #0,1: 38:[59, 20, 51] Operation: 84-33=51 Exploring Operation: 84-59=25, Resulting Numbers: [33, 20, 25] Generated Node #0,2: 38:[33, 20, 25] Operation: 84-59=25 Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[33, 20, 25], Operations: ['84-59=25'] Exploring Operation: 33-25=8, Resulting Numbers: [20, 8] Generated Node #0,2,0: 38:[20, 8] Operation: 33-25=8 Exploring Operation: 25-20=5, Resulting Numbers: [33, 5] Generated Node #0,2,1: 38:[33, 5] Operation: 25-20=5 Exploring Operation: 33-20=13, Resulting Numbers: [25, 13] Generated Node #0,2,2: 38:[25, 13] Operation: 33-20=13 Moving to Node #0,2,0 Current State: 38:[20, 8], Operations: ['84-59=25', '33-25=8'] Exploring Operation: 20+8=28, Resulting Numbers: [28] 28,38 unequal: No Solution Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,38 unequal: No Solution Exploring Operation: 20*8=160, Resulting Numbers: [160] 160,38 unequal: No Solution Moving to Node #0,2,1 Current State: 38:[33, 5], Operations: ['84-59=25', '25-20=5'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,38 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[59, 33, 84, 20], Operations: [] Exploring Operation: 84-59=25, Resulting Numbers: [33, 20, 25] Generated Node #0,2: 38:[33, 20, 25] Operation: 84-59=25 Moving to Node #0,2 Current State: 38:[33, 20, 25], Operations: ['84-59=25'] Exploring Operation: 25-20=5, Resulting Numbers: [33, 5] Generated Node #0,2,1: 38:[33, 5] Operation: 25-20=5 Moving to Node #0,2,1 Current State: 38:[33, 5], Operations: ['84-59=25', '25-20=5'] Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 18, 39, 26, 16 ]
15
[ "18+39=57", "26+16=42", "57-42=15" ]
Current State: 15:[18, 39, 26, 16], Operations: [] Exploring Operation: 18+39=57, Resulting Numbers: [26, 16, 57] Generated Node #2: [26, 16, 57] from Operation: 18+39=57 Current State: 15:[26, 16, 57], Operations: ['18+39=57'] Exploring Operation: 26+16=42, Resulting Numbers: [57, 42] Generated Node #3: [57, 42] from Operation: 26+16=42 Current State: 15:[57, 42], Operations: ['18+39=57', '26+16=42'] Exploring Operation: 57-42=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[18, 39, 26, 16], Operations: [] Exploring Operation: 39-18=21, Resulting Numbers: [26, 16, 21] Generated Node #0,0: 15:[26, 16, 21] Operation: 39-18=21 Exploring Operation: 39-26=13, Resulting Numbers: [18, 16, 13] Generated Node #0,1: 15:[18, 16, 13] Operation: 39-26=13 Exploring Operation: 26-16=10, Resulting Numbers: [18, 39, 10] Generated Node #0,2: 15:[18, 39, 10] Operation: 26-16=10 Exploring Operation: 39-16=23, Resulting Numbers: [18, 26, 23] Generated Node #0,3: 15:[18, 26, 23] Operation: 39-16=23 Exploring Operation: 26-18=8, Resulting Numbers: [39, 16, 8] Generated Node #0,4: 15:[39, 16, 8] Operation: 26-18=8 Moving to Node #0,1 Current State: 15:[18, 16, 13], Operations: ['39-26=13'] Exploring Operation: 18-13=5, Resulting Numbers: [16, 5] Generated Node #0,1,0: 15:[16, 5] Operation: 18-13=5 Exploring Operation: 16-13=3, Resulting Numbers: [18, 3] Generated Node #0,1,1: 15:[18, 3] Operation: 16-13=3 Exploring Operation: 18+13=31, Resulting Numbers: [16, 31] Generated Node #0,1,2: 15:[16, 31] Operation: 18+13=31 Exploring Operation: 18-16=2, Resulting Numbers: [13, 2] Generated Node #0,1,3: 15:[13, 2] Operation: 18-16=2 Exploring Operation: 16+13=29, Resulting Numbers: [18, 29] Generated Node #0,1,4: 15:[18, 29] Operation: 16+13=29 Moving to Node #0,0 Current State: 15:[26, 16, 21], Operations: ['39-18=21'] Exploring Operation: 26+16=42, Resulting Numbers: [21, 42] Generated Node #0,0,0: 15:[21, 42] Operation: 26+16=42 Exploring Operation: 21-16=5, Resulting Numbers: [26, 5] Generated Node #0,0,1: 15:[26, 5] Operation: 21-16=5 Exploring Operation: 26-16=10, Resulting Numbers: [21, 10] Generated Node #0,0,2: 15:[21, 10] Operation: 26-16=10 Exploring Operation: 26+21=47, Resulting Numbers: [16, 47] Generated Node #0,0,3: 15:[16, 47] Operation: 26+21=47 Exploring Operation: 26-21=5, Resulting Numbers: [16, 5] Generated Node #0,0,4: 15:[16, 5] Operation: 26-21=5 Moving to Node #0,3 Current State: 15:[18, 26, 23], Operations: ['39-16=23'] Exploring Operation: 26-18=8, Resulting Numbers: [23, 8] Generated Node #0,3,0: 15:[23, 8] Operation: 26-18=8 Exploring Operation: 18+23=41, Resulting Numbers: [26, 41] Generated Node #0,3,1: 15:[26, 41] Operation: 18+23=41 Exploring Operation: 23-18=5, Resulting Numbers: [26, 5] Generated Node #0,3,2: 15:[26, 5] Operation: 23-18=5 Exploring Operation: 18+26=44, Resulting Numbers: [23, 44] Generated Node #0,3,3: 15:[23, 44] Operation: 18+26=44 Exploring Operation: 26-23=3, Resulting Numbers: [18, 3] Generated Node #0,3,4: 15:[18, 3] Operation: 26-23=3 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 15:[18, 3], Operations: ['39-16=23', '26-23=3'] Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,15 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[18, 39, 26, 16], Operations: [] Exploring Operation: 39-16=23, Resulting Numbers: [18, 26, 23] Generated Node #0,3: 15:[18, 26, 23] Operation: 39-16=23 Moving to Node #0,3 Current State: 15:[18, 26, 23], Operations: ['39-16=23'] Exploring Operation: 26-23=3, Resulting Numbers: [18, 3] Generated Node #0,3,4: 15:[18, 3] Operation: 26-23=3 Moving to Node #0,3,4 Current State: 15:[18, 3], Operations: ['39-16=23', '26-23=3'] Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_5
mult_heuristic
[ 24, 13, 64, 67 ]
59
[ "67-64=3", "24*3=72", "72-13=59" ]
Current State: 59:[24, 13, 64, 67], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [24, 13, 3] Generated Node #2: [24, 13, 3] from Operation: 67-64=3 Current State: 59:[24, 13, 3], Operations: ['67-64=3'] Exploring Operation: 24*3=72, Resulting Numbers: [13, 72] Generated Node #3: [13, 72] from Operation: 24*3=72 Current State: 59:[13, 72], Operations: ['67-64=3', '24*3=72'] Exploring Operation: 72-13=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[24, 13, 64, 67], Operations: [] Exploring Operation: 67-13=54, Resulting Numbers: [24, 64, 54] Generated Node #0,0: 59:[24, 64, 54] Operation: 67-13=54 Exploring Operation: 24+13=37, Resulting Numbers: [64, 67, 37] Generated Node #0,1: 59:[64, 67, 37] Operation: 24+13=37 Moving to Node #0,1 Current State: 59:[64, 67, 37], Operations: ['24+13=37'] Exploring Operation: 67-37=30, Resulting Numbers: [64, 30] Generated Node #0,1,0: 59:[64, 30] Operation: 67-37=30 Exploring Operation: 64-37=27, Resulting Numbers: [67, 27] Generated Node #0,1,1: 59:[67, 27] Operation: 64-37=27 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[64, 30], Operations: ['24+13=37', '67-37=30'] Exploring Operation: 64+30=94, Resulting Numbers: [94] 94,59 unequal: No Solution Exploring Operation: 64-30=34, Resulting Numbers: [34] 34,59 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:[67, 27], Operations: ['24+13=37', '64-37=27'] Exploring Operation: 67-27=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 67+27=94, Resulting Numbers: [94] 94,59 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: 59:[24, 64, 54], Operations: ['67-13=54'] Exploring Operation: 24+54=78, Resulting Numbers: [64, 78] Generated Node #0,0,0: 59:[64, 78] Operation: 24+54=78 Exploring Operation: 64-24=40, Resulting Numbers: [54, 40] Generated Node #0,0,1: 59:[54, 40] Operation: 64-24=40 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[64, 78], Operations: ['67-13=54', '24+54=78'] Exploring Operation: 78-64=14, Resulting Numbers: [14] 14,59 unequal: No Solution Exploring Operation: 64+78=142, Resulting Numbers: [142] 142,59 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:[54, 40], Operations: ['67-13=54', '64-24=40'] Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,59 unequal: No Solution Exploring Operation: 54+40=94, Resulting Numbers: [94] 94,59 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, 98, 24, 82 ]
54
[ "36*24=864", "98-82=16", "864/16=54" ]
Current State: 54:[36, 98, 24, 82], Operations: [] Exploring Operation: 36*24=864, Resulting Numbers: [98, 82, 864] Generated Node #2: [98, 82, 864] from Operation: 36*24=864 Current State: 54:[98, 82, 864], Operations: ['36*24=864'] Exploring Operation: 98-82=16, Resulting Numbers: [864, 16] Generated Node #3: [864, 16] from Operation: 98-82=16 Current State: 54:[864, 16], Operations: ['36*24=864', '98-82=16'] Exploring Operation: 864/16=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[36, 98, 24, 82], Operations: [] Exploring Operation: 98-36=62, Resulting Numbers: [24, 82, 62] Generated Node #0,0: 54:[24, 82, 62] Operation: 98-36=62 Exploring Operation: 98-82=16, Resulting Numbers: [36, 24, 16] Generated Node #0,1: 54:[36, 24, 16] Operation: 98-82=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[36, 24, 16], Operations: ['98-82=16'] Exploring Operation: 36-24=12, Resulting Numbers: [16, 12] Generated Node #0,1,0: 54:[16, 12] Operation: 36-24=12 Exploring Operation: 36+16=52, Resulting Numbers: [24, 52] Generated Node #0,1,1: 54:[24, 52] Operation: 36+16=52 Moving to Node #0,1,0 Current State: 54:[16, 12], Operations: ['98-82=16', '36-24=12'] Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[24, 52], Operations: ['98-82=16', '36+16=52'] Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 24+52=76, Resulting Numbers: [76] 76,54 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:[24, 82, 62], Operations: ['98-36=62'] Exploring Operation: 82-62=20, Resulting Numbers: [24, 20] Generated Node #0,0,0: 54:[24, 20] Operation: 82-62=20 Exploring Operation: 82-24=58, Resulting Numbers: [62, 58] Generated Node #0,0,1: 54:[62, 58] Operation: 82-24=58 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[24, 20], Operations: ['98-36=62', '82-62=20'] Exploring Operation: 24+20=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 54:[62, 58], Operations: ['98-36=62', '82-24=58'] Exploring Operation: 62+58=120, Resulting Numbers: [120] 120,54 unequal: No Solution Exploring Operation: 62-58=4, Resulting Numbers: [4] 4,54 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_2
mult_heuristic
[ 59, 26, 15, 69 ]
39
[ "69-59=10", "26*15=390", "390/10=39" ]
Current State: 39:[59, 26, 15, 69], Operations: [] Exploring Operation: 69-59=10, Resulting Numbers: [26, 15, 10] Generated Node #2: [26, 15, 10] from Operation: 69-59=10 Current State: 39:[26, 15, 10], Operations: ['69-59=10'] Exploring Operation: 26*15=390, Resulting Numbers: [10, 390] Generated Node #3: [10, 390] from Operation: 26*15=390 Current State: 39:[10, 390], Operations: ['69-59=10', '26*15=390'] Exploring Operation: 390/10=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[59, 26, 15, 69], Operations: [] Exploring Operation: 69-59=10, Resulting Numbers: [26, 15, 10] Generated Node #0,0: 39:[26, 15, 10] Operation: 69-59=10 Exploring Operation: 69-26=43, Resulting Numbers: [59, 15, 43] Generated Node #0,1: 39:[59, 15, 43] Operation: 69-26=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[26, 15, 10], Operations: ['69-59=10'] Exploring Operation: 26-15=11, Resulting Numbers: [10, 11] Generated Node #0,0,0: 39:[10, 11] Operation: 26-15=11 Exploring Operation: 26+15=41, Resulting Numbers: [10, 41] Generated Node #0,0,1: 39:[10, 41] Operation: 26+15=41 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[10, 11], Operations: ['69-59=10', '26-15=11'] Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 39:[10, 41], Operations: ['69-59=10', '26+15=41'] Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,39 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[59, 15, 43], Operations: ['69-26=43'] Exploring Operation: 59-43=16, Resulting Numbers: [15, 16] Generated Node #0,1,0: 39:[15, 16] Operation: 59-43=16 Exploring Operation: 59-15=44, Resulting Numbers: [43, 44] Generated Node #0,1,1: 39:[43, 44] Operation: 59-15=44 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 39:[15, 16], Operations: ['69-26=43', '59-43=16'] Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 39:[43, 44], Operations: ['69-26=43', '59-15=44'] Exploring Operation: 44-43=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 43+44=87, Resulting Numbers: [87] 87,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 65, 82, 72, 66 ]
23
[ "82-65=17", "72-66=6", "17+6=23" ]
Current State: 23:[65, 82, 72, 66], Operations: [] Exploring Operation: 82-65=17, Resulting Numbers: [72, 66, 17] Generated Node #2: [72, 66, 17] from Operation: 82-65=17 Current State: 23:[72, 66, 17], Operations: ['82-65=17'] Exploring Operation: 72-66=6, Resulting Numbers: [17, 6] Generated Node #3: [17, 6] from Operation: 72-66=6 Current State: 23:[17, 6], Operations: ['82-65=17', '72-66=6'] Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[65, 82, 72, 66], Operations: [] Exploring Operation: 82-65=17, Resulting Numbers: [72, 66, 17] Generated Node #0,0: 23:[72, 66, 17] Operation: 82-65=17 Exploring Operation: 82-72=10, Resulting Numbers: [65, 66, 10] Generated Node #0,1: 23:[65, 66, 10] Operation: 82-72=10 Moving to Node #0,0 Current State: 23:[72, 66, 17], Operations: ['82-65=17'] Exploring Operation: 72-66=6, Resulting Numbers: [17, 6] Generated Node #0,0,0: 23:[17, 6] Operation: 72-66=6 Exploring Operation: 72-17=55, Resulting Numbers: [66, 55] Generated Node #0,0,1: 23:[66, 55] Operation: 72-17=55 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 23:[17, 6], Operations: ['82-65=17', '72-66=6'] Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[65, 82, 72, 66], Operations: [] Exploring Operation: 82-65=17, Resulting Numbers: [72, 66, 17] Generated Node #0,0: 23:[72, 66, 17] Operation: 82-65=17 Moving to Node #0,0 Current State: 23:[72, 66, 17], Operations: ['82-65=17'] Exploring Operation: 72-66=6, Resulting Numbers: [17, 6] Generated Node #0,0,0: 23:[17, 6] Operation: 72-66=6 Moving to Node #0,0,0 Current State: 23:[17, 6], Operations: ['82-65=17', '72-66=6'] Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 83, 58, 62, 43 ]
44
[ "83-58=25", "62-43=19", "25+19=44" ]
Current State: 44:[83, 58, 62, 43], Operations: [] Exploring Operation: 83-58=25, Resulting Numbers: [62, 43, 25] Generated Node #2: [62, 43, 25] from Operation: 83-58=25 Current State: 44:[62, 43, 25], Operations: ['83-58=25'] Exploring Operation: 62-43=19, Resulting Numbers: [25, 19] Generated Node #3: [25, 19] from Operation: 62-43=19 Current State: 44:[25, 19], Operations: ['83-58=25', '62-43=19'] Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[83, 58, 62, 43], Operations: [] Exploring Operation: 62-43=19, Resulting Numbers: [83, 58, 19] Generated Node #0,0: 44:[83, 58, 19] Operation: 62-43=19 Exploring Operation: 83-58=25, Resulting Numbers: [62, 43, 25] Generated Node #0,1: 44:[62, 43, 25] Operation: 83-58=25 Exploring Operation: 62-58=4, Resulting Numbers: [83, 43, 4] Generated Node #0,2: 44:[83, 43, 4] Operation: 62-58=4 Exploring Operation: 83-62=21, Resulting Numbers: [58, 43, 21] Generated Node #0,3: 44:[58, 43, 21] Operation: 83-62=21 Exploring Operation: 83-43=40, Resulting Numbers: [58, 62, 40] Generated Node #0,4: 44:[58, 62, 40] Operation: 83-43=40 Moving to Node #0,3 Current State: 44:[58, 43, 21], Operations: ['83-62=21'] Exploring Operation: 43-21=22, Resulting Numbers: [58, 22] Generated Node #0,3,0: 44:[58, 22] Operation: 43-21=22 Exploring Operation: 58+21=79, Resulting Numbers: [43, 79] Generated Node #0,3,1: 44:[43, 79] Operation: 58+21=79 Exploring Operation: 43+21=64, Resulting Numbers: [58, 64] Generated Node #0,3,2: 44:[58, 64] Operation: 43+21=64 Exploring Operation: 58-21=37, Resulting Numbers: [43, 37] Generated Node #0,3,3: 44:[43, 37] Operation: 58-21=37 Exploring Operation: 58-43=15, Resulting Numbers: [21, 15] Generated Node #0,3,4: 44:[21, 15] Operation: 58-43=15 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 44:[21, 15], Operations: ['83-62=21', '58-43=15'] Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,44 unequal: No Solution No 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: 44:[43, 37], Operations: ['83-62=21', '58-21=37'] Exploring Operation: 43*37=1591, Resulting Numbers: [1591] 1591,44 unequal: No Solution Exploring Operation: 43-37=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 43+37=80, Resulting Numbers: [80] 80,44 unequal: No Solution No 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: 44:[58, 22], Operations: ['83-62=21', '43-21=22'] Exploring Operation: 58-22=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 58*22=1276, Resulting Numbers: [1276] 1276,44 unequal: No Solution Exploring Operation: 58+22=80, Resulting Numbers: [80] 80,44 unequal: No Solution No 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: 44:[58, 64], Operations: ['83-62=21', '43+21=64'] Exploring Operation: 64-58=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 58+64=122, Resulting Numbers: [122] 122,44 unequal: No Solution Exploring Operation: 58*64=3712, Resulting Numbers: [3712] 3712,44 unequal: No Solution No 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: 44:[43, 79], Operations: ['83-62=21', '58+21=79'] Exploring Operation: 43*79=3397, Resulting Numbers: [3397] 3397,44 unequal: No Solution Exploring Operation: 79-43=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 43+79=122, Resulting Numbers: [122] 122,44 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: 44:[62, 43, 25], Operations: ['83-58=25'] Exploring Operation: 43-25=18, Resulting Numbers: [62, 18] Generated Node #0,1,0: 44:[62, 18] Operation: 43-25=18 Exploring Operation: 43+25=68, Resulting Numbers: [62, 68] Generated Node #0,1,1: 44:[62, 68] Operation: 43+25=68 Exploring Operation: 62-25=37, Resulting Numbers: [43, 37] Generated Node #0,1,2: 44:[43, 37] Operation: 62-25=37 Exploring Operation: 62+25=87, Resulting Numbers: [43, 87] Generated Node #0,1,3: 44:[43, 87] Operation: 62+25=87 Exploring Operation: 62-43=19, Resulting Numbers: [25, 19] Generated Node #0,1,4: 44:[25, 19] Operation: 62-43=19 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 44:[25, 19], Operations: ['83-58=25', '62-43=19'] Exploring Operation: 25*19=475, Resulting Numbers: [475] 475,44 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[83, 58, 62, 43], Operations: [] Exploring Operation: 83-58=25, Resulting Numbers: [62, 43, 25] Generated Node #0,1: 44:[62, 43, 25] Operation: 83-58=25 Moving to Node #0,1 Current State: 44:[62, 43, 25], Operations: ['83-58=25'] Exploring Operation: 62-43=19, Resulting Numbers: [25, 19] Generated Node #0,1,4: 44:[25, 19] Operation: 62-43=19 Moving to Node #0,1,4 Current State: 44:[25, 19], Operations: ['83-58=25', '62-43=19'] Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 71, 99, 7, 5 ]
20
[ "99-71=28", "28/7=4", "5*4=20" ]
Current State: 20:[71, 99, 7, 5], Operations: [] Exploring Operation: 99-71=28, Resulting Numbers: [7, 5, 28] Generated Node #2: [7, 5, 28] from Operation: 99-71=28 Current State: 20:[7, 5, 28], Operations: ['99-71=28'] Exploring Operation: 28/7=4, Resulting Numbers: [5, 4] Generated Node #3: [5, 4] from Operation: 28/7=4 Current State: 20:[5, 4], Operations: ['99-71=28', '28/7=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[71, 99, 7, 5], Operations: [] Exploring Operation: 71-7=64, Resulting Numbers: [99, 5, 64] Generated Node #0,0: 20:[99, 5, 64] Operation: 71-7=64 Exploring Operation: 99-7=92, Resulting Numbers: [71, 5, 92] Generated Node #0,1: 20:[71, 5, 92] Operation: 99-7=92 Exploring Operation: 99-71=28, Resulting Numbers: [7, 5, 28] Generated Node #0,2: 20:[7, 5, 28] Operation: 99-71=28 Start Sub Search at level 1: Moving to Node #0,2 Current State: 20:[7, 5, 28], Operations: ['99-71=28'] Exploring Operation: 28-5=23, Resulting Numbers: [7, 23] Generated Node #0,2,0: 20:[7, 23] Operation: 28-5=23 Exploring Operation: 28-7=21, Resulting Numbers: [5, 21] Generated Node #0,2,1: 20:[5, 21] Operation: 28-7=21 Exploring Operation: 28/7=4, Resulting Numbers: [5, 4] Generated Node #0,2,2: 20:[5, 4] Operation: 28/7=4 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 20:[5, 4], Operations: ['99-71=28', '28/7=4'] Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[71, 99, 7, 5], Operations: [] Exploring Operation: 99-71=28, Resulting Numbers: [7, 5, 28] Generated Node #0,2: 20:[7, 5, 28] Operation: 99-71=28 Moving to Node #0,2 Current State: 20:[7, 5, 28], Operations: ['99-71=28'] Exploring Operation: 28/7=4, Resulting Numbers: [5, 4] Generated Node #0,2,2: 20:[5, 4] Operation: 28/7=4 Moving to Node #0,2,2 Current State: 20:[5, 4], Operations: ['99-71=28', '28/7=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 43, 74, 1, 53 ]
85
[ "74-43=31", "1+53=54", "31+54=85" ]
