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
[ 62, 65, 47, 8 ]
82
[ "65-47=18", "8*18=144", "144-62=82" ]
Current State: 82:[62, 65, 47, 8], Operations: [] Exploring Operation: 65-47=18, Resulting Numbers: [62, 8, 18] Generated Node #2: [62, 8, 18] from Operation: 65-47=18 Current State: 82:[62, 8, 18], Operations: ['65-47=18'] Exploring Operation: 8*18=144, Resulting Numbers: [62, 144] Generated Node #3: [62, 144] from Operation: 8*18=144 Current State: 82:[62, 144], Operations: ['65-47=18', '8*18=144'] Exploring Operation: 144-62=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[62, 65, 47, 8], Operations: [] Exploring Operation: 65+8=73, Resulting Numbers: [62, 47, 73] Generated Node #0,0: 82:[62, 47, 73] Operation: 65+8=73 Exploring Operation: 65-62=3, Resulting Numbers: [47, 8, 3] Generated Node #0,1: 82:[47, 8, 3] Operation: 65-62=3 Exploring Operation: 62+8=70, Resulting Numbers: [65, 47, 70] Generated Node #0,2: 82:[65, 47, 70] Operation: 62+8=70 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[47, 8, 3], Operations: ['65-62=3'] Exploring Operation: 47-3=44, Resulting Numbers: [8, 44] Generated Node #0,1,0: 82:[8, 44] Operation: 47-3=44 Exploring Operation: 8-3=5, Resulting Numbers: [47, 5] Generated Node #0,1,1: 82:[47, 5] Operation: 8-3=5 Exploring Operation: 47-8=39, Resulting Numbers: [3, 39] Generated Node #0,1,2: 82:[3, 39] Operation: 47-8=39 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 82:[3, 39], Operations: ['65-62=3', '47-8=39'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,82 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,82 unequal: No Solution Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[8, 44], Operations: ['65-62=3', '47-3=44'] Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,82 unequal: No Solution Exploring Operation: 8*44=352, Resulting Numbers: [352] 352,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[47, 5], Operations: ['65-62=3', '8-3=5'] Exploring Operation: 47*5=235, Resulting Numbers: [235] 235,82 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 47+5=52, Resulting Numbers: [52] 52,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[62, 47, 73], Operations: ['65+8=73'] Exploring Operation: 73-62=11, Resulting Numbers: [47, 11] Generated Node #0,0,0: 82:[47, 11] Operation: 73-62=11 Exploring Operation: 62-47=15, Resulting Numbers: [73, 15] Generated Node #0,0,1: 82:[73, 15] Operation: 62-47=15 Exploring Operation: 73-47=26, Resulting Numbers: [62, 26] Generated Node #0,0,2: 82:[62, 26] Operation: 73-47=26 Moving to Node #0,0,0 Current State: 82:[47, 11], Operations: ['65+8=73', '73-62=11'] Exploring Operation: 47*11=517, Resulting Numbers: [517] 517,82 unequal: No Solution Exploring Operation: 47+11=58, Resulting Numbers: [58] 58,82 unequal: No Solution Exploring Operation: 47-11=36, Resulting Numbers: [36] 36,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[73, 15], Operations: ['65+8=73', '62-47=15'] Exploring Operation: 73+15=88, Resulting Numbers: [88] 88,82 unequal: No Solution Exploring Operation: 73*15=1095, Resulting Numbers: [1095] 1095,82 unequal: No Solution Exploring Operation: 73-15=58, Resulting Numbers: [58] 58,82 unequal: No Solution Moving to Node #0,0,2 Current State: 82:[62, 26], Operations: ['65+8=73', '73-47=26'] Exploring Operation: 62-26=36, Resulting Numbers: [36] 36,82 unequal: No Solution Exploring Operation: 62*26=1612, Resulting Numbers: [1612] 1612,82 unequal: No Solution Exploring Operation: 62+26=88, Resulting Numbers: [88] 88,82 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:[65, 47, 70], Operations: ['62+8=70'] Exploring Operation: 70-65=5, Resulting Numbers: [47, 5] Generated Node #0,2,0: 82:[47, 5] Operation: 70-65=5 Exploring Operation: 65-47=18, Resulting Numbers: [70, 18] Generated Node #0,2,1: 82:[70, 18] Operation: 65-47=18 Exploring Operation: 70-47=23, Resulting Numbers: [65, 23] Generated Node #0,2,2: 82:[65, 23] Operation: 70-47=23 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[47, 5], Operations: ['62+8=70', '70-65=5'] Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 47+5=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 47*5=235, Resulting Numbers: [235] 235,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[70, 18], Operations: ['62+8=70', '65-47=18'] Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 70+18=88, Resulting Numbers: [88] 88,82 unequal: No Solution Exploring Operation: 70*18=1260, Resulting Numbers: [1260] 1260,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 82:[65, 23], Operations: ['62+8=70', '70-47=23'] Exploring Operation: 65+23=88, Resulting Numbers: [88] 88,82 unequal: No Solution Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 65*23=1495, Resulting Numbers: [1495] 1495,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 33, 41, 23, 50 ]
19
[ "41-33=8", "50-23=27", "27-8=19" ]
Current State: 19:[33, 41, 23, 50], Operations: [] Exploring Operation: 41-33=8, Resulting Numbers: [23, 50, 8] Generated Node #2: [23, 50, 8] from Operation: 41-33=8 Current State: 19:[23, 50, 8], Operations: ['41-33=8'] Exploring Operation: 50-23=27, Resulting Numbers: [8, 27] Generated Node #3: [8, 27] from Operation: 50-23=27 Current State: 19:[8, 27], Operations: ['41-33=8', '50-23=27'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[33, 41, 23, 50], Operations: [] Exploring Operation: 50-33=17, Resulting Numbers: [41, 23, 17] Generated Node #0,0: 19:[41, 23, 17] Operation: 50-33=17 Exploring Operation: 50-23=27, Resulting Numbers: [33, 41, 27] Generated Node #0,1: 19:[33, 41, 27] Operation: 50-23=27 Exploring Operation: 41-33=8, Resulting Numbers: [23, 50, 8] Generated Node #0,2: 19:[23, 50, 8] Operation: 41-33=8 Exploring Operation: 50-41=9, Resulting Numbers: [33, 23, 9] Generated Node #0,3: 19:[33, 23, 9] Operation: 50-41=9 Moving to Node #0,0 Current State: 19:[41, 23, 17], Operations: ['50-33=17'] Exploring Operation: 41-23=18, Resulting Numbers: [17, 18] Generated Node #0,0,0: 19:[17, 18] Operation: 41-23=18 Exploring Operation: 41-17=24, Resulting Numbers: [23, 24] Generated Node #0,0,1: 19:[23, 24] Operation: 41-17=24 Exploring Operation: 41+17=58, Resulting Numbers: [23, 58] Generated Node #0,0,2: 19:[23, 58] Operation: 41+17=58 Exploring Operation: 23-17=6, Resulting Numbers: [41, 6] Generated Node #0,0,3: 19:[41, 6] Operation: 23-17=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[17, 18], Operations: ['50-33=17', '41-23=18'] Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 17+18=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 17*18=306, Resulting Numbers: [306] 306,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 19:[23, 24], Operations: ['50-33=17', '41-17=24'] Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 23*24=552, Resulting Numbers: [552] 552,19 unequal: No Solution Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 19:[41, 6], Operations: ['50-33=17', '23-17=6'] Exploring Operation: 41+6=47, Resulting Numbers: [47] 47,19 unequal: No Solution Exploring Operation: 41*6=246, Resulting Numbers: [246] 246,19 unequal: No Solution Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 19:[23, 58], Operations: ['50-33=17', '41+17=58'] Exploring Operation: 23*58=1334, Resulting Numbers: [1334] 1334,19 unequal: No Solution Exploring Operation: 58-23=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 23+58=81, Resulting Numbers: [81] 81,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 19:[33, 23, 9], Operations: ['50-41=9'] Exploring Operation: 33-9=24, Resulting Numbers: [23, 24] Generated Node #0,3,0: 19:[23, 24] Operation: 33-9=24 Exploring Operation: 33+9=42, Resulting Numbers: [23, 42] Generated Node #0,3,1: 19:[23, 42] Operation: 33+9=42 Exploring Operation: 33-23=10, Resulting Numbers: [9, 10] Generated Node #0,3,2: 19:[9, 10] Operation: 33-23=10 Exploring Operation: 23-9=14, Resulting Numbers: [33, 14] Generated Node #0,3,3: 19:[33, 14] Operation: 23-9=14 Moving to Node #0,1 Current State: 19:[33, 41, 27], Operations: ['50-23=27'] Exploring Operation: 33-27=6, Resulting Numbers: [41, 6] Generated Node #0,1,0: 19:[41, 6] Operation: 33-27=6 Exploring Operation: 33+41=74, Resulting Numbers: [27, 74] Generated Node #0,1,1: 19:[27, 74] Operation: 33+41=74 Exploring Operation: 41-33=8, Resulting Numbers: [27, 8] Generated Node #0,1,2: 19:[27, 8] Operation: 41-33=8 Exploring Operation: 41-27=14, Resulting Numbers: [33, 14] Generated Node #0,1,3: 19:[33, 14] Operation: 41-27=14 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 19:[27, 8], Operations: ['50-23=27', '41-33=8'] Exploring Operation: 27*8=216, Resulting Numbers: [216] 216,19 unequal: No Solution Exploring Operation: 27+8=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[33, 41, 23, 50], Operations: [] Exploring Operation: 50-23=27, Resulting Numbers: [33, 41, 27] Generated Node #0,1: 19:[33, 41, 27] Operation: 50-23=27 Moving to Node #0,1 Current State: 19:[33, 41, 27], Operations: ['50-23=27'] Exploring Operation: 41-33=8, Resulting Numbers: [27, 8] Generated Node #0,1,2: 19:[27, 8] Operation: 41-33=8 Moving to Node #0,1,2 Current State: 19:[27, 8], Operations: ['50-23=27', '41-33=8'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_4
sum_heuristic
[ 77, 2, 81, 74 ]
91
[ "81-74=7", "2*7=14", "77+14=91" ]
Current State: 91:[77, 2, 81, 74], Operations: [] Exploring Operation: 81-74=7, Resulting Numbers: [77, 2, 7] Generated Node #2: [77, 2, 7] from Operation: 81-74=7 Current State: 91:[77, 2, 7], Operations: ['81-74=7'] Exploring Operation: 2*7=14, Resulting Numbers: [77, 14] Generated Node #3: [77, 14] from Operation: 2*7=14 Current State: 91:[77, 14], Operations: ['81-74=7', '2*7=14'] Exploring Operation: 77+14=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[77, 2, 81, 74], Operations: [] Exploring Operation: 77+2=79, Resulting Numbers: [81, 74, 79] Generated Node #0,0: 91:[81, 74, 79] Operation: 77+2=79 Exploring Operation: 81-77=4, Resulting Numbers: [2, 74, 4] Generated Node #0,1: 91:[2, 74, 4] Operation: 81-77=4 Exploring Operation: 77-74=3, Resulting Numbers: [2, 81, 3] Generated Node #0,2: 91:[2, 81, 3] Operation: 77-74=3 Exploring Operation: 81-74=7, Resulting Numbers: [77, 2, 7] Generated Node #0,3: 91:[77, 2, 7] Operation: 81-74=7 Moving to Node #0,2 Current State: 91:[2, 81, 3], Operations: ['77-74=3'] Exploring Operation: 2+3=5, Resulting Numbers: [81, 5] Generated Node #0,2,0: 91:[81, 5] Operation: 2+3=5 Exploring Operation: 81+3=84, Resulting Numbers: [2, 84] Generated Node #0,2,1: 91:[2, 84] Operation: 81+3=84 Exploring Operation: 2*3=6, Resulting Numbers: [81, 6] Generated Node #0,2,2: 91:[81, 6] Operation: 2*3=6 Exploring Operation: 2+81=83, Resulting Numbers: [3, 83] Generated Node #0,2,3: 91:[3, 83] Operation: 2+81=83 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 91:[81, 6], Operations: ['77-74=3', '2*3=6'] Exploring Operation: 81+6=87, Resulting Numbers: [87] 87,91 unequal: No Solution Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,91 unequal: No Solution Exploring Operation: 81*6=486, Resulting Numbers: [486] 486,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 91:[81, 5], Operations: ['77-74=3', '2+3=5'] Exploring Operation: 81+5=86, Resulting Numbers: [86] 86,91 unequal: No Solution Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,91 unequal: No Solution Exploring Operation: 81*5=405, Resulting Numbers: [405] 405,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 91:[2, 84], Operations: ['77-74=3', '81+3=84'] Exploring Operation: 2*84=168, Resulting Numbers: [168] 168,91 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,91 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,91 unequal: No Solution Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 91:[3, 83], Operations: ['77-74=3', '2+81=83'] Exploring Operation: 83-3=80, Resulting Numbers: [80] 80,91 unequal: No Solution Exploring Operation: 3*83=249, Resulting Numbers: [249] 249,91 unequal: No Solution Exploring Operation: 3+83=86, Resulting Numbers: [86] 86,91 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: 91:[77, 2, 7], Operations: ['81-74=7'] Exploring Operation: 77+2=79, Resulting Numbers: [7, 79] Generated Node #0,3,0: 91:[7, 79] Operation: 77+2=79 Exploring Operation: 77/7=11, Resulting Numbers: [2, 11] Generated Node #0,3,1: 91:[2, 11] Operation: 77/7=11 Exploring Operation: 2*7=14, Resulting Numbers: [77, 14] Generated Node #0,3,2: 91:[77, 14] Operation: 2*7=14 Exploring Operation: 77+7=84, Resulting Numbers: [2, 84] Generated Node #0,3,3: 91:[2, 84] Operation: 77+7=84 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 91:[2, 11], Operations: ['81-74=7', '77/7=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 91:[7, 79], Operations: ['81-74=7', '77+2=79'] Exploring Operation: 7*79=553, Resulting Numbers: [553] 553,91 unequal: No Solution Exploring Operation: 7+79=86, Resulting Numbers: [86] 86,91 unequal: No Solution Exploring Operation: 79-7=72, Resulting Numbers: [72] 72,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 91:[2, 84], Operations: ['81-74=7', '77+7=84'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,91 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,91 unequal: No Solution Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,91 unequal: No Solution Exploring Operation: 2*84=168, Resulting Numbers: [168] 168,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 91:[77, 14], Operations: ['81-74=7', '2*7=14'] Exploring Operation: 77*14=1078, Resulting Numbers: [1078] 1078,91 unequal: No Solution Exploring Operation: 77+14=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[77, 2, 81, 74], Operations: [] Exploring Operation: 81-74=7, Resulting Numbers: [77, 2, 7] Generated Node #0,3: 91:[77, 2, 7] Operation: 81-74=7 Moving to Node #0,3 Current State: 91:[77, 2, 7], Operations: ['81-74=7'] Exploring Operation: 2*7=14, Resulting Numbers: [77, 14] Generated Node #0,3,2: 91:[77, 14] Operation: 2*7=14 Moving to Node #0,3,2 Current State: 91:[77, 14], Operations: ['81-74=7', '2*7=14'] Exploring Operation: 77+14=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_4
mult_heuristic
[ 12, 65, 68, 10 ]
40
[ "12*10=120", "68-65=3", "120/3=40" ]
Current State: 40:[12, 65, 68, 10], Operations: [] Exploring Operation: 12*10=120, Resulting Numbers: [65, 68, 120] Generated Node #2: [65, 68, 120] from Operation: 12*10=120 Current State: 40:[65, 68, 120], Operations: ['12*10=120'] Exploring Operation: 68-65=3, Resulting Numbers: [120, 3] Generated Node #3: [120, 3] from Operation: 68-65=3 Current State: 40:[120, 3], Operations: ['12*10=120', '68-65=3'] Exploring Operation: 120/3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[12, 65, 68, 10], Operations: [] Exploring Operation: 68-65=3, Resulting Numbers: [12, 10, 3] Generated Node #0,0: 40:[12, 10, 3] Operation: 68-65=3 Exploring Operation: 65-12=53, Resulting Numbers: [68, 10, 53] Generated Node #0,1: 40:[68, 10, 53] Operation: 65-12=53 Moving to Node #0,0 Current State: 40:[12, 10, 3], Operations: ['68-65=3'] Exploring Operation: 12/3=4, Resulting Numbers: [10, 4] Generated Node #0,0,0: 40:[10, 4] Operation: 12/3=4 Exploring Operation: 12-10=2, Resulting Numbers: [3, 2] Generated Node #0,0,1: 40:[3, 2] Operation: 12-10=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[10, 4], Operations: ['68-65=3', '12/3=4'] Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[12, 65, 68, 10], Operations: [] Exploring Operation: 68-65=3, Resulting Numbers: [12, 10, 3] Generated Node #0,0: 40:[12, 10, 3] Operation: 68-65=3 Moving to Node #0,0 Current State: 40:[12, 10, 3], Operations: ['68-65=3'] Exploring Operation: 12/3=4, Resulting Numbers: [10, 4] Generated Node #0,0,0: 40:[10, 4] Operation: 12/3=4 Moving to Node #0,0,0 Current State: 40:[10, 4], Operations: ['68-65=3', '12/3=4'] Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 60, 19, 96, 2 ]
59
[ "60+96=156", "156/2=78", "78-19=59" ]
Current State: 59:[60, 19, 96, 2], Operations: [] Exploring Operation: 60+96=156, Resulting Numbers: [19, 2, 156] Generated Node #2: [19, 2, 156] from Operation: 60+96=156 Current State: 59:[19, 2, 156], Operations: ['60+96=156'] Exploring Operation: 156/2=78, Resulting Numbers: [19, 78] Generated Node #3: [19, 78] from Operation: 156/2=78 Current State: 59:[19, 78], Operations: ['60+96=156', '156/2=78'] Exploring Operation: 78-19=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[60, 19, 96, 2], Operations: [] Exploring Operation: 96-2=94, Resulting Numbers: [60, 19, 94] Generated Node #0,0: 59:[60, 19, 94] Operation: 96-2=94 Exploring Operation: 96-19=77, Resulting Numbers: [60, 2, 77] Generated Node #0,1: 59:[60, 2, 77] Operation: 96-19=77 Exploring Operation: 96/2=48, Resulting Numbers: [60, 19, 48] Generated Node #0,2: 59:[60, 19, 48] Operation: 96/2=48 Exploring Operation: 19*2=38, Resulting Numbers: [60, 96, 38] Generated Node #0,3: 59:[60, 96, 38] Operation: 19*2=38 Exploring Operation: 19+2=21, Resulting Numbers: [60, 96, 21] Generated Node #0,4: 59:[60, 96, 21] Operation: 19+2=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[60, 19, 48], Operations: ['96/2=48'] Exploring Operation: 48-19=29, Resulting Numbers: [60, 29] Generated Node #0,2,0: 59:[60, 29] Operation: 48-19=29 Exploring Operation: 60+19=79, Resulting Numbers: [48, 79] Generated Node #0,2,1: 59:[48, 79] Operation: 60+19=79 Exploring Operation: 60-48=12, Resulting Numbers: [19, 12] Generated Node #0,2,2: 59:[19, 12] Operation: 60-48=12 Exploring Operation: 19+48=67, Resulting Numbers: [60, 67] Generated Node #0,2,3: 59:[60, 67] Operation: 19+48=67 Exploring Operation: 60-19=41, Resulting Numbers: [48, 41] Generated Node #0,2,4: 59:[48, 41] Operation: 60-19=41 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 59:[60, 67], Operations: ['96/2=48', '19+48=67'] Exploring Operation: 67-60=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 60+67=127, Resulting Numbers: [127] 127,59 unequal: No Solution Exploring Operation: 60*67=4020, Resulting Numbers: [4020] 4020,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 59:[48, 41], Operations: ['96/2=48', '60-19=41'] Exploring Operation: 48*41=1968, Resulting Numbers: [1968] 1968,59 unequal: No Solution Exploring Operation: 48-41=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 48+41=89, Resulting Numbers: [89] 89,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 59:[60, 29], Operations: ['96/2=48', '48-19=29'] Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 60*29=1740, Resulting Numbers: [1740] 1740,59 unequal: No Solution Exploring Operation: 60+29=89, Resulting Numbers: [89] 89,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 59:[48, 79], Operations: ['96/2=48', '60+19=79'] Exploring Operation: 48*79=3792, Resulting Numbers: [3792] 3792,59 unequal: No Solution Exploring Operation: 48+79=127, Resulting Numbers: [127] 127,59 unequal: No Solution Exploring Operation: 79-48=31, Resulting Numbers: [31] 31,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 59:[19, 12], Operations: ['96/2=48', '60-48=12'] Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,59 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,59 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 Start Sub Search at level 1: Moving to Node #0,3 Current State: 59:[60, 96, 38], Operations: ['19*2=38'] Exploring Operation: 96+38=134, Resulting Numbers: [60, 134] Generated Node #0,3,0: 59:[60, 134] Operation: 96+38=134 Exploring Operation: 96-38=58, Resulting Numbers: [60, 58] Generated Node #0,3,1: 59:[60, 58] Operation: 96-38=58 Exploring Operation: 96-60=36, Resulting Numbers: [38, 36] Generated Node #0,3,2: 59:[38, 36] Operation: 96-60=36 Exploring Operation: 60+38=98, Resulting Numbers: [96, 98] Generated Node #0,3,3: 59:[96, 98] Operation: 60+38=98 Exploring Operation: 60-38=22, Resulting Numbers: [96, 22] Generated Node #0,3,4: 59:[96, 22] Operation: 60-38=22 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 59:[60, 58], Operations: ['19*2=38', '96-38=58'] Exploring Operation: 60+58=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 60-58=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 60*58=3480, Resulting Numbers: [3480] 3480,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 59:[38, 36], Operations: ['19*2=38', '96-60=36'] Exploring Operation: 38*36=1368, Resulting Numbers: [1368] 1368,59 unequal: No Solution Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 38+36=74, Resulting Numbers: [74] 74,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 59:[96, 22], Operations: ['19*2=38', '60-38=22'] Exploring Operation: 96-22=74, Resulting Numbers: [74] 74,59 unequal: No Solution Exploring Operation: 96+22=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 96*22=2112, Resulting Numbers: [2112] 2112,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 59:[60, 134], Operations: ['19*2=38', '96+38=134'] Exploring Operation: 60+134=194, Resulting Numbers: [194] 194,59 unequal: No Solution Exploring Operation: 60*134=8040, Resulting Numbers: [8040] 8040,59 unequal: No Solution Exploring Operation: 134-60=74, Resulting Numbers: [74] 74,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 59:[96, 98], Operations: ['19*2=38', '60+38=98'] Exploring Operation: 98-96=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 96*98=9408, Resulting Numbers: [9408] 9408,59 unequal: No Solution Exploring Operation: 96+98=194, Resulting Numbers: [194] 194,59 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[60, 19, 94], Operations: ['96-2=94'] Exploring Operation: 19+94=113, Resulting Numbers: [60, 113] Generated Node #0,0,0: 59:[60, 113] Operation: 19+94=113 Exploring Operation: 60-19=41, Resulting Numbers: [94, 41] Generated Node #0,0,1: 59:[94, 41] Operation: 60-19=41 Exploring Operation: 60+19=79, Resulting Numbers: [94, 79] Generated Node #0,0,2: 59:[94, 79] Operation: 60+19=79 Exploring Operation: 94-60=34, Resulting Numbers: [19, 34] Generated Node #0,0,3: 59:[19, 34] Operation: 94-60=34 Exploring Operation: 94-19=75, Resulting Numbers: [60, 75] Generated Node #0,0,4: 59:[60, 75] Operation: 94-19=75 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 59:[60, 75], Operations: ['96-2=94', '94-19=75'] Exploring Operation: 60*75=4500, Resulting Numbers: [4500] 4500,59 unequal: No Solution Exploring Operation: 60+75=135, Resulting Numbers: [135] 135,59 unequal: No Solution Exploring Operation: 75-60=15, Resulting Numbers: [15] 15,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 59:[94, 41], Operations: ['96-2=94', '60-19=41'] Exploring Operation: 94+41=135, Resulting Numbers: [135] 135,59 unequal: No Solution Exploring Operation: 94*41=3854, Resulting Numbers: [3854] 3854,59 unequal: No Solution Exploring Operation: 94-41=53, Resulting Numbers: [53] 53,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[60, 113], Operations: ['96-2=94', '19+94=113'] Exploring Operation: 60*113=6780, Resulting Numbers: [6780] 6780,59 unequal: No Solution Exploring Operation: 113-60=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 60+113=173, Resulting Numbers: [173] 173,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 59:[94, 79], Operations: ['96-2=94', '60+19=79'] Exploring Operation: 94*79=7426, Resulting Numbers: [7426] 7426,59 unequal: No Solution Exploring Operation: 94-79=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 94+79=173, Resulting Numbers: [173] 173,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 59:[19, 34], Operations: ['96-2=94', '94-60=34'] Exploring Operation: 19+34=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 19*34=646, Resulting Numbers: [646] 646,59 unequal: No Solution Exploring Operation: 34-19=15, Resulting Numbers: [15] 15,59 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[60, 2, 77], Operations: ['96-19=77'] Exploring Operation: 60+2=62, Resulting Numbers: [77, 62] Generated Node #0,1,0: 59:[77, 62] Operation: 60+2=62 Exploring Operation: 60-2=58, Resulting Numbers: [77, 58] Generated Node #0,1,1: 59:[77, 58] Operation: 60-2=58 Exploring Operation: 77-2=75, Resulting Numbers: [60, 75] Generated Node #0,1,2: 59:[60, 75] Operation: 77-2=75 Exploring Operation: 2+77=79, Resulting Numbers: [60, 79] Generated Node #0,1,3: 59:[60, 79] Operation: 2+77=79 Exploring Operation: 60/2=30, Resulting Numbers: [77, 30] Generated Node #0,1,4: 59:[77, 30] Operation: 60/2=30 Moving to Node #0,1,2 Current State: 59:[60, 75], Operations: ['96-19=77', '77-2=75'] Exploring Operation: 75-60=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 60+75=135, Resulting Numbers: [135] 135,59 unequal: No Solution Exploring Operation: 60*75=4500, Resulting Numbers: [4500] 4500,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[77, 58], Operations: ['96-19=77', '60-2=58'] Exploring Operation: 77+58=135, Resulting Numbers: [135] 135,59 unequal: No Solution Exploring Operation: 77-58=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 77*58=4466, Resulting Numbers: [4466] 4466,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[77, 62], Operations: ['96-19=77', '60+2=62'] Exploring Operation: 77*62=4774, Resulting Numbers: [4774] 4774,59 unequal: No Solution Exploring Operation: 77+62=139, Resulting Numbers: [139] 139,59 unequal: No Solution Exploring Operation: 77-62=15, Resulting Numbers: [15] 15,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[60, 79], Operations: ['96-19=77', '2+77=79'] Exploring Operation: 60*79=4740, Resulting Numbers: [4740] 4740,59 unequal: No Solution Exploring Operation: 79-60=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 60+79=139, Resulting Numbers: [139] 139,59 unequal: No Solution Moving to Node #0,1,4 Current State: 59:[77, 30], Operations: ['96-19=77', '60/2=30'] Exploring Operation: 77-30=47, Resulting Numbers: [47] 47,59 unequal: No Solution Exploring Operation: 77+30=107, Resulting Numbers: [107] 107,59 unequal: No Solution Exploring Operation: 77*30=2310, Resulting Numbers: [2310] 2310,59 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 #0,4 Current State: 59:[60, 96, 21], Operations: ['19+2=21'] Exploring Operation: 96-60=36, Resulting Numbers: [21, 36] Generated Node #0,4,0: 59:[21, 36] Operation: 96-60=36 Exploring Operation: 96-21=75, Resulting Numbers: [60, 75] Generated Node #0,4,1: 59:[60, 75] Operation: 96-21=75 Exploring Operation: 60-21=39, Resulting Numbers: [96, 39] Generated Node #0,4,2: 59:[96, 39] Operation: 60-21=39 Exploring Operation: 96+21=117, Resulting Numbers: [60, 117] Generated Node #0,4,3: 59:[60, 117] Operation: 96+21=117 Exploring Operation: 60+21=81, Resulting Numbers: [96, 81] Generated Node #0,4,4: 59:[96, 81] Operation: 60+21=81 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 59:[60, 75], Operations: ['19+2=21', '96-21=75'] Exploring Operation: 75-60=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 60+75=135, Resulting Numbers: [135] 135,59 unequal: No Solution Exploring Operation: 60*75=4500, Resulting Numbers: [4500] 4500,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 59:[96, 39], Operations: ['19+2=21', '60-21=39'] Exploring Operation: 96-39=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 96*39=3744, Resulting Numbers: [3744] 3744,59 unequal: No Solution Exploring Operation: 96+39=135, Resulting Numbers: [135] 135,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 59:[60, 117], Operations: ['19+2=21', '96+21=117'] Exploring Operation: 117-60=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 60*117=7020, Resulting Numbers: [7020] 7020,59 unequal: No Solution Exploring Operation: 60+117=177, Resulting Numbers: [177] 177,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 59:[96, 81], Operations: ['19+2=21', '60+21=81'] Exploring Operation: 96+81=177, Resulting Numbers: [177] 177,59 unequal: No Solution Exploring Operation: 96*81=7776, Resulting Numbers: [7776] 7776,59 unequal: No Solution Exploring Operation: 96-81=15, Resulting Numbers: [15] 15,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 59:[21, 36], Operations: ['19+2=21', '96-60=36'] Exploring Operation: 21*36=756, Resulting Numbers: [756] 756,59 unequal: No Solution Exploring Operation: 21+36=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 36-21=15, Resulting Numbers: [15] 15,59 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_5
sum_heuristic
[ 22, 57, 6, 33 ]
88
[ "57-33=24", "22*24=528", "528/6=88" ]
Current State: 88:[22, 57, 6, 33], Operations: [] Exploring Operation: 57-33=24, Resulting Numbers: [22, 6, 24] Generated Node #2: [22, 6, 24] from Operation: 57-33=24 Current State: 88:[22, 6, 24], Operations: ['57-33=24'] Exploring Operation: 22*24=528, Resulting Numbers: [6, 528] Generated Node #3: [6, 528] from Operation: 22*24=528 Current State: 88:[6, 528], Operations: ['57-33=24', '22*24=528'] Exploring Operation: 528/6=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[22, 57, 6, 33], Operations: [] Exploring Operation: 57-33=24, Resulting Numbers: [22, 6, 24] Generated Node #0,0: 88:[22, 6, 24] Operation: 57-33=24 Exploring Operation: 33-22=11, Resulting Numbers: [57, 6, 11] Generated Node #0,1: 88:[57, 6, 11] Operation: 33-22=11 Exploring Operation: 57-6=51, Resulting Numbers: [22, 33, 51] Generated Node #0,2: 88:[22, 33, 51] Operation: 57-6=51 Exploring Operation: 57+33=90, Resulting Numbers: [22, 6, 90] Generated Node #0,3: 88:[22, 6, 90] Operation: 57+33=90 Moving to Node #0,0 Current State: 88:[22, 6, 24], Operations: ['57-33=24'] Exploring Operation: 24/6=4, Resulting Numbers: [22, 4] Generated Node #0,0,0: 88:[22, 4] Operation: 24/6=4 Exploring Operation: 24-22=2, Resulting Numbers: [6, 2] Generated Node #0,0,1: 88:[6, 2] Operation: 24-22=2 Exploring Operation: 24-6=18, Resulting Numbers: [22, 18] Generated Node #0,0,2: 88:[22, 18] Operation: 24-6=18 Exploring Operation: 22+24=46, Resulting Numbers: [6, 46] Generated Node #0,0,3: 88:[6, 46] Operation: 22+24=46 Moving to Node #0,3 Current State: 88:[22, 6, 90], Operations: ['57+33=90'] Exploring Operation: 90-6=84, Resulting Numbers: [22, 84] Generated Node #0,3,0: 88:[22, 84] Operation: 90-6=84 Exploring Operation: 90/6=15, Resulting Numbers: [22, 15] Generated Node #0,3,1: 88:[22, 15] Operation: 90/6=15 Exploring Operation: 22+6=28, Resulting Numbers: [90, 28] Generated Node #0,3,2: 88:[90, 28] Operation: 22+6=28 Exploring Operation: 22-6=16, Resulting Numbers: [90, 16] Generated Node #0,3,3: 88:[90, 16] Operation: 22-6=16 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 88:[22, 84], Operations: ['57+33=90', '90-6=84'] Exploring Operation: 22+84=106, Resulting Numbers: [106] 106,88 unequal: No Solution Exploring Operation: 22*84=1848, Resulting Numbers: [1848] 1848,88 unequal: No Solution Exploring Operation: 84-22=62, Resulting Numbers: [62] 62,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 88:[22, 15], Operations: ['57+33=90', '90/6=15'] Exploring Operation: 22*15=330, Resulting Numbers: [330] 330,88 unequal: No Solution Exploring Operation: 22+15=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 88:[90, 16], Operations: ['57+33=90', '22-6=16'] Exploring Operation: 90+16=106, Resulting Numbers: [106] 106,88 unequal: No Solution Exploring Operation: 90*16=1440, Resulting Numbers: [1440] 1440,88 unequal: No Solution Exploring Operation: 90-16=74, Resulting Numbers: [74] 74,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 88:[90, 28], Operations: ['57+33=90', '22+6=28'] Exploring Operation: 90*28=2520, Resulting Numbers: [2520] 2520,88 unequal: No Solution Exploring Operation: 90-28=62, Resulting Numbers: [62] 62,88 unequal: No Solution Exploring Operation: 90+28=118, Resulting Numbers: [118] 118,88 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: 88:[57, 6, 11], Operations: ['33-22=11'] Exploring Operation: 11-6=5, Resulting Numbers: [57, 5] Generated Node #0,1,0: 88:[57, 5] Operation: 11-6=5 Exploring Operation: 6+11=17, Resulting Numbers: [57, 17] Generated Node #0,1,1: 88:[57, 17] Operation: 6+11=17 Exploring Operation: 57-11=46, Resulting Numbers: [6, 46] Generated Node #0,1,2: 88:[6, 46] Operation: 57-11=46 Exploring Operation: 57-6=51, Resulting Numbers: [11, 51] Generated Node #0,1,3: 88:[11, 51] Operation: 57-6=51 Moving to Node #0,2 Current State: 88:[22, 33, 51], Operations: ['57-6=51'] Exploring Operation: 33-22=11, Resulting Numbers: [51, 11] Generated Node #0,2,0: 88:[51, 11] Operation: 33-22=11 Exploring Operation: 33+51=84, Resulting Numbers: [22, 84] Generated Node #0,2,1: 88:[22, 84] Operation: 33+51=84 Exploring Operation: 22+33=55, Resulting Numbers: [51, 55] Generated Node #0,2,2: 88:[51, 55] Operation: 22+33=55 Exploring Operation: 51-33=18, Resulting Numbers: [22, 18] Generated Node #0,2,3: 88:[22, 18] Operation: 51-33=18 Moving to Node #0,0,0 Current State: 88:[22, 4], Operations: ['57-33=24', '24/6=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[22, 57, 6, 33], Operations: [] Exploring Operation: 57-33=24, Resulting Numbers: [22, 6, 24] Generated Node #0,0: 88:[22, 6, 24] Operation: 57-33=24 Moving to Node #0,0 Current State: 88:[22, 6, 24], Operations: ['57-33=24'] Exploring Operation: 24/6=4, Resulting Numbers: [22, 4] Generated Node #0,0,0: 88:[22, 4] Operation: 24/6=4 Moving to Node #0,0,0 Current State: 88:[22, 4], Operations: ['57-33=24', '24/6=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.967882
hs_4
mult_heuristic
[ 11, 5, 61, 94 ]
88
[ "11*5=55", "94-61=33", "55+33=88" ]
Current State: 88:[11, 5, 61, 94], Operations: [] Exploring Operation: 11*5=55, Resulting Numbers: [61, 94, 55] Generated Node #2: [61, 94, 55] from Operation: 11*5=55 Current State: 88:[61, 94, 55], Operations: ['11*5=55'] Exploring Operation: 94-61=33, Resulting Numbers: [55, 33] Generated Node #3: [55, 33] from Operation: 94-61=33 Current State: 88:[55, 33], Operations: ['11*5=55', '94-61=33'] Exploring Operation: 55+33=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[11, 5, 61, 94], Operations: [] Exploring Operation: 94-61=33, Resulting Numbers: [11, 5, 33] Generated Node #0,0: 88:[11, 5, 33] Operation: 94-61=33 Exploring Operation: 61-11=50, Resulting Numbers: [5, 94, 50] Generated Node #0,1: 88:[5, 94, 50] Operation: 61-11=50 Moving to Node #0,0 Current State: 88:[11, 5, 33], Operations: ['94-61=33'] Exploring Operation: 33-11=22, Resulting Numbers: [5, 22] Generated Node #0,0,0: 88:[5, 22] Operation: 33-11=22 Exploring Operation: 11+33=44, Resulting Numbers: [5, 44] Generated Node #0,0,1: 88:[5, 44] Operation: 11+33=44 Moving to Node #0,1 Current State: 88:[5, 94, 50], Operations: ['61-11=50'] Exploring Operation: 94-5=89, Resulting Numbers: [50, 89] Generated Node #0,1,0: 88:[50, 89] Operation: 94-5=89 Exploring Operation: 94-50=44, Resulting Numbers: [5, 44] Generated Node #0,1,1: 88:[5, 44] Operation: 94-50=44 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 88:[5, 44], Operations: ['61-11=50', '94-50=44'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[50, 89], Operations: ['61-11=50', '94-5=89'] Exploring Operation: 50+89=139, Resulting Numbers: [139] 139,88 unequal: No Solution Exploring Operation: 89-50=39, Resulting Numbers: [39] 39,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 88:[5, 22], Operations: ['94-61=33', '33-11=22'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,88 unequal: No Solution Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[5, 44], Operations: ['94-61=33', '11+33=44'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,88 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 57, 57, 84, 62 ]
62
[ "57-57=0", "84*0=0", "62+0=62" ]
Current State: 62:[57, 57, 84, 62], Operations: [] Exploring Operation: 57-57=0, Resulting Numbers: [84, 62, 0] Generated Node #2: [84, 62, 0] from Operation: 57-57=0 Current State: 62:[84, 62, 0], Operations: ['57-57=0'] Exploring Operation: 84*0=0, Resulting Numbers: [62, 0] Generated Node #3: [62, 0] from Operation: 84*0=0 Current State: 62:[62, 0], Operations: ['57-57=0', '84*0=0'] Exploring Operation: 62+0=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[57, 57, 84, 62], Operations: [] Exploring Operation: 84-62=22, Resulting Numbers: [57, 57, 22] Generated Node #0,0: 62:[57, 57, 22] Operation: 84-62=22 Exploring Operation: 84-57=27, Resulting Numbers: [57, 62, 27] Generated Node #0,1: 62:[57, 62, 27] Operation: 84-57=27 Exploring Operation: 84-57=27, Resulting Numbers: [57, 62, 27] Generated Node #0,2: 62:[57, 62, 27] Operation: 84-57=27 Exploring Operation: 57/57=1, Resulting Numbers: [84, 62, 1] Generated Node #0,3: 62:[84, 62, 1] Operation: 57/57=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[57, 62, 27], Operations: ['84-57=27'] Exploring Operation: 62-57=5, Resulting Numbers: [27, 5] Generated Node #0,1,0: 62:[27, 5] Operation: 62-57=5 Exploring Operation: 57+27=84, Resulting Numbers: [62, 84] Generated Node #0,1,1: 62:[62, 84] Operation: 57+27=84 Exploring Operation: 62-27=35, Resulting Numbers: [57, 35] Generated Node #0,1,2: 62:[57, 35] Operation: 62-27=35 Exploring Operation: 57-27=30, Resulting Numbers: [62, 30] Generated Node #0,1,3: 62:[62, 30] Operation: 57-27=30 Moving to Node #0,1,3 Current State: 62:[62, 30], Operations: ['84-57=27', '57-27=30'] Exploring Operation: 62-30=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 62+30=92, Resulting Numbers: [92] 92,62 unequal: No Solution Exploring Operation: 62*30=1860, Resulting Numbers: [1860] 1860,62 unequal: No Solution Moving to Node #0,1,0 Current State: 62:[27, 5], Operations: ['84-57=27', '62-57=5'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,62 unequal: No Solution Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,62 unequal: No Solution Moving to Node #0,1,2 Current State: 62:[57, 35], Operations: ['84-57=27', '62-27=35'] Exploring Operation: 57*35=1995, Resulting Numbers: [1995] 1995,62 unequal: No Solution Exploring Operation: 57+35=92, Resulting Numbers: [92] 92,62 unequal: No Solution Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,62 unequal: No Solution Moving to Node #0,1,1 Current State: 62:[62, 84], Operations: ['84-57=27', '57+27=84'] Exploring Operation: 62*84=5208, Resulting Numbers: [5208] 5208,62 unequal: No Solution Exploring Operation: 84-62=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 62+84=146, Resulting Numbers: [146] 146,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[57, 62, 27], Operations: ['84-57=27'] Exploring Operation: 57-27=30, Resulting Numbers: [62, 30] Generated Node #0,2,0: 62:[62, 30] Operation: 57-27=30 Exploring Operation: 57+27=84, Resulting Numbers: [62, 84] Generated Node #0,2,1: 62:[62, 84] Operation: 57+27=84 Exploring Operation: 62-27=35, Resulting Numbers: [57, 35] Generated Node #0,2,2: 62:[57, 35] Operation: 62-27=35 Exploring Operation: 62-57=5, Resulting Numbers: [27, 5] Generated Node #0,2,3: 62:[27, 5] Operation: 62-57=5 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 62:[62, 30], Operations: ['84-57=27', '57-27=30'] Exploring Operation: 62-30=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 62*30=1860, Resulting Numbers: [1860] 1860,62 unequal: No Solution Exploring Operation: 62+30=92, Resulting Numbers: [92] 92,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 62:[27, 5], Operations: ['84-57=27', '62-57=5'] Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,62 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 62:[57, 35], Operations: ['84-57=27', '62-27=35'] Exploring Operation: 57*35=1995, Resulting Numbers: [1995] 1995,62 unequal: No Solution Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 57+35=92, Resulting Numbers: [92] 92,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 62:[62, 84], Operations: ['84-57=27', '57+27=84'] Exploring Operation: 62*84=5208, Resulting Numbers: [5208] 5208,62 unequal: No Solution Exploring Operation: 84-62=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 62+84=146, Resulting Numbers: [146] 146,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[57, 57, 22], Operations: ['84-62=22'] Exploring Operation: 57-22=35, Resulting Numbers: [57, 35] Generated Node #0,0,0: 62:[57, 35] Operation: 57-22=35 Exploring Operation: 57/57=1, Resulting Numbers: [22, 1] Generated Node #0,0,1: 62:[22, 1] Operation: 57/57=1 Exploring Operation: 57-22=35, Resulting Numbers: [57, 35] Generated Node #0,0,2: 62:[57, 35] Operation: 57-22=35 Exploring Operation: 57-57=0, Resulting Numbers: [22, 0] Generated Node #0,0,3: 62:[22, 0] Operation: 57-57=0 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[57, 35], Operations: ['84-62=22', '57-22=35'] Exploring Operation: 57*35=1995, Resulting Numbers: [1995] 1995,62 unequal: No Solution Exploring Operation: 57+35=92, Resulting Numbers: [92] 92,62 unequal: No Solution Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 62:[57, 35], Operations: ['84-62=22', '57-22=35'] Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 57+35=92, Resulting Numbers: [92] 92,62 unequal: No Solution Exploring Operation: 57*35=1995, Resulting Numbers: [1995] 1995,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 62:[22, 1], Operations: ['84-62=22', '57/57=1'] Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 22+1=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 62:[22, 0], Operations: ['84-62=22', '57-57=0'] Exploring Operation: 22+0=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 22*0=0, Resulting Numbers: [0] 0,62 unequal: No Solution Exploring Operation: 22-0=22, Resulting Numbers: [22] 22,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 62:[84, 62, 1], Operations: ['57/57=1'] Exploring Operation: 84-1=83, Resulting Numbers: [62, 83] Generated Node #0,3,0: 62:[62, 83] Operation: 84-1=83 Exploring Operation: 84*1=84, Resulting Numbers: [62, 84] Generated Node #0,3,1: 62:[62, 84] Operation: 84*1=84 Exploring Operation: 84/1=84, Resulting Numbers: [62, 84] Generated Node #0,3,2: 62:[62, 84] Operation: 84/1=84 Exploring Operation: 84-62=22, Resulting Numbers: [1, 22] Generated Node #0,3,3: 62:[1, 22] Operation: 84-62=22 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 62:[1, 22], Operations: ['57/57=1', '84-62=22'] Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 62:[62, 83], Operations: ['57/57=1', '84-1=83'] Exploring Operation: 62*83=5146, Resulting Numbers: [5146] 5146,62 unequal: No Solution Exploring Operation: 83-62=21, Resulting Numbers: [21] 21,62 unequal: No Solution Exploring Operation: 62+83=145, Resulting Numbers: [145] 145,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 62:[62, 84], Operations: ['57/57=1', '84*1=84'] Exploring Operation: 84-62=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 62*84=5208, Resulting Numbers: [5208] 5208,62 unequal: No Solution Exploring Operation: 62+84=146, Resulting Numbers: [146] 146,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 62:[62, 84], Operations: ['57/57=1', '84/1=84'] Exploring Operation: 62+84=146, Resulting Numbers: [146] 146,62 unequal: No Solution Exploring Operation: 62*84=5208, Resulting Numbers: [5208] 5208,62 unequal: No Solution Exploring Operation: 84-62=22, Resulting Numbers: [22] 22,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 37, 18, 52, 27 ]
44
[ "37-18=19", "52-27=25", "19+25=44" ]
Current State: 44:[37, 18, 52, 27], Operations: [] Exploring Operation: 37-18=19, Resulting Numbers: [52, 27, 19] Generated Node #2: [52, 27, 19] from Operation: 37-18=19 Current State: 44:[52, 27, 19], Operations: ['37-18=19'] Exploring Operation: 52-27=25, Resulting Numbers: [19, 25] Generated Node #3: [19, 25] from Operation: 52-27=25 Current State: 44:[19, 25], Operations: ['37-18=19', '52-27=25'] Exploring Operation: 19+25=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[37, 18, 52, 27], Operations: [] Exploring Operation: 37-18=19, Resulting Numbers: [52, 27, 19] Generated Node #0,0: 44:[52, 27, 19] Operation: 37-18=19 Exploring Operation: 18+27=45, Resulting Numbers: [37, 52, 45] Generated Node #0,1: 44:[37, 52, 45] Operation: 18+27=45 Exploring Operation: 37-27=10, Resulting Numbers: [18, 52, 10] Generated Node #0,2: 44:[18, 52, 10] Operation: 37-27=10 Exploring Operation: 52-27=25, Resulting Numbers: [37, 18, 25] Generated Node #0,3: 44:[37, 18, 25] Operation: 52-27=25 Exploring Operation: 52-37=15, Resulting Numbers: [18, 27, 15] Generated Node #0,4: 44:[18, 27, 15] Operation: 52-37=15 Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[18, 52, 10], Operations: ['37-27=10'] Exploring Operation: 52-18=34, Resulting Numbers: [10, 34] Generated Node #0,2,0: 44:[10, 34] Operation: 52-18=34 Exploring Operation: 52-10=42, Resulting Numbers: [18, 42] Generated Node #0,2,1: 44:[18, 42] Operation: 52-10=42 Exploring Operation: 52+10=62, Resulting Numbers: [18, 62] Generated Node #0,2,2: 44:[18, 62] Operation: 52+10=62 Exploring Operation: 18+10=28, Resulting Numbers: [52, 28] Generated Node #0,2,3: 44:[52, 28] Operation: 18+10=28 Exploring Operation: 18-10=8, Resulting Numbers: [52, 8] Generated Node #0,2,4: 44:[52, 8] Operation: 18-10=8 Moving to Node #0,2,1 Current State: 44:[18, 42], Operations: ['37-27=10', '52-10=42'] Exploring Operation: 18+42=60, Resulting Numbers: [60] 60,44 unequal: No Solution Exploring Operation: 18*42=756, Resulting Numbers: [756] 756,44 unequal: No Solution Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,44 unequal: No Solution Moving to Node #0,2,4 Current State: 44:[52, 8], Operations: ['37-27=10', '18-10=8'] Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[37, 18, 52, 27], Operations: [] Exploring Operation: 37-27=10, Resulting Numbers: [18, 52, 10] Generated Node #0,2: 44:[18, 52, 10] Operation: 37-27=10 Moving to Node #0,2 Current State: 44:[18, 52, 10], Operations: ['37-27=10'] Exploring Operation: 18-10=8, Resulting Numbers: [52, 8] Generated Node #0,2,4: 44:[52, 8] Operation: 18-10=8 Moving to Node #0,2,4 Current State: 44:[52, 8], Operations: ['37-27=10', '18-10=8'] Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 55, 48, 48, 43 ]
37
[ "48-43=5", "55/5=11", "48-11=37" ]
Current State: 37:[55, 48, 48, 43], Operations: [] Exploring Operation: 48-43=5, Resulting Numbers: [55, 5] Generated Node #2: [55, 5] from Operation: 48-43=5 Current State: 37:[55, 5], Operations: ['48-43=5'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,37 equal: Goal Reached Exploring Operation: 48-11=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[55, 48, 48, 43], Operations: [] Exploring Operation: 55-48=7, Resulting Numbers: [48, 43, 7] Generated Node #0,0: 37:[48, 43, 7] Operation: 55-48=7 Exploring Operation: 55-43=12, Resulting Numbers: [48, 48, 12] Generated Node #0,1: 37:[48, 48, 12] Operation: 55-43=12 Exploring Operation: 55-48=7, Resulting Numbers: [48, 43, 7] Generated Node #0,2: 37:[48, 43, 7] Operation: 55-48=7 Exploring Operation: 48/48=1, Resulting Numbers: [55, 43, 1] Generated Node #0,3: 37:[55, 43, 1] Operation: 48/48=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[48, 43, 7], Operations: ['55-48=7'] Exploring Operation: 43-7=36, Resulting Numbers: [48, 36] Generated Node #0,0,0: 37:[48, 36] Operation: 43-7=36 Exploring Operation: 48+7=55, Resulting Numbers: [43, 55] Generated Node #0,0,1: 37:[43, 55] Operation: 48+7=55 Exploring Operation: 48-7=41, Resulting Numbers: [43, 41] Generated Node #0,0,2: 37:[43, 41] Operation: 48-7=41 Exploring Operation: 43+7=50, Resulting Numbers: [48, 50] Generated Node #0,0,3: 37:[48, 50] Operation: 43+7=50 Moving to Node #0,0,2 Current State: 37:[43, 41], Operations: ['55-48=7', '48-7=41'] Exploring Operation: 43*41=1763, Resulting Numbers: [1763] 1763,37 unequal: No Solution Exploring Operation: 43+41=84, Resulting Numbers: [84] 84,37 unequal: No Solution Exploring Operation: 43-41=2, Resulting Numbers: [2] 2,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[48, 36], Operations: ['55-48=7', '43-7=36'] Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 48*36=1728, Resulting Numbers: [1728] 1728,37 unequal: No Solution Exploring Operation: 48+36=84, Resulting Numbers: [84] 84,37 unequal: No Solution Moving to Node #0,0,3 Current State: 37:[48, 50], Operations: ['55-48=7', '43+7=50'] Exploring Operation: 48*50=2400, Resulting Numbers: [2400] 2400,37 unequal: No Solution Exploring Operation: 48+50=98, Resulting Numbers: [98] 98,37 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[43, 55], Operations: ['55-48=7', '48+7=55'] Exploring Operation: 43*55=2365, Resulting Numbers: [2365] 2365,37 unequal: No Solution Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 43+55=98, Resulting Numbers: [98] 98,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[48, 48, 12], Operations: ['55-43=12'] Exploring Operation: 48-12=36, Resulting Numbers: [48, 36] Generated Node #0,1,0: 37:[48, 36] Operation: 48-12=36 Exploring Operation: 48+12=60, Resulting Numbers: [48, 60] Generated Node #0,1,1: 37:[48, 60] Operation: 48+12=60 Exploring Operation: 48+12=60, Resulting Numbers: [48, 60] Generated Node #0,1,2: 37:[48, 60] Operation: 48+12=60 Exploring Operation: 48-12=36, Resulting Numbers: [48, 36] Generated Node #0,1,3: 37:[48, 36] Operation: 48-12=36 Moving to Node #0,1,0 Current State: 37:[48, 36], Operations: ['55-43=12', '48-12=36'] Exploring Operation: 48*36=1728, Resulting Numbers: [1728] 1728,37 unequal: No Solution Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 48+36=84, Resulting Numbers: [84] 84,37 unequal: No Solution Moving to Node #0,1,3 Current State: 37:[48, 36], Operations: ['55-43=12', '48-12=36'] Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 48*36=1728, Resulting Numbers: [1728] 1728,37 unequal: No Solution Exploring Operation: 48+36=84, Resulting Numbers: [84] 84,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[48, 60], Operations: ['55-43=12', '48+12=60'] Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,37 unequal: No Solution Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[48, 60], Operations: ['55-43=12', '48+12=60'] Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,37 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 37:[48, 43, 7], Operations: ['55-48=7'] Exploring Operation: 48+7=55, Resulting Numbers: [43, 55] Generated Node #0,2,0: 37:[43, 55] Operation: 48+7=55 Exploring Operation: 43+7=50, Resulting Numbers: [48, 50] Generated Node #0,2,1: 37:[48, 50] Operation: 43+7=50 Exploring Operation: 48-7=41, Resulting Numbers: [43, 41] Generated Node #0,2,2: 37:[43, 41] Operation: 48-7=41 Exploring Operation: 43-7=36, Resulting Numbers: [48, 36] Generated Node #0,2,3: 37:[48, 36] Operation: 43-7=36 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 37:[43, 41], Operations: ['55-48=7', '48-7=41'] Exploring Operation: 43+41=84, Resulting Numbers: [84] 84,37 unequal: No Solution Exploring Operation: 43-41=2, Resulting Numbers: [2] 2,37 unequal: No Solution Exploring Operation: 43*41=1763, Resulting Numbers: [1763] 1763,37 unequal: No Solution No 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: 37:[48, 36], Operations: ['55-48=7', '43-7=36'] Exploring Operation: 48+36=84, Resulting Numbers: [84] 84,37 unequal: No Solution Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 48*36=1728, Resulting Numbers: [1728] 1728,37 unequal: No Solution No 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: 37:[43, 55], Operations: ['55-48=7', '48+7=55'] Exploring Operation: 43+55=98, Resulting Numbers: [98] 98,37 unequal: No Solution Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 43*55=2365, Resulting Numbers: [2365] 2365,37 unequal: No Solution No 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: 37:[48, 50], Operations: ['55-48=7', '43+7=50'] Exploring Operation: 48*50=2400, Resulting Numbers: [2400] 2400,37 unequal: No Solution Exploring Operation: 48+50=98, Resulting Numbers: [98] 98,37 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,37 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: 37:[55, 43, 1], Operations: ['48/48=1'] Exploring Operation: 55*1=55, Resulting Numbers: [43, 55] Generated Node #0,3,0: 37:[43, 55] Operation: 55*1=55 Exploring Operation: 43-1=42, Resulting Numbers: [55, 42] Generated Node #0,3,1: 37:[55, 42] Operation: 43-1=42 Exploring Operation: 55-1=54, Resulting Numbers: [43, 54] Generated Node #0,3,2: 37:[43, 54] Operation: 55-1=54 Exploring Operation: 55/1=55, Resulting Numbers: [43, 55] Generated Node #0,3,3: 37:[43, 55] Operation: 55/1=55 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 37:[55, 42], Operations: ['48/48=1', '43-1=42'] Exploring Operation: 55*42=2310, Resulting Numbers: [2310] 2310,37 unequal: No Solution Exploring Operation: 55-42=13, Resulting Numbers: [13] 13,37 unequal: No Solution Exploring Operation: 55+42=97, Resulting Numbers: [97] 97,37 unequal: No Solution No 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: 37:[43, 54], Operations: ['48/48=1', '55-1=54'] Exploring Operation: 43+54=97, Resulting Numbers: [97] 97,37 unequal: No Solution Exploring Operation: 43*54=2322, Resulting Numbers: [2322] 2322,37 unequal: No Solution Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,37 unequal: No Solution No 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: 37:[43, 55], Operations: ['48/48=1', '55*1=55'] Exploring Operation: 43+55=98, Resulting Numbers: [98] 98,37 unequal: No Solution Exploring Operation: 43*55=2365, Resulting Numbers: [2365] 2365,37 unequal: No Solution Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,37 unequal: No Solution No 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: 37:[43, 55], Operations: ['48/48=1', '55/1=55'] Exploring Operation: 43*55=2365, Resulting Numbers: [2365] 2365,37 unequal: No Solution Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 43+55=98, Resulting Numbers: [98] 98,37 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
