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
[ 11, 44, 15, 55 ]
23
[ "44*15=660", "660/55=12", "11+12=23" ]
Current State: 23:[11, 44, 15, 55], Operations: [] Exploring Operation: 44*15=660, Resulting Numbers: [11, 55, 660] Generated Node #2: [11, 55, 660] from Operation: 44*15=660 Current State: 23:[11, 55, 660], Operations: ['44*15=660'] Exploring Operation: 660/55=12, Resulting Numbers: [11, 12] Generated Node #3: [11, 12] from Operation: 660/55=12 Current State: 23:[11, 12], Operations: ['44*15=660', '660/55=12'] Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[11, 44, 15, 55], Operations: [] Exploring Operation: 44-11=33, Resulting Numbers: [15, 55, 33] Generated Node #0,0: 23:[15, 55, 33] Operation: 44-11=33 Exploring Operation: 55-44=11, Resulting Numbers: [11, 15, 11] Generated Node #0,1: 23:[11, 15, 11] Operation: 55-44=11 Exploring Operation: 55/11=5, Resulting Numbers: [44, 15, 5] Generated Node #0,2: 23:[44, 15, 5] Operation: 55/11=5 Exploring Operation: 55-11=44, Resulting Numbers: [44, 15, 44] Generated Node #0,3: 23:[44, 15, 44] Operation: 55-11=44 Moving to Node #0,1 Current State: 23:[11, 15, 11], Operations: ['55-44=11'] Exploring Operation: 15+11=26, Resulting Numbers: [11, 26] Generated Node #0,1,0: 23:[11, 26] Operation: 15+11=26 Exploring Operation: 11+15=26, Resulting Numbers: [11, 26] Generated Node #0,1,1: 23:[11, 26] Operation: 11+15=26 Exploring Operation: 11/11=1, Resulting Numbers: [15, 1] Generated Node #0,1,2: 23:[15, 1] Operation: 11/11=1 Exploring Operation: 11+11=22, Resulting Numbers: [15, 22] Generated Node #0,1,3: 23:[15, 22] Operation: 11+11=22 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 23:[15, 22], Operations: ['55-44=11', '11+11=22'] Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,23 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[11, 26], Operations: ['55-44=11', '15+11=26'] Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 11*26=286, Resulting Numbers: [286] 286,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[11, 26], Operations: ['55-44=11', '11+15=26'] Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 11*26=286, Resulting Numbers: [286] 286,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 23:[15, 1], Operations: ['55-44=11', '11/11=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,23 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 15+1=16, Resulting Numbers: [16] 16,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 23:[44, 15, 5], Operations: ['55/11=5'] Exploring Operation: 44-5=39, Resulting Numbers: [15, 39] Generated Node #0,2,0: 23:[15, 39] Operation: 44-5=39 Exploring Operation: 15+5=20, Resulting Numbers: [44, 20] Generated Node #0,2,1: 23:[44, 20] Operation: 15+5=20 Exploring Operation: 44+5=49, Resulting Numbers: [15, 49] Generated Node #0,2,2: 23:[15, 49] Operation: 44+5=49 Exploring Operation: 44-15=29, Resulting Numbers: [5, 29] Generated Node #0,2,3: 23:[5, 29] Operation: 44-15=29 Moving to Node #0,3 Current State: 23:[44, 15, 44], Operations: ['55-11=44'] Exploring Operation: 44/44=1, Resulting Numbers: [15, 1] Generated Node #0,3,0: 23:[15, 1] Operation: 44/44=1 Exploring Operation: 44-44=0, Resulting Numbers: [15, 0] Generated Node #0,3,1: 23:[15, 0] Operation: 44-44=0 Exploring Operation: 44-15=29, Resulting Numbers: [44, 29] Generated Node #0,3,2: 23:[44, 29] Operation: 44-15=29 Exploring Operation: 44-15=29, Resulting Numbers: [44, 29] Generated Node #0,3,3: 23:[44, 29] Operation: 44-15=29 Moving to Node #0,0 Current State: 23:[15, 55, 33], Operations: ['44-11=33'] Exploring Operation: 55-33=22, Resulting Numbers: [15, 22] Generated Node #0,0,0: 23:[15, 22] Operation: 55-33=22 Exploring Operation: 33-15=18, Resulting Numbers: [55, 18] Generated Node #0,0,1: 23:[55, 18] Operation: 33-15=18 Exploring Operation: 55-15=40, Resulting Numbers: [33, 40] Generated Node #0,0,2: 23:[33, 40] Operation: 55-15=40 Exploring Operation: 15+55=70, Resulting Numbers: [33, 70] Generated Node #0,0,3: 23:[33, 70] Operation: 15+55=70 Moving to Node #0,0,0 Current State: 23:[15, 22], Operations: ['44-11=33', '55-33=22'] Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[5, 29], Operations: ['55/11=5', '44-15=29'] Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 5*29=145, Resulting Numbers: [145] 145,23 unequal: No Solution Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[15, 39], Operations: ['55/11=5', '44-5=39'] Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 15*39=585, Resulting Numbers: [585] 585,23 unequal: No Solution Exploring Operation: 15+39=54, Resulting Numbers: [54] 54,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[44, 20], Operations: ['55/11=5', '15+5=20'] Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 44*20=880, Resulting Numbers: [880] 880,23 unequal: No Solution Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[44, 29], Operations: ['55-11=44', '44-15=29'] Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 44+29=73, Resulting Numbers: [73] 73,23 unequal: No Solution Exploring Operation: 44*29=1276, Resulting Numbers: [1276] 1276,23 unequal: No Solution Moving to Node #0,3,2 Current State: 23:[44, 29], Operations: ['55-11=44', '44-15=29'] Exploring Operation: 44*29=1276, Resulting Numbers: [1276] 1276,23 unequal: No Solution Exploring Operation: 44+29=73, Resulting Numbers: [73] 73,23 unequal: No Solution Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[33, 40], Operations: ['44-11=33', '55-15=40'] Exploring Operation: 33+40=73, Resulting Numbers: [73] 73,23 unequal: No Solution Exploring Operation: 33*40=1320, Resulting Numbers: [1320] 1320,23 unequal: No Solution Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[15, 1], Operations: ['55-11=44', '44/44=1'] Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 15+1=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,23 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,23 unequal: No Solution Moving to Node #0,3,1 Current State: 23:[15, 0], Operations: ['55-11=44', '44-44=0'] Exploring Operation: 15*0=0, Resulting Numbers: [0] 0,23 unequal: No Solution Exploring Operation: 15-0=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 15+0=15, Resulting Numbers: [15] 15,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[15, 49], Operations: ['55/11=5', '44+5=49'] Exploring Operation: 15*49=735, Resulting Numbers: [735] 735,23 unequal: No Solution Exploring Operation: 15+49=64, Resulting Numbers: [64] 64,23 unequal: No Solution Exploring Operation: 49-15=34, Resulting Numbers: [34] 34,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[55, 18], Operations: ['44-11=33', '33-15=18'] Exploring Operation: 55-18=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 55*18=990, Resulting Numbers: [990] 990,23 unequal: No Solution Exploring Operation: 55+18=73, Resulting Numbers: [73] 73,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[33, 70], Operations: ['44-11=33', '15+55=70'] Exploring Operation: 70-33=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 33*70=2310, Resulting Numbers: [2310] 2310,23 unequal: No Solution Exploring Operation: 33+70=103, Resulting Numbers: [103] 103,23 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 22, 45, 87, 27 ]
47
[ "22+45=67", "87+27=114", "114-67=47" ]
Current State: 47:[22, 45, 87, 27], Operations: [] Exploring Operation: 22+45=67, Resulting Numbers: [87, 27, 67] Generated Node #2: [87, 27, 67] from Operation: 22+45=67 Current State: 47:[87, 27, 67], Operations: ['22+45=67'] Exploring Operation: 87+27=114, Resulting Numbers: [67, 114] Generated Node #3: [67, 114] from Operation: 87+27=114 Current State: 47:[67, 114], Operations: ['22+45=67', '87+27=114'] Exploring Operation: 114-67=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[22, 45, 87, 27], Operations: [] Exploring Operation: 22+27=49, Resulting Numbers: [45, 87, 49] Generated Node #0,0: 47:[45, 87, 49] Operation: 22+27=49 Exploring Operation: 87-22=65, Resulting Numbers: [45, 27, 65] Generated Node #0,1: 47:[45, 27, 65] Operation: 87-22=65 Exploring Operation: 87-45=42, Resulting Numbers: [22, 27, 42] Generated Node #0,2: 47:[22, 27, 42] Operation: 87-45=42 Exploring Operation: 87-27=60, Resulting Numbers: [22, 45, 60] Generated Node #0,3: 47:[22, 45, 60] Operation: 87-27=60 Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[45, 27, 65], Operations: ['87-22=65'] Exploring Operation: 65-27=38, Resulting Numbers: [45, 38] Generated Node #0,1,0: 47:[45, 38] Operation: 65-27=38 Exploring Operation: 45+27=72, Resulting Numbers: [65, 72] Generated Node #0,1,1: 47:[65, 72] Operation: 45+27=72 Exploring Operation: 45-27=18, Resulting Numbers: [65, 18] Generated Node #0,1,2: 47:[65, 18] Operation: 45-27=18 Exploring Operation: 65-45=20, Resulting Numbers: [27, 20] Generated Node #0,1,3: 47:[27, 20] Operation: 65-45=20 Moving to Node #0,1,0 Current State: 47:[45, 38], Operations: ['87-22=65', '65-27=38'] Exploring Operation: 45*38=1710, Resulting Numbers: [1710] 1710,47 unequal: No Solution Exploring Operation: 45+38=83, Resulting Numbers: [83] 83,47 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[65, 72], Operations: ['87-22=65', '45+27=72'] Exploring Operation: 72-65=7, Resulting Numbers: [7] 7,47 unequal: No Solution Exploring Operation: 65+72=137, Resulting Numbers: [137] 137,47 unequal: No Solution Exploring Operation: 65*72=4680, Resulting Numbers: [4680] 4680,47 unequal: No Solution Moving to Node #0,1,3 Current State: 47:[27, 20], Operations: ['87-22=65', '65-45=20'] Exploring Operation: 27*20=540, Resulting Numbers: [540] 540,47 unequal: No Solution Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,47 unequal: No Solution Exploring Operation: 27+20=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[22, 45, 87, 27], Operations: [] Exploring Operation: 87-22=65, Resulting Numbers: [45, 27, 65] Generated Node #0,1: 47:[45, 27, 65] Operation: 87-22=65 Moving to Node #0,1 Current State: 47:[45, 27, 65], Operations: ['87-22=65'] Exploring Operation: 65-45=20, Resulting Numbers: [27, 20] Generated Node #0,1,3: 47:[27, 20] Operation: 65-45=20 Moving to Node #0,1,3 Current State: 47:[27, 20], Operations: ['87-22=65', '65-45=20'] Exploring Operation: 27+20=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 15, 72, 5, 6 ]
45
[ "72*5=360", "360/6=60", "60-15=45" ]
Current State: 45:[15, 72, 5, 6], Operations: [] Exploring Operation: 72*5=360, Resulting Numbers: [15, 6, 360] Generated Node #2: [15, 6, 360] from Operation: 72*5=360 Current State: 45:[15, 6, 360], Operations: ['72*5=360'] Exploring Operation: 360/6=60, Resulting Numbers: [15, 60] Generated Node #3: [15, 60] from Operation: 360/6=60 Current State: 45:[15, 60], Operations: ['72*5=360', '360/6=60'] Exploring Operation: 60-15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[15, 72, 5, 6], Operations: [] Exploring Operation: 72-15=57, Resulting Numbers: [5, 6, 57] Generated Node #0,0: 45:[5, 6, 57] Operation: 72-15=57 Exploring Operation: 72/6=12, Resulting Numbers: [15, 5, 12] Generated Node #0,1: 45:[15, 5, 12] Operation: 72/6=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[15, 5, 12], Operations: ['72/6=12'] Exploring Operation: 5+12=17, Resulting Numbers: [15, 17] Generated Node #0,1,0: 45:[15, 17] Operation: 5+12=17 Exploring Operation: 15-12=3, Resulting Numbers: [5, 3] Generated Node #0,1,1: 45:[5, 3] Operation: 15-12=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[5, 3], Operations: ['72/6=12', '15-12=3'] Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,45 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 #0,1,0 Current State: 45:[15, 17], Operations: ['72/6=12', '5+12=17'] Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,45 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,45 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 #0,0 Current State: 45:[5, 6, 57], Operations: ['72-15=57'] Exploring Operation: 57-5=52, Resulting Numbers: [6, 52] Generated Node #0,0,0: 45:[6, 52] Operation: 57-5=52 Exploring Operation: 57-6=51, Resulting Numbers: [5, 51] Generated Node #0,0,1: 45:[5, 51] Operation: 57-6=51 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 45:[5, 51], Operations: ['72-15=57', '57-6=51'] Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,45 unequal: No Solution Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,45 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 #0,0,0 Current State: 45:[6, 52], Operations: ['72-15=57', '57-5=52'] Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,45 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,45 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 No solution found.
0
hs_2
mult_heuristic
[ 71, 18, 75, 66 ]
91
[ "75-66=9", "18*9=162", "162-71=91" ]
Current State: 91:[71, 18, 75, 66], Operations: [] Exploring Operation: 75-66=9, Resulting Numbers: [71, 18, 9] Generated Node #2: [71, 18, 9] from Operation: 75-66=9 Current State: 91:[71, 18, 9], Operations: ['75-66=9'] Exploring Operation: 18*9=162, Resulting Numbers: [71, 162] Generated Node #3: [71, 162] from Operation: 18*9=162 Current State: 91:[71, 162], Operations: ['75-66=9', '18*9=162'] Exploring Operation: 162-71=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[71, 18, 75, 66], Operations: [] Exploring Operation: 75-66=9, Resulting Numbers: [71, 18, 9] Generated Node #0,0: 91:[71, 18, 9] Operation: 75-66=9 Exploring Operation: 71-66=5, Resulting Numbers: [18, 75, 5] Generated Node #0,1: 91:[18, 75, 5] Operation: 71-66=5 Exploring Operation: 75-71=4, Resulting Numbers: [18, 66, 4] Generated Node #0,2: 91:[18, 66, 4] Operation: 75-71=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[18, 75, 5], Operations: ['71-66=5'] Exploring Operation: 18+75=93, Resulting Numbers: [5, 93] Generated Node #0,1,0: 91:[5, 93] Operation: 18+75=93 Exploring Operation: 18-5=13, Resulting Numbers: [75, 13] Generated Node #0,1,1: 91:[75, 13] Operation: 18-5=13 Exploring Operation: 75/5=15, Resulting Numbers: [18, 15] Generated Node #0,1,2: 91:[18, 15] Operation: 75/5=15 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[5, 93], Operations: ['71-66=5', '18+75=93'] Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,91 unequal: No Solution Exploring Operation: 5*93=465, Resulting Numbers: [465] 465,91 unequal: No Solution Exploring Operation: 5+93=98, Resulting Numbers: [98] 98,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 91:[18, 15], Operations: ['71-66=5', '75/5=15'] Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,91 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,91 unequal: No Solution Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[75, 13], Operations: ['71-66=5', '18-5=13'] Exploring Operation: 75*13=975, Resulting Numbers: [975] 975,91 unequal: No Solution Exploring Operation: 75-13=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 75+13=88, Resulting Numbers: [88] 88,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[71, 18, 9], Operations: ['75-66=9'] Exploring Operation: 71+18=89, Resulting Numbers: [9, 89] Generated Node #0,0,0: 91:[9, 89] Operation: 71+18=89 Exploring Operation: 71+9=80, Resulting Numbers: [18, 80] Generated Node #0,0,1: 91:[18, 80] Operation: 71+9=80 Exploring Operation: 18-9=9, Resulting Numbers: [71, 9] Generated Node #0,0,2: 91:[71, 9] Operation: 18-9=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[9, 89], Operations: ['75-66=9', '71+18=89'] Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,91 unequal: No Solution Exploring Operation: 9*89=801, Resulting Numbers: [801] 801,91 unequal: No Solution Exploring Operation: 9+89=98, Resulting Numbers: [98] 98,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[18, 80], Operations: ['75-66=9', '71+9=80'] Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 18+80=98, Resulting Numbers: [98] 98,91 unequal: No Solution Exploring Operation: 18*80=1440, Resulting Numbers: [1440] 1440,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 91:[71, 9], Operations: ['75-66=9', '18-9=9'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 71*9=639, Resulting Numbers: [639] 639,91 unequal: No Solution Exploring Operation: 71+9=80, Resulting Numbers: [80] 80,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[18, 66, 4], Operations: ['75-71=4'] Exploring Operation: 66+4=70, Resulting Numbers: [18, 70] Generated Node #0,2,0: 91:[18, 70] Operation: 66+4=70 Exploring Operation: 18-4=14, Resulting Numbers: [66, 14] Generated Node #0,2,1: 91:[66, 14] Operation: 18-4=14 Exploring Operation: 18+66=84, Resulting Numbers: [4, 84] Generated Node #0,2,2: 91:[4, 84] Operation: 18+66=84 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 91:[4, 84], Operations: ['75-71=4', '18+66=84'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,91 unequal: No Solution Exploring Operation: 4+84=88, Resulting Numbers: [88] 88,91 unequal: No Solution Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 91:[18, 70], Operations: ['75-71=4', '66+4=70'] Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,91 unequal: No Solution Exploring Operation: 18+70=88, Resulting Numbers: [88] 88,91 unequal: No Solution Exploring Operation: 18*70=1260, Resulting Numbers: [1260] 1260,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 91:[66, 14], Operations: ['75-71=4', '18-4=14'] Exploring Operation: 66-14=52, Resulting Numbers: [52] 52,91 unequal: No Solution Exploring Operation: 66*14=924, Resulting Numbers: [924] 924,91 unequal: No Solution Exploring Operation: 66+14=80, Resulting Numbers: [80] 80,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 10, 58, 56, 77 ]
57
[ "58-56=2", "10*2=20", "77-20=57" ]
Current State: 57:[10, 58, 56, 77], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [10, 77, 2] Generated Node #2: [10, 77, 2] from Operation: 58-56=2 Current State: 57:[10, 77, 2], Operations: ['58-56=2'] Exploring Operation: 10*2=20, Resulting Numbers: [77, 20] Generated Node #3: [77, 20] from Operation: 10*2=20 Current State: 57:[77, 20], Operations: ['58-56=2', '10*2=20'] Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[10, 58, 56, 77], Operations: [] Exploring Operation: 77-58=19, Resulting Numbers: [10, 56, 19] Generated Node #0,0: 57:[10, 56, 19] Operation: 77-58=19 Exploring Operation: 77-10=67, Resulting Numbers: [58, 56, 67] Generated Node #0,1: 57:[58, 56, 67] Operation: 77-10=67 Exploring Operation: 77-56=21, Resulting Numbers: [10, 58, 21] Generated Node #0,2: 57:[10, 58, 21] Operation: 77-56=21 Exploring Operation: 58-10=48, Resulting Numbers: [56, 77, 48] Generated Node #0,3: 57:[56, 77, 48] Operation: 58-10=48 Exploring Operation: 58-56=2, Resulting Numbers: [10, 77, 2] Generated Node #0,4: 57:[10, 77, 2] Operation: 58-56=2 Moving to Node #0,0 Current State: 57:[10, 56, 19], Operations: ['77-58=19'] Exploring Operation: 10+56=66, Resulting Numbers: [19, 66] Generated Node #0,0,0: 57:[19, 66] Operation: 10+56=66 Exploring Operation: 56+19=75, Resulting Numbers: [10, 75] Generated Node #0,0,1: 57:[10, 75] Operation: 56+19=75 Exploring Operation: 56-10=46, Resulting Numbers: [19, 46] Generated Node #0,0,2: 57:[19, 46] Operation: 56-10=46 Exploring Operation: 19-10=9, Resulting Numbers: [56, 9] Generated Node #0,0,3: 57:[56, 9] Operation: 19-10=9 Exploring Operation: 10+19=29, Resulting Numbers: [56, 29] Generated Node #0,0,4: 57:[56, 29] Operation: 10+19=29 Moving to Node #0,2 Current State: 57:[10, 58, 21], Operations: ['77-56=21'] Exploring Operation: 58-21=37, Resulting Numbers: [10, 37] Generated Node #0,2,0: 57:[10, 37] Operation: 58-21=37 Exploring Operation: 10+21=31, Resulting Numbers: [58, 31] Generated Node #0,2,1: 57:[58, 31] Operation: 10+21=31 Exploring Operation: 58-10=48, Resulting Numbers: [21, 48] Generated Node #0,2,2: 57:[21, 48] Operation: 58-10=48 Exploring Operation: 10+58=68, Resulting Numbers: [21, 68] Generated Node #0,2,3: 57:[21, 68] Operation: 10+58=68 Exploring Operation: 21-10=11, Resulting Numbers: [58, 11] Generated Node #0,2,4: 57:[58, 11] Operation: 21-10=11 Moving to Node #0,1 Current State: 57:[58, 56, 67], Operations: ['77-10=67'] Exploring Operation: 58-56=2, Resulting Numbers: [67, 2] Generated Node #0,1,0: 57:[67, 2] Operation: 58-56=2 Exploring Operation: 58+56=114, Resulting Numbers: [67, 114] Generated Node #0,1,1: 57:[67, 114] Operation: 58+56=114 Exploring Operation: 67-58=9, Resulting Numbers: [56, 9] Generated Node #0,1,2: 57:[56, 9] Operation: 67-58=9 Exploring Operation: 67-56=11, Resulting Numbers: [58, 11] Generated Node #0,1,3: 57:[58, 11] Operation: 67-56=11 Exploring Operation: 56+67=123, Resulting Numbers: [58, 123] Generated Node #0,1,4: 57:[58, 123] Operation: 56+67=123 Moving to Node #0,4 Current State: 57:[10, 77, 2], Operations: ['58-56=2'] Exploring Operation: 10/2=5, Resulting Numbers: [77, 5] Generated Node #0,4,0: 57:[77, 5] Operation: 10/2=5 Exploring Operation: 10-2=8, Resulting Numbers: [77, 8] Generated Node #0,4,1: 57:[77, 8] Operation: 10-2=8 Exploring Operation: 77-10=67, Resulting Numbers: [2, 67] Generated Node #0,4,2: 57:[2, 67] Operation: 77-10=67 Exploring Operation: 77-2=75, Resulting Numbers: [10, 75] Generated Node #0,4,3: 57:[10, 75] Operation: 77-2=75 Exploring Operation: 10*2=20, Resulting Numbers: [77, 20] Generated Node #0,4,4: 57:[77, 20] Operation: 10*2=20 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 57:[2, 67], Operations: ['58-56=2', '77-10=67'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,57 unequal: No Solution Exploring Operation: 2*67=134, Resulting Numbers: [134] 134,57 unequal: No Solution Exploring Operation: 2+67=69, Resulting Numbers: [69] 69,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 57:[77, 20], Operations: ['58-56=2', '10*2=20'] Exploring Operation: 77+20=97, Resulting Numbers: [97] 97,57 unequal: No Solution Exploring Operation: 77*20=1540, Resulting Numbers: [1540] 1540,57 unequal: No Solution Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[10, 58, 56, 77], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [10, 77, 2] Generated Node #0,4: 57:[10, 77, 2] Operation: 58-56=2 Moving to Node #0,4 Current State: 57:[10, 77, 2], Operations: ['58-56=2'] Exploring Operation: 10*2=20, Resulting Numbers: [77, 20] Generated Node #0,4,4: 57:[77, 20] Operation: 10*2=20 Moving to Node #0,4,4 Current State: 57:[77, 20], Operations: ['58-56=2', '10*2=20'] Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
mult_heuristic
[ 97, 30, 91, 59 ]
95
[ "97+30=127", "91-59=32", "127-32=95" ]
Current State: 95:[97, 30, 91, 59], Operations: [] Exploring Operation: 97+30=127, Resulting Numbers: [91, 59, 127] Generated Node #2: [91, 59, 127] from Operation: 97+30=127 Current State: 95:[91, 59, 127], Operations: ['97+30=127'] Exploring Operation: 91-59=32, Resulting Numbers: [127, 32] Generated Node #3: [127, 32] from Operation: 91-59=32 Current State: 95:[127, 32], Operations: ['97+30=127', '91-59=32'] Exploring Operation: 127-32=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[97, 30, 91, 59], Operations: [] Exploring Operation: 30+59=89, Resulting Numbers: [97, 91, 89] Generated Node #0,0: 95:[97, 91, 89] Operation: 30+59=89 Exploring Operation: 91-59=32, Resulting Numbers: [97, 30, 32] Generated Node #0,1: 95:[97, 30, 32] Operation: 91-59=32 Exploring Operation: 97-59=38, Resulting Numbers: [30, 91, 38] Generated Node #0,2: 95:[30, 91, 38] Operation: 97-59=38 Exploring Operation: 59-30=29, Resulting Numbers: [97, 91, 29] Generated Node #0,3: 95:[97, 91, 29] Operation: 59-30=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[97, 91, 89], Operations: ['30+59=89'] Exploring Operation: 97-89=8, Resulting Numbers: [91, 8] Generated Node #0,0,0: 95:[91, 8] Operation: 97-89=8 Exploring Operation: 91+89=180, Resulting Numbers: [97, 180] Generated Node #0,0,1: 95:[97, 180] Operation: 91+89=180 Exploring Operation: 97-91=6, Resulting Numbers: [89, 6] Generated Node #0,0,2: 95:[89, 6] Operation: 97-91=6 Exploring Operation: 91-89=2, Resulting Numbers: [97, 2] Generated Node #0,0,3: 95:[97, 2] Operation: 91-89=2 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 95:[97, 2], Operations: ['30+59=89', '91-89=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,95 unequal: No Solution Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[97, 30, 91, 59], Operations: [] Exploring Operation: 30+59=89, Resulting Numbers: [97, 91, 89] Generated Node #0,0: 95:[97, 91, 89] Operation: 30+59=89 Moving to Node #0,0 Current State: 95:[97, 91, 89], Operations: ['30+59=89'] Exploring Operation: 91-89=2, Resulting Numbers: [97, 2] Generated Node #0,0,3: 95:[97, 2] Operation: 91-89=2 Moving to Node #0,0,3 Current State: 95:[97, 2], Operations: ['30+59=89', '91-89=2'] Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 2, 12, 28, 8 ]
32
[ "2*12=24", "28-24=4", "8*4=32" ]
Current State: 32:[2, 12, 28, 8], Operations: [] Exploring Operation: 2*12=24, Resulting Numbers: [28, 8, 24] Generated Node #2: [28, 8, 24] from Operation: 2*12=24 Current State: 32:[28, 8, 24], Operations: ['2*12=24'] Exploring Operation: 28-24=4, Resulting Numbers: [8, 4] Generated Node #3: [8, 4] from Operation: 28-24=4 Current State: 32:[8, 4], Operations: ['2*12=24', '28-24=4'] Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[2, 12, 28, 8], Operations: [] Exploring Operation: 28-12=16, Resulting Numbers: [2, 8, 16] Generated Node #0,0: 32:[2, 8, 16] Operation: 28-12=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[2, 8, 16], Operations: ['28-12=16'] Exploring Operation: 2*8=16, Resulting Numbers: [16, 16] Generated Node #0,0,0: 32:[16, 16] Operation: 2*8=16 Moving to Node #0,0,0 Current State: 32:[16, 16], Operations: ['28-12=16', '2*8=16'] Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[2, 12, 28, 8], Operations: [] Exploring Operation: 28-12=16, Resulting Numbers: [2, 8, 16] Generated Node #0,0: 32:[2, 8, 16] Operation: 28-12=16 Moving to Node #0,0 Current State: 32:[2, 8, 16], Operations: ['28-12=16'] Exploring Operation: 2*8=16, Resulting Numbers: [16, 16] Generated Node #0,0,0: 32:[16, 16] Operation: 2*8=16 Moving to Node #0,0,0 Current State: 32:[16, 16], Operations: ['28-12=16', '2*8=16'] Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 54, 18, 66, 3 ]
75
[ "54/18=3", "3*3=9", "66+9=75" ]
Current State: 75:[54, 18, 66, 3], Operations: [] Exploring Operation: 54/18=3, Resulting Numbers: [66, 3, 3] Generated Node #2: [66, 3, 3] from Operation: 54/18=3 Current State: 75:[66, 3, 3], Operations: ['54/18=3'] Exploring Operation: 3*3=9, Resulting Numbers: [66, 9] Generated Node #3: [66, 9] from Operation: 3*3=9 Current State: 75:[66, 9], Operations: ['54/18=3', '3*3=9'] Exploring Operation: 66+9=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[54, 18, 66, 3], Operations: [] Exploring Operation: 54/18=3, Resulting Numbers: [66, 3, 3] Generated Node #0,0: 75:[66, 3, 3] Operation: 54/18=3 Exploring Operation: 54+18=72, Resulting Numbers: [66, 3, 72] Generated Node #0,1: 75:[66, 3, 72] Operation: 54+18=72 Exploring Operation: 66-54=12, Resulting Numbers: [18, 3, 12] Generated Node #0,2: 75:[18, 3, 12] Operation: 66-54=12 Moving to Node #0,2 Current State: 75:[18, 3, 12], Operations: ['66-54=12'] Exploring Operation: 3+12=15, Resulting Numbers: [18, 15] Generated Node #0,2,0: 75:[18, 15] Operation: 3+12=15 Exploring Operation: 18-3=15, Resulting Numbers: [12, 15] Generated Node #0,2,1: 75:[12, 15] Operation: 18-3=15 Exploring Operation: 18-12=6, Resulting Numbers: [3, 6] Generated Node #0,2,2: 75:[3, 6] Operation: 18-12=6 Moving to Node #0,0 Current State: 75:[66, 3, 3], Operations: ['54/18=3'] Exploring Operation: 66/3=22, Resulting Numbers: [3, 22] Generated Node #0,0,0: 75:[3, 22] Operation: 66/3=22 Exploring Operation: 66/3=22, Resulting Numbers: [3, 22] Generated Node #0,0,1: 75:[3, 22] Operation: 66/3=22 Exploring Operation: 66+3=69, Resulting Numbers: [3, 69] Generated Node #0,0,2: 75:[3, 69] Operation: 66+3=69 Moving to Node #0,1 Current State: 75:[66, 3, 72], Operations: ['54+18=72'] Exploring Operation: 72-66=6, Resulting Numbers: [3, 6] Generated Node #0,1,0: 75:[3, 6] Operation: 72-66=6 Exploring Operation: 66/3=22, Resulting Numbers: [72, 22] Generated Node #0,1,1: 75:[72, 22] Operation: 66/3=22 Exploring Operation: 66+3=69, Resulting Numbers: [72, 69] Generated Node #0,1,2: 75:[72, 69] Operation: 66+3=69 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 75:[3, 6], Operations: ['54+18=72', '72-66=6'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 75:[72, 22], Operations: ['54+18=72', '66/3=22'] Exploring Operation: 72*22=1584, Resulting Numbers: [1584] 1584,75 unequal: No Solution Exploring Operation: 72-22=50, Resulting Numbers: [50] 50,75 unequal: No Solution Exploring Operation: 72+22=94, Resulting Numbers: [94] 94,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 75:[72, 69], Operations: ['54+18=72', '66+3=69'] Exploring Operation: 72+69=141, Resulting Numbers: [141] 141,75 unequal: No Solution Exploring Operation: 72*69=4968, Resulting Numbers: [4968] 4968,75 unequal: No Solution Exploring Operation: 72-69=3, Resulting Numbers: [3] 3,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 75:[3, 6], Operations: ['66-54=12', '18-12=6'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,75 unequal: No Solution Moving to Node #0,2,1 Current State: 75:[12, 15], Operations: ['66-54=12', '18-3=15'] Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,75 unequal: No Solution Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,75 unequal: No Solution Moving to Node #0,2,0 Current State: 75:[18, 15], Operations: ['66-54=12', '3+12=15'] Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,75 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[3, 22], Operations: ['54/18=3', '66/3=22'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 3*22=66, Resulting Numbers: [66] 66,75 unequal: No Solution Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[3, 22], Operations: ['54/18=3', '66/3=22'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 3*22=66, Resulting Numbers: [66] 66,75 unequal: No Solution Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[3, 69], Operations: ['54/18=3', '66+3=69'] Exploring Operation: 3+69=72, Resulting Numbers: [72] 72,75 unequal: No Solution Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,75 unequal: No Solution Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,75 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 16, 5, 13, 67 ]
76
[ "16-5=11", "13*11=143", "143-67=76" ]
Current State: 76:[16, 5, 13, 67], Operations: [] Exploring Operation: 16-5=11, Resulting Numbers: [13, 67, 11] Generated Node #2: [13, 67, 11] from Operation: 16-5=11 Current State: 76:[13, 67, 11], Operations: ['16-5=11'] Exploring Operation: 13*11=143, Resulting Numbers: [67, 143] Generated Node #3: [67, 143] from Operation: 13*11=143 Current State: 76:[67, 143], Operations: ['16-5=11', '13*11=143'] Exploring Operation: 143-67=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[16, 5, 13, 67], Operations: [] Exploring Operation: 16-13=3, Resulting Numbers: [5, 67, 3] Generated Node #0,0: 76:[5, 67, 3] Operation: 16-13=3 Exploring Operation: 5+67=72, Resulting Numbers: [16, 13, 72] Generated Node #0,1: 76:[16, 13, 72] Operation: 5+67=72 Exploring Operation: 13+67=80, Resulting Numbers: [16, 5, 80] Generated Node #0,2: 76:[16, 5, 80] Operation: 13+67=80 Exploring Operation: 5+13=18, Resulting Numbers: [16, 67, 18] Generated Node #0,3: 76:[16, 67, 18] Operation: 5+13=18 Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[16, 5, 80], Operations: ['13+67=80'] Exploring Operation: 80-5=75, Resulting Numbers: [16, 75] Generated Node #0,2,0: 76:[16, 75] Operation: 80-5=75 Exploring Operation: 80/5=16, Resulting Numbers: [16, 16] Generated Node #0,2,1: 76:[16, 16] Operation: 80/5=16 Exploring Operation: 80/16=5, Resulting Numbers: [5, 5] Generated Node #0,2,2: 76:[5, 5] Operation: 80/16=5 Exploring Operation: 16+5=21, Resulting Numbers: [80, 21] Generated Node #0,2,3: 76:[80, 21] Operation: 16+5=21 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 76:[5, 5], Operations: ['13+67=80', '80/16=5'] Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,76 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,76 unequal: No Solution Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 76:[16, 75], Operations: ['13+67=80', '80-5=75'] Exploring Operation: 16*75=1200, Resulting Numbers: [1200] 1200,76 unequal: No Solution Exploring Operation: 16+75=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 75-16=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 #0,2,1 Current State: 76:[16, 16], Operations: ['13+67=80', '80/5=16'] Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 16*16=256, Resulting Numbers: [256] 256,76 unequal: No Solution Exploring Operation: 16-16=0, Resulting Numbers: [0] 0,76 unequal: No Solution Exploring Operation: 16/16=1, Resulting Numbers: [1] 1,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 76:[80, 21], Operations: ['13+67=80', '16+5=21'] Exploring Operation: 80*21=1680, Resulting Numbers: [1680] 1680,76 unequal: No Solution Exploring Operation: 80+21=101, Resulting Numbers: [101] 101,76 unequal: No Solution Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,76 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:[5, 67, 3], Operations: ['16-13=3'] Exploring Operation: 5+67=72, Resulting Numbers: [3, 72] Generated Node #0,0,0: 76:[3, 72] Operation: 5+67=72 Exploring Operation: 5+3=8, Resulting Numbers: [67, 8] Generated Node #0,0,1: 76:[67, 8] Operation: 5+3=8 Exploring Operation: 5-3=2, Resulting Numbers: [67, 2] Generated Node #0,0,2: 76:[67, 2] Operation: 5-3=2 Exploring Operation: 67+3=70, Resulting Numbers: [5, 70] Generated Node #0,0,3: 76:[5, 70] Operation: 67+3=70 Moving to Node #0,0,0 Current State: 76:[3, 72], Operations: ['16-13=3', '5+67=72'] Exploring Operation: 3+72=75, Resulting Numbers: [75] 75,76 unequal: No Solution Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,76 unequal: No Solution Exploring Operation: 3*72=216, Resulting Numbers: [216] 216,76 unequal: No Solution Moving to Node #0,0,3 Current State: 76:[5, 70], Operations: ['16-13=3', '67+3=70'] Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,76 unequal: No Solution Exploring Operation: 5*70=350, Resulting Numbers: [350] 350,76 unequal: No Solution Exploring Operation: 5+70=75, Resulting Numbers: [75] 75,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[67, 2], Operations: ['16-13=3', '5-3=2'] Exploring Operation: 67*2=134, Resulting Numbers: [134] 134,76 unequal: No Solution Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[67, 8], Operations: ['16-13=3', '5+3=8'] Exploring Operation: 67+8=75, Resulting Numbers: [75] 75,76 unequal: No Solution Exploring Operation: 67-8=59, Resulting Numbers: [59] 59,76 unequal: No Solution Exploring Operation: 67*8=536, Resulting Numbers: [536] 536,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[16, 13, 72], Operations: ['5+67=72'] Exploring Operation: 16+13=29, Resulting Numbers: [72, 29] Generated Node #0,1,0: 76:[72, 29] Operation: 16+13=29 Exploring Operation: 13+72=85, Resulting Numbers: [16, 85] Generated Node #0,1,1: 76:[16, 85] Operation: 13+72=85 Exploring Operation: 16-13=3, Resulting Numbers: [72, 3] Generated Node #0,1,2: 76:[72, 3] Operation: 16-13=3 Exploring Operation: 16+72=88, Resulting Numbers: [13, 88] Generated Node #0,1,3: 76:[13, 88] Operation: 16+72=88 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 76:[72, 3], Operations: ['5+67=72', '16-13=3'] Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,76 unequal: No Solution Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,76 unequal: No Solution Exploring Operation: 72*3=216, Resulting Numbers: [216] 216,76 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:[16, 85], Operations: ['5+67=72', '13+72=85'] Exploring Operation: 85-16=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 16*85=1360, Resulting Numbers: [1360] 1360,76 unequal: No Solution Exploring Operation: 16+85=101, Resulting Numbers: [101] 101,76 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 #0,1,0 Current State: 76:[72, 29], Operations: ['5+67=72', '16+13=29'] Exploring Operation: 72*29=2088, Resulting Numbers: [2088] 2088,76 unequal: No Solution Exploring Operation: 72+29=101, Resulting Numbers: [101] 101,76 unequal: No Solution Exploring Operation: 72-29=43, Resulting Numbers: [43] 43,76 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 #0,1,3 Current State: 76:[13, 88], Operations: ['5+67=72', '16+72=88'] Exploring Operation: 13*88=1144, Resulting Numbers: [1144] 1144,76 unequal: No Solution Exploring Operation: 13+88=101, Resulting Numbers: [101] 101,76 unequal: No Solution Exploring Operation: 88-13=75, Resulting Numbers: [75] 75,76 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 #0,3 Current State: 76:[16, 67, 18], Operations: ['5+13=18'] Exploring Operation: 67+18=85, Resulting Numbers: [16, 85] Generated Node #0,3,0: 76:[16, 85] Operation: 67+18=85 Exploring Operation: 16+18=34, Resulting Numbers: [67, 34] Generated Node #0,3,1: 76:[67, 34] Operation: 16+18=34 Exploring Operation: 16+67=83, Resulting Numbers: [18, 83] Generated Node #0,3,2: 76:[18, 83] Operation: 16+67=83 Exploring Operation: 18-16=2, Resulting Numbers: [67, 2] Generated Node #0,3,3: 76:[67, 2] Operation: 18-16=2 Moving to Node #0,3,2 Current State: 76:[18, 83], Operations: ['5+13=18', '16+67=83'] Exploring Operation: 18*83=1494, Resulting Numbers: [1494] 1494,76 unequal: No Solution Exploring Operation: 18+83=101, Resulting Numbers: [101] 101,76 unequal: No Solution Exploring Operation: 83-18=65, Resulting Numbers: [65] 65,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[67, 2], Operations: ['5+13=18', '18-16=2'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,76 unequal: No Solution Exploring Operation: 67*2=134, Resulting Numbers: [134] 134,76 unequal: No Solution Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[16, 85], Operations: ['5+13=18', '67+18=85'] Exploring Operation: 16+85=101, Resulting Numbers: [101] 101,76 unequal: No Solution Exploring Operation: 85-16=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 16*85=1360, Resulting Numbers: [1360] 1360,76 unequal: No Solution Moving to Node #0,3,1 Current State: 76:[67, 34], Operations: ['5+13=18', '16+18=34'] Exploring Operation: 67+34=101, Resulting Numbers: [101] 101,76 unequal: No Solution Exploring Operation: 67-34=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 67*34=2278, Resulting Numbers: [2278] 2278,76 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
[ 23, 3, 45, 36 ]
17
[ "23+3=26", "45-36=9", "26-9=17" ]
Current State: 17:[23, 3, 45, 36], Operations: [] Exploring Operation: 23+3=26, Resulting Numbers: [45, 36, 26] Generated Node #2: [45, 36, 26] from Operation: 23+3=26 Current State: 17:[45, 36, 26], Operations: ['23+3=26'] Exploring Operation: 45-36=9, Resulting Numbers: [26, 9] Generated Node #3: [26, 9] from Operation: 45-36=9 Current State: 17:[26, 9], Operations: ['23+3=26', '45-36=9'] Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[23, 3, 45, 36], Operations: [] Exploring Operation: 45/3=15, Resulting Numbers: [23, 36, 15] Generated Node #0,0: 17:[23, 36, 15] Operation: 45/3=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[23, 36, 15], Operations: ['45/3=15'] Exploring Operation: 36-23=13, Resulting Numbers: [15, 13] Generated Node #0,0,0: 17:[15, 13] Operation: 36-23=13 Moving to Node #0,0,0 Current State: 17:[15, 13], Operations: ['45/3=15', '36-23=13'] Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 4, 10, 37, 11 ]
62
[ "4+10=14", "37+11=48", "14+48=62" ]
Current State: 62:[4, 10, 37, 11], Operations: [] Exploring Operation: 4+10=14, Resulting Numbers: [37, 11, 14] Generated Node #2: [37, 11, 14] from Operation: 4+10=14 Current State: 62:[37, 11, 14], Operations: ['4+10=14'] Exploring Operation: 37+11=48, Resulting Numbers: [14, 48] Generated Node #3: [14, 48] from Operation: 37+11=48 Current State: 62:[14, 48], Operations: ['4+10=14', '37+11=48'] Exploring Operation: 14+48=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[4, 10, 37, 11], Operations: [] Exploring Operation: 10+11=21, Resulting Numbers: [4, 37, 21] Generated Node #0,0: 62:[4, 37, 21] Operation: 10+11=21 Exploring Operation: 37-10=27, Resulting Numbers: [4, 11, 27] Generated Node #0,1: 62:[4, 11, 27] Operation: 37-10=27 Exploring Operation: 37-11=26, Resulting Numbers: [4, 10, 26] Generated Node #0,2: 62:[4, 10, 26] Operation: 37-11=26 Exploring Operation: 10-4=6, Resulting Numbers: [37, 11, 6] Generated Node #0,3: 62:[37, 11, 6] Operation: 10-4=6 Exploring Operation: 11-10=1, Resulting Numbers: [4, 37, 1] Generated Node #0,4: 62:[4, 37, 1] Operation: 11-10=1 Start Sub Search at level 1: Moving to Node #0,4 Current State: 62:[4, 37, 1], Operations: ['11-10=1'] Exploring Operation: 37-4=33, Resulting Numbers: [1, 33] Generated Node #0,4,0: 62:[1, 33] Operation: 37-4=33 Exploring Operation: 4-1=3, Resulting Numbers: [37, 3] Generated Node #0,4,1: 62:[37, 3] Operation: 4-1=3 Exploring Operation: 37-1=36, Resulting Numbers: [4, 36] Generated Node #0,4,2: 62:[4, 36] Operation: 37-1=36 Exploring Operation: 4*1=4, Resulting Numbers: [37, 4] Generated Node #0,4,3: 62:[37, 4] Operation: 4*1=4 Exploring Operation: 4/1=4, Resulting Numbers: [37, 4] Generated Node #0,4,4: 62:[37, 4] Operation: 4/1=4 Moving to Node #0,4,0 Current State: 62:[1, 33], Operations: ['11-10=1', '37-4=33'] Exploring Operation: 1*33=33, Resulting Numbers: [33] 33,62 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,62 unequal: No Solution Exploring Operation: 1+33=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,62 unequal: No Solution Moving to Node #0,4,2 Current State: 62:[4, 36], Operations: ['11-10=1', '37-1=36'] Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,62 unequal: No Solution Exploring Operation: 4*36=144, Resulting Numbers: [144] 144,62 unequal: No Solution Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,62 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,62 unequal: No Solution Moving to Node #0,4,1 Current State: 62:[37, 3], Operations: ['11-10=1', '4-1=3'] Exploring Operation: 37+3=40, Resulting Numbers: [40] 40,62 unequal: No Solution Exploring Operation: 37*3=111, Resulting Numbers: [111] 111,62 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,62 unequal: No Solution Moving to Node #0,4,3 Current State: 62:[37, 4], Operations: ['11-10=1', '4*1=4'] Exploring Operation: 37*4=148, Resulting Numbers: [148] 148,62 unequal: No Solution Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,62 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,62 unequal: No Solution Moving to Node #0,4,4 Current State: 62:[37, 4], Operations: ['11-10=1', '4/1=4'] Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,62 unequal: No Solution Exploring Operation: 37*4=148, Resulting Numbers: [148] 148,62 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[4, 11, 27], Operations: ['37-10=27'] Exploring Operation: 27-11=16, Resulting Numbers: [4, 16] Generated Node #0,1,0: 62:[4, 16] Operation: 27-11=16 Exploring Operation: 11-4=7, Resulting Numbers: [27, 7] Generated Node #0,1,1: 62:[27, 7] Operation: 11-4=7 Exploring Operation: 11+27=38, Resulting Numbers: [4, 38] Generated Node #0,1,2: 62:[4, 38] Operation: 11+27=38 Exploring Operation: 4+27=31, Resulting Numbers: [11, 31] Generated Node #0,1,3: 62:[11, 31] Operation: 4+27=31 Exploring Operation: 4+11=15, Resulting Numbers: [27, 15] Generated Node #0,1,4: 62:[27, 15] Operation: 4+11=15 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 62:[27, 7], Operations: ['37-10=27', '11-4=7'] Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,62 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,62 unequal: No Solution Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 62:[4, 38], Operations: ['37-10=27', '11+27=38'] Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,62 unequal: No Solution Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 62:[11, 31], Operations: ['37-10=27', '4+27=31'] Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,62 unequal: No Solution Exploring Operation: 11*31=341, Resulting Numbers: [341] 341,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 62:[4, 16], Operations: ['37-10=27', '27-11=16'] Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,62 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,62 unequal: No Solution Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,62 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 62:[27, 15], Operations: ['37-10=27', '4+11=15'] Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,62 unequal: No Solution Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[4, 10, 26], Operations: ['37-11=26'] Exploring Operation: 4*10=40, Resulting Numbers: [26, 40] Generated Node #0,2,0: 62:[26, 40] Operation: 4*10=40 Exploring Operation: 26-10=16, Resulting Numbers: [4, 16] Generated Node #0,2,1: 62:[4, 16] Operation: 26-10=16 Exploring Operation: 4+26=30, Resulting Numbers: [10, 30] Generated Node #0,2,2: 62:[10, 30] Operation: 4+26=30 Exploring Operation: 10-4=6, Resulting Numbers: [26, 6] Generated Node #0,2,3: 62:[26, 6] Operation: 10-4=6 Exploring Operation: 10+26=36, Resulting Numbers: [4, 36] Generated Node #0,2,4: 62:[4, 36] Operation: 10+26=36 Moving to Node #0,2,4 Current State: 62:[4, 36], Operations: ['37-11=26', '10+26=36'] Exploring Operation: 4*36=144, Resulting Numbers: [144] 144,62 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,62 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,62 unequal: No Solution Moving to Node #0,2,3 Current State: 62:[26, 6], Operations: ['37-11=26', '10-4=6'] Exploring Operation: 26*6=156, Resulting Numbers: [156] 156,62 unequal: No Solution Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[10, 30], Operations: ['37-11=26', '4+26=30'] Exploring Operation: 10*30=300, Resulting Numbers: [300] 300,62 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,62 unequal: No Solution Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,62 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[26, 40], Operations: ['37-11=26', '4*10=40'] Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 26*40=1040, Resulting Numbers: [1040] 1040,62 unequal: No Solution Exploring Operation: 26+40=66, Resulting Numbers: [66] 66,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[4, 16], Operations: ['37-11=26', '26-10=16'] Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,62 unequal: No Solution Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,62 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,62 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[4, 37, 21], Operations: ['10+11=21'] Exploring Operation: 37-4=33, Resulting Numbers: [21, 33] Generated Node #0,0,0: 62:[21, 33] Operation: 37-4=33 Exploring Operation: 4+21=25, Resulting Numbers: [37, 25] Generated Node #0,0,1: 62:[37, 25] Operation: 4+21=25 Exploring Operation: 37+21=58, Resulting Numbers: [4, 58] Generated Node #0,0,2: 62:[4, 58] Operation: 37+21=58 Exploring Operation: 4+37=41, Resulting Numbers: [21, 41] Generated Node #0,0,3: 62:[21, 41] Operation: 4+37=41 Exploring Operation: 37-21=16, Resulting Numbers: [4, 16] Generated Node #0,0,4: 62:[4, 16] Operation: 37-21=16 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 62:[4, 58], Operations: ['10+11=21', '37+21=58'] Exploring Operation: 4*58=232, Resulting Numbers: [232] 232,62 unequal: No Solution Exploring Operation: 4+58=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[4, 10, 37, 11], Operations: [] Exploring Operation: 10+11=21, Resulting Numbers: [4, 37, 21] Generated Node #0,0: 62:[4, 37, 21] Operation: 10+11=21 Moving to Node #0,0 Current State: 62:[4, 37, 21], Operations: ['10+11=21'] Exploring Operation: 37+21=58, Resulting Numbers: [4, 58] Generated Node #0,0,2: 62:[4, 58] Operation: 37+21=58 Moving to Node #0,0,2 Current State: 62:[4, 58], Operations: ['10+11=21', '37+21=58'] Exploring Operation: 4+58=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.928819
hs_5
sum_heuristic
[ 54, 14, 10, 66 ]
26
[ "54+66=120", "120/10=12", "14+12=26" ]