Current State: 85:[43, 74, 1, 53], Operations: [] Exploring Operation: 74-43=31, Resulting Numbers: [1, 53, 31] Generated Node #2: [1, 53, 31] from Operation: 74-43=31 Current State: 85:[1, 53, 31], Operations: ['74-43=31'] Exploring Operation: 1+53=54, Resulting Numbers: [31, 54] Generated Node #3: [31, 54] from Operation: 1+53=54 Current State: 85:[31, 54], Operations: ['74-43=31', '1+53=54'] Exploring Operation: 31+54=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[43, 74, 1, 53], Operations: [] Exploring Operation: 43+74=117, Resulting Numbers: [1, 53, 117] Generated Node #0,0: 85:[1, 53, 117] Operation: 43+74=117 Exploring Operation: 74-53=21, Resulting Numbers: [43, 1, 21] Generated Node #0,1: 85:[43, 1, 21] Operation: 74-53=21 Exploring Operation: 53-43=10, Resulting Numbers: [74, 1, 10] Generated Node #0,2: 85:[74, 1, 10] Operation: 53-43=10 Exploring Operation: 74-43=31, Resulting Numbers: [1, 53, 31] Generated Node #0,3: 85:[1, 53, 31] Operation: 74-43=31 Exploring Operation: 43+53=96, Resulting Numbers: [74, 1, 96] Generated Node #0,4: 85:[74, 1, 96] Operation: 43+53=96 Moving to Node #0,2 Current State: 85:[74, 1, 10], Operations: ['53-43=10'] Exploring Operation: 10-1=9, Resulting Numbers: [74, 9] Generated Node #0,2,0: 85:[74, 9] Operation: 10-1=9 Exploring Operation: 74+1=75, Resulting Numbers: [10, 75] Generated Node #0,2,1: 85:[10, 75] Operation: 74+1=75 Exploring Operation: 74+10=84, Resulting Numbers: [1, 84] Generated Node #0,2,2: 85:[1, 84] Operation: 74+10=84 Exploring Operation: 74*1=74, Resulting Numbers: [10, 74] Generated Node #0,2,3: 85:[10, 74] Operation: 74*1=74 Exploring Operation: 74/1=74, Resulting Numbers: [10, 74] Generated Node #0,2,4: 85:[10, 74] Operation: 74/1=74 Moving to Node #0,4 Current State: 85:[74, 1, 96], Operations: ['43+53=96'] Exploring Operation: 74/1=74, Resulting Numbers: [96, 74] Generated Node #0,4,0: 85:[96, 74] Operation: 74/1=74 Exploring Operation: 96-1=95, Resulting Numbers: [74, 95] Generated Node #0,4,1: 85:[74, 95] Operation: 96-1=95 Exploring Operation: 74*1=74, Resulting Numbers: [96, 74] Generated Node #0,4,2: 85:[96, 74] Operation: 74*1=74 Exploring Operation: 96-74=22, Resulting Numbers: [1, 22] Generated Node #0,4,3: 85:[1, 22] Operation: 96-74=22 Exploring Operation: 74+1=75, Resulting Numbers: [96, 75] Generated Node #0,4,4: 85:[96, 75] Operation: 74+1=75 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 85:[1, 22], Operations: ['43+53=96', '96-74=22'] Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,85 unequal: No Solution No 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: 85:[74, 95], Operations: ['43+53=96', '96-1=95'] Exploring Operation: 95-74=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 74*95=7030, Resulting Numbers: [7030] 7030,85 unequal: No Solution Exploring Operation: 74+95=169, Resulting Numbers: [169] 169,85 unequal: No Solution No 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: 85:[96, 75], Operations: ['43+53=96', '74+1=75'] Exploring Operation: 96+75=171, Resulting Numbers: [171] 171,85 unequal: No Solution Exploring Operation: 96-75=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 96*75=7200, Resulting Numbers: [7200] 7200,85 unequal: No Solution No 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: 85:[96, 74], Operations: ['43+53=96', '74/1=74'] Exploring Operation: 96*74=7104, Resulting Numbers: [7104] 7104,85 unequal: No Solution Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 96+74=170, Resulting Numbers: [170] 170,85 unequal: No Solution No 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: 85:[96, 74], Operations: ['43+53=96', '74*1=74'] Exploring Operation: 96*74=7104, Resulting Numbers: [7104] 7104,85 unequal: No Solution Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 96+74=170, Resulting Numbers: [170] 170,85 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: 85:[43, 1, 21], Operations: ['74-53=21'] Exploring Operation: 43-1=42, Resulting Numbers: [21, 42] Generated Node #0,1,0: 85:[21, 42] Operation: 43-1=42 Exploring Operation: 21-1=20, Resulting Numbers: [43, 20] Generated Node #0,1,1: 85:[43, 20] Operation: 21-1=20 Exploring Operation: 43*1=43, Resulting Numbers: [21, 43] Generated Node #0,1,2: 85:[21, 43] Operation: 43*1=43 Exploring Operation: 43+21=64, Resulting Numbers: [1, 64] Generated Node #0,1,3: 85:[1, 64] Operation: 43+21=64 Exploring Operation: 43-21=22, Resulting Numbers: [1, 22] Generated Node #0,1,4: 85:[1, 22] Operation: 43-21=22 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 85:[1, 22], Operations: ['74-53=21', '43-21=22'] Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,85 unequal: No Solution No 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: 85:[1, 64], Operations: ['74-53=21', '43+21=64'] Exploring Operation: 1*64=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 64/1=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,85 unequal: No Solution Exploring Operation: 1+64=65, Resulting Numbers: [65] 65,85 unequal: No Solution No 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: 85:[21, 42], Operations: ['74-53=21', '43-1=42'] Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 21*42=882, Resulting Numbers: [882] 882,85 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,85 unequal: No Solution No 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: 85:[43, 20], Operations: ['74-53=21', '21-1=20'] Exploring Operation: 43+20=63, Resulting Numbers: [63] 63,85 unequal: No Solution Exploring Operation: 43*20=860, Resulting Numbers: [860] 860,85 unequal: No Solution Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,85 unequal: No Solution No 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: 85:[21, 43], Operations: ['74-53=21', '43*1=43'] Exploring Operation: 21+43=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 21*43=903, Resulting Numbers: [903] 903,85 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,85 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: 85:[1, 53, 31], Operations: ['74-43=31'] Exploring Operation: 53+31=84, Resulting Numbers: [1, 84] Generated Node #0,3,0: 85:[1, 84] Operation: 53+31=84 Exploring Operation: 1+53=54, Resulting Numbers: [31, 54] Generated Node #0,3,1: 85:[31, 54] Operation: 1+53=54 Exploring Operation: 53-31=22, Resulting Numbers: [1, 22] Generated Node #0,3,2: 85:[1, 22] Operation: 53-31=22 Exploring Operation: 1*53=53, Resulting Numbers: [31, 53] Generated Node #0,3,3: 85:[31, 53] Operation: 1*53=53 Exploring Operation: 31-1=30, Resulting Numbers: [53, 30] Generated Node #0,3,4: 85:[53, 30] Operation: 31-1=30 Moving to Node #0,0 Current State: 85:[1, 53, 117], Operations: ['43+74=117'] Exploring Operation: 117-1=116, Resulting Numbers: [53, 116] Generated Node #0,0,0: 85:[53, 116] Operation: 117-1=116 Exploring Operation: 53/1=53, Resulting Numbers: [117, 53] Generated Node #0,0,1: 85:[117, 53] Operation: 53/1=53 Exploring Operation: 117-53=64, Resulting Numbers: [1, 64] Generated Node #0,0,2: 85:[1, 64] Operation: 117-53=64 Exploring Operation: 1*53=53, Resulting Numbers: [117, 53] Generated Node #0,0,3: 85:[117, 53] Operation: 1*53=53 Exploring Operation: 1+53=54, Resulting Numbers: [117, 54] Generated Node #0,0,4: 85:[117, 54] Operation: 1+53=54 Moving to Node #0,2,2 Current State: 85:[1, 84], Operations: ['53-43=10', '74+10=84'] Exploring Operation: 84/1=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 1+84=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[43, 74, 1, 53], Operations: [] Exploring Operation: 53-43=10, Resulting Numbers: [74, 1, 10] Generated Node #0,2: 85:[74, 1, 10] Operation: 53-43=10 Moving to Node #0,2 Current State: 85:[74, 1, 10], Operations: ['53-43=10'] Exploring Operation: 74+10=84, Resulting Numbers: [1, 84] Generated Node #0,2,2: 85:[1, 84] Operation: 74+10=84 Moving to Node #0,2,2 Current State: 85:[1, 84], Operations: ['53-43=10', '74+10=84'] Exploring Operation: 1+84=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
0.939236
hs_5
sum_heuristic
[ 4, 8, 7, 86 ]
26
[ "7-4=3", "86-8=78", "78/3=26" ]
Current State: 26:[4, 8, 7, 86], Operations: [] Exploring Operation: 7-4=3, Resulting Numbers: [8, 86, 3] Generated Node #2: [8, 86, 3] from Operation: 7-4=3 Current State: 26:[8, 86, 3], Operations: ['7-4=3'] Exploring Operation: 86-8=78, Resulting Numbers: [3, 78] Generated Node #3: [3, 78] from Operation: 86-8=78 Current State: 26:[3, 78], Operations: ['7-4=3', '86-8=78'] Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[4, 8, 7, 86], Operations: [] Exploring Operation: 86-7=79, Resulting Numbers: [4, 8, 79] Generated Node #0,0: 26:[4, 8, 79] Operation: 86-7=79 Exploring Operation: 86-8=78, Resulting Numbers: [4, 7, 78] Generated Node #0,1: 26:[4, 7, 78] Operation: 86-8=78 Exploring Operation: 8-7=1, Resulting Numbers: [4, 86, 1] Generated Node #0,2: 26:[4, 86, 1] Operation: 8-7=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[4, 7, 78], Operations: ['86-8=78'] Exploring Operation: 78-4=74, Resulting Numbers: [7, 74] Generated Node #0,1,0: 26:[7, 74] Operation: 78-4=74 Exploring Operation: 78-7=71, Resulting Numbers: [4, 71] Generated Node #0,1,1: 26:[4, 71] Operation: 78-7=71 Exploring Operation: 7-4=3, Resulting Numbers: [78, 3] Generated Node #0,1,2: 26:[78, 3] Operation: 7-4=3 Moving to Node #0,1,1 Current State: 26:[4, 71], Operations: ['86-8=78', '78-7=71'] Exploring Operation: 4*71=284, Resulting Numbers: [284] 284,26 unequal: No Solution Exploring Operation: 4+71=75, Resulting Numbers: [75] 75,26 unequal: No Solution Exploring Operation: 71-4=67, Resulting Numbers: [67] 67,26 unequal: No Solution Moving to Node #0,1,0 Current State: 26:[7, 74], Operations: ['86-8=78', '78-4=74'] Exploring Operation: 7+74=81, Resulting Numbers: [81] 81,26 unequal: No Solution Exploring Operation: 7*74=518, Resulting Numbers: [518] 518,26 unequal: No Solution Exploring Operation: 74-7=67, Resulting Numbers: [67] 67,26 unequal: No Solution Moving to Node #0,1,2 Current State: 26:[78, 3], Operations: ['86-8=78', '7-4=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,26 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,26 unequal: No Solution Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[4, 8, 7, 86], Operations: [] Exploring Operation: 86-8=78, Resulting Numbers: [4, 7, 78] Generated Node #0,1: 26:[4, 7, 78] Operation: 86-8=78 Moving to Node #0,1 Current State: 26:[4, 7, 78], Operations: ['86-8=78'] Exploring Operation: 7-4=3, Resulting Numbers: [78, 3] Generated Node #0,1,2: 26:[78, 3] Operation: 7-4=3 Moving to Node #0,1,2 Current State: 26:[78, 3], Operations: ['86-8=78', '7-4=3'] Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
mult_heuristic
[ 17, 30, 36, 48 ]
71
[ "30-17=13", "36+48=84", "84-13=71" ]
Current State: 71:[17, 30, 36, 48], Operations: [] Exploring Operation: 30-17=13, Resulting Numbers: [36, 48, 13] Generated Node #2: [36, 48, 13] from Operation: 30-17=13 Current State: 71:[36, 48, 13], Operations: ['30-17=13'] Exploring Operation: 36+48=84, Resulting Numbers: [13, 84] Generated Node #3: [13, 84] from Operation: 36+48=84 Current State: 71:[13, 84], Operations: ['30-17=13', '36+48=84'] Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[17, 30, 36, 48], Operations: [] Exploring Operation: 17+30=47, Resulting Numbers: [36, 48, 47] Generated Node #0,0: 71:[36, 48, 47] Operation: 17+30=47 Exploring Operation: 17+36=53, Resulting Numbers: [30, 48, 53] Generated Node #0,1: 71:[30, 48, 53] Operation: 17+36=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[36, 48, 47], Operations: ['17+30=47'] Exploring Operation: 36+47=83, Resulting Numbers: [48, 83] Generated Node #0,0,0: 71:[48, 83] Operation: 36+47=83 Exploring Operation: 36+48=84, Resulting Numbers: [47, 84] Generated Node #0,0,1: 71:[47, 84] Operation: 36+48=84 Moving to Node #0,0,0 Current State: 71:[48, 83], Operations: ['17+30=47', '36+47=83'] Exploring Operation: 83-48=35, Resulting Numbers: [35] 35,71 unequal: No Solution Exploring Operation: 48+83=131, Resulting Numbers: [131] 131,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[47, 84], Operations: ['17+30=47', '36+48=84'] Exploring Operation: 47+84=131, Resulting Numbers: [131] 131,71 unequal: No Solution Exploring Operation: 84-47=37, Resulting Numbers: [37] 37,71 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:[30, 48, 53], Operations: ['17+36=53'] Exploring Operation: 30+48=78, Resulting Numbers: [53, 78] Generated Node #0,1,0: 71:[53, 78] Operation: 30+48=78 Exploring Operation: 30+53=83, Resulting Numbers: [48, 83] Generated Node #0,1,1: 71:[48, 83] Operation: 30+53=83 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 71:[53, 78], Operations: ['17+36=53', '30+48=78'] Exploring Operation: 53+78=131, Resulting Numbers: [131] 131,71 unequal: No Solution Exploring Operation: 78-53=25, Resulting Numbers: [25] 25,71 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:[48, 83], Operations: ['17+36=53', '30+53=83'] Exploring Operation: 83-48=35, Resulting Numbers: [35] 35,71 unequal: No Solution Exploring Operation: 48+83=131, Resulting Numbers: [131] 131,71 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
[ 53, 74, 20, 78 ]
79
[ "74-53=21", "78-20=58", "21+58=79" ]
Current State: 79:[53, 74, 20, 78], Operations: [] Exploring Operation: 74-53=21, Resulting Numbers: [20, 78, 21] Generated Node #2: [20, 78, 21] from Operation: 74-53=21 Current State: 79:[20, 78, 21], Operations: ['74-53=21'] Exploring Operation: 78-20=58, Resulting Numbers: [21, 58] Generated Node #3: [21, 58] from Operation: 78-20=58 Current State: 79:[21, 58], Operations: ['74-53=21', '78-20=58'] Exploring Operation: 21+58=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[53, 74, 20, 78], Operations: [] Exploring Operation: 53+20=73, Resulting Numbers: [74, 78, 73] Generated Node #0,0: 79:[74, 78, 73] Operation: 53+20=73 Moving to Node #0,0 Current State: 79:[74, 78, 73], Operations: ['53+20=73'] Exploring Operation: 74+73=147, Resulting Numbers: [78, 147] Generated Node #0,0,0: 79:[78, 147] Operation: 74+73=147 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[78, 147], Operations: ['53+20=73', '74+73=147'] Exploring Operation: 147-78=69, Resulting Numbers: [69] 69,79 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
[ 52, 17, 61, 48 ]
72
[ "17+61=78", "48*78=3744", "3744/52=72" ]
Current State: 72:[52, 17, 61, 48], Operations: [] Exploring Operation: 17+61=78, Resulting Numbers: [52, 48, 78] Generated Node #2: [52, 48, 78] from Operation: 17+61=78 Current State: 72:[52, 48, 78], Operations: ['17+61=78'] Exploring Operation: 48*78=3744, Resulting Numbers: [52, 3744] Generated Node #3: [52, 3744] from Operation: 48*78=3744 Current State: 72:[52, 3744], Operations: ['17+61=78', '48*78=3744'] Exploring Operation: 3744/52=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[52, 17, 61, 48], Operations: [] Exploring Operation: 52-48=4, Resulting Numbers: [17, 61, 4] Generated Node #0,0: 72:[17, 61, 4] Operation: 52-48=4 Exploring Operation: 61-48=13, Resulting Numbers: [52, 17, 13] Generated Node #0,1: 72:[52, 17, 13] Operation: 61-48=13 Exploring Operation: 61-52=9, Resulting Numbers: [17, 48, 9] Generated Node #0,2: 72:[17, 48, 9] Operation: 61-52=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[17, 61, 4], Operations: ['52-48=4'] Exploring Operation: 17+61=78, Resulting Numbers: [4, 78] Generated Node #0,0,0: 72:[4, 78] Operation: 17+61=78 Exploring Operation: 61+4=65, Resulting Numbers: [17, 65] Generated Node #0,0,1: 72:[17, 65] Operation: 61+4=65 Exploring Operation: 61-17=44, Resulting Numbers: [4, 44] Generated Node #0,0,2: 72:[4, 44] Operation: 61-17=44 Moving to Node #0,0,0 Current State: 72:[4, 78], Operations: ['52-48=4', '17+61=78'] Exploring Operation: 4+78=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,72 unequal: No Solution Exploring Operation: 4*78=312, Resulting Numbers: [312] 312,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[17, 65], Operations: ['52-48=4', '61+4=65'] Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,72 unequal: No Solution Exploring Operation: 17*65=1105, Resulting Numbers: [1105] 1105,72 unequal: No Solution Exploring Operation: 17+65=82, Resulting Numbers: [82] 82,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[4, 44], Operations: ['52-48=4', '61-17=44'] Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,72 unequal: No Solution Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,72 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[17, 48, 9], Operations: ['61-52=9'] Exploring Operation: 48-9=39, Resulting Numbers: [17, 39] Generated Node #0,2,0: 72:[17, 39] Operation: 48-9=39 Exploring Operation: 48-17=31, Resulting Numbers: [9, 31] Generated Node #0,2,1: 72:[9, 31] Operation: 48-17=31 Exploring Operation: 17+48=65, Resulting Numbers: [9, 65] Generated Node #0,2,2: 72:[9, 65] Operation: 17+48=65 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 72:[17, 39], Operations: ['61-52=9', '48-9=39'] Exploring Operation: 17+39=56, Resulting Numbers: [56] 56,72 unequal: No Solution Exploring Operation: 39-17=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 17*39=663, Resulting Numbers: [663] 663,72 unequal: No Solution No 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: 72:[9, 31], Operations: ['61-52=9', '48-17=31'] Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 9+31=40, Resulting Numbers: [40] 40,72 unequal: No Solution Exploring Operation: 9*31=279, Resulting Numbers: [279] 279,72 unequal: No Solution No 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: 72:[9, 65], Operations: ['61-52=9', '17+48=65'] Exploring Operation: 9*65=585, Resulting Numbers: [585] 585,72 unequal: No Solution Exploring Operation: 9+65=74, Resulting Numbers: [74] 74,72 unequal: No Solution Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,72 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: 72:[52, 17, 13], Operations: ['61-48=13'] Exploring Operation: 52+17=69, Resulting Numbers: [13, 69] Generated Node #0,1,0: 72:[13, 69] Operation: 52+17=69 Exploring Operation: 52/13=4, Resulting Numbers: [17, 4] Generated Node #0,1,1: 72:[17, 4] Operation: 52/13=4 Exploring Operation: 52-17=35, Resulting Numbers: [13, 35] Generated Node #0,1,2: 72:[13, 35] Operation: 52-17=35 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 72:[17, 4], Operations: ['61-48=13', '52/13=4'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 17+4=21, Resulting Numbers: [21] 21,72 unequal: No Solution Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,72 unequal: No Solution No 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: 72:[13, 35], Operations: ['61-48=13', '52-17=35'] Exploring Operation: 13*35=455, Resulting Numbers: [455] 455,72 unequal: No Solution Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 13+35=48, Resulting Numbers: [48] 48,72 unequal: No Solution No 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: 72:[13, 69], Operations: ['61-48=13', '52+17=69'] Exploring Operation: 13*69=897, Resulting Numbers: [897] 897,72 unequal: No Solution Exploring Operation: 69-13=56, Resulting Numbers: [56] 56,72 unequal: No Solution Exploring Operation: 13+69=82, Resulting Numbers: [82] 82,72 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
[ 95, 76, 81, 45 ]
10
[ "95-45=50", "81-76=5", "50/5=10" ]
Current State: 10:[95, 76, 81, 45], Operations: [] Exploring Operation: 95-45=50, Resulting Numbers: [76, 81, 50] Generated Node #2: [76, 81, 50] from Operation: 95-45=50 Current State: 10:[76, 81, 50], Operations: ['95-45=50'] Exploring Operation: 81-76=5, Resulting Numbers: [50, 5] Generated Node #3: [50, 5] from Operation: 81-76=5 Current State: 10:[50, 5], Operations: ['95-45=50', '81-76=5'] Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[95, 76, 81, 45], Operations: [] Exploring Operation: 95-81=14, Resulting Numbers: [76, 45, 14] Generated Node #0,0: 10:[76, 45, 14] Operation: 95-81=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[76, 45, 14], Operations: ['95-81=14'] Exploring Operation: 76-45=31, Resulting Numbers: [14, 31] Generated Node #0,0,0: 10:[14, 31] Operation: 76-45=31 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[14, 31], Operations: ['95-81=14', '76-45=31'] Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 20, 12, 69, 16 ]
61
[ "20-12=8", "69-16=53", "8+53=61" ]
