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
[ 37, 91, 38, 43 ]
94
[ "43-38=5", "37*5=185", "185-91=94" ]
Current State: 94:[37, 91, 38, 43], Operations: [] Exploring Operation: 43-38=5, Resulting Numbers: [37, 91, 5] Generated Node #2: [37, 91, 5] from Operation: 43-38=5 Current State: 94:[37, 91, 5], Operations: ['43-38=5'] Exploring Operation: 37*5=185, Resulting Numbers: [91, 185] Generated Node #3: [91, 185] from Operation: 37*5=185 Current State: 94:[91, 185], Operations: ['43-38=5', '37*5=185'] Exploring Operation: 185-91=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[37, 91, 38, 43], Operations: [] Exploring Operation: 38-37=1, Resulting Numbers: [91, 43, 1] Generated Node #0,0: 94:[91, 43, 1] Operation: 38-37=1 Exploring Operation: 43-38=5, Resulting Numbers: [37, 91, 5] Generated Node #0,1: 94:[37, 91, 5] Operation: 43-38=5 Exploring Operation: 91-37=54, Resulting Numbers: [38, 43, 54] Generated Node #0,2: 94:[38, 43, 54] Operation: 91-37=54 Exploring Operation: 43-37=6, Resulting Numbers: [91, 38, 6] Generated Node #0,3: 94:[91, 38, 6] Operation: 43-37=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[91, 43, 1], Operations: ['38-37=1'] Exploring Operation: 91*1=91, Resulting Numbers: [43, 91] Generated Node #0,0,0: 94:[43, 91] Operation: 91*1=91 Exploring Operation: 91-43=48, Resulting Numbers: [1, 48] Generated Node #0,0,1: 94:[1, 48] Operation: 91-43=48 Exploring Operation: 43+1=44, Resulting Numbers: [91, 44] Generated Node #0,0,2: 94:[91, 44] Operation: 43+1=44 Exploring Operation: 91+1=92, Resulting Numbers: [43, 92] Generated Node #0,0,3: 94:[43, 92] Operation: 91+1=92 Moving to Node #0,0,1 Current State: 94:[1, 48], Operations: ['38-37=1', '91-43=48'] Exploring Operation: 1+48=49, Resulting Numbers: [49] 49,94 unequal: No Solution Exploring Operation: 48/1=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 1*48=48, Resulting Numbers: [48] 48,94 unequal: No Solution Moving to Node #0,0,3 Current State: 94:[43, 92], Operations: ['38-37=1', '91+1=92'] Exploring Operation: 92-43=49, Resulting Numbers: [49] 49,94 unequal: No Solution Exploring Operation: 43+92=135, Resulting Numbers: [135] 135,94 unequal: No Solution Exploring Operation: 43*92=3956, Resulting Numbers: [3956] 3956,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[91, 44], Operations: ['38-37=1', '43+1=44'] Exploring Operation: 91*44=4004, Resulting Numbers: [4004] 4004,94 unequal: No Solution Exploring Operation: 91+44=135, Resulting Numbers: [135] 135,94 unequal: No Solution Exploring Operation: 91-44=47, Resulting Numbers: [47] 47,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[43, 91], Operations: ['38-37=1', '91*1=91'] Exploring Operation: 91-43=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 43*91=3913, Resulting Numbers: [3913] 3913,94 unequal: No Solution Exploring Operation: 43+91=134, Resulting Numbers: [134] 134,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[37, 91, 5], Operations: ['43-38=5'] Exploring Operation: 37+5=42, Resulting Numbers: [91, 42] Generated Node #0,1,0: 94:[91, 42] Operation: 37+5=42 Exploring Operation: 37-5=32, Resulting Numbers: [91, 32] Generated Node #0,1,1: 94:[91, 32] Operation: 37-5=32 Exploring Operation: 91-37=54, Resulting Numbers: [5, 54] Generated Node #0,1,2: 94:[5, 54] Operation: 91-37=54 Exploring Operation: 91+5=96, Resulting Numbers: [37, 96] Generated Node #0,1,3: 94:[37, 96] Operation: 91+5=96 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[91, 42], Operations: ['43-38=5', '37+5=42'] Exploring Operation: 91-42=49, Resulting Numbers: [49] 49,94 unequal: No Solution Exploring Operation: 91+42=133, Resulting Numbers: [133] 133,94 unequal: No Solution Exploring Operation: 91*42=3822, Resulting Numbers: [3822] 3822,94 unequal: No Solution No 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: 94:[5, 54], Operations: ['43-38=5', '91-37=54'] Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,94 unequal: No Solution Exploring Operation: 5+54=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 5*54=270, Resulting Numbers: [270] 270,94 unequal: No Solution No 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: 94:[37, 96], Operations: ['43-38=5', '91+5=96'] Exploring Operation: 37*96=3552, Resulting Numbers: [3552] 3552,94 unequal: No Solution Exploring Operation: 37+96=133, Resulting Numbers: [133] 133,94 unequal: No Solution Exploring Operation: 96-37=59, Resulting Numbers: [59] 59,94 unequal: No Solution No 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: 94:[91, 32], Operations: ['43-38=5', '37-5=32'] Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 91+32=123, Resulting Numbers: [123] 123,94 unequal: No Solution Exploring Operation: 91*32=2912, Resulting Numbers: [2912] 2912,94 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: 94:[91, 38, 6], Operations: ['43-37=6'] Exploring Operation: 91-38=53, Resulting Numbers: [6, 53] Generated Node #0,3,0: 94:[6, 53] Operation: 91-38=53 Exploring Operation: 91-6=85, Resulting Numbers: [38, 85] Generated Node #0,3,1: 94:[38, 85] Operation: 91-6=85 Exploring Operation: 38+6=44, Resulting Numbers: [91, 44] Generated Node #0,3,2: 94:[91, 44] Operation: 38+6=44 Exploring Operation: 91+6=97, Resulting Numbers: [38, 97] Generated Node #0,3,3: 94:[38, 97] Operation: 91+6=97 Moving to Node #0,3,2 Current State: 94:[91, 44], Operations: ['43-37=6', '38+6=44'] Exploring Operation: 91*44=4004, Resulting Numbers: [4004] 4004,94 unequal: No Solution Exploring Operation: 91-44=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 91+44=135, Resulting Numbers: [135] 135,94 unequal: No Solution Moving to Node #0,3,0 Current State: 94:[6, 53], Operations: ['43-37=6', '91-38=53'] Exploring Operation: 6+53=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 6*53=318, Resulting Numbers: [318] 318,94 unequal: No Solution Moving to Node #0,3,3 Current State: 94:[38, 97], Operations: ['43-37=6', '91+6=97'] Exploring Operation: 97-38=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 38*97=3686, Resulting Numbers: [3686] 3686,94 unequal: No Solution Exploring Operation: 38+97=135, Resulting Numbers: [135] 135,94 unequal: No Solution Moving to Node #0,3,1 Current State: 94:[38, 85], Operations: ['43-37=6', '91-6=85'] Exploring Operation: 85-38=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 38+85=123, Resulting Numbers: [123] 123,94 unequal: No Solution Exploring Operation: 38*85=3230, Resulting Numbers: [3230] 3230,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[38, 43, 54], Operations: ['91-37=54'] Exploring Operation: 38+54=92, Resulting Numbers: [43, 92] Generated Node #0,2,0: 94:[43, 92] Operation: 38+54=92 Exploring Operation: 43-38=5, Resulting Numbers: [54, 5] Generated Node #0,2,1: 94:[54, 5] Operation: 43-38=5 Exploring Operation: 54-38=16, Resulting Numbers: [43, 16] Generated Node #0,2,2: 94:[43, 16] Operation: 54-38=16 Exploring Operation: 43+54=97, Resulting Numbers: [38, 97] Generated Node #0,2,3: 94:[38, 97] Operation: 43+54=97 Moving to Node #0,2,0 Current State: 94:[43, 92], Operations: ['91-37=54', '38+54=92'] Exploring Operation: 43+92=135, Resulting Numbers: [135] 135,94 unequal: No Solution Exploring Operation: 92-43=49, Resulting Numbers: [49] 49,94 unequal: No Solution Exploring Operation: 43*92=3956, Resulting Numbers: [3956] 3956,94 unequal: No Solution Moving to Node #0,2,1 Current State: 94:[54, 5], Operations: ['91-37=54', '43-38=5'] Exploring Operation: 54*5=270, Resulting Numbers: [270] 270,94 unequal: No Solution Exploring Operation: 54+5=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,94 unequal: No Solution Moving to Node #0,2,3 Current State: 94:[38, 97], Operations: ['91-37=54', '43+54=97'] Exploring Operation: 38+97=135, Resulting Numbers: [135] 135,94 unequal: No Solution Exploring Operation: 38*97=3686, Resulting Numbers: [3686] 3686,94 unequal: No Solution Exploring Operation: 97-38=59, Resulting Numbers: [59] 59,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[43, 16], Operations: ['91-37=54', '54-38=16'] Exploring Operation: 43*16=688, Resulting Numbers: [688] 688,94 unequal: No Solution Exploring Operation: 43+16=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 43-16=27, Resulting Numbers: [27] 27,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 11, 52, 76, 76 ]
95
[ "76-11=65", "76*65=4940", "4940/52=95" ]
Current State: 95:[11, 52, 76, 76], Operations: [] Exploring Operation: 76-11=65, Resulting Numbers: [52, 65] Generated Node #2: [52, 65] from Operation: 76-11=65 Current State: 95:[52, 65], Operations: ['76-11=65'] Exploring Operation: 76*65=4940, Resulting Numbers: [52, 4940] Generated Node #3: [52, 4940] from Operation: 76*65=4940 Current State: 95:[52, 4940], Operations: ['76-11=65', '76*65=4940'] Exploring Operation: 4940/52=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[11, 52, 76, 76], Operations: [] Exploring Operation: 76-52=24, Resulting Numbers: [11, 76, 24] Generated Node #0,0: 95:[11, 76, 24] Operation: 76-52=24 Exploring Operation: 76/76=1, Resulting Numbers: [11, 52, 1] Generated Node #0,1: 95:[11, 52, 1] Operation: 76/76=1 Exploring Operation: 76-76=0, Resulting Numbers: [11, 52, 0] Generated Node #0,2: 95:[11, 52, 0] Operation: 76-76=0 Exploring Operation: 76-52=24, Resulting Numbers: [11, 76, 24] Generated Node #0,3: 95:[11, 76, 24] Operation: 76-52=24 Moving to Node #0,0 Current State: 95:[11, 76, 24], Operations: ['76-52=24'] Exploring Operation: 11+76=87, Resulting Numbers: [24, 87] Generated Node #0,0,0: 95:[24, 87] Operation: 11+76=87 Exploring Operation: 24-11=13, Resulting Numbers: [76, 13] Generated Node #0,0,1: 95:[76, 13] Operation: 24-11=13 Exploring Operation: 76-11=65, Resulting Numbers: [24, 65] Generated Node #0,0,2: 95:[24, 65] Operation: 76-11=65 Exploring Operation: 76+24=100, Resulting Numbers: [11, 100] Generated Node #0,0,3: 95:[11, 100] Operation: 76+24=100 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 95:[11, 100], Operations: ['76-52=24', '76+24=100'] Exploring Operation: 11*100=1100, Resulting Numbers: [1100] 1100,95 unequal: No Solution Exploring Operation: 11+100=111, Resulting Numbers: [111] 111,95 unequal: No Solution Exploring Operation: 100-11=89, Resulting Numbers: [89] 89,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[24, 87], Operations: ['76-52=24', '11+76=87'] Exploring Operation: 87-24=63, Resulting Numbers: [63] 63,95 unequal: No Solution Exploring Operation: 24*87=2088, Resulting Numbers: [2088] 2088,95 unequal: No Solution Exploring Operation: 24+87=111, Resulting Numbers: [111] 111,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 95:[76, 13], Operations: ['76-52=24', '24-11=13'] Exploring Operation: 76-13=63, Resulting Numbers: [63] 63,95 unequal: No Solution Exploring Operation: 76+13=89, Resulting Numbers: [89] 89,95 unequal: No Solution Exploring Operation: 76*13=988, Resulting Numbers: [988] 988,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 95:[24, 65], Operations: ['76-52=24', '76-11=65'] Exploring Operation: 24*65=1560, Resulting Numbers: [1560] 1560,95 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,95 unequal: No Solution Exploring Operation: 24+65=89, Resulting Numbers: [89] 89,95 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: 95:[11, 76, 24], Operations: ['76-52=24'] Exploring Operation: 76+24=100, Resulting Numbers: [11, 100] Generated Node #0,3,0: 95:[11, 100] Operation: 76+24=100 Exploring Operation: 11+76=87, Resulting Numbers: [24, 87] Generated Node #0,3,1: 95:[24, 87] Operation: 11+76=87 Exploring Operation: 76-11=65, Resulting Numbers: [24, 65] Generated Node #0,3,2: 95:[24, 65] Operation: 76-11=65 Exploring Operation: 24-11=13, Resulting Numbers: [76, 13] Generated Node #0,3,3: 95:[76, 13] Operation: 24-11=13 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 95:[11, 100], Operations: ['76-52=24', '76+24=100'] Exploring Operation: 100-11=89, Resulting Numbers: [89] 89,95 unequal: No Solution Exploring Operation: 11+100=111, Resulting Numbers: [111] 111,95 unequal: No Solution Exploring Operation: 11*100=1100, Resulting Numbers: [1100] 1100,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 95:[24, 87], Operations: ['76-52=24', '11+76=87'] Exploring Operation: 24*87=2088, Resulting Numbers: [2088] 2088,95 unequal: No Solution Exploring Operation: 87-24=63, Resulting Numbers: [63] 63,95 unequal: No Solution Exploring Operation: 24+87=111, Resulting Numbers: [111] 111,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 95:[76, 13], Operations: ['76-52=24', '24-11=13'] Exploring Operation: 76-13=63, Resulting Numbers: [63] 63,95 unequal: No Solution Exploring Operation: 76*13=988, Resulting Numbers: [988] 988,95 unequal: No Solution Exploring Operation: 76+13=89, Resulting Numbers: [89] 89,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 95:[24, 65], Operations: ['76-52=24', '76-11=65'] Exploring Operation: 24*65=1560, Resulting Numbers: [1560] 1560,95 unequal: No Solution Exploring Operation: 24+65=89, Resulting Numbers: [89] 89,95 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,95 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: 95:[11, 52, 1], Operations: ['76/76=1'] Exploring Operation: 11-1=10, Resulting Numbers: [52, 10] Generated Node #0,1,0: 95:[52, 10] Operation: 11-1=10 Exploring Operation: 11+52=63, Resulting Numbers: [1, 63] Generated Node #0,1,1: 95:[1, 63] Operation: 11+52=63 Exploring Operation: 52-11=41, Resulting Numbers: [1, 41] Generated Node #0,1,2: 95:[1, 41] Operation: 52-11=41 Exploring Operation: 52-1=51, Resulting Numbers: [11, 51] Generated Node #0,1,3: 95:[11, 51] Operation: 52-1=51 Moving to Node #0,2 Current State: 95:[11, 52, 0], Operations: ['76-76=0'] Exploring Operation: 11+52=63, Resulting Numbers: [0, 63] Generated Node #0,2,0: 95:[0, 63] Operation: 11+52=63 Exploring Operation: 11*0=0, Resulting Numbers: [52, 0] Generated Node #0,2,1: 95:[52, 0] Operation: 11*0=0 Exploring Operation: 52*0=0, Resulting Numbers: [11, 0] Generated Node #0,2,2: 95:[11, 0] Operation: 52*0=0 Exploring Operation: 52-11=41, Resulting Numbers: [0, 41] Generated Node #0,2,3: 95:[0, 41] Operation: 52-11=41 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 95:[11, 0], Operations: ['76-76=0', '52*0=0'] Exploring Operation: 11+0=11, Resulting Numbers: [11] 11,95 unequal: No Solution Exploring Operation: 11*0=0, Resulting Numbers: [0] 0,95 unequal: No Solution Exploring Operation: 11-0=11, Resulting Numbers: [11] 11,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 95:[0, 41], Operations: ['76-76=0', '52-11=41'] Exploring Operation: 0+41=41, Resulting Numbers: [41] 41,95 unequal: No Solution Exploring Operation: 0*41=0, Resulting Numbers: [0] 0,95 unequal: No Solution Exploring Operation: 41-0=41, Resulting Numbers: [41] 41,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 95:[0, 63], Operations: ['76-76=0', '11+52=63'] Exploring Operation: 0+63=63, Resulting Numbers: [63] 63,95 unequal: No Solution Exploring Operation: 63-0=63, Resulting Numbers: [63] 63,95 unequal: No Solution Exploring Operation: 0*63=0, Resulting Numbers: [0] 0,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 95:[52, 0], Operations: ['76-76=0', '11*0=0'] Exploring Operation: 52*0=0, Resulting Numbers: [0] 0,95 unequal: No Solution Exploring Operation: 52+0=52, Resulting Numbers: [52] 52,95 unequal: No Solution Exploring Operation: 52-0=52, Resulting Numbers: [52] 52,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 95:[1, 41], Operations: ['76/76=1', '52-11=41'] Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,95 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,95 unequal: No Solution Exploring Operation: 1+41=42, Resulting Numbers: [42] 42,95 unequal: No Solution Exploring Operation: 1*41=41, Resulting Numbers: [41] 41,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[1, 63], Operations: ['76/76=1', '11+52=63'] Exploring Operation: 1+63=64, Resulting Numbers: [64] 64,95 unequal: No Solution Exploring Operation: 1*63=63, Resulting Numbers: [63] 63,95 unequal: No Solution Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,95 unequal: No Solution Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,95 unequal: No Solution Moving to Node #0,1,3 Current State: 95:[11, 51], Operations: ['76/76=1', '52-1=51'] Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,95 unequal: No Solution Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,95 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,95 unequal: No Solution Moving to Node #0,1,0 Current State: 95:[52, 10], Operations: ['76/76=1', '11-1=10'] Exploring Operation: 52+10=62, Resulting Numbers: [62] 62,95 unequal: No Solution Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,95 unequal: No Solution Exploring Operation: 52*10=520, Resulting Numbers: [520] 520,95 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 20, 26, 43, 58 ]
42
[ "20*58=1160", "26*43=1118", "1160-1118=42" ]
Current State: 42:[20, 26, 43, 58], Operations: [] Exploring Operation: 20*58=1160, Resulting Numbers: [26, 43, 1160] Generated Node #2: [26, 43, 1160] from Operation: 20*58=1160 Current State: 42:[26, 43, 1160], Operations: ['20*58=1160'] Exploring Operation: 26*43=1118, Resulting Numbers: [1160, 1118] Generated Node #3: [1160, 1118] from Operation: 26*43=1118 Current State: 42:[1160, 1118], Operations: ['20*58=1160', '26*43=1118'] Exploring Operation: 1160-1118=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[20, 26, 43, 58], Operations: [] Exploring Operation: 58-43=15, Resulting Numbers: [20, 26, 15] Generated Node #0,0: 42:[20, 26, 15] Operation: 58-43=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[20, 26, 15], Operations: ['58-43=15'] Exploring Operation: 26-20=6, Resulting Numbers: [15, 6] Generated Node #0,0,0: 42:[15, 6] Operation: 26-20=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[15, 6], Operations: ['58-43=15', '26-20=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 21, 40, 55, 3 ]
88
[ "21/3=7", "40+55=95", "95-7=88" ]
Current State: 88:[21, 40, 55, 3], Operations: [] Exploring Operation: 21/3=7, Resulting Numbers: [40, 55, 7] Generated Node #2: [40, 55, 7] from Operation: 21/3=7 Current State: 88:[40, 55, 7], Operations: ['21/3=7'] Exploring Operation: 40+55=95, Resulting Numbers: [7, 95] Generated Node #3: [7, 95] from Operation: 40+55=95 Current State: 88:[7, 95], Operations: ['21/3=7', '40+55=95'] Exploring Operation: 95-7=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[21, 40, 55, 3], Operations: [] Exploring Operation: 40+55=95, Resulting Numbers: [21, 3, 95] Generated Node #0,0: 88:[21, 3, 95] Operation: 40+55=95 Exploring Operation: 55-40=15, Resulting Numbers: [21, 3, 15] Generated Node #0,1: 88:[21, 3, 15] Operation: 55-40=15 Moving to Node #0,1 Current State: 88:[21, 3, 15], Operations: ['55-40=15'] Exploring Operation: 15-3=12, Resulting Numbers: [21, 12] Generated Node #0,1,0: 88:[21, 12] Operation: 15-3=12 Exploring Operation: 3*15=45, Resulting Numbers: [21, 45] Generated Node #0,1,1: 88:[21, 45] Operation: 3*15=45 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[21, 12], Operations: ['55-40=15', '15-3=12'] Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,88 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,88 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 #0,1,1 Current State: 88:[21, 45], Operations: ['55-40=15', '3*15=45'] Exploring Operation: 21+45=66, Resulting Numbers: [66] 66,88 unequal: No Solution Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 88:[21, 3, 95], Operations: ['40+55=95'] Exploring Operation: 21/3=7, Resulting Numbers: [95, 7] Generated Node #0,0,0: 88:[95, 7] Operation: 21/3=7 Exploring Operation: 95-3=92, Resulting Numbers: [21, 92] Generated Node #0,0,1: 88:[21, 92] Operation: 95-3=92 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 88:[21, 92], Operations: ['40+55=95', '95-3=92'] Exploring Operation: 21+92=113, Resulting Numbers: [113] 113,88 unequal: No Solution Exploring Operation: 92-21=71, Resulting Numbers: [71] 71,88 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 #0,0,0 Current State: 88:[95, 7], Operations: ['40+55=95', '21/3=7'] Exploring Operation: 95-7=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[21, 40, 55, 3], Operations: [] Exploring Operation: 40+55=95, Resulting Numbers: [21, 3, 95] Generated Node #0,0: 88:[21, 3, 95] Operation: 40+55=95 Moving to Node #0,0 Current State: 88:[21, 3, 95], Operations: ['40+55=95'] Exploring Operation: 21/3=7, Resulting Numbers: [95, 7] Generated Node #0,0,0: 88:[95, 7] Operation: 21/3=7 Moving to Node #0,0,0 Current State: 88:[95, 7], Operations: ['40+55=95', '21/3=7'] Exploring Operation: 95-7=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_2
mult_heuristic
[ 95, 16, 97, 3 ]
92
[ "16+3=19", "95/19=5", "97-5=92" ]
Current State: 92:[95, 16, 97, 3], Operations: [] Exploring Operation: 16+3=19, Resulting Numbers: [95, 97, 19] Generated Node #2: [95, 97, 19] from Operation: 16+3=19 Current State: 92:[95, 97, 19], Operations: ['16+3=19'] Exploring Operation: 95/19=5, Resulting Numbers: [97, 5] Generated Node #3: [97, 5] from Operation: 95/19=5 Current State: 92:[97, 5], Operations: ['16+3=19', '95/19=5'] Exploring Operation: 97-5=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[95, 16, 97, 3], Operations: [] Exploring Operation: 16*3=48, Resulting Numbers: [95, 97, 48] Generated Node #0,0: 92:[95, 97, 48] Operation: 16*3=48 Exploring Operation: 97-95=2, Resulting Numbers: [16, 3, 2] Generated Node #0,1: 92:[16, 3, 2] Operation: 97-95=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[16, 3, 2], Operations: ['97-95=2'] Exploring Operation: 16+3=19, Resulting Numbers: [2, 19] Generated Node #0,1,0: 92:[2, 19] Operation: 16+3=19 Exploring Operation: 16*3=48, Resulting Numbers: [2, 48] Generated Node #0,1,1: 92:[2, 48] Operation: 16*3=48 Moving to Node #0,1,1 Current State: 92:[2, 48], Operations: ['97-95=2', '16*3=48'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[2, 19], Operations: ['97-95=2', '16+3=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,92 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[95, 97, 48], Operations: ['16*3=48'] Exploring Operation: 95-48=47, Resulting Numbers: [97, 47] Generated Node #0,0,0: 92:[97, 47] Operation: 95-48=47 Exploring Operation: 97-95=2, Resulting Numbers: [48, 2] Generated Node #0,0,1: 92:[48, 2] Operation: 97-95=2 Moving to Node #0,0,1 Current State: 92:[48, 2], Operations: ['16*3=48', '97-95=2'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[97, 47], Operations: ['16*3=48', '95-48=47'] Exploring Operation: 97+47=144, Resulting Numbers: [144] 144,92 unequal: No Solution Exploring Operation: 97-47=50, Resulting Numbers: [50] 50,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 52, 17, 22, 72 ]
59
[ "52-17=35", "22+72=94", "94-35=59" ]
Current State: 59:[52, 17, 22, 72], Operations: [] Exploring Operation: 52-17=35, Resulting Numbers: [22, 72, 35] Generated Node #2: [22, 72, 35] from Operation: 52-17=35 Current State: 59:[22, 72, 35], Operations: ['52-17=35'] Exploring Operation: 22+72=94, Resulting Numbers: [35, 94] Generated Node #3: [35, 94] from Operation: 22+72=94 Current State: 59:[35, 94], Operations: ['52-17=35', '22+72=94'] Exploring Operation: 94-35=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[52, 17, 22, 72], Operations: [] Exploring Operation: 17+22=39, Resulting Numbers: [52, 72, 39] Generated Node #0,0: 59:[52, 72, 39] Operation: 17+22=39 Exploring Operation: 52+17=69, Resulting Numbers: [22, 72, 69] Generated Node #0,1: 59:[22, 72, 69] Operation: 52+17=69 Exploring Operation: 72-17=55, Resulting Numbers: [52, 22, 55] Generated Node #0,2: 59:[52, 22, 55] Operation: 72-17=55 Exploring Operation: 72-22=50, Resulting Numbers: [52, 17, 50] Generated Node #0,3: 59:[52, 17, 50] Operation: 72-22=50 Exploring Operation: 52+22=74, Resulting Numbers: [17, 72, 74] Generated Node #0,4: 59:[17, 72, 74] Operation: 52+22=74 Moving to Node #0,0 Current State: 59:[52, 72, 39], Operations: ['17+22=39'] Exploring Operation: 52-39=13, Resulting Numbers: [72, 13] Generated Node #0,0,0: 59:[72, 13] Operation: 52-39=13 Exploring Operation: 72-52=20, Resulting Numbers: [39, 20] Generated Node #0,0,1: 59:[39, 20] Operation: 72-52=20 Exploring Operation: 72-39=33, Resulting Numbers: [52, 33] Generated Node #0,0,2: 59:[52, 33] Operation: 72-39=33 Exploring Operation: 72+39=111, Resulting Numbers: [52, 111] Generated Node #0,0,3: 59:[52, 111] Operation: 72+39=111 Exploring Operation: 52+39=91, Resulting Numbers: [72, 91] Generated Node #0,0,4: 59:[72, 91] Operation: 52+39=91 Moving to Node #0,2 Current State: 59:[52, 22, 55], Operations: ['72-17=55'] Exploring Operation: 55-22=33, Resulting Numbers: [52, 33] Generated Node #0,2,0: 59:[52, 33] Operation: 55-22=33 Exploring Operation: 22+55=77, Resulting Numbers: [52, 77] Generated Node #0,2,1: 59:[52, 77] Operation: 22+55=77 Exploring Operation: 52+55=107, Resulting Numbers: [22, 107] Generated Node #0,2,2: 59:[22, 107] Operation: 52+55=107 Exploring Operation: 52+22=74, Resulting Numbers: [55, 74] Generated Node #0,2,3: 59:[55, 74] Operation: 52+22=74 Exploring Operation: 52-22=30, Resulting Numbers: [55, 30] Generated Node #0,2,4: 59:[55, 30] Operation: 52-22=30 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 59:[55, 74], Operations: ['72-17=55', '52+22=74'] Exploring Operation: 55+74=129, Resulting Numbers: [129] 129,59 unequal: No Solution Exploring Operation: 55*74=4070, Resulting Numbers: [4070] 4070,59 unequal: No Solution Exploring Operation: 74-55=19, Resulting Numbers: [19] 19,59 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 #0,2,1 Current State: 59:[52, 77], Operations: ['72-17=55', '22+55=77'] Exploring Operation: 77-52=25, Resulting Numbers: [25] 25,59 unequal: No Solution Exploring Operation: 52+77=129, Resulting Numbers: [129] 129,59 unequal: No Solution Exploring Operation: 52*77=4004, Resulting Numbers: [4004] 4004,59 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 #0,2,0 Current State: 59:[52, 33], Operations: ['72-17=55', '55-22=33'] Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 52+33=85, Resulting Numbers: [85] 85,59 unequal: No Solution Exploring Operation: 52*33=1716, Resulting Numbers: [1716] 1716,59 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 #0,2,4 Current State: 59:[55, 30], Operations: ['72-17=55', '52-22=30'] Exploring Operation: 55*30=1650, Resulting Numbers: [1650] 1650,59 unequal: No Solution Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,59 unequal: No Solution Exploring Operation: 55+30=85, Resulting Numbers: [85] 85,59 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 #0,2,2 Current State: 59:[22, 107], Operations: ['72-17=55', '52+55=107'] Exploring Operation: 22*107=2354, Resulting Numbers: [2354] 2354,59 unequal: No Solution Exploring Operation: 22+107=129, Resulting Numbers: [129] 129,59 unequal: No Solution Exploring Operation: 107-22=85, Resulting Numbers: [85] 85,59 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: 59:[52, 17, 50], Operations: ['72-22=50'] Exploring Operation: 52-17=35, Resulting Numbers: [50, 35] Generated Node #0,3,0: 59:[50, 35] Operation: 52-17=35 Exploring Operation: 50-17=33, Resulting Numbers: [52, 33] Generated Node #0,3,1: 59:[52, 33] Operation: 50-17=33 Exploring Operation: 17+50=67, Resulting Numbers: [52, 67] Generated Node #0,3,2: 59:[52, 67] Operation: 17+50=67 Exploring Operation: 52+50=102, Resulting Numbers: [17, 102] Generated Node #0,3,3: 59:[17, 102] Operation: 52+50=102 Exploring Operation: 52+17=69, Resulting Numbers: [50, 69] Generated Node #0,3,4: 59:[50, 69] Operation: 52+17=69 Moving to Node #0,1 Current State: 59:[22, 72, 69], Operations: ['52+17=69'] Exploring Operation: 69-22=47, Resulting Numbers: [72, 47] Generated Node #0,1,0: 59:[72, 47] Operation: 69-22=47 Exploring Operation: 22+72=94, Resulting Numbers: [69, 94] Generated Node #0,1,1: 59:[69, 94] Operation: 22+72=94 Exploring Operation: 22+69=91, Resulting Numbers: [72, 91] Generated Node #0,1,2: 59:[72, 91] Operation: 22+69=91 Exploring Operation: 72-22=50, Resulting Numbers: [69, 50] Generated Node #0,1,3: 59:[69, 50] Operation: 72-22=50 Exploring Operation: 72-69=3, Resulting Numbers: [22, 3] Generated Node #0,1,4: 59:[22, 3] Operation: 72-69=3 Moving to Node #0,4 Current State: 59:[17, 72, 74], Operations: ['52+22=74'] Exploring Operation: 72-17=55, Resulting Numbers: [74, 55] Generated Node #0,4,0: 59:[74, 55] Operation: 72-17=55 Exploring Operation: 74-17=57, Resulting Numbers: [72, 57] Generated Node #0,4,1: 59:[72, 57] Operation: 74-17=57 Exploring Operation: 74-72=2, Resulting Numbers: [17, 2] Generated Node #0,4,2: 59:[17, 2] Operation: 74-72=2 Exploring Operation: 17+74=91, Resulting Numbers: [72, 91] Generated Node #0,4,3: 59:[72, 91] Operation: 17+74=91 Exploring Operation: 17+72=89, Resulting Numbers: [74, 89] Generated Node #0,4,4: 59:[74, 89] Operation: 17+72=89 Moving to Node #0,3,2 Current State: 59:[52, 67], Operations: ['72-22=50', '17+50=67'] Exploring Operation: 52+67=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 52*67=3484, Resulting Numbers: [3484] 3484,59 unequal: No Solution Exploring Operation: 67-52=15, Resulting Numbers: [15] 15,59 unequal: No Solution Moving to Node #0,4,1 Current State: 59:[72, 57], Operations: ['52+22=74', '74-17=57'] Exploring Operation: 72-57=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 72*57=4104, Resulting Numbers: [4104] 4104,59 unequal: No Solution Exploring Operation: 72+57=129, Resulting Numbers: [129] 129,59 unequal: No Solution Moving to Node #0,3,4 Current State: 59:[50, 69], Operations: ['72-22=50', '52+17=69'] Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 50*69=3450, Resulting Numbers: [3450] 3450,59 unequal: No Solution Exploring Operation: 50+69=119, Resulting Numbers: [119] 119,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[69, 50], Operations: ['52+17=69', '72-22=50'] Exploring Operation: 69+50=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 69*50=3450, Resulting Numbers: [3450] 3450,59 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,59 unequal: No Solution Moving to Node #0,4,0 Current State: 59:[74, 55], Operations: ['52+22=74', '72-17=55'] Exploring Operation: 74-55=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 74*55=4070, Resulting Numbers: [4070] 4070,59 unequal: No Solution Exploring Operation: 74+55=129, Resulting Numbers: [129] 129,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[72, 47], Operations: ['52+17=69', '69-22=47'] Exploring Operation: 72*47=3384, Resulting Numbers: [3384] 3384,59 unequal: No Solution Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,59 unequal: No Solution Exploring Operation: 72+47=119, Resulting Numbers: [119] 119,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[52, 33], Operations: ['17+22=39', '72-39=33'] Exploring Operation: 52*33=1716, Resulting Numbers: [1716] 1716,59 unequal: No Solution Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 52+33=85, Resulting Numbers: [85] 85,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[50, 35], Operations: ['72-22=50', '52-17=35'] Exploring Operation: 50+35=85, Resulting Numbers: [85] 85,59 unequal: No Solution Exploring Operation: 50*35=1750, Resulting Numbers: [1750] 1750,59 unequal: No Solution Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,59 unequal: No Solution Moving to Node #0,3,1 Current State: 59:[52, 33], Operations: ['72-22=50', '50-17=33'] Exploring Operation: 52*33=1716, Resulting Numbers: [1716] 1716,59 unequal: No Solution Exploring Operation: 52+33=85, Resulting Numbers: [85] 85,59 unequal: No Solution Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[72, 91], Operations: ['52+17=69', '22+69=91'] Exploring Operation: 72*91=6552, Resulting Numbers: [6552] 6552,59 unequal: No Solution Exploring Operation: 91-72=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 72+91=163, Resulting Numbers: [163] 163,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[69, 94], Operations: ['52+17=69', '22+72=94'] Exploring Operation: 94-69=25, Resulting Numbers: [25] 25,59 unequal: No Solution Exploring Operation: 69+94=163, Resulting Numbers: [163] 163,59 unequal: No Solution Exploring Operation: 69*94=6486, Resulting Numbers: [6486] 6486,59 unequal: No Solution Moving to Node #0,0,4 Current State: 59:[72, 91], Operations: ['17+22=39', '52+39=91'] Exploring Operation: 72*91=6552, Resulting Numbers: [6552] 6552,59 unequal: No Solution Exploring Operation: 91-72=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 72+91=163, Resulting Numbers: [163] 163,59 unequal: No Solution Moving to Node #0,4,3 Current State: 59:[72, 91], Operations: ['52+22=74', '17+74=91'] Exploring Operation: 72*91=6552, Resulting Numbers: [6552] 6552,59 unequal: No Solution Exploring Operation: 72+91=163, Resulting Numbers: [163] 163,59 unequal: No Solution Exploring Operation: 91-72=19, Resulting Numbers: [19] 19,59 unequal: No Solution Moving to Node #0,4,4 Current State: 59:[74, 89], Operations: ['52+22=74', '17+72=89'] Exploring Operation: 89-74=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 74*89=6586, Resulting Numbers: [6586] 6586,59 unequal: No Solution Exploring Operation: 74+89=163, Resulting Numbers: [163] 163,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[39, 20], Operations: ['17+22=39', '72-52=20'] Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,59 unequal: No Solution Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[52, 17, 22, 72], Operations: [] Exploring Operation: 17+22=39, Resulting Numbers: [52, 72, 39] Generated Node #0,0: 59:[52, 72, 39] Operation: 17+22=39 Moving to Node #0,0 Current State: 59:[52, 72, 39], Operations: ['17+22=39'] Exploring Operation: 72-52=20, Resulting Numbers: [39, 20] Generated Node #0,0,1: 59:[39, 20] Operation: 72-52=20 Moving to Node #0,0,1 Current State: 59:[39, 20], Operations: ['17+22=39', '72-52=20'] Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
0.918403
hs_5
mult_heuristic
[ 85, 23, 14, 32 ]
41
[ "32-23=9", "14*9=126", "126-85=41" ]
Current State: 41:[85, 23, 14, 32], Operations: [] Exploring Operation: 32-23=9, Resulting Numbers: [85, 14, 9] Generated Node #2: [85, 14, 9] from Operation: 32-23=9 Current State: 41:[85, 14, 9], Operations: ['32-23=9'] Exploring Operation: 14*9=126, Resulting Numbers: [85, 126] Generated Node #3: [85, 126] from Operation: 14*9=126 Current State: 41:[85, 126], Operations: ['32-23=9', '14*9=126'] Exploring Operation: 126-85=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[85, 23, 14, 32], Operations: [] Exploring Operation: 85-23=62, Resulting Numbers: [14, 32, 62] Generated Node #0,0: 41:[14, 32, 62] Operation: 85-23=62 Exploring Operation: 85-14=71, Resulting Numbers: [23, 32, 71] Generated Node #0,1: 41:[23, 32, 71] Operation: 85-14=71 Exploring Operation: 85-32=53, Resulting Numbers: [23, 14, 53] Generated Node #0,2: 41:[23, 14, 53] Operation: 85-32=53 Moving to Node #0,0 Current State: 41:[14, 32, 62], Operations: ['85-23=62'] Exploring Operation: 62-14=48, Resulting Numbers: [32, 48] Generated Node #0,0,0: 41:[32, 48] Operation: 62-14=48 Exploring Operation: 62-32=30, Resulting Numbers: [14, 30] Generated Node #0,0,1: 41:[14, 30] Operation: 62-32=30 Exploring Operation: 14+32=46, Resulting Numbers: [62, 46] Generated Node #0,0,2: 41:[62, 46] Operation: 14+32=46 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[32, 48], Operations: ['85-23=62', '62-14=48'] Exploring Operation: 48-32=16, Resulting Numbers: [16] 16,41 unequal: No Solution Exploring Operation: 32+48=80, Resulting Numbers: [80] 80,41 unequal: No Solution Exploring Operation: 32*48=1536, Resulting Numbers: [1536] 1536,41 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 #0,0,2 Current State: 41:[62, 46], Operations: ['85-23=62', '14+32=46'] Exploring Operation: 62*46=2852, Resulting Numbers: [2852] 2852,41 unequal: No Solution Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,41 unequal: No Solution Exploring Operation: 62+46=108, Resulting Numbers: [108] 108,41 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 #0,0,1 Current State: 41:[14, 30], Operations: ['85-23=62', '62-32=30'] Exploring Operation: 14*30=420, Resulting Numbers: [420] 420,41 unequal: No Solution Exploring Operation: 14+30=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,41 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: 41:[23, 32, 71], Operations: ['85-14=71'] Exploring Operation: 71-23=48, Resulting Numbers: [32, 48] Generated Node #0,1,0: 41:[32, 48] Operation: 71-23=48 Exploring Operation: 23+32=55, Resulting Numbers: [71, 55] Generated Node #0,1,1: 41:[71, 55] Operation: 23+32=55 Exploring Operation: 71-32=39, Resulting Numbers: [23, 39] Generated Node #0,1,2: 41:[23, 39] Operation: 71-32=39 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[32, 48], Operations: ['85-14=71', '71-23=48'] Exploring Operation: 32*48=1536, Resulting Numbers: [1536] 1536,41 unequal: No Solution Exploring Operation: 48-32=16, Resulting Numbers: [16] 16,41 unequal: No Solution Exploring Operation: 32+48=80, Resulting Numbers: [80] 80,41 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 #0,1,2 Current State: 41:[23, 39], Operations: ['85-14=71', '71-32=39'] Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,41 unequal: No Solution Exploring Operation: 23*39=897, Resulting Numbers: [897] 897,41 unequal: No Solution Exploring Operation: 23+39=62, Resulting Numbers: [62] 62,41 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 #0,1,1 Current State: 41:[71, 55], Operations: ['85-14=71', '23+32=55'] Exploring Operation: 71+55=126, Resulting Numbers: [126] 126,41 unequal: No Solution Exploring Operation: 71*55=3905, Resulting Numbers: [3905] 3905,41 unequal: No Solution Exploring Operation: 71-55=16, Resulting Numbers: [16] 16,41 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: 41:[23, 14, 53], Operations: ['85-32=53'] Exploring Operation: 53-23=30, Resulting Numbers: [14, 30] Generated Node #0,2,0: 41:[14, 30] Operation: 53-23=30 Exploring Operation: 53-14=39, Resulting Numbers: [23, 39] Generated Node #0,2,1: 41:[23, 39] Operation: 53-14=39 Exploring Operation: 23+14=37, Resulting Numbers: [53, 37] Generated Node #0,2,2: 41:[53, 37] Operation: 23+14=37 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 41:[53, 37], Operations: ['85-32=53', '23+14=37'] Exploring Operation: 53-37=16, Resulting Numbers: [16] 16,41 unequal: No Solution Exploring Operation: 53*37=1961, Resulting Numbers: [1961] 1961,41 unequal: No Solution Exploring Operation: 53+37=90, Resulting Numbers: [90] 90,41 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 #0,2,1 Current State: 41:[23, 39], Operations: ['85-32=53', '53-14=39'] Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,41 unequal: No Solution Exploring Operation: 23+39=62, Resulting Numbers: [62] 62,41 unequal: No Solution Exploring Operation: 23*39=897, Resulting Numbers: [897] 897,41 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 #0,2,0 Current State: 41:[14, 30], Operations: ['85-32=53', '53-23=30'] Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,41 unequal: No Solution Exploring Operation: 14+30=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 14*30=420, Resulting Numbers: [420] 420,41 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
[ 84, 63, 4, 84 ]
84
[ "84+84=168", "63*4=252", "252-168=84" ]
Current State: 84:[84, 63, 4, 84], Operations: [] Exploring Operation: 84+84=168, Resulting Numbers: [63, 4, 168] Generated Node #2: [63, 4, 168] from Operation: 84+84=168 Current State: 84:[63, 4, 168], Operations: ['84+84=168'] Exploring Operation: 63*4=252, Resulting Numbers: [168, 252] Generated Node #3: [168, 252] from Operation: 63*4=252 Current State: 84:[168, 252], Operations: ['84+84=168', '63*4=252'] Exploring Operation: 252-168=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[84, 63, 4, 84], Operations: [] Exploring Operation: 84-63=21, Resulting Numbers: [4, 84, 21] Generated Node #0,0: 84:[4, 84, 21] Operation: 84-63=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[4, 84, 21], Operations: ['84-63=21'] Exploring Operation: 84/4=21, Resulting Numbers: [21, 21] Generated Node #0,0,0: 84:[21, 21] Operation: 84/4=21 Moving to Node #0,0,0 Current State: 84:[21, 21], Operations: ['84-63=21', '84/4=21'] Exploring Operation: 21+21=42, Resulting Numbers: [42] 42,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 50, 12, 90, 17 ]