Current State: 26:[54, 14, 10, 66], Operations: [] Exploring Operation: 54+66=120, Resulting Numbers: [14, 10, 120] Generated Node #2: [14, 10, 120] from Operation: 54+66=120 Current State: 26:[14, 10, 120], Operations: ['54+66=120'] Exploring Operation: 120/10=12, Resulting Numbers: [14, 12] Generated Node #3: [14, 12] from Operation: 120/10=12 Current State: 26:[14, 12], Operations: ['54+66=120', '120/10=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[54, 14, 10, 66], Operations: [] Exploring Operation: 66-54=12, Resulting Numbers: [14, 10, 12] Generated Node #0,0: 26:[14, 10, 12] Operation: 66-54=12 Exploring Operation: 54-14=40, Resulting Numbers: [10, 66, 40] Generated Node #0,1: 26:[10, 66, 40] Operation: 54-14=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[14, 10, 12], Operations: ['66-54=12'] Exploring Operation: 14+10=24, Resulting Numbers: [12, 24] Generated Node #0,0,0: 26:[12, 24] Operation: 14+10=24 Exploring Operation: 12-10=2, Resulting Numbers: [14, 2] Generated Node #0,0,1: 26:[14, 2] Operation: 12-10=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 26:[14, 2], Operations: ['66-54=12', '12-10=2'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 26:[12, 24], Operations: ['66-54=12', '14+10=24'] Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,26 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: 26:[10, 66, 40], Operations: ['54-14=40'] Exploring Operation: 66-40=26, Resulting Numbers: [10, 26] Generated Node #0,1,0: 26:[10, 26] Operation: 66-40=26 Exploring Operation: 40/10=4, Resulting Numbers: [66, 4] Generated Node #0,1,1: 26:[66, 4] Operation: 40/10=4 Moving to Node #0,1,0 Current State: 26:[10, 26], Operations: ['54-14=40', '66-40=26'] Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,26 unequal: No Solution Exploring Operation: 10+26=36, Resulting Numbers: [36] 36,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[66, 4], Operations: ['54-14=40', '40/10=4'] Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,26 unequal: No Solution Exploring Operation: 66+4=70, Resulting Numbers: [70] 70,26 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
[ 99, 41, 23, 15 ]
20
[ "99-41=58", "23+15=38", "58-38=20" ]
Current State: 20:[99, 41, 23, 15], Operations: [] Exploring Operation: 99-41=58, Resulting Numbers: [23, 15, 58] Generated Node #2: [23, 15, 58] from Operation: 99-41=58 Current State: 20:[23, 15, 58], Operations: ['99-41=58'] Exploring Operation: 23+15=38, Resulting Numbers: [58, 38] Generated Node #3: [58, 38] from Operation: 23+15=38 Current State: 20:[58, 38], Operations: ['99-41=58', '23+15=38'] Exploring Operation: 58-38=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[99, 41, 23, 15], Operations: [] Exploring Operation: 99-41=58, Resulting Numbers: [23, 15, 58] Generated Node #0,0: 20:[23, 15, 58] Operation: 99-41=58 Moving to Node #0,0 Current State: 20:[23, 15, 58], Operations: ['99-41=58'] Exploring Operation: 58-23=35, Resulting Numbers: [15, 35] Generated Node #0,0,0: 20:[15, 35] Operation: 58-23=35 Moving to Node #0,0,0 Current State: 20:[15, 35], Operations: ['99-41=58', '58-23=35'] Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[99, 41, 23, 15], Operations: [] Exploring Operation: 99-41=58, Resulting Numbers: [23, 15, 58] Generated Node #0,0: 20:[23, 15, 58] Operation: 99-41=58 Moving to Node #0,0 Current State: 20:[23, 15, 58], Operations: ['99-41=58'] Exploring Operation: 58-23=35, Resulting Numbers: [15, 35] Generated Node #0,0,0: 20:[15, 35] Operation: 58-23=35 Moving to Node #0,0,0 Current State: 20:[15, 35], Operations: ['99-41=58', '58-23=35'] Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 26, 87, 46, 86 ]
73
[ "26+87=113", "86-46=40", "113-40=73" ]
Current State: 73:[26, 87, 46, 86], Operations: [] Exploring Operation: 26+87=113, Resulting Numbers: [46, 86, 113] Generated Node #2: [46, 86, 113] from Operation: 26+87=113 Current State: 73:[46, 86, 113], Operations: ['26+87=113'] Exploring Operation: 86-46=40, Resulting Numbers: [113, 40] Generated Node #3: [113, 40] from Operation: 86-46=40 Current State: 73:[113, 40], Operations: ['26+87=113', '86-46=40'] Exploring Operation: 113-40=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[26, 87, 46, 86], Operations: [] Exploring Operation: 87-26=61, Resulting Numbers: [46, 86, 61] Generated Node #0,0: 73:[46, 86, 61] Operation: 87-26=61 Exploring Operation: 46-26=20, Resulting Numbers: [87, 86, 20] Generated Node #0,1: 73:[87, 86, 20] Operation: 46-26=20 Exploring Operation: 26+87=113, Resulting Numbers: [46, 86, 113] Generated Node #0,2: 73:[46, 86, 113] Operation: 26+87=113 Exploring Operation: 26+46=72, Resulting Numbers: [87, 86, 72] Generated Node #0,3: 73:[87, 86, 72] Operation: 26+46=72 Exploring Operation: 86-26=60, Resulting Numbers: [87, 46, 60] Generated Node #0,4: 73:[87, 46, 60] Operation: 86-26=60 Moving to Node #0,3 Current State: 73:[87, 86, 72], Operations: ['26+46=72'] Exploring Operation: 87-86=1, Resulting Numbers: [72, 1] Generated Node #0,3,0: 73:[72, 1] Operation: 87-86=1 Exploring Operation: 86-72=14, Resulting Numbers: [87, 14] Generated Node #0,3,1: 73:[87, 14] Operation: 86-72=14 Exploring Operation: 86+72=158, Resulting Numbers: [87, 158] Generated Node #0,3,2: 73:[87, 158] Operation: 86+72=158 Exploring Operation: 87+72=159, Resulting Numbers: [86, 159] Generated Node #0,3,3: 73:[86, 159] Operation: 87+72=159 Exploring Operation: 87-72=15, Resulting Numbers: [86, 15] Generated Node #0,3,4: 73:[86, 15] Operation: 87-72=15 Moving to Node #0,0 Current State: 73:[46, 86, 61], Operations: ['87-26=61'] Exploring Operation: 61-46=15, Resulting Numbers: [86, 15] Generated Node #0,0,0: 73:[86, 15] Operation: 61-46=15 Exploring Operation: 86-46=40, Resulting Numbers: [61, 40] Generated Node #0,0,1: 73:[61, 40] Operation: 86-46=40 Exploring Operation: 46+86=132, Resulting Numbers: [61, 132] Generated Node #0,0,2: 73:[61, 132] Operation: 46+86=132 Exploring Operation: 46+61=107, Resulting Numbers: [86, 107] Generated Node #0,0,3: 73:[86, 107] Operation: 46+61=107 Exploring Operation: 86-61=25, Resulting Numbers: [46, 25] Generated Node #0,0,4: 73:[46, 25] Operation: 86-61=25 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[61, 40], Operations: ['87-26=61', '86-46=40'] Exploring Operation: 61+40=101, Resulting Numbers: [101] 101,73 unequal: No Solution Exploring Operation: 61*40=2440, Resulting Numbers: [2440] 2440,73 unequal: No Solution Exploring Operation: 61-40=21, Resulting Numbers: [21] 21,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 73:[86, 107], Operations: ['87-26=61', '46+61=107'] Exploring Operation: 86+107=193, Resulting Numbers: [193] 193,73 unequal: No Solution Exploring Operation: 107-86=21, Resulting Numbers: [21] 21,73 unequal: No Solution Exploring Operation: 86*107=9202, Resulting Numbers: [9202] 9202,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[86, 15], Operations: ['87-26=61', '61-46=15'] Exploring Operation: 86*15=1290, Resulting Numbers: [1290] 1290,73 unequal: No Solution Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,73 unequal: No Solution Exploring Operation: 86+15=101, Resulting Numbers: [101] 101,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 73:[61, 132], Operations: ['87-26=61', '46+86=132'] Exploring Operation: 61+132=193, Resulting Numbers: [193] 193,73 unequal: No Solution Exploring Operation: 61*132=8052, Resulting Numbers: [8052] 8052,73 unequal: No Solution Exploring Operation: 132-61=71, Resulting Numbers: [71] 71,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 73:[46, 25], Operations: ['87-26=61', '86-61=25'] Exploring Operation: 46+25=71, Resulting Numbers: [71] 71,73 unequal: No Solution Exploring Operation: 46*25=1150, Resulting Numbers: [1150] 1150,73 unequal: No Solution Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,73 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: 73:[87, 46, 60], Operations: ['86-26=60'] Exploring Operation: 60-46=14, Resulting Numbers: [87, 14] Generated Node #0,4,0: 73:[87, 14] Operation: 60-46=14 Exploring Operation: 87-46=41, Resulting Numbers: [60, 41] Generated Node #0,4,1: 73:[60, 41] Operation: 87-46=41 Exploring Operation: 46+60=106, Resulting Numbers: [87, 106] Generated Node #0,4,2: 73:[87, 106] Operation: 46+60=106 Exploring Operation: 87+46=133, Resulting Numbers: [60, 133] Generated Node #0,4,3: 73:[60, 133] Operation: 87+46=133 Exploring Operation: 87-60=27, Resulting Numbers: [46, 27] Generated Node #0,4,4: 73:[46, 27] Operation: 87-60=27 Moving to Node #0,1 Current State: 73:[87, 86, 20], Operations: ['46-26=20'] Exploring Operation: 86+20=106, Resulting Numbers: [87, 106] Generated Node #0,1,0: 73:[87, 106] Operation: 86+20=106 Exploring Operation: 86-20=66, Resulting Numbers: [87, 66] Generated Node #0,1,1: 73:[87, 66] Operation: 86-20=66 Exploring Operation: 87-86=1, Resulting Numbers: [20, 1] Generated Node #0,1,2: 73:[20, 1] Operation: 87-86=1 Exploring Operation: 87+20=107, Resulting Numbers: [86, 107] Generated Node #0,1,3: 73:[86, 107] Operation: 87+20=107 Exploring Operation: 87-20=67, Resulting Numbers: [86, 67] Generated Node #0,1,4: 73:[86, 67] Operation: 87-20=67 Moving to Node #0,2 Current State: 73:[46, 86, 113], Operations: ['26+87=113'] Exploring Operation: 113-46=67, Resulting Numbers: [86, 67] Generated Node #0,2,0: 73:[86, 67] Operation: 113-46=67 Exploring Operation: 113-86=27, Resulting Numbers: [46, 27] Generated Node #0,2,1: 73:[46, 27] Operation: 113-86=27 Exploring Operation: 46+113=159, Resulting Numbers: [86, 159] Generated Node #0,2,2: 73:[86, 159] Operation: 46+113=159 Exploring Operation: 86-46=40, Resulting Numbers: [113, 40] Generated Node #0,2,3: 73:[113, 40] Operation: 86-46=40 Exploring Operation: 46+86=132, Resulting Numbers: [113, 132] Generated Node #0,2,4: 73:[113, 132] Operation: 46+86=132 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 73:[86, 67], Operations: ['26+87=113', '113-46=67'] Exploring Operation: 86*67=5762, Resulting Numbers: [5762] 5762,73 unequal: No Solution Exploring Operation: 86-67=19, Resulting Numbers: [19] 19,73 unequal: No Solution Exploring Operation: 86+67=153, Resulting Numbers: [153] 153,73 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 #0,2,1 Current State: 73:[46, 27], Operations: ['26+87=113', '113-86=27'] Exploring Operation: 46*27=1242, Resulting Numbers: [1242] 1242,73 unequal: No Solution Exploring Operation: 46+27=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[26, 87, 46, 86], Operations: [] Exploring Operation: 26+87=113, Resulting Numbers: [46, 86, 113] Generated Node #0,2: 73:[46, 86, 113] Operation: 26+87=113 Moving to Node #0,2 Current State: 73:[46, 86, 113], Operations: ['26+87=113'] Exploring Operation: 113-86=27, Resulting Numbers: [46, 27] Generated Node #0,2,1: 73:[46, 27] Operation: 113-86=27 Moving to Node #0,2,1 Current State: 73:[46, 27], Operations: ['26+87=113', '113-86=27'] Exploring Operation: 46+27=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.953125
hs_5
sum_heuristic
[ 23, 33, 19, 2 ]
11
[ "33-23=10", "19+2=21", "21-10=11" ]
Current State: 11:[23, 33, 19, 2], Operations: [] Exploring Operation: 33-23=10, Resulting Numbers: [19, 2, 10] Generated Node #2: [19, 2, 10] from Operation: 33-23=10 Current State: 11:[19, 2, 10], Operations: ['33-23=10'] Exploring Operation: 19+2=21, Resulting Numbers: [10, 21] Generated Node #3: [10, 21] from Operation: 19+2=21 Current State: 11:[10, 21], Operations: ['33-23=10', '19+2=21'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[23, 33, 19, 2], Operations: [] Exploring Operation: 33-23=10, Resulting Numbers: [19, 2, 10] Generated Node #0,0: 11:[19, 2, 10] Operation: 33-23=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[19, 2, 10], Operations: ['33-23=10'] Exploring Operation: 19-2=17, Resulting Numbers: [10, 17] Generated Node #0,0,0: 11:[10, 17] Operation: 19-2=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[10, 17], Operations: ['33-23=10', '19-2=17'] Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 43, 41, 4, 52 ]
22
[ "43-41=2", "52/2=26", "26-4=22" ]
Current State: 22:[43, 41, 4, 52], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [4, 52, 2] Generated Node #2: [4, 52, 2] from Operation: 43-41=2 Current State: 22:[4, 52, 2], Operations: ['43-41=2'] Exploring Operation: 52/2=26, Resulting Numbers: [4, 26] Generated Node #3: [4, 26] from Operation: 52/2=26 Current State: 22:[4, 26], Operations: ['43-41=2', '52/2=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[43, 41, 4, 52], Operations: [] Exploring Operation: 52-43=9, Resulting Numbers: [41, 4, 9] Generated Node #0,0: 22:[41, 4, 9] Operation: 52-43=9 Exploring Operation: 43-41=2, Resulting Numbers: [4, 52, 2] Generated Node #0,1: 22:[4, 52, 2] Operation: 43-41=2 Exploring Operation: 43-4=39, Resulting Numbers: [41, 52, 39] Generated Node #0,2: 22:[41, 52, 39] Operation: 43-4=39 Exploring Operation: 52-41=11, Resulting Numbers: [43, 4, 11] Generated Node #0,3: 22:[43, 4, 11] Operation: 52-41=11 Exploring Operation: 52/4=13, Resulting Numbers: [43, 41, 13] Generated Node #0,4: 22:[43, 41, 13] Operation: 52/4=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[41, 4, 9], Operations: ['52-43=9'] Exploring Operation: 9-4=5, Resulting Numbers: [41, 5] Generated Node #0,0,0: 22:[41, 5] Operation: 9-4=5 Exploring Operation: 41-9=32, Resulting Numbers: [4, 32] Generated Node #0,0,1: 22:[4, 32] Operation: 41-9=32 Exploring Operation: 41+4=45, Resulting Numbers: [9, 45] Generated Node #0,0,2: 22:[9, 45] Operation: 41+4=45 Exploring Operation: 4+9=13, Resulting Numbers: [41, 13] Generated Node #0,0,3: 22:[41, 13] Operation: 4+9=13 Exploring Operation: 41-4=37, Resulting Numbers: [9, 37] Generated Node #0,0,4: 22:[9, 37] Operation: 41-4=37 Moving to Node #0,0,1 Current State: 22:[4, 32], Operations: ['52-43=9', '41-9=32'] Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,22 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,22 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,22 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,22 unequal: No Solution Moving to Node #0,0,4 Current State: 22:[9, 37], Operations: ['52-43=9', '41-4=37'] Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,22 unequal: No Solution Exploring Operation: 9+37=46, Resulting Numbers: [46] 46,22 unequal: No Solution Exploring Operation: 9*37=333, Resulting Numbers: [333] 333,22 unequal: No Solution Moving to Node #0,0,3 Current State: 22:[41, 13], Operations: ['52-43=9', '4+9=13'] Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,22 unequal: No Solution Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,22 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,22 unequal: No Solution Moving to Node #0,0,0 Current State: 22:[41, 5], Operations: ['52-43=9', '9-4=5'] Exploring Operation: 41+5=46, Resulting Numbers: [46] 46,22 unequal: No Solution Exploring Operation: 41*5=205, Resulting Numbers: [205] 205,22 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[9, 45], Operations: ['52-43=9', '41+4=45'] Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 9*45=405, Resulting Numbers: [405] 405,22 unequal: No Solution Exploring Operation: 9+45=54, Resulting Numbers: [54] 54,22 unequal: No Solution Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,22 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 #0,3 Current State: 22:[43, 4, 11], Operations: ['52-41=11'] Exploring Operation: 43-11=32, Resulting Numbers: [4, 32] Generated Node #0,3,0: 22:[4, 32] Operation: 43-11=32 Exploring Operation: 11-4=7, Resulting Numbers: [43, 7] Generated Node #0,3,1: 22:[43, 7] Operation: 11-4=7 Exploring Operation: 43+4=47, Resulting Numbers: [11, 47] Generated Node #0,3,2: 22:[11, 47] Operation: 43+4=47 Exploring Operation: 43-4=39, Resulting Numbers: [11, 39] Generated Node #0,3,3: 22:[11, 39] Operation: 43-4=39 Exploring Operation: 4+11=15, Resulting Numbers: [43, 15] Generated Node #0,3,4: 22:[43, 15] Operation: 4+11=15 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 22:[4, 32], Operations: ['52-41=11', '43-11=32'] Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,22 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,22 unequal: No Solution Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,22 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,22 unequal: No Solution No 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: 22:[11, 39], Operations: ['52-41=11', '43-4=39'] Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,22 unequal: No Solution Exploring Operation: 11+39=50, Resulting Numbers: [50] 50,22 unequal: No Solution Exploring Operation: 11*39=429, Resulting Numbers: [429] 429,22 unequal: No Solution No 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: 22:[43, 7], Operations: ['52-41=11', '11-4=7'] Exploring Operation: 43+7=50, Resulting Numbers: [50] 50,22 unequal: No Solution Exploring Operation: 43*7=301, Resulting Numbers: [301] 301,22 unequal: No Solution Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,22 unequal: No Solution No 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: 22:[11, 47], Operations: ['52-41=11', '43+4=47'] Exploring Operation: 47-11=36, Resulting Numbers: [36] 36,22 unequal: No Solution Exploring Operation: 11+47=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 11*47=517, Resulting Numbers: [517] 517,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 22:[43, 15], Operations: ['52-41=11', '4+11=15'] Exploring Operation: 43*15=645, Resulting Numbers: [645] 645,22 unequal: No Solution Exploring Operation: 43+15=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 43-15=28, Resulting Numbers: [28] 28,22 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: 22:[4, 52, 2], Operations: ['43-41=2'] Exploring Operation: 4/2=2, Resulting Numbers: [52, 2] Generated Node #0,1,0: 22:[52, 2] Operation: 4/2=2 Exploring Operation: 52/4=13, Resulting Numbers: [2, 13] Generated Node #0,1,1: 22:[2, 13] Operation: 52/4=13 Exploring Operation: 52/2=26, Resulting Numbers: [4, 26] Generated Node #0,1,2: 22:[4, 26] Operation: 52/2=26 Exploring Operation: 4-2=2, Resulting Numbers: [52, 2] Generated Node #0,1,3: 22:[52, 2] Operation: 4-2=2 Exploring Operation: 52-4=48, Resulting Numbers: [2, 48] Generated Node #0,1,4: 22:[2, 48] Operation: 52-4=48 Moving to Node #0,1,1 Current State: 22:[2, 13], Operations: ['43-41=2', '52/4=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[4, 26], Operations: ['43-41=2', '52/2=26'] Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,22 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,22 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[43, 41, 4, 52], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [4, 52, 2] Generated Node #0,1: 22:[4, 52, 2] Operation: 43-41=2 Moving to Node #0,1 Current State: 22:[4, 52, 2], Operations: ['43-41=2'] Exploring Operation: 52/2=26, Resulting Numbers: [4, 26] Generated Node #0,1,2: 22:[4, 26] Operation: 52/2=26 Moving to Node #0,1,2 Current State: 22:[4, 26], Operations: ['43-41=2', '52/2=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.945313
hs_5
sum_heuristic
[ 59, 35, 88, 38 ]
32
[ "59+35=94", "88+38=126", "126-94=32" ]
Current State: 32:[59, 35, 88, 38], Operations: [] Exploring Operation: 59+35=94, Resulting Numbers: [88, 38, 94] Generated Node #2: [88, 38, 94] from Operation: 59+35=94 Current State: 32:[88, 38, 94], Operations: ['59+35=94'] Exploring Operation: 88+38=126, Resulting Numbers: [94, 126] Generated Node #3: [94, 126] from Operation: 88+38=126 Current State: 32:[94, 126], Operations: ['59+35=94', '88+38=126'] Exploring Operation: 126-94=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[59, 35, 88, 38], Operations: [] Exploring Operation: 88-59=29, Resulting Numbers: [35, 38, 29] Generated Node #0,0: 32:[35, 38, 29] Operation: 88-59=29 Exploring Operation: 88-38=50, Resulting Numbers: [59, 35, 50] Generated Node #0,1: 32:[59, 35, 50] Operation: 88-38=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[35, 38, 29], Operations: ['88-59=29'] Exploring Operation: 38-29=9, Resulting Numbers: [35, 9] Generated Node #0,0,0: 32:[35, 9] Operation: 38-29=9 Exploring Operation: 38-35=3, Resulting Numbers: [29, 3] Generated Node #0,0,1: 32:[29, 3] Operation: 38-35=3 Moving to Node #0,0,0 Current State: 32:[35, 9], Operations: ['88-59=29', '38-29=9'] Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,32 unequal: No Solution Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,32 unequal: No Solution Moving to Node #0,0,1 Current State: 32:[29, 3], Operations: ['88-59=29', '38-35=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[59, 35, 88, 38], Operations: [] Exploring Operation: 88-59=29, Resulting Numbers: [35, 38, 29] Generated Node #0,0: 32:[35, 38, 29] Operation: 88-59=29 Moving to Node #0,0 Current State: 32:[35, 38, 29], Operations: ['88-59=29'] Exploring Operation: 38-35=3, Resulting Numbers: [29, 3] Generated Node #0,0,1: 32:[29, 3] Operation: 38-35=3 Moving to Node #0,0,1 Current State: 32:[29, 3], Operations: ['88-59=29', '38-35=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 6, 49, 18, 89 ]
16
[ "6+49=55", "89-18=71", "71-55=16" ]
Current State: 16:[6, 49, 18, 89], Operations: [] Exploring Operation: 6+49=55, Resulting Numbers: [18, 89, 55] Generated Node #2: [18, 89, 55] from Operation: 6+49=55 Current State: 16:[18, 89, 55], Operations: ['6+49=55'] Exploring Operation: 89-18=71, Resulting Numbers: [55, 71] Generated Node #3: [55, 71] from Operation: 89-18=71 Current State: 16:[55, 71], Operations: ['6+49=55', '89-18=71'] Exploring Operation: 71-55=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[6, 49, 18, 89], Operations: [] Exploring Operation: 49-18=31, Resulting Numbers: [6, 89, 31] Generated Node #0,0: 16:[6, 89, 31] Operation: 49-18=31 Exploring Operation: 89-49=40, Resulting Numbers: [6, 18, 40] Generated Node #0,1: 16:[6, 18, 40] Operation: 89-49=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[6, 18, 40], Operations: ['89-49=40'] Exploring Operation: 40-18=22, Resulting Numbers: [6, 22] Generated Node #0,1,0: 16:[6, 22] Operation: 40-18=22 Exploring Operation: 40-6=34, Resulting Numbers: [18, 34] Generated Node #0,1,1: 16:[18, 34] Operation: 40-6=34 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[6, 22], Operations: ['89-49=40', '40-18=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[6, 49, 18, 89], Operations: [] Exploring Operation: 89-49=40, Resulting Numbers: [6, 18, 40] Generated Node #0,1: 16:[6, 18, 40] Operation: 89-49=40 Moving to Node #0,1 Current State: 16:[6, 18, 40], Operations: ['89-49=40'] Exploring Operation: 40-18=22, Resulting Numbers: [6, 22] Generated Node #0,1,0: 16:[6, 22] Operation: 40-18=22 Moving to Node #0,1,0 Current State: 16:[6, 22], Operations: ['89-49=40', '40-18=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 2, 45, 89, 19 ]
65
[ "45-2=43", "89+19=108", "108-43=65" ]
Current State: 65:[2, 45, 89, 19], Operations: [] Exploring Operation: 45-2=43, Resulting Numbers: [89, 19, 43] Generated Node #2: [89, 19, 43] from Operation: 45-2=43 Current State: 65:[89, 19, 43], Operations: ['45-2=43'] Exploring Operation: 89+19=108, Resulting Numbers: [43, 108] Generated Node #3: [43, 108] from Operation: 89+19=108 Current State: 65:[43, 108], Operations: ['45-2=43', '89+19=108'] Exploring Operation: 108-43=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[2, 45, 89, 19], Operations: [] Exploring Operation: 89-45=44, Resulting Numbers: [2, 19, 44] Generated Node #0,0: 65:[2, 19, 44] Operation: 89-45=44 Exploring Operation: 89-19=70, Resulting Numbers: [2, 45, 70] Generated Node #0,1: 65:[2, 45, 70] Operation: 89-19=70 Exploring Operation: 45+19=64, Resulting Numbers: [2, 89, 64] Generated Node #0,2: 65:[2, 89, 64] Operation: 45+19=64 Exploring Operation: 2+45=47, Resulting Numbers: [89, 19, 47] Generated Node #0,3: 65:[89, 19, 47] Operation: 2+45=47 Exploring Operation: 45-19=26, Resulting Numbers: [2, 89, 26] Generated Node #0,4: 65:[2, 89, 26] Operation: 45-19=26 Moving to Node #0,1 Current State: 65:[2, 45, 70], Operations: ['89-19=70'] Exploring Operation: 2+70=72, Resulting Numbers: [45, 72] Generated Node #0,1,0: 65:[45, 72] Operation: 2+70=72 Exploring Operation: 2+45=47, Resulting Numbers: [70, 47] Generated Node #0,1,1: 65:[70, 47] Operation: 2+45=47 Exploring Operation: 70-2=68, Resulting Numbers: [45, 68] Generated Node #0,1,2: 65:[45, 68] Operation: 70-2=68 Exploring Operation: 45-2=43, Resulting Numbers: [70, 43] Generated Node #0,1,3: 65:[70, 43] Operation: 45-2=43 Exploring Operation: 70-45=25, Resulting Numbers: [2, 25] Generated Node #0,1,4: 65:[2, 25] Operation: 70-45=25 Moving to Node #0,2 Current State: 65:[2, 89, 64], Operations: ['45+19=64'] Exploring Operation: 89-2=87, Resulting Numbers: [64, 87] Generated Node #0,2,0: 65:[64, 87] Operation: 89-2=87 Exploring Operation: 64-2=62, Resulting Numbers: [89, 62] Generated Node #0,2,1: 65:[89, 62] Operation: 64-2=62 Exploring Operation: 2+64=66, Resulting Numbers: [89, 66] Generated Node #0,2,2: 65:[89, 66] Operation: 2+64=66 Exploring Operation: 89-64=25, Resulting Numbers: [2, 25] Generated Node #0,2,3: 65:[2, 25] Operation: 89-64=25 Exploring Operation: 2+89=91, Resulting Numbers: [64, 91] Generated Node #0,2,4: 65:[64, 91] Operation: 2+89=91 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 65:[2, 25], Operations: ['45+19=64', '89-64=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,65 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 65:[64, 87], Operations: ['45+19=64', '89-2=87'] Exploring Operation: 64*87=5568, Resulting Numbers: [5568] 5568,65 unequal: No Solution Exploring Operation: 64+87=151, Resulting Numbers: [151] 151,65 unequal: No Solution Exploring Operation: 87-64=23, Resulting Numbers: [23] 23,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 65:[89, 66], Operations: ['45+19=64', '2+64=66'] Exploring Operation: 89+66=155, Resulting Numbers: [155] 155,65 unequal: No Solution Exploring Operation: 89*66=5874, Resulting Numbers: [5874] 5874,65 unequal: No Solution Exploring Operation: 89-66=23, Resulting Numbers: [23] 23,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 65:[89, 62], Operations: ['45+19=64', '64-2=62'] Exploring Operation: 89-62=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 89*62=5518, Resulting Numbers: [5518] 5518,65 unequal: No Solution Exploring Operation: 89+62=151, Resulting Numbers: [151] 151,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 65:[64, 91], Operations: ['45+19=64', '2+89=91'] Exploring Operation: 64*91=5824, Resulting Numbers: [5824] 5824,65 unequal: No Solution Exploring Operation: 64+91=155, Resulting Numbers: [155] 155,65 unequal: No Solution Exploring Operation: 91-64=27, Resulting Numbers: [27] 27,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 65:[2, 19, 44], Operations: ['89-45=44'] Exploring Operation: 2+44=46, Resulting Numbers: [19, 46] Generated Node #0,0,0: 65:[19, 46] Operation: 2+44=46 Exploring Operation: 44-19=25, Resulting Numbers: [2, 25] Generated Node #0,0,1: 65:[2, 25] Operation: 44-19=25 Exploring Operation: 44/2=22, Resulting Numbers: [19, 22] Generated Node #0,0,2: 65:[19, 22] Operation: 44/2=22 Exploring Operation: 19+44=63, Resulting Numbers: [2, 63] Generated Node #0,0,3: 65:[2, 63] Operation: 19+44=63 Exploring Operation: 19-2=17, Resulting Numbers: [44, 17] Generated Node #0,0,4: 65:[44, 17] Operation: 19-2=17 Moving to Node #0,4 Current State: 65:[2, 89, 26], Operations: ['45-19=26'] Exploring Operation: 26/2=13, Resulting Numbers: [89, 13] Generated Node #0,4,0: 65:[89, 13] Operation: 26/2=13 Exploring Operation: 89-2=87, Resulting Numbers: [26, 87] Generated Node #0,4,1: 65:[26, 87] Operation: 89-2=87 Exploring Operation: 89-26=63, Resulting Numbers: [2, 63] Generated Node #0,4,2: 65:[2, 63] Operation: 89-26=63 Exploring Operation: 2*26=52, Resulting Numbers: [89, 52] Generated Node #0,4,3: 65:[89, 52] Operation: 2*26=52 Exploring Operation: 26-2=24, Resulting Numbers: [89, 24] Generated Node #0,4,4: 65:[89, 24] Operation: 26-2=24 Moving to Node #0,3 Current State: 65:[89, 19, 47], Operations: ['2+45=47'] Exploring Operation: 89-19=70, Resulting Numbers: [47, 70] Generated Node #0,3,0: 65:[47, 70] Operation: 89-19=70 Exploring Operation: 89-47=42, Resulting Numbers: [19, 42] Generated Node #0,3,1: 65:[19, 42] Operation: 89-47=42 Exploring Operation: 19+47=66, Resulting Numbers: [89, 66] Generated Node #0,3,2: 65:[89, 66] Operation: 19+47=66 Exploring Operation: 47-19=28, Resulting Numbers: [89, 28] Generated Node #0,3,3: 65:[89, 28] Operation: 47-19=28 Exploring Operation: 89+19=108, Resulting Numbers: [47, 108] Generated Node #0,3,4: 65:[47, 108] Operation: 89+19=108 Moving to Node #0,0,3 Current State: 65:[2, 63], Operations: ['89-45=44', '19+44=63'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,65 unequal: No Solution Exploring Operation: 2*63=126, Resulting Numbers: [126] 126,65 unequal: No Solution Exploring Operation: 2+63=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[2, 45, 89, 19], Operations: [] Exploring Operation: 89-45=44, Resulting Numbers: [2, 19, 44] Generated Node #0,0: 65:[2, 19, 44] Operation: 89-45=44 Moving to Node #0,0 Current State: 65:[2, 19, 44], Operations: ['89-45=44'] Exploring Operation: 19+44=63, Resulting Numbers: [2, 63] Generated Node #0,0,3: 65:[2, 63] Operation: 19+44=63 Moving to Node #0,0,3 Current State: 65:[2, 63], Operations: ['89-45=44', '19+44=63'] Exploring Operation: 2+63=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
0.954861
hs_5
mult_heuristic
[ 26, 81, 1, 67 ]
39
[ "26+81=107", "1+67=68", "107-68=39" ]
Current State: 39:[26, 81, 1, 67], Operations: [] Exploring Operation: 26+81=107, Resulting Numbers: [1, 67, 107] Generated Node #2: [1, 67, 107] from Operation: 26+81=107 Current State: 39:[1, 67, 107], Operations: ['26+81=107'] Exploring Operation: 1+67=68, Resulting Numbers: [107, 68] Generated Node #3: [107, 68] from Operation: 1+67=68 Current State: 39:[107, 68], Operations: ['26+81=107', '1+67=68'] Exploring Operation: 107-68=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[26, 81, 1, 67], Operations: [] Exploring Operation: 67-26=41, Resulting Numbers: [81, 1, 41] Generated Node #0,0: 39:[81, 1, 41] Operation: 67-26=41 Exploring Operation: 26+1=27, Resulting Numbers: [81, 67, 27] Generated Node #0,1: 39:[81, 67, 27] Operation: 26+1=27 Exploring Operation: 81-67=14, Resulting Numbers: [26, 1, 14] Generated Node #0,2: 39:[26, 1, 14] Operation: 81-67=14 Exploring Operation: 81-26=55, Resulting Numbers: [1, 67, 55] Generated Node #0,3: 39:[1, 67, 55] Operation: 81-26=55 Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[26, 1, 14], Operations: ['81-67=14'] Exploring Operation: 26-14=12, Resulting Numbers: [1, 12] Generated Node #0,2,0: 39:[1, 12] Operation: 26-14=12 Exploring Operation: 26+1=27, Resulting Numbers: [14, 27] Generated Node #0,2,1: 39:[14, 27] Operation: 26+1=27 Exploring Operation: 26-1=25, Resulting Numbers: [14, 25] Generated Node #0,2,2: 39:[14, 25] Operation: 26-1=25 Exploring Operation: 26+14=40, Resulting Numbers: [1, 40] Generated Node #0,2,3: 39:[1, 40] Operation: 26+14=40 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 39:[1, 12], Operations: ['81-67=14', '26-14=12'] Exploring Operation: 1+12=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 39:[1, 40], Operations: ['81-67=14', '26+14=40'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[26, 81, 1, 67], Operations: [] Exploring Operation: 81-67=14, Resulting Numbers: [26, 1, 14] Generated Node #0,2: 39:[26, 1, 14] Operation: 81-67=14 Moving to Node #0,2 Current State: 39:[26, 1, 14], Operations: ['81-67=14'] Exploring Operation: 26+14=40, Resulting Numbers: [1, 40] Generated Node #0,2,3: 39:[1, 40] Operation: 26+14=40 Moving to Node #0,2,3 Current State: 39:[1, 40], Operations: ['81-67=14', '26+14=40'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 84, 24, 90, 80 ]
70
[ "84-24=60", "90-80=10", "60+10=70" ]
Current State: 70:[84, 24, 90, 80], Operations: [] Exploring Operation: 84-24=60, Resulting Numbers: [90, 80, 60] Generated Node #2: [90, 80, 60] from Operation: 84-24=60 Current State: 70:[90, 80, 60], Operations: ['84-24=60'] Exploring Operation: 90-80=10, Resulting Numbers: [60, 10] Generated Node #3: [60, 10] from Operation: 90-80=10 Current State: 70:[60, 10], Operations: ['84-24=60', '90-80=10'] Exploring Operation: 60+10=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[84, 24, 90, 80], Operations: [] Exploring Operation: 90-24=66, Resulting Numbers: [84, 80, 66] Generated Node #0,0: 70:[84, 80, 66] Operation: 90-24=66 Exploring Operation: 90-84=6, Resulting Numbers: [24, 80, 6] Generated Node #0,1: 70:[24, 80, 6] Operation: 90-84=6 Exploring Operation: 90-80=10, Resulting Numbers: [84, 24, 10] Generated Node #0,2: 70:[84, 24, 10] Operation: 90-80=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[24, 80, 6], Operations: ['90-84=6'] Exploring Operation: 80-6=74, Resulting Numbers: [24, 74] Generated Node #0,1,0: 70:[24, 74] Operation: 80-6=74 Exploring Operation: 24/6=4, Resulting Numbers: [80, 4] Generated Node #0,1,1: 70:[80, 4] Operation: 24/6=4 Exploring Operation: 24-6=18, Resulting Numbers: [80, 18] Generated Node #0,1,2: 70:[80, 18] Operation: 24-6=18 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 70:[80, 4], Operations: ['90-84=6', '24/6=4'] Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,70 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,70 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,70 unequal: No Solution No 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: 70:[24, 74], Operations: ['90-84=6', '80-6=74'] Exploring Operation: 24*74=1776, Resulting Numbers: [1776] 1776,70 unequal: No Solution Exploring Operation: 24+74=98, Resulting Numbers: [98] 98,70 unequal: No Solution Exploring Operation: 74-24=50, Resulting Numbers: [50] 50,70 unequal: No Solution No 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: 70:[80, 18], Operations: ['90-84=6', '24-6=18'] Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,70 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,70 unequal: No Solution Exploring Operation: 80*18=1440, Resulting Numbers: [1440] 1440,70 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: 70:[84, 24, 10], Operations: ['90-80=10'] Exploring Operation: 84-24=60, Resulting Numbers: [10, 60] Generated Node #0,2,0: 70:[10, 60] Operation: 84-24=60 Exploring Operation: 84-10=74, Resulting Numbers: [24, 74] Generated Node #0,2,1: 70:[24, 74] Operation: 84-10=74 Exploring Operation: 24-10=14, Resulting Numbers: [84, 14] Generated Node #0,2,2: 70:[84, 14] Operation: 24-10=14 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 70:[10, 60], Operations: ['90-80=10', '84-24=60'] Exploring Operation: 10+60=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[84, 24, 90, 80], Operations: [] Exploring Operation: 90-80=10, Resulting Numbers: [84, 24, 10] Generated Node #0,2: 70:[84, 24, 10] Operation: 90-80=10 Moving to Node #0,2 Current State: 70:[84, 24, 10], Operations: ['90-80=10'] Exploring Operation: 84-24=60, Resulting Numbers: [10, 60] Generated Node #0,2,0: 70:[10, 60] Operation: 84-24=60 Moving to Node #0,2,0 Current State: 70:[10, 60], Operations: ['90-80=10', '84-24=60'] Exploring Operation: 10+60=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 50, 58, 8, 66 ]
82
[ "58-50=8", "8+66=74", "8+74=82" ]
Current State: 82:[50, 58, 8, 66], Operations: [] Exploring Operation: 58-50=8, Resulting Numbers: [8, 66, 8] Generated Node #2: [8, 66, 8] from Operation: 58-50=8 Current State: 82:[8, 66, 8], Operations: ['58-50=8'] Exploring Operation: 8+66=74, Resulting Numbers: [74] 74,82 equal: Goal Reached Exploring Operation: 8+74=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[50, 58, 8, 66], Operations: [] Exploring Operation: 8+66=74, Resulting Numbers: [50, 58, 74] Generated Node #0,0: 82:[50, 58, 74] Operation: 8+66=74 Exploring Operation: 58-50=8, Resulting Numbers: [8, 66, 8] Generated Node #0,1: 82:[8, 66, 8] Operation: 58-50=8 Exploring Operation: 66-58=8, Resulting Numbers: [50, 8, 8] Generated Node #0,2: 82:[50, 8, 8] Operation: 66-58=8 Exploring Operation: 58-8=50, Resulting Numbers: [50, 66, 50] Generated Node #0,3: 82:[50, 66, 50] Operation: 58-8=50 Exploring Operation: 50-8=42, Resulting Numbers: [58, 66, 42] Generated Node #0,4: 82:[58, 66, 42] Operation: 50-8=42 Moving to Node #0,2 Current State: 82:[50, 8, 8], Operations: ['66-58=8'] Exploring Operation: 8/8=1, Resulting Numbers: [50, 1] Generated Node #0,2,0: 82:[50, 1] Operation: 8/8=1 Exploring Operation: 50-8=42, Resulting Numbers: [8, 42] Generated Node #0,2,1: 82:[8, 42] Operation: 50-8=42 Exploring Operation: 50+8=58, Resulting Numbers: [8, 58] Generated Node #0,2,2: 82:[8, 58] Operation: 50+8=58 Exploring Operation: 8-8=0, Resulting Numbers: [50, 0] Generated Node #0,2,3: 82:[50, 0] Operation: 8-8=0 Exploring Operation: 50-8=42, Resulting Numbers: [8, 42] Generated Node #0,2,4: 82:[8, 42] Operation: 50-8=42 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 82:[8, 42], Operations: ['66-58=8', '50-8=42'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 8+42=50, Resulting Numbers: [50] 50,82 unequal: No Solution Exploring Operation: 8*42=336, Resulting Numbers: [336] 336,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 82:[8, 42], Operations: ['66-58=8', '50-8=42'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 8*42=336, Resulting Numbers: [336] 336,82 unequal: No Solution Exploring Operation: 8+42=50, Resulting Numbers: [50] 50,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 82:[50, 1], Operations: ['66-58=8', '8/8=1'] Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,82 unequal: No Solution Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,82 unequal: No Solution Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,82 unequal: No Solution Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 82:[50, 0], Operations: ['66-58=8', '8-8=0'] Exploring Operation: 50-0=50, Resulting Numbers: [50] 50,82 unequal: No Solution Exploring Operation: 50*0=0, Resulting Numbers: [0] 0,82 unequal: No Solution Exploring Operation: 50+0=50, Resulting Numbers: [50] 50,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 82:[8, 58], Operations: ['66-58=8', '50+8=58'] Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,82 unequal: No Solution Exploring Operation: 8*58=464, Resulting Numbers: [464] 464,82 unequal: No Solution Exploring Operation: 8+58=66, Resulting Numbers: [66] 66,82 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: 82:[8, 66, 8], Operations: ['58-50=8'] Exploring Operation: 8+66=74, Resulting Numbers: [8, 74] Generated Node #0,1,0: 82:[8, 74] Operation: 8+66=74 Exploring Operation: 66+8=74, Resulting Numbers: [8, 74] Generated Node #0,1,1: 82:[8, 74] Operation: 66+8=74 Exploring Operation: 8-8=0, Resulting Numbers: [66, 0] Generated Node #0,1,2: 82:[66, 0] Operation: 8-8=0 Exploring Operation: 8/8=1, Resulting Numbers: [66, 1] Generated Node #0,1,3: 82:[66, 1] Operation: 8/8=1 Exploring Operation: 66-8=58, Resulting Numbers: [8, 58] Generated Node #0,1,4: 82:[8, 58] Operation: 66-8=58 Moving to Node #0,0 Current State: 82:[50, 58, 74], Operations: ['8+66=74'] Exploring Operation: 74-58=16, Resulting Numbers: [50, 16] Generated Node #0,0,0: 82:[50, 16] Operation: 74-58=16 Exploring Operation: 74-50=24, Resulting Numbers: [58, 24] Generated Node #0,0,1: 82:[58, 24] Operation: 74-50=24 Exploring Operation: 58-50=8, Resulting Numbers: [74, 8] Generated Node #0,0,2: 82:[74, 8] Operation: 58-50=8 Exploring Operation: 50+74=124, Resulting Numbers: [58, 124] Generated Node #0,0,3: 82:[58, 124] Operation: 50+74=124 Exploring Operation: 50+58=108, Resulting Numbers: [74, 108] Generated Node #0,0,4: 82:[74, 108] Operation: 50+58=108 Moving to Node #0,3 Current State: 82:[50, 66, 50], Operations: ['58-8=50'] Exploring Operation: 66-50=16, Resulting Numbers: [50, 16] Generated Node #0,3,0: 82:[50, 16] Operation: 66-50=16 Exploring Operation: 50+50=100, Resulting Numbers: [66, 100] Generated Node #0,3,1: 82:[66, 100] Operation: 50+50=100 Exploring Operation: 66-50=16, Resulting Numbers: [50, 16] Generated Node #0,3,2: 82:[50, 16] Operation: 66-50=16 Exploring Operation: 50-50=0, Resulting Numbers: [66, 0] Generated Node #0,3,3: 82:[66, 0] Operation: 50-50=0 Exploring Operation: 50/50=1, Resulting Numbers: [66, 1] Generated Node #0,3,4: 82:[66, 1] Operation: 50/50=1 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 82:[66, 1], Operations: ['58-8=50', '50/50=1'] Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,82 unequal: No Solution Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,82 unequal: No Solution Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,82 unequal: No Solution Exploring Operation: 66*1=66, Resulting Numbers: [66] 66,82 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 #0,3,3 Current State: 82:[66, 0], Operations: ['58-8=50', '50-50=0'] Exploring Operation: 66*0=0, Resulting Numbers: [0] 0,82 unequal: No Solution Exploring Operation: 66-0=66, Resulting Numbers: [66] 66,82 unequal: No Solution Exploring Operation: 66+0=66, Resulting Numbers: [66] 66,82 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 #0,3,0 Current State: 82:[50, 16], Operations: ['58-8=50', '66-50=16'] Exploring Operation: 50*16=800, Resulting Numbers: [800] 800,82 unequal: No Solution Exploring Operation: 50+16=66, Resulting Numbers: [66] 66,82 unequal: No Solution Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,82 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 #0,3,2 Current State: 82:[50, 16], Operations: ['58-8=50', '66-50=16'] Exploring Operation: 50*16=800, Resulting Numbers: [800] 800,82 unequal: No Solution Exploring Operation: 50+16=66, Resulting Numbers: [66] 66,82 unequal: No Solution Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,82 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 #0,3,1 Current State: 82:[66, 100], Operations: ['58-8=50', '50+50=100'] Exploring Operation: 66+100=166, Resulting Numbers: [166] 166,82 unequal: No Solution Exploring Operation: 66*100=6600, Resulting Numbers: [6600] 6600,82 unequal: No Solution Exploring Operation: 100-66=34, Resulting Numbers: [34] 34,82 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: 82:[58, 66, 42], Operations: ['50-8=42'] Exploring Operation: 58+42=100, Resulting Numbers: [66, 100] Generated Node #0,4,0: 82:[66, 100] Operation: 58+42=100 Exploring Operation: 58-42=16, Resulting Numbers: [66, 16] Generated Node #0,4,1: 82:[66, 16] Operation: 58-42=16 Exploring Operation: 58+66=124, Resulting Numbers: [42, 124] Generated Node #0,4,2: 82:[42, 124] Operation: 58+66=124 Exploring Operation: 66-42=24, Resulting Numbers: [58, 24] Generated Node #0,4,3: 82:[58, 24] Operation: 66-42=24 Exploring Operation: 66-58=8, Resulting Numbers: [42, 8] Generated Node #0,4,4: 82:[42, 8] Operation: 66-58=8 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 82:[42, 8], Operations: ['50-8=42', '66-58=8'] Exploring Operation: 42+8=50, Resulting Numbers: [50] 50,82 unequal: No Solution Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 42*8=336, Resulting Numbers: [336] 336,82 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 #0,4,1 Current State: 82:[66, 16], Operations: ['50-8=42', '58-42=16'] Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,82 unequal: No Solution Exploring Operation: 66*16=1056, Resulting Numbers: [1056] 1056,82 unequal: No Solution Exploring Operation: 66+16=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[50, 58, 8, 66], Operations: [] Exploring Operation: 50-8=42, Resulting Numbers: [58, 66, 42] Generated Node #0,4: 82:[58, 66, 42] Operation: 50-8=42 Moving to Node #0,4 Current State: 82:[58, 66, 42], Operations: ['50-8=42'] Exploring Operation: 58-42=16, Resulting Numbers: [66, 16] Generated Node #0,4,1: 82:[66, 16] Operation: 58-42=16 Moving to Node #0,4,1 Current State: 82:[66, 16], Operations: ['50-8=42', '58-42=16'] Exploring Operation: 66+16=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.9375
hs_5
mult_heuristic
[ 53, 55, 19, 51 ]
83
[ "55-53=2", "51*2=102", "102-19=83" ]
Current State: 83:[53, 55, 19, 51], Operations: [] Exploring Operation: 55-53=2, Resulting Numbers: [19, 51, 2] Generated Node #2: [19, 51, 2] from Operation: 55-53=2 Current State: 83:[19, 51, 2], Operations: ['55-53=2'] Exploring Operation: 51*2=102, Resulting Numbers: [19, 102] Generated Node #3: [19, 102] from Operation: 51*2=102 Current State: 83:[19, 102], Operations: ['55-53=2', '51*2=102'] Exploring Operation: 102-19=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[53, 55, 19, 51], Operations: [] Exploring Operation: 19+51=70, Resulting Numbers: [53, 55, 70] Generated Node #0,0: 83:[53, 55, 70] Operation: 19+51=70 Exploring Operation: 55+19=74, Resulting Numbers: [53, 51, 74] Generated Node #0,1: 83:[53, 51, 74] Operation: 55+19=74 Exploring Operation: 53+19=72, Resulting Numbers: [55, 51, 72] Generated Node #0,2: 83:[55, 51, 72] Operation: 53+19=72 Moving to Node #0,0 Current State: 83:[53, 55, 70], Operations: ['19+51=70'] Exploring Operation: 53+70=123, Resulting Numbers: [55, 123] Generated Node #0,0,0: 83:[55, 123] Operation: 53+70=123 Exploring Operation: 55+70=125, Resulting Numbers: [53, 125] Generated Node #0,0,1: 83:[53, 125] Operation: 55+70=125 Exploring Operation: 53+55=108, Resulting Numbers: [70, 108] Generated Node #0,0,2: 83:[70, 108] Operation: 53+55=108 Moving to Node #0,1 Current State: 83:[53, 51, 74], Operations: ['55+19=74'] Exploring Operation: 51+74=125, Resulting Numbers: [53, 125] Generated Node #0,1,0: 83:[53, 125] Operation: 51+74=125 Exploring Operation: 53+74=127, Resulting Numbers: [51, 127] Generated Node #0,1,1: 83:[51, 127] Operation: 53+74=127 Exploring Operation: 53+51=104, Resulting Numbers: [74, 104] Generated Node #0,1,2: 83:[74, 104] Operation: 53+51=104 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 83:[74, 104], Operations: ['55+19=74', '53+51=104'] Exploring Operation: 74+104=178, Resulting Numbers: [178] 178,83 unequal: No Solution Exploring Operation: 104-74=30, Resulting Numbers: [30] 30,83 unequal: No Solution Exploring Operation: 74*104=7696, Resulting Numbers: [7696] 7696,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 83:[53, 125], Operations: ['55+19=74', '51+74=125'] Exploring Operation: 53*125=6625, Resulting Numbers: [6625] 6625,83 unequal: No Solution Exploring Operation: 53+125=178, Resulting Numbers: [178] 178,83 unequal: No Solution Exploring Operation: 125-53=72, Resulting Numbers: [72] 72,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 83:[51, 127], Operations: ['55+19=74', '53+74=127'] Exploring Operation: 51+127=178, Resulting Numbers: [178] 178,83 unequal: No Solution Exploring Operation: 127-51=76, Resulting Numbers: [76] 76,83 unequal: No Solution Exploring Operation: 51*127=6477, Resulting Numbers: [6477] 6477,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 83:[55, 51, 72], Operations: ['53+19=72'] Exploring Operation: 51+72=123, Resulting Numbers: [55, 123] Generated Node #0,2,0: 83:[55, 123] Operation: 51+72=123 Exploring Operation: 55+72=127, Resulting Numbers: [51, 127] Generated Node #0,2,1: 83:[51, 127] Operation: 55+72=127 Exploring Operation: 55+51=106, Resulting Numbers: [72, 106] Generated Node #0,2,2: 83:[72, 106] Operation: 55+51=106 Moving to Node #0,2,2 Current State: 83:[72, 106], Operations: ['53+19=72', '55+51=106'] Exploring Operation: 106-72=34, Resulting Numbers: [34] 34,83 unequal: No Solution Exploring Operation: 72+106=178, Resulting Numbers: [178] 178,83 unequal: No Solution Exploring Operation: 72*106=7632, Resulting Numbers: [7632] 7632,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[70, 108], Operations: ['19+51=70', '53+55=108'] Exploring Operation: 70*108=7560, Resulting Numbers: [7560] 7560,83 unequal: No Solution Exploring Operation: 108-70=38, Resulting Numbers: [38] 38,83 unequal: No Solution Exploring Operation: 70+108=178, Resulting Numbers: [178] 178,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[55, 123], Operations: ['53+19=72', '51+72=123'] Exploring Operation: 55*123=6765, Resulting Numbers: [6765] 6765,83 unequal: No Solution Exploring Operation: 55+123=178, Resulting Numbers: [178] 178,83 unequal: No Solution Exploring Operation: 123-55=68, Resulting Numbers: [68] 68,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[55, 123], Operations: ['19+51=70', '53+70=123'] Exploring Operation: 123-55=68, Resulting Numbers: [68] 68,83 unequal: No Solution Exploring Operation: 55*123=6765, Resulting Numbers: [6765] 6765,83 unequal: No Solution Exploring Operation: 55+123=178, Resulting Numbers: [178] 178,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[53, 125], Operations: ['19+51=70', '55+70=125'] Exploring Operation: 53+125=178, Resulting Numbers: [178] 178,83 unequal: No Solution Exploring Operation: 53*125=6625, Resulting Numbers: [6625] 6625,83 unequal: No Solution Exploring Operation: 125-53=72, Resulting Numbers: [72] 72,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[51, 127], Operations: ['53+19=72', '55+72=127'] Exploring Operation: 51+127=178, Resulting Numbers: [178] 178,83 unequal: No Solution Exploring Operation: 51*127=6477, Resulting Numbers: [6477] 6477,83 unequal: No Solution Exploring Operation: 127-51=76, Resulting Numbers: [76] 76,83 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 44, 57, 64, 26 ]
32
[ "57-44=13", "64*13=832", "832/26=32" ]