Current State: 61:[20, 12, 69, 16], Operations: [] Exploring Operation: 20-12=8, Resulting Numbers: [69, 16, 8] Generated Node #2: [69, 16, 8] from Operation: 20-12=8 Current State: 61:[69, 16, 8], Operations: ['20-12=8'] Exploring Operation: 69-16=53, Resulting Numbers: [8, 53] Generated Node #3: [8, 53] from Operation: 69-16=53 Current State: 61:[8, 53], Operations: ['20-12=8', '69-16=53'] Exploring Operation: 8+53=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[20, 12, 69, 16], Operations: [] Exploring Operation: 20+12=32, Resulting Numbers: [69, 16, 32] Generated Node #0,0: 61:[69, 16, 32] Operation: 20+12=32 Exploring Operation: 20+16=36, Resulting Numbers: [12, 69, 36] Generated Node #0,1: 61:[12, 69, 36] Operation: 20+16=36 Exploring Operation: 12+16=28, Resulting Numbers: [20, 69, 28] Generated Node #0,2: 61:[20, 69, 28] Operation: 12+16=28 Moving to Node #0,0 Current State: 61:[69, 16, 32], Operations: ['20+12=32'] Exploring Operation: 16+32=48, Resulting Numbers: [69, 48] Generated Node #0,0,0: 61:[69, 48] Operation: 16+32=48 Exploring Operation: 69-16=53, Resulting Numbers: [32, 53] Generated Node #0,0,1: 61:[32, 53] Operation: 69-16=53 Exploring Operation: 69+16=85, Resulting Numbers: [32, 85] Generated Node #0,0,2: 61:[32, 85] Operation: 69+16=85 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[69, 48], Operations: ['20+12=32', '16+32=48'] Exploring Operation: 69*48=3312, Resulting Numbers: [3312] 3312,61 unequal: No Solution Exploring Operation: 69+48=117, Resulting Numbers: [117] 117,61 unequal: No Solution Exploring Operation: 69-48=21, Resulting Numbers: [21] 21,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[32, 53], Operations: ['20+12=32', '69-16=53'] Exploring Operation: 32+53=85, Resulting Numbers: [85] 85,61 unequal: No Solution Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,61 unequal: No Solution Exploring Operation: 32*53=1696, Resulting Numbers: [1696] 1696,61 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 #0,0,2 Current State: 61:[32, 85], Operations: ['20+12=32', '69+16=85'] Exploring Operation: 85-32=53, Resulting Numbers: [53] 53,61 unequal: No Solution Exploring Operation: 32*85=2720, Resulting Numbers: [2720] 2720,61 unequal: No Solution Exploring Operation: 32+85=117, Resulting Numbers: [117] 117,61 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: 61:[12, 69, 36], Operations: ['20+16=36'] Exploring Operation: 12+36=48, Resulting Numbers: [69, 48] Generated Node #0,1,0: 61:[69, 48] Operation: 12+36=48 Exploring Operation: 69-12=57, Resulting Numbers: [36, 57] Generated Node #0,1,1: 61:[36, 57] Operation: 69-12=57 Exploring Operation: 12+69=81, Resulting Numbers: [36, 81] Generated Node #0,1,2: 61:[36, 81] Operation: 12+69=81 Moving to Node #0,2 Current State: 61:[20, 69, 28], Operations: ['12+16=28'] Exploring Operation: 20+28=48, Resulting Numbers: [69, 48] Generated Node #0,2,0: 61:[69, 48] Operation: 20+28=48 Exploring Operation: 20+69=89, Resulting Numbers: [28, 89] Generated Node #0,2,1: 61:[28, 89] Operation: 20+69=89 Exploring Operation: 69-20=49, Resulting Numbers: [28, 49] Generated Node #0,2,2: 61:[28, 49] Operation: 69-20=49 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[69, 48], Operations: ['12+16=28', '20+28=48'] Exploring Operation: 69*48=3312, Resulting Numbers: [3312] 3312,61 unequal: No Solution Exploring Operation: 69-48=21, Resulting Numbers: [21] 21,61 unequal: No Solution Exploring Operation: 69+48=117, Resulting Numbers: [117] 117,61 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 #0,2,2 Current State: 61:[28, 49], Operations: ['12+16=28', '69-20=49'] Exploring Operation: 49-28=21, Resulting Numbers: [21] 21,61 unequal: No Solution Exploring Operation: 28+49=77, Resulting Numbers: [77] 77,61 unequal: No Solution Exploring Operation: 28*49=1372, Resulting Numbers: [1372] 1372,61 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 #0,2,1 Current State: 61:[28, 89], Operations: ['12+16=28', '20+69=89'] Exploring Operation: 89-28=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[20, 12, 69, 16], Operations: [] Exploring Operation: 12+16=28, Resulting Numbers: [20, 69, 28] Generated Node #0,2: 61:[20, 69, 28] Operation: 12+16=28 Moving to Node #0,2 Current State: 61:[20, 69, 28], Operations: ['12+16=28'] Exploring Operation: 20+69=89, Resulting Numbers: [28, 89] Generated Node #0,2,1: 61:[28, 89] Operation: 20+69=89 Moving to Node #0,2,1 Current State: 61:[28, 89], Operations: ['12+16=28', '20+69=89'] Exploring Operation: 89-28=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_3
sum_heuristic
[ 19, 47, 36, 77 ]
42
[ "19+47=66", "36*77=2772", "2772/66=42" ]
Current State: 42:[19, 47, 36, 77], Operations: [] Exploring Operation: 19+47=66, Resulting Numbers: [36, 77, 66] Generated Node #2: [36, 77, 66] from Operation: 19+47=66 Current State: 42:[36, 77, 66], Operations: ['19+47=66'] Exploring Operation: 36*77=2772, Resulting Numbers: [66, 2772] Generated Node #3: [66, 2772] from Operation: 36*77=2772 Current State: 42:[66, 2772], Operations: ['19+47=66', '36*77=2772'] Exploring Operation: 2772/66=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[19, 47, 36, 77], Operations: [] Exploring Operation: 77-36=41, Resulting Numbers: [19, 47, 41] Generated Node #0,0: 42:[19, 47, 41] Operation: 77-36=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[19, 47, 41], Operations: ['77-36=41'] Exploring Operation: 47-41=6, Resulting Numbers: [19, 6] Generated Node #0,0,0: 42:[19, 6] Operation: 47-41=6 Moving to Node #0,0,0 Current State: 42:[19, 6], Operations: ['77-36=41', '47-41=6'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 10, 98, 2, 73 ]
45
[ "10*2=20", "98-73=25", "20+25=45" ]
Current State: 45:[10, 98, 2, 73], Operations: [] Exploring Operation: 10*2=20, Resulting Numbers: [98, 73, 20] Generated Node #2: [98, 73, 20] from Operation: 10*2=20 Current State: 45:[98, 73, 20], Operations: ['10*2=20'] Exploring Operation: 98-73=25, Resulting Numbers: [20, 25] Generated Node #3: [20, 25] from Operation: 98-73=25 Current State: 45:[20, 25], Operations: ['10*2=20', '98-73=25'] Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[10, 98, 2, 73], Operations: [] Exploring Operation: 98-73=25, Resulting Numbers: [10, 2, 25] Generated Node #0,0: 45:[10, 2, 25] Operation: 98-73=25 Exploring Operation: 98/2=49, Resulting Numbers: [10, 73, 49] Generated Node #0,1: 45:[10, 73, 49] Operation: 98/2=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[10, 2, 25], Operations: ['98-73=25'] Exploring Operation: 25-10=15, Resulting Numbers: [2, 15] Generated Node #0,0,0: 45:[2, 15] Operation: 25-10=15 Exploring Operation: 2*25=50, Resulting Numbers: [10, 50] Generated Node #0,0,1: 45:[10, 50] Operation: 2*25=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[2, 15], Operations: ['98-73=25', '25-10=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,45 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,45 unequal: No Solution No 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: 45:[10, 50], Operations: ['98-73=25', '2*25=50'] Exploring Operation: 50/10=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,45 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: 45:[10, 73, 49], Operations: ['98/2=49'] Exploring Operation: 73-49=24, Resulting Numbers: [10, 24] Generated Node #0,1,0: 45:[10, 24] Operation: 73-49=24 Exploring Operation: 73-10=63, Resulting Numbers: [49, 63] Generated Node #0,1,1: 45:[49, 63] Operation: 73-10=63 Moving to Node #0,1,0 Current State: 45:[10, 24], Operations: ['98/2=49', '73-49=24'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,45 unequal: No Solution Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[49, 63], Operations: ['98/2=49', '73-10=63'] Exploring Operation: 49+63=112, Resulting Numbers: [112] 112,45 unequal: No Solution Exploring Operation: 63-49=14, Resulting Numbers: [14] 14,45 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
[ 25, 45, 40, 52 ]
54
[ "45-25=20", "40/20=2", "52+2=54" ]
Current State: 54:[25, 45, 40, 52], Operations: [] Exploring Operation: 45-25=20, Resulting Numbers: [40, 52, 20] Generated Node #2: [40, 52, 20] from Operation: 45-25=20 Current State: 54:[40, 52, 20], Operations: ['45-25=20'] Exploring Operation: 40/20=2, Resulting Numbers: [52, 2] Generated Node #3: [52, 2] from Operation: 40/20=2 Current State: 54:[52, 2], Operations: ['45-25=20', '40/20=2'] Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[25, 45, 40, 52], Operations: [] Exploring Operation: 45-40=5, Resulting Numbers: [25, 52, 5] Generated Node #0,0: 54:[25, 52, 5] Operation: 45-40=5 Exploring Operation: 40-25=15, Resulting Numbers: [45, 52, 15] Generated Node #0,1: 54:[45, 52, 15] Operation: 40-25=15 Moving to Node #0,0 Current State: 54:[25, 52, 5], Operations: ['45-40=5'] Exploring Operation: 52-25=27, Resulting Numbers: [5, 27] Generated Node #0,0,0: 54:[5, 27] Operation: 52-25=27 Exploring Operation: 25/5=5, Resulting Numbers: [52, 5] Generated Node #0,0,1: 54:[52, 5] Operation: 25/5=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[5, 27], Operations: ['45-40=5', '52-25=27'] Exploring Operation: 5+27=32, Resulting Numbers: [32] 32,54 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,54 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 #0,0,1 Current State: 54:[52, 5], Operations: ['45-40=5', '25/5=5'] Exploring Operation: 52+5=57, Resulting Numbers: [57] 57,54 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,54 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: 54:[45, 52, 15], Operations: ['40-25=15'] Exploring Operation: 52-45=7, Resulting Numbers: [15, 7] Generated Node #0,1,0: 54:[15, 7] Operation: 52-45=7 Exploring Operation: 45/15=3, Resulting Numbers: [52, 3] Generated Node #0,1,1: 54:[52, 3] Operation: 45/15=3 Moving to Node #0,1,1 Current State: 54:[52, 3], Operations: ['40-25=15', '45/15=3'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,54 unequal: No Solution Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[15, 7], Operations: ['40-25=15', '52-45=7'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,54 unequal: No Solution Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,54 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 25, 21, 4, 20 ]
12
[ "25-21=4", "20-4=16", "16-4=12" ]
Current State: 12:[25, 21, 4, 20], Operations: [] Exploring Operation: 25-21=4, Resulting Numbers: [4, 20, 4] Generated Node #2: [4, 20, 4] from Operation: 25-21=4 Current State: 12:[4, 20, 4], Operations: ['25-21=4'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,12 equal: Goal Reached Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[25, 21, 4, 20], Operations: [] Exploring Operation: 25-21=4, Resulting Numbers: [4, 20, 4] Generated Node #0,0: 12:[4, 20, 4] Operation: 25-21=4 Moving to Node #0,0 Current State: 12:[4, 20, 4], Operations: ['25-21=4'] Exploring Operation: 20/4=5, Resulting Numbers: [4, 5] Generated Node #0,0,0: 12:[4, 5] Operation: 20/4=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[4, 5], Operations: ['25-21=4', '20/4=5'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 44, 9, 27, 50 ]
82
[ "44*27=1188", "1188/9=132", "132-50=82" ]
Current State: 82:[44, 9, 27, 50], Operations: [] Exploring Operation: 44*27=1188, Resulting Numbers: [9, 50, 1188] Generated Node #2: [9, 50, 1188] from Operation: 44*27=1188 Current State: 82:[9, 50, 1188], Operations: ['44*27=1188'] Exploring Operation: 1188/9=132, Resulting Numbers: [50, 132] Generated Node #3: [50, 132] from Operation: 1188/9=132 Current State: 82:[50, 132], Operations: ['44*27=1188', '1188/9=132'] Exploring Operation: 132-50=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[44, 9, 27, 50], Operations: [] Exploring Operation: 27/9=3, Resulting Numbers: [44, 50, 3] Generated Node #0,0: 82:[44, 50, 3] Operation: 27/9=3 Exploring Operation: 27+50=77, Resulting Numbers: [44, 9, 77] Generated Node #0,1: 82:[44, 9, 77] Operation: 27+50=77 Exploring Operation: 9+27=36, Resulting Numbers: [44, 50, 36] Generated Node #0,2: 82:[44, 50, 36] Operation: 9+27=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[44, 50, 3], Operations: ['27/9=3'] Exploring Operation: 50-44=6, Resulting Numbers: [3, 6] Generated Node #0,0,0: 82:[3, 6] Operation: 50-44=6 Exploring Operation: 44-3=41, Resulting Numbers: [50, 41] Generated Node #0,0,1: 82:[50, 41] Operation: 44-3=41 Exploring Operation: 50-3=47, Resulting Numbers: [44, 47] Generated Node #0,0,2: 82:[44, 47] Operation: 50-3=47 Moving to Node #0,0,0 Current State: 82:[3, 6], Operations: ['27/9=3', '50-44=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[50, 41], Operations: ['27/9=3', '44-3=41'] Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,82 unequal: No Solution Exploring Operation: 50*41=2050, Resulting Numbers: [2050] 2050,82 unequal: No Solution Exploring Operation: 50+41=91, Resulting Numbers: [91] 91,82 unequal: No Solution Moving to Node #0,0,2 Current State: 82:[44, 47], Operations: ['27/9=3', '50-3=47'] Exploring Operation: 44*47=2068, Resulting Numbers: [2068] 2068,82 unequal: No Solution Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,82 unequal: No Solution Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[44, 9, 77], Operations: ['27+50=77'] Exploring Operation: 77-44=33, Resulting Numbers: [9, 33] Generated Node #0,1,0: 82:[9, 33] Operation: 77-44=33 Exploring Operation: 44-9=35, Resulting Numbers: [77, 35] Generated Node #0,1,1: 82:[77, 35] Operation: 44-9=35 Exploring Operation: 9+77=86, Resulting Numbers: [44, 86] Generated Node #0,1,2: 82:[44, 86] Operation: 9+77=86 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 82:[44, 86], Operations: ['27+50=77', '9+77=86'] Exploring Operation: 44+86=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 86-44=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 44*86=3784, Resulting Numbers: [3784] 3784,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[77, 35], Operations: ['27+50=77', '44-9=35'] Exploring Operation: 77+35=112, Resulting Numbers: [112] 112,82 unequal: No Solution Exploring Operation: 77*35=2695, Resulting Numbers: [2695] 2695,82 unequal: No Solution Exploring Operation: 77-35=42, Resulting Numbers: [42] 42,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[9, 33], Operations: ['27+50=77', '77-44=33'] Exploring Operation: 9+33=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 9*33=297, Resulting Numbers: [297] 297,82 unequal: No Solution Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[44, 50, 36], Operations: ['9+27=36'] Exploring Operation: 50-44=6, Resulting Numbers: [36, 6] Generated Node #0,2,0: 82:[36, 6] Operation: 50-44=6 Exploring Operation: 50+36=86, Resulting Numbers: [44, 86] Generated Node #0,2,1: 82:[44, 86] Operation: 50+36=86 Exploring Operation: 44+36=80, Resulting Numbers: [50, 80] Generated Node #0,2,2: 82:[50, 80] Operation: 44+36=80 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[44, 86], Operations: ['9+27=36', '50+36=86'] Exploring Operation: 44+86=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 44*86=3784, Resulting Numbers: [3784] 3784,82 unequal: No Solution Exploring Operation: 86-44=42, Resulting Numbers: [42] 42,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[36, 6], Operations: ['9+27=36', '50-44=6'] Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,82 unequal: No Solution Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 82:[50, 80], Operations: ['9+27=36', '44+36=80'] Exploring Operation: 50*80=4000, Resulting Numbers: [4000] 4000,82 unequal: No Solution Exploring Operation: 80-50=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 50+80=130, Resulting Numbers: [130] 130,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 99, 9, 14, 42 ]
39
[ "99/9=11", "42-14=28", "11+28=39" ]
Current State: 39:[99, 9, 14, 42], Operations: [] Exploring Operation: 99/9=11, Resulting Numbers: [14, 42, 11] Generated Node #2: [14, 42, 11] from Operation: 99/9=11 Current State: 39:[14, 42, 11], Operations: ['99/9=11'] Exploring Operation: 42-14=28, Resulting Numbers: [11, 28] Generated Node #3: [11, 28] from Operation: 42-14=28 Current State: 39:[11, 28], Operations: ['99/9=11', '42-14=28'] Exploring Operation: 11+28=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[99, 9, 14, 42], Operations: [] Exploring Operation: 99/9=11, Resulting Numbers: [14, 42, 11] Generated Node #0,0: 39:[14, 42, 11] Operation: 99/9=11 Exploring Operation: 99-42=57, Resulting Numbers: [9, 14, 57] Generated Node #0,1: 39:[9, 14, 57] Operation: 99-42=57 Moving to Node #0,0 Current State: 39:[14, 42, 11], Operations: ['99/9=11'] Exploring Operation: 42/14=3, Resulting Numbers: [11, 3] Generated Node #0,0,0: 39:[11, 3] Operation: 42/14=3 Exploring Operation: 14-11=3, Resulting Numbers: [42, 3] Generated Node #0,0,1: 39:[42, 3] Operation: 14-11=3 Moving to Node #0,1 Current State: 39:[9, 14, 57], Operations: ['99-42=57'] Exploring Operation: 57-9=48, Resulting Numbers: [14, 48] Generated Node #0,1,0: 39:[14, 48] Operation: 57-9=48 Exploring Operation: 57-14=43, Resulting Numbers: [9, 43] Generated Node #0,1,1: 39:[9, 43] Operation: 57-14=43 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[9, 43], Operations: ['99-42=57', '57-14=43'] Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,39 unequal: No Solution Exploring Operation: 9+43=52, Resulting Numbers: [52] 52,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[14, 48], Operations: ['99-42=57', '57-9=48'] Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,39 unequal: No Solution Exploring Operation: 14+48=62, Resulting Numbers: [62] 62,39 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: 39:[11, 3], Operations: ['99/9=11', '42/14=3'] Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,39 unequal: No Solution Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[42, 3], Operations: ['99/9=11', '14-11=3'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[99, 9, 14, 42], Operations: [] Exploring Operation: 99/9=11, Resulting Numbers: [14, 42, 11] Generated Node #0,0: 39:[14, 42, 11] Operation: 99/9=11 Moving to Node #0,0 Current State: 39:[14, 42, 11], Operations: ['99/9=11'] Exploring Operation: 14-11=3, Resulting Numbers: [42, 3] Generated Node #0,0,1: 39:[42, 3] Operation: 14-11=3 Moving to Node #0,0,1 Current State: 39:[42, 3], Operations: ['99/9=11', '14-11=3'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
0.985243
hs_2
mult_heuristic
[ 14, 52, 45, 38 ]
59
[ "14+52=66", "45-38=7", "66-7=59" ]
Current State: 59:[14, 52, 45, 38], Operations: [] Exploring Operation: 14+52=66, Resulting Numbers: [45, 38, 66] Generated Node #2: [45, 38, 66] from Operation: 14+52=66 Current State: 59:[45, 38, 66], Operations: ['14+52=66'] Exploring Operation: 45-38=7, Resulting Numbers: [66, 7] Generated Node #3: [66, 7] from Operation: 45-38=7 Current State: 59:[66, 7], Operations: ['14+52=66', '45-38=7'] Exploring Operation: 66-7=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[14, 52, 45, 38], Operations: [] Exploring Operation: 14+45=59, Resulting Numbers: [52, 38, 59] Generated Node #0,0: 59:[52, 38, 59] Operation: 14+45=59 Exploring Operation: 14+38=52, Resulting Numbers: [52, 45, 52] Generated Node #0,1: 59:[52, 45, 52] Operation: 14+38=52 Exploring Operation: 52-14=38, Resulting Numbers: [45, 38, 38] Generated Node #0,2: 59:[45, 38, 38] Operation: 52-14=38 Exploring Operation: 14+52=66, Resulting Numbers: [45, 38, 66] Generated Node #0,3: 59:[45, 38, 66] Operation: 14+52=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[52, 38, 59], Operations: ['14+45=59'] Exploring Operation: 38+59=97, Resulting Numbers: [52, 97] Generated Node #0,0,0: 59:[52, 97] Operation: 38+59=97 Exploring Operation: 52+38=90, Resulting Numbers: [59, 90] Generated Node #0,0,1: 59:[59, 90] Operation: 52+38=90 Exploring Operation: 59-38=21, Resulting Numbers: [52, 21] Generated Node #0,0,2: 59:[52, 21] Operation: 59-38=21 Exploring Operation: 52-38=14, Resulting Numbers: [59, 14] Generated Node #0,0,3: 59:[59, 14] Operation: 52-38=14 Moving to Node #0,0,1 Current State: 59:[59, 90], Operations: ['14+45=59', '52+38=90'] Exploring Operation: 59*90=5310, Resulting Numbers: [5310] 5310,59 unequal: No Solution Exploring Operation: 90-59=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 59+90=149, Resulting Numbers: [149] 149,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[52, 21], Operations: ['14+45=59', '59-38=21'] Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,59 unequal: No Solution Exploring Operation: 52*21=1092, Resulting Numbers: [1092] 1092,59 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[52, 97], Operations: ['14+45=59', '38+59=97'] Exploring Operation: 52*97=5044, Resulting Numbers: [5044] 5044,59 unequal: No Solution Exploring Operation: 97-52=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 52+97=149, Resulting Numbers: [149] 149,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[59, 14], Operations: ['14+45=59', '52-38=14'] Exploring Operation: 59+14=73, Resulting Numbers: [73] 73,59 unequal: No Solution Exploring Operation: 59-14=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 59*14=826, Resulting Numbers: [826] 826,59 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 Current State: 59:[52, 45, 52], Operations: ['14+38=52'] Exploring Operation: 52-45=7, Resulting Numbers: [52, 7] Generated Node #0,1,0: 59:[52, 7] Operation: 52-45=7 Exploring Operation: 52+45=97, Resulting Numbers: [52, 97] Generated Node #0,1,1: 59:[52, 97] Operation: 52+45=97 Exploring Operation: 45+52=97, Resulting Numbers: [52, 97] Generated Node #0,1,2: 59:[52, 97] Operation: 45+52=97 Exploring Operation: 52+52=104, Resulting Numbers: [45, 104] Generated Node #0,1,3: 59:[45, 104] Operation: 52+52=104 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 59:[52, 97], Operations: ['14+38=52', '52+45=97'] Exploring Operation: 52*97=5044, Resulting Numbers: [5044] 5044,59 unequal: No Solution Exploring Operation: 52+97=149, Resulting Numbers: [149] 149,59 unequal: No Solution Exploring Operation: 97-52=45, Resulting Numbers: [45] 45,59 unequal: No Solution No 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: 59:[52, 97], Operations: ['14+38=52', '45+52=97'] Exploring Operation: 52+97=149, Resulting Numbers: [149] 149,59 unequal: No Solution Exploring Operation: 97-52=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 52*97=5044, Resulting Numbers: [5044] 5044,59 unequal: No Solution No 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: 59:[52, 7], Operations: ['14+38=52', '52-45=7'] Exploring Operation: 52+7=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[14, 52, 45, 38], Operations: [] Exploring Operation: 14+38=52, Resulting Numbers: [52, 45, 52] Generated Node #0,1: 59:[52, 45, 52] Operation: 14+38=52 Moving to Node #0,1 Current State: 59:[52, 45, 52], Operations: ['14+38=52'] Exploring Operation: 52-45=7, Resulting Numbers: [52, 7] Generated Node #0,1,0: 59:[52, 7] Operation: 52-45=7 Moving to Node #0,1,0 Current State: 59:[52, 7], Operations: ['14+38=52', '52-45=7'] Exploring Operation: 52+7=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_4