11
[ "50+12=62", "90-17=73", "73-62=11" ]
Current State: 11:[50, 12, 90, 17], Operations: [] Exploring Operation: 50+12=62, Resulting Numbers: [90, 17, 62] Generated Node #2: [90, 17, 62] from Operation: 50+12=62 Current State: 11:[90, 17, 62], Operations: ['50+12=62'] Exploring Operation: 90-17=73, Resulting Numbers: [62, 73] Generated Node #3: [62, 73] from Operation: 90-17=73 Current State: 11:[62, 73], Operations: ['50+12=62', '90-17=73'] Exploring Operation: 73-62=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[50, 12, 90, 17], Operations: [] Exploring Operation: 50-17=33, Resulting Numbers: [12, 90, 33] Generated Node #0,0: 11:[12, 90, 33] Operation: 50-17=33 Exploring Operation: 90-17=73, Resulting Numbers: [50, 12, 73] Generated Node #0,1: 11:[50, 12, 73] Operation: 90-17=73 Exploring Operation: 90-50=40, Resulting Numbers: [12, 17, 40] Generated Node #0,2: 11:[12, 17, 40] Operation: 90-50=40 Exploring Operation: 50-12=38, Resulting Numbers: [90, 17, 38] Generated Node #0,3: 11:[90, 17, 38] Operation: 50-12=38 Moving to Node #0,2 Current State: 11:[12, 17, 40], Operations: ['90-50=40'] Exploring Operation: 40-17=23, Resulting Numbers: [12, 23] Generated Node #0,2,0: 11:[12, 23] Operation: 40-17=23 Exploring Operation: 17-12=5, Resulting Numbers: [40, 5] Generated Node #0,2,1: 11:[40, 5] Operation: 17-12=5 Exploring Operation: 40-12=28, Resulting Numbers: [17, 28] Generated Node #0,2,2: 11:[17, 28] Operation: 40-12=28 Exploring Operation: 12+17=29, Resulting Numbers: [40, 29] Generated Node #0,2,3: 11:[40, 29] Operation: 12+17=29 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[12, 23], Operations: ['90-50=40', '40-17=23'] Exploring Operation: 12*23=276, Resulting Numbers: [276] 276,11 unequal: No Solution Exploring Operation: 12+23=35, Resulting Numbers: [35] 35,11 unequal: No Solution Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[50, 12, 90, 17], Operations: [] Exploring Operation: 90-50=40, Resulting Numbers: [12, 17, 40] Generated Node #0,2: 11:[12, 17, 40] Operation: 90-50=40 Moving to Node #0,2 Current State: 11:[12, 17, 40], Operations: ['90-50=40'] Exploring Operation: 40-17=23, Resulting Numbers: [12, 23] Generated Node #0,2,0: 11:[12, 23] Operation: 40-17=23 Moving to Node #0,2,0 Current State: 11:[12, 23], Operations: ['90-50=40', '40-17=23'] Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 32, 23, 48, 74 ]
17
[ "32-23=9", "74-48=26", "26-9=17" ]
Current State: 17:[32, 23, 48, 74], Operations: [] Exploring Operation: 32-23=9, Resulting Numbers: [48, 74, 9] Generated Node #2: [48, 74, 9] from Operation: 32-23=9 Current State: 17:[48, 74, 9], Operations: ['32-23=9'] Exploring Operation: 74-48=26, Resulting Numbers: [9, 26] Generated Node #3: [9, 26] from Operation: 74-48=26 Current State: 17:[9, 26], Operations: ['32-23=9', '74-48=26'] Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[32, 23, 48, 74], Operations: [] Exploring Operation: 74-48=26, Resulting Numbers: [32, 23, 26] Generated Node #0,0: 17:[32, 23, 26] Operation: 74-48=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[32, 23, 26], Operations: ['74-48=26'] Exploring Operation: 32-23=9, Resulting Numbers: [26, 9] Generated Node #0,0,0: 17:[26, 9] Operation: 32-23=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[26, 9], Operations: ['74-48=26', '32-23=9'] Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[32, 23, 48, 74], Operations: [] Exploring Operation: 74-48=26, Resulting Numbers: [32, 23, 26] Generated Node #0,0: 17:[32, 23, 26] Operation: 74-48=26 Moving to Node #0,0 Current State: 17:[32, 23, 26], Operations: ['74-48=26'] Exploring Operation: 32-23=9, Resulting Numbers: [26, 9] Generated Node #0,0,0: 17:[26, 9] Operation: 32-23=9 Moving to Node #0,0,0 Current State: 17:[26, 9], Operations: ['74-48=26', '32-23=9'] Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 40, 27, 65, 79 ]
74
[ "40-27=13", "65/13=5", "79-5=74" ]
Current State: 74:[40, 27, 65, 79], Operations: [] Exploring Operation: 40-27=13, Resulting Numbers: [65, 79, 13] Generated Node #2: [65, 79, 13] from Operation: 40-27=13 Current State: 74:[65, 79, 13], Operations: ['40-27=13'] Exploring Operation: 65/13=5, Resulting Numbers: [79, 5] Generated Node #3: [79, 5] from Operation: 65/13=5 Current State: 74:[79, 5], Operations: ['40-27=13', '65/13=5'] Exploring Operation: 79-5=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[40, 27, 65, 79], Operations: [] Exploring Operation: 65-27=38, Resulting Numbers: [40, 79, 38] Generated Node #0,0: 74:[40, 79, 38] Operation: 65-27=38 Exploring Operation: 40+27=67, Resulting Numbers: [65, 79, 67] Generated Node #0,1: 74:[65, 79, 67] Operation: 40+27=67 Exploring Operation: 79-40=39, Resulting Numbers: [27, 65, 39] Generated Node #0,2: 74:[27, 65, 39] Operation: 79-40=39 Exploring Operation: 40-27=13, Resulting Numbers: [65, 79, 13] Generated Node #0,3: 74:[65, 79, 13] Operation: 40-27=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[40, 79, 38], Operations: ['65-27=38'] Exploring Operation: 40+38=78, Resulting Numbers: [79, 78] Generated Node #0,0,0: 74:[79, 78] Operation: 40+38=78 Exploring Operation: 40-38=2, Resulting Numbers: [79, 2] Generated Node #0,0,1: 74:[79, 2] Operation: 40-38=2 Exploring Operation: 79-40=39, Resulting Numbers: [38, 39] Generated Node #0,0,2: 74:[38, 39] Operation: 79-40=39 Exploring Operation: 79-38=41, Resulting Numbers: [40, 41] Generated Node #0,0,3: 74:[40, 41] Operation: 79-38=41 Moving to Node #0,0,2 Current State: 74:[38, 39], Operations: ['65-27=38', '79-40=39'] Exploring Operation: 38*39=1482, Resulting Numbers: [1482] 1482,74 unequal: No Solution Exploring Operation: 38+39=77, Resulting Numbers: [77] 77,74 unequal: No Solution Exploring Operation: 39-38=1, Resulting Numbers: [1] 1,74 unequal: No Solution Moving to Node #0,0,1 Current State: 74:[79, 2], Operations: ['65-27=38', '40-38=2'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,74 unequal: No Solution Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,74 unequal: No Solution Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,74 unequal: No Solution Moving to Node #0,0,3 Current State: 74:[40, 41], Operations: ['65-27=38', '79-38=41'] Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,74 unequal: No Solution Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,74 unequal: No Solution Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,74 unequal: No Solution Moving to Node #0,0,0 Current State: 74:[79, 78], Operations: ['65-27=38', '40+38=78'] Exploring Operation: 79*78=6162, Resulting Numbers: [6162] 6162,74 unequal: No Solution Exploring Operation: 79+78=157, Resulting Numbers: [157] 157,74 unequal: No Solution Exploring Operation: 79-78=1, Resulting Numbers: [1] 1,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[65, 79, 67], Operations: ['40+27=67'] Exploring Operation: 67-65=2, Resulting Numbers: [79, 2] Generated Node #0,1,0: 74:[79, 2] Operation: 67-65=2 Exploring Operation: 79-65=14, Resulting Numbers: [67, 14] Generated Node #0,1,1: 74:[67, 14] Operation: 79-65=14 Exploring Operation: 65+67=132, Resulting Numbers: [79, 132] Generated Node #0,1,2: 74:[79, 132] Operation: 65+67=132 Exploring Operation: 79-67=12, Resulting Numbers: [65, 12] Generated Node #0,1,3: 74:[65, 12] Operation: 79-67=12 Moving to Node #0,1,0 Current State: 74:[79, 2], Operations: ['40+27=67', '67-65=2'] Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,74 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,74 unequal: No Solution Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,74 unequal: No Solution Moving to Node #0,1,3 Current State: 74:[65, 12], Operations: ['40+27=67', '79-67=12'] Exploring Operation: 65*12=780, Resulting Numbers: [780] 780,74 unequal: No Solution Exploring Operation: 65-12=53, Resulting Numbers: [53] 53,74 unequal: No Solution Exploring Operation: 65+12=77, Resulting Numbers: [77] 77,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[67, 14], Operations: ['40+27=67', '79-65=14'] Exploring Operation: 67*14=938, Resulting Numbers: [938] 938,74 unequal: No Solution Exploring Operation: 67-14=53, Resulting Numbers: [53] 53,74 unequal: No Solution Exploring Operation: 67+14=81, Resulting Numbers: [81] 81,74 unequal: No Solution Moving to Node #0,1,2 Current State: 74:[79, 132], Operations: ['40+27=67', '65+67=132'] Exploring Operation: 79*132=10428, Resulting Numbers: [10428] 10428,74 unequal: No Solution Exploring Operation: 132-79=53, Resulting Numbers: [53] 53,74 unequal: No Solution Exploring Operation: 79+132=211, Resulting Numbers: [211] 211,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[27, 65, 39], Operations: ['79-40=39'] Exploring Operation: 39-27=12, Resulting Numbers: [65, 12] Generated Node #0,2,0: 74:[65, 12] Operation: 39-27=12 Exploring Operation: 65-27=38, Resulting Numbers: [39, 38] Generated Node #0,2,1: 74:[39, 38] Operation: 65-27=38 Exploring Operation: 27+65=92, Resulting Numbers: [39, 92] Generated Node #0,2,2: 74:[39, 92] Operation: 27+65=92 Exploring Operation: 27+39=66, Resulting Numbers: [65, 66] Generated Node #0,2,3: 74:[65, 66] Operation: 27+39=66 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 74:[39, 38], Operations: ['79-40=39', '65-27=38'] Exploring Operation: 39-38=1, Resulting Numbers: [1] 1,74 unequal: No Solution Exploring Operation: 39*38=1482, Resulting Numbers: [1482] 1482,74 unequal: No Solution Exploring Operation: 39+38=77, Resulting Numbers: [77] 77,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 74:[65, 66], Operations: ['79-40=39', '27+39=66'] Exploring Operation: 65+66=131, Resulting Numbers: [131] 131,74 unequal: No Solution Exploring Operation: 65*66=4290, Resulting Numbers: [4290] 4290,74 unequal: No Solution Exploring Operation: 66-65=1, Resulting Numbers: [1] 1,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 74:[65, 12], Operations: ['79-40=39', '39-27=12'] Exploring Operation: 65*12=780, Resulting Numbers: [780] 780,74 unequal: No Solution Exploring Operation: 65+12=77, Resulting Numbers: [77] 77,74 unequal: No Solution Exploring Operation: 65-12=53, Resulting Numbers: [53] 53,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 74:[39, 92], Operations: ['79-40=39', '27+65=92'] Exploring Operation: 39*92=3588, Resulting Numbers: [3588] 3588,74 unequal: No Solution Exploring Operation: 92-39=53, Resulting Numbers: [53] 53,74 unequal: No Solution Exploring Operation: 39+92=131, Resulting Numbers: [131] 131,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 74:[65, 79, 13], Operations: ['40-27=13'] Exploring Operation: 79-13=66, Resulting Numbers: [65, 66] Generated Node #0,3,0: 74:[65, 66] Operation: 79-13=66 Exploring Operation: 65+13=78, Resulting Numbers: [79, 78] Generated Node #0,3,1: 74:[79, 78] Operation: 65+13=78 Exploring Operation: 65-13=52, Resulting Numbers: [79, 52] Generated Node #0,3,2: 74:[79, 52] Operation: 65-13=52 Exploring Operation: 65/13=5, Resulting Numbers: [79, 5] Generated Node #0,3,3: 74:[79, 5] Operation: 65/13=5 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 74:[79, 5], Operations: ['40-27=13', '65/13=5'] Exploring Operation: 79+5=84, Resulting Numbers: [84] 84,74 unequal: No Solution Exploring Operation: 79*5=395, Resulting Numbers: [395] 395,74 unequal: No Solution Exploring Operation: 79-5=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[40, 27, 65, 79], Operations: [] Exploring Operation: 40-27=13, Resulting Numbers: [65, 79, 13] Generated Node #0,3: 74:[65, 79, 13] Operation: 40-27=13 Moving to Node #0,3 Current State: 74:[65, 79, 13], Operations: ['40-27=13'] Exploring Operation: 65/13=5, Resulting Numbers: [79, 5] Generated Node #0,3,3: 74:[79, 5] Operation: 65/13=5 Moving to Node #0,3,3 Current State: 74:[79, 5], Operations: ['40-27=13', '65/13=5'] Exploring Operation: 79-5=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.945313
hs_4
mult_heuristic
[ 7, 64, 47, 44 ]
19
[ "64-7=57", "47-44=3", "57/3=19" ]
Current State: 19:[7, 64, 47, 44], Operations: [] Exploring Operation: 64-7=57, Resulting Numbers: [47, 44, 57] Generated Node #2: [47, 44, 57] from Operation: 64-7=57 Current State: 19:[47, 44, 57], Operations: ['64-7=57'] Exploring Operation: 47-44=3, Resulting Numbers: [57, 3] Generated Node #3: [57, 3] from Operation: 47-44=3 Current State: 19:[57, 3], Operations: ['64-7=57', '47-44=3'] Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[7, 64, 47, 44], Operations: [] Exploring Operation: 64-7=57, Resulting Numbers: [47, 44, 57] Generated Node #0,0: 19:[47, 44, 57] Operation: 64-7=57 Exploring Operation: 64-47=17, Resulting Numbers: [7, 44, 17] Generated Node #0,1: 19:[7, 44, 17] Operation: 64-47=17 Exploring Operation: 47-44=3, Resulting Numbers: [7, 64, 3] Generated Node #0,2: 19:[7, 64, 3] Operation: 47-44=3 Exploring Operation: 64-44=20, Resulting Numbers: [7, 47, 20] Generated Node #0,3: 19:[7, 47, 20] Operation: 64-44=20 Moving to Node #0,1 Current State: 19:[7, 44, 17], Operations: ['64-47=17'] Exploring Operation: 7+17=24, Resulting Numbers: [44, 24] Generated Node #0,1,0: 19:[44, 24] Operation: 7+17=24 Exploring Operation: 44-7=37, Resulting Numbers: [17, 37] Generated Node #0,1,1: 19:[17, 37] Operation: 44-7=37 Exploring Operation: 7+44=51, Resulting Numbers: [17, 51] Generated Node #0,1,2: 19:[17, 51] Operation: 7+44=51 Exploring Operation: 44-17=27, Resulting Numbers: [7, 27] Generated Node #0,1,3: 19:[7, 27] Operation: 44-17=27 Moving to Node #0,3 Current State: 19:[7, 47, 20], Operations: ['64-44=20'] Exploring Operation: 47-20=27, Resulting Numbers: [7, 27] Generated Node #0,3,0: 19:[7, 27] Operation: 47-20=27 Exploring Operation: 7+47=54, Resulting Numbers: [20, 54] Generated Node #0,3,1: 19:[20, 54] Operation: 7+47=54 Exploring Operation: 20-7=13, Resulting Numbers: [47, 13] Generated Node #0,3,2: 19:[47, 13] Operation: 20-7=13 Exploring Operation: 47-7=40, Resulting Numbers: [20, 40] Generated Node #0,3,3: 19:[20, 40] Operation: 47-7=40 Moving to Node #0,2 Current State: 19:[7, 64, 3], Operations: ['47-44=3'] Exploring Operation: 64-3=61, Resulting Numbers: [7, 61] Generated Node #0,2,0: 19:[7, 61] Operation: 64-3=61 Exploring Operation: 7+3=10, Resulting Numbers: [64, 10] Generated Node #0,2,1: 19:[64, 10] Operation: 7+3=10 Exploring Operation: 7*3=21, Resulting Numbers: [64, 21] Generated Node #0,2,2: 19:[64, 21] Operation: 7*3=21 Exploring Operation: 64-7=57, Resulting Numbers: [3, 57] Generated Node #0,2,3: 19:[3, 57] Operation: 64-7=57 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 19:[64, 21], Operations: ['47-44=3', '7*3=21'] Exploring Operation: 64+21=85, Resulting Numbers: [85] 85,19 unequal: No Solution Exploring Operation: 64*21=1344, Resulting Numbers: [1344] 1344,19 unequal: No Solution Exploring Operation: 64-21=43, Resulting Numbers: [43] 43,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 19:[7, 61], Operations: ['47-44=3', '64-3=61'] Exploring Operation: 7*61=427, Resulting Numbers: [427] 427,19 unequal: No Solution Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 7+61=68, Resulting Numbers: [68] 68,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 19:[64, 10], Operations: ['47-44=3', '7+3=10'] Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 64*10=640, Resulting Numbers: [640] 640,19 unequal: No Solution Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 19:[3, 57], Operations: ['47-44=3', '64-7=57'] Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 3*57=171, Resulting Numbers: [171] 171,19 unequal: No Solution Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[7, 64, 47, 44], Operations: [] Exploring Operation: 47-44=3, Resulting Numbers: [7, 64, 3] Generated Node #0,2: 19:[7, 64, 3] Operation: 47-44=3 Moving to Node #0,2 Current State: 19:[7, 64, 3], Operations: ['47-44=3'] Exploring Operation: 64-7=57, Resulting Numbers: [3, 57] Generated Node #0,2,3: 19:[3, 57] Operation: 64-7=57 Moving to Node #0,2,3 Current State: 19:[3, 57], Operations: ['47-44=3', '64-7=57'] Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 5, 58, 75, 89 ]
46
[ "75/5=15", "89-58=31", "15+31=46" ]
Current State: 46:[5, 58, 75, 89], Operations: [] Exploring Operation: 75/5=15, Resulting Numbers: [58, 89, 15] Generated Node #2: [58, 89, 15] from Operation: 75/5=15 Current State: 46:[58, 89, 15], Operations: ['75/5=15'] Exploring Operation: 89-58=31, Resulting Numbers: [15, 31] Generated Node #3: [15, 31] from Operation: 89-58=31 Current State: 46:[15, 31], Operations: ['75/5=15', '89-58=31'] Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[5, 58, 75, 89], Operations: [] Exploring Operation: 89-75=14, Resulting Numbers: [5, 58, 14] Generated Node #0,0: 46:[5, 58, 14] Operation: 89-75=14 Exploring Operation: 89-58=31, Resulting Numbers: [5, 75, 31] Generated Node #0,1: 46:[5, 75, 31] Operation: 89-58=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[5, 58, 14], Operations: ['89-75=14'] Exploring Operation: 58-14=44, Resulting Numbers: [5, 44] Generated Node #0,0,0: 46:[5, 44] Operation: 58-14=44 Exploring Operation: 58-5=53, Resulting Numbers: [14, 53] Generated Node #0,0,1: 46:[14, 53] Operation: 58-5=53 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[5, 44], Operations: ['89-75=14', '58-14=44'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,46 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:[14, 53], Operations: ['89-75=14', '58-5=53'] Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,46 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:[5, 75, 31], Operations: ['89-58=31'] Exploring Operation: 75/5=15, Resulting Numbers: [31, 15] Generated Node #0,1,0: 46:[31, 15] Operation: 75/5=15 Exploring Operation: 75-31=44, Resulting Numbers: [5, 44] Generated Node #0,1,1: 46:[5, 44] Operation: 75-31=44 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 46:[5, 44], Operations: ['89-58=31', '75-31=44'] Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,46 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:[31, 15], Operations: ['89-58=31', '75/5=15'] Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,46 unequal: No Solution Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[5, 58, 75, 89], Operations: [] Exploring Operation: 89-58=31, Resulting Numbers: [5, 75, 31] Generated Node #0,1: 46:[5, 75, 31] Operation: 89-58=31 Moving to Node #0,1 Current State: 46:[5, 75, 31], Operations: ['89-58=31'] Exploring Operation: 75/5=15, Resulting Numbers: [31, 15] Generated Node #0,1,0: 46:[31, 15] Operation: 75/5=15 Moving to Node #0,1,0 Current State: 46:[31, 15], Operations: ['89-58=31', '75/5=15'] Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 7, 23, 24, 54 ]
35
[ "23+54=77", "77/7=11", "24+11=35" ]
Current State: 35:[7, 23, 24, 54], Operations: [] Exploring Operation: 23+54=77, Resulting Numbers: [7, 24, 77] Generated Node #2: [7, 24, 77] from Operation: 23+54=77 Current State: 35:[7, 24, 77], Operations: ['23+54=77'] Exploring Operation: 77/7=11, Resulting Numbers: [24, 11] Generated Node #3: [24, 11] from Operation: 77/7=11 Current State: 35:[24, 11], Operations: ['23+54=77', '77/7=11'] Exploring Operation: 24+11=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[7, 23, 24, 54], Operations: [] Exploring Operation: 24-23=1, Resulting Numbers: [7, 54, 1] Generated Node #0,0: 35:[7, 54, 1] Operation: 24-23=1 Exploring Operation: 23+24=47, Resulting Numbers: [7, 54, 47] Generated Node #0,1: 35:[7, 54, 47] Operation: 23+24=47 Exploring Operation: 54-23=31, Resulting Numbers: [7, 24, 31] Generated Node #0,2: 35:[7, 24, 31] Operation: 54-23=31 Exploring Operation: 54-24=30, Resulting Numbers: [7, 23, 30] Generated Node #0,3: 35:[7, 23, 30] Operation: 54-24=30 Moving to Node #0,2 Current State: 35:[7, 24, 31], Operations: ['54-23=31'] Exploring Operation: 7+31=38, Resulting Numbers: [24, 38] Generated Node #0,2,0: 35:[24, 38] Operation: 7+31=38 Exploring Operation: 7+24=31, Resulting Numbers: [31, 31] Generated Node #0,2,1: 35:[31, 31] Operation: 7+24=31 Exploring Operation: 31-24=7, Resulting Numbers: [7, 7] Generated Node #0,2,2: 35:[7, 7] Operation: 31-24=7 Exploring Operation: 24-7=17, Resulting Numbers: [31, 17] Generated Node #0,2,3: 35:[31, 17] Operation: 24-7=17 Moving to Node #0,3 Current State: 35:[7, 23, 30], Operations: ['54-24=30'] Exploring Operation: 7+30=37, Resulting Numbers: [23, 37] Generated Node #0,3,0: 35:[23, 37] Operation: 7+30=37 Exploring Operation: 7+23=30, Resulting Numbers: [30, 30] Generated Node #0,3,1: 35:[30, 30] Operation: 7+23=30 Exploring Operation: 23-7=16, Resulting Numbers: [30, 16] Generated Node #0,3,2: 35:[30, 16] Operation: 23-7=16 Exploring Operation: 30-23=7, Resulting Numbers: [7, 7] Generated Node #0,3,3: 35:[7, 7] Operation: 30-23=7 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 35:[7, 7], Operations: ['54-24=30', '30-23=7'] Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,35 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 #0,3,1 Current State: 35:[30, 30], Operations: ['54-24=30', '7+23=30'] Exploring Operation: 30-30=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 30*30=900, Resulting Numbers: [900] 900,35 unequal: No Solution Exploring Operation: 30/30=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 30+30=60, Resulting Numbers: [60] 60,35 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 #0,3,0 Current State: 35:[23, 37], Operations: ['54-24=30', '7+30=37'] Exploring Operation: 23+37=60, Resulting Numbers: [60] 60,35 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 23*37=851, Resulting Numbers: [851] 851,35 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 #0,3,2 Current State: 35:[30, 16], Operations: ['54-24=30', '23-7=16'] Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 30+16=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 30*16=480, Resulting Numbers: [480] 480,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 35:[7, 54, 1], Operations: ['24-23=1'] Exploring Operation: 7*1=7, Resulting Numbers: [54, 7] Generated Node #0,0,0: 35:[54, 7] Operation: 7*1=7 Exploring Operation: 54-1=53, Resulting Numbers: [7, 53] Generated Node #0,0,1: 35:[7, 53] Operation: 54-1=53 Exploring Operation: 7/1=7, Resulting Numbers: [54, 7] Generated Node #0,0,2: 35:[54, 7] Operation: 7/1=7 Exploring Operation: 54-7=47, Resulting Numbers: [1, 47] Generated Node #0,0,3: 35:[1, 47] Operation: 54-7=47 Moving to Node #0,1 Current State: 35:[7, 54, 47], Operations: ['23+24=47'] Exploring Operation: 7+54=61, Resulting Numbers: [47, 61] Generated Node #0,1,0: 35:[47, 61] Operation: 7+54=61 Exploring Operation: 54-7=47, Resulting Numbers: [47, 47] Generated Node #0,1,1: 35:[47, 47] Operation: 54-7=47 Exploring Operation: 54-47=7, Resulting Numbers: [7, 7] Generated Node #0,1,2: 35:[7, 7] Operation: 54-47=7 Exploring Operation: 47-7=40, Resulting Numbers: [54, 40] Generated Node #0,1,3: 35:[54, 40] Operation: 47-7=40 Moving to Node #0,2,2 Current State: 35:[7, 7], Operations: ['54-23=31', '31-24=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,35 unequal: No Solution Moving to Node #0,1,2 Current State: 35:[7, 7], Operations: ['23+24=47', '54-47=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,35 unequal: No Solution Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,35 unequal: No Solution Moving to Node #0,2,1 Current State: 35:[31, 31], Operations: ['54-23=31', '7+24=31'] Exploring Operation: 31-31=0, Resulting Numbers: [0] 0,35 unequal: No Solution Exploring Operation: 31/31=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 31*31=961, Resulting Numbers: [961] 961,35 unequal: No Solution Exploring Operation: 31+31=62, Resulting Numbers: [62] 62,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[24, 38], Operations: ['54-23=31', '7+31=38'] Exploring Operation: 24*38=912, Resulting Numbers: [912] 912,35 unequal: No Solution Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 24+38=62, Resulting Numbers: [62] 62,35 unequal: No Solution Moving to Node #0,2,3 Current State: 35:[31, 17], Operations: ['54-23=31', '24-7=17'] Exploring Operation: 31+17=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 31*17=527, Resulting Numbers: [527] 527,35 unequal: No Solution Exploring Operation: 31-17=14, Resulting Numbers: [14] 14,35 unequal: No Solution Moving to Node #0,0,3 Current State: 35:[1, 47], Operations: ['24-23=1', '54-7=47'] Exploring Operation: 1+47=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 1*47=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[7, 53], Operations: ['24-23=1', '54-1=53'] Exploring Operation: 7*53=371, Resulting Numbers: [371] 371,35 unequal: No Solution Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 7+53=60, Resulting Numbers: [60] 60,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[54, 7], Operations: ['24-23=1', '7*1=7'] Exploring Operation: 54+7=61, Resulting Numbers: [61] 61,35 unequal: No Solution Exploring Operation: 54-7=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 54*7=378, Resulting Numbers: [378] 378,35 unequal: No Solution Moving to Node #0,0,2 Current State: 35:[54, 7], Operations: ['24-23=1', '7/1=7'] Exploring Operation: 54-7=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 54+7=61, Resulting Numbers: [61] 61,35 unequal: No Solution Exploring Operation: 54*7=378, Resulting Numbers: [378] 378,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[47, 47], Operations: ['23+24=47', '54-7=47'] Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,35 unequal: No Solution Exploring Operation: 47/47=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 47*47=2209, Resulting Numbers: [2209] 2209,35 unequal: No Solution Exploring Operation: 47-47=0, Resulting Numbers: [0] 0,35 unequal: No Solution Moving to Node #0,1,3 Current State: 35:[54, 40], Operations: ['23+24=47', '47-7=40'] Exploring Operation: 54*40=2160, Resulting Numbers: [2160] 2160,35 unequal: No Solution Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 54+40=94, Resulting Numbers: [94] 94,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[47, 61], Operations: ['23+24=47', '7+54=61'] Exploring Operation: 61-47=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 47+61=108, Resulting Numbers: [108] 108,35 unequal: No Solution Exploring Operation: 47*61=2867, Resulting Numbers: [2867] 2867,35 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 3, 64, 1, 91 ]
78
[ "64+1=65", "91-65=26", "3*26=78" ]
Current State: 78:[3, 64, 1, 91], Operations: [] Exploring Operation: 64+1=65, Resulting Numbers: [3, 91, 65] Generated Node #2: [3, 91, 65] from Operation: 64+1=65 Current State: 78:[3, 91, 65], Operations: ['64+1=65'] Exploring Operation: 91-65=26, Resulting Numbers: [3, 26] Generated Node #3: [3, 26] from Operation: 91-65=26 Current State: 78:[3, 26], Operations: ['64+1=65', '91-65=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[3, 64, 1, 91], Operations: [] Exploring Operation: 91-3=88, Resulting Numbers: [64, 1, 88] Generated Node #0,0: 78:[64, 1, 88] Operation: 91-3=88 Exploring Operation: 91-1=90, Resulting Numbers: [3, 64, 90] Generated Node #0,1: 78:[3, 64, 90] Operation: 91-1=90 Exploring Operation: 3+64=67, Resulting Numbers: [1, 91, 67] Generated Node #0,2: 78:[1, 91, 67] Operation: 3+64=67 Exploring Operation: 91-64=27, Resulting Numbers: [3, 1, 27] Generated Node #0,3: 78:[3, 1, 27] Operation: 91-64=27 Exploring Operation: 64+1=65, Resulting Numbers: [3, 91, 65] Generated Node #0,4: 78:[3, 91, 65] Operation: 64+1=65 Start Sub Search at level 1: Moving to Node #0,3 Current State: 78:[3, 1, 27], Operations: ['91-64=27'] Exploring Operation: 3/1=3, Resulting Numbers: [27, 3] Generated Node #0,3,0: 78:[27, 3] Operation: 3/1=3 Exploring Operation: 3-1=2, Resulting Numbers: [27, 2] Generated Node #0,3,1: 78:[27, 2] Operation: 3-1=2 Exploring Operation: 3*1=3, Resulting Numbers: [27, 3] Generated Node #0,3,2: 78:[27, 3] Operation: 3*1=3 Exploring Operation: 27-1=26, Resulting Numbers: [3, 26] Generated Node #0,3,3: 78:[3, 26] Operation: 27-1=26 Exploring Operation: 1*27=27, Resulting Numbers: [3, 27] Generated Node #0,3,4: 78:[3, 27] Operation: 1*27=27 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 78:[3, 26], Operations: ['91-64=27', '27-1=26'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[3, 64, 1, 91], Operations: [] Exploring Operation: 91-64=27, Resulting Numbers: [3, 1, 27] Generated Node #0,3: 78:[3, 1, 27] Operation: 91-64=27 Moving to Node #0,3 Current State: 78:[3, 1, 27], Operations: ['91-64=27'] Exploring Operation: 27-1=26, Resulting Numbers: [3, 26] Generated Node #0,3,3: 78:[3, 26] Operation: 27-1=26 Moving to Node #0,3,3 Current State: 78:[3, 26], Operations: ['91-64=27', '27-1=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 29, 26, 60, 4 ]
27
[ "26+4=30", "60/30=2", "29-2=27" ]
Current State: 27:[29, 26, 60, 4], Operations: [] Exploring Operation: 26+4=30, Resulting Numbers: [29, 60, 30] Generated Node #2: [29, 60, 30] from Operation: 26+4=30 Current State: 27:[29, 60, 30], Operations: ['26+4=30'] Exploring Operation: 60/30=2, Resulting Numbers: [29, 2] Generated Node #3: [29, 2] from Operation: 60/30=2 Current State: 27:[29, 2], Operations: ['26+4=30', '60/30=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[29, 26, 60, 4], Operations: [] Exploring Operation: 60-29=31, Resulting Numbers: [26, 4, 31] Generated Node #0,0: 27:[26, 4, 31] Operation: 60-29=31 Exploring Operation: 60/4=15, Resulting Numbers: [29, 26, 15] Generated Node #0,1: 27:[29, 26, 15] Operation: 60/4=15 Exploring Operation: 60-26=34, Resulting Numbers: [29, 4, 34] Generated Node #0,2: 27:[29, 4, 34] Operation: 60-26=34 Moving to Node #0,0 Current State: 27:[26, 4, 31], Operations: ['60-29=31'] Exploring Operation: 26+4=30, Resulting Numbers: [31, 30] Generated Node #0,0,0: 27:[31, 30] Operation: 26+4=30 Exploring Operation: 31-26=5, Resulting Numbers: [4, 5] Generated Node #0,0,1: 27:[4, 5] Operation: 31-26=5 Exploring Operation: 31-4=27, Resulting Numbers: [26, 27] Generated Node #0,0,2: 27:[26, 27] Operation: 31-4=27 Moving to Node #0,1 Current State: 27:[29, 26, 15], Operations: ['60/4=15'] Exploring Operation: 26-15=11, Resulting Numbers: [29, 11] Generated Node #0,1,0: 27:[29, 11] Operation: 26-15=11 Exploring Operation: 29-26=3, Resulting Numbers: [15, 3] Generated Node #0,1,1: 27:[15, 3] Operation: 29-26=3 Exploring Operation: 29-15=14, Resulting Numbers: [26, 14] Generated Node #0,1,2: 27:[26, 14] Operation: 29-15=14 Moving to Node #0,2 Current State: 27:[29, 4, 34], Operations: ['60-26=34'] Exploring Operation: 34-29=5, Resulting Numbers: [4, 5] Generated Node #0,2,0: 27:[4, 5] Operation: 34-29=5 Exploring Operation: 34-4=30, Resulting Numbers: [29, 30] Generated Node #0,2,1: 27:[29, 30] Operation: 34-4=30 Exploring Operation: 29-4=25, Resulting Numbers: [34, 25] Generated Node #0,2,2: 27:[34, 25] Operation: 29-4=25 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 27:[4, 5], Operations: ['60-26=34', '34-29=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,27 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 27:[29, 30], Operations: ['60-26=34', '34-4=30'] Exploring Operation: 29*30=870, Resulting Numbers: [870] 870,27 unequal: No Solution Exploring Operation: 29+30=59, Resulting Numbers: [59] 59,27 unequal: No Solution Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 27:[34, 25], Operations: ['60-26=34', '29-4=25'] Exploring Operation: 34-25=9, Resulting Numbers: [9] 9,27 unequal: No Solution Exploring Operation: 34*25=850, Resulting Numbers: [850] 850,27 unequal: No Solution Exploring Operation: 34+25=59, Resulting Numbers: [59] 59,27 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: 27:[26, 27], Operations: ['60-29=31', '31-4=27'] Exploring Operation: 26*27=702, Resulting Numbers: [702] 702,27 unequal: No Solution Exploring Operation: 26+27=53, Resulting Numbers: [53] 53,27 unequal: No Solution Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,27 unequal: No Solution Moving to Node #0,0,1 Current State: 27:[4, 5], Operations: ['60-29=31', '31-26=5'] Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,27 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,27 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,27 unequal: No Solution Moving to Node #0,1,0 Current State: 27:[29, 11], Operations: ['60/4=15', '26-15=11'] Exploring Operation: 29*11=319, Resulting Numbers: [319] 319,27 unequal: No Solution Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 29+11=40, Resulting Numbers: [40] 40,27 unequal: No Solution Moving to Node #0,1,2 Current State: 27:[26, 14], Operations: ['60/4=15', '29-15=14'] Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[15, 3], Operations: ['60/4=15', '29-26=3'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,27 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[31, 30], Operations: ['60-29=31', '26+4=30'] Exploring Operation: 31+30=61, Resulting Numbers: [61] 61,27 unequal: No Solution Exploring Operation: 31*30=930, Resulting Numbers: [930] 930,27 unequal: No Solution Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,27 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 76, 11, 88, 78 ]
74
[ "76+78=154", "154/11=14", "88-14=74" ]
Current State: 74:[76, 11, 88, 78], Operations: [] Exploring Operation: 76+78=154, Resulting Numbers: [11, 88, 154] Generated Node #2: [11, 88, 154] from Operation: 76+78=154 Current State: 74:[11, 88, 154], Operations: ['76+78=154'] Exploring Operation: 154/11=14, Resulting Numbers: [88, 14] Generated Node #3: [88, 14] from Operation: 154/11=14 Current State: 74:[88, 14], Operations: ['76+78=154', '154/11=14'] Exploring Operation: 88-14=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[76, 11, 88, 78], Operations: [] Exploring Operation: 88-11=77, Resulting Numbers: [76, 78, 77] Generated Node #0,0: 74:[76, 78, 77] Operation: 88-11=77 Exploring Operation: 88/11=8, Resulting Numbers: [76, 78, 8] Generated Node #0,1: 74:[76, 78, 8] Operation: 88/11=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[76, 78, 77], Operations: ['88-11=77'] Exploring Operation: 78-77=1, Resulting Numbers: [76, 1] Generated Node #0,0,0: 74:[76, 1] Operation: 78-77=1 Exploring Operation: 78-76=2, Resulting Numbers: [77, 2] Generated Node #0,0,1: 74:[77, 2] Operation: 78-76=2 Moving to Node #0,0,0 Current State: 74:[76, 1], Operations: ['88-11=77', '78-77=1'] Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,74 unequal: No Solution Exploring Operation: 76*1=76, Resulting Numbers: [76] 76,74 unequal: No Solution Moving to Node #0,0,1 Current State: 74:[77, 2], Operations: ['88-11=77', '78-76=2'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,74 unequal: No Solution Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[76, 78, 8], Operations: ['88/11=8'] Exploring Operation: 78-8=70, Resulting Numbers: [76, 70] Generated Node #0,1,0: 74:[76, 70] Operation: 78-8=70 Exploring Operation: 78-76=2, Resulting Numbers: [8, 2] Generated Node #0,1,1: 74:[8, 2] Operation: 78-76=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 74:[76, 70], Operations: ['88/11=8', '78-8=70'] Exploring Operation: 76-70=6, Resulting Numbers: [6] 6,74 unequal: No Solution Exploring Operation: 76+70=146, Resulting Numbers: [146] 146,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 74:[8, 2], Operations: ['88/11=8', '78-76=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,74 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 66, 95, 5, 14 ]
75
[ "95-66=29", "29-14=15", "5*15=75" ]
Current State: 75:[66, 95, 5, 14], Operations: [] Exploring Operation: 95-66=29, Resulting Numbers: [5, 14, 29] Generated Node #2: [5, 14, 29] from Operation: 95-66=29 Current State: 75:[5, 14, 29], Operations: ['95-66=29'] Exploring Operation: 29-14=15, Resulting Numbers: [5, 15] Generated Node #3: [5, 15] from Operation: 29-14=15 Current State: 75:[5, 15], Operations: ['95-66=29', '29-14=15'] Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[66, 95, 5, 14], Operations: [] Exploring Operation: 95/5=19, Resulting Numbers: [66, 14, 19] Generated Node #0,0: 75:[66, 14, 19] Operation: 95/5=19 Exploring Operation: 95-66=29, Resulting Numbers: [5, 14, 29] Generated Node #0,1: 75:[5, 14, 29] Operation: 95-66=29 Exploring Operation: 95-14=81, Resulting Numbers: [66, 5, 81] Generated Node #0,2: 75:[66, 5, 81] Operation: 95-14=81 Exploring Operation: 66+5=71, Resulting Numbers: [95, 14, 71] Generated Node #0,3: 75:[95, 14, 71] Operation: 66+5=71 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[5, 14, 29], Operations: ['95-66=29'] Exploring Operation: 29-5=24, Resulting Numbers: [14, 24] Generated Node #0,1,0: 75:[14, 24] Operation: 29-5=24 Exploring Operation: 29-14=15, Resulting Numbers: [5, 15] Generated Node #0,1,1: 75:[5, 15] Operation: 29-14=15 Exploring Operation: 5+14=19, Resulting Numbers: [29, 19] Generated Node #0,1,2: 75:[29, 19] Operation: 5+14=19 Exploring Operation: 14-5=9, Resulting Numbers: [29, 9] Generated Node #0,1,3: 75:[29, 9] Operation: 14-5=9 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[5, 15], Operations: ['95-66=29', '29-14=15'] Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,75 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,75 unequal: No Solution Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[66, 95, 5, 14], Operations: [] Exploring Operation: 95-66=29, Resulting Numbers: [5, 14, 29] Generated Node #0,1: 75:[5, 14, 29] Operation: 95-66=29 Moving to Node #0,1 Current State: 75:[5, 14, 29], Operations: ['95-66=29'] Exploring Operation: 29-14=15, Resulting Numbers: [5, 15] Generated Node #0,1,1: 75:[5, 15] Operation: 29-14=15 Moving to Node #0,1,1 Current State: 75:[5, 15], Operations: ['95-66=29', '29-14=15'] Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 6, 24, 22, 17 ]
64
[ "24-17=7", "6*7=42", "22+42=64" ]
Current State: 64:[6, 24, 22, 17], Operations: [] Exploring Operation: 24-17=7, Resulting Numbers: [6, 22, 7] Generated Node #2: [6, 22, 7] from Operation: 24-17=7 Current State: 64:[6, 22, 7], Operations: ['24-17=7'] Exploring Operation: 6*7=42, Resulting Numbers: [22, 42] Generated Node #3: [22, 42] from Operation: 6*7=42 Current State: 64:[22, 42], Operations: ['24-17=7', '6*7=42'] Exploring Operation: 22+42=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[6, 24, 22, 17], Operations: [] Exploring Operation: 24/6=4, Resulting Numbers: [22, 17, 4] Generated Node #0,0: 64:[22, 17, 4] Operation: 24/6=4 Exploring Operation: 24-22=2, Resulting Numbers: [6, 17, 2] Generated Node #0,1: 64:[6, 17, 2] Operation: 24-22=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[6, 17, 2], Operations: ['24-22=2'] Exploring Operation: 6+2=8, Resulting Numbers: [17, 8] Generated Node #0,1,0: 64:[17, 8] Operation: 6+2=8 Exploring Operation: 6-2=4, Resulting Numbers: [17, 4] Generated Node #0,1,1: 64:[17, 4] Operation: 6-2=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 64:[17, 8], Operations: ['24-22=2', '6+2=8'] Exploring Operation: 17+8=25, Resulting Numbers: [25] 25,64 unequal: No Solution Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,64 unequal: No Solution No 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: 64:[17, 4], Operations: ['24-22=2', '6-2=4'] Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,64 unequal: No Solution Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,64 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: 64:[22, 17, 4], Operations: ['24/6=4'] Exploring Operation: 22-17=5, Resulting Numbers: [4, 5] Generated Node #0,0,0: 64:[4, 5] Operation: 22-17=5 Exploring Operation: 22-4=18, Resulting Numbers: [17, 18] Generated Node #0,0,1: 64:[17, 18] Operation: 22-4=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 64:[4, 5], Operations: ['24/6=4', '22-17=5'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,64 unequal: No Solution No 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: 64:[17, 18], Operations: ['24/6=4', '22-4=18'] Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 17+18=35, Resulting Numbers: [35] 35,64 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