[ 80, 6, 98, 44 ]
86
[ "80+98=178", "6*44=264", "264-178=86" ]
Current State: 86:[80, 6, 98, 44], Operations: [] Exploring Operation: 80+98=178, Resulting Numbers: [6, 44, 178] Generated Node #2: [6, 44, 178] from Operation: 80+98=178 Current State: 86:[6, 44, 178], Operations: ['80+98=178'] Exploring Operation: 6*44=264, Resulting Numbers: [178, 264] Generated Node #3: [178, 264] from Operation: 6*44=264 Current State: 86:[178, 264], Operations: ['80+98=178', '6*44=264'] Exploring Operation: 264-178=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[80, 6, 98, 44], Operations: [] Exploring Operation: 80+6=86, Resulting Numbers: [98, 44, 86] Generated Node #0,0: 86:[98, 44, 86] Operation: 80+6=86 Exploring Operation: 98-6=92, Resulting Numbers: [80, 44, 92] Generated Node #0,1: 86:[80, 44, 92] Operation: 98-6=92 Exploring Operation: 98-80=18, Resulting Numbers: [6, 44, 18] Generated Node #0,2: 86:[6, 44, 18] Operation: 98-80=18 Exploring Operation: 80-44=36, Resulting Numbers: [6, 98, 36] Generated Node #0,3: 86:[6, 98, 36] Operation: 80-44=36 Exploring Operation: 98-44=54, Resulting Numbers: [80, 6, 54] Generated Node #0,4: 86:[80, 6, 54] Operation: 98-44=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[98, 44, 86], Operations: ['80+6=86'] Exploring Operation: 98-44=54, Resulting Numbers: [86, 54] Generated Node #0,0,0: 86:[86, 54] Operation: 98-44=54 Exploring Operation: 98+44=142, Resulting Numbers: [86, 142] Generated Node #0,0,1: 86:[86, 142] Operation: 98+44=142 Exploring Operation: 86-44=42, Resulting Numbers: [98, 42] Generated Node #0,0,2: 86:[98, 42] Operation: 86-44=42 Exploring Operation: 98-86=12, Resulting Numbers: [44, 12] Generated Node #0,0,3: 86:[44, 12] Operation: 98-86=12 Exploring Operation: 44+86=130, Resulting Numbers: [98, 130] Generated Node #0,0,4: 86:[98, 130] Operation: 44+86=130 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[86, 54], Operations: ['80+6=86', '98-44=54'] Exploring Operation: 86+54=140, Resulting Numbers: [140] 140,86 unequal: No Solution Exploring Operation: 86*54=4644, Resulting Numbers: [4644] 4644,86 unequal: No Solution Exploring Operation: 86-54=32, Resulting Numbers: [32] 32,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 86:[44, 12], Operations: ['80+6=86', '98-86=12'] Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 44+12=56, Resulting Numbers: [56] 56,86 unequal: No Solution Exploring Operation: 44*12=528, Resulting Numbers: [528] 528,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 86:[98, 42], Operations: ['80+6=86', '86-44=42'] Exploring Operation: 98+42=140, Resulting Numbers: [140] 140,86 unequal: No Solution Exploring Operation: 98-42=56, Resulting Numbers: [56] 56,86 unequal: No Solution Exploring Operation: 98*42=4116, Resulting Numbers: [4116] 4116,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[86, 142], Operations: ['80+6=86', '98+44=142'] Exploring Operation: 86*142=12212, Resulting Numbers: [12212] 12212,86 unequal: No Solution Exploring Operation: 142-86=56, Resulting Numbers: [56] 56,86 unequal: No Solution Exploring Operation: 86+142=228, Resulting Numbers: [228] 228,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 86:[98, 130], Operations: ['80+6=86', '44+86=130'] Exploring Operation: 98*130=12740, Resulting Numbers: [12740] 12740,86 unequal: No Solution Exploring Operation: 98+130=228, Resulting Numbers: [228] 228,86 unequal: No Solution Exploring Operation: 130-98=32, Resulting Numbers: [32] 32,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[80, 44, 92], Operations: ['98-6=92'] Exploring Operation: 80+44=124, Resulting Numbers: [92, 124] Generated Node #0,1,0: 86:[92, 124] Operation: 80+44=124 Exploring Operation: 92-44=48, Resulting Numbers: [80, 48] Generated Node #0,1,1: 86:[80, 48] Operation: 92-44=48 Exploring Operation: 44+92=136, Resulting Numbers: [80, 136] Generated Node #0,1,2: 86:[80, 136] Operation: 44+92=136 Exploring Operation: 80-44=36, Resulting Numbers: [92, 36] Generated Node #0,1,3: 86:[92, 36] Operation: 80-44=36 Exploring Operation: 92-80=12, Resulting Numbers: [44, 12] Generated Node #0,1,4: 86:[44, 12] Operation: 92-80=12 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 86:[80, 48], Operations: ['98-6=92', '92-44=48'] Exploring Operation: 80+48=128, Resulting Numbers: [128] 128,86 unequal: No Solution Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 80*48=3840, Resulting Numbers: [3840] 3840,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 86:[44, 12], Operations: ['98-6=92', '92-80=12'] Exploring Operation: 44*12=528, Resulting Numbers: [528] 528,86 unequal: No Solution Exploring Operation: 44+12=56, Resulting Numbers: [56] 56,86 unequal: No Solution Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 86:[92, 36], Operations: ['98-6=92', '80-44=36'] Exploring Operation: 92+36=128, Resulting Numbers: [128] 128,86 unequal: No Solution Exploring Operation: 92*36=3312, Resulting Numbers: [3312] 3312,86 unequal: No Solution Exploring Operation: 92-36=56, Resulting Numbers: [56] 56,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 86:[92, 124], Operations: ['98-6=92', '80+44=124'] Exploring Operation: 92+124=216, Resulting Numbers: [216] 216,86 unequal: No Solution Exploring Operation: 124-92=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 92*124=11408, Resulting Numbers: [11408] 11408,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 86:[80, 136], Operations: ['98-6=92', '44+92=136'] Exploring Operation: 136-80=56, Resulting Numbers: [56] 56,86 unequal: No Solution Exploring Operation: 80*136=10880, Resulting Numbers: [10880] 10880,86 unequal: No Solution Exploring Operation: 80+136=216, Resulting Numbers: [216] 216,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[6, 44, 18], Operations: ['98-80=18'] Exploring Operation: 18/6=3, Resulting Numbers: [44, 3] Generated Node #0,2,0: 86:[44, 3] Operation: 18/6=3 Exploring Operation: 44-18=26, Resulting Numbers: [6, 26] Generated Node #0,2,1: 86:[6, 26] Operation: 44-18=26 Exploring Operation: 44-6=38, Resulting Numbers: [18, 38] Generated Node #0,2,2: 86:[18, 38] Operation: 44-6=38 Exploring Operation: 6+18=24, Resulting Numbers: [44, 24] Generated Node #0,2,3: 86:[44, 24] Operation: 6+18=24 Exploring Operation: 18-6=12, Resulting Numbers: [44, 12] Generated Node #0,2,4: 86:[44, 12] Operation: 18-6=12 Moving to Node #0,2,0 Current State: 86:[44, 3], Operations: ['98-80=18', '18/6=3'] Exploring Operation: 44*3=132, Resulting Numbers: [132] 132,86 unequal: No Solution Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,86 unequal: No Solution Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,86 unequal: No Solution Moving to Node #0,2,4 Current State: 86:[44, 12], Operations: ['98-80=18', '18-6=12'] Exploring Operation: 44*12=528, Resulting Numbers: [528] 528,86 unequal: No Solution Exploring Operation: 44+12=56, Resulting Numbers: [56] 56,86 unequal: No Solution Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,86 unequal: No Solution Moving to Node #0,2,3 Current State: 86:[44, 24], Operations: ['98-80=18', '6+18=24'] Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,86 unequal: No Solution Exploring Operation: 44+24=68, Resulting Numbers: [68] 68,86 unequal: No Solution Exploring Operation: 44*24=1056, Resulting Numbers: [1056] 1056,86 unequal: No Solution Moving to Node #0,2,1 Current State: 86:[6, 26], Operations: ['98-80=18', '44-18=26'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,86 unequal: No Solution Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 6*26=156, Resulting Numbers: [156] 156,86 unequal: No Solution Moving to Node #0,2,2 Current State: 86:[18, 38], Operations: ['98-80=18', '44-6=38'] Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,86 unequal: No Solution Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,86 unequal: No Solution Exploring Operation: 18*38=684, Resulting Numbers: [684] 684,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 86:[80, 6, 54], Operations: ['98-44=54'] Exploring Operation: 80-54=26, Resulting Numbers: [6, 26] Generated Node #0,4,0: 86:[6, 26] Operation: 80-54=26 Exploring Operation: 54/6=9, Resulting Numbers: [80, 9] Generated Node #0,4,1: 86:[80, 9] Operation: 54/6=9 Exploring Operation: 54-6=48, Resulting Numbers: [80, 48] Generated Node #0,4,2: 86:[80, 48] Operation: 54-6=48 Exploring Operation: 80+6=86, Resulting Numbers: [54, 86] Generated Node #0,4,3: 86:[54, 86] Operation: 80+6=86 Exploring Operation: 80-6=74, Resulting Numbers: [54, 74] Generated Node #0,4,4: 86:[54, 74] Operation: 80-6=74 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 86:[80, 48], Operations: ['98-44=54', '54-6=48'] Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 80*48=3840, Resulting Numbers: [3840] 3840,86 unequal: No Solution Exploring Operation: 80+48=128, Resulting Numbers: [128] 128,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 86:[54, 86], Operations: ['98-44=54', '80+6=86'] Exploring Operation: 86-54=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 54*86=4644, Resulting Numbers: [4644] 4644,86 unequal: No Solution Exploring Operation: 54+86=140, Resulting Numbers: [140] 140,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 86:[80, 9], Operations: ['98-44=54', '54/6=9'] Exploring Operation: 80*9=720, Resulting Numbers: [720] 720,86 unequal: No Solution Exploring Operation: 80+9=89, Resulting Numbers: [89] 89,86 unequal: No Solution Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 86:[6, 26], Operations: ['98-44=54', '80-54=26'] Exploring Operation: 6*26=156, Resulting Numbers: [156] 156,86 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,86 unequal: No Solution Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 86:[54, 74], Operations: ['98-44=54', '80-6=74'] Exploring Operation: 54*74=3996, Resulting Numbers: [3996] 3996,86 unequal: No Solution Exploring Operation: 74-54=20, Resulting Numbers: [20] 20,86 unequal: No Solution Exploring Operation: 54+74=128, Resulting Numbers: [128] 128,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[6, 98, 36], Operations: ['80-44=36'] Exploring Operation: 98-36=62, Resulting Numbers: [6, 62] Generated Node #0,3,0: 86:[6, 62] Operation: 98-36=62 Exploring Operation: 36/6=6, Resulting Numbers: [98, 6] Generated Node #0,3,1: 86:[98, 6] Operation: 36/6=6 Exploring Operation: 6+98=104, Resulting Numbers: [36, 104] Generated Node #0,3,2: 86:[36, 104] Operation: 6+98=104 Exploring Operation: 6+36=42, Resulting Numbers: [98, 42] Generated Node #0,3,3: 86:[98, 42] Operation: 6+36=42 Exploring Operation: 98-6=92, Resulting Numbers: [36, 92] Generated Node #0,3,4: 86:[36, 92] Operation: 98-6=92 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 86:[98, 42], Operations: ['80-44=36', '6+36=42'] Exploring Operation: 98*42=4116, Resulting Numbers: [4116] 4116,86 unequal: No Solution Exploring Operation: 98+42=140, Resulting Numbers: [140] 140,86 unequal: No Solution Exploring Operation: 98-42=56, Resulting Numbers: [56] 56,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 86:[36, 92], Operations: ['80-44=36', '98-6=92'] Exploring Operation: 36+92=128, Resulting Numbers: [128] 128,86 unequal: No Solution Exploring Operation: 36*92=3312, Resulting Numbers: [3312] 3312,86 unequal: No Solution Exploring Operation: 92-36=56, Resulting Numbers: [56] 56,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 86:[98, 6], Operations: ['80-44=36', '36/6=6'] Exploring Operation: 98*6=588, Resulting Numbers: [588] 588,86 unequal: No Solution Exploring Operation: 98-6=92, Resulting Numbers: [92] 92,86 unequal: No Solution Exploring Operation: 98+6=104, Resulting Numbers: [104] 104,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 86:[6, 62], Operations: ['80-44=36', '98-36=62'] Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,86 unequal: No Solution Exploring Operation: 6*62=372, Resulting Numbers: [372] 372,86 unequal: No Solution Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 86:[36, 104], Operations: ['80-44=36', '6+98=104'] Exploring Operation: 104-36=68, Resulting Numbers: [68] 68,86 unequal: No Solution Exploring Operation: 36*104=3744, Resulting Numbers: [3744] 3744,86 unequal: No Solution Exploring Operation: 36+104=140, Resulting Numbers: [140] 140,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 84, 73, 15, 77 ]
32
[ "84-77=7", "15*7=105", "105-73=32" ]
Current State: 32:[84, 73, 15, 77], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [73, 15, 7] Generated Node #2: [73, 15, 7] from Operation: 84-77=7 Current State: 32:[73, 15, 7], Operations: ['84-77=7'] Exploring Operation: 15*7=105, Resulting Numbers: [73, 105] Generated Node #3: [73, 105] from Operation: 15*7=105 Current State: 32:[73, 105], Operations: ['84-77=7', '15*7=105'] Exploring Operation: 105-73=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[84, 73, 15, 77], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [73, 15, 7] Generated Node #0,0: 32:[73, 15, 7] Operation: 84-77=7 Exploring Operation: 84-15=69, Resulting Numbers: [73, 77, 69] Generated Node #0,1: 32:[73, 77, 69] Operation: 84-15=69 Exploring Operation: 77-73=4, Resulting Numbers: [84, 15, 4] Generated Node #0,2: 32:[84, 15, 4] Operation: 77-73=4 Exploring Operation: 84-73=11, Resulting Numbers: [15, 77, 11] Generated Node #0,3: 32:[15, 77, 11] Operation: 84-73=11 Moving to Node #0,0 Current State: 32:[73, 15, 7], Operations: ['84-77=7'] Exploring Operation: 73-15=58, Resulting Numbers: [7, 58] Generated Node #0,0,0: 32:[7, 58] Operation: 73-15=58 Exploring Operation: 15-7=8, Resulting Numbers: [73, 8] Generated Node #0,0,1: 32:[73, 8] Operation: 15-7=8 Exploring Operation: 73-7=66, Resulting Numbers: [15, 66] Generated Node #0,0,2: 32:[15, 66] Operation: 73-7=66 Exploring Operation: 15+7=22, Resulting Numbers: [73, 22] Generated Node #0,0,3: 32:[73, 22] Operation: 15+7=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[7, 58], Operations: ['84-77=7', '73-15=58'] Exploring Operation: 7*58=406, Resulting Numbers: [406] 406,32 unequal: No Solution Exploring Operation: 7+58=65, Resulting Numbers: [65] 65,32 unequal: No Solution Exploring Operation: 58-7=51, Resulting Numbers: [51] 51,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 32:[15, 66], Operations: ['84-77=7', '73-7=66'] Exploring Operation: 15*66=990, Resulting Numbers: [990] 990,32 unequal: No Solution Exploring Operation: 66-15=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 15+66=81, Resulting Numbers: [81] 81,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[73, 8], Operations: ['84-77=7', '15-7=8'] Exploring Operation: 73*8=584, Resulting Numbers: [584] 584,32 unequal: No Solution Exploring Operation: 73+8=81, Resulting Numbers: [81] 81,32 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 32:[73, 22], Operations: ['84-77=7', '15+7=22'] Exploring Operation: 73+22=95, Resulting Numbers: [95] 95,32 unequal: No Solution Exploring Operation: 73*22=1606, Resulting Numbers: [1606] 1606,32 unequal: No Solution Exploring Operation: 73-22=51, Resulting Numbers: [51] 51,32 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: 32:[15, 77, 11], Operations: ['84-73=11'] Exploring Operation: 77-15=62, Resulting Numbers: [11, 62] Generated Node #0,3,0: 32:[11, 62] Operation: 77-15=62 Exploring Operation: 15-11=4, Resulting Numbers: [77, 4] Generated Node #0,3,1: 32:[77, 4] Operation: 15-11=4 Exploring Operation: 77-11=66, Resulting Numbers: [15, 66] Generated Node #0,3,2: 32:[15, 66] Operation: 77-11=66 Exploring Operation: 77/11=7, Resulting Numbers: [15, 7] Generated Node #0,3,3: 32:[15, 7] Operation: 77/11=7 Moving to Node #0,2 Current State: 32:[84, 15, 4], Operations: ['77-73=4'] Exploring Operation: 84-15=69, Resulting Numbers: [4, 69] Generated Node #0,2,0: 32:[4, 69] Operation: 84-15=69 Exploring Operation: 15+4=19, Resulting Numbers: [84, 19] Generated Node #0,2,1: 32:[84, 19] Operation: 15+4=19 Exploring Operation: 84/4=21, Resulting Numbers: [15, 21] Generated Node #0,2,2: 32:[15, 21] Operation: 84/4=21 Exploring Operation: 84-4=80, Resulting Numbers: [15, 80] Generated Node #0,2,3: 32:[15, 80] Operation: 84-4=80 Moving to Node #0,1 Current State: 32:[73, 77, 69], Operations: ['84-15=69'] Exploring Operation: 77-73=4, Resulting Numbers: [69, 4] Generated Node #0,1,0: 32:[69, 4] Operation: 77-73=4 Exploring Operation: 73+77=150, Resulting Numbers: [69, 150] Generated Node #0,1,1: 32:[69, 150] Operation: 73+77=150 Exploring Operation: 77-69=8, Resulting Numbers: [73, 8] Generated Node #0,1,2: 32:[73, 8] Operation: 77-69=8 Exploring Operation: 73-69=4, Resulting Numbers: [77, 4] Generated Node #0,1,3: 32:[77, 4] Operation: 73-69=4 Moving to Node #0,3,3 Current State: 32:[15, 7], Operations: ['84-73=11', '77/11=7'] Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,32 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,32 unequal: No Solution Exploring Operation: 15*7=105, Resulting Numbers: [105] 105,32 unequal: No Solution Moving to Node #0,2,2 Current State: 32:[15, 21], Operations: ['77-73=4', '84/4=21'] Exploring Operation: 15+21=36, Resulting Numbers: [36] 36,32 unequal: No Solution Exploring Operation: 15*21=315, Resulting Numbers: [315] 315,32 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,32 unequal: No Solution Moving to Node #0,3,0 Current State: 32:[11, 62], Operations: ['84-73=11', '77-15=62'] Exploring Operation: 62-11=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 11+62=73, Resulting Numbers: [73] 73,32 unequal: No Solution Exploring Operation: 11*62=682, Resulting Numbers: [682] 682,32 unequal: No Solution Moving to Node #0,3,2 Current State: 32:[15, 66], Operations: ['84-73=11', '77-11=66'] Exploring Operation: 15*66=990, Resulting Numbers: [990] 990,32 unequal: No Solution Exploring Operation: 15+66=81, Resulting Numbers: [81] 81,32 unequal: No Solution Exploring Operation: 66-15=51, Resulting Numbers: [51] 51,32 unequal: No Solution Moving to Node #0,2,0 Current State: 32:[4, 69], Operations: ['77-73=4', '84-15=69'] Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,32 unequal: No Solution Exploring Operation: 4*69=276, Resulting Numbers: [276] 276,32 unequal: No Solution Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,32 unequal: No Solution Moving to Node #0,1,0 Current State: 32:[69, 4], Operations: ['84-15=69', '77-73=4'] Exploring Operation: 69*4=276, Resulting Numbers: [276] 276,32 unequal: No Solution Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,32 unequal: No Solution Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,32 unequal: No Solution Moving to Node #0,1,2 Current State: 32:[73, 8], Operations: ['84-15=69', '77-69=8'] Exploring Operation: 73*8=584, Resulting Numbers: [584] 584,32 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,32 unequal: No Solution Exploring Operation: 73+8=81, Resulting Numbers: [81] 81,32 unequal: No Solution Moving to Node #0,1,3 Current State: 32:[77, 4], Operations: ['84-15=69', '73-69=4'] Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,32 unequal: No Solution Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,32 unequal: No Solution Exploring Operation: 77*4=308, Resulting Numbers: [308] 308,32 unequal: No Solution Moving to Node #0,3,1 Current State: 32:[77, 4], Operations: ['84-73=11', '15-11=4'] Exploring Operation: 77*4=308, Resulting Numbers: [308] 308,32 unequal: No Solution Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,32 unequal: No Solution Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,32 unequal: No Solution Moving to Node #0,2,3 Current State: 32:[15, 80], Operations: ['77-73=4', '84-4=80'] Exploring Operation: 80-15=65, Resulting Numbers: [65] 65,32 unequal: No Solution Exploring Operation: 15*80=1200, Resulting Numbers: [1200] 1200,32 unequal: No Solution Exploring Operation: 15+80=95, Resulting Numbers: [95] 95,32 unequal: No Solution Moving to Node #0,2,1 Current State: 32:[84, 19], Operations: ['77-73=4', '15+4=19'] Exploring Operation: 84*19=1596, Resulting Numbers: [1596] 1596,32 unequal: No Solution Exploring Operation: 84+19=103, Resulting Numbers: [103] 103,32 unequal: No Solution Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,32 unequal: No Solution Moving to Node #0,1,1 Current State: 32:[69, 150], Operations: ['84-15=69', '73+77=150'] Exploring Operation: 69*150=10350, Resulting Numbers: [10350] 10350,32 unequal: No Solution Exploring Operation: 150-69=81, Resulting Numbers: [81] 81,32 unequal: No Solution Exploring Operation: 69+150=219, Resulting Numbers: [219] 219,32 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 53, 53, 13, 67 ]
79
[ "53/53=1", "13+67=80", "80-1=79" ]
Current State: 79:[53, 53, 13, 67], Operations: [] Exploring Operation: 53/53=1, Resulting Numbers: [13, 67, 1] Generated Node #2: [13, 67, 1] from Operation: 53/53=1 Current State: 79:[13, 67, 1], Operations: ['53/53=1'] Exploring Operation: 13+67=80, Resulting Numbers: [1, 80] Generated Node #3: [1, 80] from Operation: 13+67=80 Current State: 79:[1, 80], Operations: ['53/53=1', '13+67=80'] Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[53, 53, 13, 67], Operations: [] Exploring Operation: 53+13=66, Resulting Numbers: [53, 67, 66] Generated Node #0,0: 79:[53, 67, 66] Operation: 53+13=66 Exploring Operation: 53-13=40, Resulting Numbers: [53, 67, 40] Generated Node #0,1: 79:[53, 67, 40] Operation: 53-13=40 Exploring Operation: 53+13=66, Resulting Numbers: [53, 67, 66] Generated Node #0,2: 79:[53, 67, 66] Operation: 53+13=66 Exploring Operation: 13+67=80, Resulting Numbers: [53, 53, 80] Generated Node #0,3: 79:[53, 53, 80] Operation: 13+67=80 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[53, 67, 66], Operations: ['53+13=66'] Exploring Operation: 53+66=119, Resulting Numbers: [67, 119] Generated Node #0,0,0: 79:[67, 119] Operation: 53+66=119 Exploring Operation: 53+67=120, Resulting Numbers: [66, 120] Generated Node #0,0,1: 79:[66, 120] Operation: 53+67=120 Exploring Operation: 67-53=14, Resulting Numbers: [66, 14] Generated Node #0,0,2: 79:[66, 14] Operation: 67-53=14 Exploring Operation: 66-53=13, Resulting Numbers: [67, 13] Generated Node #0,0,3: 79:[67, 13] Operation: 66-53=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[67, 119], Operations: ['53+13=66', '53+66=119'] Exploring Operation: 67*119=7973, Resulting Numbers: [7973] 7973,79 unequal: No Solution Exploring Operation: 67+119=186, Resulting Numbers: [186] 186,79 unequal: No Solution Exploring Operation: 119-67=52, Resulting Numbers: [52] 52,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 79:[66, 120], Operations: ['53+13=66', '53+67=120'] Exploring Operation: 66*120=7920, Resulting Numbers: [7920] 7920,79 unequal: No Solution Exploring Operation: 120-66=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 66+120=186, Resulting Numbers: [186] 186,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 79:[66, 14], Operations: ['53+13=66', '67-53=14'] Exploring Operation: 66-14=52, Resulting Numbers: [52] 52,79 unequal: No Solution Exploring Operation: 66*14=924, Resulting Numbers: [924] 924,79 unequal: No Solution Exploring Operation: 66+14=80, Resulting Numbers: [80] 80,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 79:[67, 13], Operations: ['53+13=66', '66-53=13'] Exploring Operation: 67+13=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 67*13=871, Resulting Numbers: [871] 871,79 unequal: No Solution Exploring Operation: 67-13=54, Resulting Numbers: [54] 54,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[53, 67, 66], Operations: ['53+13=66'] Exploring Operation: 53+66=119, Resulting Numbers: [67, 119] Generated Node #0,2,0: 79:[67, 119] Operation: 53+66=119 Exploring Operation: 67-53=14, Resulting Numbers: [66, 14] Generated Node #0,2,1: 79:[66, 14] Operation: 67-53=14 Exploring Operation: 53+67=120, Resulting Numbers: [66, 120] Generated Node #0,2,2: 79:[66, 120] Operation: 53+67=120 Exploring Operation: 66-53=13, Resulting Numbers: [67, 13] Generated Node #0,2,3: 79:[67, 13] Operation: 66-53=13 Moving to Node #0,2,0 Current State: 79:[67, 119], Operations: ['53+13=66', '53+66=119'] Exploring Operation: 67*119=7973, Resulting Numbers: [7973] 7973,79 unequal: No Solution Exploring Operation: 67+119=186, Resulting Numbers: [186] 186,79 unequal: No Solution Exploring Operation: 119-67=52, Resulting Numbers: [52] 52,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[66, 120], Operations: ['53+13=66', '53+67=120'] Exploring Operation: 66*120=7920, Resulting Numbers: [7920] 7920,79 unequal: No Solution Exploring Operation: 120-66=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 66+120=186, Resulting Numbers: [186] 186,79 unequal: No Solution Moving to Node #0,2,3 Current State: 79:[67, 13], Operations: ['53+13=66', '66-53=13'] Exploring Operation: 67-13=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 67*13=871, Resulting Numbers: [871] 871,79 unequal: No Solution Exploring Operation: 67+13=80, Resulting Numbers: [80] 80,79 unequal: No Solution Moving to Node #0,2,1 Current State: 79:[66, 14], Operations: ['53+13=66', '67-53=14'] Exploring Operation: 66-14=52, Resulting Numbers: [52] 52,79 unequal: No Solution Exploring Operation: 66+14=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 66*14=924, Resulting Numbers: [924] 924,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 79:[53, 53, 80], Operations: ['13+67=80'] Exploring Operation: 53/53=1, Resulting Numbers: [80, 1] Generated Node #0,3,0: 79:[80, 1] Operation: 53/53=1 Exploring Operation: 53+53=106, Resulting Numbers: [80, 106] Generated Node #0,3,1: 79:[80, 106] Operation: 53+53=106 Exploring Operation: 80-53=27, Resulting Numbers: [53, 27] Generated Node #0,3,2: 79:[53, 27] Operation: 80-53=27 Exploring Operation: 80-53=27, Resulting Numbers: [53, 27] Generated Node #0,3,3: 79:[53, 27] Operation: 80-53=27 Moving to Node #0,3,1 Current State: 79:[80, 106], Operations: ['13+67=80', '53+53=106'] Exploring Operation: 106-80=26, Resulting Numbers: [26] 26,79 unequal: No Solution Exploring Operation: 80+106=186, Resulting Numbers: [186] 186,79 unequal: No Solution Exploring Operation: 80*106=8480, Resulting Numbers: [8480] 8480,79 unequal: No Solution Moving to Node #0,3,3 Current State: 79:[53, 27], Operations: ['13+67=80', '80-53=27'] Exploring Operation: 53*27=1431, Resulting Numbers: [1431] 1431,79 unequal: No Solution Exploring Operation: 53+27=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[53, 27], Operations: ['13+67=80', '80-53=27'] Exploring Operation: 53+27=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 53*27=1431, Resulting Numbers: [1431] 1431,79 unequal: No Solution Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,79 unequal: No Solution Moving to Node #0,3,0 Current State: 79:[80, 1], Operations: ['13+67=80', '53/53=1'] Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[53, 53, 13, 67], Operations: [] Exploring Operation: 13+67=80, Resulting Numbers: [53, 53, 80] Generated Node #0,3: 79:[53, 53, 80] Operation: 13+67=80 Moving to Node #0,3 Current State: 79:[53, 53, 80], Operations: ['13+67=80'] Exploring Operation: 53/53=1, Resulting Numbers: [80, 1] Generated Node #0,3,0: 79:[80, 1] Operation: 53/53=1 Moving to Node #0,3,0 Current State: 79:[80, 1], Operations: ['13+67=80', '53/53=1'] Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.953125
hs_4
mult_heuristic
[ 9, 4, 52, 99 ]
52
[ "9-4=5", "99-52=47", "5+47=52" ]
Current State: 52:[9, 4, 52, 99], Operations: [] Exploring Operation: 9-4=5, Resulting Numbers: [52, 99, 5] Generated Node #2: [52, 99, 5] from Operation: 9-4=5 Current State: 52:[52, 99, 5], Operations: ['9-4=5'] Exploring Operation: 99-52=47, Resulting Numbers: [5, 47] Generated Node #3: [5, 47] from Operation: 99-52=47 Current State: 52:[5, 47], Operations: ['9-4=5', '99-52=47'] Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[9, 4, 52, 99], Operations: [] Exploring Operation: 99-52=47, Resulting Numbers: [9, 4, 47] Generated Node #0,0: 52:[9, 4, 47] Operation: 99-52=47 Exploring Operation: 99/9=11, Resulting Numbers: [4, 52, 11] Generated Node #0,1: 52:[4, 52, 11] Operation: 99/9=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[4, 52, 11], Operations: ['99/9=11'] Exploring Operation: 52/4=13, Resulting Numbers: [11, 13] Generated Node #0,1,0: 52:[11, 13] Operation: 52/4=13 Exploring Operation: 4+11=15, Resulting Numbers: [52, 15] Generated Node #0,1,1: 52:[52, 15] Operation: 4+11=15 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[11, 13], Operations: ['99/9=11', '52/4=13'] Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[52, 15], Operations: ['99/9=11', '4+11=15'] Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,52 unequal: No Solution Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[9, 4, 47], Operations: ['99-52=47'] Exploring Operation: 9+4=13, Resulting Numbers: [47, 13] Generated Node #0,0,0: 52:[47, 13] Operation: 9+4=13 Exploring Operation: 9+47=56, Resulting Numbers: [4, 56] Generated Node #0,0,1: 52:[4, 56] Operation: 9+47=56 Moving to Node #0,0,1 Current State: 52:[4, 56], Operations: ['99-52=47', '9+47=56'] Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[9, 4, 52, 99], Operations: [] Exploring Operation: 99-52=47, Resulting Numbers: [9, 4, 47] Generated Node #0,0: 52:[9, 4, 47] Operation: 99-52=47 Moving to Node #0,0 Current State: 52:[9, 4, 47], Operations: ['99-52=47'] Exploring Operation: 9+47=56, Resulting Numbers: [4, 56] Generated Node #0,0,1: 52:[4, 56] Operation: 9+47=56 Moving to Node #0,0,1 Current State: 52:[4, 56], Operations: ['99-52=47', '9+47=56'] Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 47, 62, 4, 37 ]
22
[ "47-37=10", "4*10=40", "62-40=22" ]
Current State: 22:[47, 62, 4, 37], Operations: [] Exploring Operation: 47-37=10, Resulting Numbers: [62, 4, 10] Generated Node #2: [62, 4, 10] from Operation: 47-37=10 Current State: 22:[62, 4, 10], Operations: ['47-37=10'] Exploring Operation: 4*10=40, Resulting Numbers: [62, 40] Generated Node #3: [62, 40] from Operation: 4*10=40 Current State: 22:[62, 40], Operations: ['47-37=10', '4*10=40'] Exploring Operation: 62-40=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[47, 62, 4, 37], Operations: [] Exploring Operation: 62-47=15, Resulting Numbers: [4, 37, 15] Generated Node #0,0: 22:[4, 37, 15] Operation: 62-47=15 Exploring Operation: 62-37=25, Resulting Numbers: [47, 4, 25] Generated Node #0,1: 22:[47, 4, 25] Operation: 62-37=25 Exploring Operation: 47-37=10, Resulting Numbers: [62, 4, 10] Generated Node #0,2: 22:[62, 4, 10] Operation: 47-37=10 Moving to Node #0,0 Current State: 22:[4, 37, 15], Operations: ['62-47=15'] Exploring Operation: 37-15=22, Resulting Numbers: [4, 22] Generated Node #0,0,0: 22:[4, 22] Operation: 37-15=22 Exploring Operation: 15-4=11, Resulting Numbers: [37, 11] Generated Node #0,0,1: 22:[37, 11] Operation: 15-4=11 Exploring Operation: 37-4=33, Resulting Numbers: [15, 33] Generated Node #0,0,2: 22:[15, 33] Operation: 37-4=33 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[4, 22], Operations: ['62-47=15', '37-15=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,22 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 22:[37, 11], Operations: ['62-47=15', '15-4=11'] Exploring Operation: 37+11=48, Resulting Numbers: [48] 48,22 unequal: No Solution Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,22 unequal: No Solution Exploring Operation: 37*11=407, Resulting Numbers: [407] 407,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 22:[15, 33], Operations: ['62-47=15', '37-4=33'] Exploring Operation: 15*33=495, Resulting Numbers: [495] 495,22 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 15+33=48, Resulting Numbers: [48] 48,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 22:[47, 4, 25], Operations: ['62-37=25'] Exploring Operation: 47-25=22, Resulting Numbers: [4, 22] Generated Node #0,1,0: 22:[4, 22] Operation: 47-25=22 Exploring Operation: 25-4=21, Resulting Numbers: [47, 21] Generated Node #0,1,1: 22:[47, 21] Operation: 25-4=21 Exploring Operation: 47-4=43, Resulting Numbers: [25, 43] Generated Node #0,1,2: 22:[25, 43] Operation: 47-4=43 Moving to Node #0,2 Current State: 22:[62, 4, 10], Operations: ['47-37=10'] Exploring Operation: 62-10=52, Resulting Numbers: [4, 52] Generated Node #0,2,0: 22:[4, 52] Operation: 62-10=52 Exploring Operation: 4+10=14, Resulting Numbers: [62, 14] Generated Node #0,2,1: 22:[62, 14] Operation: 4+10=14 Exploring Operation: 62-4=58, Resulting Numbers: [10, 58] Generated Node #0,2,2: 22:[10, 58] Operation: 62-4=58 Moving to Node #0,1,0 Current State: 22:[4, 22], Operations: ['62-37=25', '47-25=22'] Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,22 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,22 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[25, 43], Operations: ['62-37=25', '47-4=43'] Exploring Operation: 43-25=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 25*43=1075, Resulting Numbers: [1075] 1075,22 unequal: No Solution Exploring Operation: 25+43=68, Resulting Numbers: [68] 68,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[47, 21], Operations: ['62-37=25', '25-4=21'] Exploring Operation: 47-21=26, Resulting Numbers: [26] 26,22 unequal: No Solution Exploring Operation: 47+21=68, Resulting Numbers: [68] 68,22 unequal: No Solution Exploring Operation: 47*21=987, Resulting Numbers: [987] 987,22 unequal: No Solution Moving to Node #0,2,0 Current State: 22:[4, 52], Operations: ['47-37=10', '62-10=52'] Exploring Operation: 4+52=56, Resulting Numbers: [56] 56,22 unequal: No Solution Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,22 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[10, 58], Operations: ['47-37=10', '62-4=58'] Exploring Operation: 10*58=580, Resulting Numbers: [580] 580,22 unequal: No Solution Exploring Operation: 10+58=68, Resulting Numbers: [68] 68,22 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,22 unequal: No Solution Moving to Node #0,2,1 Current State: 22:[62, 14], Operations: ['47-37=10', '4+10=14'] Exploring Operation: 62-14=48, Resulting Numbers: [48] 48,22 unequal: No Solution Exploring Operation: 62*14=868, Resulting Numbers: [868] 868,22 unequal: No Solution Exploring Operation: 62+14=76, Resulting Numbers: [76] 76,22 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 26, 72, 54, 1 ]
100
[ "72-26=46", "54*1=54", "46+54=100" ]
Current State: 100:[26, 72, 54, 1], Operations: [] Exploring Operation: 72-26=46, Resulting Numbers: [54, 1, 46] Generated Node #2: [54, 1, 46] from Operation: 72-26=46 Current State: 100:[54, 1, 46], Operations: ['72-26=46'] Exploring Operation: 54*1=54, Resulting Numbers: [46, 54] Generated Node #3: [46, 54] from Operation: 54*1=54 Current State: 100:[46, 54], Operations: ['72-26=46', '54*1=54'] Exploring Operation: 46+54=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[26, 72, 54, 1], Operations: [] Exploring Operation: 26+72=98, Resulting Numbers: [54, 1, 98] Generated Node #0,0: 100:[54, 1, 98] Operation: 26+72=98 Exploring Operation: 72-26=46, Resulting Numbers: [54, 1, 46] Generated Node #0,1: 100:[54, 1, 46] Operation: 72-26=46 Exploring Operation: 72-54=18, Resulting Numbers: [26, 1, 18] Generated Node #0,2: 100:[26, 1, 18] Operation: 72-54=18 Exploring Operation: 54-26=28, Resulting Numbers: [72, 1, 28] Generated Node #0,3: 100:[72, 1, 28] Operation: 54-26=28 Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[26, 1, 18], Operations: ['72-54=18'] Exploring Operation: 26*1=26, Resulting Numbers: [18, 26] Generated Node #0,2,0: 100:[18, 26] Operation: 26*1=26 Exploring Operation: 1+18=19, Resulting Numbers: [26, 19] Generated Node #0,2,1: 100:[26, 19] Operation: 1+18=19 Exploring Operation: 26-1=25, Resulting Numbers: [18, 25] Generated Node #0,2,2: 100:[18, 25] Operation: 26-1=25 Exploring Operation: 26/1=26, Resulting Numbers: [18, 26] Generated Node #0,2,3: 100:[18, 26] Operation: 26/1=26 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 100:[26, 19], Operations: ['72-54=18', '1+18=19'] Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,100 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,100 unequal: No Solution Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,100 unequal: No Solution No 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: 100:[18, 25], Operations: ['72-54=18', '26-1=25'] Exploring Operation: 18*25=450, Resulting Numbers: [450] 450,100 unequal: No Solution Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,100 unequal: No Solution Exploring Operation: 18+25=43, Resulting Numbers: [43] 43,100 unequal: No Solution No 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: 100:[18, 26], Operations: ['72-54=18', '26*1=26'] Exploring Operation: 18+26=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 26-18=8, Resulting Numbers: [8] 8,100 unequal: No Solution Exploring Operation: 18*26=468, Resulting Numbers: [468] 468,100 unequal: No Solution No 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: 100:[18, 26], Operations: ['72-54=18', '26/1=26'] Exploring Operation: 18*26=468, Resulting Numbers: [468] 468,100 unequal: No Solution Exploring Operation: 26-18=8, Resulting Numbers: [8] 8,100 unequal: No Solution Exploring Operation: 18+26=44, Resulting Numbers: [44] 44,100 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: 100:[54, 1, 98], Operations: ['26+72=98'] Exploring Operation: 54/1=54, Resulting Numbers: [98, 54] Generated Node #0,0,0: 100:[98, 54] Operation: 54/1=54 Exploring Operation: 54-1=53, Resulting Numbers: [98, 53] Generated Node #0,0,1: 100:[98, 53] Operation: 54-1=53 Exploring Operation: 54*1=54, Resulting Numbers: [98, 54] Generated Node #0,0,2: 100:[98, 54] Operation: 54*1=54 Exploring Operation: 1+98=99, Resulting Numbers: [54, 99] Generated Node #0,0,3: 100:[54, 99] Operation: 1+98=99 Moving to Node #0,0,1 Current State: 100:[98, 53], Operations: ['26+72=98', '54-1=53'] Exploring Operation: 98*53=5194, Resulting Numbers: [5194] 5194,100 unequal: No Solution Exploring Operation: 98-53=45, Resulting Numbers: [45] 45,100 unequal: No Solution Exploring Operation: 98+53=151, Resulting Numbers: [151] 151,100 unequal: No Solution Moving to Node #0,0,3 Current State: 100:[54, 99], Operations: ['26+72=98', '1+98=99'] Exploring Operation: 54*99=5346, Resulting Numbers: [5346] 5346,100 unequal: No Solution Exploring Operation: 54+99=153, Resulting Numbers: [153] 153,100 unequal: No Solution Exploring Operation: 99-54=45, Resulting Numbers: [45] 45,100 unequal: No Solution Moving to Node #0,0,2 Current State: 100:[98, 54], Operations: ['26+72=98', '54*1=54'] Exploring Operation: 98*54=5292, Resulting Numbers: [5292] 5292,100 unequal: No Solution Exploring Operation: 98+54=152, Resulting Numbers: [152] 152,100 unequal: No Solution Exploring Operation: 98-54=44, Resulting Numbers: [44] 44,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[98, 54], Operations: ['26+72=98', '54/1=54'] Exploring Operation: 98*54=5292, Resulting Numbers: [5292] 5292,100 unequal: No Solution Exploring Operation: 98-54=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 98+54=152, Resulting Numbers: [152] 152,100 unequal: No Solution No 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: 100:[54, 1, 46], Operations: ['72-26=46'] Exploring Operation: 54-46=8, Resulting Numbers: [1, 8] Generated Node #0,1,0: 100:[1, 8] Operation: 54-46=8 Exploring Operation: 54-1=53, Resulting Numbers: [46, 53] Generated Node #0,1,1: 100:[46, 53] Operation: 54-1=53 Exploring Operation: 54+46=100, Resulting Numbers: [1, 100] Generated Node #0,1,2: 100:[1, 100] Operation: 54+46=100 Exploring Operation: 1+46=47, Resulting Numbers: [54, 47] Generated Node #0,1,3: 100:[54, 47] Operation: 1+46=47 Moving to Node #0,1,2 Current State: 100:[1, 100], Operations: ['72-26=46', '54+46=100'] Exploring Operation: 1*100=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[26, 72, 54, 1], Operations: [] Exploring Operation: 72-26=46, Resulting Numbers: [54, 1, 46] Generated Node #0,1: 100:[54, 1, 46] Operation: 72-26=46 Moving to Node #0,1 Current State: 100:[54, 1, 46], Operations: ['72-26=46'] Exploring Operation: 54+46=100, Resulting Numbers: [1, 100] Generated Node #0,1,2: 100:[1, 100] Operation: 54+46=100 Moving to Node #0,1,2 Current State: 100:[1, 100], Operations: ['72-26=46', '54+46=100'] Exploring Operation: 1*100=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.960938
hs_4
mult_heuristic
[ 78, 9, 40, 6 ]
14
[ "9-6=3", "78/3=26", "40-26=14" ]
Current State: 14:[78, 9, 40, 6], Operations: [] Exploring Operation: 9-6=3, Resulting Numbers: [78, 40, 3] Generated Node #2: [78, 40, 3] from Operation: 9-6=3 Current State: 14:[78, 40, 3], Operations: ['9-6=3'] Exploring Operation: 78/3=26, Resulting Numbers: [40, 26] Generated Node #3: [40, 26] from Operation: 78/3=26 Current State: 14:[40, 26], Operations: ['9-6=3', '78/3=26'] Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[78, 9, 40, 6], Operations: [] Exploring Operation: 78-40=38, Resulting Numbers: [9, 6, 38] Generated Node #0,0: 14:[9, 6, 38] Operation: 78-40=38 Exploring Operation: 78/6=13, Resulting Numbers: [9, 40, 13] Generated Node #0,1: 14:[9, 40, 13] Operation: 78/6=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[9, 6, 38], Operations: ['78-40=38'] Exploring Operation: 38-6=32, Resulting Numbers: [9, 32] Generated Node #0,0,0: 14:[9, 32] Operation: 38-6=32 Exploring Operation: 38-9=29, Resulting Numbers: [6, 29] Generated Node #0,0,1: 14:[6, 29] Operation: 38-9=29 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 14:[6, 29], Operations: ['78-40=38', '38-9=29'] Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,14 unequal: No Solution No 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: 14:[9, 32], Operations: ['78-40=38', '38-6=32'] Exploring Operation: 9+32=41, Resulting Numbers: [41] 41,14 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,14 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: 14:[9, 40, 13], Operations: ['78/6=13'] Exploring Operation: 40-13=27, Resulting Numbers: [9, 27] Generated Node #0,1,0: 14:[9, 27] Operation: 40-13=27 Exploring Operation: 40-9=31, Resulting Numbers: [13, 31] Generated Node #0,1,1: 14:[13, 31] Operation: 40-9=31 Moving to Node #0,1,0 Current State: 14:[9, 27], Operations: ['78/6=13', '40-13=27'] Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,14 unequal: No Solution Moving to Node #0,1,1 Current State: 14:[13, 31], Operations: ['78/6=13', '40-9=31'] Exploring Operation: 13+31=44, Resulting Numbers: [44] 44,14 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,14 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
[ 94, 91, 59, 32 ]
37
[ "94-91=3", "32*3=96", "96-59=37" ]
Current State: 37:[94, 91, 59, 32], Operations: [] Exploring Operation: 94-91=3, Resulting Numbers: [59, 32, 3] Generated Node #2: [59, 32, 3] from Operation: 94-91=3 Current State: 37:[59, 32, 3], Operations: ['94-91=3'] Exploring Operation: 32*3=96, Resulting Numbers: [59, 96] Generated Node #3: [59, 96] from Operation: 32*3=96 Current State: 37:[59, 96], Operations: ['94-91=3', '32*3=96'] Exploring Operation: 96-59=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[94, 91, 59, 32], Operations: [] Exploring Operation: 94-91=3, Resulting Numbers: [59, 32, 3] Generated Node #0,0: 37:[59, 32, 3] Operation: 94-91=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[59, 32, 3], Operations: ['94-91=3'] Exploring Operation: 59-3=56, Resulting Numbers: [32, 56] Generated Node #0,0,0: 37:[32, 56] Operation: 59-3=56 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[32, 56], Operations: ['94-91=3', '59-3=56'] Exploring Operation: 56-32=24, Resulting Numbers: [24] 24,37 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
[ 74, 69, 77, 4 ]
86
[ "74-69=5", "77+4=81", "5+81=86" ]
Current State: 86:[74, 69, 77, 4], Operations: [] Exploring Operation: 74-69=5, Resulting Numbers: [77, 4, 5] Generated Node #2: [77, 4, 5] from Operation: 74-69=5 Current State: 86:[77, 4, 5], Operations: ['74-69=5'] Exploring Operation: 77+4=81, Resulting Numbers: [5, 81] Generated Node #3: [5, 81] from Operation: 77+4=81 Current State: 86:[5, 81], Operations: ['74-69=5', '77+4=81'] Exploring Operation: 5+81=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[74, 69, 77, 4], Operations: [] Exploring Operation: 74-69=5, Resulting Numbers: [77, 4, 5] Generated Node #0,0: 86:[77, 4, 5] Operation: 74-69=5 Exploring Operation: 74+4=78, Resulting Numbers: [69, 77, 78] Generated Node #0,1: 86:[69, 77, 78] Operation: 74+4=78 Exploring Operation: 77-74=3, Resulting Numbers: [69, 4, 3] Generated Node #0,2: 86:[69, 4, 3] Operation: 77-74=3 Exploring Operation: 77-69=8, Resulting Numbers: [74, 4, 8] Generated Node #0,3: 86:[74, 4, 8] Operation: 77-69=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[77, 4, 5], Operations: ['74-69=5'] Exploring Operation: 5-4=1, Resulting Numbers: [77, 1] Generated Node #0,0,0: 86:[77, 1] Operation: 5-4=1 Exploring Operation: 77-4=73, Resulting Numbers: [5, 73] Generated Node #0,0,1: 86:[5, 73] Operation: 77-4=73 Exploring Operation: 77+4=81, Resulting Numbers: [5, 81] Generated Node #0,0,2: 86:[5, 81] Operation: 77+4=81 Exploring Operation: 77+5=82, Resulting Numbers: [4, 82] Generated Node #0,0,3: 86:[4, 82] Operation: 77+5=82 Moving to Node #0,0,3 Current State: 86:[4, 82], Operations: ['74-69=5', '77+5=82'] Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,86 unequal: No Solution Exploring Operation: 4*82=328, Resulting Numbers: [328] 328,86 unequal: No Solution Exploring Operation: 4+82=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[74, 69, 77, 4], Operations: [] Exploring Operation: 74-69=5, Resulting Numbers: [77, 4, 5] Generated Node #0,0: 86:[77, 4, 5] Operation: 74-69=5 Moving to Node #0,0 Current State: 86:[77, 4, 5], Operations: ['74-69=5'] Exploring Operation: 77+5=82, Resulting Numbers: [4, 82] Generated Node #0,0,3: 86:[4, 82] Operation: 77+5=82 Moving to Node #0,0,3 Current State: 86:[4, 82], Operations: ['74-69=5', '77+5=82'] Exploring Operation: 4+82=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 59, 90, 50, 81 ]
62
[ "90-59=31", "81-50=31", "31+31=62" ]
Current State: 62:[59, 90, 50, 81], Operations: [] Exploring Operation: 90-59=31, Resulting Numbers: [50, 81, 31] Generated Node #2: [50, 81, 31] from Operation: 90-59=31 Current State: 62:[50, 81, 31], Operations: ['90-59=31'] Exploring Operation: 81-50=31, Resulting Numbers: [31, 31] Generated Node #3: [31, 31] from Operation: 81-50=31 Current State: 62:[31, 31], Operations: ['90-59=31', '81-50=31'] Exploring Operation: 31+31=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[59, 90, 50, 81], Operations: [] Exploring Operation: 90-59=31, Resulting Numbers: [50, 81, 31] Generated Node #0,0: 62:[50, 81, 31] Operation: 90-59=31 Exploring Operation: 90-81=9, Resulting Numbers: [59, 50, 9] Generated Node #0,1: 62:[59, 50, 9] Operation: 90-81=9 Moving to Node #0,1 Current State: 62:[59, 50, 9], Operations: ['90-81=9'] Exploring Operation: 50-9=41, Resulting Numbers: [59, 41] Generated Node #0,1,0: 62:[59, 41] Operation: 50-9=41 Exploring Operation: 50+9=59, Resulting Numbers: [59, 59] Generated Node #0,1,1: 62:[59, 59] Operation: 50+9=59 Moving to Node #0,0 Current State: 62:[50, 81, 31], Operations: ['90-59=31'] Exploring Operation: 81-50=31, Resulting Numbers: [31, 31] Generated Node #0,0,0: 62:[31, 31] Operation: 81-50=31 Exploring Operation: 81-31=50, Resulting Numbers: [50, 50] Generated Node #0,0,1: 62:[50, 50] Operation: 81-31=50 Moving to Node #0,0,0 Current State: 62:[31, 31], Operations: ['90-59=31', '81-50=31'] Exploring Operation: 31+31=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[59, 90, 50, 81], Operations: [] Exploring Operation: 90-59=31, Resulting Numbers: [50, 81, 31] Generated Node #0,0: 62:[50, 81, 31] Operation: 90-59=31 Moving to Node #0,0 Current State: 62:[50, 81, 31], Operations: ['90-59=31'] Exploring Operation: 81-50=31, Resulting Numbers: [31, 31] Generated Node #0,0,0: 62:[31, 31] Operation: 81-50=31 Moving to Node #0,0,0 Current State: 62:[31, 31], Operations: ['90-59=31', '81-50=31'] Exploring Operation: 31+31=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.990451
hs_2
mult_heuristic
[ 99, 5, 33, 24 ]
48
[ "99/33=3", "5-3=2", "24*2=48" ]
Current State: 48:[99, 5, 33, 24], Operations: [] Exploring Operation: 99/33=3, Resulting Numbers: [5, 24, 3] Generated Node #2: [5, 24, 3] from Operation: 99/33=3 Current State: 48:[5, 24, 3], Operations: ['99/33=3'] Exploring Operation: 5-3=2, Resulting Numbers: [24, 2] Generated Node #3: [24, 2] from Operation: 5-3=2 Current State: 48:[24, 2], Operations: ['99/33=3', '5-3=2'] Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[99, 5, 33, 24], Operations: [] Exploring Operation: 99/33=3, Resulting Numbers: [5, 24, 3] Generated Node #0,0: 48:[5, 24, 3] Operation: 99/33=3 Exploring Operation: 99-33=66, Resulting Numbers: [5, 24, 66] Generated Node #0,1: 48:[5, 24, 66] Operation: 99-33=66 Moving to Node #0,0 Current State: 48:[5, 24, 3], Operations: ['99/33=3'] Exploring Operation: 5+3=8, Resulting Numbers: [24, 8] Generated Node #0,0,0: 48:[24, 8] Operation: 5+3=8 Exploring Operation: 5-3=2, Resulting Numbers: [24, 2] Generated Node #0,0,1: 48:[24, 2] Operation: 5-3=2 Moving to Node #0,1 Current State: 48:[5, 24, 66], Operations: ['99-33=66'] Exploring Operation: 66-5=61, Resulting Numbers: [24, 61] Generated Node #0,1,0: 48:[24, 61] Operation: 66-5=61 Exploring Operation: 66-24=42, Resulting Numbers: [5, 42] Generated Node #0,1,1: 48:[5, 42] Operation: 66-24=42 Moving to Node #0,0,0 Current State: 48:[24, 8], Operations: ['99/33=3', '5+3=8'] Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[24, 2], Operations: ['99/33=3', '5-3=2'] Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[99, 5, 33, 24], Operations: [] Exploring Operation: 99/33=3, Resulting Numbers: [5, 24, 3] Generated Node #0,0: 48:[5, 24, 3] Operation: 99/33=3 Moving to Node #0,0 Current State: 48:[5, 24, 3], Operations: ['99/33=3'] Exploring Operation: 5-3=2, Resulting Numbers: [24, 2] Generated Node #0,0,1: 48:[24, 2] Operation: 5-3=2 Moving to Node #0,0,1 Current State: 48:[24, 2], Operations: ['99/33=3', '5-3=2'] Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.988715
hs_2
mult_heuristic
[ 64, 16, 86, 21 ]
27
[ "64+16=80", "86+21=107", "107-80=27" ]
Current State: 27:[64, 16, 86, 21], Operations: [] Exploring Operation: 64+16=80, Resulting Numbers: [86, 21, 80] Generated Node #2: [86, 21, 80] from Operation: 64+16=80 Current State: 27:[86, 21, 80], Operations: ['64+16=80'] Exploring Operation: 86+21=107, Resulting Numbers: [80, 107] Generated Node #3: [80, 107] from Operation: 86+21=107 Current State: 27:[80, 107], Operations: ['64+16=80', '86+21=107'] Exploring Operation: 107-80=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[64, 16, 86, 21], Operations: [] Exploring Operation: 64-21=43, Resulting Numbers: [16, 86, 43] Generated Node #0,0: 27:[16, 86, 43] Operation: 64-21=43 Exploring Operation: 64/16=4, Resulting Numbers: [86, 21, 4] Generated Node #0,1: 27:[86, 21, 4] Operation: 64/16=4 Exploring Operation: 86-64=22, Resulting Numbers: [16, 21, 22] Generated Node #0,2: 27:[16, 21, 22] Operation: 86-64=22 Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[16, 21, 22], Operations: ['86-64=22'] Exploring Operation: 22-16=6, Resulting Numbers: [21, 6] Generated Node #0,2,0: 27:[21, 6] Operation: 22-16=6 Exploring Operation: 21-16=5, Resulting Numbers: [22, 5] Generated Node #0,2,1: 27:[22, 5] Operation: 21-16=5 Exploring Operation: 22-21=1, Resulting Numbers: [16, 1] Generated Node #0,2,2: 27:[16, 1] Operation: 22-21=1 Moving to Node #0,2,1 Current State: 27:[22, 5], Operations: ['86-64=22', '21-16=5'] Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[64, 16, 86, 21], Operations: [] Exploring Operation: 86-64=22, Resulting Numbers: [16, 21, 22] Generated Node #0,2: 27:[16, 21, 22] Operation: 86-64=22 Moving to Node #0,2 Current State: 27:[16, 21, 22], Operations: ['86-64=22'] Exploring Operation: 21-16=5, Resulting Numbers: [22, 5] Generated Node #0,2,1: 27:[22, 5] Operation: 21-16=5 Moving to Node #0,2,1 Current State: 27:[22, 5], Operations: ['86-64=22', '21-16=5'] Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 33, 85, 41, 87 ]
72
[ "33+85=118", "87-41=46", "118-46=72" ]