mult_heuristic
[ 16, 71, 45, 64 ]
19
[ "71+64=135", "135/45=3", "16+3=19" ]
Current State: 19:[16, 71, 45, 64], Operations: [] Exploring Operation: 71+64=135, Resulting Numbers: [16, 45, 135] Generated Node #2: [16, 45, 135] from Operation: 71+64=135 Current State: 19:[16, 45, 135], Operations: ['71+64=135'] Exploring Operation: 135/45=3, Resulting Numbers: [16, 3] Generated Node #3: [16, 3] from Operation: 135/45=3 Current State: 19:[16, 3], Operations: ['71+64=135', '135/45=3'] Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[16, 71, 45, 64], Operations: [] Exploring Operation: 71-64=7, Resulting Numbers: [16, 45, 7] Generated Node #0,0: 19:[16, 45, 7] Operation: 71-64=7 Exploring Operation: 64-45=19, Resulting Numbers: [16, 71, 19] Generated Node #0,1: 19:[16, 71, 19] Operation: 64-45=19 Exploring Operation: 71-45=26, Resulting Numbers: [16, 64, 26] Generated Node #0,2: 19:[16, 64, 26] Operation: 71-45=26 Exploring Operation: 64/16=4, Resulting Numbers: [71, 45, 4] Generated Node #0,3: 19:[71, 45, 4] Operation: 64/16=4 Exploring Operation: 71-16=55, Resulting Numbers: [45, 64, 55] Generated Node #0,4: 19:[45, 64, 55] Operation: 71-16=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[16, 45, 7], Operations: ['71-64=7'] Exploring Operation: 45+7=52, Resulting Numbers: [16, 52] Generated Node #0,0,0: 19:[16, 52] Operation: 45+7=52 Exploring Operation: 45-7=38, Resulting Numbers: [16, 38] Generated Node #0,0,1: 19:[16, 38] Operation: 45-7=38 Exploring Operation: 45-16=29, Resulting Numbers: [7, 29] Generated Node #0,0,2: 19:[7, 29] Operation: 45-16=29 Exploring Operation: 16-7=9, Resulting Numbers: [45, 9] Generated Node #0,0,3: 19:[45, 9] Operation: 16-7=9 Exploring Operation: 16+7=23, Resulting Numbers: [45, 23] Generated Node #0,0,4: 19:[45, 23] Operation: 16+7=23 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 19:[16, 38], Operations: ['71-64=7', '45-7=38'] Exploring Operation: 16*38=608, Resulting Numbers: [608] 608,19 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 16+38=54, Resulting Numbers: [54] 54,19 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 #0,0,2 Current State: 19:[7, 29], Operations: ['71-64=7', '45-16=29'] Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,19 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,19 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 #0,0,4 Current State: 19:[45, 23], Operations: ['71-64=7', '16+7=23'] Exploring Operation: 45+23=68, Resulting Numbers: [68] 68,19 unequal: No Solution Exploring Operation: 45*23=1035, Resulting Numbers: [1035] 1035,19 unequal: No Solution Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,19 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 #0,0,0 Current State: 19:[16, 52], Operations: ['71-64=7', '45+7=52'] Exploring Operation: 52-16=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 16+52=68, Resulting Numbers: [68] 68,19 unequal: No Solution Exploring Operation: 16*52=832, Resulting Numbers: [832] 832,19 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 #0,0,3 Current State: 19:[45, 9], Operations: ['71-64=7', '16-7=9'] Exploring Operation: 45*9=405, Resulting Numbers: [405] 405,19 unequal: No Solution Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 45+9=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,19 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:[16, 71, 19], Operations: ['64-45=19'] Exploring Operation: 71-16=55, Resulting Numbers: [19, 55] Generated Node #0,1,0: 19:[19, 55] Operation: 71-16=55 Exploring Operation: 19-16=3, Resulting Numbers: [71, 3] Generated Node #0,1,1: 19:[71, 3] Operation: 19-16=3 Exploring Operation: 16+19=35, Resulting Numbers: [71, 35] Generated Node #0,1,2: 19:[71, 35] Operation: 16+19=35 Exploring Operation: 71-19=52, Resulting Numbers: [16, 52] Generated Node #0,1,3: 19:[16, 52] Operation: 71-19=52 Exploring Operation: 16+71=87, Resulting Numbers: [19, 87] Generated Node #0,1,4: 19:[19, 87] Operation: 16+71=87 Moving to Node #0,1,0 Current State: 19:[19, 55], Operations: ['64-45=19', '71-16=55'] Exploring Operation: 19+55=74, Resulting Numbers: [74] 74,19 unequal: No Solution Exploring Operation: 19*55=1045, Resulting Numbers: [1045] 1045,19 unequal: No Solution Exploring Operation: 55-19=36, Resulting Numbers: [36] 36,19 unequal: No Solution Moving to Node #0,1,3 Current State: 19:[16, 52], Operations: ['64-45=19', '71-19=52'] Exploring Operation: 52-16=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 16+52=68, Resulting Numbers: [68] 68,19 unequal: No Solution Exploring Operation: 16*52=832, Resulting Numbers: [832] 832,19 unequal: No Solution Moving to Node #0,1,1 Current State: 19:[71, 3], Operations: ['64-45=19', '19-16=3'] Exploring Operation: 71*3=213, Resulting Numbers: [213] 213,19 unequal: No Solution Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,19 unequal: No Solution Exploring Operation: 71+3=74, Resulting Numbers: [74] 74,19 unequal: No Solution Moving to Node #0,1,2 Current State: 19:[71, 35], Operations: ['64-45=19', '16+19=35'] Exploring Operation: 71+35=106, Resulting Numbers: [106] 106,19 unequal: No Solution Exploring Operation: 71*35=2485, Resulting Numbers: [2485] 2485,19 unequal: No Solution Exploring Operation: 71-35=36, Resulting Numbers: [36] 36,19 unequal: No Solution Moving to Node #0,1,4 Current State: 19:[19, 87], Operations: ['64-45=19', '16+71=87'] Exploring Operation: 19*87=1653, Resulting Numbers: [1653] 1653,19 unequal: No Solution Exploring Operation: 19+87=106, Resulting Numbers: [106] 106,19 unequal: No Solution Exploring Operation: 87-19=68, Resulting Numbers: [68] 68,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[16, 64, 26], Operations: ['71-45=26'] Exploring Operation: 64-26=38, Resulting Numbers: [16, 38] Generated Node #0,2,0: 19:[16, 38] Operation: 64-26=38 Exploring Operation: 26-16=10, Resulting Numbers: [64, 10] Generated Node #0,2,1: 19:[64, 10] Operation: 26-16=10 Exploring Operation: 64-16=48, Resulting Numbers: [26, 48] Generated Node #0,2,2: 19:[26, 48] Operation: 64-16=48 Exploring Operation: 16+64=80, Resulting Numbers: [26, 80] Generated Node #0,2,3: 19:[26, 80] Operation: 16+64=80 Exploring Operation: 64/16=4, Resulting Numbers: [26, 4] Generated Node #0,2,4: 19:[26, 4] Operation: 64/16=4 Moving to Node #0,2,0 Current State: 19:[16, 38], Operations: ['71-45=26', '64-26=38'] Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 16*38=608, Resulting Numbers: [608] 608,19 unequal: No Solution Exploring Operation: 16+38=54, Resulting Numbers: [54] 54,19 unequal: No Solution Moving to Node #0,2,4 Current State: 19:[26, 4], Operations: ['71-45=26', '64/16=4'] Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,19 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,19 unequal: No Solution Moving to Node #0,2,2 Current State: 19:[26, 48], Operations: ['71-45=26', '64-16=48'] Exploring Operation: 48-26=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 26*48=1248, Resulting Numbers: [1248] 1248,19 unequal: No Solution Exploring Operation: 26+48=74, Resulting Numbers: [74] 74,19 unequal: No Solution Moving to Node #0,2,1 Current State: 19:[64, 10], Operations: ['71-45=26', '26-16=10'] Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 64*10=640, Resulting Numbers: [640] 640,19 unequal: No Solution Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,19 unequal: No Solution Moving to Node #0,2,3 Current State: 19:[26, 80], Operations: ['71-45=26', '16+64=80'] Exploring Operation: 26*80=2080, Resulting Numbers: [2080] 2080,19 unequal: No Solution Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 26+80=106, Resulting Numbers: [106] 106,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 19:[71, 45, 4], Operations: ['64/16=4'] Exploring Operation: 71-4=67, Resulting Numbers: [45, 67] Generated Node #0,3,0: 19:[45, 67] Operation: 71-4=67 Exploring Operation: 45-4=41, Resulting Numbers: [71, 41] Generated Node #0,3,1: 19:[71, 41] Operation: 45-4=41 Exploring Operation: 71+4=75, Resulting Numbers: [45, 75] Generated Node #0,3,2: 19:[45, 75] Operation: 71+4=75 Exploring Operation: 45+4=49, Resulting Numbers: [71, 49] Generated Node #0,3,3: 19:[71, 49] Operation: 45+4=49 Exploring Operation: 71-45=26, Resulting Numbers: [4, 26] Generated Node #0,3,4: 19:[4, 26] Operation: 71-45=26 Moving to Node #0,3,4 Current State: 19:[4, 26], Operations: ['64/16=4', '71-45=26'] Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,19 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,19 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,19 unequal: No Solution Moving to Node #0,3,1 Current State: 19:[71, 41], Operations: ['64/16=4', '45-4=41'] Exploring Operation: 71-41=30, Resulting Numbers: [30] 30,19 unequal: No Solution Exploring Operation: 71*41=2911, Resulting Numbers: [2911] 2911,19 unequal: No Solution Exploring Operation: 71+41=112, Resulting Numbers: [112] 112,19 unequal: No Solution Moving to Node #0,3,0 Current State: 19:[45, 67], Operations: ['64/16=4', '71-4=67'] Exploring Operation: 45*67=3015, Resulting Numbers: [3015] 3015,19 unequal: No Solution Exploring Operation: 45+67=112, Resulting Numbers: [112] 112,19 unequal: No Solution Exploring Operation: 67-45=22, Resulting Numbers: [22] 22,19 unequal: No Solution Moving to Node #0,3,2 Current State: 19:[45, 75], Operations: ['64/16=4', '71+4=75'] Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,19 unequal: No Solution Exploring Operation: 45+75=120, Resulting Numbers: [120] 120,19 unequal: No Solution Exploring Operation: 45*75=3375, Resulting Numbers: [3375] 3375,19 unequal: No Solution Moving to Node #0,3,3 Current State: 19:[71, 49], Operations: ['64/16=4', '45+4=49'] Exploring Operation: 71*49=3479, Resulting Numbers: [3479] 3479,19 unequal: No Solution Exploring Operation: 71+49=120, Resulting Numbers: [120] 120,19 unequal: No Solution Exploring Operation: 71-49=22, Resulting Numbers: [22] 22,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 19:[45, 64, 55], Operations: ['71-16=55'] Exploring Operation: 45+64=109, Resulting Numbers: [55, 109] Generated Node #0,4,0: 19:[55, 109] Operation: 45+64=109 Exploring Operation: 64-45=19, Resulting Numbers: [55, 19] Generated Node #0,4,1: 19:[55, 19] Operation: 64-45=19 Exploring Operation: 64-55=9, Resulting Numbers: [45, 9] Generated Node #0,4,2: 19:[45, 9] Operation: 64-55=9 Exploring Operation: 55-45=10, Resulting Numbers: [64, 10] Generated Node #0,4,3: 19:[64, 10] Operation: 55-45=10 Exploring Operation: 45+55=100, Resulting Numbers: [64, 100] Generated Node #0,4,4: 19:[64, 100] Operation: 45+55=100 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 19:[55, 19], Operations: ['71-16=55', '64-45=19'] Exploring Operation: 55+19=74, Resulting Numbers: [74] 74,19 unequal: No Solution Exploring Operation: 55*19=1045, Resulting Numbers: [1045] 1045,19 unequal: No Solution Exploring Operation: 55-19=36, Resulting Numbers: [36] 36,19 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 #0,4,2 Current State: 19:[45, 9], Operations: ['71-16=55', '64-55=9'] Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 45*9=405, Resulting Numbers: [405] 405,19 unequal: No Solution Exploring Operation: 45+9=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,19 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 #0,4,3 Current State: 19:[64, 10], Operations: ['71-16=55', '55-45=10'] Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,19 unequal: No Solution Exploring Operation: 64*10=640, Resulting Numbers: [640] 640,19 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 #0,4,0 Current State: 19:[55, 109], Operations: ['71-16=55', '45+64=109'] Exploring Operation: 55+109=164, Resulting Numbers: [164] 164,19 unequal: No Solution Exploring Operation: 55*109=5995, Resulting Numbers: [5995] 5995,19 unequal: No Solution Exploring Operation: 109-55=54, Resulting Numbers: [54] 54,19 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 #0,4,4 Current State: 19:[64, 100], Operations: ['71-16=55', '45+55=100'] Exploring Operation: 100-64=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 64*100=6400, Resulting Numbers: [6400] 6400,19 unequal: No Solution Exploring Operation: 64+100=164, Resulting Numbers: [164] 164,19 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 No solution found.
0
hs_5
mult_heuristic
[ 22, 7, 40, 12 ]
13
[ "22-7=15", "40-12=28", "28-15=13" ]
Current State: 13:[22, 7, 40, 12], Operations: [] Exploring Operation: 22-7=15, Resulting Numbers: [40, 12, 15] Generated Node #2: [40, 12, 15] from Operation: 22-7=15 Current State: 13:[40, 12, 15], Operations: ['22-7=15'] Exploring Operation: 40-12=28, Resulting Numbers: [15, 28] Generated Node #3: [15, 28] from Operation: 40-12=28 Current State: 13:[15, 28], Operations: ['22-7=15', '40-12=28'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[22, 7, 40, 12], Operations: [] Exploring Operation: 40-22=18, Resulting Numbers: [7, 12, 18] Generated Node #0,0: 13:[7, 12, 18] Operation: 40-22=18 Moving to Node #0,0 Current State: 13:[7, 12, 18], Operations: ['40-22=18'] Exploring Operation: 18-7=11, Resulting Numbers: [12, 11] Generated Node #0,0,0: 13:[12, 11] Operation: 18-7=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 13:[12, 11], Operations: ['40-22=18', '18-7=11'] Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,13 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
[ 37, 55, 84, 28 ]
20
[ "37+55=92", "84+28=112", "112-92=20" ]
Current State: 20:[37, 55, 84, 28], Operations: [] Exploring Operation: 37+55=92, Resulting Numbers: [84, 28, 92] Generated Node #2: [84, 28, 92] from Operation: 37+55=92 Current State: 20:[84, 28, 92], Operations: ['37+55=92'] Exploring Operation: 84+28=112, Resulting Numbers: [92, 112] Generated Node #3: [92, 112] from Operation: 84+28=112 Current State: 20:[92, 112], Operations: ['37+55=92', '84+28=112'] Exploring Operation: 112-92=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[37, 55, 84, 28], Operations: [] Exploring Operation: 84-37=47, Resulting Numbers: [55, 28, 47] Generated Node #0,0: 20:[55, 28, 47] Operation: 84-37=47 Exploring Operation: 84-55=29, Resulting Numbers: [37, 28, 29] Generated Node #0,1: 20:[37, 28, 29] Operation: 84-55=29 Exploring Operation: 84/28=3, Resulting Numbers: [37, 55, 3] Generated Node #0,2: 20:[37, 55, 3] Operation: 84/28=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[37, 28, 29], Operations: ['84-55=29'] Exploring Operation: 37-29=8, Resulting Numbers: [28, 8] Generated Node #0,1,0: 20:[28, 8] Operation: 37-29=8 Exploring Operation: 37-28=9, Resulting Numbers: [29, 9] Generated Node #0,1,1: 20:[29, 9] Operation: 37-28=9 Exploring Operation: 29-28=1, Resulting Numbers: [37, 1] Generated Node #0,1,2: 20:[37, 1] Operation: 29-28=1 Moving to Node #0,1,0 Current State: 20:[28, 8], Operations: ['84-55=29', '37-29=8'] Exploring Operation: 28*8=224, Resulting Numbers: [224] 224,20 unequal: No Solution Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,20 unequal: No Solution Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[37, 55, 84, 28], Operations: [] Exploring Operation: 84-55=29, Resulting Numbers: [37, 28, 29] Generated Node #0,1: 20:[37, 28, 29] Operation: 84-55=29 Moving to Node #0,1 Current State: 20:[37, 28, 29], Operations: ['84-55=29'] Exploring Operation: 37-29=8, Resulting Numbers: [28, 8] Generated Node #0,1,0: 20:[28, 8] Operation: 37-29=8 Moving to Node #0,1,0 Current State: 20:[28, 8], Operations: ['84-55=29', '37-29=8'] Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 4, 82, 54, 49 ]
73
[ "82-4=78", "54-49=5", "78-5=73" ]
Current State: 73:[4, 82, 54, 49], Operations: [] Exploring Operation: 82-4=78, Resulting Numbers: [54, 49, 78] Generated Node #2: [54, 49, 78] from Operation: 82-4=78 Current State: 73:[54, 49, 78], Operations: ['82-4=78'] Exploring Operation: 54-49=5, Resulting Numbers: [78, 5] Generated Node #3: [78, 5] from Operation: 54-49=5 Current State: 73:[78, 5], Operations: ['82-4=78', '54-49=5'] Exploring Operation: 78-5=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[4, 82, 54, 49], Operations: [] Exploring Operation: 4+49=53, Resulting Numbers: [82, 54, 53] Generated Node #0,0: 73:[82, 54, 53] Operation: 4+49=53 Exploring Operation: 4+82=86, Resulting Numbers: [54, 49, 86] Generated Node #0,1: 73:[54, 49, 86] Operation: 4+82=86 Exploring Operation: 82-4=78, Resulting Numbers: [54, 49, 78] Generated Node #0,2: 73:[54, 49, 78] Operation: 82-4=78 Exploring Operation: 4+54=58, Resulting Numbers: [82, 49, 58] Generated Node #0,3: 73:[82, 49, 58] Operation: 4+54=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[82, 54, 53], Operations: ['4+49=53'] Exploring Operation: 82-53=29, Resulting Numbers: [54, 29] Generated Node #0,0,0: 73:[54, 29] Operation: 82-53=29 Exploring Operation: 54+53=107, Resulting Numbers: [82, 107] Generated Node #0,0,1: 73:[82, 107] Operation: 54+53=107 Exploring Operation: 82-54=28, Resulting Numbers: [53, 28] Generated Node #0,0,2: 73:[53, 28] Operation: 82-54=28 Exploring Operation: 82+53=135, Resulting Numbers: [54, 135] Generated Node #0,0,3: 73:[54, 135] Operation: 82+53=135 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[82, 107], Operations: ['4+49=53', '54+53=107'] Exploring Operation: 107-82=25, Resulting Numbers: [25] 25,73 unequal: No Solution Exploring Operation: 82*107=8774, Resulting Numbers: [8774] 8774,73 unequal: No Solution Exploring Operation: 82+107=189, Resulting Numbers: [189] 189,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[54, 29], Operations: ['4+49=53', '82-53=29'] Exploring Operation: 54+29=83, Resulting Numbers: [83] 83,73 unequal: No Solution Exploring Operation: 54*29=1566, Resulting Numbers: [1566] 1566,73 unequal: No Solution Exploring Operation: 54-29=25, Resulting Numbers: [25] 25,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 73:[53, 28], Operations: ['4+49=53', '82-54=28'] Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,73 unequal: No Solution Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,73 unequal: No Solution Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 73:[54, 135], Operations: ['4+49=53', '82+53=135'] Exploring Operation: 54+135=189, Resulting Numbers: [189] 189,73 unequal: No Solution Exploring Operation: 135-54=81, Resulting Numbers: [81] 81,73 unequal: No Solution Exploring Operation: 54*135=7290, Resulting Numbers: [7290] 7290,73 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:[54, 49, 78], Operations: ['82-4=78'] Exploring Operation: 78-54=24, Resulting Numbers: [49, 24] Generated Node #0,2,0: 73:[49, 24] Operation: 78-54=24 Exploring Operation: 54+49=103, Resulting Numbers: [78, 103] Generated Node #0,2,1: 73:[78, 103] Operation: 54+49=103 Exploring Operation: 78-49=29, Resulting Numbers: [54, 29] Generated Node #0,2,2: 73:[54, 29] Operation: 78-49=29 Exploring Operation: 54-49=5, Resulting Numbers: [78, 5] Generated Node #0,2,3: 73:[78, 5] Operation: 54-49=5 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 73:[78, 103], Operations: ['82-4=78', '54+49=103'] Exploring Operation: 103-78=25, Resulting Numbers: [25] 25,73 unequal: No Solution Exploring Operation: 78*103=8034, Resulting Numbers: [8034] 8034,73 unequal: No Solution Exploring Operation: 78+103=181, Resulting Numbers: [181] 181,73 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 #0,2,2 Current State: 73:[54, 29], Operations: ['82-4=78', '78-49=29'] Exploring Operation: 54-29=25, Resulting Numbers: [25] 25,73 unequal: No Solution Exploring Operation: 54*29=1566, Resulting Numbers: [1566] 1566,73 unequal: No Solution Exploring Operation: 54+29=83, Resulting Numbers: [83] 83,73 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 #0,2,0 Current State: 73:[49, 24], Operations: ['82-4=78', '78-54=24'] Exploring Operation: 49*24=1176, Resulting Numbers: [1176] 1176,73 unequal: No Solution Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[4, 82, 54, 49], Operations: [] Exploring Operation: 82-4=78, Resulting Numbers: [54, 49, 78] Generated Node #0,2: 73:[54, 49, 78] Operation: 82-4=78 Moving to Node #0,2 Current State: 73:[54, 49, 78], Operations: ['82-4=78'] Exploring Operation: 78-54=24, Resulting Numbers: [49, 24] Generated Node #0,2,0: 73:[49, 24] Operation: 78-54=24 Moving to Node #0,2,0 Current State: 73:[49, 24], Operations: ['82-4=78', '78-54=24'] Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_4