Current State: 32:[44, 57, 64, 26], Operations: [] Exploring Operation: 57-44=13, Resulting Numbers: [64, 26, 13] Generated Node #2: [64, 26, 13] from Operation: 57-44=13 Current State: 32:[64, 26, 13], Operations: ['57-44=13'] Exploring Operation: 64*13=832, Resulting Numbers: [26, 832] Generated Node #3: [26, 832] from Operation: 64*13=832 Current State: 32:[26, 832], Operations: ['57-44=13', '64*13=832'] Exploring Operation: 832/26=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[44, 57, 64, 26], Operations: [] Exploring Operation: 64-57=7, Resulting Numbers: [44, 26, 7] Generated Node #0,0: 32:[44, 26, 7] Operation: 64-57=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[44, 26, 7], Operations: ['64-57=7'] Exploring Operation: 44-26=18, Resulting Numbers: [7, 18] Generated Node #0,0,0: 32:[7, 18] Operation: 44-26=18 Moving to Node #0,0,0 Current State: 32:[7, 18], Operations: ['64-57=7', '44-26=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 1, 1, 59, 96 ]
39
[ "1+1=2", "96-59=37", "2+37=39" ]
Current State: 39:[1, 1, 59, 96], Operations: [] Exploring Operation: 1+1=2, Resulting Numbers: [59, 96, 2] Generated Node #2: [59, 96, 2] from Operation: 1+1=2 Current State: 39:[59, 96, 2], Operations: ['1+1=2'] Exploring Operation: 96-59=37, Resulting Numbers: [2, 37] Generated Node #3: [2, 37] from Operation: 96-59=37 Current State: 39:[2, 37], Operations: ['1+1=2', '96-59=37'] Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[1, 1, 59, 96], Operations: [] Exploring Operation: 96-59=37, Resulting Numbers: [1, 1, 37] Generated Node #0,0: 39:[1, 1, 37] Operation: 96-59=37 Moving to Node #0,0 Current State: 39:[1, 1, 37], Operations: ['96-59=37'] Exploring Operation: 1+1=2, Resulting Numbers: [37, 2] Generated Node #0,0,0: 39:[37, 2] Operation: 1+1=2 Moving to Node #0,0,0 Current State: 39:[37, 2], Operations: ['96-59=37', '1+1=2'] Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[1, 1, 59, 96], Operations: [] Exploring Operation: 96-59=37, Resulting Numbers: [1, 1, 37] Generated Node #0,0: 39:[1, 1, 37] Operation: 96-59=37 Moving to Node #0,0 Current State: 39:[1, 1, 37], Operations: ['96-59=37'] Exploring Operation: 1+1=2, Resulting Numbers: [37, 2] Generated Node #0,0,0: 39:[37, 2] Operation: 1+1=2 Moving to Node #0,0,0 Current State: 39:[37, 2], Operations: ['96-59=37', '1+1=2'] Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 10, 25, 6, 28 ]
42
[ "10+25=35", "35-28=7", "6*7=42" ]
Current State: 42:[10, 25, 6, 28], Operations: [] Exploring Operation: 10+25=35, Resulting Numbers: [6, 28, 35] Generated Node #2: [6, 28, 35] from Operation: 10+25=35 Current State: 42:[6, 28, 35], Operations: ['10+25=35'] Exploring Operation: 35-28=7, Resulting Numbers: [6, 7] Generated Node #3: [6, 7] from Operation: 35-28=7 Current State: 42:[6, 7], Operations: ['10+25=35', '35-28=7'] Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[10, 25, 6, 28], Operations: [] Exploring Operation: 28-10=18, Resulting Numbers: [25, 6, 18] Generated Node #0,0: 42:[25, 6, 18] Operation: 28-10=18 Exploring Operation: 28-6=22, Resulting Numbers: [10, 25, 22] Generated Node #0,1: 42:[10, 25, 22] Operation: 28-6=22 Exploring Operation: 28-25=3, Resulting Numbers: [10, 6, 3] Generated Node #0,2: 42:[10, 6, 3] Operation: 28-25=3 Exploring Operation: 10+28=38, Resulting Numbers: [25, 6, 38] Generated Node #0,3: 42:[25, 6, 38] Operation: 10+28=38 Exploring Operation: 25-10=15, Resulting Numbers: [6, 28, 15] Generated Node #0,4: 42:[6, 28, 15] Operation: 25-10=15 Moving to Node #0,2 Current State: 42:[10, 6, 3], Operations: ['28-25=3'] Exploring Operation: 10-3=7, Resulting Numbers: [6, 7] Generated Node #0,2,0: 42:[6, 7] Operation: 10-3=7 Exploring Operation: 6-3=3, Resulting Numbers: [10, 3] Generated Node #0,2,1: 42:[10, 3] Operation: 6-3=3 Exploring Operation: 10+3=13, Resulting Numbers: [6, 13] Generated Node #0,2,2: 42:[6, 13] Operation: 10+3=13 Exploring Operation: 10+6=16, Resulting Numbers: [3, 16] Generated Node #0,2,3: 42:[3, 16] Operation: 10+6=16 Exploring Operation: 10-6=4, Resulting Numbers: [3, 4] Generated Node #0,2,4: 42:[3, 4] Operation: 10-6=4 Moving to Node #0,0 Current State: 42:[25, 6, 18], Operations: ['28-10=18'] Exploring Operation: 25-18=7, Resulting Numbers: [6, 7] Generated Node #0,0,0: 42:[6, 7] Operation: 25-18=7 Exploring Operation: 25-6=19, Resulting Numbers: [18, 19] Generated Node #0,0,1: 42:[18, 19] Operation: 25-6=19 Exploring Operation: 18-6=12, Resulting Numbers: [25, 12] Generated Node #0,0,2: 42:[25, 12] Operation: 18-6=12 Exploring Operation: 25+18=43, Resulting Numbers: [6, 43] Generated Node #0,0,3: 42:[6, 43] Operation: 25+18=43 Exploring Operation: 18/6=3, Resulting Numbers: [25, 3] Generated Node #0,0,4: 42:[25, 3] Operation: 18/6=3 Moving to Node #0,1 Current State: 42:[10, 25, 22], Operations: ['28-6=22'] Exploring Operation: 22-10=12, Resulting Numbers: [25, 12] Generated Node #0,1,0: 42:[25, 12] Operation: 22-10=12 Exploring Operation: 25-10=15, Resulting Numbers: [22, 15] Generated Node #0,1,1: 42:[22, 15] Operation: 25-10=15 Exploring Operation: 25-22=3, Resulting Numbers: [10, 3] Generated Node #0,1,2: 42:[10, 3] Operation: 25-22=3 Exploring Operation: 10+25=35, Resulting Numbers: [22, 35] Generated Node #0,1,3: 42:[22, 35] Operation: 10+25=35 Exploring Operation: 25+22=47, Resulting Numbers: [10, 47] Generated Node #0,1,4: 42:[10, 47] Operation: 25+22=47 Moving to Node #0,3 Current State: 42:[25, 6, 38], Operations: ['10+28=38'] Exploring Operation: 25+6=31, Resulting Numbers: [38, 31] Generated Node #0,3,0: 42:[38, 31] Operation: 25+6=31 Exploring Operation: 6+38=44, Resulting Numbers: [25, 44] Generated Node #0,3,1: 42:[25, 44] Operation: 6+38=44 Exploring Operation: 38-6=32, Resulting Numbers: [25, 32] Generated Node #0,3,2: 42:[25, 32] Operation: 38-6=32 Exploring Operation: 38-25=13, Resulting Numbers: [6, 13] Generated Node #0,3,3: 42:[6, 13] Operation: 38-25=13 Exploring Operation: 25-6=19, Resulting Numbers: [38, 19] Generated Node #0,3,4: 42:[38, 19] Operation: 25-6=19 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 42:[6, 13], Operations: ['10+28=38', '38-25=13'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,42 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 42:[25, 44], Operations: ['10+28=38', '6+38=44'] Exploring Operation: 25+44=69, Resulting Numbers: [69] 69,42 unequal: No Solution Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 25*44=1100, Resulting Numbers: [1100] 1100,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 42:[38, 19], Operations: ['10+28=38', '25-6=19'] Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 38+19=57, Resulting Numbers: [57] 57,42 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 38*19=722, Resulting Numbers: [722] 722,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 42:[38, 31], Operations: ['10+28=38', '25+6=31'] Exploring Operation: 38+31=69, Resulting Numbers: [69] 69,42 unequal: No Solution Exploring Operation: 38*31=1178, Resulting Numbers: [1178] 1178,42 unequal: No Solution Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 42:[25, 32], Operations: ['10+28=38', '38-6=32'] Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,42 unequal: No Solution Exploring Operation: 25+32=57, Resulting Numbers: [57] 57,42 unequal: No Solution Exploring Operation: 25*32=800, Resulting Numbers: [800] 800,42 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: 42:[6, 28, 15], Operations: ['25-10=15'] Exploring Operation: 6+15=21, Resulting Numbers: [28, 21] Generated Node #0,4,0: 42:[28, 21] Operation: 6+15=21 Exploring Operation: 6+28=34, Resulting Numbers: [15, 34] Generated Node #0,4,1: 42:[15, 34] Operation: 6+28=34 Exploring Operation: 28+15=43, Resulting Numbers: [6, 43] Generated Node #0,4,2: 42:[6, 43] Operation: 28+15=43 Exploring Operation: 28-6=22, Resulting Numbers: [15, 22] Generated Node #0,4,3: 42:[15, 22] Operation: 28-6=22 Exploring Operation: 28-15=13, Resulting Numbers: [6, 13] Generated Node #0,4,4: 42:[6, 13] Operation: 28-15=13 Moving to Node #0,2,0 Current State: 42:[6, 7], Operations: ['28-25=3', '10-3=7'] Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[10, 25, 6, 28], Operations: [] Exploring Operation: 28-25=3, Resulting Numbers: [10, 6, 3] Generated Node #0,2: 42:[10, 6, 3] Operation: 28-25=3 Moving to Node #0,2 Current State: 42:[10, 6, 3], Operations: ['28-25=3'] Exploring Operation: 10-3=7, Resulting Numbers: [6, 7] Generated Node #0,2,0: 42:[6, 7] Operation: 10-3=7 Moving to Node #0,2,0 Current State: 42:[6, 7], Operations: ['28-25=3', '10-3=7'] Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
0.954861
hs_5
sum_heuristic
[ 24, 58, 60, 57 ]
69
[ "60-58=2", "24/2=12", "57+12=69" ]
Current State: 69:[24, 58, 60, 57], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [24, 57, 2] Generated Node #2: [24, 57, 2] from Operation: 60-58=2 Current State: 69:[24, 57, 2], Operations: ['60-58=2'] Exploring Operation: 24/2=12, Resulting Numbers: [57, 12] Generated Node #3: [57, 12] from Operation: 24/2=12 Current State: 69:[57, 12], Operations: ['60-58=2', '24/2=12'] Exploring Operation: 57+12=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[24, 58, 60, 57], Operations: [] Exploring Operation: 60-57=3, Resulting Numbers: [24, 58, 3] Generated Node #0,0: 69:[24, 58, 3] Operation: 60-57=3 Exploring Operation: 57-24=33, Resulting Numbers: [58, 60, 33] Generated Node #0,1: 69:[58, 60, 33] Operation: 57-24=33 Exploring Operation: 60-58=2, Resulting Numbers: [24, 57, 2] Generated Node #0,2: 69:[24, 57, 2] Operation: 60-58=2 Exploring Operation: 58-57=1, Resulting Numbers: [24, 60, 1] Generated Node #0,3: 69:[24, 60, 1] Operation: 58-57=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[24, 58, 3], Operations: ['60-57=3'] Exploring Operation: 24+58=82, Resulting Numbers: [3, 82] Generated Node #0,0,0: 69:[3, 82] Operation: 24+58=82 Exploring Operation: 58-24=34, Resulting Numbers: [3, 34] Generated Node #0,0,1: 69:[3, 34] Operation: 58-24=34 Exploring Operation: 24-3=21, Resulting Numbers: [58, 21] Generated Node #0,0,2: 69:[58, 21] Operation: 24-3=21 Exploring Operation: 58+3=61, Resulting Numbers: [24, 61] Generated Node #0,0,3: 69:[24, 61] Operation: 58+3=61 Moving to Node #0,0,3 Current State: 69:[24, 61], Operations: ['60-57=3', '58+3=61'] Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,69 unequal: No Solution Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,69 unequal: No Solution Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,69 unequal: No Solution Moving to Node #0,0,1 Current State: 69:[3, 34], Operations: ['60-57=3', '58-24=34'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,69 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,69 unequal: No Solution Moving to Node #0,0,2 Current State: 69:[58, 21], Operations: ['60-57=3', '24-3=21'] Exploring Operation: 58*21=1218, Resulting Numbers: [1218] 1218,69 unequal: No Solution Exploring Operation: 58-21=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 58+21=79, Resulting Numbers: [79] 79,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[3, 82], Operations: ['60-57=3', '24+58=82'] Exploring Operation: 3+82=85, Resulting Numbers: [85] 85,69 unequal: No Solution Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,69 unequal: No Solution Exploring Operation: 3*82=246, Resulting Numbers: [246] 246,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 69:[24, 60, 1], Operations: ['58-57=1'] Exploring Operation: 60+1=61, Resulting Numbers: [24, 61] Generated Node #0,3,0: 69:[24, 61] Operation: 60+1=61 Exploring Operation: 24-1=23, Resulting Numbers: [60, 23] Generated Node #0,3,1: 69:[60, 23] Operation: 24-1=23 Exploring Operation: 24/1=24, Resulting Numbers: [60, 24] Generated Node #0,3,2: 69:[60, 24] Operation: 24/1=24 Exploring Operation: 24*1=24, Resulting Numbers: [60, 24] Generated Node #0,3,3: 69:[60, 24] Operation: 24*1=24 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 69:[24, 61], Operations: ['58-57=1', '60+1=61'] Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,69 unequal: No Solution Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,69 unequal: No Solution No 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: 69:[60, 23], Operations: ['58-57=1', '24-1=23'] Exploring Operation: 60*23=1380, Resulting Numbers: [1380] 1380,69 unequal: No Solution Exploring Operation: 60-23=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 60+23=83, Resulting Numbers: [83] 83,69 unequal: No Solution No 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: 69:[60, 24], Operations: ['58-57=1', '24/1=24'] Exploring Operation: 60-24=36, Resulting Numbers: [36] 36,69 unequal: No Solution Exploring Operation: 60+24=84, Resulting Numbers: [84] 84,69 unequal: No Solution Exploring Operation: 60*24=1440, Resulting Numbers: [1440] 1440,69 unequal: No Solution No 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: 69:[60, 24], Operations: ['58-57=1', '24*1=24'] Exploring Operation: 60-24=36, Resulting Numbers: [36] 36,69 unequal: No Solution Exploring Operation: 60*24=1440, Resulting Numbers: [1440] 1440,69 unequal: No Solution Exploring Operation: 60+24=84, Resulting Numbers: [84] 84,69 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: 69:[24, 57, 2], Operations: ['60-58=2'] Exploring Operation: 24+57=81, Resulting Numbers: [2, 81] Generated Node #0,2,0: 69:[2, 81] Operation: 24+57=81 Exploring Operation: 57+2=59, Resulting Numbers: [24, 59] Generated Node #0,2,1: 69:[24, 59] Operation: 57+2=59 Exploring Operation: 57-24=33, Resulting Numbers: [2, 33] Generated Node #0,2,2: 69:[2, 33] Operation: 57-24=33 Exploring Operation: 24-2=22, Resulting Numbers: [57, 22] Generated Node #0,2,3: 69:[57, 22] Operation: 24-2=22 Moving to Node #0,2,1 Current State: 69:[24, 59], Operations: ['60-58=2', '57+2=59'] Exploring Operation: 24*59=1416, Resulting Numbers: [1416] 1416,69 unequal: No Solution Exploring Operation: 24+59=83, Resulting Numbers: [83] 83,69 unequal: No Solution Exploring Operation: 59-24=35, Resulting Numbers: [35] 35,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[2, 33], Operations: ['60-58=2', '57-24=33'] Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,69 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[57, 22], Operations: ['60-58=2', '24-2=22'] Exploring Operation: 57+22=79, Resulting Numbers: [79] 79,69 unequal: No Solution Exploring Operation: 57-22=35, Resulting Numbers: [35] 35,69 unequal: No Solution Exploring Operation: 57*22=1254, Resulting Numbers: [1254] 1254,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[2, 81], Operations: ['60-58=2', '24+57=81'] Exploring Operation: 2*81=162, Resulting Numbers: [162] 162,69 unequal: No Solution Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,69 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[58, 60, 33], Operations: ['57-24=33'] Exploring Operation: 60-58=2, Resulting Numbers: [33, 2] Generated Node #0,1,0: 69:[33, 2] Operation: 60-58=2 Exploring Operation: 58+33=91, Resulting Numbers: [60, 91] Generated Node #0,1,1: 69:[60, 91] Operation: 58+33=91 Exploring Operation: 58-33=25, Resulting Numbers: [60, 25] Generated Node #0,1,2: 69:[60, 25] Operation: 58-33=25 Exploring Operation: 60-33=27, Resulting Numbers: [58, 27] Generated Node #0,1,3: 69:[58, 27] Operation: 60-33=27 Moving to Node #0,1,0 Current State: 69:[33, 2], Operations: ['57-24=33', '60-58=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,69 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[60, 25], Operations: ['57-24=33', '58-33=25'] Exploring Operation: 60+25=85, Resulting Numbers: [85] 85,69 unequal: No Solution Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,69 unequal: No Solution Exploring Operation: 60*25=1500, Resulting Numbers: [1500] 1500,69 unequal: No Solution Moving to Node #0,1,3 Current State: 69:[58, 27], Operations: ['57-24=33', '60-33=27'] Exploring Operation: 58*27=1566, Resulting Numbers: [1566] 1566,69 unequal: No Solution Exploring Operation: 58-27=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 58+27=85, Resulting Numbers: [85] 85,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[60, 91], Operations: ['57-24=33', '58+33=91'] Exploring Operation: 91-60=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 60+91=151, Resulting Numbers: [151] 151,69 unequal: No Solution Exploring Operation: 60*91=5460, Resulting Numbers: [5460] 5460,69 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
[ 4, 28, 84, 42 ]
30
[ "4+28=32", "84/42=2", "32-2=30" ]
Current State: 30:[4, 28, 84, 42], Operations: [] Exploring Operation: 4+28=32, Resulting Numbers: [84, 42, 32] Generated Node #2: [84, 42, 32] from Operation: 4+28=32 Current State: 30:[84, 42, 32], Operations: ['4+28=32'] Exploring Operation: 84/42=2, Resulting Numbers: [32, 2] Generated Node #3: [32, 2] from Operation: 84/42=2 Current State: 30:[32, 2], Operations: ['4+28=32', '84/42=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[4, 28, 84, 42], Operations: [] Exploring Operation: 84/42=2, Resulting Numbers: [4, 28, 2] Generated Node #0,0: 30:[4, 28, 2] Operation: 84/42=2 Exploring Operation: 84/28=3, Resulting Numbers: [4, 42, 3] Generated Node #0,1: 30:[4, 42, 3] Operation: 84/28=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[4, 28, 2], Operations: ['84/42=2'] Exploring Operation: 28/4=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 30:[2, 7] Operation: 28/4=7 Exploring Operation: 28+2=30, Resulting Numbers: [4, 30] Generated Node #0,0,1: 30:[4, 30] Operation: 28+2=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[2, 7], Operations: ['84/42=2', '28/4=7'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[4, 30], Operations: ['84/42=2', '28+2=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[4, 42, 3], Operations: ['84/28=3'] Exploring Operation: 42-4=38, Resulting Numbers: [3, 38] Generated Node #0,1,0: 30:[3, 38] Operation: 42-4=38 Exploring Operation: 42/3=14, Resulting Numbers: [4, 14] Generated Node #0,1,1: 30:[4, 14] Operation: 42/3=14 Moving to Node #0,1,1 Current State: 30:[4, 14], Operations: ['84/28=3', '42/3=14'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,30 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[3, 38], Operations: ['84/28=3', '42-4=38'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,30 unequal: No Solution Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 19, 11, 76, 4 ]
48
[ "76/19=4", "11*4=44", "4+44=48" ]
Current State: 48:[19, 11, 76, 4], Operations: [] Exploring Operation: 76/19=4, Resulting Numbers: [11, 4, 4] Generated Node #2: [11, 4, 4] from Operation: 76/19=4 Current State: 48:[11, 4, 4], Operations: ['76/19=4'] Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,48 equal: Goal Reached Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[19, 11, 76, 4], Operations: [] Exploring Operation: 76/4=19, Resulting Numbers: [19, 11, 19] Generated Node #0,0: 48:[19, 11, 19] Operation: 76/4=19 Exploring Operation: 76/19=4, Resulting Numbers: [11, 4, 4] Generated Node #0,1: 48:[11, 4, 4] Operation: 76/19=4 Exploring Operation: 76-11=65, Resulting Numbers: [19, 4, 65] Generated Node #0,2: 48:[19, 4, 65] Operation: 76-11=65 Exploring Operation: 76-19=57, Resulting Numbers: [11, 4, 57] Generated Node #0,3: 48:[11, 4, 57] Operation: 76-19=57 Moving to Node #0,1 Current State: 48:[11, 4, 4], Operations: ['76/19=4'] Exploring Operation: 11-4=7, Resulting Numbers: [4, 7] Generated Node #0,1,0: 48:[4, 7] Operation: 11-4=7 Exploring Operation: 11+4=15, Resulting Numbers: [4, 15] Generated Node #0,1,1: 48:[4, 15] Operation: 11+4=15 Exploring Operation: 11-4=7, Resulting Numbers: [4, 7] Generated Node #0,1,2: 48:[4, 7] Operation: 11-4=7 Exploring Operation: 11+4=15, Resulting Numbers: [4, 15] Generated Node #0,1,3: 48:[4, 15] Operation: 11+4=15 Moving to Node #0,0 Current State: 48:[19, 11, 19], Operations: ['76/4=19'] Exploring Operation: 19-19=0, Resulting Numbers: [11, 0] Generated Node #0,0,0: 48:[11, 0] Operation: 19-19=0 Exploring Operation: 19-11=8, Resulting Numbers: [19, 8] Generated Node #0,0,1: 48:[19, 8] Operation: 19-11=8 Exploring Operation: 19-11=8, Resulting Numbers: [19, 8] Generated Node #0,0,2: 48:[19, 8] Operation: 19-11=8 Exploring Operation: 19/19=1, Resulting Numbers: [11, 1] Generated Node #0,0,3: 48:[11, 1] Operation: 19/19=1 Moving to Node #0,3 Current State: 48:[11, 4, 57], Operations: ['76-19=57'] Exploring Operation: 57-4=53, Resulting Numbers: [11, 53] Generated Node #0,3,0: 48:[11, 53] Operation: 57-4=53 Exploring Operation: 11+4=15, Resulting Numbers: [57, 15] Generated Node #0,3,1: 48:[57, 15] Operation: 11+4=15 Exploring Operation: 11-4=7, Resulting Numbers: [57, 7] Generated Node #0,3,2: 48:[57, 7] Operation: 11-4=7 Exploring Operation: 57-11=46, Resulting Numbers: [4, 46] Generated Node #0,3,3: 48:[4, 46] Operation: 57-11=46 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 48:[4, 46], Operations: ['76-19=57', '57-11=46'] Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,48 unequal: No Solution Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,48 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 48:[11, 53], Operations: ['76-19=57', '57-4=53'] Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 11*53=583, Resulting Numbers: [583] 583,48 unequal: No Solution Exploring Operation: 11+53=64, Resulting Numbers: [64] 64,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 48:[57, 15], Operations: ['76-19=57', '11+4=15'] Exploring Operation: 57-15=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 57*15=855, Resulting Numbers: [855] 855,48 unequal: No Solution Exploring Operation: 57+15=72, Resulting Numbers: [72] 72,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 48:[57, 7], Operations: ['76-19=57', '11-4=7'] Exploring Operation: 57+7=64, Resulting Numbers: [64] 64,48 unequal: No Solution Exploring Operation: 57*7=399, Resulting Numbers: [399] 399,48 unequal: No Solution Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,48 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: 48:[19, 4, 65], Operations: ['76-11=65'] Exploring Operation: 19-4=15, Resulting Numbers: [65, 15] Generated Node #0,2,0: 48:[65, 15] Operation: 19-4=15 Exploring Operation: 65-4=61, Resulting Numbers: [19, 61] Generated Node #0,2,1: 48:[19, 61] Operation: 65-4=61 Exploring Operation: 65-19=46, Resulting Numbers: [4, 46] Generated Node #0,2,2: 48:[4, 46] Operation: 65-19=46 Exploring Operation: 19+4=23, Resulting Numbers: [65, 23] Generated Node #0,2,3: 48:[65, 23] Operation: 19+4=23 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 48:[4, 46], Operations: ['76-11=65', '65-19=46'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,48 unequal: No Solution Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 48:[19, 61], Operations: ['76-11=65', '65-4=61'] Exploring Operation: 61-19=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 19*61=1159, Resulting Numbers: [1159] 1159,48 unequal: No Solution Exploring Operation: 19+61=80, Resulting Numbers: [80] 80,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 48:[65, 15], Operations: ['76-11=65', '19-4=15'] Exploring Operation: 65+15=80, Resulting Numbers: [80] 80,48 unequal: No Solution Exploring Operation: 65*15=975, Resulting Numbers: [975] 975,48 unequal: No Solution Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 48:[65, 23], Operations: ['76-11=65', '19+4=23'] Exploring Operation: 65+23=88, Resulting Numbers: [88] 88,48 unequal: No Solution Exploring Operation: 65*23=1495, Resulting Numbers: [1495] 1495,48 unequal: No Solution Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,48 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: 48:[4, 7], Operations: ['76/19=4', '11-4=7'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,48 unequal: No Solution Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,48 unequal: No Solution Moving to Node #0,1,2 Current State: 48:[4, 7], Operations: ['76/19=4', '11-4=7'] Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[4, 15], Operations: ['76/19=4', '11+4=15'] Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,48 unequal: No Solution Moving to Node #0,1,3 Current State: 48:[4, 15], Operations: ['76/19=4', '11+4=15'] Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,48 unequal: No Solution Moving to Node #0,0,3 Current State: 48:[11, 1], Operations: ['76/4=19', '19/19=1'] Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[19, 8], Operations: ['76/4=19', '19-11=8'] Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,48 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,48 unequal: No Solution Moving to Node #0,0,2 Current State: 48:[19, 8], Operations: ['76/4=19', '19-11=8'] Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,48 unequal: No Solution Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,48 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,48 unequal: No Solution Moving to Node #0,0,0 Current State: 48:[11, 0], Operations: ['76/4=19', '19-19=0'] Exploring Operation: 11+0=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 11*0=0, Resulting Numbers: [0] 0,48 unequal: No Solution Exploring Operation: 11-0=11, Resulting Numbers: [11] 11,48 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 53, 25, 39, 90 ]
27
[ "53+25=78", "90-39=51", "78-51=27" ]
Current State: 27:[53, 25, 39, 90], Operations: [] Exploring Operation: 53+25=78, Resulting Numbers: [39, 90, 78] Generated Node #2: [39, 90, 78] from Operation: 53+25=78 Current State: 27:[39, 90, 78], Operations: ['53+25=78'] Exploring Operation: 90-39=51, Resulting Numbers: [78, 51] Generated Node #3: [78, 51] from Operation: 90-39=51 Current State: 27:[78, 51], Operations: ['53+25=78', '90-39=51'] Exploring Operation: 78-51=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[53, 25, 39, 90], Operations: [] Exploring Operation: 90-53=37, Resulting Numbers: [25, 39, 37] Generated Node #0,0: 27:[25, 39, 37] Operation: 90-53=37 Moving to Node #0,0 Current State: 27:[25, 39, 37], Operations: ['90-53=37'] Exploring Operation: 39-37=2, Resulting Numbers: [25, 2] Generated Node #0,0,0: 27:[25, 2] Operation: 39-37=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[25, 2], Operations: ['90-53=37', '39-37=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[53, 25, 39, 90], Operations: [] Exploring Operation: 90-53=37, Resulting Numbers: [25, 39, 37] Generated Node #0,0: 27:[25, 39, 37] Operation: 90-53=37 Moving to Node #0,0 Current State: 27:[25, 39, 37], Operations: ['90-53=37'] Exploring Operation: 39-37=2, Resulting Numbers: [25, 2] Generated Node #0,0,0: 27:[25, 2] Operation: 39-37=2 Moving to Node #0,0,0 Current State: 27:[25, 2], Operations: ['90-53=37', '39-37=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 45, 12, 13, 50 ]
94
[ "45+12=57", "50-13=37", "57+37=94" ]
Current State: 94:[45, 12, 13, 50], Operations: [] Exploring Operation: 45+12=57, Resulting Numbers: [13, 50, 57] Generated Node #2: [13, 50, 57] from Operation: 45+12=57 Current State: 94:[13, 50, 57], Operations: ['45+12=57'] Exploring Operation: 50-13=37, Resulting Numbers: [57, 37] Generated Node #3: [57, 37] from Operation: 50-13=37 Current State: 94:[57, 37], Operations: ['45+12=57', '50-13=37'] Exploring Operation: 57+37=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[45, 12, 13, 50], Operations: [] Exploring Operation: 50-12=38, Resulting Numbers: [45, 13, 38] Generated Node #0,0: 94:[45, 13, 38] Operation: 50-12=38 Exploring Operation: 50-13=37, Resulting Numbers: [45, 12, 37] Generated Node #0,1: 94:[45, 12, 37] Operation: 50-13=37 Exploring Operation: 45+50=95, Resulting Numbers: [12, 13, 95] Generated Node #0,2: 94:[12, 13, 95] Operation: 45+50=95 Exploring Operation: 13-12=1, Resulting Numbers: [45, 50, 1] Generated Node #0,3: 94:[45, 50, 1] Operation: 13-12=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[45, 50, 1], Operations: ['13-12=1'] Exploring Operation: 50-45=5, Resulting Numbers: [1, 5] Generated Node #0,3,0: 94:[1, 5] Operation: 50-45=5 Exploring Operation: 50-1=49, Resulting Numbers: [45, 49] Generated Node #0,3,1: 94:[45, 49] Operation: 50-1=49 Exploring Operation: 45+50=95, Resulting Numbers: [1, 95] Generated Node #0,3,2: 94:[1, 95] Operation: 45+50=95 Exploring Operation: 45+1=46, Resulting Numbers: [50, 46] Generated Node #0,3,3: 94:[50, 46] Operation: 45+1=46 Moving to Node #0,3,2 Current State: 94:[1, 95], Operations: ['13-12=1', '45+50=95'] Exploring Operation: 1+95=96, Resulting Numbers: [96] 96,94 unequal: No Solution Exploring Operation: 95/1=95, Resulting Numbers: [95] 95,94 unequal: No Solution Exploring Operation: 95-1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[45, 12, 13, 50], Operations: [] Exploring Operation: 13-12=1, Resulting Numbers: [45, 50, 1] Generated Node #0,3: 94:[45, 50, 1] Operation: 13-12=1 Moving to Node #0,3 Current State: 94:[45, 50, 1], Operations: ['13-12=1'] Exploring Operation: 45+50=95, Resulting Numbers: [1, 95] Generated Node #0,3,2: 94:[1, 95] Operation: 45+50=95 Moving to Node #0,3,2 Current State: 94:[1, 95], Operations: ['13-12=1', '45+50=95'] Exploring Operation: 95-1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 75, 43, 67, 61 ]
38
[ "75-43=32", "67-61=6", "32+6=38" ]
Current State: 38:[75, 43, 67, 61], Operations: [] Exploring Operation: 75-43=32, Resulting Numbers: [67, 61, 32] Generated Node #2: [67, 61, 32] from Operation: 75-43=32 Current State: 38:[67, 61, 32], Operations: ['75-43=32'] Exploring Operation: 67-61=6, Resulting Numbers: [32, 6] Generated Node #3: [32, 6] from Operation: 67-61=6 Current State: 38:[32, 6], Operations: ['75-43=32', '67-61=6'] Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[75, 43, 67, 61], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [75, 43, 6] Generated Node #0,0: 38:[75, 43, 6] Operation: 67-61=6 Exploring Operation: 75-61=14, Resulting Numbers: [43, 67, 14] Generated Node #0,1: 38:[43, 67, 14] Operation: 75-61=14 Exploring Operation: 75-43=32, Resulting Numbers: [67, 61, 32] Generated Node #0,2: 38:[67, 61, 32] Operation: 75-43=32 Exploring Operation: 75-67=8, Resulting Numbers: [43, 61, 8] Generated Node #0,3: 38:[43, 61, 8] Operation: 75-67=8 Exploring Operation: 67-43=24, Resulting Numbers: [75, 61, 24] Generated Node #0,4: 38:[75, 61, 24] Operation: 67-43=24 Start Sub Search at level 1: Moving to Node #0,3 Current State: 38:[43, 61, 8], Operations: ['75-67=8'] Exploring Operation: 61+8=69, Resulting Numbers: [43, 69] Generated Node #0,3,0: 38:[43, 69] Operation: 61+8=69 Exploring Operation: 43+8=51, Resulting Numbers: [61, 51] Generated Node #0,3,1: 38:[61, 51] Operation: 43+8=51 Exploring Operation: 43-8=35, Resulting Numbers: [61, 35] Generated Node #0,3,2: 38:[61, 35] Operation: 43-8=35 Exploring Operation: 61-8=53, Resulting Numbers: [43, 53] Generated Node #0,3,3: 38:[43, 53] Operation: 61-8=53 Exploring Operation: 61-43=18, Resulting Numbers: [8, 18] Generated Node #0,3,4: 38:[8, 18] Operation: 61-43=18 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 38:[8, 18], Operations: ['75-67=8', '61-43=18'] Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,38 unequal: No Solution Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,38 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,38 unequal: No Solution No 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: 38:[43, 53], Operations: ['75-67=8', '61-8=53'] Exploring Operation: 43*53=2279, Resulting Numbers: [2279] 2279,38 unequal: No Solution Exploring Operation: 53-43=10, Resulting Numbers: [10] 10,38 unequal: No Solution Exploring Operation: 43+53=96, Resulting Numbers: [96] 96,38 unequal: No Solution No 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: 38:[61, 35], Operations: ['75-67=8', '43-8=35'] Exploring Operation: 61+35=96, Resulting Numbers: [96] 96,38 unequal: No Solution Exploring Operation: 61*35=2135, Resulting Numbers: [2135] 2135,38 unequal: No Solution Exploring Operation: 61-35=26, Resulting Numbers: [26] 26,38 unequal: No Solution No 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: 38:[43, 69], Operations: ['75-67=8', '61+8=69'] Exploring Operation: 43*69=2967, Resulting Numbers: [2967] 2967,38 unequal: No Solution Exploring Operation: 43+69=112, Resulting Numbers: [112] 112,38 unequal: No Solution Exploring Operation: 69-43=26, Resulting Numbers: [26] 26,38 unequal: No Solution No 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: 38:[61, 51], Operations: ['75-67=8', '43+8=51'] Exploring Operation: 61*51=3111, Resulting Numbers: [3111] 3111,38 unequal: No Solution Exploring Operation: 61-51=10, Resulting Numbers: [10] 10,38 unequal: No Solution Exploring Operation: 61+51=112, Resulting Numbers: [112] 112,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[43, 67, 14], Operations: ['75-61=14'] Exploring Operation: 43+14=57, Resulting Numbers: [67, 57] Generated Node #0,1,0: 38:[67, 57] Operation: 43+14=57 Exploring Operation: 67+14=81, Resulting Numbers: [43, 81] Generated Node #0,1,1: 38:[43, 81] Operation: 67+14=81 Exploring Operation: 67-43=24, Resulting Numbers: [14, 24] Generated Node #0,1,2: 38:[14, 24] Operation: 67-43=24 Exploring Operation: 67-14=53, Resulting Numbers: [43, 53] Generated Node #0,1,3: 38:[43, 53] Operation: 67-14=53 Exploring Operation: 43-14=29, Resulting Numbers: [67, 29] Generated Node #0,1,4: 38:[67, 29] Operation: 43-14=29 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 38:[14, 24], Operations: ['75-61=14', '67-43=24'] Exploring Operation: 14+24=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[75, 43, 67, 61], Operations: [] Exploring Operation: 75-61=14, Resulting Numbers: [43, 67, 14] Generated Node #0,1: 38:[43, 67, 14] Operation: 75-61=14 Moving to Node #0,1 Current State: 38:[43, 67, 14], Operations: ['75-61=14'] Exploring Operation: 67-43=24, Resulting Numbers: [14, 24] Generated Node #0,1,2: 38:[14, 24] Operation: 67-43=24 Moving to Node #0,1,2 Current State: 38:[14, 24], Operations: ['75-61=14', '67-43=24'] Exploring Operation: 14+24=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_5
sum_heuristic
[ 15, 18, 53, 71 ]
21
[ "18-15=3", "71-53=18", "3+18=21" ]
Current State: 21:[15, 18, 53, 71], Operations: [] Exploring Operation: 18-15=3, Resulting Numbers: [53, 71, 3] Generated Node #2: [53, 71, 3] from Operation: 18-15=3 Current State: 21:[53, 71, 3], Operations: ['18-15=3'] Exploring Operation: 71-53=18, Resulting Numbers: [3, 18] Generated Node #3: [3, 18] from Operation: 71-53=18 Current State: 21:[3, 18], Operations: ['18-15=3', '71-53=18'] Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[15, 18, 53, 71], Operations: [] Exploring Operation: 53-15=38, Resulting Numbers: [18, 71, 38] Generated Node #0,0: 21:[18, 71, 38] Operation: 53-15=38 Exploring Operation: 53-18=35, Resulting Numbers: [15, 71, 35] Generated Node #0,1: 21:[15, 71, 35] Operation: 53-18=35 Exploring Operation: 71-15=56, Resulting Numbers: [18, 53, 56] Generated Node #0,2: 21:[18, 53, 56] Operation: 71-15=56 Exploring Operation: 71-53=18, Resulting Numbers: [15, 18, 18] Generated Node #0,3: 21:[15, 18, 18] Operation: 71-53=18 Exploring Operation: 71-18=53, Resulting Numbers: [15, 53, 53] Generated Node #0,4: 21:[15, 53, 53] Operation: 71-18=53 Moving to Node #0,3 Current State: 21:[15, 18, 18], Operations: ['71-53=18'] Exploring Operation: 18-18=0, Resulting Numbers: [15, 0] Generated Node #0,3,0: 21:[15, 0] Operation: 18-18=0 Exploring Operation: 15+18=33, Resulting Numbers: [18, 33] Generated Node #0,3,1: 21:[18, 33] Operation: 15+18=33 Exploring Operation: 18/18=1, Resulting Numbers: [15, 1] Generated Node #0,3,2: 21:[15, 1] Operation: 18/18=1 Exploring Operation: 18-15=3, Resulting Numbers: [18, 3] Generated Node #0,3,3: 21:[18, 3] Operation: 18-15=3 Exploring Operation: 18-15=3, Resulting Numbers: [18, 3] Generated Node #0,3,4: 21:[18, 3] Operation: 18-15=3 Moving to Node #0,1 Current State: 21:[15, 71, 35], Operations: ['53-18=35'] Exploring Operation: 71-35=36, Resulting Numbers: [15, 36] Generated Node #0,1,0: 21:[15, 36] Operation: 71-35=36 Exploring Operation: 15+35=50, Resulting Numbers: [71, 50] Generated Node #0,1,1: 21:[71, 50] Operation: 15+35=50 Exploring Operation: 35-15=20, Resulting Numbers: [71, 20] Generated Node #0,1,2: 21:[71, 20] Operation: 35-15=20 Exploring Operation: 71-15=56, Resulting Numbers: [35, 56] Generated Node #0,1,3: 21:[35, 56] Operation: 71-15=56 Exploring Operation: 15+71=86, Resulting Numbers: [35, 86] Generated Node #0,1,4: 21:[35, 86] Operation: 15+71=86 Moving to Node #0,4 Current State: 21:[15, 53, 53], Operations: ['71-18=53'] Exploring Operation: 53/53=1, Resulting Numbers: [15, 1] Generated Node #0,4,0: 21:[15, 1] Operation: 53/53=1 Exploring Operation: 53-53=0, Resulting Numbers: [15, 0] Generated Node #0,4,1: 21:[15, 0] Operation: 53-53=0 Exploring Operation: 53-15=38, Resulting Numbers: [53, 38] Generated Node #0,4,2: 21:[53, 38] Operation: 53-15=38 Exploring Operation: 15+53=68, Resulting Numbers: [53, 68] Generated Node #0,4,3: 21:[53, 68] Operation: 15+53=68 Exploring Operation: 53-15=38, Resulting Numbers: [53, 38] Generated Node #0,4,4: 21:[53, 38] Operation: 53-15=38 Moving to Node #0,0 Current State: 21:[18, 71, 38], Operations: ['53-15=38'] Exploring Operation: 71-18=53, Resulting Numbers: [38, 53] Generated Node #0,0,0: 21:[38, 53] Operation: 71-18=53 Exploring Operation: 71-38=33, Resulting Numbers: [18, 33] Generated Node #0,0,1: 21:[18, 33] Operation: 71-38=33 Exploring Operation: 18+38=56, Resulting Numbers: [71, 56] Generated Node #0,0,2: 21:[71, 56] Operation: 18+38=56 Exploring Operation: 18+71=89, Resulting Numbers: [38, 89] Generated Node #0,0,3: 21:[38, 89] Operation: 18+71=89 Exploring Operation: 38-18=20, Resulting Numbers: [71, 20] Generated Node #0,0,4: 21:[71, 20] Operation: 38-18=20 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[18, 33], Operations: ['53-15=38', '71-38=33'] Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 18*33=594, Resulting Numbers: [594] 594,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[38, 53], Operations: ['53-15=38', '71-18=53'] Exploring Operation: 53-38=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 38+53=91, Resulting Numbers: [91] 91,21 unequal: No Solution Exploring Operation: 38*53=2014, Resulting Numbers: [2014] 2014,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 21:[71, 20], Operations: ['53-15=38', '38-18=20'] Exploring Operation: 71-20=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 71*20=1420, Resulting Numbers: [1420] 1420,21 unequal: No Solution Exploring Operation: 71+20=91, Resulting Numbers: [91] 91,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 21:[71, 56], Operations: ['53-15=38', '18+38=56'] Exploring Operation: 71-56=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 71+56=127, Resulting Numbers: [127] 127,21 unequal: No Solution Exploring Operation: 71*56=3976, Resulting Numbers: [3976] 3976,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 21:[38, 89], Operations: ['53-15=38', '18+71=89'] Exploring Operation: 38+89=127, Resulting Numbers: [127] 127,21 unequal: No Solution Exploring Operation: 38*89=3382, Resulting Numbers: [3382] 3382,21 unequal: No Solution Exploring Operation: 89-38=51, Resulting Numbers: [51] 51,21 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: 21:[18, 53, 56], Operations: ['71-15=56'] Exploring Operation: 56-53=3, Resulting Numbers: [18, 3] Generated Node #0,2,0: 21:[18, 3] Operation: 56-53=3 Exploring Operation: 18+53=71, Resulting Numbers: [56, 71] Generated Node #0,2,1: 21:[56, 71] Operation: 18+53=71 Exploring Operation: 18+56=74, Resulting Numbers: [53, 74] Generated Node #0,2,2: 21:[53, 74] Operation: 18+56=74 Exploring Operation: 53-18=35, Resulting Numbers: [56, 35] Generated Node #0,2,3: 21:[56, 35] Operation: 53-18=35 Exploring Operation: 56-18=38, Resulting Numbers: [53, 38] Generated Node #0,2,4: 21:[53, 38] Operation: 56-18=38 Moving to Node #0,3,3 Current State: 21:[18, 3], Operations: ['71-53=18', '18-15=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[15, 18, 53, 71], Operations: [] Exploring Operation: 71-53=18, Resulting Numbers: [15, 18, 18] Generated Node #0,3: 21:[15, 18, 18] Operation: 71-53=18 Moving to Node #0,3 Current State: 21:[15, 18, 18], Operations: ['71-53=18'] Exploring Operation: 18-15=3, Resulting Numbers: [18, 3] Generated Node #0,3,3: 21:[18, 3] Operation: 18-15=3 Moving to Node #0,3,3 Current State: 21:[18, 3], Operations: ['71-53=18', '18-15=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.956597
hs_5
mult_heuristic
[ 37, 85, 5, 22 ]
75
[ "85-37=48", "5+22=27", "48+27=75" ]
Current State: 75:[37, 85, 5, 22], Operations: [] Exploring Operation: 85-37=48, Resulting Numbers: [5, 22, 48] Generated Node #2: [5, 22, 48] from Operation: 85-37=48 Current State: 75:[5, 22, 48], Operations: ['85-37=48'] Exploring Operation: 5+22=27, Resulting Numbers: [48, 27] Generated Node #3: [48, 27] from Operation: 5+22=27 Current State: 75:[48, 27], Operations: ['85-37=48', '5+22=27'] Exploring Operation: 48+27=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[37, 85, 5, 22], Operations: [] Exploring Operation: 37-22=15, Resulting Numbers: [85, 5, 15] Generated Node #0,0: 75:[85, 5, 15] Operation: 37-22=15 Exploring Operation: 37-5=32, Resulting Numbers: [85, 22, 32] Generated Node #0,1: 75:[85, 22, 32] Operation: 37-5=32 Exploring Operation: 85/5=17, Resulting Numbers: [37, 22, 17] Generated Node #0,2: 75:[37, 22, 17] Operation: 85/5=17 Moving to Node #0,0 Current State: 75:[85, 5, 15], Operations: ['37-22=15'] Exploring Operation: 85-15=70, Resulting Numbers: [5, 70] Generated Node #0,0,0: 75:[5, 70] Operation: 85-15=70 Exploring Operation: 85/5=17, Resulting Numbers: [15, 17] Generated Node #0,0,1: 75:[15, 17] Operation: 85/5=17 Exploring Operation: 85-5=80, Resulting Numbers: [15, 80] Generated Node #0,0,2: 75:[15, 80] Operation: 85-5=80 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 75:[15, 17], Operations: ['37-22=15', '85/5=17'] Exploring Operation: 15*17=255, Resulting Numbers: [255] 255,75 unequal: No Solution Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,75 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[5, 70], Operations: ['37-22=15', '85-15=70'] Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 5+70=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[37, 85, 5, 22], Operations: [] Exploring Operation: 37-22=15, Resulting Numbers: [85, 5, 15] Generated Node #0,0: 75:[85, 5, 15] Operation: 37-22=15 Moving to Node #0,0 Current State: 75:[85, 5, 15], Operations: ['37-22=15'] Exploring Operation: 85-15=70, Resulting Numbers: [5, 70] Generated Node #0,0,0: 75:[5, 70] Operation: 85-15=70 Moving to Node #0,0,0 Current State: 75:[5, 70], Operations: ['37-22=15', '85-15=70'] Exploring Operation: 5+70=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 33, 68, 41, 91 ]
72
[ "41+91=132", "132/33=4", "68+4=72" ]
Current State: 72:[33, 68, 41, 91], Operations: [] Exploring Operation: 41+91=132, Resulting Numbers: [33, 68, 132] Generated Node #2: [33, 68, 132] from Operation: 41+91=132 Current State: 72:[33, 68, 132], Operations: ['41+91=132'] Exploring Operation: 132/33=4, Resulting Numbers: [68, 4] Generated Node #3: [68, 4] from Operation: 132/33=4 Current State: 72:[68, 4], Operations: ['41+91=132', '132/33=4'] Exploring Operation: 68+4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[33, 68, 41, 91], Operations: [] Exploring Operation: 91-68=23, Resulting Numbers: [33, 41, 23] Generated Node #0,0: 72:[33, 41, 23] Operation: 91-68=23 Exploring Operation: 41-33=8, Resulting Numbers: [68, 91, 8] Generated Node #0,1: 72:[68, 91, 8] Operation: 41-33=8 Exploring Operation: 68-33=35, Resulting Numbers: [41, 91, 35] Generated Node #0,2: 72:[41, 91, 35] Operation: 68-33=35 Exploring Operation: 91-41=50, Resulting Numbers: [33, 68, 50] Generated Node #0,3: 72:[33, 68, 50] Operation: 91-41=50 Exploring Operation: 91-33=58, Resulting Numbers: [68, 41, 58] Generated Node #0,4: 72:[68, 41, 58] Operation: 91-33=58 Moving to Node #0,0 Current State: 72:[33, 41, 23], Operations: ['91-68=23'] Exploring Operation: 33+41=74, Resulting Numbers: [23, 74] Generated Node #0,0,0: 72:[23, 74] Operation: 33+41=74 Exploring Operation: 41+23=64, Resulting Numbers: [33, 64] Generated Node #0,0,1: 72:[33, 64] Operation: 41+23=64 Exploring Operation: 33-23=10, Resulting Numbers: [41, 10] Generated Node #0,0,2: 72:[41, 10] Operation: 33-23=10 Exploring Operation: 41-23=18, Resulting Numbers: [33, 18] Generated Node #0,0,3: 72:[33, 18] Operation: 41-23=18 Exploring Operation: 41-33=8, Resulting Numbers: [23, 8] Generated Node #0,0,4: 72:[23, 8] Operation: 41-33=8 Moving to Node #0,3 Current State: 72:[33, 68, 50], Operations: ['91-41=50'] Exploring Operation: 50-33=17, Resulting Numbers: [68, 17] Generated Node #0,3,0: 72:[68, 17] Operation: 50-33=17 Exploring Operation: 68-50=18, Resulting Numbers: [33, 18] Generated Node #0,3,1: 72:[33, 18] Operation: 68-50=18 Exploring Operation: 33+68=101, Resulting Numbers: [50, 101] Generated Node #0,3,2: 72:[50, 101] Operation: 33+68=101 Exploring Operation: 33+50=83, Resulting Numbers: [68, 83] Generated Node #0,3,3: 72:[68, 83] Operation: 33+50=83 Exploring Operation: 68-33=35, Resulting Numbers: [50, 35] Generated Node #0,3,4: 72:[50, 35] Operation: 68-33=35 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 72:[33, 18], Operations: ['91-41=50', '68-50=18'] Exploring Operation: 33*18=594, Resulting Numbers: [594] 594,72 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 33+18=51, Resulting Numbers: [51] 51,72 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 #0,3,0 Current State: 72:[68, 17], Operations: ['91-41=50', '50-33=17'] Exploring Operation: 68-17=51, Resulting Numbers: [51] 51,72 unequal: No Solution Exploring Operation: 68*17=1156, Resulting Numbers: [1156] 1156,72 unequal: No Solution Exploring Operation: 68+17=85, Resulting Numbers: [85] 85,72 unequal: No Solution Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,72 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 #0,3,3 Current State: 72:[68, 83], Operations: ['91-41=50', '33+50=83'] Exploring Operation: 68+83=151, Resulting Numbers: [151] 151,72 unequal: No Solution Exploring Operation: 68*83=5644, Resulting Numbers: [5644] 5644,72 unequal: No Solution Exploring Operation: 83-68=15, Resulting Numbers: [15] 15,72 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 #0,3,4 Current State: 72:[50, 35], Operations: ['91-41=50', '68-33=35'] Exploring Operation: 50+35=85, Resulting Numbers: [85] 85,72 unequal: No Solution Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 50*35=1750, Resulting Numbers: [1750] 1750,72 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 #0,3,2 Current State: 72:[50, 101], Operations: ['91-41=50', '33+68=101'] Exploring Operation: 50+101=151, Resulting Numbers: [151] 151,72 unequal: No Solution Exploring Operation: 101-50=51, Resulting Numbers: [51] 51,72 unequal: No Solution Exploring Operation: 50*101=5050, Resulting Numbers: [5050] 5050,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 72:[68, 91, 8], Operations: ['41-33=8'] Exploring Operation: 91-8=83, Resulting Numbers: [68, 83] Generated Node #0,1,0: 72:[68, 83] Operation: 91-8=83 Exploring Operation: 68-8=60, Resulting Numbers: [91, 60] Generated Node #0,1,1: 72:[91, 60] Operation: 68-8=60 Exploring Operation: 91-68=23, Resulting Numbers: [8, 23] Generated Node #0,1,2: 72:[8, 23] Operation: 91-68=23 Exploring Operation: 68+8=76, Resulting Numbers: [91, 76] Generated Node #0,1,3: 72:[91, 76] Operation: 68+8=76 Exploring Operation: 91+8=99, Resulting Numbers: [68, 99] Generated Node #0,1,4: 72:[68, 99] Operation: 91+8=99 Moving to Node #0,4 Current State: 72:[68, 41, 58], Operations: ['91-33=58'] Exploring Operation: 68+41=109, Resulting Numbers: [58, 109] Generated Node #0,4,0: 72:[58, 109] Operation: 68+41=109 Exploring Operation: 58-41=17, Resulting Numbers: [68, 17] Generated Node #0,4,1: 72:[68, 17] Operation: 58-41=17 Exploring Operation: 68-41=27, Resulting Numbers: [58, 27] Generated Node #0,4,2: 72:[58, 27] Operation: 68-41=27 Exploring Operation: 68-58=10, Resulting Numbers: [41, 10] Generated Node #0,4,3: 72:[41, 10] Operation: 68-58=10 Exploring Operation: 41+58=99, Resulting Numbers: [68, 99] Generated Node #0,4,4: 72:[68, 99] Operation: 41+58=99 Moving to Node #0,2 Current State: 72:[41, 91, 35], Operations: ['68-33=35'] Exploring Operation: 41+35=76, Resulting Numbers: [91, 76] Generated Node #0,2,0: 72:[91, 76] Operation: 41+35=76 Exploring Operation: 41-35=6, Resulting Numbers: [91, 6] Generated Node #0,2,1: 72:[91, 6] Operation: 41-35=6 Exploring Operation: 91+35=126, Resulting Numbers: [41, 126] Generated Node #0,2,2: 72:[41, 126] Operation: 91+35=126 Exploring Operation: 91-35=56, Resulting Numbers: [41, 56] Generated Node #0,2,3: 72:[41, 56] Operation: 91-35=56 Exploring Operation: 91-41=50, Resulting Numbers: [35, 50] Generated Node #0,2,4: 72:[35, 50] Operation: 91-41=50 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 72:[35, 50], Operations: ['68-33=35', '91-41=50'] Exploring Operation: 35*50=1750, Resulting Numbers: [1750] 1750,72 unequal: No Solution Exploring Operation: 35+50=85, Resulting Numbers: [85] 85,72 unequal: No Solution Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 72:[91, 6], Operations: ['68-33=35', '41-35=6'] Exploring Operation: 91-6=85, Resulting Numbers: [85] 85,72 unequal: No Solution Exploring Operation: 91+6=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 91*6=546, Resulting Numbers: [546] 546,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 72:[41, 56], Operations: ['68-33=35', '91-35=56'] Exploring Operation: 56-41=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 41+56=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 41*56=2296, Resulting Numbers: [2296] 2296,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 72:[91, 76], Operations: ['68-33=35', '41+35=76'] Exploring Operation: 91*76=6916, Resulting Numbers: [6916] 6916,72 unequal: No Solution Exploring Operation: 91+76=167, Resulting Numbers: [167] 167,72 unequal: No Solution Exploring Operation: 91-76=15, Resulting Numbers: [15] 15,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 72:[41, 126], Operations: ['68-33=35', '91+35=126'] Exploring Operation: 41*126=5166, Resulting Numbers: [5166] 5166,72 unequal: No Solution Exploring Operation: 126-41=85, Resulting Numbers: [85] 85,72 unequal: No Solution Exploring Operation: 41+126=167, Resulting Numbers: [167] 167,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,4 Current State: 72:[23, 8], Operations: ['91-68=23', '41-33=8'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,72 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[8, 23], Operations: ['41-33=8', '91-68=23'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 8*23=184, Resulting Numbers: [184] 184,72 unequal: No Solution Exploring Operation: 8+23=31, Resulting Numbers: [31] 31,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[33, 18], Operations: ['91-68=23', '41-23=18'] Exploring Operation: 33+18=51, Resulting Numbers: [51] 51,72 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 33*18=594, Resulting Numbers: [594] 594,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[23, 74], Operations: ['91-68=23', '33+41=74'] Exploring Operation: 74-23=51, Resulting Numbers: [51] 51,72 unequal: No Solution Exploring Operation: 23+74=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 23*74=1702, Resulting Numbers: [1702] 1702,72 unequal: No Solution Moving to Node #0,4,1 Current State: 72:[68, 17], Operations: ['91-33=58', '58-41=17'] Exploring Operation: 68-17=51, Resulting Numbers: [51] 51,72 unequal: No Solution Exploring Operation: 68*17=1156, Resulting Numbers: [1156] 1156,72 unequal: No Solution Exploring Operation: 68+17=85, Resulting Numbers: [85] 85,72 unequal: No Solution Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,72 unequal: No Solution Moving to Node #0,4,3 Current State: 72:[41, 10], Operations: ['91-33=58', '68-58=10'] Exploring Operation: 41+10=51, Resulting Numbers: [51] 51,72 unequal: No Solution Exploring Operation: 41*10=410, Resulting Numbers: [410] 410,72 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[41, 10], Operations: ['91-68=23', '33-23=10'] Exploring Operation: 41+10=51, Resulting Numbers: [51] 51,72 unequal: No Solution Exploring Operation: 41*10=410, Resulting Numbers: [410] 410,72 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[33, 64], Operations: ['91-68=23', '41+23=64'] Exploring Operation: 33*64=2112, Resulting Numbers: [2112] 2112,72 unequal: No Solution Exploring Operation: 33+64=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 64-33=31, Resulting Numbers: [31] 31,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[68, 83], Operations: ['41-33=8', '91-8=83'] Exploring Operation: 68*83=5644, Resulting Numbers: [5644] 5644,72 unequal: No Solution Exploring Operation: 68+83=151, Resulting Numbers: [151] 151,72 unequal: No Solution Exploring Operation: 83-68=15, Resulting Numbers: [15] 15,72 unequal: No Solution Moving to Node #0,4,2 Current State: 72:[58, 27], Operations: ['91-33=58', '68-41=27'] Exploring Operation: 58+27=85, Resulting Numbers: [85] 85,72 unequal: No Solution Exploring Operation: 58*27=1566, Resulting Numbers: [1566] 1566,72 unequal: No Solution Exploring Operation: 58-27=31, Resulting Numbers: [31] 31,72 unequal: No Solution Moving to Node #0,1,3 Current State: 72:[91, 76], Operations: ['41-33=8', '68+8=76'] Exploring Operation: 91*76=6916, Resulting Numbers: [6916] 6916,72 unequal: No Solution Exploring Operation: 91+76=167, Resulting Numbers: [167] 167,72 unequal: No Solution Exploring Operation: 91-76=15, Resulting Numbers: [15] 15,72 unequal: No Solution Moving to Node #0,4,4 Current State: 72:[68, 99], Operations: ['91-33=58', '41+58=99'] Exploring Operation: 68*99=6732, Resulting Numbers: [6732] 6732,72 unequal: No Solution Exploring Operation: 68+99=167, Resulting Numbers: [167] 167,72 unequal: No Solution Exploring Operation: 99-68=31, Resulting Numbers: [31] 31,72 unequal: No Solution Moving to Node #0,1,4 Current State: 72:[68, 99], Operations: ['41-33=8', '91+8=99'] Exploring Operation: 99-68=31, Resulting Numbers: [31] 31,72 unequal: No Solution Exploring Operation: 68*99=6732, Resulting Numbers: [6732] 6732,72 unequal: No Solution Exploring Operation: 68+99=167, Resulting Numbers: [167] 167,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[91, 60], Operations: ['41-33=8', '68-8=60'] Exploring Operation: 91+60=151, Resulting Numbers: [151] 151,72 unequal: No Solution Exploring Operation: 91*60=5460, Resulting Numbers: [5460] 5460,72 unequal: No Solution Exploring Operation: 91-60=31, Resulting Numbers: [31] 31,72 unequal: No Solution Moving to Node #0,4,0 Current State: 72:[58, 109], Operations: ['91-33=58', '68+41=109'] Exploring Operation: 58*109=6322, Resulting Numbers: [6322] 6322,72 unequal: No Solution Exploring Operation: 58+109=167, Resulting Numbers: [167] 167,72 unequal: No Solution Exploring Operation: 109-58=51, Resulting Numbers: [51] 51,72 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 97, 3, 14, 21 ]