[ 35, 53, 24, 78 ]
36
[ "53-35=18", "78-24=54", "54-18=36" ]
Current State: 36:[35, 53, 24, 78], Operations: [] Exploring Operation: 53-35=18, Resulting Numbers: [24, 78, 18] Generated Node #2: [24, 78, 18] from Operation: 53-35=18 Current State: 36:[24, 78, 18], Operations: ['53-35=18'] Exploring Operation: 78-24=54, Resulting Numbers: [18, 54] Generated Node #3: [18, 54] from Operation: 78-24=54 Current State: 36:[18, 54], Operations: ['53-35=18', '78-24=54'] Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[35, 53, 24, 78], Operations: [] Exploring Operation: 78-53=25, Resulting Numbers: [35, 24, 25] Generated Node #0,0: 36:[35, 24, 25] Operation: 78-53=25 Moving to Node #0,0 Current State: 36:[35, 24, 25], Operations: ['78-53=25'] Exploring Operation: 25-24=1, Resulting Numbers: [35, 1] Generated Node #0,0,0: 36:[35, 1] Operation: 25-24=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[35, 1], Operations: ['78-53=25', '25-24=1'] Exploring Operation: 35+1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[35, 53, 24, 78], Operations: [] Exploring Operation: 78-53=25, Resulting Numbers: [35, 24, 25] Generated Node #0,0: 36:[35, 24, 25] Operation: 78-53=25 Moving to Node #0,0 Current State: 36:[35, 24, 25], Operations: ['78-53=25'] Exploring Operation: 25-24=1, Resulting Numbers: [35, 1] Generated Node #0,0,0: 36:[35, 1] Operation: 25-24=1 Moving to Node #0,0,0 Current State: 36:[35, 1], Operations: ['78-53=25', '25-24=1'] Exploring Operation: 35+1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 67, 16, 49, 44 ]
13
[ "16*44=704", "704-67=637", "637/49=13" ]
Current State: 13:[67, 16, 49, 44], Operations: [] Exploring Operation: 16*44=704, Resulting Numbers: [67, 49, 704] Generated Node #2: [67, 49, 704] from Operation: 16*44=704 Current State: 13:[67, 49, 704], Operations: ['16*44=704'] Exploring Operation: 704-67=637, Resulting Numbers: [49, 637] Generated Node #3: [49, 637] from Operation: 704-67=637 Current State: 13:[49, 637], Operations: ['16*44=704', '704-67=637'] Exploring Operation: 637/49=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[67, 16, 49, 44], Operations: [] Exploring Operation: 67-49=18, Resulting Numbers: [16, 44, 18] Generated Node #0,0: 13:[16, 44, 18] Operation: 67-49=18 Exploring Operation: 67-44=23, Resulting Numbers: [16, 49, 23] Generated Node #0,1: 13:[16, 49, 23] Operation: 67-44=23 Exploring Operation: 49-44=5, Resulting Numbers: [67, 16, 5] Generated Node #0,2: 13:[67, 16, 5] Operation: 49-44=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[16, 44, 18], Operations: ['67-49=18'] Exploring Operation: 44-16=28, Resulting Numbers: [18, 28] Generated Node #0,0,0: 13:[18, 28] Operation: 44-16=28 Exploring Operation: 44-18=26, Resulting Numbers: [16, 26] Generated Node #0,0,1: 13:[16, 26] Operation: 44-18=26 Exploring Operation: 18-16=2, Resulting Numbers: [44, 2] Generated Node #0,0,2: 13:[44, 2] Operation: 18-16=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 13:[16, 26], Operations: ['67-49=18', '44-18=26'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,13 unequal: No Solution Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[18, 28], Operations: ['67-49=18', '44-16=28'] Exploring Operation: 18+28=46, Resulting Numbers: [46] 46,13 unequal: No Solution Exploring Operation: 18*28=504, Resulting Numbers: [504] 504,13 unequal: No Solution Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 13:[44, 2], Operations: ['67-49=18', '18-16=2'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,13 unequal: No Solution Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,13 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[16, 49, 23], Operations: ['67-44=23'] Exploring Operation: 23-16=7, Resulting Numbers: [49, 7] Generated Node #0,1,0: 13:[49, 7] Operation: 23-16=7 Exploring Operation: 49-16=33, Resulting Numbers: [23, 33] Generated Node #0,1,1: 13:[23, 33] Operation: 49-16=33 Exploring Operation: 49-23=26, Resulting Numbers: [16, 26] Generated Node #0,1,2: 13:[16, 26] Operation: 49-23=26 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 13:[16, 26], Operations: ['67-44=23', '49-23=26'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,13 unequal: No Solution Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[23, 33], Operations: ['67-44=23', '49-16=33'] Exploring Operation: 23+33=56, Resulting Numbers: [56] 56,13 unequal: No Solution Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 23*33=759, Resulting Numbers: [759] 759,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 13:[49, 7], Operations: ['67-44=23', '23-16=7'] Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,13 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[67, 16, 5], Operations: ['49-44=5'] Exploring Operation: 67-16=51, Resulting Numbers: [5, 51] Generated Node #0,2,0: 13:[5, 51] Operation: 67-16=51 Exploring Operation: 67-5=62, Resulting Numbers: [16, 62] Generated Node #0,2,1: 13:[16, 62] Operation: 67-5=62 Exploring Operation: 16-5=11, Resulting Numbers: [67, 11] Generated Node #0,2,2: 13:[67, 11] Operation: 16-5=11 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 13:[5, 51], Operations: ['49-44=5', '67-16=51'] Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,13 unequal: No Solution Exploring Operation: 5*51=255, Resulting Numbers: [255] 255,13 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 13:[16, 62], Operations: ['49-44=5', '67-5=62'] Exploring Operation: 16*62=992, Resulting Numbers: [992] 992,13 unequal: No Solution Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,13 unequal: No Solution Exploring Operation: 16+62=78, Resulting Numbers: [78] 78,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 13:[67, 11], Operations: ['49-44=5', '16-5=11'] Exploring Operation: 67+11=78, Resulting Numbers: [78] 78,13 unequal: No Solution Exploring Operation: 67*11=737, Resulting Numbers: [737] 737,13 unequal: No Solution Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 24, 50, 83, 2 ]
82
[ "24+83=107", "50/2=25", "107-25=82" ]
Current State: 82:[24, 50, 83, 2], Operations: [] Exploring Operation: 24+83=107, Resulting Numbers: [50, 2, 107] Generated Node #2: [50, 2, 107] from Operation: 24+83=107 Current State: 82:[50, 2, 107], Operations: ['24+83=107'] Exploring Operation: 50/2=25, Resulting Numbers: [107, 25] Generated Node #3: [107, 25] from Operation: 50/2=25 Current State: 82:[107, 25], Operations: ['24+83=107', '50/2=25'] Exploring Operation: 107-25=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[24, 50, 83, 2], Operations: [] Exploring Operation: 24+50=74, Resulting Numbers: [83, 2, 74] Generated Node #0,0: 82:[83, 2, 74] Operation: 24+50=74 Moving to Node #0,0 Current State: 82:[83, 2, 74], Operations: ['24+50=74'] Exploring Operation: 74/2=37, Resulting Numbers: [83, 37] Generated Node #0,0,0: 82:[83, 37] Operation: 74/2=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 82:[83, 37], Operations: ['24+50=74', '74/2=37'] Exploring Operation: 83-37=46, Resulting Numbers: [46] 46,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 13, 38, 10, 60 ]
40
[ "13*60=780", "780/10=78", "78-38=40" ]
Current State: 40:[13, 38, 10, 60], Operations: [] Exploring Operation: 13*60=780, Resulting Numbers: [38, 10, 780] Generated Node #2: [38, 10, 780] from Operation: 13*60=780 Current State: 40:[38, 10, 780], Operations: ['13*60=780'] Exploring Operation: 780/10=78, Resulting Numbers: [38, 78] Generated Node #3: [38, 78] from Operation: 780/10=78 Current State: 40:[38, 78], Operations: ['13*60=780', '780/10=78'] Exploring Operation: 78-38=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[13, 38, 10, 60], Operations: [] Exploring Operation: 60/10=6, Resulting Numbers: [13, 38, 6] Generated Node #0,0: 40:[13, 38, 6] Operation: 60/10=6 Exploring Operation: 60-38=22, Resulting Numbers: [13, 10, 22] Generated Node #0,1: 40:[13, 10, 22] Operation: 60-38=22 Exploring Operation: 60-13=47, Resulting Numbers: [38, 10, 47] Generated Node #0,2: 40:[38, 10, 47] Operation: 60-13=47 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[13, 10, 22], Operations: ['60-38=22'] Exploring Operation: 13+10=23, Resulting Numbers: [22, 23] Generated Node #0,1,0: 40:[22, 23] Operation: 13+10=23 Exploring Operation: 22-13=9, Resulting Numbers: [10, 9] Generated Node #0,1,1: 40:[10, 9] Operation: 22-13=9 Exploring Operation: 13-10=3, Resulting Numbers: [22, 3] Generated Node #0,1,2: 40:[22, 3] Operation: 13-10=3 Moving to Node #0,1,1 Current State: 40:[10, 9], Operations: ['60-38=22', '22-13=9'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,40 unequal: No Solution Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,40 unequal: No Solution Moving to Node #0,1,2 Current State: 40:[22, 3], Operations: ['60-38=22', '13-10=3'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,40 unequal: No Solution Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,40 unequal: No Solution Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,40 unequal: No Solution Moving to Node #0,1,0 Current State: 40:[22, 23], Operations: ['60-38=22', '13+10=23'] Exploring Operation: 22*23=506, Resulting Numbers: [506] 506,40 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 22+23=45, Resulting Numbers: [45] 45,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[13, 38, 6], Operations: ['60/10=6'] Exploring Operation: 13-6=7, Resulting Numbers: [38, 7] Generated Node #0,0,0: 40:[38, 7] Operation: 13-6=7 Exploring Operation: 38-13=25, Resulting Numbers: [6, 25] Generated Node #0,0,1: 40:[6, 25] Operation: 38-13=25 Exploring Operation: 13+6=19, Resulting Numbers: [38, 19] Generated Node #0,0,2: 40:[38, 19] Operation: 13+6=19 Moving to Node #0,0,0 Current State: 40:[38, 7], Operations: ['60/10=6', '13-6=7'] Exploring Operation: 38*7=266, Resulting Numbers: [266] 266,40 unequal: No Solution Exploring Operation: 38+7=45, Resulting Numbers: [45] 45,40 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,40 unequal: No Solution Moving to Node #0,0,2 Current State: 40:[38, 19], Operations: ['60/10=6', '13+6=19'] Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,40 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 38+19=57, Resulting Numbers: [57] 57,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[6, 25], Operations: ['60/10=6', '38-13=25'] Exploring Operation: 6*25=150, Resulting Numbers: [150] 150,40 unequal: No Solution Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,40 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,40 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 #0,2 Current State: 40:[38, 10, 47], Operations: ['60-13=47'] Exploring Operation: 47-10=37, Resulting Numbers: [38, 37] Generated Node #0,2,0: 40:[38, 37] Operation: 47-10=37 Exploring Operation: 38+10=48, Resulting Numbers: [47, 48] Generated Node #0,2,1: 40:[47, 48] Operation: 38+10=48 Exploring Operation: 47-38=9, Resulting Numbers: [10, 9] Generated Node #0,2,2: 40:[10, 9] Operation: 47-38=9 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 40:[10, 9], Operations: ['60-13=47', '47-38=9'] Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,40 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 40:[38, 37], Operations: ['60-13=47', '47-10=37'] Exploring Operation: 38*37=1406, Resulting Numbers: [1406] 1406,40 unequal: No Solution Exploring Operation: 38-37=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 38+37=75, Resulting Numbers: [75] 75,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 40:[47, 48], Operations: ['60-13=47', '38+10=48'] Exploring Operation: 47*48=2256, Resulting Numbers: [2256] 2256,40 unequal: No Solution Exploring Operation: 47+48=95, Resulting Numbers: [95] 95,40 unequal: No Solution Exploring Operation: 48-47=1, Resulting Numbers: [1] 1,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 34, 18, 15, 38 ]
37
[ "34-18=16", "15+38=53", "53-16=37" ]
Current State: 37:[34, 18, 15, 38], Operations: [] Exploring Operation: 34-18=16, Resulting Numbers: [15, 38, 16] Generated Node #2: [15, 38, 16] from Operation: 34-18=16 Current State: 37:[15, 38, 16], Operations: ['34-18=16'] Exploring Operation: 15+38=53, Resulting Numbers: [16, 53] Generated Node #3: [16, 53] from Operation: 15+38=53 Current State: 37:[16, 53], Operations: ['34-18=16', '15+38=53'] Exploring Operation: 53-16=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[34, 18, 15, 38], Operations: [] Exploring Operation: 34+15=49, Resulting Numbers: [18, 38, 49] Generated Node #0,0: 37:[18, 38, 49] Operation: 34+15=49 Exploring Operation: 18+15=33, Resulting Numbers: [34, 38, 33] Generated Node #0,1: 37:[34, 38, 33] Operation: 18+15=33 Exploring Operation: 38-15=23, Resulting Numbers: [34, 18, 23] Generated Node #0,2: 37:[34, 18, 23] Operation: 38-15=23 Exploring Operation: 34+18=52, Resulting Numbers: [15, 38, 52] Generated Node #0,3: 37:[15, 38, 52] Operation: 34+18=52 Moving to Node #0,1 Current State: 37:[34, 38, 33], Operations: ['18+15=33'] Exploring Operation: 34-33=1, Resulting Numbers: [38, 1] Generated Node #0,1,0: 37:[38, 1] Operation: 34-33=1 Exploring Operation: 38-33=5, Resulting Numbers: [34, 5] Generated Node #0,1,1: 37:[34, 5] Operation: 38-33=5 Exploring Operation: 34+33=67, Resulting Numbers: [38, 67] Generated Node #0,1,2: 37:[38, 67] Operation: 34+33=67 Exploring Operation: 38-34=4, Resulting Numbers: [33, 4] Generated Node #0,1,3: 37:[33, 4] Operation: 38-34=4 Moving to Node #0,0 Current State: 37:[18, 38, 49], Operations: ['34+15=49'] Exploring Operation: 18+49=67, Resulting Numbers: [38, 67] Generated Node #0,0,0: 37:[38, 67] Operation: 18+49=67 Exploring Operation: 18+38=56, Resulting Numbers: [49, 56] Generated Node #0,0,1: 37:[49, 56] Operation: 18+38=56 Exploring Operation: 49-18=31, Resulting Numbers: [38, 31] Generated Node #0,0,2: 37:[38, 31] Operation: 49-18=31 Exploring Operation: 38-18=20, Resulting Numbers: [49, 20] Generated Node #0,0,3: 37:[49, 20] Operation: 38-18=20 Moving to Node #0,2 Current State: 37:[34, 18, 23], Operations: ['38-15=23'] Exploring Operation: 34-18=16, Resulting Numbers: [23, 16] Generated Node #0,2,0: 37:[23, 16] Operation: 34-18=16 Exploring Operation: 23-18=5, Resulting Numbers: [34, 5] Generated Node #0,2,1: 37:[34, 5] Operation: 23-18=5 Exploring Operation: 34+18=52, Resulting Numbers: [23, 52] Generated Node #0,2,2: 37:[23, 52] Operation: 34+18=52 Exploring Operation: 18+23=41, Resulting Numbers: [34, 41] Generated Node #0,2,3: 37:[34, 41] Operation: 18+23=41 Moving to Node #0,3 Current State: 37:[15, 38, 52], Operations: ['34+18=52'] Exploring Operation: 38-15=23, Resulting Numbers: [52, 23] Generated Node #0,3,0: 37:[52, 23] Operation: 38-15=23 Exploring Operation: 52-15=37, Resulting Numbers: [38, 37] Generated Node #0,3,1: 37:[38, 37] Operation: 52-15=37 Exploring Operation: 15+52=67, Resulting Numbers: [38, 67] Generated Node #0,3,2: 37:[38, 67] Operation: 15+52=67 Exploring Operation: 15+38=53, Resulting Numbers: [52, 53] Generated Node #0,3,3: 37:[52, 53] Operation: 15+38=53 Moving to Node #0,3,1 Current State: 37:[38, 37], Operations: ['34+18=52', '52-15=37'] Exploring Operation: 38*37=1406, Resulting Numbers: [1406] 1406,37 unequal: No Solution Exploring Operation: 38+37=75, Resulting Numbers: [75] 75,37 unequal: No Solution Exploring Operation: 38-37=1, Resulting Numbers: [1] 1,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[38, 31], Operations: ['34+15=49', '49-18=31'] Exploring Operation: 38*31=1178, Resulting Numbers: [1178] 1178,37 unequal: No Solution Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 38+31=69, Resulting Numbers: [69] 69,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[34, 41], Operations: ['38-15=23', '18+23=41'] Exploring Operation: 34+41=75, Resulting Numbers: [75] 75,37 unequal: No Solution Exploring Operation: 34*41=1394, Resulting Numbers: [1394] 1394,37 unequal: No Solution Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,37 unequal: No Solution Moving to Node #0,3,0 Current State: 37:[52, 23], Operations: ['34+18=52', '38-15=23'] Exploring Operation: 52+23=75, Resulting Numbers: [75] 75,37 unequal: No Solution Exploring Operation: 52-23=29, Resulting Numbers: [29] 29,37 unequal: No Solution Exploring Operation: 52*23=1196, Resulting Numbers: [1196] 1196,37 unequal: No Solution Moving to Node #0,0,3 Current State: 37:[49, 20], Operations: ['34+15=49', '38-18=20'] Exploring Operation: 49*20=980, Resulting Numbers: [980] 980,37 unequal: No Solution Exploring Operation: 49+20=69, Resulting Numbers: [69] 69,37 unequal: No Solution Exploring Operation: 49-20=29, Resulting Numbers: [29] 29,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[23, 52], Operations: ['38-15=23', '34+18=52'] Exploring Operation: 23*52=1196, Resulting Numbers: [1196] 1196,37 unequal: No Solution Exploring Operation: 23+52=75, Resulting Numbers: [75] 75,37 unequal: No Solution Exploring Operation: 52-23=29, Resulting Numbers: [29] 29,37 unequal: No Solution Moving to Node #0,3,2 Current State: 37:[38, 67], Operations: ['34+18=52', '15+52=67'] Exploring Operation: 38+67=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,37 unequal: No Solution Exploring Operation: 38*67=2546, Resulting Numbers: [2546] 2546,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[38, 67], Operations: ['34+15=49', '18+49=67'] Exploring Operation: 38+67=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,37 unequal: No Solution Exploring Operation: 38*67=2546, Resulting Numbers: [2546] 2546,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[38, 67], Operations: ['18+15=33', '34+33=67'] Exploring Operation: 38*67=2546, Resulting Numbers: [2546] 2546,37 unequal: No Solution Exploring Operation: 38+67=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[49, 56], Operations: ['34+15=49', '18+38=56'] Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,37 unequal: No Solution Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,37 unequal: No Solution Moving to Node #0,3,3 Current State: 37:[52, 53], Operations: ['34+18=52', '15+38=53'] Exploring Operation: 52+53=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 52*53=2756, Resulting Numbers: [2756] 2756,37 unequal: No Solution Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[34, 5], Operations: ['38-15=23', '23-18=5'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,37 unequal: No Solution Exploring Operation: 34+5=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 34*5=170, Resulting Numbers: [170] 170,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[23, 16], Operations: ['38-15=23', '34-18=16'] Exploring Operation: 23*16=368, Resulting Numbers: [368] 368,37 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 23+16=39, Resulting Numbers: [39] 39,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[34, 5], Operations: ['18+15=33', '38-33=5'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,37 unequal: No Solution Exploring Operation: 34+5=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 34*5=170, Resulting Numbers: [170] 170,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[38, 1], Operations: ['18+15=33', '34-33=1'] Exploring Operation: 38+1=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[34, 18, 15, 38], Operations: [] Exploring Operation: 18+15=33, Resulting Numbers: [34, 38, 33] Generated Node #0,1: 37:[34, 38, 33] Operation: 18+15=33 Moving to Node #0,1 Current State: 37:[34, 38, 33], Operations: ['18+15=33'] Exploring Operation: 34-33=1, Resulting Numbers: [38, 1] Generated Node #0,1,0: 37:[38, 1] Operation: 34-33=1 Moving to Node #0,1,0 Current State: 37:[38, 1], Operations: ['18+15=33', '34-33=1'] Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
0.939236
hs_4
sum_heuristic
[ 9, 51, 18, 53 ]
77
[ "51-9=42", "53-18=35", "42+35=77" ]
Current State: 77:[9, 51, 18, 53], Operations: [] Exploring Operation: 51-9=42, Resulting Numbers: [18, 53, 42] Generated Node #2: [18, 53, 42] from Operation: 51-9=42 Current State: 77:[18, 53, 42], Operations: ['51-9=42'] Exploring Operation: 53-18=35, Resulting Numbers: [42, 35] Generated Node #3: [42, 35] from Operation: 53-18=35 Current State: 77:[42, 35], Operations: ['51-9=42', '53-18=35'] Exploring Operation: 42+35=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[9, 51, 18, 53], Operations: [] Exploring Operation: 18+53=71, Resulting Numbers: [9, 51, 71] Generated Node #0,0: 77:[9, 51, 71] Operation: 18+53=71 Exploring Operation: 51+18=69, Resulting Numbers: [9, 53, 69] Generated Node #0,1: 77:[9, 53, 69] Operation: 51+18=69 Exploring Operation: 51+53=104, Resulting Numbers: [9, 18, 104] Generated Node #0,2: 77:[9, 18, 104] Operation: 51+53=104 Exploring Operation: 53-51=2, Resulting Numbers: [9, 18, 2] Generated Node #0,3: 77:[9, 18, 2] Operation: 53-51=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[9, 18, 2], Operations: ['53-51=2'] Exploring Operation: 18-9=9, Resulting Numbers: [2, 9] Generated Node #0,3,0: 77:[2, 9] Operation: 18-9=9 Exploring Operation: 9+2=11, Resulting Numbers: [18, 11] Generated Node #0,3,1: 77:[18, 11] Operation: 9+2=11 Exploring Operation: 18/2=9, Resulting Numbers: [9, 9] Generated Node #0,3,2: 77:[9, 9] Operation: 18/2=9 Exploring Operation: 9-2=7, Resulting Numbers: [18, 7] Generated Node #0,3,3: 77:[18, 7] Operation: 9-2=7 Moving to Node #0,3,2 Current State: 77:[9, 9], Operations: ['53-51=2', '18/2=9'] Exploring Operation: 9/9=1, Resulting Numbers: [1] 1,77 unequal: No Solution Exploring Operation: 9*9=81, Resulting Numbers: [81] 81,77 unequal: No Solution Exploring Operation: 9-9=0, Resulting Numbers: [0] 0,77 unequal: No Solution Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,77 unequal: No Solution Moving to Node #0,3,1 Current State: 77:[18, 11], Operations: ['53-51=2', '9+2=11'] Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 18*11=198, Resulting Numbers: [198] 198,77 unequal: No Solution Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,77 unequal: No Solution Moving to Node #0,3,0 Current State: 77:[2, 9], Operations: ['53-51=2', '18-9=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,77 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,77 unequal: No Solution Moving to Node #0,3,3 Current State: 77:[18, 7], Operations: ['53-51=2', '9-2=7'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,77 unequal: No Solution Exploring Operation: 18+7=25, Resulting Numbers: [25] 25,77 unequal: No Solution Exploring Operation: 18*7=126, Resulting Numbers: [126] 126,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[9, 51, 71], Operations: ['18+53=71'] Exploring Operation: 9+51=60, Resulting Numbers: [71, 60] Generated Node #0,0,0: 77:[71, 60] Operation: 9+51=60 Exploring Operation: 71-51=20, Resulting Numbers: [9, 20] Generated Node #0,0,1: 77:[9, 20] Operation: 71-51=20 Exploring Operation: 51-9=42, Resulting Numbers: [71, 42] Generated Node #0,0,2: 77:[71, 42] Operation: 51-9=42 Exploring Operation: 9+71=80, Resulting Numbers: [51, 80] Generated Node #0,0,3: 77:[51, 80] Operation: 9+71=80 Moving to Node #0,0,1 Current State: 77:[9, 20], Operations: ['18+53=71', '71-51=20'] Exploring Operation: 9+20=29, Resulting Numbers: [29] 29,77 unequal: No Solution Exploring Operation: 9*20=180, Resulting Numbers: [180] 180,77 unequal: No Solution Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,77 unequal: No Solution Moving to Node #0,0,0 Current State: 77:[71, 60], Operations: ['18+53=71', '9+51=60'] Exploring Operation: 71-60=11, Resulting Numbers: [11] 11,77 unequal: No Solution Exploring Operation: 71+60=131, Resulting Numbers: [131] 131,77 unequal: No Solution Exploring Operation: 71*60=4260, Resulting Numbers: [4260] 4260,77 unequal: No Solution Moving to Node #0,0,3 Current State: 77:[51, 80], Operations: ['18+53=71', '9+71=80'] Exploring Operation: 51*80=4080, Resulting Numbers: [4080] 4080,77 unequal: No Solution Exploring Operation: 80-51=29, Resulting Numbers: [29] 29,77 unequal: No Solution Exploring Operation: 51+80=131, Resulting Numbers: [131] 131,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[71, 42], Operations: ['18+53=71', '51-9=42'] Exploring Operation: 71-42=29, Resulting Numbers: [29] 29,77 unequal: No Solution Exploring Operation: 71+42=113, Resulting Numbers: [113] 113,77 unequal: No Solution Exploring Operation: 71*42=2982, Resulting Numbers: [2982] 2982,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[9, 53, 69], Operations: ['51+18=69'] Exploring Operation: 9+53=62, Resulting Numbers: [69, 62] Generated Node #0,1,0: 77:[69, 62] Operation: 9+53=62 Exploring Operation: 9+69=78, Resulting Numbers: [53, 78] Generated Node #0,1,1: 77:[53, 78] Operation: 9+69=78 Exploring Operation: 69-53=16, Resulting Numbers: [9, 16] Generated Node #0,1,2: 77:[9, 16] Operation: 69-53=16 Exploring Operation: 53-9=44, Resulting Numbers: [69, 44] Generated Node #0,1,3: 77:[69, 44] Operation: 53-9=44 Moving to Node #0,1,2 Current State: 77:[9, 16], Operations: ['51+18=69', '69-53=16'] Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,77 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[69, 62], Operations: ['51+18=69', '9+53=62'] Exploring Operation: 69+62=131, Resulting Numbers: [131] 131,77 unequal: No Solution Exploring Operation: 69*62=4278, Resulting Numbers: [4278] 4278,77 unequal: No Solution Exploring Operation: 69-62=7, Resulting Numbers: [7] 7,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[53, 78], Operations: ['51+18=69', '9+69=78'] Exploring Operation: 53+78=131, Resulting Numbers: [131] 131,77 unequal: No Solution Exploring Operation: 53*78=4134, Resulting Numbers: [4134] 4134,77 unequal: No Solution Exploring Operation: 78-53=25, Resulting Numbers: [25] 25,77 unequal: No Solution Moving to Node #0,1,3 Current State: 77:[69, 44], Operations: ['51+18=69', '53-9=44'] Exploring Operation: 69*44=3036, Resulting Numbers: [3036] 3036,77 unequal: No Solution Exploring Operation: 69-44=25, Resulting Numbers: [25] 25,77 unequal: No Solution Exploring Operation: 69+44=113, Resulting Numbers: [113] 113,77 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 #0,2 Current State: 77:[9, 18, 104], Operations: ['51+53=104'] Exploring Operation: 18/9=2, Resulting Numbers: [104, 2] Generated Node #0,2,0: 77:[104, 2] Operation: 18/9=2 Exploring Operation: 104-9=95, Resulting Numbers: [18, 95] Generated Node #0,2,1: 77:[18, 95] Operation: 104-9=95 Exploring Operation: 18-9=9, Resulting Numbers: [104, 9] Generated Node #0,2,2: 77:[104, 9] Operation: 18-9=9 Exploring Operation: 104-18=86, Resulting Numbers: [9, 86] Generated Node #0,2,3: 77:[9, 86] Operation: 104-18=86 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 77:[9, 86], Operations: ['51+53=104', '104-18=86'] Exploring Operation: 9+86=95, Resulting Numbers: [95] 95,77 unequal: No Solution Exploring Operation: 9*86=774, Resulting Numbers: [774] 774,77 unequal: No Solution Exploring Operation: 86-9=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[9, 51, 18, 53], Operations: [] Exploring Operation: 51+53=104, Resulting Numbers: [9, 18, 104] Generated Node #0,2: 77:[9, 18, 104] Operation: 51+53=104 Moving to Node #0,2 Current State: 77:[9, 18, 104], Operations: ['51+53=104'] Exploring Operation: 104-18=86, Resulting Numbers: [9, 86] Generated Node #0,2,3: 77:[9, 86] Operation: 104-18=86 Moving to Node #0,2,3 Current State: 77:[9, 86], Operations: ['51+53=104', '104-18=86'] Exploring Operation: 86-9=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.944444
hs_4
sum_heuristic
[ 60, 44, 3, 3 ]
25
[ "60-44=16", "3*3=9", "16+9=25" ]
Current State: 25:[60, 44, 3, 3], Operations: [] Exploring Operation: 60-44=16, Resulting Numbers: [3, 3, 16] Generated Node #2: [3, 3, 16] from Operation: 60-44=16 Current State: 25:[3, 3, 16], Operations: ['60-44=16'] Exploring Operation: 3*3=9, Resulting Numbers: [16, 9] Generated Node #3: [16, 9] from Operation: 3*3=9 Current State: 25:[16, 9], Operations: ['60-44=16', '3*3=9'] Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[60, 44, 3, 3], Operations: [] Exploring Operation: 60-3=57, Resulting Numbers: [44, 3, 57] Generated Node #0,0: 25:[44, 3, 57] Operation: 60-3=57 Exploring Operation: 60/3=20, Resulting Numbers: [44, 3, 20] Generated Node #0,1: 25:[44, 3, 20] Operation: 60/3=20 Exploring Operation: 60-44=16, Resulting Numbers: [3, 3, 16] Generated Node #0,2: 25:[3, 3, 16] Operation: 60-44=16 Exploring Operation: 60/3=20, Resulting Numbers: [44, 3, 20] Generated Node #0,3: 25:[44, 3, 20] Operation: 60/3=20 Moving to Node #0,2 Current State: 25:[3, 3, 16], Operations: ['60-44=16'] Exploring Operation: 3+16=19, Resulting Numbers: [3, 19] Generated Node #0,2,0: 25:[3, 19] Operation: 3+16=19 Exploring Operation: 3+16=19, Resulting Numbers: [3, 19] Generated Node #0,2,1: 25:[3, 19] Operation: 3+16=19 Exploring Operation: 16-3=13, Resulting Numbers: [3, 13] Generated Node #0,2,2: 25:[3, 13] Operation: 16-3=13 Exploring Operation: 3+3=6, Resulting Numbers: [16, 6] Generated Node #0,2,3: 25:[16, 6] Operation: 3+3=6 Moving to Node #0,3 Current State: 25:[44, 3, 20], Operations: ['60/3=20'] Exploring Operation: 44+3=47, Resulting Numbers: [20, 47] Generated Node #0,3,0: 25:[20, 47] Operation: 44+3=47 Exploring Operation: 44-20=24, Resulting Numbers: [3, 24] Generated Node #0,3,1: 25:[3, 24] Operation: 44-20=24 Exploring Operation: 44-3=41, Resulting Numbers: [20, 41] Generated Node #0,3,2: 25:[20, 41] Operation: 44-3=41 Exploring Operation: 3+20=23, Resulting Numbers: [44, 23] Generated Node #0,3,3: 25:[44, 23] Operation: 3+20=23 Moving to Node #0,1 Current State: 25:[44, 3, 20], Operations: ['60/3=20'] Exploring Operation: 44-3=41, Resulting Numbers: [20, 41] Generated Node #0,1,0: 25:[20, 41] Operation: 44-3=41 Exploring Operation: 3+20=23, Resulting Numbers: [44, 23] Generated Node #0,1,1: 25:[44, 23] Operation: 3+20=23 Exploring Operation: 44+3=47, Resulting Numbers: [20, 47] Generated Node #0,1,2: 25:[20, 47] Operation: 44+3=47 Exploring Operation: 44-20=24, Resulting Numbers: [3, 24] Generated Node #0,1,3: 25:[3, 24] Operation: 44-20=24 Moving to Node #0,0 Current State: 25:[44, 3, 57], Operations: ['60-3=57'] Exploring Operation: 44-3=41, Resulting Numbers: [57, 41] Generated Node #0,0,0: 25:[57, 41] Operation: 44-3=41 Exploring Operation: 57/3=19, Resulting Numbers: [44, 19] Generated Node #0,0,1: 25:[44, 19] Operation: 57/3=19 Exploring Operation: 57-44=13, Resulting Numbers: [3, 13] Generated Node #0,0,2: 25:[3, 13] Operation: 57-44=13 Exploring Operation: 57-3=54, Resulting Numbers: [44, 54] Generated Node #0,0,3: 25:[44, 54] Operation: 57-3=54 Moving to Node #0,3,1 Current State: 25:[3, 24], Operations: ['60/3=20', '44-20=24'] Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,25 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,25 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,25 unequal: No Solution Moving to Node #0,1,3 Current State: 25:[3, 24], Operations: ['60/3=20', '44-20=24'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,25 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,25 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,25 unequal: No Solution Moving to Node #0,2,1 Current State: 25:[3, 19], Operations: ['60-44=16', '3+16=19'] Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,25 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,25 unequal: No Solution Moving to Node #0,2,0 Current State: 25:[3, 19], Operations: ['60-44=16', '3+16=19'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,25 unequal: No Solution Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,25 unequal: No Solution Moving to Node #0,2,2 Current State: 25:[3, 13], Operations: ['60-44=16', '16-3=13'] Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,25 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,25 unequal: No Solution Moving to Node #0,0,2 Current State: 25:[3, 13], Operations: ['60-3=57', '57-44=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,25 unequal: No Solution Moving to Node #0,2,3 Current State: 25:[16, 6], Operations: ['60-44=16', '3+3=6'] Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,25 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,25 unequal: No Solution Moving to Node #0,3,3 Current State: 25:[44, 23], Operations: ['60/3=20', '3+20=23'] Exploring Operation: 44+23=67, Resulting Numbers: [67] 67,25 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 44*23=1012, Resulting Numbers: [1012] 1012,25 unequal: No Solution Moving to Node #0,3,2 Current State: 25:[20, 41], Operations: ['60/3=20', '44-3=41'] Exploring Operation: 20*41=820, Resulting Numbers: [820] 820,25 unequal: No Solution Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 20+41=61, Resulting Numbers: [61] 61,25 unequal: No Solution Moving to Node #0,1,1 Current State: 25:[44, 23], Operations: ['60/3=20', '3+20=23'] Exploring Operation: 44+23=67, Resulting Numbers: [67] 67,25 unequal: No Solution Exploring Operation: 44*23=1012, Resulting Numbers: [1012] 1012,25 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,25 unequal: No Solution Moving to Node #0,1,0 Current State: 25:[20, 41], Operations: ['60/3=20', '44-3=41'] Exploring Operation: 20*41=820, Resulting Numbers: [820] 820,25 unequal: No Solution Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 20+41=61, Resulting Numbers: [61] 61,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[44, 19], Operations: ['60-3=57', '57/3=19'] Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[60, 44, 3, 3], Operations: [] Exploring Operation: 60-3=57, Resulting Numbers: [44, 3, 57] Generated Node #0,0: 25:[44, 3, 57] Operation: 60-3=57 Moving to Node #0,0 Current State: 25:[44, 3, 57], Operations: ['60-3=57'] Exploring Operation: 57/3=19, Resulting Numbers: [44, 19] Generated Node #0,0,1: 25:[44, 19] Operation: 57/3=19 Moving to Node #0,0,1 Current State: 25:[44, 19], Operations: ['60-3=57', '57/3=19'] Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
0.947917
hs_4
sum_heuristic
[ 20, 75, 70, 3 ]
65
[ "20+70=90", "75/3=25", "90-25=65" ]
Current State: 65:[20, 75, 70, 3], Operations: [] Exploring Operation: 20+70=90, Resulting Numbers: [75, 3, 90] Generated Node #2: [75, 3, 90] from Operation: 20+70=90 Current State: 65:[75, 3, 90], Operations: ['20+70=90'] Exploring Operation: 75/3=25, Resulting Numbers: [90, 25] Generated Node #3: [90, 25] from Operation: 75/3=25 Current State: 65:[90, 25], Operations: ['20+70=90', '75/3=25'] Exploring Operation: 90-25=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[20, 75, 70, 3], Operations: [] Exploring Operation: 75-20=55, Resulting Numbers: [70, 3, 55] Generated Node #0,0: 65:[70, 3, 55] Operation: 75-20=55 Exploring Operation: 75-70=5, Resulting Numbers: [20, 3, 5] Generated Node #0,1: 65:[20, 3, 5] Operation: 75-70=5 Exploring Operation: 20-3=17, Resulting Numbers: [75, 70, 17] Generated Node #0,2: 65:[75, 70, 17] Operation: 20-3=17 Moving to Node #0,1 Current State: 65:[20, 3, 5], Operations: ['75-70=5'] Exploring Operation: 20/5=4, Resulting Numbers: [3, 4] Generated Node #0,1,0: 65:[3, 4] Operation: 20/5=4 Exploring Operation: 20-5=15, Resulting Numbers: [3, 15] Generated Node #0,1,1: 65:[3, 15] Operation: 20-5=15 Exploring Operation: 20-3=17, Resulting Numbers: [5, 17] Generated Node #0,1,2: 65:[5, 17] Operation: 20-3=17 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[3, 4], Operations: ['75-70=5', '20/5=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,65 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[3, 15], Operations: ['75-70=5', '20-5=15'] Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,65 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[5, 17], Operations: ['75-70=5', '20-3=17'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 5+17=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 5*17=85, Resulting Numbers: [85] 85,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 65:[70, 3, 55], Operations: ['75-20=55'] Exploring Operation: 3+55=58, Resulting Numbers: [70, 58] Generated Node #0,0,0: 65:[70, 58] Operation: 3+55=58 Exploring Operation: 70-55=15, Resulting Numbers: [3, 15] Generated Node #0,0,1: 65:[3, 15] Operation: 70-55=15 Exploring Operation: 70-3=67, Resulting Numbers: [55, 67] Generated Node #0,0,2: 65:[55, 67] Operation: 70-3=67 Moving to Node #0,2 Current State: 65:[75, 70, 17], Operations: ['20-3=17'] Exploring Operation: 75-17=58, Resulting Numbers: [70, 58] Generated Node #0,2,0: 65:[70, 58] Operation: 75-17=58 Exploring Operation: 70-17=53, Resulting Numbers: [75, 53] Generated Node #0,2,1: 65:[75, 53] Operation: 70-17=53 Exploring Operation: 75-70=5, Resulting Numbers: [17, 5] Generated Node #0,2,2: 65:[17, 5] Operation: 75-70=5 Moving to Node #0,0,1 Current State: 65:[3, 15], Operations: ['75-20=55', '70-55=15'] Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,65 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[17, 5], Operations: ['20-3=17', '75-70=5'] Exploring Operation: 17*5=85, Resulting Numbers: [85] 85,65 unequal: No Solution Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,65 unequal: No Solution Moving to Node #0,0,2 Current State: 65:[55, 67], Operations: ['75-20=55', '70-3=67'] Exploring Operation: 67-55=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 55+67=122, Resulting Numbers: [122] 122,65 unequal: No Solution Exploring Operation: 55*67=3685, Resulting Numbers: [3685] 3685,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[70, 58], Operations: ['20-3=17', '75-17=58'] Exploring Operation: 70-58=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 70*58=4060, Resulting Numbers: [4060] 4060,65 unequal: No Solution Exploring Operation: 70+58=128, Resulting Numbers: [128] 128,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[70, 58], Operations: ['75-20=55', '3+55=58'] Exploring Operation: 70*58=4060, Resulting Numbers: [4060] 4060,65 unequal: No Solution Exploring Operation: 70-58=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 70+58=128, Resulting Numbers: [128] 128,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[75, 53], Operations: ['20-3=17', '70-17=53'] Exploring Operation: 75+53=128, Resulting Numbers: [128] 128,65 unequal: No Solution Exploring Operation: 75-53=22, Resulting Numbers: [22] 22,65 unequal: No Solution Exploring Operation: 75*53=3975, Resulting Numbers: [3975] 3975,65 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 19, 73, 78, 42 ]
66
[ "73-19=54", "78+42=120", "120-54=66" ]
Current State: 66:[19, 73, 78, 42], Operations: [] Exploring Operation: 73-19=54, Resulting Numbers: [78, 42, 54] Generated Node #2: [78, 42, 54] from Operation: 73-19=54 Current State: 66:[78, 42, 54], Operations: ['73-19=54'] Exploring Operation: 78+42=120, Resulting Numbers: [54, 120] Generated Node #3: [54, 120] from Operation: 78+42=120 Current State: 66:[54, 120], Operations: ['73-19=54', '78+42=120'] Exploring Operation: 120-54=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[19, 73, 78, 42], Operations: [] Exploring Operation: 78-42=36, Resulting Numbers: [19, 73, 36] Generated Node #0,0: 66:[19, 73, 36] Operation: 78-42=36 Exploring Operation: 73-42=31, Resulting Numbers: [19, 78, 31] Generated Node #0,1: 66:[19, 78, 31] Operation: 73-42=31 Exploring Operation: 78-19=59, Resulting Numbers: [73, 42, 59] Generated Node #0,2: 66:[73, 42, 59] Operation: 78-19=59 Exploring Operation: 42-19=23, Resulting Numbers: [73, 78, 23] Generated Node #0,3: 66:[73, 78, 23] Operation: 42-19=23 Exploring Operation: 78-73=5, Resulting Numbers: [19, 42, 5] Generated Node #0,4: 66:[19, 42, 5] Operation: 78-73=5 Moving to Node #0,0 Current State: 66:[19, 73, 36], Operations: ['78-42=36'] Exploring Operation: 36-19=17, Resulting Numbers: [73, 17] Generated Node #0,0,0: 66:[73, 17] Operation: 36-19=17 Exploring Operation: 73-19=54, Resulting Numbers: [36, 54] Generated Node #0,0,1: 66:[36, 54] Operation: 73-19=54 Exploring Operation: 19+73=92, Resulting Numbers: [36, 92] Generated Node #0,0,2: 66:[36, 92] Operation: 19+73=92 Exploring Operation: 19+36=55, Resulting Numbers: [73, 55] Generated Node #0,0,3: 66:[73, 55] Operation: 19+36=55 Exploring Operation: 73-36=37, Resulting Numbers: [19, 37] Generated Node #0,0,4: 66:[19, 37] Operation: 73-36=37 Moving to Node #0,4 Current State: 66:[19, 42, 5], Operations: ['78-73=5'] Exploring Operation: 19-5=14, Resulting Numbers: [42, 14] Generated Node #0,4,0: 66:[42, 14] Operation: 19-5=14 Exploring Operation: 42-19=23, Resulting Numbers: [5, 23] Generated Node #0,4,1: 66:[5, 23] Operation: 42-19=23 Exploring Operation: 42-5=37, Resulting Numbers: [19, 37] Generated Node #0,4,2: 66:[19, 37] Operation: 42-5=37 Exploring Operation: 19+42=61, Resulting Numbers: [5, 61] Generated Node #0,4,3: 66:[5, 61] Operation: 19+42=61 Exploring Operation: 19+5=24, Resulting Numbers: [42, 24] Generated Node #0,4,4: 66:[42, 24] Operation: 19+5=24 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 66:[5, 23], Operations: ['78-73=5', '42-19=23'] Exploring Operation: 5*23=115, Resulting Numbers: [115] 115,66 unequal: No Solution Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,66 unequal: No Solution Exploring Operation: 5+23=28, Resulting Numbers: [28] 28,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 66:[5, 61], Operations: ['78-73=5', '19+42=61'] Exploring Operation: 5+61=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[19, 73, 78, 42], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [19, 42, 5] Generated Node #0,4: 66:[19, 42, 5] Operation: 78-73=5 Moving to Node #0,4 Current State: 66:[19, 42, 5], Operations: ['78-73=5'] Exploring Operation: 19+42=61, Resulting Numbers: [5, 61] Generated Node #0,4,3: 66:[5, 61] Operation: 19+42=61 Moving to Node #0,4,3 Current State: 66:[5, 61], Operations: ['78-73=5', '19+42=61'] Exploring Operation: 5+61=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 36, 40, 44, 86 ]