Current State: 72:[33, 85, 41, 87], Operations: [] Exploring Operation: 33+85=118, Resulting Numbers: [41, 87, 118] Generated Node #2: [41, 87, 118] from Operation: 33+85=118 Current State: 72:[41, 87, 118], Operations: ['33+85=118'] Exploring Operation: 87-41=46, Resulting Numbers: [118, 46] Generated Node #3: [118, 46] from Operation: 87-41=46 Current State: 72:[118, 46], Operations: ['33+85=118', '87-41=46'] Exploring Operation: 118-46=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[33, 85, 41, 87], Operations: [] Exploring Operation: 85-41=44, Resulting Numbers: [33, 87, 44] Generated Node #0,0: 72:[33, 87, 44] Operation: 85-41=44 Exploring Operation: 41-33=8, Resulting Numbers: [85, 87, 8] Generated Node #0,1: 72:[85, 87, 8] Operation: 41-33=8 Exploring Operation: 87-85=2, Resulting Numbers: [33, 41, 2] Generated Node #0,2: 72:[33, 41, 2] Operation: 87-85=2 Exploring Operation: 87-41=46, Resulting Numbers: [33, 85, 46] Generated Node #0,3: 72:[33, 85, 46] Operation: 87-41=46 Moving to Node #0,2 Current State: 72:[33, 41, 2], Operations: ['87-85=2'] Exploring Operation: 41-33=8, Resulting Numbers: [2, 8] Generated Node #0,2,0: 72:[2, 8] Operation: 41-33=8 Exploring Operation: 33+2=35, Resulting Numbers: [41, 35] Generated Node #0,2,1: 72:[41, 35] Operation: 33+2=35 Exploring Operation: 41-2=39, Resulting Numbers: [33, 39] Generated Node #0,2,2: 72:[33, 39] Operation: 41-2=39 Exploring Operation: 33+41=74, Resulting Numbers: [2, 74] Generated Node #0,2,3: 72:[2, 74] Operation: 33+41=74 Moving to Node #0,3 Current State: 72:[33, 85, 46], Operations: ['87-41=46'] Exploring Operation: 85-33=52, Resulting Numbers: [46, 52] Generated Node #0,3,0: 72:[46, 52] Operation: 85-33=52 Exploring Operation: 46-33=13, Resulting Numbers: [85, 13] Generated Node #0,3,1: 72:[85, 13] Operation: 46-33=13 Exploring Operation: 33+46=79, Resulting Numbers: [85, 79] Generated Node #0,3,2: 72:[85, 79] Operation: 33+46=79 Exploring Operation: 85-46=39, Resulting Numbers: [33, 39] Generated Node #0,3,3: 72:[33, 39] Operation: 85-46=39 Moving to Node #0,0 Current State: 72:[33, 87, 44], Operations: ['85-41=44'] Exploring Operation: 44-33=11, Resulting Numbers: [87, 11] Generated Node #0,0,0: 72:[87, 11] Operation: 44-33=11 Exploring Operation: 33+44=77, Resulting Numbers: [87, 77] Generated Node #0,0,1: 72:[87, 77] Operation: 33+44=77 Exploring Operation: 87-44=43, Resulting Numbers: [33, 43] Generated Node #0,0,2: 72:[33, 43] Operation: 87-44=43 Exploring Operation: 87-33=54, Resulting Numbers: [44, 54] Generated Node #0,0,3: 72:[44, 54] Operation: 87-33=54 Moving to Node #0,1 Current State: 72:[85, 87, 8], Operations: ['41-33=8'] Exploring Operation: 87-8=79, Resulting Numbers: [85, 79] Generated Node #0,1,0: 72:[85, 79] Operation: 87-8=79 Exploring Operation: 85+8=93, Resulting Numbers: [87, 93] Generated Node #0,1,1: 72:[87, 93] Operation: 85+8=93 Exploring Operation: 87-85=2, Resulting Numbers: [8, 2] Generated Node #0,1,2: 72:[8, 2] Operation: 87-85=2 Exploring Operation: 85-8=77, Resulting Numbers: [87, 77] Generated Node #0,1,3: 72:[87, 77] Operation: 85-8=77 Moving to Node #0,2,0 Current State: 72:[2, 8], Operations: ['87-85=2', '41-33=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,72 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[8, 2], Operations: ['41-33=8', '87-85=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,72 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,72 unequal: No Solution Moving to Node #0,2,3 Current State: 72:[2, 74], Operations: ['87-85=2', '33+41=74'] Exploring Operation: 2+74=76, Resulting Numbers: [76] 76,72 unequal: No Solution Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[33, 85, 41, 87], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [33, 41, 2] Generated Node #0,2: 72:[33, 41, 2] Operation: 87-85=2 Moving to Node #0,2 Current State: 72:[33, 41, 2], Operations: ['87-85=2'] Exploring Operation: 33+41=74, Resulting Numbers: [2, 74] Generated Node #0,2,3: 72:[2, 74] Operation: 33+41=74 Moving to Node #0,2,3 Current State: 72:[2, 74], Operations: ['87-85=2', '33+41=74'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.969618
hs_4
sum_heuristic
[ 9, 25, 59, 27 ]
28
[ "27/9=3", "25+59=84", "84/3=28" ]
Current State: 28:[9, 25, 59, 27], Operations: [] Exploring Operation: 27/9=3, Resulting Numbers: [25, 59, 3] Generated Node #2: [25, 59, 3] from Operation: 27/9=3 Current State: 28:[25, 59, 3], Operations: ['27/9=3'] Exploring Operation: 25+59=84, Resulting Numbers: [3, 84] Generated Node #3: [3, 84] from Operation: 25+59=84 Current State: 28:[3, 84], Operations: ['27/9=3', '25+59=84'] Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[9, 25, 59, 27], Operations: [] Exploring Operation: 59-25=34, Resulting Numbers: [9, 27, 34] Generated Node #0,0: 28:[9, 27, 34] Operation: 59-25=34 Exploring Operation: 59-27=32, Resulting Numbers: [9, 25, 32] Generated Node #0,1: 28:[9, 25, 32] Operation: 59-27=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[9, 27, 34], Operations: ['59-25=34'] Exploring Operation: 34-27=7, Resulting Numbers: [9, 7] Generated Node #0,0,0: 28:[9, 7] Operation: 34-27=7 Exploring Operation: 34-9=25, Resulting Numbers: [27, 25] Generated Node #0,0,1: 28:[27, 25] Operation: 34-9=25 Moving to Node #0,0,0 Current State: 28:[9, 7], Operations: ['59-25=34', '34-27=7'] Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,28 unequal: No Solution Moving to Node #0,0,1 Current State: 28:[27, 25], Operations: ['59-25=34', '34-9=25'] Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 27+25=52, Resulting Numbers: [52] 52,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[9, 25, 32], Operations: ['59-27=32'] Exploring Operation: 32-25=7, Resulting Numbers: [9, 7] Generated Node #0,1,0: 28:[9, 7] Operation: 32-25=7 Exploring Operation: 25-9=16, Resulting Numbers: [32, 16] Generated Node #0,1,1: 28:[32, 16] Operation: 25-9=16 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 28:[9, 7], Operations: ['59-27=32', '32-25=7'] Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 9-7=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 #0,1,1 Current State: 28:[32, 16], Operations: ['59-27=32', '25-9=16'] Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 11, 23, 57, 66 ]
86
[ "66/11=6", "23+57=80", "6+80=86" ]
Current State: 86:[11, 23, 57, 66], Operations: [] Exploring Operation: 66/11=6, Resulting Numbers: [23, 57, 6] Generated Node #2: [23, 57, 6] from Operation: 66/11=6 Current State: 86:[23, 57, 6], Operations: ['66/11=6'] Exploring Operation: 23+57=80, Resulting Numbers: [6, 80] Generated Node #3: [6, 80] from Operation: 23+57=80 Current State: 86:[6, 80], Operations: ['66/11=6', '23+57=80'] Exploring Operation: 6+80=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[11, 23, 57, 66], Operations: [] Exploring Operation: 66-23=43, Resulting Numbers: [11, 57, 43] Generated Node #0,0: 86:[11, 57, 43] Operation: 66-23=43 Moving to Node #0,0 Current State: 86:[11, 57, 43], Operations: ['66-23=43'] Exploring Operation: 57-11=46, Resulting Numbers: [43, 46] Generated Node #0,0,0: 86:[43, 46] Operation: 57-11=46 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[43, 46], Operations: ['66-23=43', '57-11=46'] Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 2, 44, 40, 1 ]
35
[ "2*40=80", "44+1=45", "80-45=35" ]
Current State: 35:[2, 44, 40, 1], Operations: [] Exploring Operation: 2*40=80, Resulting Numbers: [44, 1, 80] Generated Node #2: [44, 1, 80] from Operation: 2*40=80 Current State: 35:[44, 1, 80], Operations: ['2*40=80'] Exploring Operation: 44+1=45, Resulting Numbers: [80, 45] Generated Node #3: [80, 45] from Operation: 44+1=45 Current State: 35:[80, 45], Operations: ['2*40=80', '44+1=45'] Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[2, 44, 40, 1], Operations: [] Exploring Operation: 44-40=4, Resulting Numbers: [2, 1, 4] Generated Node #0,0: 35:[2, 1, 4] Operation: 44-40=4 Exploring Operation: 40-2=38, Resulting Numbers: [44, 1, 38] Generated Node #0,1: 35:[44, 1, 38] Operation: 40-2=38 Exploring Operation: 2+1=3, Resulting Numbers: [44, 40, 3] Generated Node #0,2: 35:[44, 40, 3] Operation: 2+1=3 Exploring Operation: 44-2=42, Resulting Numbers: [40, 1, 42] Generated Node #0,3: 35:[40, 1, 42] Operation: 44-2=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[2, 1, 4], Operations: ['44-40=4'] Exploring Operation: 2/1=2, Resulting Numbers: [4, 2] Generated Node #0,0,0: 35:[4, 2] Operation: 2/1=2 Exploring Operation: 2*1=2, Resulting Numbers: [4, 2] Generated Node #0,0,1: 35:[4, 2] Operation: 2*1=2 Exploring Operation: 1+4=5, Resulting Numbers: [2, 5] Generated Node #0,0,2: 35:[2, 5] Operation: 1+4=5 Exploring Operation: 2+1=3, Resulting Numbers: [4, 3] Generated Node #0,0,3: 35:[4, 3] Operation: 2+1=3 Moving to Node #0,0,2 Current State: 35:[2, 5], Operations: ['44-40=4', '1+4=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,35 unequal: No Solution Moving to Node #0,0,3 Current State: 35:[4, 3], Operations: ['44-40=4', '2+1=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[4, 2], Operations: ['44-40=4', '2*1=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[4, 2], Operations: ['44-40=4', '2/1=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[44, 1, 38], Operations: ['40-2=38'] Exploring Operation: 44-1=43, Resulting Numbers: [38, 43] Generated Node #0,1,0: 35:[38, 43] Operation: 44-1=43 Exploring Operation: 38-1=37, Resulting Numbers: [44, 37] Generated Node #0,1,1: 35:[44, 37] Operation: 38-1=37 Exploring Operation: 44-38=6, Resulting Numbers: [1, 6] Generated Node #0,1,2: 35:[1, 6] Operation: 44-38=6 Exploring Operation: 44*1=44, Resulting Numbers: [38, 44] Generated Node #0,1,3: 35:[38, 44] Operation: 44*1=44 Moving to Node #0,1,2 Current State: 35:[1, 6], Operations: ['40-2=38', '44-38=6'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 1+6=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[44, 37], Operations: ['40-2=38', '38-1=37'] Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,35 unequal: No Solution Exploring Operation: 44*37=1628, Resulting Numbers: [1628] 1628,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[38, 43], Operations: ['40-2=38', '44-1=43'] Exploring Operation: 38+43=81, Resulting Numbers: [81] 81,35 unequal: No Solution Exploring Operation: 43-38=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 38*43=1634, Resulting Numbers: [1634] 1634,35 unequal: No Solution Moving to Node #0,1,3 Current State: 35:[38, 44], Operations: ['40-2=38', '44*1=44'] Exploring Operation: 44-38=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 38+44=82, Resulting Numbers: [82] 82,35 unequal: No Solution Exploring Operation: 38*44=1672, Resulting Numbers: [1672] 1672,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[44, 40, 3], Operations: ['2+1=3'] Exploring Operation: 40-3=37, Resulting Numbers: [44, 37] Generated Node #0,2,0: 35:[44, 37] Operation: 40-3=37 Exploring Operation: 44-40=4, Resulting Numbers: [3, 4] Generated Node #0,2,1: 35:[3, 4] Operation: 44-40=4 Exploring Operation: 44+3=47, Resulting Numbers: [40, 47] Generated Node #0,2,2: 35:[40, 47] Operation: 44+3=47 Exploring Operation: 44-3=41, Resulting Numbers: [40, 41] Generated Node #0,2,3: 35:[40, 41] Operation: 44-3=41 Moving to Node #0,2,1 Current State: 35:[3, 4], Operations: ['2+1=3', '44-40=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,35 unequal: No Solution Moving to Node #0,2,3 Current State: 35:[40, 41], Operations: ['2+1=3', '44-3=41'] Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,35 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[44, 37], Operations: ['2+1=3', '40-3=37'] Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 44*37=1628, Resulting Numbers: [1628] 1628,35 unequal: No Solution Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,35 unequal: No Solution Moving to Node #0,2,2 Current State: 35:[40, 47], Operations: ['2+1=3', '44+3=47'] Exploring Operation: 40*47=1880, Resulting Numbers: [1880] 1880,35 unequal: No Solution Exploring Operation: 40+47=87, Resulting Numbers: [87] 87,35 unequal: No Solution Exploring Operation: 47-40=7, Resulting Numbers: [7] 7,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 35:[40, 1, 42], Operations: ['44-2=42'] Exploring Operation: 42-40=2, Resulting Numbers: [1, 2] Generated Node #0,3,0: 35:[1, 2] Operation: 42-40=2 Exploring Operation: 42-1=41, Resulting Numbers: [40, 41] Generated Node #0,3,1: 35:[40, 41] Operation: 42-1=41 Exploring Operation: 40-1=39, Resulting Numbers: [42, 39] Generated Node #0,3,2: 35:[42, 39] Operation: 40-1=39 Exploring Operation: 40*1=40, Resulting Numbers: [42, 40] Generated Node #0,3,3: 35:[42, 40] Operation: 40*1=40 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 35:[1, 2], Operations: ['44-2=42', '42-40=2'] Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 35:[40, 41], Operations: ['44-2=42', '42-1=41'] Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,35 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 35:[42, 39], Operations: ['44-2=42', '40-1=39'] Exploring Operation: 42*39=1638, Resulting Numbers: [1638] 1638,35 unequal: No Solution Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 42+39=81, Resulting Numbers: [81] 81,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 35:[42, 40], Operations: ['44-2=42', '40*1=40'] Exploring Operation: 42*40=1680, Resulting Numbers: [1680] 1680,35 unequal: No Solution Exploring Operation: 42+40=82, Resulting Numbers: [82] 82,35 unequal: No Solution Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 84, 12, 54, 63 ]
16
[ "84/12=7", "63-54=9", "7+9=16" ]
Current State: 16:[84, 12, 54, 63], Operations: [] Exploring Operation: 84/12=7, Resulting Numbers: [54, 63, 7] Generated Node #2: [54, 63, 7] from Operation: 84/12=7 Current State: 16:[54, 63, 7], Operations: ['84/12=7'] Exploring Operation: 63-54=9, Resulting Numbers: [7, 9] Generated Node #3: [7, 9] from Operation: 63-54=9 Current State: 16:[7, 9], Operations: ['84/12=7', '63-54=9'] Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[84, 12, 54, 63], Operations: [] Exploring Operation: 84-63=21, Resulting Numbers: [12, 54, 21] Generated Node #0,0: 16:[12, 54, 21] Operation: 84-63=21 Exploring Operation: 84-54=30, Resulting Numbers: [12, 63, 30] Generated Node #0,1: 16:[12, 63, 30] Operation: 84-54=30 Exploring Operation: 63-54=9, Resulting Numbers: [84, 12, 9] Generated Node #0,2: 16:[84, 12, 9] Operation: 63-54=9 Exploring Operation: 84/12=7, Resulting Numbers: [54, 63, 7] Generated Node #0,3: 16:[54, 63, 7] Operation: 84/12=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[12, 54, 21], Operations: ['84-63=21'] Exploring Operation: 54-21=33, Resulting Numbers: [12, 33] Generated Node #0,0,0: 16:[12, 33] Operation: 54-21=33 Exploring Operation: 21-12=9, Resulting Numbers: [54, 9] Generated Node #0,0,1: 16:[54, 9] Operation: 21-12=9 Exploring Operation: 12+54=66, Resulting Numbers: [21, 66] Generated Node #0,0,2: 16:[21, 66] Operation: 12+54=66 Exploring Operation: 54-12=42, Resulting Numbers: [21, 42] Generated Node #0,0,3: 16:[21, 42] Operation: 54-12=42 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 16:[12, 33], Operations: ['84-63=21', '54-21=33'] Exploring Operation: 12*33=396, Resulting Numbers: [396] 396,16 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,16 unequal: No Solution Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 16:[21, 42], Operations: ['84-63=21', '54-12=42'] Exploring Operation: 21*42=882, Resulting Numbers: [882] 882,16 unequal: No Solution Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,16 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,16 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 16:[54, 9], Operations: ['84-63=21', '21-12=9'] Exploring Operation: 54+9=63, Resulting Numbers: [63] 63,16 unequal: No Solution Exploring Operation: 54*9=486, Resulting Numbers: [486] 486,16 unequal: No Solution Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,16 unequal: No Solution Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 16:[21, 66], Operations: ['84-63=21', '12+54=66'] Exploring Operation: 21+66=87, Resulting Numbers: [87] 87,16 unequal: No Solution Exploring Operation: 66-21=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 21*66=1386, Resulting Numbers: [1386] 1386,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[12, 63, 30], Operations: ['84-54=30'] Exploring Operation: 63-30=33, Resulting Numbers: [12, 33] Generated Node #0,1,0: 16:[12, 33] Operation: 63-30=33 Exploring Operation: 30-12=18, Resulting Numbers: [63, 18] Generated Node #0,1,1: 16:[63, 18] Operation: 30-12=18 Exploring Operation: 12+63=75, Resulting Numbers: [30, 75] Generated Node #0,1,2: 16:[30, 75] Operation: 12+63=75 Exploring Operation: 63-12=51, Resulting Numbers: [30, 51] Generated Node #0,1,3: 16:[30, 51] Operation: 63-12=51 Moving to Node #0,1,0 Current State: 16:[12, 33], Operations: ['84-54=30', '63-30=33'] Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,16 unequal: No Solution Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 12*33=396, Resulting Numbers: [396] 396,16 unequal: No Solution Moving to Node #0,1,3 Current State: 16:[30, 51], Operations: ['84-54=30', '63-12=51'] Exploring Operation: 30+51=81, Resulting Numbers: [81] 81,16 unequal: No Solution Exploring Operation: 30*51=1530, Resulting Numbers: [1530] 1530,16 unequal: No Solution Exploring Operation: 51-30=21, Resulting Numbers: [21] 21,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[63, 18], Operations: ['84-54=30', '30-12=18'] Exploring Operation: 63-18=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 63+18=81, Resulting Numbers: [81] 81,16 unequal: No Solution Exploring Operation: 63*18=1134, Resulting Numbers: [1134] 1134,16 unequal: No Solution Moving to Node #0,1,2 Current State: 16:[30, 75], Operations: ['84-54=30', '12+63=75'] Exploring Operation: 75-30=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 30+75=105, Resulting Numbers: [105] 105,16 unequal: No Solution Exploring Operation: 30*75=2250, Resulting Numbers: [2250] 2250,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[84, 12, 9], Operations: ['63-54=9'] Exploring Operation: 12-9=3, Resulting Numbers: [84, 3] Generated Node #0,2,0: 16:[84, 3] Operation: 12-9=3 Exploring Operation: 84-12=72, Resulting Numbers: [9, 72] Generated Node #0,2,1: 16:[9, 72] Operation: 84-12=72 Exploring Operation: 84/12=7, Resulting Numbers: [9, 7] Generated Node #0,2,2: 16:[9, 7] Operation: 84/12=7 Exploring Operation: 84-9=75, Resulting Numbers: [12, 75] Generated Node #0,2,3: 16:[12, 75] Operation: 84-9=75 Moving to Node #0,2,2 Current State: 16:[9, 7], Operations: ['63-54=9', '84/12=7'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,16 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[84, 12, 54, 63], Operations: [] Exploring Operation: 63-54=9, Resulting Numbers: [84, 12, 9] Generated Node #0,2: 16:[84, 12, 9] Operation: 63-54=9 Moving to Node #0,2 Current State: 16:[84, 12, 9], Operations: ['63-54=9'] Exploring Operation: 84/12=7, Resulting Numbers: [9, 7] Generated Node #0,2,2: 16:[9, 7] Operation: 84/12=7 Moving to Node #0,2,2 Current State: 16:[9, 7], Operations: ['63-54=9', '84/12=7'] Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.957465
hs_4
sum_heuristic
[ 87, 63, 38, 2 ]
52
[ "87-63=24", "38*2=76", "76-24=52" ]
Current State: 52:[87, 63, 38, 2], Operations: [] Exploring Operation: 87-63=24, Resulting Numbers: [38, 2, 24] Generated Node #2: [38, 2, 24] from Operation: 87-63=24 Current State: 52:[38, 2, 24], Operations: ['87-63=24'] Exploring Operation: 38*2=76, Resulting Numbers: [24, 76] Generated Node #3: [24, 76] from Operation: 38*2=76 Current State: 52:[24, 76], Operations: ['87-63=24', '38*2=76'] Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[87, 63, 38, 2], Operations: [] Exploring Operation: 87-38=49, Resulting Numbers: [63, 2, 49] Generated Node #0,0: 52:[63, 2, 49] Operation: 87-38=49 Exploring Operation: 87-63=24, Resulting Numbers: [38, 2, 24] Generated Node #0,1: 52:[38, 2, 24] Operation: 87-63=24 Exploring Operation: 87-2=85, Resulting Numbers: [63, 38, 85] Generated Node #0,2: 52:[63, 38, 85] Operation: 87-2=85 Exploring Operation: 38/2=19, Resulting Numbers: [87, 63, 19] Generated Node #0,3: 52:[87, 63, 19] Operation: 38/2=19 Exploring Operation: 63-38=25, Resulting Numbers: [87, 2, 25] Generated Node #0,4: 52:[87, 2, 25] Operation: 63-38=25 Moving to Node #0,0 Current State: 52:[63, 2, 49], Operations: ['87-38=49'] Exploring Operation: 2+49=51, Resulting Numbers: [63, 51] Generated Node #0,0,0: 52:[63, 51] Operation: 2+49=51 Exploring Operation: 63+2=65, Resulting Numbers: [49, 65] Generated Node #0,0,1: 52:[49, 65] Operation: 63+2=65 Exploring Operation: 63-49=14, Resulting Numbers: [2, 14] Generated Node #0,0,2: 52:[2, 14] Operation: 63-49=14 Exploring Operation: 63-2=61, Resulting Numbers: [49, 61] Generated Node #0,0,3: 52:[49, 61] Operation: 63-2=61 Exploring Operation: 49-2=47, Resulting Numbers: [63, 47] Generated Node #0,0,4: 52:[63, 47] Operation: 49-2=47 Moving to Node #0,1 Current State: 52:[38, 2, 24], Operations: ['87-63=24'] Exploring Operation: 38-2=36, Resulting Numbers: [24, 36] Generated Node #0,1,0: 52:[24, 36] Operation: 38-2=36 Exploring Operation: 38-24=14, Resulting Numbers: [2, 14] Generated Node #0,1,1: 52:[2, 14] Operation: 38-24=14 Exploring Operation: 2+24=26, Resulting Numbers: [38, 26] Generated Node #0,1,2: 52:[38, 26] Operation: 2+24=26 Exploring Operation: 38/2=19, Resulting Numbers: [24, 19] Generated Node #0,1,3: 52:[24, 19] Operation: 38/2=19 Exploring Operation: 38+24=62, Resulting Numbers: [2, 62] Generated Node #0,1,4: 52:[2, 62] Operation: 38+24=62 Moving to Node #0,4 Current State: 52:[87, 2, 25], Operations: ['63-38=25'] Exploring Operation: 87+2=89, Resulting Numbers: [25, 89] Generated Node #0,4,0: 52:[25, 89] Operation: 87+2=89 Exploring Operation: 87-2=85, Resulting Numbers: [25, 85] Generated Node #0,4,1: 52:[25, 85] Operation: 87-2=85 Exploring Operation: 87-25=62, Resulting Numbers: [2, 62] Generated Node #0,4,2: 52:[2, 62] Operation: 87-25=62 Exploring Operation: 2+25=27, Resulting Numbers: [87, 27] Generated Node #0,4,3: 52:[87, 27] Operation: 2+25=27 Exploring Operation: 2*25=50, Resulting Numbers: [87, 50] Generated Node #0,4,4: 52:[87, 50] Operation: 2*25=50 Moving to Node #0,3 Current State: 52:[87, 63, 19], Operations: ['38/2=19'] Exploring Operation: 63-19=44, Resulting Numbers: [87, 44] Generated Node #0,3,0: 52:[87, 44] Operation: 63-19=44 Exploring Operation: 87-19=68, Resulting Numbers: [63, 68] Generated Node #0,3,1: 52:[63, 68] Operation: 87-19=68 Exploring Operation: 63+19=82, Resulting Numbers: [87, 82] Generated Node #0,3,2: 52:[87, 82] Operation: 63+19=82 Exploring Operation: 87-63=24, Resulting Numbers: [19, 24] Generated Node #0,3,3: 52:[19, 24] Operation: 87-63=24 Exploring Operation: 87+19=106, Resulting Numbers: [63, 106] Generated Node #0,3,4: 52:[63, 106] Operation: 87+19=106 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 52:[19, 24], Operations: ['38/2=19', '87-63=24'] Exploring Operation: 24-19=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 19*24=456, Resulting Numbers: [456] 456,52 unequal: No Solution Exploring Operation: 19+24=43, Resulting Numbers: [43] 43,52 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 #0,3,1 Current State: 52:[63, 68], Operations: ['38/2=19', '87-19=68'] Exploring Operation: 63+68=131, Resulting Numbers: [131] 131,52 unequal: No Solution Exploring Operation: 68-63=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 63*68=4284, Resulting Numbers: [4284] 4284,52 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 #0,3,0 Current State: 52:[87, 44], Operations: ['38/2=19', '63-19=44'] Exploring Operation: 87+44=131, Resulting Numbers: [131] 131,52 unequal: No Solution Exploring Operation: 87-44=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 87*44=3828, Resulting Numbers: [3828] 3828,52 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 #0,3,2 Current State: 52:[87, 82], Operations: ['38/2=19', '63+19=82'] Exploring Operation: 87-82=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 87*82=7134, Resulting Numbers: [7134] 7134,52 unequal: No Solution Exploring Operation: 87+82=169, Resulting Numbers: [169] 169,52 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 #0,3,4 Current State: 52:[63, 106], Operations: ['38/2=19', '87+19=106'] Exploring Operation: 106-63=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 63+106=169, Resulting Numbers: [169] 169,52 unequal: No Solution Exploring Operation: 63*106=6678, Resulting Numbers: [6678] 6678,52 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: 52:[63, 38, 85], Operations: ['87-2=85'] Exploring Operation: 85-38=47, Resulting Numbers: [63, 47] Generated Node #0,2,0: 52:[63, 47] Operation: 85-38=47 Exploring Operation: 38+85=123, Resulting Numbers: [63, 123] Generated Node #0,2,1: 52:[63, 123] Operation: 38+85=123 Exploring Operation: 63+38=101, Resulting Numbers: [85, 101] Generated Node #0,2,2: 52:[85, 101] Operation: 63+38=101 Exploring Operation: 85-63=22, Resulting Numbers: [38, 22] Generated Node #0,2,3: 52:[38, 22] Operation: 85-63=22 Exploring Operation: 63-38=25, Resulting Numbers: [85, 25] Generated Node #0,2,4: 52:[85, 25] Operation: 63-38=25 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 52:[63, 47], Operations: ['87-2=85', '85-38=47'] Exploring Operation: 63*47=2961, Resulting Numbers: [2961] 2961,52 unequal: No Solution Exploring Operation: 63+47=110, Resulting Numbers: [110] 110,52 unequal: No Solution Exploring Operation: 63-47=16, Resulting Numbers: [16] 16,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 52:[38, 22], Operations: ['87-2=85', '85-63=22'] Exploring Operation: 38*22=836, Resulting Numbers: [836] 836,52 unequal: No Solution Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 38+22=60, Resulting Numbers: [60] 60,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 52:[85, 25], Operations: ['87-2=85', '63-38=25'] Exploring Operation: 85*25=2125, Resulting Numbers: [2125] 2125,52 unequal: No Solution Exploring Operation: 85-25=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 85+25=110, Resulting Numbers: [110] 110,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 52:[63, 123], Operations: ['87-2=85', '38+85=123'] Exploring Operation: 123-63=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 63*123=7749, Resulting Numbers: [7749] 7749,52 unequal: No Solution Exploring Operation: 63+123=186, Resulting Numbers: [186] 186,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 52:[85, 101], Operations: ['87-2=85', '63+38=101'] Exploring Operation: 101-85=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 85*101=8585, Resulting Numbers: [8585] 8585,52 unequal: No Solution Exploring Operation: 85+101=186, Resulting Numbers: [186] 186,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 52:[2, 14], Operations: ['87-38=49', '63-49=14'] Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,52 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[2, 14], Operations: ['87-63=24', '38-24=14'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,52 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,52 unequal: No Solution Moving to Node #0,1,3 Current State: 52:[24, 19], Operations: ['87-63=24', '38/2=19'] Exploring Operation: 24*19=456, Resulting Numbers: [456] 456,52 unequal: No Solution Exploring Operation: 24+19=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 24-19=5, Resulting Numbers: [5] 5,52 unequal: No Solution Moving to Node #0,1,4 Current State: 52:[2, 62], Operations: ['87-63=24', '38+24=62'] Exploring Operation: 2*62=124, Resulting Numbers: [124] 124,52 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,52 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,52 unequal: No Solution Moving to Node #0,4,2 Current State: 52:[2, 62], Operations: ['63-38=25', '87-25=62'] Exploring Operation: 2*62=124, Resulting Numbers: [124] 124,52 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,52 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,52 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,52 unequal: No Solution Moving to Node #0,0,3 Current State: 52:[49, 61], Operations: ['87-38=49', '63-2=61'] Exploring Operation: 61-49=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 49*61=2989, Resulting Numbers: [2989] 2989,52 unequal: No Solution Exploring Operation: 49+61=110, Resulting Numbers: [110] 110,52 unequal: No Solution Moving to Node #0,1,2 Current State: 52:[38, 26], Operations: ['87-63=24', '2+24=26'] Exploring Operation: 38*26=988, Resulting Numbers: [988] 988,52 unequal: No Solution Exploring Operation: 38-26=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 38+26=64, Resulting Numbers: [64] 64,52 unequal: No Solution Moving to Node #0,0,0 Current State: 52:[63, 51], Operations: ['87-38=49', '2+49=51'] Exploring Operation: 63-51=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 63+51=114, Resulting Numbers: [114] 114,52 unequal: No Solution Exploring Operation: 63*51=3213, Resulting Numbers: [3213] 3213,52 unequal: No Solution Moving to Node #0,1,0 Current State: 52:[24, 36], Operations: ['87-63=24', '38-2=36'] Exploring Operation: 24+36=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 36-24=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 24*36=864, Resulting Numbers: [864] 864,52 unequal: No Solution Moving to Node #0,0,4 Current State: 52:[63, 47], Operations: ['87-38=49', '49-2=47'] Exploring Operation: 63+47=110, Resulting Numbers: [110] 110,52 unequal: No Solution Exploring Operation: 63-47=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 63*47=2961, Resulting Numbers: [2961] 2961,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[49, 65], Operations: ['87-38=49', '63+2=65'] Exploring Operation: 49+65=114, Resulting Numbers: [114] 114,52 unequal: No Solution Exploring Operation: 49*65=3185, Resulting Numbers: [3185] 3185,52 unequal: No Solution Exploring Operation: 65-49=16, Resulting Numbers: [16] 16,52 unequal: No Solution Moving to Node #0,4,1 Current State: 52:[25, 85], Operations: ['63-38=25', '87-2=85'] Exploring Operation: 25*85=2125, Resulting Numbers: [2125] 2125,52 unequal: No Solution Exploring Operation: 85-25=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 25+85=110, Resulting Numbers: [110] 110,52 unequal: No Solution Moving to Node #0,4,3 Current State: 52:[87, 27], Operations: ['63-38=25', '2+25=27'] Exploring Operation: 87+27=114, Resulting Numbers: [114] 114,52 unequal: No Solution Exploring Operation: 87*27=2349, Resulting Numbers: [2349] 2349,52 unequal: No Solution Exploring Operation: 87-27=60, Resulting Numbers: [60] 60,52 unequal: No Solution Moving to Node #0,4,4 Current State: 52:[87, 50], Operations: ['63-38=25', '2*25=50'] Exploring Operation: 87*50=4350, Resulting Numbers: [4350] 4350,52 unequal: No Solution Exploring Operation: 87+50=137, Resulting Numbers: [137] 137,52 unequal: No Solution Exploring Operation: 87-50=37, Resulting Numbers: [37] 37,52 unequal: No Solution Moving to Node #0,4,0 Current State: 52:[25, 89], Operations: ['63-38=25', '87+2=89'] Exploring Operation: 25+89=114, Resulting Numbers: [114] 114,52 unequal: No Solution Exploring Operation: 25*89=2225, Resulting Numbers: [2225] 2225,52 unequal: No Solution Exploring Operation: 89-25=64, Resulting Numbers: [64] 64,52 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 46, 14, 33, 12 ]
89
[ "46+33=79", "14*12=168", "168-79=89" ]
Current State: 89:[46, 14, 33, 12], Operations: [] Exploring Operation: 46+33=79, Resulting Numbers: [14, 12, 79] Generated Node #2: [14, 12, 79] from Operation: 46+33=79 Current State: 89:[14, 12, 79], Operations: ['46+33=79'] Exploring Operation: 14*12=168, Resulting Numbers: [79, 168] Generated Node #3: [79, 168] from Operation: 14*12=168 Current State: 89:[79, 168], Operations: ['46+33=79', '14*12=168'] Exploring Operation: 168-79=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[46, 14, 33, 12], Operations: [] Exploring Operation: 14+33=47, Resulting Numbers: [46, 12, 47] Generated Node #0,0: 89:[46, 12, 47] Operation: 14+33=47 Exploring Operation: 46+14=60, Resulting Numbers: [33, 12, 60] Generated Node #0,1: 89:[33, 12, 60] Operation: 46+14=60 Exploring Operation: 46+33=79, Resulting Numbers: [14, 12, 79] Generated Node #0,2: 89:[14, 12, 79] Operation: 46+33=79 Exploring Operation: 46+12=58, Resulting Numbers: [14, 33, 58] Generated Node #0,3: 89:[14, 33, 58] Operation: 46+12=58 Moving to Node #0,0 Current State: 89:[46, 12, 47], Operations: ['14+33=47'] Exploring Operation: 46+47=93, Resulting Numbers: [12, 93] Generated Node #0,0,0: 89:[12, 93] Operation: 46+47=93 Exploring Operation: 12+47=59, Resulting Numbers: [46, 59] Generated Node #0,0,1: 89:[46, 59] Operation: 12+47=59 Exploring Operation: 46+12=58, Resulting Numbers: [47, 58] Generated Node #0,0,2: 89:[47, 58] Operation: 46+12=58 Exploring Operation: 46-12=34, Resulting Numbers: [47, 34] Generated Node #0,0,3: 89:[47, 34] Operation: 46-12=34 Moving to Node #0,2 Current State: 89:[14, 12, 79], Operations: ['46+33=79'] Exploring Operation: 12+79=91, Resulting Numbers: [14, 91] Generated Node #0,2,0: 89:[14, 91] Operation: 12+79=91 Exploring Operation: 14+12=26, Resulting Numbers: [79, 26] Generated Node #0,2,1: 89:[79, 26] Operation: 14+12=26 Exploring Operation: 14+79=93, Resulting Numbers: [12, 93] Generated Node #0,2,2: 89:[12, 93] Operation: 14+79=93 Exploring Operation: 14*12=168, Resulting Numbers: [79, 168] Generated Node #0,2,3: 89:[79, 168] Operation: 14*12=168 Moving to Node #0,1 Current State: 89:[33, 12, 60], Operations: ['46+14=60'] Exploring Operation: 33-12=21, Resulting Numbers: [60, 21] Generated Node #0,1,0: 89:[60, 21] Operation: 33-12=21 Exploring Operation: 33+12=45, Resulting Numbers: [60, 45] Generated Node #0,1,1: 89:[60, 45] Operation: 33+12=45 Exploring Operation: 12+60=72, Resulting Numbers: [33, 72] Generated Node #0,1,2: 89:[33, 72] Operation: 12+60=72 Exploring Operation: 33+60=93, Resulting Numbers: [12, 93] Generated Node #0,1,3: 89:[12, 93] Operation: 33+60=93 Moving to Node #0,3 Current State: 89:[14, 33, 58], Operations: ['46+12=58'] Exploring Operation: 33+58=91, Resulting Numbers: [14, 91] Generated Node #0,3,0: 89:[14, 91] Operation: 33+58=91 Exploring Operation: 14+58=72, Resulting Numbers: [33, 72] Generated Node #0,3,1: 89:[33, 72] Operation: 14+58=72 Exploring Operation: 33-14=19, Resulting Numbers: [58, 19] Generated Node #0,3,2: 89:[58, 19] Operation: 33-14=19 Exploring Operation: 14+33=47, Resulting Numbers: [58, 47] Generated Node #0,3,3: 89:[58, 47] Operation: 14+33=47 Moving to Node #0,0,1 Current State: 89:[46, 59], Operations: ['14+33=47', '12+47=59'] Exploring Operation: 46+59=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,89 unequal: No Solution Exploring Operation: 46*59=2714, Resulting Numbers: [2714] 2714,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[33, 72], Operations: ['46+12=58', '14+58=72'] Exploring Operation: 33+72=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 72-33=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 33*72=2376, Resulting Numbers: [2376] 2376,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[58, 47], Operations: ['46+12=58', '14+33=47'] Exploring Operation: 58-47=11, Resulting Numbers: [11] 11,89 unequal: No Solution Exploring Operation: 58*47=2726, Resulting Numbers: [2726] 2726,89 unequal: No Solution Exploring Operation: 58+47=105, Resulting Numbers: [105] 105,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[47, 58], Operations: ['14+33=47', '46+12=58'] Exploring Operation: 47+58=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 58-47=11, Resulting Numbers: [11] 11,89 unequal: No Solution Exploring Operation: 47*58=2726, Resulting Numbers: [2726] 2726,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[79, 26], Operations: ['46+33=79', '14+12=26'] Exploring Operation: 79+26=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 79-26=53, Resulting Numbers: [53] 53,89 unequal: No Solution Exploring Operation: 79*26=2054, Resulting Numbers: [2054] 2054,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[33, 72], Operations: ['46+14=60', '12+60=72'] Exploring Operation: 33*72=2376, Resulting Numbers: [2376] 2376,89 unequal: No Solution Exploring Operation: 72-33=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 33+72=105, Resulting Numbers: [105] 105,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[60, 45], Operations: ['46+14=60', '33+12=45'] Exploring Operation: 60*45=2700, Resulting Numbers: [2700] 2700,89 unequal: No Solution Exploring Operation: 60+45=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 60-45=15, Resulting Numbers: [15] 15,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[14, 91], Operations: ['46+12=58', '33+58=91'] Exploring Operation: 14*91=1274, Resulting Numbers: [1274] 1274,89 unequal: No Solution Exploring Operation: 14+91=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 91-14=77, Resulting Numbers: [77] 77,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[14, 91], Operations: ['46+33=79', '12+79=91'] Exploring Operation: 91-14=77, Resulting Numbers: [77] 77,89 unequal: No Solution Exploring Operation: 14+91=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 14*91=1274, Resulting Numbers: [1274] 1274,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[12, 93], Operations: ['46+33=79', '14+79=93'] Exploring Operation: 12+93=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 12*93=1116, Resulting Numbers: [1116] 1116,89 unequal: No Solution Exploring Operation: 93-12=81, Resulting Numbers: [81] 81,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[12, 93], Operations: ['46+14=60', '33+60=93'] Exploring Operation: 12+93=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 12*93=1116, Resulting Numbers: [1116] 1116,89 unequal: No Solution Exploring Operation: 93-12=81, Resulting Numbers: [81] 81,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[12, 93], Operations: ['14+33=47', '46+47=93'] Exploring Operation: 12+93=105, Resulting Numbers: [105] 105,89 unequal: No Solution Exploring Operation: 93-12=81, Resulting Numbers: [81] 81,89 unequal: No Solution Exploring Operation: 12*93=1116, Resulting Numbers: [1116] 1116,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[79, 168], Operations: ['46+33=79', '14*12=168'] Exploring Operation: 168-79=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[46, 14, 33, 12], Operations: [] Exploring Operation: 46+33=79, Resulting Numbers: [14, 12, 79] Generated Node #0,2: 89:[14, 12, 79] Operation: 46+33=79 Moving to Node #0,2 Current State: 89:[14, 12, 79], Operations: ['46+33=79'] Exploring Operation: 14*12=168, Resulting Numbers: [79, 168] Generated Node #0,2,3: 89:[79, 168] Operation: 14*12=168 Moving to Node #0,2,3 Current State: 89:[79, 168], Operations: ['46+33=79', '14*12=168'] Exploring Operation: 168-79=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
0.947049
hs_4
mult_heuristic
[ 19, 19, 52, 7 ]
44
[ "19/19=1", "52-7=45", "45-1=44" ]
Current State: 44:[19, 19, 52, 7], Operations: [] Exploring Operation: 19/19=1, Resulting Numbers: [52, 7, 1] Generated Node #2: [52, 7, 1] from Operation: 19/19=1 Current State: 44:[52, 7, 1], Operations: ['19/19=1'] Exploring Operation: 52-7=45, Resulting Numbers: [1, 45] Generated Node #3: [1, 45] from Operation: 52-7=45 Current State: 44:[1, 45], Operations: ['19/19=1', '52-7=45'] Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[19, 19, 52, 7], Operations: [] Exploring Operation: 52-7=45, Resulting Numbers: [19, 19, 45] Generated Node #0,0: 44:[19, 19, 45] Operation: 52-7=45 Exploring Operation: 19/19=1, Resulting Numbers: [52, 7, 1] Generated Node #0,1: 44:[52, 7, 1] Operation: 19/19=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[19, 19, 45], Operations: ['52-7=45'] Exploring Operation: 19/19=1, Resulting Numbers: [45, 1] Generated Node #0,0,0: 44:[45, 1] Operation: 19/19=1 Exploring Operation: 19-19=0, Resulting Numbers: [45, 0] Generated Node #0,0,1: 44:[45, 0] Operation: 19-19=0 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[45, 1], Operations: ['52-7=45', '19/19=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,44 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[19, 19, 52, 7], Operations: [] Exploring Operation: 52-7=45, Resulting Numbers: [19, 19, 45] Generated Node #0,0: 44:[19, 19, 45] Operation: 52-7=45 Moving to Node #0,0 Current State: 44:[19, 19, 45], Operations: ['52-7=45'] Exploring Operation: 19/19=1, Resulting Numbers: [45, 1] Generated Node #0,0,0: 44:[45, 1] Operation: 19/19=1 Moving to Node #0,0,0 Current State: 44:[45, 1], Operations: ['52-7=45', '19/19=1'] Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 17, 76, 94, 34 ]
22
[ "76+94=170", "170/34=5", "17+5=22" ]
Current State: 22:[17, 76, 94, 34], Operations: [] Exploring Operation: 76+94=170, Resulting Numbers: [17, 34, 170] Generated Node #2: [17, 34, 170] from Operation: 76+94=170 Current State: 22:[17, 34, 170], Operations: ['76+94=170'] Exploring Operation: 170/34=5, Resulting Numbers: [17, 5] Generated Node #3: [17, 5] from Operation: 170/34=5 Current State: 22:[17, 5], Operations: ['76+94=170', '170/34=5'] Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[17, 76, 94, 34], Operations: [] Exploring Operation: 94-76=18, Resulting Numbers: [17, 34, 18] Generated Node #0,0: 22:[17, 34, 18] Operation: 94-76=18 Exploring Operation: 76-34=42, Resulting Numbers: [17, 94, 42] Generated Node #0,1: 22:[17, 94, 42] Operation: 76-34=42 Moving to Node #0,0 Current State: 22:[17, 34, 18], Operations: ['94-76=18'] Exploring Operation: 34-17=17, Resulting Numbers: [18, 17] Generated Node #0,0,0: 22:[18, 17] Operation: 34-17=17 Exploring Operation: 34/17=2, Resulting Numbers: [18, 2] Generated Node #0,0,1: 22:[18, 2] Operation: 34/17=2 Moving to Node #0,1 Current State: 22:[17, 94, 42], Operations: ['76-34=42'] Exploring Operation: 94-42=52, Resulting Numbers: [17, 52] Generated Node #0,1,0: 22:[17, 52] Operation: 94-42=52 Exploring Operation: 94-17=77, Resulting Numbers: [42, 77] Generated Node #0,1,1: 22:[42, 77] Operation: 94-17=77 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[17, 52], Operations: ['76-34=42', '94-42=52'] Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,22 unequal: No Solution Exploring Operation: 17+52=69, Resulting Numbers: [69] 69,22 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 #0,1,1 Current State: 22:[42, 77], Operations: ['76-34=42', '94-17=77'] Exploring Operation: 42+77=119, Resulting Numbers: [119] 119,22 unequal: No Solution Exploring Operation: 77-42=35, Resulting Numbers: [35] 35,22 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: 22:[18, 2], Operations: ['94-76=18', '34/17=2'] Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,22 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,22 unequal: No Solution Moving to Node #0,0,0 Current State: 22:[18, 17], Operations: ['94-76=18', '34-17=17'] Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,22 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 61, 44, 10, 84 ]
11
[ "61+44=105", "10+84=94", "105-94=11" ]
Current State: 11:[61, 44, 10, 84], Operations: [] Exploring Operation: 61+44=105, Resulting Numbers: [10, 84, 105] Generated Node #2: [10, 84, 105] from Operation: 61+44=105 Current State: 11:[10, 84, 105], Operations: ['61+44=105'] Exploring Operation: 10+84=94, Resulting Numbers: [105, 94] Generated Node #3: [105, 94] from Operation: 10+84=94 Current State: 11:[105, 94], Operations: ['61+44=105', '10+84=94'] Exploring Operation: 105-94=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[61, 44, 10, 84], Operations: [] Exploring Operation: 84-61=23, Resulting Numbers: [44, 10, 23] Generated Node #0,0: 11:[44, 10, 23] Operation: 84-61=23 Exploring Operation: 84-44=40, Resulting Numbers: [61, 10, 40] Generated Node #0,1: 11:[61, 10, 40] Operation: 84-44=40 Exploring Operation: 61-10=51, Resulting Numbers: [44, 84, 51] Generated Node #0,2: 11:[44, 84, 51] Operation: 61-10=51 Exploring Operation: 61-44=17, Resulting Numbers: [10, 84, 17] Generated Node #0,3: 11:[10, 84, 17] Operation: 61-44=17 Moving to Node #0,0 Current State: 11:[44, 10, 23], Operations: ['84-61=23'] Exploring Operation: 44-23=21, Resulting Numbers: [10, 21] Generated Node #0,0,0: 11:[10, 21] Operation: 44-23=21 Exploring Operation: 23-10=13, Resulting Numbers: [44, 13] Generated Node #0,0,1: 11:[44, 13] Operation: 23-10=13 Exploring Operation: 44-10=34, Resulting Numbers: [23, 34] Generated Node #0,0,2: 11:[23, 34] Operation: 44-10=34 Exploring Operation: 44+10=54, Resulting Numbers: [23, 54] Generated Node #0,0,3: 11:[23, 54] Operation: 44+10=54 Moving to Node #0,3 Current State: 11:[10, 84, 17], Operations: ['61-44=17'] Exploring Operation: 10+84=94, Resulting Numbers: [17, 94] Generated Node #0,3,0: 11:[17, 94] Operation: 10+84=94 Exploring Operation: 84-10=74, Resulting Numbers: [17, 74] Generated Node #0,3,1: 11:[17, 74] Operation: 84-10=74 Exploring Operation: 84-17=67, Resulting Numbers: [10, 67] Generated Node #0,3,2: 11:[10, 67] Operation: 84-17=67 Exploring Operation: 17-10=7, Resulting Numbers: [84, 7] Generated Node #0,3,3: 11:[84, 7] Operation: 17-10=7 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 11:[10, 67], Operations: ['61-44=17', '84-17=67'] Exploring Operation: 67-10=57, Resulting Numbers: [57] 57,11 unequal: No Solution Exploring Operation: 10+67=77, Resulting Numbers: [77] 77,11 unequal: No Solution Exploring Operation: 10*67=670, Resulting Numbers: [670] 670,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 11:[17, 74], Operations: ['61-44=17', '84-10=74'] Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,11 unequal: No Solution Exploring Operation: 17*74=1258, Resulting Numbers: [1258] 1258,11 unequal: No Solution Exploring Operation: 17+74=91, Resulting Numbers: [91] 91,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 11:[84, 7], Operations: ['61-44=17', '17-10=7'] Exploring Operation: 84+7=91, Resulting Numbers: [91] 91,11 unequal: No Solution Exploring Operation: 84-7=77, Resulting Numbers: [77] 77,11 unequal: No Solution Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 84*7=588, Resulting Numbers: [588] 588,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 11:[17, 94], Operations: ['61-44=17', '10+84=94'] Exploring Operation: 17+94=111, Resulting Numbers: [111] 111,11 unequal: No Solution Exploring Operation: 17*94=1598, Resulting Numbers: [1598] 1598,11 unequal: No Solution Exploring Operation: 94-17=77, Resulting Numbers: [77] 77,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 11:[61, 10, 40], Operations: ['84-44=40'] Exploring Operation: 40-10=30, Resulting Numbers: [61, 30] Generated Node #0,1,0: 11:[61, 30] Operation: 40-10=30 Exploring Operation: 61-40=21, Resulting Numbers: [10, 21] Generated Node #0,1,1: 11:[10, 21] Operation: 61-40=21 Exploring Operation: 40/10=4, Resulting Numbers: [61, 4] Generated Node #0,1,2: 11:[61, 4] Operation: 40/10=4 Exploring Operation: 61-10=51, Resulting Numbers: [40, 51] Generated Node #0,1,3: 11:[40, 51] Operation: 61-10=51 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 11:[10, 21], Operations: ['84-44=40', '61-40=21'] Exploring Operation: 10*21=210, Resulting Numbers: [210] 210,11 unequal: No Solution Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[61, 44, 10, 84], Operations: [] Exploring Operation: 84-44=40, Resulting Numbers: [61, 10, 40] Generated Node #0,1: 11:[61, 10, 40] Operation: 84-44=40 Moving to Node #0,1 Current State: 11:[61, 10, 40], Operations: ['84-44=40'] Exploring Operation: 61-40=21, Resulting Numbers: [10, 21] Generated Node #0,1,1: 11:[10, 21] Operation: 61-40=21 Moving to Node #0,1,1 Current State: 11:[10, 21], Operations: ['84-44=40', '61-40=21'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_4
sum_heuristic
[ 98, 21, 60, 17 ]
76
[ "98+21=119", "60-17=43", "119-43=76" ]
Current State: 76:[98, 21, 60, 17], Operations: [] Exploring Operation: 98+21=119, Resulting Numbers: [60, 17, 119] Generated Node #2: [60, 17, 119] from Operation: 98+21=119 Current State: 76:[60, 17, 119], Operations: ['98+21=119'] Exploring Operation: 60-17=43, Resulting Numbers: [119, 43] Generated Node #3: [119, 43] from Operation: 60-17=43 Current State: 76:[119, 43], Operations: ['98+21=119', '60-17=43'] Exploring Operation: 119-43=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[98, 21, 60, 17], Operations: [] Exploring Operation: 98-60=38, Resulting Numbers: [21, 17, 38] Generated Node #0,0: 76:[21, 17, 38] Operation: 98-60=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[21, 17, 38], Operations: ['98-60=38'] Exploring Operation: 21+17=38, Resulting Numbers: [38, 38] Generated Node #0,0,0: 76:[38, 38] Operation: 21+17=38 Moving to Node #0,0,0 Current State: 76:[38, 38], Operations: ['98-60=38', '21+17=38'] Exploring Operation: 38+38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[98, 21, 60, 17], Operations: [] Exploring Operation: 98-60=38, Resulting Numbers: [21, 17, 38] Generated Node #0,0: 76:[21, 17, 38] Operation: 98-60=38 Moving to Node #0,0 Current State: 76:[21, 17, 38], Operations: ['98-60=38'] Exploring Operation: 21+17=38, Resulting Numbers: [38, 38] Generated Node #0,0,0: 76:[38, 38] Operation: 21+17=38 Moving to Node #0,0,0 Current State: 76:[38, 38], Operations: ['98-60=38', '21+17=38'] Exploring Operation: 38+38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 97, 64, 16, 65 ]
66
[ "97-65=32", "32/16=2", "64+2=66" ]
Current State: 66:[97, 64, 16, 65], Operations: [] Exploring Operation: 97-65=32, Resulting Numbers: [64, 16, 32] Generated Node #2: [64, 16, 32] from Operation: 97-65=32 Current State: 66:[64, 16, 32], Operations: ['97-65=32'] Exploring Operation: 32/16=2, Resulting Numbers: [64, 2] Generated Node #3: [64, 2] from Operation: 32/16=2 Current State: 66:[64, 2], Operations: ['97-65=32', '32/16=2'] Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[97, 64, 16, 65], Operations: [] Exploring Operation: 97-64=33, Resulting Numbers: [16, 65, 33] Generated Node #0,0: 66:[16, 65, 33] Operation: 97-64=33 Exploring Operation: 97-16=81, Resulting Numbers: [64, 65, 81] Generated Node #0,1: 66:[64, 65, 81] Operation: 97-16=81 Exploring Operation: 97-65=32, Resulting Numbers: [64, 16, 32] Generated Node #0,2: 66:[64, 16, 32] Operation: 97-65=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[16, 65, 33], Operations: ['97-64=33'] Exploring Operation: 65-33=32, Resulting Numbers: [16, 32] Generated Node #0,0,0: 66:[16, 32] Operation: 65-33=32 Exploring Operation: 16+65=81, Resulting Numbers: [33, 81] Generated Node #0,0,1: 66:[33, 81] Operation: 16+65=81 Exploring Operation: 33-16=17, Resulting Numbers: [65, 17] Generated Node #0,0,2: 66:[65, 17] Operation: 33-16=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 66:[16, 32], Operations: ['97-64=33', '65-33=32'] Exploring Operation: 16+32=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,66 unequal: No Solution Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 66:[65, 17], Operations: ['97-64=33', '33-16=17'] Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 65+17=82, Resulting Numbers: [82] 82,66 unequal: No Solution Exploring Operation: 65*17=1105, Resulting Numbers: [1105] 1105,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 66:[33, 81], Operations: ['97-64=33', '16+65=81'] Exploring Operation: 81-33=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 33*81=2673, Resulting Numbers: [2673] 2673,66 unequal: No Solution Exploring Operation: 33+81=114, Resulting Numbers: [114] 114,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 66:[64, 16, 32], Operations: ['97-65=32'] Exploring Operation: 32/16=2, Resulting Numbers: [64, 2] Generated Node #0,2,0: 66:[64, 2] Operation: 32/16=2 Exploring Operation: 64/16=4, Resulting Numbers: [32, 4] Generated Node #0,2,1: 66:[32, 4] Operation: 64/16=4 Exploring Operation: 64/32=2, Resulting Numbers: [16, 2] Generated Node #0,2,2: 66:[16, 2] Operation: 64/32=2 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 66:[64, 2], Operations: ['97-65=32', '32/16=2'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,66 unequal: No Solution Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[97, 64, 16, 65], Operations: [] Exploring Operation: 97-65=32, Resulting Numbers: [64, 16, 32] Generated Node #0,2: 66:[64, 16, 32] Operation: 97-65=32 Moving to Node #0,2 Current State: 66:[64, 16, 32], Operations: ['97-65=32'] Exploring Operation: 32/16=2, Resulting Numbers: [64, 2] Generated Node #0,2,0: 66:[64, 2] Operation: 32/16=2 Moving to Node #0,2,0 Current State: 66:[64, 2], Operations: ['97-65=32', '32/16=2'] Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 11, 59, 18, 24 ]
20
[ "59-11=48", "48/24=2", "18+2=20" ]
Current State: 20:[11, 59, 18, 24], Operations: [] Exploring Operation: 59-11=48, Resulting Numbers: [18, 24, 48] Generated Node #2: [18, 24, 48] from Operation: 59-11=48 Current State: 20:[18, 24, 48], Operations: ['59-11=48'] Exploring Operation: 48/24=2, Resulting Numbers: [18, 2] Generated Node #3: [18, 2] from Operation: 48/24=2 Current State: 20:[18, 2], Operations: ['59-11=48', '48/24=2'] Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[11, 59, 18, 24], Operations: [] Exploring Operation: 59-24=35, Resulting Numbers: [11, 18, 35] Generated Node #0,0: 20:[11, 18, 35] Operation: 59-24=35 Exploring Operation: 59-11=48, Resulting Numbers: [18, 24, 48] Generated Node #0,1: 20:[18, 24, 48] Operation: 59-11=48 Exploring Operation: 59-18=41, Resulting Numbers: [11, 24, 41] Generated Node #0,2: 20:[11, 24, 41] Operation: 59-18=41 Moving to Node #0,0 Current State: 20:[11, 18, 35], Operations: ['59-24=35'] Exploring Operation: 18-11=7, Resulting Numbers: [35, 7] Generated Node #0,0,0: 20:[35, 7] Operation: 18-11=7 Exploring Operation: 35-18=17, Resulting Numbers: [11, 17] Generated Node #0,0,1: 20:[11, 17] Operation: 35-18=17 Exploring Operation: 35-11=24, Resulting Numbers: [18, 24] Generated Node #0,0,2: 20:[18, 24] Operation: 35-11=24 Moving to Node #0,2 Current State: 20:[11, 24, 41], Operations: ['59-18=41'] Exploring Operation: 41-24=17, Resulting Numbers: [11, 17] Generated Node #0,2,0: 20:[11, 17] Operation: 41-24=17 Exploring Operation: 41-11=30, Resulting Numbers: [24, 30] Generated Node #0,2,1: 20:[24, 30] Operation: 41-11=30 Exploring Operation: 24-11=13, Resulting Numbers: [41, 13] Generated Node #0,2,2: 20:[41, 13] Operation: 24-11=13 Moving to Node #0,1 Current State: 20:[18, 24, 48], Operations: ['59-11=48'] Exploring Operation: 48-18=30, Resulting Numbers: [24, 30] Generated Node #0,1,0: 20:[24, 30] Operation: 48-18=30 Exploring Operation: 48-24=24, Resulting Numbers: [18, 24] Generated Node #0,1,1: 20:[18, 24] Operation: 48-24=24 Exploring Operation: 48/24=2, Resulting Numbers: [18, 2] Generated Node #0,1,2: 20:[18, 2] Operation: 48/24=2 Moving to Node #0,1,2 Current State: 20:[18, 2], Operations: ['59-11=48', '48/24=2'] Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[11, 59, 18, 24], Operations: [] Exploring Operation: 59-11=48, Resulting Numbers: [18, 24, 48] Generated Node #0,1: 20:[18, 24, 48] Operation: 59-11=48 Moving to Node #0,1 Current State: 20:[18, 24, 48], Operations: ['59-11=48'] Exploring Operation: 48/24=2, Resulting Numbers: [18, 2] Generated Node #0,1,2: 20:[18, 2] Operation: 48/24=2 Moving to Node #0,1,2 Current State: 20:[18, 2], Operations: ['59-11=48', '48/24=2'] Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