59
[ "97-3=94", "14+21=35", "94-35=59" ]
Current State: 59:[97, 3, 14, 21], Operations: [] Exploring Operation: 97-3=94, Resulting Numbers: [14, 21, 94] Generated Node #2: [14, 21, 94] from Operation: 97-3=94 Current State: 59:[14, 21, 94], Operations: ['97-3=94'] Exploring Operation: 14+21=35, Resulting Numbers: [94, 35] Generated Node #3: [94, 35] from Operation: 14+21=35 Current State: 59:[94, 35], Operations: ['97-3=94', '14+21=35'] Exploring Operation: 94-35=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[97, 3, 14, 21], Operations: [] Exploring Operation: 3*21=63, Resulting Numbers: [97, 14, 63] Generated Node #0,0: 59:[97, 14, 63] Operation: 3*21=63 Exploring Operation: 3*14=42, Resulting Numbers: [97, 21, 42] Generated Node #0,1: 59:[97, 21, 42] Operation: 3*14=42 Moving to Node #0,0 Current State: 59:[97, 14, 63], Operations: ['3*21=63'] Exploring Operation: 63-14=49, Resulting Numbers: [97, 49] Generated Node #0,0,0: 59:[97, 49] Operation: 63-14=49 Exploring Operation: 97-14=83, Resulting Numbers: [63, 83] Generated Node #0,0,1: 59:[63, 83] Operation: 97-14=83 Moving to Node #0,1 Current State: 59:[97, 21, 42], Operations: ['3*14=42'] Exploring Operation: 97-42=55, Resulting Numbers: [21, 55] Generated Node #0,1,0: 59:[21, 55] Operation: 97-42=55 Exploring Operation: 97-21=76, Resulting Numbers: [42, 76] Generated Node #0,1,1: 59:[42, 76] Operation: 97-21=76 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[42, 76], Operations: ['3*14=42', '97-21=76'] Exploring Operation: 76-42=34, Resulting Numbers: [34] 34,59 unequal: No Solution Exploring Operation: 42+76=118, Resulting Numbers: [118] 118,59 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 #0,1,0 Current State: 59:[21, 55], Operations: ['3*14=42', '97-42=55'] Exploring Operation: 21+55=76, Resulting Numbers: [76] 76,59 unequal: No Solution Exploring Operation: 55-21=34, Resulting Numbers: [34] 34,59 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: 59:[63, 83], Operations: ['3*21=63', '97-14=83'] Exploring Operation: 63+83=146, Resulting Numbers: [146] 146,59 unequal: No Solution Exploring Operation: 83-63=20, Resulting Numbers: [20] 20,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[97, 49], Operations: ['3*21=63', '63-14=49'] Exploring Operation: 97-49=48, Resulting Numbers: [48] 48,59 unequal: No Solution Exploring Operation: 97+49=146, Resulting Numbers: [146] 146,59 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 89, 8, 93, 85 ]
53
[ "93-89=4", "8*4=32", "85-32=53" ]
Current State: 53:[89, 8, 93, 85], Operations: [] Exploring Operation: 93-89=4, Resulting Numbers: [8, 85, 4] Generated Node #2: [8, 85, 4] from Operation: 93-89=4 Current State: 53:[8, 85, 4], Operations: ['93-89=4'] Exploring Operation: 8*4=32, Resulting Numbers: [85, 32] Generated Node #3: [85, 32] from Operation: 8*4=32 Current State: 53:[85, 32], Operations: ['93-89=4', '8*4=32'] Exploring Operation: 85-32=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[89, 8, 93, 85], Operations: [] Exploring Operation: 89+8=97, Resulting Numbers: [93, 85, 97] Generated Node #0,0: 53:[93, 85, 97] Operation: 89+8=97 Exploring Operation: 89-8=81, Resulting Numbers: [93, 85, 81] Generated Node #0,1: 53:[93, 85, 81] Operation: 89-8=81 Exploring Operation: 93-8=85, Resulting Numbers: [89, 85, 85] Generated Node #0,2: 53:[89, 85, 85] Operation: 93-8=85 Exploring Operation: 85-8=77, Resulting Numbers: [89, 93, 77] Generated Node #0,3: 53:[89, 93, 77] Operation: 85-8=77 Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[93, 85, 81], Operations: ['89-8=81'] Exploring Operation: 93-81=12, Resulting Numbers: [85, 12] Generated Node #0,1,0: 53:[85, 12] Operation: 93-81=12 Exploring Operation: 93-85=8, Resulting Numbers: [81, 8] Generated Node #0,1,1: 53:[81, 8] Operation: 93-85=8 Exploring Operation: 85-81=4, Resulting Numbers: [93, 4] Generated Node #0,1,2: 53:[93, 4] Operation: 85-81=4 Exploring Operation: 93+85=178, Resulting Numbers: [81, 178] Generated Node #0,1,3: 53:[81, 178] Operation: 93+85=178 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[85, 12], Operations: ['89-8=81', '93-81=12'] Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,53 unequal: No Solution Exploring Operation: 85*12=1020, Resulting Numbers: [1020] 1020,53 unequal: No Solution Exploring Operation: 85+12=97, Resulting Numbers: [97] 97,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[81, 8], Operations: ['89-8=81', '93-85=8'] Exploring Operation: 81*8=648, Resulting Numbers: [648] 648,53 unequal: No Solution Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,53 unequal: No Solution Exploring Operation: 81+8=89, Resulting Numbers: [89] 89,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 53:[93, 4], Operations: ['89-8=81', '85-81=4'] Exploring Operation: 93*4=372, Resulting Numbers: [372] 372,53 unequal: No Solution Exploring Operation: 93-4=89, Resulting Numbers: [89] 89,53 unequal: No Solution Exploring Operation: 93+4=97, Resulting Numbers: [97] 97,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 53:[81, 178], Operations: ['89-8=81', '93+85=178'] Exploring Operation: 178-81=97, Resulting Numbers: [97] 97,53 unequal: No Solution Exploring Operation: 81*178=14418, Resulting Numbers: [14418] 14418,53 unequal: No Solution Exploring Operation: 81+178=259, Resulting Numbers: [259] 259,53 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: 53:[89, 85, 85], Operations: ['93-8=85'] Exploring Operation: 89-85=4, Resulting Numbers: [85, 4] Generated Node #0,2,0: 53:[85, 4] Operation: 89-85=4 Exploring Operation: 85/85=1, Resulting Numbers: [89, 1] Generated Node #0,2,1: 53:[89, 1] Operation: 85/85=1 Exploring Operation: 89-85=4, Resulting Numbers: [85, 4] Generated Node #0,2,2: 53:[85, 4] Operation: 89-85=4 Exploring Operation: 85-85=0, Resulting Numbers: [89, 0] Generated Node #0,2,3: 53:[89, 0] Operation: 85-85=0 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 53:[85, 4], Operations: ['93-8=85', '89-85=4'] Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 85*4=340, Resulting Numbers: [340] 340,53 unequal: No Solution Exploring Operation: 85+4=89, Resulting Numbers: [89] 89,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 53:[85, 4], Operations: ['93-8=85', '89-85=4'] Exploring Operation: 85+4=89, Resulting Numbers: [89] 89,53 unequal: No Solution Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 85*4=340, Resulting Numbers: [340] 340,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 53:[89, 1], Operations: ['93-8=85', '85/85=1'] Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,53 unequal: No Solution Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,53 unequal: No Solution Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,53 unequal: No Solution Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 53:[89, 0], Operations: ['93-8=85', '85-85=0'] Exploring Operation: 89+0=89, Resulting Numbers: [89] 89,53 unequal: No Solution Exploring Operation: 89-0=89, Resulting Numbers: [89] 89,53 unequal: No Solution Exploring Operation: 89*0=0, Resulting Numbers: [0] 0,53 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: 53:[89, 93, 77], Operations: ['85-8=77'] Exploring Operation: 93-89=4, Resulting Numbers: [77, 4] Generated Node #0,3,0: 53:[77, 4] Operation: 93-89=4 Exploring Operation: 89-77=12, Resulting Numbers: [93, 12] Generated Node #0,3,1: 53:[93, 12] Operation: 89-77=12 Exploring Operation: 89+93=182, Resulting Numbers: [77, 182] Generated Node #0,3,2: 53:[77, 182] Operation: 89+93=182 Exploring Operation: 93-77=16, Resulting Numbers: [89, 16] Generated Node #0,3,3: 53:[89, 16] Operation: 93-77=16 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 53:[77, 4], Operations: ['85-8=77', '93-89=4'] Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,53 unequal: No Solution Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 77*4=308, Resulting Numbers: [308] 308,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 53:[89, 16], Operations: ['85-8=77', '93-77=16'] Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,53 unequal: No Solution Exploring Operation: 89*16=1424, Resulting Numbers: [1424] 1424,53 unequal: No Solution Exploring Operation: 89+16=105, Resulting Numbers: [105] 105,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 53:[93, 12], Operations: ['85-8=77', '89-77=12'] Exploring Operation: 93+12=105, Resulting Numbers: [105] 105,53 unequal: No Solution Exploring Operation: 93*12=1116, Resulting Numbers: [1116] 1116,53 unequal: No Solution Exploring Operation: 93-12=81, Resulting Numbers: [81] 81,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 53:[77, 182], Operations: ['85-8=77', '89+93=182'] Exploring Operation: 77+182=259, Resulting Numbers: [259] 259,53 unequal: No Solution Exploring Operation: 182-77=105, Resulting Numbers: [105] 105,53 unequal: No Solution Exploring Operation: 77*182=14014, Resulting Numbers: [14014] 14014,53 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: 53:[93, 85, 97], Operations: ['89+8=97'] Exploring Operation: 93+85=178, Resulting Numbers: [97, 178] Generated Node #0,0,0: 53:[97, 178] Operation: 93+85=178 Exploring Operation: 97-93=4, Resulting Numbers: [85, 4] Generated Node #0,0,1: 53:[85, 4] Operation: 97-93=4 Exploring Operation: 93-85=8, Resulting Numbers: [97, 8] Generated Node #0,0,2: 53:[97, 8] Operation: 93-85=8 Exploring Operation: 97-85=12, Resulting Numbers: [93, 12] Generated Node #0,0,3: 53:[93, 12] Operation: 97-85=12 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 53:[85, 4], Operations: ['89+8=97', '97-93=4'] Exploring Operation: 85+4=89, Resulting Numbers: [89] 89,53 unequal: No Solution Exploring Operation: 85*4=340, Resulting Numbers: [340] 340,53 unequal: No Solution Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 53:[93, 12], Operations: ['89+8=97', '97-85=12'] Exploring Operation: 93*12=1116, Resulting Numbers: [1116] 1116,53 unequal: No Solution Exploring Operation: 93-12=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 93+12=105, Resulting Numbers: [105] 105,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 53:[97, 8], Operations: ['89+8=97', '93-85=8'] Exploring Operation: 97+8=105, Resulting Numbers: [105] 105,53 unequal: No Solution Exploring Operation: 97*8=776, Resulting Numbers: [776] 776,53 unequal: No Solution Exploring Operation: 97-8=89, Resulting Numbers: [89] 89,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 53:[97, 178], Operations: ['89+8=97', '93+85=178'] Exploring Operation: 97+178=275, Resulting Numbers: [275] 275,53 unequal: No Solution Exploring Operation: 178-97=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 97*178=17266, Resulting Numbers: [17266] 17266,53 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
[ 4, 5, 40, 43 ]
12
[ "4+5=9", "43-40=3", "9+3=12" ]
Current State: 12:[4, 5, 40, 43], Operations: [] Exploring Operation: 4+5=9, Resulting Numbers: [40, 43, 9] Generated Node #2: [40, 43, 9] from Operation: 4+5=9 Current State: 12:[40, 43, 9], Operations: ['4+5=9'] Exploring Operation: 43-40=3, Resulting Numbers: [9, 3] Generated Node #3: [9, 3] from Operation: 43-40=3 Current State: 12:[9, 3], Operations: ['4+5=9', '43-40=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[4, 5, 40, 43], Operations: [] Exploring Operation: 43-40=3, Resulting Numbers: [4, 5, 3] Generated Node #0,0: 12:[4, 5, 3] Operation: 43-40=3 Exploring Operation: 40/4=10, Resulting Numbers: [5, 43, 10] Generated Node #0,1: 12:[5, 43, 10] Operation: 40/4=10 Exploring Operation: 40/5=8, Resulting Numbers: [4, 43, 8] Generated Node #0,2: 12:[4, 43, 8] Operation: 40/5=8 Exploring Operation: 40-5=35, Resulting Numbers: [4, 43, 35] Generated Node #0,3: 12:[4, 43, 35] Operation: 40-5=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[4, 5, 3], Operations: ['43-40=3'] Exploring Operation: 4+3=7, Resulting Numbers: [5, 7] Generated Node #0,0,0: 12:[5, 7] Operation: 4+3=7 Exploring Operation: 4*3=12, Resulting Numbers: [5, 12] Generated Node #0,0,1: 12:[5, 12] Operation: 4*3=12 Exploring Operation: 5-4=1, Resulting Numbers: [3, 1] Generated Node #0,0,2: 12:[3, 1] Operation: 5-4=1 Exploring Operation: 5-3=2, Resulting Numbers: [4, 2] Generated Node #0,0,3: 12:[4, 2] Operation: 5-3=2 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 12:[4, 2], Operations: ['43-40=3', '5-3=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 12:[5, 12], Operations: ['43-40=3', '4*3=12'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,12 unequal: No Solution Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,12 unequal: No Solution Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 12:[3, 1], Operations: ['43-40=3', '5-4=1'] Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[5, 7], Operations: ['43-40=3', '4+3=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[4, 5, 40, 43], Operations: [] Exploring Operation: 43-40=3, Resulting Numbers: [4, 5, 3] Generated Node #0,0: 12:[4, 5, 3] Operation: 43-40=3 Moving to Node #0,0 Current State: 12:[4, 5, 3], Operations: ['43-40=3'] Exploring Operation: 4+3=7, Resulting Numbers: [5, 7] Generated Node #0,0,0: 12:[5, 7] Operation: 4+3=7 Moving to Node #0,0,0 Current State: 12:[5, 7], Operations: ['43-40=3', '4+3=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_4
mult_heuristic
[ 47, 18, 2, 63 ]
50
[ "63-47=16", "2*16=32", "18+32=50" ]
Current State: 50:[47, 18, 2, 63], Operations: [] Exploring Operation: 63-47=16, Resulting Numbers: [18, 2, 16] Generated Node #2: [18, 2, 16] from Operation: 63-47=16 Current State: 50:[18, 2, 16], Operations: ['63-47=16'] Exploring Operation: 2*16=32, Resulting Numbers: [18, 32] Generated Node #3: [18, 32] from Operation: 2*16=32 Current State: 50:[18, 32], Operations: ['63-47=16', '2*16=32'] Exploring Operation: 18+32=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[47, 18, 2, 63], Operations: [] Exploring Operation: 63-18=45, Resulting Numbers: [47, 2, 45] Generated Node #0,0: 50:[47, 2, 45] Operation: 63-18=45 Exploring Operation: 63-47=16, Resulting Numbers: [18, 2, 16] Generated Node #0,1: 50:[18, 2, 16] Operation: 63-47=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[47, 2, 45], Operations: ['63-18=45'] Exploring Operation: 47-45=2, Resulting Numbers: [2, 2] Generated Node #0,0,0: 50:[2, 2] Operation: 47-45=2 Exploring Operation: 47+2=49, Resulting Numbers: [45, 49] Generated Node #0,0,1: 50:[45, 49] Operation: 47+2=49 Moving to Node #0,0,0 Current State: 50:[2, 2], Operations: ['63-18=45', '47-45=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[45, 49], Operations: ['63-18=45', '47+2=49'] Exploring Operation: 45+49=94, Resulting Numbers: [94] 94,50 unequal: No Solution Exploring Operation: 49-45=4, Resulting Numbers: [4] 4,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[18, 2, 16], Operations: ['63-47=16'] Exploring Operation: 18-16=2, Resulting Numbers: [2, 2] Generated Node #0,1,0: 50:[2, 2] Operation: 18-16=2 Exploring Operation: 18/2=9, Resulting Numbers: [16, 9] Generated Node #0,1,1: 50:[16, 9] Operation: 18/2=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 50:[2, 2], Operations: ['63-47=16', '18-16=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,50 unequal: No Solution No 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: 50:[16, 9], Operations: ['63-47=16', '18/2=9'] Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,50 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,50 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
[ 30, 60, 47, 90 ]
92
[ "60/30=2", "90/2=45", "47+45=92" ]
Current State: 92:[30, 60, 47, 90], Operations: [] Exploring Operation: 60/30=2, Resulting Numbers: [47, 90, 2] Generated Node #2: [47, 90, 2] from Operation: 60/30=2 Current State: 92:[47, 90, 2], Operations: ['60/30=2'] Exploring Operation: 90/2=45, Resulting Numbers: [47, 45] Generated Node #3: [47, 45] from Operation: 90/2=45 Current State: 92:[47, 45], Operations: ['60/30=2', '90/2=45'] Exploring Operation: 47+45=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[30, 60, 47, 90], Operations: [] Exploring Operation: 30+60=90, Resulting Numbers: [47, 90, 90] Generated Node #0,0: 92:[47, 90, 90] Operation: 30+60=90 Exploring Operation: 60-30=30, Resulting Numbers: [47, 90, 30] Generated Node #0,1: 92:[47, 90, 30] Operation: 60-30=30 Exploring Operation: 60/30=2, Resulting Numbers: [47, 90, 2] Generated Node #0,2: 92:[47, 90, 2] Operation: 60/30=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[47, 90, 2], Operations: ['60/30=2'] Exploring Operation: 90+2=92, Resulting Numbers: [47, 92] Generated Node #0,2,0: 92:[47, 92] Operation: 90+2=92 Exploring Operation: 90-47=43, Resulting Numbers: [2, 43] Generated Node #0,2,1: 92:[2, 43] Operation: 90-47=43 Exploring Operation: 90/2=45, Resulting Numbers: [47, 45] Generated Node #0,2,2: 92:[47, 45] Operation: 90/2=45 Moving to Node #0,2,0 Current State: 92:[47, 92], Operations: ['60/30=2', '90+2=92'] Exploring Operation: 47+92=139, Resulting Numbers: [139] 139,92 unequal: No Solution Exploring Operation: 92-47=45, Resulting Numbers: [45] 45,92 unequal: No Solution Exploring Operation: 47*92=4324, Resulting Numbers: [4324] 4324,92 unequal: No Solution Moving to Node #0,2,2 Current State: 92:[47, 45], Operations: ['60/30=2', '90/2=45'] Exploring Operation: 47+45=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[30, 60, 47, 90], Operations: [] Exploring Operation: 60/30=2, Resulting Numbers: [47, 90, 2] Generated Node #0,2: 92:[47, 90, 2] Operation: 60/30=2 Moving to Node #0,2 Current State: 92:[47, 90, 2], Operations: ['60/30=2'] Exploring Operation: 90/2=45, Resulting Numbers: [47, 45] Generated Node #0,2,2: 92:[47, 45] Operation: 90/2=45 Moving to Node #0,2,2 Current State: 92:[47, 45], Operations: ['60/30=2', '90/2=45'] Exploring Operation: 47+45=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 6, 83, 10, 11 ]
14
[ "83-10=73", "11+73=84", "84/6=14" ]
Current State: 14:[6, 83, 10, 11], Operations: [] Exploring Operation: 83-10=73, Resulting Numbers: [6, 11, 73] Generated Node #2: [6, 11, 73] from Operation: 83-10=73 Current State: 14:[6, 11, 73], Operations: ['83-10=73'] Exploring Operation: 11+73=84, Resulting Numbers: [6, 84] Generated Node #3: [6, 84] from Operation: 11+73=84 Current State: 14:[6, 84], Operations: ['83-10=73', '11+73=84'] Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[6, 83, 10, 11], Operations: [] Exploring Operation: 83-6=77, Resulting Numbers: [10, 11, 77] Generated Node #0,0: 14:[10, 11, 77] Operation: 83-6=77 Exploring Operation: 83-11=72, Resulting Numbers: [6, 10, 72] Generated Node #0,1: 14:[6, 10, 72] Operation: 83-11=72 Exploring Operation: 6+10=16, Resulting Numbers: [83, 11, 16] Generated Node #0,2: 14:[83, 11, 16] Operation: 6+10=16 Exploring Operation: 11-10=1, Resulting Numbers: [6, 83, 1] Generated Node #0,3: 14:[6, 83, 1] Operation: 11-10=1 Exploring Operation: 83-10=73, Resulting Numbers: [6, 11, 73] Generated Node #0,4: 14:[6, 11, 73] Operation: 83-10=73 Moving to Node #0,1 Current State: 14:[6, 10, 72], Operations: ['83-11=72'] Exploring Operation: 72-6=66, Resulting Numbers: [10, 66] Generated Node #0,1,0: 14:[10, 66] Operation: 72-6=66 Exploring Operation: 10-6=4, Resulting Numbers: [72, 4] Generated Node #0,1,1: 14:[72, 4] Operation: 10-6=4 Exploring Operation: 6+10=16, Resulting Numbers: [72, 16] Generated Node #0,1,2: 14:[72, 16] Operation: 6+10=16 Exploring Operation: 72/6=12, Resulting Numbers: [10, 12] Generated Node #0,1,3: 14:[10, 12] Operation: 72/6=12 Exploring Operation: 72-10=62, Resulting Numbers: [6, 62] Generated Node #0,1,4: 14:[6, 62] Operation: 72-10=62 Moving to Node #0,4 Current State: 14:[6, 11, 73], Operations: ['83-10=73'] Exploring Operation: 73-11=62, Resulting Numbers: [6, 62] Generated Node #0,4,0: 14:[6, 62] Operation: 73-11=62 Exploring Operation: 11-6=5, Resulting Numbers: [73, 5] Generated Node #0,4,1: 14:[73, 5] Operation: 11-6=5 Exploring Operation: 6+73=79, Resulting Numbers: [11, 79] Generated Node #0,4,2: 14:[11, 79] Operation: 6+73=79 Exploring Operation: 6+11=17, Resulting Numbers: [73, 17] Generated Node #0,4,3: 14:[73, 17] Operation: 6+11=17 Exploring Operation: 73-6=67, Resulting Numbers: [11, 67] Generated Node #0,4,4: 14:[11, 67] Operation: 73-6=67 Moving to Node #0,0 Current State: 14:[10, 11, 77], Operations: ['83-6=77'] Exploring Operation: 77-10=67, Resulting Numbers: [11, 67] Generated Node #0,0,0: 14:[11, 67] Operation: 77-10=67 Exploring Operation: 10+11=21, Resulting Numbers: [77, 21] Generated Node #0,0,1: 14:[77, 21] Operation: 10+11=21 Exploring Operation: 77/11=7, Resulting Numbers: [10, 7] Generated Node #0,0,2: 14:[10, 7] Operation: 77/11=7 Exploring Operation: 77-11=66, Resulting Numbers: [10, 66] Generated Node #0,0,3: 14:[10, 66] Operation: 77-11=66 Exploring Operation: 11-10=1, Resulting Numbers: [77, 1] Generated Node #0,0,4: 14:[77, 1] Operation: 11-10=1 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 14:[10, 7], Operations: ['83-6=77', '77/11=7'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,14 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 14:[10, 66], Operations: ['83-6=77', '77-11=66'] Exploring Operation: 66-10=56, Resulting Numbers: [56] 56,14 unequal: No Solution Exploring Operation: 10*66=660, Resulting Numbers: [660] 660,14 unequal: No Solution Exploring Operation: 10+66=76, Resulting Numbers: [76] 76,14 unequal: No Solution No 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: 14:[11, 67], Operations: ['83-6=77', '77-10=67'] Exploring Operation: 11*67=737, Resulting Numbers: [737] 737,14 unequal: No Solution Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,14 unequal: No Solution Exploring Operation: 11+67=78, Resulting Numbers: [78] 78,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 14:[77, 1], Operations: ['83-6=77', '11-10=1'] Exploring Operation: 77/1=77, Resulting Numbers: [77] 77,14 unequal: No Solution Exploring Operation: 77*1=77, Resulting Numbers: [77] 77,14 unequal: No Solution Exploring Operation: 77+1=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,14 unequal: No Solution No 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: 14:[77, 21], Operations: ['83-6=77', '10+11=21'] Exploring Operation: 77+21=98, Resulting Numbers: [98] 98,14 unequal: No Solution Exploring Operation: 77*21=1617, Resulting Numbers: [1617] 1617,14 unequal: No Solution Exploring Operation: 77-21=56, Resulting Numbers: [56] 56,14 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: 14:[6, 83, 1], Operations: ['11-10=1'] Exploring Operation: 83-1=82, Resulting Numbers: [6, 82] Generated Node #0,3,0: 14:[6, 82] Operation: 83-1=82 Exploring Operation: 83-6=77, Resulting Numbers: [1, 77] Generated Node #0,3,1: 14:[1, 77] Operation: 83-6=77 Exploring Operation: 6+1=7, Resulting Numbers: [83, 7] Generated Node #0,3,2: 14:[83, 7] Operation: 6+1=7 Exploring Operation: 6*1=6, Resulting Numbers: [83, 6] Generated Node #0,3,3: 14:[83, 6] Operation: 6*1=6 Exploring Operation: 6/1=6, Resulting Numbers: [83, 6] Generated Node #0,3,4: 14:[83, 6] Operation: 6/1=6 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 14:[1, 77], Operations: ['11-10=1', '83-6=77'] Exploring Operation: 1*77=77, Resulting Numbers: [77] 77,14 unequal: No Solution Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 77/1=77, Resulting Numbers: [77] 77,14 unequal: No Solution Exploring Operation: 1+77=78, Resulting Numbers: [78] 78,14 unequal: No Solution No 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: 14:[6, 82], Operations: ['11-10=1', '83-1=82'] Exploring Operation: 6*82=492, Resulting Numbers: [492] 492,14 unequal: No Solution Exploring Operation: 82-6=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 6+82=88, Resulting Numbers: [88] 88,14 unequal: No Solution No 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: 14:[83, 7], Operations: ['11-10=1', '6+1=7'] Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 83*7=581, Resulting Numbers: [581] 581,14 unequal: No Solution Exploring Operation: 83+7=90, Resulting Numbers: [90] 90,14 unequal: No Solution No 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: 14:[83, 6], Operations: ['11-10=1', '6*1=6'] Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,14 unequal: No Solution Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,14 unequal: No Solution Exploring Operation: 83*6=498, Resulting Numbers: [498] 498,14 unequal: No Solution No 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: 14:[83, 6], Operations: ['11-10=1', '6/1=6'] Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,14 unequal: No Solution Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,14 unequal: No Solution Exploring Operation: 83*6=498, Resulting Numbers: [498] 498,14 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: 14:[83, 11, 16], Operations: ['6+10=16'] Exploring Operation: 83-11=72, Resulting Numbers: [16, 72] Generated Node #0,2,0: 14:[16, 72] Operation: 83-11=72 Exploring Operation: 83-16=67, Resulting Numbers: [11, 67] Generated Node #0,2,1: 14:[11, 67] Operation: 83-16=67 Exploring Operation: 11+16=27, Resulting Numbers: [83, 27] Generated Node #0,2,2: 14:[83, 27] Operation: 11+16=27 Exploring Operation: 83+11=94, Resulting Numbers: [16, 94] Generated Node #0,2,3: 14:[16, 94] Operation: 83+11=94 Exploring Operation: 16-11=5, Resulting Numbers: [83, 5] Generated Node #0,2,4: 14:[83, 5] Operation: 16-11=5 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 14:[11, 67], Operations: ['6+10=16', '83-16=67'] Exploring Operation: 11*67=737, Resulting Numbers: [737] 737,14 unequal: No Solution Exploring Operation: 11+67=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,14 unequal: No Solution No 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: 14:[16, 72], Operations: ['6+10=16', '83-11=72'] Exploring Operation: 16+72=88, Resulting Numbers: [88] 88,14 unequal: No Solution Exploring Operation: 16*72=1152, Resulting Numbers: [1152] 1152,14 unequal: No Solution Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,14 unequal: No Solution No 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: 14:[83, 5], Operations: ['6+10=16', '16-11=5'] Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 83*5=415, Resulting Numbers: [415] 415,14 unequal: No Solution Exploring Operation: 83+5=88, Resulting Numbers: [88] 88,14 unequal: No Solution No 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: 14:[83, 27], Operations: ['6+10=16', '11+16=27'] Exploring Operation: 83-27=56, Resulting Numbers: [56] 56,14 unequal: No Solution Exploring Operation: 83*27=2241, Resulting Numbers: [2241] 2241,14 unequal: No Solution Exploring Operation: 83+27=110, Resulting Numbers: [110] 110,14 unequal: No Solution No 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: 14:[16, 94], Operations: ['6+10=16', '83+11=94'] Exploring Operation: 94-16=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 16+94=110, Resulting Numbers: [110] 110,14 unequal: No Solution Exploring Operation: 16*94=1504, Resulting Numbers: [1504] 1504,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 14:[10, 12], Operations: ['83-11=72', '72/6=12'] Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 10*12=120, Resulting Numbers: [120] 120,14 unequal: No Solution Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,14 unequal: No Solution Moving to Node #0,4,0 Current State: 14:[6, 62], Operations: ['83-10=73', '73-11=62'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,14 unequal: No Solution Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,14 unequal: No Solution Exploring Operation: 6*62=372, Resulting Numbers: [372] 372,14 unequal: No Solution Moving to Node #0,1,4 Current State: 14:[6, 62], Operations: ['83-11=72', '72-10=62'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,14 unequal: No Solution Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,14 unequal: No Solution Exploring Operation: 6*62=372, Resulting Numbers: [372] 372,14 unequal: No Solution Moving to Node #0,1,0 Current State: 14:[10, 66], Operations: ['83-11=72', '72-6=66'] Exploring Operation: 10+66=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 66-10=56, Resulting Numbers: [56] 56,14 unequal: No Solution Exploring Operation: 10*66=660, Resulting Numbers: [660] 660,14 unequal: No Solution Moving to Node #0,4,4 Current State: 14:[11, 67], Operations: ['83-10=73', '73-6=67'] Exploring Operation: 11+67=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 11*67=737, Resulting Numbers: [737] 737,14 unequal: No Solution Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,14 unequal: No Solution Moving to Node #0,1,2 Current State: 14:[72, 16], Operations: ['83-11=72', '6+10=16'] Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,14 unequal: No Solution Exploring Operation: 72*16=1152, Resulting Numbers: [1152] 1152,14 unequal: No Solution Exploring Operation: 72+16=88, Resulting Numbers: [88] 88,14 unequal: No Solution Moving to Node #0,1,1 Current State: 14:[72, 4], Operations: ['83-11=72', '10-6=4'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,14 unequal: No Solution Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 72*4=288, Resulting Numbers: [288] 288,14 unequal: No Solution Moving to Node #0,4,1 Current State: 14:[73, 5], Operations: ['83-10=73', '11-6=5'] Exploring Operation: 73*5=365, Resulting Numbers: [365] 365,14 unequal: No Solution Exploring Operation: 73+5=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 73-5=68, Resulting Numbers: [68] 68,14 unequal: No Solution Moving to Node #0,4,3 Current State: 14:[73, 17], Operations: ['83-10=73', '6+11=17'] Exploring Operation: 73*17=1241, Resulting Numbers: [1241] 1241,14 unequal: No Solution Exploring Operation: 73+17=90, Resulting Numbers: [90] 90,14 unequal: No Solution Exploring Operation: 73-17=56, Resulting Numbers: [56] 56,14 unequal: No Solution Moving to Node #0,4,2 Current State: 14:[11, 79], Operations: ['83-10=73', '6+73=79'] Exploring Operation: 11+79=90, Resulting Numbers: [90] 90,14 unequal: No Solution Exploring Operation: 79-11=68, Resulting Numbers: [68] 68,14 unequal: No Solution Exploring Operation: 11*79=869, Resulting Numbers: [869] 869,14 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 14, 6, 25, 70 ]
95
[ "70/14=5", "25-6=19", "5*19=95" ]
Current State: 95:[14, 6, 25, 70], Operations: [] Exploring Operation: 70/14=5, Resulting Numbers: [6, 25, 5] Generated Node #2: [6, 25, 5] from Operation: 70/14=5 Current State: 95:[6, 25, 5], Operations: ['70/14=5'] Exploring Operation: 25-6=19, Resulting Numbers: [5, 19] Generated Node #3: [5, 19] from Operation: 25-6=19 Current State: 95:[5, 19], Operations: ['70/14=5', '25-6=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[14, 6, 25, 70], Operations: [] Exploring Operation: 70/14=5, Resulting Numbers: [6, 25, 5] Generated Node #0,0: 95:[6, 25, 5] Operation: 70/14=5 Exploring Operation: 25+70=95, Resulting Numbers: [14, 6, 95] Generated Node #0,1: 95:[14, 6, 95] Operation: 25+70=95 Moving to Node #0,1 Current State: 95:[14, 6, 95], Operations: ['25+70=95'] Exploring Operation: 14+6=20, Resulting Numbers: [95, 20] Generated Node #0,1,0: 95:[95, 20] Operation: 14+6=20 Exploring Operation: 14-6=8, Resulting Numbers: [95, 8] Generated Node #0,1,1: 95:[95, 8] Operation: 14-6=8 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 95:[95, 20], Operations: ['25+70=95', '14+6=20'] Exploring Operation: 95+20=115, Resulting Numbers: [115] 115,95 unequal: No Solution Exploring Operation: 95-20=75, Resulting Numbers: [75] 75,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 95:[95, 8], Operations: ['25+70=95', '14-6=8'] Exploring Operation: 95+8=103, Resulting Numbers: [103] 103,95 unequal: No Solution Exploring Operation: 95-8=87, Resulting Numbers: [87] 87,95 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: 95:[6, 25, 5], Operations: ['70/14=5'] Exploring Operation: 25-6=19, Resulting Numbers: [5, 19] Generated Node #0,0,0: 95:[5, 19] Operation: 25-6=19 Exploring Operation: 25/5=5, Resulting Numbers: [6, 5] Generated Node #0,0,1: 95:[6, 5] Operation: 25/5=5 Moving to Node #0,0,0 Current State: 95:[5, 19], Operations: ['70/14=5', '25-6=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[14, 6, 25, 70], Operations: [] Exploring Operation: 70/14=5, Resulting Numbers: [6, 25, 5] Generated Node #0,0: 95:[6, 25, 5] Operation: 70/14=5 Moving to Node #0,0 Current State: 95:[6, 25, 5], Operations: ['70/14=5'] Exploring Operation: 25-6=19, Resulting Numbers: [5, 19] Generated Node #0,0,0: 95:[5, 19] Operation: 25-6=19 Moving to Node #0,0,0 Current State: 95:[5, 19], Operations: ['70/14=5', '25-6=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 54, 74, 39, 74 ]
15
[ "54+74=128", "39+74=113", "128-113=15" ]
Current State: 15:[54, 74, 39, 74], Operations: [] Exploring Operation: 54+74=128, Resulting Numbers: [39, 128] Generated Node #2: [39, 128] from Operation: 54+74=128 Current State: 15:[39, 128], Operations: ['54+74=128'] Exploring Operation: 39+74=113, Resulting Numbers: [128, 113] Generated Node #3: [128, 113] from Operation: 39+74=113 Current State: 15:[128, 113], Operations: ['54+74=128', '39+74=113'] Exploring Operation: 128-113=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[54, 74, 39, 74], Operations: [] Exploring Operation: 74-54=20, Resulting Numbers: [39, 74, 20] Generated Node #0,0: 15:[39, 74, 20] Operation: 74-54=20 Exploring Operation: 74/74=1, Resulting Numbers: [54, 39, 1] Generated Node #0,1: 15:[54, 39, 1] Operation: 74/74=1 Exploring Operation: 74-54=20, Resulting Numbers: [74, 39, 20] Generated Node #0,2: 15:[74, 39, 20] Operation: 74-54=20 Exploring Operation: 74-74=0, Resulting Numbers: [54, 39, 0] Generated Node #0,3: 15:[54, 39, 0] Operation: 74-74=0 Moving to Node #0,1 Current State: 15:[54, 39, 1], Operations: ['74/74=1'] Exploring Operation: 54-39=15, Resulting Numbers: [1, 15] Generated Node #0,1,0: 15:[1, 15] Operation: 54-39=15 Exploring Operation: 39-1=38, Resulting Numbers: [54, 38] Generated Node #0,1,1: 15:[54, 38] Operation: 39-1=38 Exploring Operation: 54-1=53, Resulting Numbers: [39, 53] Generated Node #0,1,2: 15:[39, 53] Operation: 54-1=53 Exploring Operation: 54*1=54, Resulting Numbers: [39, 54] Generated Node #0,1,3: 15:[39, 54] Operation: 54*1=54 Moving to Node #0,3 Current State: 15:[54, 39, 0], Operations: ['74-74=0'] Exploring Operation: 54-39=15, Resulting Numbers: [0, 15] Generated Node #0,3,0: 15:[0, 15] Operation: 54-39=15 Exploring Operation: 54+0=54, Resulting Numbers: [39, 54] Generated Node #0,3,1: 15:[39, 54] Operation: 54+0=54 Exploring Operation: 54*0=0, Resulting Numbers: [39, 0] Generated Node #0,3,2: 15:[39, 0] Operation: 54*0=0 Exploring Operation: 39*0=0, Resulting Numbers: [54, 0] Generated Node #0,3,3: 15:[54, 0] Operation: 39*0=0 Moving to Node #0,2 Current State: 15:[74, 39, 20], Operations: ['74-54=20'] Exploring Operation: 74-20=54, Resulting Numbers: [39, 54] Generated Node #0,2,0: 15:[39, 54] Operation: 74-20=54 Exploring Operation: 74+39=113, Resulting Numbers: [20, 113] Generated Node #0,2,1: 15:[20, 113] Operation: 74+39=113 Exploring Operation: 74-39=35, Resulting Numbers: [20, 35] Generated Node #0,2,2: 15:[20, 35] Operation: 74-39=35 Exploring Operation: 39-20=19, Resulting Numbers: [74, 19] Generated Node #0,2,3: 15:[74, 19] Operation: 39-20=19 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 15:[20, 35], Operations: ['74-54=20', '74-39=35'] Exploring Operation: 20+35=55, Resulting Numbers: [55] 55,15 unequal: No Solution Exploring Operation: 20*35=700, Resulting Numbers: [700] 700,15 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[54, 74, 39, 74], Operations: [] Exploring Operation: 74-54=20, Resulting Numbers: [74, 39, 20] Generated Node #0,2: 15:[74, 39, 20] Operation: 74-54=20 Moving to Node #0,2 Current State: 15:[74, 39, 20], Operations: ['74-54=20'] Exploring Operation: 74-39=35, Resulting Numbers: [20, 35] Generated Node #0,2,2: 15:[20, 35] Operation: 74-39=35 Moving to Node #0,2,2 Current State: 15:[20, 35], Operations: ['74-54=20', '74-39=35'] Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
sum_heuristic
[ 28, 58, 70, 44 ]
33
[ "58-44=14", "70/14=5", "28+5=33" ]
Current State: 33:[28, 58, 70, 44], Operations: [] Exploring Operation: 58-44=14, Resulting Numbers: [28, 70, 14] Generated Node #2: [28, 70, 14] from Operation: 58-44=14 Current State: 33:[28, 70, 14], Operations: ['58-44=14'] Exploring Operation: 70/14=5, Resulting Numbers: [28, 5] Generated Node #3: [28, 5] from Operation: 70/14=5 Current State: 33:[28, 5], Operations: ['58-44=14', '70/14=5'] Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[28, 58, 70, 44], Operations: [] Exploring Operation: 70-44=26, Resulting Numbers: [28, 58, 26] Generated Node #0,0: 33:[28, 58, 26] Operation: 70-44=26 Exploring Operation: 70-58=12, Resulting Numbers: [28, 44, 12] Generated Node #0,1: 33:[28, 44, 12] Operation: 70-58=12 Moving to Node #0,1 Current State: 33:[28, 44, 12], Operations: ['70-58=12'] Exploring Operation: 44-28=16, Resulting Numbers: [12, 16] Generated Node #0,1,0: 33:[12, 16] Operation: 44-28=16 Exploring Operation: 44-12=32, Resulting Numbers: [28, 32] Generated Node #0,1,1: 33:[28, 32] Operation: 44-12=32 Moving to Node #0,0 Current State: 33:[28, 58, 26], Operations: ['70-44=26'] Exploring Operation: 58-28=30, Resulting Numbers: [26, 30] Generated Node #0,0,0: 33:[26, 30] Operation: 58-28=30 Exploring Operation: 58-26=32, Resulting Numbers: [28, 32] Generated Node #0,0,1: 33:[28, 32] Operation: 58-26=32 Moving to Node #0,1,0 Current State: 33:[12, 16], Operations: ['70-58=12', '44-28=16'] Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,33 unequal: No Solution Exploring Operation: 12+16=28, Resulting Numbers: [28] 28,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[28, 32], Operations: ['70-44=26', '58-26=32'] Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,33 unequal: No Solution Exploring Operation: 28+32=60, Resulting Numbers: [60] 60,33 unequal: No Solution Moving to Node #0,1,1 Current State: 33:[28, 32], Operations: ['70-58=12', '44-12=32'] Exploring Operation: 28+32=60, Resulting Numbers: [60] 60,33 unequal: No Solution Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,33 unequal: No Solution Moving to Node #0,0,0 Current State: 33:[26, 30], Operations: ['70-44=26', '58-28=30'] Exploring Operation: 30-26=4, Resulting Numbers: [4] 4,33 unequal: No Solution Exploring Operation: 26+30=56, Resulting Numbers: [56] 56,33 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 14, 98, 9, 94 ]
50
[ "98-94=4", "9*4=36", "14+36=50" ]