sum_heuristic
[ 31, 54, 42, 34 ]
93
[ "31+54=85", "42-34=8", "85+8=93" ]
Current State: 93:[31, 54, 42, 34], Operations: [] Exploring Operation: 31+54=85, Resulting Numbers: [42, 34, 85] Generated Node #2: [42, 34, 85] from Operation: 31+54=85 Current State: 93:[42, 34, 85], Operations: ['31+54=85'] Exploring Operation: 42-34=8, Resulting Numbers: [85, 8] Generated Node #3: [85, 8] from Operation: 42-34=8 Current State: 93:[85, 8], Operations: ['31+54=85', '42-34=8'] Exploring Operation: 85+8=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[31, 54, 42, 34], Operations: [] Exploring Operation: 54+42=96, Resulting Numbers: [31, 34, 96] Generated Node #0,0: 93:[31, 34, 96] Operation: 54+42=96 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[31, 34, 96], Operations: ['54+42=96'] Exploring Operation: 34-31=3, Resulting Numbers: [96, 3] Generated Node #0,0,0: 93:[96, 3] Operation: 34-31=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 93:[96, 3], Operations: ['54+42=96', '34-31=3'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[31, 54, 42, 34], Operations: [] Exploring Operation: 54+42=96, Resulting Numbers: [31, 34, 96] Generated Node #0,0: 93:[31, 34, 96] Operation: 54+42=96 Moving to Node #0,0 Current State: 93:[31, 34, 96], Operations: ['54+42=96'] Exploring Operation: 34-31=3, Resulting Numbers: [96, 3] Generated Node #0,0,0: 93:[96, 3] Operation: 34-31=3 Moving to Node #0,0,0 Current State: 93:[96, 3], Operations: ['54+42=96', '34-31=3'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 65, 68, 43, 2 ]
47
[ "65+68=133", "43*2=86", "133-86=47" ]
Current State: 47:[65, 68, 43, 2], Operations: [] Exploring Operation: 65+68=133, Resulting Numbers: [43, 2, 133] Generated Node #2: [43, 2, 133] from Operation: 65+68=133 Current State: 47:[43, 2, 133], Operations: ['65+68=133'] Exploring Operation: 43*2=86, Resulting Numbers: [133, 86] Generated Node #3: [133, 86] from Operation: 43*2=86 Current State: 47:[133, 86], Operations: ['65+68=133', '43*2=86'] Exploring Operation: 133-86=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[65, 68, 43, 2], Operations: [] Exploring Operation: 68-2=66, Resulting Numbers: [65, 43, 66] Generated Node #0,0: 47:[65, 43, 66] Operation: 68-2=66 Exploring Operation: 65-2=63, Resulting Numbers: [68, 43, 63] Generated Node #0,1: 47:[68, 43, 63] Operation: 65-2=63 Exploring Operation: 68/2=34, Resulting Numbers: [65, 43, 34] Generated Node #0,2: 47:[65, 43, 34] Operation: 68/2=34 Start Sub Search at level 1: Moving to Node #0,2 Current State: 47:[65, 43, 34], Operations: ['68/2=34'] Exploring Operation: 65-43=22, Resulting Numbers: [34, 22] Generated Node #0,2,0: 47:[34, 22] Operation: 65-43=22 Exploring Operation: 43+34=77, Resulting Numbers: [65, 77] Generated Node #0,2,1: 47:[65, 77] Operation: 43+34=77 Exploring Operation: 65-34=31, Resulting Numbers: [43, 31] Generated Node #0,2,2: 47:[43, 31] Operation: 65-34=31 Moving to Node #0,2,2 Current State: 47:[43, 31], Operations: ['68/2=34', '65-34=31'] Exploring Operation: 43+31=74, Resulting Numbers: [74] 74,47 unequal: No Solution Exploring Operation: 43-31=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 43*31=1333, Resulting Numbers: [1333] 1333,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[34, 22], Operations: ['68/2=34', '65-43=22'] Exploring Operation: 34+22=56, Resulting Numbers: [56] 56,47 unequal: No Solution Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 34*22=748, Resulting Numbers: [748] 748,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[65, 77], Operations: ['68/2=34', '43+34=77'] Exploring Operation: 65*77=5005, Resulting Numbers: [5005] 5005,47 unequal: No Solution Exploring Operation: 77-65=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 65+77=142, Resulting Numbers: [142] 142,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[65, 43, 66], Operations: ['68-2=66'] Exploring Operation: 66-43=23, Resulting Numbers: [65, 23] Generated Node #0,0,0: 47:[65, 23] Operation: 66-43=23 Exploring Operation: 65-43=22, Resulting Numbers: [66, 22] Generated Node #0,0,1: 47:[66, 22] Operation: 65-43=22 Exploring Operation: 66-65=1, Resulting Numbers: [43, 1] Generated Node #0,0,2: 47:[43, 1] Operation: 66-65=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[65, 23], Operations: ['68-2=66', '66-43=23'] Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,47 unequal: No Solution Exploring Operation: 65+23=88, Resulting Numbers: [88] 88,47 unequal: No Solution Exploring Operation: 65*23=1495, Resulting Numbers: [1495] 1495,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 47:[66, 22], Operations: ['68-2=66', '65-43=22'] Exploring Operation: 66/22=3, Resulting Numbers: [3] 3,47 unequal: No Solution Exploring Operation: 66+22=88, Resulting Numbers: [88] 88,47 unequal: No Solution Exploring Operation: 66-22=44, Resulting Numbers: [44] 44,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 47:[43, 1], Operations: ['68-2=66', '66-65=1'] Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 43+1=44, Resulting Numbers: [44] 44,47 unequal: No Solution Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[68, 43, 63], Operations: ['65-2=63'] Exploring Operation: 68-43=25, Resulting Numbers: [63, 25] Generated Node #0,1,0: 47:[63, 25] Operation: 68-43=25 Exploring Operation: 68-63=5, Resulting Numbers: [43, 5] Generated Node #0,1,1: 47:[43, 5] Operation: 68-63=5 Exploring Operation: 63-43=20, Resulting Numbers: [68, 20] Generated Node #0,1,2: 47:[68, 20] Operation: 63-43=20 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 47:[63, 25], Operations: ['65-2=63', '68-43=25'] Exploring Operation: 63*25=1575, Resulting Numbers: [1575] 1575,47 unequal: No Solution Exploring Operation: 63+25=88, Resulting Numbers: [88] 88,47 unequal: No Solution Exploring Operation: 63-25=38, Resulting Numbers: [38] 38,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 47:[43, 5], Operations: ['65-2=63', '68-63=5'] Exploring Operation: 43+5=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 43*5=215, Resulting Numbers: [215] 215,47 unequal: No Solution Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 47:[68, 20], Operations: ['65-2=63', '63-43=20'] Exploring Operation: 68-20=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 68*20=1360, Resulting Numbers: [1360] 1360,47 unequal: No Solution Exploring Operation: 68+20=88, Resulting Numbers: [88] 88,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 24, 49, 37, 35 ]
71
[ "24+49=73", "37-35=2", "73-2=71" ]
Current State: 71:[24, 49, 37, 35], Operations: [] Exploring Operation: 24+49=73, Resulting Numbers: [37, 35, 73] Generated Node #2: [37, 35, 73] from Operation: 24+49=73 Current State: 71:[37, 35, 73], Operations: ['24+49=73'] Exploring Operation: 37-35=2, Resulting Numbers: [73, 2] Generated Node #3: [73, 2] from Operation: 37-35=2 Current State: 71:[73, 2], Operations: ['24+49=73', '37-35=2'] Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[24, 49, 37, 35], Operations: [] Exploring Operation: 24+35=59, Resulting Numbers: [49, 37, 59] Generated Node #0,0: 71:[49, 37, 59] Operation: 24+35=59 Exploring Operation: 37+35=72, Resulting Numbers: [24, 49, 72] Generated Node #0,1: 71:[24, 49, 72] Operation: 37+35=72 Exploring Operation: 24+37=61, Resulting Numbers: [49, 35, 61] Generated Node #0,2: 71:[49, 35, 61] Operation: 24+37=61 Exploring Operation: 24+49=73, Resulting Numbers: [37, 35, 73] Generated Node #0,3: 71:[37, 35, 73] Operation: 24+49=73 Moving to Node #0,0 Current State: 71:[49, 37, 59], Operations: ['24+35=59'] Exploring Operation: 49+37=86, Resulting Numbers: [59, 86] Generated Node #0,0,0: 71:[59, 86] Operation: 49+37=86 Exploring Operation: 49+59=108, Resulting Numbers: [37, 108] Generated Node #0,0,1: 71:[37, 108] Operation: 49+59=108 Exploring Operation: 49-37=12, Resulting Numbers: [59, 12] Generated Node #0,0,2: 71:[59, 12] Operation: 49-37=12 Exploring Operation: 37+59=96, Resulting Numbers: [49, 96] Generated Node #0,0,3: 71:[49, 96] Operation: 37+59=96 Moving to Node #0,2 Current State: 71:[49, 35, 61], Operations: ['24+37=61'] Exploring Operation: 49-35=14, Resulting Numbers: [61, 14] Generated Node #0,2,0: 71:[61, 14] Operation: 49-35=14 Exploring Operation: 49+35=84, Resulting Numbers: [61, 84] Generated Node #0,2,1: 71:[61, 84] Operation: 49+35=84 Exploring Operation: 35+61=96, Resulting Numbers: [49, 96] Generated Node #0,2,2: 71:[49, 96] Operation: 35+61=96 Exploring Operation: 61-35=26, Resulting Numbers: [49, 26] Generated Node #0,2,3: 71:[49, 26] Operation: 61-35=26 Moving to Node #0,1 Current State: 71:[24, 49, 72], Operations: ['37+35=72'] Exploring Operation: 49-24=25, Resulting Numbers: [72, 25] Generated Node #0,1,0: 71:[72, 25] Operation: 49-24=25 Exploring Operation: 24+72=96, Resulting Numbers: [49, 96] Generated Node #0,1,1: 71:[49, 96] Operation: 24+72=96 Exploring Operation: 24+49=73, Resulting Numbers: [72, 73] Generated Node #0,1,2: 71:[72, 73] Operation: 24+49=73 Exploring Operation: 72-24=48, Resulting Numbers: [49, 48] Generated Node #0,1,3: 71:[49, 48] Operation: 72-24=48 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 71:[72, 73], Operations: ['37+35=72', '24+49=73'] Exploring Operation: 72*73=5256, Resulting Numbers: [5256] 5256,71 unequal: No Solution Exploring Operation: 73-72=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 72+73=145, Resulting Numbers: [145] 145,71 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 #0,1,3 Current State: 71:[49, 48], Operations: ['37+35=72', '72-24=48'] Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,71 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,71 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 #0,1,0 Current State: 71:[72, 25], Operations: ['37+35=72', '49-24=25'] Exploring Operation: 72+25=97, Resulting Numbers: [97] 97,71 unequal: No Solution Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,71 unequal: No Solution Exploring Operation: 72*25=1800, Resulting Numbers: [1800] 1800,71 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 #0,1,1 Current State: 71:[49, 96], Operations: ['37+35=72', '24+72=96'] Exploring Operation: 49+96=145, Resulting Numbers: [145] 145,71 unequal: No Solution Exploring Operation: 49*96=4704, Resulting Numbers: [4704] 4704,71 unequal: No Solution Exploring Operation: 96-49=47, Resulting Numbers: [47] 47,71 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: 71:[37, 35, 73], Operations: ['24+49=73'] Exploring Operation: 37+35=72, Resulting Numbers: [73, 72] Generated Node #0,3,0: 71:[73, 72] Operation: 37+35=72 Exploring Operation: 73-35=38, Resulting Numbers: [37, 38] Generated Node #0,3,1: 71:[37, 38] Operation: 73-35=38 Exploring Operation: 73-37=36, Resulting Numbers: [35, 36] Generated Node #0,3,2: 71:[35, 36] Operation: 73-37=36 Exploring Operation: 37-35=2, Resulting Numbers: [73, 2] Generated Node #0,3,3: 71:[73, 2] Operation: 37-35=2 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 71:[73, 72], Operations: ['24+49=73', '37+35=72'] Exploring Operation: 73-72=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 73+72=145, Resulting Numbers: [145] 145,71 unequal: No Solution Exploring Operation: 73*72=5256, Resulting Numbers: [5256] 5256,71 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 #0,3,1 Current State: 71:[37, 38], Operations: ['24+49=73', '73-35=38'] Exploring Operation: 37+38=75, Resulting Numbers: [75] 75,71 unequal: No Solution Exploring Operation: 37*38=1406, Resulting Numbers: [1406] 1406,71 unequal: No Solution Exploring Operation: 38-37=1, Resulting Numbers: [1] 1,71 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 #0,3,2 Current State: 71:[35, 36], Operations: ['24+49=73', '73-37=36'] Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[24, 49, 37, 35], Operations: [] Exploring Operation: 24+49=73, Resulting Numbers: [37, 35, 73] Generated Node #0,3: 71:[37, 35, 73] Operation: 24+49=73 Moving to Node #0,3 Current State: 71:[37, 35, 73], Operations: ['24+49=73'] Exploring Operation: 73-37=36, Resulting Numbers: [35, 36] Generated Node #0,3,2: 71:[35, 36] Operation: 73-37=36 Moving to Node #0,3,2 Current State: 71:[35, 36], Operations: ['24+49=73', '73-37=36'] Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_4
mult_heuristic
[ 6, 71, 54, 4 ]
40
[ "6*54=324", "71*4=284", "324-284=40" ]
Current State: 40:[6, 71, 54, 4], Operations: [] Exploring Operation: 6*54=324, Resulting Numbers: [71, 4, 324] Generated Node #2: [71, 4, 324] from Operation: 6*54=324 Current State: 40:[71, 4, 324], Operations: ['6*54=324'] Exploring Operation: 71*4=284, Resulting Numbers: [324, 284] Generated Node #3: [324, 284] from Operation: 71*4=284 Current State: 40:[324, 284], Operations: ['6*54=324', '71*4=284'] Exploring Operation: 324-284=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[6, 71, 54, 4], Operations: [] Exploring Operation: 71-6=65, Resulting Numbers: [54, 4, 65] Generated Node #0,0: 40:[54, 4, 65] Operation: 71-6=65 Exploring Operation: 71-54=17, Resulting Numbers: [6, 4, 17] Generated Node #0,1: 40:[6, 4, 17] Operation: 71-54=17 Exploring Operation: 54/6=9, Resulting Numbers: [71, 4, 9] Generated Node #0,2: 40:[71, 4, 9] Operation: 54/6=9 Exploring Operation: 54-6=48, Resulting Numbers: [71, 4, 48] Generated Node #0,3: 40:[71, 4, 48] Operation: 54-6=48 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[6, 4, 17], Operations: ['71-54=17'] Exploring Operation: 17-6=11, Resulting Numbers: [4, 11] Generated Node #0,1,0: 40:[4, 11] Operation: 17-6=11 Exploring Operation: 6+4=10, Resulting Numbers: [17, 10] Generated Node #0,1,1: 40:[17, 10] Operation: 6+4=10 Exploring Operation: 4+17=21, Resulting Numbers: [6, 21] Generated Node #0,1,2: 40:[6, 21] Operation: 4+17=21 Exploring Operation: 6-4=2, Resulting Numbers: [17, 2] Generated Node #0,1,3: 40:[17, 2] Operation: 6-4=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 40:[4, 11], Operations: ['71-54=17', '17-6=11'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,40 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 40:[6, 21], Operations: ['71-54=17', '4+17=21'] Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,40 unequal: No Solution Exploring Operation: 6*21=126, Resulting Numbers: [126] 126,40 unequal: No Solution Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 40:[17, 10], Operations: ['71-54=17', '6+4=10'] Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,40 unequal: No Solution Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,40 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 40:[17, 2], Operations: ['71-54=17', '6-4=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,40 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,40 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[71, 4, 9], Operations: ['54/6=9'] Exploring Operation: 71-4=67, Resulting Numbers: [9, 67] Generated Node #0,2,0: 40:[9, 67] Operation: 71-4=67 Exploring Operation: 71-9=62, Resulting Numbers: [4, 62] Generated Node #0,2,1: 40:[4, 62] Operation: 71-9=62 Exploring Operation: 9-4=5, Resulting Numbers: [71, 5] Generated Node #0,2,2: 40:[71, 5] Operation: 9-4=5 Exploring Operation: 4+9=13, Resulting Numbers: [71, 13] Generated Node #0,2,3: 40:[71, 13] Operation: 4+9=13 Moving to Node #0,2,1 Current State: 40:[4, 62], Operations: ['54/6=9', '71-9=62'] Exploring Operation: 4+62=66, Resulting Numbers: [66] 66,40 unequal: No Solution Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,40 unequal: No Solution Exploring Operation: 4*62=248, Resulting Numbers: [248] 248,40 unequal: No Solution Moving to Node #0,2,0 Current State: 40:[9, 67], Operations: ['54/6=9', '71-4=67'] Exploring Operation: 9+67=76, Resulting Numbers: [76] 76,40 unequal: No Solution Exploring Operation: 67-9=58, Resulting Numbers: [58] 58,40 unequal: No Solution Exploring Operation: 9*67=603, Resulting Numbers: [603] 603,40 unequal: No Solution Moving to Node #0,2,2 Current State: 40:[71, 5], Operations: ['54/6=9', '9-4=5'] Exploring Operation: 71*5=355, Resulting Numbers: [355] 355,40 unequal: No Solution Exploring Operation: 71+5=76, Resulting Numbers: [76] 76,40 unequal: No Solution Exploring Operation: 71-5=66, Resulting Numbers: [66] 66,40 unequal: No Solution Moving to Node #0,2,3 Current State: 40:[71, 13], Operations: ['54/6=9', '4+9=13'] Exploring Operation: 71-13=58, Resulting Numbers: [58] 58,40 unequal: No Solution Exploring Operation: 71*13=923, Resulting Numbers: [923] 923,40 unequal: No Solution Exploring Operation: 71+13=84, Resulting Numbers: [84] 84,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[54, 4, 65], Operations: ['71-6=65'] Exploring Operation: 54+4=58, Resulting Numbers: [65, 58] Generated Node #0,0,0: 40:[65, 58] Operation: 54+4=58 Exploring Operation: 65-4=61, Resulting Numbers: [54, 61] Generated Node #0,0,1: 40:[54, 61] Operation: 65-4=61 Exploring Operation: 65-54=11, Resulting Numbers: [4, 11] Generated Node #0,0,2: 40:[4, 11] Operation: 65-54=11 Exploring Operation: 54-4=50, Resulting Numbers: [65, 50] Generated Node #0,0,3: 40:[65, 50] Operation: 54-4=50 Moving to Node #0,0,2 Current State: 40:[4, 11], Operations: ['71-6=65', '65-54=11'] Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,40 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,40 unequal: No Solution Moving to Node #0,0,3 Current State: 40:[65, 50], Operations: ['71-6=65', '54-4=50'] Exploring Operation: 65-50=15, Resulting Numbers: [15] 15,40 unequal: No Solution Exploring Operation: 65*50=3250, Resulting Numbers: [3250] 3250,40 unequal: No Solution Exploring Operation: 65+50=115, Resulting Numbers: [115] 115,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[54, 61], Operations: ['71-6=65', '65-4=61'] Exploring Operation: 54+61=115, Resulting Numbers: [115] 115,40 unequal: No Solution Exploring Operation: 54*61=3294, Resulting Numbers: [3294] 3294,40 unequal: No Solution Exploring Operation: 61-54=7, Resulting Numbers: [7] 7,40 unequal: No Solution Moving to Node #0,0,0 Current State: 40:[65, 58], Operations: ['71-6=65', '54+4=58'] Exploring Operation: 65+58=123, Resulting Numbers: [123] 123,40 unequal: No Solution Exploring Operation: 65*58=3770, Resulting Numbers: [3770] 3770,40 unequal: No Solution Exploring Operation: 65-58=7, Resulting Numbers: [7] 7,40 unequal: No Solution No 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: 40:[71, 4, 48], Operations: ['54-6=48'] Exploring Operation: 48/4=12, Resulting Numbers: [71, 12] Generated Node #0,3,0: 40:[71, 12] Operation: 48/4=12 Exploring Operation: 48-4=44, Resulting Numbers: [71, 44] Generated Node #0,3,1: 40:[71, 44] Operation: 48-4=44 Exploring Operation: 71-4=67, Resulting Numbers: [48, 67] Generated Node #0,3,2: 40:[48, 67] Operation: 71-4=67 Exploring Operation: 71-48=23, Resulting Numbers: [4, 23] Generated Node #0,3,3: 40:[4, 23] Operation: 71-48=23 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 40:[4, 23], Operations: ['54-6=48', '71-48=23'] Exploring Operation: 4+23=27, Resulting Numbers: [27] 27,40 unequal: No Solution Exploring Operation: 4*23=92, Resulting Numbers: [92] 92,40 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 40:[71, 12], Operations: ['54-6=48', '48/4=12'] Exploring Operation: 71-12=59, Resulting Numbers: [59] 59,40 unequal: No Solution Exploring Operation: 71+12=83, Resulting Numbers: [83] 83,40 unequal: No Solution Exploring Operation: 71*12=852, Resulting Numbers: [852] 852,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 40:[71, 44], Operations: ['54-6=48', '48-4=44'] Exploring Operation: 71+44=115, Resulting Numbers: [115] 115,40 unequal: No Solution Exploring Operation: 71*44=3124, Resulting Numbers: [3124] 3124,40 unequal: No Solution Exploring Operation: 71-44=27, Resulting Numbers: [27] 27,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 40:[48, 67], Operations: ['54-6=48', '71-4=67'] Exploring Operation: 48+67=115, Resulting Numbers: [115] 115,40 unequal: No Solution Exploring Operation: 67-48=19, Resulting Numbers: [19] 19,40 unequal: No Solution Exploring Operation: 48*67=3216, Resulting Numbers: [3216] 3216,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 89, 37, 98, 40 ]