0.985243
hs_3
mult_heuristic
[ 4, 23, 15, 10 ]
27
[ "4*15=60", "23+10=33", "60-33=27" ]
Current State: 27:[4, 23, 15, 10], Operations: [] Exploring Operation: 4*15=60, Resulting Numbers: [23, 10, 60] Generated Node #2: [23, 10, 60] from Operation: 4*15=60 Current State: 27:[23, 10, 60], Operations: ['4*15=60'] Exploring Operation: 23+10=33, Resulting Numbers: [60, 33] Generated Node #3: [60, 33] from Operation: 23+10=33 Current State: 27:[60, 33], Operations: ['4*15=60', '23+10=33'] Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[4, 23, 15, 10], Operations: [] Exploring Operation: 4+23=27, Resulting Numbers: [15, 10, 27] Generated Node #0,0: 27:[15, 10, 27] Operation: 4+23=27 Exploring Operation: 23-15=8, Resulting Numbers: [4, 10, 8] Generated Node #0,1: 27:[4, 10, 8] Operation: 23-15=8 Exploring Operation: 15-4=11, Resulting Numbers: [23, 10, 11] Generated Node #0,2: 27:[23, 10, 11] Operation: 15-4=11 Moving to Node #0,1 Current State: 27:[4, 10, 8], Operations: ['23-15=8'] Exploring Operation: 8/4=2, Resulting Numbers: [10, 2] Generated Node #0,1,0: 27:[10, 2] Operation: 8/4=2 Exploring Operation: 8-4=4, Resulting Numbers: [10, 4] Generated Node #0,1,1: 27:[10, 4] Operation: 8-4=4 Exploring Operation: 10-8=2, Resulting Numbers: [4, 2] Generated Node #0,1,2: 27:[4, 2] Operation: 10-8=2 Moving to Node #0,0 Current State: 27:[15, 10, 27], Operations: ['4+23=27'] Exploring Operation: 15-10=5, Resulting Numbers: [27, 5] Generated Node #0,0,0: 27:[27, 5] Operation: 15-10=5 Exploring Operation: 15+10=25, Resulting Numbers: [27, 25] Generated Node #0,0,1: 27:[27, 25] Operation: 15+10=25 Exploring Operation: 27-15=12, Resulting Numbers: [10, 12] Generated Node #0,0,2: 27:[10, 12] Operation: 27-15=12 Moving to Node #0,2 Current State: 27:[23, 10, 11], Operations: ['15-4=11'] Exploring Operation: 11-10=1, Resulting Numbers: [23, 1] Generated Node #0,2,0: 27:[23, 1] Operation: 11-10=1 Exploring Operation: 23-11=12, Resulting Numbers: [10, 12] Generated Node #0,2,1: 27:[10, 12] Operation: 23-11=12 Exploring Operation: 23-10=13, Resulting Numbers: [11, 13] Generated Node #0,2,2: 27:[11, 13] Operation: 23-10=13 Moving to Node #0,1,0 Current State: 27:[10, 2], Operations: ['23-15=8', '8/4=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,27 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,27 unequal: No Solution Moving to Node #0,1,2 Current State: 27:[4, 2], Operations: ['23-15=8', '10-8=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[10, 4], Operations: ['23-15=8', '8-4=4'] Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,27 unequal: No Solution Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,27 unequal: No Solution Moving to Node #0,0,1 Current State: 27:[27, 25], Operations: ['4+23=27', '15+10=25'] Exploring Operation: 27+25=52, Resulting Numbers: [52] 52,27 unequal: No Solution Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 27*25=675, Resulting Numbers: [675] 675,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[27, 5], Operations: ['4+23=27', '15-10=5'] Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,27 unequal: No Solution Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,27 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,27 unequal: No Solution Moving to Node #0,2,1 Current State: 27:[10, 12], Operations: ['15-4=11', '23-11=12'] Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 10*12=120, Resulting Numbers: [120] 120,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[10, 12], Operations: ['4+23=27', '27-15=12'] Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 10*12=120, Resulting Numbers: [120] 120,27 unequal: No Solution Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,27 unequal: No Solution Moving to Node #0,2,2 Current State: 27:[11, 13], Operations: ['15-4=11', '23-10=13'] Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 11*13=143, Resulting Numbers: [143] 143,27 unequal: No Solution Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,27 unequal: No Solution Moving to Node #0,2,0 Current State: 27:[23, 1], Operations: ['15-4=11', '11-10=1'] Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,27 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,27 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,27 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 99, 88, 99, 54 ]
88
[ "99-99=0", "54*0=0", "88+0=88" ]
Current State: 88:[99, 88, 99, 54], Operations: [] Exploring Operation: 99-99=0, Resulting Numbers: [88, 54, 0] Generated Node #2: [88, 54, 0] from Operation: 99-99=0 Current State: 88:[88, 54, 0], Operations: ['99-99=0'] Exploring Operation: 54*0=0, Resulting Numbers: [88, 0] Generated Node #3: [88, 0] from Operation: 54*0=0 Current State: 88:[88, 0], Operations: ['99-99=0', '54*0=0'] Exploring Operation: 88+0=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[99, 88, 99, 54], Operations: [] Exploring Operation: 99/99=1, Resulting Numbers: [88, 54, 1] Generated Node #0,0: 88:[88, 54, 1] Operation: 99/99=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[88, 54, 1], Operations: ['99/99=1'] Exploring Operation: 54-1=53, Resulting Numbers: [88, 53] Generated Node #0,0,0: 88:[88, 53] Operation: 54-1=53 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[88, 53], Operations: ['99/99=1', '54-1=53'] Exploring Operation: 88-53=35, Resulting Numbers: [35] 35,88 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
[ 36, 99, 4, 20 ]
47
[ "99-36=63", "20-4=16", "63-16=47" ]
Current State: 47:[36, 99, 4, 20], Operations: [] Exploring Operation: 99-36=63, Resulting Numbers: [4, 20, 63] Generated Node #2: [4, 20, 63] from Operation: 99-36=63 Current State: 47:[4, 20, 63], Operations: ['99-36=63'] Exploring Operation: 20-4=16, Resulting Numbers: [63, 16] Generated Node #3: [63, 16] from Operation: 20-4=16 Current State: 47:[63, 16], Operations: ['99-36=63', '20-4=16'] Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[36, 99, 4, 20], Operations: [] Exploring Operation: 99-36=63, Resulting Numbers: [4, 20, 63] Generated Node #0,0: 47:[4, 20, 63] Operation: 99-36=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[4, 20, 63], Operations: ['99-36=63'] Exploring Operation: 4+20=24, Resulting Numbers: [63, 24] Generated Node #0,0,0: 47:[63, 24] Operation: 4+20=24 Moving to Node #0,0,0 Current State: 47:[63, 24], Operations: ['99-36=63', '4+20=24'] Exploring Operation: 63-24=39, Resulting Numbers: [39] 39,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 79, 32, 5, 70 ]
97
[ "79+32=111", "70/5=14", "111-14=97" ]
Current State: 97:[79, 32, 5, 70], Operations: [] Exploring Operation: 79+32=111, Resulting Numbers: [5, 70, 111] Generated Node #2: [5, 70, 111] from Operation: 79+32=111 Current State: 97:[5, 70, 111], Operations: ['79+32=111'] Exploring Operation: 70/5=14, Resulting Numbers: [111, 14] Generated Node #3: [111, 14] from Operation: 70/5=14 Current State: 97:[111, 14], Operations: ['79+32=111', '70/5=14'] Exploring Operation: 111-14=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[79, 32, 5, 70], Operations: [] Exploring Operation: 79+5=84, Resulting Numbers: [32, 70, 84] Generated Node #0,0: 97:[32, 70, 84] Operation: 79+5=84 Moving to Node #0,0 Current State: 97:[32, 70, 84], Operations: ['79+5=84'] Exploring Operation: 32+70=102, Resulting Numbers: [84, 102] Generated Node #0,0,0: 97:[84, 102] Operation: 32+70=102 Moving to Node #0,0,0 Current State: 97:[84, 102], Operations: ['79+5=84', '32+70=102'] Exploring Operation: 102-84=18, Resulting Numbers: [18] 18,97 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 75, 98, 15, 45 ]
31
[ "98*15=1470", "1470-75=1395", "1395/45=31" ]
Current State: 31:[75, 98, 15, 45], Operations: [] Exploring Operation: 98*15=1470, Resulting Numbers: [75, 45, 1470] Generated Node #2: [75, 45, 1470] from Operation: 98*15=1470 Current State: 31:[75, 45, 1470], Operations: ['98*15=1470'] Exploring Operation: 1470-75=1395, Resulting Numbers: [45, 1395] Generated Node #3: [45, 1395] from Operation: 1470-75=1395 Current State: 31:[45, 1395], Operations: ['98*15=1470', '1470-75=1395'] Exploring Operation: 1395/45=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[75, 98, 15, 45], Operations: [] Exploring Operation: 75/15=5, Resulting Numbers: [98, 45, 5] Generated Node #0,0: 31:[98, 45, 5] Operation: 75/15=5 Exploring Operation: 98-45=53, Resulting Numbers: [75, 15, 53] Generated Node #0,1: 31:[75, 15, 53] Operation: 98-45=53 Exploring Operation: 98-75=23, Resulting Numbers: [15, 45, 23] Generated Node #0,2: 31:[15, 45, 23] Operation: 98-75=23 Exploring Operation: 75-45=30, Resulting Numbers: [98, 15, 30] Generated Node #0,3: 31:[98, 15, 30] Operation: 75-45=30 Start Sub Search at level 1: Moving to Node #0,2 Current State: 31:[15, 45, 23], Operations: ['98-75=23'] Exploring Operation: 45-15=30, Resulting Numbers: [23, 30] Generated Node #0,2,0: 31:[23, 30] Operation: 45-15=30 Exploring Operation: 15+23=38, Resulting Numbers: [45, 38] Generated Node #0,2,1: 31:[45, 38] Operation: 15+23=38 Exploring Operation: 45-23=22, Resulting Numbers: [15, 22] Generated Node #0,2,2: 31:[15, 22] Operation: 45-23=22 Exploring Operation: 45/15=3, Resulting Numbers: [23, 3] Generated Node #0,2,3: 31:[23, 3] Operation: 45/15=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 31:[23, 30], Operations: ['98-75=23', '45-15=30'] Exploring Operation: 23*30=690, Resulting Numbers: [690] 690,31 unequal: No Solution Exploring Operation: 30-23=7, Resulting Numbers: [7] 7,31 unequal: No Solution Exploring Operation: 23+30=53, Resulting Numbers: [53] 53,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 31:[45, 38], Operations: ['98-75=23', '15+23=38'] Exploring Operation: 45+38=83, Resulting Numbers: [83] 83,31 unequal: No Solution Exploring Operation: 45*38=1710, Resulting Numbers: [1710] 1710,31 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 31:[15, 22], Operations: ['98-75=23', '45-23=22'] Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,31 unequal: No Solution Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,31 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 31:[23, 3], Operations: ['98-75=23', '45/15=3'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,31 unequal: No Solution Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[75, 15, 53], Operations: ['98-45=53'] Exploring Operation: 75-53=22, Resulting Numbers: [15, 22] Generated Node #0,1,0: 31:[15, 22] Operation: 75-53=22 Exploring Operation: 75/15=5, Resulting Numbers: [53, 5] Generated Node #0,1,1: 31:[53, 5] Operation: 75/15=5 Exploring Operation: 75-15=60, Resulting Numbers: [53, 60] Generated Node #0,1,2: 31:[53, 60] Operation: 75-15=60 Exploring Operation: 53-15=38, Resulting Numbers: [75, 38] Generated Node #0,1,3: 31:[75, 38] Operation: 53-15=38 Moving to Node #0,1,0 Current State: 31:[15, 22], Operations: ['98-45=53', '75-53=22'] Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,31 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,31 unequal: No Solution Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[53, 5], Operations: ['98-45=53', '75/15=5'] Exploring Operation: 53*5=265, Resulting Numbers: [265] 265,31 unequal: No Solution Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,31 unequal: No Solution Exploring Operation: 53+5=58, Resulting Numbers: [58] 58,31 unequal: No Solution Moving to Node #0,1,3 Current State: 31:[75, 38], Operations: ['98-45=53', '53-15=38'] Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,31 unequal: No Solution Exploring Operation: 75*38=2850, Resulting Numbers: [2850] 2850,31 unequal: No Solution Exploring Operation: 75+38=113, Resulting Numbers: [113] 113,31 unequal: No Solution Moving to Node #0,1,2 Current State: 31:[53, 60], Operations: ['98-45=53', '75-15=60'] Exploring Operation: 53+60=113, Resulting Numbers: [113] 113,31 unequal: No Solution Exploring Operation: 53*60=3180, Resulting Numbers: [3180] 3180,31 unequal: No Solution Exploring Operation: 60-53=7, Resulting Numbers: [7] 7,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 31:[98, 15, 30], Operations: ['75-45=30'] Exploring Operation: 15+30=45, Resulting Numbers: [98, 45] Generated Node #0,3,0: 31:[98, 45] Operation: 15+30=45 Exploring Operation: 98+15=113, Resulting Numbers: [30, 113] Generated Node #0,3,1: 31:[30, 113] Operation: 98+15=113 Exploring Operation: 98-15=83, Resulting Numbers: [30, 83] Generated Node #0,3,2: 31:[30, 83] Operation: 98-15=83 Exploring Operation: 98-30=68, Resulting Numbers: [15, 68] Generated Node #0,3,3: 31:[15, 68] Operation: 98-30=68 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 31:[30, 83], Operations: ['75-45=30', '98-15=83'] Exploring Operation: 30*83=2490, Resulting Numbers: [2490] 2490,31 unequal: No Solution Exploring Operation: 83-30=53, Resulting Numbers: [53] 53,31 unequal: No Solution Exploring Operation: 30+83=113, Resulting Numbers: [113] 113,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 31:[15, 68], Operations: ['75-45=30', '98-30=68'] Exploring Operation: 15*68=1020, Resulting Numbers: [1020] 1020,31 unequal: No Solution Exploring Operation: 68-15=53, Resulting Numbers: [53] 53,31 unequal: No Solution Exploring Operation: 15+68=83, Resulting Numbers: [83] 83,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 31:[98, 45], Operations: ['75-45=30', '15+30=45'] Exploring Operation: 98*45=4410, Resulting Numbers: [4410] 4410,31 unequal: No Solution Exploring Operation: 98+45=143, Resulting Numbers: [143] 143,31 unequal: No Solution Exploring Operation: 98-45=53, Resulting Numbers: [53] 53,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 31:[30, 113], Operations: ['75-45=30', '98+15=113'] Exploring Operation: 30+113=143, Resulting Numbers: [143] 143,31 unequal: No Solution Exploring Operation: 113-30=83, Resulting Numbers: [83] 83,31 unequal: No Solution Exploring Operation: 30*113=3390, Resulting Numbers: [3390] 3390,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[98, 45, 5], Operations: ['75/15=5'] Exploring Operation: 98-45=53, Resulting Numbers: [5, 53] Generated Node #0,0,0: 31:[5, 53] Operation: 98-45=53 Exploring Operation: 45-5=40, Resulting Numbers: [98, 40] Generated Node #0,0,1: 31:[98, 40] Operation: 45-5=40 Exploring Operation: 98-5=93, Resulting Numbers: [45, 93] Generated Node #0,0,2: 31:[45, 93] Operation: 98-5=93 Exploring Operation: 98+5=103, Resulting Numbers: [45, 103] Generated Node #0,0,3: 31:[45, 103] Operation: 98+5=103 Moving to Node #0,0,0 Current State: 31:[5, 53], Operations: ['75/15=5', '98-45=53'] Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,31 unequal: No Solution Exploring Operation: 5+53=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 5*53=265, Resulting Numbers: [265] 265,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[45, 93], Operations: ['75/15=5', '98-5=93'] Exploring Operation: 93-45=48, Resulting Numbers: [48] 48,31 unequal: No Solution Exploring Operation: 45*93=4185, Resulting Numbers: [4185] 4185,31 unequal: No Solution Exploring Operation: 45+93=138, Resulting Numbers: [138] 138,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[98, 40], Operations: ['75/15=5', '45-5=40'] Exploring Operation: 98-40=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 98*40=3920, Resulting Numbers: [3920] 3920,31 unequal: No Solution Exploring Operation: 98+40=138, Resulting Numbers: [138] 138,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[45, 103], Operations: ['75/15=5', '98+5=103'] Exploring Operation: 45+103=148, Resulting Numbers: [148] 148,31 unequal: No Solution Exploring Operation: 103-45=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 45*103=4635, Resulting Numbers: [4635] 4635,31 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
[ 9, 27, 54, 2 ]
72
[ "9+27=36", "54*2=108", "108-36=72" ]
Current State: 72:[9, 27, 54, 2], Operations: [] Exploring Operation: 9+27=36, Resulting Numbers: [54, 2, 36] Generated Node #2: [54, 2, 36] from Operation: 9+27=36 Current State: 72:[54, 2, 36], Operations: ['9+27=36'] Exploring Operation: 54*2=108, Resulting Numbers: [36, 108] Generated Node #3: [36, 108] from Operation: 54*2=108 Current State: 72:[36, 108], Operations: ['9+27=36', '54*2=108'] Exploring Operation: 108-36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[9, 27, 54, 2], Operations: [] Exploring Operation: 54/27=2, Resulting Numbers: [9, 2, 2] Generated Node #0,0: 72:[9, 2, 2] Operation: 54/27=2 Exploring Operation: 27+54=81, Resulting Numbers: [9, 2, 81] Generated Node #0,1: 72:[9, 2, 81] Operation: 27+54=81 Exploring Operation: 54-27=27, Resulting Numbers: [9, 2, 27] Generated Node #0,2: 72:[9, 2, 27] Operation: 54-27=27 Exploring Operation: 54/9=6, Resulting Numbers: [27, 2, 6] Generated Node #0,3: 72:[27, 2, 6] Operation: 54/9=6 Exploring Operation: 54/2=27, Resulting Numbers: [9, 27, 27] Generated Node #0,4: 72:[9, 27, 27] Operation: 54/2=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[9, 2, 2], Operations: ['54/27=2'] Exploring Operation: 9*2=18, Resulting Numbers: [2, 18] Generated Node #0,0,0: 72:[2, 18] Operation: 9*2=18 Exploring Operation: 9+2=11, Resulting Numbers: [2, 11] Generated Node #0,0,1: 72:[2, 11] Operation: 9+2=11 Exploring Operation: 2*2=4, Resulting Numbers: [9, 4] Generated Node #0,0,2: 72:[9, 4] Operation: 2*2=4 Exploring Operation: 2+2=4, Resulting Numbers: [9, 4] Generated Node #0,0,3: 72:[9, 4] Operation: 2+2=4 Exploring Operation: 9*2=18, Resulting Numbers: [2, 18] Generated Node #0,0,4: 72:[2, 18] Operation: 9*2=18 Moving to Node #0,0,0 Current State: 72:[2, 18], Operations: ['54/27=2', '9*2=18'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,72 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[9, 4], Operations: ['54/27=2', '2+2=4'] Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,72 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[9, 4], Operations: ['54/27=2', '2*2=4'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,72 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,72 unequal: No Solution Moving to Node #0,0,4 Current State: 72:[2, 18], Operations: ['54/27=2', '9*2=18'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,72 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[2, 11], Operations: ['54/27=2', '9+2=11'] Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[9, 2, 27], Operations: ['54-27=27'] Exploring Operation: 27/9=3, Resulting Numbers: [2, 3] Generated Node #0,2,0: 72:[2, 3] Operation: 27/9=3 Exploring Operation: 27-2=25, Resulting Numbers: [9, 25] Generated Node #0,2,1: 72:[9, 25] Operation: 27-2=25 Exploring Operation: 9+27=36, Resulting Numbers: [2, 36] Generated Node #0,2,2: 72:[2, 36] Operation: 9+27=36 Exploring Operation: 27-9=18, Resulting Numbers: [2, 18] Generated Node #0,2,3: 72:[2, 18] Operation: 27-9=18 Exploring Operation: 9*2=18, Resulting Numbers: [27, 18] Generated Node #0,2,4: 72:[27, 18] Operation: 9*2=18 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 72:[2, 3], Operations: ['54-27=27', '27/9=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,72 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,72 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 72:[2, 36], Operations: ['54-27=27', '9+27=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,72 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[9, 27, 54, 2], Operations: [] Exploring Operation: 54-27=27, Resulting Numbers: [9, 2, 27] Generated Node #0,2: 72:[9, 2, 27] Operation: 54-27=27 Moving to Node #0,2 Current State: 72:[9, 2, 27], Operations: ['54-27=27'] Exploring Operation: 9+27=36, Resulting Numbers: [2, 36] Generated Node #0,2,2: 72:[2, 36] Operation: 9+27=36 Moving to Node #0,2,2 Current State: 72:[2, 36], Operations: ['54-27=27', '9+27=36'] Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.963542
hs_5
sum_heuristic
[ 11, 65, 7, 39 ]
51
[ "11*7=77", "65-39=26", "77-26=51" ]
Current State: 51:[11, 65, 7, 39], Operations: [] Exploring Operation: 11*7=77, Resulting Numbers: [65, 39, 77] Generated Node #2: [65, 39, 77] from Operation: 11*7=77 Current State: 51:[65, 39, 77], Operations: ['11*7=77'] Exploring Operation: 65-39=26, Resulting Numbers: [77, 26] Generated Node #3: [77, 26] from Operation: 65-39=26 Current State: 51:[77, 26], Operations: ['11*7=77', '65-39=26'] Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[11, 65, 7, 39], Operations: [] Exploring Operation: 65-11=54, Resulting Numbers: [7, 39, 54] Generated Node #0,0: 51:[7, 39, 54] Operation: 65-11=54 Moving to Node #0,0 Current State: 51:[7, 39, 54], Operations: ['65-11=54'] Exploring Operation: 54-39=15, Resulting Numbers: [7, 15] Generated Node #0,0,0: 51:[7, 15] Operation: 54-39=15 Moving to Node #0,0,0 Current State: 51:[7, 15], Operations: ['65-11=54', '54-39=15'] Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,51 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 6, 4, 12, 47 ]
73
[ "6+4=10", "12*10=120", "120-47=73" ]
Current State: 73:[6, 4, 12, 47], Operations: [] Exploring Operation: 6+4=10, Resulting Numbers: [12, 47, 10] Generated Node #2: [12, 47, 10] from Operation: 6+4=10 Current State: 73:[12, 47, 10], Operations: ['6+4=10'] Exploring Operation: 12*10=120, Resulting Numbers: [47, 120] Generated Node #3: [47, 120] from Operation: 12*10=120 Current State: 73:[47, 120], Operations: ['6+4=10', '12*10=120'] Exploring Operation: 120-47=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[6, 4, 12, 47], Operations: [] Exploring Operation: 6*4=24, Resulting Numbers: [12, 47, 24] Generated Node #0,0: 73:[12, 47, 24] Operation: 6*4=24 Exploring Operation: 6*12=72, Resulting Numbers: [4, 47, 72] Generated Node #0,1: 73:[4, 47, 72] Operation: 6*12=72 Exploring Operation: 4*12=48, Resulting Numbers: [6, 47, 48] Generated Node #0,2: 73:[6, 47, 48] Operation: 4*12=48 Moving to Node #0,1 Current State: 73:[4, 47, 72], Operations: ['6*12=72'] Exploring Operation: 4+72=76, Resulting Numbers: [47, 76] Generated Node #0,1,0: 73:[47, 76] Operation: 4+72=76 Exploring Operation: 4+47=51, Resulting Numbers: [72, 51] Generated Node #0,1,1: 73:[72, 51] Operation: 4+47=51 Exploring Operation: 47-4=43, Resulting Numbers: [72, 43] Generated Node #0,1,2: 73:[72, 43] Operation: 47-4=43 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[72, 51], Operations: ['6*12=72', '4+47=51'] Exploring Operation: 72*51=3672, Resulting Numbers: [3672] 3672,73 unequal: No Solution Exploring Operation: 72+51=123, Resulting Numbers: [123] 123,73 unequal: No Solution Exploring Operation: 72-51=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 #0,1,0 Current State: 73:[47, 76], Operations: ['6*12=72', '4+72=76'] Exploring Operation: 76-47=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 47+76=123, Resulting Numbers: [123] 123,73 unequal: No Solution Exploring Operation: 47*76=3572, Resulting Numbers: [3572] 3572,73 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 #0,1,2 Current State: 73:[72, 43], Operations: ['6*12=72', '47-4=43'] Exploring Operation: 72*43=3096, Resulting Numbers: [3096] 3096,73 unequal: No Solution Exploring Operation: 72+43=115, Resulting Numbers: [115] 115,73 unequal: No Solution Exploring Operation: 72-43=29, Resulting Numbers: [29] 29,73 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: 73:[6, 47, 48], Operations: ['4*12=48'] Exploring Operation: 6+48=54, Resulting Numbers: [47, 54] Generated Node #0,2,0: 73:[47, 54] Operation: 6+48=54 Exploring Operation: 6+47=53, Resulting Numbers: [48, 53] Generated Node #0,2,1: 73:[48, 53] Operation: 6+47=53 Exploring Operation: 47-6=41, Resulting Numbers: [48, 41] Generated Node #0,2,2: 73:[48, 41] Operation: 47-6=41 Moving to Node #0,0 Current State: 73:[12, 47, 24], Operations: ['6*4=24'] Exploring Operation: 12+47=59, Resulting Numbers: [24, 59] Generated Node #0,0,0: 73:[24, 59] Operation: 12+47=59 Exploring Operation: 12+24=36, Resulting Numbers: [47, 36] Generated Node #0,0,1: 73:[47, 36] Operation: 12+24=36 Exploring Operation: 47+24=71, Resulting Numbers: [12, 71] Generated Node #0,0,2: 73:[12, 71] Operation: 47+24=71 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[24, 59], Operations: ['6*4=24', '12+47=59'] Exploring Operation: 24+59=83, Resulting Numbers: [83] 83,73 unequal: No Solution Exploring Operation: 59-24=35, Resulting Numbers: [35] 35,73 unequal: No Solution Exploring Operation: 24*59=1416, Resulting Numbers: [1416] 1416,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[47, 36], Operations: ['6*4=24', '12+24=36'] Exploring Operation: 47*36=1692, Resulting Numbers: [1692] 1692,73 unequal: No Solution Exploring Operation: 47+36=83, Resulting Numbers: [83] 83,73 unequal: No Solution Exploring Operation: 47-36=11, Resulting Numbers: [11] 11,73 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:[12, 71], Operations: ['6*4=24', '47+24=71'] Exploring Operation: 71-12=59, Resulting Numbers: [59] 59,73 unequal: No Solution Exploring Operation: 12+71=83, Resulting Numbers: [83] 83,73 unequal: No Solution Exploring Operation: 12*71=852, Resulting Numbers: [852] 852,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 73:[47, 54], Operations: ['4*12=48', '6+48=54'] Exploring Operation: 47+54=101, Resulting Numbers: [101] 101,73 unequal: No Solution Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,73 unequal: No Solution Exploring Operation: 47*54=2538, Resulting Numbers: [2538] 2538,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[48, 53], Operations: ['4*12=48', '6+47=53'] Exploring Operation: 48*53=2544, Resulting Numbers: [2544] 2544,73 unequal: No Solution Exploring Operation: 48+53=101, Resulting Numbers: [101] 101,73 unequal: No Solution Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[48, 41], Operations: ['4*12=48', '47-6=41'] Exploring Operation: 48+41=89, Resulting Numbers: [89] 89,73 unequal: No Solution Exploring Operation: 48-41=7, Resulting Numbers: [7] 7,73 unequal: No Solution Exploring Operation: 48*41=1968, Resulting Numbers: [1968] 1968,73 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 18, 2, 71, 73 ]
38
[ "18*2=36", "73-71=2", "36+2=38" ]
Current State: 38:[18, 2, 71, 73], Operations: [] Exploring Operation: 18*2=36, Resulting Numbers: [71, 73, 36] Generated Node #2: [71, 73, 36] from Operation: 18*2=36 Current State: 38:[71, 73, 36], Operations: ['18*2=36'] Exploring Operation: 73-71=2, Resulting Numbers: [36, 2] Generated Node #3: [36, 2] from Operation: 73-71=2 Current State: 38:[36, 2], Operations: ['18*2=36', '73-71=2'] Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[18, 2, 71, 73], Operations: [] Exploring Operation: 73-71=2, Resulting Numbers: [18, 2, 2] Generated Node #0,0: 38:[18, 2, 2] Operation: 73-71=2 Moving to Node #0,0 Current State: 38:[18, 2, 2], Operations: ['73-71=2'] Exploring Operation: 18+2=20, Resulting Numbers: [2, 20] Generated Node #0,0,0: 38:[2, 20] Operation: 18+2=20 Moving to Node #0,0,0 Current State: 38:[2, 20], Operations: ['73-71=2', '18+2=20'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,38 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 66, 34, 78, 33 ]
56
[ "66/33=2", "34+78=112", "112/2=56" ]
Current State: 56:[66, 34, 78, 33], Operations: [] Exploring Operation: 66/33=2, Resulting Numbers: [34, 78, 2] Generated Node #2: [34, 78, 2] from Operation: 66/33=2 Current State: 56:[34, 78, 2], Operations: ['66/33=2'] Exploring Operation: 34+78=112, Resulting Numbers: [2, 112] Generated Node #3: [2, 112] from Operation: 34+78=112 Current State: 56:[2, 112], Operations: ['66/33=2', '34+78=112'] Exploring Operation: 112/2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[66, 34, 78, 33], Operations: [] Exploring Operation: 78-66=12, Resulting Numbers: [34, 33, 12] Generated Node #0,0: 56:[34, 33, 12] Operation: 78-66=12 Exploring Operation: 78-34=44, Resulting Numbers: [66, 33, 44] Generated Node #0,1: 56:[66, 33, 44] Operation: 78-34=44 Exploring Operation: 78-33=45, Resulting Numbers: [66, 34, 45] Generated Node #0,2: 56:[66, 34, 45] Operation: 78-33=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[34, 33, 12], Operations: ['78-66=12'] Exploring Operation: 34+33=67, Resulting Numbers: [12, 67] Generated Node #0,0,0: 56:[12, 67] Operation: 34+33=67 Exploring Operation: 34-12=22, Resulting Numbers: [33, 22] Generated Node #0,0,1: 56:[33, 22] Operation: 34-12=22 Exploring Operation: 34-33=1, Resulting Numbers: [12, 1] Generated Node #0,0,2: 56:[12, 1] Operation: 34-33=1 Moving to Node #0,0,2 Current State: 56:[12, 1], Operations: ['78-66=12', '34-33=1'] Exploring Operation: 12+1=13, Resulting Numbers: [13] 13,56 unequal: No Solution Exploring Operation: 12*1=12, Resulting Numbers: [12] 12,56 unequal: No Solution Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[33, 22], Operations: ['78-66=12', '34-12=22'] Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,56 unequal: No Solution Exploring Operation: 33+22=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 33*22=726, Resulting Numbers: [726] 726,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[12, 67], Operations: ['78-66=12', '34+33=67'] Exploring Operation: 12+67=79, Resulting Numbers: [79] 79,56 unequal: No Solution Exploring Operation: 67-12=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 12*67=804, Resulting Numbers: [804] 804,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[66, 33, 44], Operations: ['78-34=44'] Exploring Operation: 66-44=22, Resulting Numbers: [33, 22] Generated Node #0,1,0: 56:[33, 22] Operation: 66-44=22 Exploring Operation: 66/33=2, Resulting Numbers: [44, 2] Generated Node #0,1,1: 56:[44, 2] Operation: 66/33=2 Exploring Operation: 44-33=11, Resulting Numbers: [66, 11] Generated Node #0,1,2: 56:[66, 11] Operation: 44-33=11 Moving to Node #0,1,0 Current State: 56:[33, 22], Operations: ['78-34=44', '66-44=22'] Exploring Operation: 33+22=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 33*22=726, Resulting Numbers: [726] 726,56 unequal: No Solution Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[44, 2], Operations: ['78-34=44', '66/33=2'] Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,56 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,56 unequal: No Solution Moving to Node #0,1,2 Current State: 56:[66, 11], Operations: ['78-34=44', '44-33=11'] Exploring Operation: 66/11=6, Resulting Numbers: [6] 6,56 unequal: No Solution Exploring Operation: 66+11=77, Resulting Numbers: [77] 77,56 unequal: No Solution Exploring Operation: 66-11=55, Resulting Numbers: [55] 55,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[66, 34, 45], Operations: ['78-33=45'] Exploring Operation: 45-34=11, Resulting Numbers: [66, 11] Generated Node #0,2,0: 56:[66, 11] Operation: 45-34=11 Exploring Operation: 66-34=32, Resulting Numbers: [45, 32] Generated Node #0,2,1: 56:[45, 32] Operation: 66-34=32 Exploring Operation: 66-45=21, Resulting Numbers: [34, 21] Generated Node #0,2,2: 56:[34, 21] Operation: 66-45=21 Moving to Node #0,2,0 Current State: 56:[66, 11], Operations: ['78-33=45', '45-34=11'] Exploring Operation: 66-11=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 66/11=6, Resulting Numbers: [6] 6,56 unequal: No Solution Exploring Operation: 66+11=77, Resulting Numbers: [77] 77,56 unequal: No Solution Moving to Node #0,2,2 Current State: 56:[34, 21], Operations: ['78-33=45', '66-45=21'] Exploring Operation: 34+21=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 34*21=714, Resulting Numbers: [714] 714,56 unequal: No Solution Exploring Operation: 34-21=13, Resulting Numbers: [13] 13,56 unequal: No Solution Moving to Node #0,2,1 Current State: 56:[45, 32], Operations: ['78-33=45', '66-34=32'] Exploring Operation: 45-32=13, Resulting Numbers: [13] 13,56 unequal: No Solution Exploring Operation: 45*32=1440, Resulting Numbers: [1440] 1440,56 unequal: No Solution Exploring Operation: 45+32=77, Resulting Numbers: [77] 77,56 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
[ 87, 59, 70, 97 ]
21
[ "87+59=146", "70+97=167", "167-146=21" ]
Current State: 21:[87, 59, 70, 97], Operations: [] Exploring Operation: 87+59=146, Resulting Numbers: [70, 97, 146] Generated Node #2: [70, 97, 146] from Operation: 87+59=146 Current State: 21:[70, 97, 146], Operations: ['87+59=146'] Exploring Operation: 70+97=167, Resulting Numbers: [146, 167] Generated Node #3: [146, 167] from Operation: 70+97=167 Current State: 21:[146, 167], Operations: ['87+59=146', '70+97=167'] Exploring Operation: 167-146=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[87, 59, 70, 97], Operations: [] Exploring Operation: 97-87=10, Resulting Numbers: [59, 70, 10] Generated Node #0,0: 21:[59, 70, 10] Operation: 97-87=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[59, 70, 10], Operations: ['97-87=10'] Exploring Operation: 70-59=11, Resulting Numbers: [10, 11] Generated Node #0,0,0: 21:[10, 11] Operation: 70-59=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[10, 11], Operations: ['97-87=10', '70-59=11'] Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[87, 59, 70, 97], Operations: [] Exploring Operation: 97-87=10, Resulting Numbers: [59, 70, 10] Generated Node #0,0: 21:[59, 70, 10] Operation: 97-87=10 Moving to Node #0,0 Current State: 21:[59, 70, 10], Operations: ['97-87=10'] Exploring Operation: 70-59=11, Resulting Numbers: [10, 11] Generated Node #0,0,0: 21:[10, 11] Operation: 70-59=11 Moving to Node #0,0,0 Current State: 21:[10, 11], Operations: ['97-87=10', '70-59=11'] Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 11, 39, 19, 35 ]
32
[ "19-11=8", "39-35=4", "8*4=32" ]
Current State: 32:[11, 39, 19, 35], Operations: [] Exploring Operation: 19-11=8, Resulting Numbers: [39, 35, 8] Generated Node #2: [39, 35, 8] from Operation: 19-11=8 Current State: 32:[39, 35, 8], Operations: ['19-11=8'] Exploring Operation: 39-35=4, Resulting Numbers: [8, 4] Generated Node #3: [8, 4] from Operation: 39-35=4 Current State: 32:[8, 4], Operations: ['19-11=8', '39-35=4'] Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[11, 39, 19, 35], Operations: [] Exploring Operation: 39-11=28, Resulting Numbers: [19, 35, 28] Generated Node #0,0: 32:[19, 35, 28] Operation: 39-11=28 Exploring Operation: 19-11=8, Resulting Numbers: [39, 35, 8] Generated Node #0,1: 32:[39, 35, 8] Operation: 19-11=8 Exploring Operation: 39-35=4, Resulting Numbers: [11, 19, 4] Generated Node #0,2: 32:[11, 19, 4] Operation: 39-35=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[11, 19, 4], Operations: ['39-35=4'] Exploring Operation: 11+19=30, Resulting Numbers: [4, 30] Generated Node #0,2,0: 32:[4, 30] Operation: 11+19=30 Exploring Operation: 19-11=8, Resulting Numbers: [4, 8] Generated Node #0,2,1: 32:[4, 8] Operation: 19-11=8 Exploring Operation: 11+4=15, Resulting Numbers: [19, 15] Generated Node #0,2,2: 32:[19, 15] Operation: 11+4=15 Moving to Node #0,2,1 Current State: 32:[4, 8], Operations: ['39-35=4', '19-11=8'] Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[11, 39, 19, 35], Operations: [] Exploring Operation: 39-35=4, Resulting Numbers: [11, 19, 4] Generated Node #0,2: 32:[11, 19, 4] Operation: 39-35=4 Moving to Node #0,2 Current State: 32:[11, 19, 4], Operations: ['39-35=4'] Exploring Operation: 19-11=8, Resulting Numbers: [4, 8] Generated Node #0,2,1: 32:[4, 8] Operation: 19-11=8 Moving to Node #0,2,1 Current State: 32:[4, 8], Operations: ['39-35=4', '19-11=8'] Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 39, 36, 87, 29 ]
25
[ "39+36=75", "87/29=3", "75/3=25" ]
Current State: 25:[39, 36, 87, 29], Operations: [] Exploring Operation: 39+36=75, Resulting Numbers: [87, 29, 75] Generated Node #2: [87, 29, 75] from Operation: 39+36=75 Current State: 25:[87, 29, 75], Operations: ['39+36=75'] Exploring Operation: 87/29=3, Resulting Numbers: [75, 3] Generated Node #3: [75, 3] from Operation: 87/29=3 Current State: 25:[75, 3], Operations: ['39+36=75', '87/29=3'] Exploring Operation: 75/3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[39, 36, 87, 29], Operations: [] Exploring Operation: 87-36=51, Resulting Numbers: [39, 29, 51] Generated Node #0,0: 25:[39, 29, 51] Operation: 87-36=51 Exploring Operation: 87/29=3, Resulting Numbers: [39, 36, 3] Generated Node #0,1: 25:[39, 36, 3] Operation: 87/29=3 Exploring Operation: 87-29=58, Resulting Numbers: [39, 36, 58] Generated Node #0,2: 25:[39, 36, 58] Operation: 87-29=58 Exploring Operation: 87-39=48, Resulting Numbers: [36, 29, 48] Generated Node #0,3: 25:[36, 29, 48] Operation: 87-39=48 Moving to Node #0,1 Current State: 25:[39, 36, 3], Operations: ['87/29=3'] Exploring Operation: 39-36=3, Resulting Numbers: [3, 3] Generated Node #0,1,0: 25:[3, 3] Operation: 39-36=3 Exploring Operation: 39-3=36, Resulting Numbers: [36, 36] Generated Node #0,1,1: 25:[36, 36] Operation: 39-3=36 Exploring Operation: 36/3=12, Resulting Numbers: [39, 12] Generated Node #0,1,2: 25:[39, 12] Operation: 36/3=12 Exploring Operation: 39/3=13, Resulting Numbers: [36, 13] Generated Node #0,1,3: 25:[36, 13] Operation: 39/3=13 Moving to Node #0,3 Current State: 25:[36, 29, 48], Operations: ['87-39=48'] Exploring Operation: 48-29=19, Resulting Numbers: [36, 19] Generated Node #0,3,0: 25:[36, 19] Operation: 48-29=19 Exploring Operation: 36-29=7, Resulting Numbers: [48, 7] Generated Node #0,3,1: 25:[48, 7] Operation: 36-29=7 Exploring Operation: 36+29=65, Resulting Numbers: [48, 65] Generated Node #0,3,2: 25:[48, 65] Operation: 36+29=65 Exploring Operation: 48-36=12, Resulting Numbers: [29, 12] Generated Node #0,3,3: 25:[29, 12] Operation: 48-36=12 Moving to Node #0,0 Current State: 25:[39, 29, 51], Operations: ['87-36=51'] Exploring Operation: 39-29=10, Resulting Numbers: [51, 10] Generated Node #0,0,0: 25:[51, 10] Operation: 39-29=10 Exploring Operation: 39+29=68, Resulting Numbers: [51, 68] Generated Node #0,0,1: 25:[51, 68] Operation: 39+29=68 Exploring Operation: 51-39=12, Resulting Numbers: [29, 12] Generated Node #0,0,2: 25:[29, 12] Operation: 51-39=12 Exploring Operation: 51-29=22, Resulting Numbers: [39, 22] Generated Node #0,0,3: 25:[39, 22] Operation: 51-29=22 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 25:[29, 12], Operations: ['87-36=51', '51-39=12'] Exploring Operation: 29*12=348, Resulting Numbers: [348] 348,25 unequal: No Solution Exploring Operation: 29+12=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 25:[39, 22], Operations: ['87-36=51', '51-29=22'] Exploring Operation: 39-22=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 39*22=858, Resulting Numbers: [858] 858,25 unequal: No Solution Exploring Operation: 39+22=61, Resulting Numbers: [61] 61,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[51, 10], Operations: ['87-36=51', '39-29=10'] Exploring Operation: 51-10=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 51*10=510, Resulting Numbers: [510] 510,25 unequal: No Solution Exploring Operation: 51+10=61, Resulting Numbers: [61] 61,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 25:[51, 68], Operations: ['87-36=51', '39+29=68'] Exploring Operation: 68-51=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 51+68=119, Resulting Numbers: [119] 119,25 unequal: No Solution Exploring Operation: 51*68=3468, Resulting Numbers: [3468] 3468,25 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: 25:[39, 36, 58], Operations: ['87-29=58'] Exploring Operation: 39+36=75, Resulting Numbers: [58, 75] Generated Node #0,2,0: 25:[58, 75] Operation: 39+36=75 Exploring Operation: 58-39=19, Resulting Numbers: [36, 19] Generated Node #0,2,1: 25:[36, 19] Operation: 58-39=19 Exploring Operation: 39-36=3, Resulting Numbers: [58, 3] Generated Node #0,2,2: 25:[58, 3] Operation: 39-36=3 Exploring Operation: 58-36=22, Resulting Numbers: [39, 22] Generated Node #0,2,3: 25:[39, 22] Operation: 58-36=22 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 25:[36, 19], Operations: ['87-29=58', '58-39=19'] Exploring Operation: 36*19=684, Resulting Numbers: [684] 684,25 unequal: No Solution Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,25 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 25:[39, 22], Operations: ['87-29=58', '58-36=22'] Exploring Operation: 39+22=61, Resulting Numbers: [61] 61,25 unequal: No Solution Exploring Operation: 39*22=858, Resulting Numbers: [858] 858,25 unequal: No Solution Exploring Operation: 39-22=17, Resulting Numbers: [17] 17,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 25:[58, 3], Operations: ['87-29=58', '39-36=3'] Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,25 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,25 unequal: No Solution Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 25:[58, 75], Operations: ['87-29=58', '39+36=75'] Exploring Operation: 58*75=4350, Resulting Numbers: [4350] 4350,25 unequal: No Solution Exploring Operation: 58+75=133, Resulting Numbers: [133] 133,25 unequal: No Solution Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,25 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: 25:[3, 3], Operations: ['87/29=3', '39-36=3'] Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,25 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,25 unequal: No Solution Moving to Node #0,3,3 Current State: 25:[29, 12], Operations: ['87-39=48', '48-36=12'] Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 29*12=348, Resulting Numbers: [348] 348,25 unequal: No Solution Exploring Operation: 29+12=41, Resulting Numbers: [41] 41,25 unequal: No Solution Moving to Node #0,3,0 Current State: 25:[36, 19], Operations: ['87-39=48', '48-29=19'] Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,25 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 36*19=684, Resulting Numbers: [684] 684,25 unequal: No Solution Moving to Node #0,1,3 Current State: 25:[36, 13], Operations: ['87/29=3', '39/3=13'] Exploring Operation: 36*13=468, Resulting Numbers: [468] 468,25 unequal: No Solution Exploring Operation: 36+13=49, Resulting Numbers: [49] 49,25 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,25 unequal: No Solution Moving to Node #0,1,2 Current State: 25:[39, 12], Operations: ['87/29=3', '36/3=12'] Exploring Operation: 39-12=27, Resulting Numbers: [27] 27,25 unequal: No Solution Exploring Operation: 39*12=468, Resulting Numbers: [468] 468,25 unequal: No Solution Exploring Operation: 39+12=51, Resulting Numbers: [51] 51,25 unequal: No Solution Moving to Node #0,1,1 Current State: 25:[36, 36], Operations: ['87/29=3', '39-3=36'] Exploring Operation: 36+36=72, Resulting Numbers: [72] 72,25 unequal: No Solution Exploring Operation: 36/36=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 36-36=0, Resulting Numbers: [0] 0,25 unequal: No Solution Exploring Operation: 36*36=1296, Resulting Numbers: [1296] 1296,25 unequal: No Solution Moving to Node #0,3,1 Current State: 25:[48, 7], Operations: ['87-39=48', '36-29=7'] Exploring Operation: 48+7=55, Resulting Numbers: [55] 55,25 unequal: No Solution Exploring Operation: 48*7=336, Resulting Numbers: [336] 336,25 unequal: No Solution Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,25 unequal: No Solution Moving to Node #0,3,2 Current State: 25:[48, 65], Operations: ['87-39=48', '36+29=65'] Exploring Operation: 48*65=3120, Resulting Numbers: [3120] 3120,25 unequal: No Solution Exploring Operation: 65-48=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 48+65=113, Resulting Numbers: [113] 113,25 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 9, 70, 6, 65 ]
40
[ "9*70=630", "630/6=105", "105-65=40" ]
Current State: 40:[9, 70, 6, 65], Operations: [] Exploring Operation: 9*70=630, Resulting Numbers: [6, 65, 630] Generated Node #2: [6, 65, 630] from Operation: 9*70=630 Current State: 40:[6, 65, 630], Operations: ['9*70=630'] Exploring Operation: 630/6=105, Resulting Numbers: [65, 105] Generated Node #3: [65, 105] from Operation: 630/6=105 Current State: 40:[65, 105], Operations: ['9*70=630', '630/6=105'] Exploring Operation: 105-65=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[9, 70, 6, 65], Operations: [] Exploring Operation: 70-65=5, Resulting Numbers: [9, 6, 5] Generated Node #0,0: 40:[9, 6, 5] Operation: 70-65=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[9, 6, 5], Operations: ['70-65=5'] Exploring Operation: 9-6=3, Resulting Numbers: [5, 3] Generated Node #0,0,0: 40:[5, 3] Operation: 9-6=3 Moving to Node #0,0,0 Current State: 40:[5, 3], Operations: ['70-65=5', '9-6=3'] Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,40 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
[ 98, 26, 44, 23 ]
46
[ "26+23=49", "98/49=2", "44+2=46" ]
Current State: 46:[98, 26, 44, 23], Operations: [] Exploring Operation: 26+23=49, Resulting Numbers: [98, 44, 49] Generated Node #2: [98, 44, 49] from Operation: 26+23=49 Current State: 46:[98, 44, 49], Operations: ['26+23=49'] Exploring Operation: 98/49=2, Resulting Numbers: [44, 2] Generated Node #3: [44, 2] from Operation: 98/49=2 Current State: 46:[44, 2], Operations: ['26+23=49', '98/49=2'] Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[98, 26, 44, 23], Operations: [] Exploring Operation: 98-23=75, Resulting Numbers: [26, 44, 75] Generated Node #0,0: 46:[26, 44, 75] Operation: 98-23=75 Exploring Operation: 98-44=54, Resulting Numbers: [26, 23, 54] Generated Node #0,1: 46:[26, 23, 54] Operation: 98-44=54 Exploring Operation: 98-26=72, Resulting Numbers: [44, 23, 72] Generated Node #0,2: 46:[44, 23, 72] Operation: 98-26=72 Moving to Node #0,1 Current State: 46:[26, 23, 54], Operations: ['98-44=54'] Exploring Operation: 54-26=28, Resulting Numbers: [23, 28] Generated Node #0,1,0: 46:[23, 28] Operation: 54-26=28 Exploring Operation: 26-23=3, Resulting Numbers: [54, 3] Generated Node #0,1,1: 46:[54, 3] Operation: 26-23=3 Exploring Operation: 26+23=49, Resulting Numbers: [54, 49] Generated Node #0,1,2: 46:[54, 49] Operation: 26+23=49 Moving to Node #0,2 Current State: 46:[44, 23, 72], Operations: ['98-26=72'] Exploring Operation: 72-44=28, Resulting Numbers: [23, 28] Generated Node #0,2,0: 46:[23, 28] Operation: 72-44=28 Exploring Operation: 72-23=49, Resulting Numbers: [44, 49] Generated Node #0,2,1: 46:[44, 49] Operation: 72-23=49 Exploring Operation: 44-23=21, Resulting Numbers: [72, 21] Generated Node #0,2,2: 46:[72, 21] Operation: 44-23=21 Moving to Node #0,0 Current State: 46:[26, 44, 75], Operations: ['98-23=75'] Exploring Operation: 75-26=49, Resulting Numbers: [44, 49] Generated Node #0,0,0: 46:[44, 49] Operation: 75-26=49 Exploring Operation: 44-26=18, Resulting Numbers: [75, 18] Generated Node #0,0,1: 46:[75, 18] Operation: 44-26=18 Exploring Operation: 75-44=31, Resulting Numbers: [26, 31] Generated Node #0,0,2: 46:[26, 31] Operation: 75-44=31 Moving to Node #0,1,0 Current State: 46:[23, 28], Operations: ['98-44=54', '54-26=28'] Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 23*28=644, Resulting Numbers: [644] 644,46 unequal: No Solution Exploring Operation: 23+28=51, Resulting Numbers: [51] 51,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[44, 49], Operations: ['98-23=75', '75-26=49'] Exploring Operation: 44*49=2156, Resulting Numbers: [2156] 2156,46 unequal: No Solution Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 44+49=93, Resulting Numbers: [93] 93,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[23, 28], Operations: ['98-26=72', '72-44=28'] Exploring Operation: 23*28=644, Resulting Numbers: [644] 644,46 unequal: No Solution Exploring Operation: 23+28=51, Resulting Numbers: [51] 51,46 unequal: No Solution Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[44, 49], Operations: ['98-26=72', '72-23=49'] Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 44*49=2156, Resulting Numbers: [2156] 2156,46 unequal: No Solution Exploring Operation: 44+49=93, Resulting Numbers: [93] 93,46 unequal: No Solution Moving to Node #0,1,1 Current State: 46:[54, 3], Operations: ['98-44=54', '26-23=3'] Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,46 unequal: No Solution Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,46 unequal: No Solution Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,46 unequal: No Solution Moving to Node #0,1,2 Current State: 46:[54, 49], Operations: ['98-44=54', '26+23=49'] Exploring Operation: 54*49=2646, Resulting Numbers: [2646] 2646,46 unequal: No Solution Exploring Operation: 54+49=103, Resulting Numbers: [103] 103,46 unequal: No Solution Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[26, 31], Operations: ['98-23=75', '75-44=31'] Exploring Operation: 26*31=806, Resulting Numbers: [806] 806,46 unequal: No Solution Exploring Operation: 31-26=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 26+31=57, Resulting Numbers: [57] 57,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[72, 21], Operations: ['98-26=72', '44-23=21'] Exploring Operation: 72-21=51, Resulting Numbers: [51] 51,46 unequal: No Solution Exploring Operation: 72*21=1512, Resulting Numbers: [1512] 1512,46 unequal: No Solution Exploring Operation: 72+21=93, Resulting Numbers: [93] 93,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[75, 18], Operations: ['98-23=75', '44-26=18'] Exploring Operation: 75+18=93, Resulting Numbers: [93] 93,46 unequal: No Solution Exploring Operation: 75-18=57, Resulting Numbers: [57] 57,46 unequal: No Solution Exploring Operation: 75*18=1350, Resulting Numbers: [1350] 1350,46 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 77, 24, 94, 66 ]
66
[ "77*24=1848", "94-66=28", "1848/28=66" ]
Current State: 66:[77, 24, 94, 66], Operations: [] Exploring Operation: 77*24=1848, Resulting Numbers: [94, 66, 1848] Generated Node #2: [94, 66, 1848] from Operation: 77*24=1848 Current State: 66:[94, 66, 1848], Operations: ['77*24=1848'] Exploring Operation: 94-66=28, Resulting Numbers: [1848, 28] Generated Node #3: [1848, 28] from Operation: 94-66=28 Current State: 66:[1848, 28], Operations: ['77*24=1848', '94-66=28'] Exploring Operation: 1848/28=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[77, 24, 94, 66], Operations: [] Exploring Operation: 94-77=17, Resulting Numbers: [24, 66, 17] Generated Node #0,0: 66:[24, 66, 17] Operation: 94-77=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[24, 66, 17], Operations: ['94-77=17'] Exploring Operation: 24-17=7, Resulting Numbers: [66, 7] Generated Node #0,0,0: 66:[66, 7] Operation: 24-17=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 66:[66, 7], Operations: ['94-77=17', '24-17=7'] Exploring Operation: 66+7=73, Resulting Numbers: [73] 73,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 76, 74, 34, 17 ]
68
[ "76-74=2", "17*2=34", "34+34=68" ]
Current State: 68:[76, 74, 34, 17], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [34, 17, 2] Generated Node #2: [34, 17, 2] from Operation: 76-74=2 Current State: 68:[34, 17, 2], Operations: ['76-74=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34, 34] Generated Node #3: [34, 34] from Operation: 17*2=34 Current State: 68:[34, 34], Operations: ['76-74=2', '17*2=34'] Exploring Operation: 34+34=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[76, 74, 34, 17], Operations: [] Exploring Operation: 76-34=42, Resulting Numbers: [74, 17, 42] Generated Node #0,0: 68:[74, 17, 42] Operation: 76-34=42 Exploring Operation: 76-74=2, Resulting Numbers: [34, 17, 2] Generated Node #0,1: 68:[34, 17, 2] Operation: 76-74=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[34, 17, 2], Operations: ['76-74=2'] Exploring Operation: 34-17=17, Resulting Numbers: [2, 17] Generated Node #0,1,0: 68:[2, 17] Operation: 34-17=17 Exploring Operation: 34/17=2, Resulting Numbers: [2, 2] Generated Node #0,1,1: 68:[2, 2] Operation: 34/17=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 68:[2, 17], Operations: ['76-74=2', '34-17=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,68 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,68 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 #0,1,1 Current State: 68:[2, 2], Operations: ['76-74=2', '34/17=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,68 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,68 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 #0,0 Current State: 68:[74, 17, 42], Operations: ['76-34=42'] Exploring Operation: 42-17=25, Resulting Numbers: [74, 25] Generated Node #0,0,0: 68:[74, 25] Operation: 42-17=25 Exploring Operation: 74-42=32, Resulting Numbers: [17, 32] Generated Node #0,0,1: 68:[17, 32] Operation: 74-42=32 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 68:[17, 32], Operations: ['76-34=42', '74-42=32'] Exploring Operation: 17+32=49, Resulting Numbers: [49] 49,68 unequal: No Solution Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,68 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:[74, 25], Operations: ['76-34=42', '42-17=25'] Exploring Operation: 74-25=49, Resulting Numbers: [49] 49,68 unequal: No Solution Exploring Operation: 74+25=99, Resulting Numbers: [99] 99,68 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 No solution found.