Current State: 50:[14, 98, 9, 94], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [14, 9, 4] Generated Node #2: [14, 9, 4] from Operation: 98-94=4 Current State: 50:[14, 9, 4], Operations: ['98-94=4'] Exploring Operation: 9*4=36, Resulting Numbers: [14, 36] Generated Node #3: [14, 36] from Operation: 9*4=36 Current State: 50:[14, 36], Operations: ['98-94=4', '9*4=36'] Exploring Operation: 14+36=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[14, 98, 9, 94], Operations: [] Exploring Operation: 98-9=89, Resulting Numbers: [14, 94, 89] Generated Node #0,0: 50:[14, 94, 89] Operation: 98-9=89 Exploring Operation: 98-14=84, Resulting Numbers: [9, 94, 84] Generated Node #0,1: 50:[9, 94, 84] Operation: 98-14=84 Exploring Operation: 98/14=7, Resulting Numbers: [9, 94, 7] Generated Node #0,2: 50:[9, 94, 7] Operation: 98/14=7 Exploring Operation: 98-94=4, Resulting Numbers: [14, 9, 4] Generated Node #0,3: 50:[14, 9, 4] Operation: 98-94=4 Exploring Operation: 94-14=80, Resulting Numbers: [98, 9, 80] Generated Node #0,4: 50:[98, 9, 80] Operation: 94-14=80 Moving to Node #0,3 Current State: 50:[14, 9, 4], Operations: ['98-94=4'] Exploring Operation: 14-4=10, Resulting Numbers: [9, 10] Generated Node #0,3,0: 50:[9, 10] Operation: 14-4=10 Exploring Operation: 14+9=23, Resulting Numbers: [4, 23] Generated Node #0,3,1: 50:[4, 23] Operation: 14+9=23 Exploring Operation: 14-9=5, Resulting Numbers: [4, 5] Generated Node #0,3,2: 50:[4, 5] Operation: 14-9=5 Exploring Operation: 14*4=56, Resulting Numbers: [9, 56] Generated Node #0,3,3: 50:[9, 56] Operation: 14*4=56 Exploring Operation: 9-4=5, Resulting Numbers: [14, 5] Generated Node #0,3,4: 50:[14, 5] Operation: 9-4=5 Moving to Node #0,2 Current State: 50:[9, 94, 7], Operations: ['98/14=7'] Exploring Operation: 9+7=16, Resulting Numbers: [94, 16] Generated Node #0,2,0: 50:[94, 16] Operation: 9+7=16 Exploring Operation: 94+7=101, Resulting Numbers: [9, 101] Generated Node #0,2,1: 50:[9, 101] Operation: 94+7=101 Exploring Operation: 94-7=87, Resulting Numbers: [9, 87] Generated Node #0,2,2: 50:[9, 87] Operation: 94-7=87 Exploring Operation: 94-9=85, Resulting Numbers: [7, 85] Generated Node #0,2,3: 50:[7, 85] Operation: 94-9=85 Exploring Operation: 9-7=2, Resulting Numbers: [94, 2] Generated Node #0,2,4: 50:[94, 2] Operation: 9-7=2 Moving to Node #0,1 Current State: 50:[9, 94, 84], Operations: ['98-14=84'] Exploring Operation: 9+84=93, Resulting Numbers: [94, 93] Generated Node #0,1,0: 50:[94, 93] Operation: 9+84=93 Exploring Operation: 94-9=85, Resulting Numbers: [84, 85] Generated Node #0,1,1: 50:[84, 85] Operation: 94-9=85 Exploring Operation: 94-84=10, Resulting Numbers: [9, 10] Generated Node #0,1,2: 50:[9, 10] Operation: 94-84=10 Exploring Operation: 9+94=103, Resulting Numbers: [84, 103] Generated Node #0,1,3: 50:[84, 103] Operation: 9+94=103 Exploring Operation: 84-9=75, Resulting Numbers: [94, 75] Generated Node #0,1,4: 50:[94, 75] Operation: 84-9=75 Moving to Node #0,4 Current State: 50:[98, 9, 80], Operations: ['94-14=80'] Exploring Operation: 98-80=18, Resulting Numbers: [9, 18] Generated Node #0,4,0: 50:[9, 18] Operation: 98-80=18 Exploring Operation: 80-9=71, Resulting Numbers: [98, 71] Generated Node #0,4,1: 50:[98, 71] Operation: 80-9=71 Exploring Operation: 98+9=107, Resulting Numbers: [80, 107] Generated Node #0,4,2: 50:[80, 107] Operation: 98+9=107 Exploring Operation: 9+80=89, Resulting Numbers: [98, 89] Generated Node #0,4,3: 50:[98, 89] Operation: 9+80=89 Exploring Operation: 98-9=89, Resulting Numbers: [80, 89] Generated Node #0,4,4: 50:[80, 89] Operation: 98-9=89 Moving to Node #0,0 Current State: 50:[14, 94, 89], Operations: ['98-9=89'] Exploring Operation: 14+94=108, Resulting Numbers: [89, 108] Generated Node #0,0,0: 50:[89, 108] Operation: 14+94=108 Exploring Operation: 89-14=75, Resulting Numbers: [94, 75] Generated Node #0,0,1: 50:[94, 75] Operation: 89-14=75 Exploring Operation: 94-89=5, Resulting Numbers: [14, 5] Generated Node #0,0,2: 50:[14, 5] Operation: 94-89=5 Exploring Operation: 14+89=103, Resulting Numbers: [94, 103] Generated Node #0,0,3: 50:[94, 103] Operation: 14+89=103 Exploring Operation: 94-14=80, Resulting Numbers: [89, 80] Generated Node #0,0,4: 50:[89, 80] Operation: 94-14=80 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 50:[14, 5], Operations: ['98-9=89', '94-89=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,50 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,50 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 50:[94, 75], Operations: ['98-9=89', '89-14=75'] Exploring Operation: 94*75=7050, Resulting Numbers: [7050] 7050,50 unequal: No Solution Exploring Operation: 94+75=169, Resulting Numbers: [169] 169,50 unequal: No Solution Exploring Operation: 94-75=19, Resulting Numbers: [19] 19,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 50:[89, 80], Operations: ['98-9=89', '94-14=80'] Exploring Operation: 89-80=9, Resulting Numbers: [9] 9,50 unequal: No Solution Exploring Operation: 89+80=169, Resulting Numbers: [169] 169,50 unequal: No Solution Exploring Operation: 89*80=7120, Resulting Numbers: [7120] 7120,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[89, 108], Operations: ['98-9=89', '14+94=108'] Exploring Operation: 89*108=9612, Resulting Numbers: [9612] 9612,50 unequal: No Solution Exploring Operation: 108-89=19, Resulting Numbers: [19] 19,50 unequal: No Solution Exploring Operation: 89+108=197, Resulting Numbers: [197] 197,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 50:[94, 103], Operations: ['98-9=89', '14+89=103'] Exploring Operation: 103-94=9, Resulting Numbers: [9] 9,50 unequal: No Solution Exploring Operation: 94+103=197, Resulting Numbers: [197] 197,50 unequal: No Solution Exploring Operation: 94*103=9682, Resulting Numbers: [9682] 9682,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 50:[9, 10], Operations: ['98-94=4', '14-4=10'] Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,50 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,50 unequal: No Solution Moving to Node #0,3,2 Current State: 50:[4, 5], Operations: ['98-94=4', '14-9=5'] Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,50 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,50 unequal: No Solution Moving to Node #0,1,2 Current State: 50:[9, 10], Operations: ['98-14=84', '94-84=10'] Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,50 unequal: No Solution Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,50 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,50 unequal: No Solution Moving to Node #0,3,1 Current State: 50:[4, 23], Operations: ['98-94=4', '14+9=23'] Exploring Operation: 4*23=92, Resulting Numbers: [92] 92,50 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,50 unequal: No Solution Exploring Operation: 4+23=27, Resulting Numbers: [27] 27,50 unequal: No Solution Moving to Node #0,3,4 Current State: 50:[14, 5], Operations: ['98-94=4', '9-4=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,50 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,50 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,50 unequal: No Solution Moving to Node #0,3,3 Current State: 50:[9, 56], Operations: ['98-94=4', '14*4=56'] Exploring Operation: 9*56=504, Resulting Numbers: [504] 504,50 unequal: No Solution Exploring Operation: 9+56=65, Resulting Numbers: [65] 65,50 unequal: No Solution Exploring Operation: 56-9=47, Resulting Numbers: [47] 47,50 unequal: No Solution Moving to Node #0,4,0 Current State: 50:[9, 18], Operations: ['94-14=80', '98-80=18'] Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,50 unequal: No Solution Exploring Operation: 9*18=162, Resulting Numbers: [162] 162,50 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,50 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,50 unequal: No Solution Moving to Node #0,2,3 Current State: 50:[7, 85], Operations: ['98/14=7', '94-9=85'] Exploring Operation: 85-7=78, Resulting Numbers: [78] 78,50 unequal: No Solution Exploring Operation: 7*85=595, Resulting Numbers: [595] 595,50 unequal: No Solution Exploring Operation: 7+85=92, Resulting Numbers: [92] 92,50 unequal: No Solution Moving to Node #0,2,2 Current State: 50:[9, 87], Operations: ['98/14=7', '94-7=87'] Exploring Operation: 9*87=783, Resulting Numbers: [783] 783,50 unequal: No Solution Exploring Operation: 9+87=96, Resulting Numbers: [96] 96,50 unequal: No Solution Exploring Operation: 87-9=78, Resulting Numbers: [78] 78,50 unequal: No Solution Moving to Node #0,2,4 Current State: 50:[94, 2], Operations: ['98/14=7', '9-7=2'] Exploring Operation: 94*2=188, Resulting Numbers: [188] 188,50 unequal: No Solution Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,50 unequal: No Solution Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,50 unequal: No Solution Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,50 unequal: No Solution Moving to Node #0,2,0 Current State: 50:[94, 16], Operations: ['98/14=7', '9+7=16'] Exploring Operation: 94*16=1504, Resulting Numbers: [1504] 1504,50 unequal: No Solution Exploring Operation: 94-16=78, Resulting Numbers: [78] 78,50 unequal: No Solution Exploring Operation: 94+16=110, Resulting Numbers: [110] 110,50 unequal: No Solution Moving to Node #0,2,1 Current State: 50:[9, 101], Operations: ['98/14=7', '94+7=101'] Exploring Operation: 101-9=92, Resulting Numbers: [92] 92,50 unequal: No Solution Exploring Operation: 9+101=110, Resulting Numbers: [110] 110,50 unequal: No Solution Exploring Operation: 9*101=909, Resulting Numbers: [909] 909,50 unequal: No Solution Moving to Node #0,1,4 Current State: 50:[94, 75], Operations: ['98-14=84', '84-9=75'] Exploring Operation: 94-75=19, Resulting Numbers: [19] 19,50 unequal: No Solution Exploring Operation: 94*75=7050, Resulting Numbers: [7050] 7050,50 unequal: No Solution Exploring Operation: 94+75=169, Resulting Numbers: [169] 169,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[84, 85], Operations: ['98-14=84', '94-9=85'] Exploring Operation: 84+85=169, Resulting Numbers: [169] 169,50 unequal: No Solution Exploring Operation: 84*85=7140, Resulting Numbers: [7140] 7140,50 unequal: No Solution Exploring Operation: 85-84=1, Resulting Numbers: [1] 1,50 unequal: No Solution Moving to Node #0,4,1 Current State: 50:[98, 71], Operations: ['94-14=80', '80-9=71'] Exploring Operation: 98+71=169, Resulting Numbers: [169] 169,50 unequal: No Solution Exploring Operation: 98-71=27, Resulting Numbers: [27] 27,50 unequal: No Solution Exploring Operation: 98*71=6958, Resulting Numbers: [6958] 6958,50 unequal: No Solution Moving to Node #0,4,4 Current State: 50:[80, 89], Operations: ['94-14=80', '98-9=89'] Exploring Operation: 80+89=169, Resulting Numbers: [169] 169,50 unequal: No Solution Exploring Operation: 89-80=9, Resulting Numbers: [9] 9,50 unequal: No Solution Exploring Operation: 80*89=7120, Resulting Numbers: [7120] 7120,50 unequal: No Solution Moving to Node #0,1,0 Current State: 50:[94, 93], Operations: ['98-14=84', '9+84=93'] Exploring Operation: 94+93=187, Resulting Numbers: [187] 187,50 unequal: No Solution Exploring Operation: 94*93=8742, Resulting Numbers: [8742] 8742,50 unequal: No Solution Exploring Operation: 94-93=1, Resulting Numbers: [1] 1,50 unequal: No Solution Moving to Node #0,1,3 Current State: 50:[84, 103], Operations: ['98-14=84', '9+94=103'] Exploring Operation: 84*103=8652, Resulting Numbers: [8652] 8652,50 unequal: No Solution Exploring Operation: 103-84=19, Resulting Numbers: [19] 19,50 unequal: No Solution Exploring Operation: 84+103=187, Resulting Numbers: [187] 187,50 unequal: No Solution Moving to Node #0,4,3 Current State: 50:[98, 89], Operations: ['94-14=80', '9+80=89'] Exploring Operation: 98*89=8722, Resulting Numbers: [8722] 8722,50 unequal: No Solution Exploring Operation: 98+89=187, Resulting Numbers: [187] 187,50 unequal: No Solution Exploring Operation: 98-89=9, Resulting Numbers: [9] 9,50 unequal: No Solution Moving to Node #0,4,2 Current State: 50:[80, 107], Operations: ['94-14=80', '98+9=107'] Exploring Operation: 80*107=8560, Resulting Numbers: [8560] 8560,50 unequal: No Solution Exploring Operation: 107-80=27, Resulting Numbers: [27] 27,50 unequal: No Solution Exploring Operation: 80+107=187, Resulting Numbers: [187] 187,50 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 34, 57, 70, 17 ]
26
[ "34/17=2", "70-57=13", "2*13=26" ]
Current State: 26:[34, 57, 70, 17], Operations: [] Exploring Operation: 34/17=2, Resulting Numbers: [57, 70, 2] Generated Node #2: [57, 70, 2] from Operation: 34/17=2 Current State: 26:[57, 70, 2], Operations: ['34/17=2'] Exploring Operation: 70-57=13, Resulting Numbers: [2, 13] Generated Node #3: [2, 13] from Operation: 70-57=13 Current State: 26:[2, 13], Operations: ['34/17=2', '70-57=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[34, 57, 70, 17], Operations: [] Exploring Operation: 70-34=36, Resulting Numbers: [57, 17, 36] Generated Node #0,0: 26:[57, 17, 36] Operation: 70-34=36 Exploring Operation: 70-57=13, Resulting Numbers: [34, 17, 13] Generated Node #0,1: 26:[34, 17, 13] Operation: 70-57=13 Exploring Operation: 57-34=23, Resulting Numbers: [70, 17, 23] Generated Node #0,2: 26:[70, 17, 23] Operation: 57-34=23 Moving to Node #0,1 Current State: 26:[34, 17, 13], Operations: ['70-57=13'] Exploring Operation: 34-17=17, Resulting Numbers: [13, 17] Generated Node #0,1,0: 26:[13, 17] Operation: 34-17=17 Exploring Operation: 34-13=21, Resulting Numbers: [17, 21] Generated Node #0,1,1: 26:[17, 21] Operation: 34-13=21 Exploring Operation: 34/17=2, Resulting Numbers: [13, 2] Generated Node #0,1,2: 26:[13, 2] Operation: 34/17=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[13, 2], Operations: ['70-57=13', '34/17=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,26 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[34, 57, 70, 17], Operations: [] Exploring Operation: 70-57=13, Resulting Numbers: [34, 17, 13] Generated Node #0,1: 26:[34, 17, 13] Operation: 70-57=13 Moving to Node #0,1 Current State: 26:[34, 17, 13], Operations: ['70-57=13'] Exploring Operation: 34/17=2, Resulting Numbers: [13, 2] Generated Node #0,1,2: 26:[13, 2] Operation: 34/17=2 Moving to Node #0,1,2 Current State: 26:[13, 2], Operations: ['70-57=13', '34/17=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 15, 8, 75, 45 ]
42
[ "75/15=5", "45-8=37", "5+37=42" ]
Current State: 42:[15, 8, 75, 45], Operations: [] Exploring Operation: 75/15=5, Resulting Numbers: [8, 45, 5] Generated Node #2: [8, 45, 5] from Operation: 75/15=5 Current State: 42:[8, 45, 5], Operations: ['75/15=5'] Exploring Operation: 45-8=37, Resulting Numbers: [5, 37] Generated Node #3: [5, 37] from Operation: 45-8=37 Current State: 42:[5, 37], Operations: ['75/15=5', '45-8=37'] Exploring Operation: 5+37=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[15, 8, 75, 45], Operations: [] Exploring Operation: 75-45=30, Resulting Numbers: [15, 8, 30] Generated Node #0,0: 42:[15, 8, 30] Operation: 75-45=30 Exploring Operation: 75/15=5, Resulting Numbers: [8, 45, 5] Generated Node #0,1: 42:[8, 45, 5] Operation: 75/15=5 Moving to Node #0,1 Current State: 42:[8, 45, 5], Operations: ['75/15=5'] Exploring Operation: 45-5=40, Resulting Numbers: [8, 40] Generated Node #0,1,0: 42:[8, 40] Operation: 45-5=40 Exploring Operation: 8-5=3, Resulting Numbers: [45, 3] Generated Node #0,1,1: 42:[45, 3] Operation: 8-5=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 42:[8, 40], Operations: ['75/15=5', '45-5=40'] Exploring Operation: 8+40=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 42:[45, 3], Operations: ['75/15=5', '8-5=3'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[15, 8, 75, 45], Operations: [] Exploring Operation: 75/15=5, Resulting Numbers: [8, 45, 5] Generated Node #0,1: 42:[8, 45, 5] Operation: 75/15=5 Moving to Node #0,1 Current State: 42:[8, 45, 5], Operations: ['75/15=5'] Exploring Operation: 8-5=3, Resulting Numbers: [45, 3] Generated Node #0,1,1: 42:[45, 3] Operation: 8-5=3 Moving to Node #0,1,1 Current State: 42:[45, 3], Operations: ['75/15=5', '8-5=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 92, 48, 83, 2 ]
79
[ "92+83=175", "48*2=96", "175-96=79" ]
Current State: 79:[92, 48, 83, 2], Operations: [] Exploring Operation: 92+83=175, Resulting Numbers: [48, 2, 175] Generated Node #2: [48, 2, 175] from Operation: 92+83=175 Current State: 79:[48, 2, 175], Operations: ['92+83=175'] Exploring Operation: 48*2=96, Resulting Numbers: [175, 96] Generated Node #3: [175, 96] from Operation: 48*2=96 Current State: 79:[175, 96], Operations: ['92+83=175', '48*2=96'] Exploring Operation: 175-96=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[92, 48, 83, 2], Operations: [] Exploring Operation: 83-2=81, Resulting Numbers: [92, 48, 81] Generated Node #0,0: 79:[92, 48, 81] Operation: 83-2=81 Exploring Operation: 92+2=94, Resulting Numbers: [48, 83, 94] Generated Node #0,1: 79:[48, 83, 94] Operation: 92+2=94 Exploring Operation: 48*2=96, Resulting Numbers: [92, 83, 96] Generated Node #0,2: 79:[92, 83, 96] Operation: 48*2=96 Exploring Operation: 92-2=90, Resulting Numbers: [48, 83, 90] Generated Node #0,3: 79:[48, 83, 90] Operation: 92-2=90 Exploring Operation: 48+2=50, Resulting Numbers: [92, 83, 50] Generated Node #0,4: 79:[92, 83, 50] Operation: 48+2=50 Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[92, 83, 96], Operations: ['48*2=96'] Exploring Operation: 92-83=9, Resulting Numbers: [96, 9] Generated Node #0,2,0: 79:[96, 9] Operation: 92-83=9 Exploring Operation: 96-83=13, Resulting Numbers: [92, 13] Generated Node #0,2,1: 79:[92, 13] Operation: 96-83=13 Exploring Operation: 92+96=188, Resulting Numbers: [83, 188] Generated Node #0,2,2: 79:[83, 188] Operation: 92+96=188 Exploring Operation: 92+83=175, Resulting Numbers: [96, 175] Generated Node #0,2,3: 79:[96, 175] Operation: 92+83=175 Exploring Operation: 96-92=4, Resulting Numbers: [83, 4] Generated Node #0,2,4: 79:[83, 4] Operation: 96-92=4 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 79:[92, 13], Operations: ['48*2=96', '96-83=13'] Exploring Operation: 92+13=105, Resulting Numbers: [105] 105,79 unequal: No Solution Exploring Operation: 92*13=1196, Resulting Numbers: [1196] 1196,79 unequal: No Solution Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[92, 48, 83, 2], Operations: [] Exploring Operation: 48*2=96, Resulting Numbers: [92, 83, 96] Generated Node #0,2: 79:[92, 83, 96] Operation: 48*2=96 Moving to Node #0,2 Current State: 79:[92, 83, 96], Operations: ['48*2=96'] Exploring Operation: 96-83=13, Resulting Numbers: [92, 13] Generated Node #0,2,1: 79:[92, 13] Operation: 96-83=13 Moving to Node #0,2,1 Current State: 79:[92, 13], Operations: ['48*2=96', '96-83=13'] Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 90, 74, 80, 18 ]
13
[ "90-74=16", "80/16=5", "18-5=13" ]
Current State: 13:[90, 74, 80, 18], Operations: [] Exploring Operation: 90-74=16, Resulting Numbers: [80, 18, 16] Generated Node #2: [80, 18, 16] from Operation: 90-74=16 Current State: 13:[80, 18, 16], Operations: ['90-74=16'] Exploring Operation: 80/16=5, Resulting Numbers: [18, 5] Generated Node #3: [18, 5] from Operation: 80/16=5 Current State: 13:[18, 5], Operations: ['90-74=16', '80/16=5'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[90, 74, 80, 18], Operations: [] Exploring Operation: 80-74=6, Resulting Numbers: [90, 18, 6] Generated Node #0,0: 13:[90, 18, 6] Operation: 80-74=6 Exploring Operation: 90-74=16, Resulting Numbers: [80, 18, 16] Generated Node #0,1: 13:[80, 18, 16] Operation: 90-74=16 Exploring Operation: 90-80=10, Resulting Numbers: [74, 18, 10] Generated Node #0,2: 13:[74, 18, 10] Operation: 90-80=10 Moving to Node #0,2 Current State: 13:[74, 18, 10], Operations: ['90-80=10'] Exploring Operation: 74-18=56, Resulting Numbers: [10, 56] Generated Node #0,2,0: 13:[10, 56] Operation: 74-18=56 Exploring Operation: 74-10=64, Resulting Numbers: [18, 64] Generated Node #0,2,1: 13:[18, 64] Operation: 74-10=64 Exploring Operation: 18-10=8, Resulting Numbers: [74, 8] Generated Node #0,2,2: 13:[74, 8] Operation: 18-10=8 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 13:[10, 56], Operations: ['90-80=10', '74-18=56'] Exploring Operation: 10*56=560, Resulting Numbers: [560] 560,13 unequal: No Solution Exploring Operation: 10+56=66, Resulting Numbers: [66] 66,13 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,13 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:[18, 64], Operations: ['90-80=10', '74-10=64'] Exploring Operation: 18*64=1152, Resulting Numbers: [1152] 1152,13 unequal: No Solution Exploring Operation: 18+64=82, Resulting Numbers: [82] 82,13 unequal: No Solution Exploring Operation: 64-18=46, Resulting Numbers: [46] 46,13 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 #0,2,2 Current State: 13:[74, 8], Operations: ['90-80=10', '18-10=8'] Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,13 unequal: No Solution Exploring Operation: 74+8=82, Resulting Numbers: [82] 82,13 unequal: No Solution Exploring Operation: 74*8=592, Resulting Numbers: [592] 592,13 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: 13:[80, 18, 16], Operations: ['90-74=16'] Exploring Operation: 80-18=62, Resulting Numbers: [16, 62] Generated Node #0,1,0: 13:[16, 62] Operation: 80-18=62 Exploring Operation: 80/16=5, Resulting Numbers: [18, 5] Generated Node #0,1,1: 13:[18, 5] Operation: 80/16=5 Exploring Operation: 80-16=64, Resulting Numbers: [18, 64] Generated Node #0,1,2: 13:[18, 64] Operation: 80-16=64 Moving to Node #0,0 Current State: 13:[90, 18, 6], Operations: ['80-74=6'] Exploring Operation: 90-18=72, Resulting Numbers: [6, 72] Generated Node #0,0,0: 13:[6, 72] Operation: 90-18=72 Exploring Operation: 90/18=5, Resulting Numbers: [6, 5] Generated Node #0,0,1: 13:[6, 5] Operation: 90/18=5 Exploring Operation: 90/6=15, Resulting Numbers: [18, 15] Generated Node #0,0,2: 13:[18, 15] Operation: 90/6=15 Moving to Node #0,0,2 Current State: 13:[18, 15], Operations: ['80-74=6', '90/6=15'] Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,13 unequal: No Solution Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,13 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[18, 5], Operations: ['90-74=16', '80/16=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,13 unequal: No Solution Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,13 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[90, 74, 80, 18], Operations: [] Exploring Operation: 90-74=16, Resulting Numbers: [80, 18, 16] Generated Node #0,1: 13:[80, 18, 16] Operation: 90-74=16 Moving to Node #0,1 Current State: 13:[80, 18, 16], Operations: ['90-74=16'] Exploring Operation: 80/16=5, Resulting Numbers: [18, 5] Generated Node #0,1,1: 13:[18, 5] Operation: 80/16=5 Moving to Node #0,1,1 Current State: 13:[18, 5], Operations: ['90-74=16', '80/16=5'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
0.97309
hs_3
mult_heuristic
[ 25, 27, 16, 31 ]
93
[ "25-16=9", "27*31=837", "837/9=93" ]
Current State: 93:[25, 27, 16, 31], Operations: [] Exploring Operation: 25-16=9, Resulting Numbers: [27, 31, 9] Generated Node #2: [27, 31, 9] from Operation: 25-16=9 Current State: 93:[27, 31, 9], Operations: ['25-16=9'] Exploring Operation: 27*31=837, Resulting Numbers: [9, 837] Generated Node #3: [9, 837] from Operation: 27*31=837 Current State: 93:[9, 837], Operations: ['25-16=9', '27*31=837'] Exploring Operation: 837/9=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[25, 27, 16, 31], Operations: [] Exploring Operation: 27-25=2, Resulting Numbers: [16, 31, 2] Generated Node #0,0: 93:[16, 31, 2] Operation: 27-25=2 Exploring Operation: 25-16=9, Resulting Numbers: [27, 31, 9] Generated Node #0,1: 93:[27, 31, 9] Operation: 25-16=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[27, 31, 9], Operations: ['25-16=9'] Exploring Operation: 27+9=36, Resulting Numbers: [31, 36] Generated Node #0,1,0: 93:[31, 36] Operation: 27+9=36 Exploring Operation: 27/9=3, Resulting Numbers: [31, 3] Generated Node #0,1,1: 93:[31, 3] Operation: 27/9=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 93:[31, 3], Operations: ['25-16=9', '27/9=3'] Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[25, 27, 16, 31], Operations: [] Exploring Operation: 25-16=9, Resulting Numbers: [27, 31, 9] Generated Node #0,1: 93:[27, 31, 9] Operation: 25-16=9 Moving to Node #0,1 Current State: 93:[27, 31, 9], Operations: ['25-16=9'] Exploring Operation: 27/9=3, Resulting Numbers: [31, 3] Generated Node #0,1,1: 93:[31, 3] Operation: 27/9=3 Moving to Node #0,1,1 Current State: 93:[31, 3], Operations: ['25-16=9', '27/9=3'] Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 66, 85, 70, 71 ]
20
[ "85-66=19", "71-70=1", "19+1=20" ]
Current State: 20:[66, 85, 70, 71], Operations: [] Exploring Operation: 85-66=19, Resulting Numbers: [70, 71, 19] Generated Node #2: [70, 71, 19] from Operation: 85-66=19 Current State: 20:[70, 71, 19], Operations: ['85-66=19'] Exploring Operation: 71-70=1, Resulting Numbers: [19, 1] Generated Node #3: [19, 1] from Operation: 71-70=1 Current State: 20:[19, 1], Operations: ['85-66=19', '71-70=1'] Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[66, 85, 70, 71], Operations: [] Exploring Operation: 85-71=14, Resulting Numbers: [66, 70, 14] Generated Node #0,0: 20:[66, 70, 14] Operation: 85-71=14 Exploring Operation: 85-66=19, Resulting Numbers: [70, 71, 19] Generated Node #0,1: 20:[70, 71, 19] Operation: 85-66=19 Exploring Operation: 85-70=15, Resulting Numbers: [66, 71, 15] Generated Node #0,2: 20:[66, 71, 15] Operation: 85-70=15 Exploring Operation: 71-70=1, Resulting Numbers: [66, 85, 1] Generated Node #0,3: 20:[66, 85, 1] Operation: 71-70=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[66, 70, 14], Operations: ['85-71=14'] Exploring Operation: 70/14=5, Resulting Numbers: [66, 5] Generated Node #0,0,0: 20:[66, 5] Operation: 70/14=5 Exploring Operation: 70-66=4, Resulting Numbers: [14, 4] Generated Node #0,0,1: 20:[14, 4] Operation: 70-66=4 Exploring Operation: 70-14=56, Resulting Numbers: [66, 56] Generated Node #0,0,2: 20:[66, 56] Operation: 70-14=56 Exploring Operation: 66-14=52, Resulting Numbers: [70, 52] Generated Node #0,0,3: 20:[70, 52] Operation: 66-14=52 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 20:[14, 4], Operations: ['85-71=14', '70-66=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,20 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,20 unequal: No Solution No 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: 20:[66, 5], Operations: ['85-71=14', '70/14=5'] Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,20 unequal: No Solution Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 66*5=330, Resulting Numbers: [330] 330,20 unequal: No Solution No 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: 20:[66, 56], Operations: ['85-71=14', '70-14=56'] Exploring Operation: 66+56=122, Resulting Numbers: [122] 122,20 unequal: No Solution Exploring Operation: 66*56=3696, Resulting Numbers: [3696] 3696,20 unequal: No Solution Exploring Operation: 66-56=10, Resulting Numbers: [10] 10,20 unequal: No Solution No 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: 20:[70, 52], Operations: ['85-71=14', '66-14=52'] Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,20 unequal: No Solution Exploring Operation: 70+52=122, Resulting Numbers: [122] 122,20 unequal: No Solution Exploring Operation: 70*52=3640, Resulting Numbers: [3640] 3640,20 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: 20:[70, 71, 19], Operations: ['85-66=19'] Exploring Operation: 71-70=1, Resulting Numbers: [19, 1] Generated Node #0,1,0: 20:[19, 1] Operation: 71-70=1 Exploring Operation: 71-19=52, Resulting Numbers: [70, 52] Generated Node #0,1,1: 20:[70, 52] Operation: 71-19=52 Exploring Operation: 70-19=51, Resulting Numbers: [71, 51] Generated Node #0,1,2: 20:[71, 51] Operation: 70-19=51 Exploring Operation: 70+19=89, Resulting Numbers: [71, 89] Generated Node #0,1,3: 20:[71, 89] Operation: 70+19=89 Moving to Node #0,1,0 Current State: 20:[19, 1], Operations: ['85-66=19', '71-70=1'] Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,20 unequal: No Solution Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,20 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,20 unequal: No Solution Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[66, 85, 70, 71], Operations: [] Exploring Operation: 85-66=19, Resulting Numbers: [70, 71, 19] Generated Node #0,1: 20:[70, 71, 19] Operation: 85-66=19 Moving to Node #0,1 Current State: 20:[70, 71, 19], Operations: ['85-66=19'] Exploring Operation: 71-70=1, Resulting Numbers: [19, 1] Generated Node #0,1,0: 20:[19, 1] Operation: 71-70=1 Moving to Node #0,1,0 Current State: 20:[19, 1], Operations: ['85-66=19', '71-70=1'] Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 14, 31, 98, 18 ]
99
[ "31-14=17", "98+18=116", "116-17=99" ]
Current State: 99:[14, 31, 98, 18], Operations: [] Exploring Operation: 31-14=17, Resulting Numbers: [98, 18, 17] Generated Node #2: [98, 18, 17] from Operation: 31-14=17 Current State: 99:[98, 18, 17], Operations: ['31-14=17'] Exploring Operation: 98+18=116, Resulting Numbers: [17, 116] Generated Node #3: [17, 116] from Operation: 98+18=116 Current State: 99:[17, 116], Operations: ['31-14=17', '98+18=116'] Exploring Operation: 116-17=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[14, 31, 98, 18], Operations: [] Exploring Operation: 14+18=32, Resulting Numbers: [31, 98, 32] Generated Node #0,0: 99:[31, 98, 32] Operation: 14+18=32 Exploring Operation: 18-14=4, Resulting Numbers: [31, 98, 4] Generated Node #0,1: 99:[31, 98, 4] Operation: 18-14=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[31, 98, 32], Operations: ['14+18=32'] Exploring Operation: 32-31=1, Resulting Numbers: [98, 1] Generated Node #0,0,0: 99:[98, 1] Operation: 32-31=1 Exploring Operation: 31+98=129, Resulting Numbers: [32, 129] Generated Node #0,0,1: 99:[32, 129] Operation: 31+98=129 Moving to Node #0,0,0 Current State: 99:[98, 1], Operations: ['14+18=32', '32-31=1'] Exploring Operation: 98+1=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[14, 31, 98, 18], Operations: [] Exploring Operation: 14+18=32, Resulting Numbers: [31, 98, 32] Generated Node #0,0: 99:[31, 98, 32] Operation: 14+18=32 Moving to Node #0,0 Current State: 99:[31, 98, 32], Operations: ['14+18=32'] Exploring Operation: 32-31=1, Resulting Numbers: [98, 1] Generated Node #0,0,0: 99:[98, 1] Operation: 32-31=1 Moving to Node #0,0,0 Current State: 99:[98, 1], Operations: ['14+18=32', '32-31=1'] Exploring Operation: 98+1=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 61, 2, 26, 4 ]
52
[ "61+4=65", "26/2=13", "65-13=52" ]
Current State: 52:[61, 2, 26, 4], Operations: [] Exploring Operation: 61+4=65, Resulting Numbers: [2, 26, 65] Generated Node #2: [2, 26, 65] from Operation: 61+4=65 Current State: 52:[2, 26, 65], Operations: ['61+4=65'] Exploring Operation: 26/2=13, Resulting Numbers: [65, 13] Generated Node #3: [65, 13] from Operation: 26/2=13 Current State: 52:[65, 13], Operations: ['61+4=65', '26/2=13'] Exploring Operation: 65-13=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[61, 2, 26, 4], Operations: [] Exploring Operation: 61-2=59, Resulting Numbers: [26, 4, 59] Generated Node #0,0: 52:[26, 4, 59] Operation: 61-2=59 Exploring Operation: 61-4=57, Resulting Numbers: [2, 26, 57] Generated Node #0,1: 52:[2, 26, 57] Operation: 61-4=57 Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[2, 26, 57], Operations: ['61-4=57'] Exploring Operation: 57-2=55, Resulting Numbers: [26, 55] Generated Node #0,1,0: 52:[26, 55] Operation: 57-2=55 Exploring Operation: 2*26=52, Resulting Numbers: [57, 52] Generated Node #0,1,1: 52:[57, 52] Operation: 2*26=52 Moving to Node #0,1,0 Current State: 52:[26, 55], Operations: ['61-4=57', '57-2=55'] Exploring Operation: 55-26=29, Resulting Numbers: [29] 29,52 unequal: No Solution Exploring Operation: 26+55=81, Resulting Numbers: [81] 81,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[57, 52], Operations: ['61-4=57', '2*26=52'] Exploring Operation: 57-52=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 57+52=109, Resulting Numbers: [109] 109,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[26, 4, 59], Operations: ['61-2=59'] Exploring Operation: 59-4=55, Resulting Numbers: [26, 55] Generated Node #0,0,0: 52:[26, 55] Operation: 59-4=55 Exploring Operation: 59-26=33, Resulting Numbers: [4, 33] Generated Node #0,0,1: 52:[4, 33] Operation: 59-26=33 Moving to Node #0,0,0 Current State: 52:[26, 55], Operations: ['61-2=59', '59-4=55'] Exploring Operation: 26+55=81, Resulting Numbers: [81] 81,52 unequal: No Solution Exploring Operation: 55-26=29, Resulting Numbers: [29] 29,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[4, 33], Operations: ['61-2=59', '59-26=33'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,52 unequal: No Solution Exploring Operation: 4+33=37, Resulting Numbers: [37] 37,52 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
[ 38, 30, 62, 8 ]
46
[ "38-30=8", "62-8=54", "54-8=46" ]
Current State: 46:[38, 30, 62, 8], Operations: [] Exploring Operation: 38-30=8, Resulting Numbers: [62, 8, 8] Generated Node #2: [62, 8, 8] from Operation: 38-30=8 Current State: 46:[62, 8, 8], Operations: ['38-30=8'] Exploring Operation: 62-8=54, Resulting Numbers: [54] 54,46 equal: Goal Reached Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[38, 30, 62, 8], Operations: [] Exploring Operation: 62-38=24, Resulting Numbers: [30, 8, 24] Generated Node #0,0: 46:[30, 8, 24] Operation: 62-38=24 Moving to Node #0,0 Current State: 46:[30, 8, 24], Operations: ['62-38=24'] Exploring Operation: 30-8=22, Resulting Numbers: [24, 22] Generated Node #0,0,0: 46:[24, 22] Operation: 30-8=22 Moving to Node #0,0,0 Current State: 46:[24, 22], Operations: ['62-38=24', '30-8=22'] Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[38, 30, 62, 8], Operations: [] Exploring Operation: 62-38=24, Resulting Numbers: [30, 8, 24] Generated Node #0,0: 46:[30, 8, 24] Operation: 62-38=24 Moving to Node #0,0 Current State: 46:[30, 8, 24], Operations: ['62-38=24'] Exploring Operation: 30-8=22, Resulting Numbers: [24, 22] Generated Node #0,0,0: 46:[24, 22] Operation: 30-8=22 Moving to Node #0,0,0 Current State: 46:[24, 22], Operations: ['62-38=24', '30-8=22'] Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 48, 18, 67, 47 ]
86
[ "48+18=66", "67-47=20", "66+20=86" ]
Current State: 86:[48, 18, 67, 47], Operations: [] Exploring Operation: 48+18=66, Resulting Numbers: [67, 47, 66] Generated Node #2: [67, 47, 66] from Operation: 48+18=66 Current State: 86:[67, 47, 66], Operations: ['48+18=66'] Exploring Operation: 67-47=20, Resulting Numbers: [66, 20] Generated Node #3: [66, 20] from Operation: 67-47=20 Current State: 86:[66, 20], Operations: ['48+18=66', '67-47=20'] Exploring Operation: 66+20=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[48, 18, 67, 47], Operations: [] Exploring Operation: 48-18=30, Resulting Numbers: [67, 47, 30] Generated Node #0,0: 86:[67, 47, 30] Operation: 48-18=30 Exploring Operation: 48-47=1, Resulting Numbers: [18, 67, 1] Generated Node #0,1: 86:[18, 67, 1] Operation: 48-47=1 Exploring Operation: 67-18=49, Resulting Numbers: [48, 47, 49] Generated Node #0,2: 86:[48, 47, 49] Operation: 67-18=49 Exploring Operation: 18+67=85, Resulting Numbers: [48, 47, 85] Generated Node #0,3: 86:[48, 47, 85] Operation: 18+67=85 Moving to Node #0,3 Current State: 86:[48, 47, 85], Operations: ['18+67=85'] Exploring Operation: 48-47=1, Resulting Numbers: [85, 1] Generated Node #0,3,0: 86:[85, 1] Operation: 48-47=1 Exploring Operation: 85-48=37, Resulting Numbers: [47, 37] Generated Node #0,3,1: 86:[47, 37] Operation: 85-48=37 Exploring Operation: 48+47=95, Resulting Numbers: [85, 95] Generated Node #0,3,2: 86:[85, 95] Operation: 48+47=95 Exploring Operation: 85-47=38, Resulting Numbers: [48, 38] Generated Node #0,3,3: 86:[48, 38] Operation: 85-47=38 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 86:[85, 1], Operations: ['18+67=85', '48-47=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,86 unequal: No Solution Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,86 unequal: No Solution Exploring Operation: 85+1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[48, 18, 67, 47], Operations: [] Exploring Operation: 18+67=85, Resulting Numbers: [48, 47, 85] Generated Node #0,3: 86:[48, 47, 85] Operation: 18+67=85 Moving to Node #0,3 Current State: 86:[48, 47, 85], Operations: ['18+67=85'] Exploring Operation: 48-47=1, Resulting Numbers: [85, 1] Generated Node #0,3,0: 86:[85, 1] Operation: 48-47=1 Moving to Node #0,3,0 Current State: 86:[85, 1], Operations: ['18+67=85', '48-47=1'] Exploring Operation: 85+1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 96, 81, 7, 74 ]
96
[ "96+81=177", "7+74=81", "177-81=96" ]
Current State: 96:[96, 81, 7, 74], Operations: [] Exploring Operation: 96+81=177, Resulting Numbers: [7, 74, 177] Generated Node #2: [7, 74, 177] from Operation: 96+81=177 Current State: 96:[7, 74, 177], Operations: ['96+81=177'] Exploring Operation: 7+74=81, Resulting Numbers: [177, 81] Generated Node #3: [177, 81] from Operation: 7+74=81 Current State: 96:[177, 81], Operations: ['96+81=177', '7+74=81'] Exploring Operation: 177-81=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[96, 81, 7, 74], Operations: [] Exploring Operation: 81-74=7, Resulting Numbers: [96, 7, 7] Generated Node #0,0: 96:[96, 7, 7] Operation: 81-74=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[96, 7, 7], Operations: ['81-74=7'] Exploring Operation: 7*7=49, Resulting Numbers: [96, 49] Generated Node #0,0,0: 96:[96, 49] Operation: 7*7=49 Moving to Node #0,0,0 Current State: 96:[96, 49], Operations: ['81-74=7', '7*7=49'] Exploring Operation: 96-49=47, Resulting Numbers: [47] 47,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 34, 21, 63, 26 ]
11
[ "34-26=8", "63/21=3", "8+3=11" ]
Current State: 11:[34, 21, 63, 26], Operations: [] Exploring Operation: 34-26=8, Resulting Numbers: [21, 63, 8] Generated Node #2: [21, 63, 8] from Operation: 34-26=8 Current State: 11:[21, 63, 8], Operations: ['34-26=8'] Exploring Operation: 63/21=3, Resulting Numbers: [8, 3] Generated Node #3: [8, 3] from Operation: 63/21=3 Current State: 11:[8, 3], Operations: ['34-26=8', '63/21=3'] Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[34, 21, 63, 26], Operations: [] Exploring Operation: 63/21=3, Resulting Numbers: [34, 26, 3] Generated Node #0,0: 11:[34, 26, 3] Operation: 63/21=3 Exploring Operation: 34-26=8, Resulting Numbers: [21, 63, 8] Generated Node #0,1: 11:[21, 63, 8] Operation: 34-26=8 Exploring Operation: 63-26=37, Resulting Numbers: [34, 21, 37] Generated Node #0,2: 11:[34, 21, 37] Operation: 63-26=37 Exploring Operation: 63-34=29, Resulting Numbers: [21, 26, 29] Generated Node #0,3: 11:[21, 26, 29] Operation: 63-34=29 Start Sub Search at level 1: Moving to Node #0,3 Current State: 11:[21, 26, 29], Operations: ['63-34=29'] Exploring Operation: 21+26=47, Resulting Numbers: [29, 47] Generated Node #0,3,0: 11:[29, 47] Operation: 21+26=47 Exploring Operation: 29-21=8, Resulting Numbers: [26, 8] Generated Node #0,3,1: 11:[26, 8] Operation: 29-21=8 Exploring Operation: 29-26=3, Resulting Numbers: [21, 3] Generated Node #0,3,2: 11:[21, 3] Operation: 29-26=3 Exploring Operation: 26-21=5, Resulting Numbers: [29, 5] Generated Node #0,3,3: 11:[29, 5] Operation: 26-21=5 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 11:[26, 8], Operations: ['63-34=29', '29-21=8'] Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,11 unequal: No Solution Exploring Operation: 26*8=208, Resulting Numbers: [208] 208,11 unequal: No Solution Exploring Operation: 26+8=34, Resulting Numbers: [34] 34,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 11:[21, 3], Operations: ['63-34=29', '29-26=3'] Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,11 unequal: No Solution Exploring Operation: 21*3=63, Resulting Numbers: [63] 63,11 unequal: No Solution Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 11:[29, 5], Operations: ['63-34=29', '26-21=5'] Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,11 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 11:[29, 47], Operations: ['63-34=29', '21+26=47'] Exploring Operation: 29+47=76, Resulting Numbers: [76] 76,11 unequal: No Solution Exploring Operation: 47-29=18, Resulting Numbers: [18] 18,11 unequal: No Solution Exploring Operation: 29*47=1363, Resulting Numbers: [1363] 1363,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[34, 26, 3], Operations: ['63/21=3'] Exploring Operation: 34+3=37, Resulting Numbers: [26, 37] Generated Node #0,0,0: 11:[26, 37] Operation: 34+3=37 Exploring Operation: 34-3=31, Resulting Numbers: [26, 31] Generated Node #0,0,1: 11:[26, 31] Operation: 34-3=31 Exploring Operation: 34-26=8, Resulting Numbers: [3, 8] Generated Node #0,0,2: 11:[3, 8] Operation: 34-26=8 Exploring Operation: 26-3=23, Resulting Numbers: [34, 23] Generated Node #0,0,3: 11:[34, 23] Operation: 26-3=23 Moving to Node #0,0,2 Current State: 11:[3, 8], Operations: ['63/21=3', '34-26=8'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,11 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[34, 21, 63, 26], Operations: [] Exploring Operation: 63/21=3, Resulting Numbers: [34, 26, 3] Generated Node #0,0: 11:[34, 26, 3] Operation: 63/21=3 Moving to Node #0,0 Current State: 11:[34, 26, 3], Operations: ['63/21=3'] Exploring Operation: 34-26=8, Resulting Numbers: [3, 8] Generated Node #0,0,2: 11:[3, 8] Operation: 34-26=8 Moving to Node #0,0,2 Current State: 11:[3, 8], Operations: ['63/21=3', '34-26=8'] Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 60, 85, 17, 97 ]
22
[ "97-85=12", "60/12=5", "17+5=22" ]
Current State: 22:[60, 85, 17, 97], Operations: [] Exploring Operation: 97-85=12, Resulting Numbers: [60, 17, 12] Generated Node #2: [60, 17, 12] from Operation: 97-85=12 Current State: 22:[60, 17, 12], Operations: ['97-85=12'] Exploring Operation: 60/12=5, Resulting Numbers: [17, 5] Generated Node #3: [17, 5] from Operation: 60/12=5 Current State: 22:[17, 5], Operations: ['97-85=12', '60/12=5'] Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[60, 85, 17, 97], Operations: [] Exploring Operation: 85-60=25, Resulting Numbers: [17, 97, 25] Generated Node #0,0: 22:[17, 97, 25] Operation: 85-60=25 Exploring Operation: 97-85=12, Resulting Numbers: [60, 17, 12] Generated Node #0,1: 22:[60, 17, 12] Operation: 97-85=12 Moving to Node #0,1 Current State: 22:[60, 17, 12], Operations: ['97-85=12'] Exploring Operation: 60/12=5, Resulting Numbers: [17, 5] Generated Node #0,1,0: 22:[17, 5] Operation: 60/12=5 Exploring Operation: 60-17=43, Resulting Numbers: [12, 43] Generated Node #0,1,1: 22:[12, 43] Operation: 60-17=43 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[17, 5], Operations: ['97-85=12', '60/12=5'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,22 unequal: No Solution Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[60, 85, 17, 97], Operations: [] Exploring Operation: 97-85=12, Resulting Numbers: [60, 17, 12] Generated Node #0,1: 22:[60, 17, 12] Operation: 97-85=12 Moving to Node #0,1 Current State: 22:[60, 17, 12], Operations: ['97-85=12'] Exploring Operation: 60/12=5, Resulting Numbers: [17, 5] Generated Node #0,1,0: 22:[17, 5] Operation: 60/12=5 Moving to Node #0,1,0 Current State: 22:[17, 5], Operations: ['97-85=12', '60/12=5'] Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 75, 57, 2, 19 ]
74
[ "75-57=18", "19+18=37", "2*37=74" ]
Current State: 74:[75, 57, 2, 19], Operations: [] Exploring Operation: 75-57=18, Resulting Numbers: [2, 19, 18] Generated Node #2: [2, 19, 18] from Operation: 75-57=18 Current State: 74:[2, 19, 18], Operations: ['75-57=18'] Exploring Operation: 19+18=37, Resulting Numbers: [2, 37] Generated Node #3: [2, 37] from Operation: 19+18=37 Current State: 74:[2, 37], Operations: ['75-57=18', '19+18=37'] Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[75, 57, 2, 19], Operations: [] Exploring Operation: 57-19=38, Resulting Numbers: [75, 2, 38] Generated Node #0,0: 74:[75, 2, 38] Operation: 57-19=38 Exploring Operation: 57/19=3, Resulting Numbers: [75, 2, 3] Generated Node #0,1: 74:[75, 2, 3] Operation: 57/19=3 Moving to Node #0,0 Current State: 74:[75, 2, 38], Operations: ['57-19=38'] Exploring Operation: 75-38=37, Resulting Numbers: [2, 37] Generated Node #0,0,0: 74:[2, 37] Operation: 75-38=37 Exploring Operation: 75-2=73, Resulting Numbers: [38, 73] Generated Node #0,0,1: 74:[38, 73] Operation: 75-2=73 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[2, 37], Operations: ['57-19=38', '75-38=37'] Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[75, 57, 2, 19], Operations: [] Exploring Operation: 57-19=38, Resulting Numbers: [75, 2, 38] Generated Node #0,0: 74:[75, 2, 38] Operation: 57-19=38 Moving to Node #0,0 Current State: 74:[75, 2, 38], Operations: ['57-19=38'] Exploring Operation: 75-38=37, Resulting Numbers: [2, 37] Generated Node #0,0,0: 74:[2, 37] Operation: 75-38=37 Moving to Node #0,0,0 Current State: 74:[2, 37], Operations: ['57-19=38', '75-38=37'] Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 11, 47, 68, 79 ]
89
[ "11+47=58", "68+79=147", "147-58=89" ]
Current State: 89:[11, 47, 68, 79], Operations: [] Exploring Operation: 11+47=58, Resulting Numbers: [68, 79, 58] Generated Node #2: [68, 79, 58] from Operation: 11+47=58 Current State: 89:[68, 79, 58], Operations: ['11+47=58'] Exploring Operation: 68+79=147, Resulting Numbers: [58, 147] Generated Node #3: [58, 147] from Operation: 68+79=147 Current State: 89:[58, 147], Operations: ['11+47=58', '68+79=147'] Exploring Operation: 147-58=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[11, 47, 68, 79], Operations: [] Exploring Operation: 11+79=90, Resulting Numbers: [47, 68, 90] Generated Node #0,0: 89:[47, 68, 90] Operation: 11+79=90 Exploring Operation: 11+47=58, Resulting Numbers: [68, 79, 58] Generated Node #0,1: 89:[68, 79, 58] Operation: 11+47=58 Exploring Operation: 11+68=79, Resulting Numbers: [47, 79, 79] Generated Node #0,2: 89:[47, 79, 79] Operation: 11+68=79 Exploring Operation: 47-11=36, Resulting Numbers: [68, 79, 36] Generated Node #0,3: 89:[68, 79, 36] Operation: 47-11=36 Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[68, 79, 58], Operations: ['11+47=58'] Exploring Operation: 68+79=147, Resulting Numbers: [58, 147] Generated Node #0,1,0: 89:[58, 147] Operation: 68+79=147 Exploring Operation: 79+58=137, Resulting Numbers: [68, 137] Generated Node #0,1,1: 89:[68, 137] Operation: 79+58=137 Exploring Operation: 68-58=10, Resulting Numbers: [79, 10] Generated Node #0,1,2: 89:[79, 10] Operation: 68-58=10 Exploring Operation: 68+58=126, Resulting Numbers: [79, 126] Generated Node #0,1,3: 89:[79, 126] Operation: 68+58=126 Moving to Node #0,1,3 Current State: 89:[79, 126], Operations: ['11+47=58', '68+58=126'] Exploring Operation: 79+126=205, Resulting Numbers: [205] 205,89 unequal: No Solution Exploring Operation: 79*126=9954, Resulting Numbers: [9954] 9954,89 unequal: No Solution Exploring Operation: 126-79=47, Resulting Numbers: [47] 47,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[68, 137], Operations: ['11+47=58', '79+58=137'] Exploring Operation: 68+137=205, Resulting Numbers: [205] 205,89 unequal: No Solution Exploring Operation: 137-68=69, Resulting Numbers: [69] 69,89 unequal: No Solution Exploring Operation: 68*137=9316, Resulting Numbers: [9316] 9316,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[79, 10], Operations: ['11+47=58', '68-58=10'] Exploring Operation: 79-10=69, Resulting Numbers: [69] 69,89 unequal: No Solution Exploring Operation: 79+10=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[11, 47, 68, 79], Operations: [] Exploring Operation: 11+47=58, Resulting Numbers: [68, 79, 58] Generated Node #0,1: 89:[68, 79, 58] Operation: 11+47=58 Moving to Node #0,1 Current State: 89:[68, 79, 58], Operations: ['11+47=58'] Exploring Operation: 68-58=10, Resulting Numbers: [79, 10] Generated Node #0,1,2: 89:[79, 10] Operation: 68-58=10 Moving to Node #0,1,2 Current State: 89:[79, 10], Operations: ['11+47=58', '68-58=10'] Exploring Operation: 79+10=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 20, 16, 98, 8 ]
50
[ "98-20=78", "16*8=128", "128-78=50" ]
Current State: 50:[20, 16, 98, 8], Operations: [] Exploring Operation: 98-20=78, Resulting Numbers: [16, 8, 78] Generated Node #2: [16, 8, 78] from Operation: 98-20=78 Current State: 50:[16, 8, 78], Operations: ['98-20=78'] Exploring Operation: 16*8=128, Resulting Numbers: [78, 128] Generated Node #3: [78, 128] from Operation: 16*8=128 Current State: 50:[78, 128], Operations: ['98-20=78', '16*8=128'] Exploring Operation: 128-78=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[20, 16, 98, 8], Operations: [] Exploring Operation: 98-20=78, Resulting Numbers: [16, 8, 78] Generated Node #0,0: 50:[16, 8, 78] Operation: 98-20=78 Moving to Node #0,0 Current State: 50:[16, 8, 78], Operations: ['98-20=78'] Exploring Operation: 78-16=62, Resulting Numbers: [8, 62] Generated Node #0,0,0: 50:[8, 62] Operation: 78-16=62 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[8, 62], Operations: ['98-20=78', '78-16=62'] Exploring Operation: 62-8=54, Resulting Numbers: [54] 54,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 87, 45, 39, 60 ]
36
[ "87-39=48", "45*48=2160", "2160/60=36" ]
Current State: 36:[87, 45, 39, 60], Operations: [] Exploring Operation: 87-39=48, Resulting Numbers: [45, 60, 48] Generated Node #2: [45, 60, 48] from Operation: 87-39=48 Current State: 36:[45, 60, 48], Operations: ['87-39=48'] Exploring Operation: 45*48=2160, Resulting Numbers: [60, 2160] Generated Node #3: [60, 2160] from Operation: 45*48=2160 Current State: 36:[60, 2160], Operations: ['87-39=48', '45*48=2160'] Exploring Operation: 2160/60=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[87, 45, 39, 60], Operations: [] Exploring Operation: 87-39=48, Resulting Numbers: [45, 60, 48] Generated Node #0,0: 36:[45, 60, 48] Operation: 87-39=48 Exploring Operation: 87-60=27, Resulting Numbers: [45, 39, 27] Generated Node #0,1: 36:[45, 39, 27] Operation: 87-60=27 Exploring Operation: 87-45=42, Resulting Numbers: [39, 60, 42] Generated Node #0,2: 36:[39, 60, 42] Operation: 87-45=42 Moving to Node #0,1 Current State: 36:[45, 39, 27], Operations: ['87-60=27'] Exploring Operation: 45-39=6, Resulting Numbers: [27, 6] Generated Node #0,1,0: 36:[27, 6] Operation: 45-39=6 Exploring Operation: 45-27=18, Resulting Numbers: [39, 18] Generated Node #0,1,1: 36:[39, 18] Operation: 45-27=18 Exploring Operation: 39-27=12, Resulting Numbers: [45, 12] Generated Node #0,1,2: 36:[45, 12] Operation: 39-27=12 Moving to Node #0,2 Current State: 36:[39, 60, 42], Operations: ['87-45=42'] Exploring Operation: 42-39=3, Resulting Numbers: [60, 3] Generated Node #0,2,0: 36:[60, 3] Operation: 42-39=3 Exploring Operation: 60-42=18, Resulting Numbers: [39, 18] Generated Node #0,2,1: 36:[39, 18] Operation: 60-42=18 Exploring Operation: 60-39=21, Resulting Numbers: [42, 21] Generated Node #0,2,2: 36:[42, 21] Operation: 60-39=21 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 36:[39, 18], Operations: ['87-45=42', '60-42=18'] Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,36 unequal: No Solution Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 39*18=702, Resulting Numbers: [702] 702,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 36:[42, 21], Operations: ['87-45=42', '60-39=21'] Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 42+21=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 36:[60, 3], Operations: ['87-45=42', '42-39=3'] Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,36 unequal: No Solution Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 36:[45, 60, 48], Operations: ['87-39=48'] Exploring Operation: 60-45=15, Resulting Numbers: [48, 15] Generated Node #0,0,0: 36:[48, 15] Operation: 60-45=15 Exploring Operation: 48-45=3, Resulting Numbers: [60, 3] Generated Node #0,0,1: 36:[60, 3] Operation: 48-45=3 Exploring Operation: 60-48=12, Resulting Numbers: [45, 12] Generated Node #0,0,2: 36:[45, 12] Operation: 60-48=12 Moving to Node #0,1,1 Current State: 36:[39, 18], Operations: ['87-60=27', '45-27=18'] Exploring Operation: 39*18=702, Resulting Numbers: [702] 702,36 unequal: No Solution Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,36 unequal: No Solution Moving to Node #0,1,2 Current State: 36:[45, 12], Operations: ['87-60=27', '39-27=12'] Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,36 unequal: No Solution Exploring Operation: 45*12=540, Resulting Numbers: [540] 540,36 unequal: No Solution Exploring Operation: 45+12=57, Resulting Numbers: [57] 57,36 unequal: No Solution Moving to Node #0,1,0 Current State: 36:[27, 6], Operations: ['87-60=27', '45-39=6'] Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,36 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,36 unequal: No Solution Moving to Node #0,0,2 Current State: 36:[45, 12], Operations: ['87-39=48', '60-48=12'] Exploring Operation: 45+12=57, Resulting Numbers: [57] 57,36 unequal: No Solution Exploring Operation: 45*12=540, Resulting Numbers: [540] 540,36 unequal: No Solution Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,36 unequal: No Solution Moving to Node #0,0,0 Current State: 36:[48, 15], Operations: ['87-39=48', '60-45=15'] Exploring Operation: 48+15=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 48*15=720, Resulting Numbers: [720] 720,36 unequal: No Solution Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,36 unequal: No Solution Moving to Node #0,0,1 Current State: 36:[60, 3], Operations: ['87-39=48', '48-45=3'] Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,36 unequal: No Solution Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,36 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 14, 79, 11, 11 ]