12
[ "89+37=126", "98+40=138", "138-126=12" ]
Current State: 12:[89, 37, 98, 40], Operations: [] Exploring Operation: 89+37=126, Resulting Numbers: [98, 40, 126] Generated Node #2: [98, 40, 126] from Operation: 89+37=126 Current State: 12:[98, 40, 126], Operations: ['89+37=126'] Exploring Operation: 98+40=138, Resulting Numbers: [126, 138] Generated Node #3: [126, 138] from Operation: 98+40=138 Current State: 12:[126, 138], Operations: ['89+37=126', '98+40=138'] Exploring Operation: 138-126=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[89, 37, 98, 40], Operations: [] Exploring Operation: 89-37=52, Resulting Numbers: [98, 40, 52] Generated Node #0,0: 12:[98, 40, 52] Operation: 89-37=52 Exploring Operation: 98-37=61, Resulting Numbers: [89, 40, 61] Generated Node #0,1: 12:[89, 40, 61] Operation: 98-37=61 Exploring Operation: 89-40=49, Resulting Numbers: [37, 98, 49] Generated Node #0,2: 12:[37, 98, 49] Operation: 89-40=49 Exploring Operation: 98-40=58, Resulting Numbers: [89, 37, 58] Generated Node #0,3: 12:[89, 37, 58] Operation: 98-40=58 Exploring Operation: 98-89=9, Resulting Numbers: [37, 40, 9] Generated Node #0,4: 12:[37, 40, 9] Operation: 98-89=9 Start Sub Search at level 1: Moving to Node #0,4 Current State: 12:[37, 40, 9], Operations: ['98-89=9'] Exploring Operation: 37+9=46, Resulting Numbers: [40, 46] Generated Node #0,4,0: 12:[40, 46] Operation: 37+9=46 Exploring Operation: 40-9=31, Resulting Numbers: [37, 31] Generated Node #0,4,1: 12:[37, 31] Operation: 40-9=31 Exploring Operation: 40+9=49, Resulting Numbers: [37, 49] Generated Node #0,4,2: 12:[37, 49] Operation: 40+9=49 Exploring Operation: 37-9=28, Resulting Numbers: [40, 28] Generated Node #0,4,3: 12:[40, 28] Operation: 37-9=28 Exploring Operation: 40-37=3, Resulting Numbers: [9, 3] Generated Node #0,4,4: 12:[9, 3] Operation: 40-37=3 Moving to Node #0,4,4 Current State: 12:[9, 3], Operations: ['98-89=9', '40-37=3'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[89, 37, 98, 40], Operations: [] Exploring Operation: 98-89=9, Resulting Numbers: [37, 40, 9] Generated Node #0,4: 12:[37, 40, 9] Operation: 98-89=9 Moving to Node #0,4 Current State: 12:[37, 40, 9], Operations: ['98-89=9'] Exploring Operation: 40-37=3, Resulting Numbers: [9, 3] Generated Node #0,4,4: 12:[9, 3] Operation: 40-37=3 Moving to Node #0,4,4 Current State: 12:[9, 3], Operations: ['98-89=9', '40-37=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 97, 81, 9, 83 ]
86
[ "97+81=178", "9+83=92", "178-92=86" ]
Current State: 86:[97, 81, 9, 83], Operations: [] Exploring Operation: 97+81=178, Resulting Numbers: [9, 83, 178] Generated Node #2: [9, 83, 178] from Operation: 97+81=178 Current State: 86:[9, 83, 178], Operations: ['97+81=178'] Exploring Operation: 9+83=92, Resulting Numbers: [178, 92] Generated Node #3: [178, 92] from Operation: 9+83=92 Current State: 86:[178, 92], Operations: ['97+81=178', '9+83=92'] Exploring Operation: 178-92=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[97, 81, 9, 83], Operations: [] Exploring Operation: 81+9=90, Resulting Numbers: [97, 83, 90] Generated Node #0,0: 86:[97, 83, 90] Operation: 81+9=90 Exploring Operation: 97-9=88, Resulting Numbers: [81, 83, 88] Generated Node #0,1: 86:[81, 83, 88] Operation: 97-9=88 Exploring Operation: 83-81=2, Resulting Numbers: [97, 9, 2] Generated Node #0,2: 86:[97, 9, 2] Operation: 83-81=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[81, 83, 88], Operations: ['97-9=88'] Exploring Operation: 83-81=2, Resulting Numbers: [88, 2] Generated Node #0,1,0: 86:[88, 2] Operation: 83-81=2 Exploring Operation: 88-81=7, Resulting Numbers: [83, 7] Generated Node #0,1,1: 86:[83, 7] Operation: 88-81=7 Exploring Operation: 88-83=5, Resulting Numbers: [81, 5] Generated Node #0,1,2: 86:[81, 5] Operation: 88-83=5 Moving to Node #0,1,0 Current State: 86:[88, 2], Operations: ['97-9=88', '83-81=2'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[97, 81, 9, 83], Operations: [] Exploring Operation: 97-9=88, Resulting Numbers: [81, 83, 88] Generated Node #0,1: 86:[81, 83, 88] Operation: 97-9=88 Moving to Node #0,1 Current State: 86:[81, 83, 88], Operations: ['97-9=88'] Exploring Operation: 83-81=2, Resulting Numbers: [88, 2] Generated Node #0,1,0: 86:[88, 2] Operation: 83-81=2 Moving to Node #0,1,0 Current State: 86:[88, 2], Operations: ['97-9=88', '83-81=2'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 1, 24, 4, 9 ]
63
[ "4-1=3", "24*3=72", "72-9=63" ]
Current State: 63:[1, 24, 4, 9], Operations: [] Exploring Operation: 4-1=3, Resulting Numbers: [24, 9, 3] Generated Node #2: [24, 9, 3] from Operation: 4-1=3 Current State: 63:[24, 9, 3], Operations: ['4-1=3'] Exploring Operation: 24*3=72, Resulting Numbers: [9, 72] Generated Node #3: [9, 72] from Operation: 24*3=72 Current State: 63:[9, 72], Operations: ['4-1=3', '24*3=72'] Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[1, 24, 4, 9], Operations: [] Exploring Operation: 24-1=23, Resulting Numbers: [4, 9, 23] Generated Node #0,0: 63:[4, 9, 23] Operation: 24-1=23 Exploring Operation: 4-1=3, Resulting Numbers: [24, 9, 3] Generated Node #0,1: 63:[24, 9, 3] Operation: 4-1=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[4, 9, 23], Operations: ['24-1=23'] Exploring Operation: 23-4=19, Resulting Numbers: [9, 19] Generated Node #0,0,0: 63:[9, 19] Operation: 23-4=19 Exploring Operation: 9-4=5, Resulting Numbers: [23, 5] Generated Node #0,0,1: 63:[23, 5] Operation: 9-4=5 Moving to Node #0,0,0 Current State: 63:[9, 19], Operations: ['24-1=23', '23-4=19'] Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,63 unequal: No Solution Exploring Operation: 9+19=28, Resulting Numbers: [28] 28,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[23, 5], Operations: ['24-1=23', '9-4=5'] Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,63 unequal: No Solution Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[24, 9, 3], Operations: ['4-1=3'] Exploring Operation: 24/3=8, Resulting Numbers: [9, 8] Generated Node #0,1,0: 63:[9, 8] Operation: 24/3=8 Exploring Operation: 24-3=21, Resulting Numbers: [9, 21] Generated Node #0,1,1: 63:[9, 21] Operation: 24-3=21 Moving to Node #0,1,1 Current State: 63:[9, 21], Operations: ['4-1=3', '24-3=21'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,63 unequal: No Solution Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[9, 8], Operations: ['4-1=3', '24/3=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 27, 99, 80, 61 ]
91
[ "99-27=72", "80-61=19", "72+19=91" ]
Current State: 91:[27, 99, 80, 61], Operations: [] Exploring Operation: 99-27=72, Resulting Numbers: [80, 61, 72] Generated Node #2: [80, 61, 72] from Operation: 99-27=72 Current State: 91:[80, 61, 72], Operations: ['99-27=72'] Exploring Operation: 80-61=19, Resulting Numbers: [72, 19] Generated Node #3: [72, 19] from Operation: 80-61=19 Current State: 91:[72, 19], Operations: ['99-27=72', '80-61=19'] Exploring Operation: 72+19=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[27, 99, 80, 61], Operations: [] Exploring Operation: 27+61=88, Resulting Numbers: [99, 80, 88] Generated Node #0,0: 91:[99, 80, 88] Operation: 27+61=88 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[99, 80, 88], Operations: ['27+61=88'] Exploring Operation: 99-80=19, Resulting Numbers: [88, 19] Generated Node #0,0,0: 91:[88, 19] Operation: 99-80=19 Moving to Node #0,0,0 Current State: 91:[88, 19], Operations: ['27+61=88', '99-80=19'] Exploring Operation: 88+19=107, Resulting Numbers: [107] 107,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 16, 14, 13, 36 ]
21
[ "16-14=2", "36-13=23", "23-2=21" ]
Current State: 21:[16, 14, 13, 36], Operations: [] Exploring Operation: 16-14=2, Resulting Numbers: [13, 36, 2] Generated Node #2: [13, 36, 2] from Operation: 16-14=2 Current State: 21:[13, 36, 2], Operations: ['16-14=2'] Exploring Operation: 36-13=23, Resulting Numbers: [2, 23] Generated Node #3: [2, 23] from Operation: 36-13=23 Current State: 21:[2, 23], Operations: ['16-14=2', '36-13=23'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[16, 14, 13, 36], Operations: [] Exploring Operation: 36-14=22, Resulting Numbers: [16, 13, 22] Generated Node #0,0: 21:[16, 13, 22] Operation: 36-14=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[16, 13, 22], Operations: ['36-14=22'] Exploring Operation: 16-13=3, Resulting Numbers: [22, 3] Generated Node #0,0,0: 21:[22, 3] Operation: 16-13=3 Moving to Node #0,0,0 Current State: 21:[22, 3], Operations: ['36-14=22', '16-13=3'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 24, 36, 60, 30 ]
12
[ "24*60=1440", "1440/30=48", "48-36=12" ]
Current State: 12:[24, 36, 60, 30], Operations: [] Exploring Operation: 24*60=1440, Resulting Numbers: [36, 30, 1440] Generated Node #2: [36, 30, 1440] from Operation: 24*60=1440 Current State: 12:[36, 30, 1440], Operations: ['24*60=1440'] Exploring Operation: 1440/30=48, Resulting Numbers: [36, 48] Generated Node #3: [36, 48] from Operation: 1440/30=48 Current State: 12:[36, 48], Operations: ['24*60=1440', '1440/30=48'] Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[24, 36, 60, 30], Operations: [] Exploring Operation: 60/30=2, Resulting Numbers: [24, 36, 2] Generated Node #0,0: 12:[24, 36, 2] Operation: 60/30=2 Exploring Operation: 60-30=30, Resulting Numbers: [24, 36, 30] Generated Node #0,1: 12:[24, 36, 30] Operation: 60-30=30 Exploring Operation: 36-30=6, Resulting Numbers: [24, 60, 6] Generated Node #0,2: 12:[24, 60, 6] Operation: 36-30=6 Exploring Operation: 60-36=24, Resulting Numbers: [24, 30, 24] Generated Node #0,3: 12:[24, 30, 24] Operation: 60-36=24 Moving to Node #0,0 Current State: 12:[24, 36, 2], Operations: ['60/30=2'] Exploring Operation: 24-2=22, Resulting Numbers: [36, 22] Generated Node #0,0,0: 12:[36, 22] Operation: 24-2=22 Exploring Operation: 24/2=12, Resulting Numbers: [36, 12] Generated Node #0,0,1: 12:[36, 12] Operation: 24/2=12 Exploring Operation: 36-24=12, Resulting Numbers: [2, 12] Generated Node #0,0,2: 12:[2, 12] Operation: 36-24=12 Exploring Operation: 36/2=18, Resulting Numbers: [24, 18] Generated Node #0,0,3: 12:[24, 18] Operation: 36/2=18 Moving to Node #0,3 Current State: 12:[24, 30, 24], Operations: ['60-36=24'] Exploring Operation: 30-24=6, Resulting Numbers: [24, 6] Generated Node #0,3,0: 12:[24, 6] Operation: 30-24=6 Exploring Operation: 30-24=6, Resulting Numbers: [24, 6] Generated Node #0,3,1: 12:[24, 6] Operation: 30-24=6 Exploring Operation: 24-24=0, Resulting Numbers: [30, 0] Generated Node #0,3,2: 12:[30, 0] Operation: 24-24=0 Exploring Operation: 24/24=1, Resulting Numbers: [30, 1] Generated Node #0,3,3: 12:[30, 1] Operation: 24/24=1 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 12:[24, 6], Operations: ['60-36=24', '30-24=6'] Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 24*6=144, Resulting Numbers: [144] 144,12 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 24+6=30, Resulting Numbers: [30] 30,12 unequal: No Solution No 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: 12:[24, 6], Operations: ['60-36=24', '30-24=6'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 24+6=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 24*6=144, Resulting Numbers: [144] 144,12 unequal: No Solution No 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: 12:[30, 1], Operations: ['60-36=24', '24/24=1'] Exploring Operation: 30/1=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 30+1=31, Resulting Numbers: [31] 31,12 unequal: No Solution Exploring Operation: 30*1=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,12 unequal: No Solution No 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: 12:[30, 0], Operations: ['60-36=24', '24-24=0'] Exploring Operation: 30-0=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 30*0=0, Resulting Numbers: [0] 0,12 unequal: No Solution Exploring Operation: 30+0=30, Resulting Numbers: [30] 30,12 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: 12:[24, 36, 30], Operations: ['60-30=30'] Exploring Operation: 24+36=60, Resulting Numbers: [30, 60] Generated Node #0,1,0: 12:[30, 60] Operation: 24+36=60 Exploring Operation: 30-24=6, Resulting Numbers: [36, 6] Generated Node #0,1,1: 12:[36, 6] Operation: 30-24=6 Exploring Operation: 36-24=12, Resulting Numbers: [30, 12] Generated Node #0,1,2: 12:[30, 12] Operation: 36-24=12 Exploring Operation: 36-30=6, Resulting Numbers: [24, 6] Generated Node #0,1,3: 12:[24, 6] Operation: 36-30=6 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 12:[24, 6], Operations: ['60-30=30', '36-30=6'] Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 24*6=144, Resulting Numbers: [144] 144,12 unequal: No Solution Exploring Operation: 24+6=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,12 unequal: No Solution No 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: 12:[30, 12], Operations: ['60-30=30', '36-24=12'] Exploring Operation: 30+12=42, Resulting Numbers: [42] 42,12 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 30*12=360, Resulting Numbers: [360] 360,12 unequal: No Solution No 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: 12:[36, 6], Operations: ['60-30=30', '30-24=6'] Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,12 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 36*6=216, Resulting Numbers: [216] 216,12 unequal: No Solution No 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: 12:[30, 60], Operations: ['60-30=30', '24+36=60'] Exploring Operation: 30+60=90, Resulting Numbers: [90] 90,12 unequal: No Solution Exploring Operation: 60-30=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 30*60=1800, Resulting Numbers: [1800] 1800,12 unequal: No Solution Exploring Operation: 60/30=2, Resulting Numbers: [2] 2,12 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: 12:[24, 60, 6], Operations: ['36-30=6'] Exploring Operation: 24/6=4, Resulting Numbers: [60, 4] Generated Node #0,2,0: 12:[60, 4] Operation: 24/6=4 Exploring Operation: 60/6=10, Resulting Numbers: [24, 10] Generated Node #0,2,1: 12:[24, 10] Operation: 60/6=10 Exploring Operation: 24-6=18, Resulting Numbers: [60, 18] Generated Node #0,2,2: 12:[60, 18] Operation: 24-6=18 Exploring Operation: 60-24=36, Resulting Numbers: [6, 36] Generated Node #0,2,3: 12:[6, 36] Operation: 60-24=36 Moving to Node #0,0,2 Current State: 12:[2, 12], Operations: ['60/30=2', '36-24=12'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,12 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[24, 10], Operations: ['36-30=6', '60/6=10'] Exploring Operation: 24*10=240, Resulting Numbers: [240] 240,12 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,12 unequal: No Solution Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,12 unequal: No Solution Moving to Node #0,0,3 Current State: 12:[24, 18], Operations: ['60/30=2', '36/2=18'] Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,12 unequal: No Solution Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[36, 12], Operations: ['60/30=2', '24/2=12'] Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,12 unequal: No Solution Exploring Operation: 36*12=432, Resulting Numbers: [432] 432,12 unequal: No Solution Exploring Operation: 36+12=48, Resulting Numbers: [48] 48,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[6, 36], Operations: ['36-30=6', '60-24=36'] Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 6+36=42, Resulting Numbers: [42] 42,12 unequal: No Solution Exploring Operation: 6*36=216, Resulting Numbers: [216] 216,12 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[36, 22], Operations: ['60/30=2', '24-2=22'] Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,12 unequal: No Solution Exploring Operation: 36*22=792, Resulting Numbers: [792] 792,12 unequal: No Solution Exploring Operation: 36+22=58, Resulting Numbers: [58] 58,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[60, 4], Operations: ['36-30=6', '24/6=4'] Exploring Operation: 60-4=56, Resulting Numbers: [56] 56,12 unequal: No Solution Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,12 unequal: No Solution Exploring Operation: 60*4=240, Resulting Numbers: [240] 240,12 unequal: No Solution Exploring Operation: 60+4=64, Resulting Numbers: [64] 64,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[60, 18], Operations: ['36-30=6', '24-6=18'] Exploring Operation: 60-18=42, Resulting Numbers: [42] 42,12 unequal: No Solution Exploring Operation: 60+18=78, Resulting Numbers: [78] 78,12 unequal: No Solution Exploring Operation: 60*18=1080, Resulting Numbers: [1080] 1080,12 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 37, 45, 87, 3 ]
35
[ "87-37=50", "45/3=15", "50-15=35" ]
Current State: 35:[37, 45, 87, 3], Operations: [] Exploring Operation: 87-37=50, Resulting Numbers: [45, 3, 50] Generated Node #2: [45, 3, 50] from Operation: 87-37=50 Current State: 35:[45, 3, 50], Operations: ['87-37=50'] Exploring Operation: 45/3=15, Resulting Numbers: [50, 15] Generated Node #3: [50, 15] from Operation: 45/3=15 Current State: 35:[50, 15], Operations: ['87-37=50', '45/3=15'] Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[37, 45, 87, 3], Operations: [] Exploring Operation: 87-45=42, Resulting Numbers: [37, 3, 42] Generated Node #0,0: 35:[37, 3, 42] Operation: 87-45=42 Exploring Operation: 87-37=50, Resulting Numbers: [45, 3, 50] Generated Node #0,1: 35:[45, 3, 50] Operation: 87-37=50 Exploring Operation: 87/3=29, Resulting Numbers: [37, 45, 29] Generated Node #0,2: 35:[37, 45, 29] Operation: 87/3=29 Moving to Node #0,0 Current State: 35:[37, 3, 42], Operations: ['87-45=42'] Exploring Operation: 37-3=34, Resulting Numbers: [42, 34] Generated Node #0,0,0: 35:[42, 34] Operation: 37-3=34 Exploring Operation: 42-37=5, Resulting Numbers: [3, 5] Generated Node #0,0,1: 35:[3, 5] Operation: 42-37=5 Exploring Operation: 42-3=39, Resulting Numbers: [37, 39] Generated Node #0,0,2: 35:[37, 39] Operation: 42-3=39 Moving to Node #0,2 Current State: 35:[37, 45, 29], Operations: ['87/3=29'] Exploring Operation: 37-29=8, Resulting Numbers: [45, 8] Generated Node #0,2,0: 35:[45, 8] Operation: 37-29=8 Exploring Operation: 45-29=16, Resulting Numbers: [37, 16] Generated Node #0,2,1: 35:[37, 16] Operation: 45-29=16 Exploring Operation: 45-37=8, Resulting Numbers: [29, 8] Generated Node #0,2,2: 35:[29, 8] Operation: 45-37=8 Moving to Node #0,1 Current State: 35:[45, 3, 50], Operations: ['87-37=50'] Exploring Operation: 45-3=42, Resulting Numbers: [50, 42] Generated Node #0,1,0: 35:[50, 42] Operation: 45-3=42 Exploring Operation: 50-3=47, Resulting Numbers: [45, 47] Generated Node #0,1,1: 35:[45, 47] Operation: 50-3=47 Exploring Operation: 50-45=5, Resulting Numbers: [3, 5] Generated Node #0,1,2: 35:[3, 5] Operation: 50-45=5 Moving to Node #0,0,1 Current State: 35:[3, 5], Operations: ['87-45=42', '42-37=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,35 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,35 unequal: No Solution Moving to Node #0,1,2 Current State: 35:[3, 5], Operations: ['87-37=50', '50-45=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,35 unequal: No Solution Moving to Node #0,0,2 Current State: 35:[37, 39], Operations: ['87-45=42', '42-3=39'] Exploring Operation: 37+39=76, Resulting Numbers: [76] 76,35 unequal: No Solution Exploring Operation: 37*39=1443, Resulting Numbers: [1443] 1443,35 unequal: No Solution Exploring Operation: 39-37=2, Resulting Numbers: [2] 2,35 unequal: No Solution Moving to Node #0,2,2 Current State: 35:[29, 8], Operations: ['87/3=29', '45-37=8'] Exploring Operation: 29*8=232, Resulting Numbers: [232] 232,35 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,35 unequal: No Solution Exploring Operation: 29+8=37, Resulting Numbers: [37] 37,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[42, 34], Operations: ['87-45=42', '37-3=34'] Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 42+34=76, Resulting Numbers: [76] 76,35 unequal: No Solution Exploring Operation: 42*34=1428, Resulting Numbers: [1428] 1428,35 unequal: No Solution Moving to Node #0,2,1 Current State: 35:[37, 16], Operations: ['87/3=29', '45-29=16'] Exploring Operation: 37*16=592, Resulting Numbers: [592] 592,35 unequal: No Solution Exploring Operation: 37+16=53, Resulting Numbers: [53] 53,35 unequal: No Solution Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[45, 8], Operations: ['87/3=29', '37-29=8'] Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,35 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,35 unequal: No Solution Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[50, 42], Operations: ['87-37=50', '45-3=42'] Exploring Operation: 50*42=2100, Resulting Numbers: [2100] 2100,35 unequal: No Solution Exploring Operation: 50+42=92, Resulting Numbers: [92] 92,35 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[45, 47], Operations: ['87-37=50', '50-3=47'] Exploring Operation: 45*47=2115, Resulting Numbers: [2115] 2115,35 unequal: No Solution Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 45+47=92, Resulting Numbers: [92] 92,35 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 53, 44, 78, 7 ]