0
hs_2
mult_heuristic
[ 55, 35, 28, 41 ]
77
[ "55+35=90", "41-28=13", "90-13=77" ]
Current State: 77:[55, 35, 28, 41], Operations: [] Exploring Operation: 55+35=90, Resulting Numbers: [28, 41, 90] Generated Node #2: [28, 41, 90] from Operation: 55+35=90 Current State: 77:[28, 41, 90], Operations: ['55+35=90'] Exploring Operation: 41-28=13, Resulting Numbers: [90, 13] Generated Node #3: [90, 13] from Operation: 41-28=13 Current State: 77:[90, 13], Operations: ['55+35=90', '41-28=13'] Exploring Operation: 90-13=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[55, 35, 28, 41], Operations: [] Exploring Operation: 41-28=13, Resulting Numbers: [55, 35, 13] Generated Node #0,0: 77:[55, 35, 13] Operation: 41-28=13 Exploring Operation: 35+41=76, Resulting Numbers: [55, 28, 76] Generated Node #0,1: 77:[55, 28, 76] Operation: 35+41=76 Exploring Operation: 55-41=14, Resulting Numbers: [35, 28, 14] Generated Node #0,2: 77:[35, 28, 14] Operation: 55-41=14 Exploring Operation: 41-35=6, Resulting Numbers: [55, 28, 6] Generated Node #0,3: 77:[55, 28, 6] Operation: 41-35=6 Moving to Node #0,1 Current State: 77:[55, 28, 76], Operations: ['35+41=76'] Exploring Operation: 28+76=104, Resulting Numbers: [55, 104] Generated Node #0,1,0: 77:[55, 104] Operation: 28+76=104 Exploring Operation: 55+28=83, Resulting Numbers: [76, 83] Generated Node #0,1,1: 77:[76, 83] Operation: 55+28=83 Exploring Operation: 76-55=21, Resulting Numbers: [28, 21] Generated Node #0,1,2: 77:[28, 21] Operation: 76-55=21 Exploring Operation: 55-28=27, Resulting Numbers: [76, 27] Generated Node #0,1,3: 77:[76, 27] Operation: 55-28=27 Moving to Node #0,3 Current State: 77:[55, 28, 6], Operations: ['41-35=6'] Exploring Operation: 28-6=22, Resulting Numbers: [55, 22] Generated Node #0,3,0: 77:[55, 22] Operation: 28-6=22 Exploring Operation: 55+28=83, Resulting Numbers: [6, 83] Generated Node #0,3,1: 77:[6, 83] Operation: 55+28=83 Exploring Operation: 55-28=27, Resulting Numbers: [6, 27] Generated Node #0,3,2: 77:[6, 27] Operation: 55-28=27 Exploring Operation: 55+6=61, Resulting Numbers: [28, 61] Generated Node #0,3,3: 77:[28, 61] Operation: 55+6=61 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 77:[6, 83], Operations: ['41-35=6', '55+28=83'] Exploring Operation: 6+83=89, Resulting Numbers: [89] 89,77 unequal: No Solution Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[55, 35, 28, 41], Operations: [] Exploring Operation: 41-35=6, Resulting Numbers: [55, 28, 6] Generated Node #0,3: 77:[55, 28, 6] Operation: 41-35=6 Moving to Node #0,3 Current State: 77:[55, 28, 6], Operations: ['41-35=6'] Exploring Operation: 55+28=83, Resulting Numbers: [6, 83] Generated Node #0,3,1: 77:[6, 83] Operation: 55+28=83 Moving to Node #0,3,1 Current State: 77:[6, 83], Operations: ['41-35=6', '55+28=83'] Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 13, 97, 42, 50 ]
52
[ "97-13=84", "84/42=2", "50+2=52" ]
Current State: 52:[13, 97, 42, 50], Operations: [] Exploring Operation: 97-13=84, Resulting Numbers: [42, 50, 84] Generated Node #2: [42, 50, 84] from Operation: 97-13=84 Current State: 52:[42, 50, 84], Operations: ['97-13=84'] Exploring Operation: 84/42=2, Resulting Numbers: [50, 2] Generated Node #3: [50, 2] from Operation: 84/42=2 Current State: 52:[50, 2], Operations: ['97-13=84', '84/42=2'] Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[13, 97, 42, 50], Operations: [] Exploring Operation: 97-42=55, Resulting Numbers: [13, 50, 55] Generated Node #0,0: 52:[13, 50, 55] Operation: 97-42=55 Exploring Operation: 97-50=47, Resulting Numbers: [13, 42, 47] Generated Node #0,1: 52:[13, 42, 47] Operation: 97-50=47 Exploring Operation: 97-13=84, Resulting Numbers: [42, 50, 84] Generated Node #0,2: 52:[42, 50, 84] Operation: 97-13=84 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[13, 50, 55], Operations: ['97-42=55'] Exploring Operation: 55-13=42, Resulting Numbers: [50, 42] Generated Node #0,0,0: 52:[50, 42] Operation: 55-13=42 Exploring Operation: 55-50=5, Resulting Numbers: [13, 5] Generated Node #0,0,1: 52:[13, 5] Operation: 55-50=5 Exploring Operation: 13+50=63, Resulting Numbers: [55, 63] Generated Node #0,0,2: 52:[55, 63] Operation: 13+50=63 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[13, 5], Operations: ['97-42=55', '55-50=5'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,52 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[50, 42], Operations: ['97-42=55', '55-13=42'] Exploring Operation: 50*42=2100, Resulting Numbers: [2100] 2100,52 unequal: No Solution Exploring Operation: 50+42=92, Resulting Numbers: [92] 92,52 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 52:[55, 63], Operations: ['97-42=55', '13+50=63'] Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 55+63=118, Resulting Numbers: [118] 118,52 unequal: No Solution Exploring Operation: 55*63=3465, Resulting Numbers: [3465] 3465,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[13, 42, 47], Operations: ['97-50=47'] Exploring Operation: 13+42=55, Resulting Numbers: [47, 55] Generated Node #0,1,0: 52:[47, 55] Operation: 13+42=55 Exploring Operation: 47-42=5, Resulting Numbers: [13, 5] Generated Node #0,1,1: 52:[13, 5] Operation: 47-42=5 Exploring Operation: 42-13=29, Resulting Numbers: [47, 29] Generated Node #0,1,2: 52:[47, 29] Operation: 42-13=29 Moving to Node #0,1,1 Current State: 52:[13, 5], Operations: ['97-50=47', '47-42=5'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,52 unequal: No Solution Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,52 unequal: No Solution Moving to Node #0,1,0 Current State: 52:[47, 55], Operations: ['97-50=47', '13+42=55'] Exploring Operation: 47+55=102, Resulting Numbers: [102] 102,52 unequal: No Solution Exploring Operation: 47*55=2585, Resulting Numbers: [2585] 2585,52 unequal: No Solution Exploring Operation: 55-47=8, Resulting Numbers: [8] 8,52 unequal: No Solution Moving to Node #0,1,2 Current State: 52:[47, 29], Operations: ['97-50=47', '42-13=29'] Exploring Operation: 47*29=1363, Resulting Numbers: [1363] 1363,52 unequal: No Solution Exploring Operation: 47-29=18, Resulting Numbers: [18] 18,52 unequal: No Solution Exploring Operation: 47+29=76, Resulting Numbers: [76] 76,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[42, 50, 84], Operations: ['97-13=84'] Exploring Operation: 84/42=2, Resulting Numbers: [50, 2] Generated Node #0,2,0: 52:[50, 2] Operation: 84/42=2 Exploring Operation: 84-50=34, Resulting Numbers: [42, 34] Generated Node #0,2,1: 52:[42, 34] Operation: 84-50=34 Exploring Operation: 84-42=42, Resulting Numbers: [50, 42] Generated Node #0,2,2: 52:[50, 42] Operation: 84-42=42 Moving to Node #0,2,0 Current State: 52:[50, 2], Operations: ['97-13=84', '84/42=2'] Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,52 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,52 unequal: No Solution Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[13, 97, 42, 50], Operations: [] Exploring Operation: 97-13=84, Resulting Numbers: [42, 50, 84] Generated Node #0,2: 52:[42, 50, 84] Operation: 97-13=84 Moving to Node #0,2 Current State: 52:[42, 50, 84], Operations: ['97-13=84'] Exploring Operation: 84/42=2, Resulting Numbers: [50, 2] Generated Node #0,2,0: 52:[50, 2] Operation: 84/42=2 Moving to Node #0,2,0 Current State: 52:[50, 2], Operations: ['97-13=84', '84/42=2'] Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_3
mult_heuristic
[ 46, 66, 64, 88 ]
67
[ "46+88=134", "66-64=2", "134/2=67" ]
Current State: 67:[46, 66, 64, 88], Operations: [] Exploring Operation: 46+88=134, Resulting Numbers: [66, 64, 134] Generated Node #2: [66, 64, 134] from Operation: 46+88=134 Current State: 67:[66, 64, 134], Operations: ['46+88=134'] Exploring Operation: 66-64=2, Resulting Numbers: [134, 2] Generated Node #3: [134, 2] from Operation: 66-64=2 Current State: 67:[134, 2], Operations: ['46+88=134', '66-64=2'] Exploring Operation: 134/2=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[46, 66, 64, 88], Operations: [] Exploring Operation: 88-46=42, Resulting Numbers: [66, 64, 42] Generated Node #0,0: 67:[66, 64, 42] Operation: 88-46=42 Moving to Node #0,0 Current State: 67:[66, 64, 42], Operations: ['88-46=42'] Exploring Operation: 64+42=106, Resulting Numbers: [66, 106] Generated Node #0,0,0: 67:[66, 106] Operation: 64+42=106 Moving to Node #0,0,0 Current State: 67:[66, 106], Operations: ['88-46=42', '64+42=106'] Exploring Operation: 106-66=40, Resulting Numbers: [40] 40,67 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 98, 54, 28, 24 ]
100
[ "98+54=152", "28+24=52", "152-52=100" ]
Current State: 100:[98, 54, 28, 24], Operations: [] Exploring Operation: 98+54=152, Resulting Numbers: [28, 24, 152] Generated Node #2: [28, 24, 152] from Operation: 98+54=152 Current State: 100:[28, 24, 152], Operations: ['98+54=152'] Exploring Operation: 28+24=52, Resulting Numbers: [152, 52] Generated Node #3: [152, 52] from Operation: 28+24=52 Current State: 100:[152, 52], Operations: ['98+54=152', '28+24=52'] Exploring Operation: 152-52=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[98, 54, 28, 24], Operations: [] Exploring Operation: 28+24=52, Resulting Numbers: [98, 54, 52] Generated Node #0,0: 100:[98, 54, 52] Operation: 28+24=52 Exploring Operation: 28-24=4, Resulting Numbers: [98, 54, 4] Generated Node #0,1: 100:[98, 54, 4] Operation: 28-24=4 Exploring Operation: 98-54=44, Resulting Numbers: [28, 24, 44] Generated Node #0,2: 100:[28, 24, 44] Operation: 98-54=44 Exploring Operation: 54-28=26, Resulting Numbers: [98, 24, 26] Generated Node #0,3: 100:[98, 24, 26] Operation: 54-28=26 Exploring Operation: 54-24=30, Resulting Numbers: [98, 28, 30] Generated Node #0,4: 100:[98, 28, 30] Operation: 54-24=30 Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[98, 24, 26], Operations: ['54-28=26'] Exploring Operation: 98+24=122, Resulting Numbers: [26, 122] Generated Node #0,3,0: 100:[26, 122] Operation: 98+24=122 Exploring Operation: 24+26=50, Resulting Numbers: [98, 50] Generated Node #0,3,1: 100:[98, 50] Operation: 24+26=50 Exploring Operation: 26-24=2, Resulting Numbers: [98, 2] Generated Node #0,3,2: 100:[98, 2] Operation: 26-24=2 Exploring Operation: 98-26=72, Resulting Numbers: [24, 72] Generated Node #0,3,3: 100:[24, 72] Operation: 98-26=72 Exploring Operation: 98-24=74, Resulting Numbers: [26, 74] Generated Node #0,3,4: 100:[26, 74] Operation: 98-24=74 Moving to Node #0,3,1 Current State: 100:[98, 50], Operations: ['54-28=26', '24+26=50'] Exploring Operation: 98+50=148, Resulting Numbers: [148] 148,100 unequal: No Solution Exploring Operation: 98*50=4900, Resulting Numbers: [4900] 4900,100 unequal: No Solution Exploring Operation: 98-50=48, Resulting Numbers: [48] 48,100 unequal: No Solution Moving to Node #0,3,2 Current State: 100:[98, 2], Operations: ['54-28=26', '26-24=2'] Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,100 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,100 unequal: No Solution Exploring Operation: 98*2=196, Resulting Numbers: [196] 196,100 unequal: No Solution Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[98, 54, 28, 24], Operations: [] Exploring Operation: 54-28=26, Resulting Numbers: [98, 24, 26] Generated Node #0,3: 100:[98, 24, 26] Operation: 54-28=26 Moving to Node #0,3 Current State: 100:[98, 24, 26], Operations: ['54-28=26'] Exploring Operation: 26-24=2, Resulting Numbers: [98, 2] Generated Node #0,3,2: 100:[98, 2] Operation: 26-24=2 Moving to Node #0,3,2 Current State: 100:[98, 2], Operations: ['54-28=26', '26-24=2'] Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 64, 63, 46, 84 ]
89
[ "64+63=127", "84-46=38", "127-38=89" ]
Current State: 89:[64, 63, 46, 84], Operations: [] Exploring Operation: 64+63=127, Resulting Numbers: [46, 84, 127] Generated Node #2: [46, 84, 127] from Operation: 64+63=127 Current State: 89:[46, 84, 127], Operations: ['64+63=127'] Exploring Operation: 84-46=38, Resulting Numbers: [127, 38] Generated Node #3: [127, 38] from Operation: 84-46=38 Current State: 89:[127, 38], Operations: ['64+63=127', '84-46=38'] Exploring Operation: 127-38=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[64, 63, 46, 84], Operations: [] Exploring Operation: 64+46=110, Resulting Numbers: [63, 84, 110] Generated Node #0,0: 89:[63, 84, 110] Operation: 64+46=110 Exploring Operation: 64+63=127, Resulting Numbers: [46, 84, 127] Generated Node #0,1: 89:[46, 84, 127] Operation: 64+63=127 Exploring Operation: 46+84=130, Resulting Numbers: [64, 63, 130] Generated Node #0,2: 89:[64, 63, 130] Operation: 46+84=130 Exploring Operation: 63+46=109, Resulting Numbers: [64, 84, 109] Generated Node #0,3: 89:[64, 84, 109] Operation: 63+46=109 Start Sub Search at level 1: Moving to Node #0,3 Current State: 89:[64, 84, 109], Operations: ['63+46=109'] Exploring Operation: 64+84=148, Resulting Numbers: [109, 148] Generated Node #0,3,0: 89:[109, 148] Operation: 64+84=148 Exploring Operation: 64+109=173, Resulting Numbers: [84, 173] Generated Node #0,3,1: 89:[84, 173] Operation: 64+109=173 Exploring Operation: 109-64=45, Resulting Numbers: [84, 45] Generated Node #0,3,2: 89:[84, 45] Operation: 109-64=45 Exploring Operation: 84-64=20, Resulting Numbers: [109, 20] Generated Node #0,3,3: 89:[109, 20] Operation: 84-64=20 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 89:[84, 45], Operations: ['63+46=109', '109-64=45'] Exploring Operation: 84-45=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 84+45=129, Resulting Numbers: [129] 129,89 unequal: No Solution Exploring Operation: 84*45=3780, Resulting Numbers: [3780] 3780,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 89:[109, 148], Operations: ['63+46=109', '64+84=148'] Exploring Operation: 109*148=16132, Resulting Numbers: [16132] 16132,89 unequal: No Solution Exploring Operation: 109+148=257, Resulting Numbers: [257] 257,89 unequal: No Solution Exploring Operation: 148-109=39, Resulting Numbers: [39] 39,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 89:[84, 173], Operations: ['63+46=109', '64+109=173'] Exploring Operation: 173-84=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[64, 63, 46, 84], Operations: [] Exploring Operation: 63+46=109, Resulting Numbers: [64, 84, 109] Generated Node #0,3: 89:[64, 84, 109] Operation: 63+46=109 Moving to Node #0,3 Current State: 89:[64, 84, 109], Operations: ['63+46=109'] Exploring Operation: 64+109=173, Resulting Numbers: [84, 173] Generated Node #0,3,1: 89:[84, 173] Operation: 64+109=173 Moving to Node #0,3,1 Current State: 89:[84, 173], Operations: ['63+46=109', '64+109=173'] Exploring Operation: 173-84=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 65, 42, 93, 63 ]
53
[ "65-42=23", "93-63=30", "23+30=53" ]
Current State: 53:[65, 42, 93, 63], Operations: [] Exploring Operation: 65-42=23, Resulting Numbers: [93, 63, 23] Generated Node #2: [93, 63, 23] from Operation: 65-42=23 Current State: 53:[93, 63, 23], Operations: ['65-42=23'] Exploring Operation: 93-63=30, Resulting Numbers: [23, 30] Generated Node #3: [23, 30] from Operation: 93-63=30 Current State: 53:[23, 30], Operations: ['65-42=23', '93-63=30'] Exploring Operation: 23+30=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[65, 42, 93, 63], Operations: [] Exploring Operation: 93-42=51, Resulting Numbers: [65, 63, 51] Generated Node #0,0: 53:[65, 63, 51] Operation: 93-42=51 Exploring Operation: 63-42=21, Resulting Numbers: [65, 93, 21] Generated Node #0,1: 53:[65, 93, 21] Operation: 63-42=21 Exploring Operation: 93-63=30, Resulting Numbers: [65, 42, 30] Generated Node #0,2: 53:[65, 42, 30] Operation: 93-63=30 Exploring Operation: 93-65=28, Resulting Numbers: [42, 63, 28] Generated Node #0,3: 53:[42, 63, 28] Operation: 93-65=28 Exploring Operation: 65-42=23, Resulting Numbers: [93, 63, 23] Generated Node #0,4: 53:[93, 63, 23] Operation: 65-42=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[65, 63, 51], Operations: ['93-42=51'] Exploring Operation: 65+51=116, Resulting Numbers: [63, 116] Generated Node #0,0,0: 53:[63, 116] Operation: 65+51=116 Exploring Operation: 65-51=14, Resulting Numbers: [63, 14] Generated Node #0,0,1: 53:[63, 14] Operation: 65-51=14 Exploring Operation: 63+51=114, Resulting Numbers: [65, 114] Generated Node #0,0,2: 53:[65, 114] Operation: 63+51=114 Exploring Operation: 65-63=2, Resulting Numbers: [51, 2] Generated Node #0,0,3: 53:[51, 2] Operation: 65-63=2 Exploring Operation: 63-51=12, Resulting Numbers: [65, 12] Generated Node #0,0,4: 53:[65, 12] Operation: 63-51=12 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 53:[63, 14], Operations: ['93-42=51', '65-51=14'] Exploring Operation: 63*14=882, Resulting Numbers: [882] 882,53 unequal: No Solution Exploring Operation: 63+14=77, Resulting Numbers: [77] 77,53 unequal: No Solution Exploring Operation: 63-14=49, Resulting Numbers: [49] 49,53 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:[51, 2], Operations: ['93-42=51', '65-63=2'] Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[65, 42, 93, 63], Operations: [] Exploring Operation: 93-42=51, Resulting Numbers: [65, 63, 51] Generated Node #0,0: 53:[65, 63, 51] Operation: 93-42=51 Moving to Node #0,0 Current State: 53:[65, 63, 51], Operations: ['93-42=51'] Exploring Operation: 65-63=2, Resulting Numbers: [51, 2] Generated Node #0,0,3: 53:[51, 2] Operation: 65-63=2 Moving to Node #0,0,3 Current State: 53:[51, 2], Operations: ['93-42=51', '65-63=2'] Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 1, 27, 9, 39 ]
58
[ "1+27=28", "39-9=30", "28+30=58" ]
Current State: 58:[1, 27, 9, 39], Operations: [] Exploring Operation: 1+27=28, Resulting Numbers: [9, 39, 28] Generated Node #2: [9, 39, 28] from Operation: 1+27=28 Current State: 58:[9, 39, 28], Operations: ['1+27=28'] Exploring Operation: 39-9=30, Resulting Numbers: [28, 30] Generated Node #3: [28, 30] from Operation: 39-9=30 Current State: 58:[28, 30], Operations: ['1+27=28', '39-9=30'] Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[1, 27, 9, 39], Operations: [] Exploring Operation: 27+39=66, Resulting Numbers: [1, 9, 66] Generated Node #0,0: 58:[1, 9, 66] Operation: 27+39=66 Exploring Operation: 27/9=3, Resulting Numbers: [1, 39, 3] Generated Node #0,1: 58:[1, 39, 3] Operation: 27/9=3 Exploring Operation: 39-9=30, Resulting Numbers: [1, 27, 30] Generated Node #0,2: 58:[1, 27, 30] Operation: 39-9=30 Exploring Operation: 9+39=48, Resulting Numbers: [1, 27, 48] Generated Node #0,3: 58:[1, 27, 48] Operation: 9+39=48 Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[1, 27, 30], Operations: ['39-9=30'] Exploring Operation: 1+27=28, Resulting Numbers: [30, 28] Generated Node #0,2,0: 58:[30, 28] Operation: 1+27=28 Exploring Operation: 30-1=29, Resulting Numbers: [27, 29] Generated Node #0,2,1: 58:[27, 29] Operation: 30-1=29 Exploring Operation: 27+30=57, Resulting Numbers: [1, 57] Generated Node #0,2,2: 58:[1, 57] Operation: 27+30=57 Exploring Operation: 30-27=3, Resulting Numbers: [1, 3] Generated Node #0,2,3: 58:[1, 3] Operation: 30-27=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 58:[30, 28], Operations: ['39-9=30', '1+27=28'] Exploring Operation: 30*28=840, Resulting Numbers: [840] 840,58 unequal: No Solution Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[1, 27, 9, 39], Operations: [] Exploring Operation: 39-9=30, Resulting Numbers: [1, 27, 30] Generated Node #0,2: 58:[1, 27, 30] Operation: 39-9=30 Moving to Node #0,2 Current State: 58:[1, 27, 30], Operations: ['39-9=30'] Exploring Operation: 1+27=28, Resulting Numbers: [30, 28] Generated Node #0,2,0: 58:[30, 28] Operation: 1+27=28 Moving to Node #0,2,0 Current State: 58:[30, 28], Operations: ['39-9=30', '1+27=28'] Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 8, 9, 12, 8 ]
22
[ "8/8=1", "9+12=21", "1+21=22" ]
Current State: 22:[8, 9, 12, 8], Operations: [] Exploring Operation: 8/8=1, Resulting Numbers: [9, 12, 1] Generated Node #2: [9, 12, 1] from Operation: 8/8=1 Current State: 22:[9, 12, 1], Operations: ['8/8=1'] Exploring Operation: 9+12=21, Resulting Numbers: [1, 21] Generated Node #3: [1, 21] from Operation: 9+12=21 Current State: 22:[1, 21], Operations: ['8/8=1', '9+12=21'] Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[8, 9, 12, 8], Operations: [] Exploring Operation: 9-8=1, Resulting Numbers: [12, 8, 1] Generated Node #0,0: 22:[12, 8, 1] Operation: 9-8=1 Exploring Operation: 8/8=1, Resulting Numbers: [9, 12, 1] Generated Node #0,1: 22:[9, 12, 1] Operation: 8/8=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[9, 12, 1], Operations: ['8/8=1'] Exploring Operation: 12-9=3, Resulting Numbers: [1, 3] Generated Node #0,1,0: 22:[1, 3] Operation: 12-9=3 Exploring Operation: 9+12=21, Resulting Numbers: [1, 21] Generated Node #0,1,1: 22:[1, 21] Operation: 9+12=21 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 22:[1, 3], Operations: ['8/8=1', '12-9=3'] Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,22 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,22 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 #0,1,1 Current State: 22:[1, 21], Operations: ['8/8=1', '9+12=21'] Exploring Operation: 1*21=21, Resulting Numbers: [21] 21,22 unequal: No Solution Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[8, 9, 12, 8], Operations: [] Exploring Operation: 8/8=1, Resulting Numbers: [9, 12, 1] Generated Node #0,1: 22:[9, 12, 1] Operation: 8/8=1 Moving to Node #0,1 Current State: 22:[9, 12, 1], Operations: ['8/8=1'] Exploring Operation: 9+12=21, Resulting Numbers: [1, 21] Generated Node #0,1,1: 22:[1, 21] Operation: 9+12=21 Moving to Node #0,1,1 Current State: 22:[1, 21], Operations: ['8/8=1', '9+12=21'] Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 20, 59, 20, 15 ]
41
[ "20-15=5", "20*5=100", "100-59=41" ]
Current State: 41:[20, 59, 20, 15], Operations: [] Exploring Operation: 20-15=5, Resulting Numbers: [59, 5] Generated Node #2: [59, 5] from Operation: 20-15=5 Current State: 41:[59, 5], Operations: ['20-15=5'] Exploring Operation: 20*5=100, Resulting Numbers: [59, 100] Generated Node #3: [59, 100] from Operation: 20*5=100 Current State: 41:[59, 100], Operations: ['20-15=5', '20*5=100'] Exploring Operation: 100-59=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[20, 59, 20, 15], Operations: [] Exploring Operation: 20+20=40, Resulting Numbers: [59, 15, 40] Generated Node #0,0: 41:[59, 15, 40] Operation: 20+20=40 Exploring Operation: 20+15=35, Resulting Numbers: [59, 20, 35] Generated Node #0,1: 41:[59, 20, 35] Operation: 20+15=35 Exploring Operation: 59-15=44, Resulting Numbers: [20, 20, 44] Generated Node #0,2: 41:[20, 20, 44] Operation: 59-15=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[59, 15, 40], Operations: ['20+20=40'] Exploring Operation: 59+15=74, Resulting Numbers: [40, 74] Generated Node #0,0,0: 41:[40, 74] Operation: 59+15=74 Exploring Operation: 15+40=55, Resulting Numbers: [59, 55] Generated Node #0,0,1: 41:[59, 55] Operation: 15+40=55 Exploring Operation: 59-15=44, Resulting Numbers: [40, 44] Generated Node #0,0,2: 41:[40, 44] Operation: 59-15=44 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 41:[40, 44], Operations: ['20+20=40', '59-15=44'] Exploring Operation: 40*44=1760, Resulting Numbers: [1760] 1760,41 unequal: No Solution Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,41 unequal: No Solution Exploring Operation: 40+44=84, Resulting Numbers: [84] 84,41 unequal: No Solution No 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: 41:[59, 55], Operations: ['20+20=40', '15+40=55'] Exploring Operation: 59+55=114, Resulting Numbers: [114] 114,41 unequal: No Solution Exploring Operation: 59*55=3245, Resulting Numbers: [3245] 3245,41 unequal: No Solution Exploring Operation: 59-55=4, Resulting Numbers: [4] 4,41 unequal: No Solution No 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: 41:[40, 74], Operations: ['20+20=40', '59+15=74'] Exploring Operation: 40*74=2960, Resulting Numbers: [2960] 2960,41 unequal: No Solution Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,41 unequal: No Solution Exploring Operation: 40+74=114, Resulting Numbers: [114] 114,41 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: 41:[59, 20, 35], Operations: ['20+15=35'] Exploring Operation: 59-20=39, Resulting Numbers: [35, 39] Generated Node #0,1,0: 41:[35, 39] Operation: 59-20=39 Exploring Operation: 59-35=24, Resulting Numbers: [20, 24] Generated Node #0,1,1: 41:[20, 24] Operation: 59-35=24 Exploring Operation: 20+35=55, Resulting Numbers: [59, 55] Generated Node #0,1,2: 41:[59, 55] Operation: 20+35=55 Moving to Node #0,1,0 Current State: 41:[35, 39], Operations: ['20+15=35', '59-20=39'] Exploring Operation: 35*39=1365, Resulting Numbers: [1365] 1365,41 unequal: No Solution Exploring Operation: 35+39=74, Resulting Numbers: [74] 74,41 unequal: No Solution Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[59, 55], Operations: ['20+15=35', '20+35=55'] Exploring Operation: 59*55=3245, Resulting Numbers: [3245] 3245,41 unequal: No Solution Exploring Operation: 59+55=114, Resulting Numbers: [114] 114,41 unequal: No Solution Exploring Operation: 59-55=4, Resulting Numbers: [4] 4,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[20, 24], Operations: ['20+15=35', '59-35=24'] Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,41 unequal: No Solution Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,41 unequal: No Solution No 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: 41:[20, 20, 44], Operations: ['59-15=44'] Exploring Operation: 44-20=24, Resulting Numbers: [20, 24] Generated Node #0,2,0: 41:[20, 24] Operation: 44-20=24 Exploring Operation: 44-20=24, Resulting Numbers: [20, 24] Generated Node #0,2,1: 41:[20, 24] Operation: 44-20=24 Exploring Operation: 20+20=40, Resulting Numbers: [44, 40] Generated Node #0,2,2: 41:[44, 40] Operation: 20+20=40 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 41:[44, 40], Operations: ['59-15=44', '20+20=40'] Exploring Operation: 44+40=84, Resulting Numbers: [84] 84,41 unequal: No Solution Exploring Operation: 44*40=1760, Resulting Numbers: [1760] 1760,41 unequal: No Solution Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,41 unequal: No Solution No 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: 41:[20, 24], Operations: ['59-15=44', '44-20=24'] Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,41 unequal: No Solution Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,41 unequal: No Solution Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,41 unequal: No Solution No 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: 41:[20, 24], Operations: ['59-15=44', '44-20=24'] Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,41 unequal: No Solution Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,41 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
[ 12, 67, 11, 46 ]
44
[ "12+67=79", "46-11=35", "79-35=44" ]
Current State: 44:[12, 67, 11, 46], Operations: [] Exploring Operation: 12+67=79, Resulting Numbers: [11, 46, 79] Generated Node #2: [11, 46, 79] from Operation: 12+67=79 Current State: 44:[11, 46, 79], Operations: ['12+67=79'] Exploring Operation: 46-11=35, Resulting Numbers: [79, 35] Generated Node #3: [79, 35] from Operation: 46-11=35 Current State: 44:[79, 35], Operations: ['12+67=79', '46-11=35'] Exploring Operation: 79-35=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[12, 67, 11, 46], Operations: [] Exploring Operation: 67-11=56, Resulting Numbers: [12, 46, 56] Generated Node #0,0: 44:[12, 46, 56] Operation: 67-11=56 Exploring Operation: 67-46=21, Resulting Numbers: [12, 11, 21] Generated Node #0,1: 44:[12, 11, 21] Operation: 67-46=21 Exploring Operation: 67-12=55, Resulting Numbers: [11, 46, 55] Generated Node #0,2: 44:[11, 46, 55] Operation: 67-12=55 Moving to Node #0,1 Current State: 44:[12, 11, 21], Operations: ['67-46=21'] Exploring Operation: 21-12=9, Resulting Numbers: [11, 9] Generated Node #0,1,0: 44:[11, 9] Operation: 21-12=9 Exploring Operation: 12+11=23, Resulting Numbers: [21, 23] Generated Node #0,1,1: 44:[21, 23] Operation: 12+11=23 Exploring Operation: 12-11=1, Resulting Numbers: [21, 1] Generated Node #0,1,2: 44:[21, 1] Operation: 12-11=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 44:[11, 9], Operations: ['67-46=21', '21-12=9'] Exploring Operation: 11+9=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 11*9=99, Resulting Numbers: [99] 99,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 44:[21, 23], Operations: ['67-46=21', '12+11=23'] Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 21*23=483, Resulting Numbers: [483] 483,44 unequal: No Solution Exploring Operation: 21+23=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[12, 67, 11, 46], Operations: [] Exploring Operation: 67-46=21, Resulting Numbers: [12, 11, 21] Generated Node #0,1: 44:[12, 11, 21] Operation: 67-46=21 Moving to Node #0,1 Current State: 44:[12, 11, 21], Operations: ['67-46=21'] Exploring Operation: 12+11=23, Resulting Numbers: [21, 23] Generated Node #0,1,1: 44:[21, 23] Operation: 12+11=23 Moving to Node #0,1,1 Current State: 44:[21, 23], Operations: ['67-46=21', '12+11=23'] Exploring Operation: 21+23=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 40, 19, 41, 18 ]
59
[ "40*18=720", "19*41=779", "779-720=59" ]
Current State: 59:[40, 19, 41, 18], Operations: [] Exploring Operation: 40*18=720, Resulting Numbers: [19, 41, 720] Generated Node #2: [19, 41, 720] from Operation: 40*18=720 Current State: 59:[19, 41, 720], Operations: ['40*18=720'] Exploring Operation: 19*41=779, Resulting Numbers: [720, 779] Generated Node #3: [720, 779] from Operation: 19*41=779 Current State: 59:[720, 779], Operations: ['40*18=720', '19*41=779'] Exploring Operation: 779-720=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[40, 19, 41, 18], Operations: [] Exploring Operation: 19+18=37, Resulting Numbers: [40, 41, 37] Generated Node #0,0: 59:[40, 41, 37] Operation: 19+18=37 Exploring Operation: 19+41=60, Resulting Numbers: [40, 18, 60] Generated Node #0,1: 59:[40, 18, 60] Operation: 19+41=60 Exploring Operation: 40+19=59, Resulting Numbers: [41, 18, 59] Generated Node #0,2: 59:[41, 18, 59] Operation: 40+19=59 Exploring Operation: 40+18=58, Resulting Numbers: [19, 41, 58] Generated Node #0,3: 59:[19, 41, 58] Operation: 40+18=58 Exploring Operation: 41+18=59, Resulting Numbers: [40, 19, 59] Generated Node #0,4: 59:[40, 19, 59] Operation: 41+18=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[40, 41, 37], Operations: ['19+18=37'] Exploring Operation: 41-37=4, Resulting Numbers: [40, 4] Generated Node #0,0,0: 59:[40, 4] Operation: 41-37=4 Exploring Operation: 40+41=81, Resulting Numbers: [37, 81] Generated Node #0,0,1: 59:[37, 81] Operation: 40+41=81 Exploring Operation: 41+37=78, Resulting Numbers: [40, 78] Generated Node #0,0,2: 59:[40, 78] Operation: 41+37=78 Exploring Operation: 40-37=3, Resulting Numbers: [41, 3] Generated Node #0,0,3: 59:[41, 3] Operation: 40-37=3 Exploring Operation: 40+37=77, Resulting Numbers: [41, 77] Generated Node #0,0,4: 59:[41, 77] Operation: 40+37=77 Moving to Node #0,0,4 Current State: 59:[41, 77], Operations: ['19+18=37', '40+37=77'] Exploring Operation: 41+77=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 77-41=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 41*77=3157, Resulting Numbers: [3157] 3157,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[40, 78], Operations: ['19+18=37', '41+37=78'] Exploring Operation: 40+78=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 78-40=38, Resulting Numbers: [38] 38,59 unequal: No Solution Exploring Operation: 40*78=3120, Resulting Numbers: [3120] 3120,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[37, 81], Operations: ['19+18=37', '40+41=81'] Exploring Operation: 37+81=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 37*81=2997, Resulting Numbers: [2997] 2997,59 unequal: No Solution Exploring Operation: 81-37=44, Resulting Numbers: [44] 44,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[40, 4], Operations: ['19+18=37', '41-37=4'] Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 40+4=44, Resulting Numbers: [44] 44,59 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,59 unequal: No Solution Exploring Operation: 40*4=160, Resulting Numbers: [160] 160,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[41, 3], Operations: ['19+18=37', '40-37=3'] Exploring Operation: 41*3=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,59 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,59 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 #0,2 Current State: 59:[41, 18, 59], Operations: ['40+19=59'] Exploring Operation: 41-18=23, Resulting Numbers: [59, 23] Generated Node #0,2,0: 59:[59, 23] Operation: 41-18=23 Exploring Operation: 41+59=100, Resulting Numbers: [18, 100] Generated Node #0,2,1: 59:[18, 100] Operation: 41+59=100 Exploring Operation: 59-18=41, Resulting Numbers: [41, 41] Generated Node #0,2,2: 59:[41, 41] Operation: 59-18=41 Exploring Operation: 41+18=59, Resulting Numbers: [59, 59] Generated Node #0,2,3: 59:[59, 59] Operation: 41+18=59 Exploring Operation: 18+59=77, Resulting Numbers: [41, 77] Generated Node #0,2,4: 59:[41, 77] Operation: 18+59=77 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 59:[59, 59], Operations: ['40+19=59', '41+18=59'] Exploring Operation: 59+59=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 59-59=0, Resulting Numbers: [0] 0,59 unequal: No Solution Exploring Operation: 59*59=3481, Resulting Numbers: [3481] 3481,59 unequal: No Solution Exploring Operation: 59/59=1, Resulting Numbers: [1] 1,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 59:[59, 23], Operations: ['40+19=59', '41-18=23'] Exploring Operation: 59*23=1357, Resulting Numbers: [1357] 1357,59 unequal: No Solution Exploring Operation: 59-23=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 59+23=82, Resulting Numbers: [82] 82,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 59:[41, 41], Operations: ['40+19=59', '59-18=41'] Exploring Operation: 41*41=1681, Resulting Numbers: [1681] 1681,59 unequal: No Solution Exploring Operation: 41/41=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 41-41=0, Resulting Numbers: [0] 0,59 unequal: No Solution Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 59:[41, 77], Operations: ['40+19=59', '18+59=77'] Exploring Operation: 77-41=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 41*77=3157, Resulting Numbers: [3157] 3157,59 unequal: No Solution Exploring Operation: 41+77=118, Resulting Numbers: [118] 118,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 59:[18, 100], Operations: ['40+19=59', '41+59=100'] Exploring Operation: 18*100=1800, Resulting Numbers: [1800] 1800,59 unequal: No Solution Exploring Operation: 18+100=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 100-18=82, Resulting Numbers: [82] 82,59 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 Start Sub Search at level 1: Moving to Node #0,3 Current State: 59:[19, 41, 58], Operations: ['40+18=58'] Exploring Operation: 58-19=39, Resulting Numbers: [41, 39] Generated Node #0,3,0: 59:[41, 39] Operation: 58-19=39 Exploring Operation: 19+41=60, Resulting Numbers: [58, 60] Generated Node #0,3,1: 59:[58, 60] Operation: 19+41=60 Exploring Operation: 41+58=99, Resulting Numbers: [19, 99] Generated Node #0,3,2: 59:[19, 99] Operation: 41+58=99 Exploring Operation: 19+58=77, Resulting Numbers: [41, 77] Generated Node #0,3,3: 59:[41, 77] Operation: 19+58=77 Exploring Operation: 41-19=22, Resulting Numbers: [58, 22] Generated Node #0,3,4: 59:[58, 22] Operation: 41-19=22 Moving to Node #0,3,1 Current State: 59:[58, 60], Operations: ['40+18=58', '19+41=60'] Exploring Operation: 58*60=3480, Resulting Numbers: [3480] 3480,59 unequal: No Solution Exploring Operation: 58+60=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 60-58=2, Resulting Numbers: [2] 2,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[41, 77], Operations: ['40+18=58', '19+58=77'] Exploring Operation: 41*77=3157, Resulting Numbers: [3157] 3157,59 unequal: No Solution Exploring Operation: 41+77=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 77-41=36, Resulting Numbers: [36] 36,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[41, 39], Operations: ['40+18=58', '58-19=39'] Exploring Operation: 41*39=1599, Resulting Numbers: [1599] 1599,59 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,59 unequal: No Solution Moving to Node #0,3,4 Current State: 59:[58, 22], Operations: ['40+18=58', '41-19=22'] Exploring Operation: 58*22=1276, Resulting Numbers: [1276] 1276,59 unequal: No Solution Exploring Operation: 58-22=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 58+22=80, Resulting Numbers: [80] 80,59 unequal: No Solution Moving to Node #0,3,2 Current State: 59:[19, 99], Operations: ['40+18=58', '41+58=99'] Exploring Operation: 19*99=1881, Resulting Numbers: [1881] 1881,59 unequal: No Solution Exploring Operation: 19+99=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 99-19=80, Resulting Numbers: [80] 80,59 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 #0,4 Current State: 59:[40, 19, 59], Operations: ['41+18=59'] Exploring Operation: 19+59=78, Resulting Numbers: [40, 78] Generated Node #0,4,0: 59:[40, 78] Operation: 19+59=78 Exploring Operation: 40+19=59, Resulting Numbers: [59, 59] Generated Node #0,4,1: 59:[59, 59] Operation: 40+19=59 Exploring Operation: 59-19=40, Resulting Numbers: [40, 40] Generated Node #0,4,2: 59:[40, 40] Operation: 59-19=40 Exploring Operation: 40-19=21, Resulting Numbers: [59, 21] Generated Node #0,4,3: 59:[59, 21] Operation: 40-19=21 Exploring Operation: 40+59=99, Resulting Numbers: [19, 99] Generated Node #0,4,4: 59:[19, 99] Operation: 40+59=99 Moving to Node #0,4,1 Current State: 59:[59, 59], Operations: ['41+18=59', '40+19=59'] Exploring Operation: 59*59=3481, Resulting Numbers: [3481] 3481,59 unequal: No Solution Exploring Operation: 59/59=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 59+59=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 59-59=0, Resulting Numbers: [0] 0,59 unequal: No Solution Moving to Node #0,4,2 Current State: 59:[40, 40], Operations: ['41+18=59', '59-19=40'] Exploring Operation: 40*40=1600, Resulting Numbers: [1600] 1600,59 unequal: No Solution Exploring Operation: 40/40=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 40+40=80, Resulting Numbers: [80] 80,59 unequal: No Solution Exploring Operation: 40-40=0, Resulting Numbers: [0] 0,59 unequal: No Solution Moving to Node #0,4,0 Current State: 59:[40, 78], Operations: ['41+18=59', '19+59=78'] Exploring Operation: 40*78=3120, Resulting Numbers: [3120] 3120,59 unequal: No Solution Exploring Operation: 78-40=38, Resulting Numbers: [38] 38,59 unequal: No Solution Exploring Operation: 40+78=118, Resulting Numbers: [118] 118,59 unequal: No Solution Moving to Node #0,4,3 Current State: 59:[59, 21], Operations: ['41+18=59', '40-19=21'] Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,59 unequal: No Solution Exploring Operation: 59*21=1239, Resulting Numbers: [1239] 1239,59 unequal: No Solution Exploring Operation: 59+21=80, Resulting Numbers: [80] 80,59 unequal: No Solution Moving to Node #0,4,4 Current State: 59:[19, 99], Operations: ['41+18=59', '40+59=99'] Exploring Operation: 19+99=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 19*99=1881, Resulting Numbers: [1881] 1881,59 unequal: No Solution Exploring Operation: 99-19=80, Resulting Numbers: [80] 80,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[40, 18, 60], Operations: ['19+41=60'] Exploring Operation: 40+18=58, Resulting Numbers: [60, 58] Generated Node #0,1,0: 59:[60, 58] Operation: 40+18=58 Exploring Operation: 40-18=22, Resulting Numbers: [60, 22] Generated Node #0,1,1: 59:[60, 22] Operation: 40-18=22 Exploring Operation: 18+60=78, Resulting Numbers: [40, 78] Generated Node #0,1,2: 59:[40, 78] Operation: 18+60=78 Exploring Operation: 60-40=20, Resulting Numbers: [18, 20] Generated Node #0,1,3: 59:[18, 20] Operation: 60-40=20 Exploring Operation: 60-18=42, Resulting Numbers: [40, 42] Generated Node #0,1,4: 59:[40, 42] Operation: 60-18=42 Moving to Node #0,1,0 Current State: 59:[60, 58], Operations: ['19+41=60', '40+18=58'] Exploring Operation: 60-58=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 60*58=3480, Resulting Numbers: [3480] 3480,59 unequal: No Solution Exploring Operation: 60+58=118, Resulting Numbers: [118] 118,59 unequal: No Solution Moving to Node #0,1,4 Current State: 59:[40, 42], Operations: ['19+41=60', '60-18=42'] Exploring Operation: 40*42=1680, Resulting Numbers: [1680] 1680,59 unequal: No Solution Exploring Operation: 40+42=82, Resulting Numbers: [82] 82,59 unequal: No Solution Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[60, 22], Operations: ['19+41=60', '40-18=22'] Exploring Operation: 60-22=38, Resulting Numbers: [38] 38,59 unequal: No Solution Exploring Operation: 60+22=82, Resulting Numbers: [82] 82,59 unequal: No Solution Exploring Operation: 60*22=1320, Resulting Numbers: [1320] 1320,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[40, 78], Operations: ['19+41=60', '18+60=78'] Exploring Operation: 40+78=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 78-40=38, Resulting Numbers: [38] 38,59 unequal: No Solution Exploring Operation: 40*78=3120, Resulting Numbers: [3120] 3120,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[18, 20], Operations: ['19+41=60', '60-40=20'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 18*20=360, Resulting Numbers: [360] 360,59 unequal: No Solution Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 63, 80, 71, 51 ]
67
[ "71-51=20", "80/20=4", "63+4=67" ]
Current State: 67:[63, 80, 71, 51], Operations: [] Exploring Operation: 71-51=20, Resulting Numbers: [63, 80, 20] Generated Node #2: [63, 80, 20] from Operation: 71-51=20 Current State: 67:[63, 80, 20], Operations: ['71-51=20'] Exploring Operation: 80/20=4, Resulting Numbers: [63, 4] Generated Node #3: [63, 4] from Operation: 80/20=4 Current State: 67:[63, 4], Operations: ['71-51=20', '80/20=4'] Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[63, 80, 71, 51], Operations: [] Exploring Operation: 80-51=29, Resulting Numbers: [63, 71, 29] Generated Node #0,0: 67:[63, 71, 29] Operation: 80-51=29 Exploring Operation: 63+51=114, Resulting Numbers: [80, 71, 114] Generated Node #0,1: 67:[80, 71, 114] Operation: 63+51=114 Moving to Node #0,0 Current State: 67:[63, 71, 29], Operations: ['80-51=29'] Exploring Operation: 71-29=42, Resulting Numbers: [63, 42] Generated Node #0,0,0: 67:[63, 42] Operation: 71-29=42 Exploring Operation: 63+29=92, Resulting Numbers: [71, 92] Generated Node #0,0,1: 67:[71, 92] Operation: 63+29=92 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[63, 42], Operations: ['80-51=29', '71-29=42'] Exploring Operation: 63-42=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 63+42=105, Resulting Numbers: [105] 105,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[71, 92], Operations: ['80-51=29', '63+29=92'] Exploring Operation: 92-71=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 71+92=163, Resulting Numbers: [163] 163,67 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: 67:[80, 71, 114], Operations: ['63+51=114'] Exploring Operation: 114-71=43, Resulting Numbers: [80, 43] Generated Node #0,1,0: 67:[80, 43] Operation: 114-71=43 Exploring Operation: 114-80=34, Resulting Numbers: [71, 34] Generated Node #0,1,1: 67:[71, 34] Operation: 114-80=34 Moving to Node #0,1,0 Current State: 67:[80, 43], Operations: ['63+51=114', '114-71=43'] Exploring Operation: 80-43=37, Resulting Numbers: [37] 37,67 unequal: No Solution Exploring Operation: 80+43=123, Resulting Numbers: [123] 123,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[71, 34], Operations: ['63+51=114', '114-80=34'] Exploring Operation: 71+34=105, Resulting Numbers: [105] 105,67 unequal: No Solution Exploring Operation: 71-34=37, Resulting Numbers: [37] 37,67 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 17, 9, 2, 64 ]
28
[ "17-9=8", "64-8=56", "56/2=28" ]
Current State: 28:[17, 9, 2, 64], Operations: [] Exploring Operation: 17-9=8, Resulting Numbers: [2, 64, 8] Generated Node #2: [2, 64, 8] from Operation: 17-9=8 Current State: 28:[2, 64, 8], Operations: ['17-9=8'] Exploring Operation: 64-8=56, Resulting Numbers: [2, 56] Generated Node #3: [2, 56] from Operation: 64-8=56 Current State: 28:[2, 56], Operations: ['17-9=8', '64-8=56'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[17, 9, 2, 64], Operations: [] Exploring Operation: 64/2=32, Resulting Numbers: [17, 9, 32] Generated Node #0,0: 28:[17, 9, 32] Operation: 64/2=32 Exploring Operation: 64-9=55, Resulting Numbers: [17, 2, 55] Generated Node #0,1: 28:[17, 2, 55] Operation: 64-9=55 Exploring Operation: 17+9=26, Resulting Numbers: [2, 64, 26] Generated Node #0,2: 28:[2, 64, 26] Operation: 17+9=26 Exploring Operation: 64-17=47, Resulting Numbers: [9, 2, 47] Generated Node #0,3: 28:[9, 2, 47] Operation: 64-17=47 Exploring Operation: 17-9=8, Resulting Numbers: [2, 64, 8] Generated Node #0,4: 28:[2, 64, 8] Operation: 17-9=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[17, 9, 32], Operations: ['64/2=32'] Exploring Operation: 32-9=23, Resulting Numbers: [17, 23] Generated Node #0,0,0: 28:[17, 23] Operation: 32-9=23 Exploring Operation: 17-9=8, Resulting Numbers: [32, 8] Generated Node #0,0,1: 28:[32, 8] Operation: 17-9=8 Exploring Operation: 9+32=41, Resulting Numbers: [17, 41] Generated Node #0,0,2: 28:[17, 41] Operation: 9+32=41 Exploring Operation: 17+9=26, Resulting Numbers: [32, 26] Generated Node #0,0,3: 28:[32, 26] Operation: 17+9=26 Exploring Operation: 32-17=15, Resulting Numbers: [9, 15] Generated Node #0,0,4: 28:[9, 15] Operation: 32-17=15 Moving to Node #0,0,4 Current State: 28:[9, 15], Operations: ['64/2=32', '32-17=15'] Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,28 unequal: No Solution Exploring Operation: 9*15=135, Resulting Numbers: [135] 135,28 unequal: No Solution Moving to Node #0,0,1 Current State: 28:[32, 8], Operations: ['64/2=32', '17-9=8'] Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,28 unequal: No Solution Exploring Operation: 32+8=40, Resulting Numbers: [40] 40,28 unequal: No Solution Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 32*8=256, Resulting Numbers: [256] 256,28 unequal: No Solution Moving to Node #0,0,3 Current State: 28:[32, 26], Operations: ['64/2=32', '17+9=26'] Exploring Operation: 32+26=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 32*26=832, Resulting Numbers: [832] 832,28 unequal: No Solution Exploring Operation: 32-26=6, Resulting Numbers: [6] 6,28 unequal: No Solution Moving to Node #0,0,0 Current State: 28:[17, 23], Operations: ['64/2=32', '32-9=23'] Exploring Operation: 17+23=40, Resulting Numbers: [40] 40,28 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 17*23=391, Resulting Numbers: [391] 391,28 unequal: No Solution Moving to Node #0,0,2 Current State: 28:[17, 41], Operations: ['64/2=32', '9+32=41'] Exploring Operation: 17*41=697, Resulting Numbers: [697] 697,28 unequal: No Solution Exploring Operation: 41-17=24, Resulting Numbers: [24] 24,28 unequal: No Solution Exploring Operation: 17+41=58, Resulting Numbers: [58] 58,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 28:[9, 2, 47], Operations: ['64-17=47'] Exploring Operation: 9+2=11, Resulting Numbers: [47, 11] Generated Node #0,3,0: 28:[47, 11] Operation: 9+2=11 Exploring Operation: 47-9=38, Resulting Numbers: [2, 38] Generated Node #0,3,1: 28:[2, 38] Operation: 47-9=38 Exploring Operation: 9-2=7, Resulting Numbers: [47, 7] Generated Node #0,3,2: 28:[47, 7] Operation: 9-2=7 Exploring Operation: 9*2=18, Resulting Numbers: [47, 18] Generated Node #0,3,3: 28:[47, 18] Operation: 9*2=18 Exploring Operation: 47-2=45, Resulting Numbers: [9, 45] Generated Node #0,3,4: 28:[9, 45] Operation: 47-2=45 Moving to Node #0,3,1 Current State: 28:[2, 38], Operations: ['64-17=47', '47-9=38'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,28 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,28 unequal: No Solution Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,28 unequal: No Solution Exploring Operation: 2+38=40, Resulting Numbers: [40] 40,28 unequal: No Solution Moving to Node #0,3,4 Current State: 28:[9, 45], Operations: ['64-17=47', '47-2=45'] Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,28 unequal: No Solution Exploring Operation: 9+45=54, Resulting Numbers: [54] 54,28 unequal: No Solution Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,28 unequal: No Solution Exploring Operation: 9*45=405, Resulting Numbers: [405] 405,28 unequal: No Solution Moving to Node #0,3,2 Current State: 28:[47, 7], Operations: ['64-17=47', '9-2=7'] Exploring Operation: 47+7=54, Resulting Numbers: [54] 54,28 unequal: No Solution Exploring Operation: 47*7=329, Resulting Numbers: [329] 329,28 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,28 unequal: No Solution Moving to Node #0,3,0 Current State: 28:[47, 11], Operations: ['64-17=47', '9+2=11'] Exploring Operation: 47+11=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 47*11=517, Resulting Numbers: [517] 517,28 unequal: No Solution Exploring Operation: 47-11=36, Resulting Numbers: [36] 36,28 unequal: No Solution Moving to Node #0,3,3 Current State: 28:[47, 18], Operations: ['64-17=47', '9*2=18'] Exploring Operation: 47-18=29, Resulting Numbers: [29] 29,28 unequal: No Solution Exploring Operation: 47*18=846, Resulting Numbers: [846] 846,28 unequal: No Solution Exploring Operation: 47+18=65, Resulting Numbers: [65] 65,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[17, 2, 55], Operations: ['64-9=55'] Exploring Operation: 2+55=57, Resulting Numbers: [17, 57] Generated Node #0,1,0: 28:[17, 57] Operation: 2+55=57 Exploring Operation: 17-2=15, Resulting Numbers: [55, 15] Generated Node #0,1,1: 28:[55, 15] Operation: 17-2=15 Exploring Operation: 55-17=38, Resulting Numbers: [2, 38] Generated Node #0,1,2: 28:[2, 38] Operation: 55-17=38 Exploring Operation: 17+2=19, Resulting Numbers: [55, 19] Generated Node #0,1,3: 28:[55, 19] Operation: 17+2=19 Exploring Operation: 55-2=53, Resulting Numbers: [17, 53] Generated Node #0,1,4: 28:[17, 53] Operation: 55-2=53 Moving to Node #0,1,2 Current State: 28:[2, 38], Operations: ['64-9=55', '55-17=38'] Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,28 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,28 unequal: No Solution Exploring Operation: 2+38=40, Resulting Numbers: [40] 40,28 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,28 unequal: No Solution Moving to Node #0,1,4 Current State: 28:[17, 53], Operations: ['64-9=55', '55-2=53'] Exploring Operation: 17+53=70, Resulting Numbers: [70] 70,28 unequal: No Solution Exploring Operation: 17*53=901, Resulting Numbers: [901] 901,28 unequal: No Solution Exploring Operation: 53-17=36, Resulting Numbers: [36] 36,28 unequal: No Solution Moving to Node #0,1,1 Current State: 28:[55, 15], Operations: ['64-9=55', '17-2=15'] Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,28 unequal: No Solution Exploring Operation: 55*15=825, Resulting Numbers: [825] 825,28 unequal: No Solution Exploring Operation: 55+15=70, Resulting Numbers: [70] 70,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[17, 57], Operations: ['64-9=55', '2+55=57'] Exploring Operation: 17*57=969, Resulting Numbers: [969] 969,28 unequal: No Solution Exploring Operation: 17+57=74, Resulting Numbers: [74] 74,28 unequal: No Solution Exploring Operation: 57-17=40, Resulting Numbers: [40] 40,28 unequal: No Solution Moving to Node #0,1,3 Current State: 28:[55, 19], Operations: ['64-9=55', '17+2=19'] Exploring Operation: 55+19=74, Resulting Numbers: [74] 74,28 unequal: No Solution Exploring Operation: 55-19=36, Resulting Numbers: [36] 36,28 unequal: No Solution Exploring Operation: 55*19=1045, Resulting Numbers: [1045] 1045,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 28:[2, 64, 8], Operations: ['17-9=8'] Exploring Operation: 64/2=32, Resulting Numbers: [8, 32] Generated Node #0,4,0: 28:[8, 32] Operation: 64/2=32 Exploring Operation: 64/8=8, Resulting Numbers: [2, 8] Generated Node #0,4,1: 28:[2, 8] Operation: 64/8=8 Exploring Operation: 64-2=62, Resulting Numbers: [8, 62] Generated Node #0,4,2: 28:[8, 62] Operation: 64-2=62 Exploring Operation: 64-8=56, Resulting Numbers: [2, 56] Generated Node #0,4,3: 28:[2, 56] Operation: 64-8=56 Exploring Operation: 8/2=4, Resulting Numbers: [64, 4] Generated Node #0,4,4: 28:[64, 4] Operation: 8/2=4 Moving to Node #0,4,1 Current State: 28:[2, 8], Operations: ['17-9=8', '64/8=8'] Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,28 unequal: No Solution Moving to Node #0,4,0 Current State: 28:[8, 32], Operations: ['17-9=8', '64/2=32'] Exploring Operation: 8+32=40, Resulting Numbers: [40] 40,28 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,28 unequal: No Solution Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 8*32=256, Resulting Numbers: [256] 256,28 unequal: No Solution Moving to Node #0,4,3 Current State: 28:[2, 56], Operations: ['17-9=8', '64-8=56'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,28 unequal: No Solution Exploring Operation: 2*56=112, Resulting Numbers: [112] 112,28 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[17, 9, 2, 64], Operations: [] Exploring Operation: 17-9=8, Resulting Numbers: [2, 64, 8] Generated Node #0,4: 28:[2, 64, 8] Operation: 17-9=8 Moving to Node #0,4 Current State: 28:[2, 64, 8], Operations: ['17-9=8'] Exploring Operation: 64-8=56, Resulting Numbers: [2, 56] Generated Node #0,4,3: 28:[2, 56] Operation: 64-8=56 Moving to Node #0,4,3 Current State: 28:[2, 56], Operations: ['17-9=8', '64-8=56'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.922743
hs_5
mult_heuristic
[ 54, 32, 10, 9 ]
16
[ "54/9=6", "32-10=22", "22-6=16" ]
Current State: 16:[54, 32, 10, 9], Operations: [] Exploring Operation: 54/9=6, Resulting Numbers: [32, 10, 6] Generated Node #2: [32, 10, 6] from Operation: 54/9=6 Current State: 16:[32, 10, 6], Operations: ['54/9=6'] Exploring Operation: 32-10=22, Resulting Numbers: [6, 22] Generated Node #3: [6, 22] from Operation: 32-10=22 Current State: 16:[6, 22], Operations: ['54/9=6', '32-10=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[54, 32, 10, 9], Operations: [] Exploring Operation: 54-10=44, Resulting Numbers: [32, 9, 44] Generated Node #0,0: 16:[32, 9, 44] Operation: 54-10=44 Exploring Operation: 54/9=6, Resulting Numbers: [32, 10, 6] Generated Node #0,1: 16:[32, 10, 6] Operation: 54/9=6 Exploring Operation: 54-32=22, Resulting Numbers: [10, 9, 22] Generated Node #0,2: 16:[10, 9, 22] Operation: 54-32=22 Exploring Operation: 32-10=22, Resulting Numbers: [54, 9, 22] Generated Node #0,3: 16:[54, 9, 22] Operation: 32-10=22 Moving to Node #0,2 Current State: 16:[10, 9, 22], Operations: ['54-32=22'] Exploring Operation: 22-10=12, Resulting Numbers: [9, 12] Generated Node #0,2,0: 16:[9, 12] Operation: 22-10=12 Exploring Operation: 22-9=13, Resulting Numbers: [10, 13] Generated Node #0,2,1: 16:[10, 13] Operation: 22-9=13 Exploring Operation: 10+9=19, Resulting Numbers: [22, 19] Generated Node #0,2,2: 16:[22, 19] Operation: 10+9=19 Exploring Operation: 10-9=1, Resulting Numbers: [22, 1] Generated Node #0,2,3: 16:[22, 1] Operation: 10-9=1 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 16:[9, 12], Operations: ['54-32=22', '22-10=12'] Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 9*12=108, Resulting Numbers: [108] 108,16 unequal: No Solution Exploring Operation: 9+12=21, Resulting Numbers: [21] 21,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 16:[10, 13], Operations: ['54-32=22', '22-9=13'] Exploring Operation: 10*13=130, Resulting Numbers: [130] 130,16 unequal: No Solution Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,16 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 16:[22, 1], Operations: ['54-32=22', '10-9=1'] Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,16 unequal: No Solution Exploring Operation: 22+1=23, Resulting Numbers: [23] 23,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 16:[22, 19], Operations: ['54-32=22', '10+9=19'] Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,16 unequal: No Solution Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 16:[32, 10, 6], Operations: ['54/9=6'] Exploring Operation: 10-6=4, Resulting Numbers: [32, 4] Generated Node #0,1,0: 16:[32, 4] Operation: 10-6=4 Exploring Operation: 32-6=26, Resulting Numbers: [10, 26] Generated Node #0,1,1: 16:[10, 26] Operation: 32-6=26 Exploring Operation: 10+6=16, Resulting Numbers: [32, 16] Generated Node #0,1,2: 16:[32, 16] Operation: 10+6=16 Exploring Operation: 32-10=22, Resulting Numbers: [6, 22] Generated Node #0,1,3: 16:[6, 22] Operation: 32-10=22 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 16:[6, 22], Operations: ['54/9=6', '32-10=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[54, 32, 10, 9], Operations: [] Exploring Operation: 54/9=6, Resulting Numbers: [32, 10, 6] Generated Node #0,1: 16:[32, 10, 6] Operation: 54/9=6 Moving to Node #0,1 Current State: 16:[32, 10, 6], Operations: ['54/9=6'] Exploring Operation: 32-10=22, Resulting Numbers: [6, 22] Generated Node #0,1,3: 16:[6, 22] Operation: 32-10=22 Moving to Node #0,1,3 Current State: 16:[6, 22], Operations: ['54/9=6', '32-10=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 47, 64, 55, 74 ]
82
[ "55-47=8", "64/8=8", "74+8=82" ]