92
[ "14+79=93", "11/11=1", "93-1=92" ]
Current State: 92:[14, 79, 11, 11], Operations: [] Exploring Operation: 14+79=93, Resulting Numbers: [11, 11, 93] Generated Node #2: [11, 11, 93] from Operation: 14+79=93 Current State: 92:[11, 11, 93], Operations: ['14+79=93'] Exploring Operation: 11/11=1, Resulting Numbers: [93, 1] Generated Node #3: [93, 1] from Operation: 11/11=1 Current State: 92:[93, 1], Operations: ['14+79=93', '11/11=1'] Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[14, 79, 11, 11], Operations: [] Exploring Operation: 14+79=93, Resulting Numbers: [11, 11, 93] Generated Node #0,0: 92:[11, 11, 93] Operation: 14+79=93 Moving to Node #0,0 Current State: 92:[11, 11, 93], Operations: ['14+79=93'] Exploring Operation: 11+11=22, Resulting Numbers: [93, 22] Generated Node #0,0,0: 92:[93, 22] Operation: 11+11=22 Moving to Node #0,0,0 Current State: 92:[93, 22], Operations: ['14+79=93', '11+11=22'] Exploring Operation: 93-22=71, Resulting Numbers: [71] 71,92 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 70, 54, 5, 38 ]
59
[ "70-54=16", "5+38=43", "16+43=59" ]
Current State: 59:[70, 54, 5, 38], Operations: [] Exploring Operation: 70-54=16, Resulting Numbers: [5, 38, 16] Generated Node #2: [5, 38, 16] from Operation: 70-54=16 Current State: 59:[5, 38, 16], Operations: ['70-54=16'] Exploring Operation: 5+38=43, Resulting Numbers: [16, 43] Generated Node #3: [16, 43] from Operation: 5+38=43 Current State: 59:[16, 43], Operations: ['70-54=16', '5+38=43'] Exploring Operation: 16+43=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[70, 54, 5, 38], Operations: [] Exploring Operation: 70-5=65, Resulting Numbers: [54, 38, 65] Generated Node #0,0: 59:[54, 38, 65] Operation: 70-5=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[54, 38, 65], Operations: ['70-5=65'] Exploring Operation: 65-38=27, Resulting Numbers: [54, 27] Generated Node #0,0,0: 59:[54, 27] Operation: 65-38=27 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[54, 27], Operations: ['70-5=65', '65-38=27'] Exploring Operation: 54+27=81, Resulting Numbers: [81] 81,59 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
[ 2, 69, 53, 21 ]
82
[ "69+53=122", "122/2=61", "21+61=82" ]
Current State: 82:[2, 69, 53, 21], Operations: [] Exploring Operation: 69+53=122, Resulting Numbers: [2, 21, 122] Generated Node #2: [2, 21, 122] from Operation: 69+53=122 Current State: 82:[2, 21, 122], Operations: ['69+53=122'] Exploring Operation: 122/2=61, Resulting Numbers: [21, 61] Generated Node #3: [21, 61] from Operation: 122/2=61 Current State: 82:[21, 61], Operations: ['69+53=122', '122/2=61'] Exploring Operation: 21+61=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[2, 69, 53, 21], Operations: [] Exploring Operation: 69-21=48, Resulting Numbers: [2, 53, 48] Generated Node #0,0: 82:[2, 53, 48] Operation: 69-21=48 Exploring Operation: 53+21=74, Resulting Numbers: [2, 69, 74] Generated Node #0,1: 82:[2, 69, 74] Operation: 53+21=74 Exploring Operation: 69+21=90, Resulting Numbers: [2, 53, 90] Generated Node #0,2: 82:[2, 53, 90] Operation: 69+21=90 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[2, 53, 48], Operations: ['69-21=48'] Exploring Operation: 53-2=51, Resulting Numbers: [48, 51] Generated Node #0,0,0: 82:[48, 51] Operation: 53-2=51 Exploring Operation: 48-2=46, Resulting Numbers: [53, 46] Generated Node #0,0,1: 82:[53, 46] Operation: 48-2=46 Exploring Operation: 53-48=5, Resulting Numbers: [2, 5] Generated Node #0,0,2: 82:[2, 5] Operation: 53-48=5 Moving to Node #0,0,2 Current State: 82:[2, 5], Operations: ['69-21=48', '53-48=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,82 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,82 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[48, 51], Operations: ['69-21=48', '53-2=51'] Exploring Operation: 48*51=2448, Resulting Numbers: [2448] 2448,82 unequal: No Solution Exploring Operation: 48+51=99, Resulting Numbers: [99] 99,82 unequal: No Solution Exploring Operation: 51-48=3, Resulting Numbers: [3] 3,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[53, 46], Operations: ['69-21=48', '48-2=46'] Exploring Operation: 53*46=2438, Resulting Numbers: [2438] 2438,82 unequal: No Solution Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,82 unequal: No Solution Exploring Operation: 53+46=99, Resulting Numbers: [99] 99,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[2, 53, 90], Operations: ['69+21=90'] Exploring Operation: 90-53=37, Resulting Numbers: [2, 37] Generated Node #0,2,0: 82:[2, 37] Operation: 90-53=37 Exploring Operation: 90/2=45, Resulting Numbers: [53, 45] Generated Node #0,2,1: 82:[53, 45] Operation: 90/2=45 Exploring Operation: 53-2=51, Resulting Numbers: [90, 51] Generated Node #0,2,2: 82:[90, 51] Operation: 53-2=51 Moving to Node #0,2,0 Current State: 82:[2, 37], Operations: ['69+21=90', '90-53=37'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,82 unequal: No Solution Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,82 unequal: No Solution Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,82 unequal: No Solution Moving to Node #0,2,1 Current State: 82:[53, 45], Operations: ['69+21=90', '90/2=45'] Exploring Operation: 53-45=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 53+45=98, Resulting Numbers: [98] 98,82 unequal: No Solution Exploring Operation: 53*45=2385, Resulting Numbers: [2385] 2385,82 unequal: No Solution Moving to Node #0,2,2 Current State: 82:[90, 51], Operations: ['69+21=90', '53-2=51'] Exploring Operation: 90*51=4590, Resulting Numbers: [4590] 4590,82 unequal: No Solution Exploring Operation: 90-51=39, Resulting Numbers: [39] 39,82 unequal: No Solution Exploring Operation: 90+51=141, Resulting Numbers: [141] 141,82 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:[2, 69, 74], Operations: ['53+21=74'] Exploring Operation: 2+69=71, Resulting Numbers: [74, 71] Generated Node #0,1,0: 82:[74, 71] Operation: 2+69=71 Exploring Operation: 74-69=5, Resulting Numbers: [2, 5] Generated Node #0,1,1: 82:[2, 5] Operation: 74-69=5 Exploring Operation: 74/2=37, Resulting Numbers: [69, 37] Generated Node #0,1,2: 82:[69, 37] Operation: 74/2=37 Moving to Node #0,1,1 Current State: 82:[2, 5], Operations: ['53+21=74', '74-69=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,82 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[69, 37], Operations: ['53+21=74', '74/2=37'] Exploring Operation: 69-37=32, Resulting Numbers: [32] 32,82 unequal: No Solution Exploring Operation: 69*37=2553, Resulting Numbers: [2553] 2553,82 unequal: No Solution Exploring Operation: 69+37=106, Resulting Numbers: [106] 106,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[74, 71], Operations: ['53+21=74', '2+69=71'] Exploring Operation: 74-71=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 74+71=145, Resulting Numbers: [145] 145,82 unequal: No Solution Exploring Operation: 74*71=5254, Resulting Numbers: [5254] 5254,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 34, 3, 62, 66 ]
98
[ "34*3=102", "66-62=4", "102-4=98" ]
Current State: 98:[34, 3, 62, 66], Operations: [] Exploring Operation: 34*3=102, Resulting Numbers: [62, 66, 102] Generated Node #2: [62, 66, 102] from Operation: 34*3=102 Current State: 98:[62, 66, 102], Operations: ['34*3=102'] Exploring Operation: 66-62=4, Resulting Numbers: [102, 4] Generated Node #3: [102, 4] from Operation: 66-62=4 Current State: 98:[102, 4], Operations: ['34*3=102', '66-62=4'] Exploring Operation: 102-4=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[34, 3, 62, 66], Operations: [] Exploring Operation: 34+66=100, Resulting Numbers: [3, 62, 100] Generated Node #0,0: 98:[3, 62, 100] Operation: 34+66=100 Exploring Operation: 34+62=96, Resulting Numbers: [3, 66, 96] Generated Node #0,1: 98:[3, 66, 96] Operation: 34+62=96 Exploring Operation: 66-34=32, Resulting Numbers: [3, 62, 32] Generated Node #0,2: 98:[3, 62, 32] Operation: 66-34=32 Exploring Operation: 66-62=4, Resulting Numbers: [34, 3, 4] Generated Node #0,3: 98:[34, 3, 4] Operation: 66-62=4 Moving to Node #0,0 Current State: 98:[3, 62, 100], Operations: ['34+66=100'] Exploring Operation: 3+62=65, Resulting Numbers: [100, 65] Generated Node #0,0,0: 98:[100, 65] Operation: 3+62=65 Exploring Operation: 62-3=59, Resulting Numbers: [100, 59] Generated Node #0,0,1: 98:[100, 59] Operation: 62-3=59 Exploring Operation: 100-3=97, Resulting Numbers: [62, 97] Generated Node #0,0,2: 98:[62, 97] Operation: 100-3=97 Exploring Operation: 100-62=38, Resulting Numbers: [3, 38] Generated Node #0,0,3: 98:[3, 38] Operation: 100-62=38 Moving to Node #0,3 Current State: 98:[34, 3, 4], Operations: ['66-62=4'] Exploring Operation: 34+4=38, Resulting Numbers: [3, 38] Generated Node #0,3,0: 98:[3, 38] Operation: 34+4=38 Exploring Operation: 34+3=37, Resulting Numbers: [4, 37] Generated Node #0,3,1: 98:[4, 37] Operation: 34+3=37 Exploring Operation: 34*3=102, Resulting Numbers: [4, 102] Generated Node #0,3,2: 98:[4, 102] Operation: 34*3=102 Exploring Operation: 3+4=7, Resulting Numbers: [34, 7] Generated Node #0,3,3: 98:[34, 7] Operation: 3+4=7 Moving to Node #0,1 Current State: 98:[3, 66, 96], Operations: ['34+62=96'] Exploring Operation: 66-3=63, Resulting Numbers: [96, 63] Generated Node #0,1,0: 98:[96, 63] Operation: 66-3=63 Exploring Operation: 3+96=99, Resulting Numbers: [66, 99] Generated Node #0,1,1: 98:[66, 99] Operation: 3+96=99 Exploring Operation: 96-66=30, Resulting Numbers: [3, 30] Generated Node #0,1,2: 98:[3, 30] Operation: 96-66=30 Exploring Operation: 66/3=22, Resulting Numbers: [96, 22] Generated Node #0,1,3: 98:[96, 22] Operation: 66/3=22 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 98:[96, 22], Operations: ['34+62=96', '66/3=22'] Exploring Operation: 96-22=74, Resulting Numbers: [74] 74,98 unequal: No Solution Exploring Operation: 96+22=118, Resulting Numbers: [118] 118,98 unequal: No Solution Exploring Operation: 96*22=2112, Resulting Numbers: [2112] 2112,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 98:[96, 63], Operations: ['34+62=96', '66-3=63'] Exploring Operation: 96*63=6048, Resulting Numbers: [6048] 6048,98 unequal: No Solution Exploring Operation: 96+63=159, Resulting Numbers: [159] 159,98 unequal: No Solution Exploring Operation: 96-63=33, Resulting Numbers: [33] 33,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 98:[3, 30], Operations: ['34+62=96', '96-66=30'] Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,98 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,98 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,98 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 98:[66, 99], Operations: ['34+62=96', '3+96=99'] Exploring Operation: 99-66=33, Resulting Numbers: [33] 33,98 unequal: No Solution Exploring Operation: 66+99=165, Resulting Numbers: [165] 165,98 unequal: No Solution Exploring Operation: 66*99=6534, Resulting Numbers: [6534] 6534,98 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: 98:[3, 62, 32], Operations: ['66-34=32'] Exploring Operation: 3*32=96, Resulting Numbers: [62, 96] Generated Node #0,2,0: 98:[62, 96] Operation: 3*32=96 Exploring Operation: 62+32=94, Resulting Numbers: [3, 94] Generated Node #0,2,1: 98:[3, 94] Operation: 62+32=94 Exploring Operation: 62-32=30, Resulting Numbers: [3, 30] Generated Node #0,2,2: 98:[3, 30] Operation: 62-32=30 Exploring Operation: 62-3=59, Resulting Numbers: [32, 59] Generated Node #0,2,3: 98:[32, 59] Operation: 62-3=59 Moving to Node #0,2,1 Current State: 98:[3, 94], Operations: ['66-34=32', '62+32=94'] Exploring Operation: 3*94=282, Resulting Numbers: [282] 282,98 unequal: No Solution Exploring Operation: 3+94=97, Resulting Numbers: [97] 97,98 unequal: No Solution Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,98 unequal: No Solution Moving to Node #0,3,2 Current State: 98:[4, 102], Operations: ['66-62=4', '34*3=102'] Exploring Operation: 102-4=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[34, 3, 62, 66], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [34, 3, 4] Generated Node #0,3: 98:[34, 3, 4] Operation: 66-62=4 Moving to Node #0,3 Current State: 98:[34, 3, 4], Operations: ['66-62=4'] Exploring Operation: 34*3=102, Resulting Numbers: [4, 102] Generated Node #0,3,2: 98:[4, 102] Operation: 34*3=102 Moving to Node #0,3,2 Current State: 98:[4, 102], Operations: ['66-62=4', '34*3=102'] Exploring Operation: 102-4=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
0.96441
hs_4
sum_heuristic
[ 50, 1, 37, 9 ]
22
[ "50*1=50", "37-9=28", "50-28=22" ]
Current State: 22:[50, 1, 37, 9], Operations: [] Exploring Operation: 50*1=50, Resulting Numbers: [37, 9, 50] Generated Node #2: [37, 9, 50] from Operation: 50*1=50 Current State: 22:[37, 9, 50], Operations: ['50*1=50'] Exploring Operation: 37-9=28, Resulting Numbers: [50, 28] Generated Node #3: [50, 28] from Operation: 37-9=28 Current State: 22:[50, 28], Operations: ['50*1=50', '37-9=28'] Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[50, 1, 37, 9], Operations: [] Exploring Operation: 50-37=13, Resulting Numbers: [1, 9, 13] Generated Node #0,0: 22:[1, 9, 13] Operation: 50-37=13 Exploring Operation: 50-1=49, Resulting Numbers: [37, 9, 49] Generated Node #0,1: 22:[37, 9, 49] Operation: 50-1=49 Exploring Operation: 37-9=28, Resulting Numbers: [50, 1, 28] Generated Node #0,2: 22:[50, 1, 28] Operation: 37-9=28 Exploring Operation: 37-1=36, Resulting Numbers: [50, 9, 36] Generated Node #0,3: 22:[50, 9, 36] Operation: 37-1=36 Exploring Operation: 50-9=41, Resulting Numbers: [1, 37, 41] Generated Node #0,4: 22:[1, 37, 41] Operation: 50-9=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[1, 9, 13], Operations: ['50-37=13'] Exploring Operation: 9+13=22, Resulting Numbers: [1, 22] Generated Node #0,0,0: 22:[1, 22] Operation: 9+13=22 Exploring Operation: 13-1=12, Resulting Numbers: [9, 12] Generated Node #0,0,1: 22:[9, 12] Operation: 13-1=12 Exploring Operation: 13-9=4, Resulting Numbers: [1, 4] Generated Node #0,0,2: 22:[1, 4] Operation: 13-9=4 Exploring Operation: 1+9=10, Resulting Numbers: [13, 10] Generated Node #0,0,3: 22:[13, 10] Operation: 1+9=10 Exploring Operation: 1*9=9, Resulting Numbers: [13, 9] Generated Node #0,0,4: 22:[13, 9] Operation: 1*9=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 22:[1, 22], Operations: ['50-37=13', '9+13=22'] Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,22 unequal: No Solution Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[50, 1, 37, 9], Operations: [] Exploring Operation: 50-37=13, Resulting Numbers: [1, 9, 13] Generated Node #0,0: 22:[1, 9, 13] Operation: 50-37=13 Moving to Node #0,0 Current State: 22:[1, 9, 13], Operations: ['50-37=13'] Exploring Operation: 9+13=22, Resulting Numbers: [1, 22] Generated Node #0,0,0: 22:[1, 22] Operation: 9+13=22 Moving to Node #0,0,0 Current State: 22:[1, 22], Operations: ['50-37=13', '9+13=22'] Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 60, 35, 7, 36 ]
24
[ "60*7=420", "420/35=12", "36-12=24" ]
Current State: 24:[60, 35, 7, 36], Operations: [] Exploring Operation: 60*7=420, Resulting Numbers: [35, 36, 420] Generated Node #2: [35, 36, 420] from Operation: 60*7=420 Current State: 24:[35, 36, 420], Operations: ['60*7=420'] Exploring Operation: 420/35=12, Resulting Numbers: [36, 12] Generated Node #3: [36, 12] from Operation: 420/35=12 Current State: 24:[36, 12], Operations: ['60*7=420', '420/35=12'] Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[60, 35, 7, 36], Operations: [] Exploring Operation: 36-35=1, Resulting Numbers: [60, 7, 1] Generated Node #0,0: 24:[60, 7, 1] Operation: 36-35=1 Exploring Operation: 60-36=24, Resulting Numbers: [35, 7, 24] Generated Node #0,1: 24:[35, 7, 24] Operation: 60-36=24 Exploring Operation: 35/7=5, Resulting Numbers: [60, 36, 5] Generated Node #0,2: 24:[60, 36, 5] Operation: 35/7=5 Exploring Operation: 60-35=25, Resulting Numbers: [7, 36, 25] Generated Node #0,3: 24:[7, 36, 25] Operation: 60-35=25 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[35, 7, 24], Operations: ['60-36=24'] Exploring Operation: 35-24=11, Resulting Numbers: [7, 11] Generated Node #0,1,0: 24:[7, 11] Operation: 35-24=11 Exploring Operation: 35/7=5, Resulting Numbers: [24, 5] Generated Node #0,1,1: 24:[24, 5] Operation: 35/7=5 Exploring Operation: 24-7=17, Resulting Numbers: [35, 17] Generated Node #0,1,2: 24:[35, 17] Operation: 24-7=17 Exploring Operation: 35-7=28, Resulting Numbers: [24, 28] Generated Node #0,1,3: 24:[24, 28] Operation: 35-7=28 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 24:[24, 5], Operations: ['60-36=24', '35/7=5'] Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,24 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,24 unequal: No Solution Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 24:[7, 11], Operations: ['60-36=24', '35-24=11'] Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,24 unequal: No Solution Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,24 unequal: No Solution Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 24:[24, 28], Operations: ['60-36=24', '35-7=28'] Exploring Operation: 24+28=52, Resulting Numbers: [52] 52,24 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 24*28=672, Resulting Numbers: [672] 672,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 24:[35, 17], Operations: ['60-36=24', '24-7=17'] Exploring Operation: 35+17=52, Resulting Numbers: [52] 52,24 unequal: No Solution Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,24 unequal: No Solution Exploring Operation: 35*17=595, Resulting Numbers: [595] 595,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 24:[7, 36, 25], Operations: ['60-35=25'] Exploring Operation: 7+36=43, Resulting Numbers: [25, 43] Generated Node #0,3,0: 24:[25, 43] Operation: 7+36=43 Exploring Operation: 36-25=11, Resulting Numbers: [7, 11] Generated Node #0,3,1: 24:[7, 11] Operation: 36-25=11 Exploring Operation: 36-7=29, Resulting Numbers: [25, 29] Generated Node #0,3,2: 24:[25, 29] Operation: 36-7=29 Exploring Operation: 25-7=18, Resulting Numbers: [36, 18] Generated Node #0,3,3: 24:[36, 18] Operation: 25-7=18 Moving to Node #0,3,1 Current State: 24:[7, 11], Operations: ['60-35=25', '36-25=11'] Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,24 unequal: No Solution Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[25, 29], Operations: ['60-35=25', '36-7=29'] Exploring Operation: 25+29=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 25*29=725, Resulting Numbers: [725] 725,24 unequal: No Solution Moving to Node #0,3,3 Current State: 24:[36, 18], Operations: ['60-35=25', '25-7=18'] Exploring Operation: 36/18=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 36+18=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 36*18=648, Resulting Numbers: [648] 648,24 unequal: No Solution Exploring Operation: 36-18=18, Resulting Numbers: [18] 18,24 unequal: No Solution Moving to Node #0,3,0 Current State: 24:[25, 43], Operations: ['60-35=25', '7+36=43'] Exploring Operation: 25+43=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 43-25=18, Resulting Numbers: [18] 18,24 unequal: No Solution Exploring Operation: 25*43=1075, Resulting Numbers: [1075] 1075,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[60, 7, 1], Operations: ['36-35=1'] Exploring Operation: 7+1=8, Resulting Numbers: [60, 8] Generated Node #0,0,0: 24:[60, 8] Operation: 7+1=8 Exploring Operation: 60-7=53, Resulting Numbers: [1, 53] Generated Node #0,0,1: 24:[1, 53] Operation: 60-7=53 Exploring Operation: 7-1=6, Resulting Numbers: [60, 6] Generated Node #0,0,2: 24:[60, 6] Operation: 7-1=6 Exploring Operation: 60-1=59, Resulting Numbers: [7, 59] Generated Node #0,0,3: 24:[7, 59] Operation: 60-1=59 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 24:[1, 53], Operations: ['36-35=1', '60-7=53'] Exploring Operation: 1+53=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 1*53=53, Resulting Numbers: [53] 53,24 unequal: No Solution Exploring Operation: 53/1=53, Resulting Numbers: [53] 53,24 unequal: No Solution Exploring Operation: 53-1=52, Resulting Numbers: [52] 52,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[60, 8], Operations: ['36-35=1', '7+1=8'] Exploring Operation: 60+8=68, Resulting Numbers: [68] 68,24 unequal: No Solution Exploring Operation: 60*8=480, Resulting Numbers: [480] 480,24 unequal: No Solution Exploring Operation: 60-8=52, Resulting Numbers: [52] 52,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 24:[60, 6], Operations: ['36-35=1', '7-1=6'] Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 60+6=66, Resulting Numbers: [66] 66,24 unequal: No Solution Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,24 unequal: No Solution Exploring Operation: 60*6=360, Resulting Numbers: [360] 360,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 24:[7, 59], Operations: ['36-35=1', '60-1=59'] Exploring Operation: 7+59=66, Resulting Numbers: [66] 66,24 unequal: No Solution Exploring Operation: 7*59=413, Resulting Numbers: [413] 413,24 unequal: No Solution Exploring Operation: 59-7=52, Resulting Numbers: [52] 52,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[60, 36, 5], Operations: ['35/7=5'] Exploring Operation: 36-5=31, Resulting Numbers: [60, 31] Generated Node #0,2,0: 24:[60, 31] Operation: 36-5=31 Exploring Operation: 60-5=55, Resulting Numbers: [36, 55] Generated Node #0,2,1: 24:[36, 55] Operation: 60-5=55 Exploring Operation: 60-36=24, Resulting Numbers: [5, 24] Generated Node #0,2,2: 24:[5, 24] Operation: 60-36=24 Exploring Operation: 60/5=12, Resulting Numbers: [36, 12] Generated Node #0,2,3: 24:[36, 12] Operation: 60/5=12 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 24:[5, 24], Operations: ['35/7=5', '60-36=24'] Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,24 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,24 unequal: No Solution Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 24:[36, 12], Operations: ['35/7=5', '60/5=12'] Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[60, 35, 7, 36], Operations: [] Exploring Operation: 35/7=5, Resulting Numbers: [60, 36, 5] Generated Node #0,2: 24:[60, 36, 5] Operation: 35/7=5 Moving to Node #0,2 Current State: 24:[60, 36, 5], Operations: ['35/7=5'] Exploring Operation: 60/5=12, Resulting Numbers: [36, 12] Generated Node #0,2,3: 24:[36, 12] Operation: 60/5=12 Moving to Node #0,2,3 Current State: 24:[36, 12], Operations: ['35/7=5', '60/5=12'] Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.94184
hs_4
sum_heuristic
[ 89, 4, 31, 14 ]
21
[ "89+14=103", "4*31=124", "124-103=21" ]
Current State: 21:[89, 4, 31, 14], Operations: [] Exploring Operation: 89+14=103, Resulting Numbers: [4, 31, 103] Generated Node #2: [4, 31, 103] from Operation: 89+14=103 Current State: 21:[4, 31, 103], Operations: ['89+14=103'] Exploring Operation: 4*31=124, Resulting Numbers: [103, 124] Generated Node #3: [103, 124] from Operation: 4*31=124 Current State: 21:[103, 124], Operations: ['89+14=103', '4*31=124'] Exploring Operation: 124-103=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[89, 4, 31, 14], Operations: [] Exploring Operation: 89-31=58, Resulting Numbers: [4, 14, 58] Generated Node #0,0: 21:[4, 14, 58] Operation: 89-31=58 Exploring Operation: 89-14=75, Resulting Numbers: [4, 31, 75] Generated Node #0,1: 21:[4, 31, 75] Operation: 89-14=75 Exploring Operation: 31-14=17, Resulting Numbers: [89, 4, 17] Generated Node #0,2: 21:[89, 4, 17] Operation: 31-14=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[4, 14, 58], Operations: ['89-31=58'] Exploring Operation: 4+14=18, Resulting Numbers: [58, 18] Generated Node #0,0,0: 21:[58, 18] Operation: 4+14=18 Exploring Operation: 14-4=10, Resulting Numbers: [58, 10] Generated Node #0,0,1: 21:[58, 10] Operation: 14-4=10 Exploring Operation: 58-14=44, Resulting Numbers: [4, 44] Generated Node #0,0,2: 21:[4, 44] Operation: 58-14=44 Moving to Node #0,0,2 Current State: 21:[4, 44], Operations: ['89-31=58', '58-14=44'] Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[58, 18], Operations: ['89-31=58', '4+14=18'] Exploring Operation: 58+18=76, Resulting Numbers: [76] 76,21 unequal: No Solution Exploring Operation: 58-18=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 58*18=1044, Resulting Numbers: [1044] 1044,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[58, 10], Operations: ['89-31=58', '14-4=10'] Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,21 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 58*10=580, Resulting Numbers: [580] 580,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[4, 31, 75], Operations: ['89-14=75'] Exploring Operation: 31-4=27, Resulting Numbers: [75, 27] Generated Node #0,1,0: 21:[75, 27] Operation: 31-4=27 Exploring Operation: 75-31=44, Resulting Numbers: [4, 44] Generated Node #0,1,1: 21:[4, 44] Operation: 75-31=44 Exploring Operation: 75-4=71, Resulting Numbers: [31, 71] Generated Node #0,1,2: 21:[31, 71] Operation: 75-4=71 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 21:[4, 44], Operations: ['89-14=75', '75-31=44'] Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 21:[75, 27], Operations: ['89-14=75', '31-4=27'] Exploring Operation: 75+27=102, Resulting Numbers: [102] 102,21 unequal: No Solution Exploring Operation: 75*27=2025, Resulting Numbers: [2025] 2025,21 unequal: No Solution Exploring Operation: 75-27=48, Resulting Numbers: [48] 48,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 21:[31, 71], Operations: ['89-14=75', '75-4=71'] Exploring Operation: 31*71=2201, Resulting Numbers: [2201] 2201,21 unequal: No Solution Exploring Operation: 71-31=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 31+71=102, Resulting Numbers: [102] 102,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[89, 4, 17], Operations: ['31-14=17'] Exploring Operation: 4+17=21, Resulting Numbers: [89, 21] Generated Node #0,2,0: 21:[89, 21] Operation: 4+17=21 Exploring Operation: 89-17=72, Resulting Numbers: [4, 72] Generated Node #0,2,1: 21:[4, 72] Operation: 89-17=72 Exploring Operation: 89-4=85, Resulting Numbers: [17, 85] Generated Node #0,2,2: 21:[17, 85] Operation: 89-4=85 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 21:[4, 72], Operations: ['31-14=17', '89-17=72'] Exploring Operation: 4+72=76, Resulting Numbers: [76] 76,21 unequal: No Solution Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 21:[89, 21], Operations: ['31-14=17', '4+17=21'] Exploring Operation: 89+21=110, Resulting Numbers: [110] 110,21 unequal: No Solution Exploring Operation: 89*21=1869, Resulting Numbers: [1869] 1869,21 unequal: No Solution Exploring Operation: 89-21=68, Resulting Numbers: [68] 68,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 21:[17, 85], Operations: ['31-14=17', '89-4=85'] Exploring Operation: 85/17=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 17+85=102, Resulting Numbers: [102] 102,21 unequal: No Solution Exploring Operation: 85-17=68, Resulting Numbers: [68] 68,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 25, 29, 75, 2 ]
93
[ "75/25=3", "29+2=31", "3*31=93" ]
Current State: 93:[25, 29, 75, 2], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [29, 2, 3] Generated Node #2: [29, 2, 3] from Operation: 75/25=3 Current State: 93:[29, 2, 3], Operations: ['75/25=3'] Exploring Operation: 29+2=31, Resulting Numbers: [3, 31] Generated Node #3: [3, 31] from Operation: 29+2=31 Current State: 93:[3, 31], Operations: ['75/25=3', '29+2=31'] Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[25, 29, 75, 2], Operations: [] Exploring Operation: 29+75=104, Resulting Numbers: [25, 2, 104] Generated Node #0,0: 93:[25, 2, 104] Operation: 29+75=104 Exploring Operation: 75/25=3, Resulting Numbers: [29, 2, 3] Generated Node #0,1: 93:[29, 2, 3] Operation: 75/25=3 Exploring Operation: 25+75=100, Resulting Numbers: [29, 2, 100] Generated Node #0,2: 93:[29, 2, 100] Operation: 25+75=100 Exploring Operation: 29-25=4, Resulting Numbers: [75, 2, 4] Generated Node #0,3: 93:[75, 2, 4] Operation: 29-25=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[29, 2, 3], Operations: ['75/25=3'] Exploring Operation: 2+3=5, Resulting Numbers: [29, 5] Generated Node #0,1,0: 93:[29, 5] Operation: 2+3=5 Exploring Operation: 29-2=27, Resulting Numbers: [3, 27] Generated Node #0,1,1: 93:[3, 27] Operation: 29-2=27 Exploring Operation: 29+2=31, Resulting Numbers: [3, 31] Generated Node #0,1,2: 93:[3, 31] Operation: 29+2=31 Exploring Operation: 29+3=32, Resulting Numbers: [2, 32] Generated Node #0,1,3: 93:[2, 32] Operation: 29+3=32 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 93:[3, 31], Operations: ['75/25=3', '29+2=31'] Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[25, 29, 75, 2], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [29, 2, 3] Generated Node #0,1: 93:[29, 2, 3] Operation: 75/25=3 Moving to Node #0,1 Current State: 93:[29, 2, 3], Operations: ['75/25=3'] Exploring Operation: 29+2=31, Resulting Numbers: [3, 31] Generated Node #0,1,2: 93:[3, 31] Operation: 29+2=31 Moving to Node #0,1,2 Current State: 93:[3, 31], Operations: ['75/25=3', '29+2=31'] Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 30, 33, 84, 42 ]
36
[ "33*84=2772", "2772/42=66", "66-30=36" ]
Current State: 36:[30, 33, 84, 42], Operations: [] Exploring Operation: 33*84=2772, Resulting Numbers: [30, 42, 2772] Generated Node #2: [30, 42, 2772] from Operation: 33*84=2772 Current State: 36:[30, 42, 2772], Operations: ['33*84=2772'] Exploring Operation: 2772/42=66, Resulting Numbers: [30, 66] Generated Node #3: [30, 66] from Operation: 2772/42=66 Current State: 36:[30, 66], Operations: ['33*84=2772', '2772/42=66'] Exploring Operation: 66-30=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[30, 33, 84, 42], Operations: [] Exploring Operation: 84-30=54, Resulting Numbers: [33, 42, 54] Generated Node #0,0: 36:[33, 42, 54] Operation: 84-30=54 Exploring Operation: 84-33=51, Resulting Numbers: [30, 42, 51] Generated Node #0,1: 36:[30, 42, 51] Operation: 84-33=51 Exploring Operation: 84-42=42, Resulting Numbers: [30, 33, 42] Generated Node #0,2: 36:[30, 33, 42] Operation: 84-42=42 Exploring Operation: 84/42=2, Resulting Numbers: [30, 33, 2] Generated Node #0,3: 36:[30, 33, 2] Operation: 84/42=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 36:[30, 33, 2], Operations: ['84/42=2'] Exploring Operation: 30/2=15, Resulting Numbers: [33, 15] Generated Node #0,3,0: 36:[33, 15] Operation: 30/2=15 Exploring Operation: 33+2=35, Resulting Numbers: [30, 35] Generated Node #0,3,1: 36:[30, 35] Operation: 33+2=35 Exploring Operation: 33-30=3, Resulting Numbers: [2, 3] Generated Node #0,3,2: 36:[2, 3] Operation: 33-30=3 Exploring Operation: 30+2=32, Resulting Numbers: [33, 32] Generated Node #0,3,3: 36:[33, 32] Operation: 30+2=32 Moving to Node #0,3,2 Current State: 36:[2, 3], Operations: ['84/42=2', '33-30=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,36 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,36 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,36 unequal: No Solution Moving to Node #0,3,0 Current State: 36:[33, 15], Operations: ['84/42=2', '30/2=15'] Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,36 unequal: No Solution Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,36 unequal: No Solution Moving to Node #0,3,3 Current State: 36:[33, 32], Operations: ['84/42=2', '30+2=32'] Exploring Operation: 33*32=1056, Resulting Numbers: [1056] 1056,36 unequal: No Solution Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,36 unequal: No Solution Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,36 unequal: No Solution Moving to Node #0,3,1 Current State: 36:[30, 35], Operations: ['84/42=2', '33+2=35'] Exploring Operation: 30*35=1050, Resulting Numbers: [1050] 1050,36 unequal: No Solution Exploring Operation: 35-30=5, Resulting Numbers: [5] 5,36 unequal: No Solution Exploring Operation: 30+35=65, Resulting Numbers: [65] 65,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 36:[30, 33, 42], Operations: ['84-42=42'] Exploring Operation: 42-30=12, Resulting Numbers: [33, 12] Generated Node #0,2,0: 36:[33, 12] Operation: 42-30=12 Exploring Operation: 33-30=3, Resulting Numbers: [42, 3] Generated Node #0,2,1: 36:[42, 3] Operation: 33-30=3 Exploring Operation: 30+33=63, Resulting Numbers: [42, 63] Generated Node #0,2,2: 36:[42, 63] Operation: 30+33=63 Exploring Operation: 42-33=9, Resulting Numbers: [30, 9] Generated Node #0,2,3: 36:[30, 9] Operation: 42-33=9 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 36:[33, 12], Operations: ['84-42=42', '42-30=12'] Exploring Operation: 33+12=45, Resulting Numbers: [45] 45,36 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 33*12=396, Resulting Numbers: [396] 396,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 36:[42, 3], Operations: ['84-42=42', '33-30=3'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,36 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,36 unequal: No Solution Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,36 unequal: No Solution Exploring Operation: 42*3=126, Resulting Numbers: [126] 126,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 36:[30, 9], Operations: ['84-42=42', '42-33=9'] Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 30+9=39, Resulting Numbers: [39] 39,36 unequal: No Solution Exploring Operation: 30*9=270, Resulting Numbers: [270] 270,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 36:[42, 63], Operations: ['84-42=42', '30+33=63'] Exploring Operation: 42*63=2646, Resulting Numbers: [2646] 2646,36 unequal: No Solution Exploring Operation: 42+63=105, Resulting Numbers: [105] 105,36 unequal: No Solution Exploring Operation: 63-42=21, Resulting Numbers: [21] 21,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[33, 42, 54], Operations: ['84-30=54'] Exploring Operation: 54-42=12, Resulting Numbers: [33, 12] Generated Node #0,0,0: 36:[33, 12] Operation: 54-42=12 Exploring Operation: 33+42=75, Resulting Numbers: [54, 75] Generated Node #0,0,1: 36:[54, 75] Operation: 33+42=75 Exploring Operation: 42-33=9, Resulting Numbers: [54, 9] Generated Node #0,0,2: 36:[54, 9] Operation: 42-33=9 Exploring Operation: 54-33=21, Resulting Numbers: [42, 21] Generated Node #0,0,3: 36:[42, 21] Operation: 54-33=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[33, 12], Operations: ['84-30=54', '54-42=12'] Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 33*12=396, Resulting Numbers: [396] 396,36 unequal: No Solution Exploring Operation: 33+12=45, Resulting Numbers: [45] 45,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 36:[42, 21], Operations: ['84-30=54', '54-33=21'] Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 42*21=882, Resulting Numbers: [882] 882,36 unequal: No Solution Exploring Operation: 42+21=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 36:[54, 9], Operations: ['84-30=54', '42-33=9'] Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,36 unequal: No Solution Exploring Operation: 54*9=486, Resulting Numbers: [486] 486,36 unequal: No Solution Exploring Operation: 54+9=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 36:[54, 75], Operations: ['84-30=54', '33+42=75'] Exploring Operation: 75-54=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 54+75=129, Resulting Numbers: [129] 129,36 unequal: No Solution Exploring Operation: 54*75=4050, Resulting Numbers: [4050] 4050,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[30, 42, 51], Operations: ['84-33=51'] Exploring Operation: 51-42=9, Resulting Numbers: [30, 9] Generated Node #0,1,0: 36:[30, 9] Operation: 51-42=9 Exploring Operation: 42-30=12, Resulting Numbers: [51, 12] Generated Node #0,1,1: 36:[51, 12] Operation: 42-30=12 Exploring Operation: 51-30=21, Resulting Numbers: [42, 21] Generated Node #0,1,2: 36:[42, 21] Operation: 51-30=21 Exploring Operation: 30+42=72, Resulting Numbers: [51, 72] Generated Node #0,1,3: 36:[51, 72] Operation: 30+42=72 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 36:[30, 9], Operations: ['84-33=51', '51-42=9'] Exploring Operation: 30*9=270, Resulting Numbers: [270] 270,36 unequal: No Solution Exploring Operation: 30+9=39, Resulting Numbers: [39] 39,36 unequal: No Solution Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 36:[42, 21], Operations: ['84-33=51', '51-30=21'] Exploring Operation: 42*21=882, Resulting Numbers: [882] 882,36 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 42+21=63, Resulting Numbers: [63] 63,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 36:[51, 12], Operations: ['84-33=51', '42-30=12'] Exploring Operation: 51*12=612, Resulting Numbers: [612] 612,36 unequal: No Solution Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 36:[51, 72], Operations: ['84-33=51', '30+42=72'] Exploring Operation: 51+72=123, Resulting Numbers: [123] 123,36 unequal: No Solution Exploring Operation: 72-51=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 51*72=3672, Resulting Numbers: [3672] 3672,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 24, 61, 72, 44 ]
51
[ "72/24=3", "61-44=17", "3*17=51" ]
Current State: 51:[24, 61, 72, 44], Operations: [] Exploring Operation: 72/24=3, Resulting Numbers: [61, 44, 3] Generated Node #2: [61, 44, 3] from Operation: 72/24=3 Current State: 51:[61, 44, 3], Operations: ['72/24=3'] Exploring Operation: 61-44=17, Resulting Numbers: [3, 17] Generated Node #3: [3, 17] from Operation: 61-44=17 Current State: 51:[3, 17], Operations: ['72/24=3', '61-44=17'] Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[24, 61, 72, 44], Operations: [] Exploring Operation: 72/24=3, Resulting Numbers: [61, 44, 3] Generated Node #0,0: 51:[61, 44, 3] Operation: 72/24=3 Exploring Operation: 72-24=48, Resulting Numbers: [61, 44, 48] Generated Node #0,1: 51:[61, 44, 48] Operation: 72-24=48 Exploring Operation: 72-61=11, Resulting Numbers: [24, 44, 11] Generated Node #0,2: 51:[24, 44, 11] Operation: 72-61=11 Exploring Operation: 61-44=17, Resulting Numbers: [24, 72, 17] Generated Node #0,3: 51:[24, 72, 17] Operation: 61-44=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[61, 44, 3], Operations: ['72/24=3'] Exploring Operation: 44+3=47, Resulting Numbers: [61, 47] Generated Node #0,0,0: 51:[61, 47] Operation: 44+3=47 Exploring Operation: 61-44=17, Resulting Numbers: [3, 17] Generated Node #0,0,1: 51:[3, 17] Operation: 61-44=17 Exploring Operation: 61-3=58, Resulting Numbers: [44, 58] Generated Node #0,0,2: 51:[44, 58] Operation: 61-3=58 Exploring Operation: 61+3=64, Resulting Numbers: [44, 64] Generated Node #0,0,3: 51:[44, 64] Operation: 61+3=64 Moving to Node #0,0,1 Current State: 51:[3, 17], Operations: ['72/24=3', '61-44=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,51 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[24, 61, 72, 44], Operations: [] Exploring Operation: 72/24=3, Resulting Numbers: [61, 44, 3] Generated Node #0,0: 51:[61, 44, 3] Operation: 72/24=3 Moving to Node #0,0 Current State: 51:[61, 44, 3], Operations: ['72/24=3'] Exploring Operation: 61-44=17, Resulting Numbers: [3, 17] Generated Node #0,0,1: 51:[3, 17] Operation: 61-44=17 Moving to Node #0,0,1 Current State: 51:[3, 17], Operations: ['72/24=3', '61-44=17'] Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 21, 48, 3, 17 ]
64
[ "48-21=27", "3*27=81", "81-17=64" ]
Current State: 64:[21, 48, 3, 17], Operations: [] Exploring Operation: 48-21=27, Resulting Numbers: [3, 17, 27] Generated Node #2: [3, 17, 27] from Operation: 48-21=27 Current State: 64:[3, 17, 27], Operations: ['48-21=27'] Exploring Operation: 3*27=81, Resulting Numbers: [17, 81] Generated Node #3: [17, 81] from Operation: 3*27=81 Current State: 64:[17, 81], Operations: ['48-21=27', '3*27=81'] Exploring Operation: 81-17=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[21, 48, 3, 17], Operations: [] Exploring Operation: 21+48=69, Resulting Numbers: [3, 17, 69] Generated Node #0,0: 64:[3, 17, 69] Operation: 21+48=69 Exploring Operation: 48/3=16, Resulting Numbers: [21, 17, 16] Generated Node #0,1: 64:[21, 17, 16] Operation: 48/3=16 Exploring Operation: 48+17=65, Resulting Numbers: [21, 3, 65] Generated Node #0,2: 64:[21, 3, 65] Operation: 48+17=65 Exploring Operation: 48-17=31, Resulting Numbers: [21, 3, 31] Generated Node #0,3: 64:[21, 3, 31] Operation: 48-17=31 Exploring Operation: 48-21=27, Resulting Numbers: [3, 17, 27] Generated Node #0,4: 64:[3, 17, 27] Operation: 48-21=27 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[21, 17, 16], Operations: ['48/3=16'] Exploring Operation: 17+16=33, Resulting Numbers: [21, 33] Generated Node #0,1,0: 64:[21, 33] Operation: 17+16=33 Exploring Operation: 21+17=38, Resulting Numbers: [16, 38] Generated Node #0,1,1: 64:[16, 38] Operation: 21+17=38 Exploring Operation: 21+16=37, Resulting Numbers: [17, 37] Generated Node #0,1,2: 64:[17, 37] Operation: 21+16=37 Exploring Operation: 21-17=4, Resulting Numbers: [16, 4] Generated Node #0,1,3: 64:[16, 4] Operation: 21-17=4 Exploring Operation: 21-16=5, Resulting Numbers: [17, 5] Generated Node #0,1,4: 64:[17, 5] Operation: 21-16=5 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 64:[16, 4], Operations: ['48/3=16', '21-17=4'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,64 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[21, 48, 3, 17], Operations: [] Exploring Operation: 48/3=16, Resulting Numbers: [21, 17, 16] Generated Node #0,1: 64:[21, 17, 16] Operation: 48/3=16 Moving to Node #0,1 Current State: 64:[21, 17, 16], Operations: ['48/3=16'] Exploring Operation: 21-17=4, Resulting Numbers: [16, 4] Generated Node #0,1,3: 64:[16, 4] Operation: 21-17=4 Moving to Node #0,1,3 Current State: 64:[16, 4], Operations: ['48/3=16', '21-17=4'] Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 52, 6, 46, 44 ]
94
[ "52-44=8", "6*8=48", "46+48=94" ]
Current State: 94:[52, 6, 46, 44], Operations: [] Exploring Operation: 52-44=8, Resulting Numbers: [6, 46, 8] Generated Node #2: [6, 46, 8] from Operation: 52-44=8 Current State: 94:[6, 46, 8], Operations: ['52-44=8'] Exploring Operation: 6*8=48, Resulting Numbers: [46, 48] Generated Node #3: [46, 48] from Operation: 6*8=48 Current State: 94:[46, 48], Operations: ['52-44=8', '6*8=48'] Exploring Operation: 46+48=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[52, 6, 46, 44], Operations: [] Exploring Operation: 52+44=96, Resulting Numbers: [6, 46, 96] Generated Node #0,0: 94:[6, 46, 96] Operation: 52+44=96 Exploring Operation: 52-6=46, Resulting Numbers: [46, 44, 46] Generated Node #0,1: 94:[46, 44, 46] Operation: 52-6=46 Exploring Operation: 6+44=50, Resulting Numbers: [52, 46, 50] Generated Node #0,2: 94:[52, 46, 50] Operation: 6+44=50 Exploring Operation: 46-44=2, Resulting Numbers: [52, 6, 2] Generated Node #0,3: 94:[52, 6, 2] Operation: 46-44=2 Moving to Node #0,1 Current State: 94:[46, 44, 46], Operations: ['52-6=46'] Exploring Operation: 46+44=90, Resulting Numbers: [46, 90] Generated Node #0,1,0: 94:[46, 90] Operation: 46+44=90 Exploring Operation: 46-44=2, Resulting Numbers: [46, 2] Generated Node #0,1,1: 94:[46, 2] Operation: 46-44=2 Exploring Operation: 46/46=1, Resulting Numbers: [44, 1] Generated Node #0,1,2: 94:[44, 1] Operation: 46/46=1 Exploring Operation: 46-44=2, Resulting Numbers: [46, 2] Generated Node #0,1,3: 94:[46, 2] Operation: 46-44=2 Moving to Node #0,0 Current State: 94:[6, 46, 96], Operations: ['52+44=96'] Exploring Operation: 6+46=52, Resulting Numbers: [96, 52] Generated Node #0,0,0: 94:[96, 52] Operation: 6+46=52 Exploring Operation: 96-6=90, Resulting Numbers: [46, 90] Generated Node #0,0,1: 94:[46, 90] Operation: 96-6=90 Exploring Operation: 46-6=40, Resulting Numbers: [96, 40] Generated Node #0,0,2: 94:[96, 40] Operation: 46-6=40 Exploring Operation: 96-46=50, Resulting Numbers: [6, 50] Generated Node #0,0,3: 94:[6, 50] Operation: 96-46=50 Moving to Node #0,3 Current State: 94:[52, 6, 2], Operations: ['46-44=2'] Exploring Operation: 6/2=3, Resulting Numbers: [52, 3] Generated Node #0,3,0: 94:[52, 3] Operation: 6/2=3 Exploring Operation: 6-2=4, Resulting Numbers: [52, 4] Generated Node #0,3,1: 94:[52, 4] Operation: 6-2=4 Exploring Operation: 52-6=46, Resulting Numbers: [2, 46] Generated Node #0,3,2: 94:[2, 46] Operation: 52-6=46 Exploring Operation: 52-2=50, Resulting Numbers: [6, 50] Generated Node #0,3,3: 94:[6, 50] Operation: 52-2=50 Moving to Node #0,2 Current State: 94:[52, 46, 50], Operations: ['6+44=50'] Exploring Operation: 46+50=96, Resulting Numbers: [52, 96] Generated Node #0,2,0: 94:[52, 96] Operation: 46+50=96 Exploring Operation: 52+46=98, Resulting Numbers: [50, 98] Generated Node #0,2,1: 94:[50, 98] Operation: 52+46=98 Exploring Operation: 52-46=6, Resulting Numbers: [50, 6] Generated Node #0,2,2: 94:[50, 6] Operation: 52-46=6 Exploring Operation: 52-50=2, Resulting Numbers: [46, 2] Generated Node #0,2,3: 94:[46, 2] Operation: 52-50=2 Moving to Node #0,1,1 Current State: 94:[46, 2], Operations: ['52-6=46', '46-44=2'] Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,94 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,94 unequal: No Solution Moving to Node #0,2,3 Current State: 94:[46, 2], Operations: ['6+44=50', '52-50=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,94 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,94 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,94 unequal: No Solution Moving to Node #0,1,3 Current State: 94:[46, 2], Operations: ['52-6=46', '46-44=2'] Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,94 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,94 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,94 unequal: No Solution Moving to Node #0,3,2 Current State: 94:[2, 46], Operations: ['46-44=2', '52-6=46'] Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,94 unequal: No Solution Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[44, 1], Operations: ['52-6=46', '46/46=1'] Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[46, 90], Operations: ['52+44=96', '96-6=90'] Exploring Operation: 90-46=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 46+90=136, Resulting Numbers: [136] 136,94 unequal: No Solution Exploring Operation: 46*90=4140, Resulting Numbers: [4140] 4140,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[46, 90], Operations: ['52-6=46', '46+44=90'] Exploring Operation: 46+90=136, Resulting Numbers: [136] 136,94 unequal: No Solution Exploring Operation: 90-46=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 46*90=4140, Resulting Numbers: [4140] 4140,94 unequal: No Solution Moving to Node #0,3,0 Current State: 94:[52, 3], Operations: ['46-44=2', '6/2=3'] Exploring Operation: 52*3=156, Resulting Numbers: [156] 156,94 unequal: No Solution Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,94 unequal: No Solution Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,94 unequal: No Solution Moving to Node #0,0,3 Current State: 94:[6, 50], Operations: ['52+44=96', '96-46=50'] Exploring Operation: 6*50=300, Resulting Numbers: [300] 300,94 unequal: No Solution Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 6+50=56, Resulting Numbers: [56] 56,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[96, 52], Operations: ['52+44=96', '6+46=52'] Exploring Operation: 96-52=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 96+52=148, Resulting Numbers: [148] 148,94 unequal: No Solution Exploring Operation: 96*52=4992, Resulting Numbers: [4992] 4992,94 unequal: No Solution Moving to Node #0,3,3 Current State: 94:[6, 50], Operations: ['46-44=2', '52-2=50'] Exploring Operation: 6+50=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 6*50=300, Resulting Numbers: [300] 300,94 unequal: No Solution Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[50, 6], Operations: ['6+44=50', '52-46=6'] Exploring Operation: 50*6=300, Resulting Numbers: [300] 300,94 unequal: No Solution Exploring Operation: 50+6=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,94 unequal: No Solution Moving to Node #0,2,0 Current State: 94:[52, 96], Operations: ['6+44=50', '46+50=96'] Exploring Operation: 52*96=4992, Resulting Numbers: [4992] 4992,94 unequal: No Solution Exploring Operation: 96-52=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 52+96=148, Resulting Numbers: [148] 148,94 unequal: No Solution Moving to Node #0,2,1 Current State: 94:[50, 98], Operations: ['6+44=50', '52+46=98'] Exploring Operation: 50*98=4900, Resulting Numbers: [4900] 4900,94 unequal: No Solution Exploring Operation: 50+98=148, Resulting Numbers: [148] 148,94 unequal: No Solution Exploring Operation: 98-50=48, Resulting Numbers: [48] 48,94 unequal: No Solution Moving to Node #0,3,1 Current State: 94:[52, 4], Operations: ['46-44=2', '6-2=4'] Exploring Operation: 52+4=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 52*4=208, Resulting Numbers: [208] 208,94 unequal: No Solution Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[96, 40], Operations: ['52+44=96', '46-6=40'] Exploring Operation: 96-40=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 96*40=3840, Resulting Numbers: [3840] 3840,94 unequal: No Solution Exploring Operation: 96+40=136, Resulting Numbers: [136] 136,94 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 83, 24, 72, 20 ]