76
[ "53-44=9", "78+7=85", "85-9=76" ]
Current State: 76:[53, 44, 78, 7], Operations: [] Exploring Operation: 53-44=9, Resulting Numbers: [78, 7, 9] Generated Node #2: [78, 7, 9] from Operation: 53-44=9 Current State: 76:[78, 7, 9], Operations: ['53-44=9'] Exploring Operation: 78+7=85, Resulting Numbers: [9, 85] Generated Node #3: [9, 85] from Operation: 78+7=85 Current State: 76:[9, 85], Operations: ['53-44=9', '78+7=85'] Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[53, 44, 78, 7], Operations: [] Exploring Operation: 53-7=46, Resulting Numbers: [44, 78, 46] Generated Node #0,0: 76:[44, 78, 46] Operation: 53-7=46 Exploring Operation: 53-44=9, Resulting Numbers: [78, 7, 9] Generated Node #0,1: 76:[78, 7, 9] Operation: 53-44=9 Exploring Operation: 78-53=25, Resulting Numbers: [44, 7, 25] Generated Node #0,2: 76:[44, 7, 25] Operation: 78-53=25 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[78, 7, 9], Operations: ['53-44=9'] Exploring Operation: 9-7=2, Resulting Numbers: [78, 2] Generated Node #0,1,0: 76:[78, 2] Operation: 9-7=2 Exploring Operation: 78-7=71, Resulting Numbers: [9, 71] Generated Node #0,1,1: 76:[9, 71] Operation: 78-7=71 Exploring Operation: 7+9=16, Resulting Numbers: [78, 16] Generated Node #0,1,2: 76:[78, 16] Operation: 7+9=16 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 76:[78, 2], Operations: ['53-44=9', '9-7=2'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,76 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[53, 44, 78, 7], Operations: [] Exploring Operation: 53-44=9, Resulting Numbers: [78, 7, 9] Generated Node #0,1: 76:[78, 7, 9] Operation: 53-44=9 Moving to Node #0,1 Current State: 76:[78, 7, 9], Operations: ['53-44=9'] Exploring Operation: 9-7=2, Resulting Numbers: [78, 2] Generated Node #0,1,0: 76:[78, 2] Operation: 9-7=2 Moving to Node #0,1,0 Current State: 76:[78, 2], Operations: ['53-44=9', '9-7=2'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 84, 28, 26, 14 ]
36
[ "84/28=3", "26-14=12", "3*12=36" ]
Current State: 36:[84, 28, 26, 14], Operations: [] Exploring Operation: 84/28=3, Resulting Numbers: [26, 14, 3] Generated Node #2: [26, 14, 3] from Operation: 84/28=3 Current State: 36:[26, 14, 3], Operations: ['84/28=3'] Exploring Operation: 26-14=12, Resulting Numbers: [3, 12] Generated Node #3: [3, 12] from Operation: 26-14=12 Current State: 36:[3, 12], Operations: ['84/28=3', '26-14=12'] Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[84, 28, 26, 14], Operations: [] Exploring Operation: 84/28=3, Resulting Numbers: [26, 14, 3] Generated Node #0,0: 36:[26, 14, 3] Operation: 84/28=3 Exploring Operation: 84/14=6, Resulting Numbers: [28, 26, 6] Generated Node #0,1: 36:[28, 26, 6] Operation: 84/14=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[26, 14, 3], Operations: ['84/28=3'] Exploring Operation: 26+14=40, Resulting Numbers: [3, 40] Generated Node #0,0,0: 36:[3, 40] Operation: 26+14=40 Exploring Operation: 26-14=12, Resulting Numbers: [3, 12] Generated Node #0,0,1: 36:[3, 12] Operation: 26-14=12 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 36:[3, 12], Operations: ['84/28=3', '26-14=12'] Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[84, 28, 26, 14], Operations: [] Exploring Operation: 84/28=3, Resulting Numbers: [26, 14, 3] Generated Node #0,0: 36:[26, 14, 3] Operation: 84/28=3 Moving to Node #0,0 Current State: 36:[26, 14, 3], Operations: ['84/28=3'] Exploring Operation: 26-14=12, Resulting Numbers: [3, 12] Generated Node #0,0,1: 36:[3, 12] Operation: 26-14=12 Moving to Node #0,0,1 Current State: 36:[3, 12], Operations: ['84/28=3', '26-14=12'] Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 59, 77, 93, 45 ]
66
[ "77-59=18", "93-45=48", "18+48=66" ]
Current State: 66:[59, 77, 93, 45], Operations: [] Exploring Operation: 77-59=18, Resulting Numbers: [93, 45, 18] Generated Node #2: [93, 45, 18] from Operation: 77-59=18 Current State: 66:[93, 45, 18], Operations: ['77-59=18'] Exploring Operation: 93-45=48, Resulting Numbers: [18, 48] Generated Node #3: [18, 48] from Operation: 93-45=48 Current State: 66:[18, 48], Operations: ['77-59=18', '93-45=48'] Exploring Operation: 18+48=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[59, 77, 93, 45], Operations: [] Exploring Operation: 93-45=48, Resulting Numbers: [59, 77, 48] Generated Node #0,0: 66:[59, 77, 48] Operation: 93-45=48 Exploring Operation: 93-77=16, Resulting Numbers: [59, 45, 16] Generated Node #0,1: 66:[59, 45, 16] Operation: 93-77=16 Exploring Operation: 93-59=34, Resulting Numbers: [77, 45, 34] Generated Node #0,2: 66:[77, 45, 34] Operation: 93-59=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[59, 45, 16], Operations: ['93-77=16'] Exploring Operation: 45-16=29, Resulting Numbers: [59, 29] Generated Node #0,1,0: 66:[59, 29] Operation: 45-16=29 Exploring Operation: 45+16=61, Resulting Numbers: [59, 61] Generated Node #0,1,1: 66:[59, 61] Operation: 45+16=61 Exploring Operation: 59-45=14, Resulting Numbers: [16, 14] Generated Node #0,1,2: 66:[16, 14] Operation: 59-45=14 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 66:[16, 14], Operations: ['93-77=16', '59-45=14'] Exploring Operation: 16*14=224, Resulting Numbers: [224] 224,66 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,66 unequal: No Solution Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,66 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:[59, 29], Operations: ['93-77=16', '45-16=29'] Exploring Operation: 59+29=88, Resulting Numbers: [88] 88,66 unequal: No Solution Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 59*29=1711, Resulting Numbers: [1711] 1711,66 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 #0,1,1 Current State: 66:[59, 61], Operations: ['93-77=16', '45+16=61'] Exploring Operation: 61-59=2, Resulting Numbers: [2] 2,66 unequal: No Solution Exploring Operation: 59+61=120, Resulting Numbers: [120] 120,66 unequal: No Solution Exploring Operation: 59*61=3599, Resulting Numbers: [3599] 3599,66 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 #0,2 Current State: 66:[77, 45, 34], Operations: ['93-59=34'] Exploring Operation: 77-34=43, Resulting Numbers: [45, 43] Generated Node #0,2,0: 66:[45, 43] Operation: 77-34=43 Exploring Operation: 45-34=11, Resulting Numbers: [77, 11] Generated Node #0,2,1: 66:[77, 11] Operation: 45-34=11 Exploring Operation: 77-45=32, Resulting Numbers: [34, 32] Generated Node #0,2,2: 66:[34, 32] Operation: 77-45=32 Moving to Node #0,2,2 Current State: 66:[34, 32], Operations: ['93-59=34', '77-45=32'] Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,66 unequal: No Solution Exploring Operation: 34+32=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[59, 77, 93, 45], Operations: [] Exploring Operation: 93-59=34, Resulting Numbers: [77, 45, 34] Generated Node #0,2: 66:[77, 45, 34] Operation: 93-59=34 Moving to Node #0,2 Current State: 66:[77, 45, 34], Operations: ['93-59=34'] Exploring Operation: 77-45=32, Resulting Numbers: [34, 32] Generated Node #0,2,2: 66:[34, 32] Operation: 77-45=32 Moving to Node #0,2,2 Current State: 66:[34, 32], Operations: ['93-59=34', '77-45=32'] Exploring Operation: 34+32=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 47, 15, 27, 75 ]
100
[ "47-27=20", "75/15=5", "20*5=100" ]
Current State: 100:[47, 15, 27, 75], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [15, 75, 20] Generated Node #2: [15, 75, 20] from Operation: 47-27=20 Current State: 100:[15, 75, 20], Operations: ['47-27=20'] Exploring Operation: 75/15=5, Resulting Numbers: [20, 5] Generated Node #3: [20, 5] from Operation: 75/15=5 Current State: 100:[20, 5], Operations: ['47-27=20', '75/15=5'] Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[47, 15, 27, 75], Operations: [] Exploring Operation: 75/15=5, Resulting Numbers: [47, 27, 5] Generated Node #0,0: 100:[47, 27, 5] Operation: 75/15=5 Exploring Operation: 75-47=28, Resulting Numbers: [15, 27, 28] Generated Node #0,1: 100:[15, 27, 28] Operation: 75-47=28 Exploring Operation: 27+75=102, Resulting Numbers: [47, 15, 102] Generated Node #0,2: 100:[47, 15, 102] Operation: 27+75=102 Moving to Node #0,0 Current State: 100:[47, 27, 5], Operations: ['75/15=5'] Exploring Operation: 27-5=22, Resulting Numbers: [47, 22] Generated Node #0,0,0: 100:[47, 22] Operation: 27-5=22 Exploring Operation: 47-27=20, Resulting Numbers: [5, 20] Generated Node #0,0,1: 100:[5, 20] Operation: 47-27=20 Exploring Operation: 47+5=52, Resulting Numbers: [27, 52] Generated Node #0,0,2: 100:[27, 52] Operation: 47+5=52 Moving to Node #0,1 Current State: 100:[15, 27, 28], Operations: ['75-47=28'] Exploring Operation: 28-27=1, Resulting Numbers: [15, 1] Generated Node #0,1,0: 100:[15, 1] Operation: 28-27=1 Exploring Operation: 28-15=13, Resulting Numbers: [27, 13] Generated Node #0,1,1: 100:[27, 13] Operation: 28-15=13 Exploring Operation: 27-15=12, Resulting Numbers: [28, 12] Generated Node #0,1,2: 100:[28, 12] Operation: 27-15=12 Moving to Node #0,2 Current State: 100:[47, 15, 102], Operations: ['27+75=102'] Exploring Operation: 102-47=55, Resulting Numbers: [15, 55] Generated Node #0,2,0: 100:[15, 55] Operation: 102-47=55 Exploring Operation: 47-15=32, Resulting Numbers: [102, 32] Generated Node #0,2,1: 100:[102, 32] Operation: 47-15=32 Exploring Operation: 47+15=62, Resulting Numbers: [102, 62] Generated Node #0,2,2: 100:[102, 62] Operation: 47+15=62 Moving to Node #0,0,1 Current State: 100:[5, 20], Operations: ['75/15=5', '47-27=20'] Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[47, 15, 27, 75], Operations: [] Exploring Operation: 75/15=5, Resulting Numbers: [47, 27, 5] Generated Node #0,0: 100:[47, 27, 5] Operation: 75/15=5 Moving to Node #0,0 Current State: 100:[47, 27, 5], Operations: ['75/15=5'] Exploring Operation: 47-27=20, Resulting Numbers: [5, 20] Generated Node #0,0,1: 100:[5, 20] Operation: 47-27=20 Moving to Node #0,0,1 Current State: 100:[5, 20], Operations: ['75/15=5', '47-27=20'] Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.983507
hs_3
mult_heuristic
[ 11, 5, 90, 55 ]
13
[ "11*90=990", "990/55=18", "18-5=13" ]
Current State: 13:[11, 5, 90, 55], Operations: [] Exploring Operation: 11*90=990, Resulting Numbers: [5, 55, 990] Generated Node #2: [5, 55, 990] from Operation: 11*90=990 Current State: 13:[5, 55, 990], Operations: ['11*90=990'] Exploring Operation: 990/55=18, Resulting Numbers: [5, 18] Generated Node #3: [5, 18] from Operation: 990/55=18 Current State: 13:[5, 18], Operations: ['11*90=990', '990/55=18'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[11, 5, 90, 55], Operations: [] Exploring Operation: 90-55=35, Resulting Numbers: [11, 5, 35] Generated Node #0,0: 13:[11, 5, 35] Operation: 90-55=35 Exploring Operation: 55/5=11, Resulting Numbers: [11, 90, 11] Generated Node #0,1: 13:[11, 90, 11] Operation: 55/5=11 Exploring Operation: 90/5=18, Resulting Numbers: [11, 55, 18] Generated Node #0,2: 13:[11, 55, 18] Operation: 90/5=18 Moving to Node #0,0 Current State: 13:[11, 5, 35], Operations: ['90-55=35'] Exploring Operation: 35-5=30, Resulting Numbers: [11, 30] Generated Node #0,0,0: 13:[11, 30] Operation: 35-5=30 Exploring Operation: 35-11=24, Resulting Numbers: [5, 24] Generated Node #0,0,1: 13:[5, 24] Operation: 35-11=24 Exploring Operation: 35/5=7, Resulting Numbers: [11, 7] Generated Node #0,0,2: 13:[11, 7] Operation: 35/5=7 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 13:[11, 7], Operations: ['90-55=35', '35/5=7'] Exploring Operation: 11+7=18, Resulting Numbers: [18] 18,13 unequal: No Solution Exploring Operation: 11*7=77, Resulting Numbers: [77] 77,13 unequal: No Solution Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 13:[11, 30], Operations: ['90-55=35', '35-5=30'] Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,13 unequal: No Solution Exploring Operation: 11*30=330, Resulting Numbers: [330] 330,13 unequal: No Solution Exploring Operation: 11+30=41, Resulting Numbers: [41] 41,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 13:[5, 24], Operations: ['90-55=35', '35-11=24'] Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,13 unequal: No Solution Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,13 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,13 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: 13:[11, 55, 18], Operations: ['90/5=18'] Exploring Operation: 55/11=5, Resulting Numbers: [18, 5] Generated Node #0,2,0: 13:[18, 5] Operation: 55/11=5 Exploring Operation: 55-18=37, Resulting Numbers: [11, 37] Generated Node #0,2,1: 13:[11, 37] Operation: 55-18=37 Exploring Operation: 55-11=44, Resulting Numbers: [18, 44] Generated Node #0,2,2: 13:[18, 44] Operation: 55-11=44 Moving to Node #0,1 Current State: 13:[11, 90, 11], Operations: ['55/5=11'] Exploring Operation: 11+11=22, Resulting Numbers: [90, 22] Generated Node #0,1,0: 13:[90, 22] Operation: 11+11=22 Exploring Operation: 90-11=79, Resulting Numbers: [11, 79] Generated Node #0,1,1: 13:[11, 79] Operation: 90-11=79 Exploring Operation: 90-11=79, Resulting Numbers: [11, 79] Generated Node #0,1,2: 13:[11, 79] Operation: 90-11=79 Moving to Node #0,2,0 Current State: 13:[18, 5], Operations: ['90/5=18', '55/11=5'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[11, 5, 90, 55], Operations: [] Exploring Operation: 90/5=18, Resulting Numbers: [11, 55, 18] Generated Node #0,2: 13:[11, 55, 18] Operation: 90/5=18 Moving to Node #0,2 Current State: 13:[11, 55, 18], Operations: ['90/5=18'] Exploring Operation: 55/11=5, Resulting Numbers: [18, 5] Generated Node #0,2,0: 13:[18, 5] Operation: 55/11=5 Moving to Node #0,2,0 Current State: 13:[18, 5], Operations: ['90/5=18', '55/11=5'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
0.977431
hs_3
sum_heuristic
[ 50, 16, 52, 11 ]
42
[ "16-11=5", "50/5=10", "52-10=42" ]
Current State: 42:[50, 16, 52, 11], Operations: [] Exploring Operation: 16-11=5, Resulting Numbers: [50, 52, 5] Generated Node #2: [50, 52, 5] from Operation: 16-11=5 Current State: 42:[50, 52, 5], Operations: ['16-11=5'] Exploring Operation: 50/5=10, Resulting Numbers: [52, 10] Generated Node #3: [52, 10] from Operation: 50/5=10 Current State: 42:[52, 10], Operations: ['16-11=5', '50/5=10'] Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[50, 16, 52, 11], Operations: [] Exploring Operation: 52-50=2, Resulting Numbers: [16, 11, 2] Generated Node #0,0: 42:[16, 11, 2] Operation: 52-50=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[16, 11, 2], Operations: ['52-50=2'] Exploring Operation: 16-11=5, Resulting Numbers: [2, 5] Generated Node #0,0,0: 42:[2, 5] Operation: 16-11=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[2, 5], Operations: ['52-50=2', '16-11=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 40, 9, 35, 8 ]
39
[ "40/8=5", "9+35=44", "44-5=39" ]
Current State: 39:[40, 9, 35, 8], Operations: [] Exploring Operation: 40/8=5, Resulting Numbers: [9, 35, 5] Generated Node #2: [9, 35, 5] from Operation: 40/8=5 Current State: 39:[9, 35, 5], Operations: ['40/8=5'] Exploring Operation: 9+35=44, Resulting Numbers: [5, 44] Generated Node #3: [5, 44] from Operation: 9+35=44 Current State: 39:[5, 44], Operations: ['40/8=5', '9+35=44'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[40, 9, 35, 8], Operations: [] Exploring Operation: 9+8=17, Resulting Numbers: [40, 35, 17] Generated Node #0,0: 39:[40, 35, 17] Operation: 9+8=17 Exploring Operation: 35+8=43, Resulting Numbers: [40, 9, 43] Generated Node #0,1: 39:[40, 9, 43] Operation: 35+8=43 Exploring Operation: 9-8=1, Resulting Numbers: [40, 35, 1] Generated Node #0,2: 39:[40, 35, 1] Operation: 9-8=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[40, 35, 1], Operations: ['9-8=1'] Exploring Operation: 40-35=5, Resulting Numbers: [1, 5] Generated Node #0,2,0: 39:[1, 5] Operation: 40-35=5 Exploring Operation: 35+1=36, Resulting Numbers: [40, 36] Generated Node #0,2,1: 39:[40, 36] Operation: 35+1=36 Exploring Operation: 40-1=39, Resulting Numbers: [35, 39] Generated Node #0,2,2: 39:[35, 39] Operation: 40-1=39 Moving to Node #0,2,0 Current State: 39:[1, 5], Operations: ['9-8=1', '40-35=5'] Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,39 unequal: No Solution Moving to Node #0,2,1 Current State: 39:[40, 36], Operations: ['9-8=1', '35+1=36'] Exploring Operation: 40*36=1440, Resulting Numbers: [1440] 1440,39 unequal: No Solution Exploring Operation: 40+36=76, Resulting Numbers: [76] 76,39 unequal: No Solution Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,39 unequal: No Solution Moving to Node #0,2,2 Current State: 39:[35, 39], Operations: ['9-8=1', '40-1=39'] Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 35+39=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 35*39=1365, Resulting Numbers: [1365] 1365,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[40, 35, 17], Operations: ['9+8=17'] Exploring Operation: 40-35=5, Resulting Numbers: [17, 5] Generated Node #0,0,0: 39:[17, 5] Operation: 40-35=5 Exploring Operation: 40-17=23, Resulting Numbers: [35, 23] Generated Node #0,0,1: 39:[35, 23] Operation: 40-17=23 Exploring Operation: 35-17=18, Resulting Numbers: [40, 18] Generated Node #0,0,2: 39:[40, 18] Operation: 35-17=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[17, 5], Operations: ['9+8=17', '40-35=5'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 17*5=85, Resulting Numbers: [85] 85,39 unequal: No Solution Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 39:[40, 18], Operations: ['9+8=17', '35-17=18'] Exploring Operation: 40*18=720, Resulting Numbers: [720] 720,39 unequal: No Solution Exploring Operation: 40-18=22, Resulting Numbers: [22] 22,39 unequal: No Solution Exploring Operation: 40+18=58, Resulting Numbers: [58] 58,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 39:[35, 23], Operations: ['9+8=17', '40-17=23'] Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 35*23=805, Resulting Numbers: [805] 805,39 unequal: No Solution Exploring Operation: 35+23=58, Resulting Numbers: [58] 58,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[40, 9, 43], Operations: ['35+8=43'] Exploring Operation: 43-40=3, Resulting Numbers: [9, 3] Generated Node #0,1,0: 39:[9, 3] Operation: 43-40=3 Exploring Operation: 43-9=34, Resulting Numbers: [40, 34] Generated Node #0,1,1: 39:[40, 34] Operation: 43-9=34 Exploring Operation: 40-9=31, Resulting Numbers: [43, 31] Generated Node #0,1,2: 39:[43, 31] Operation: 40-9=31 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 39:[9, 3], Operations: ['35+8=43', '43-40=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 39:[40, 34], Operations: ['35+8=43', '43-9=34'] Exploring Operation: 40*34=1360, Resulting Numbers: [1360] 1360,39 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 39:[43, 31], Operations: ['35+8=43', '40-9=31'] Exploring Operation: 43*31=1333, Resulting Numbers: [1333] 1333,39 unequal: No Solution Exploring Operation: 43+31=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 43-31=12, Resulting Numbers: [12] 12,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 58, 90, 2, 2 ]
76
[ "58+90=148", "148/2=74", "2+74=76" ]
Current State: 76:[58, 90, 2, 2], Operations: [] Exploring Operation: 58+90=148, Resulting Numbers: [2, 2, 148] Generated Node #2: [2, 2, 148] from Operation: 58+90=148 Current State: 76:[2, 2, 148], Operations: ['58+90=148'] Exploring Operation: 148/2=74, Resulting Numbers: [74] 74,76 equal: Goal Reached Exploring Operation: 2+74=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[58, 90, 2, 2], Operations: [] Exploring Operation: 58/2=29, Resulting Numbers: [90, 2, 29] Generated Node #0,0: 76:[90, 2, 29] Operation: 58/2=29 Exploring Operation: 90-58=32, Resulting Numbers: [2, 2, 32] Generated Node #0,1: 76:[2, 2, 32] Operation: 90-58=32 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[2, 2, 32], Operations: ['90-58=32'] Exploring Operation: 32/2=16, Resulting Numbers: [2, 16] Generated Node #0,1,0: 76:[2, 16] Operation: 32/2=16 Exploring Operation: 32/2=16, Resulting Numbers: [2, 16] Generated Node #0,1,1: 76:[2, 16] Operation: 32/2=16 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 76:[2, 16], Operations: ['90-58=32', '32/2=16'] Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,76 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 #0,1,1 Current State: 76:[2, 16], Operations: ['90-58=32', '32/2=16'] Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[90, 2, 29], Operations: ['58/2=29'] Exploring Operation: 90-29=61, Resulting Numbers: [2, 61] Generated Node #0,0,0: 76:[2, 61] Operation: 90-29=61 Exploring Operation: 90/2=45, Resulting Numbers: [29, 45] Generated Node #0,0,1: 76:[29, 45] Operation: 90/2=45 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 76:[2, 61], Operations: ['58/2=29', '90-29=61'] Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,76 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,76 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 #0,0,1 Current State: 76:[29, 45], Operations: ['58/2=29', '90/2=45'] Exploring Operation: 45-29=16, Resulting Numbers: [16] 16,76 unequal: No Solution Exploring Operation: 29+45=74, Resulting Numbers: [74] 74,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 13, 44, 2, 14 ]