Current State: 82:[47, 64, 55, 74], Operations: [] Exploring Operation: 55-47=8, Resulting Numbers: [64, 74, 8] Generated Node #2: [64, 74, 8] from Operation: 55-47=8 Current State: 82:[64, 74, 8], Operations: ['55-47=8'] Exploring Operation: 64/8=8, Resulting Numbers: [74, 8] Generated Node #3: [74, 8] from Operation: 64/8=8 Current State: 82:[74, 8], Operations: ['55-47=8', '64/8=8'] Exploring Operation: 74+8=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[47, 64, 55, 74], Operations: [] Exploring Operation: 55-47=8, Resulting Numbers: [64, 74, 8] Generated Node #0,0: 82:[64, 74, 8] Operation: 55-47=8 Exploring Operation: 64-55=9, Resulting Numbers: [47, 74, 9] Generated Node #0,1: 82:[47, 74, 9] Operation: 64-55=9 Exploring Operation: 74-55=19, Resulting Numbers: [47, 64, 19] Generated Node #0,2: 82:[47, 64, 19] Operation: 74-55=19 Exploring Operation: 74-64=10, Resulting Numbers: [47, 55, 10] Generated Node #0,3: 82:[47, 55, 10] Operation: 74-64=10 Exploring Operation: 64-47=17, Resulting Numbers: [55, 74, 17] Generated Node #0,4: 82:[55, 74, 17] Operation: 64-47=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[47, 74, 9], Operations: ['64-55=9'] Exploring Operation: 47-9=38, Resulting Numbers: [74, 38] Generated Node #0,1,0: 82:[74, 38] Operation: 47-9=38 Exploring Operation: 47+9=56, Resulting Numbers: [74, 56] Generated Node #0,1,1: 82:[74, 56] Operation: 47+9=56 Exploring Operation: 74+9=83, Resulting Numbers: [47, 83] Generated Node #0,1,2: 82:[47, 83] Operation: 74+9=83 Exploring Operation: 74-47=27, Resulting Numbers: [9, 27] Generated Node #0,1,3: 82:[9, 27] Operation: 74-47=27 Exploring Operation: 74-9=65, Resulting Numbers: [47, 65] Generated Node #0,1,4: 82:[47, 65] Operation: 74-9=65 Moving to Node #0,1,2 Current State: 82:[47, 83], Operations: ['64-55=9', '74+9=83'] Exploring Operation: 47*83=3901, Resulting Numbers: [3901] 3901,82 unequal: No Solution Exploring Operation: 47+83=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 83-47=36, Resulting Numbers: [36] 36,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[74, 38], Operations: ['64-55=9', '47-9=38'] Exploring Operation: 74-38=36, Resulting Numbers: [36] 36,82 unequal: No Solution Exploring Operation: 74*38=2812, Resulting Numbers: [2812] 2812,82 unequal: No Solution Exploring Operation: 74+38=112, Resulting Numbers: [112] 112,82 unequal: No Solution Moving to Node #0,1,3 Current State: 82:[9, 27], Operations: ['64-55=9', '74-47=27'] Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 9*27=243, Resulting Numbers: [243] 243,82 unequal: No Solution Exploring Operation: 9+27=36, Resulting Numbers: [36] 36,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[74, 56], Operations: ['64-55=9', '47+9=56'] Exploring Operation: 74+56=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 74-56=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 74*56=4144, Resulting Numbers: [4144] 4144,82 unequal: No Solution Moving to Node #0,1,4 Current State: 82:[47, 65], Operations: ['64-55=9', '74-9=65'] Exploring Operation: 47*65=3055, Resulting Numbers: [3055] 3055,82 unequal: No Solution Exploring Operation: 65-47=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 47+65=112, Resulting Numbers: [112] 112,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[47, 55, 10], Operations: ['74-64=10'] Exploring Operation: 55-10=45, Resulting Numbers: [47, 45] Generated Node #0,3,0: 82:[47, 45] Operation: 55-10=45 Exploring Operation: 55+10=65, Resulting Numbers: [47, 65] Generated Node #0,3,1: 82:[47, 65] Operation: 55+10=65 Exploring Operation: 47-10=37, Resulting Numbers: [55, 37] Generated Node #0,3,2: 82:[55, 37] Operation: 47-10=37 Exploring Operation: 47+55=102, Resulting Numbers: [10, 102] Generated Node #0,3,3: 82:[10, 102] Operation: 47+55=102 Exploring Operation: 55-47=8, Resulting Numbers: [10, 8] Generated Node #0,3,4: 82:[10, 8] Operation: 55-47=8 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 82:[47, 45], Operations: ['74-64=10', '55-10=45'] Exploring Operation: 47*45=2115, Resulting Numbers: [2115] 2115,82 unequal: No Solution Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 47+45=92, Resulting Numbers: [92] 92,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 82:[10, 8], Operations: ['74-64=10', '55-47=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,82 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 82:[55, 37], Operations: ['74-64=10', '47-10=37'] Exploring Operation: 55+37=92, Resulting Numbers: [92] 92,82 unequal: No Solution Exploring Operation: 55*37=2035, Resulting Numbers: [2035] 2035,82 unequal: No Solution Exploring Operation: 55-37=18, Resulting Numbers: [18] 18,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 82:[47, 65], Operations: ['74-64=10', '55+10=65'] Exploring Operation: 65-47=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 47*65=3055, Resulting Numbers: [3055] 3055,82 unequal: No Solution Exploring Operation: 47+65=112, Resulting Numbers: [112] 112,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 82:[10, 102], Operations: ['74-64=10', '47+55=102'] Exploring Operation: 102-10=92, Resulting Numbers: [92] 92,82 unequal: No Solution Exploring Operation: 10*102=1020, Resulting Numbers: [1020] 1020,82 unequal: No Solution Exploring Operation: 10+102=112, Resulting Numbers: [112] 112,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[64, 74, 8], Operations: ['55-47=8'] Exploring Operation: 64-8=56, Resulting Numbers: [74, 56] Generated Node #0,0,0: 82:[74, 56] Operation: 64-8=56 Exploring Operation: 74+8=82, Resulting Numbers: [64, 82] Generated Node #0,0,1: 82:[64, 82] Operation: 74+8=82 Exploring Operation: 64/8=8, Resulting Numbers: [74, 8] Generated Node #0,0,2: 82:[74, 8] Operation: 64/8=8 Exploring Operation: 74-64=10, Resulting Numbers: [8, 10] Generated Node #0,0,3: 82:[8, 10] Operation: 74-64=10 Exploring Operation: 64+8=72, Resulting Numbers: [74, 72] Generated Node #0,0,4: 82:[74, 72] Operation: 64+8=72 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[74, 8], Operations: ['55-47=8', '64/8=8'] Exploring Operation: 74*8=592, Resulting Numbers: [592] 592,82 unequal: No Solution Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,82 unequal: No Solution Exploring Operation: 74+8=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[47, 64, 55, 74], Operations: [] Exploring Operation: 55-47=8, Resulting Numbers: [64, 74, 8] Generated Node #0,0: 82:[64, 74, 8] Operation: 55-47=8 Moving to Node #0,0 Current State: 82:[64, 74, 8], Operations: ['55-47=8'] Exploring Operation: 64/8=8, Resulting Numbers: [74, 8] Generated Node #0,0,2: 82:[74, 8] Operation: 64/8=8 Moving to Node #0,0,2 Current State: 82:[74, 8], Operations: ['55-47=8', '64/8=8'] Exploring Operation: 74+8=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.949653
hs_5
sum_heuristic
[ 47, 8, 79, 24 ]
42
[ "47+79=126", "24/8=3", "126/3=42" ]
Current State: 42:[47, 8, 79, 24], Operations: [] Exploring Operation: 47+79=126, Resulting Numbers: [8, 24, 126] Generated Node #2: [8, 24, 126] from Operation: 47+79=126 Current State: 42:[8, 24, 126], Operations: ['47+79=126'] Exploring Operation: 24/8=3, Resulting Numbers: [126, 3] Generated Node #3: [126, 3] from Operation: 24/8=3 Current State: 42:[126, 3], Operations: ['47+79=126', '24/8=3'] Exploring Operation: 126/3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[47, 8, 79, 24], Operations: [] Exploring Operation: 79-8=71, Resulting Numbers: [47, 24, 71] Generated Node #0,0: 42:[47, 24, 71] Operation: 79-8=71 Exploring Operation: 79-47=32, Resulting Numbers: [8, 24, 32] Generated Node #0,1: 42:[8, 24, 32] Operation: 79-47=32 Exploring Operation: 47-24=23, Resulting Numbers: [8, 79, 23] Generated Node #0,2: 42:[8, 79, 23] Operation: 47-24=23 Exploring Operation: 79-24=55, Resulting Numbers: [47, 8, 55] Generated Node #0,3: 42:[47, 8, 55] Operation: 79-24=55 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[8, 24, 32], Operations: ['79-47=32'] Exploring Operation: 32/8=4, Resulting Numbers: [24, 4] Generated Node #0,1,0: 42:[24, 4] Operation: 32/8=4 Exploring Operation: 32-8=24, Resulting Numbers: [24, 24] Generated Node #0,1,1: 42:[24, 24] Operation: 32-8=24 Exploring Operation: 8+32=40, Resulting Numbers: [24, 40] Generated Node #0,1,2: 42:[24, 40] Operation: 8+32=40 Exploring Operation: 32-24=8, Resulting Numbers: [8, 8] Generated Node #0,1,3: 42:[8, 8] Operation: 32-24=8 Moving to Node #0,1,3 Current State: 42:[8, 8], Operations: ['79-47=32', '32-24=8'] Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,42 unequal: No Solution Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,42 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[24, 4], Operations: ['79-47=32', '32/8=4'] Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,42 unequal: No Solution Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,42 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,42 unequal: No Solution Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[24, 40], Operations: ['79-47=32', '8+32=40'] Exploring Operation: 24+40=64, Resulting Numbers: [64] 64,42 unequal: No Solution Exploring Operation: 24*40=960, Resulting Numbers: [960] 960,42 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[24, 24], Operations: ['79-47=32', '32-8=24'] Exploring Operation: 24-24=0, Resulting Numbers: [0] 0,42 unequal: No Solution Exploring Operation: 24*24=576, Resulting Numbers: [576] 576,42 unequal: No Solution Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,42 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 Current State: 42:[47, 8, 55], Operations: ['79-24=55'] Exploring Operation: 47+8=55, Resulting Numbers: [55, 55] Generated Node #0,3,0: 42:[55, 55] Operation: 47+8=55 Exploring Operation: 55-8=47, Resulting Numbers: [47, 47] Generated Node #0,3,1: 42:[47, 47] Operation: 55-8=47 Exploring Operation: 47-8=39, Resulting Numbers: [55, 39] Generated Node #0,3,2: 42:[55, 39] Operation: 47-8=39 Exploring Operation: 55-47=8, Resulting Numbers: [8, 8] Generated Node #0,3,3: 42:[8, 8] Operation: 55-47=8 Moving to Node #0,3,3 Current State: 42:[8, 8], Operations: ['79-24=55', '55-47=8'] Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,42 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,42 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,42 unequal: No Solution Moving to Node #0,3,1 Current State: 42:[47, 47], Operations: ['79-24=55', '55-8=47'] Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,42 unequal: No Solution Exploring Operation: 47*47=2209, Resulting Numbers: [2209] 2209,42 unequal: No Solution Exploring Operation: 47/47=1, Resulting Numbers: [1] 1,42 unequal: No Solution Exploring Operation: 47-47=0, Resulting Numbers: [0] 0,42 unequal: No Solution Moving to Node #0,3,2 Current State: 42:[55, 39], Operations: ['79-24=55', '47-8=39'] Exploring Operation: 55-39=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 55*39=2145, Resulting Numbers: [2145] 2145,42 unequal: No Solution Exploring Operation: 55+39=94, Resulting Numbers: [94] 94,42 unequal: No Solution Moving to Node #0,3,0 Current State: 42:[55, 55], Operations: ['79-24=55', '47+8=55'] Exploring Operation: 55*55=3025, Resulting Numbers: [3025] 3025,42 unequal: No Solution Exploring Operation: 55+55=110, Resulting Numbers: [110] 110,42 unequal: No Solution Exploring Operation: 55/55=1, Resulting Numbers: [1] 1,42 unequal: No Solution Exploring Operation: 55-55=0, Resulting Numbers: [0] 0,42 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 #0,0 Current State: 42:[47, 24, 71], Operations: ['79-8=71'] Exploring Operation: 71-24=47, Resulting Numbers: [47, 47] Generated Node #0,0,0: 42:[47, 47] Operation: 71-24=47 Exploring Operation: 47-24=23, Resulting Numbers: [71, 23] Generated Node #0,0,1: 42:[71, 23] Operation: 47-24=23 Exploring Operation: 47+24=71, Resulting Numbers: [71, 71] Generated Node #0,0,2: 42:[71, 71] Operation: 47+24=71 Exploring Operation: 71-47=24, Resulting Numbers: [24, 24] Generated Node #0,0,3: 42:[24, 24] Operation: 71-47=24 Moving to Node #0,0,3 Current State: 42:[24, 24], Operations: ['79-8=71', '71-47=24'] Exploring Operation: 24-24=0, Resulting Numbers: [0] 0,42 unequal: No Solution Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 24*24=576, Resulting Numbers: [576] 576,42 unequal: No Solution Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,42 unequal: No Solution Moving to Node #0,0,0 Current State: 42:[47, 47], Operations: ['79-8=71', '71-24=47'] Exploring Operation: 47-47=0, Resulting Numbers: [0] 0,42 unequal: No Solution Exploring Operation: 47*47=2209, Resulting Numbers: [2209] 2209,42 unequal: No Solution Exploring Operation: 47/47=1, Resulting Numbers: [1] 1,42 unequal: No Solution Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[71, 23], Operations: ['79-8=71', '47-24=23'] Exploring Operation: 71+23=94, Resulting Numbers: [94] 94,42 unequal: No Solution Exploring Operation: 71*23=1633, Resulting Numbers: [1633] 1633,42 unequal: No Solution Exploring Operation: 71-23=48, Resulting Numbers: [48] 48,42 unequal: No Solution Moving to Node #0,0,2 Current State: 42:[71, 71], Operations: ['79-8=71', '47+24=71'] Exploring Operation: 71+71=142, Resulting Numbers: [142] 142,42 unequal: No Solution Exploring Operation: 71/71=1, Resulting Numbers: [1] 1,42 unequal: No Solution Exploring Operation: 71-71=0, Resulting Numbers: [0] 0,42 unequal: No Solution Exploring Operation: 71*71=5041, Resulting Numbers: [5041] 5041,42 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 #0,2 Current State: 42:[8, 79, 23], Operations: ['47-24=23'] Exploring Operation: 79-23=56, Resulting Numbers: [8, 56] Generated Node #0,2,0: 42:[8, 56] Operation: 79-23=56 Exploring Operation: 79-8=71, Resulting Numbers: [23, 71] Generated Node #0,2,1: 42:[23, 71] Operation: 79-8=71 Exploring Operation: 8+79=87, Resulting Numbers: [23, 87] Generated Node #0,2,2: 42:[23, 87] Operation: 8+79=87 Exploring Operation: 23-8=15, Resulting Numbers: [79, 15] Generated Node #0,2,3: 42:[79, 15] Operation: 23-8=15 Moving to Node #0,2,0 Current State: 42:[8, 56], Operations: ['47-24=23', '79-23=56'] Exploring Operation: 8*56=448, Resulting Numbers: [448] 448,42 unequal: No Solution Exploring Operation: 8+56=64, Resulting Numbers: [64] 64,42 unequal: No Solution Exploring Operation: 56-8=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 56/8=7, Resulting Numbers: [7] 7,42 unequal: No Solution Moving to Node #0,2,1 Current State: 42:[23, 71], Operations: ['47-24=23', '79-8=71'] Exploring Operation: 71-23=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 23*71=1633, Resulting Numbers: [1633] 1633,42 unequal: No Solution Exploring Operation: 23+71=94, Resulting Numbers: [94] 94,42 unequal: No Solution Moving to Node #0,2,3 Current State: 42:[79, 15], Operations: ['47-24=23', '23-8=15'] Exploring Operation: 79-15=64, Resulting Numbers: [64] 64,42 unequal: No Solution Exploring Operation: 79+15=94, Resulting Numbers: [94] 94,42 unequal: No Solution Exploring Operation: 79*15=1185, Resulting Numbers: [1185] 1185,42 unequal: No Solution Moving to Node #0,2,2 Current State: 42:[23, 87], Operations: ['47-24=23', '8+79=87'] Exploring Operation: 23+87=110, Resulting Numbers: [110] 110,42 unequal: No Solution Exploring Operation: 23*87=2001, Resulting Numbers: [2001] 2001,42 unequal: No Solution Exploring Operation: 87-23=64, Resulting Numbers: [64] 64,42 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
[ 37, 19, 33, 98 ]
30
[ "33-19=14", "98/14=7", "37-7=30" ]
Current State: 30:[37, 19, 33, 98], Operations: [] Exploring Operation: 33-19=14, Resulting Numbers: [37, 98, 14] Generated Node #2: [37, 98, 14] from Operation: 33-19=14 Current State: 30:[37, 98, 14], Operations: ['33-19=14'] Exploring Operation: 98/14=7, Resulting Numbers: [37, 7] Generated Node #3: [37, 7] from Operation: 98/14=7 Current State: 30:[37, 7], Operations: ['33-19=14', '98/14=7'] Exploring Operation: 37-7=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[37, 19, 33, 98], Operations: [] Exploring Operation: 98-37=61, Resulting Numbers: [19, 33, 61] Generated Node #0,0: 30:[19, 33, 61] Operation: 98-37=61 Exploring Operation: 98-33=65, Resulting Numbers: [37, 19, 65] Generated Node #0,1: 30:[37, 19, 65] Operation: 98-33=65 Moving to Node #0,0 Current State: 30:[19, 33, 61], Operations: ['98-37=61'] Exploring Operation: 61-19=42, Resulting Numbers: [33, 42] Generated Node #0,0,0: 30:[33, 42] Operation: 61-19=42 Exploring Operation: 61-33=28, Resulting Numbers: [19, 28] Generated Node #0,0,1: 30:[19, 28] Operation: 61-33=28 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[19, 28], Operations: ['98-37=61', '61-33=28'] Exploring Operation: 19+28=47, Resulting Numbers: [47] 47,30 unequal: No Solution Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[33, 42], Operations: ['98-37=61', '61-19=42'] Exploring Operation: 42-33=9, Resulting Numbers: [9] 9,30 unequal: No Solution Exploring Operation: 33+42=75, Resulting Numbers: [75] 75,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 30:[37, 19, 65], Operations: ['98-33=65'] Exploring Operation: 65-19=46, Resulting Numbers: [37, 46] Generated Node #0,1,0: 30:[37, 46] Operation: 65-19=46 Exploring Operation: 65-37=28, Resulting Numbers: [19, 28] Generated Node #0,1,1: 30:[19, 28] Operation: 65-37=28 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 30:[19, 28], Operations: ['98-33=65', '65-37=28'] Exploring Operation: 19+28=47, Resulting Numbers: [47] 47,30 unequal: No Solution Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,30 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 #0,1,0 Current State: 30:[37, 46], Operations: ['98-33=65', '65-19=46'] Exploring Operation: 37+46=83, Resulting Numbers: [83] 83,30 unequal: No Solution Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 69, 90, 2, 98 ]
13
[ "69+98=167", "90*2=180", "180-167=13" ]
Current State: 13:[69, 90, 2, 98], Operations: [] Exploring Operation: 69+98=167, Resulting Numbers: [90, 2, 167] Generated Node #2: [90, 2, 167] from Operation: 69+98=167 Current State: 13:[90, 2, 167], Operations: ['69+98=167'] Exploring Operation: 90*2=180, Resulting Numbers: [167, 180] Generated Node #3: [167, 180] from Operation: 90*2=180 Current State: 13:[167, 180], Operations: ['69+98=167', '90*2=180'] Exploring Operation: 180-167=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[69, 90, 2, 98], Operations: [] Exploring Operation: 90-69=21, Resulting Numbers: [2, 98, 21] Generated Node #0,0: 13:[2, 98, 21] Operation: 90-69=21 Exploring Operation: 98/2=49, Resulting Numbers: [69, 90, 49] Generated Node #0,1: 13:[69, 90, 49] Operation: 98/2=49 Exploring Operation: 90/2=45, Resulting Numbers: [69, 98, 45] Generated Node #0,2: 13:[69, 98, 45] Operation: 90/2=45 Exploring Operation: 98-69=29, Resulting Numbers: [90, 2, 29] Generated Node #0,3: 13:[90, 2, 29] Operation: 98-69=29 Exploring Operation: 98-90=8, Resulting Numbers: [69, 2, 8] Generated Node #0,4: 13:[69, 2, 8] Operation: 98-90=8 Moving to Node #0,4 Current State: 13:[69, 2, 8], Operations: ['98-90=8'] Exploring Operation: 69+2=71, Resulting Numbers: [8, 71] Generated Node #0,4,0: 13:[8, 71] Operation: 69+2=71 Exploring Operation: 2*8=16, Resulting Numbers: [69, 16] Generated Node #0,4,1: 13:[69, 16] Operation: 2*8=16 Exploring Operation: 69-2=67, Resulting Numbers: [8, 67] Generated Node #0,4,2: 13:[8, 67] Operation: 69-2=67 Exploring Operation: 69-8=61, Resulting Numbers: [2, 61] Generated Node #0,4,3: 13:[2, 61] Operation: 69-8=61 Exploring Operation: 2+8=10, Resulting Numbers: [69, 10] Generated Node #0,4,4: 13:[69, 10] Operation: 2+8=10 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 13:[69, 16], Operations: ['98-90=8', '2*8=16'] Exploring Operation: 69-16=53, Resulting Numbers: [53] 53,13 unequal: No Solution Exploring Operation: 69+16=85, Resulting Numbers: [85] 85,13 unequal: No Solution Exploring Operation: 69*16=1104, Resulting Numbers: [1104] 1104,13 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 #0,4,2 Current State: 13:[8, 67], Operations: ['98-90=8', '69-2=67'] Exploring Operation: 67-8=59, Resulting Numbers: [59] 59,13 unequal: No Solution Exploring Operation: 8+67=75, Resulting Numbers: [75] 75,13 unequal: No Solution Exploring Operation: 8*67=536, Resulting Numbers: [536] 536,13 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 #0,4,3 Current State: 13:[2, 61], Operations: ['98-90=8', '69-8=61'] Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,13 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,13 unequal: No Solution Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,13 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 #0,4,4 Current State: 13:[69, 10], Operations: ['98-90=8', '2+8=10'] Exploring Operation: 69+10=79, Resulting Numbers: [79] 79,13 unequal: No Solution Exploring Operation: 69-10=59, Resulting Numbers: [59] 59,13 unequal: No Solution Exploring Operation: 69*10=690, Resulting Numbers: [690] 690,13 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 #0,4,0 Current State: 13:[8, 71], Operations: ['98-90=8', '69+2=71'] Exploring Operation: 8+71=79, Resulting Numbers: [79] 79,13 unequal: No Solution Exploring Operation: 71-8=63, Resulting Numbers: [63] 63,13 unequal: No Solution Exploring Operation: 8*71=568, Resulting Numbers: [568] 568,13 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: 13:[90, 2, 29], Operations: ['98-69=29'] Exploring Operation: 90+2=92, Resulting Numbers: [29, 92] Generated Node #0,3,0: 13:[29, 92] Operation: 90+2=92 Exploring Operation: 90/2=45, Resulting Numbers: [29, 45] Generated Node #0,3,1: 13:[29, 45] Operation: 90/2=45 Exploring Operation: 29-2=27, Resulting Numbers: [90, 27] Generated Node #0,3,2: 13:[90, 27] Operation: 29-2=27 Exploring Operation: 90-29=61, Resulting Numbers: [2, 61] Generated Node #0,3,3: 13:[2, 61] Operation: 90-29=61 Exploring Operation: 90-2=88, Resulting Numbers: [29, 88] Generated Node #0,3,4: 13:[29, 88] Operation: 90-2=88 Moving to Node #0,0 Current State: 13:[2, 98, 21], Operations: ['90-69=21'] Exploring Operation: 98-2=96, Resulting Numbers: [21, 96] Generated Node #0,0,0: 13:[21, 96] Operation: 98-2=96 Exploring Operation: 98-21=77, Resulting Numbers: [2, 77] Generated Node #0,0,1: 13:[2, 77] Operation: 98-21=77 Exploring Operation: 21-2=19, Resulting Numbers: [98, 19] Generated Node #0,0,2: 13:[98, 19] Operation: 21-2=19 Exploring Operation: 2+98=100, Resulting Numbers: [21, 100] Generated Node #0,0,3: 13:[21, 100] Operation: 2+98=100 Exploring Operation: 98/2=49, Resulting Numbers: [21, 49] Generated Node #0,0,4: 13:[21, 49] Operation: 98/2=49 Moving to Node #0,1 Current State: 13:[69, 90, 49], Operations: ['98/2=49'] Exploring Operation: 69-49=20, Resulting Numbers: [90, 20] Generated Node #0,1,0: 13:[90, 20] Operation: 69-49=20 Exploring Operation: 90-49=41, Resulting Numbers: [69, 41] Generated Node #0,1,1: 13:[69, 41] Operation: 90-49=41 Exploring Operation: 69+49=118, Resulting Numbers: [90, 118] Generated Node #0,1,2: 13:[90, 118] Operation: 69+49=118 Exploring Operation: 69+90=159, Resulting Numbers: [49, 159] Generated Node #0,1,3: 13:[49, 159] Operation: 69+90=159 Exploring Operation: 90-69=21, Resulting Numbers: [49, 21] Generated Node #0,1,4: 13:[49, 21] Operation: 90-69=21 Moving to Node #0,2 Current State: 13:[69, 98, 45], Operations: ['90/2=45'] Exploring Operation: 69-45=24, Resulting Numbers: [98, 24] Generated Node #0,2,0: 13:[98, 24] Operation: 69-45=24 Exploring Operation: 98-69=29, Resulting Numbers: [45, 29] Generated Node #0,2,1: 13:[45, 29] Operation: 98-69=29 Exploring Operation: 98-45=53, Resulting Numbers: [69, 53] Generated Node #0,2,2: 13:[69, 53] Operation: 98-45=53 Exploring Operation: 69+45=114, Resulting Numbers: [98, 114] Generated Node #0,2,3: 13:[98, 114] Operation: 69+45=114 Exploring Operation: 69+98=167, Resulting Numbers: [45, 167] Generated Node #0,2,4: 13:[45, 167] Operation: 69+98=167 Moving to Node #0,0,4 Current State: 13:[21, 49], Operations: ['90-69=21', '98/2=49'] Exploring Operation: 21*49=1029, Resulting Numbers: [1029] 1029,13 unequal: No Solution Exploring Operation: 49-21=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 21+49=70, Resulting Numbers: [70] 70,13 unequal: No Solution Moving to Node #0,1,4 Current State: 13:[49, 21], Operations: ['98/2=49', '90-69=21'] Exploring Operation: 49-21=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 49*21=1029, Resulting Numbers: [1029] 1029,13 unequal: No Solution Exploring Operation: 49+21=70, Resulting Numbers: [70] 70,13 unequal: No Solution Moving to Node #0,3,1 Current State: 13:[29, 45], Operations: ['98-69=29', '90/2=45'] Exploring Operation: 29+45=74, Resulting Numbers: [74] 74,13 unequal: No Solution Exploring Operation: 45-29=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 29*45=1305, Resulting Numbers: [1305] 1305,13 unequal: No Solution Moving to Node #0,2,1 Current State: 13:[45, 29], Operations: ['90/2=45', '98-69=29'] Exploring Operation: 45*29=1305, Resulting Numbers: [1305] 1305,13 unequal: No Solution Exploring Operation: 45-29=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 45+29=74, Resulting Numbers: [74] 74,13 unequal: No Solution Moving to Node #0,3,3 Current State: 13:[2, 61], Operations: ['98-69=29', '90-29=61'] Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,13 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,13 unequal: No Solution Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[2, 77], Operations: ['90-69=21', '98-21=77'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,13 unequal: No Solution Exploring Operation: 2+77=79, Resulting Numbers: [79] 79,13 unequal: No Solution Exploring Operation: 2*77=154, Resulting Numbers: [154] 154,13 unequal: No Solution Moving to Node #0,1,0 Current State: 13:[90, 20], Operations: ['98/2=49', '69-49=20'] Exploring Operation: 90*20=1800, Resulting Numbers: [1800] 1800,13 unequal: No Solution Exploring Operation: 90+20=110, Resulting Numbers: [110] 110,13 unequal: No Solution Exploring Operation: 90-20=70, Resulting Numbers: [70] 70,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[69, 41], Operations: ['98/2=49', '90-49=41'] Exploring Operation: 69+41=110, Resulting Numbers: [110] 110,13 unequal: No Solution Exploring Operation: 69-41=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 69*41=2829, Resulting Numbers: [2829] 2829,13 unequal: No Solution Moving to Node #0,3,2 Current State: 13:[90, 27], Operations: ['98-69=29', '29-2=27'] Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,13 unequal: No Solution Exploring Operation: 90+27=117, Resulting Numbers: [117] 117,13 unequal: No Solution Exploring Operation: 90*27=2430, Resulting Numbers: [2430] 2430,13 unequal: No Solution Moving to Node #0,0,2 Current State: 13:[98, 19], Operations: ['90-69=21', '21-2=19'] Exploring Operation: 98-19=79, Resulting Numbers: [79] 79,13 unequal: No Solution Exploring Operation: 98*19=1862, Resulting Numbers: [1862] 1862,13 unequal: No Solution Exploring Operation: 98+19=117, Resulting Numbers: [117] 117,13 unequal: No Solution Moving to Node #0,3,4 Current State: 13:[29, 88], Operations: ['98-69=29', '90-2=88'] Exploring Operation: 88-29=59, Resulting Numbers: [59] 59,13 unequal: No Solution Exploring Operation: 29+88=117, Resulting Numbers: [117] 117,13 unequal: No Solution Exploring Operation: 29*88=2552, Resulting Numbers: [2552] 2552,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[21, 96], Operations: ['90-69=21', '98-2=96'] Exploring Operation: 21*96=2016, Resulting Numbers: [2016] 2016,13 unequal: No Solution Exploring Operation: 96-21=75, Resulting Numbers: [75] 75,13 unequal: No Solution Exploring Operation: 21+96=117, Resulting Numbers: [117] 117,13 unequal: No Solution Moving to Node #0,3,0 Current State: 13:[29, 92], Operations: ['98-69=29', '90+2=92'] Exploring Operation: 29+92=121, Resulting Numbers: [121] 121,13 unequal: No Solution Exploring Operation: 29*92=2668, Resulting Numbers: [2668] 2668,13 unequal: No Solution Exploring Operation: 92-29=63, Resulting Numbers: [63] 63,13 unequal: No Solution Moving to Node #0,0,3 Current State: 13:[21, 100], Operations: ['90-69=21', '2+98=100'] Exploring Operation: 100-21=79, Resulting Numbers: [79] 79,13 unequal: No Solution Exploring Operation: 21*100=2100, Resulting Numbers: [2100] 2100,13 unequal: No Solution Exploring Operation: 21+100=121, Resulting Numbers: [121] 121,13 unequal: No Solution Moving to Node #0,2,0 Current State: 13:[98, 24], Operations: ['90/2=45', '69-45=24'] Exploring Operation: 98*24=2352, Resulting Numbers: [2352] 2352,13 unequal: No Solution Exploring Operation: 98-24=74, Resulting Numbers: [74] 74,13 unequal: No Solution Exploring Operation: 98+24=122, Resulting Numbers: [122] 122,13 unequal: No Solution Moving to Node #0,2,2 Current State: 13:[69, 53], Operations: ['90/2=45', '98-45=53'] Exploring Operation: 69-53=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 69+53=122, Resulting Numbers: [122] 122,13 unequal: No Solution Exploring Operation: 69*53=3657, Resulting Numbers: [3657] 3657,13 unequal: No Solution Moving to Node #0,1,2 Current State: 13:[90, 118], Operations: ['98/2=49', '69+49=118'] Exploring Operation: 90+118=208, Resulting Numbers: [208] 208,13 unequal: No Solution Exploring Operation: 118-90=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 90*118=10620, Resulting Numbers: [10620] 10620,13 unequal: No Solution Moving to Node #0,1,3 Current State: 13:[49, 159], Operations: ['98/2=49', '69+90=159'] Exploring Operation: 49*159=7791, Resulting Numbers: [7791] 7791,13 unequal: No Solution Exploring Operation: 49+159=208, Resulting Numbers: [208] 208,13 unequal: No Solution Exploring Operation: 159-49=110, Resulting Numbers: [110] 110,13 unequal: No Solution Moving to Node #0,2,3 Current State: 13:[98, 114], Operations: ['90/2=45', '69+45=114'] Exploring Operation: 114-98=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 98+114=212, Resulting Numbers: [212] 212,13 unequal: No Solution Exploring Operation: 98*114=11172, Resulting Numbers: [11172] 11172,13 unequal: No Solution Moving to Node #0,2,4 Current State: 13:[45, 167], Operations: ['90/2=45', '69+98=167'] Exploring Operation: 45*167=7515, Resulting Numbers: [7515] 7515,13 unequal: No Solution Exploring Operation: 167-45=122, Resulting Numbers: [122] 122,13 unequal: No Solution Exploring Operation: 45+167=212, Resulting Numbers: [212] 212,13 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 40, 16, 8, 80 ]
40
[ "40-8=32", "16*80=1280", "1280/32=40" ]
Current State: 40:[40, 16, 8, 80], Operations: [] Exploring Operation: 40-8=32, Resulting Numbers: [16, 80, 32] Generated Node #2: [16, 80, 32] from Operation: 40-8=32 Current State: 40:[16, 80, 32], Operations: ['40-8=32'] Exploring Operation: 16*80=1280, Resulting Numbers: [32, 1280] Generated Node #3: [32, 1280] from Operation: 16*80=1280 Current State: 40:[32, 1280], Operations: ['40-8=32', '16*80=1280'] Exploring Operation: 1280/32=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[40, 16, 8, 80], Operations: [] Exploring Operation: 80-40=40, Resulting Numbers: [16, 8, 40] Generated Node #0,0: 40:[16, 8, 40] Operation: 80-40=40 Exploring Operation: 80/16=5, Resulting Numbers: [40, 8, 5] Generated Node #0,1: 40:[40, 8, 5] Operation: 80/16=5 Moving to Node #0,1 Current State: 40:[40, 8, 5], Operations: ['80/16=5'] Exploring Operation: 40/8=5, Resulting Numbers: [5, 5] Generated Node #0,1,0: 40:[5, 5] Operation: 40/8=5 Exploring Operation: 40/5=8, Resulting Numbers: [8, 8] Generated Node #0,1,1: 40:[8, 8] Operation: 40/5=8 Moving to Node #0,0 Current State: 40:[16, 8, 40], Operations: ['80-40=40'] Exploring Operation: 16-8=8, Resulting Numbers: [40, 8] Generated Node #0,0,0: 40:[40, 8] Operation: 16-8=8 Exploring Operation: 16/8=2, Resulting Numbers: [40, 2] Generated Node #0,0,1: 40:[40, 2] Operation: 16/8=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[40, 8], Operations: ['80-40=40', '16-8=8'] Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[40, 2], Operations: ['80-40=40', '16/8=2'] Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,40 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: 40:[5, 5], Operations: ['80/16=5', '40/8=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,40 unequal: No Solution Moving to Node #0,1,1 Current State: 40:[8, 8], Operations: ['80/16=5', '40/5=8'] Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,40 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 1, 32, 96, 89 ]
40
[ "1+32=33", "96-89=7", "33+7=40" ]
Current State: 40:[1, 32, 96, 89], Operations: [] Exploring Operation: 1+32=33, Resulting Numbers: [96, 89, 33] Generated Node #2: [96, 89, 33] from Operation: 1+32=33 Current State: 40:[96, 89, 33], Operations: ['1+32=33'] Exploring Operation: 96-89=7, Resulting Numbers: [33, 7] Generated Node #3: [33, 7] from Operation: 96-89=7 Current State: 40:[33, 7], Operations: ['1+32=33', '96-89=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[1, 32, 96, 89], Operations: [] Exploring Operation: 96-32=64, Resulting Numbers: [1, 89, 64] Generated Node #0,0: 40:[1, 89, 64] Operation: 96-32=64 Exploring Operation: 96/32=3, Resulting Numbers: [1, 89, 3] Generated Node #0,1: 40:[1, 89, 3] Operation: 96/32=3 Exploring Operation: 96-89=7, Resulting Numbers: [1, 32, 7] Generated Node #0,2: 40:[1, 32, 7] Operation: 96-89=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[1, 32, 7], Operations: ['96-89=7'] Exploring Operation: 1+32=33, Resulting Numbers: [7, 33] Generated Node #0,2,0: 40:[7, 33] Operation: 1+32=33 Exploring Operation: 32+7=39, Resulting Numbers: [1, 39] Generated Node #0,2,1: 40:[1, 39] Operation: 32+7=39 Exploring Operation: 32-7=25, Resulting Numbers: [1, 25] Generated Node #0,2,2: 40:[1, 25] Operation: 32-7=25 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 40:[1, 39], Operations: ['96-89=7', '32+7=39'] Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[1, 32, 96, 89], Operations: [] Exploring Operation: 96-89=7, Resulting Numbers: [1, 32, 7] Generated Node #0,2: 40:[1, 32, 7] Operation: 96-89=7 Moving to Node #0,2 Current State: 40:[1, 32, 7], Operations: ['96-89=7'] Exploring Operation: 32+7=39, Resulting Numbers: [1, 39] Generated Node #0,2,1: 40:[1, 39] Operation: 32+7=39 Moving to Node #0,2,1 Current State: 40:[1, 39], Operations: ['96-89=7', '32+7=39'] Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 20, 23, 45, 55 ]
21
[ "55-45=10", "20/10=2", "23-2=21" ]
Current State: 21:[20, 23, 45, 55], Operations: [] Exploring Operation: 55-45=10, Resulting Numbers: [20, 23, 10] Generated Node #2: [20, 23, 10] from Operation: 55-45=10 Current State: 21:[20, 23, 10], Operations: ['55-45=10'] Exploring Operation: 20/10=2, Resulting Numbers: [23, 2] Generated Node #3: [23, 2] from Operation: 20/10=2 Current State: 21:[23, 2], Operations: ['55-45=10', '20/10=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[20, 23, 45, 55], Operations: [] Exploring Operation: 45-23=22, Resulting Numbers: [20, 55, 22] Generated Node #0,0: 21:[20, 55, 22] Operation: 45-23=22 Exploring Operation: 55-45=10, Resulting Numbers: [20, 23, 10] Generated Node #0,1: 21:[20, 23, 10] Operation: 55-45=10 Moving to Node #0,1 Current State: 21:[20, 23, 10], Operations: ['55-45=10'] Exploring Operation: 20/10=2, Resulting Numbers: [23, 2] Generated Node #0,1,0: 21:[23, 2] Operation: 20/10=2 Exploring Operation: 23-20=3, Resulting Numbers: [10, 3] Generated Node #0,1,1: 21:[10, 3] Operation: 23-20=3 Moving to Node #0,0 Current State: 21:[20, 55, 22], Operations: ['45-23=22'] Exploring Operation: 55-22=33, Resulting Numbers: [20, 33] Generated Node #0,0,0: 21:[20, 33] Operation: 55-22=33 Exploring Operation: 55-20=35, Resulting Numbers: [22, 35] Generated Node #0,0,1: 21:[22, 35] Operation: 55-20=35 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[20, 33], Operations: ['45-23=22', '55-22=33'] Exploring Operation: 33-20=13, Resulting Numbers: [13] 13,21 unequal: No Solution Exploring Operation: 20+33=53, Resulting Numbers: [53] 53,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[22, 35], Operations: ['45-23=22', '55-20=35'] Exploring Operation: 22+35=57, Resulting Numbers: [57] 57,21 unequal: No Solution Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,21 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: 21:[23, 2], Operations: ['55-45=10', '20/10=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,21 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[20, 23, 45, 55], Operations: [] Exploring Operation: 55-45=10, Resulting Numbers: [20, 23, 10] Generated Node #0,1: 21:[20, 23, 10] Operation: 55-45=10 Moving to Node #0,1 Current State: 21:[20, 23, 10], Operations: ['55-45=10'] Exploring Operation: 20/10=2, Resulting Numbers: [23, 2] Generated Node #0,1,0: 21:[23, 2] Operation: 20/10=2 Moving to Node #0,1,0 Current State: 21:[23, 2], Operations: ['55-45=10', '20/10=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 8, 23, 34, 84 ]
30
[ "8+84=92", "92/23=4", "34-4=30" ]
Current State: 30:[8, 23, 34, 84], Operations: [] Exploring Operation: 8+84=92, Resulting Numbers: [23, 34, 92] Generated Node #2: [23, 34, 92] from Operation: 8+84=92 Current State: 30:[23, 34, 92], Operations: ['8+84=92'] Exploring Operation: 92/23=4, Resulting Numbers: [34, 4] Generated Node #3: [34, 4] from Operation: 92/23=4 Current State: 30:[34, 4], Operations: ['8+84=92', '92/23=4'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[8, 23, 34, 84], Operations: [] Exploring Operation: 34-23=11, Resulting Numbers: [8, 84, 11] Generated Node #0,0: 30:[8, 84, 11] Operation: 34-23=11 Exploring Operation: 23-8=15, Resulting Numbers: [34, 84, 15] Generated Node #0,1: 30:[34, 84, 15] Operation: 23-8=15 Exploring Operation: 84-8=76, Resulting Numbers: [23, 34, 76] Generated Node #0,2: 30:[23, 34, 76] Operation: 84-8=76 Exploring Operation: 84-23=61, Resulting Numbers: [8, 34, 61] Generated Node #0,3: 30:[8, 34, 61] Operation: 84-23=61 Exploring Operation: 84-34=50, Resulting Numbers: [8, 23, 50] Generated Node #0,4: 30:[8, 23, 50] Operation: 84-34=50 Moving to Node #0,4 Current State: 30:[8, 23, 50], Operations: ['84-34=50'] Exploring Operation: 23-8=15, Resulting Numbers: [50, 15] Generated Node #0,4,0: 30:[50, 15] Operation: 23-8=15 Exploring Operation: 50-23=27, Resulting Numbers: [8, 27] Generated Node #0,4,1: 30:[8, 27] Operation: 50-23=27 Exploring Operation: 8+23=31, Resulting Numbers: [50, 31] Generated Node #0,4,2: 30:[50, 31] Operation: 8+23=31 Exploring Operation: 50-8=42, Resulting Numbers: [23, 42] Generated Node #0,4,3: 30:[23, 42] Operation: 50-8=42 Exploring Operation: 8+50=58, Resulting Numbers: [23, 58] Generated Node #0,4,4: 30:[23, 58] Operation: 8+50=58 Moving to Node #0,3 Current State: 30:[8, 34, 61], Operations: ['84-23=61'] Exploring Operation: 61-34=27, Resulting Numbers: [8, 27] Generated Node #0,3,0: 30:[8, 27] Operation: 61-34=27 Exploring Operation: 8+34=42, Resulting Numbers: [61, 42] Generated Node #0,3,1: 30:[61, 42] Operation: 8+34=42 Exploring Operation: 34-8=26, Resulting Numbers: [61, 26] Generated Node #0,3,2: 30:[61, 26] Operation: 34-8=26 Exploring Operation: 61-8=53, Resulting Numbers: [34, 53] Generated Node #0,3,3: 30:[34, 53] Operation: 61-8=53 Exploring Operation: 8+61=69, Resulting Numbers: [34, 69] Generated Node #0,3,4: 30:[34, 69] Operation: 8+61=69 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 30:[8, 27], Operations: ['84-23=61', '61-34=27'] Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,30 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,30 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 30:[34, 53], Operations: ['84-23=61', '61-8=53'] Exploring Operation: 34*53=1802, Resulting Numbers: [1802] 1802,30 unequal: No Solution Exploring Operation: 34+53=87, Resulting Numbers: [87] 87,30 unequal: No Solution Exploring Operation: 53-34=19, Resulting Numbers: [19] 19,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 30:[61, 26], Operations: ['84-23=61', '34-8=26'] Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,30 unequal: No Solution Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,30 unequal: No Solution Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 30:[61, 42], Operations: ['84-23=61', '8+34=42'] Exploring Operation: 61+42=103, Resulting Numbers: [103] 103,30 unequal: No Solution Exploring Operation: 61-42=19, Resulting Numbers: [19] 19,30 unequal: No Solution Exploring Operation: 61*42=2562, Resulting Numbers: [2562] 2562,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 30:[34, 69], Operations: ['84-23=61', '8+61=69'] Exploring Operation: 69-34=35, Resulting Numbers: [35] 35,30 unequal: No Solution Exploring Operation: 34*69=2346, Resulting Numbers: [2346] 2346,30 unequal: No Solution Exploring Operation: 34+69=103, Resulting Numbers: [103] 103,30 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: 30:[8, 84, 11], Operations: ['34-23=11'] Exploring Operation: 84-11=73, Resulting Numbers: [8, 73] Generated Node #0,0,0: 30:[8, 73] Operation: 84-11=73 Exploring Operation: 11-8=3, Resulting Numbers: [84, 3] Generated Node #0,0,1: 30:[84, 3] Operation: 11-8=3 Exploring Operation: 84-8=76, Resulting Numbers: [11, 76] Generated Node #0,0,2: 30:[11, 76] Operation: 84-8=76 Exploring Operation: 8+84=92, Resulting Numbers: [11, 92] Generated Node #0,0,3: 30:[11, 92] Operation: 8+84=92 Exploring Operation: 8+11=19, Resulting Numbers: [84, 19] Generated Node #0,0,4: 30:[84, 19] Operation: 8+11=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[8, 73], Operations: ['34-23=11', '84-11=73'] Exploring Operation: 8+73=81, Resulting Numbers: [81] 81,30 unequal: No Solution Exploring Operation: 8*73=584, Resulting Numbers: [584] 584,30 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 30:[11, 76], Operations: ['34-23=11', '84-8=76'] Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,30 unequal: No Solution Exploring Operation: 11+76=87, Resulting Numbers: [87] 87,30 unequal: No Solution Exploring Operation: 11*76=836, Resulting Numbers: [836] 836,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[84, 3], Operations: ['34-23=11', '11-8=3'] Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,30 unequal: No Solution Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,30 unequal: No Solution Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,30 unequal: No Solution Exploring Operation: 84*3=252, Resulting Numbers: [252] 252,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 30:[84, 19], Operations: ['34-23=11', '8+11=19'] Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,30 unequal: No Solution Exploring Operation: 84*19=1596, Resulting Numbers: [1596] 1596,30 unequal: No Solution Exploring Operation: 84+19=103, Resulting Numbers: [103] 103,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 30:[11, 92], Operations: ['34-23=11', '8+84=92'] Exploring Operation: 11*92=1012, Resulting Numbers: [1012] 1012,30 unequal: No Solution Exploring Operation: 92-11=81, Resulting Numbers: [81] 81,30 unequal: No Solution Exploring Operation: 11+92=103, Resulting Numbers: [103] 103,30 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: 30:[23, 34, 76], Operations: ['84-8=76'] Exploring Operation: 76-23=53, Resulting Numbers: [34, 53] Generated Node #0,2,0: 30:[34, 53] Operation: 76-23=53 Exploring Operation: 23+34=57, Resulting Numbers: [76, 57] Generated Node #0,2,1: 30:[76, 57] Operation: 23+34=57 Exploring Operation: 76-34=42, Resulting Numbers: [23, 42] Generated Node #0,2,2: 30:[23, 42] Operation: 76-34=42 Exploring Operation: 34-23=11, Resulting Numbers: [76, 11] Generated Node #0,2,3: 30:[76, 11] Operation: 34-23=11 Exploring Operation: 23+76=99, Resulting Numbers: [34, 99] Generated Node #0,2,4: 30:[34, 99] Operation: 23+76=99 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 30:[23, 42], Operations: ['84-8=76', '76-34=42'] Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,30 unequal: No Solution Exploring Operation: 23*42=966, Resulting Numbers: [966] 966,30 unequal: No Solution Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,30 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 #0,2,0 Current State: 30:[34, 53], Operations: ['84-8=76', '76-23=53'] Exploring Operation: 34*53=1802, Resulting Numbers: [1802] 1802,30 unequal: No Solution 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 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 30:[76, 11], Operations: ['84-8=76', '34-23=11'] Exploring Operation: 76*11=836, Resulting Numbers: [836] 836,30 unequal: No Solution Exploring Operation: 76+11=87, Resulting Numbers: [87] 87,30 unequal: No Solution Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,30 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 #0,2,1 Current State: 30:[76, 57], Operations: ['84-8=76', '23+34=57'] Exploring Operation: 76*57=4332, Resulting Numbers: [4332] 4332,30 unequal: No Solution Exploring Operation: 76+57=133, Resulting Numbers: [133] 133,30 unequal: No Solution Exploring Operation: 76-57=19, Resulting Numbers: [19] 19,30 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 #0,2,4 Current State: 30:[34, 99], Operations: ['84-8=76', '23+76=99'] Exploring Operation: 34*99=3366, Resulting Numbers: [3366] 3366,30 unequal: No Solution Exploring Operation: 99-34=65, Resulting Numbers: [65] 65,30 unequal: No Solution Exploring Operation: 34+99=133, Resulting Numbers: [133] 133,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 30:[34, 84, 15], Operations: ['23-8=15'] Exploring Operation: 84-15=69, Resulting Numbers: [34, 69] Generated Node #0,1,0: 30:[34, 69] Operation: 84-15=69 Exploring Operation: 34+15=49, Resulting Numbers: [84, 49] Generated Node #0,1,1: 30:[84, 49] Operation: 34+15=49 Exploring Operation: 84+15=99, Resulting Numbers: [34, 99] Generated Node #0,1,2: 30:[34, 99] Operation: 84+15=99 Exploring Operation: 34-15=19, Resulting Numbers: [84, 19] Generated Node #0,1,3: 30:[84, 19] Operation: 34-15=19 Exploring Operation: 84-34=50, Resulting Numbers: [15, 50] Generated Node #0,1,4: 30:[15, 50] Operation: 84-34=50 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 30:[15, 50], Operations: ['23-8=15', '84-34=50'] Exploring Operation: 15*50=750, Resulting Numbers: [750] 750,30 unequal: No Solution Exploring Operation: 15+50=65, Resulting Numbers: [65] 65,30 unequal: No Solution Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,30 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 #0,1,0 Current State: 30:[34, 69], Operations: ['23-8=15', '84-15=69'] Exploring Operation: 69-34=35, Resulting Numbers: [35] 35,30 unequal: No Solution Exploring Operation: 34*69=2346, Resulting Numbers: [2346] 2346,30 unequal: No Solution Exploring Operation: 34+69=103, Resulting Numbers: [103] 103,30 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 #0,1,3 Current State: 30:[84, 19], Operations: ['23-8=15', '34-15=19'] Exploring Operation: 84+19=103, Resulting Numbers: [103] 103,30 unequal: No Solution Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,30 unequal: No Solution Exploring Operation: 84*19=1596, Resulting Numbers: [1596] 1596,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 30:[84, 49], Operations: ['23-8=15', '34+15=49'] Exploring Operation: 84+49=133, Resulting Numbers: [133] 133,30 unequal: No Solution Exploring Operation: 84*49=4116, Resulting Numbers: [4116] 4116,30 unequal: No Solution Exploring Operation: 84-49=35, Resulting Numbers: [35] 35,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 30:[34, 99], Operations: ['23-8=15', '84+15=99'] Exploring Operation: 34+99=133, Resulting Numbers: [133] 133,30 unequal: No Solution Exploring Operation: 34*99=3366, Resulting Numbers: [3366] 3366,30 unequal: No Solution Exploring Operation: 99-34=65, Resulting Numbers: [65] 65,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,1 Current State: 30:[8, 27], Operations: ['84-34=50', '50-23=27'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,30 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,30 unequal: No Solution Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,30 unequal: No Solution Moving to Node #0,4,3 Current State: 30:[23, 42], Operations: ['84-34=50', '50-8=42'] Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,30 unequal: No Solution Exploring Operation: 23*42=966, Resulting Numbers: [966] 966,30 unequal: No Solution Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,30 unequal: No Solution Moving to Node #0,4,0 Current State: 30:[50, 15], Operations: ['84-34=50', '23-8=15'] Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,30 unequal: No Solution Exploring Operation: 50*15=750, Resulting Numbers: [750] 750,30 unequal: No Solution Exploring Operation: 50+15=65, Resulting Numbers: [65] 65,30 unequal: No Solution Moving to Node #0,4,2 Current State: 30:[50, 31], Operations: ['84-34=50', '8+23=31'] Exploring Operation: 50*31=1550, Resulting Numbers: [1550] 1550,30 unequal: No Solution Exploring Operation: 50-31=19, Resulting Numbers: [19] 19,30 unequal: No Solution Exploring Operation: 50+31=81, Resulting Numbers: [81] 81,30 unequal: No Solution Moving to Node #0,4,4 Current State: 30:[23, 58], Operations: ['84-34=50', '8+50=58'] Exploring Operation: 58-23=35, Resulting Numbers: [35] 35,30 unequal: No Solution Exploring Operation: 23*58=1334, Resulting Numbers: [1334] 1334,30 unequal: No Solution Exploring Operation: 23+58=81, Resulting Numbers: [81] 81,30 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 71, 20, 89, 9 ]
75
[ "89-9=80", "80/20=4", "71+4=75" ]
Current State: 75:[71, 20, 89, 9], Operations: [] Exploring Operation: 89-9=80, Resulting Numbers: [71, 20, 80] Generated Node #2: [71, 20, 80] from Operation: 89-9=80 Current State: 75:[71, 20, 80], Operations: ['89-9=80'] Exploring Operation: 80/20=4, Resulting Numbers: [71, 4] Generated Node #3: [71, 4] from Operation: 80/20=4 Current State: 75:[71, 4], Operations: ['89-9=80', '80/20=4'] Exploring Operation: 71+4=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[71, 20, 89, 9], Operations: [] Exploring Operation: 89-20=69, Resulting Numbers: [71, 9, 69] Generated Node #0,0: 75:[71, 9, 69] Operation: 89-20=69 Exploring Operation: 89-71=18, Resulting Numbers: [20, 9, 18] Generated Node #0,1: 75:[20, 9, 18] Operation: 89-71=18 Moving to Node #0,1 Current State: 75:[20, 9, 18], Operations: ['89-71=18'] Exploring Operation: 18/9=2, Resulting Numbers: [20, 2] Generated Node #0,1,0: 75:[20, 2] Operation: 18/9=2 Exploring Operation: 20-18=2, Resulting Numbers: [9, 2] Generated Node #0,1,1: 75:[9, 2] Operation: 20-18=2 Moving to Node #0,0 Current State: 75:[71, 9, 69], Operations: ['89-20=69'] Exploring Operation: 9+69=78, Resulting Numbers: [71, 78] Generated Node #0,0,0: 75:[71, 78] Operation: 9+69=78 Exploring Operation: 71-69=2, Resulting Numbers: [9, 2] Generated Node #0,0,1: 75:[9, 2] Operation: 71-69=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 75:[9, 2], Operations: ['89-20=69', '71-69=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,75 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:[71, 78], Operations: ['89-20=69', '9+69=78'] Exploring Operation: 71+78=149, Resulting Numbers: [149] 149,75 unequal: No Solution Exploring Operation: 78-71=7, Resulting Numbers: [7] 7,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 75:[9, 2], Operations: ['89-71=18', '20-18=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[20, 2], Operations: ['89-71=18', '18/9=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,75 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 94, 56, 68, 52 ]
77
[ "56-52=4", "68/4=17", "94-17=77" ]
Current State: 77:[94, 56, 68, 52], Operations: [] Exploring Operation: 56-52=4, Resulting Numbers: [94, 68, 4] Generated Node #2: [94, 68, 4] from Operation: 56-52=4 Current State: 77:[94, 68, 4], Operations: ['56-52=4'] Exploring Operation: 68/4=17, Resulting Numbers: [94, 17] Generated Node #3: [94, 17] from Operation: 68/4=17 Current State: 77:[94, 17], Operations: ['56-52=4', '68/4=17'] Exploring Operation: 94-17=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[94, 56, 68, 52], Operations: [] Exploring Operation: 56-52=4, Resulting Numbers: [94, 68, 4] Generated Node #0,0: 77:[94, 68, 4] Operation: 56-52=4 Exploring Operation: 56+52=108, Resulting Numbers: [94, 68, 108] Generated Node #0,1: 77:[94, 68, 108] Operation: 56+52=108 Exploring Operation: 68-56=12, Resulting Numbers: [94, 52, 12] Generated Node #0,2: 77:[94, 52, 12] Operation: 68-56=12 Exploring Operation: 68-52=16, Resulting Numbers: [94, 56, 16] Generated Node #0,3: 77:[94, 56, 16] Operation: 68-52=16 Moving to Node #0,0 Current State: 77:[94, 68, 4], Operations: ['56-52=4'] Exploring Operation: 68+4=72, Resulting Numbers: [94, 72] Generated Node #0,0,0: 77:[94, 72] Operation: 68+4=72 Exploring Operation: 68/4=17, Resulting Numbers: [94, 17] Generated Node #0,0,1: 77:[94, 17] Operation: 68/4=17 Exploring Operation: 94-4=90, Resulting Numbers: [68, 90] Generated Node #0,0,2: 77:[68, 90] Operation: 94-4=90 Exploring Operation: 94-68=26, Resulting Numbers: [4, 26] Generated Node #0,0,3: 77:[4, 26] Operation: 94-68=26 Moving to Node #0,3 Current State: 77:[94, 56, 16], Operations: ['68-52=16'] Exploring Operation: 56+16=72, Resulting Numbers: [94, 72] Generated Node #0,3,0: 77:[94, 72] Operation: 56+16=72 Exploring Operation: 94-16=78, Resulting Numbers: [56, 78] Generated Node #0,3,1: 77:[56, 78] Operation: 94-16=78 Exploring Operation: 56-16=40, Resulting Numbers: [94, 40] Generated Node #0,3,2: 77:[94, 40] Operation: 56-16=40 Exploring Operation: 94-56=38, Resulting Numbers: [16, 38] Generated Node #0,3,3: 77:[16, 38] Operation: 94-56=38 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 77:[94, 72], Operations: ['68-52=16', '56+16=72'] Exploring Operation: 94+72=166, Resulting Numbers: [166] 166,77 unequal: No Solution Exploring Operation: 94-72=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 94*72=6768, Resulting Numbers: [6768] 6768,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 77:[56, 78], Operations: ['68-52=16', '94-16=78'] Exploring Operation: 56+78=134, Resulting Numbers: [134] 134,77 unequal: No Solution Exploring Operation: 56*78=4368, Resulting Numbers: [4368] 4368,77 unequal: No Solution Exploring Operation: 78-56=22, Resulting Numbers: [22] 22,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 77:[16, 38], Operations: ['68-52=16', '94-56=38'] Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 16+38=54, Resulting Numbers: [54] 54,77 unequal: No Solution Exploring Operation: 16*38=608, Resulting Numbers: [608] 608,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 77:[94, 40], Operations: ['68-52=16', '56-16=40'] Exploring Operation: 94-40=54, Resulting Numbers: [54] 54,77 unequal: No Solution Exploring Operation: 94*40=3760, Resulting Numbers: [3760] 3760,77 unequal: No Solution Exploring Operation: 94+40=134, Resulting Numbers: [134] 134,77 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: 77:[94, 52, 12], Operations: ['68-56=12'] Exploring Operation: 94-12=82, Resulting Numbers: [52, 82] Generated Node #0,2,0: 77:[52, 82] Operation: 94-12=82 Exploring Operation: 52+12=64, Resulting Numbers: [94, 64] Generated Node #0,2,1: 77:[94, 64] Operation: 52+12=64 Exploring Operation: 94-52=42, Resulting Numbers: [12, 42] Generated Node #0,2,2: 77:[12, 42] Operation: 94-52=42 Exploring Operation: 52-12=40, Resulting Numbers: [94, 40] Generated Node #0,2,3: 77:[94, 40] Operation: 52-12=40 Moving to Node #0,1 Current State: 77:[94, 68, 108], Operations: ['56+52=108'] Exploring Operation: 108-94=14, Resulting Numbers: [68, 14] Generated Node #0,1,0: 77:[68, 14] Operation: 108-94=14 Exploring Operation: 108-68=40, Resulting Numbers: [94, 40] Generated Node #0,1,1: 77:[94, 40] Operation: 108-68=40 Exploring Operation: 94-68=26, Resulting Numbers: [108, 26] Generated Node #0,1,2: 77:[108, 26] Operation: 94-68=26 Exploring Operation: 94+68=162, Resulting Numbers: [108, 162] Generated Node #0,1,3: 77:[108, 162] Operation: 94+68=162 Moving to Node #0,1,0 Current State: 77:[68, 14], Operations: ['56+52=108', '108-94=14'] Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,77 unequal: No Solution Exploring Operation: 68+14=82, Resulting Numbers: [82] 82,77 unequal: No Solution Exploring Operation: 68*14=952, Resulting Numbers: [952] 952,77 unequal: No Solution Moving to Node #0,0,3 Current State: 77:[4, 26], Operations: ['56-52=4', '94-68=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,77 unequal: No Solution Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[68, 90], Operations: ['56-52=4', '94-4=90'] Exploring Operation: 90-68=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 68+90=158, Resulting Numbers: [158] 158,77 unequal: No Solution Exploring Operation: 68*90=6120, Resulting Numbers: [6120] 6120,77 unequal: No Solution Moving to Node #0,0,0 Current State: 77:[94, 72], Operations: ['56-52=4', '68+4=72'] Exploring Operation: 94-72=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 94*72=6768, Resulting Numbers: [6768] 6768,77 unequal: No Solution Exploring Operation: 94+72=166, Resulting Numbers: [166] 166,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[94, 17], Operations: ['56-52=4', '68/4=17'] Exploring Operation: 94-17=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[94, 56, 68, 52], Operations: [] Exploring Operation: 56-52=4, Resulting Numbers: [94, 68, 4] Generated Node #0,0: 77:[94, 68, 4] Operation: 56-52=4 Moving to Node #0,0 Current State: 77:[94, 68, 4], Operations: ['56-52=4'] Exploring Operation: 68/4=17, Resulting Numbers: [94, 17] Generated Node #0,0,1: 77:[94, 17] Operation: 68/4=17 Moving to Node #0,0,1 Current State: 77:[94, 17], Operations: ['56-52=4', '68/4=17'] Exploring Operation: 94-17=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
0.957465
hs_4
sum_heuristic
[ 41, 70, 21, 4 ]
86
[ "41+70=111", "21+4=25", "111-25=86" ]