88
[ "36+44=80", "80/40=2", "86+2=88" ]
Current State: 88:[36, 40, 44, 86], Operations: [] Exploring Operation: 36+44=80, Resulting Numbers: [40, 86, 80] Generated Node #2: [40, 86, 80] from Operation: 36+44=80 Current State: 88:[40, 86, 80], Operations: ['36+44=80'] Exploring Operation: 80/40=2, Resulting Numbers: [86, 2] Generated Node #3: [86, 2] from Operation: 80/40=2 Current State: 88:[86, 2], Operations: ['36+44=80', '80/40=2'] Exploring Operation: 86+2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[36, 40, 44, 86], Operations: [] Exploring Operation: 86-36=50, Resulting Numbers: [40, 44, 50] Generated Node #0,0: 88:[40, 44, 50] Operation: 86-36=50 Exploring Operation: 40-36=4, Resulting Numbers: [44, 86, 4] Generated Node #0,1: 88:[44, 86, 4] Operation: 40-36=4 Exploring Operation: 44-36=8, Resulting Numbers: [40, 86, 8] Generated Node #0,2: 88:[40, 86, 8] Operation: 44-36=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[44, 86, 4], Operations: ['40-36=4'] Exploring Operation: 86+4=90, Resulting Numbers: [44, 90] Generated Node #0,1,0: 88:[44, 90] Operation: 86+4=90 Exploring Operation: 44/4=11, Resulting Numbers: [86, 11] Generated Node #0,1,1: 88:[86, 11] Operation: 44/4=11 Exploring Operation: 86-44=42, Resulting Numbers: [4, 42] Generated Node #0,1,2: 88:[4, 42] Operation: 86-44=42 Moving to Node #0,1,0 Current State: 88:[44, 90], Operations: ['40-36=4', '86+4=90'] Exploring Operation: 44*90=3960, Resulting Numbers: [3960] 3960,88 unequal: No Solution Exploring Operation: 44+90=134, Resulting Numbers: [134] 134,88 unequal: No Solution Exploring Operation: 90-44=46, Resulting Numbers: [46] 46,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[86, 11], Operations: ['40-36=4', '44/4=11'] Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 86+11=97, Resulting Numbers: [97] 97,88 unequal: No Solution Exploring Operation: 86*11=946, Resulting Numbers: [946] 946,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[4, 42], Operations: ['40-36=4', '86-44=42'] Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 4*42=168, Resulting Numbers: [168] 168,88 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[40, 86, 8], Operations: ['44-36=8'] Exploring Operation: 40/8=5, Resulting Numbers: [86, 5] Generated Node #0,2,0: 88:[86, 5] Operation: 40/8=5 Exploring Operation: 40+8=48, Resulting Numbers: [86, 48] Generated Node #0,2,1: 88:[86, 48] Operation: 40+8=48 Exploring Operation: 86-40=46, Resulting Numbers: [8, 46] Generated Node #0,2,2: 88:[8, 46] Operation: 86-40=46 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 88:[8, 46], Operations: ['44-36=8', '86-40=46'] Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,88 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,88 unequal: No Solution Exploring Operation: 8*46=368, Resulting Numbers: [368] 368,88 unequal: No Solution No 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: 88:[86, 5], Operations: ['44-36=8', '40/8=5'] Exploring Operation: 86*5=430, Resulting Numbers: [430] 430,88 unequal: No Solution Exploring Operation: 86+5=91, Resulting Numbers: [91] 91,88 unequal: No Solution Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,88 unequal: No Solution No 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: 88:[86, 48], Operations: ['44-36=8', '40+8=48'] Exploring Operation: 86-48=38, Resulting Numbers: [38] 38,88 unequal: No Solution Exploring Operation: 86+48=134, Resulting Numbers: [134] 134,88 unequal: No Solution Exploring Operation: 86*48=4128, Resulting Numbers: [4128] 4128,88 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[40, 44, 50], Operations: ['86-36=50'] Exploring Operation: 40+50=90, Resulting Numbers: [44, 90] Generated Node #0,0,0: 88:[44, 90] Operation: 40+50=90 Exploring Operation: 50-40=10, Resulting Numbers: [44, 10] Generated Node #0,0,1: 88:[44, 10] Operation: 50-40=10 Exploring Operation: 44-40=4, Resulting Numbers: [50, 4] Generated Node #0,0,2: 88:[50, 4] Operation: 44-40=4 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[44, 10], Operations: ['86-36=50', '50-40=10'] Exploring Operation: 44*10=440, Resulting Numbers: [440] 440,88 unequal: No Solution Exploring Operation: 44+10=54, Resulting Numbers: [54] 54,88 unequal: No Solution Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,88 unequal: No Solution No 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: 88:[44, 90], Operations: ['86-36=50', '40+50=90'] Exploring Operation: 90-44=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 44+90=134, Resulting Numbers: [134] 134,88 unequal: No Solution Exploring Operation: 44*90=3960, Resulting Numbers: [3960] 3960,88 unequal: No Solution No 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: 88:[50, 4], Operations: ['86-36=50', '44-40=4'] Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,88 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,88 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_3
sum_heuristic
[ 64, 92, 29, 65 ]
64
[ "92-64=28", "65-29=36", "28+36=64" ]
Current State: 64:[64, 92, 29, 65], Operations: [] Exploring Operation: 92-64=28, Resulting Numbers: [29, 65, 28] Generated Node #2: [29, 65, 28] from Operation: 92-64=28 Current State: 64:[29, 65, 28], Operations: ['92-64=28'] Exploring Operation: 65-29=36, Resulting Numbers: [28, 36] Generated Node #3: [28, 36] from Operation: 65-29=36 Current State: 64:[28, 36], Operations: ['92-64=28', '65-29=36'] Exploring Operation: 28+36=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[64, 92, 29, 65], Operations: [] Exploring Operation: 92-64=28, Resulting Numbers: [29, 65, 28] Generated Node #0,0: 64:[29, 65, 28] Operation: 92-64=28 Exploring Operation: 92-29=63, Resulting Numbers: [64, 65, 63] Generated Node #0,1: 64:[64, 65, 63] Operation: 92-29=63 Exploring Operation: 92-65=27, Resulting Numbers: [64, 29, 27] Generated Node #0,2: 64:[64, 29, 27] Operation: 92-65=27 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[64, 65, 63], Operations: ['92-29=63'] Exploring Operation: 65-63=2, Resulting Numbers: [64, 2] Generated Node #0,1,0: 64:[64, 2] Operation: 65-63=2 Exploring Operation: 64-63=1, Resulting Numbers: [65, 1] Generated Node #0,1,1: 64:[65, 1] Operation: 64-63=1 Exploring Operation: 65-64=1, Resulting Numbers: [63, 1] Generated Node #0,1,2: 64:[63, 1] Operation: 65-64=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 64:[64, 2], Operations: ['92-29=63', '65-63=2'] Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,64 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,64 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,64 unequal: No Solution No 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: 64:[65, 1], Operations: ['92-29=63', '64-63=1'] Exploring Operation: 65*1=65, Resulting Numbers: [65] 65,64 unequal: No Solution Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[64, 92, 29, 65], Operations: [] Exploring Operation: 92-29=63, Resulting Numbers: [64, 65, 63] Generated Node #0,1: 64:[64, 65, 63] Operation: 92-29=63 Moving to Node #0,1 Current State: 64:[64, 65, 63], Operations: ['92-29=63'] Exploring Operation: 64-63=1, Resulting Numbers: [65, 1] Generated Node #0,1,1: 64:[65, 1] Operation: 64-63=1 Moving to Node #0,1,1 Current State: 64:[65, 1], Operations: ['92-29=63', '64-63=1'] Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 32, 69, 99, 56 ]
54
[ "32+69=101", "99+56=155", "155-101=54" ]
Current State: 54:[32, 69, 99, 56], Operations: [] Exploring Operation: 32+69=101, Resulting Numbers: [99, 56, 101] Generated Node #2: [99, 56, 101] from Operation: 32+69=101 Current State: 54:[99, 56, 101], Operations: ['32+69=101'] Exploring Operation: 99+56=155, Resulting Numbers: [101, 155] Generated Node #3: [101, 155] from Operation: 99+56=155 Current State: 54:[101, 155], Operations: ['32+69=101', '99+56=155'] Exploring Operation: 155-101=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[32, 69, 99, 56], Operations: [] Exploring Operation: 99-69=30, Resulting Numbers: [32, 56, 30] Generated Node #0,0: 54:[32, 56, 30] Operation: 99-69=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[32, 56, 30], Operations: ['99-69=30'] Exploring Operation: 32-30=2, Resulting Numbers: [56, 2] Generated Node #0,0,0: 54:[56, 2] Operation: 32-30=2 Moving to Node #0,0,0 Current State: 54:[56, 2], Operations: ['99-69=30', '32-30=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[32, 69, 99, 56], Operations: [] Exploring Operation: 99-69=30, Resulting Numbers: [32, 56, 30] Generated Node #0,0: 54:[32, 56, 30] Operation: 99-69=30 Moving to Node #0,0 Current State: 54:[32, 56, 30], Operations: ['99-69=30'] Exploring Operation: 32-30=2, Resulting Numbers: [56, 2] Generated Node #0,0,0: 54:[56, 2] Operation: 32-30=2 Moving to Node #0,0,0 Current State: 54:[56, 2], Operations: ['99-69=30', '32-30=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 69, 98, 96, 39 ]
60
[ "69-39=30", "98-96=2", "30*2=60" ]
Current State: 60:[69, 98, 96, 39], Operations: [] Exploring Operation: 69-39=30, Resulting Numbers: [98, 96, 30] Generated Node #2: [98, 96, 30] from Operation: 69-39=30 Current State: 60:[98, 96, 30], Operations: ['69-39=30'] Exploring Operation: 98-96=2, Resulting Numbers: [30, 2] Generated Node #3: [30, 2] from Operation: 98-96=2 Current State: 60:[30, 2], Operations: ['69-39=30', '98-96=2'] Exploring Operation: 30*2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[69, 98, 96, 39], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [69, 39, 2] Generated Node #0,0: 60:[69, 39, 2] Operation: 98-96=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[69, 39, 2], Operations: ['98-96=2'] Exploring Operation: 69-39=30, Resulting Numbers: [2, 30] Generated Node #0,0,0: 60:[2, 30] Operation: 69-39=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[2, 30], Operations: ['98-96=2', '69-39=30'] Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[69, 98, 96, 39], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [69, 39, 2] Generated Node #0,0: 60:[69, 39, 2] Operation: 98-96=2 Moving to Node #0,0 Current State: 60:[69, 39, 2], Operations: ['98-96=2'] Exploring Operation: 69-39=30, Resulting Numbers: [2, 30] Generated Node #0,0,0: 60:[2, 30] Operation: 69-39=30 Moving to Node #0,0,0 Current State: 60:[2, 30], Operations: ['98-96=2', '69-39=30'] Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 83, 83, 13, 86 ]
74
[ "83/83=1", "86-13=73", "1+73=74" ]
Current State: 74:[83, 83, 13, 86], Operations: [] Exploring Operation: 83/83=1, Resulting Numbers: [13, 86, 1] Generated Node #2: [13, 86, 1] from Operation: 83/83=1 Current State: 74:[13, 86, 1], Operations: ['83/83=1'] Exploring Operation: 86-13=73, Resulting Numbers: [1, 73] Generated Node #3: [1, 73] from Operation: 86-13=73 Current State: 74:[1, 73], Operations: ['83/83=1', '86-13=73'] Exploring Operation: 1+73=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[83, 83, 13, 86], Operations: [] Exploring Operation: 86-83=3, Resulting Numbers: [83, 13, 3] Generated Node #0,0: 74:[83, 13, 3] Operation: 86-83=3 Exploring Operation: 86-13=73, Resulting Numbers: [83, 83, 73] Generated Node #0,1: 74:[83, 83, 73] Operation: 86-13=73 Exploring Operation: 86-83=3, Resulting Numbers: [83, 13, 3] Generated Node #0,2: 74:[83, 13, 3] Operation: 86-83=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[83, 83, 73], Operations: ['86-13=73'] Exploring Operation: 83-83=0, Resulting Numbers: [73, 0] Generated Node #0,1,0: 74:[73, 0] Operation: 83-83=0 Exploring Operation: 83-73=10, Resulting Numbers: [83, 10] Generated Node #0,1,1: 74:[83, 10] Operation: 83-73=10 Exploring Operation: 83/83=1, Resulting Numbers: [73, 1] Generated Node #0,1,2: 74:[73, 1] Operation: 83/83=1 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 74:[73, 1], Operations: ['86-13=73', '83/83=1'] Exploring Operation: 73*1=73, Resulting Numbers: [73] 73,74 unequal: No Solution Exploring Operation: 73/1=73, Resulting Numbers: [73] 73,74 unequal: No Solution Exploring Operation: 73+1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[83, 83, 13, 86], Operations: [] Exploring Operation: 86-13=73, Resulting Numbers: [83, 83, 73] Generated Node #0,1: 74:[83, 83, 73] Operation: 86-13=73 Moving to Node #0,1 Current State: 74:[83, 83, 73], Operations: ['86-13=73'] Exploring Operation: 83/83=1, Resulting Numbers: [73, 1] Generated Node #0,1,2: 74:[73, 1] Operation: 83/83=1 Moving to Node #0,1,2 Current State: 74:[73, 1], Operations: ['86-13=73', '83/83=1'] Exploring Operation: 73+1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 92, 76, 59, 94 ]
21
[ "94-92=2", "76/2=38", "59-38=21" ]
Current State: 21:[92, 76, 59, 94], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [76, 59, 2] Generated Node #2: [76, 59, 2] from Operation: 94-92=2 Current State: 21:[76, 59, 2], Operations: ['94-92=2'] Exploring Operation: 76/2=38, Resulting Numbers: [59, 38] Generated Node #3: [59, 38] from Operation: 76/2=38 Current State: 21:[59, 38], Operations: ['94-92=2', '76/2=38'] Exploring Operation: 59-38=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[92, 76, 59, 94], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [76, 59, 2] Generated Node #0,0: 21:[76, 59, 2] Operation: 94-92=2 Moving to Node #0,0 Current State: 21:[76, 59, 2], Operations: ['94-92=2'] Exploring Operation: 76-59=17, Resulting Numbers: [2, 17] Generated Node #0,0,0: 21:[2, 17] Operation: 76-59=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[2, 17], Operations: ['94-92=2', '76-59=17'] Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 11, 46, 13, 38 ]
86
[ "46-11=35", "13+38=51", "35+51=86" ]
Current State: 86:[11, 46, 13, 38], Operations: [] Exploring Operation: 46-11=35, Resulting Numbers: [13, 38, 35] Generated Node #2: [13, 38, 35] from Operation: 46-11=35 Current State: 86:[13, 38, 35], Operations: ['46-11=35'] Exploring Operation: 13+38=51, Resulting Numbers: [35, 51] Generated Node #3: [35, 51] from Operation: 13+38=51 Current State: 86:[35, 51], Operations: ['46-11=35', '13+38=51'] Exploring Operation: 35+51=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[11, 46, 13, 38], Operations: [] Exploring Operation: 11+38=49, Resulting Numbers: [46, 13, 49] Generated Node #0,0: 86:[46, 13, 49] Operation: 11+38=49 Exploring Operation: 13+38=51, Resulting Numbers: [11, 46, 51] Generated Node #0,1: 86:[11, 46, 51] Operation: 13+38=51 Exploring Operation: 13-11=2, Resulting Numbers: [46, 38, 2] Generated Node #0,2: 86:[46, 38, 2] Operation: 13-11=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[46, 38, 2], Operations: ['13-11=2'] Exploring Operation: 46+38=84, Resulting Numbers: [2, 84] Generated Node #0,2,0: 86:[2, 84] Operation: 46+38=84 Exploring Operation: 46-2=44, Resulting Numbers: [38, 44] Generated Node #0,2,1: 86:[38, 44] Operation: 46-2=44 Exploring Operation: 46-38=8, Resulting Numbers: [2, 8] Generated Node #0,2,2: 86:[2, 8] Operation: 46-38=8 Moving to Node #0,2,0 Current State: 86:[2, 84], Operations: ['13-11=2', '46+38=84'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,86 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,86 unequal: No Solution Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[11, 46, 13, 38], Operations: [] Exploring Operation: 13-11=2, Resulting Numbers: [46, 38, 2] Generated Node #0,2: 86:[46, 38, 2] Operation: 13-11=2 Moving to Node #0,2 Current State: 86:[46, 38, 2], Operations: ['13-11=2'] Exploring Operation: 46+38=84, Resulting Numbers: [2, 84] Generated Node #0,2,0: 86:[2, 84] Operation: 46+38=84 Moving to Node #0,2,0 Current State: 86:[2, 84], Operations: ['13-11=2', '46+38=84'] Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 67, 2, 17, 57 ]
37
[ "67-57=10", "2*10=20", "17+20=37" ]
Current State: 37:[67, 2, 17, 57], Operations: [] Exploring Operation: 67-57=10, Resulting Numbers: [2, 17, 10] Generated Node #2: [2, 17, 10] from Operation: 67-57=10 Current State: 37:[2, 17, 10], Operations: ['67-57=10'] Exploring Operation: 2*10=20, Resulting Numbers: [17, 20] Generated Node #3: [17, 20] from Operation: 2*10=20 Current State: 37:[17, 20], Operations: ['67-57=10', '2*10=20'] Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[67, 2, 17, 57], Operations: [] Exploring Operation: 2*17=34, Resulting Numbers: [67, 57, 34] Generated Node #0,0: 37:[67, 57, 34] Operation: 2*17=34 Exploring Operation: 2+17=19, Resulting Numbers: [67, 57, 19] Generated Node #0,1: 37:[67, 57, 19] Operation: 2+17=19 Exploring Operation: 67-17=50, Resulting Numbers: [2, 57, 50] Generated Node #0,2: 37:[2, 57, 50] Operation: 67-17=50 Exploring Operation: 67-2=65, Resulting Numbers: [17, 57, 65] Generated Node #0,3: 37:[17, 57, 65] Operation: 67-2=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[67, 57, 34], Operations: ['2*17=34'] Exploring Operation: 67-57=10, Resulting Numbers: [34, 10] Generated Node #0,0,0: 37:[34, 10] Operation: 67-57=10 Exploring Operation: 67+34=101, Resulting Numbers: [57, 101] Generated Node #0,0,1: 37:[57, 101] Operation: 67+34=101 Exploring Operation: 57-34=23, Resulting Numbers: [67, 23] Generated Node #0,0,2: 37:[67, 23] Operation: 57-34=23 Exploring Operation: 67-34=33, Resulting Numbers: [57, 33] Generated Node #0,0,3: 37:[57, 33] Operation: 67-34=33 Moving to Node #0,0,3 Current State: 37:[57, 33], Operations: ['2*17=34', '67-34=33'] Exploring Operation: 57+33=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,37 unequal: No Solution Exploring Operation: 57*33=1881, Resulting Numbers: [1881] 1881,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[34, 10], Operations: ['2*17=34', '67-57=10'] Exploring Operation: 34*10=340, Resulting Numbers: [340] 340,37 unequal: No Solution Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,37 unequal: No Solution Exploring Operation: 34+10=44, Resulting Numbers: [44] 44,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[67, 23], Operations: ['2*17=34', '57-34=23'] Exploring Operation: 67*23=1541, Resulting Numbers: [1541] 1541,37 unequal: No Solution Exploring Operation: 67+23=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 67-23=44, Resulting Numbers: [44] 44,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[57, 101], Operations: ['2*17=34', '67+34=101'] Exploring Operation: 57*101=5757, Resulting Numbers: [5757] 5757,37 unequal: No Solution Exploring Operation: 101-57=44, Resulting Numbers: [44] 44,37 unequal: No Solution Exploring Operation: 57+101=158, Resulting Numbers: [158] 158,37 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:[67, 57, 19], Operations: ['2+17=19'] Exploring Operation: 67-57=10, Resulting Numbers: [19, 10] Generated Node #0,1,0: 37:[19, 10] Operation: 67-57=10 Exploring Operation: 67-19=48, Resulting Numbers: [57, 48] Generated Node #0,1,1: 37:[57, 48] Operation: 67-19=48 Exploring Operation: 57-19=38, Resulting Numbers: [67, 38] Generated Node #0,1,2: 37:[67, 38] Operation: 57-19=38 Exploring Operation: 57/19=3, Resulting Numbers: [67, 3] Generated Node #0,1,3: 37:[67, 3] Operation: 57/19=3 Moving to Node #0,1,1 Current State: 37:[57, 48], Operations: ['2+17=19', '67-19=48'] Exploring Operation: 57+48=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 57-48=9, Resulting Numbers: [9] 9,37 unequal: No Solution Exploring Operation: 57*48=2736, Resulting Numbers: [2736] 2736,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[67, 38], Operations: ['2+17=19', '57-19=38'] Exploring Operation: 67+38=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,37 unequal: No Solution Exploring Operation: 67*38=2546, Resulting Numbers: [2546] 2546,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[19, 10], Operations: ['2+17=19', '67-57=10'] Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,37 unequal: No Solution Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,37 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,37 unequal: No Solution Moving to Node #0,1,3 Current State: 37:[67, 3], Operations: ['2+17=19', '57/19=3'] Exploring Operation: 67*3=201, Resulting Numbers: [201] 201,37 unequal: No Solution Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,37 unequal: No Solution Exploring Operation: 67+3=70, Resulting Numbers: [70] 70,37 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:[2, 57, 50], Operations: ['67-17=50'] Exploring Operation: 50/2=25, Resulting Numbers: [57, 25] Generated Node #0,2,0: 37:[57, 25] Operation: 50/2=25 Exploring Operation: 2+57=59, Resulting Numbers: [50, 59] Generated Node #0,2,1: 37:[50, 59] Operation: 2+57=59 Exploring Operation: 57-2=55, Resulting Numbers: [50, 55] Generated Node #0,2,2: 37:[50, 55] Operation: 57-2=55 Exploring Operation: 50-2=48, Resulting Numbers: [57, 48] Generated Node #0,2,3: 37:[57, 48] Operation: 50-2=48 Moving to Node #0,2,2 Current State: 37:[50, 55], Operations: ['67-17=50', '57-2=55'] Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,37 unequal: No Solution Exploring Operation: 50+55=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 50*55=2750, Resulting Numbers: [2750] 2750,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[57, 48], Operations: ['67-17=50', '50-2=48'] Exploring Operation: 57+48=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 57*48=2736, Resulting Numbers: [2736] 2736,37 unequal: No Solution Exploring Operation: 57-48=9, Resulting Numbers: [9] 9,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[57, 25], Operations: ['67-17=50', '50/2=25'] Exploring Operation: 57+25=82, Resulting Numbers: [82] 82,37 unequal: No Solution Exploring Operation: 57*25=1425, Resulting Numbers: [1425] 1425,37 unequal: No Solution Exploring Operation: 57-25=32, Resulting Numbers: [32] 32,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[50, 59], Operations: ['67-17=50', '2+57=59'] Exploring Operation: 50*59=2950, Resulting Numbers: [2950] 2950,37 unequal: No Solution Exploring Operation: 59-50=9, Resulting Numbers: [9] 9,37 unequal: No Solution Exploring Operation: 50+59=109, Resulting Numbers: [109] 109,37 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 #0,3 Current State: 37:[17, 57, 65], Operations: ['67-2=65'] Exploring Operation: 17+57=74, Resulting Numbers: [65, 74] Generated Node #0,3,0: 37:[65, 74] Operation: 17+57=74 Exploring Operation: 65-57=8, Resulting Numbers: [17, 8] Generated Node #0,3,1: 37:[17, 8] Operation: 65-57=8 Exploring Operation: 65-17=48, Resulting Numbers: [57, 48] Generated Node #0,3,2: 37:[57, 48] Operation: 65-17=48 Exploring Operation: 57-17=40, Resulting Numbers: [65, 40] Generated Node #0,3,3: 37:[65, 40] Operation: 57-17=40 Moving to Node #0,3,2 Current State: 37:[57, 48], Operations: ['67-2=65', '65-17=48'] Exploring Operation: 57+48=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 57-48=9, Resulting Numbers: [9] 9,37 unequal: No Solution Exploring Operation: 57*48=2736, Resulting Numbers: [2736] 2736,37 unequal: No Solution Moving to Node #0,3,3 Current State: 37:[65, 40], Operations: ['67-2=65', '57-17=40'] Exploring Operation: 65+40=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 65-40=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 65*40=2600, Resulting Numbers: [2600] 2600,37 unequal: No Solution Moving to Node #0,3,1 Current State: 37:[17, 8], Operations: ['67-2=65', '65-57=8'] Exploring Operation: 17+8=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,37 unequal: No Solution Exploring Operation: 17*8=136, Resulting Numbers: [136] 136,37 unequal: No Solution Moving to Node #0,3,0 Current State: 37:[65, 74], Operations: ['67-2=65', '17+57=74'] Exploring Operation: 74-65=9, Resulting Numbers: [9] 9,37 unequal: No Solution Exploring Operation: 65*74=4810, Resulting Numbers: [4810] 4810,37 unequal: No Solution Exploring Operation: 65+74=139, Resulting Numbers: [139] 139,37 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
[ 25, 40, 24, 49 ]
41
[ "25+24=49", "49/49=1", "40+1=41" ]
Current State: 41:[25, 40, 24, 49], Operations: [] Exploring Operation: 25+24=49, Resulting Numbers: [40, 49, 49] Generated Node #2: [40, 49, 49] from Operation: 25+24=49 Current State: 41:[40, 49, 49], Operations: ['25+24=49'] Exploring Operation: 49/49=1, Resulting Numbers: [40, 1] Generated Node #3: [40, 1] from Operation: 49/49=1 Current State: 41:[40, 1], Operations: ['25+24=49', '49/49=1'] Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[25, 40, 24, 49], Operations: [] Exploring Operation: 25+24=49, Resulting Numbers: [40, 49, 49] Generated Node #0,0: 41:[40, 49, 49] Operation: 25+24=49 Moving to Node #0,0 Current State: 41:[40, 49, 49], Operations: ['25+24=49'] Exploring Operation: 49-40=9, Resulting Numbers: [49, 9] Generated Node #0,0,0: 41:[49, 9] Operation: 49-40=9 Moving to Node #0,0,0 Current State: 41:[49, 9], Operations: ['25+24=49', '49-40=9'] Exploring Operation: 49-9=40, Resulting Numbers: [40] 40,41 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 96, 95, 93, 74 ]
91
[ "93-74=19", "95/19=5", "96-5=91" ]
Current State: 91:[96, 95, 93, 74], Operations: [] Exploring Operation: 93-74=19, Resulting Numbers: [96, 95, 19] Generated Node #2: [96, 95, 19] from Operation: 93-74=19 Current State: 91:[96, 95, 19], Operations: ['93-74=19'] Exploring Operation: 95/19=5, Resulting Numbers: [96, 5] Generated Node #3: [96, 5] from Operation: 95/19=5 Current State: 91:[96, 5], Operations: ['93-74=19', '95/19=5'] Exploring Operation: 96-5=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[96, 95, 93, 74], Operations: [] Exploring Operation: 95-74=21, Resulting Numbers: [96, 93, 21] Generated Node #0,0: 91:[96, 93, 21] Operation: 95-74=21 Exploring Operation: 93-74=19, Resulting Numbers: [96, 95, 19] Generated Node #0,1: 91:[96, 95, 19] Operation: 93-74=19 Exploring Operation: 96-95=1, Resulting Numbers: [93, 74, 1] Generated Node #0,2: 91:[93, 74, 1] Operation: 96-95=1 Exploring Operation: 96-74=22, Resulting Numbers: [95, 93, 22] Generated Node #0,3: 91:[95, 93, 22] Operation: 96-74=22 Moving to Node #0,0 Current State: 91:[96, 93, 21], Operations: ['95-74=21'] Exploring Operation: 96-21=75, Resulting Numbers: [93, 75] Generated Node #0,0,0: 91:[93, 75] Operation: 96-21=75 Exploring Operation: 96+21=117, Resulting Numbers: [93, 117] Generated Node #0,0,1: 91:[93, 117] Operation: 96+21=117 Exploring Operation: 93-21=72, Resulting Numbers: [96, 72] Generated Node #0,0,2: 91:[96, 72] Operation: 93-21=72 Exploring Operation: 96-93=3, Resulting Numbers: [21, 3] Generated Node #0,0,3: 91:[21, 3] Operation: 96-93=3 Moving to Node #0,3 Current State: 91:[95, 93, 22], Operations: ['96-74=22'] Exploring Operation: 95-93=2, Resulting Numbers: [22, 2] Generated Node #0,3,0: 91:[22, 2] Operation: 95-93=2 Exploring Operation: 95-22=73, Resulting Numbers: [93, 73] Generated Node #0,3,1: 91:[93, 73] Operation: 95-22=73 Exploring Operation: 95+22=117, Resulting Numbers: [93, 117] Generated Node #0,3,2: 91:[93, 117] Operation: 95+22=117 Exploring Operation: 93-22=71, Resulting Numbers: [95, 71] Generated Node #0,3,3: 91:[95, 71] Operation: 93-22=71 Moving to Node #0,1 Current State: 91:[96, 95, 19], Operations: ['93-74=19'] Exploring Operation: 96-19=77, Resulting Numbers: [95, 77] Generated Node #0,1,0: 91:[95, 77] Operation: 96-19=77 Exploring Operation: 95-19=76, Resulting Numbers: [96, 76] Generated Node #0,1,1: 91:[96, 76] Operation: 95-19=76 Exploring Operation: 95/19=5, Resulting Numbers: [96, 5] Generated Node #0,1,2: 91:[96, 5] Operation: 95/19=5 Exploring Operation: 96-95=1, Resulting Numbers: [19, 1] Generated Node #0,1,3: 91:[19, 1] Operation: 96-95=1 Moving to Node #0,2 Current State: 91:[93, 74, 1], Operations: ['96-95=1'] Exploring Operation: 74+1=75, Resulting Numbers: [93, 75] Generated Node #0,2,0: 91:[93, 75] Operation: 74+1=75 Exploring Operation: 93*1=93, Resulting Numbers: [74, 93] Generated Node #0,2,1: 91:[74, 93] Operation: 93*1=93 Exploring Operation: 93-1=92, Resulting Numbers: [74, 92] Generated Node #0,2,2: 91:[74, 92] Operation: 93-1=92 Exploring Operation: 93-74=19, Resulting Numbers: [1, 19] Generated Node #0,2,3: 91:[1, 19] Operation: 93-74=19 Moving to Node #0,1,2 Current State: 91:[96, 5], Operations: ['93-74=19', '95/19=5'] Exploring Operation: 96+5=101, Resulting Numbers: [101] 101,91 unequal: No Solution Exploring Operation: 96-5=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[96, 95, 93, 74], Operations: [] Exploring Operation: 93-74=19, Resulting Numbers: [96, 95, 19] Generated Node #0,1: 91:[96, 95, 19] Operation: 93-74=19 Moving to Node #0,1 Current State: 91:[96, 95, 19], Operations: ['93-74=19'] Exploring Operation: 95/19=5, Resulting Numbers: [96, 5] Generated Node #0,1,2: 91:[96, 5] Operation: 95/19=5 Moving to Node #0,1,2 Current State: 91:[96, 5], Operations: ['93-74=19', '95/19=5'] Exploring Operation: 96-5=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
0.977431
hs_4
sum_heuristic
[ 23, 25, 15, 45 ]
62
[ "25-23=2", "15+45=60", "2+60=62" ]
Current State: 62:[23, 25, 15, 45], Operations: [] Exploring Operation: 25-23=2, Resulting Numbers: [15, 45, 2] Generated Node #2: [15, 45, 2] from Operation: 25-23=2 Current State: 62:[15, 45, 2], Operations: ['25-23=2'] Exploring Operation: 15+45=60, Resulting Numbers: [2, 60] Generated Node #3: [2, 60] from Operation: 15+45=60 Current State: 62:[2, 60], Operations: ['25-23=2', '15+45=60'] Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[23, 25, 15, 45], Operations: [] Exploring Operation: 45-15=30, Resulting Numbers: [23, 25, 30] Generated Node #0,0: 62:[23, 25, 30] Operation: 45-15=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[23, 25, 30], Operations: ['45-15=30'] Exploring Operation: 25-23=2, Resulting Numbers: [30, 2] Generated Node #0,0,0: 62:[30, 2] Operation: 25-23=2 Moving to Node #0,0,0 Current State: 62:[30, 2], Operations: ['45-15=30', '25-23=2'] Exploring Operation: 30+2=32, Resulting Numbers: [32] 32,62 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
[ 23, 30, 17, 63 ]
87
[ "30-23=7", "17+63=80", "7+80=87" ]
Current State: 87:[23, 30, 17, 63], Operations: [] Exploring Operation: 30-23=7, Resulting Numbers: [17, 63, 7] Generated Node #2: [17, 63, 7] from Operation: 30-23=7 Current State: 87:[17, 63, 7], Operations: ['30-23=7'] Exploring Operation: 17+63=80, Resulting Numbers: [7, 80] Generated Node #3: [7, 80] from Operation: 17+63=80 Current State: 87:[7, 80], Operations: ['30-23=7', '17+63=80'] Exploring Operation: 7+80=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[23, 30, 17, 63], Operations: [] Exploring Operation: 63-30=33, Resulting Numbers: [23, 17, 33] Generated Node #0,0: 87:[23, 17, 33] Operation: 63-30=33 Exploring Operation: 17+63=80, Resulting Numbers: [23, 30, 80] Generated Node #0,1: 87:[23, 30, 80] Operation: 17+63=80 Exploring Operation: 63-23=40, Resulting Numbers: [30, 17, 40] Generated Node #0,2: 87:[30, 17, 40] Operation: 63-23=40 Exploring Operation: 23+63=86, Resulting Numbers: [30, 17, 86] Generated Node #0,3: 87:[30, 17, 86] Operation: 23+63=86 Moving to Node #0,1 Current State: 87:[23, 30, 80], Operations: ['17+63=80'] Exploring Operation: 23+80=103, Resulting Numbers: [30, 103] Generated Node #0,1,0: 87:[30, 103] Operation: 23+80=103 Exploring Operation: 30-23=7, Resulting Numbers: [80, 7] Generated Node #0,1,1: 87:[80, 7] Operation: 30-23=7 Exploring Operation: 80-23=57, Resulting Numbers: [30, 57] Generated Node #0,1,2: 87:[30, 57] Operation: 80-23=57 Exploring Operation: 80-30=50, Resulting Numbers: [23, 50] Generated Node #0,1,3: 87:[23, 50] Operation: 80-30=50 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 87:[80, 7], Operations: ['17+63=80', '30-23=7'] Exploring Operation: 80-7=73, Resulting Numbers: [73] 73,87 unequal: No Solution Exploring Operation: 80*7=560, Resulting Numbers: [560] 560,87 unequal: No Solution Exploring Operation: 80+7=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[23, 30, 17, 63], Operations: [] Exploring Operation: 17+63=80, Resulting Numbers: [23, 30, 80] Generated Node #0,1: 87:[23, 30, 80] Operation: 17+63=80 Moving to Node #0,1 Current State: 87:[23, 30, 80], Operations: ['17+63=80'] Exploring Operation: 30-23=7, Resulting Numbers: [80, 7] Generated Node #0,1,1: 87:[80, 7] Operation: 30-23=7 Moving to Node #0,1,1 Current State: 87:[80, 7], Operations: ['17+63=80', '30-23=7'] Exploring Operation: 80+7=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 71, 43, 57, 16 ]
13
[ "71-43=28", "57-16=41", "41-28=13" ]
Current State: 13:[71, 43, 57, 16], Operations: [] Exploring Operation: 71-43=28, Resulting Numbers: [57, 16, 28] Generated Node #2: [57, 16, 28] from Operation: 71-43=28 Current State: 13:[57, 16, 28], Operations: ['71-43=28'] Exploring Operation: 57-16=41, Resulting Numbers: [28, 41] Generated Node #3: [28, 41] from Operation: 57-16=41 Current State: 13:[28, 41], Operations: ['71-43=28', '57-16=41'] Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[71, 43, 57, 16], Operations: [] Exploring Operation: 71-43=28, Resulting Numbers: [57, 16, 28] Generated Node #0,0: 13:[57, 16, 28] Operation: 71-43=28 Exploring Operation: 71-57=14, Resulting Numbers: [43, 16, 14] Generated Node #0,1: 13:[43, 16, 14] Operation: 71-57=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[43, 16, 14], Operations: ['71-57=14'] Exploring Operation: 43-16=27, Resulting Numbers: [14, 27] Generated Node #0,1,0: 13:[14, 27] Operation: 43-16=27 Exploring Operation: 43-14=29, Resulting Numbers: [16, 29] Generated Node #0,1,1: 13:[16, 29] Operation: 43-14=29 Moving to Node #0,1,0 Current State: 13:[14, 27], Operations: ['71-57=14', '43-16=27'] Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[71, 43, 57, 16], Operations: [] Exploring Operation: 71-57=14, Resulting Numbers: [43, 16, 14] Generated Node #0,1: 13:[43, 16, 14] Operation: 71-57=14 Moving to Node #0,1 Current State: 13:[43, 16, 14], Operations: ['71-57=14'] Exploring Operation: 43-16=27, Resulting Numbers: [14, 27] Generated Node #0,1,0: 13:[14, 27] Operation: 43-16=27 Moving to Node #0,1,0 Current State: 13:[14, 27], Operations: ['71-57=14', '43-16=27'] Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 68, 25, 72, 45 ]
70
[ "68-25=43", "72-45=27", "43+27=70" ]
Current State: 70:[68, 25, 72, 45], Operations: [] Exploring Operation: 68-25=43, Resulting Numbers: [72, 45, 43] Generated Node #2: [72, 45, 43] from Operation: 68-25=43 Current State: 70:[72, 45, 43], Operations: ['68-25=43'] Exploring Operation: 72-45=27, Resulting Numbers: [43, 27] Generated Node #3: [43, 27] from Operation: 72-45=27 Current State: 70:[43, 27], Operations: ['68-25=43', '72-45=27'] Exploring Operation: 43+27=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[68, 25, 72, 45], Operations: [] Exploring Operation: 45-25=20, Resulting Numbers: [68, 72, 20] Generated Node #0,0: 70:[68, 72, 20] Operation: 45-25=20 Exploring Operation: 72-45=27, Resulting Numbers: [68, 25, 27] Generated Node #0,1: 70:[68, 25, 27] Operation: 72-45=27 Exploring Operation: 68-25=43, Resulting Numbers: [72, 45, 43] Generated Node #0,2: 70:[72, 45, 43] Operation: 68-25=43 Exploring Operation: 25+45=70, Resulting Numbers: [68, 72, 70] Generated Node #0,3: 70:[68, 72, 70] Operation: 25+45=70 Start Sub Search at level 1: Moving to Node #0,3 Current State: 70:[68, 72, 70], Operations: ['25+45=70'] Exploring Operation: 68+72=140, Resulting Numbers: [70, 140] Generated Node #0,3,0: 70:[70, 140] Operation: 68+72=140 Exploring Operation: 70-68=2, Resulting Numbers: [72, 2] Generated Node #0,3,1: 70:[72, 2] Operation: 70-68=2 Exploring Operation: 72-70=2, Resulting Numbers: [68, 2] Generated Node #0,3,2: 70:[68, 2] Operation: 72-70=2 Exploring Operation: 72-68=4, Resulting Numbers: [70, 4] Generated Node #0,3,3: 70:[70, 4] Operation: 72-68=4 Moving to Node #0,3,3 Current State: 70:[70, 4], Operations: ['25+45=70', '72-68=4'] Exploring Operation: 70*4=280, Resulting Numbers: [280] 280,70 unequal: No Solution Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,70 unequal: No Solution Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,70 unequal: No Solution Moving to Node #0,3,2 Current State: 70:[68, 2], Operations: ['25+45=70', '72-70=2'] Exploring Operation: 68*2=136, Resulting Numbers: [136] 136,70 unequal: No Solution Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,70 unequal: No Solution Exploring Operation: 68+2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[68, 25, 72, 45], Operations: [] Exploring Operation: 25+45=70, Resulting Numbers: [68, 72, 70] Generated Node #0,3: 70:[68, 72, 70] Operation: 25+45=70 Moving to Node #0,3 Current State: 70:[68, 72, 70], Operations: ['25+45=70'] Exploring Operation: 72-70=2, Resulting Numbers: [68, 2] Generated Node #0,3,2: 70:[68, 2] Operation: 72-70=2 Moving to Node #0,3,2 Current State: 70:[68, 2], Operations: ['25+45=70', '72-70=2'] Exploring Operation: 68+2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 38, 89, 34, 78 ]
61
[ "89-38=51", "34+78=112", "112-51=61" ]
Current State: 61:[38, 89, 34, 78], Operations: [] Exploring Operation: 89-38=51, Resulting Numbers: [34, 78, 51] Generated Node #2: [34, 78, 51] from Operation: 89-38=51 Current State: 61:[34, 78, 51], Operations: ['89-38=51'] Exploring Operation: 34+78=112, Resulting Numbers: [51, 112] Generated Node #3: [51, 112] from Operation: 34+78=112 Current State: 61:[51, 112], Operations: ['89-38=51', '34+78=112'] Exploring Operation: 112-51=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[38, 89, 34, 78], Operations: [] Exploring Operation: 89-38=51, Resulting Numbers: [34, 78, 51] Generated Node #0,0: 61:[34, 78, 51] Operation: 89-38=51 Exploring Operation: 89-34=55, Resulting Numbers: [38, 78, 55] Generated Node #0,1: 61:[38, 78, 55] Operation: 89-34=55 Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[38, 78, 55], Operations: ['89-34=55'] Exploring Operation: 78-38=40, Resulting Numbers: [55, 40] Generated Node #0,1,0: 61:[55, 40] Operation: 78-38=40 Exploring Operation: 38+55=93, Resulting Numbers: [78, 93] Generated Node #0,1,1: 61:[78, 93] Operation: 38+55=93 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[55, 40], Operations: ['89-34=55', '78-38=40'] Exploring Operation: 55+40=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 55-40=15, Resulting Numbers: [15] 15,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[78, 93], Operations: ['89-34=55', '38+55=93'] Exploring Operation: 78+93=171, Resulting Numbers: [171] 171,61 unequal: No Solution Exploring Operation: 93-78=15, Resulting Numbers: [15] 15,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[34, 78, 51], Operations: ['89-38=51'] Exploring Operation: 78-34=44, Resulting Numbers: [51, 44] Generated Node #0,0,0: 61:[51, 44] Operation: 78-34=44 Exploring Operation: 34+51=85, Resulting Numbers: [78, 85] Generated Node #0,0,1: 61:[78, 85] Operation: 34+51=85 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[51, 44], Operations: ['89-38=51', '78-34=44'] Exploring Operation: 51+44=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 51-44=7, Resulting Numbers: [7] 7,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 61:[78, 85], Operations: ['89-38=51', '34+51=85'] Exploring Operation: 85-78=7, Resulting Numbers: [7] 7,61 unequal: No Solution Exploring Operation: 78+85=163, Resulting Numbers: [163] 163,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 48, 71, 64, 60 ]