43
[ "44-13=31", "14-2=12", "31+12=43" ]
Current State: 43:[13, 44, 2, 14], Operations: [] Exploring Operation: 44-13=31, Resulting Numbers: [2, 14, 31] Generated Node #2: [2, 14, 31] from Operation: 44-13=31 Current State: 43:[2, 14, 31], Operations: ['44-13=31'] Exploring Operation: 14-2=12, Resulting Numbers: [31, 12] Generated Node #3: [31, 12] from Operation: 14-2=12 Current State: 43:[31, 12], Operations: ['44-13=31', '14-2=12'] Exploring Operation: 31+12=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[13, 44, 2, 14], Operations: [] Exploring Operation: 2*14=28, Resulting Numbers: [13, 44, 28] Generated Node #0,0: 43:[13, 44, 28] Operation: 2*14=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[13, 44, 28], Operations: ['2*14=28'] Exploring Operation: 13+28=41, Resulting Numbers: [44, 41] Generated Node #0,0,0: 43:[44, 41] Operation: 13+28=41 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[44, 41], Operations: ['2*14=28', '13+28=41'] Exploring Operation: 44-41=3, Resulting Numbers: [3] 3,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 23, 56, 65, 8 ]
22
[ "23+56=79", "65-8=57", "79-57=22" ]
Current State: 22:[23, 56, 65, 8], Operations: [] Exploring Operation: 23+56=79, Resulting Numbers: [65, 8, 79] Generated Node #2: [65, 8, 79] from Operation: 23+56=79 Current State: 22:[65, 8, 79], Operations: ['23+56=79'] Exploring Operation: 65-8=57, Resulting Numbers: [79, 57] Generated Node #3: [79, 57] from Operation: 65-8=57 Current State: 22:[79, 57], Operations: ['23+56=79', '65-8=57'] Exploring Operation: 79-57=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[23, 56, 65, 8], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [23, 65, 7] Generated Node #0,0: 22:[23, 65, 7] Operation: 56/8=7 Exploring Operation: 65-56=9, Resulting Numbers: [23, 8, 9] Generated Node #0,1: 22:[23, 8, 9] Operation: 65-56=9 Moving to Node #0,1 Current State: 22:[23, 8, 9], Operations: ['65-56=9'] Exploring Operation: 23-8=15, Resulting Numbers: [9, 15] Generated Node #0,1,0: 22:[9, 15] Operation: 23-8=15 Exploring Operation: 9-8=1, Resulting Numbers: [23, 1] Generated Node #0,1,1: 22:[23, 1] Operation: 9-8=1 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[23, 1], Operations: ['65-56=9', '9-8=1'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[23, 56, 65, 8], Operations: [] Exploring Operation: 65-56=9, Resulting Numbers: [23, 8, 9] Generated Node #0,1: 22:[23, 8, 9] Operation: 65-56=9 Moving to Node #0,1 Current State: 22:[23, 8, 9], Operations: ['65-56=9'] Exploring Operation: 9-8=1, Resulting Numbers: [23, 1] Generated Node #0,1,1: 22:[23, 1] Operation: 9-8=1 Moving to Node #0,1,1 Current State: 22:[23, 1], Operations: ['65-56=9', '9-8=1'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 69, 63, 65, 71 ]
22
[ "69+63=132", "71-65=6", "132/6=22" ]
Current State: 22:[69, 63, 65, 71], Operations: [] Exploring Operation: 69+63=132, Resulting Numbers: [65, 71, 132] Generated Node #2: [65, 71, 132] from Operation: 69+63=132 Current State: 22:[65, 71, 132], Operations: ['69+63=132'] Exploring Operation: 71-65=6, Resulting Numbers: [132, 6] Generated Node #3: [132, 6] from Operation: 71-65=6 Current State: 22:[132, 6], Operations: ['69+63=132', '71-65=6'] Exploring Operation: 132/6=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[69, 63, 65, 71], Operations: [] Exploring Operation: 71-69=2, Resulting Numbers: [63, 65, 2] Generated Node #0,0: 22:[63, 65, 2] Operation: 71-69=2 Exploring Operation: 71-65=6, Resulting Numbers: [69, 63, 6] Generated Node #0,1: 22:[69, 63, 6] Operation: 71-65=6 Exploring Operation: 69-65=4, Resulting Numbers: [63, 71, 4] Generated Node #0,2: 22:[63, 71, 4] Operation: 69-65=4 Moving to Node #0,0 Current State: 22:[63, 65, 2], Operations: ['71-69=2'] Exploring Operation: 63-2=61, Resulting Numbers: [65, 61] Generated Node #0,0,0: 22:[65, 61] Operation: 63-2=61 Exploring Operation: 65-2=63, Resulting Numbers: [63, 63] Generated Node #0,0,1: 22:[63, 63] Operation: 65-2=63 Exploring Operation: 65-63=2, Resulting Numbers: [2, 2] Generated Node #0,0,2: 22:[2, 2] Operation: 65-63=2 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 22:[2, 2], Operations: ['71-69=2', '65-63=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,22 unequal: No Solution No 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: 22:[65, 61], Operations: ['71-69=2', '63-2=61'] Exploring Operation: 65-61=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 65+61=126, Resulting Numbers: [126] 126,22 unequal: No Solution Exploring Operation: 65*61=3965, Resulting Numbers: [3965] 3965,22 unequal: No Solution No 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: 22:[63, 63], Operations: ['71-69=2', '65-2=63'] Exploring Operation: 63/63=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 63+63=126, Resulting Numbers: [126] 126,22 unequal: No Solution Exploring Operation: 63-63=0, Resulting Numbers: [0] 0,22 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: 22:[69, 63, 6], Operations: ['71-65=6'] Exploring Operation: 69-6=63, Resulting Numbers: [63, 63] Generated Node #0,1,0: 22:[63, 63] Operation: 69-6=63 Exploring Operation: 69-63=6, Resulting Numbers: [6, 6] Generated Node #0,1,1: 22:[6, 6] Operation: 69-63=6 Exploring Operation: 63-6=57, Resulting Numbers: [69, 57] Generated Node #0,1,2: 22:[69, 57] Operation: 63-6=57 Moving to Node #0,2 Current State: 22:[63, 71, 4], Operations: ['69-65=4'] Exploring Operation: 71-63=8, Resulting Numbers: [4, 8] Generated Node #0,2,0: 22:[4, 8] Operation: 71-63=8 Exploring Operation: 63-4=59, Resulting Numbers: [71, 59] Generated Node #0,2,1: 22:[71, 59] Operation: 63-4=59 Exploring Operation: 71-4=67, Resulting Numbers: [63, 67] Generated Node #0,2,2: 22:[63, 67] Operation: 71-4=67 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 22:[4, 8], Operations: ['69-65=4', '71-63=8'] Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,22 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,22 unequal: No Solution No 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: 22:[71, 59], Operations: ['69-65=4', '63-4=59'] Exploring Operation: 71*59=4189, Resulting Numbers: [4189] 4189,22 unequal: No Solution Exploring Operation: 71+59=130, Resulting Numbers: [130] 130,22 unequal: No Solution Exploring Operation: 71-59=12, Resulting Numbers: [12] 12,22 unequal: No Solution No 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: 22:[63, 67], Operations: ['69-65=4', '71-4=67'] Exploring Operation: 63+67=130, Resulting Numbers: [130] 130,22 unequal: No Solution Exploring Operation: 63*67=4221, Resulting Numbers: [4221] 4221,22 unequal: No Solution Exploring Operation: 67-63=4, Resulting Numbers: [4] 4,22 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: 22:[6, 6], Operations: ['71-65=6', '69-63=6'] Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,22 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,22 unequal: No Solution Moving to Node #0,1,0 Current State: 22:[63, 63], Operations: ['71-65=6', '69-6=63'] Exploring Operation: 63/63=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 63-63=0, Resulting Numbers: [0] 0,22 unequal: No Solution Exploring Operation: 63+63=126, Resulting Numbers: [126] 126,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[69, 57], Operations: ['71-65=6', '63-6=57'] Exploring Operation: 69*57=3933, Resulting Numbers: [3933] 3933,22 unequal: No Solution Exploring Operation: 69-57=12, Resulting Numbers: [12] 12,22 unequal: No Solution Exploring Operation: 69+57=126, Resulting Numbers: [126] 126,22 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 54, 20, 63, 86 ]
94
[ "63-54=9", "20*9=180", "180-86=94" ]
Current State: 94:[54, 20, 63, 86], Operations: [] Exploring Operation: 63-54=9, Resulting Numbers: [20, 86, 9] Generated Node #2: [20, 86, 9] from Operation: 63-54=9 Current State: 94:[20, 86, 9], Operations: ['63-54=9'] Exploring Operation: 20*9=180, Resulting Numbers: [86, 180] Generated Node #3: [86, 180] from Operation: 20*9=180 Current State: 94:[86, 180], Operations: ['63-54=9', '20*9=180'] Exploring Operation: 180-86=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[54, 20, 63, 86], Operations: [] Exploring Operation: 63-54=9, Resulting Numbers: [20, 86, 9] Generated Node #0,0: 94:[20, 86, 9] Operation: 63-54=9 Exploring Operation: 20+86=106, Resulting Numbers: [54, 63, 106] Generated Node #0,1: 94:[54, 63, 106] Operation: 20+86=106 Exploring Operation: 54-20=34, Resulting Numbers: [63, 86, 34] Generated Node #0,2: 94:[63, 86, 34] Operation: 54-20=34 Exploring Operation: 20+63=83, Resulting Numbers: [54, 86, 83] Generated Node #0,3: 94:[54, 86, 83] Operation: 20+63=83 Exploring Operation: 63-20=43, Resulting Numbers: [54, 86, 43] Generated Node #0,4: 94:[54, 86, 43] Operation: 63-20=43 Moving to Node #0,4 Current State: 94:[54, 86, 43], Operations: ['63-20=43'] Exploring Operation: 86/43=2, Resulting Numbers: [54, 2] Generated Node #0,4,0: 94:[54, 2] Operation: 86/43=2 Exploring Operation: 86-43=43, Resulting Numbers: [54, 43] Generated Node #0,4,1: 94:[54, 43] Operation: 86-43=43 Exploring Operation: 54-43=11, Resulting Numbers: [86, 11] Generated Node #0,4,2: 94:[86, 11] Operation: 54-43=11 Exploring Operation: 86-54=32, Resulting Numbers: [43, 32] Generated Node #0,4,3: 94:[43, 32] Operation: 86-54=32 Exploring Operation: 54+43=97, Resulting Numbers: [86, 97] Generated Node #0,4,4: 94:[86, 97] Operation: 54+43=97 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 94:[54, 2], Operations: ['63-20=43', '86/43=2'] Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,94 unequal: No Solution Exploring Operation: 54*2=108, Resulting Numbers: [108] 108,94 unequal: No Solution Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,94 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:[54, 43], Operations: ['63-20=43', '86-43=43'] Exploring Operation: 54+43=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,94 unequal: No Solution Exploring Operation: 54*43=2322, Resulting Numbers: [2322] 2322,94 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 #0,4,4 Current State: 94:[86, 97], Operations: ['63-20=43', '54+43=97'] Exploring Operation: 86*97=8342, Resulting Numbers: [8342] 8342,94 unequal: No Solution Exploring Operation: 86+97=183, Resulting Numbers: [183] 183,94 unequal: No Solution Exploring Operation: 97-86=11, Resulting Numbers: [11] 11,94 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:[86, 11], Operations: ['63-20=43', '54-43=11'] Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,94 unequal: No Solution Exploring Operation: 86*11=946, Resulting Numbers: [946] 946,94 unequal: No Solution Exploring Operation: 86+11=97, Resulting Numbers: [97] 97,94 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:[43, 32], Operations: ['63-20=43', '86-54=32'] Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,94 unequal: No Solution Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,94 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,94 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: 94:[54, 86, 83], Operations: ['20+63=83'] Exploring Operation: 54+86=140, Resulting Numbers: [83, 140] Generated Node #0,3,0: 94:[83, 140] Operation: 54+86=140 Exploring Operation: 86-83=3, Resulting Numbers: [54, 3] Generated Node #0,3,1: 94:[54, 3] Operation: 86-83=3 Exploring Operation: 83-54=29, Resulting Numbers: [86, 29] Generated Node #0,3,2: 94:[86, 29] Operation: 83-54=29 Exploring Operation: 54+83=137, Resulting Numbers: [86, 137] Generated Node #0,3,3: 94:[86, 137] Operation: 54+83=137 Exploring Operation: 86-54=32, Resulting Numbers: [83, 32] Generated Node #0,3,4: 94:[83, 32] Operation: 86-54=32 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 94:[54, 3], Operations: ['20+63=83', '86-83=3'] Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,94 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 54*3=162, Resulting Numbers: [162] 162,94 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 #0,3,2 Current State: 94:[86, 29], Operations: ['20+63=83', '83-54=29'] Exploring Operation: 86+29=115, Resulting Numbers: [115] 115,94 unequal: No Solution Exploring Operation: 86*29=2494, Resulting Numbers: [2494] 2494,94 unequal: No Solution Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,94 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 #0,3,4 Current State: 94:[83, 32], Operations: ['20+63=83', '86-54=32'] Exploring Operation: 83-32=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 83+32=115, Resulting Numbers: [115] 115,94 unequal: No Solution Exploring Operation: 83*32=2656, Resulting Numbers: [2656] 2656,94 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 #0,3,3 Current State: 94:[86, 137], Operations: ['20+63=83', '54+83=137'] Exploring Operation: 86+137=223, Resulting Numbers: [223] 223,94 unequal: No Solution Exploring Operation: 86*137=11782, Resulting Numbers: [11782] 11782,94 unequal: No Solution Exploring Operation: 137-86=51, Resulting Numbers: [51] 51,94 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 #0,3,0 Current State: 94:[83, 140], Operations: ['20+63=83', '54+86=140'] Exploring Operation: 140-83=57, Resulting Numbers: [57] 57,94 unequal: No Solution Exploring Operation: 83+140=223, Resulting Numbers: [223] 223,94 unequal: No Solution Exploring Operation: 83*140=11620, Resulting Numbers: [11620] 11620,94 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:[20, 86, 9], Operations: ['63-54=9'] Exploring Operation: 86-20=66, Resulting Numbers: [9, 66] Generated Node #0,0,0: 94:[9, 66] Operation: 86-20=66 Exploring Operation: 20+9=29, Resulting Numbers: [86, 29] Generated Node #0,0,1: 94:[86, 29] Operation: 20+9=29 Exploring Operation: 86+9=95, Resulting Numbers: [20, 95] Generated Node #0,0,2: 94:[20, 95] Operation: 86+9=95 Exploring Operation: 20-9=11, Resulting Numbers: [86, 11] Generated Node #0,0,3: 94:[86, 11] Operation: 20-9=11 Exploring Operation: 20+86=106, Resulting Numbers: [9, 106] Generated Node #0,0,4: 94:[9, 106] Operation: 20+86=106 Moving to Node #0,1 Current State: 94:[54, 63, 106], Operations: ['20+86=106'] Exploring Operation: 106-54=52, Resulting Numbers: [63, 52] Generated Node #0,1,0: 94:[63, 52] Operation: 106-54=52 Exploring Operation: 63-54=9, Resulting Numbers: [106, 9] Generated Node #0,1,1: 94:[106, 9] Operation: 63-54=9 Exploring Operation: 54+106=160, Resulting Numbers: [63, 160] Generated Node #0,1,2: 94:[63, 160] Operation: 54+106=160 Exploring Operation: 54+63=117, Resulting Numbers: [106, 117] Generated Node #0,1,3: 94:[106, 117] Operation: 54+63=117 Exploring Operation: 106-63=43, Resulting Numbers: [54, 43] Generated Node #0,1,4: 94:[54, 43] Operation: 106-63=43 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 94:[54, 43], Operations: ['20+86=106', '106-63=43'] Exploring Operation: 54*43=2322, Resulting Numbers: [2322] 2322,94 unequal: No Solution Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,94 unequal: No Solution Exploring Operation: 54+43=97, Resulting Numbers: [97] 97,94 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 #0,1,1 Current State: 94:[106, 9], Operations: ['20+86=106', '63-54=9'] Exploring Operation: 106*9=954, Resulting Numbers: [954] 954,94 unequal: No Solution Exploring Operation: 106+9=115, Resulting Numbers: [115] 115,94 unequal: No Solution Exploring Operation: 106-9=97, Resulting Numbers: [97] 97,94 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 #0,1,0 Current State: 94:[63, 52], Operations: ['20+86=106', '106-54=52'] Exploring Operation: 63+52=115, Resulting Numbers: [115] 115,94 unequal: No Solution Exploring Operation: 63-52=11, Resulting Numbers: [11] 11,94 unequal: No Solution Exploring Operation: 63*52=3276, Resulting Numbers: [3276] 3276,94 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 #0,1,3 Current State: 94:[106, 117], Operations: ['20+86=106', '54+63=117'] Exploring Operation: 106+117=223, Resulting Numbers: [223] 223,94 unequal: No Solution Exploring Operation: 106*117=12402, Resulting Numbers: [12402] 12402,94 unequal: No Solution Exploring Operation: 117-106=11, Resulting Numbers: [11] 11,94 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 #0,1,2 Current State: 94:[63, 160], Operations: ['20+86=106', '54+106=160'] Exploring Operation: 160-63=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 63+160=223, Resulting Numbers: [223] 223,94 unequal: No Solution Exploring Operation: 63*160=10080, Resulting Numbers: [10080] 10080,94 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: 94:[63, 86, 34], Operations: ['54-20=34'] Exploring Operation: 63+34=97, Resulting Numbers: [86, 97] Generated Node #0,2,0: 94:[86, 97] Operation: 63+34=97 Exploring Operation: 86-34=52, Resulting Numbers: [63, 52] Generated Node #0,2,1: 94:[63, 52] Operation: 86-34=52 Exploring Operation: 86-63=23, Resulting Numbers: [34, 23] Generated Node #0,2,2: 94:[34, 23] Operation: 86-63=23 Exploring Operation: 86+34=120, Resulting Numbers: [63, 120] Generated Node #0,2,3: 94:[63, 120] Operation: 86+34=120 Exploring Operation: 63-34=29, Resulting Numbers: [86, 29] Generated Node #0,2,4: 94:[86, 29] Operation: 63-34=29 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 94:[86, 97], Operations: ['54-20=34', '63+34=97'] Exploring Operation: 86*97=8342, Resulting Numbers: [8342] 8342,94 unequal: No Solution Exploring Operation: 97-86=11, Resulting Numbers: [11] 11,94 unequal: No Solution Exploring Operation: 86+97=183, Resulting Numbers: [183] 183,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 94:[63, 52], Operations: ['54-20=34', '86-34=52'] Exploring Operation: 63*52=3276, Resulting Numbers: [3276] 3276,94 unequal: No Solution Exploring Operation: 63+52=115, Resulting Numbers: [115] 115,94 unequal: No Solution Exploring Operation: 63-52=11, Resulting Numbers: [11] 11,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 94:[86, 29], Operations: ['54-20=34', '63-34=29'] Exploring Operation: 86+29=115, Resulting Numbers: [115] 115,94 unequal: No Solution Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,94 unequal: No Solution Exploring Operation: 86*29=2494, Resulting Numbers: [2494] 2494,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 94:[34, 23], Operations: ['54-20=34', '86-63=23'] Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,94 unequal: No Solution Exploring Operation: 34+23=57, Resulting Numbers: [57] 57,94 unequal: No Solution Exploring Operation: 34*23=782, Resulting Numbers: [782] 782,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 94:[63, 120], Operations: ['54-20=34', '86+34=120'] Exploring Operation: 120-63=57, Resulting Numbers: [57] 57,94 unequal: No Solution Exploring Operation: 63*120=7560, Resulting Numbers: [7560] 7560,94 unequal: No Solution Exploring Operation: 63+120=183, Resulting Numbers: [183] 183,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 94:[86, 11], Operations: ['63-54=9', '20-9=11'] Exploring Operation: 86+11=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,94 unequal: No Solution Exploring Operation: 86*11=946, Resulting Numbers: [946] 946,94 unequal: No Solution Moving to Node #0,0,4 Current State: 94:[9, 106], Operations: ['63-54=9', '20+86=106'] Exploring Operation: 9*106=954, Resulting Numbers: [954] 954,94 unequal: No Solution Exploring Operation: 9+106=115, Resulting Numbers: [115] 115,94 unequal: No Solution Exploring Operation: 106-9=97, Resulting Numbers: [97] 97,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[20, 95], Operations: ['63-54=9', '86+9=95'] Exploring Operation: 95-20=75, Resulting Numbers: [75] 75,94 unequal: No Solution Exploring Operation: 20*95=1900, Resulting Numbers: [1900] 1900,94 unequal: No Solution Exploring Operation: 20+95=115, Resulting Numbers: [115] 115,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[9, 66], Operations: ['63-54=9', '86-20=66'] Exploring Operation: 9+66=75, Resulting Numbers: [75] 75,94 unequal: No Solution Exploring Operation: 9*66=594, Resulting Numbers: [594] 594,94 unequal: No Solution Exploring Operation: 66-9=57, Resulting Numbers: [57] 57,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[86, 29], Operations: ['63-54=9', '20+9=29'] Exploring Operation: 86*29=2494, Resulting Numbers: [2494] 2494,94 unequal: No Solution Exploring Operation: 86+29=115, Resulting Numbers: [115] 115,94 unequal: No Solution Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,94 unequal: No Solution No solution found.
0
hs_5
sum_heuristic