Current State: 86:[41, 70, 21, 4], Operations: [] Exploring Operation: 41+70=111, Resulting Numbers: [21, 4, 111] Generated Node #2: [21, 4, 111] from Operation: 41+70=111 Current State: 86:[21, 4, 111], Operations: ['41+70=111'] Exploring Operation: 21+4=25, Resulting Numbers: [111, 25] Generated Node #3: [111, 25] from Operation: 21+4=25 Current State: 86:[111, 25], Operations: ['41+70=111', '21+4=25'] Exploring Operation: 111-25=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[41, 70, 21, 4], Operations: [] Exploring Operation: 70-21=49, Resulting Numbers: [41, 4, 49] Generated Node #0,0: 86:[41, 4, 49] Operation: 70-21=49 Exploring Operation: 70+21=91, Resulting Numbers: [41, 4, 91] Generated Node #0,1: 86:[41, 4, 91] Operation: 70+21=91 Moving to Node #0,1 Current State: 86:[41, 4, 91], Operations: ['70+21=91'] Exploring Operation: 91-4=87, Resulting Numbers: [41, 87] Generated Node #0,1,0: 86:[41, 87] Operation: 91-4=87 Exploring Operation: 41+4=45, Resulting Numbers: [91, 45] Generated Node #0,1,1: 86:[91, 45] Operation: 41+4=45 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[41, 87], Operations: ['70+21=91', '91-4=87'] Exploring Operation: 41+87=128, Resulting Numbers: [128] 128,86 unequal: No Solution Exploring Operation: 87-41=46, Resulting Numbers: [46] 46,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[91, 45], Operations: ['70+21=91', '41+4=45'] Exploring Operation: 91+45=136, Resulting Numbers: [136] 136,86 unequal: No Solution Exploring Operation: 91-45=46, Resulting Numbers: [46] 46,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 86:[41, 4, 49], Operations: ['70-21=49'] Exploring Operation: 41+49=90, Resulting Numbers: [4, 90] Generated Node #0,0,0: 86:[4, 90] Operation: 41+49=90 Exploring Operation: 49-4=45, Resulting Numbers: [41, 45] Generated Node #0,0,1: 86:[41, 45] Operation: 49-4=45 Moving to Node #0,0,1 Current State: 86:[41, 45], Operations: ['70-21=49', '49-4=45'] Exploring Operation: 45-41=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 41+45=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[41, 70, 21, 4], Operations: [] Exploring Operation: 70-21=49, Resulting Numbers: [41, 4, 49] Generated Node #0,0: 86:[41, 4, 49] Operation: 70-21=49 Moving to Node #0,0 Current State: 86:[41, 4, 49], Operations: ['70-21=49'] Exploring Operation: 49-4=45, Resulting Numbers: [41, 45] Generated Node #0,0,1: 86:[41, 45] Operation: 49-4=45 Moving to Node #0,0,1 Current State: 86:[41, 45], Operations: ['70-21=49', '49-4=45'] Exploring Operation: 41+45=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 8, 46, 7, 34 ]
81
[ "8+46=54", "34-7=27", "54+27=81" ]
Current State: 81:[8, 46, 7, 34], Operations: [] Exploring Operation: 8+46=54, Resulting Numbers: [7, 34, 54] Generated Node #2: [7, 34, 54] from Operation: 8+46=54 Current State: 81:[7, 34, 54], Operations: ['8+46=54'] Exploring Operation: 34-7=27, Resulting Numbers: [54, 27] Generated Node #3: [54, 27] from Operation: 34-7=27 Current State: 81:[54, 27], Operations: ['8+46=54', '34-7=27'] Exploring Operation: 54+27=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[8, 46, 7, 34], Operations: [] Exploring Operation: 46+34=80, Resulting Numbers: [8, 7, 80] Generated Node #0,0: 81:[8, 7, 80] Operation: 46+34=80 Moving to Node #0,0 Current State: 81:[8, 7, 80], Operations: ['46+34=80'] Exploring Operation: 8-7=1, Resulting Numbers: [80, 1] Generated Node #0,0,0: 81:[80, 1] Operation: 8-7=1 Moving to Node #0,0,0 Current State: 81:[80, 1], Operations: ['46+34=80', '8-7=1'] Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[8, 46, 7, 34], Operations: [] Exploring Operation: 46+34=80, Resulting Numbers: [8, 7, 80] Generated Node #0,0: 81:[8, 7, 80] Operation: 46+34=80 Moving to Node #0,0 Current State: 81:[8, 7, 80], Operations: ['46+34=80'] Exploring Operation: 8-7=1, Resulting Numbers: [80, 1] Generated Node #0,0,0: 81:[80, 1] Operation: 8-7=1 Moving to Node #0,0,0 Current State: 81:[80, 1], Operations: ['46+34=80', '8-7=1'] Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 18, 32, 61, 8 ]
11
[ "18*32=576", "576/8=72", "72-61=11" ]
Current State: 11:[18, 32, 61, 8], Operations: [] Exploring Operation: 18*32=576, Resulting Numbers: [61, 8, 576] Generated Node #2: [61, 8, 576] from Operation: 18*32=576 Current State: 11:[61, 8, 576], Operations: ['18*32=576'] Exploring Operation: 576/8=72, Resulting Numbers: [61, 72] Generated Node #3: [61, 72] from Operation: 576/8=72 Current State: 11:[61, 72], Operations: ['18*32=576', '576/8=72'] Exploring Operation: 72-61=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[18, 32, 61, 8], Operations: [] Exploring Operation: 32/8=4, Resulting Numbers: [18, 61, 4] Generated Node #0,0: 11:[18, 61, 4] Operation: 32/8=4 Exploring Operation: 61-18=43, Resulting Numbers: [32, 8, 43] Generated Node #0,1: 11:[32, 8, 43] Operation: 61-18=43 Exploring Operation: 32-8=24, Resulting Numbers: [18, 61, 24] Generated Node #0,2: 11:[18, 61, 24] Operation: 32-8=24 Exploring Operation: 61-32=29, Resulting Numbers: [18, 8, 29] Generated Node #0,3: 11:[18, 8, 29] Operation: 61-32=29 Exploring Operation: 32-18=14, Resulting Numbers: [61, 8, 14] Generated Node #0,4: 11:[61, 8, 14] Operation: 32-18=14 Start Sub Search at level 1: Moving to Node #0,3 Current State: 11:[18, 8, 29], Operations: ['61-32=29'] Exploring Operation: 29-8=21, Resulting Numbers: [18, 21] Generated Node #0,3,0: 11:[18, 21] Operation: 29-8=21 Exploring Operation: 18-8=10, Resulting Numbers: [29, 10] Generated Node #0,3,1: 11:[29, 10] Operation: 18-8=10 Exploring Operation: 8+29=37, Resulting Numbers: [18, 37] Generated Node #0,3,2: 11:[18, 37] Operation: 8+29=37 Exploring Operation: 18+8=26, Resulting Numbers: [29, 26] Generated Node #0,3,3: 11:[29, 26] Operation: 18+8=26 Exploring Operation: 29-18=11, Resulting Numbers: [8, 11] Generated Node #0,3,4: 11:[8, 11] Operation: 29-18=11 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 11:[8, 11], Operations: ['61-32=29', '29-18=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,11 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:[18, 21], Operations: ['61-32=29', '29-8=21'] Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 18+21=39, Resulting Numbers: [39] 39,11 unequal: No Solution Exploring Operation: 18*21=378, Resulting Numbers: [378] 378,11 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 #0,3,1 Current State: 11:[29, 10], Operations: ['61-32=29', '18-8=10'] Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 29*10=290, Resulting Numbers: [290] 290,11 unequal: No Solution Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,11 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:[18, 37], Operations: ['61-32=29', '8+29=37'] Exploring Operation: 18*37=666, Resulting Numbers: [666] 666,11 unequal: No Solution Exploring Operation: 18+37=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,11 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, 26], Operations: ['61-32=29', '18+8=26'] Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 29+26=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 29*26=754, Resulting Numbers: [754] 754,11 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 #0,1 Current State: 11:[32, 8, 43], Operations: ['61-18=43'] Exploring Operation: 32-8=24, Resulting Numbers: [43, 24] Generated Node #0,1,0: 11:[43, 24] Operation: 32-8=24 Exploring Operation: 32/8=4, Resulting Numbers: [43, 4] Generated Node #0,1,1: 11:[43, 4] Operation: 32/8=4 Exploring Operation: 32+8=40, Resulting Numbers: [43, 40] Generated Node #0,1,2: 11:[43, 40] Operation: 32+8=40 Exploring Operation: 43-8=35, Resulting Numbers: [32, 35] Generated Node #0,1,3: 11:[32, 35] Operation: 43-8=35 Exploring Operation: 43-32=11, Resulting Numbers: [8, 11] Generated Node #0,1,4: 11:[8, 11] Operation: 43-32=11 Moving to Node #0,1,4 Current State: 11:[8, 11], Operations: ['61-18=43', '43-32=11'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[43, 4], Operations: ['61-18=43', '32/8=4'] Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,11 unequal: No Solution Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[43, 24], Operations: ['61-18=43', '32-8=24'] Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,11 unequal: No Solution Exploring Operation: 43*24=1032, Resulting Numbers: [1032] 1032,11 unequal: No Solution Moving to Node #0,1,3 Current State: 11:[32, 35], Operations: ['61-18=43', '43-8=35'] Exploring Operation: 32+35=67, Resulting Numbers: [67] 67,11 unequal: No Solution Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 32*35=1120, Resulting Numbers: [1120] 1120,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[43, 40], Operations: ['61-18=43', '32+8=40'] Exploring Operation: 43+40=83, Resulting Numbers: [83] 83,11 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 43*40=1720, Resulting Numbers: [1720] 1720,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 11:[61, 8, 14], Operations: ['32-18=14'] Exploring Operation: 61-8=53, Resulting Numbers: [14, 53] Generated Node #0,4,0: 11:[14, 53] Operation: 61-8=53 Exploring Operation: 61-14=47, Resulting Numbers: [8, 47] Generated Node #0,4,1: 11:[8, 47] Operation: 61-14=47 Exploring Operation: 61+8=69, Resulting Numbers: [14, 69] Generated Node #0,4,2: 11:[14, 69] Operation: 61+8=69 Exploring Operation: 8+14=22, Resulting Numbers: [61, 22] Generated Node #0,4,3: 11:[61, 22] Operation: 8+14=22 Exploring Operation: 14-8=6, Resulting Numbers: [61, 6] Generated Node #0,4,4: 11:[61, 6] Operation: 14-8=6 Moving to Node #0,4,1 Current State: 11:[8, 47], Operations: ['32-18=14', '61-14=47'] Exploring Operation: 8+47=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 8*47=376, Resulting Numbers: [376] 376,11 unequal: No Solution Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,11 unequal: No Solution Moving to Node #0,4,0 Current State: 11:[14, 53], Operations: ['32-18=14', '61-8=53'] Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,11 unequal: No Solution Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,11 unequal: No Solution Exploring Operation: 14*53=742, Resulting Numbers: [742] 742,11 unequal: No Solution Moving to Node #0,4,4 Current State: 11:[61, 6], Operations: ['32-18=14', '14-8=6'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 61*6=366, Resulting Numbers: [366] 366,11 unequal: No Solution Exploring Operation: 61+6=67, Resulting Numbers: [67] 67,11 unequal: No Solution Moving to Node #0,4,2 Current State: 11:[14, 69], Operations: ['32-18=14', '61+8=69'] Exploring Operation: 14+69=83, Resulting Numbers: [83] 83,11 unequal: No Solution Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 14*69=966, Resulting Numbers: [966] 966,11 unequal: No Solution Moving to Node #0,4,3 Current State: 11:[61, 22], Operations: ['32-18=14', '8+14=22'] Exploring Operation: 61+22=83, Resulting Numbers: [83] 83,11 unequal: No Solution Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,11 unequal: No Solution Exploring Operation: 61*22=1342, Resulting Numbers: [1342] 1342,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[18, 61, 4], Operations: ['32/8=4'] Exploring Operation: 18-4=14, Resulting Numbers: [61, 14] Generated Node #0,0,0: 11:[61, 14] Operation: 18-4=14 Exploring Operation: 61-18=43, Resulting Numbers: [4, 43] Generated Node #0,0,1: 11:[4, 43] Operation: 61-18=43 Exploring Operation: 18+4=22, Resulting Numbers: [61, 22] Generated Node #0,0,2: 11:[61, 22] Operation: 18+4=22 Exploring Operation: 61-4=57, Resulting Numbers: [18, 57] Generated Node #0,0,3: 11:[18, 57] Operation: 61-4=57 Exploring Operation: 61+4=65, Resulting Numbers: [18, 65] Generated Node #0,0,4: 11:[18, 65] Operation: 61+4=65 Moving to Node #0,0,1 Current State: 11:[4, 43], Operations: ['32/8=4', '61-18=43'] Exploring Operation: 4+43=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,11 unequal: No Solution Exploring Operation: 4*43=172, Resulting Numbers: [172] 172,11 unequal: No Solution Moving to Node #0,0,3 Current State: 11:[18, 57], Operations: ['32/8=4', '61-4=57'] Exploring Operation: 18+57=75, Resulting Numbers: [75] 75,11 unequal: No Solution Exploring Operation: 57-18=39, Resulting Numbers: [39] 39,11 unequal: No Solution Exploring Operation: 18*57=1026, Resulting Numbers: [1026] 1026,11 unequal: No Solution Moving to Node #0,0,0 Current State: 11:[61, 14], Operations: ['32/8=4', '18-4=14'] Exploring Operation: 61+14=75, Resulting Numbers: [75] 75,11 unequal: No Solution Exploring Operation: 61-14=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 61*14=854, Resulting Numbers: [854] 854,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[61, 22], Operations: ['32/8=4', '18+4=22'] Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,11 unequal: No Solution Exploring Operation: 61*22=1342, Resulting Numbers: [1342] 1342,11 unequal: No Solution Exploring Operation: 61+22=83, Resulting Numbers: [83] 83,11 unequal: No Solution Moving to Node #0,0,4 Current State: 11:[18, 65], Operations: ['32/8=4', '61+4=65'] Exploring Operation: 18*65=1170, Resulting Numbers: [1170] 1170,11 unequal: No Solution Exploring Operation: 65-18=47, Resulting Numbers: [47] 47,11 unequal: No Solution Exploring Operation: 18+65=83, Resulting Numbers: [83] 83,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 11:[18, 61, 24], Operations: ['32-8=24'] Exploring Operation: 61-18=43, Resulting Numbers: [24, 43] Generated Node #0,2,0: 11:[24, 43] Operation: 61-18=43 Exploring Operation: 18+61=79, Resulting Numbers: [24, 79] Generated Node #0,2,1: 11:[24, 79] Operation: 18+61=79 Exploring Operation: 24-18=6, Resulting Numbers: [61, 6] Generated Node #0,2,2: 11:[61, 6] Operation: 24-18=6 Exploring Operation: 61-24=37, Resulting Numbers: [18, 37] Generated Node #0,2,3: 11:[18, 37] Operation: 61-24=37 Exploring Operation: 18+24=42, Resulting Numbers: [61, 42] Generated Node #0,2,4: 11:[61, 42] Operation: 18+24=42 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 11:[18, 37], Operations: ['32-8=24', '61-24=37'] Exploring Operation: 18+37=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 18*37=666, Resulting Numbers: [666] 666,11 unequal: No Solution Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,11 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 #0,2,0 Current State: 11:[24, 43], Operations: ['32-8=24', '61-18=43'] Exploring Operation: 24*43=1032, Resulting Numbers: [1032] 1032,11 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,11 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 #0,2,2 Current State: 11:[61, 6], Operations: ['32-8=24', '24-18=6'] Exploring Operation: 61+6=67, Resulting Numbers: [67] 67,11 unequal: No Solution Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 61*6=366, Resulting Numbers: [366] 366,11 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 #0,2,1 Current State: 11:[24, 79], Operations: ['32-8=24', '18+61=79'] Exploring Operation: 24*79=1896, Resulting Numbers: [1896] 1896,11 unequal: No Solution Exploring Operation: 79-24=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 24+79=103, Resulting Numbers: [103] 103,11 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 #0,2,4 Current State: 11:[61, 42], Operations: ['32-8=24', '18+24=42'] Exploring Operation: 61-42=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 61*42=2562, Resulting Numbers: [2562] 2562,11 unequal: No Solution Exploring Operation: 61+42=103, Resulting Numbers: [103] 103,11 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_5
sum_heuristic
[ 53, 54, 42, 47 ]
90
[ "54-53=1", "42+47=89", "1+89=90" ]
Current State: 90:[53, 54, 42, 47], Operations: [] Exploring Operation: 54-53=1, Resulting Numbers: [42, 47, 1] Generated Node #2: [42, 47, 1] from Operation: 54-53=1 Current State: 90:[42, 47, 1], Operations: ['54-53=1'] Exploring Operation: 42+47=89, Resulting Numbers: [1, 89] Generated Node #3: [1, 89] from Operation: 42+47=89 Current State: 90:[1, 89], Operations: ['54-53=1', '42+47=89'] Exploring Operation: 1+89=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[53, 54, 42, 47], Operations: [] Exploring Operation: 54-47=7, Resulting Numbers: [53, 42, 7] Generated Node #0,0: 90:[53, 42, 7] Operation: 54-47=7 Exploring Operation: 53-42=11, Resulting Numbers: [54, 47, 11] Generated Node #0,1: 90:[54, 47, 11] Operation: 53-42=11 Exploring Operation: 54-53=1, Resulting Numbers: [42, 47, 1] Generated Node #0,2: 90:[42, 47, 1] Operation: 54-53=1 Exploring Operation: 54-42=12, Resulting Numbers: [53, 47, 12] Generated Node #0,3: 90:[53, 47, 12] Operation: 54-42=12 Exploring Operation: 53-47=6, Resulting Numbers: [54, 42, 6] Generated Node #0,4: 90:[54, 42, 6] Operation: 53-47=6 Moving to Node #0,2 Current State: 90:[42, 47, 1], Operations: ['54-53=1'] Exploring Operation: 47-42=5, Resulting Numbers: [1, 5] Generated Node #0,2,0: 90:[1, 5] Operation: 47-42=5 Exploring Operation: 42+1=43, Resulting Numbers: [47, 43] Generated Node #0,2,1: 90:[47, 43] Operation: 42+1=43 Exploring Operation: 42+47=89, Resulting Numbers: [1, 89] Generated Node #0,2,2: 90:[1, 89] Operation: 42+47=89 Exploring Operation: 47-1=46, Resulting Numbers: [42, 46] Generated Node #0,2,3: 90:[42, 46] Operation: 47-1=46 Exploring Operation: 42*1=42, Resulting Numbers: [47, 42] Generated Node #0,2,4: 90:[47, 42] Operation: 42*1=42 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 90:[1, 5], Operations: ['54-53=1', '47-42=5'] Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 90:[1, 89], Operations: ['54-53=1', '42+47=89'] Exploring Operation: 1+89=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[53, 54, 42, 47], Operations: [] Exploring Operation: 54-53=1, Resulting Numbers: [42, 47, 1] Generated Node #0,2: 90:[42, 47, 1] Operation: 54-53=1 Moving to Node #0,2 Current State: 90:[42, 47, 1], Operations: ['54-53=1'] Exploring Operation: 42+47=89, Resulting Numbers: [1, 89] Generated Node #0,2,2: 90:[1, 89] Operation: 42+47=89 Moving to Node #0,2,2 Current State: 90:[1, 89], Operations: ['54-53=1', '42+47=89'] Exploring Operation: 1+89=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 3, 29, 6, 33 ]
46
[ "33/3=11", "29+6=35", "11+35=46" ]
Current State: 46:[3, 29, 6, 33], Operations: [] Exploring Operation: 33/3=11, Resulting Numbers: [29, 6, 11] Generated Node #2: [29, 6, 11] from Operation: 33/3=11 Current State: 46:[29, 6, 11], Operations: ['33/3=11'] Exploring Operation: 29+6=35, Resulting Numbers: [11, 35] Generated Node #3: [11, 35] from Operation: 29+6=35 Current State: 46:[11, 35], Operations: ['33/3=11', '29+6=35'] Exploring Operation: 11+35=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[3, 29, 6, 33], Operations: [] Exploring Operation: 6+33=39, Resulting Numbers: [3, 29, 39] Generated Node #0,0: 46:[3, 29, 39] Operation: 6+33=39 Exploring Operation: 33-6=27, Resulting Numbers: [3, 29, 27] Generated Node #0,1: 46:[3, 29, 27] Operation: 33-6=27 Exploring Operation: 33-29=4, Resulting Numbers: [3, 6, 4] Generated Node #0,2: 46:[3, 6, 4] Operation: 33-29=4 Exploring Operation: 29-6=23, Resulting Numbers: [3, 33, 23] Generated Node #0,3: 46:[3, 33, 23] Operation: 29-6=23 Exploring Operation: 6/3=2, Resulting Numbers: [29, 33, 2] Generated Node #0,4: 46:[29, 33, 2] Operation: 6/3=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[3, 6, 4], Operations: ['33-29=4'] Exploring Operation: 6-4=2, Resulting Numbers: [3, 2] Generated Node #0,2,0: 46:[3, 2] Operation: 6-4=2 Exploring Operation: 6-3=3, Resulting Numbers: [4, 3] Generated Node #0,2,1: 46:[4, 3] Operation: 6-3=3 Exploring Operation: 4-3=1, Resulting Numbers: [6, 1] Generated Node #0,2,2: 46:[6, 1] Operation: 4-3=1 Exploring Operation: 6/3=2, Resulting Numbers: [4, 2] Generated Node #0,2,3: 46:[4, 2] Operation: 6/3=2 Exploring Operation: 6*4=24, Resulting Numbers: [3, 24] Generated Node #0,2,4: 46:[3, 24] Operation: 6*4=24 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 46:[3, 2], Operations: ['33-29=4', '6-4=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,46 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 46:[4, 2], Operations: ['33-29=4', '6/3=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,46 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,46 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 46:[3, 24], Operations: ['33-29=4', '6*4=24'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,46 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 46:[4, 3], Operations: ['33-29=4', '6-3=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 46:[6, 1], Operations: ['33-29=4', '4-3=1'] Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,46 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[3, 29, 27], Operations: ['33-6=27'] Exploring Operation: 29+27=56, Resulting Numbers: [3, 56] Generated Node #0,1,0: 46:[3, 56] Operation: 29+27=56 Exploring Operation: 29-27=2, Resulting Numbers: [3, 2] Generated Node #0,1,1: 46:[3, 2] Operation: 29-27=2 Exploring Operation: 3+29=32, Resulting Numbers: [27, 32] Generated Node #0,1,2: 46:[27, 32] Operation: 3+29=32 Exploring Operation: 27-3=24, Resulting Numbers: [29, 24] Generated Node #0,1,3: 46:[29, 24] Operation: 27-3=24 Exploring Operation: 29-3=26, Resulting Numbers: [27, 26] Generated Node #0,1,4: 46:[27, 26] Operation: 29-3=26 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 46:[3, 2], Operations: ['33-6=27', '29-27=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,46 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 46:[29, 24], Operations: ['33-6=27', '27-3=24'] Exploring Operation: 29-24=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 29+24=53, Resulting Numbers: [53] 53,46 unequal: No Solution Exploring Operation: 29*24=696, Resulting Numbers: [696] 696,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 46:[27, 26], Operations: ['33-6=27', '29-3=26'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 27+26=53, Resulting Numbers: [53] 53,46 unequal: No Solution Exploring Operation: 27*26=702, Resulting Numbers: [702] 702,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[3, 56], Operations: ['33-6=27', '29+27=56'] Exploring Operation: 3*56=168, Resulting Numbers: [168] 168,46 unequal: No Solution Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,46 unequal: No Solution Exploring Operation: 3+56=59, Resulting Numbers: [59] 59,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 46:[27, 32], Operations: ['33-6=27', '3+29=32'] Exploring Operation: 27+32=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 27*32=864, Resulting Numbers: [864] 864,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 46:[3, 33, 23], Operations: ['29-6=23'] Exploring Operation: 33+23=56, Resulting Numbers: [3, 56] Generated Node #0,3,0: 46:[3, 56] Operation: 33+23=56 Exploring Operation: 3+33=36, Resulting Numbers: [23, 36] Generated Node #0,3,1: 46:[23, 36] Operation: 3+33=36 Exploring Operation: 33/3=11, Resulting Numbers: [23, 11] Generated Node #0,3,2: 46:[23, 11] Operation: 33/3=11 Exploring Operation: 33-23=10, Resulting Numbers: [3, 10] Generated Node #0,3,3: 46:[3, 10] Operation: 33-23=10 Exploring Operation: 33-3=30, Resulting Numbers: [23, 30] Generated Node #0,3,4: 46:[23, 30] Operation: 33-3=30 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 46:[23, 30], Operations: ['29-6=23', '33-3=30'] Exploring Operation: 30-23=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 23+30=53, Resulting Numbers: [53] 53,46 unequal: No Solution Exploring Operation: 23*30=690, Resulting Numbers: [690] 690,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 46:[23, 11], Operations: ['29-6=23', '33/3=11'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 23*11=253, Resulting Numbers: [253] 253,46 unequal: No Solution Exploring Operation: 23+11=34, Resulting Numbers: [34] 34,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 46:[3, 10], Operations: ['29-6=23', '33-23=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 46:[23, 36], Operations: ['29-6=23', '3+33=36'] Exploring Operation: 23+36=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 23*36=828, Resulting Numbers: [828] 828,46 unequal: No Solution Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 46:[3, 56], Operations: ['29-6=23', '33+23=56'] Exploring Operation: 3+56=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,46 unequal: No Solution Exploring Operation: 3*56=168, Resulting Numbers: [168] 168,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[3, 29, 39], Operations: ['6+33=39'] Exploring Operation: 39-3=36, Resulting Numbers: [29, 36] Generated Node #0,0,0: 46:[29, 36] Operation: 39-3=36 Exploring Operation: 29-3=26, Resulting Numbers: [39, 26] Generated Node #0,0,1: 46:[39, 26] Operation: 29-3=26 Exploring Operation: 3+39=42, Resulting Numbers: [29, 42] Generated Node #0,0,2: 46:[29, 42] Operation: 3+39=42 Exploring Operation: 3+29=32, Resulting Numbers: [39, 32] Generated Node #0,0,3: 46:[39, 32] Operation: 3+29=32 Exploring Operation: 39-29=10, Resulting Numbers: [3, 10] Generated Node #0,0,4: 46:[3, 10] Operation: 39-29=10 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 46:[3, 10], Operations: ['6+33=39', '39-29=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 46:[39, 26], Operations: ['6+33=39', '29-3=26'] Exploring Operation: 39*26=1014, Resulting Numbers: [1014] 1014,46 unequal: No Solution Exploring Operation: 39-26=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 39+26=65, Resulting Numbers: [65] 65,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 46:[29, 42], Operations: ['6+33=39', '3+39=42'] Exploring Operation: 29*42=1218, Resulting Numbers: [1218] 1218,46 unequal: No Solution Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 29+42=71, Resulting Numbers: [71] 71,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[29, 36], Operations: ['6+33=39', '39-3=36'] Exploring Operation: 29+36=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 36-29=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 29*36=1044, Resulting Numbers: [1044] 1044,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 46:[39, 32], Operations: ['6+33=39', '3+29=32'] Exploring Operation: 39*32=1248, Resulting Numbers: [1248] 1248,46 unequal: No Solution Exploring Operation: 39+32=71, Resulting Numbers: [71] 71,46 unequal: No Solution Exploring Operation: 39-32=7, Resulting Numbers: [7] 7,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 46:[29, 33, 2], Operations: ['6/3=2'] Exploring Operation: 33-29=4, Resulting Numbers: [2, 4] Generated Node #0,4,0: 46:[2, 4] Operation: 33-29=4 Exploring Operation: 29+33=62, Resulting Numbers: [2, 62] Generated Node #0,4,1: 46:[2, 62] Operation: 29+33=62 Exploring Operation: 33-2=31, Resulting Numbers: [29, 31] Generated Node #0,4,2: 46:[29, 31] Operation: 33-2=31 Exploring Operation: 33+2=35, Resulting Numbers: [29, 35] Generated Node #0,4,3: 46:[29, 35] Operation: 33+2=35 Exploring Operation: 29-2=27, Resulting Numbers: [33, 27] Generated Node #0,4,4: 46:[33, 27] Operation: 29-2=27 Moving to Node #0,4,0 Current State: 46:[2, 4], Operations: ['6/3=2', '33-29=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,46 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,46 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,46 unequal: No Solution Moving to Node #0,4,4 Current State: 46:[33, 27], Operations: ['6/3=2', '29-2=27'] Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,46 unequal: No Solution Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,46 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,46 unequal: No Solution Moving to Node #0,4,2 Current State: 46:[29, 31], Operations: ['6/3=2', '33-2=31'] Exploring Operation: 29*31=899, Resulting Numbers: [899] 899,46 unequal: No Solution Exploring Operation: 29+31=60, Resulting Numbers: [60] 60,46 unequal: No Solution Exploring Operation: 31-29=2, Resulting Numbers: [2] 2,46 unequal: No Solution Moving to Node #0,4,1 Current State: 46:[2, 62], Operations: ['6/3=2', '29+33=62'] Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,46 unequal: No Solution Exploring Operation: 2*62=124, Resulting Numbers: [124] 124,46 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,46 unequal: No Solution Moving to Node #0,4,3 Current State: 46:[29, 35], Operations: ['6/3=2', '33+2=35'] Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,46 unequal: No Solution Exploring Operation: 29*35=1015, Resulting Numbers: [1015] 1015,46 unequal: No Solution Exploring Operation: 29+35=64, Resulting Numbers: [64] 64,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 4, 2, 45, 2 ]
55
[ "4*2=8", "45+2=47", "8+47=55" ]
Current State: 55:[4, 2, 45, 2], Operations: [] Exploring Operation: 4*2=8, Resulting Numbers: [45, 8] Generated Node #2: [45, 8] from Operation: 4*2=8 Current State: 55:[45, 8], Operations: ['4*2=8'] Exploring Operation: 45+2=47, Resulting Numbers: [8, 47] Generated Node #3: [8, 47] from Operation: 45+2=47 Current State: 55:[8, 47], Operations: ['4*2=8', '45+2=47'] Exploring Operation: 8+47=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[4, 2, 45, 2], Operations: [] Exploring Operation: 2+2=4, Resulting Numbers: [4, 45, 4] Generated Node #0,0: 55:[4, 45, 4] Operation: 2+2=4 Exploring Operation: 2*2=4, Resulting Numbers: [4, 45, 4] Generated Node #0,1: 55:[4, 45, 4] Operation: 2*2=4 Exploring Operation: 2+45=47, Resulting Numbers: [4, 2, 47] Generated Node #0,2: 55:[4, 2, 47] Operation: 2+45=47 Exploring Operation: 4+45=49, Resulting Numbers: [2, 2, 49] Generated Node #0,3: 55:[2, 2, 49] Operation: 4+45=49 Moving to Node #0,0 Current State: 55:[4, 45, 4], Operations: ['2+2=4'] Exploring Operation: 4/4=1, Resulting Numbers: [45, 1] Generated Node #0,0,0: 55:[45, 1] Operation: 4/4=1 Exploring Operation: 4+4=8, Resulting Numbers: [45, 8] Generated Node #0,0,1: 55:[45, 8] Operation: 4+4=8 Exploring Operation: 4+45=49, Resulting Numbers: [4, 49] Generated Node #0,0,2: 55:[4, 49] Operation: 4+45=49 Exploring Operation: 45+4=49, Resulting Numbers: [4, 49] Generated Node #0,0,3: 55:[4, 49] Operation: 45+4=49 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 55:[4, 49], Operations: ['2+2=4', '4+45=49'] Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,55 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,55 unequal: No Solution Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,55 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, 49], Operations: ['2+2=4', '45+4=49'] Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,55 unequal: No Solution Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,55 unequal: No Solution Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,55 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:[45, 8], Operations: ['2+2=4', '4+4=8'] Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,55 unequal: No Solution Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,55 unequal: No Solution Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,55 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 #0,0,0 Current State: 55:[45, 1], Operations: ['2+2=4', '4/4=1'] Exploring Operation: 45+1=46, Resulting Numbers: [46] 46,55 unequal: No Solution Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,55 unequal: No Solution Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,55 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,55 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: 55:[4, 2, 47], Operations: ['2+45=47'] Exploring Operation: 4+47=51, Resulting Numbers: [2, 51] Generated Node #0,2,0: 55:[2, 51] Operation: 4+47=51 Exploring Operation: 4*2=8, Resulting Numbers: [47, 8] Generated Node #0,2,1: 55:[47, 8] Operation: 4*2=8 Exploring Operation: 4+2=6, Resulting Numbers: [47, 6] Generated Node #0,2,2: 55:[47, 6] Operation: 4+2=6 Exploring Operation: 2+47=49, Resulting Numbers: [4, 49] Generated Node #0,2,3: 55:[4, 49] Operation: 2+47=49 Moving to Node #0,1 Current State: 55:[4, 45, 4], Operations: ['2*2=4'] Exploring Operation: 4+4=8, Resulting Numbers: [45, 8] Generated Node #0,1,0: 55:[45, 8] Operation: 4+4=8 Exploring Operation: 45+4=49, Resulting Numbers: [4, 49] Generated Node #0,1,1: 55:[4, 49] Operation: 45+4=49 Exploring Operation: 4/4=1, Resulting Numbers: [45, 1] Generated Node #0,1,2: 55:[45, 1] Operation: 4/4=1 Exploring Operation: 4+45=49, Resulting Numbers: [4, 49] Generated Node #0,1,3: 55:[4, 49] Operation: 4+45=49 Moving to Node #0,3 Current State: 55:[2, 2, 49], Operations: ['4+45=49'] Exploring Operation: 2+49=51, Resulting Numbers: [2, 51] Generated Node #0,3,0: 55:[2, 51] Operation: 2+49=51 Exploring Operation: 2+2=4, Resulting Numbers: [49, 4] Generated Node #0,3,1: 55:[49, 4] Operation: 2+2=4 Exploring Operation: 2+49=51, Resulting Numbers: [2, 51] Generated Node #0,3,2: 55:[2, 51] Operation: 2+49=51 Exploring Operation: 2*2=4, Resulting Numbers: [49, 4] Generated Node #0,3,3: 55:[49, 4] Operation: 2*2=4 Moving to Node #0,2,0 Current State: 55:[2, 51], Operations: ['2+45=47', '4+47=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,55 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,55 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,55 unequal: No Solution Moving to Node #0,1,3 Current State: 55:[4, 49], Operations: ['2*2=4', '4+45=49'] Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,55 unequal: No Solution Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,55 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,55 unequal: No Solution Moving to Node #0,3,3 Current State: 55:[49, 4], Operations: ['4+45=49', '2*2=4'] Exploring Operation: 49*4=196, Resulting Numbers: [196] 196,55 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,55 unequal: No Solution Exploring Operation: 49+4=53, Resulting Numbers: [53] 53,55 unequal: No Solution Moving to Node #0,3,2 Current State: 55:[2, 51], Operations: ['4+45=49', '2+49=51'] Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,55 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,55 unequal: No Solution Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,55 unequal: No Solution Moving to Node #0,3,1 Current State: 55:[49, 4], Operations: ['4+45=49', '2+2=4'] Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,55 unequal: No Solution Exploring Operation: 49*4=196, Resulting Numbers: [196] 196,55 unequal: No Solution Exploring Operation: 49+4=53, Resulting Numbers: [53] 53,55 unequal: No Solution Moving to Node #0,2,3 Current State: 55:[4, 49], Operations: ['2+45=47', '2+47=49'] Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,55 unequal: No Solution Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,55 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[4, 49], Operations: ['2*2=4', '45+4=49'] Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,55 unequal: No Solution Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,55 unequal: No Solution Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,55 unequal: No Solution Moving to Node #0,3,0 Current State: 55:[2, 51], Operations: ['4+45=49', '2+49=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,55 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,55 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[47, 6], Operations: ['2+45=47', '4+2=6'] Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,55 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,55 unequal: No Solution Exploring Operation: 47*6=282, Resulting Numbers: [282] 282,55 unequal: No Solution Moving to Node #0,2,1 Current State: 55:[47, 8], Operations: ['2+45=47', '4*2=8'] Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,55 unequal: No Solution Exploring Operation: 47+8=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[4, 2, 45, 2], Operations: [] Exploring Operation: 2+45=47, Resulting Numbers: [4, 2, 47] Generated Node #0,2: 55:[4, 2, 47] Operation: 2+45=47 Moving to Node #0,2 Current State: 55:[4, 2, 47], Operations: ['2+45=47'] Exploring Operation: 4*2=8, Resulting Numbers: [47, 8] Generated Node #0,2,1: 55:[47, 8] Operation: 4*2=8 Moving to Node #0,2,1 Current State: 55:[47, 8], Operations: ['2+45=47', '4*2=8'] Exploring Operation: 47+8=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
0.942708
hs_4
mult_heuristic
[ 21, 50, 75, 29 ]
43
[ "21*50=1050", "1050/75=14", "29+14=43" ]
Current State: 43:[21, 50, 75, 29], Operations: [] Exploring Operation: 21*50=1050, Resulting Numbers: [75, 29, 1050] Generated Node #2: [75, 29, 1050] from Operation: 21*50=1050 Current State: 43:[75, 29, 1050], Operations: ['21*50=1050'] Exploring Operation: 1050/75=14, Resulting Numbers: [29, 14] Generated Node #3: [29, 14] from Operation: 1050/75=14 Current State: 43:[29, 14], Operations: ['21*50=1050', '1050/75=14'] Exploring Operation: 29+14=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[21, 50, 75, 29], Operations: [] Exploring Operation: 75-21=54, Resulting Numbers: [50, 29, 54] Generated Node #0,0: 43:[50, 29, 54] Operation: 75-21=54 Exploring Operation: 21+29=50, Resulting Numbers: [50, 75, 50] Generated Node #0,1: 43:[50, 75, 50] Operation: 21+29=50 Exploring Operation: 75-29=46, Resulting Numbers: [21, 50, 46] Generated Node #0,2: 43:[21, 50, 46] Operation: 75-29=46 Moving to Node #0,0 Current State: 43:[50, 29, 54], Operations: ['75-21=54'] Exploring Operation: 54-29=25, Resulting Numbers: [50, 25] Generated Node #0,0,0: 43:[50, 25] Operation: 54-29=25 Exploring Operation: 50-29=21, Resulting Numbers: [54, 21] Generated Node #0,0,1: 43:[54, 21] Operation: 50-29=21 Exploring Operation: 50+29=79, Resulting Numbers: [54, 79] Generated Node #0,0,2: 43:[54, 79] Operation: 50+29=79 Moving to Node #0,2 Current State: 43:[21, 50, 46], Operations: ['75-29=46'] Exploring Operation: 46-21=25, Resulting Numbers: [50, 25] Generated Node #0,2,0: 43:[50, 25] Operation: 46-21=25 Exploring Operation: 21+50=71, Resulting Numbers: [46, 71] Generated Node #0,2,1: 43:[46, 71] Operation: 21+50=71 Exploring Operation: 50-21=29, Resulting Numbers: [46, 29] Generated Node #0,2,2: 43:[46, 29] Operation: 50-21=29 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 43:[46, 29], Operations: ['75-29=46', '50-21=29'] Exploring Operation: 46+29=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 46*29=1334, Resulting Numbers: [1334] 1334,43 unequal: No Solution Exploring Operation: 46-29=17, Resulting Numbers: [17] 17,43 unequal: No Solution No 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: 43:[50, 25], Operations: ['75-29=46', '46-21=25'] Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 50+25=75, Resulting Numbers: [75] 75,43 unequal: No Solution No 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: 43:[46, 71], Operations: ['75-29=46', '21+50=71'] Exploring Operation: 71-46=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 46+71=117, Resulting Numbers: [117] 117,43 unequal: No Solution Exploring Operation: 46*71=3266, Resulting Numbers: [3266] 3266,43 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: 43:[50, 75, 50], Operations: ['21+29=50'] Exploring Operation: 50/50=1, Resulting Numbers: [75, 1] Generated Node #0,1,0: 43:[75, 1] Operation: 50/50=1 Exploring Operation: 75-50=25, Resulting Numbers: [50, 25] Generated Node #0,1,1: 43:[50, 25] Operation: 75-50=25 Exploring Operation: 75-50=25, Resulting Numbers: [50, 25] Generated Node #0,1,2: 43:[50, 25] Operation: 75-50=25 Moving to Node #0,0,0 Current State: 43:[50, 25], Operations: ['75-21=54', '54-29=25'] Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 50+25=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[50, 25], Operations: ['21+29=50', '75-50=25'] Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 50+25=75, Resulting Numbers: [75] 75,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[50, 25], Operations: ['21+29=50', '75-50=25'] Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 50+25=75, Resulting Numbers: [75] 75,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[54, 21], Operations: ['75-21=54', '50-29=21'] Exploring Operation: 54*21=1134, Resulting Numbers: [1134] 1134,43 unequal: No Solution Exploring Operation: 54-21=33, Resulting Numbers: [33] 33,43 unequal: No Solution Exploring Operation: 54+21=75, Resulting Numbers: [75] 75,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[54, 79], Operations: ['75-21=54', '50+29=79'] Exploring Operation: 79-54=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 54*79=4266, Resulting Numbers: [4266] 4266,43 unequal: No Solution Exploring Operation: 54+79=133, Resulting Numbers: [133] 133,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[75, 1], Operations: ['21+29=50', '50/50=1'] Exploring Operation: 75*1=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 75-1=74, Resulting Numbers: [74] 74,43 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 81, 87, 78, 14 ]
43
[ "81-78=3", "87/3=29", "14+29=43" ]
Current State: 43:[81, 87, 78, 14], Operations: [] Exploring Operation: 81-78=3, Resulting Numbers: [87, 14, 3] Generated Node #2: [87, 14, 3] from Operation: 81-78=3 Current State: 43:[87, 14, 3], Operations: ['81-78=3'] Exploring Operation: 87/3=29, Resulting Numbers: [14, 29] Generated Node #3: [14, 29] from Operation: 87/3=29 Current State: 43:[14, 29], Operations: ['81-78=3', '87/3=29'] Exploring Operation: 14+29=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[81, 87, 78, 14], Operations: [] Exploring Operation: 87-81=6, Resulting Numbers: [78, 14, 6] Generated Node #0,0: 43:[78, 14, 6] Operation: 87-81=6 Moving to Node #0,0 Current State: 43:[78, 14, 6], Operations: ['87-81=6'] Exploring Operation: 78-14=64, Resulting Numbers: [6, 64] Generated Node #0,0,0: 43:[6, 64] Operation: 78-14=64 Moving to Node #0,0,0 Current State: 43:[6, 64], Operations: ['87-81=6', '78-14=64'] Exploring Operation: 64-6=58, Resulting Numbers: [58] 58,43 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 97, 8, 47, 15 ]
43
[ "97+8=105", "47+15=62", "105-62=43" ]
Current State: 43:[97, 8, 47, 15], Operations: [] Exploring Operation: 97+8=105, Resulting Numbers: [47, 15, 105] Generated Node #2: [47, 15, 105] from Operation: 97+8=105 Current State: 43:[47, 15, 105], Operations: ['97+8=105'] Exploring Operation: 47+15=62, Resulting Numbers: [105, 62] Generated Node #3: [105, 62] from Operation: 47+15=62 Current State: 43:[105, 62], Operations: ['97+8=105', '47+15=62'] Exploring Operation: 105-62=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[97, 8, 47, 15], Operations: [] Exploring Operation: 97-15=82, Resulting Numbers: [8, 47, 82] Generated Node #0,0: 43:[8, 47, 82] Operation: 97-15=82 Exploring Operation: 8+15=23, Resulting Numbers: [97, 47, 23] Generated Node #0,1: 43:[97, 47, 23] Operation: 8+15=23 Exploring Operation: 97-47=50, Resulting Numbers: [8, 15, 50] Generated Node #0,2: 43:[8, 15, 50] Operation: 97-47=50 Exploring Operation: 97-8=89, Resulting Numbers: [47, 15, 89] Generated Node #0,3: 43:[47, 15, 89] Operation: 97-8=89 Moving to Node #0,2 Current State: 43:[8, 15, 50], Operations: ['97-47=50'] Exploring Operation: 15-8=7, Resulting Numbers: [50, 7] Generated Node #0,2,0: 43:[50, 7] Operation: 15-8=7 Exploring Operation: 8+50=58, Resulting Numbers: [15, 58] Generated Node #0,2,1: 43:[15, 58] Operation: 8+50=58 Exploring Operation: 8+15=23, Resulting Numbers: [50, 23] Generated Node #0,2,2: 43:[50, 23] Operation: 8+15=23 Exploring Operation: 50-8=42, Resulting Numbers: [15, 42] Generated Node #0,2,3: 43:[15, 42] Operation: 50-8=42 Moving to Node #0,1 Current State: 43:[97, 47, 23], Operations: ['8+15=23'] Exploring Operation: 97-23=74, Resulting Numbers: [47, 74] Generated Node #0,1,0: 43:[47, 74] Operation: 97-23=74 Exploring Operation: 47-23=24, Resulting Numbers: [97, 24] Generated Node #0,1,1: 43:[97, 24] Operation: 47-23=24 Exploring Operation: 97+23=120, Resulting Numbers: [47, 120] Generated Node #0,1,2: 43:[47, 120] Operation: 97+23=120 Exploring Operation: 97-47=50, Resulting Numbers: [23, 50] Generated Node #0,1,3: 43:[23, 50] Operation: 97-47=50 Moving to Node #0,0 Current State: 43:[8, 47, 82], Operations: ['97-15=82'] Exploring Operation: 82-8=74, Resulting Numbers: [47, 74] Generated Node #0,0,0: 43:[47, 74] Operation: 82-8=74 Exploring Operation: 8+47=55, Resulting Numbers: [82, 55] Generated Node #0,0,1: 43:[82, 55] Operation: 8+47=55 Exploring Operation: 47-8=39, Resulting Numbers: [82, 39] Generated Node #0,0,2: 43:[82, 39] Operation: 47-8=39 Exploring Operation: 82-47=35, Resulting Numbers: [8, 35] Generated Node #0,0,3: 43:[8, 35] Operation: 82-47=35 Moving to Node #0,3 Current State: 43:[47, 15, 89], Operations: ['97-8=89'] Exploring Operation: 89-47=42, Resulting Numbers: [15, 42] Generated Node #0,3,0: 43:[15, 42] Operation: 89-47=42 Exploring Operation: 47-15=32, Resulting Numbers: [89, 32] Generated Node #0,3,1: 43:[89, 32] Operation: 47-15=32 Exploring Operation: 47+15=62, Resulting Numbers: [89, 62] Generated Node #0,3,2: 43:[89, 62] Operation: 47+15=62 Exploring Operation: 89-15=74, Resulting Numbers: [47, 74] Generated Node #0,3,3: 43:[47, 74] Operation: 89-15=74 Moving to Node #0,2,2 Current State: 43:[50, 23], Operations: ['97-47=50', '8+15=23'] Exploring Operation: 50*23=1150, Resulting Numbers: [1150] 1150,43 unequal: No Solution Exploring Operation: 50+23=73, Resulting Numbers: [73] 73,43 unequal: No Solution Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[23, 50], Operations: ['8+15=23', '97-47=50'] Exploring Operation: 23+50=73, Resulting Numbers: [73] 73,43 unequal: No Solution Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,43 unequal: No Solution Exploring Operation: 23*50=1150, Resulting Numbers: [1150] 1150,43 unequal: No Solution Moving to Node #0,3,0 Current State: 43:[15, 42], Operations: ['97-8=89', '89-47=42'] Exploring Operation: 15+42=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 15*42=630, Resulting Numbers: [630] 630,43 unequal: No Solution Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,43 unequal: No Solution Moving to Node #0,2,3 Current State: 43:[15, 42], Operations: ['97-47=50', '50-8=42'] Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,43 unequal: No Solution Exploring Operation: 15+42=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 15*42=630, Resulting Numbers: [630] 630,43 unequal: No Solution Moving to Node #0,3,3 Current State: 43:[47, 74], Operations: ['97-8=89', '89-15=74'] Exploring Operation: 47+74=121, Resulting Numbers: [121] 121,43 unequal: No Solution Exploring Operation: 47*74=3478, Resulting Numbers: [3478] 3478,43 unequal: No Solution Exploring Operation: 74-47=27, Resulting Numbers: [27] 27,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[47, 74], Operations: ['8+15=23', '97-23=74'] Exploring Operation: 47*74=3478, Resulting Numbers: [3478] 3478,43 unequal: No Solution Exploring Operation: 47+74=121, Resulting Numbers: [121] 121,43 unequal: No Solution Exploring Operation: 74-47=27, Resulting Numbers: [27] 27,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[47, 74], Operations: ['97-15=82', '82-8=74'] Exploring Operation: 74-47=27, Resulting Numbers: [27] 27,43 unequal: No Solution Exploring Operation: 47*74=3478, Resulting Numbers: [3478] 3478,43 unequal: No Solution Exploring Operation: 47+74=121, Resulting Numbers: [121] 121,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[50, 7], Operations: ['97-47=50', '15-8=7'] Exploring Operation: 50*7=350, Resulting Numbers: [350] 350,43 unequal: No Solution Exploring Operation: 50+7=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[97, 8, 47, 15], Operations: [] Exploring Operation: 97-47=50, Resulting Numbers: [8, 15, 50] Generated Node #0,2: 43:[8, 15, 50] Operation: 97-47=50 Moving to Node #0,2 Current State: 43:[8, 15, 50], Operations: ['97-47=50'] Exploring Operation: 15-8=7, Resulting Numbers: [50, 7] Generated Node #0,2,0: 43:[50, 7] Operation: 15-8=7 Moving to Node #0,2,0 Current State: 43:[50, 7], Operations: ['97-47=50', '15-8=7'] Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
0.958333
hs_4
mult_heuristic
[ 66, 58, 73, 54 ]
27
[ "66-58=8", "73-54=19", "8+19=27" ]
Current State: 27:[66, 58, 73, 54], Operations: [] Exploring Operation: 66-58=8, Resulting Numbers: [73, 54, 8] Generated Node #2: [73, 54, 8] from Operation: 66-58=8 Current State: 27:[73, 54, 8], Operations: ['66-58=8'] Exploring Operation: 73-54=19, Resulting Numbers: [8, 19] Generated Node #3: [8, 19] from Operation: 73-54=19 Current State: 27:[8, 19], Operations: ['66-58=8', '73-54=19'] Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[66, 58, 73, 54], Operations: [] Exploring Operation: 73-66=7, Resulting Numbers: [58, 54, 7] Generated Node #0,0: 27:[58, 54, 7] Operation: 73-66=7 Moving to Node #0,0 Current State: 27:[58, 54, 7], Operations: ['73-66=7'] Exploring Operation: 58-54=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 27:[7, 4] Operation: 58-54=4 Moving to Node #0,0,0 Current State: 27:[7, 4], Operations: ['73-66=7', '58-54=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,27 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 40, 25, 50, 89 ]
80
[ "89-25=64", "50*64=3200", "3200/40=80" ]
Current State: 80:[40, 25, 50, 89], Operations: [] Exploring Operation: 89-25=64, Resulting Numbers: [40, 50, 64] Generated Node #2: [40, 50, 64] from Operation: 89-25=64 Current State: 80:[40, 50, 64], Operations: ['89-25=64'] Exploring Operation: 50*64=3200, Resulting Numbers: [40, 3200] Generated Node #3: [40, 3200] from Operation: 50*64=3200 Current State: 80:[40, 3200], Operations: ['89-25=64', '50*64=3200'] Exploring Operation: 3200/40=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[40, 25, 50, 89], Operations: [] Exploring Operation: 50-25=25, Resulting Numbers: [40, 89, 25] Generated Node #0,0: 80:[40, 89, 25] Operation: 50-25=25 Exploring Operation: 50-40=10, Resulting Numbers: [25, 89, 10] Generated Node #0,1: 80:[25, 89, 10] Operation: 50-40=10 Exploring Operation: 50/25=2, Resulting Numbers: [40, 89, 2] Generated Node #0,2: 80:[40, 89, 2] Operation: 50/25=2 Exploring Operation: 89-50=39, Resulting Numbers: [40, 25, 39] Generated Node #0,3: 80:[40, 25, 39] Operation: 89-50=39 Exploring Operation: 25+50=75, Resulting Numbers: [40, 89, 75] Generated Node #0,4: 80:[40, 89, 75] Operation: 25+50=75 Moving to Node #0,3 Current State: 80:[40, 25, 39], Operations: ['89-50=39'] Exploring Operation: 39-25=14, Resulting Numbers: [40, 14] Generated Node #0,3,0: 80:[40, 14] Operation: 39-25=14 Exploring Operation: 40-25=15, Resulting Numbers: [39, 15] Generated Node #0,3,1: 80:[39, 15] Operation: 40-25=15 Exploring Operation: 40+39=79, Resulting Numbers: [25, 79] Generated Node #0,3,2: 80:[25, 79] Operation: 40+39=79 Exploring Operation: 40+25=65, Resulting Numbers: [39, 65] Generated Node #0,3,3: 80:[39, 65] Operation: 40+25=65 Exploring Operation: 40-39=1, Resulting Numbers: [25, 1] Generated Node #0,3,4: 80:[25, 1] Operation: 40-39=1 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 80:[40, 14], Operations: ['89-50=39', '39-25=14'] Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,80 unequal: No Solution Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,80 unequal: No Solution Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 80:[39, 15], Operations: ['89-50=39', '40-25=15'] Exploring Operation: 39+15=54, Resulting Numbers: [54] 54,80 unequal: No Solution Exploring Operation: 39*15=585, Resulting Numbers: [585] 585,80 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 80:[25, 79], Operations: ['89-50=39', '40+39=79'] Exploring Operation: 25*79=1975, Resulting Numbers: [1975] 1975,80 unequal: No Solution Exploring Operation: 79-25=54, Resulting Numbers: [54] 54,80 unequal: No Solution Exploring Operation: 25+79=104, Resulting Numbers: [104] 104,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 80:[25, 1], Operations: ['89-50=39', '40-39=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 80:[39, 65], Operations: ['89-50=39', '40+25=65'] Exploring Operation: 39+65=104, Resulting Numbers: [104] 104,80 unequal: No Solution Exploring Operation: 39*65=2535, Resulting Numbers: [2535] 2535,80 unequal: No Solution Exploring Operation: 65-39=26, Resulting Numbers: [26] 26,80 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: 80:[40, 89, 2], Operations: ['50/25=2'] Exploring Operation: 89-40=49, Resulting Numbers: [2, 49] Generated Node #0,2,0: 80:[2, 49] Operation: 89-40=49 Exploring Operation: 40/2=20, Resulting Numbers: [89, 20] Generated Node #0,2,1: 80:[89, 20] Operation: 40/2=20 Exploring Operation: 40*2=80, Resulting Numbers: [89, 80] Generated Node #0,2,2: 80:[89, 80] Operation: 40*2=80 Exploring Operation: 89-2=87, Resulting Numbers: [40, 87] Generated Node #0,2,3: 80:[40, 87] Operation: 89-2=87 Exploring Operation: 40+2=42, Resulting Numbers: [89, 42] Generated Node #0,2,4: 80:[89, 42] Operation: 40+2=42 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 80:[40, 87], Operations: ['50/25=2', '89-2=87'] Exploring Operation: 87-40=47, Resulting Numbers: [47] 47,80 unequal: No Solution Exploring Operation: 40+87=127, Resulting Numbers: [127] 127,80 unequal: No Solution Exploring Operation: 40*87=3480, Resulting Numbers: [3480] 3480,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[2, 49], Operations: ['50/25=2', '89-40=49'] Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,80 unequal: No Solution Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,80 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 80:[89, 20], Operations: ['50/25=2', '40/2=20'] Exploring Operation: 89*20=1780, Resulting Numbers: [1780] 1780,80 unequal: No Solution Exploring Operation: 89+20=109, Resulting Numbers: [109] 109,80 unequal: No Solution Exploring Operation: 89-20=69, Resulting Numbers: [69] 69,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 80:[89, 80], Operations: ['50/25=2', '40*2=80'] Exploring Operation: 89*80=7120, Resulting Numbers: [7120] 7120,80 unequal: No Solution Exploring Operation: 89-80=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 89+80=169, Resulting Numbers: [169] 169,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 80:[89, 42], Operations: ['50/25=2', '40+2=42'] Exploring Operation: 89+42=131, Resulting Numbers: [131] 131,80 unequal: No Solution Exploring Operation: 89*42=3738, Resulting Numbers: [3738] 3738,80 unequal: No Solution Exploring Operation: 89-42=47, Resulting Numbers: [47] 47,80 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: 80:[40, 89, 25], Operations: ['50-25=25'] Exploring Operation: 89-25=64, Resulting Numbers: [40, 64] Generated Node #0,0,0: 80:[40, 64] Operation: 89-25=64 Exploring Operation: 89+25=114, Resulting Numbers: [40, 114] Generated Node #0,0,1: 80:[40, 114] Operation: 89+25=114 Exploring Operation: 40+25=65, Resulting Numbers: [89, 65] Generated Node #0,0,2: 80:[89, 65] Operation: 40+25=65 Exploring Operation: 40-25=15, Resulting Numbers: [89, 15] Generated Node #0,0,3: 80:[89, 15] Operation: 40-25=15 Exploring Operation: 89-40=49, Resulting Numbers: [25, 49] Generated Node #0,0,4: 80:[25, 49] Operation: 89-40=49 Moving to Node #0,1 Current State: 80:[25, 89, 10], Operations: ['50-40=10'] Exploring Operation: 89-25=64, Resulting Numbers: [10, 64] Generated Node #0,1,0: 80:[10, 64] Operation: 89-25=64 Exploring Operation: 89-10=79, Resulting Numbers: [25, 79] Generated Node #0,1,1: 80:[25, 79] Operation: 89-10=79 Exploring Operation: 25-10=15, Resulting Numbers: [89, 15] Generated Node #0,1,2: 80:[89, 15] Operation: 25-10=15 Exploring Operation: 25+10=35, Resulting Numbers: [89, 35] Generated Node #0,1,3: 80:[89, 35] Operation: 25+10=35 Exploring Operation: 89+10=99, Resulting Numbers: [25, 99] Generated Node #0,1,4: 80:[25, 99] Operation: 89+10=99 Moving to Node #0,4 Current State: 80:[40, 89, 75], Operations: ['25+50=75'] Exploring Operation: 75-40=35, Resulting Numbers: [89, 35] Generated Node #0,4,0: 80:[89, 35] Operation: 75-40=35 Exploring Operation: 40+75=115, Resulting Numbers: [89, 115] Generated Node #0,4,1: 80:[89, 115] Operation: 40+75=115 Exploring Operation: 89-75=14, Resulting Numbers: [40, 14] Generated Node #0,4,2: 80:[40, 14] Operation: 89-75=14 Exploring Operation: 89-40=49, Resulting Numbers: [75, 49] Generated Node #0,4,3: 80:[75, 49] Operation: 89-40=49 Exploring Operation: 40+89=129, Resulting Numbers: [75, 129] Generated Node #0,4,4: 80:[75, 129] Operation: 40+89=129 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 80:[40, 14], Operations: ['25+50=75', '89-75=14'] Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,80 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,80 unequal: No Solution Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 80:[89, 35], Operations: ['25+50=75', '75-40=35'] Exploring Operation: 89+35=124, Resulting Numbers: [124] 124,80 unequal: No Solution Exploring Operation: 89-35=54, Resulting Numbers: [54] 54,80 unequal: No Solution Exploring Operation: 89*35=3115, Resulting Numbers: [3115] 3115,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 80:[75, 49], Operations: ['25+50=75', '89-40=49'] Exploring Operation: 75+49=124, Resulting Numbers: [124] 124,80 unequal: No Solution Exploring Operation: 75-49=26, Resulting Numbers: [26] 26,80 unequal: No Solution Exploring Operation: 75*49=3675, Resulting Numbers: [3675] 3675,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 80:[89, 115], Operations: ['25+50=75', '40+75=115'] Exploring Operation: 115-89=26, Resulting Numbers: [26] 26,80 unequal: No Solution Exploring Operation: 89+115=204, Resulting Numbers: [204] 204,80 unequal: No Solution Exploring Operation: 89*115=10235, Resulting Numbers: [10235] 10235,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 80:[75, 129], Operations: ['25+50=75', '40+89=129'] Exploring Operation: 75*129=9675, Resulting Numbers: [9675] 9675,80 unequal: No Solution Exploring Operation: 75+129=204, Resulting Numbers: [204] 204,80 unequal: No Solution Exploring Operation: 129-75=54, Resulting Numbers: [54] 54,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 80:[25, 79], Operations: ['50-40=10', '89-10=79'] Exploring Operation: 79-25=54, Resulting Numbers: [54] 54,80 unequal: No Solution Exploring Operation: 25+79=104, Resulting Numbers: [104] 104,80 unequal: No Solution Exploring Operation: 25*79=1975, Resulting Numbers: [1975] 1975,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[89, 15], Operations: ['50-25=25', '40-25=15'] Exploring Operation: 89+15=104, Resulting Numbers: [104] 104,80 unequal: No Solution Exploring Operation: 89*15=1335, Resulting Numbers: [1335] 1335,80 unequal: No Solution Exploring Operation: 89-15=74, Resulting Numbers: [74] 74,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[89, 15], Operations: ['50-40=10', '25-10=15'] Exploring Operation: 89-15=74, Resulting Numbers: [74] 74,80 unequal: No Solution Exploring Operation: 89*15=1335, Resulting Numbers: [1335] 1335,80 unequal: No Solution Exploring Operation: 89+15=104, Resulting Numbers: [104] 104,80 unequal: No Solution Moving to Node #0,0,4 Current State: 80:[25, 49], Operations: ['50-25=25', '89-40=49'] Exploring Operation: 25*49=1225, Resulting Numbers: [1225] 1225,80 unequal: No Solution Exploring Operation: 25+49=74, Resulting Numbers: [74] 74,80 unequal: No Solution Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,80 unequal: No Solution Moving to Node #0,1,3 Current State: 80:[89, 35], Operations: ['50-40=10', '25+10=35'] Exploring Operation: 89*35=3115, Resulting Numbers: [3115] 3115,80 unequal: No Solution Exploring Operation: 89+35=124, Resulting Numbers: [124] 124,80 unequal: No Solution Exploring Operation: 89-35=54, Resulting Numbers: [54] 54,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[40, 64], Operations: ['50-25=25', '89-25=64'] Exploring Operation: 40+64=104, Resulting Numbers: [104] 104,80 unequal: No Solution Exploring Operation: 64-40=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 40*64=2560, Resulting Numbers: [2560] 2560,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[10, 64], Operations: ['50-40=10', '89-25=64'] Exploring Operation: 10*64=640, Resulting Numbers: [640] 640,80 unequal: No Solution Exploring Operation: 10+64=74, Resulting Numbers: [74] 74,80 unequal: No Solution Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,80 unequal: No Solution Moving to Node #0,1,4 Current State: 80:[25, 99], Operations: ['50-40=10', '89+10=99'] Exploring Operation: 99-25=74, Resulting Numbers: [74] 74,80 unequal: No Solution Exploring Operation: 25*99=2475, Resulting Numbers: [2475] 2475,80 unequal: No Solution Exploring Operation: 25+99=124, Resulting Numbers: [124] 124,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[89, 65], Operations: ['50-25=25', '40+25=65'] Exploring Operation: 89+65=154, Resulting Numbers: [154] 154,80 unequal: No Solution Exploring Operation: 89*65=5785, Resulting Numbers: [5785] 5785,80 unequal: No Solution Exploring Operation: 89-65=24, Resulting Numbers: [24] 24,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[40, 114], Operations: ['50-25=25', '89+25=114'] Exploring Operation: 40*114=4560, Resulting Numbers: [4560] 4560,80 unequal: No Solution Exploring Operation: 40+114=154, Resulting Numbers: [154] 154,80 unequal: No Solution Exploring Operation: 114-40=74, Resulting Numbers: [74] 74,80 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 41, 2, 30, 67 ]