27
[ "71-48=23", "64-60=4", "23+4=27" ]
Current State: 27:[48, 71, 64, 60], Operations: [] Exploring Operation: 71-48=23, Resulting Numbers: [64, 60, 23] Generated Node #2: [64, 60, 23] from Operation: 71-48=23 Current State: 27:[64, 60, 23], Operations: ['71-48=23'] Exploring Operation: 64-60=4, Resulting Numbers: [23, 4] Generated Node #3: [23, 4] from Operation: 64-60=4 Current State: 27:[23, 4], Operations: ['71-48=23', '64-60=4'] Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[48, 71, 64, 60], Operations: [] Exploring Operation: 71-60=11, Resulting Numbers: [48, 64, 11] Generated Node #0,0: 27:[48, 64, 11] Operation: 71-60=11 Exploring Operation: 71-64=7, Resulting Numbers: [48, 60, 7] Generated Node #0,1: 27:[48, 60, 7] Operation: 71-64=7 Exploring Operation: 64-60=4, Resulting Numbers: [48, 71, 4] Generated Node #0,2: 27:[48, 71, 4] Operation: 64-60=4 Moving to Node #0,1 Current State: 27:[48, 60, 7], Operations: ['71-64=7'] Exploring Operation: 60-7=53, Resulting Numbers: [48, 53] Generated Node #0,1,0: 27:[48, 53] Operation: 60-7=53 Exploring Operation: 48-7=41, Resulting Numbers: [60, 41] Generated Node #0,1,1: 27:[60, 41] Operation: 48-7=41 Exploring Operation: 60-48=12, Resulting Numbers: [7, 12] Generated Node #0,1,2: 27:[7, 12] Operation: 60-48=12 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 27:[7, 12], Operations: ['71-64=7', '60-48=12'] Exploring Operation: 7+12=19, Resulting Numbers: [19] 19,27 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,27 unequal: No Solution Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 27:[48, 53], Operations: ['71-64=7', '60-7=53'] Exploring Operation: 48+53=101, Resulting Numbers: [101] 101,27 unequal: No Solution Exploring Operation: 48*53=2544, Resulting Numbers: [2544] 2544,27 unequal: No Solution Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 27:[60, 41], Operations: ['71-64=7', '48-7=41'] Exploring Operation: 60*41=2460, Resulting Numbers: [2460] 2460,27 unequal: No Solution Exploring Operation: 60-41=19, Resulting Numbers: [19] 19,27 unequal: No Solution Exploring Operation: 60+41=101, Resulting Numbers: [101] 101,27 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: 27:[48, 64, 11], Operations: ['71-60=11'] Exploring Operation: 64-11=53, Resulting Numbers: [48, 53] Generated Node #0,0,0: 27:[48, 53] Operation: 64-11=53 Exploring Operation: 64-48=16, Resulting Numbers: [11, 16] Generated Node #0,0,1: 27:[11, 16] Operation: 64-48=16 Exploring Operation: 48-11=37, Resulting Numbers: [64, 37] Generated Node #0,0,2: 27:[64, 37] Operation: 48-11=37 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 27:[11, 16], Operations: ['71-60=11', '64-48=16'] Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,27 unequal: No Solution Exploring Operation: 11*16=176, Resulting Numbers: [176] 176,27 unequal: No Solution Exploring Operation: 11+16=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[48, 71, 64, 60], Operations: [] Exploring Operation: 71-60=11, Resulting Numbers: [48, 64, 11] Generated Node #0,0: 27:[48, 64, 11] Operation: 71-60=11 Moving to Node #0,0 Current State: 27:[48, 64, 11], Operations: ['71-60=11'] Exploring Operation: 64-48=16, Resulting Numbers: [11, 16] Generated Node #0,0,1: 27:[11, 16] Operation: 64-48=16 Moving to Node #0,0,1 Current State: 27:[11, 16], Operations: ['71-60=11', '64-48=16'] Exploring Operation: 11+16=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 91, 98, 92, 83 ]
29
[ "91+83=174", "98-92=6", "174/6=29" ]
Current State: 29:[91, 98, 92, 83], Operations: [] Exploring Operation: 91+83=174, Resulting Numbers: [98, 92, 174] Generated Node #2: [98, 92, 174] from Operation: 91+83=174 Current State: 29:[98, 92, 174], Operations: ['91+83=174'] Exploring Operation: 98-92=6, Resulting Numbers: [174, 6] Generated Node #3: [174, 6] from Operation: 98-92=6 Current State: 29:[174, 6], Operations: ['91+83=174', '98-92=6'] Exploring Operation: 174/6=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[91, 98, 92, 83], Operations: [] Exploring Operation: 98-91=7, Resulting Numbers: [92, 83, 7] Generated Node #0,0: 29:[92, 83, 7] Operation: 98-91=7 Exploring Operation: 98-92=6, Resulting Numbers: [91, 83, 6] Generated Node #0,1: 29:[91, 83, 6] Operation: 98-92=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[92, 83, 7], Operations: ['98-91=7'] Exploring Operation: 92-83=9, Resulting Numbers: [7, 9] Generated Node #0,0,0: 29:[7, 9] Operation: 92-83=9 Exploring Operation: 92-7=85, Resulting Numbers: [83, 85] Generated Node #0,0,1: 29:[83, 85] Operation: 92-7=85 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[7, 9], Operations: ['98-91=7', '92-83=9'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,29 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,29 unequal: No Solution No 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: 29:[83, 85], Operations: ['98-91=7', '92-7=85'] Exploring Operation: 83+85=168, Resulting Numbers: [168] 168,29 unequal: No Solution Exploring Operation: 85-83=2, Resulting Numbers: [2] 2,29 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: 29:[91, 83, 6], Operations: ['98-92=6'] Exploring Operation: 91-6=85, Resulting Numbers: [83, 85] Generated Node #0,1,0: 29:[83, 85] Operation: 91-6=85 Exploring Operation: 91-83=8, Resulting Numbers: [6, 8] Generated Node #0,1,1: 29:[6, 8] Operation: 91-83=8 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 29:[6, 8], Operations: ['98-92=6', '91-83=8'] Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,29 unequal: No Solution No 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: 29:[83, 85], Operations: ['98-92=6', '91-6=85'] Exploring Operation: 85-83=2, Resulting Numbers: [2] 2,29 unequal: No Solution Exploring Operation: 83+85=168, Resulting Numbers: [168] 168,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 56, 68, 70, 51 ]
79
[ "70-68=2", "56/2=28", "51+28=79" ]
Current State: 79:[56, 68, 70, 51], Operations: [] Exploring Operation: 70-68=2, Resulting Numbers: [56, 51, 2] Generated Node #2: [56, 51, 2] from Operation: 70-68=2 Current State: 79:[56, 51, 2], Operations: ['70-68=2'] Exploring Operation: 56/2=28, Resulting Numbers: [51, 28] Generated Node #3: [51, 28] from Operation: 56/2=28 Current State: 79:[51, 28], Operations: ['70-68=2', '56/2=28'] Exploring Operation: 51+28=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[56, 68, 70, 51], Operations: [] Exploring Operation: 56+51=107, Resulting Numbers: [68, 70, 107] Generated Node #0,0: 79:[68, 70, 107] Operation: 56+51=107 Exploring Operation: 56+70=126, Resulting Numbers: [68, 51, 126] Generated Node #0,1: 79:[68, 51, 126] Operation: 56+70=126 Exploring Operation: 56+68=124, Resulting Numbers: [70, 51, 124] Generated Node #0,2: 79:[70, 51, 124] Operation: 56+68=124 Exploring Operation: 68+51=119, Resulting Numbers: [56, 70, 119] Generated Node #0,3: 79:[56, 70, 119] Operation: 68+51=119 Exploring Operation: 70+51=121, Resulting Numbers: [56, 68, 121] Generated Node #0,4: 79:[56, 68, 121] Operation: 70+51=121 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[68, 70, 107], Operations: ['56+51=107'] Exploring Operation: 68+70=138, Resulting Numbers: [107, 138] Generated Node #0,0,0: 79:[107, 138] Operation: 68+70=138 Exploring Operation: 107-68=39, Resulting Numbers: [70, 39] Generated Node #0,0,1: 79:[70, 39] Operation: 107-68=39 Exploring Operation: 70-68=2, Resulting Numbers: [107, 2] Generated Node #0,0,2: 79:[107, 2] Operation: 70-68=2 Exploring Operation: 68+107=175, Resulting Numbers: [70, 175] Generated Node #0,0,3: 79:[70, 175] Operation: 68+107=175 Exploring Operation: 107-70=37, Resulting Numbers: [68, 37] Generated Node #0,0,4: 79:[68, 37] Operation: 107-70=37 Moving to Node #0,0,1 Current State: 79:[70, 39], Operations: ['56+51=107', '107-68=39'] Exploring Operation: 70+39=109, Resulting Numbers: [109] 109,79 unequal: No Solution Exploring Operation: 70-39=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 70*39=2730, Resulting Numbers: [2730] 2730,79 unequal: No Solution Moving to Node #0,0,4 Current State: 79:[68, 37], Operations: ['56+51=107', '107-70=37'] Exploring Operation: 68-37=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 68+37=105, Resulting Numbers: [105] 105,79 unequal: No Solution Exploring Operation: 68*37=2516, Resulting Numbers: [2516] 2516,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[107, 138], Operations: ['56+51=107', '68+70=138'] Exploring Operation: 107*138=14766, Resulting Numbers: [14766] 14766,79 unequal: No Solution Exploring Operation: 138-107=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 107+138=245, Resulting Numbers: [245] 245,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[107, 2], Operations: ['56+51=107', '70-68=2'] Exploring Operation: 107+2=109, Resulting Numbers: [109] 109,79 unequal: No Solution Exploring Operation: 107-2=105, Resulting Numbers: [105] 105,79 unequal: No Solution Exploring Operation: 107*2=214, Resulting Numbers: [214] 214,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[70, 175], Operations: ['56+51=107', '68+107=175'] Exploring Operation: 70*175=12250, Resulting Numbers: [12250] 12250,79 unequal: No Solution Exploring Operation: 70+175=245, Resulting Numbers: [245] 245,79 unequal: No Solution Exploring Operation: 175-70=105, Resulting Numbers: [105] 105,79 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:[56, 70, 119], Operations: ['68+51=119'] Exploring Operation: 56+70=126, Resulting Numbers: [119, 126] Generated Node #0,3,0: 79:[119, 126] Operation: 56+70=126 Exploring Operation: 119-56=63, Resulting Numbers: [70, 63] Generated Node #0,3,1: 79:[70, 63] Operation: 119-56=63 Exploring Operation: 70-56=14, Resulting Numbers: [119, 14] Generated Node #0,3,2: 79:[119, 14] Operation: 70-56=14 Exploring Operation: 119-70=49, Resulting Numbers: [56, 49] Generated Node #0,3,3: 79:[56, 49] Operation: 119-70=49 Exploring Operation: 56+119=175, Resulting Numbers: [70, 175] Generated Node #0,3,4: 79:[70, 175] Operation: 56+119=175 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 79:[70, 63], Operations: ['68+51=119', '119-56=63'] Exploring Operation: 70-63=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 70+63=133, Resulting Numbers: [133] 133,79 unequal: No Solution Exploring Operation: 70*63=4410, Resulting Numbers: [4410] 4410,79 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 #0,3,3 Current State: 79:[56, 49], Operations: ['68+51=119', '119-70=49'] Exploring Operation: 56*49=2744, Resulting Numbers: [2744] 2744,79 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 56+49=105, Resulting Numbers: [105] 105,79 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 #0,3,0 Current State: 79:[119, 126], Operations: ['68+51=119', '56+70=126'] Exploring Operation: 119*126=14994, Resulting Numbers: [14994] 14994,79 unequal: No Solution Exploring Operation: 126-119=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 119+126=245, Resulting Numbers: [245] 245,79 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 #0,3,2 Current State: 79:[119, 14], Operations: ['68+51=119', '70-56=14'] Exploring Operation: 119*14=1666, Resulting Numbers: [1666] 1666,79 unequal: No Solution Exploring Operation: 119+14=133, Resulting Numbers: [133] 133,79 unequal: No Solution Exploring Operation: 119-14=105, Resulting Numbers: [105] 105,79 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 #0,3,4 Current State: 79:[70, 175], Operations: ['68+51=119', '56+119=175'] Exploring Operation: 175-70=105, Resulting Numbers: [105] 105,79 unequal: No Solution Exploring Operation: 70+175=245, Resulting Numbers: [245] 245,79 unequal: No Solution Exploring Operation: 70*175=12250, Resulting Numbers: [12250] 12250,79 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 #0,4 Current State: 79:[56, 68, 121], Operations: ['70+51=121'] Exploring Operation: 68-56=12, Resulting Numbers: [121, 12] Generated Node #0,4,0: 79:[121, 12] Operation: 68-56=12 Exploring Operation: 56+68=124, Resulting Numbers: [121, 124] Generated Node #0,4,1: 79:[121, 124] Operation: 56+68=124 Exploring Operation: 121-56=65, Resulting Numbers: [68, 65] Generated Node #0,4,2: 79:[68, 65] Operation: 121-56=65 Exploring Operation: 121-68=53, Resulting Numbers: [56, 53] Generated Node #0,4,3: 79:[56, 53] Operation: 121-68=53 Exploring Operation: 56+121=177, Resulting Numbers: [68, 177] Generated Node #0,4,4: 79:[68, 177] Operation: 56+121=177 Moving to Node #0,4,2 Current State: 79:[68, 65], Operations: ['70+51=121', '121-56=65'] Exploring Operation: 68*65=4420, Resulting Numbers: [4420] 4420,79 unequal: No Solution Exploring Operation: 68+65=133, Resulting Numbers: [133] 133,79 unequal: No Solution Exploring Operation: 68-65=3, Resulting Numbers: [3] 3,79 unequal: No Solution Moving to Node #0,4,3 Current State: 79:[56, 53], Operations: ['70+51=121', '121-68=53'] Exploring Operation: 56*53=2968, Resulting Numbers: [2968] 2968,79 unequal: No Solution Exploring Operation: 56+53=109, Resulting Numbers: [109] 109,79 unequal: No Solution Exploring Operation: 56-53=3, Resulting Numbers: [3] 3,79 unequal: No Solution Moving to Node #0,4,1 Current State: 79:[121, 124], Operations: ['70+51=121', '56+68=124'] Exploring Operation: 124-121=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 121+124=245, Resulting Numbers: [245] 245,79 unequal: No Solution Exploring Operation: 121*124=15004, Resulting Numbers: [15004] 15004,79 unequal: No Solution Moving to Node #0,4,0 Current State: 79:[121, 12], Operations: ['70+51=121', '68-56=12'] Exploring Operation: 121+12=133, Resulting Numbers: [133] 133,79 unequal: No Solution Exploring Operation: 121-12=109, Resulting Numbers: [109] 109,79 unequal: No Solution Exploring Operation: 121*12=1452, Resulting Numbers: [1452] 1452,79 unequal: No Solution Moving to Node #0,4,4 Current State: 79:[68, 177], Operations: ['70+51=121', '56+121=177'] Exploring Operation: 68+177=245, Resulting Numbers: [245] 245,79 unequal: No Solution Exploring Operation: 68*177=12036, Resulting Numbers: [12036] 12036,79 unequal: No Solution Exploring Operation: 177-68=109, Resulting Numbers: [109] 109,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[70, 51, 124], Operations: ['56+68=124'] Exploring Operation: 70+51=121, Resulting Numbers: [124, 121] Generated Node #0,2,0: 79:[124, 121] Operation: 70+51=121 Exploring Operation: 124-51=73, Resulting Numbers: [70, 73] Generated Node #0,2,1: 79:[70, 73] Operation: 124-51=73 Exploring Operation: 124-70=54, Resulting Numbers: [51, 54] Generated Node #0,2,2: 79:[51, 54] Operation: 124-70=54 Exploring Operation: 70-51=19, Resulting Numbers: [124, 19] Generated Node #0,2,3: 79:[124, 19] Operation: 70-51=19 Exploring Operation: 51+124=175, Resulting Numbers: [70, 175] Generated Node #0,2,4: 79:[70, 175] Operation: 51+124=175 Moving to Node #0,2,1 Current State: 79:[70, 73], Operations: ['56+68=124', '124-51=73'] Exploring Operation: 73-70=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 70*73=5110, Resulting Numbers: [5110] 5110,79 unequal: No Solution Exploring Operation: 70+73=143, Resulting Numbers: [143] 143,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[51, 54], Operations: ['56+68=124', '124-70=54'] Exploring Operation: 54-51=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 51+54=105, Resulting Numbers: [105] 105,79 unequal: No Solution Exploring Operation: 51*54=2754, Resulting Numbers: [2754] 2754,79 unequal: No Solution Moving to Node #0,2,0 Current State: 79:[124, 121], Operations: ['56+68=124', '70+51=121'] Exploring Operation: 124-121=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 124+121=245, Resulting Numbers: [245] 245,79 unequal: No Solution Exploring Operation: 124*121=15004, Resulting Numbers: [15004] 15004,79 unequal: No Solution Moving to Node #0,2,3 Current State: 79:[124, 19], Operations: ['56+68=124', '70-51=19'] Exploring Operation: 124*19=2356, Resulting Numbers: [2356] 2356,79 unequal: No Solution Exploring Operation: 124-19=105, Resulting Numbers: [105] 105,79 unequal: No Solution Exploring Operation: 124+19=143, Resulting Numbers: [143] 143,79 unequal: No Solution Moving to Node #0,2,4 Current State: 79:[70, 175], Operations: ['56+68=124', '51+124=175'] Exploring Operation: 70+175=245, Resulting Numbers: [245] 245,79 unequal: No Solution Exploring Operation: 175-70=105, Resulting Numbers: [105] 105,79 unequal: No Solution Exploring Operation: 70*175=12250, Resulting Numbers: [12250] 12250,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[68, 51, 126], Operations: ['56+70=126'] Exploring Operation: 51+126=177, Resulting Numbers: [68, 177] Generated Node #0,1,0: 79:[68, 177] Operation: 51+126=177 Exploring Operation: 126-68=58, Resulting Numbers: [51, 58] Generated Node #0,1,1: 79:[51, 58] Operation: 126-68=58 Exploring Operation: 68-51=17, Resulting Numbers: [126, 17] Generated Node #0,1,2: 79:[126, 17] Operation: 68-51=17 Exploring Operation: 126-51=75, Resulting Numbers: [68, 75] Generated Node #0,1,3: 79:[68, 75] Operation: 126-51=75 Exploring Operation: 68+51=119, Resulting Numbers: [126, 119] Generated Node #0,1,4: 79:[126, 119] Operation: 68+51=119 Moving to Node #0,1,3 Current State: 79:[68, 75], Operations: ['56+70=126', '126-51=75'] Exploring Operation: 75-68=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 68*75=5100, Resulting Numbers: [5100] 5100,79 unequal: No Solution Exploring Operation: 68+75=143, Resulting Numbers: [143] 143,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[51, 58], Operations: ['56+70=126', '126-68=58'] Exploring Operation: 51*58=2958, Resulting Numbers: [2958] 2958,79 unequal: No Solution Exploring Operation: 51+58=109, Resulting Numbers: [109] 109,79 unequal: No Solution Exploring Operation: 58-51=7, Resulting Numbers: [7] 7,79 unequal: No Solution Moving to Node #0,1,4 Current State: 79:[126, 119], Operations: ['56+70=126', '68+51=119'] Exploring Operation: 126-119=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 126+119=245, Resulting Numbers: [245] 245,79 unequal: No Solution Exploring Operation: 126*119=14994, Resulting Numbers: [14994] 14994,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[68, 177], Operations: ['56+70=126', '51+126=177'] Exploring Operation: 68*177=12036, Resulting Numbers: [12036] 12036,79 unequal: No Solution Exploring Operation: 177-68=109, Resulting Numbers: [109] 109,79 unequal: No Solution Exploring Operation: 68+177=245, Resulting Numbers: [245] 245,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[126, 17], Operations: ['56+70=126', '68-51=17'] Exploring Operation: 126+17=143, Resulting Numbers: [143] 143,79 unequal: No Solution Exploring Operation: 126-17=109, Resulting Numbers: [109] 109,79 unequal: No Solution Exploring Operation: 126*17=2142, Resulting Numbers: [2142] 2142,79 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
[ 15, 10, 73, 2 ]
39
[ "15-10=5", "73+5=78", "78/2=39" ]
Current State: 39:[15, 10, 73, 2], Operations: [] Exploring Operation: 15-10=5, Resulting Numbers: [73, 2, 5] Generated Node #2: [73, 2, 5] from Operation: 15-10=5 Current State: 39:[73, 2, 5], Operations: ['15-10=5'] Exploring Operation: 73+5=78, Resulting Numbers: [2, 78] Generated Node #3: [2, 78] from Operation: 73+5=78 Current State: 39:[2, 78], Operations: ['15-10=5', '73+5=78'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[15, 10, 73, 2], Operations: [] Exploring Operation: 15-10=5, Resulting Numbers: [73, 2, 5] Generated Node #0,0: 39:[73, 2, 5] Operation: 15-10=5 Exploring Operation: 73-15=58, Resulting Numbers: [10, 2, 58] Generated Node #0,1: 39:[10, 2, 58] Operation: 73-15=58 Exploring Operation: 10+2=12, Resulting Numbers: [15, 73, 12] Generated Node #0,2: 39:[15, 73, 12] Operation: 10+2=12 Exploring Operation: 15-2=13, Resulting Numbers: [10, 73, 13] Generated Node #0,3: 39:[10, 73, 13] Operation: 15-2=13 Exploring Operation: 73-10=63, Resulting Numbers: [15, 2, 63] Generated Node #0,4: 39:[15, 2, 63] Operation: 73-10=63 Moving to Node #0,1 Current State: 39:[10, 2, 58], Operations: ['73-15=58'] Exploring Operation: 10+2=12, Resulting Numbers: [58, 12] Generated Node #0,1,0: 39:[58, 12] Operation: 10+2=12 Exploring Operation: 58/2=29, Resulting Numbers: [10, 29] Generated Node #0,1,1: 39:[10, 29] Operation: 58/2=29 Exploring Operation: 10/2=5, Resulting Numbers: [58, 5] Generated Node #0,1,2: 39:[58, 5] Operation: 10/2=5 Exploring Operation: 58-2=56, Resulting Numbers: [10, 56] Generated Node #0,1,3: 39:[10, 56] Operation: 58-2=56 Exploring Operation: 58-10=48, Resulting Numbers: [2, 48] Generated Node #0,1,4: 39:[2, 48] Operation: 58-10=48 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 39:[2, 48], Operations: ['73-15=58', '58-10=48'] Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,39 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,39 unequal: No Solution Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[10, 29], Operations: ['73-15=58', '58/2=29'] Exploring Operation: 10*29=290, Resulting Numbers: [290] 290,39 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,39 unequal: No Solution Exploring Operation: 10+29=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[15, 10, 73, 2], Operations: [] Exploring Operation: 73-15=58, Resulting Numbers: [10, 2, 58] Generated Node #0,1: 39:[10, 2, 58] Operation: 73-15=58 Moving to Node #0,1 Current State: 39:[10, 2, 58], Operations: ['73-15=58'] Exploring Operation: 58/2=29, Resulting Numbers: [10, 29] Generated Node #0,1,1: 39:[10, 29] Operation: 58/2=29 Moving to Node #0,1,1 Current State: 39:[10, 29], Operations: ['73-15=58', '58/2=29'] Exploring Operation: 10+29=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 72, 2, 20, 40 ]
71
[ "2*20=40", "40/40=1", "72-1=71" ]
Current State: 71:[72, 2, 20, 40], Operations: [] Exploring Operation: 2*20=40, Resulting Numbers: [72, 40, 40] Generated Node #2: [72, 40, 40] from Operation: 2*20=40 Current State: 71:[72, 40, 40], Operations: ['2*20=40'] Exploring Operation: 40/40=1, Resulting Numbers: [72, 1] Generated Node #3: [72, 1] from Operation: 40/40=1 Current State: 71:[72, 1], Operations: ['2*20=40', '40/40=1'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[72, 2, 20, 40], Operations: [] Exploring Operation: 2*40=80, Resulting Numbers: [72, 20, 80] Generated Node #0,0: 71:[72, 20, 80] Operation: 2*40=80 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[72, 20, 80], Operations: ['2*40=80'] Exploring Operation: 80-20=60, Resulting Numbers: [72, 60] Generated Node #0,0,0: 71:[72, 60] Operation: 80-20=60 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[72, 60], Operations: ['2*40=80', '80-20=60'] Exploring Operation: 72-60=12, Resulting Numbers: [12] 12,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 50, 89, 42, 49 ]
100
[ "89-42=47", "49-47=2", "50*2=100" ]
Current State: 100:[50, 89, 42, 49], Operations: [] Exploring Operation: 89-42=47, Resulting Numbers: [50, 49, 47] Generated Node #2: [50, 49, 47] from Operation: 89-42=47 Current State: 100:[50, 49, 47], Operations: ['89-42=47'] Exploring Operation: 49-47=2, Resulting Numbers: [50, 2] Generated Node #3: [50, 2] from Operation: 49-47=2 Current State: 100:[50, 2], Operations: ['89-42=47', '49-47=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[50, 89, 42, 49], Operations: [] Exploring Operation: 89-42=47, Resulting Numbers: [50, 49, 47] Generated Node #0,0: 100:[50, 49, 47] Operation: 89-42=47 Moving to Node #0,0 Current State: 100:[50, 49, 47], Operations: ['89-42=47'] Exploring Operation: 49-47=2, Resulting Numbers: [50, 2] Generated Node #0,0,0: 100:[50, 2] Operation: 49-47=2 Moving to Node #0,0,0 Current State: 100:[50, 2], Operations: ['89-42=47', '49-47=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[50, 89, 42, 49], Operations: [] Exploring Operation: 89-42=47, Resulting Numbers: [50, 49, 47] Generated Node #0,0: 100:[50, 49, 47] Operation: 89-42=47 Moving to Node #0,0 Current State: 100:[50, 49, 47], Operations: ['89-42=47'] Exploring Operation: 49-47=2, Resulting Numbers: [50, 2] Generated Node #0,0,0: 100:[50, 2] Operation: 49-47=2 Moving to Node #0,0,0 Current State: 100:[50, 2], Operations: ['89-42=47', '49-47=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 71, 33, 71, 11 ]
44
[ "71+33=104", "71-11=60", "104-60=44" ]
Current State: 44:[71, 33, 71, 11], Operations: [] Exploring Operation: 71+33=104, Resulting Numbers: [11, 104] Generated Node #2: [11, 104] from Operation: 71+33=104 Current State: 44:[11, 104], Operations: ['71+33=104'] Exploring Operation: 71-11=60, Resulting Numbers: [104, 60] Generated Node #3: [104, 60] from Operation: 71-11=60 Current State: 44:[104, 60], Operations: ['71+33=104', '71-11=60'] Exploring Operation: 104-60=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[71, 33, 71, 11], Operations: [] Exploring Operation: 71/71=1, Resulting Numbers: [33, 11, 1] Generated Node #0,0: 44:[33, 11, 1] Operation: 71/71=1 Moving to Node #0,0 Current State: 44:[33, 11, 1], Operations: ['71/71=1'] Exploring Operation: 33+11=44, Resulting Numbers: [1, 44] Generated Node #0,0,0: 44:[1, 44] Operation: 33+11=44 Moving to Node #0,0,0 Current State: 44:[1, 44], Operations: ['71/71=1', '33+11=44'] Exploring Operation: 1*44=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[71, 33, 71, 11], Operations: [] Exploring Operation: 71/71=1, Resulting Numbers: [33, 11, 1] Generated Node #0,0: 44:[33, 11, 1] Operation: 71/71=1 Moving to Node #0,0 Current State: 44:[33, 11, 1], Operations: ['71/71=1'] Exploring Operation: 33+11=44, Resulting Numbers: [1, 44] Generated Node #0,0,0: 44:[1, 44] Operation: 33+11=44 Moving to Node #0,0,0 Current State: 44:[1, 44], Operations: ['71/71=1', '33+11=44'] Exploring Operation: 1*44=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 54, 42, 1, 48 ]
60
[ "54-42=12", "1*48=48", "12+48=60" ]
Current State: 60:[54, 42, 1, 48], Operations: [] Exploring Operation: 54-42=12, Resulting Numbers: [1, 48, 12] Generated Node #2: [1, 48, 12] from Operation: 54-42=12 Current State: 60:[1, 48, 12], Operations: ['54-42=12'] Exploring Operation: 1*48=48, Resulting Numbers: [12, 48] Generated Node #3: [12, 48] from Operation: 1*48=48 Current State: 60:[12, 48], Operations: ['54-42=12', '1*48=48'] Exploring Operation: 12+48=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[54, 42, 1, 48], Operations: [] Exploring Operation: 48-42=6, Resulting Numbers: [54, 1, 6] Generated Node #0,0: 60:[54, 1, 6] Operation: 48-42=6 Moving to Node #0,0 Current State: 60:[54, 1, 6], Operations: ['48-42=6'] Exploring Operation: 54+6=60, Resulting Numbers: [1, 60] Generated Node #0,0,0: 60:[1, 60] Operation: 54+6=60 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[1, 60], Operations: ['48-42=6', '54+6=60'] Exploring Operation: 1*60=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[54, 42, 1, 48], Operations: [] Exploring Operation: 48-42=6, Resulting Numbers: [54, 1, 6] Generated Node #0,0: 60:[54, 1, 6] Operation: 48-42=6 Moving to Node #0,0 Current State: 60:[54, 1, 6], Operations: ['48-42=6'] Exploring Operation: 54+6=60, Resulting Numbers: [1, 60] Generated Node #0,0,0: 60:[1, 60] Operation: 54+6=60 Moving to Node #0,0,0 Current State: 60:[1, 60], Operations: ['48-42=6', '54+6=60'] Exploring Operation: 1*60=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 34, 52, 54, 41 ]
73
[ "34+52=86", "54-41=13", "86-13=73" ]
Current State: 73:[34, 52, 54, 41], Operations: [] Exploring Operation: 34+52=86, Resulting Numbers: [54, 41, 86] Generated Node #2: [54, 41, 86] from Operation: 34+52=86 Current State: 73:[54, 41, 86], Operations: ['34+52=86'] Exploring Operation: 54-41=13, Resulting Numbers: [86, 13] Generated Node #3: [86, 13] from Operation: 54-41=13 Current State: 73:[86, 13], Operations: ['34+52=86', '54-41=13'] Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[34, 52, 54, 41], Operations: [] Exploring Operation: 34+54=88, Resulting Numbers: [52, 41, 88] Generated Node #0,0: 73:[52, 41, 88] Operation: 34+54=88 Exploring Operation: 34+41=75, Resulting Numbers: [52, 54, 75] Generated Node #0,1: 73:[52, 54, 75] Operation: 34+41=75 Exploring Operation: 34+52=86, Resulting Numbers: [54, 41, 86] Generated Node #0,2: 73:[54, 41, 86] Operation: 34+52=86 Exploring Operation: 54+41=95, Resulting Numbers: [34, 52, 95] Generated Node #0,3: 73:[34, 52, 95] Operation: 54+41=95 Exploring Operation: 52+41=93, Resulting Numbers: [34, 54, 93] Generated Node #0,4: 73:[34, 54, 93] Operation: 52+41=93 Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[52, 54, 75], Operations: ['34+41=75'] Exploring Operation: 52+54=106, Resulting Numbers: [75, 106] Generated Node #0,1,0: 73:[75, 106] Operation: 52+54=106 Exploring Operation: 75-54=21, Resulting Numbers: [52, 21] Generated Node #0,1,1: 73:[52, 21] Operation: 75-54=21 Exploring Operation: 54-52=2, Resulting Numbers: [75, 2] Generated Node #0,1,2: 73:[75, 2] Operation: 54-52=2 Exploring Operation: 75-52=23, Resulting Numbers: [54, 23] Generated Node #0,1,3: 73:[54, 23] Operation: 75-52=23 Exploring Operation: 52+75=127, Resulting Numbers: [54, 127] Generated Node #0,1,4: 73:[54, 127] Operation: 52+75=127 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[75, 106], Operations: ['34+41=75', '52+54=106'] Exploring Operation: 106-75=31, Resulting Numbers: [31] 31,73 unequal: No Solution Exploring Operation: 75+106=181, Resulting Numbers: [181] 181,73 unequal: No Solution Exploring Operation: 75*106=7950, Resulting Numbers: [7950] 7950,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 73:[54, 23], Operations: ['34+41=75', '75-52=23'] Exploring Operation: 54+23=77, Resulting Numbers: [77] 77,73 unequal: No Solution Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,73 unequal: No Solution Exploring Operation: 54*23=1242, Resulting Numbers: [1242] 1242,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[52, 21], Operations: ['34+41=75', '75-54=21'] Exploring Operation: 52*21=1092, Resulting Numbers: [1092] 1092,73 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,73 unequal: No Solution Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[34, 52, 54, 41], Operations: [] Exploring Operation: 34+41=75, Resulting Numbers: [52, 54, 75] Generated Node #0,1: 73:[52, 54, 75] Operation: 34+41=75 Moving to Node #0,1 Current State: 73:[52, 54, 75], Operations: ['34+41=75'] Exploring Operation: 75-54=21, Resulting Numbers: [52, 21] Generated Node #0,1,1: 73:[52, 21] Operation: 75-54=21 Moving to Node #0,1,1 Current State: 73:[52, 21], Operations: ['34+41=75', '75-54=21'] Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 31, 62, 44, 19 ]
61
[ "62/31=2", "44+19=63", "63-2=61" ]
Current State: 61:[31, 62, 44, 19], Operations: [] Exploring Operation: 62/31=2, Resulting Numbers: [44, 19, 2] Generated Node #2: [44, 19, 2] from Operation: 62/31=2 Current State: 61:[44, 19, 2], Operations: ['62/31=2'] Exploring Operation: 44+19=63, Resulting Numbers: [2, 63] Generated Node #3: [2, 63] from Operation: 44+19=63 Current State: 61:[2, 63], Operations: ['62/31=2', '44+19=63'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[31, 62, 44, 19], Operations: [] Exploring Operation: 31+19=50, Resulting Numbers: [62, 44, 50] Generated Node #0,0: 61:[62, 44, 50] Operation: 31+19=50 Exploring Operation: 31+44=75, Resulting Numbers: [62, 19, 75] Generated Node #0,1: 61:[62, 19, 75] Operation: 31+44=75 Exploring Operation: 44+19=63, Resulting Numbers: [31, 62, 63] Generated Node #0,2: 61:[31, 62, 63] Operation: 44+19=63 Moving to Node #0,0 Current State: 61:[62, 44, 50], Operations: ['31+19=50'] Exploring Operation: 62-44=18, Resulting Numbers: [50, 18] Generated Node #0,0,0: 61:[50, 18] Operation: 62-44=18 Exploring Operation: 62+44=106, Resulting Numbers: [50, 106] Generated Node #0,0,1: 61:[50, 106] Operation: 62+44=106 Exploring Operation: 44+50=94, Resulting Numbers: [62, 94] Generated Node #0,0,2: 61:[62, 94] Operation: 44+50=94 Moving to Node #0,2 Current State: 61:[31, 62, 63], Operations: ['44+19=63'] Exploring Operation: 31+62=93, Resulting Numbers: [63, 93] Generated Node #0,2,0: 61:[63, 93] Operation: 31+62=93 Exploring Operation: 63-31=32, Resulting Numbers: [62, 32] Generated Node #0,2,1: 61:[62, 32] Operation: 63-31=32 Exploring Operation: 62-31=31, Resulting Numbers: [63, 31] Generated Node #0,2,2: 61:[63, 31] Operation: 62-31=31 Moving to Node #0,1 Current State: 61:[62, 19, 75], Operations: ['31+44=75'] Exploring Operation: 75-19=56, Resulting Numbers: [62, 56] Generated Node #0,1,0: 61:[62, 56] Operation: 75-19=56 Exploring Operation: 62+19=81, Resulting Numbers: [75, 81] Generated Node #0,1,1: 61:[75, 81] Operation: 62+19=81 Exploring Operation: 62-19=43, Resulting Numbers: [75, 43] Generated Node #0,1,2: 61:[75, 43] Operation: 62-19=43 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 61:[62, 56], Operations: ['31+44=75', '75-19=56'] Exploring Operation: 62*56=3472, Resulting Numbers: [3472] 3472,61 unequal: No Solution Exploring Operation: 62+56=118, Resulting Numbers: [118] 118,61 unequal: No Solution Exploring Operation: 62-56=6, Resulting Numbers: [6] 6,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 61:[75, 43], Operations: ['31+44=75', '62-19=43'] Exploring Operation: 75-43=32, Resulting Numbers: [32] 32,61 unequal: No Solution Exploring Operation: 75*43=3225, Resulting Numbers: [3225] 3225,61 unequal: No Solution Exploring Operation: 75+43=118, Resulting Numbers: [118] 118,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[75, 81], Operations: ['31+44=75', '62+19=81'] Exploring Operation: 75+81=156, Resulting Numbers: [156] 156,61 unequal: No Solution Exploring Operation: 81-75=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 75*81=6075, Resulting Numbers: [6075] 6075,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 61:[62, 32], Operations: ['44+19=63', '63-31=32'] Exploring Operation: 62+32=94, Resulting Numbers: [94] 94,61 unequal: No Solution Exploring Operation: 62*32=1984, Resulting Numbers: [1984] 1984,61 unequal: No Solution Exploring Operation: 62-32=30, Resulting Numbers: [30] 30,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[63, 31], Operations: ['44+19=63', '62-31=31'] Exploring Operation: 63-31=32, Resulting Numbers: [32] 32,61 unequal: No Solution Exploring Operation: 63+31=94, Resulting Numbers: [94] 94,61 unequal: No Solution Exploring Operation: 63*31=1953, Resulting Numbers: [1953] 1953,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[63, 93], Operations: ['44+19=63', '31+62=93'] Exploring Operation: 63*93=5859, Resulting Numbers: [5859] 5859,61 unequal: No Solution Exploring Operation: 93-63=30, Resulting Numbers: [30] 30,61 unequal: No Solution Exploring Operation: 63+93=156, Resulting Numbers: [156] 156,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[62, 94], Operations: ['31+19=50', '44+50=94'] Exploring Operation: 62*94=5828, Resulting Numbers: [5828] 5828,61 unequal: No Solution Exploring Operation: 62+94=156, Resulting Numbers: [156] 156,61 unequal: No Solution Exploring Operation: 94-62=32, Resulting Numbers: [32] 32,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[50, 18], Operations: ['31+19=50', '62-44=18'] Exploring Operation: 50+18=68, Resulting Numbers: [68] 68,61 unequal: No Solution Exploring Operation: 50*18=900, Resulting Numbers: [900] 900,61 unequal: No Solution Exploring Operation: 50-18=32, Resulting Numbers: [32] 32,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[50, 106], Operations: ['31+19=50', '62+44=106'] Exploring Operation: 106-50=56, Resulting Numbers: [56] 56,61 unequal: No Solution Exploring Operation: 50+106=156, Resulting Numbers: [156] 156,61 unequal: No Solution Exploring Operation: 50*106=5300, Resulting Numbers: [5300] 5300,61 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 76, 54, 8, 51 ]
71
[ "76+54=130", "8+51=59", "130-59=71" ]
Current State: 71:[76, 54, 8, 51], Operations: [] Exploring Operation: 76+54=130, Resulting Numbers: [8, 51, 130] Generated Node #2: [8, 51, 130] from Operation: 76+54=130 Current State: 71:[8, 51, 130], Operations: ['76+54=130'] Exploring Operation: 8+51=59, Resulting Numbers: [130, 59] Generated Node #3: [130, 59] from Operation: 8+51=59 Current State: 71:[130, 59], Operations: ['76+54=130', '8+51=59'] Exploring Operation: 130-59=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[76, 54, 8, 51], Operations: [] Exploring Operation: 54+8=62, Resulting Numbers: [76, 51, 62] Generated Node #0,0: 71:[76, 51, 62] Operation: 54+8=62 Moving to Node #0,0 Current State: 71:[76, 51, 62], Operations: ['54+8=62'] Exploring Operation: 51+62=113, Resulting Numbers: [76, 113] Generated Node #0,0,0: 71:[76, 113] Operation: 51+62=113 Moving to Node #0,0,0 Current State: 71:[76, 113], Operations: ['54+8=62', '51+62=113'] Exploring Operation: 113-76=37, Resulting Numbers: [37] 37,71 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 24, 8, 52, 10 ]
26
[ "24-8=16", "52-10=42", "42-16=26" ]
Current State: 26:[24, 8, 52, 10], Operations: [] Exploring Operation: 24-8=16, Resulting Numbers: [52, 10, 16] Generated Node #2: [52, 10, 16] from Operation: 24-8=16 Current State: 26:[52, 10, 16], Operations: ['24-8=16'] Exploring Operation: 52-10=42, Resulting Numbers: [16, 42] Generated Node #3: [16, 42] from Operation: 52-10=42 Current State: 26:[16, 42], Operations: ['24-8=16', '52-10=42'] Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[24, 8, 52, 10], Operations: [] Exploring Operation: 52-10=42, Resulting Numbers: [24, 8, 42] Generated Node #0,0: 26:[24, 8, 42] Operation: 52-10=42 Exploring Operation: 10-8=2, Resulting Numbers: [24, 52, 2] Generated Node #0,1: 26:[24, 52, 2] Operation: 10-8=2 Exploring Operation: 52-8=44, Resulting Numbers: [24, 10, 44] Generated Node #0,2: 26:[24, 10, 44] Operation: 52-8=44 Exploring Operation: 52-24=28, Resulting Numbers: [8, 10, 28] Generated Node #0,3: 26:[8, 10, 28] Operation: 52-24=28 Start Sub Search at level 1: Moving to Node #0,3 Current State: 26:[8, 10, 28], Operations: ['52-24=28'] Exploring Operation: 8+10=18, Resulting Numbers: [28, 18] Generated Node #0,3,0: 26:[28, 18] Operation: 8+10=18 Exploring Operation: 28-8=20, Resulting Numbers: [10, 20] Generated Node #0,3,1: 26:[10, 20] Operation: 28-8=20 Exploring Operation: 10-8=2, Resulting Numbers: [28, 2] Generated Node #0,3,2: 26:[28, 2] Operation: 10-8=2 Exploring Operation: 28-10=18, Resulting Numbers: [8, 18] Generated Node #0,3,3: 26:[8, 18] Operation: 28-10=18 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 26:[28, 2], Operations: ['52-24=28', '10-8=2'] Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,26 unequal: No Solution Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[24, 8, 52, 10], Operations: [] Exploring Operation: 52-24=28, Resulting Numbers: [8, 10, 28] Generated Node #0,3: 26:[8, 10, 28] Operation: 52-24=28 Moving to Node #0,3 Current State: 26:[8, 10, 28], Operations: ['52-24=28'] Exploring Operation: 10-8=2, Resulting Numbers: [28, 2] Generated Node #0,3,2: 26:[28, 2] Operation: 10-8=2 Moving to Node #0,3,2 Current State: 26:[28, 2], Operations: ['52-24=28', '10-8=2'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 50, 2, 73, 9 ]
45
[ "50+9=59", "2*59=118", "118-73=45" ]
Current State: 45:[50, 2, 73, 9], Operations: [] Exploring Operation: 50+9=59, Resulting Numbers: [2, 73, 59] Generated Node #2: [2, 73, 59] from Operation: 50+9=59 Current State: 45:[2, 73, 59], Operations: ['50+9=59'] Exploring Operation: 2*59=118, Resulting Numbers: [73, 118] Generated Node #3: [73, 118] from Operation: 2*59=118 Current State: 45:[73, 118], Operations: ['50+9=59', '2*59=118'] Exploring Operation: 118-73=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[50, 2, 73, 9], Operations: [] Exploring Operation: 73-50=23, Resulting Numbers: [2, 9, 23] Generated Node #0,0: 45:[2, 9, 23] Operation: 73-50=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[2, 9, 23], Operations: ['73-50=23'] Exploring Operation: 2*23=46, Resulting Numbers: [9, 46] Generated Node #0,0,0: 45:[9, 46] Operation: 2*23=46 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[9, 46], Operations: ['73-50=23', '2*23=46'] Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 63, 60, 48, 75 ]
73
[ "63-60=3", "75/3=25", "48+25=73" ]
Current State: 73:[63, 60, 48, 75], Operations: [] Exploring Operation: 63-60=3, Resulting Numbers: [48, 75, 3] Generated Node #2: [48, 75, 3] from Operation: 63-60=3 Current State: 73:[48, 75, 3], Operations: ['63-60=3'] Exploring Operation: 75/3=25, Resulting Numbers: [48, 25] Generated Node #3: [48, 25] from Operation: 75/3=25 Current State: 73:[48, 25], Operations: ['63-60=3', '75/3=25'] Exploring Operation: 48+25=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[63, 60, 48, 75], Operations: [] Exploring Operation: 60+48=108, Resulting Numbers: [63, 75, 108] Generated Node #0,0: 73:[63, 75, 108] Operation: 60+48=108 Moving to Node #0,0 Current State: 73:[63, 75, 108], Operations: ['60+48=108'] Exploring Operation: 108-63=45, Resulting Numbers: [75, 45] Generated Node #0,0,0: 73:[75, 45] Operation: 108-63=45 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[75, 45], Operations: ['60+48=108', '108-63=45'] Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 90, 40, 83, 52 ]
19
[ "90-40=50", "83-52=31", "50-31=19" ]
Current State: 19:[90, 40, 83, 52], Operations: [] Exploring Operation: 90-40=50, Resulting Numbers: [83, 52, 50] Generated Node #2: [83, 52, 50] from Operation: 90-40=50 Current State: 19:[83, 52, 50], Operations: ['90-40=50'] Exploring Operation: 83-52=31, Resulting Numbers: [50, 31] Generated Node #3: [50, 31] from Operation: 83-52=31 Current State: 19:[50, 31], Operations: ['90-40=50', '83-52=31'] Exploring Operation: 50-31=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[90, 40, 83, 52], Operations: [] Exploring Operation: 90-83=7, Resulting Numbers: [40, 52, 7] Generated Node #0,0: 19:[40, 52, 7] Operation: 90-83=7 Moving to Node #0,0 Current State: 19:[40, 52, 7], Operations: ['90-83=7'] Exploring Operation: 52-40=12, Resulting Numbers: [7, 12] Generated Node #0,0,0: 19:[7, 12] Operation: 52-40=12 Moving to Node #0,0,0 Current State: 19:[7, 12], Operations: ['90-83=7', '52-40=12'] Exploring Operation: 7+12=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[90, 40, 83, 52], Operations: [] Exploring Operation: 90-83=7, Resulting Numbers: [40, 52, 7] Generated Node #0,0: 19:[40, 52, 7] Operation: 90-83=7 Moving to Node #0,0 Current State: 19:[40, 52, 7], Operations: ['90-83=7'] Exploring Operation: 52-40=12, Resulting Numbers: [7, 12] Generated Node #0,0,0: 19:[7, 12] Operation: 52-40=12 Moving to Node #0,0,0 Current State: 19:[7, 12], Operations: ['90-83=7', '52-40=12'] Exploring Operation: 7+12=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 33, 13, 12, 30 ]
75
[ "33-30=3", "13+12=25", "3*25=75" ]
Current State: 75:[33, 13, 12, 30], Operations: [] Exploring Operation: 33-30=3, Resulting Numbers: [13, 12, 3] Generated Node #2: [13, 12, 3] from Operation: 33-30=3 Current State: 75:[13, 12, 3], Operations: ['33-30=3'] Exploring Operation: 13+12=25, Resulting Numbers: [3, 25] Generated Node #3: [3, 25] from Operation: 13+12=25 Current State: 75:[3, 25], Operations: ['33-30=3', '13+12=25'] Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[33, 13, 12, 30], Operations: [] Exploring Operation: 33-12=21, Resulting Numbers: [13, 30, 21] Generated Node #0,0: 75:[13, 30, 21] Operation: 33-12=21 Exploring Operation: 33-30=3, Resulting Numbers: [13, 12, 3] Generated Node #0,1: 75:[13, 12, 3] Operation: 33-30=3 Moving to Node #0,1 Current State: 75:[13, 12, 3], Operations: ['33-30=3'] Exploring Operation: 13+12=25, Resulting Numbers: [3, 25] Generated Node #0,1,0: 75:[3, 25] Operation: 13+12=25 Exploring Operation: 13-12=1, Resulting Numbers: [3, 1] Generated Node #0,1,1: 75:[3, 1] Operation: 13-12=1 Moving to Node #0,0 Current State: 75:[13, 30, 21], Operations: ['33-12=21'] Exploring Operation: 30-21=9, Resulting Numbers: [13, 9] Generated Node #0,0,0: 75:[13, 9] Operation: 30-21=9 Exploring Operation: 30-13=17, Resulting Numbers: [21, 17] Generated Node #0,0,1: 75:[21, 17] Operation: 30-13=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[13, 9], Operations: ['33-12=21', '30-21=9'] Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,75 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 #0,0,1 Current State: 75:[21, 17], Operations: ['33-12=21', '30-13=17'] Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 21+17=38, Resulting Numbers: [38] 38,75 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: 75:[3, 25], Operations: ['33-30=3', '13+12=25'] Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[33, 13, 12, 30], Operations: [] Exploring Operation: 33-30=3, Resulting Numbers: [13, 12, 3] Generated Node #0,1: 75:[13, 12, 3] Operation: 33-30=3 Moving to Node #0,1 Current State: 75:[13, 12, 3], Operations: ['33-30=3'] Exploring Operation: 13+12=25, Resulting Numbers: [3, 25] Generated Node #0,1,0: 75:[3, 25] Operation: 13+12=25 Moving to Node #0,1,0 Current State: 75:[3, 25], Operations: ['33-30=3', '13+12=25'] Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 61, 45, 18, 64 ]
30
[ "61-45=16", "64-18=46", "46-16=30" ]
Current State: 30:[61, 45, 18, 64], Operations: [] Exploring Operation: 61-45=16, Resulting Numbers: [18, 64, 16] Generated Node #2: [18, 64, 16] from Operation: 61-45=16 Current State: 30:[18, 64, 16], Operations: ['61-45=16'] Exploring Operation: 64-18=46, Resulting Numbers: [16, 46] Generated Node #3: [16, 46] from Operation: 64-18=46 Current State: 30:[16, 46], Operations: ['61-45=16', '64-18=46'] Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[61, 45, 18, 64], Operations: [] Exploring Operation: 64-45=19, Resulting Numbers: [61, 18, 19] Generated Node #0,0: 30:[61, 18, 19] Operation: 64-45=19 Exploring Operation: 61-18=43, Resulting Numbers: [45, 64, 43] Generated Node #0,1: 30:[45, 64, 43] Operation: 61-18=43 Exploring Operation: 61-45=16, Resulting Numbers: [18, 64, 16] Generated Node #0,2: 30:[18, 64, 16] Operation: 61-45=16 Exploring Operation: 64-61=3, Resulting Numbers: [45, 18, 3] Generated Node #0,3: 30:[45, 18, 3] Operation: 64-61=3 Exploring Operation: 64-18=46, Resulting Numbers: [61, 45, 46] Generated Node #0,4: 30:[61, 45, 46] Operation: 64-18=46 Moving to Node #0,3 Current State: 30:[45, 18, 3], Operations: ['64-61=3'] Exploring Operation: 45/3=15, Resulting Numbers: [18, 15] Generated Node #0,3,0: 30:[18, 15] Operation: 45/3=15 Exploring Operation: 45-18=27, Resulting Numbers: [3, 27] Generated Node #0,3,1: 30:[3, 27] Operation: 45-18=27 Exploring Operation: 18/3=6, Resulting Numbers: [45, 6] Generated Node #0,3,2: 30:[45, 6] Operation: 18/3=6 Exploring Operation: 45-3=42, Resulting Numbers: [18, 42] Generated Node #0,3,3: 30:[18, 42] Operation: 45-3=42 Exploring Operation: 18-3=15, Resulting Numbers: [45, 15] Generated Node #0,3,4: 30:[45, 15] Operation: 18-3=15 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 30:[18, 15], Operations: ['64-61=3', '45/3=15'] Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,30 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,30 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:[3, 27], Operations: ['64-61=3', '45-18=27'] Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,30 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[61, 45, 18, 64], Operations: [] Exploring Operation: 64-61=3, Resulting Numbers: [45, 18, 3] Generated Node #0,3: 30:[45, 18, 3] Operation: 64-61=3 Moving to Node #0,3 Current State: 30:[45, 18, 3], Operations: ['64-61=3'] Exploring Operation: 45-18=27, Resulting Numbers: [3, 27] Generated Node #0,3,1: 30:[3, 27] Operation: 45-18=27 Moving to Node #0,3,1 Current State: 30:[3, 27], Operations: ['64-61=3', '45-18=27'] Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 8, 45, 38, 56 ]
57
[ "45-8=37", "38+56=94", "94-37=57" ]
Current State: 57:[8, 45, 38, 56], Operations: [] Exploring Operation: 45-8=37, Resulting Numbers: [38, 56, 37] Generated Node #2: [38, 56, 37] from Operation: 45-8=37 Current State: 57:[38, 56, 37], Operations: ['45-8=37'] Exploring Operation: 38+56=94, Resulting Numbers: [37, 94] Generated Node #3: [37, 94] from Operation: 38+56=94 Current State: 57:[37, 94], Operations: ['45-8=37', '38+56=94'] Exploring Operation: 94-37=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[8, 45, 38, 56], Operations: [] Exploring Operation: 56-38=18, Resulting Numbers: [8, 45, 18] Generated Node #0,0: 57:[8, 45, 18] Operation: 56-38=18 Exploring Operation: 45-38=7, Resulting Numbers: [8, 56, 7] Generated Node #0,1: 57:[8, 56, 7] Operation: 45-38=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[8, 56, 7], Operations: ['45-38=7'] Exploring Operation: 8*7=56, Resulting Numbers: [56, 56] Generated Node #0,1,0: 57:[56, 56] Operation: 8*7=56 Exploring Operation: 8-7=1, Resulting Numbers: [56, 1] Generated Node #0,1,1: 57:[56, 1] Operation: 8-7=1 Moving to Node #0,1,0 Current State: 57:[56, 56], Operations: ['45-38=7', '8*7=56'] Exploring Operation: 56-56=0, Resulting Numbers: [0] 0,57 unequal: No Solution Exploring Operation: 56/56=1, Resulting Numbers: [1] 1,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[56, 1], Operations: ['45-38=7', '8-7=1'] Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[8, 45, 38, 56], Operations: [] Exploring Operation: 45-38=7, Resulting Numbers: [8, 56, 7] Generated Node #0,1: 57:[8, 56, 7] Operation: 45-38=7 Moving to Node #0,1 Current State: 57:[8, 56, 7], Operations: ['45-38=7'] Exploring Operation: 8-7=1, Resulting Numbers: [56, 1] Generated Node #0,1,1: 57:[56, 1] Operation: 8-7=1 Moving to Node #0,1,1 Current State: 57:[56, 1], Operations: ['45-38=7', '8-7=1'] Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 45, 35, 23, 24 ]
90
[ "45*24=1080", "35-23=12", "1080/12=90" ]
Current State: 90:[45, 35, 23, 24], Operations: [] Exploring Operation: 45*24=1080, Resulting Numbers: [35, 23, 1080] Generated Node #2: [35, 23, 1080] from Operation: 45*24=1080 Current State: 90:[35, 23, 1080], Operations: ['45*24=1080'] Exploring Operation: 35-23=12, Resulting Numbers: [1080, 12] Generated Node #3: [1080, 12] from Operation: 35-23=12 Current State: 90:[1080, 12], Operations: ['45*24=1080', '35-23=12'] Exploring Operation: 1080/12=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[45, 35, 23, 24], Operations: [] Exploring Operation: 35-24=11, Resulting Numbers: [45, 23, 11] Generated Node #0,0: 90:[45, 23, 11] Operation: 35-24=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[45, 23, 11], Operations: ['35-24=11'] Exploring Operation: 23-11=12, Resulting Numbers: [45, 12] Generated Node #0,0,0: 90:[45, 12] Operation: 23-11=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[45, 12], Operations: ['35-24=11', '23-11=12'] Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 80, 91, 1, 20 ]
88
[ "80/20=4", "91+1=92", "92-4=88" ]
Current State: 88:[80, 91, 1, 20], Operations: [] Exploring Operation: 80/20=4, Resulting Numbers: [91, 1, 4] Generated Node #2: [91, 1, 4] from Operation: 80/20=4 Current State: 88:[91, 1, 4], Operations: ['80/20=4'] Exploring Operation: 91+1=92, Resulting Numbers: [4, 92] Generated Node #3: [4, 92] from Operation: 91+1=92 Current State: 88:[4, 92], Operations: ['80/20=4', '91+1=92'] Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[80, 91, 1, 20], Operations: [] Exploring Operation: 80/20=4, Resulting Numbers: [91, 1, 4] Generated Node #0,0: 88:[91, 1, 4] Operation: 80/20=4 Exploring Operation: 91-80=11, Resulting Numbers: [1, 20, 11] Generated Node #0,1: 88:[1, 20, 11] Operation: 91-80=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[1, 20, 11], Operations: ['91-80=11'] Exploring Operation: 1+20=21, Resulting Numbers: [11, 21] Generated Node #0,1,0: 88:[11, 21] Operation: 1+20=21 Exploring Operation: 1*20=20, Resulting Numbers: [11, 20] Generated Node #0,1,1: 88:[11, 20] Operation: 1*20=20 Moving to Node #0,1,0 Current State: 88:[11, 21], Operations: ['91-80=11', '1+20=21'] Exploring Operation: 11+21=32, Resulting Numbers: [32] 32,88 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[11, 20], Operations: ['91-80=11', '1*20=20'] Exploring Operation: 11+20=31, Resulting Numbers: [31] 31,88 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,88 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 #0,0 Current State: 88:[91, 1, 4], Operations: ['80/20=4'] Exploring Operation: 91-4=87, Resulting Numbers: [1, 87] Generated Node #0,0,0: 88:[1, 87] Operation: 91-4=87 Exploring Operation: 91-1=90, Resulting Numbers: [4, 90] Generated Node #0,0,1: 88:[4, 90] Operation: 91-1=90 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[1, 87], Operations: ['80/20=4', '91-4=87'] Exploring Operation: 1*87=87, Resulting Numbers: [87] 87,88 unequal: No Solution Exploring Operation: 1+87=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[80, 91, 1, 20], Operations: [] Exploring Operation: 80/20=4, Resulting Numbers: [91, 1, 4] Generated Node #0,0: 88:[91, 1, 4] Operation: 80/20=4 Moving to Node #0,0 Current State: 88:[91, 1, 4], Operations: ['80/20=4'] Exploring Operation: 91-4=87, Resulting Numbers: [1, 87] Generated Node #0,0,0: 88:[1, 87] Operation: 91-4=87 Moving to Node #0,0,0 Current State: 88:[1, 87], Operations: ['80/20=4', '91-4=87'] Exploring Operation: 1+87=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 36, 35, 94, 63 ]
86
[ "36+35=71", "94+63=157", "157-71=86" ]
Current State: 86:[36, 35, 94, 63], Operations: [] Exploring Operation: 36+35=71, Resulting Numbers: [94, 63, 71] Generated Node #2: [94, 63, 71] from Operation: 36+35=71 Current State: 86:[94, 63, 71], Operations: ['36+35=71'] Exploring Operation: 94+63=157, Resulting Numbers: [71, 157] Generated Node #3: [71, 157] from Operation: 94+63=157 Current State: 86:[71, 157], Operations: ['36+35=71', '94+63=157'] Exploring Operation: 157-71=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[36, 35, 94, 63], Operations: [] Exploring Operation: 63-35=28, Resulting Numbers: [36, 94, 28] Generated Node #0,0: 86:[36, 94, 28] Operation: 63-35=28 Exploring Operation: 35+63=98, Resulting Numbers: [36, 94, 98] Generated Node #0,1: 86:[36, 94, 98] Operation: 35+63=98 Exploring Operation: 36+63=99, Resulting Numbers: [35, 94, 99] Generated Node #0,2: 86:[35, 94, 99] Operation: 36+63=99 Exploring Operation: 36-35=1, Resulting Numbers: [94, 63, 1] Generated Node #0,3: 86:[94, 63, 1] Operation: 36-35=1 Exploring Operation: 94-63=31, Resulting Numbers: [36, 35, 31] Generated Node #0,4: 86:[36, 35, 31] Operation: 94-63=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[36, 94, 98], Operations: ['35+63=98'] Exploring Operation: 98-36=62, Resulting Numbers: [94, 62] Generated Node #0,1,0: 86:[94, 62] Operation: 98-36=62 Exploring Operation: 98-94=4, Resulting Numbers: [36, 4] Generated Node #0,1,1: 86:[36, 4] Operation: 98-94=4 Exploring Operation: 94-36=58, Resulting Numbers: [98, 58] Generated Node #0,1,2: 86:[98, 58] Operation: 94-36=58 Exploring Operation: 36+94=130, Resulting Numbers: [98, 130] Generated Node #0,1,3: 86:[98, 130] Operation: 36+94=130 Exploring Operation: 36+98=134, Resulting Numbers: [94, 134] Generated Node #0,1,4: 86:[94, 134] Operation: 36+98=134 Moving to Node #0,1,1 Current State: 86:[36, 4], Operations: ['35+63=98', '98-94=4'] Exploring Operation: 36+4=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 36*4=144, Resulting Numbers: [144] 144,86 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,86 unequal: No Solution Moving to Node #0,1,2 Current State: 86:[98, 58], Operations: ['35+63=98', '94-36=58'] Exploring Operation: 98+58=156, Resulting Numbers: [156] 156,86 unequal: No Solution Exploring Operation: 98*58=5684, Resulting Numbers: [5684] 5684,86 unequal: No Solution Exploring Operation: 98-58=40, Resulting Numbers: [40] 40,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[94, 62], Operations: ['35+63=98', '98-36=62'] Exploring Operation: 94*62=5828, Resulting Numbers: [5828] 5828,86 unequal: No Solution Exploring Operation: 94-62=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 94+62=156, Resulting Numbers: [156] 156,86 unequal: No Solution Moving to Node #0,1,3 Current State: 86:[98, 130], Operations: ['35+63=98', '36+94=130'] Exploring Operation: 98*130=12740, Resulting Numbers: [12740] 12740,86 unequal: No Solution Exploring Operation: 130-98=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 98+130=228, Resulting Numbers: [228] 228,86 unequal: No Solution Moving to Node #0,1,4 Current State: 86:[94, 134], Operations: ['35+63=98', '36+98=134'] Exploring Operation: 134-94=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 94+134=228, Resulting Numbers: [228] 228,86 unequal: No Solution Exploring Operation: 94*134=12596, Resulting Numbers: [12596] 12596,86 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:[36, 35, 31], Operations: ['94-63=31'] Exploring Operation: 35-31=4, Resulting Numbers: [36, 4] Generated Node #0,4,0: 86:[36, 4] Operation: 35-31=4 Exploring Operation: 36+35=71, Resulting Numbers: [31, 71] Generated Node #0,4,1: 86:[31, 71] Operation: 36+35=71 Exploring Operation: 36-35=1, Resulting Numbers: [31, 1] Generated Node #0,4,2: 86:[31, 1] Operation: 36-35=1 Exploring Operation: 36-31=5, Resulting Numbers: [35, 5] Generated Node #0,4,3: 86:[35, 5] Operation: 36-31=5 Exploring Operation: 36+31=67, Resulting Numbers: [35, 67] Generated Node #0,4,4: 86:[35, 67] Operation: 36+31=67 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 86:[36, 4], Operations: ['94-63=31', '35-31=4'] Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 36*4=144, Resulting Numbers: [144] 144,86 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 36+4=40, Resulting Numbers: [40] 40,86 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:[35, 5], Operations: ['94-63=31', '36-31=5'] Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,86 unequal: No Solution Exploring Operation: 35*5=175, Resulting Numbers: [175] 175,86 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 #0,4,2 Current State: 86:[31, 1], Operations: ['94-63=31', '36-35=1'] Exploring Operation: 31*1=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 31-1=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 31+1=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 #0,4,1 Current State: 86:[31, 71], Operations: ['94-63=31', '36+35=71'] Exploring Operation: 31*71=2201, Resulting Numbers: [2201] 2201,86 unequal: No Solution Exploring Operation: 31+71=102, Resulting Numbers: [102] 102,86 unequal: No Solution Exploring Operation: 71-31=40, Resulting Numbers: [40] 40,86 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:[35, 67], Operations: ['94-63=31', '36+31=67'] Exploring Operation: 35*67=2345, Resulting Numbers: [2345] 2345,86 unequal: No Solution Exploring Operation: 67-35=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 35+67=102, Resulting Numbers: [102] 102,86 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:[35, 94, 99], Operations: ['36+63=99'] Exploring Operation: 99-35=64, Resulting Numbers: [94, 64] Generated Node #0,2,0: 86:[94, 64] Operation: 99-35=64 Exploring Operation: 35+99=134, Resulting Numbers: [94, 134] Generated Node #0,2,1: 86:[94, 134] Operation: 35+99=134 Exploring Operation: 94-35=59, Resulting Numbers: [99, 59] Generated Node #0,2,2: 86:[99, 59] Operation: 94-35=59 Exploring Operation: 99-94=5, Resulting Numbers: [35, 5] Generated Node #0,2,3: 86:[35, 5] Operation: 99-94=5 Exploring Operation: 35+94=129, Resulting Numbers: [99, 129] Generated Node #0,2,4: 86:[99, 129] Operation: 35+94=129 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 86:[35, 5], Operations: ['36+63=99', '99-94=5'] Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,86 unequal: No Solution Exploring Operation: 35*5=175, Resulting Numbers: [175] 175,86 unequal: No Solution Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 86:[94, 64], Operations: ['36+63=99', '99-35=64'] Exploring Operation: 94+64=158, Resulting Numbers: [158] 158,86 unequal: No Solution Exploring Operation: 94-64=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 94*64=6016, Resulting Numbers: [6016] 6016,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 86:[99, 59], Operations: ['36+63=99', '94-35=59'] Exploring Operation: 99*59=5841, Resulting Numbers: [5841] 5841,86 unequal: No Solution Exploring Operation: 99+59=158, Resulting Numbers: [158] 158,86 unequal: No Solution Exploring Operation: 99-59=40, Resulting Numbers: [40] 40,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 86:[94, 134], Operations: ['36+63=99', '35+99=134'] Exploring Operation: 94*134=12596, Resulting Numbers: [12596] 12596,86 unequal: No Solution Exploring Operation: 94+134=228, Resulting Numbers: [228] 228,86 unequal: No Solution Exploring Operation: 134-94=40, Resulting Numbers: [40] 40,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 86:[99, 129], Operations: ['36+63=99', '35+94=129'] Exploring Operation: 99*129=12771, Resulting Numbers: [12771] 12771,86 unequal: No Solution Exploring Operation: 99+129=228, Resulting Numbers: [228] 228,86 unequal: No Solution Exploring Operation: 129-99=30, Resulting Numbers: [30] 30,86 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:[94, 63, 1], Operations: ['36-35=1'] Exploring Operation: 94*1=94, Resulting Numbers: [63, 94] Generated Node #0,3,0: 86:[63, 94] Operation: 94*1=94 Exploring Operation: 94-1=93, Resulting Numbers: [63, 93] Generated Node #0,3,1: 86:[63, 93] Operation: 94-1=93 Exploring Operation: 63-1=62, Resulting Numbers: [94, 62] Generated Node #0,3,2: 86:[94, 62] Operation: 63-1=62 Exploring Operation: 94/1=94, Resulting Numbers: [63, 94] Generated Node #0,3,3: 86:[63, 94] Operation: 94/1=94 Exploring Operation: 94-63=31, Resulting Numbers: [1, 31] Generated Node #0,3,4: 86:[1, 31] Operation: 94-63=31 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 86:[1, 31], Operations: ['36-35=1', '94-63=31'] Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 31-1=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 1+31=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 1*31=31, Resulting Numbers: [31] 31,86 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:[63, 93], Operations: ['36-35=1', '94-1=93'] Exploring Operation: 63*93=5859, Resulting Numbers: [5859] 5859,86 unequal: No Solution Exploring Operation: 93-63=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 63+93=156, Resulting Numbers: [156] 156,86 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:[94, 62], Operations: ['36-35=1', '63-1=62'] Exploring Operation: 94*62=5828, Resulting Numbers: [5828] 5828,86 unequal: No Solution Exploring Operation: 94+62=156, Resulting Numbers: [156] 156,86 unequal: No Solution Exploring Operation: 94-62=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 #0,3,0 Current State: 86:[63, 94], Operations: ['36-35=1', '94*1=94'] Exploring Operation: 63*94=5922, Resulting Numbers: [5922] 5922,86 unequal: No Solution Exploring Operation: 63+94=157, Resulting Numbers: [157] 157,86 unequal: No Solution Exploring Operation: 94-63=31, Resulting Numbers: [31] 31,86 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 #0,3,3 Current State: 86:[63, 94], Operations: ['36-35=1', '94/1=94'] Exploring Operation: 63+94=157, Resulting Numbers: [157] 157,86 unequal: No Solution Exploring Operation: 94-63=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 63*94=5922, Resulting Numbers: [5922] 5922,86 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 #0,0 Current State: 86:[36, 94, 28], Operations: ['63-35=28'] Exploring Operation: 36-28=8, Resulting Numbers: [94, 8] Generated Node #0,0,0: 86:[94, 8] Operation: 36-28=8 Exploring Operation: 94-28=66, Resulting Numbers: [36, 66] Generated Node #0,0,1: 86:[36, 66] Operation: 94-28=66 Exploring Operation: 94+28=122, Resulting Numbers: [36, 122] Generated Node #0,0,2: 86:[36, 122] Operation: 94+28=122 Exploring Operation: 36+28=64, Resulting Numbers: [94, 64] Generated Node #0,0,3: 86:[94, 64] Operation: 36+28=64 Exploring Operation: 94-36=58, Resulting Numbers: [28, 58] Generated Node #0,0,4: 86:[28, 58] Operation: 94-36=58 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[94, 8], Operations: ['63-35=28', '36-28=8'] Exploring Operation: 94+8=102, Resulting Numbers: [102] 102,86 unequal: No Solution Exploring Operation: 94*8=752, Resulting Numbers: [752] 752,86 unequal: No Solution Exploring Operation: 94-8=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[36, 35, 94, 63], Operations: [] Exploring Operation: 63-35=28, Resulting Numbers: [36, 94, 28] Generated Node #0,0: 86:[36, 94, 28] Operation: 63-35=28 Moving to Node #0,0 Current State: 86:[36, 94, 28], Operations: ['63-35=28'] Exploring Operation: 36-28=8, Resulting Numbers: [94, 8] Generated Node #0,0,0: 86:[94, 8] Operation: 36-28=8 Moving to Node #0,0,0 Current State: 86:[94, 8], Operations: ['63-35=28', '36-28=8'] Exploring Operation: 94-8=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.91059
hs_5
sum_heuristic
[ 41, 86, 56, 51 ]
62
[ "86-41=45", "56+51=107", "107-45=62" ]
Current State: 62:[41, 86, 56, 51], Operations: [] Exploring Operation: 86-41=45, Resulting Numbers: [56, 51, 45] Generated Node #2: [56, 51, 45] from Operation: 86-41=45 Current State: 62:[56, 51, 45], Operations: ['86-41=45'] Exploring Operation: 56+51=107, Resulting Numbers: [45, 107] Generated Node #3: [45, 107] from Operation: 56+51=107 Current State: 62:[45, 107], Operations: ['86-41=45', '56+51=107'] Exploring Operation: 107-45=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[41, 86, 56, 51], Operations: [] Exploring Operation: 86-51=35, Resulting Numbers: [41, 56, 35] Generated Node #0,0: 62:[41, 56, 35] Operation: 86-51=35 Exploring Operation: 86-41=45, Resulting Numbers: [56, 51, 45] Generated Node #0,1: 62:[56, 51, 45] Operation: 86-41=45 Exploring Operation: 86-56=30, Resulting Numbers: [41, 51, 30] Generated Node #0,2: 62:[41, 51, 30] Operation: 86-56=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[41, 56, 35], Operations: ['86-51=35'] Exploring Operation: 41-35=6, Resulting Numbers: [56, 6] Generated Node #0,0,0: 62:[56, 6] Operation: 41-35=6 Exploring Operation: 56-41=15, Resulting Numbers: [35, 15] Generated Node #0,0,1: 62:[35, 15] Operation: 56-41=15 Exploring Operation: 41+35=76, Resulting Numbers: [56, 76] Generated Node #0,0,2: 62:[56, 76] Operation: 41+35=76 Moving to Node #0,0,0 Current State: 62:[56, 6], Operations: ['86-51=35', '41-35=6'] Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,62 unequal: No Solution Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[41, 86, 56, 51], Operations: [] Exploring Operation: 86-51=35, Resulting Numbers: [41, 56, 35] Generated Node #0,0: 62:[41, 56, 35] Operation: 86-51=35 Moving to Node #0,0 Current State: 62:[41, 56, 35], Operations: ['86-51=35'] Exploring Operation: 41-35=6, Resulting Numbers: [56, 6] Generated Node #0,0,0: 62:[56, 6] Operation: 41-35=6 Moving to Node #0,0,0 Current State: 62:[56, 6], Operations: ['86-51=35', '41-35=6'] Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 29, 78, 12, 24 ]
13
[ "78-29=49", "12+24=36", "49-36=13" ]
Current State: 13:[29, 78, 12, 24], Operations: [] Exploring Operation: 78-29=49, Resulting Numbers: [12, 24, 49] Generated Node #2: [12, 24, 49] from Operation: 78-29=49 Current State: 13:[12, 24, 49], Operations: ['78-29=49'] Exploring Operation: 12+24=36, Resulting Numbers: [49, 36] Generated Node #3: [49, 36] from Operation: 12+24=36 Current State: 13:[49, 36], Operations: ['78-29=49', '12+24=36'] Exploring Operation: 49-36=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[29, 78, 12, 24], Operations: [] Exploring Operation: 78-29=49, Resulting Numbers: [12, 24, 49] Generated Node #0,0: 13:[12, 24, 49] Operation: 78-29=49 Exploring Operation: 78-24=54, Resulting Numbers: [29, 12, 54] Generated Node #0,1: 13:[29, 12, 54] Operation: 78-24=54 Moving to Node #0,0 Current State: 13:[12, 24, 49], Operations: ['78-29=49'] Exploring Operation: 49-24=25, Resulting Numbers: [12, 25] Generated Node #0,0,0: 13:[12, 25] Operation: 49-24=25 Exploring Operation: 49-12=37, Resulting Numbers: [24, 37] Generated Node #0,0,1: 13:[24, 37] Operation: 49-12=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 13:[12, 25], Operations: ['78-29=49', '49-24=25'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[29, 78, 12, 24], Operations: [] Exploring Operation: 78-29=49, Resulting Numbers: [12, 24, 49] Generated Node #0,0: 13:[12, 24, 49] Operation: 78-29=49 Moving to Node #0,0 Current State: 13:[12, 24, 49], Operations: ['78-29=49'] Exploring Operation: 49-24=25, Resulting Numbers: [12, 25] Generated Node #0,0,0: 13:[12, 25] Operation: 49-24=25 Moving to Node #0,0,0 Current State: 13:[12, 25], Operations: ['78-29=49', '49-24=25'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 13, 54, 44, 48 ]
25
[ "13+54=67", "44+48=92", "92-67=25" ]
Current State: 25:[13, 54, 44, 48], Operations: [] Exploring Operation: 13+54=67, Resulting Numbers: [44, 48, 67] Generated Node #2: [44, 48, 67] from Operation: 13+54=67 Current State: 25:[44, 48, 67], Operations: ['13+54=67'] Exploring Operation: 44+48=92, Resulting Numbers: [67, 92] Generated Node #3: [67, 92] from Operation: 44+48=92 Current State: 25:[67, 92], Operations: ['13+54=67', '44+48=92'] Exploring Operation: 92-67=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[13, 54, 44, 48], Operations: [] Exploring Operation: 48-44=4, Resulting Numbers: [13, 54, 4] Generated Node #0,0: 25:[13, 54, 4] Operation: 48-44=4 Exploring Operation: 54-48=6, Resulting Numbers: [13, 44, 6] Generated Node #0,1: 25:[13, 44, 6] Operation: 54-48=6 Exploring Operation: 54-44=10, Resulting Numbers: [13, 48, 10] Generated Node #0,2: 25:[13, 48, 10] Operation: 54-44=10 Exploring Operation: 54-13=41, Resulting Numbers: [44, 48, 41] Generated Node #0,3: 25:[44, 48, 41] Operation: 54-13=41 Moving to Node #0,1 Current State: 25:[13, 44, 6], Operations: ['54-48=6'] Exploring Operation: 44-6=38, Resulting Numbers: [13, 38] Generated Node #0,1,0: 25:[13, 38] Operation: 44-6=38 Exploring Operation: 13-6=7, Resulting Numbers: [44, 7] Generated Node #0,1,1: 25:[44, 7] Operation: 13-6=7 Exploring Operation: 13+6=19, Resulting Numbers: [44, 19] Generated Node #0,1,2: 25:[44, 19] Operation: 13+6=19 Exploring Operation: 44-13=31, Resulting Numbers: [6, 31] Generated Node #0,1,3: 25:[6, 31] Operation: 44-13=31 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 25:[6, 31], Operations: ['54-48=6', '44-13=31'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[13, 54, 44, 48], Operations: [] Exploring Operation: 54-48=6, Resulting Numbers: [13, 44, 6] Generated Node #0,1: 25:[13, 44, 6] Operation: 54-48=6 Moving to Node #0,1 Current State: 25:[13, 44, 6], Operations: ['54-48=6'] Exploring Operation: 44-13=31, Resulting Numbers: [6, 31] Generated Node #0,1,3: 25:[6, 31] Operation: 44-13=31 Moving to Node #0,1,3 Current State: 25:[6, 31], Operations: ['54-48=6', '44-13=31'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 75, 59, 65, 37 ]
86
[ "75-59=16", "65+37=102", "102-16=86" ]
Current State: 86:[75, 59, 65, 37], Operations: [] Exploring Operation: 75-59=16, Resulting Numbers: [65, 37, 16] Generated Node #2: [65, 37, 16] from Operation: 75-59=16 Current State: 86:[65, 37, 16], Operations: ['75-59=16'] Exploring Operation: 65+37=102, Resulting Numbers: [16, 102] Generated Node #3: [16, 102] from Operation: 65+37=102 Current State: 86:[16, 102], Operations: ['75-59=16', '65+37=102'] Exploring Operation: 102-16=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[75, 59, 65, 37], Operations: [] Exploring Operation: 75-65=10, Resulting Numbers: [59, 37, 10] Generated Node #0,0: 86:[59, 37, 10] Operation: 75-65=10 Exploring Operation: 65-59=6, Resulting Numbers: [75, 37, 6] Generated Node #0,1: 86:[75, 37, 6] Operation: 65-59=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[75, 37, 6], Operations: ['65-59=6'] Exploring Operation: 75-37=38, Resulting Numbers: [6, 38] Generated Node #0,1,0: 86:[6, 38] Operation: 75-37=38 Exploring Operation: 75+6=81, Resulting Numbers: [37, 81] Generated Node #0,1,1: 86:[37, 81] Operation: 75+6=81 Moving to Node #0,1,0 Current State: 86:[6, 38], Operations: ['65-59=6', '75-37=38'] Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,86 unequal: No Solution Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[37, 81], Operations: ['65-59=6', '75+6=81'] Exploring Operation: 37+81=118, Resulting Numbers: [118] 118,86 unequal: No Solution Exploring Operation: 81-37=44, Resulting Numbers: [44] 44,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[59, 37, 10], Operations: ['75-65=10'] Exploring Operation: 59-10=49, Resulting Numbers: [37, 49] Generated Node #0,0,0: 86:[37, 49] Operation: 59-10=49 Exploring Operation: 59+37=96, Resulting Numbers: [10, 96] Generated Node #0,0,1: 86:[10, 96] Operation: 59+37=96 Moving to Node #0,0,0 Current State: 86:[37, 49], Operations: ['75-65=10', '59-10=49'] Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,86 unequal: No Solution Exploring Operation: 37+49=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[75, 59, 65, 37], Operations: [] Exploring Operation: 75-65=10, Resulting Numbers: [59, 37, 10] Generated Node #0,0: 86:[59, 37, 10] Operation: 75-65=10 Moving to Node #0,0 Current State: 86:[59, 37, 10], Operations: ['75-65=10'] Exploring Operation: 59-10=49, Resulting Numbers: [37, 49] Generated Node #0,0,0: 86:[37, 49] Operation: 59-10=49 Moving to Node #0,0,0 Current State: 86:[37, 49], Operations: ['75-65=10', '59-10=49'] Exploring Operation: 37+49=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 74, 35, 11, 72 ]
71
[ "35-11=24", "72/24=3", "74-3=71" ]
Current State: 71:[74, 35, 11, 72], Operations: [] Exploring Operation: 35-11=24, Resulting Numbers: [74, 72, 24] Generated Node #2: [74, 72, 24] from Operation: 35-11=24 Current State: 71:[74, 72, 24], Operations: ['35-11=24'] Exploring Operation: 72/24=3, Resulting Numbers: [74, 3] Generated Node #3: [74, 3] from Operation: 72/24=3 Current State: 71:[74, 3], Operations: ['35-11=24', '72/24=3'] Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[74, 35, 11, 72], Operations: [] Exploring Operation: 35+11=46, Resulting Numbers: [74, 72, 46] Generated Node #0,0: 71:[74, 72, 46] Operation: 35+11=46 Moving to Node #0,0 Current State: 71:[74, 72, 46], Operations: ['35+11=46'] Exploring Operation: 74-46=28, Resulting Numbers: [72, 28] Generated Node #0,0,0: 71:[72, 28] Operation: 74-46=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[72, 28], Operations: ['35+11=46', '74-46=28'] Exploring Operation: 72-28=44, Resulting Numbers: [44] 44,71 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
[ 19, 98, 92, 80 ]
55
[ "19+98=117", "92+80=172", "172-117=55" ]
Current State: 55:[19, 98, 92, 80], Operations: [] Exploring Operation: 19+98=117, Resulting Numbers: [92, 80, 117] Generated Node #2: [92, 80, 117] from Operation: 19+98=117 Current State: 55:[92, 80, 117], Operations: ['19+98=117'] Exploring Operation: 92+80=172, Resulting Numbers: [117, 172] Generated Node #3: [117, 172] from Operation: 92+80=172 Current State: 55:[117, 172], Operations: ['19+98=117', '92+80=172'] Exploring Operation: 172-117=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[19, 98, 92, 80], Operations: [] Exploring Operation: 92-80=12, Resulting Numbers: [19, 98, 12] Generated Node #0,0: 55:[19, 98, 12] Operation: 92-80=12 Exploring Operation: 98-92=6, Resulting Numbers: [19, 80, 6] Generated Node #0,1: 55:[19, 80, 6] Operation: 98-92=6 Exploring Operation: 98-80=18, Resulting Numbers: [19, 92, 18] Generated Node #0,2: 55:[19, 92, 18] Operation: 98-80=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[19, 80, 6], Operations: ['98-92=6'] Exploring Operation: 80-19=61, Resulting Numbers: [6, 61] Generated Node #0,1,0: 55:[6, 61] Operation: 80-19=61 Exploring Operation: 80-6=74, Resulting Numbers: [19, 74] Generated Node #0,1,1: 55:[19, 74] Operation: 80-6=74 Exploring Operation: 19-6=13, Resulting Numbers: [80, 13] Generated Node #0,1,2: 55:[80, 13] Operation: 19-6=13 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[6, 61], Operations: ['98-92=6', '80-19=61'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[19, 98, 92, 80], Operations: [] Exploring Operation: 98-92=6, Resulting Numbers: [19, 80, 6] Generated Node #0,1: 55:[19, 80, 6] Operation: 98-92=6 Moving to Node #0,1 Current State: 55:[19, 80, 6], Operations: ['98-92=6'] Exploring Operation: 80-19=61, Resulting Numbers: [6, 61] Generated Node #0,1,0: 55:[6, 61] Operation: 80-19=61 Moving to Node #0,1,0 Current State: 55:[6, 61], Operations: ['98-92=6', '80-19=61'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 60, 66, 18, 68 ]
65
[ "66-60=6", "18/6=3", "68-3=65" ]
Current State: 65:[60, 66, 18, 68], Operations: [] Exploring Operation: 66-60=6, Resulting Numbers: [18, 68, 6] Generated Node #2: [18, 68, 6] from Operation: 66-60=6 Current State: 65:[18, 68, 6], Operations: ['66-60=6'] Exploring Operation: 18/6=3, Resulting Numbers: [68, 3] Generated Node #3: [68, 3] from Operation: 18/6=3 Current State: 65:[68, 3], Operations: ['66-60=6', '18/6=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[60, 66, 18, 68], Operations: [] Exploring Operation: 66-60=6, Resulting Numbers: [18, 68, 6] Generated Node #0,0: 65:[18, 68, 6] Operation: 66-60=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[18, 68, 6], Operations: ['66-60=6'] Exploring Operation: 18-6=12, Resulting Numbers: [68, 12] Generated Node #0,0,0: 65:[68, 12] Operation: 18-6=12 Moving to Node #0,0,0 Current State: 65:[68, 12], Operations: ['66-60=6', '18-6=12'] Exploring Operation: 68-12=56, Resulting Numbers: [56] 56,65 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
[ 36, 11, 32, 20 ]
14
[ "32-20=12", "36/12=3", "11+3=14" ]
Current State: 14:[36, 11, 32, 20], Operations: [] Exploring Operation: 32-20=12, Resulting Numbers: [36, 11, 12] Generated Node #2: [36, 11, 12] from Operation: 32-20=12 Current State: 14:[36, 11, 12], Operations: ['32-20=12'] Exploring Operation: 36/12=3, Resulting Numbers: [11, 3] Generated Node #3: [11, 3] from Operation: 36/12=3 Current State: 14:[11, 3], Operations: ['32-20=12', '36/12=3'] Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[36, 11, 32, 20], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [11, 20, 4] Generated Node #0,0: 14:[11, 20, 4] Operation: 36-32=4 Exploring Operation: 36-20=16, Resulting Numbers: [11, 32, 16] Generated Node #0,1: 14:[11, 32, 16] Operation: 36-20=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[11, 20, 4], Operations: ['36-32=4'] Exploring Operation: 20-11=9, Resulting Numbers: [4, 9] Generated Node #0,0,0: 14:[4, 9] Operation: 20-11=9 Exploring Operation: 20-4=16, Resulting Numbers: [11, 16] Generated Node #0,0,1: 14:[11, 16] Operation: 20-4=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 14:[4, 9], Operations: ['36-32=4', '20-11=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,14 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,14 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 #0,0,1 Current State: 14:[11, 16], Operations: ['36-32=4', '20-4=16'] Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 11+16=27, Resulting Numbers: [27] 27,14 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:[11, 32, 16], Operations: ['36-20=16'] Exploring Operation: 32-16=16, Resulting Numbers: [11, 16] Generated Node #0,1,0: 14:[11, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [11, 2] Generated Node #0,1,1: 14:[11, 2] Operation: 32/16=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 14:[11, 2], Operations: ['36-20=16', '32/16=2'] Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,14 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,14 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 #0,1,0 Current State: 14:[11, 16], Operations: ['36-20=16', '32-16=16'] Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 11+16=27, Resulting Numbers: [27] 27,14 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 No solution found.
0
hs_2
sum_heuristic
[ 51, 80, 51, 28 ]
80
[ "51-51=0", "28*0=0", "80+0=80" ]
Current State: 80:[51, 80, 51, 28], Operations: [] Exploring Operation: 51-51=0, Resulting Numbers: [80, 28, 0] Generated Node #2: [80, 28, 0] from Operation: 51-51=0 Current State: 80:[80, 28, 0], Operations: ['51-51=0'] Exploring Operation: 28*0=0, Resulting Numbers: [80, 0] Generated Node #3: [80, 0] from Operation: 28*0=0 Current State: 80:[80, 0], Operations: ['51-51=0', '28*0=0'] Exploring Operation: 80+0=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[51, 80, 51, 28], Operations: [] Exploring Operation: 51/51=1, Resulting Numbers: [80, 28, 1] Generated Node #0,0: 80:[80, 28, 1] Operation: 51/51=1 Exploring Operation: 51-51=0, Resulting Numbers: [80, 28, 0] Generated Node #0,1: 80:[80, 28, 0] Operation: 51-51=0 Exploring Operation: 51+28=79, Resulting Numbers: [80, 51, 79] Generated Node #0,2: 80:[80, 51, 79] Operation: 51+28=79 Moving to Node #0,0 Current State: 80:[80, 28, 1], Operations: ['51/51=1'] Exploring Operation: 28-1=27, Resulting Numbers: [80, 27] Generated Node #0,0,0: 80:[80, 27] Operation: 28-1=27 Exploring Operation: 80/1=80, Resulting Numbers: [28, 80] Generated Node #0,0,1: 80:[28, 80] Operation: 80/1=80 Exploring Operation: 80*1=80, Resulting Numbers: [28, 80] Generated Node #0,0,2: 80:[28, 80] Operation: 80*1=80 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[80, 27], Operations: ['51/51=1', '28-1=27'] Exploring Operation: 80+27=107, Resulting Numbers: [107] 107,80 unequal: No Solution Exploring Operation: 80-27=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 80*27=2160, Resulting Numbers: [2160] 2160,80 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 #0,0,1 Current State: 80:[28, 80], Operations: ['51/51=1', '80/1=80'] Exploring Operation: 28+80=108, Resulting Numbers: [108] 108,80 unequal: No Solution Exploring Operation: 28*80=2240, Resulting Numbers: [2240] 2240,80 unequal: No Solution Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,80 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 #0,0,2 Current State: 80:[28, 80], Operations: ['51/51=1', '80*1=80'] Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 28+80=108, Resulting Numbers: [108] 108,80 unequal: No Solution Exploring Operation: 28*80=2240, Resulting Numbers: [2240] 2240,80 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: 80:[80, 28, 0], Operations: ['51-51=0'] Exploring Operation: 80-0=80, Resulting Numbers: [28, 80] Generated Node #0,1,0: 80:[28, 80] Operation: 80-0=80 Exploring Operation: 80+0=80, Resulting Numbers: [28, 80] Generated Node #0,1,1: 80:[28, 80] Operation: 80+0=80 Exploring Operation: 28*0=0, Resulting Numbers: [80, 0] Generated Node #0,1,2: 80:[80, 0] Operation: 28*0=0 Moving to Node #0,2 Current State: 80:[80, 51, 79], Operations: ['51+28=79'] Exploring Operation: 80-79=1, Resulting Numbers: [51, 1] Generated Node #0,2,0: 80:[51, 1] Operation: 80-79=1 Exploring Operation: 79-51=28, Resulting Numbers: [80, 28] Generated Node #0,2,1: 80:[80, 28] Operation: 79-51=28 Exploring Operation: 80-51=29, Resulting Numbers: [79, 29] Generated Node #0,2,2: 80:[79, 29] Operation: 80-51=29 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 80:[80, 28], Operations: ['51+28=79', '79-51=28'] Exploring Operation: 80*28=2240, Resulting Numbers: [2240] 2240,80 unequal: No Solution Exploring Operation: 80+28=108, Resulting Numbers: [108] 108,80 unequal: No Solution Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,80 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:[79, 29], Operations: ['51+28=79', '80-51=29'] Exploring Operation: 79+29=108, Resulting Numbers: [108] 108,80 unequal: No Solution Exploring Operation: 79*29=2291, Resulting Numbers: [2291] 2291,80 unequal: No Solution Exploring Operation: 79-29=50, Resulting Numbers: [50] 50,80 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:[51, 1], Operations: ['51+28=79', '80-79=1'] Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,80 unequal: No Solution Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,80 unequal: No Solution Exploring Operation: 51*1=51, Resulting Numbers: [51] 51,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 80:[80, 0], Operations: ['51-51=0', '28*0=0'] Exploring Operation: 80*0=0, Resulting Numbers: [0] 0,80 unequal: No Solution Exploring Operation: 80+0=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[51, 80, 51, 28], Operations: [] Exploring Operation: 51-51=0, Resulting Numbers: [80, 28, 0] Generated Node #0,1: 80:[80, 28, 0] Operation: 51-51=0 Moving to Node #0,1 Current State: 80:[80, 28, 0], Operations: ['51-51=0'] Exploring Operation: 28*0=0, Resulting Numbers: [80, 0] Generated Node #0,1,2: 80:[80, 0] Operation: 28*0=0 Moving to Node #0,1,2 Current State: 80:[80, 0], Operations: ['51-51=0', '28*0=0'] Exploring Operation: 80+0=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
0.96875
hs_3
mult_heuristic
[ 3, 53, 62, 8 ]
47
[ "53-8=45", "45/3=15", "62-15=47" ]
Current State: 47:[3, 53, 62, 8], Operations: [] Exploring Operation: 53-8=45, Resulting Numbers: [3, 62, 45] Generated Node #2: [3, 62, 45] from Operation: 53-8=45 Current State: 47:[3, 62, 45], Operations: ['53-8=45'] Exploring Operation: 45/3=15, Resulting Numbers: [62, 15] Generated Node #3: [62, 15] from Operation: 45/3=15 Current State: 47:[62, 15], Operations: ['53-8=45', '45/3=15'] Exploring Operation: 62-15=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[3, 53, 62, 8], Operations: [] Exploring Operation: 3*8=24, Resulting Numbers: [53, 62, 24] Generated Node #0,0: 47:[53, 62, 24] Operation: 3*8=24 Moving to Node #0,0 Current State: 47:[53, 62, 24], Operations: ['3*8=24'] Exploring Operation: 62-24=38, Resulting Numbers: [53, 38] Generated Node #0,0,0: 47:[53, 38] Operation: 62-24=38 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[53, 38], Operations: ['3*8=24', '62-24=38'] Exploring Operation: 53-38=15, Resulting Numbers: [15] 15,47 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
[ 2, 18, 28, 89 ]
84
[ "28-18=10", "10/2=5", "89-5=84" ]
Current State: 84:[2, 18, 28, 89], Operations: [] Exploring Operation: 28-18=10, Resulting Numbers: [2, 89, 10] Generated Node #2: [2, 89, 10] from Operation: 28-18=10 Current State: 84:[2, 89, 10], Operations: ['28-18=10'] Exploring Operation: 10/2=5, Resulting Numbers: [89, 5] Generated Node #3: [89, 5] from Operation: 10/2=5 Current State: 84:[89, 5], Operations: ['28-18=10', '10/2=5'] Exploring Operation: 89-5=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[2, 18, 28, 89], Operations: [] Exploring Operation: 89-2=87, Resulting Numbers: [18, 28, 87] Generated Node #0,0: 84:[18, 28, 87] Operation: 89-2=87 Exploring Operation: 28-18=10, Resulting Numbers: [2, 89, 10] Generated Node #0,1: 84:[2, 89, 10] Operation: 28-18=10 Exploring Operation: 2+18=20, Resulting Numbers: [28, 89, 20] Generated Node #0,2: 84:[28, 89, 20] Operation: 2+18=20 Exploring Operation: 18/2=9, Resulting Numbers: [28, 89, 9] Generated Node #0,3: 84:[28, 89, 9] Operation: 18/2=9 Exploring Operation: 18-2=16, Resulting Numbers: [28, 89, 16] Generated Node #0,4: 84:[28, 89, 16] Operation: 18-2=16 Moving to Node #0,0 Current State: 84:[18, 28, 87], Operations: ['89-2=87'] Exploring Operation: 18+28=46, Resulting Numbers: [87, 46] Generated Node #0,0,0: 84:[87, 46] Operation: 18+28=46 Exploring Operation: 28-18=10, Resulting Numbers: [87, 10] Generated Node #0,0,1: 84:[87, 10] Operation: 28-18=10 Exploring Operation: 18+87=105, Resulting Numbers: [28, 105] Generated Node #0,0,2: 84:[28, 105] Operation: 18+87=105 Exploring Operation: 87-18=69, Resulting Numbers: [28, 69] Generated Node #0,0,3: 84:[28, 69] Operation: 87-18=69 Exploring Operation: 87-28=59, Resulting Numbers: [18, 59] Generated Node #0,0,4: 84:[18, 59] Operation: 87-28=59 Moving to Node #0,2 Current State: 84:[28, 89, 20], Operations: ['2+18=20'] Exploring Operation: 89+20=109, Resulting Numbers: [28, 109] Generated Node #0,2,0: 84:[28, 109] Operation: 89+20=109 Exploring Operation: 89-20=69, Resulting Numbers: [28, 69] Generated Node #0,2,1: 84:[28, 69] Operation: 89-20=69 Exploring Operation: 28-20=8, Resulting Numbers: [89, 8] Generated Node #0,2,2: 84:[89, 8] Operation: 28-20=8 Exploring Operation: 89-28=61, Resulting Numbers: [20, 61] Generated Node #0,2,3: 84:[20, 61] Operation: 89-28=61 Exploring Operation: 28+20=48, Resulting Numbers: [89, 48] Generated Node #0,2,4: 84:[89, 48] Operation: 28+20=48 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 84:[89, 8], Operations: ['2+18=20', '28-20=8'] Exploring Operation: 89+8=97, Resulting Numbers: [97] 97,84 unequal: No Solution Exploring Operation: 89*8=712, Resulting Numbers: [712] 712,84 unequal: No Solution Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 84:[89, 48], Operations: ['2+18=20', '28+20=48'] Exploring Operation: 89-48=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 89+48=137, Resulting Numbers: [137] 137,84 unequal: No Solution Exploring Operation: 89*48=4272, Resulting Numbers: [4272] 4272,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 84:[28, 69], Operations: ['2+18=20', '89-20=69'] Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 28+69=97, Resulting Numbers: [97] 97,84 unequal: No Solution Exploring Operation: 28*69=1932, Resulting Numbers: [1932] 1932,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 84:[20, 61], Operations: ['2+18=20', '89-28=61'] Exploring Operation: 20*61=1220, Resulting Numbers: [1220] 1220,84 unequal: No Solution Exploring Operation: 20+61=81, Resulting Numbers: [81] 81,84 unequal: No Solution Exploring Operation: 61-20=41, Resulting Numbers: [41] 41,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[28, 109], Operations: ['2+18=20', '89+20=109'] Exploring Operation: 28+109=137, Resulting Numbers: [137] 137,84 unequal: No Solution Exploring Operation: 109-28=81, Resulting Numbers: [81] 81,84 unequal: No Solution Exploring Operation: 28*109=3052, Resulting Numbers: [3052] 3052,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 84:[2, 89, 10], Operations: ['28-18=10'] Exploring Operation: 10-2=8, Resulting Numbers: [89, 8] Generated Node #0,1,0: 84:[89, 8] Operation: 10-2=8 Exploring Operation: 2+10=12, Resulting Numbers: [89, 12] Generated Node #0,1,1: 84:[89, 12] Operation: 2+10=12 Exploring Operation: 89-10=79, Resulting Numbers: [2, 79] Generated Node #0,1,2: 84:[2, 79] Operation: 89-10=79 Exploring Operation: 2*10=20, Resulting Numbers: [89, 20] Generated Node #0,1,3: 84:[89, 20] Operation: 2*10=20 Exploring Operation: 89-2=87, Resulting Numbers: [10, 87] Generated Node #0,1,4: 84:[10, 87] Operation: 89-2=87 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[89, 12], Operations: ['28-18=10', '2+10=12'] Exploring Operation: 89+12=101, Resulting Numbers: [101] 101,84 unequal: No Solution Exploring Operation: 89*12=1068, Resulting Numbers: [1068] 1068,84 unequal: No Solution Exploring Operation: 89-12=77, Resulting Numbers: [77] 77,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 84:[2, 79], Operations: ['28-18=10', '89-10=79'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,84 unequal: No Solution Exploring Operation: 2*79=158, Resulting Numbers: [158] 158,84 unequal: No Solution Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 84:[10, 87], Operations: ['28-18=10', '89-2=87'] Exploring Operation: 10*87=870, Resulting Numbers: [870] 870,84 unequal: No Solution Exploring Operation: 10+87=97, Resulting Numbers: [97] 97,84 unequal: No Solution Exploring Operation: 87-10=77, Resulting Numbers: [77] 77,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 84:[89, 8], Operations: ['28-18=10', '10-2=8'] Exploring Operation: 89*8=712, Resulting Numbers: [712] 712,84 unequal: No Solution Exploring Operation: 89+8=97, Resulting Numbers: [97] 97,84 unequal: No Solution Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 84:[89, 20], Operations: ['28-18=10', '2*10=20'] Exploring Operation: 89-20=69, Resulting Numbers: [69] 69,84 unequal: No Solution Exploring Operation: 89*20=1780, Resulting Numbers: [1780] 1780,84 unequal: No Solution Exploring Operation: 89+20=109, Resulting Numbers: [109] 109,84 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: 84:[28, 89, 9], Operations: ['18/2=9'] Exploring Operation: 89+9=98, Resulting Numbers: [28, 98] Generated Node #0,3,0: 84:[28, 98] Operation: 89+9=98 Exploring Operation: 89-9=80, Resulting Numbers: [28, 80] Generated Node #0,3,1: 84:[28, 80] Operation: 89-9=80 Exploring Operation: 28+9=37, Resulting Numbers: [89, 37] Generated Node #0,3,2: 84:[89, 37] Operation: 28+9=37 Exploring Operation: 28-9=19, Resulting Numbers: [89, 19] Generated Node #0,3,3: 84:[89, 19] Operation: 28-9=19 Exploring Operation: 89-28=61, Resulting Numbers: [9, 61] Generated Node #0,3,4: 84:[9, 61] Operation: 89-28=61 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 84:[28, 80], Operations: ['18/2=9', '89-9=80'] Exploring Operation: 28*80=2240, Resulting Numbers: [2240] 2240,84 unequal: No Solution Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,84 unequal: No Solution Exploring Operation: 28+80=108, Resulting Numbers: [108] 108,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 84:[89, 19], Operations: ['18/2=9', '28-9=19'] Exploring Operation: 89*19=1691, Resulting Numbers: [1691] 1691,84 unequal: No Solution Exploring Operation: 89+19=108, Resulting Numbers: [108] 108,84 unequal: No Solution Exploring Operation: 89-19=70, Resulting Numbers: [70] 70,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 84:[89, 37], Operations: ['18/2=9', '28+9=37'] Exploring Operation: 89+37=126, Resulting Numbers: [126] 126,84 unequal: No Solution Exploring Operation: 89*37=3293, Resulting Numbers: [3293] 3293,84 unequal: No Solution Exploring Operation: 89-37=52, Resulting Numbers: [52] 52,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 84:[28, 98], Operations: ['18/2=9', '89+9=98'] Exploring Operation: 98-28=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 28+98=126, Resulting Numbers: [126] 126,84 unequal: No Solution Exploring Operation: 28*98=2744, Resulting Numbers: [2744] 2744,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 84:[9, 61], Operations: ['18/2=9', '89-28=61'] Exploring Operation: 9*61=549, Resulting Numbers: [549] 549,84 unequal: No Solution Exploring Operation: 9+61=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 84:[28, 89, 16], Operations: ['18-2=16'] Exploring Operation: 89-16=73, Resulting Numbers: [28, 73] Generated Node #0,4,0: 84:[28, 73] Operation: 89-16=73 Exploring Operation: 28+16=44, Resulting Numbers: [89, 44] Generated Node #0,4,1: 84:[89, 44] Operation: 28+16=44 Exploring Operation: 89+16=105, Resulting Numbers: [28, 105] Generated Node #0,4,2: 84:[28, 105] Operation: 89+16=105 Exploring Operation: 89-28=61, Resulting Numbers: [16, 61] Generated Node #0,4,3: 84:[16, 61] Operation: 89-28=61 Exploring Operation: 28-16=12, Resulting Numbers: [89, 12] Generated Node #0,4,4: 84:[89, 12] Operation: 28-16=12 Moving to Node #0,0,1 Current State: 84:[87, 10], Operations: ['89-2=87', '28-18=10'] Exploring Operation: 87-10=77, Resulting Numbers: [77] 77,84 unequal: No Solution Exploring Operation: 87+10=97, Resulting Numbers: [97] 97,84 unequal: No Solution Exploring Operation: 87*10=870, Resulting Numbers: [870] 870,84 unequal: No Solution Moving to Node #0,4,4 Current State: 84:[89, 12], Operations: ['18-2=16', '28-16=12'] Exploring Operation: 89+12=101, Resulting Numbers: [101] 101,84 unequal: No Solution Exploring Operation: 89*12=1068, Resulting Numbers: [1068] 1068,84 unequal: No Solution Exploring Operation: 89-12=77, Resulting Numbers: [77] 77,84 unequal: No Solution Moving to Node #0,4,1 Current State: 84:[89, 44], Operations: ['18-2=16', '28+16=44'] Exploring Operation: 89-44=45, Resulting Numbers: [45] 45,84 unequal: No Solution Exploring Operation: 89*44=3916, Resulting Numbers: [3916] 3916,84 unequal: No Solution Exploring Operation: 89+44=133, Resulting Numbers: [133] 133,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[87, 46], Operations: ['89-2=87', '18+28=46'] Exploring Operation: 87-46=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 87+46=133, Resulting Numbers: [133] 133,84 unequal: No Solution Exploring Operation: 87*46=4002, Resulting Numbers: [4002] 4002,84 unequal: No Solution Moving to Node #0,4,0 Current State: 84:[28, 73], Operations: ['18-2=16', '89-16=73'] Exploring Operation: 28+73=101, Resulting Numbers: [101] 101,84 unequal: No Solution Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,84 unequal: No Solution Exploring Operation: 28*73=2044, Resulting Numbers: [2044] 2044,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[28, 69], Operations: ['89-2=87', '87-18=69'] Exploring Operation: 28*69=1932, Resulting Numbers: [1932] 1932,84 unequal: No Solution Exploring Operation: 28+69=97, Resulting Numbers: [97] 97,84 unequal: No Solution Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,84 unequal: No Solution Moving to Node #0,0,4 Current State: 84:[18, 59], Operations: ['89-2=87', '87-28=59'] Exploring Operation: 18+59=77, Resulting Numbers: [77] 77,84 unequal: No Solution Exploring Operation: 59-18=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 18*59=1062, Resulting Numbers: [1062] 1062,84 unequal: No Solution Moving to Node #0,4,2 Current State: 84:[28, 105], Operations: ['18-2=16', '89+16=105'] Exploring Operation: 28+105=133, Resulting Numbers: [133] 133,84 unequal: No Solution Exploring Operation: 28*105=2940, Resulting Numbers: [2940] 2940,84 unequal: No Solution Exploring Operation: 105-28=77, Resulting Numbers: [77] 77,84 unequal: No Solution Moving to Node #0,4,3 Current State: 84:[16, 61], Operations: ['18-2=16', '89-28=61'] Exploring Operation: 61-16=45, Resulting Numbers: [45] 45,84 unequal: No Solution Exploring Operation: 16*61=976, Resulting Numbers: [976] 976,84 unequal: No Solution Exploring Operation: 16+61=77, Resulting Numbers: [77] 77,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[28, 105], Operations: ['89-2=87', '18+87=105'] Exploring Operation: 28+105=133, Resulting Numbers: [133] 133,84 unequal: No Solution Exploring Operation: 105-28=77, Resulting Numbers: [77] 77,84 unequal: No Solution Exploring Operation: 28*105=2940, Resulting Numbers: [2940] 2940,84 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 9, 62, 33, 39 ]
81
[ "33*39=1287", "1287/9=143", "143-62=81" ]
Current State: 81:[9, 62, 33, 39], Operations: [] Exploring Operation: 33*39=1287, Resulting Numbers: [9, 62, 1287] Generated Node #2: [9, 62, 1287] from Operation: 33*39=1287 Current State: 81:[9, 62, 1287], Operations: ['33*39=1287'] Exploring Operation: 1287/9=143, Resulting Numbers: [62, 143] Generated Node #3: [62, 143] from Operation: 1287/9=143 Current State: 81:[62, 143], Operations: ['33*39=1287', '1287/9=143'] Exploring Operation: 143-62=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[9, 62, 33, 39], Operations: [] Exploring Operation: 62-39=23, Resulting Numbers: [9, 33, 23] Generated Node #0,0: 81:[9, 33, 23] Operation: 62-39=23 Exploring Operation: 62-33=29, Resulting Numbers: [9, 39, 29] Generated Node #0,1: 81:[9, 39, 29] Operation: 62-33=29 Moving to Node #0,0 Current State: 81:[9, 33, 23], Operations: ['62-39=23'] Exploring Operation: 33-9=24, Resulting Numbers: [23, 24] Generated Node #0,0,0: 81:[23, 24] Operation: 33-9=24 Exploring Operation: 33-23=10, Resulting Numbers: [9, 10] Generated Node #0,0,1: 81:[9, 10] Operation: 33-23=10 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[9, 10], Operations: ['62-39=23', '33-23=10'] Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,81 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[23, 24], Operations: ['62-39=23', '33-9=24'] Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,81 unequal: No Solution Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,81 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: 81:[9, 39, 29], Operations: ['62-33=29'] Exploring Operation: 39-29=10, Resulting Numbers: [9, 10] Generated Node #0,1,0: 81:[9, 10] Operation: 39-29=10 Exploring Operation: 39-9=30, Resulting Numbers: [29, 30] Generated Node #0,1,1: 81:[29, 30] Operation: 39-9=30 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 81:[9, 10], Operations: ['62-33=29', '39-29=10'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,81 unequal: No Solution Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 81:[29, 30], Operations: ['62-33=29', '39-9=30'] Exploring Operation: 29+30=59, Resulting Numbers: [59] 59,81 unequal: No Solution Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,81 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
[ 86, 87, 11, 96 ]
86
[ "87-86=1", "96-11=85", "1+85=86" ]
Current State: 86:[86, 87, 11, 96], Operations: [] Exploring Operation: 87-86=1, Resulting Numbers: [11, 96, 1] Generated Node #2: [11, 96, 1] from Operation: 87-86=1 Current State: 86:[11, 96, 1], Operations: ['87-86=1'] Exploring Operation: 96-11=85, Resulting Numbers: [1, 85] Generated Node #3: [1, 85] from Operation: 96-11=85 Current State: 86:[1, 85], Operations: ['87-86=1', '96-11=85'] Exploring Operation: 1+85=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[86, 87, 11, 96], Operations: [] Exploring Operation: 96-11=85, Resulting Numbers: [86, 87, 85] Generated Node #0,0: 86:[86, 87, 85] Operation: 96-11=85 Exploring Operation: 96-87=9, Resulting Numbers: [86, 11, 9] Generated Node #0,1: 86:[86, 11, 9] Operation: 96-87=9 Exploring Operation: 96-86=10, Resulting Numbers: [87, 11, 10] Generated Node #0,2: 86:[87, 11, 10] Operation: 96-86=10 Moving to Node #0,0 Current State: 86:[86, 87, 85], Operations: ['96-11=85'] Exploring Operation: 87-85=2, Resulting Numbers: [86, 2] Generated Node #0,0,0: 86:[86, 2] Operation: 87-85=2 Exploring Operation: 87-86=1, Resulting Numbers: [85, 1] Generated Node #0,0,1: 86:[85, 1] Operation: 87-86=1 Exploring Operation: 86-85=1, Resulting Numbers: [87, 1] Generated Node #0,0,2: 86:[87, 1] Operation: 86-85=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[86, 2], Operations: ['96-11=85', '87-85=2'] Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,86 unequal: No Solution Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 86+2=88, Resulting Numbers: [88] 88,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 86:[85, 1], Operations: ['96-11=85', '87-86=1'] Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,86 unequal: No Solution Exploring Operation: 85*1=85, Resulting Numbers: [85] 85,86 unequal: No Solution Exploring Operation: 85+1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[86, 87, 11, 96], Operations: [] Exploring Operation: 96-11=85, Resulting Numbers: [86, 87, 85] Generated Node #0,0: 86:[86, 87, 85] Operation: 96-11=85 Moving to Node #0,0 Current State: 86:[86, 87, 85], Operations: ['96-11=85'] Exploring Operation: 87-86=1, Resulting Numbers: [85, 1] Generated Node #0,0,1: 86:[85, 1] Operation: 87-86=1 Moving to Node #0,0,1 Current State: 86:[85, 1], Operations: ['96-11=85', '87-86=1'] Exploring Operation: 85+1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 45, 71, 11, 2 ]
69
[ "45+71=116", "116/2=58", "11+58=69" ]
Current State: 69:[45, 71, 11, 2], Operations: [] Exploring Operation: 45+71=116, Resulting Numbers: [11, 2, 116] Generated Node #2: [11, 2, 116] from Operation: 45+71=116 Current State: 69:[11, 2, 116], Operations: ['45+71=116'] Exploring Operation: 116/2=58, Resulting Numbers: [11, 58] Generated Node #3: [11, 58] from Operation: 116/2=58 Current State: 69:[11, 58], Operations: ['45+71=116', '116/2=58'] Exploring Operation: 11+58=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[45, 71, 11, 2], Operations: [] Exploring Operation: 71-45=26, Resulting Numbers: [11, 2, 26] Generated Node #0,0: 69:[11, 2, 26] Operation: 71-45=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[11, 2, 26], Operations: ['71-45=26'] Exploring Operation: 11*2=22, Resulting Numbers: [26, 22] Generated Node #0,0,0: 69:[26, 22] Operation: 11*2=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[26, 22], Operations: ['71-45=26', '11*2=22'] Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 59, 76, 31, 38 ]
56
[ "59-31=28", "76/38=2", "28*2=56" ]
Current State: 56:[59, 76, 31, 38], Operations: [] Exploring Operation: 59-31=28, Resulting Numbers: [76, 38, 28] Generated Node #2: [76, 38, 28] from Operation: 59-31=28 Current State: 56:[76, 38, 28], Operations: ['59-31=28'] Exploring Operation: 76/38=2, Resulting Numbers: [28, 2] Generated Node #3: [28, 2] from Operation: 76/38=2 Current State: 56:[28, 2], Operations: ['59-31=28', '76/38=2'] Exploring Operation: 28*2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[59, 76, 31, 38], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [59, 31, 2] Generated Node #0,0: 56:[59, 31, 2] Operation: 76/38=2 Exploring Operation: 76-59=17, Resulting Numbers: [31, 38, 17] Generated Node #0,1: 56:[31, 38, 17] Operation: 76-59=17 Moving to Node #0,0 Current State: 56:[59, 31, 2], Operations: ['76/38=2'] Exploring Operation: 59-2=57, Resulting Numbers: [31, 57] Generated Node #0,0,0: 56:[31, 57] Operation: 59-2=57 Exploring Operation: 59-31=28, Resulting Numbers: [2, 28] Generated Node #0,0,1: 56:[2, 28] Operation: 59-31=28 Moving to Node #0,1 Current State: 56:[31, 38, 17], Operations: ['76-59=17'] Exploring Operation: 38+17=55, Resulting Numbers: [31, 55] Generated Node #0,1,0: 56:[31, 55] Operation: 38+17=55 Exploring Operation: 38-31=7, Resulting Numbers: [17, 7] Generated Node #0,1,1: 56:[17, 7] Operation: 38-31=7 Moving to Node #0,0,1 Current State: 56:[2, 28], Operations: ['76/38=2', '59-31=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[59, 76, 31, 38], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [59, 31, 2] Generated Node #0,0: 56:[59, 31, 2] Operation: 76/38=2 Moving to Node #0,0 Current State: 56:[59, 31, 2], Operations: ['76/38=2'] Exploring Operation: 59-31=28, Resulting Numbers: [2, 28] Generated Node #0,0,1: 56:[2, 28] Operation: 59-31=28 Moving to Node #0,0,1 Current State: 56:[2, 28], Operations: ['76/38=2', '59-31=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 41, 56, 2, 80 ]
15
[ "41+56=97", "2+80=82", "97-82=15" ]
Current State: 15:[41, 56, 2, 80], Operations: [] Exploring Operation: 41+56=97, Resulting Numbers: [2, 80, 97] Generated Node #2: [2, 80, 97] from Operation: 41+56=97 Current State: 15:[2, 80, 97], Operations: ['41+56=97'] Exploring Operation: 2+80=82, Resulting Numbers: [97, 82] Generated Node #3: [97, 82] from Operation: 2+80=82 Current State: 15:[97, 82], Operations: ['41+56=97', '2+80=82'] Exploring Operation: 97-82=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[41, 56, 2, 80], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [41, 2, 24] Generated Node #0,0: 15:[41, 2, 24] Operation: 80-56=24 Exploring Operation: 80-41=39, Resulting Numbers: [56, 2, 39] Generated Node #0,1: 15:[56, 2, 39] Operation: 80-41=39 Exploring Operation: 56-41=15, Resulting Numbers: [2, 80, 15] Generated Node #0,2: 15:[2, 80, 15] Operation: 56-41=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[41, 2, 24], Operations: ['80-56=24'] Exploring Operation: 41-24=17, Resulting Numbers: [2, 17] Generated Node #0,0,0: 15:[2, 17] Operation: 41-24=17 Exploring Operation: 41-2=39, Resulting Numbers: [24, 39] Generated Node #0,0,1: 15:[24, 39] Operation: 41-2=39 Exploring Operation: 24/2=12, Resulting Numbers: [41, 12] Generated Node #0,0,2: 15:[41, 12] Operation: 24/2=12 Moving to Node #0,0,0 Current State: 15:[2, 17], Operations: ['80-56=24', '41-24=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[41, 56, 2, 80], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [41, 2, 24] Generated Node #0,0: 15:[41, 2, 24] Operation: 80-56=24 Moving to Node #0,0 Current State: 15:[41, 2, 24], Operations: ['80-56=24'] Exploring Operation: 41-24=17, Resulting Numbers: [2, 17] Generated Node #0,0,0: 15:[2, 17] Operation: 41-24=17 Moving to Node #0,0,0 Current State: 15:[2, 17], Operations: ['80-56=24', '41-24=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 14, 41, 69, 41 ]
14
[ "41-41=0", "69*0=0", "14+0=14" ]
Current State: 14:[14, 41, 69, 41], Operations: [] Exploring Operation: 41-41=0, Resulting Numbers: [14, 69, 0] Generated Node #2: [14, 69, 0] from Operation: 41-41=0 Current State: 14:[14, 69, 0], Operations: ['41-41=0'] Exploring Operation: 69*0=0, Resulting Numbers: [14, 0] Generated Node #3: [14, 0] from Operation: 69*0=0 Current State: 14:[14, 0], Operations: ['41-41=0', '69*0=0'] Exploring Operation: 14+0=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[14, 41, 69, 41], Operations: [] Exploring Operation: 69-41=28, Resulting Numbers: [14, 41, 28] Generated Node #0,0: 14:[14, 41, 28] Operation: 69-41=28 Exploring Operation: 69-41=28, Resulting Numbers: [14, 41, 28] Generated Node #0,1: 14:[14, 41, 28] Operation: 69-41=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[14, 41, 28], Operations: ['69-41=28'] Exploring Operation: 41-28=13, Resulting Numbers: [14, 13] Generated Node #0,0,0: 14:[14, 13] Operation: 41-28=13 Exploring Operation: 41-14=27, Resulting Numbers: [28, 27] Generated Node #0,0,1: 14:[28, 27] Operation: 41-14=27 Moving to Node #0,0,0 Current State: 14:[14, 13], Operations: ['69-41=28', '41-28=13'] Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[28, 27], Operations: ['69-41=28', '41-14=27'] Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,14 unequal: No Solution Exploring Operation: 28+27=55, Resulting Numbers: [55] 55,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[14, 41, 28], Operations: ['69-41=28'] Exploring Operation: 41-28=13, Resulting Numbers: [14, 13] Generated Node #0,1,0: 14:[14, 13] Operation: 41-28=13 Exploring Operation: 41-14=27, Resulting Numbers: [28, 27] Generated Node #0,1,1: 14:[28, 27] Operation: 41-14=27 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 14:[14, 13], Operations: ['69-41=28', '41-28=13'] Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,14 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 #0,1,1 Current State: 14:[28, 27], Operations: ['69-41=28', '41-14=27'] Exploring Operation: 28+27=55, Resulting Numbers: [55] 55,14 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,14 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 No solution found.
0
hs_2
sum_heuristic
[ 94, 68, 31, 64 ]
69
[ "94-68=26", "31+64=95", "95-26=69" ]
Current State: 69:[94, 68, 31, 64], Operations: [] Exploring Operation: 94-68=26, Resulting Numbers: [31, 64, 26] Generated Node #2: [31, 64, 26] from Operation: 94-68=26 Current State: 69:[31, 64, 26], Operations: ['94-68=26'] Exploring Operation: 31+64=95, Resulting Numbers: [26, 95] Generated Node #3: [26, 95] from Operation: 31+64=95 Current State: 69:[26, 95], Operations: ['94-68=26', '31+64=95'] Exploring Operation: 95-26=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[94, 68, 31, 64], Operations: [] Exploring Operation: 94-64=30, Resulting Numbers: [68, 31, 30] Generated Node #0,0: 69:[68, 31, 30] Operation: 94-64=30 Exploring Operation: 94-68=26, Resulting Numbers: [31, 64, 26] Generated Node #0,1: 69:[31, 64, 26] Operation: 94-68=26 Exploring Operation: 68-64=4, Resulting Numbers: [94, 31, 4] Generated Node #0,2: 69:[94, 31, 4] Operation: 68-64=4 Exploring Operation: 94-31=63, Resulting Numbers: [68, 64, 63] Generated Node #0,3: 69:[68, 64, 63] Operation: 94-31=63 Moving to Node #0,3 Current State: 69:[68, 64, 63], Operations: ['94-31=63'] Exploring Operation: 64+63=127, Resulting Numbers: [68, 127] Generated Node #0,3,0: 69:[68, 127] Operation: 64+63=127 Exploring Operation: 68-64=4, Resulting Numbers: [63, 4] Generated Node #0,3,1: 69:[63, 4] Operation: 68-64=4 Exploring Operation: 64-63=1, Resulting Numbers: [68, 1] Generated Node #0,3,2: 69:[68, 1] Operation: 64-63=1 Exploring Operation: 68-63=5, Resulting Numbers: [64, 5] Generated Node #0,3,3: 69:[64, 5] Operation: 68-63=5 Moving to Node #0,1 Current State: 69:[31, 64, 26], Operations: ['94-68=26'] Exploring Operation: 31-26=5, Resulting Numbers: [64, 5] Generated Node #0,1,0: 69:[64, 5] Operation: 31-26=5 Exploring Operation: 31+26=57, Resulting Numbers: [64, 57] Generated Node #0,1,1: 69:[64, 57] Operation: 31+26=57 Exploring Operation: 64-26=38, Resulting Numbers: [31, 38] Generated Node #0,1,2: 69:[31, 38] Operation: 64-26=38 Exploring Operation: 64-31=33, Resulting Numbers: [26, 33] Generated Node #0,1,3: 69:[26, 33] Operation: 64-31=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[64, 5], Operations: ['94-68=26', '31-26=5'] Exploring Operation: 64-5=59, Resulting Numbers: [59] 59,69 unequal: No Solution Exploring Operation: 64+5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[94, 68, 31, 64], Operations: [] Exploring Operation: 94-68=26, Resulting Numbers: [31, 64, 26] Generated Node #0,1: 69:[31, 64, 26] Operation: 94-68=26 Moving to Node #0,1 Current State: 69:[31, 64, 26], Operations: ['94-68=26'] Exploring Operation: 31-26=5, Resulting Numbers: [64, 5] Generated Node #0,1,0: 69:[64, 5] Operation: 31-26=5 Moving to Node #0,1,0 Current State: 69:[64, 5], Operations: ['94-68=26', '31-26=5'] Exploring Operation: 64+5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 49, 96, 78, 47 ]
16
[ "96-49=47", "78-47=31", "47-31=16" ]
Current State: 16:[49, 96, 78, 47], Operations: [] Exploring Operation: 96-49=47, Resulting Numbers: [78, 47, 47] Generated Node #2: [78, 47, 47] from Operation: 96-49=47 Current State: 16:[78, 47, 47], Operations: ['96-49=47'] Exploring Operation: 78-47=31, Resulting Numbers: [31] 31,16 equal: Goal Reached Exploring Operation: 47-31=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[49, 96, 78, 47], Operations: [] Exploring Operation: 96-78=18, Resulting Numbers: [49, 47, 18] Generated Node #0,0: 16:[49, 47, 18] Operation: 96-78=18 Moving to Node #0,0 Current State: 16:[49, 47, 18], Operations: ['96-78=18'] Exploring Operation: 49-47=2, Resulting Numbers: [18, 2] Generated Node #0,0,0: 16:[18, 2] Operation: 49-47=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[18, 2], Operations: ['96-78=18', '49-47=2'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[49, 96, 78, 47], Operations: [] Exploring Operation: 96-78=18, Resulting Numbers: [49, 47, 18] Generated Node #0,0: 16:[49, 47, 18] Operation: 96-78=18 Moving to Node #0,0 Current State: 16:[49, 47, 18], Operations: ['96-78=18'] Exploring Operation: 49-47=2, Resulting Numbers: [18, 2] Generated Node #0,0,0: 16:[18, 2] Operation: 49-47=2 Moving to Node #0,0,0 Current State: 16:[18, 2], Operations: ['96-78=18', '49-47=2'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 84, 49, 13, 61 ]
91
[ "84*13=1092", "61-49=12", "1092/12=91" ]
Current State: 91:[84, 49, 13, 61], Operations: [] Exploring Operation: 84*13=1092, Resulting Numbers: [49, 61, 1092] Generated Node #2: [49, 61, 1092] from Operation: 84*13=1092 Current State: 91:[49, 61, 1092], Operations: ['84*13=1092'] Exploring Operation: 61-49=12, Resulting Numbers: [1092, 12] Generated Node #3: [1092, 12] from Operation: 61-49=12 Current State: 91:[1092, 12], Operations: ['84*13=1092', '61-49=12'] Exploring Operation: 1092/12=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[84, 49, 13, 61], Operations: [] Exploring Operation: 49+61=110, Resulting Numbers: [84, 13, 110] Generated Node #0,0: 91:[84, 13, 110] Operation: 49+61=110 Exploring Operation: 84-49=35, Resulting Numbers: [13, 61, 35] Generated Node #0,1: 91:[13, 61, 35] Operation: 84-49=35 Exploring Operation: 84-61=23, Resulting Numbers: [49, 13, 23] Generated Node #0,2: 91:[49, 13, 23] Operation: 84-61=23 Exploring Operation: 61-49=12, Resulting Numbers: [84, 13, 12] Generated Node #0,3: 91:[84, 13, 12] Operation: 61-49=12 Moving to Node #0,3 Current State: 91:[84, 13, 12], Operations: ['61-49=12'] Exploring Operation: 84+12=96, Resulting Numbers: [13, 96] Generated Node #0,3,0: 91:[13, 96] Operation: 84+12=96 Exploring Operation: 84/12=7, Resulting Numbers: [13, 7] Generated Node #0,3,1: 91:[13, 7] Operation: 84/12=7 Exploring Operation: 84+13=97, Resulting Numbers: [12, 97] Generated Node #0,3,2: 91:[12, 97] Operation: 84+13=97 Exploring Operation: 13-12=1, Resulting Numbers: [84, 1] Generated Node #0,3,3: 91:[84, 1] Operation: 13-12=1 Moving to Node #0,0 Current State: 91:[84, 13, 110], Operations: ['49+61=110'] Exploring Operation: 84+13=97, Resulting Numbers: [110, 97] Generated Node #0,0,0: 91:[110, 97] Operation: 84+13=97 Exploring Operation: 84-13=71, Resulting Numbers: [110, 71] Generated Node #0,0,1: 91:[110, 71] Operation: 84-13=71 Exploring Operation: 110-84=26, Resulting Numbers: [13, 26] Generated Node #0,0,2: 91:[13, 26] Operation: 110-84=26 Exploring Operation: 110-13=97, Resulting Numbers: [84, 97] Generated Node #0,0,3: 91:[84, 97] Operation: 110-13=97 Moving to Node #0,2 Current State: 91:[49, 13, 23], Operations: ['84-61=23'] Exploring Operation: 49+13=62, Resulting Numbers: [23, 62] Generated Node #0,2,0: 91:[23, 62] Operation: 49+13=62 Exploring Operation: 49+23=72, Resulting Numbers: [13, 72] Generated Node #0,2,1: 91:[13, 72] Operation: 49+23=72 Exploring Operation: 49-23=26, Resulting Numbers: [13, 26] Generated Node #0,2,2: 91:[13, 26] Operation: 49-23=26 Exploring Operation: 49-13=36, Resulting Numbers: [23, 36] Generated Node #0,2,3: 91:[23, 36] Operation: 49-13=36 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 91:[13, 26], Operations: ['84-61=23', '49-23=26'] Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 13*26=338, Resulting Numbers: [338] 338,91 unequal: No Solution Exploring Operation: 13+26=39, Resulting Numbers: [39] 39,91 unequal: No Solution Exploring Operation: 26-13=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 #0,2,1 Current State: 91:[13, 72], Operations: ['84-61=23', '49+23=72'] Exploring Operation: 13+72=85, Resulting Numbers: [85] 85,91 unequal: No Solution Exploring Operation: 13*72=936, Resulting Numbers: [936] 936,91 unequal: No Solution Exploring Operation: 72-13=59, Resulting Numbers: [59] 59,91 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:[23, 36], Operations: ['84-61=23', '49-13=36'] Exploring Operation: 23+36=59, Resulting Numbers: [59] 59,91 unequal: No Solution Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,91 unequal: No Solution Exploring Operation: 23*36=828, Resulting Numbers: [828] 828,91 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:[23, 62], Operations: ['84-61=23', '49+13=62'] Exploring Operation: 23*62=1426, Resulting Numbers: [1426] 1426,91 unequal: No Solution Exploring Operation: 23+62=85, Resulting Numbers: [85] 85,91 unequal: No Solution Exploring Operation: 62-23=39, Resulting Numbers: [39] 39,91 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: 91:[13, 61, 35], Operations: ['84-49=35'] Exploring Operation: 35-13=22, Resulting Numbers: [61, 22] Generated Node #0,1,0: 91:[61, 22] Operation: 35-13=22 Exploring Operation: 61-35=26, Resulting Numbers: [13, 26] Generated Node #0,1,1: 91:[13, 26] Operation: 61-35=26 Exploring Operation: 61+35=96, Resulting Numbers: [13, 96] Generated Node #0,1,2: 91:[13, 96] Operation: 61+35=96 Exploring Operation: 13+61=74, Resulting Numbers: [35, 74] Generated Node #0,1,3: 91:[35, 74] Operation: 13+61=74 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 91:[13, 96], Operations: ['84-49=35', '61+35=96'] Exploring Operation: 13+96=109, Resulting Numbers: [109] 109,91 unequal: No Solution Exploring Operation: 13*96=1248, Resulting Numbers: [1248] 1248,91 unequal: No Solution Exploring Operation: 96-13=83, Resulting Numbers: [83] 83,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 91:[13, 26], Operations: ['84-49=35', '61-35=26'] Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,91 unequal: No Solution Exploring Operation: 13+26=39, Resulting Numbers: [39] 39,91 unequal: No Solution Exploring Operation: 13*26=338, Resulting Numbers: [338] 338,91 unequal: No Solution Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 91:[61, 22], Operations: ['84-49=35', '35-13=22'] Exploring Operation: 61*22=1342, Resulting Numbers: [1342] 1342,91 unequal: No Solution Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,91 unequal: No Solution Exploring Operation: 61+22=83, Resulting Numbers: [83] 83,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 91:[35, 74], Operations: ['84-49=35', '13+61=74'] Exploring Operation: 74-35=39, Resulting Numbers: [39] 39,91 unequal: No Solution Exploring Operation: 35*74=2590, Resulting Numbers: [2590] 2590,91 unequal: No Solution Exploring Operation: 35+74=109, Resulting Numbers: [109] 109,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 91:[13, 7], Operations: ['61-49=12', '84/12=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,91 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,91 unequal: No Solution Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[84, 49, 13, 61], Operations: [] Exploring Operation: 61-49=12, Resulting Numbers: [84, 13, 12] Generated Node #0,3: 91:[84, 13, 12] Operation: 61-49=12 Moving to Node #0,3 Current State: 91:[84, 13, 12], Operations: ['61-49=12'] Exploring Operation: 84/12=7, Resulting Numbers: [13, 7] Generated Node #0,3,1: 91:[13, 7] Operation: 84/12=7 Moving to Node #0,3,1 Current State: 91:[13, 7], Operations: ['61-49=12', '84/12=7'] Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
0.953993
hs_4
mult_heuristic
[ 11, 34, 49, 64 ]
22
[ "34+64=98", "11*98=1078", "1078/49=22" ]
Current State: 22:[11, 34, 49, 64], Operations: [] Exploring Operation: 34+64=98, Resulting Numbers: [11, 49, 98] Generated Node #2: [11, 49, 98] from Operation: 34+64=98 Current State: 22:[11, 49, 98], Operations: ['34+64=98'] Exploring Operation: 11*98=1078, Resulting Numbers: [49, 1078] Generated Node #3: [49, 1078] from Operation: 11*98=1078 Current State: 22:[49, 1078], Operations: ['34+64=98', '11*98=1078'] Exploring Operation: 1078/49=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[11, 34, 49, 64], Operations: [] Exploring Operation: 64-49=15, Resulting Numbers: [11, 34, 15] Generated Node #0,0: 22:[11, 34, 15] Operation: 64-49=15 Exploring Operation: 64-34=30, Resulting Numbers: [11, 49, 30] Generated Node #0,1: 22:[11, 49, 30] Operation: 64-34=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[11, 34, 15], Operations: ['64-49=15'] Exploring Operation: 34-15=19, Resulting Numbers: [11, 19] Generated Node #0,0,0: 22:[11, 19] Operation: 34-15=19 Exploring Operation: 34-11=23, Resulting Numbers: [15, 23] Generated Node #0,0,1: 22:[15, 23] Operation: 34-11=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 22:[11, 19], Operations: ['64-49=15', '34-15=19'] Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,22 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 22:[15, 23], Operations: ['64-49=15', '34-11=23'] Exploring Operation: 15+23=38, Resulting Numbers: [38] 38,22 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[11, 49, 30], Operations: ['64-34=30'] Exploring Operation: 49-11=38, Resulting Numbers: [30, 38] Generated Node #0,1,0: 22:[30, 38] Operation: 49-11=38 Exploring Operation: 49-30=19, Resulting Numbers: [11, 19] Generated Node #0,1,1: 22:[11, 19] Operation: 49-30=19 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 22:[11, 19], Operations: ['64-34=30', '49-30=19'] Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,22 unequal: No Solution Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,22 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 #0,1,0 Current State: 22:[30, 38], Operations: ['64-34=30', '49-11=38'] Exploring Operation: 30+38=68, Resulting Numbers: [68] 68,22 unequal: No Solution Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 2, 1, 11, 95 ]
59
[ "1+95=96", "96/2=48", "11+48=59" ]
Current State: 59:[2, 1, 11, 95], Operations: [] Exploring Operation: 1+95=96, Resulting Numbers: [2, 11, 96] Generated Node #2: [2, 11, 96] from Operation: 1+95=96 Current State: 59:[2, 11, 96], Operations: ['1+95=96'] Exploring Operation: 96/2=48, Resulting Numbers: [11, 48] Generated Node #3: [11, 48] from Operation: 96/2=48 Current State: 59:[11, 48], Operations: ['1+95=96', '96/2=48'] Exploring Operation: 11+48=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[2, 1, 11, 95], Operations: [] Exploring Operation: 2+11=13, Resulting Numbers: [1, 95, 13] Generated Node #0,0: 59:[1, 95, 13] Operation: 2+11=13 Exploring Operation: 2+1=3, Resulting Numbers: [11, 95, 3] Generated Node #0,1: 59:[11, 95, 3] Operation: 2+1=3 Exploring Operation: 2*11=22, Resulting Numbers: [1, 95, 22] Generated Node #0,2: 59:[1, 95, 22] Operation: 2*11=22 Moving to Node #0,2 Current State: 59:[1, 95, 22], Operations: ['2*11=22'] Exploring Operation: 95-1=94, Resulting Numbers: [22, 94] Generated Node #0,2,0: 59:[22, 94] Operation: 95-1=94 Exploring Operation: 95-22=73, Resulting Numbers: [1, 73] Generated Node #0,2,1: 59:[1, 73] Operation: 95-22=73 Exploring Operation: 1+22=23, Resulting Numbers: [95, 23] Generated Node #0,2,2: 59:[95, 23] Operation: 1+22=23 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[22, 94], Operations: ['2*11=22', '95-1=94'] Exploring Operation: 22+94=116, Resulting Numbers: [116] 116,59 unequal: No Solution Exploring Operation: 94-22=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 22*94=2068, Resulting Numbers: [2068] 2068,59 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 #0,2,1 Current State: 59:[1, 73], Operations: ['2*11=22', '95-22=73'] Exploring Operation: 1*73=73, Resulting Numbers: [73] 73,59 unequal: No Solution Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 73/1=73, Resulting Numbers: [73] 73,59 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 #0,2,2 Current State: 59:[95, 23], Operations: ['2*11=22', '1+22=23'] Exploring Operation: 95*23=2185, Resulting Numbers: [2185] 2185,59 unequal: No Solution Exploring Operation: 95-23=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 95+23=118, Resulting Numbers: [118] 118,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 59:[1, 95, 13], Operations: ['2+11=13'] Exploring Operation: 95-1=94, Resulting Numbers: [13, 94] Generated Node #0,0,0: 59:[13, 94] Operation: 95-1=94 Exploring Operation: 95-13=82, Resulting Numbers: [1, 82] Generated Node #0,0,1: 59:[1, 82] Operation: 95-13=82 Exploring Operation: 1+13=14, Resulting Numbers: [95, 14] Generated Node #0,0,2: 59:[95, 14] Operation: 1+13=14 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[13, 94], Operations: ['2+11=13', '95-1=94'] Exploring Operation: 13*94=1222, Resulting Numbers: [1222] 1222,59 unequal: No Solution Exploring Operation: 13+94=107, Resulting Numbers: [107] 107,59 unequal: No Solution Exploring Operation: 94-13=81, Resulting Numbers: [81] 81,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[1, 82], Operations: ['2+11=13', '95-13=82'] Exploring Operation: 1*82=82, Resulting Numbers: [82] 82,59 unequal: No Solution Exploring Operation: 82/1=82, Resulting Numbers: [82] 82,59 unequal: No Solution Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 59:[95, 14], Operations: ['2+11=13', '1+13=14'] Exploring Operation: 95+14=109, Resulting Numbers: [109] 109,59 unequal: No Solution Exploring Operation: 95*14=1330, Resulting Numbers: [1330] 1330,59 unequal: No Solution Exploring Operation: 95-14=81, Resulting Numbers: [81] 81,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 59:[11, 95, 3], Operations: ['2+1=3'] Exploring Operation: 95-11=84, Resulting Numbers: [3, 84] Generated Node #0,1,0: 59:[3, 84] Operation: 95-11=84 Exploring Operation: 11*3=33, Resulting Numbers: [95, 33] Generated Node #0,1,1: 59:[95, 33] Operation: 11*3=33 Exploring Operation: 11+3=14, Resulting Numbers: [95, 14] Generated Node #0,1,2: 59:[95, 14] Operation: 11+3=14 Moving to Node #0,1,1 Current State: 59:[95, 33], Operations: ['2+1=3', '11*3=33'] Exploring Operation: 95-33=62, Resulting Numbers: [62] 62,59 unequal: No Solution Exploring Operation: 95+33=128, Resulting Numbers: [128] 128,59 unequal: No Solution Exploring Operation: 95*33=3135, Resulting Numbers: [3135] 3135,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[3, 84], Operations: ['2+1=3', '95-11=84'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,59 unequal: No Solution Exploring Operation: 3+84=87, Resulting Numbers: [87] 87,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[95, 14], Operations: ['2+1=3', '11+3=14'] Exploring Operation: 95*14=1330, Resulting Numbers: [1330] 1330,59 unequal: No Solution Exploring Operation: 95+14=109, Resulting Numbers: [109] 109,59 unequal: No Solution Exploring Operation: 95-14=81, Resulting Numbers: [81] 81,59 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 96, 98, 99, 21 ]
39
[ "98-96=2", "99-21=78", "78/2=39" ]
Current State: 39:[96, 98, 99, 21], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [99, 21, 2] Generated Node #2: [99, 21, 2] from Operation: 98-96=2 Current State: 39:[99, 21, 2], Operations: ['98-96=2'] Exploring Operation: 99-21=78, Resulting Numbers: [2, 78] Generated Node #3: [2, 78] from Operation: 99-21=78 Current State: 39:[2, 78], Operations: ['98-96=2', '99-21=78'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[96, 98, 99, 21], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [96, 21, 1] Generated Node #0,0: 39:[96, 21, 1] Operation: 99-98=1 Exploring Operation: 99-96=3, Resulting Numbers: [98, 21, 3] Generated Node #0,1: 39:[98, 21, 3] Operation: 99-96=3 Moving to Node #0,0 Current State: 39:[96, 21, 1], Operations: ['99-98=1'] Exploring Operation: 96-21=75, Resulting Numbers: [1, 75] Generated Node #0,0,0: 39:[1, 75] Operation: 96-21=75 Exploring Operation: 96-1=95, Resulting Numbers: [21, 95] Generated Node #0,0,1: 39:[21, 95] Operation: 96-1=95 Moving to Node #0,1 Current State: 39:[98, 21, 3], Operations: ['99-96=3'] Exploring Operation: 98-21=77, Resulting Numbers: [3, 77] Generated Node #0,1,0: 39:[3, 77] Operation: 98-21=77 Exploring Operation: 21/3=7, Resulting Numbers: [98, 7] Generated Node #0,1,1: 39:[98, 7] Operation: 21/3=7 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[3, 77], Operations: ['99-96=3', '98-21=77'] Exploring Operation: 3+77=80, Resulting Numbers: [80] 80,39 unequal: No Solution Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[98, 7], Operations: ['99-96=3', '21/3=7'] Exploring Operation: 98/7=14, Resulting Numbers: [14] 14,39 unequal: No Solution Exploring Operation: 98-7=91, Resulting Numbers: [91] 91,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 39:[1, 75], Operations: ['99-98=1', '96-21=75'] Exploring Operation: 75-1=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 1*75=75, Resulting Numbers: [75] 75,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[21, 95], Operations: ['99-98=1', '96-1=95'] Exploring Operation: 95-21=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 21+95=116, Resulting Numbers: [116] 116,39 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 67, 18, 68, 81 ]
100
[ "67-18=49", "68+81=149", "149-49=100" ]
Current State: 100:[67, 18, 68, 81], Operations: [] Exploring Operation: 67-18=49, Resulting Numbers: [68, 81, 49] Generated Node #2: [68, 81, 49] from Operation: 67-18=49 Current State: 100:[68, 81, 49], Operations: ['67-18=49'] Exploring Operation: 68+81=149, Resulting Numbers: [49, 149] Generated Node #3: [49, 149] from Operation: 68+81=149 Current State: 100:[49, 149], Operations: ['67-18=49', '68+81=149'] Exploring Operation: 149-49=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[67, 18, 68, 81], Operations: [] Exploring Operation: 81-68=13, Resulting Numbers: [67, 18, 13] Generated Node #0,0: 100:[67, 18, 13] Operation: 81-68=13 Exploring Operation: 68-67=1, Resulting Numbers: [18, 81, 1] Generated Node #0,1: 100:[18, 81, 1] Operation: 68-67=1 Moving to Node #0,0 Current State: 100:[67, 18, 13], Operations: ['81-68=13'] Exploring Operation: 67-13=54, Resulting Numbers: [18, 54] Generated Node #0,0,0: 100:[18, 54] Operation: 67-13=54 Exploring Operation: 67-18=49, Resulting Numbers: [13, 49] Generated Node #0,0,1: 100:[13, 49] Operation: 67-18=49 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[13, 49], Operations: ['81-68=13', '67-18=49'] Exploring Operation: 13+49=62, Resulting Numbers: [62] 62,100 unequal: No Solution Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,100 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 #0,0,0 Current State: 100:[18, 54], Operations: ['81-68=13', '67-13=54'] Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,100 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: 100:[18, 81, 1], Operations: ['68-67=1'] Exploring Operation: 18+81=99, Resulting Numbers: [1, 99] Generated Node #0,1,0: 100:[1, 99] Operation: 18+81=99 Exploring Operation: 81-18=63, Resulting Numbers: [1, 63] Generated Node #0,1,1: 100:[1, 63] Operation: 81-18=63 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 100:[1, 99], Operations: ['68-67=1', '18+81=99'] Exploring Operation: 1+99=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[67, 18, 68, 81], Operations: [] Exploring Operation: 68-67=1, Resulting Numbers: [18, 81, 1] Generated Node #0,1: 100:[18, 81, 1] Operation: 68-67=1 Moving to Node #0,1 Current State: 100:[18, 81, 1], Operations: ['68-67=1'] Exploring Operation: 18+81=99, Resulting Numbers: [1, 99] Generated Node #0,1,0: 100:[1, 99] Operation: 18+81=99 Moving to Node #0,1,0 Current State: 100:[1, 99], Operations: ['68-67=1', '18+81=99'] Exploring Operation: 1+99=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 60, 13, 12, 22 ]
13
[ "60-13=47", "12+22=34", "47-34=13" ]
Current State: 13:[60, 13, 12, 22], Operations: [] Exploring Operation: 60-13=47, Resulting Numbers: [12, 22, 47] Generated Node #2: [12, 22, 47] from Operation: 60-13=47 Current State: 13:[12, 22, 47], Operations: ['60-13=47'] Exploring Operation: 12+22=34, Resulting Numbers: [47, 34] Generated Node #3: [47, 34] from Operation: 12+22=34 Current State: 13:[47, 34], Operations: ['60-13=47', '12+22=34'] Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[60, 13, 12, 22], Operations: [] Exploring Operation: 60-22=38, Resulting Numbers: [13, 12, 38] Generated Node #0,0: 13:[13, 12, 38] Operation: 60-22=38 Exploring Operation: 60/12=5, Resulting Numbers: [13, 22, 5] Generated Node #0,1: 13:[13, 22, 5] Operation: 60/12=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[13, 22, 5], Operations: ['60/12=5'] Exploring Operation: 22-13=9, Resulting Numbers: [5, 9] Generated Node #0,1,0: 13:[5, 9] Operation: 22-13=9 Exploring Operation: 22-5=17, Resulting Numbers: [13, 17] Generated Node #0,1,1: 13:[13, 17] Operation: 22-5=17 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[13, 17], Operations: ['60/12=5', '22-5=17'] Exploring Operation: 13+17=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 17-13=4, Resulting Numbers: [4] 4,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 13:[5, 9], Operations: ['60/12=5', '22-13=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[13, 12, 38], Operations: ['60-22=38'] Exploring Operation: 38-12=26, Resulting Numbers: [13, 26] Generated Node #0,0,0: 13:[13, 26] Operation: 38-12=26 Exploring Operation: 38-13=25, Resulting Numbers: [12, 25] Generated Node #0,0,1: 13:[12, 25] Operation: 38-13=25 Moving to Node #0,0,0 Current State: 13:[13, 26], Operations: ['60-22=38', '38-12=26'] Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[60, 13, 12, 22], Operations: [] Exploring Operation: 60-22=38, Resulting Numbers: [13, 12, 38] Generated Node #0,0: 13:[13, 12, 38] Operation: 60-22=38 Moving to Node #0,0 Current State: 13:[13, 12, 38], Operations: ['60-22=38'] Exploring Operation: 38-12=26, Resulting Numbers: [13, 26] Generated Node #0,0,0: 13:[13, 26] Operation: 38-12=26 Moving to Node #0,0,0 Current State: 13:[13, 26], Operations: ['60-22=38', '38-12=26'] Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 40, 38, 38, 11 ]
60
[ "40-38=2", "11*2=22", "38+22=60" ]
Current State: 60:[40, 38, 38, 11], Operations: [] Exploring Operation: 40-38=2, Resulting Numbers: [11, 2] Generated Node #2: [11, 2] from Operation: 40-38=2 Current State: 60:[11, 2], Operations: ['40-38=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,60 equal: Goal Reached Exploring Operation: 38+22=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[40, 38, 38, 11], Operations: [] Exploring Operation: 40-38=2, Resulting Numbers: [38, 11, 2] Generated Node #0,0: 60:[38, 11, 2] Operation: 40-38=2 Moving to Node #0,0 Current State: 60:[38, 11, 2], Operations: ['40-38=2'] Exploring Operation: 38/2=19, Resulting Numbers: [11, 19] Generated Node #0,0,0: 60:[11, 19] Operation: 38/2=19 Moving to Node #0,0,0 Current State: 60:[11, 19], Operations: ['40-38=2', '38/2=19'] Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,60 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 30, 74, 3, 81 ]
37
[ "30+81=111", "111/3=37", "74-37=37" ]
Current State: 37:[30, 74, 3, 81], Operations: [] Exploring Operation: 30+81=111, Resulting Numbers: [74, 3, 111] Generated Node #2: [74, 3, 111] from Operation: 30+81=111 Current State: 37:[74, 3, 111], Operations: ['30+81=111'] Exploring Operation: 111/3=37, Resulting Numbers: [74, 37] Generated Node #3: [74, 37] from Operation: 111/3=37 Current State: 37:[74, 37], Operations: ['30+81=111', '111/3=37'] Exploring Operation: 74-37=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[30, 74, 3, 81], Operations: [] Exploring Operation: 74-30=44, Resulting Numbers: [3, 81, 44] Generated Node #0,0: 37:[3, 81, 44] Operation: 74-30=44 Exploring Operation: 30+3=33, Resulting Numbers: [74, 81, 33] Generated Node #0,1: 37:[74, 81, 33] Operation: 30+3=33 Exploring Operation: 81/3=27, Resulting Numbers: [30, 74, 27] Generated Node #0,2: 37:[30, 74, 27] Operation: 81/3=27 Exploring Operation: 81-74=7, Resulting Numbers: [30, 3, 7] Generated Node #0,3: 37:[30, 3, 7] Operation: 81-74=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 37:[30, 74, 27], Operations: ['81/3=27'] Exploring Operation: 74-27=47, Resulting Numbers: [30, 47] Generated Node #0,2,0: 37:[30, 47] Operation: 74-27=47 Exploring Operation: 30-27=3, Resulting Numbers: [74, 3] Generated Node #0,2,1: 37:[74, 3] Operation: 30-27=3 Exploring Operation: 30+27=57, Resulting Numbers: [74, 57] Generated Node #0,2,2: 37:[74, 57] Operation: 30+27=57 Exploring Operation: 74-30=44, Resulting Numbers: [27, 44] Generated Node #0,2,3: 37:[27, 44] Operation: 74-30=44 Moving to Node #0,2,0 Current State: 37:[30, 47], Operations: ['81/3=27', '74-27=47'] Exploring Operation: 30+47=77, Resulting Numbers: [77] 77,37 unequal: No Solution Exploring Operation: 30*47=1410, Resulting Numbers: [1410] 1410,37 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[27, 44], Operations: ['81/3=27', '74-30=44'] Exploring Operation: 27+44=71, Resulting Numbers: [71] 71,37 unequal: No Solution Exploring Operation: 27*44=1188, Resulting Numbers: [1188] 1188,37 unequal: No Solution Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[74, 57], Operations: ['81/3=27', '30+27=57'] Exploring Operation: 74+57=131, Resulting Numbers: [131] 131,37 unequal: No Solution Exploring Operation: 74*57=4218, Resulting Numbers: [4218] 4218,37 unequal: No Solution Exploring Operation: 74-57=17, Resulting Numbers: [17] 17,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[74, 3], Operations: ['81/3=27', '30-27=3'] Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,37 unequal: No Solution Exploring Operation: 74*3=222, Resulting Numbers: [222] 222,37 unequal: No Solution Exploring Operation: 74+3=77, Resulting Numbers: [77] 77,37 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 #0,3 Current State: 37:[30, 3, 7], Operations: ['81-74=7'] Exploring Operation: 3*7=21, Resulting Numbers: [30, 21] Generated Node #0,3,0: 37:[30, 21] Operation: 3*7=21 Exploring Operation: 3+7=10, Resulting Numbers: [30, 10] Generated Node #0,3,1: 37:[30, 10] Operation: 3+7=10 Exploring Operation: 30+3=33, Resulting Numbers: [7, 33] Generated Node #0,3,2: 37:[7, 33] Operation: 30+3=33 Exploring Operation: 30+7=37, Resulting Numbers: [3, 37] Generated Node #0,3,3: 37:[3, 37] Operation: 30+7=37 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 37:[30, 21], Operations: ['81-74=7', '3*7=21'] Exploring Operation: 30-21=9, Resulting Numbers: [9] 9,37 unequal: No Solution Exploring Operation: 30+21=51, Resulting Numbers: [51] 51,37 unequal: No Solution Exploring Operation: 30*21=630, Resulting Numbers: [630] 630,37 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 #0,3,1 Current State: 37:[30, 10], Operations: ['81-74=7', '3+7=10'] Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,37 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,37 unequal: No Solution Exploring Operation: 30*10=300, Resulting Numbers: [300] 300,37 unequal: No Solution Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,37 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:[7, 33], Operations: ['81-74=7', '30+3=33'] Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 7*33=231, Resulting Numbers: [231] 231,37 unequal: No Solution Exploring Operation: 7+33=40, Resulting Numbers: [40] 40,37 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:[3, 37], Operations: ['81-74=7', '30+7=37'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,37 unequal: No Solution Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 3*37=111, Resulting Numbers: [111] 111,37 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 #0,0 Current State: 37:[3, 81, 44], Operations: ['74-30=44'] Exploring Operation: 44-3=41, Resulting Numbers: [81, 41] Generated Node #0,0,0: 37:[81, 41] Operation: 44-3=41 Exploring Operation: 81-44=37, Resulting Numbers: [3, 37] Generated Node #0,0,1: 37:[3, 37] Operation: 81-44=37 Exploring Operation: 81-3=78, Resulting Numbers: [44, 78] Generated Node #0,0,2: 37:[44, 78] Operation: 81-3=78 Exploring Operation: 81/3=27, Resulting Numbers: [44, 27] Generated Node #0,0,3: 37:[44, 27] Operation: 81/3=27 Moving to Node #0,0,3 Current State: 37:[44, 27], Operations: ['74-30=44', '81/3=27'] Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 44+27=71, Resulting Numbers: [71] 71,37 unequal: No Solution Exploring Operation: 44*27=1188, Resulting Numbers: [1188] 1188,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[3, 37], Operations: ['74-30=44', '81-44=37'] Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 3*37=111, Resulting Numbers: [111] 111,37 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[44, 78], Operations: ['74-30=44', '81-3=78'] Exploring Operation: 44*78=3432, Resulting Numbers: [3432] 3432,37 unequal: No Solution Exploring Operation: 44+78=122, Resulting Numbers: [122] 122,37 unequal: No Solution Exploring Operation: 78-44=34, Resulting Numbers: [34] 34,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[81, 41], Operations: ['74-30=44', '44-3=41'] Exploring Operation: 81+41=122, Resulting Numbers: [122] 122,37 unequal: No Solution Exploring Operation: 81*41=3321, Resulting Numbers: [3321] 3321,37 unequal: No Solution Exploring Operation: 81-41=40, Resulting Numbers: [40] 40,37 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:[74, 81, 33], Operations: ['30+3=33'] Exploring Operation: 74+33=107, Resulting Numbers: [81, 107] Generated Node #0,1,0: 37:[81, 107] Operation: 74+33=107 Exploring Operation: 81-74=7, Resulting Numbers: [33, 7] Generated Node #0,1,1: 37:[33, 7] Operation: 81-74=7 Exploring Operation: 81-33=48, Resulting Numbers: [74, 48] Generated Node #0,1,2: 37:[74, 48] Operation: 81-33=48 Exploring Operation: 74-33=41, Resulting Numbers: [81, 41] Generated Node #0,1,3: 37:[81, 41] Operation: 74-33=41 Moving to Node #0,1,1 Current State: 37:[33, 7], Operations: ['30+3=33', '81-74=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,37 unequal: No Solution Moving to Node #0,1,3 Current State: 37:[81, 41], Operations: ['30+3=33', '74-33=41'] Exploring Operation: 81-41=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 81+41=122, Resulting Numbers: [122] 122,37 unequal: No Solution Exploring Operation: 81*41=3321, Resulting Numbers: [3321] 3321,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[74, 48], Operations: ['30+3=33', '81-33=48'] Exploring Operation: 74+48=122, Resulting Numbers: [122] 122,37 unequal: No Solution Exploring Operation: 74*48=3552, Resulting Numbers: [3552] 3552,37 unequal: No Solution Exploring Operation: 74-48=26, Resulting Numbers: [26] 26,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[81, 107], Operations: ['30+3=33', '74+33=107'] Exploring Operation: 107-81=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 81*107=8667, Resulting Numbers: [8667] 8667,37 unequal: No Solution Exploring Operation: 81+107=188, Resulting Numbers: [188] 188,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 61, 7, 36, 99 ]
70
[ "99-36=63", "63/7=9", "61+9=70" ]
Current State: 70:[61, 7, 36, 99], Operations: [] Exploring Operation: 99-36=63, Resulting Numbers: [61, 7, 63] Generated Node #2: [61, 7, 63] from Operation: 99-36=63 Current State: 70:[61, 7, 63], Operations: ['99-36=63'] Exploring Operation: 63/7=9, Resulting Numbers: [61, 9] Generated Node #3: [61, 9] from Operation: 63/7=9 Current State: 70:[61, 9], Operations: ['99-36=63', '63/7=9'] Exploring Operation: 61+9=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[61, 7, 36, 99], Operations: [] Exploring Operation: 99-61=38, Resulting Numbers: [7, 36, 38] Generated Node #0,0: 70:[7, 36, 38] Operation: 99-61=38 Moving to Node #0,0 Current State: 70:[7, 36, 38], Operations: ['99-61=38'] Exploring Operation: 38-36=2, Resulting Numbers: [7, 2] Generated Node #0,0,0: 70:[7, 2] Operation: 38-36=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[7, 2], Operations: ['99-61=38', '38-36=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,70 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
[ 34, 21, 13, 76 ]
75
[ "34-21=13", "13/13=1", "76-1=75" ]
Current State: 75:[34, 21, 13, 76], Operations: [] Exploring Operation: 34-21=13, Resulting Numbers: [13, 76, 13] Generated Node #2: [13, 76, 13] from Operation: 34-21=13 Current State: 75:[13, 76, 13], Operations: ['34-21=13'] Exploring Operation: 13/13=1, Resulting Numbers: [76, 1] Generated Node #3: [76, 1] from Operation: 13/13=1 Current State: 75:[76, 1], Operations: ['34-21=13', '13/13=1'] Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[34, 21, 13, 76], Operations: [] Exploring Operation: 34-13=21, Resulting Numbers: [21, 76, 21] Generated Node #0,0: 75:[21, 76, 21] Operation: 34-13=21 Exploring Operation: 34-21=13, Resulting Numbers: [13, 76, 13] Generated Node #0,1: 75:[13, 76, 13] Operation: 34-21=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[13, 76, 13], Operations: ['34-21=13'] Exploring Operation: 13/13=1, Resulting Numbers: [76, 1] Generated Node #0,1,0: 75:[76, 1] Operation: 13/13=1 Exploring Operation: 13+13=26, Resulting Numbers: [76, 26] Generated Node #0,1,1: 75:[76, 26] Operation: 13+13=26 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[76, 26], Operations: ['34-21=13', '13+13=26'] Exploring Operation: 76+26=102, Resulting Numbers: [102] 102,75 unequal: No Solution Exploring Operation: 76-26=50, Resulting Numbers: [50] 50,75 unequal: No Solution No 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: 75:[76, 1], Operations: ['34-21=13', '13/13=1'] Exploring Operation: 76*1=76, Resulting Numbers: [76] 76,75 unequal: No Solution Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[34, 21, 13, 76], Operations: [] Exploring Operation: 34-21=13, Resulting Numbers: [13, 76, 13] Generated Node #0,1: 75:[13, 76, 13] Operation: 34-21=13 Moving to Node #0,1 Current State: 75:[13, 76, 13], Operations: ['34-21=13'] Exploring Operation: 13/13=1, Resulting Numbers: [76, 1] Generated Node #0,1,0: 75:[76, 1] Operation: 13/13=1 Moving to Node #0,1,0 Current State: 75:[76, 1], Operations: ['34-21=13', '13/13=1'] Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 29, 87, 44, 79 ]
32
[ "87/29=3", "79-44=35", "35-3=32" ]
Current State: 32:[29, 87, 44, 79], Operations: [] Exploring Operation: 87/29=3, Resulting Numbers: [44, 79, 3] Generated Node #2: [44, 79, 3] from Operation: 87/29=3 Current State: 32:[44, 79, 3], Operations: ['87/29=3'] Exploring Operation: 79-44=35, Resulting Numbers: [3, 35] Generated Node #3: [3, 35] from Operation: 79-44=35 Current State: 32:[3, 35], Operations: ['87/29=3', '79-44=35'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[29, 87, 44, 79], Operations: [] Exploring Operation: 87/29=3, Resulting Numbers: [44, 79, 3] Generated Node #0,0: 32:[44, 79, 3] Operation: 87/29=3 Exploring Operation: 87-44=43, Resulting Numbers: [29, 79, 43] Generated Node #0,1: 32:[29, 79, 43] Operation: 87-44=43 Exploring Operation: 79-44=35, Resulting Numbers: [29, 87, 35] Generated Node #0,2: 32:[29, 87, 35] Operation: 79-44=35 Exploring Operation: 87-79=8, Resulting Numbers: [29, 44, 8] Generated Node #0,3: 32:[29, 44, 8] Operation: 87-79=8 Start Sub Search at level 1: Moving to Node #0,3 Current State: 32:[29, 44, 8], Operations: ['87-79=8'] Exploring Operation: 29+8=37, Resulting Numbers: [44, 37] Generated Node #0,3,0: 32:[44, 37] Operation: 29+8=37 Exploring Operation: 44-8=36, Resulting Numbers: [29, 36] Generated Node #0,3,1: 32:[29, 36] Operation: 44-8=36 Exploring Operation: 44-29=15, Resulting Numbers: [8, 15] Generated Node #0,3,2: 32:[8, 15] Operation: 44-29=15 Exploring Operation: 29-8=21, Resulting Numbers: [44, 21] Generated Node #0,3,3: 32:[44, 21] Operation: 29-8=21 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 32:[8, 15], Operations: ['87-79=8', '44-29=15'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,32 unequal: No Solution Exploring Operation: 8*15=120, Resulting Numbers: [120] 120,32 unequal: No Solution Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 32:[29, 36], Operations: ['87-79=8', '44-8=36'] Exploring Operation: 36-29=7, Resulting Numbers: [7] 7,32 unequal: No Solution Exploring Operation: 29*36=1044, Resulting Numbers: [1044] 1044,32 unequal: No Solution Exploring Operation: 29+36=65, Resulting Numbers: [65] 65,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 32:[44, 37], Operations: ['87-79=8', '29+8=37'] Exploring Operation: 44*37=1628, Resulting Numbers: [1628] 1628,32 unequal: No Solution Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,32 unequal: No Solution Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 32:[44, 21], Operations: ['87-79=8', '29-8=21'] Exploring Operation: 44+21=65, Resulting Numbers: [65] 65,32 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,32 unequal: No Solution Exploring Operation: 44*21=924, Resulting Numbers: [924] 924,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[44, 79, 3], Operations: ['87/29=3'] Exploring Operation: 79-44=35, Resulting Numbers: [3, 35] Generated Node #0,0,0: 32:[3, 35] Operation: 79-44=35 Exploring Operation: 44+3=47, Resulting Numbers: [79, 47] Generated Node #0,0,1: 32:[79, 47] Operation: 44+3=47 Exploring Operation: 79-3=76, Resulting Numbers: [44, 76] Generated Node #0,0,2: 32:[44, 76] Operation: 79-3=76 Exploring Operation: 44-3=41, Resulting Numbers: [79, 41] Generated Node #0,0,3: 32:[79, 41] Operation: 44-3=41 Moving to Node #0,0,0 Current State: 32:[3, 35], Operations: ['87/29=3', '79-44=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,32 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[29, 87, 44, 79], Operations: [] Exploring Operation: 87/29=3, Resulting Numbers: [44, 79, 3] Generated Node #0,0: 32:[44, 79, 3] Operation: 87/29=3 Moving to Node #0,0 Current State: 32:[44, 79, 3], Operations: ['87/29=3'] Exploring Operation: 79-44=35, Resulting Numbers: [3, 35] Generated Node #0,0,0: 32:[3, 35] Operation: 79-44=35 Moving to Node #0,0,0 Current State: 32:[3, 35], Operations: ['87/29=3', '79-44=35'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 85, 22, 2, 5 ]
60
[ "85-22=63", "5-2=3", "63-3=60" ]
Current State: 60:[85, 22, 2, 5], Operations: [] Exploring Operation: 85-22=63, Resulting Numbers: [2, 5, 63] Generated Node #2: [2, 5, 63] from Operation: 85-22=63 Current State: 60:[2, 5, 63], Operations: ['85-22=63'] Exploring Operation: 5-2=3, Resulting Numbers: [63, 3] Generated Node #3: [63, 3] from Operation: 5-2=3 Current State: 60:[63, 3], Operations: ['85-22=63', '5-2=3'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[85, 22, 2, 5], Operations: [] Exploring Operation: 85-22=63, Resulting Numbers: [2, 5, 63] Generated Node #0,0: 60:[2, 5, 63] Operation: 85-22=63 Exploring Operation: 22-2=20, Resulting Numbers: [85, 5, 20] Generated Node #0,1: 60:[85, 5, 20] Operation: 22-2=20 Exploring Operation: 85/5=17, Resulting Numbers: [22, 2, 17] Generated Node #0,2: 60:[22, 2, 17] Operation: 85/5=17 Exploring Operation: 85-5=80, Resulting Numbers: [22, 2, 80] Generated Node #0,3: 60:[22, 2, 80] Operation: 85-5=80 Exploring Operation: 85-2=83, Resulting Numbers: [22, 5, 83] Generated Node #0,4: 60:[22, 5, 83] Operation: 85-2=83 Moving to Node #0,0 Current State: 60:[2, 5, 63], Operations: ['85-22=63'] Exploring Operation: 2+5=7, Resulting Numbers: [63, 7] Generated Node #0,0,0: 60:[63, 7] Operation: 2+5=7 Exploring Operation: 63-5=58, Resulting Numbers: [2, 58] Generated Node #0,0,1: 60:[2, 58] Operation: 63-5=58 Exploring Operation: 5-2=3, Resulting Numbers: [63, 3] Generated Node #0,0,2: 60:[63, 3] Operation: 5-2=3 Exploring Operation: 63-2=61, Resulting Numbers: [5, 61] Generated Node #0,0,3: 60:[5, 61] Operation: 63-2=61 Exploring Operation: 2*5=10, Resulting Numbers: [63, 10] Generated Node #0,0,4: 60:[63, 10] Operation: 2*5=10 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 60:[5, 61], Operations: ['85-22=63', '63-2=61'] Exploring Operation: 5*61=305, Resulting Numbers: [305] 305,60 unequal: No Solution Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,60 unequal: No Solution Exploring Operation: 5+61=66, Resulting Numbers: [66] 66,60 unequal: No Solution No 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: 60:[2, 58], Operations: ['85-22=63', '63-5=58'] Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[85, 22, 2, 5], Operations: [] Exploring Operation: 85-22=63, Resulting Numbers: [2, 5, 63] Generated Node #0,0: 60:[2, 5, 63] Operation: 85-22=63 Moving to Node #0,0 Current State: 60:[2, 5, 63], Operations: ['85-22=63'] Exploring Operation: 63-5=58, Resulting Numbers: [2, 58] Generated Node #0,0,1: 60:[2, 58] Operation: 63-5=58 Moving to Node #0,0,1 Current State: 60:[2, 58], Operations: ['85-22=63', '63-5=58'] Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 27, 45, 48, 56 ]
80
[ "27+45=72", "56-48=8", "72+8=80" ]
Current State: 80:[27, 45, 48, 56], Operations: [] Exploring Operation: 27+45=72, Resulting Numbers: [48, 56, 72] Generated Node #2: [48, 56, 72] from Operation: 27+45=72 Current State: 80:[48, 56, 72], Operations: ['27+45=72'] Exploring Operation: 56-48=8, Resulting Numbers: [72, 8] Generated Node #3: [72, 8] from Operation: 56-48=8 Current State: 80:[72, 8], Operations: ['27+45=72', '56-48=8'] Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[27, 45, 48, 56], Operations: [] Exploring Operation: 56-48=8, Resulting Numbers: [27, 45, 8] Generated Node #0,0: 80:[27, 45, 8] Operation: 56-48=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[27, 45, 8], Operations: ['56-48=8'] Exploring Operation: 45-27=18, Resulting Numbers: [8, 18] Generated Node #0,0,0: 80:[8, 18] Operation: 45-27=18 Moving to Node #0,0,0 Current State: 80:[8, 18], Operations: ['56-48=8', '45-27=18'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,80 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
[ 43, 21, 87, 27 ]
92
[ "43-21=22", "87+27=114", "114-22=92" ]
Current State: 92:[43, 21, 87, 27], Operations: [] Exploring Operation: 43-21=22, Resulting Numbers: [87, 27, 22] Generated Node #2: [87, 27, 22] from Operation: 43-21=22 Current State: 92:[87, 27, 22], Operations: ['43-21=22'] Exploring Operation: 87+27=114, Resulting Numbers: [22, 114] Generated Node #3: [22, 114] from Operation: 87+27=114 Current State: 92:[22, 114], Operations: ['43-21=22', '87+27=114'] Exploring Operation: 114-22=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[43, 21, 87, 27], Operations: [] Exploring Operation: 87-43=44, Resulting Numbers: [21, 27, 44] Generated Node #0,0: 92:[21, 27, 44] Operation: 87-43=44 Moving to Node #0,0 Current State: 92:[21, 27, 44], Operations: ['87-43=44'] Exploring Operation: 21+27=48, Resulting Numbers: [44, 48] Generated Node #0,0,0: 92:[44, 48] Operation: 21+27=48 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[44, 48], Operations: ['87-43=44', '21+27=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[43, 21, 87, 27], Operations: [] Exploring Operation: 87-43=44, Resulting Numbers: [21, 27, 44] Generated Node #0,0: 92:[21, 27, 44] Operation: 87-43=44 Moving to Node #0,0 Current State: 92:[21, 27, 44], Operations: ['87-43=44'] Exploring Operation: 21+27=48, Resulting Numbers: [44, 48] Generated Node #0,0,0: 92:[44, 48] Operation: 21+27=48 Moving to Node #0,0,0 Current State: 92:[44, 48], Operations: ['87-43=44', '21+27=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 20, 94, 99, 38 ]
96
[ "20+94=114", "114/38=3", "99-3=96" ]
Current State: 96:[20, 94, 99, 38], Operations: [] Exploring Operation: 20+94=114, Resulting Numbers: [99, 38, 114] Generated Node #2: [99, 38, 114] from Operation: 20+94=114 Current State: 96:[99, 38, 114], Operations: ['20+94=114'] Exploring Operation: 114/38=3, Resulting Numbers: [99, 3] Generated Node #3: [99, 3] from Operation: 114/38=3 Current State: 96:[99, 3], Operations: ['20+94=114', '114/38=3'] Exploring Operation: 99-3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[20, 94, 99, 38], Operations: [] Exploring Operation: 38-20=18, Resulting Numbers: [94, 99, 18] Generated Node #0,0: 96:[94, 99, 18] Operation: 38-20=18 Exploring Operation: 99-94=5, Resulting Numbers: [20, 38, 5] Generated Node #0,1: 96:[20, 38, 5] Operation: 99-94=5 Exploring Operation: 20+38=58, Resulting Numbers: [94, 99, 58] Generated Node #0,2: 96:[94, 99, 58] Operation: 20+38=58 Moving to Node #0,0 Current State: 96:[94, 99, 18], Operations: ['38-20=18'] Exploring Operation: 94+18=112, Resulting Numbers: [99, 112] Generated Node #0,0,0: 96:[99, 112] Operation: 94+18=112 Exploring Operation: 99-18=81, Resulting Numbers: [94, 81] Generated Node #0,0,1: 96:[94, 81] Operation: 99-18=81 Exploring Operation: 99-94=5, Resulting Numbers: [18, 5] Generated Node #0,0,2: 96:[18, 5] Operation: 99-94=5 Moving to Node #0,1 Current State: 96:[20, 38, 5], Operations: ['99-94=5'] Exploring Operation: 38-20=18, Resulting Numbers: [5, 18] Generated Node #0,1,0: 96:[5, 18] Operation: 38-20=18 Exploring Operation: 38-5=33, Resulting Numbers: [20, 33] Generated Node #0,1,1: 96:[20, 33] Operation: 38-5=33 Exploring Operation: 20/5=4, Resulting Numbers: [38, 4] Generated Node #0,1,2: 96:[38, 4] Operation: 20/5=4 Moving to Node #0,2 Current State: 96:[94, 99, 58], Operations: ['20+38=58'] Exploring Operation: 99-58=41, Resulting Numbers: [94, 41] Generated Node #0,2,0: 96:[94, 41] Operation: 99-58=41 Exploring Operation: 99-94=5, Resulting Numbers: [58, 5] Generated Node #0,2,1: 96:[58, 5] Operation: 99-94=5 Exploring Operation: 94-58=36, Resulting Numbers: [99, 36] Generated Node #0,2,2: 96:[99, 36] Operation: 94-58=36 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 96:[99, 36], Operations: ['20+38=58', '94-58=36'] Exploring Operation: 99+36=135, Resulting Numbers: [135] 135,96 unequal: No Solution Exploring Operation: 99-36=63, Resulting Numbers: [63] 63,96 unequal: No Solution Exploring Operation: 99*36=3564, Resulting Numbers: [3564] 3564,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 96:[94, 41], Operations: ['20+38=58', '99-58=41'] Exploring Operation: 94-41=53, Resulting Numbers: [53] 53,96 unequal: No Solution Exploring Operation: 94*41=3854, Resulting Numbers: [3854] 3854,96 unequal: No Solution Exploring Operation: 94+41=135, Resulting Numbers: [135] 135,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 96:[58, 5], Operations: ['20+38=58', '99-94=5'] Exploring Operation: 58*5=290, Resulting Numbers: [290] 290,96 unequal: No Solution Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,96 unequal: No Solution Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,96 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: 96:[18, 5], Operations: ['38-20=18', '99-94=5'] Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,96 unequal: No Solution Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[5, 18], Operations: ['99-94=5', '38-20=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,96 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[20, 33], Operations: ['99-94=5', '38-5=33'] Exploring Operation: 33-20=13, Resulting Numbers: [13] 13,96 unequal: No Solution Exploring Operation: 20*33=660, Resulting Numbers: [660] 660,96 unequal: No Solution Exploring Operation: 20+33=53, Resulting Numbers: [53] 53,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[38, 4], Operations: ['99-94=5', '20/5=4'] Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,96 unequal: No Solution Exploring Operation: 38*4=152, Resulting Numbers: [152] 152,96 unequal: No Solution Exploring Operation: 38+4=42, Resulting Numbers: [42] 42,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[94, 81], Operations: ['38-20=18', '99-18=81'] Exploring Operation: 94*81=7614, Resulting Numbers: [7614] 7614,96 unequal: No Solution Exploring Operation: 94+81=175, Resulting Numbers: [175] 175,96 unequal: No Solution Exploring Operation: 94-81=13, Resulting Numbers: [13] 13,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[99, 112], Operations: ['38-20=18', '94+18=112'] Exploring Operation: 99*112=11088, Resulting Numbers: [11088] 11088,96 unequal: No Solution Exploring Operation: 99+112=211, Resulting Numbers: [211] 211,96 unequal: No Solution Exploring Operation: 112-99=13, Resulting Numbers: [13] 13,96 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 21, 53, 4, 43 ]
94
[ "21*4=84", "53-43=10", "84+10=94" ]
Current State: 94:[21, 53, 4, 43], Operations: [] Exploring Operation: 21*4=84, Resulting Numbers: [53, 43, 84] Generated Node #2: [53, 43, 84] from Operation: 21*4=84 Current State: 94:[53, 43, 84], Operations: ['21*4=84'] Exploring Operation: 53-43=10, Resulting Numbers: [84, 10] Generated Node #3: [84, 10] from Operation: 53-43=10 Current State: 94:[84, 10], Operations: ['21*4=84', '53-43=10'] Exploring Operation: 84+10=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[21, 53, 4, 43], Operations: [] Exploring Operation: 21*4=84, Resulting Numbers: [53, 43, 84] Generated Node #0,0: 94:[53, 43, 84] Operation: 21*4=84 Exploring Operation: 53-21=32, Resulting Numbers: [4, 43, 32] Generated Node #0,1: 94:[4, 43, 32] Operation: 53-21=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[53, 43, 84], Operations: ['21*4=84'] Exploring Operation: 53+43=96, Resulting Numbers: [84, 96] Generated Node #0,0,0: 94:[84, 96] Operation: 53+43=96 Exploring Operation: 84-43=41, Resulting Numbers: [53, 41] Generated Node #0,0,1: 94:[53, 41] Operation: 84-43=41 Moving to Node #0,0,0 Current State: 94:[84, 96], Operations: ['21*4=84', '53+43=96'] Exploring Operation: 84+96=180, Resulting Numbers: [180] 180,94 unequal: No Solution Exploring Operation: 96-84=12, Resulting Numbers: [12] 12,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[53, 41], Operations: ['21*4=84', '84-43=41'] Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[21, 53, 4, 43], Operations: [] Exploring Operation: 21*4=84, Resulting Numbers: [53, 43, 84] Generated Node #0,0: 94:[53, 43, 84] Operation: 21*4=84 Moving to Node #0,0 Current State: 94:[53, 43, 84], Operations: ['21*4=84'] Exploring Operation: 84-43=41, Resulting Numbers: [53, 41] Generated Node #0,0,1: 94:[53, 41] Operation: 84-43=41 Moving to Node #0,0,1 Current State: 94:[53, 41], Operations: ['21*4=84', '84-43=41'] Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 94, 14, 6, 8 ]
38
[ "14+8=22", "6*22=132", "132-94=38" ]
Current State: 38:[94, 14, 6, 8], Operations: [] Exploring Operation: 14+8=22, Resulting Numbers: [94, 6, 22] Generated Node #2: [94, 6, 22] from Operation: 14+8=22 Current State: 38:[94, 6, 22], Operations: ['14+8=22'] Exploring Operation: 6*22=132, Resulting Numbers: [94, 132] Generated Node #3: [94, 132] from Operation: 6*22=132 Current State: 38:[94, 132], Operations: ['14+8=22', '6*22=132'] Exploring Operation: 132-94=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[94, 14, 6, 8], Operations: [] Exploring Operation: 8-6=2, Resulting Numbers: [94, 14, 2] Generated Node #0,0: 38:[94, 14, 2] Operation: 8-6=2 Exploring Operation: 94-6=88, Resulting Numbers: [14, 8, 88] Generated Node #0,1: 38:[14, 8, 88] Operation: 94-6=88 Exploring Operation: 94-8=86, Resulting Numbers: [14, 6, 86] Generated Node #0,2: 38:[14, 6, 86] Operation: 94-8=86 Exploring Operation: 94-14=80, Resulting Numbers: [6, 8, 80] Generated Node #0,3: 38:[6, 8, 80] Operation: 94-14=80 Start Sub Search at level 1: Moving to Node #0,3 Current State: 38:[6, 8, 80], Operations: ['94-14=80'] Exploring Operation: 80-8=72, Resulting Numbers: [6, 72] Generated Node #0,3,0: 38:[6, 72] Operation: 80-8=72 Exploring Operation: 80/8=10, Resulting Numbers: [6, 10] Generated Node #0,3,1: 38:[6, 10] Operation: 80/8=10 Exploring Operation: 80-6=74, Resulting Numbers: [8, 74] Generated Node #0,3,2: 38:[8, 74] Operation: 80-6=74 Exploring Operation: 8-6=2, Resulting Numbers: [80, 2] Generated Node #0,3,3: 38:[80, 2] Operation: 8-6=2 Moving to Node #0,3,1 Current State: 38:[6, 10], Operations: ['94-14=80', '80/8=10'] Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,38 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,38 unequal: No Solution Moving to Node #0,3,0 Current State: 38:[6, 72], Operations: ['94-14=80', '80-8=72'] Exploring Operation: 72-6=66, Resulting Numbers: [66] 66,38 unequal: No Solution Exploring Operation: 6+72=78, Resulting Numbers: [78] 78,38 unequal: No Solution Exploring Operation: 6*72=432, Resulting Numbers: [432] 432,38 unequal: No Solution Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,38 unequal: No Solution Moving to Node #0,3,3 Current State: 38:[80, 2], Operations: ['94-14=80', '8-6=2'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,38 unequal: No Solution Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,38 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,38 unequal: No Solution Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,38 unequal: No Solution Moving to Node #0,3,2 Current State: 38:[8, 74], Operations: ['94-14=80', '80-6=74'] Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,38 unequal: No Solution Exploring Operation: 8+74=82, Resulting Numbers: [82] 82,38 unequal: No Solution Exploring Operation: 8*74=592, Resulting Numbers: [592] 592,38 unequal: No Solution No 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: 38:[14, 6, 86], Operations: ['94-8=86'] Exploring Operation: 86-6=80, Resulting Numbers: [14, 80] Generated Node #0,2,0: 38:[14, 80] Operation: 86-6=80 Exploring Operation: 14+6=20, Resulting Numbers: [86, 20] Generated Node #0,2,1: 38:[86, 20] Operation: 14+6=20 Exploring Operation: 14-6=8, Resulting Numbers: [86, 8] Generated Node #0,2,2: 38:[86, 8] Operation: 14-6=8 Exploring Operation: 86-14=72, Resulting Numbers: [6, 72] Generated Node #0,2,3: 38:[6, 72] Operation: 86-14=72 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 38:[6, 72], Operations: ['94-8=86', '86-14=72'] Exploring Operation: 6+72=78, Resulting Numbers: [78] 78,38 unequal: No Solution Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,38 unequal: No Solution Exploring Operation: 6*72=432, Resulting Numbers: [432] 432,38 unequal: No Solution Exploring Operation: 72-6=66, Resulting Numbers: [66] 66,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 38:[14, 80], Operations: ['94-8=86', '86-6=80'] Exploring Operation: 14+80=94, Resulting Numbers: [94] 94,38 unequal: No Solution Exploring Operation: 14*80=1120, Resulting Numbers: [1120] 1120,38 unequal: No Solution Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 38:[86, 20], Operations: ['94-8=86', '14+6=20'] Exploring Operation: 86-20=66, Resulting Numbers: [66] 66,38 unequal: No Solution Exploring Operation: 86+20=106, Resulting Numbers: [106] 106,38 unequal: No Solution Exploring Operation: 86*20=1720, Resulting Numbers: [1720] 1720,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 38:[86, 8], Operations: ['94-8=86', '14-6=8'] Exploring Operation: 86-8=78, Resulting Numbers: [78] 78,38 unequal: No Solution Exploring Operation: 86*8=688, Resulting Numbers: [688] 688,38 unequal: No Solution Exploring Operation: 86+8=94, Resulting Numbers: [94] 94,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[94, 14, 2], Operations: ['8-6=2'] Exploring Operation: 94-2=92, Resulting Numbers: [14, 92] Generated Node #0,0,0: 38:[14, 92] Operation: 94-2=92 Exploring Operation: 94/2=47, Resulting Numbers: [14, 47] Generated Node #0,0,1: 38:[14, 47] Operation: 94/2=47 Exploring Operation: 94-14=80, Resulting Numbers: [2, 80] Generated Node #0,0,2: 38:[2, 80] Operation: 94-14=80 Exploring Operation: 14+2=16, Resulting Numbers: [94, 16] Generated Node #0,0,3: 38:[94, 16] Operation: 14+2=16 Moving to Node #0,0,1 Current State: 38:[14, 47], Operations: ['8-6=2', '94/2=47'] Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,38 unequal: No Solution Exploring Operation: 14*47=658, Resulting Numbers: [658] 658,38 unequal: No Solution Exploring Operation: 14+47=61, Resulting Numbers: [61] 61,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[2, 80], Operations: ['8-6=2', '94-14=80'] Exploring Operation: 2+80=82, Resulting Numbers: [82] 82,38 unequal: No Solution Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,38 unequal: No Solution Exploring Operation: 2*80=160, Resulting Numbers: [160] 160,38 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,38 unequal: No Solution Moving to Node #0,0,3 Current State: 38:[94, 16], Operations: ['8-6=2', '14+2=16'] Exploring Operation: 94+16=110, Resulting Numbers: [110] 110,38 unequal: No Solution Exploring Operation: 94*16=1504, Resulting Numbers: [1504] 1504,38 unequal: No Solution Exploring Operation: 94-16=78, Resulting Numbers: [78] 78,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[14, 92], Operations: ['8-6=2', '94-2=92'] Exploring Operation: 92-14=78, Resulting Numbers: [78] 78,38 unequal: No Solution Exploring Operation: 14+92=106, Resulting Numbers: [106] 106,38 unequal: No Solution Exploring Operation: 14*92=1288, Resulting Numbers: [1288] 1288,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[14, 8, 88], Operations: ['94-6=88'] Exploring Operation: 88-14=74, Resulting Numbers: [8, 74] Generated Node #0,1,0: 38:[8, 74] Operation: 88-14=74 Exploring Operation: 88-8=80, Resulting Numbers: [14, 80] Generated Node #0,1,1: 38:[14, 80] Operation: 88-8=80 Exploring Operation: 88/8=11, Resulting Numbers: [14, 11] Generated Node #0,1,2: 38:[14, 11] Operation: 88/8=11 Exploring Operation: 14+8=22, Resulting Numbers: [88, 22] Generated Node #0,1,3: 38:[88, 22] Operation: 14+8=22 Moving to Node #0,1,2 Current State: 38:[14, 11], Operations: ['94-6=88', '88/8=11'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 14+11=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 14*11=154, Resulting Numbers: [154] 154,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[8, 74], Operations: ['94-6=88', '88-14=74'] Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,38 unequal: No Solution Exploring Operation: 8*74=592, Resulting Numbers: [592] 592,38 unequal: No Solution Exploring Operation: 8+74=82, Resulting Numbers: [82] 82,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[14, 80], Operations: ['94-6=88', '88-8=80'] Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,38 unequal: No Solution Exploring Operation: 14+80=94, Resulting Numbers: [94] 94,38 unequal: No Solution Exploring Operation: 14*80=1120, Resulting Numbers: [1120] 1120,38 unequal: No Solution Moving to Node #0,1,3 Current State: 38:[88, 22], Operations: ['94-6=88', '14+8=22'] Exploring Operation: 88-22=66, Resulting Numbers: [66] 66,38 unequal: No Solution Exploring Operation: 88/22=4, Resulting Numbers: [4] 4,38 unequal: No Solution Exploring Operation: 88+22=110, Resulting Numbers: [110] 110,38 unequal: No Solution Exploring Operation: 88*22=1936, Resulting Numbers: [1936] 1936,38 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