23
[ "72/24=3", "20*3=60", "83-60=23" ]
Current State: 23:[83, 24, 72, 20], Operations: [] Exploring Operation: 72/24=3, Resulting Numbers: [83, 20, 3] Generated Node #2: [83, 20, 3] from Operation: 72/24=3 Current State: 23:[83, 20, 3], Operations: ['72/24=3'] Exploring Operation: 20*3=60, Resulting Numbers: [83, 60] Generated Node #3: [83, 60] from Operation: 20*3=60 Current State: 23:[83, 60], Operations: ['72/24=3', '20*3=60'] Exploring Operation: 83-60=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[83, 24, 72, 20], Operations: [] Exploring Operation: 83-72=11, Resulting Numbers: [24, 20, 11] Generated Node #0,0: 23:[24, 20, 11] Operation: 83-72=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[24, 20, 11], Operations: ['83-72=11'] Exploring Operation: 20+11=31, Resulting Numbers: [24, 31] Generated Node #0,0,0: 23:[24, 31] Operation: 20+11=31 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[24, 31], Operations: ['83-72=11', '20+11=31'] Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 60, 56, 4, 84 ]
55
[ "60+56=116", "116/4=29", "84-29=55" ]
Current State: 55:[60, 56, 4, 84], Operations: [] Exploring Operation: 60+56=116, Resulting Numbers: [4, 84, 116] Generated Node #2: [4, 84, 116] from Operation: 60+56=116 Current State: 55:[4, 84, 116], Operations: ['60+56=116'] Exploring Operation: 116/4=29, Resulting Numbers: [84, 29] Generated Node #3: [84, 29] from Operation: 116/4=29 Current State: 55:[84, 29], Operations: ['60+56=116', '116/4=29'] Exploring Operation: 84-29=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[60, 56, 4, 84], Operations: [] Exploring Operation: 60-56=4, Resulting Numbers: [4, 84, 4] Generated Node #0,0: 55:[4, 84, 4] Operation: 60-56=4 Exploring Operation: 84-60=24, Resulting Numbers: [56, 4, 24] Generated Node #0,1: 55:[56, 4, 24] Operation: 84-60=24 Exploring Operation: 84-56=28, Resulting Numbers: [60, 4, 28] Generated Node #0,2: 55:[60, 4, 28] Operation: 84-56=28 Exploring Operation: 84/4=21, Resulting Numbers: [60, 56, 21] Generated Node #0,3: 55:[60, 56, 21] Operation: 84/4=21 Moving to Node #0,1 Current State: 55:[56, 4, 24], Operations: ['84-60=24'] Exploring Operation: 24/4=6, Resulting Numbers: [56, 6] Generated Node #0,1,0: 55:[56, 6] Operation: 24/4=6 Exploring Operation: 56-4=52, Resulting Numbers: [24, 52] Generated Node #0,1,1: 55:[24, 52] Operation: 56-4=52 Exploring Operation: 56/4=14, Resulting Numbers: [24, 14] Generated Node #0,1,2: 55:[24, 14] Operation: 56/4=14 Exploring Operation: 24-4=20, Resulting Numbers: [56, 20] Generated Node #0,1,3: 55:[56, 20] Operation: 24-4=20 Moving to Node #0,3 Current State: 55:[60, 56, 21], Operations: ['84/4=21'] Exploring Operation: 60-56=4, Resulting Numbers: [21, 4] Generated Node #0,3,0: 55:[21, 4] Operation: 60-56=4 Exploring Operation: 60-21=39, Resulting Numbers: [56, 39] Generated Node #0,3,1: 55:[56, 39] Operation: 60-21=39 Exploring Operation: 56-21=35, Resulting Numbers: [60, 35] Generated Node #0,3,2: 55:[60, 35] Operation: 56-21=35 Exploring Operation: 60+21=81, Resulting Numbers: [56, 81] Generated Node #0,3,3: 55:[56, 81] Operation: 60+21=81 Moving to Node #0,2 Current State: 55:[60, 4, 28], Operations: ['84-56=28'] Exploring Operation: 28-4=24, Resulting Numbers: [60, 24] Generated Node #0,2,0: 55:[60, 24] Operation: 28-4=24 Exploring Operation: 60/4=15, Resulting Numbers: [28, 15] Generated Node #0,2,1: 55:[28, 15] Operation: 60/4=15 Exploring Operation: 60-4=56, Resulting Numbers: [28, 56] Generated Node #0,2,2: 55:[28, 56] Operation: 60-4=56 Exploring Operation: 28/4=7, Resulting Numbers: [60, 7] Generated Node #0,2,3: 55:[60, 7] Operation: 28/4=7 Moving to Node #0,0 Current State: 55:[4, 84, 4], Operations: ['60-56=4'] Exploring Operation: 84/4=21, Resulting Numbers: [4, 21] Generated Node #0,0,0: 55:[4, 21] Operation: 84/4=21 Exploring Operation: 84-4=80, Resulting Numbers: [4, 80] Generated Node #0,0,1: 55:[4, 80] Operation: 84-4=80 Exploring Operation: 84-4=80, Resulting Numbers: [4, 80] Generated Node #0,0,2: 55:[4, 80] Operation: 84-4=80 Exploring Operation: 84/4=21, Resulting Numbers: [4, 21] Generated Node #0,0,3: 55:[4, 21] Operation: 84/4=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 55:[4, 21], Operations: ['60-56=4', '84/4=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,55 unequal: No Solution Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 55:[4, 21], Operations: ['60-56=4', '84/4=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,55 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 55:[4, 80], Operations: ['60-56=4', '84-4=80'] Exploring Operation: 4*80=320, Resulting Numbers: [320] 320,55 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,55 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,55 unequal: No Solution Exploring Operation: 4+80=84, Resulting Numbers: [84] 84,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 55:[4, 80], Operations: ['60-56=4', '84-4=80'] Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,55 unequal: No Solution Exploring Operation: 4+80=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,55 unequal: No Solution Exploring Operation: 4*80=320, Resulting Numbers: [320] 320,55 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: 55:[56, 6], Operations: ['84-60=24', '24/4=6'] Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,55 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,55 unequal: No Solution Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,55 unequal: No Solution Moving to Node #0,2,3 Current State: 55:[60, 7], Operations: ['84-56=28', '28/4=7'] Exploring Operation: 60-7=53, Resulting Numbers: [53] 53,55 unequal: No Solution Exploring Operation: 60+7=67, Resulting Numbers: [67] 67,55 unequal: No Solution Exploring Operation: 60*7=420, Resulting Numbers: [420] 420,55 unequal: No Solution Moving to Node #0,1,3 Current State: 55:[56, 20], Operations: ['84-60=24', '24-4=20'] Exploring Operation: 56-20=36, Resulting Numbers: [36] 36,55 unequal: No Solution Exploring Operation: 56+20=76, Resulting Numbers: [76] 76,55 unequal: No Solution Exploring Operation: 56*20=1120, Resulting Numbers: [1120] 1120,55 unequal: No Solution Moving to Node #0,3,0 Current State: 55:[21, 4], Operations: ['84/4=21', '60-56=4'] Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,55 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[24, 52], Operations: ['84-60=24', '56-4=52'] Exploring Operation: 24*52=1248, Resulting Numbers: [1248] 1248,55 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,55 unequal: No Solution Exploring Operation: 24+52=76, Resulting Numbers: [76] 76,55 unequal: No Solution Moving to Node #0,1,2 Current State: 55:[24, 14], Operations: ['84-60=24', '56/4=14'] Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,55 unequal: No Solution Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 24*14=336, Resulting Numbers: [336] 336,55 unequal: No Solution Moving to Node #0,3,1 Current State: 55:[56, 39], Operations: ['84/4=21', '60-21=39'] Exploring Operation: 56*39=2184, Resulting Numbers: [2184] 2184,55 unequal: No Solution Exploring Operation: 56+39=95, Resulting Numbers: [95] 95,55 unequal: No Solution Exploring Operation: 56-39=17, Resulting Numbers: [17] 17,55 unequal: No Solution Moving to Node #0,2,0 Current State: 55:[60, 24], Operations: ['84-56=28', '28-4=24'] Exploring Operation: 60+24=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 60*24=1440, Resulting Numbers: [1440] 1440,55 unequal: No Solution Exploring Operation: 60-24=36, Resulting Numbers: [36] 36,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[28, 56], Operations: ['84-56=28', '60-4=56'] Exploring Operation: 56-28=28, Resulting Numbers: [28] 28,55 unequal: No Solution Exploring Operation: 28*56=1568, Resulting Numbers: [1568] 1568,55 unequal: No Solution Exploring Operation: 56/28=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 28+56=84, Resulting Numbers: [84] 84,55 unequal: No Solution Moving to Node #0,2,1 Current State: 55:[28, 15], Operations: ['84-56=28', '60/4=15'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,55 unequal: No Solution Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,55 unequal: No Solution Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,55 unequal: No Solution Moving to Node #0,3,2 Current State: 55:[60, 35], Operations: ['84/4=21', '56-21=35'] Exploring Operation: 60*35=2100, Resulting Numbers: [2100] 2100,55 unequal: No Solution Exploring Operation: 60+35=95, Resulting Numbers: [95] 95,55 unequal: No Solution Exploring Operation: 60-35=25, Resulting Numbers: [25] 25,55 unequal: No Solution Moving to Node #0,3,3 Current State: 55:[56, 81], Operations: ['84/4=21', '60+21=81'] Exploring Operation: 56*81=4536, Resulting Numbers: [4536] 4536,55 unequal: No Solution Exploring Operation: 81-56=25, Resulting Numbers: [25] 25,55 unequal: No Solution Exploring Operation: 56+81=137, Resulting Numbers: [137] 137,55 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 32, 72, 48, 44 ]
68
[ "44-32=12", "48/12=4", "72-4=68" ]
Current State: 68:[32, 72, 48, 44], Operations: [] Exploring Operation: 44-32=12, Resulting Numbers: [72, 48, 12] Generated Node #2: [72, 48, 12] from Operation: 44-32=12 Current State: 68:[72, 48, 12], Operations: ['44-32=12'] Exploring Operation: 48/12=4, Resulting Numbers: [72, 4] Generated Node #3: [72, 4] from Operation: 48/12=4 Current State: 68:[72, 4], Operations: ['44-32=12', '48/12=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[32, 72, 48, 44], Operations: [] Exploring Operation: 72-48=24, Resulting Numbers: [32, 44, 24] Generated Node #0,0: 68:[32, 44, 24] Operation: 72-48=24 Exploring Operation: 72-44=28, Resulting Numbers: [32, 48, 28] Generated Node #0,1: 68:[32, 48, 28] Operation: 72-44=28 Exploring Operation: 48-44=4, Resulting Numbers: [32, 72, 4] Generated Node #0,2: 68:[32, 72, 4] Operation: 48-44=4 Exploring Operation: 48-32=16, Resulting Numbers: [72, 44, 16] Generated Node #0,3: 68:[72, 44, 16] Operation: 48-32=16 Exploring Operation: 44-32=12, Resulting Numbers: [72, 48, 12] Generated Node #0,4: 68:[72, 48, 12] Operation: 44-32=12 Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[32, 72, 4], Operations: ['48-44=4'] Exploring Operation: 72/4=18, Resulting Numbers: [32, 18] Generated Node #0,2,0: 68:[32, 18] Operation: 72/4=18 Exploring Operation: 32/4=8, Resulting Numbers: [72, 8] Generated Node #0,2,1: 68:[72, 8] Operation: 32/4=8 Exploring Operation: 72-4=68, Resulting Numbers: [32, 68] Generated Node #0,2,2: 68:[32, 68] Operation: 72-4=68 Exploring Operation: 72-32=40, Resulting Numbers: [4, 40] Generated Node #0,2,3: 68:[4, 40] Operation: 72-32=40 Exploring Operation: 32+4=36, Resulting Numbers: [72, 36] Generated Node #0,2,4: 68:[72, 36] Operation: 32+4=36 Moving to Node #0,2,2 Current State: 68:[32, 68], Operations: ['48-44=4', '72-4=68'] Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 32*68=2176, Resulting Numbers: [2176] 2176,68 unequal: No Solution Exploring Operation: 32+68=100, Resulting Numbers: [100] 100,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[32, 18], Operations: ['48-44=4', '72/4=18'] Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,68 unequal: No Solution Exploring Operation: 32*18=576, Resulting Numbers: [576] 576,68 unequal: No Solution Exploring Operation: 32+18=50, Resulting Numbers: [50] 50,68 unequal: No Solution Moving to Node #0,2,3 Current State: 68:[4, 40], Operations: ['48-44=4', '72-32=40'] Exploring Operation: 4*40=160, Resulting Numbers: [160] 160,68 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,68 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 4+40=44, Resulting Numbers: [44] 44,68 unequal: No Solution Moving to Node #0,2,4 Current State: 68:[72, 36], Operations: ['48-44=4', '32+4=36'] Exploring Operation: 72+36=108, Resulting Numbers: [108] 108,68 unequal: No Solution Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 72*36=2592, Resulting Numbers: [2592] 2592,68 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,68 unequal: No Solution Moving to Node #0,2,1 Current State: 68:[72, 8], Operations: ['48-44=4', '32/4=8'] Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,68 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,68 unequal: No Solution Exploring Operation: 72*8=576, Resulting Numbers: [576] 576,68 unequal: No Solution Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 68:[72, 44, 16], Operations: ['48-32=16'] Exploring Operation: 72-16=56, Resulting Numbers: [44, 56] Generated Node #0,3,0: 68:[44, 56] Operation: 72-16=56 Exploring Operation: 44-16=28, Resulting Numbers: [72, 28] Generated Node #0,3,1: 68:[72, 28] Operation: 44-16=28 Exploring Operation: 72-44=28, Resulting Numbers: [16, 28] Generated Node #0,3,2: 68:[16, 28] Operation: 72-44=28 Exploring Operation: 72+16=88, Resulting Numbers: [44, 88] Generated Node #0,3,3: 68:[44, 88] Operation: 72+16=88 Exploring Operation: 44+16=60, Resulting Numbers: [72, 60] Generated Node #0,3,4: 68:[72, 60] Operation: 44+16=60 Moving to Node #0,3,2 Current State: 68:[16, 28], Operations: ['48-32=16', '72-44=28'] Exploring Operation: 16+28=44, Resulting Numbers: [44] 44,68 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 16*28=448, Resulting Numbers: [448] 448,68 unequal: No Solution Moving to Node #0,3,1 Current State: 68:[72, 28], Operations: ['48-32=16', '44-16=28'] Exploring Operation: 72+28=100, Resulting Numbers: [100] 100,68 unequal: No Solution Exploring Operation: 72-28=44, Resulting Numbers: [44] 44,68 unequal: No Solution Exploring Operation: 72*28=2016, Resulting Numbers: [2016] 2016,68 unequal: No Solution Moving to Node #0,3,4 Current State: 68:[72, 60], Operations: ['48-32=16', '44+16=60'] Exploring Operation: 72-60=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 72+60=132, Resulting Numbers: [132] 132,68 unequal: No Solution Exploring Operation: 72*60=4320, Resulting Numbers: [4320] 4320,68 unequal: No Solution Moving to Node #0,3,0 Current State: 68:[44, 56], Operations: ['48-32=16', '72-16=56'] Exploring Operation: 56-44=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 44+56=100, Resulting Numbers: [100] 100,68 unequal: No Solution Exploring Operation: 44*56=2464, Resulting Numbers: [2464] 2464,68 unequal: No Solution Moving to Node #0,3,3 Current State: 68:[44, 88], Operations: ['48-32=16', '72+16=88'] Exploring Operation: 88/44=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 44+88=132, Resulting Numbers: [132] 132,68 unequal: No Solution Exploring Operation: 44*88=3872, Resulting Numbers: [3872] 3872,68 unequal: No Solution Exploring Operation: 88-44=44, Resulting Numbers: [44] 44,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[32, 44, 24], Operations: ['72-48=24'] Exploring Operation: 32+44=76, Resulting Numbers: [24, 76] Generated Node #0,0,0: 68:[24, 76] Operation: 32+44=76 Exploring Operation: 44-24=20, Resulting Numbers: [32, 20] Generated Node #0,0,1: 68:[32, 20] Operation: 44-24=20 Exploring Operation: 32-24=8, Resulting Numbers: [44, 8] Generated Node #0,0,2: 68:[44, 8] Operation: 32-24=8 Exploring Operation: 44-32=12, Resulting Numbers: [24, 12] Generated Node #0,0,3: 68:[24, 12] Operation: 44-32=12 Exploring Operation: 44+24=68, Resulting Numbers: [32, 68] Generated Node #0,0,4: 68:[32, 68] Operation: 44+24=68 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 68:[32, 68], Operations: ['72-48=24', '44+24=68'] Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 32*68=2176, Resulting Numbers: [2176] 2176,68 unequal: No Solution Exploring Operation: 32+68=100, Resulting Numbers: [100] 100,68 unequal: No Solution No 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: 68:[32, 20], Operations: ['72-48=24', '44-24=20'] Exploring Operation: 32*20=640, Resulting Numbers: [640] 640,68 unequal: No Solution Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 32+20=52, Resulting Numbers: [52] 52,68 unequal: No Solution No 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: 68:[24, 12], Operations: ['72-48=24', '44-32=12'] Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 24+12=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 24*12=288, Resulting Numbers: [288] 288,68 unequal: No Solution No 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: 68:[44, 8], Operations: ['72-48=24', '32-24=8'] Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 44*8=352, Resulting Numbers: [352] 352,68 unequal: No Solution Exploring Operation: 44+8=52, Resulting Numbers: [52] 52,68 unequal: No Solution No 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: 68:[24, 76], Operations: ['72-48=24', '32+44=76'] Exploring Operation: 24*76=1824, Resulting Numbers: [1824] 1824,68 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 24+76=100, Resulting Numbers: [100] 100,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[32, 48, 28], Operations: ['72-44=28'] Exploring Operation: 32+48=80, Resulting Numbers: [28, 80] Generated Node #0,1,0: 68:[28, 80] Operation: 32+48=80 Exploring Operation: 48-28=20, Resulting Numbers: [32, 20] Generated Node #0,1,1: 68:[32, 20] Operation: 48-28=20 Exploring Operation: 48+28=76, Resulting Numbers: [32, 76] Generated Node #0,1,2: 68:[32, 76] Operation: 48+28=76 Exploring Operation: 32-28=4, Resulting Numbers: [48, 4] Generated Node #0,1,3: 68:[48, 4] Operation: 32-28=4 Exploring Operation: 48-32=16, Resulting Numbers: [28, 16] Generated Node #0,1,4: 68:[28, 16] Operation: 48-32=16 Moving to Node #0,1,1 Current State: 68:[32, 20], Operations: ['72-44=28', '48-28=20'] Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 32*20=640, Resulting Numbers: [640] 640,68 unequal: No Solution Exploring Operation: 32+20=52, Resulting Numbers: [52] 52,68 unequal: No Solution Moving to Node #0,1,4 Current State: 68:[28, 16], Operations: ['72-44=28', '48-32=16'] Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,68 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[32, 76], Operations: ['72-44=28', '48+28=76'] Exploring Operation: 32*76=2432, Resulting Numbers: [2432] 2432,68 unequal: No Solution Exploring Operation: 32+76=108, Resulting Numbers: [108] 108,68 unequal: No Solution Exploring Operation: 76-32=44, Resulting Numbers: [44] 44,68 unequal: No Solution Moving to Node #0,1,3 Current State: 68:[48, 4], Operations: ['72-44=28', '32-28=4'] Exploring Operation: 48/4=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 48*4=192, Resulting Numbers: [192] 192,68 unequal: No Solution Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,68 unequal: No Solution Exploring Operation: 48+4=52, Resulting Numbers: [52] 52,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[28, 80], Operations: ['72-44=28', '32+48=80'] Exploring Operation: 28*80=2240, Resulting Numbers: [2240] 2240,68 unequal: No Solution Exploring Operation: 28+80=108, Resulting Numbers: [108] 108,68 unequal: No Solution Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 68:[72, 48, 12], Operations: ['44-32=12'] Exploring Operation: 48+12=60, Resulting Numbers: [72, 60] Generated Node #0,4,0: 68:[72, 60] Operation: 48+12=60 Exploring Operation: 72/12=6, Resulting Numbers: [48, 6] Generated Node #0,4,1: 68:[48, 6] Operation: 72/12=6 Exploring Operation: 72-48=24, Resulting Numbers: [12, 24] Generated Node #0,4,2: 68:[12, 24] Operation: 72-48=24 Exploring Operation: 48-12=36, Resulting Numbers: [72, 36] Generated Node #0,4,3: 68:[72, 36] Operation: 48-12=36 Exploring Operation: 48/12=4, Resulting Numbers: [72, 4] Generated Node #0,4,4: 68:[72, 4] Operation: 48/12=4 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 68:[72, 4], Operations: ['44-32=12', '48/12=4'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,68 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[32, 72, 48, 44], Operations: [] Exploring Operation: 44-32=12, Resulting Numbers: [72, 48, 12] Generated Node #0,4: 68:[72, 48, 12] Operation: 44-32=12 Moving to Node #0,4 Current State: 68:[72, 48, 12], Operations: ['44-32=12'] Exploring Operation: 48/12=4, Resulting Numbers: [72, 4] Generated Node #0,4,4: 68:[72, 4] Operation: 48/12=4 Moving to Node #0,4,4 Current State: 68:[72, 4], Operations: ['44-32=12', '48/12=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.911458
hs_5
mult_heuristic
[ 77, 30, 79, 1 ]
32
[ "77-30=47", "79*1=79", "79-47=32" ]
Current State: 32:[77, 30, 79, 1], Operations: [] Exploring Operation: 77-30=47, Resulting Numbers: [79, 1, 47] Generated Node #2: [79, 1, 47] from Operation: 77-30=47 Current State: 32:[79, 1, 47], Operations: ['77-30=47'] Exploring Operation: 79*1=79, Resulting Numbers: [47, 79] Generated Node #3: [47, 79] from Operation: 79*1=79 Current State: 32:[47, 79], Operations: ['77-30=47', '79*1=79'] Exploring Operation: 79-47=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[77, 30, 79, 1], Operations: [] Exploring Operation: 77-30=47, Resulting Numbers: [79, 1, 47] Generated Node #0,0: 32:[79, 1, 47] Operation: 77-30=47 Exploring Operation: 77-1=76, Resulting Numbers: [30, 79, 76] Generated Node #0,1: 32:[30, 79, 76] Operation: 77-1=76 Exploring Operation: 79-30=49, Resulting Numbers: [77, 1, 49] Generated Node #0,2: 32:[77, 1, 49] Operation: 79-30=49 Exploring Operation: 79-77=2, Resulting Numbers: [30, 1, 2] Generated Node #0,3: 32:[30, 1, 2] Operation: 79-77=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 32:[30, 1, 2], Operations: ['79-77=2'] Exploring Operation: 30+2=32, Resulting Numbers: [1, 32] Generated Node #0,3,0: 32:[1, 32] Operation: 30+2=32 Exploring Operation: 30+1=31, Resulting Numbers: [2, 31] Generated Node #0,3,1: 32:[2, 31] Operation: 30+1=31 Exploring Operation: 30/1=30, Resulting Numbers: [2, 30] Generated Node #0,3,2: 32:[2, 30] Operation: 30/1=30 Exploring Operation: 30*1=30, Resulting Numbers: [2, 30] Generated Node #0,3,3: 32:[2, 30] Operation: 30*1=30 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 32:[1, 32], Operations: ['79-77=2', '30+2=32'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 1+32=33, Resulting Numbers: [33] 33,32 unequal: No Solution Exploring Operation: 1*32=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[77, 30, 79, 1], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [30, 1, 2] Generated Node #0,3: 32:[30, 1, 2] Operation: 79-77=2 Moving to Node #0,3 Current State: 32:[30, 1, 2], Operations: ['79-77=2'] Exploring Operation: 30+2=32, Resulting Numbers: [1, 32] Generated Node #0,3,0: 32:[1, 32] Operation: 30+2=32 Moving to Node #0,3,0 Current State: 32:[1, 32], Operations: ['79-77=2', '30+2=32'] Exploring Operation: 1*32=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 70, 27, 36, 73 ]
12
[ "70+27=97", "36+73=109", "109-97=12" ]
Current State: 12:[70, 27, 36, 73], Operations: [] Exploring Operation: 70+27=97, Resulting Numbers: [36, 73, 97] Generated Node #2: [36, 73, 97] from Operation: 70+27=97 Current State: 12:[36, 73, 97], Operations: ['70+27=97'] Exploring Operation: 36+73=109, Resulting Numbers: [97, 109] Generated Node #3: [97, 109] from Operation: 36+73=109 Current State: 12:[97, 109], Operations: ['70+27=97', '36+73=109'] Exploring Operation: 109-97=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[70, 27, 36, 73], Operations: [] Exploring Operation: 73-70=3, Resulting Numbers: [27, 36, 3] Generated Node #0,0: 12:[27, 36, 3] Operation: 73-70=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[27, 36, 3], Operations: ['73-70=3'] Exploring Operation: 36-27=9, Resulting Numbers: [3, 9] Generated Node #0,0,0: 12:[3, 9] Operation: 36-27=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[3, 9], Operations: ['73-70=3', '36-27=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[70, 27, 36, 73], Operations: [] Exploring Operation: 73-70=3, Resulting Numbers: [27, 36, 3] Generated Node #0,0: 12:[27, 36, 3] Operation: 73-70=3 Moving to Node #0,0 Current State: 12:[27, 36, 3], Operations: ['73-70=3'] Exploring Operation: 36-27=9, Resulting Numbers: [3, 9] Generated Node #0,0,0: 12:[3, 9] Operation: 36-27=9 Moving to Node #0,0,0 Current State: 12:[3, 9], Operations: ['73-70=3', '36-27=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 77, 93, 29, 53 ]
40
[ "93-77=16", "53-29=24", "16+24=40" ]
Current State: 40:[77, 93, 29, 53], Operations: [] Exploring Operation: 93-77=16, Resulting Numbers: [29, 53, 16] Generated Node #2: [29, 53, 16] from Operation: 93-77=16 Current State: 40:[29, 53, 16], Operations: ['93-77=16'] Exploring Operation: 53-29=24, Resulting Numbers: [16, 24] Generated Node #3: [16, 24] from Operation: 53-29=24 Current State: 40:[16, 24], Operations: ['93-77=16', '53-29=24'] Exploring Operation: 16+24=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[77, 93, 29, 53], Operations: [] Exploring Operation: 93-77=16, Resulting Numbers: [29, 53, 16] Generated Node #0,0: 40:[29, 53, 16] Operation: 93-77=16 Moving to Node #0,0 Current State: 40:[29, 53, 16], Operations: ['93-77=16'] Exploring Operation: 53-29=24, Resulting Numbers: [16, 24] Generated Node #0,0,0: 40:[16, 24] Operation: 53-29=24 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[16, 24], Operations: ['93-77=16', '53-29=24'] Exploring Operation: 16+24=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[77, 93, 29, 53], Operations: [] Exploring Operation: 93-77=16, Resulting Numbers: [29, 53, 16] Generated Node #0,0: 40:[29, 53, 16] Operation: 93-77=16 Moving to Node #0,0 Current State: 40:[29, 53, 16], Operations: ['93-77=16'] Exploring Operation: 53-29=24, Resulting Numbers: [16, 24] Generated Node #0,0,0: 40:[16, 24] Operation: 53-29=24 Moving to Node #0,0,0 Current State: 40:[16, 24], Operations: ['93-77=16', '53-29=24'] Exploring Operation: 16+24=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 25, 97, 12, 53 ]
47
[ "97-25=72", "72/12=6", "53-6=47" ]
Current State: 47:[25, 97, 12, 53], Operations: [] Exploring Operation: 97-25=72, Resulting Numbers: [12, 53, 72] Generated Node #2: [12, 53, 72] from Operation: 97-25=72 Current State: 47:[12, 53, 72], Operations: ['97-25=72'] Exploring Operation: 72/12=6, Resulting Numbers: [53, 6] Generated Node #3: [53, 6] from Operation: 72/12=6 Current State: 47:[53, 6], Operations: ['97-25=72', '72/12=6'] Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[25, 97, 12, 53], Operations: [] Exploring Operation: 97-53=44, Resulting Numbers: [25, 12, 44] Generated Node #0,0: 47:[25, 12, 44] Operation: 97-53=44 Moving to Node #0,0 Current State: 47:[25, 12, 44], Operations: ['97-53=44'] Exploring Operation: 25+12=37, Resulting Numbers: [44, 37] Generated Node #0,0,0: 47:[44, 37] Operation: 25+12=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[44, 37], Operations: ['97-53=44', '25+12=37'] Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 34, 88, 97, 78 ]
73
[ "88-34=54", "97-78=19", "54+19=73" ]
Current State: 73:[34, 88, 97, 78], Operations: [] Exploring Operation: 88-34=54, Resulting Numbers: [97, 78, 54] Generated Node #2: [97, 78, 54] from Operation: 88-34=54 Current State: 73:[97, 78, 54], Operations: ['88-34=54'] Exploring Operation: 97-78=19, Resulting Numbers: [54, 19] Generated Node #3: [54, 19] from Operation: 97-78=19 Current State: 73:[54, 19], Operations: ['88-34=54', '97-78=19'] Exploring Operation: 54+19=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[34, 88, 97, 78], Operations: [] Exploring Operation: 97-34=63, Resulting Numbers: [88, 78, 63] Generated Node #0,0: 73:[88, 78, 63] Operation: 97-34=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[88, 78, 63], Operations: ['97-34=63'] Exploring Operation: 88-63=25, Resulting Numbers: [78, 25] Generated Node #0,0,0: 73:[78, 25] Operation: 88-63=25 Moving to Node #0,0,0 Current State: 73:[78, 25], Operations: ['97-34=63', '88-63=25'] Exploring Operation: 78-25=53, Resulting Numbers: [53] 53,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 4, 83, 50, 75 ]
27
[ "83-50=33", "75+33=108", "108/4=27" ]
Current State: 27:[4, 83, 50, 75], Operations: [] Exploring Operation: 83-50=33, Resulting Numbers: [4, 75, 33] Generated Node #2: [4, 75, 33] from Operation: 83-50=33 Current State: 27:[4, 75, 33], Operations: ['83-50=33'] Exploring Operation: 75+33=108, Resulting Numbers: [4, 108] Generated Node #3: [4, 108] from Operation: 75+33=108 Current State: 27:[4, 108], Operations: ['83-50=33', '75+33=108'] Exploring Operation: 108/4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[4, 83, 50, 75], Operations: [] Exploring Operation: 83-4=79, Resulting Numbers: [50, 75, 79] Generated Node #0,0: 27:[50, 75, 79] Operation: 83-4=79 Exploring Operation: 83-50=33, Resulting Numbers: [4, 75, 33] Generated Node #0,1: 27:[4, 75, 33] Operation: 83-50=33 Exploring Operation: 50-4=46, Resulting Numbers: [83, 75, 46] Generated Node #0,2: 27:[83, 75, 46] Operation: 50-4=46 Exploring Operation: 83-75=8, Resulting Numbers: [4, 50, 8] Generated Node #0,3: 27:[4, 50, 8] Operation: 83-75=8 Exploring Operation: 75-50=25, Resulting Numbers: [4, 83, 25] Generated Node #0,4: 27:[4, 83, 25] Operation: 75-50=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 27:[4, 50, 8], Operations: ['83-75=8'] Exploring Operation: 4+8=12, Resulting Numbers: [50, 12] Generated Node #0,3,0: 27:[50, 12] Operation: 4+8=12 Exploring Operation: 50-4=46, Resulting Numbers: [8, 46] Generated Node #0,3,1: 27:[8, 46] Operation: 50-4=46 Exploring Operation: 8-4=4, Resulting Numbers: [50, 4] Generated Node #0,3,2: 27:[50, 4] Operation: 8-4=4 Exploring Operation: 50-8=42, Resulting Numbers: [4, 42] Generated Node #0,3,3: 27:[4, 42] Operation: 50-8=42 Exploring Operation: 8/4=2, Resulting Numbers: [50, 2] Generated Node #0,3,4: 27:[50, 2] Operation: 8/4=2 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 27:[4, 42], Operations: ['83-75=8', '50-8=42'] Exploring Operation: 4*42=168, Resulting Numbers: [168] 168,27 unequal: No Solution Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,27 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,27 unequal: No Solution No 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: 27:[8, 46], Operations: ['83-75=8', '50-4=46'] Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,27 unequal: No Solution Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 8*46=368, Resulting Numbers: [368] 368,27 unequal: No Solution No 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: 27:[50, 4], Operations: ['83-75=8', '8-4=4'] Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,27 unequal: No Solution Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 27:[50, 2], Operations: ['83-75=8', '8/4=2'] Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,27 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,27 unequal: No Solution Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,27 unequal: No Solution No 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: 27:[50, 12], Operations: ['83-75=8', '4+8=12'] Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,27 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,27 unequal: No Solution Exploring Operation: 50*12=600, Resulting Numbers: [600] 600,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[4, 75, 33], Operations: ['83-50=33'] Exploring Operation: 4+75=79, Resulting Numbers: [33, 79] Generated Node #0,1,0: 27:[33, 79] Operation: 4+75=79 Exploring Operation: 75-33=42, Resulting Numbers: [4, 42] Generated Node #0,1,1: 27:[4, 42] Operation: 75-33=42 Exploring Operation: 75-4=71, Resulting Numbers: [33, 71] Generated Node #0,1,2: 27:[33, 71] Operation: 75-4=71 Exploring Operation: 4+33=37, Resulting Numbers: [75, 37] Generated Node #0,1,3: 27:[75, 37] Operation: 4+33=37 Exploring Operation: 33-4=29, Resulting Numbers: [75, 29] Generated Node #0,1,4: 27:[75, 29] Operation: 33-4=29 Moving to Node #0,1,1 Current State: 27:[4, 42], Operations: ['83-50=33', '75-33=42'] Exploring Operation: 4*42=168, Resulting Numbers: [168] 168,27 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,27 unequal: No Solution Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,27 unequal: No Solution Moving to Node #0,1,4 Current State: 27:[75, 29], Operations: ['83-50=33', '33-4=29'] Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,27 unequal: No Solution Exploring Operation: 75*29=2175, Resulting Numbers: [2175] 2175,27 unequal: No Solution Exploring Operation: 75+29=104, Resulting Numbers: [104] 104,27 unequal: No Solution Moving to Node #0,1,2 Current State: 27:[33, 71], Operations: ['83-50=33', '75-4=71'] Exploring Operation: 33*71=2343, Resulting Numbers: [2343] 2343,27 unequal: No Solution Exploring Operation: 71-33=38, Resulting Numbers: [38] 38,27 unequal: No Solution Exploring Operation: 33+71=104, Resulting Numbers: [104] 104,27 unequal: No Solution Moving to Node #0,1,0 Current State: 27:[33, 79], Operations: ['83-50=33', '4+75=79'] Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,27 unequal: No Solution Exploring Operation: 33+79=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 33*79=2607, Resulting Numbers: [2607] 2607,27 unequal: No Solution Moving to Node #0,1,3 Current State: 27:[75, 37], Operations: ['83-50=33', '4+33=37'] Exploring Operation: 75+37=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 75*37=2775, Resulting Numbers: [2775] 2775,27 unequal: No Solution Exploring Operation: 75-37=38, Resulting Numbers: [38] 38,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 27:[4, 83, 25], Operations: ['75-50=25'] Exploring Operation: 83-4=79, Resulting Numbers: [25, 79] Generated Node #0,4,0: 27:[25, 79] Operation: 83-4=79 Exploring Operation: 25-4=21, Resulting Numbers: [83, 21] Generated Node #0,4,1: 27:[83, 21] Operation: 25-4=21 Exploring Operation: 4+25=29, Resulting Numbers: [83, 29] Generated Node #0,4,2: 27:[83, 29] Operation: 4+25=29 Exploring Operation: 83-25=58, Resulting Numbers: [4, 58] Generated Node #0,4,3: 27:[4, 58] Operation: 83-25=58 Exploring Operation: 4+83=87, Resulting Numbers: [25, 87] Generated Node #0,4,4: 27:[25, 87] Operation: 4+83=87 Moving to Node #0,4,3 Current State: 27:[4, 58], Operations: ['75-50=25', '83-25=58'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 4*58=232, Resulting Numbers: [232] 232,27 unequal: No Solution Exploring Operation: 4+58=62, Resulting Numbers: [62] 62,27 unequal: No Solution Moving to Node #0,4,0 Current State: 27:[25, 79], Operations: ['75-50=25', '83-4=79'] Exploring Operation: 79-25=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 25+79=104, Resulting Numbers: [104] 104,27 unequal: No Solution Exploring Operation: 25*79=1975, Resulting Numbers: [1975] 1975,27 unequal: No Solution Moving to Node #0,4,2 Current State: 27:[83, 29], Operations: ['75-50=25', '4+25=29'] Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 83+29=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 83*29=2407, Resulting Numbers: [2407] 2407,27 unequal: No Solution Moving to Node #0,4,1 Current State: 27:[83, 21], Operations: ['75-50=25', '25-4=21'] Exploring Operation: 83-21=62, Resulting Numbers: [62] 62,27 unequal: No Solution Exploring Operation: 83+21=104, Resulting Numbers: [104] 104,27 unequal: No Solution Exploring Operation: 83*21=1743, Resulting Numbers: [1743] 1743,27 unequal: No Solution Moving to Node #0,4,4 Current State: 27:[25, 87], Operations: ['75-50=25', '4+83=87'] Exploring Operation: 87-25=62, Resulting Numbers: [62] 62,27 unequal: No Solution Exploring Operation: 25+87=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 25*87=2175, Resulting Numbers: [2175] 2175,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[50, 75, 79], Operations: ['83-4=79'] Exploring Operation: 79-50=29, Resulting Numbers: [75, 29] Generated Node #0,0,0: 27:[75, 29] Operation: 79-50=29 Exploring Operation: 50+79=129, Resulting Numbers: [75, 129] Generated Node #0,0,1: 27:[75, 129] Operation: 50+79=129 Exploring Operation: 75-50=25, Resulting Numbers: [79, 25] Generated Node #0,0,2: 27:[79, 25] Operation: 75-50=25 Exploring Operation: 79-75=4, Resulting Numbers: [50, 4] Generated Node #0,0,3: 27:[50, 4] Operation: 79-75=4 Exploring Operation: 50+75=125, Resulting Numbers: [79, 125] Generated Node #0,0,4: 27:[79, 125] Operation: 50+75=125 Moving to Node #0,0,3 Current State: 27:[50, 4], Operations: ['83-4=79', '79-75=4'] Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,27 unequal: No Solution Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[75, 29], Operations: ['83-4=79', '79-50=29'] Exploring Operation: 75*29=2175, Resulting Numbers: [2175] 2175,27 unequal: No Solution Exploring Operation: 75+29=104, Resulting Numbers: [104] 104,27 unequal: No Solution Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[79, 25], Operations: ['83-4=79', '75-50=25'] Exploring Operation: 79*25=1975, Resulting Numbers: [1975] 1975,27 unequal: No Solution Exploring Operation: 79-25=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 79+25=104, Resulting Numbers: [104] 104,27 unequal: No Solution Moving to Node #0,0,1 Current State: 27:[75, 129], Operations: ['83-4=79', '50+79=129'] Exploring Operation: 75*129=9675, Resulting Numbers: [9675] 9675,27 unequal: No Solution Exploring Operation: 129-75=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 75+129=204, Resulting Numbers: [204] 204,27 unequal: No Solution Moving to Node #0,0,4 Current State: 27:[79, 125], Operations: ['83-4=79', '50+75=125'] Exploring Operation: 79*125=9875, Resulting Numbers: [9875] 9875,27 unequal: No Solution Exploring Operation: 125-79=46, Resulting Numbers: [46] 46,27 unequal: No Solution Exploring Operation: 79+125=204, Resulting Numbers: [204] 204,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[83, 75, 46], Operations: ['50-4=46'] Exploring Operation: 83+46=129, Resulting Numbers: [75, 129] Generated Node #0,2,0: 27:[75, 129] Operation: 83+46=129 Exploring Operation: 75-46=29, Resulting Numbers: [83, 29] Generated Node #0,2,1: 27:[83, 29] Operation: 75-46=29 Exploring Operation: 83-46=37, Resulting Numbers: [75, 37] Generated Node #0,2,2: 27:[75, 37] Operation: 83-46=37 Exploring Operation: 83+75=158, Resulting Numbers: [46, 158] Generated Node #0,2,3: 27:[46, 158] Operation: 83+75=158 Exploring Operation: 83-75=8, Resulting Numbers: [46, 8] Generated Node #0,2,4: 27:[46, 8] Operation: 83-75=8 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 27:[46, 8], Operations: ['50-4=46', '83-75=8'] Exploring Operation: 46*8=368, Resulting Numbers: [368] 368,27 unequal: No Solution Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,27 unequal: No Solution No 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: 27:[83, 29], Operations: ['50-4=46', '75-46=29'] Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 83+29=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 83*29=2407, Resulting Numbers: [2407] 2407,27 unequal: No Solution No 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: 27:[75, 37], Operations: ['50-4=46', '83-46=37'] Exploring Operation: 75*37=2775, Resulting Numbers: [2775] 2775,27 unequal: No Solution Exploring Operation: 75-37=38, Resulting Numbers: [38] 38,27 unequal: No Solution Exploring Operation: 75+37=112, Resulting Numbers: [112] 112,27 unequal: No Solution No 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: 27:[75, 129], Operations: ['50-4=46', '83+46=129'] Exploring Operation: 129-75=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 75+129=204, Resulting Numbers: [204] 204,27 unequal: No Solution Exploring Operation: 75*129=9675, Resulting Numbers: [9675] 9675,27 unequal: No Solution No 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: 27:[46, 158], Operations: ['50-4=46', '83+75=158'] Exploring Operation: 158-46=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 46*158=7268, Resulting Numbers: [7268] 7268,27 unequal: No Solution Exploring Operation: 46+158=204, Resulting Numbers: [204] 204,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 85, 70, 66, 30 ]
51
[ "85-70=15", "66-30=36", "15+36=51" ]
Current State: 51:[85, 70, 66, 30], Operations: [] Exploring Operation: 85-70=15, Resulting Numbers: [66, 30, 15] Generated Node #2: [66, 30, 15] from Operation: 85-70=15 Current State: 51:[66, 30, 15], Operations: ['85-70=15'] Exploring Operation: 66-30=36, Resulting Numbers: [15, 36] Generated Node #3: [15, 36] from Operation: 66-30=36 Current State: 51:[15, 36], Operations: ['85-70=15', '66-30=36'] Exploring Operation: 15+36=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[85, 70, 66, 30], Operations: [] Exploring Operation: 85-30=55, Resulting Numbers: [70, 66, 55] Generated Node #0,0: 51:[70, 66, 55] Operation: 85-30=55 Exploring Operation: 85-66=19, Resulting Numbers: [70, 30, 19] Generated Node #0,1: 51:[70, 30, 19] Operation: 85-66=19 Exploring Operation: 85-70=15, Resulting Numbers: [66, 30, 15] Generated Node #0,2: 51:[66, 30, 15] Operation: 85-70=15 Moving to Node #0,2 Current State: 51:[66, 30, 15], Operations: ['85-70=15'] Exploring Operation: 66-15=51, Resulting Numbers: [30, 51] Generated Node #0,2,0: 51:[30, 51] Operation: 66-15=51 Exploring Operation: 66-30=36, Resulting Numbers: [15, 36] Generated Node #0,2,1: 51:[15, 36] Operation: 66-30=36 Exploring Operation: 30/15=2, Resulting Numbers: [66, 2] Generated Node #0,2,2: 51:[66, 2] Operation: 30/15=2 Moving to Node #0,1 Current State: 51:[70, 30, 19], Operations: ['85-66=19'] Exploring Operation: 70-19=51, Resulting Numbers: [30, 51] Generated Node #0,1,0: 51:[30, 51] Operation: 70-19=51 Exploring Operation: 30+19=49, Resulting Numbers: [70, 49] Generated Node #0,1,1: 51:[70, 49] Operation: 30+19=49 Exploring Operation: 70-30=40, Resulting Numbers: [19, 40] Generated Node #0,1,2: 51:[19, 40] Operation: 70-30=40 Moving to Node #0,0 Current State: 51:[70, 66, 55], Operations: ['85-30=55'] Exploring Operation: 70-66=4, Resulting Numbers: [55, 4] Generated Node #0,0,0: 51:[55, 4] Operation: 70-66=4 Exploring Operation: 66-55=11, Resulting Numbers: [70, 11] Generated Node #0,0,1: 51:[70, 11] Operation: 66-55=11 Exploring Operation: 70-55=15, Resulting Numbers: [66, 15] Generated Node #0,0,2: 51:[66, 15] Operation: 70-55=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[55, 4], Operations: ['85-30=55', '70-66=4'] Exploring Operation: 55+4=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[85, 70, 66, 30], Operations: [] Exploring Operation: 85-30=55, Resulting Numbers: [70, 66, 55] Generated Node #0,0: 51:[70, 66, 55] Operation: 85-30=55 Moving to Node #0,0 Current State: 51:[70, 66, 55], Operations: ['85-30=55'] Exploring Operation: 70-66=4, Resulting Numbers: [55, 4] Generated Node #0,0,0: 51:[55, 4] Operation: 70-66=4 Moving to Node #0,0,0 Current State: 51:[55, 4], Operations: ['85-30=55', '70-66=4'] Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 56, 46, 80, 3 ]
30
[ "56-46=10", "80+10=90", "90/3=30" ]
Current State: 30:[56, 46, 80, 3], Operations: [] Exploring Operation: 56-46=10, Resulting Numbers: [80, 3, 10] Generated Node #2: [80, 3, 10] from Operation: 56-46=10 Current State: 30:[80, 3, 10], Operations: ['56-46=10'] Exploring Operation: 80+10=90, Resulting Numbers: [3, 90] Generated Node #3: [3, 90] from Operation: 80+10=90 Current State: 30:[3, 90], Operations: ['56-46=10', '80+10=90'] Exploring Operation: 90/3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[56, 46, 80, 3], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [46, 3, 24] Generated Node #0,0: 30:[46, 3, 24] Operation: 80-56=24 Exploring Operation: 80-46=34, Resulting Numbers: [56, 3, 34] Generated Node #0,1: 30:[56, 3, 34] Operation: 80-46=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[46, 3, 24], Operations: ['80-56=24'] Exploring Operation: 46-24=22, Resulting Numbers: [3, 22] Generated Node #0,0,0: 30:[3, 22] Operation: 46-24=22 Exploring Operation: 24/3=8, Resulting Numbers: [46, 8] Generated Node #0,0,1: 30:[46, 8] Operation: 24/3=8 Moving to Node #0,0,0 Current State: 30:[3, 22], Operations: ['80-56=24', '46-24=22'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,30 unequal: No Solution Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,30 unequal: No Solution Moving to Node #0,0,1 Current State: 30:[46, 8], Operations: ['80-56=24', '24/3=8'] Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,30 unequal: No Solution Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[56, 3, 34], Operations: ['80-46=34'] Exploring Operation: 56-34=22, Resulting Numbers: [3, 22] Generated Node #0,1,0: 30:[3, 22] Operation: 56-34=22 Exploring Operation: 56-3=53, Resulting Numbers: [34, 53] Generated Node #0,1,1: 30:[34, 53] Operation: 56-3=53 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[3, 22], Operations: ['80-46=34', '56-34=22'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,30 unequal: No Solution Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[34, 53], Operations: ['80-46=34', '56-3=53'] Exploring Operation: 53-34=19, Resulting Numbers: [19] 19,30 unequal: No Solution Exploring Operation: 34+53=87, Resulting Numbers: [87] 87,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 5, 26, 20, 10 ]
20
[ "20/5=4", "26-10=16", "4+16=20" ]
Current State: 20:[5, 26, 20, 10], Operations: [] Exploring Operation: 20/5=4, Resulting Numbers: [26, 10, 4] Generated Node #2: [26, 10, 4] from Operation: 20/5=4 Current State: 20:[26, 10, 4], Operations: ['20/5=4'] Exploring Operation: 26-10=16, Resulting Numbers: [4, 16] Generated Node #3: [4, 16] from Operation: 26-10=16 Current State: 20:[4, 16], Operations: ['20/5=4', '26-10=16'] Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[5, 26, 20, 10], Operations: [] Exploring Operation: 26-10=16, Resulting Numbers: [5, 20, 16] Generated Node #0,0: 20:[5, 20, 16] Operation: 26-10=16 Exploring Operation: 20/5=4, Resulting Numbers: [26, 10, 4] Generated Node #0,1: 20:[26, 10, 4] Operation: 20/5=4 Exploring Operation: 26-5=21, Resulting Numbers: [20, 10, 21] Generated Node #0,2: 20:[20, 10, 21] Operation: 26-5=21 Exploring Operation: 26-20=6, Resulting Numbers: [5, 10, 6] Generated Node #0,3: 20:[5, 10, 6] Operation: 26-20=6 Moving to Node #0,2 Current State: 20:[20, 10, 21], Operations: ['26-5=21'] Exploring Operation: 20/10=2, Resulting Numbers: [21, 2] Generated Node #0,2,0: 20:[21, 2] Operation: 20/10=2 Exploring Operation: 21-20=1, Resulting Numbers: [10, 1] Generated Node #0,2,1: 20:[10, 1] Operation: 21-20=1 Exploring Operation: 21-10=11, Resulting Numbers: [20, 11] Generated Node #0,2,2: 20:[20, 11] Operation: 21-10=11 Exploring Operation: 20-10=10, Resulting Numbers: [21, 10] Generated Node #0,2,3: 20:[21, 10] Operation: 20-10=10 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 20:[21, 2], Operations: ['26-5=21', '20/10=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,20 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,20 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,20 unequal: No Solution No 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: 20:[10, 1], Operations: ['26-5=21', '21-20=1'] Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,20 unequal: No Solution No 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: 20:[20, 11], Operations: ['26-5=21', '21-10=11'] Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 20*11=220, Resulting Numbers: [220] 220,20 unequal: No Solution Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,20 unequal: No Solution No 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: 20:[21, 10], Operations: ['26-5=21', '20-10=10'] Exploring Operation: 21*10=210, Resulting Numbers: [210] 210,20 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,20 unequal: No Solution Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,20 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: 20:[5, 10, 6], Operations: ['26-20=6'] Exploring Operation: 10/5=2, Resulting Numbers: [6, 2] Generated Node #0,3,0: 20:[6, 2] Operation: 10/5=2 Exploring Operation: 5+6=11, Resulting Numbers: [10, 11] Generated Node #0,3,1: 20:[10, 11] Operation: 5+6=11 Exploring Operation: 10-5=5, Resulting Numbers: [6, 5] Generated Node #0,3,2: 20:[6, 5] Operation: 10-5=5 Exploring Operation: 10-6=4, Resulting Numbers: [5, 4] Generated Node #0,3,3: 20:[5, 4] Operation: 10-6=4 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 20:[5, 4], Operations: ['26-20=6', '10-6=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:[5, 26, 20, 10], Operations: [] Exploring Operation: 26-20=6, Resulting Numbers: [5, 10, 6] Generated Node #0,3: 20:[5, 10, 6] Operation: 26-20=6 Moving to Node #0,3 Current State: 20:[5, 10, 6], Operations: ['26-20=6'] Exploring Operation: 10-6=4, Resulting Numbers: [5, 4] Generated Node #0,3,3: 20:[5, 4] Operation: 10-6=4 Moving to Node #0,3,3 Current State: 20:[5, 4], Operations: ['26-20=6', '10-6=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 73, 49, 76, 51 ]
49
[ "73-49=24", "76-51=25", "24+25=49" ]
Current State: 49:[73, 49, 76, 51], Operations: [] Exploring Operation: 73-49=24, Resulting Numbers: [76, 51, 24] Generated Node #2: [76, 51, 24] from Operation: 73-49=24 Current State: 49:[76, 51, 24], Operations: ['73-49=24'] Exploring Operation: 76-51=25, Resulting Numbers: [24, 25] Generated Node #3: [24, 25] from Operation: 76-51=25 Current State: 49:[24, 25], Operations: ['73-49=24', '76-51=25'] Exploring Operation: 24+25=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[73, 49, 76, 51], Operations: [] Exploring Operation: 76-49=27, Resulting Numbers: [73, 51, 27] Generated Node #0,0: 49:[73, 51, 27] Operation: 76-49=27 Exploring Operation: 73-49=24, Resulting Numbers: [76, 51, 24] Generated Node #0,1: 49:[76, 51, 24] Operation: 73-49=24 Exploring Operation: 73-51=22, Resulting Numbers: [49, 76, 22] Generated Node #0,2: 49:[49, 76, 22] Operation: 73-51=22 Exploring Operation: 76-73=3, Resulting Numbers: [49, 51, 3] Generated Node #0,3: 49:[49, 51, 3] Operation: 76-73=3 Exploring Operation: 76-51=25, Resulting Numbers: [73, 49, 25] Generated Node #0,4: 49:[73, 49, 25] Operation: 76-51=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 49:[49, 51, 3], Operations: ['76-73=3'] Exploring Operation: 51+3=54, Resulting Numbers: [49, 54] Generated Node #0,3,0: 49:[49, 54] Operation: 51+3=54 Exploring Operation: 49+3=52, Resulting Numbers: [51, 52] Generated Node #0,3,1: 49:[51, 52] Operation: 49+3=52 Exploring Operation: 51-49=2, Resulting Numbers: [3, 2] Generated Node #0,3,2: 49:[3, 2] Operation: 51-49=2 Exploring Operation: 49-3=46, Resulting Numbers: [51, 46] Generated Node #0,3,3: 49:[51, 46] Operation: 49-3=46 Exploring Operation: 51-3=48, Resulting Numbers: [49, 48] Generated Node #0,3,4: 49:[49, 48] Operation: 51-3=48 Moving to Node #0,3,4 Current State: 49:[49, 48], Operations: ['76-73=3', '51-3=48'] Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,49 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,49 unequal: No Solution Moving to Node #0,3,1 Current State: 49:[51, 52], Operations: ['76-73=3', '49+3=52'] Exploring Operation: 51*52=2652, Resulting Numbers: [2652] 2652,49 unequal: No Solution Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 51+52=103, Resulting Numbers: [103] 103,49 unequal: No Solution Moving to Node #0,3,0 Current State: 49:[49, 54], Operations: ['76-73=3', '51+3=54'] Exploring Operation: 49*54=2646, Resulting Numbers: [2646] 2646,49 unequal: No Solution Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 49+54=103, Resulting Numbers: [103] 103,49 unequal: No Solution Moving to Node #0,3,3 Current State: 49:[51, 46], Operations: ['76-73=3', '49-3=46'] Exploring Operation: 51+46=97, Resulting Numbers: [97] 97,49 unequal: No Solution Exploring Operation: 51-46=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 51*46=2346, Resulting Numbers: [2346] 2346,49 unequal: No Solution Moving to Node #0,3,2 Current State: 49:[3, 2], Operations: ['76-73=3', '51-49=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,49 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,49 unequal: No Solution No 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: 49:[49, 76, 22], Operations: ['73-51=22'] Exploring Operation: 76-22=54, Resulting Numbers: [49, 54] Generated Node #0,2,0: 49:[49, 54] Operation: 76-22=54 Exploring Operation: 76-49=27, Resulting Numbers: [22, 27] Generated Node #0,2,1: 49:[22, 27] Operation: 76-49=27 Exploring Operation: 49+22=71, Resulting Numbers: [76, 71] Generated Node #0,2,2: 49:[76, 71] Operation: 49+22=71 Exploring Operation: 49-22=27, Resulting Numbers: [76, 27] Generated Node #0,2,3: 49:[76, 27] Operation: 49-22=27 Exploring Operation: 76+22=98, Resulting Numbers: [49, 98] Generated Node #0,2,4: 49:[49, 98] Operation: 76+22=98 Moving to Node #0,2,0 Current State: 49:[49, 54], Operations: ['73-51=22', '76-22=54'] Exploring Operation: 49*54=2646, Resulting Numbers: [2646] 2646,49 unequal: No Solution Exploring Operation: 49+54=103, Resulting Numbers: [103] 103,49 unequal: No Solution Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[22, 27], Operations: ['73-51=22', '76-49=27'] Exploring Operation: 22+27=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[73, 49, 76, 51], Operations: [] Exploring Operation: 73-51=22, Resulting Numbers: [49, 76, 22] Generated Node #0,2: 49:[49, 76, 22] Operation: 73-51=22 Moving to Node #0,2 Current State: 49:[49, 76, 22], Operations: ['73-51=22'] Exploring Operation: 76-49=27, Resulting Numbers: [22, 27] Generated Node #0,2,1: 49:[22, 27] Operation: 76-49=27 Moving to Node #0,2,1 Current State: 49:[22, 27], Operations: ['73-51=22', '76-49=27'] Exploring Operation: 22+27=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
mult_heuristic
[ 9, 2, 8, 81 ]
28
[ "81-9=72", "72/2=36", "36-8=28" ]
Current State: 28:[9, 2, 8, 81], Operations: [] Exploring Operation: 81-9=72, Resulting Numbers: [2, 8, 72] Generated Node #2: [2, 8, 72] from Operation: 81-9=72 Current State: 28:[2, 8, 72], Operations: ['81-9=72'] Exploring Operation: 72/2=36, Resulting Numbers: [8, 36] Generated Node #3: [8, 36] from Operation: 72/2=36 Current State: 28:[8, 36], Operations: ['81-9=72', '72/2=36'] Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[9, 2, 8, 81], Operations: [] Exploring Operation: 81-8=73, Resulting Numbers: [9, 2, 73] Generated Node #0,0: 28:[9, 2, 73] Operation: 81-8=73 Exploring Operation: 81-9=72, Resulting Numbers: [2, 8, 72] Generated Node #0,1: 28:[2, 8, 72] Operation: 81-9=72 Exploring Operation: 81/9=9, Resulting Numbers: [2, 8, 9] Generated Node #0,2: 28:[2, 8, 9] Operation: 81/9=9 Start Sub Search at level 1: Moving to Node #0,2 Current State: 28:[2, 8, 9], Operations: ['81/9=9'] Exploring Operation: 8/2=4, Resulting Numbers: [9, 4] Generated Node #0,2,0: 28:[9, 4] Operation: 8/2=4 Exploring Operation: 9-8=1, Resulting Numbers: [2, 1] Generated Node #0,2,1: 28:[2, 1] Operation: 9-8=1 Exploring Operation: 9-2=7, Resulting Numbers: [8, 7] Generated Node #0,2,2: 28:[8, 7] Operation: 9-2=7 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 28:[2, 1], Operations: ['81/9=9', '9-8=1'] Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,28 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,28 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 #0,2,2 Current State: 28:[8, 7], Operations: ['81/9=9', '9-2=7'] Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,28 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,28 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 #0,2,0 Current State: 28:[9, 4], Operations: ['81/9=9', '8/2=4'] Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,28 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,28 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[2, 8, 72], Operations: ['81-9=72'] Exploring Operation: 72/2=36, Resulting Numbers: [8, 36] Generated Node #0,1,0: 28:[8, 36] Operation: 72/2=36 Exploring Operation: 72/8=9, Resulting Numbers: [2, 9] Generated Node #0,1,1: 28:[2, 9] Operation: 72/8=9 Exploring Operation: 72-8=64, Resulting Numbers: [2, 64] Generated Node #0,1,2: 28:[2, 64] Operation: 72-8=64 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 28:[2, 9], Operations: ['81-9=72', '72/8=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,28 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,28 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,28 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 #0,1,0 Current State: 28:[8, 36], Operations: ['81-9=72', '72/2=36'] Exploring Operation: 8*36=288, Resulting Numbers: [288] 288,28 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[9, 2, 8, 81], Operations: [] Exploring Operation: 81-9=72, Resulting Numbers: [2, 8, 72] Generated Node #0,1: 28:[2, 8, 72] Operation: 81-9=72 Moving to Node #0,1 Current State: 28:[2, 8, 72], Operations: ['81-9=72'] Exploring Operation: 72/2=36, Resulting Numbers: [8, 36] Generated Node #0,1,0: 28:[8, 36] Operation: 72/2=36 Moving to Node #0,1,0 Current State: 28:[8, 36], Operations: ['81-9=72', '72/2=36'] Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.976563
hs_3
sum_heuristic
[ 30, 97, 5, 99 ]
27
[ "97-30=67", "99-5=94", "94-67=27" ]
Current State: 27:[30, 97, 5, 99], Operations: [] Exploring Operation: 97-30=67, Resulting Numbers: [5, 99, 67] Generated Node #2: [5, 99, 67] from Operation: 97-30=67 Current State: 27:[5, 99, 67], Operations: ['97-30=67'] Exploring Operation: 99-5=94, Resulting Numbers: [67, 94] Generated Node #3: [67, 94] from Operation: 99-5=94 Current State: 27:[67, 94], Operations: ['97-30=67', '99-5=94'] Exploring Operation: 94-67=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[30, 97, 5, 99], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [30, 5, 2] Generated Node #0,0: 27:[30, 5, 2] Operation: 99-97=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[30, 5, 2], Operations: ['99-97=2'] Exploring Operation: 30-5=25, Resulting Numbers: [2, 25] Generated Node #0,0,0: 27:[2, 25] Operation: 30-5=25 Moving to Node #0,0,0 Current State: 27:[2, 25], Operations: ['99-97=2', '30-5=25'] Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[30, 97, 5, 99], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [30, 5, 2] Generated Node #0,0: 27:[30, 5, 2] Operation: 99-97=2 Moving to Node #0,0 Current State: 27:[30, 5, 2], Operations: ['99-97=2'] Exploring Operation: 30-5=25, Resulting Numbers: [2, 25] Generated Node #0,0,0: 27:[2, 25] Operation: 30-5=25 Moving to Node #0,0,0 Current State: 27:[2, 25], Operations: ['99-97=2', '30-5=25'] Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 75, 66, 60, 48 ]
83
[ "66-60=6", "48/6=8", "75+8=83" ]
Current State: 83:[75, 66, 60, 48], Operations: [] Exploring Operation: 66-60=6, Resulting Numbers: [75, 48, 6] Generated Node #2: [75, 48, 6] from Operation: 66-60=6 Current State: 83:[75, 48, 6], Operations: ['66-60=6'] Exploring Operation: 48/6=8, Resulting Numbers: [75, 8] Generated Node #3: [75, 8] from Operation: 48/6=8 Current State: 83:[75, 8], Operations: ['66-60=6', '48/6=8'] Exploring Operation: 75+8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[75, 66, 60, 48], Operations: [] Exploring Operation: 66+60=126, Resulting Numbers: [75, 48, 126] Generated Node #0,0: 83:[75, 48, 126] Operation: 66+60=126 Exploring Operation: 66+48=114, Resulting Numbers: [75, 60, 114] Generated Node #0,1: 83:[75, 60, 114] Operation: 66+48=114 Exploring Operation: 75+48=123, Resulting Numbers: [66, 60, 123] Generated Node #0,2: 83:[66, 60, 123] Operation: 75+48=123 Exploring Operation: 75-48=27, Resulting Numbers: [66, 60, 27] Generated Node #0,3: 83:[66, 60, 27] Operation: 75-48=27 Exploring Operation: 60+48=108, Resulting Numbers: [75, 66, 108] Generated Node #0,4: 83:[75, 66, 108] Operation: 60+48=108 Moving to Node #0,4 Current State: 83:[75, 66, 108], Operations: ['60+48=108'] Exploring Operation: 108-75=33, Resulting Numbers: [66, 33] Generated Node #0,4,0: 83:[66, 33] Operation: 108-75=33 Exploring Operation: 66+108=174, Resulting Numbers: [75, 174] Generated Node #0,4,1: 83:[75, 174] Operation: 66+108=174 Exploring Operation: 75+66=141, Resulting Numbers: [108, 141] Generated Node #0,4,2: 83:[108, 141] Operation: 75+66=141 Exploring Operation: 75-66=9, Resulting Numbers: [108, 9] Generated Node #0,4,3: 83:[108, 9] Operation: 75-66=9 Exploring Operation: 108-66=42, Resulting Numbers: [75, 42] Generated Node #0,4,4: 83:[75, 42] Operation: 108-66=42 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 83:[75, 42], Operations: ['60+48=108', '108-66=42'] Exploring Operation: 75+42=117, Resulting Numbers: [117] 117,83 unequal: No Solution Exploring Operation: 75-42=33, Resulting Numbers: [33] 33,83 unequal: No Solution Exploring Operation: 75*42=3150, Resulting Numbers: [3150] 3150,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 83:[66, 33], Operations: ['60+48=108', '108-75=33'] Exploring Operation: 66/33=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 66-33=33, Resulting Numbers: [33] 33,83 unequal: No Solution Exploring Operation: 66+33=99, Resulting Numbers: [99] 99,83 unequal: No Solution Exploring Operation: 66*33=2178, Resulting Numbers: [2178] 2178,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 83:[108, 141], Operations: ['60+48=108', '75+66=141'] Exploring Operation: 108*141=15228, Resulting Numbers: [15228] 15228,83 unequal: No Solution Exploring Operation: 108+141=249, Resulting Numbers: [249] 249,83 unequal: No Solution Exploring Operation: 141-108=33, Resulting Numbers: [33] 33,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 83:[75, 174], Operations: ['60+48=108', '66+108=174'] Exploring Operation: 75*174=13050, Resulting Numbers: [13050] 13050,83 unequal: No Solution Exploring Operation: 75+174=249, Resulting Numbers: [249] 249,83 unequal: No Solution Exploring Operation: 174-75=99, Resulting Numbers: [99] 99,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 83:[108, 9], Operations: ['60+48=108', '75-66=9'] Exploring Operation: 108+9=117, Resulting Numbers: [117] 117,83 unequal: No Solution Exploring Operation: 108-9=99, Resulting Numbers: [99] 99,83 unequal: No Solution Exploring Operation: 108/9=12, Resulting Numbers: [12] 12,83 unequal: No Solution Exploring Operation: 108*9=972, Resulting Numbers: [972] 972,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 83:[75, 60, 114], Operations: ['66+48=114'] Exploring Operation: 75-60=15, Resulting Numbers: [114, 15] Generated Node #0,1,0: 83:[114, 15] Operation: 75-60=15 Exploring Operation: 114-60=54, Resulting Numbers: [75, 54] Generated Node #0,1,1: 83:[75, 54] Operation: 114-60=54 Exploring Operation: 75+60=135, Resulting Numbers: [114, 135] Generated Node #0,1,2: 83:[114, 135] Operation: 75+60=135 Exploring Operation: 60+114=174, Resulting Numbers: [75, 174] Generated Node #0,1,3: 83:[75, 174] Operation: 60+114=174 Exploring Operation: 114-75=39, Resulting Numbers: [60, 39] Generated Node #0,1,4: 83:[60, 39] Operation: 114-75=39 Moving to Node #0,2 Current State: 83:[66, 60, 123], Operations: ['75+48=123'] Exploring Operation: 66+60=126, Resulting Numbers: [123, 126] Generated Node #0,2,0: 83:[123, 126] Operation: 66+60=126 Exploring Operation: 123-60=63, Resulting Numbers: [66, 63] Generated Node #0,2,1: 83:[66, 63] Operation: 123-60=63 Exploring Operation: 60+123=183, Resulting Numbers: [66, 183] Generated Node #0,2,2: 83:[66, 183] Operation: 60+123=183 Exploring Operation: 123-66=57, Resulting Numbers: [60, 57] Generated Node #0,2,3: 83:[60, 57] Operation: 123-66=57 Exploring Operation: 66-60=6, Resulting Numbers: [123, 6] Generated Node #0,2,4: 83:[123, 6] Operation: 66-60=6 Moving to Node #0,0 Current State: 83:[75, 48, 126], Operations: ['66+60=126'] Exploring Operation: 75+48=123, Resulting Numbers: [126, 123] Generated Node #0,0,0: 83:[126, 123] Operation: 75+48=123 Exploring Operation: 126-48=78, Resulting Numbers: [75, 78] Generated Node #0,0,1: 83:[75, 78] Operation: 126-48=78 Exploring Operation: 48+126=174, Resulting Numbers: [75, 174] Generated Node #0,0,2: 83:[75, 174] Operation: 48+126=174 Exploring Operation: 126-75=51, Resulting Numbers: [48, 51] Generated Node #0,0,3: 83:[48, 51] Operation: 126-75=51 Exploring Operation: 75-48=27, Resulting Numbers: [126, 27] Generated Node #0,0,4: 83:[126, 27] Operation: 75-48=27 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[75, 78], Operations: ['66+60=126', '126-48=78'] Exploring Operation: 75+78=153, Resulting Numbers: [153] 153,83 unequal: No Solution Exploring Operation: 75*78=5850, Resulting Numbers: [5850] 5850,83 unequal: No Solution Exploring Operation: 78-75=3, Resulting Numbers: [3] 3,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 83:[48, 51], Operations: ['66+60=126', '126-75=51'] Exploring Operation: 51-48=3, Resulting Numbers: [3] 3,83 unequal: No Solution Exploring Operation: 48*51=2448, Resulting Numbers: [2448] 2448,83 unequal: No Solution Exploring Operation: 48+51=99, Resulting Numbers: [99] 99,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[126, 123], Operations: ['66+60=126', '75+48=123'] Exploring Operation: 126-123=3, Resulting Numbers: [3] 3,83 unequal: No Solution Exploring Operation: 126+123=249, Resulting Numbers: [249] 249,83 unequal: No Solution Exploring Operation: 126*123=15498, Resulting Numbers: [15498] 15498,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[75, 174], Operations: ['66+60=126', '48+126=174'] Exploring Operation: 75*174=13050, Resulting Numbers: [13050] 13050,83 unequal: No Solution Exploring Operation: 174-75=99, Resulting Numbers: [99] 99,83 unequal: No Solution Exploring Operation: 75+174=249, Resulting Numbers: [249] 249,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 83:[126, 27], Operations: ['66+60=126', '75-48=27'] Exploring Operation: 126+27=153, Resulting Numbers: [153] 153,83 unequal: No Solution Exploring Operation: 126*27=3402, Resulting Numbers: [3402] 3402,83 unequal: No Solution Exploring Operation: 126-27=99, Resulting Numbers: [99] 99,83 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: 83:[66, 60, 27], Operations: ['75-48=27'] Exploring Operation: 66+60=126, Resulting Numbers: [27, 126] Generated Node #0,3,0: 83:[27, 126] Operation: 66+60=126 Exploring Operation: 66+27=93, Resulting Numbers: [60, 93] Generated Node #0,3,1: 83:[60, 93] Operation: 66+27=93 Exploring Operation: 60-27=33, Resulting Numbers: [66, 33] Generated Node #0,3,2: 83:[66, 33] Operation: 60-27=33 Exploring Operation: 66-27=39, Resulting Numbers: [60, 39] Generated Node #0,3,3: 83:[60, 39] Operation: 66-27=39 Exploring Operation: 60+27=87, Resulting Numbers: [66, 87] Generated Node #0,3,4: 83:[66, 87] Operation: 60+27=87 Moving to Node #0,3,4 Current State: 83:[66, 87], Operations: ['75-48=27', '60+27=87'] Exploring Operation: 66*87=5742, Resulting Numbers: [5742] 5742,83 unequal: No Solution Exploring Operation: 66+87=153, Resulting Numbers: [153] 153,83 unequal: No Solution Exploring Operation: 87-66=21, Resulting Numbers: [21] 21,83 unequal: No Solution Moving to Node #0,3,1 Current State: 83:[60, 93], Operations: ['75-48=27', '66+27=93'] Exploring Operation: 93-60=33, Resulting Numbers: [33] 33,83 unequal: No Solution Exploring Operation: 60*93=5580, Resulting Numbers: [5580] 5580,83 unequal: No Solution Exploring Operation: 60+93=153, Resulting Numbers: [153] 153,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[66, 63], Operations: ['75+48=123', '123-60=63'] Exploring Operation: 66+63=129, Resulting Numbers: [129] 129,83 unequal: No Solution Exploring Operation: 66*63=4158, Resulting Numbers: [4158] 4158,83 unequal: No Solution Exploring Operation: 66-63=3, Resulting Numbers: [3] 3,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[75, 54], Operations: ['66+48=114', '114-60=54'] Exploring Operation: 75*54=4050, Resulting Numbers: [4050] 4050,83 unequal: No Solution Exploring Operation: 75-54=21, Resulting Numbers: [21] 21,83 unequal: No Solution Exploring Operation: 75+54=129, Resulting Numbers: [129] 129,83 unequal: No Solution Moving to Node #0,2,3 Current State: 83:[60, 57], Operations: ['75+48=123', '123-66=57'] Exploring Operation: 60*57=3420, Resulting Numbers: [3420] 3420,83 unequal: No Solution Exploring Operation: 60+57=117, Resulting Numbers: [117] 117,83 unequal: No Solution Exploring Operation: 60-57=3, Resulting Numbers: [3] 3,83 unequal: No Solution Moving to Node #0,3,3 Current State: 83:[60, 39], Operations: ['75-48=27', '66-27=39'] Exploring Operation: 60*39=2340, Resulting Numbers: [2340] 2340,83 unequal: No Solution Exploring Operation: 60+39=99, Resulting Numbers: [99] 99,83 unequal: No Solution Exploring Operation: 60-39=21, Resulting Numbers: [21] 21,83 unequal: No Solution Moving to Node #0,3,2 Current State: 83:[66, 33], Operations: ['75-48=27', '60-27=33'] Exploring Operation: 66-33=33, Resulting Numbers: [33] 33,83 unequal: No Solution Exploring Operation: 66*33=2178, Resulting Numbers: [2178] 2178,83 unequal: No Solution Exploring Operation: 66/33=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 66+33=99, Resulting Numbers: [99] 99,83 unequal: No Solution Moving to Node #0,1,4 Current State: 83:[60, 39], Operations: ['66+48=114', '114-75=39'] Exploring Operation: 60*39=2340, Resulting Numbers: [2340] 2340,83 unequal: No Solution Exploring Operation: 60+39=99, Resulting Numbers: [99] 99,83 unequal: No Solution Exploring Operation: 60-39=21, Resulting Numbers: [21] 21,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[114, 135], Operations: ['66+48=114', '75+60=135'] Exploring Operation: 114+135=249, Resulting Numbers: [249] 249,83 unequal: No Solution Exploring Operation: 135-114=21, Resulting Numbers: [21] 21,83 unequal: No Solution Exploring Operation: 114*135=15390, Resulting Numbers: [15390] 15390,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[123, 126], Operations: ['75+48=123', '66+60=126'] Exploring Operation: 126-123=3, Resulting Numbers: [3] 3,83 unequal: No Solution Exploring Operation: 123+126=249, Resulting Numbers: [249] 249,83 unequal: No Solution Exploring Operation: 123*126=15498, Resulting Numbers: [15498] 15498,83 unequal: No Solution Moving to Node #0,3,0 Current State: 83:[27, 126], Operations: ['75-48=27', '66+60=126'] Exploring Operation: 27+126=153, Resulting Numbers: [153] 153,83 unequal: No Solution Exploring Operation: 126-27=99, Resulting Numbers: [99] 99,83 unequal: No Solution Exploring Operation: 27*126=3402, Resulting Numbers: [3402] 3402,83 unequal: No Solution Moving to Node #0,1,3 Current State: 83:[75, 174], Operations: ['66+48=114', '60+114=174'] Exploring Operation: 174-75=99, Resulting Numbers: [99] 99,83 unequal: No Solution Exploring Operation: 75+174=249, Resulting Numbers: [249] 249,83 unequal: No Solution Exploring Operation: 75*174=13050, Resulting Numbers: [13050] 13050,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[114, 15], Operations: ['66+48=114', '75-60=15'] Exploring Operation: 114*15=1710, Resulting Numbers: [1710] 1710,83 unequal: No Solution Exploring Operation: 114+15=129, Resulting Numbers: [129] 129,83 unequal: No Solution Exploring Operation: 114-15=99, Resulting Numbers: [99] 99,83 unequal: No Solution Moving to Node #0,2,4 Current State: 83:[123, 6], Operations: ['75+48=123', '66-60=6'] Exploring Operation: 123+6=129, Resulting Numbers: [129] 129,83 unequal: No Solution Exploring Operation: 123*6=738, Resulting Numbers: [738] 738,83 unequal: No Solution Exploring Operation: 123-6=117, Resulting Numbers: [117] 117,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[66, 183], Operations: ['75+48=123', '60+123=183'] Exploring Operation: 183-66=117, Resulting Numbers: [117] 117,83 unequal: No Solution Exploring Operation: 66+183=249, Resulting Numbers: [249] 249,83 unequal: No Solution Exploring Operation: 66*183=12078, Resulting Numbers: [12078] 12078,83 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 6, 99, 40, 34 ]
100
[ "40-6=34", "34/34=1", "99+1=100" ]
Current State: 100:[6, 99, 40, 34], Operations: [] Exploring Operation: 40-6=34, Resulting Numbers: [99, 34, 34] Generated Node #2: [99, 34, 34] from Operation: 40-6=34 Current State: 100:[99, 34, 34], Operations: ['40-6=34'] Exploring Operation: 34/34=1, Resulting Numbers: [99, 1] Generated Node #3: [99, 1] from Operation: 34/34=1 Current State: 100:[99, 1], Operations: ['40-6=34', '34/34=1'] Exploring Operation: 99+1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[6, 99, 40, 34], Operations: [] Exploring Operation: 6+40=46, Resulting Numbers: [99, 34, 46] Generated Node #0,0: 100:[99, 34, 46] Operation: 6+40=46 Exploring Operation: 34-6=28, Resulting Numbers: [99, 40, 28] Generated Node #0,1: 100:[99, 40, 28] Operation: 34-6=28 Exploring Operation: 40-6=34, Resulting Numbers: [99, 34, 34] Generated Node #0,2: 100:[99, 34, 34] Operation: 40-6=34 Exploring Operation: 40-34=6, Resulting Numbers: [6, 99, 6] Generated Node #0,3: 100:[6, 99, 6] Operation: 40-34=6 Moving to Node #0,3 Current State: 100:[6, 99, 6], Operations: ['40-34=6'] Exploring Operation: 6+99=105, Resulting Numbers: [6, 105] Generated Node #0,3,0: 100:[6, 105] Operation: 6+99=105 Exploring Operation: 6-6=0, Resulting Numbers: [99, 0] Generated Node #0,3,1: 100:[99, 0] Operation: 6-6=0 Exploring Operation: 6/6=1, Resulting Numbers: [99, 1] Generated Node #0,3,2: 100:[99, 1] Operation: 6/6=1 Exploring Operation: 6+6=12, Resulting Numbers: [99, 12] Generated Node #0,3,3: 100:[99, 12] Operation: 6+6=12 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 100:[99, 1], Operations: ['40-34=6', '6/6=1'] Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,100 unequal: No Solution Exploring Operation: 99*1=99, Resulting Numbers: [99] 99,100 unequal: No Solution Exploring Operation: 99/1=99, Resulting Numbers: [99] 99,100 unequal: No Solution Exploring Operation: 99+1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[6, 99, 40, 34], Operations: [] Exploring Operation: 40-34=6, Resulting Numbers: [6, 99, 6] Generated Node #0,3: 100:[6, 99, 6] Operation: 40-34=6 Moving to Node #0,3 Current State: 100:[6, 99, 6], Operations: ['40-34=6'] Exploring Operation: 6/6=1, Resulting Numbers: [99, 1] Generated Node #0,3,2: 100:[99, 1] Operation: 6/6=1 Moving to Node #0,3,2 Current State: 100:[99, 1], Operations: ['40-34=6', '6/6=1'] Exploring Operation: 99+1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 13, 39, 15, 1 ]
45
[ "39/13=3", "15*1=15", "3*15=45" ]
Current State: 45:[13, 39, 15, 1], Operations: [] Exploring Operation: 39/13=3, Resulting Numbers: [15, 1, 3] Generated Node #2: [15, 1, 3] from Operation: 39/13=3 Current State: 45:[15, 1, 3], Operations: ['39/13=3'] Exploring Operation: 15*1=15, Resulting Numbers: [3, 15] Generated Node #3: [3, 15] from Operation: 15*1=15 Current State: 45:[3, 15], Operations: ['39/13=3', '15*1=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[13, 39, 15, 1], Operations: [] Exploring Operation: 39/13=3, Resulting Numbers: [15, 1, 3] Generated Node #0,0: 45:[15, 1, 3] Operation: 39/13=3 Moving to Node #0,0 Current State: 45:[15, 1, 3], Operations: ['39/13=3'] Exploring Operation: 15*1=15, Resulting Numbers: [3, 15] Generated Node #0,0,0: 45:[3, 15] Operation: 15*1=15 Moving to Node #0,0,0 Current State: 45:[3, 15], Operations: ['39/13=3', '15*1=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[13, 39, 15, 1], Operations: [] Exploring Operation: 39/13=3, Resulting Numbers: [15, 1, 3] Generated Node #0,0: 45:[15, 1, 3] Operation: 39/13=3 Moving to Node #0,0 Current State: 45:[15, 1, 3], Operations: ['39/13=3'] Exploring Operation: 15*1=15, Resulting Numbers: [3, 15] Generated Node #0,0,0: 45:[3, 15] Operation: 15*1=15 Moving to Node #0,0,0 Current State: 45:[3, 15], Operations: ['39/13=3', '15*1=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 82, 17, 70, 5 ]
20
[ "82*5=410", "410-70=340", "340/17=20" ]
Current State: 20:[82, 17, 70, 5], Operations: [] Exploring Operation: 82*5=410, Resulting Numbers: [17, 70, 410] Generated Node #2: [17, 70, 410] from Operation: 82*5=410 Current State: 20:[17, 70, 410], Operations: ['82*5=410'] Exploring Operation: 410-70=340, Resulting Numbers: [17, 340] Generated Node #3: [17, 340] from Operation: 410-70=340 Current State: 20:[17, 340], Operations: ['82*5=410', '410-70=340'] Exploring Operation: 340/17=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[82, 17, 70, 5], Operations: [] Exploring Operation: 82-17=65, Resulting Numbers: [70, 5, 65] Generated Node #0,0: 20:[70, 5, 65] Operation: 82-17=65 Exploring Operation: 70/5=14, Resulting Numbers: [82, 17, 14] Generated Node #0,1: 20:[82, 17, 14] Operation: 70/5=14 Exploring Operation: 82-70=12, Resulting Numbers: [17, 5, 12] Generated Node #0,2: 20:[17, 5, 12] Operation: 82-70=12 Moving to Node #0,2 Current State: 20:[17, 5, 12], Operations: ['82-70=12'] Exploring Operation: 17-5=12, Resulting Numbers: [12, 12] Generated Node #0,2,0: 20:[12, 12] Operation: 17-5=12 Exploring Operation: 17+5=22, Resulting Numbers: [12, 22] Generated Node #0,2,1: 20:[12, 22] Operation: 17+5=22 Exploring Operation: 17-12=5, Resulting Numbers: [5, 5] Generated Node #0,2,2: 20:[5, 5] Operation: 17-12=5 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 20:[5, 5], Operations: ['82-70=12', '17-12=5'] Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,20 unequal: No Solution Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,20 unequal: No Solution No 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: 20:[12, 12], Operations: ['82-70=12', '17-5=12'] Exploring Operation: 12-12=0, Resulting Numbers: [0] 0,20 unequal: No Solution Exploring Operation: 12/12=1, Resulting Numbers: [1] 1,20 unequal: No Solution Exploring Operation: 12+12=24, Resulting Numbers: [24] 24,20 unequal: No Solution No 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: 20:[12, 22], Operations: ['82-70=12', '17+5=22'] Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,20 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: 20:[82, 17, 14], Operations: ['70/5=14'] Exploring Operation: 17-14=3, Resulting Numbers: [82, 3] Generated Node #0,1,0: 20:[82, 3] Operation: 17-14=3 Exploring Operation: 82-17=65, Resulting Numbers: [14, 65] Generated Node #0,1,1: 20:[14, 65] Operation: 82-17=65 Exploring Operation: 82-14=68, Resulting Numbers: [17, 68] Generated Node #0,1,2: 20:[17, 68] Operation: 82-14=68 Moving to Node #0,0 Current State: 20:[70, 5, 65], Operations: ['82-17=65'] Exploring Operation: 65/5=13, Resulting Numbers: [70, 13] Generated Node #0,0,0: 20:[70, 13] Operation: 65/5=13 Exploring Operation: 70-65=5, Resulting Numbers: [5, 5] Generated Node #0,0,1: 20:[5, 5] Operation: 70-65=5 Exploring Operation: 70/5=14, Resulting Numbers: [65, 14] Generated Node #0,0,2: 20:[65, 14] Operation: 70/5=14 Moving to Node #0,0,1 Current State: 20:[5, 5], Operations: ['82-17=65', '70-65=5'] Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,20 unequal: No Solution Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[14, 65], Operations: ['70/5=14', '82-17=65'] Exploring Operation: 14+65=79, Resulting Numbers: [79] 79,20 unequal: No Solution Exploring Operation: 65-14=51, Resulting Numbers: [51] 51,20 unequal: No Solution Exploring Operation: 14*65=910, Resulting Numbers: [910] 910,20 unequal: No Solution Moving to Node #0,0,2 Current State: 20:[65, 14], Operations: ['82-17=65', '70/5=14'] Exploring Operation: 65*14=910, Resulting Numbers: [910] 910,20 unequal: No Solution Exploring Operation: 65-14=51, Resulting Numbers: [51] 51,20 unequal: No Solution Exploring Operation: 65+14=79, Resulting Numbers: [79] 79,20 unequal: No Solution Moving to Node #0,1,2 Current State: 20:[17, 68], Operations: ['70/5=14', '82-14=68'] Exploring Operation: 68-17=51, Resulting Numbers: [51] 51,20 unequal: No Solution Exploring Operation: 17+68=85, Resulting Numbers: [85] 85,20 unequal: No Solution Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,20 unequal: No Solution Moving to Node #0,0,0 Current State: 20:[70, 13], Operations: ['82-17=65', '65/5=13'] Exploring Operation: 70+13=83, Resulting Numbers: [83] 83,20 unequal: No Solution Exploring Operation: 70*13=910, Resulting Numbers: [910] 910,20 unequal: No Solution Exploring Operation: 70-13=57, Resulting Numbers: [57] 57,20 unequal: No Solution Moving to Node #0,1,0 Current State: 20:[82, 3], Operations: ['70/5=14', '17-14=3'] Exploring Operation: 82+3=85, Resulting Numbers: [85] 85,20 unequal: No Solution Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,20 unequal: No Solution Exploring Operation: 82*3=246, Resulting Numbers: [246] 246,20 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 45, 87, 68, 83 ]
84
[ "83-68=15", "45/15=3", "87-3=84" ]
Current State: 84:[45, 87, 68, 83], Operations: [] Exploring Operation: 83-68=15, Resulting Numbers: [45, 87, 15] Generated Node #2: [45, 87, 15] from Operation: 83-68=15 Current State: 84:[45, 87, 15], Operations: ['83-68=15'] Exploring Operation: 45/15=3, Resulting Numbers: [87, 3] Generated Node #3: [87, 3] from Operation: 45/15=3 Current State: 84:[87, 3], Operations: ['83-68=15', '45/15=3'] Exploring Operation: 87-3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[45, 87, 68, 83], Operations: [] Exploring Operation: 68-45=23, Resulting Numbers: [87, 83, 23] Generated Node #0,0: 84:[87, 83, 23] Operation: 68-45=23 Moving to Node #0,0 Current State: 84:[87, 83, 23], Operations: ['68-45=23'] Exploring Operation: 87-83=4, Resulting Numbers: [23, 4] Generated Node #0,0,0: 84:[23, 4] Operation: 87-83=4 Moving to Node #0,0,0 Current State: 84:[23, 4], Operations: ['68-45=23', '87-83=4'] Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,84 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 12, 4, 47, 55 ]
92
[ "55-47=8", "12*8=96", "96-4=92" ]
Current State: 92:[12, 4, 47, 55], Operations: [] Exploring Operation: 55-47=8, Resulting Numbers: [12, 4, 8] Generated Node #2: [12, 4, 8] from Operation: 55-47=8 Current State: 92:[12, 4, 8], Operations: ['55-47=8'] Exploring Operation: 12*8=96, Resulting Numbers: [4, 96] Generated Node #3: [4, 96] from Operation: 12*8=96 Current State: 92:[4, 96], Operations: ['55-47=8', '12*8=96'] Exploring Operation: 96-4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[12, 4, 47, 55], Operations: [] Exploring Operation: 12/4=3, Resulting Numbers: [47, 55, 3] Generated Node #0,0: 92:[47, 55, 3] Operation: 12/4=3 Exploring Operation: 55-12=43, Resulting Numbers: [4, 47, 43] Generated Node #0,1: 92:[4, 47, 43] Operation: 55-12=43 Moving to Node #0,1 Current State: 92:[4, 47, 43], Operations: ['55-12=43'] Exploring Operation: 4+43=47, Resulting Numbers: [47, 47] Generated Node #0,1,0: 92:[47, 47] Operation: 4+43=47 Exploring Operation: 47-43=4, Resulting Numbers: [4, 4] Generated Node #0,1,1: 92:[4, 4] Operation: 47-43=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[4, 4], Operations: ['55-12=43', '47-43=4'] Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[47, 47], Operations: ['55-12=43', '4+43=47'] Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,92 unequal: No Solution Exploring Operation: 47/47=1, Resulting Numbers: [1] 1,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 92:[47, 55, 3], Operations: ['12/4=3'] Exploring Operation: 55-47=8, Resulting Numbers: [3, 8] Generated Node #0,0,0: 92:[3, 8] Operation: 55-47=8 Exploring Operation: 55-3=52, Resulting Numbers: [47, 52] Generated Node #0,0,1: 92:[47, 52] Operation: 55-3=52 Moving to Node #0,0,0 Current State: 92:[3, 8], Operations: ['12/4=3', '55-47=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[47, 52], Operations: ['12/4=3', '55-3=52'] Exploring Operation: 47+52=99, Resulting Numbers: [99] 99,92 unequal: No Solution Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,92 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 15, 91, 89, 12 ]
39
[ "91-89=2", "12*2=24", "15+24=39" ]
Current State: 39:[15, 91, 89, 12], Operations: [] Exploring Operation: 91-89=2, Resulting Numbers: [15, 12, 2] Generated Node #2: [15, 12, 2] from Operation: 91-89=2 Current State: 39:[15, 12, 2], Operations: ['91-89=2'] Exploring Operation: 12*2=24, Resulting Numbers: [15, 24] Generated Node #3: [15, 24] from Operation: 12*2=24 Current State: 39:[15, 24], Operations: ['91-89=2', '12*2=24'] Exploring Operation: 15+24=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[15, 91, 89, 12], Operations: [] Exploring Operation: 91-89=2, Resulting Numbers: [15, 12, 2] Generated Node #0,0: 39:[15, 12, 2] Operation: 91-89=2 Exploring Operation: 91-15=76, Resulting Numbers: [89, 12, 76] Generated Node #0,1: 39:[89, 12, 76] Operation: 91-15=76 Exploring Operation: 89-15=74, Resulting Numbers: [91, 12, 74] Generated Node #0,2: 39:[91, 12, 74] Operation: 89-15=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[15, 12, 2], Operations: ['91-89=2'] Exploring Operation: 12+2=14, Resulting Numbers: [15, 14] Generated Node #0,0,0: 39:[15, 14] Operation: 12+2=14 Exploring Operation: 15-2=13, Resulting Numbers: [12, 13] Generated Node #0,0,1: 39:[12, 13] Operation: 15-2=13 Exploring Operation: 15-12=3, Resulting Numbers: [2, 3] Generated Node #0,0,2: 39:[2, 3] Operation: 15-12=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 39:[12, 13], Operations: ['91-89=2', '15-2=13'] Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,39 unequal: No Solution Exploring Operation: 13-12=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 #0,0,2 Current State: 39:[2, 3], Operations: ['91-89=2', '15-12=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,39 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 #0,0,0 Current State: 39:[15, 14], Operations: ['91-89=2', '12+2=14'] Exploring Operation: 15*14=210, Resulting Numbers: [210] 210,39 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,39 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:[89, 12, 76], Operations: ['91-15=76'] Exploring Operation: 76-12=64, Resulting Numbers: [89, 64] Generated Node #0,1,0: 39:[89, 64] Operation: 76-12=64 Exploring Operation: 89-76=13, Resulting Numbers: [12, 13] Generated Node #0,1,1: 39:[12, 13] Operation: 89-76=13 Exploring Operation: 89-12=77, Resulting Numbers: [76, 77] Generated Node #0,1,2: 39:[76, 77] Operation: 89-12=77 Moving to Node #0,1,1 Current State: 39:[12, 13], Operations: ['91-15=76', '89-76=13'] Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,39 unequal: No Solution Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[89, 64], Operations: ['91-15=76', '76-12=64'] Exploring Operation: 89+64=153, Resulting Numbers: [153] 153,39 unequal: No Solution Exploring Operation: 89*64=5696, Resulting Numbers: [5696] 5696,39 unequal: No Solution Exploring Operation: 89-64=25, Resulting Numbers: [25] 25,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[76, 77], Operations: ['91-15=76', '89-12=77'] Exploring Operation: 76*77=5852, Resulting Numbers: [5852] 5852,39 unequal: No Solution Exploring Operation: 76+77=153, Resulting Numbers: [153] 153,39 unequal: No Solution Exploring Operation: 77-76=1, Resulting Numbers: [1] 1,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[91, 12, 74], Operations: ['89-15=74'] Exploring Operation: 91-74=17, Resulting Numbers: [12, 17] Generated Node #0,2,0: 39:[12, 17] Operation: 91-74=17 Exploring Operation: 91-12=79, Resulting Numbers: [74, 79] Generated Node #0,2,1: 39:[74, 79] Operation: 91-12=79 Exploring Operation: 74-12=62, Resulting Numbers: [91, 62] Generated Node #0,2,2: 39:[91, 62] Operation: 74-12=62 Moving to Node #0,2,0 Current State: 39:[12, 17], Operations: ['89-15=74', '91-74=17'] Exploring Operation: 12*17=204, Resulting Numbers: [204] 204,39 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 12+17=29, Resulting Numbers: [29] 29,39 unequal: No Solution Moving to Node #0,2,1 Current State: 39:[74, 79], Operations: ['89-15=74', '91-12=79'] Exploring Operation: 74+79=153, Resulting Numbers: [153] 153,39 unequal: No Solution Exploring Operation: 79-74=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 74*79=5846, Resulting Numbers: [5846] 5846,39 unequal: No Solution Moving to Node #0,2,2 Current State: 39:[91, 62], Operations: ['89-15=74', '74-12=62'] Exploring Operation: 91*62=5642, Resulting Numbers: [5642] 5642,39 unequal: No Solution Exploring Operation: 91-62=29, Resulting Numbers: [29] 29,39 unequal: No Solution Exploring Operation: 91+62=153, Resulting Numbers: [153] 153,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 42, 10, 87, 27 ]
48
[ "87-27=60", "60/10=6", "42+6=48" ]
Current State: 48:[42, 10, 87, 27], Operations: [] Exploring Operation: 87-27=60, Resulting Numbers: [42, 10, 60] Generated Node #2: [42, 10, 60] from Operation: 87-27=60 Current State: 48:[42, 10, 60], Operations: ['87-27=60'] Exploring Operation: 60/10=6, Resulting Numbers: [42, 6] Generated Node #3: [42, 6] from Operation: 60/10=6 Current State: 48:[42, 6], Operations: ['87-27=60', '60/10=6'] Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[42, 10, 87, 27], Operations: [] Exploring Operation: 87-10=77, Resulting Numbers: [42, 27, 77] Generated Node #0,0: 48:[42, 27, 77] Operation: 87-10=77 Exploring Operation: 87-27=60, Resulting Numbers: [42, 10, 60] Generated Node #0,1: 48:[42, 10, 60] Operation: 87-27=60 Exploring Operation: 87-42=45, Resulting Numbers: [10, 27, 45] Generated Node #0,2: 48:[10, 27, 45] Operation: 87-42=45 Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[10, 27, 45], Operations: ['87-42=45'] Exploring Operation: 45-27=18, Resulting Numbers: [10, 18] Generated Node #0,2,0: 48:[10, 18] Operation: 45-27=18 Exploring Operation: 10+45=55, Resulting Numbers: [27, 55] Generated Node #0,2,1: 48:[27, 55] Operation: 10+45=55 Exploring Operation: 27-10=17, Resulting Numbers: [45, 17] Generated Node #0,2,2: 48:[45, 17] Operation: 27-10=17 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 48:[10, 18], Operations: ['87-42=45', '45-27=18'] Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,48 unequal: No Solution Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 48:[45, 17], Operations: ['87-42=45', '27-10=17'] Exploring Operation: 45*17=765, Resulting Numbers: [765] 765,48 unequal: No Solution Exploring Operation: 45+17=62, Resulting Numbers: [62] 62,48 unequal: No Solution Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 48:[27, 55], Operations: ['87-42=45', '10+45=55'] Exploring Operation: 55-27=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 27+55=82, Resulting Numbers: [82] 82,48 unequal: No Solution Exploring Operation: 27*55=1485, Resulting Numbers: [1485] 1485,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[42, 10, 60], Operations: ['87-27=60'] Exploring Operation: 60-42=18, Resulting Numbers: [10, 18] Generated Node #0,1,0: 48:[10, 18] Operation: 60-42=18 Exploring Operation: 60/10=6, Resulting Numbers: [42, 6] Generated Node #0,1,1: 48:[42, 6] Operation: 60/10=6 Exploring Operation: 60-10=50, Resulting Numbers: [42, 50] Generated Node #0,1,2: 48:[42, 50] Operation: 60-10=50 Moving to Node #0,1,0 Current State: 48:[10, 18], Operations: ['87-27=60', '60-42=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[42, 6], Operations: ['87-27=60', '60/10=6'] Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,48 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[42, 10, 87, 27], Operations: [] Exploring Operation: 87-27=60, Resulting Numbers: [42, 10, 60] Generated Node #0,1: 48:[42, 10, 60] Operation: 87-27=60 Moving to Node #0,1 Current State: 48:[42, 10, 60], Operations: ['87-27=60'] Exploring Operation: 60/10=6, Resulting Numbers: [42, 6] Generated Node #0,1,1: 48:[42, 6] Operation: 60/10=6 Moving to Node #0,1,1 Current State: 48:[42, 6], Operations: ['87-27=60', '60/10=6'] Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_3
sum_heuristic
[ 5, 64, 34, 40 ]
86
[ "64-40=24", "5*24=120", "120-34=86" ]
Current State: 86:[5, 64, 34, 40], Operations: [] Exploring Operation: 64-40=24, Resulting Numbers: [5, 34, 24] Generated Node #2: [5, 34, 24] from Operation: 64-40=24 Current State: 86:[5, 34, 24], Operations: ['64-40=24'] Exploring Operation: 5*24=120, Resulting Numbers: [34, 120] Generated Node #3: [34, 120] from Operation: 5*24=120 Current State: 86:[34, 120], Operations: ['64-40=24', '5*24=120'] Exploring Operation: 120-34=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[5, 64, 34, 40], Operations: [] Exploring Operation: 64+34=98, Resulting Numbers: [5, 40, 98] Generated Node #0,0: 86:[5, 40, 98] Operation: 64+34=98 Moving to Node #0,0 Current State: 86:[5, 40, 98], Operations: ['64+34=98'] Exploring Operation: 98-5=93, Resulting Numbers: [40, 93] Generated Node #0,0,0: 86:[40, 93] Operation: 98-5=93 Moving to Node #0,0,0 Current State: 86:[40, 93], Operations: ['64+34=98', '98-5=93'] Exploring Operation: 93-40=53, Resulting Numbers: [53] 53,86 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 50, 53, 66, 23 ]
86
[ "53-50=3", "66+23=89", "89-3=86" ]
Current State: 86:[50, 53, 66, 23], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [66, 23, 3] Generated Node #2: [66, 23, 3] from Operation: 53-50=3 Current State: 86:[66, 23, 3], Operations: ['53-50=3'] Exploring Operation: 66+23=89, Resulting Numbers: [3, 89] Generated Node #3: [3, 89] from Operation: 66+23=89 Current State: 86:[3, 89], Operations: ['53-50=3', '66+23=89'] Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[50, 53, 66, 23], Operations: [] Exploring Operation: 66-23=43, Resulting Numbers: [50, 53, 43] Generated Node #0,0: 86:[50, 53, 43] Operation: 66-23=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[50, 53, 43], Operations: ['66-23=43'] Exploring Operation: 53-50=3, Resulting Numbers: [43, 3] Generated Node #0,0,0: 86:[43, 3] Operation: 53-50=3 Moving to Node #0,0,0 Current State: 86:[43, 3], Operations: ['66-23=43', '53-50=3'] Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,86 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
[ 73, 11, 40, 37 ]
59
[ "73-11=62", "40-37=3", "62-3=59" ]
Current State: 59:[73, 11, 40, 37], Operations: [] Exploring Operation: 73-11=62, Resulting Numbers: [40, 37, 62] Generated Node #2: [40, 37, 62] from Operation: 73-11=62 Current State: 59:[40, 37, 62], Operations: ['73-11=62'] Exploring Operation: 40-37=3, Resulting Numbers: [62, 3] Generated Node #3: [62, 3] from Operation: 40-37=3 Current State: 59:[62, 3], Operations: ['73-11=62', '40-37=3'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[73, 11, 40, 37], Operations: [] Exploring Operation: 73-11=62, Resulting Numbers: [40, 37, 62] Generated Node #0,0: 59:[40, 37, 62] Operation: 73-11=62 Exploring Operation: 11+37=48, Resulting Numbers: [73, 40, 48] Generated Node #0,1: 59:[73, 40, 48] Operation: 11+37=48 Exploring Operation: 73+11=84, Resulting Numbers: [40, 37, 84] Generated Node #0,2: 59:[40, 37, 84] Operation: 73+11=84 Exploring Operation: 11+40=51, Resulting Numbers: [73, 37, 51] Generated Node #0,3: 59:[73, 37, 51] Operation: 11+40=51 Moving to Node #0,0 Current State: 59:[40, 37, 62], Operations: ['73-11=62'] Exploring Operation: 62-40=22, Resulting Numbers: [37, 22] Generated Node #0,0,0: 59:[37, 22] Operation: 62-40=22 Exploring Operation: 62-37=25, Resulting Numbers: [40, 25] Generated Node #0,0,1: 59:[40, 25] Operation: 62-37=25 Exploring Operation: 40-37=3, Resulting Numbers: [62, 3] Generated Node #0,0,2: 59:[62, 3] Operation: 40-37=3 Exploring Operation: 40+37=77, Resulting Numbers: [62, 77] Generated Node #0,0,3: 59:[62, 77] Operation: 40+37=77 Moving to Node #0,3 Current State: 59:[73, 37, 51], Operations: ['11+40=51'] Exploring Operation: 73+37=110, Resulting Numbers: [51, 110] Generated Node #0,3,0: 59:[51, 110] Operation: 73+37=110 Exploring Operation: 73-37=36, Resulting Numbers: [51, 36] Generated Node #0,3,1: 59:[51, 36] Operation: 73-37=36 Exploring Operation: 73-51=22, Resulting Numbers: [37, 22] Generated Node #0,3,2: 59:[37, 22] Operation: 73-51=22 Exploring Operation: 37+51=88, Resulting Numbers: [73, 88] Generated Node #0,3,3: 59:[73, 88] Operation: 37+51=88 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 59:[51, 36], Operations: ['11+40=51', '73-37=36'] Exploring Operation: 51*36=1836, Resulting Numbers: [1836] 1836,59 unequal: No Solution Exploring Operation: 51+36=87, Resulting Numbers: [87] 87,59 unequal: No Solution Exploring Operation: 51-36=15, Resulting Numbers: [15] 15,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 59:[73, 88], Operations: ['11+40=51', '37+51=88'] Exploring Operation: 73+88=161, Resulting Numbers: [161] 161,59 unequal: No Solution Exploring Operation: 73*88=6424, Resulting Numbers: [6424] 6424,59 unequal: No Solution Exploring Operation: 88-73=15, Resulting Numbers: [15] 15,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 59:[51, 110], Operations: ['11+40=51', '73+37=110'] Exploring Operation: 51+110=161, Resulting Numbers: [161] 161,59 unequal: No Solution Exploring Operation: 110-51=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[73, 11, 40, 37], Operations: [] Exploring Operation: 11+40=51, Resulting Numbers: [73, 37, 51] Generated Node #0,3: 59:[73, 37, 51] Operation: 11+40=51 Moving to Node #0,3 Current State: 59:[73, 37, 51], Operations: ['11+40=51'] Exploring Operation: 73+37=110, Resulting Numbers: [51, 110] Generated Node #0,3,0: 59:[51, 110] Operation: 73+37=110 Moving to Node #0,3,0 Current State: 59:[51, 110], Operations: ['11+40=51', '73+37=110'] Exploring Operation: 110-51=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_4
sum_heuristic