54
[ "41+2=43", "30+67=97", "97-43=54" ]
Current State: 54:[41, 2, 30, 67], Operations: [] Exploring Operation: 41+2=43, Resulting Numbers: [30, 67, 43] Generated Node #2: [30, 67, 43] from Operation: 41+2=43 Current State: 54:[30, 67, 43], Operations: ['41+2=43'] Exploring Operation: 30+67=97, Resulting Numbers: [43, 97] Generated Node #3: [43, 97] from Operation: 30+67=97 Current State: 54:[43, 97], Operations: ['41+2=43', '30+67=97'] Exploring Operation: 97-43=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[41, 2, 30, 67], Operations: [] Exploring Operation: 67-41=26, Resulting Numbers: [2, 30, 26] Generated Node #0,0: 54:[2, 30, 26] Operation: 67-41=26 Exploring Operation: 41-30=11, Resulting Numbers: [2, 67, 11] Generated Node #0,1: 54:[2, 67, 11] Operation: 41-30=11 Moving to Node #0,0 Current State: 54:[2, 30, 26], Operations: ['67-41=26'] Exploring Operation: 30-26=4, Resulting Numbers: [2, 4] Generated Node #0,0,0: 54:[2, 4] Operation: 30-26=4 Exploring Operation: 30-2=28, Resulting Numbers: [26, 28] Generated Node #0,0,1: 54:[26, 28] Operation: 30-2=28 Moving to Node #0,1 Current State: 54:[2, 67, 11], Operations: ['41-30=11'] Exploring Operation: 67-2=65, Resulting Numbers: [11, 65] Generated Node #0,1,0: 54:[11, 65] Operation: 67-2=65 Exploring Operation: 67-11=56, Resulting Numbers: [2, 56] Generated Node #0,1,1: 54:[2, 56] Operation: 67-11=56 Moving to Node #0,0,0 Current State: 54:[2, 4], Operations: ['67-41=26', '30-26=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[2, 56], Operations: ['41-30=11', '67-11=56'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[41, 2, 30, 67], Operations: [] Exploring Operation: 41-30=11, Resulting Numbers: [2, 67, 11] Generated Node #0,1: 54:[2, 67, 11] Operation: 41-30=11 Moving to Node #0,1 Current State: 54:[2, 67, 11], Operations: ['41-30=11'] Exploring Operation: 67-11=56, Resulting Numbers: [2, 56] Generated Node #0,1,1: 54:[2, 56] Operation: 67-11=56 Moving to Node #0,1,1 Current State: 54:[2, 56], Operations: ['41-30=11', '67-11=56'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
0.988715
hs_2
mult_heuristic
[ 7, 28, 75, 2 ]
46
[ "7*28=196", "75*2=150", "196-150=46" ]
Current State: 46:[7, 28, 75, 2], Operations: [] Exploring Operation: 7*28=196, Resulting Numbers: [75, 2, 196] Generated Node #2: [75, 2, 196] from Operation: 7*28=196 Current State: 46:[75, 2, 196], Operations: ['7*28=196'] Exploring Operation: 75*2=150, Resulting Numbers: [196, 150] Generated Node #3: [196, 150] from Operation: 75*2=150 Current State: 46:[196, 150], Operations: ['7*28=196', '75*2=150'] Exploring Operation: 196-150=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[7, 28, 75, 2], Operations: [] Exploring Operation: 75-7=68, Resulting Numbers: [28, 2, 68] Generated Node #0,0: 46:[28, 2, 68] Operation: 75-7=68 Exploring Operation: 7-2=5, Resulting Numbers: [28, 75, 5] Generated Node #0,1: 46:[28, 75, 5] Operation: 7-2=5 Exploring Operation: 75-28=47, Resulting Numbers: [7, 2, 47] Generated Node #0,2: 46:[7, 2, 47] Operation: 75-28=47 Exploring Operation: 28/7=4, Resulting Numbers: [75, 2, 4] Generated Node #0,3: 46:[75, 2, 4] Operation: 28/7=4 Exploring Operation: 28-7=21, Resulting Numbers: [75, 2, 21] Generated Node #0,4: 46:[75, 2, 21] Operation: 28-7=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[7, 2, 47], Operations: ['75-28=47'] Exploring Operation: 7+2=9, Resulting Numbers: [47, 9] Generated Node #0,2,0: 46:[47, 9] Operation: 7+2=9 Exploring Operation: 7+47=54, Resulting Numbers: [2, 54] Generated Node #0,2,1: 46:[2, 54] Operation: 7+47=54 Exploring Operation: 7-2=5, Resulting Numbers: [47, 5] Generated Node #0,2,2: 46:[47, 5] Operation: 7-2=5 Exploring Operation: 47-2=45, Resulting Numbers: [7, 45] Generated Node #0,2,3: 46:[7, 45] Operation: 47-2=45 Exploring Operation: 47-7=40, Resulting Numbers: [2, 40] Generated Node #0,2,4: 46:[2, 40] Operation: 47-7=40 Moving to Node #0,2,2 Current State: 46:[47, 5], Operations: ['75-28=47', '7-2=5'] Exploring Operation: 47+5=52, Resulting Numbers: [52] 52,46 unequal: No Solution Exploring Operation: 47*5=235, Resulting Numbers: [235] 235,46 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,46 unequal: No Solution Moving to Node #0,2,4 Current State: 46:[2, 40], Operations: ['75-28=47', '47-7=40'] Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,46 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,46 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,46 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,46 unequal: No Solution Moving to Node #0,2,3 Current State: 46:[7, 45], Operations: ['75-28=47', '47-2=45'] Exploring Operation: 7*45=315, Resulting Numbers: [315] 315,46 unequal: No Solution Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,46 unequal: No Solution Exploring Operation: 7+45=52, Resulting Numbers: [52] 52,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[47, 9], Operations: ['75-28=47', '7+2=9'] Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,46 unequal: No Solution Exploring Operation: 47*9=423, Resulting Numbers: [423] 423,46 unequal: No Solution Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[2, 54], Operations: ['75-28=47', '7+47=54'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,46 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 2+54=56, Resulting Numbers: [56] 56,46 unequal: No Solution Exploring Operation: 2*54=108, Resulting Numbers: [108] 108,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[28, 2, 68], Operations: ['75-7=68'] Exploring Operation: 68-28=40, Resulting Numbers: [2, 40] Generated Node #0,0,0: 46:[2, 40] Operation: 68-28=40 Exploring Operation: 68/2=34, Resulting Numbers: [28, 34] Generated Node #0,0,1: 46:[28, 34] Operation: 68/2=34 Exploring Operation: 68-2=66, Resulting Numbers: [28, 66] Generated Node #0,0,2: 46:[28, 66] Operation: 68-2=66 Exploring Operation: 28+2=30, Resulting Numbers: [68, 30] Generated Node #0,0,3: 46:[68, 30] Operation: 28+2=30 Exploring Operation: 28-2=26, Resulting Numbers: [68, 26] Generated Node #0,0,4: 46:[68, 26] Operation: 28-2=26 Moving to Node #0,0,0 Current State: 46:[2, 40], Operations: ['75-7=68', '68-28=40'] Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,46 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,46 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,46 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[28, 34], Operations: ['75-7=68', '68/2=34'] Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,46 unequal: No Solution Exploring Operation: 28*34=952, Resulting Numbers: [952] 952,46 unequal: No Solution Exploring Operation: 28+34=62, Resulting Numbers: [62] 62,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[28, 66], Operations: ['75-7=68', '68-2=66'] Exploring Operation: 28*66=1848, Resulting Numbers: [1848] 1848,46 unequal: No Solution Exploring Operation: 28+66=94, Resulting Numbers: [94] 94,46 unequal: No Solution Exploring Operation: 66-28=38, Resulting Numbers: [38] 38,46 unequal: No Solution Moving to Node #0,0,4 Current State: 46:[68, 26], Operations: ['75-7=68', '28-2=26'] Exploring Operation: 68-26=42, Resulting Numbers: [42] 42,46 unequal: No Solution Exploring Operation: 68+26=94, Resulting Numbers: [94] 94,46 unequal: No Solution Exploring Operation: 68*26=1768, Resulting Numbers: [1768] 1768,46 unequal: No Solution Moving to Node #0,0,3 Current State: 46:[68, 30], Operations: ['75-7=68', '28+2=30'] Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,46 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,46 unequal: No Solution Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 46:[75, 2, 4], Operations: ['28/7=4'] Exploring Operation: 75-4=71, Resulting Numbers: [2, 71] Generated Node #0,3,0: 46:[2, 71] Operation: 75-4=71 Exploring Operation: 4-2=2, Resulting Numbers: [75, 2] Generated Node #0,3,1: 46:[75, 2] Operation: 4-2=2 Exploring Operation: 75+2=77, Resulting Numbers: [4, 77] Generated Node #0,3,2: 46:[4, 77] Operation: 75+2=77 Exploring Operation: 4/2=2, Resulting Numbers: [75, 2] Generated Node #0,3,3: 46:[75, 2] Operation: 4/2=2 Exploring Operation: 75-2=73, Resulting Numbers: [4, 73] Generated Node #0,3,4: 46:[4, 73] Operation: 75-2=73 Moving to Node #0,3,0 Current State: 46:[2, 71], Operations: ['28/7=4', '75-4=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,46 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,46 unequal: No Solution Exploring Operation: 2*71=142, Resulting Numbers: [142] 142,46 unequal: No Solution Moving to Node #0,3,3 Current State: 46:[75, 2], Operations: ['28/7=4', '4/2=2'] Exploring Operation: 75*2=150, Resulting Numbers: [150] 150,46 unequal: No Solution Exploring Operation: 75+2=77, Resulting Numbers: [77] 77,46 unequal: No Solution Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,46 unequal: No Solution Moving to Node #0,3,1 Current State: 46:[75, 2], Operations: ['28/7=4', '4-2=2'] Exploring Operation: 75*2=150, Resulting Numbers: [150] 150,46 unequal: No Solution Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,46 unequal: No Solution Exploring Operation: 75+2=77, Resulting Numbers: [77] 77,46 unequal: No Solution Moving to Node #0,3,4 Current State: 46:[4, 73], Operations: ['28/7=4', '75-2=73'] Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,46 unequal: No Solution Exploring Operation: 4*73=292, Resulting Numbers: [292] 292,46 unequal: No Solution Exploring Operation: 4+73=77, Resulting Numbers: [77] 77,46 unequal: No Solution Moving to Node #0,3,2 Current State: 46:[4, 77], Operations: ['28/7=4', '75+2=77'] Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,46 unequal: No Solution Exploring Operation: 4*77=308, Resulting Numbers: [308] 308,46 unequal: No Solution Exploring Operation: 4+77=81, Resulting Numbers: [81] 81,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 46:[75, 2, 21], Operations: ['28-7=21'] Exploring Operation: 2+21=23, Resulting Numbers: [75, 23] Generated Node #0,4,0: 46:[75, 23] Operation: 2+21=23 Exploring Operation: 2*21=42, Resulting Numbers: [75, 42] Generated Node #0,4,1: 46:[75, 42] Operation: 2*21=42 Exploring Operation: 75-2=73, Resulting Numbers: [21, 73] Generated Node #0,4,2: 46:[21, 73] Operation: 75-2=73 Exploring Operation: 75-21=54, Resulting Numbers: [2, 54] Generated Node #0,4,3: 46:[2, 54] Operation: 75-21=54 Exploring Operation: 75+2=77, Resulting Numbers: [21, 77] Generated Node #0,4,4: 46:[21, 77] Operation: 75+2=77 Moving to Node #0,4,3 Current State: 46:[2, 54], Operations: ['28-7=21', '75-21=54'] Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 2*54=108, Resulting Numbers: [108] 108,46 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,46 unequal: No Solution Exploring Operation: 2+54=56, Resulting Numbers: [56] 56,46 unequal: No Solution Moving to Node #0,4,2 Current State: 46:[21, 73], Operations: ['28-7=21', '75-2=73'] Exploring Operation: 21+73=94, Resulting Numbers: [94] 94,46 unequal: No Solution Exploring Operation: 21*73=1533, Resulting Numbers: [1533] 1533,46 unequal: No Solution Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,46 unequal: No Solution Moving to Node #0,4,0 Current State: 46:[75, 23], Operations: ['28-7=21', '2+21=23'] Exploring Operation: 75+23=98, Resulting Numbers: [98] 98,46 unequal: No Solution Exploring Operation: 75-23=52, Resulting Numbers: [52] 52,46 unequal: No Solution Exploring Operation: 75*23=1725, Resulting Numbers: [1725] 1725,46 unequal: No Solution Moving to Node #0,4,1 Current State: 46:[75, 42], Operations: ['28-7=21', '2*21=42'] Exploring Operation: 75+42=117, Resulting Numbers: [117] 117,46 unequal: No Solution Exploring Operation: 75*42=3150, Resulting Numbers: [3150] 3150,46 unequal: No Solution Exploring Operation: 75-42=33, Resulting Numbers: [33] 33,46 unequal: No Solution Moving to Node #0,4,4 Current State: 46:[21, 77], Operations: ['28-7=21', '75+2=77'] Exploring Operation: 21*77=1617, Resulting Numbers: [1617] 1617,46 unequal: No Solution Exploring Operation: 21+77=98, Resulting Numbers: [98] 98,46 unequal: No Solution Exploring Operation: 77-21=56, Resulting Numbers: [56] 56,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[28, 75, 5], Operations: ['7-2=5'] Exploring Operation: 75-5=70, Resulting Numbers: [28, 70] Generated Node #0,1,0: 46:[28, 70] Operation: 75-5=70 Exploring Operation: 28+5=33, Resulting Numbers: [75, 33] Generated Node #0,1,1: 46:[75, 33] Operation: 28+5=33 Exploring Operation: 28-5=23, Resulting Numbers: [75, 23] Generated Node #0,1,2: 46:[75, 23] Operation: 28-5=23 Exploring Operation: 75-28=47, Resulting Numbers: [5, 47] Generated Node #0,1,3: 46:[5, 47] Operation: 75-28=47 Exploring Operation: 75/5=15, Resulting Numbers: [28, 15] Generated Node #0,1,4: 46:[28, 15] Operation: 75/5=15 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 46:[5, 47], Operations: ['7-2=5', '75-28=47'] Exploring Operation: 5*47=235, Resulting Numbers: [235] 235,46 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,46 unequal: No Solution Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 46:[28, 15], Operations: ['7-2=5', '75/5=15'] Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,46 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[28, 70], Operations: ['7-2=5', '75-5=70'] Exploring Operation: 28+70=98, Resulting Numbers: [98] 98,46 unequal: No Solution Exploring Operation: 70-28=42, Resulting Numbers: [42] 42,46 unequal: No Solution Exploring Operation: 28*70=1960, Resulting Numbers: [1960] 1960,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 46:[75, 23], Operations: ['7-2=5', '28-5=23'] Exploring Operation: 75*23=1725, Resulting Numbers: [1725] 1725,46 unequal: No Solution Exploring Operation: 75-23=52, Resulting Numbers: [52] 52,46 unequal: No Solution Exploring Operation: 75+23=98, Resulting Numbers: [98] 98,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 46:[75, 33], Operations: ['7-2=5', '28+5=33'] Exploring Operation: 75+33=108, Resulting Numbers: [108] 108,46 unequal: No Solution Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,46 unequal: No Solution Exploring Operation: 75*33=2475, Resulting Numbers: [2475] 2475,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 6, 19, 47, 47 ]
36
[ "19+47=66", "66/6=11", "47-11=36" ]
Current State: 36:[6, 19, 47, 47], Operations: [] Exploring Operation: 19+47=66, Resulting Numbers: [6, 66] Generated Node #2: [6, 66] from Operation: 19+47=66 Current State: 36:[6, 66], Operations: ['19+47=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,36 equal: Goal Reached Exploring Operation: 47-11=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[6, 19, 47, 47], Operations: [] Exploring Operation: 47-6=41, Resulting Numbers: [19, 47, 41] Generated Node #0,0: 36:[19, 47, 41] Operation: 47-6=41 Exploring Operation: 47-6=41, Resulting Numbers: [19, 47, 41] Generated Node #0,1: 36:[19, 47, 41] Operation: 47-6=41 Exploring Operation: 47/47=1, Resulting Numbers: [6, 19, 1] Generated Node #0,2: 36:[6, 19, 1] Operation: 47/47=1 Exploring Operation: 47-47=0, Resulting Numbers: [6, 19, 0] Generated Node #0,3: 36:[6, 19, 0] Operation: 47-47=0 Moving to Node #0,2 Current State: 36:[6, 19, 1], Operations: ['47/47=1'] Exploring Operation: 19*1=19, Resulting Numbers: [6, 19] Generated Node #0,2,0: 36:[6, 19] Operation: 19*1=19 Exploring Operation: 6*1=6, Resulting Numbers: [19, 6] Generated Node #0,2,1: 36:[19, 6] Operation: 6*1=6 Exploring Operation: 6/1=6, Resulting Numbers: [19, 6] Generated Node #0,2,2: 36:[19, 6] Operation: 6/1=6 Exploring Operation: 19-1=18, Resulting Numbers: [6, 18] Generated Node #0,2,3: 36:[6, 18] Operation: 19-1=18 Moving to Node #0,3 Current State: 36:[6, 19, 0], Operations: ['47-47=0'] Exploring Operation: 6+0=6, Resulting Numbers: [19, 6] Generated Node #0,3,0: 36:[19, 6] Operation: 6+0=6 Exploring Operation: 19+0=19, Resulting Numbers: [6, 19] Generated Node #0,3,1: 36:[6, 19] Operation: 19+0=19 Exploring Operation: 6-0=6, Resulting Numbers: [19, 6] Generated Node #0,3,2: 36:[19, 6] Operation: 6-0=6 Exploring Operation: 19-0=19, Resulting Numbers: [6, 19] Generated Node #0,3,3: 36:[6, 19] Operation: 19-0=19 Moving to Node #0,1 Current State: 36:[19, 47, 41], Operations: ['47-6=41'] Exploring Operation: 19+47=66, Resulting Numbers: [41, 66] Generated Node #0,1,0: 36:[41, 66] Operation: 19+47=66 Exploring Operation: 41-19=22, Resulting Numbers: [47, 22] Generated Node #0,1,1: 36:[47, 22] Operation: 41-19=22 Exploring Operation: 47-19=28, Resulting Numbers: [41, 28] Generated Node #0,1,2: 36:[41, 28] Operation: 47-19=28 Exploring Operation: 47-41=6, Resulting Numbers: [19, 6] Generated Node #0,1,3: 36:[19, 6] Operation: 47-41=6 Moving to Node #0,0 Current State: 36:[19, 47, 41], Operations: ['47-6=41'] Exploring Operation: 47-19=28, Resulting Numbers: [41, 28] Generated Node #0,0,0: 36:[41, 28] Operation: 47-19=28 Exploring Operation: 19+47=66, Resulting Numbers: [41, 66] Generated Node #0,0,1: 36:[41, 66] Operation: 19+47=66 Exploring Operation: 47-41=6, Resulting Numbers: [19, 6] Generated Node #0,0,2: 36:[19, 6] Operation: 47-41=6 Exploring Operation: 41-19=22, Resulting Numbers: [47, 22] Generated Node #0,0,3: 36:[47, 22] Operation: 41-19=22 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 36:[19, 6], Operations: ['47-6=41', '47-41=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,36 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[41, 28], Operations: ['47-6=41', '47-19=28'] Exploring Operation: 41*28=1148, Resulting Numbers: [1148] 1148,36 unequal: No Solution Exploring Operation: 41+28=69, Resulting Numbers: [69] 69,36 unequal: No Solution Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 36:[47, 22], Operations: ['47-6=41', '41-19=22'] Exploring Operation: 47*22=1034, Resulting Numbers: [1034] 1034,36 unequal: No Solution Exploring Operation: 47+22=69, Resulting Numbers: [69] 69,36 unequal: No Solution Exploring Operation: 47-22=25, Resulting Numbers: [25] 25,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[41, 66], Operations: ['47-6=41', '19+47=66'] Exploring Operation: 41*66=2706, Resulting Numbers: [2706] 2706,36 unequal: No Solution Exploring Operation: 41+66=107, Resulting Numbers: [107] 107,36 unequal: No Solution Exploring Operation: 66-41=25, Resulting Numbers: [25] 25,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,3 Current State: 36:[6, 18], Operations: ['47/47=1', '19-1=18'] Exploring Operation: 6*18=108, Resulting Numbers: [108] 108,36 unequal: No Solution Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,36 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,36 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,36 unequal: No Solution Moving to Node #0,2,1 Current State: 36:[19, 6], Operations: ['47/47=1', '6*1=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,36 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,36 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,36 unequal: No Solution Moving to Node #0,3,2 Current State: 36:[19, 6], Operations: ['47-47=0', '6-0=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,36 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,36 unequal: No Solution Moving to Node #0,3,1 Current State: 36:[6, 19], Operations: ['47-47=0', '19+0=19'] Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,36 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,36 unequal: No Solution Moving to Node #0,2,0 Current State: 36:[6, 19], Operations: ['47/47=1', '19*1=19'] Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,36 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,36 unequal: No Solution Moving to Node #0,3,0 Current State: 36:[19, 6], Operations: ['47-47=0', '6+0=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,36 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,36 unequal: No Solution Moving to Node #0,1,3 Current State: 36:[19, 6], Operations: ['47-6=41', '47-41=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,36 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,36 unequal: No Solution Moving to Node #0,3,3 Current State: 36:[6, 19], Operations: ['47-47=0', '19-0=19'] Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,36 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,36 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,36 unequal: No Solution Moving to Node #0,2,2 Current State: 36:[19, 6], Operations: ['47/47=1', '6/1=6'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,36 unequal: No Solution Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,36 unequal: No Solution Moving to Node #0,1,2 Current State: 36:[41, 28], Operations: ['47-6=41', '47-19=28'] Exploring Operation: 41*28=1148, Resulting Numbers: [1148] 1148,36 unequal: No Solution Exploring Operation: 41+28=69, Resulting Numbers: [69] 69,36 unequal: No Solution Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,36 unequal: No Solution Moving to Node #0,1,1 Current State: 36:[47, 22], Operations: ['47-6=41', '41-19=22'] Exploring Operation: 47+22=69, Resulting Numbers: [69] 69,36 unequal: No Solution Exploring Operation: 47*22=1034, Resulting Numbers: [1034] 1034,36 unequal: No Solution Exploring Operation: 47-22=25, Resulting Numbers: [25] 25,36 unequal: No Solution Moving to Node #0,1,0 Current State: 36:[41, 66], Operations: ['47-6=41', '19+47=66'] Exploring Operation: 41*66=2706, Resulting Numbers: [2706] 2706,36 unequal: No Solution Exploring Operation: 66-41=25, Resulting Numbers: [25] 25,36 unequal: No Solution Exploring Operation: 41+66=107, Resulting Numbers: [107] 107,36 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 30, 28, 33, 98 ]
72
[ "30*98=2940", "2940/28=105", "105-33=72" ]
Current State: 72:[30, 28, 33, 98], Operations: [] Exploring Operation: 30*98=2940, Resulting Numbers: [28, 33, 2940] Generated Node #2: [28, 33, 2940] from Operation: 30*98=2940 Current State: 72:[28, 33, 2940], Operations: ['30*98=2940'] Exploring Operation: 2940/28=105, Resulting Numbers: [33, 105] Generated Node #3: [33, 105] from Operation: 2940/28=105 Current State: 72:[33, 105], Operations: ['30*98=2940', '2940/28=105'] Exploring Operation: 105-33=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[30, 28, 33, 98], Operations: [] Exploring Operation: 98-33=65, Resulting Numbers: [30, 28, 65] Generated Node #0,0: 72:[30, 28, 65] Operation: 98-33=65 Exploring Operation: 98-28=70, Resulting Numbers: [30, 33, 70] Generated Node #0,1: 72:[30, 33, 70] Operation: 98-28=70 Exploring Operation: 98-30=68, Resulting Numbers: [28, 33, 68] Generated Node #0,2: 72:[28, 33, 68] Operation: 98-30=68 Moving to Node #0,1 Current State: 72:[30, 33, 70], Operations: ['98-28=70'] Exploring Operation: 70-30=40, Resulting Numbers: [33, 40] Generated Node #0,1,0: 72:[33, 40] Operation: 70-30=40 Exploring Operation: 33-30=3, Resulting Numbers: [70, 3] Generated Node #0,1,1: 72:[70, 3] Operation: 33-30=3 Exploring Operation: 70-33=37, Resulting Numbers: [30, 37] Generated Node #0,1,2: 72:[30, 37] Operation: 70-33=37 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 72:[70, 3], Operations: ['98-28=70', '33-30=3'] Exploring Operation: 70*3=210, Resulting Numbers: [210] 210,72 unequal: No Solution Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,72 unequal: No Solution Exploring Operation: 70+3=73, Resulting Numbers: [73] 73,72 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 #0,1,0 Current State: 72:[33, 40], Operations: ['98-28=70', '70-30=40'] Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 33*40=1320, Resulting Numbers: [1320] 1320,72 unequal: No Solution Exploring Operation: 33+40=73, Resulting Numbers: [73] 73,72 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 #0,1,2 Current State: 72:[30, 37], Operations: ['98-28=70', '70-33=37'] Exploring Operation: 37-30=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 30+37=67, Resulting Numbers: [67] 67,72 unequal: No Solution Exploring Operation: 30*37=1110, Resulting Numbers: [1110] 1110,72 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: 72:[28, 33, 68], Operations: ['98-30=68'] Exploring Operation: 33-28=5, Resulting Numbers: [68, 5] Generated Node #0,2,0: 72:[68, 5] Operation: 33-28=5 Exploring Operation: 68-33=35, Resulting Numbers: [28, 35] Generated Node #0,2,1: 72:[28, 35] Operation: 68-33=35 Exploring Operation: 68-28=40, Resulting Numbers: [33, 40] Generated Node #0,2,2: 72:[33, 40] Operation: 68-28=40 Moving to Node #0,0 Current State: 72:[30, 28, 65], Operations: ['98-33=65'] Exploring Operation: 65-30=35, Resulting Numbers: [28, 35] Generated Node #0,0,0: 72:[28, 35] Operation: 65-30=35 Exploring Operation: 65-28=37, Resulting Numbers: [30, 37] Generated Node #0,0,1: 72:[30, 37] Operation: 65-28=37 Exploring Operation: 30-28=2, Resulting Numbers: [65, 2] Generated Node #0,0,2: 72:[65, 2] Operation: 30-28=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[28, 35], Operations: ['98-33=65', '65-30=35'] Exploring Operation: 28*35=980, Resulting Numbers: [980] 980,72 unequal: No Solution Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 28+35=63, Resulting Numbers: [63] 63,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[30, 37], Operations: ['98-33=65', '65-28=37'] Exploring Operation: 37-30=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 30+37=67, Resulting Numbers: [67] 67,72 unequal: No Solution Exploring Operation: 30*37=1110, Resulting Numbers: [1110] 1110,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 72:[65, 2], Operations: ['98-33=65', '30-28=2'] Exploring Operation: 65+2=67, Resulting Numbers: [67] 67,72 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,72 unequal: No Solution Exploring Operation: 65*2=130, Resulting Numbers: [130] 130,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 72:[68, 5], Operations: ['98-30=68', '33-28=5'] Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,72 unequal: No Solution Exploring Operation: 68+5=73, Resulting Numbers: [73] 73,72 unequal: No Solution Exploring Operation: 68*5=340, Resulting Numbers: [340] 340,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[28, 35], Operations: ['98-30=68', '68-33=35'] Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 28+35=63, Resulting Numbers: [63] 63,72 unequal: No Solution Exploring Operation: 28*35=980, Resulting Numbers: [980] 980,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[33, 40], Operations: ['98-30=68', '68-28=40'] Exploring Operation: 33*40=1320, Resulting Numbers: [1320] 1320,72 unequal: No Solution Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 33+40=73, Resulting Numbers: [73] 73,72 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 24, 38, 19, 12 ]
98
[ "38-24=14", "19-12=7", "14*7=98" ]
Current State: 98:[24, 38, 19, 12], Operations: [] Exploring Operation: 38-24=14, Resulting Numbers: [19, 12, 14] Generated Node #2: [19, 12, 14] from Operation: 38-24=14 Current State: 98:[19, 12, 14], Operations: ['38-24=14'] Exploring Operation: 19-12=7, Resulting Numbers: [14, 7] Generated Node #3: [14, 7] from Operation: 19-12=7 Current State: 98:[14, 7], Operations: ['38-24=14', '19-12=7'] Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[24, 38, 19, 12], Operations: [] Exploring Operation: 24-19=5, Resulting Numbers: [38, 12, 5] Generated Node #0,0: 98:[38, 12, 5] Operation: 24-19=5 Exploring Operation: 24/12=2, Resulting Numbers: [38, 19, 2] Generated Node #0,1: 98:[38, 19, 2] Operation: 24/12=2 Exploring Operation: 38/19=2, Resulting Numbers: [24, 12, 2] Generated Node #0,2: 98:[24, 12, 2] Operation: 38/19=2 Exploring Operation: 38-24=14, Resulting Numbers: [19, 12, 14] Generated Node #0,3: 98:[19, 12, 14] Operation: 38-24=14 Moving to Node #0,3 Current State: 98:[19, 12, 14], Operations: ['38-24=14'] Exploring Operation: 19-14=5, Resulting Numbers: [12, 5] Generated Node #0,3,0: 98:[12, 5] Operation: 19-14=5 Exploring Operation: 14-12=2, Resulting Numbers: [19, 2] Generated Node #0,3,1: 98:[19, 2] Operation: 14-12=2 Exploring Operation: 19+12=31, Resulting Numbers: [14, 31] Generated Node #0,3,2: 98:[14, 31] Operation: 19+12=31 Exploring Operation: 19-12=7, Resulting Numbers: [14, 7] Generated Node #0,3,3: 98:[14, 7] Operation: 19-12=7 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 98:[14, 7], Operations: ['38-24=14', '19-12=7'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[24, 38, 19, 12], Operations: [] Exploring Operation: 38-24=14, Resulting Numbers: [19, 12, 14] Generated Node #0,3: 98:[19, 12, 14] Operation: 38-24=14 Moving to Node #0,3 Current State: 98:[19, 12, 14], Operations: ['38-24=14'] Exploring Operation: 19-12=7, Resulting Numbers: [14, 7] Generated Node #0,3,3: 98:[14, 7] Operation: 19-12=7 Moving to Node #0,3,3 Current State: 98:[14, 7], Operations: ['38-24=14', '19-12=7'] Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 42, 40, 86, 66 ]
84
[ "42*40=1680", "86-66=20", "1680/20=84" ]
Current State: 84:[42, 40, 86, 66], Operations: [] Exploring Operation: 42*40=1680, Resulting Numbers: [86, 66, 1680] Generated Node #2: [86, 66, 1680] from Operation: 42*40=1680 Current State: 84:[86, 66, 1680], Operations: ['42*40=1680'] Exploring Operation: 86-66=20, Resulting Numbers: [1680, 20] Generated Node #3: [1680, 20] from Operation: 86-66=20 Current State: 84:[1680, 20], Operations: ['42*40=1680', '86-66=20'] Exploring Operation: 1680/20=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[42, 40, 86, 66], Operations: [] Exploring Operation: 86-66=20, Resulting Numbers: [42, 40, 20] Generated Node #0,0: 84:[42, 40, 20] Operation: 86-66=20 Exploring Operation: 66-40=26, Resulting Numbers: [42, 86, 26] Generated Node #0,1: 84:[42, 86, 26] Operation: 66-40=26 Moving to Node #0,0 Current State: 84:[42, 40, 20], Operations: ['86-66=20'] Exploring Operation: 40/20=2, Resulting Numbers: [42, 2] Generated Node #0,0,0: 84:[42, 2] Operation: 40/20=2 Exploring Operation: 42-40=2, Resulting Numbers: [20, 2] Generated Node #0,0,1: 84:[20, 2] Operation: 42-40=2 Moving to Node #0,1 Current State: 84:[42, 86, 26], Operations: ['66-40=26'] Exploring Operation: 42-26=16, Resulting Numbers: [86, 16] Generated Node #0,1,0: 84:[86, 16] Operation: 42-26=16 Exploring Operation: 86-42=44, Resulting Numbers: [26, 44] Generated Node #0,1,1: 84:[26, 44] Operation: 86-42=44 Moving to Node #0,0,0 Current State: 84:[42, 2], Operations: ['86-66=20', '40/20=2'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[42, 40, 86, 66], Operations: [] Exploring Operation: 86-66=20, Resulting Numbers: [42, 40, 20] Generated Node #0,0: 84:[42, 40, 20] Operation: 86-66=20 Moving to Node #0,0 Current State: 84:[42, 40, 20], Operations: ['86-66=20'] Exploring Operation: 40/20=2, Resulting Numbers: [42, 2] Generated Node #0,0,0: 84:[42, 2] Operation: 40/20=2 Moving to Node #0,0,0 Current State: 84:[42, 2], Operations: ['86-66=20', '40/20=2'] Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.989583
hs_2
mult_heuristic
[ 21, 90, 34, 13 ]
91
[ "34-21=13", "13/13=1", "90+1=91" ]
Current State: 91:[21, 90, 34, 13], Operations: [] Exploring Operation: 34-21=13, Resulting Numbers: [90, 13, 13] Generated Node #2: [90, 13, 13] from Operation: 34-21=13 Current State: 91:[90, 13, 13], Operations: ['34-21=13'] Exploring Operation: 13/13=1, Resulting Numbers: [90, 1] Generated Node #3: [90, 1] from Operation: 13/13=1 Current State: 91:[90, 1], Operations: ['34-21=13', '13/13=1'] Exploring Operation: 90+1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[21, 90, 34, 13], Operations: [] Exploring Operation: 21-13=8, Resulting Numbers: [90, 34, 8] Generated Node #0,0: 91:[90, 34, 8] Operation: 21-13=8 Exploring Operation: 34-21=13, Resulting Numbers: [90, 13, 13] Generated Node #0,1: 91:[90, 13, 13] Operation: 34-21=13 Exploring Operation: 34-13=21, Resulting Numbers: [21, 90, 21] Generated Node #0,2: 91:[21, 90, 21] Operation: 34-13=21 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[90, 13, 13], Operations: ['34-21=13'] Exploring Operation: 90+13=103, Resulting Numbers: [13, 103] Generated Node #0,1,0: 91:[13, 103] Operation: 90+13=103 Exploring Operation: 13/13=1, Resulting Numbers: [90, 1] Generated Node #0,1,1: 91:[90, 1] Operation: 13/13=1 Exploring Operation: 13-13=0, Resulting Numbers: [90, 0] Generated Node #0,1,2: 91:[90, 0] Operation: 13-13=0 Moving to Node #0,1,1 Current State: 91:[90, 1], Operations: ['34-21=13', '13/13=1'] Exploring Operation: 90*1=90, Resulting Numbers: [90] 90,91 unequal: No Solution Exploring Operation: 90+1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[21, 90, 34, 13], Operations: [] Exploring Operation: 34-21=13, Resulting Numbers: [90, 13, 13] Generated Node #0,1: 91:[90, 13, 13] Operation: 34-21=13 Moving to Node #0,1 Current State: 91:[90, 13, 13], Operations: ['34-21=13'] Exploring Operation: 13/13=1, Resulting Numbers: [90, 1] Generated Node #0,1,1: 91:[90, 1] Operation: 13/13=1 Moving to Node #0,1,1 Current State: 91:[90, 1], Operations: ['34-21=13', '13/13=1'] Exploring Operation: 90+1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 24, 74, 80, 68 ]
62
[ "74-24=50", "80-68=12", "50+12=62" ]
Current State: 62:[24, 74, 80, 68], Operations: [] Exploring Operation: 74-24=50, Resulting Numbers: [80, 68, 50] Generated Node #2: [80, 68, 50] from Operation: 74-24=50 Current State: 62:[80, 68, 50], Operations: ['74-24=50'] Exploring Operation: 80-68=12, Resulting Numbers: [50, 12] Generated Node #3: [50, 12] from Operation: 80-68=12 Current State: 62:[50, 12], Operations: ['74-24=50', '80-68=12'] Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[24, 74, 80, 68], Operations: [] Exploring Operation: 80-68=12, Resulting Numbers: [24, 74, 12] Generated Node #0,0: 62:[24, 74, 12] Operation: 80-68=12 Exploring Operation: 80-24=56, Resulting Numbers: [74, 68, 56] Generated Node #0,1: 62:[74, 68, 56] Operation: 80-24=56 Exploring Operation: 74-68=6, Resulting Numbers: [24, 80, 6] Generated Node #0,2: 62:[24, 80, 6] Operation: 74-68=6 Exploring Operation: 80-74=6, Resulting Numbers: [24, 68, 6] Generated Node #0,3: 62:[24, 68, 6] Operation: 80-74=6 Moving to Node #0,3 Current State: 62:[24, 68, 6], Operations: ['80-74=6'] Exploring Operation: 24/6=4, Resulting Numbers: [68, 4] Generated Node #0,3,0: 62:[68, 4] Operation: 24/6=4 Exploring Operation: 68-24=44, Resulting Numbers: [6, 44] Generated Node #0,3,1: 62:[6, 44] Operation: 68-24=44 Exploring Operation: 24+6=30, Resulting Numbers: [68, 30] Generated Node #0,3,2: 62:[68, 30] Operation: 24+6=30 Exploring Operation: 68-6=62, Resulting Numbers: [24, 62] Generated Node #0,3,3: 62:[24, 62] Operation: 68-6=62 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 62:[68, 30], Operations: ['80-74=6', '24+6=30'] Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,62 unequal: No Solution Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,62 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 #0,3,3 Current State: 62:[24, 62], Operations: ['80-74=6', '68-6=62'] Exploring Operation: 24*62=1488, Resulting Numbers: [1488] 1488,62 unequal: No Solution Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,62 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,62 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 #0,3,0 Current State: 62:[68, 4], Operations: ['80-74=6', '24/6=4'] Exploring Operation: 68*4=272, Resulting Numbers: [272] 272,62 unequal: No Solution Exploring Operation: 68+4=72, Resulting Numbers: [72] 72,62 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,62 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,62 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 #0,3,1 Current State: 62:[6, 44], Operations: ['80-74=6', '68-24=44'] Exploring Operation: 6*44=264, Resulting Numbers: [264] 264,62 unequal: No Solution Exploring Operation: 6+44=50, Resulting Numbers: [50] 50,62 unequal: No Solution Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 62:[74, 68, 56], Operations: ['80-24=56'] Exploring Operation: 74-68=6, Resulting Numbers: [56, 6] Generated Node #0,1,0: 62:[56, 6] Operation: 74-68=6 Exploring Operation: 74-56=18, Resulting Numbers: [68, 18] Generated Node #0,1,1: 62:[68, 18] Operation: 74-56=18 Exploring Operation: 74+56=130, Resulting Numbers: [68, 130] Generated Node #0,1,2: 62:[68, 130] Operation: 74+56=130 Exploring Operation: 68-56=12, Resulting Numbers: [74, 12] Generated Node #0,1,3: 62:[74, 12] Operation: 68-56=12 Moving to Node #0,2 Current State: 62:[24, 80, 6], Operations: ['74-68=6'] Exploring Operation: 80-6=74, Resulting Numbers: [24, 74] Generated Node #0,2,0: 62:[24, 74] Operation: 80-6=74 Exploring Operation: 24+6=30, Resulting Numbers: [80, 30] Generated Node #0,2,1: 62:[80, 30] Operation: 24+6=30 Exploring Operation: 80-24=56, Resulting Numbers: [6, 56] Generated Node #0,2,2: 62:[6, 56] Operation: 80-24=56 Exploring Operation: 24/6=4, Resulting Numbers: [80, 4] Generated Node #0,2,3: 62:[80, 4] Operation: 24/6=4 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 62:[6, 56], Operations: ['74-68=6', '80-24=56'] Exploring Operation: 6*56=336, Resulting Numbers: [336] 336,62 unequal: No Solution Exploring Operation: 6+56=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[24, 74, 80, 68], Operations: [] Exploring Operation: 74-68=6, Resulting Numbers: [24, 80, 6] Generated Node #0,2: 62:[24, 80, 6] Operation: 74-68=6 Moving to Node #0,2 Current State: 62:[24, 80, 6], Operations: ['74-68=6'] Exploring Operation: 80-24=56, Resulting Numbers: [6, 56] Generated Node #0,2,2: 62:[6, 56] Operation: 80-24=56 Moving to Node #0,2,2 Current State: 62:[6, 56], Operations: ['74-68=6', '80-24=56'] Exploring Operation: 6+56=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_4
sum_heuristic
[ 7, 84, 23, 90 ]
10
[ "84-7=77", "90-23=67", "77-67=10" ]
Current State: 10:[7, 84, 23, 90], Operations: [] Exploring Operation: 84-7=77, Resulting Numbers: [23, 90, 77] Generated Node #2: [23, 90, 77] from Operation: 84-7=77 Current State: 10:[23, 90, 77], Operations: ['84-7=77'] Exploring Operation: 90-23=67, Resulting Numbers: [77, 67] Generated Node #3: [77, 67] from Operation: 90-23=67 Current State: 10:[77, 67], Operations: ['84-7=77', '90-23=67'] Exploring Operation: 77-67=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[7, 84, 23, 90], Operations: [] Exploring Operation: 84-23=61, Resulting Numbers: [7, 90, 61] Generated Node #0,0: 10:[7, 90, 61] Operation: 84-23=61 Exploring Operation: 90-84=6, Resulting Numbers: [7, 23, 6] Generated Node #0,1: 10:[7, 23, 6] Operation: 90-84=6 Exploring Operation: 84/7=12, Resulting Numbers: [23, 90, 12] Generated Node #0,2: 10:[23, 90, 12] Operation: 84/7=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[7, 23, 6], Operations: ['90-84=6'] Exploring Operation: 7-6=1, Resulting Numbers: [23, 1] Generated Node #0,1,0: 10:[23, 1] Operation: 7-6=1 Exploring Operation: 23-7=16, Resulting Numbers: [6, 16] Generated Node #0,1,1: 10:[6, 16] Operation: 23-7=16 Exploring Operation: 23-6=17, Resulting Numbers: [7, 17] Generated Node #0,1,2: 10:[7, 17] Operation: 23-6=17 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 10:[6, 16], Operations: ['90-84=6', '23-7=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,10 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,10 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[7, 84, 23, 90], Operations: [] Exploring Operation: 90-84=6, Resulting Numbers: [7, 23, 6] Generated Node #0,1: 10:[7, 23, 6] Operation: 90-84=6 Moving to Node #0,1 Current State: 10:[7, 23, 6], Operations: ['90-84=6'] Exploring Operation: 23-7=16, Resulting Numbers: [6, 16] Generated Node #0,1,1: 10:[6, 16] Operation: 23-7=16 Moving to Node #0,1,1 Current State: 10:[6, 16], Operations: ['90-84=6', '23-7=16'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 61, 44, 2, 23 ]
16
[ "61-23=38", "44/2=22", "38-22=16" ]
Current State: 16:[61, 44, 2, 23], Operations: [] Exploring Operation: 61-23=38, Resulting Numbers: [44, 2, 38] Generated Node #2: [44, 2, 38] from Operation: 61-23=38 Current State: 16:[44, 2, 38], Operations: ['61-23=38'] Exploring Operation: 44/2=22, Resulting Numbers: [38, 22] Generated Node #3: [38, 22] from Operation: 44/2=22 Current State: 16:[38, 22], Operations: ['61-23=38', '44/2=22'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[61, 44, 2, 23], Operations: [] Exploring Operation: 61-44=17, Resulting Numbers: [2, 23, 17] Generated Node #0,0: 16:[2, 23, 17] Operation: 61-44=17 Exploring Operation: 44-23=21, Resulting Numbers: [61, 2, 21] Generated Node #0,1: 16:[61, 2, 21] Operation: 44-23=21 Exploring Operation: 44/2=22, Resulting Numbers: [61, 23, 22] Generated Node #0,2: 16:[61, 23, 22] Operation: 44/2=22 Exploring Operation: 61-23=38, Resulting Numbers: [44, 2, 38] Generated Node #0,3: 16:[44, 2, 38] Operation: 61-23=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[2, 23, 17], Operations: ['61-44=17'] Exploring Operation: 17-2=15, Resulting Numbers: [23, 15] Generated Node #0,0,0: 16:[23, 15] Operation: 17-2=15 Exploring Operation: 23-17=6, Resulting Numbers: [2, 6] Generated Node #0,0,1: 16:[2, 6] Operation: 23-17=6 Exploring Operation: 2+23=25, Resulting Numbers: [17, 25] Generated Node #0,0,2: 16:[17, 25] Operation: 2+23=25 Exploring Operation: 23-2=21, Resulting Numbers: [17, 21] Generated Node #0,0,3: 16:[17, 21] Operation: 23-2=21 Moving to Node #0,0,1 Current State: 16:[2, 6], Operations: ['61-44=17', '23-17=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,16 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,16 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,16 unequal: No Solution Moving to Node #0,0,3 Current State: 16:[17, 21], Operations: ['61-44=17', '23-2=21'] Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,16 unequal: No Solution Exploring Operation: 17+21=38, Resulting Numbers: [38] 38,16 unequal: No Solution Exploring Operation: 17*21=357, Resulting Numbers: [357] 357,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[23, 15], Operations: ['61-44=17', '17-2=15'] Exploring Operation: 23+15=38, Resulting Numbers: [38] 38,16 unequal: No Solution Exploring Operation: 23*15=345, Resulting Numbers: [345] 345,16 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,16 unequal: No Solution Moving to Node #0,0,2 Current State: 16:[17, 25], Operations: ['61-44=17', '2+23=25'] Exploring Operation: 17*25=425, Resulting Numbers: [425] 425,16 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[61, 2, 21], Operations: ['44-23=21'] Exploring Operation: 21-2=19, Resulting Numbers: [61, 19] Generated Node #0,1,0: 16:[61, 19] Operation: 21-2=19 Exploring Operation: 61-21=40, Resulting Numbers: [2, 40] Generated Node #0,1,1: 16:[2, 40] Operation: 61-21=40 Exploring Operation: 61+2=63, Resulting Numbers: [21, 63] Generated Node #0,1,2: 16:[21, 63] Operation: 61+2=63 Exploring Operation: 61-2=59, Resulting Numbers: [21, 59] Generated Node #0,1,3: 16:[21, 59] Operation: 61-2=59 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[2, 40], Operations: ['44-23=21', '61-21=40'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,16 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,16 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,16 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[61, 19], Operations: ['44-23=21', '21-2=19'] Exploring Operation: 61+19=80, Resulting Numbers: [80] 80,16 unequal: No Solution Exploring Operation: 61*19=1159, Resulting Numbers: [1159] 1159,16 unequal: No Solution Exploring Operation: 61-19=42, Resulting Numbers: [42] 42,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 16:[21, 59], Operations: ['44-23=21', '61-2=59'] Exploring Operation: 21*59=1239, Resulting Numbers: [1239] 1239,16 unequal: No Solution Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,16 unequal: No Solution Exploring Operation: 21+59=80, Resulting Numbers: [80] 80,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 16:[21, 63], Operations: ['44-23=21', '61+2=63'] Exploring Operation: 21+63=84, Resulting Numbers: [84] 84,16 unequal: No Solution Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,16 unequal: No Solution Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 21*63=1323, Resulting Numbers: [1323] 1323,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 16:[44, 2, 38], Operations: ['61-23=38'] Exploring Operation: 44-38=6, Resulting Numbers: [2, 6] Generated Node #0,3,0: 16:[2, 6] Operation: 44-38=6 Exploring Operation: 44-2=42, Resulting Numbers: [38, 42] Generated Node #0,3,1: 16:[38, 42] Operation: 44-2=42 Exploring Operation: 38/2=19, Resulting Numbers: [44, 19] Generated Node #0,3,2: 16:[44, 19] Operation: 38/2=19 Exploring Operation: 44/2=22, Resulting Numbers: [38, 22] Generated Node #0,3,3: 16:[38, 22] Operation: 44/2=22 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 16:[2, 6], Operations: ['61-23=38', '44-38=6'] Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,16 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 16:[38, 22], Operations: ['61-23=38', '44/2=22'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[61, 44, 2, 23], Operations: [] Exploring Operation: 61-23=38, Resulting Numbers: [44, 2, 38] Generated Node #0,3: 16:[44, 2, 38] Operation: 61-23=38 Moving to Node #0,3 Current State: 16:[44, 2, 38], Operations: ['61-23=38'] Exploring Operation: 44/2=22, Resulting Numbers: [38, 22] Generated Node #0,3,3: 16:[38, 22] Operation: 44/2=22 Moving to Node #0,3,3 Current State: 16:[38, 22], Operations: ['61-23=38', '44/2=22'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.954861
hs_4
mult_heuristic
[ 53, 52, 6, 7 ]
49
[ "53-52=1", "6+1=7", "7*7=49" ]
Current State: 49:[53, 52, 6, 7], Operations: [] Exploring Operation: 53-52=1, Resulting Numbers: [6, 7, 1] Generated Node #2: [6, 7, 1] from Operation: 53-52=1 Current State: 49:[6, 7, 1], Operations: ['53-52=1'] Exploring Operation: 6+1=7, Resulting Numbers: [7, 7] Generated Node #3: [7, 7] from Operation: 6+1=7 Current State: 49:[7, 7], Operations: ['53-52=1', '6+1=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[53, 52, 6, 7], Operations: [] Exploring Operation: 52-6=46, Resulting Numbers: [53, 7, 46] Generated Node #0,0: 49:[53, 7, 46] Operation: 52-6=46 Exploring Operation: 53-6=47, Resulting Numbers: [52, 7, 47] Generated Node #0,1: 49:[52, 7, 47] Operation: 53-6=47 Exploring Operation: 53-7=46, Resulting Numbers: [52, 6, 46] Generated Node #0,2: 49:[52, 6, 46] Operation: 53-7=46 Exploring Operation: 52-7=45, Resulting Numbers: [53, 6, 45] Generated Node #0,3: 49:[53, 6, 45] Operation: 52-7=45 Exploring Operation: 53-52=1, Resulting Numbers: [6, 7, 1] Generated Node #0,4: 49:[6, 7, 1] Operation: 53-52=1 Moving to Node #0,1 Current State: 49:[52, 7, 47], Operations: ['53-6=47'] Exploring Operation: 52-47=5, Resulting Numbers: [7, 5] Generated Node #0,1,0: 49:[7, 5] Operation: 52-47=5 Exploring Operation: 52+7=59, Resulting Numbers: [47, 59] Generated Node #0,1,1: 49:[47, 59] Operation: 52+7=59 Exploring Operation: 47-7=40, Resulting Numbers: [52, 40] Generated Node #0,1,2: 49:[52, 40] Operation: 47-7=40 Exploring Operation: 52-7=45, Resulting Numbers: [47, 45] Generated Node #0,1,3: 49:[47, 45] Operation: 52-7=45 Exploring Operation: 7+47=54, Resulting Numbers: [52, 54] Generated Node #0,1,4: 49:[52, 54] Operation: 7+47=54 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 49:[7, 5], Operations: ['53-6=47', '52-47=5'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,49 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,49 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 #0,1,3 Current State: 49:[47, 45], Operations: ['53-6=47', '52-7=45'] Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 47*45=2115, Resulting Numbers: [2115] 2115,49 unequal: No Solution Exploring Operation: 47+45=92, Resulting Numbers: [92] 92,49 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 #0,1,4 Current State: 49:[52, 54], Operations: ['53-6=47', '7+47=54'] Exploring Operation: 52+54=106, Resulting Numbers: [106] 106,49 unequal: No Solution Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 52*54=2808, Resulting Numbers: [2808] 2808,49 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 #0,1,1 Current State: 49:[47, 59], Operations: ['53-6=47', '52+7=59'] Exploring Operation: 59-47=12, Resulting Numbers: [12] 12,49 unequal: No Solution Exploring Operation: 47*59=2773, Resulting Numbers: [2773] 2773,49 unequal: No Solution Exploring Operation: 47+59=106, Resulting Numbers: [106] 106,49 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 #0,1,2 Current State: 49:[52, 40], Operations: ['53-6=47', '47-7=40'] Exploring Operation: 52+40=92, Resulting Numbers: [92] 92,49 unequal: No Solution Exploring Operation: 52*40=2080, Resulting Numbers: [2080] 2080,49 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,49 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: 49:[52, 6, 46], Operations: ['53-7=46'] Exploring Operation: 52-46=6, Resulting Numbers: [6, 6] Generated Node #0,2,0: 49:[6, 6] Operation: 52-46=6 Exploring Operation: 46-6=40, Resulting Numbers: [52, 40] Generated Node #0,2,1: 49:[52, 40] Operation: 46-6=40 Exploring Operation: 6+46=52, Resulting Numbers: [52, 52] Generated Node #0,2,2: 49:[52, 52] Operation: 6+46=52 Exploring Operation: 52+6=58, Resulting Numbers: [46, 58] Generated Node #0,2,3: 49:[46, 58] Operation: 52+6=58 Exploring Operation: 52-6=46, Resulting Numbers: [46, 46] Generated Node #0,2,4: 49:[46, 46] Operation: 52-6=46 Moving to Node #0,0 Current State: 49:[53, 7, 46], Operations: ['52-6=46'] Exploring Operation: 53-46=7, Resulting Numbers: [7, 7] Generated Node #0,0,0: 49:[7, 7] Operation: 53-46=7 Exploring Operation: 7+46=53, Resulting Numbers: [53, 53] Generated Node #0,0,1: 49:[53, 53] Operation: 7+46=53 Exploring Operation: 46-7=39, Resulting Numbers: [53, 39] Generated Node #0,0,2: 49:[53, 39] Operation: 46-7=39 Exploring Operation: 53+7=60, Resulting Numbers: [46, 60] Generated Node #0,0,3: 49:[46, 60] Operation: 53+7=60 Exploring Operation: 53-7=46, Resulting Numbers: [46, 46] Generated Node #0,0,4: 49:[46, 46] Operation: 53-7=46 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 49:[7, 7], Operations: ['52-6=46', '53-46=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[53, 52, 6, 7], Operations: [] Exploring Operation: 52-6=46, Resulting Numbers: [53, 7, 46] Generated Node #0,0: 49:[53, 7, 46] Operation: 52-6=46 Moving to Node #0,0 Current State: 49:[53, 7, 46], Operations: ['52-6=46'] Exploring Operation: 53-46=7, Resulting Numbers: [7, 7] Generated Node #0,0,0: 49:[7, 7] Operation: 53-46=7 Moving to Node #0,0,0 Current State: 49:[7, 7], Operations: ['52-6=46', '53-46=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_5
sum_heuristic
[ 60, 64, 89, 67 ]
32
[ "60+64=124", "89+67=156", "156-124=32" ]
Current State: 32:[60, 64, 89, 67], Operations: [] Exploring Operation: 60+64=124, Resulting Numbers: [89, 67, 124] Generated Node #2: [89, 67, 124] from Operation: 60+64=124 Current State: 32:[89, 67, 124], Operations: ['60+64=124'] Exploring Operation: 89+67=156, Resulting Numbers: [124, 156] Generated Node #3: [124, 156] from Operation: 89+67=156 Current State: 32:[124, 156], Operations: ['60+64=124', '89+67=156'] Exploring Operation: 156-124=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[60, 64, 89, 67], Operations: [] Exploring Operation: 89-67=22, Resulting Numbers: [60, 64, 22] Generated Node #0,0: 32:[60, 64, 22] Operation: 89-67=22 Exploring Operation: 89-64=25, Resulting Numbers: [60, 67, 25] Generated Node #0,1: 32:[60, 67, 25] Operation: 89-64=25 Exploring Operation: 89-60=29, Resulting Numbers: [64, 67, 29] Generated Node #0,2: 32:[64, 67, 29] Operation: 89-60=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[60, 64, 22], Operations: ['89-67=22'] Exploring Operation: 64-22=42, Resulting Numbers: [60, 42] Generated Node #0,0,0: 32:[60, 42] Operation: 64-22=42 Exploring Operation: 64-60=4, Resulting Numbers: [22, 4] Generated Node #0,0,1: 32:[22, 4] Operation: 64-60=4 Exploring Operation: 60-22=38, Resulting Numbers: [64, 38] Generated Node #0,0,2: 32:[64, 38] Operation: 60-22=38 Moving to Node #0,0,1 Current State: 32:[22, 4], Operations: ['89-67=22', '64-60=4'] Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,32 unequal: No Solution Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,32 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,32 unequal: No Solution Moving to Node #0,0,0 Current State: 32:[60, 42], Operations: ['89-67=22', '64-22=42'] Exploring Operation: 60-42=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 60*42=2520, Resulting Numbers: [2520] 2520,32 unequal: No Solution Exploring Operation: 60+42=102, Resulting Numbers: [102] 102,32 unequal: No Solution Moving to Node #0,0,2 Current State: 32:[64, 38], Operations: ['89-67=22', '60-22=38'] Exploring Operation: 64+38=102, Resulting Numbers: [102] 102,32 unequal: No Solution Exploring Operation: 64*38=2432, Resulting Numbers: [2432] 2432,32 unequal: No Solution Exploring Operation: 64-38=26, Resulting Numbers: [26] 26,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[60, 67, 25], Operations: ['89-64=25'] Exploring Operation: 60-25=35, Resulting Numbers: [67, 35] Generated Node #0,1,0: 32:[67, 35] Operation: 60-25=35 Exploring Operation: 67-60=7, Resulting Numbers: [25, 7] Generated Node #0,1,1: 32:[25, 7] Operation: 67-60=7 Exploring Operation: 67-25=42, Resulting Numbers: [60, 42] Generated Node #0,1,2: 32:[60, 42] Operation: 67-25=42 Moving to Node #0,1,1 Current State: 32:[25, 7], Operations: ['89-64=25', '67-60=7'] Exploring Operation: 25*7=175, Resulting Numbers: [175] 175,32 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[60, 64, 89, 67], Operations: [] Exploring Operation: 89-64=25, Resulting Numbers: [60, 67, 25] Generated Node #0,1: 32:[60, 67, 25] Operation: 89-64=25 Moving to Node #0,1 Current State: 32:[60, 67, 25], Operations: ['89-64=25'] Exploring Operation: 67-60=7, Resulting Numbers: [25, 7] Generated Node #0,1,1: 32:[25, 7] Operation: 67-60=7 Moving to Node #0,1,1 Current State: 32:[25, 7], Operations: ['89-64=25', '67-60=7'] Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
sum_heuristic
[ 85, 31, 21, 98 ]
39
[ "85+31=116", "98-21=77", "116-77=39" ]
Current State: 39:[85, 31, 21, 98], Operations: [] Exploring Operation: 85+31=116, Resulting Numbers: [21, 98, 116] Generated Node #2: [21, 98, 116] from Operation: 85+31=116 Current State: 39:[21, 98, 116], Operations: ['85+31=116'] Exploring Operation: 98-21=77, Resulting Numbers: [116, 77] Generated Node #3: [116, 77] from Operation: 98-21=77 Current State: 39:[116, 77], Operations: ['85+31=116', '98-21=77'] Exploring Operation: 116-77=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[85, 31, 21, 98], Operations: [] Exploring Operation: 98-31=67, Resulting Numbers: [85, 21, 67] Generated Node #0,0: 39:[85, 21, 67] Operation: 98-31=67 Exploring Operation: 98-85=13, Resulting Numbers: [31, 21, 13] Generated Node #0,1: 39:[31, 21, 13] Operation: 98-85=13 Exploring Operation: 85-31=54, Resulting Numbers: [21, 98, 54] Generated Node #0,2: 39:[21, 98, 54] Operation: 85-31=54 Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[31, 21, 13], Operations: ['98-85=13'] Exploring Operation: 31+13=44, Resulting Numbers: [21, 44] Generated Node #0,1,0: 39:[21, 44] Operation: 31+13=44 Exploring Operation: 31+21=52, Resulting Numbers: [13, 52] Generated Node #0,1,1: 39:[13, 52] Operation: 31+21=52 Exploring Operation: 31-21=10, Resulting Numbers: [13, 10] Generated Node #0,1,2: 39:[13, 10] Operation: 31-21=10 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 39:[13, 10], Operations: ['98-85=13', '31-21=10'] Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,39 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 39:[21, 44], Operations: ['98-85=13', '31+13=44'] Exploring Operation: 21*44=924, Resulting Numbers: [924] 924,39 unequal: No Solution Exploring Operation: 21+44=65, Resulting Numbers: [65] 65,39 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 39:[13, 52], Operations: ['98-85=13', '31+21=52'] Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[85, 31, 21, 98], Operations: [] Exploring Operation: 98-85=13, Resulting Numbers: [31, 21, 13] Generated Node #0,1: 39:[31, 21, 13] Operation: 98-85=13 Moving to Node #0,1 Current State: 39:[31, 21, 13], Operations: ['98-85=13'] Exploring Operation: 31+21=52, Resulting Numbers: [13, 52] Generated Node #0,1,1: 39:[13, 52] Operation: 31+21=52 Moving to Node #0,1,1 Current State: 39:[13, 52], Operations: ['98-85=13', '31+21=52'] Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic