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
[ 90, 32, 7, 36 ]
30
[ "32+7=39", "39-36=3", "90/3=30" ]
Current State: 30:[90, 32, 7, 36], Operations: [] Exploring Operation: 32+7=39, Resulting Numbers: [90, 36, 39] Generated Node #2: [90, 36, 39] from Operation: 32+7=39 Current State: 30:[90, 36, 39], Operations: ['32+7=39'] Exploring Operation: 39-36=3, Resulting Numbers: [90, 3] Generated Node #3: [90, 3] from Operation: 39-36=3 Current State: 30:[90, 3], Operations: ['32+7=39', '39-36=3'] Exploring Operation: 90/3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[90, 32, 7, 36], Operations: [] Exploring Operation: 90-36=54, Resulting Numbers: [32, 7, 54] Generated Node #0,0: 30:[32, 7, 54] Operation: 90-36=54 Exploring Operation: 90-7=83, Resulting Numbers: [32, 36, 83] Generated Node #0,1: 30:[32, 36, 83] Operation: 90-7=83 Exploring Operation: 90-32=58, Resulting Numbers: [7, 36, 58] Generated Node #0,2: 30:[7, 36, 58] Operation: 90-32=58 Moving to Node #0,0 Current State: 30:[32, 7, 54], Operations: ['90-36=54'] Exploring Operation: 32-7=25, Resulting Numbers: [54, 25] Generated Node #0,0,0: 30:[54, 25] Operation: 32-7=25 Exploring Operation: 54-7=47, Resulting Numbers: [32, 47] Generated Node #0,0,1: 30:[32, 47] Operation: 54-7=47 Exploring Operation: 54-32=22, Resulting Numbers: [7, 22] Generated Node #0,0,2: 30:[7, 22] Operation: 54-32=22 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 30:[7, 22], Operations: ['90-36=54', '54-32=22'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 7*22=154, Resulting Numbers: [154] 154,30 unequal: No Solution Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[32, 47], Operations: ['90-36=54', '54-7=47'] Exploring Operation: 32+47=79, Resulting Numbers: [79] 79,30 unequal: No Solution Exploring Operation: 32*47=1504, Resulting Numbers: [1504] 1504,30 unequal: No Solution Exploring Operation: 47-32=15, Resulting Numbers: [15] 15,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[54, 25], Operations: ['90-36=54', '32-7=25'] Exploring Operation: 54*25=1350, Resulting Numbers: [1350] 1350,30 unequal: No Solution Exploring Operation: 54-25=29, Resulting Numbers: [29] 29,30 unequal: No Solution Exploring Operation: 54+25=79, Resulting Numbers: [79] 79,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 30:[7, 36, 58], Operations: ['90-32=58'] Exploring Operation: 58-7=51, Resulting Numbers: [36, 51] Generated Node #0,2,0: 30:[36, 51] Operation: 58-7=51 Exploring Operation: 36-7=29, Resulting Numbers: [58, 29] Generated Node #0,2,1: 30:[58, 29] Operation: 36-7=29 Exploring Operation: 58-36=22, Resulting Numbers: [7, 22] Generated Node #0,2,2: 30:[7, 22] Operation: 58-36=22 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 30:[7, 22], Operations: ['90-32=58', '58-36=22'] Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,30 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 7*22=154, Resulting Numbers: [154] 154,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 30:[36, 51], Operations: ['90-32=58', '58-7=51'] Exploring Operation: 36*51=1836, Resulting Numbers: [1836] 1836,30 unequal: No Solution Exploring Operation: 36+51=87, Resulting Numbers: [87] 87,30 unequal: No Solution Exploring Operation: 51-36=15, Resulting Numbers: [15] 15,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 30:[58, 29], Operations: ['90-32=58', '36-7=29'] Exploring Operation: 58-29=29, Resulting Numbers: [29] 29,30 unequal: No Solution Exploring Operation: 58/29=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 58+29=87, Resulting Numbers: [87] 87,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 30:[32, 36, 83], Operations: ['90-7=83'] Exploring Operation: 83-32=51, Resulting Numbers: [36, 51] Generated Node #0,1,0: 30:[36, 51] Operation: 83-32=51 Exploring Operation: 83-36=47, Resulting Numbers: [32, 47] Generated Node #0,1,1: 30:[32, 47] Operation: 83-36=47 Exploring Operation: 36-32=4, Resulting Numbers: [83, 4] Generated Node #0,1,2: 30:[83, 4] Operation: 36-32=4 Moving to Node #0,1,1 Current State: 30:[32, 47], Operations: ['90-7=83', '83-36=47'] Exploring Operation: 32+47=79, Resulting Numbers: [79] 79,30 unequal: No Solution Exploring Operation: 47-32=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 32*47=1504, Resulting Numbers: [1504] 1504,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[36, 51], Operations: ['90-7=83', '83-32=51'] Exploring Operation: 51-36=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 36*51=1836, Resulting Numbers: [1836] 1836,30 unequal: No Solution Exploring Operation: 36+51=87, Resulting Numbers: [87] 87,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[83, 4], Operations: ['90-7=83', '36-32=4'] Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,30 unequal: No Solution Exploring Operation: 83+4=87, Resulting Numbers: [87] 87,30 unequal: No Solution Exploring Operation: 83*4=332, Resulting Numbers: [332] 332,30 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 2, 84, 15, 46 ]
23
[ "2*46=92", "84-15=69", "92-69=23" ]
Current State: 23:[2, 84, 15, 46], Operations: [] Exploring Operation: 2*46=92, Resulting Numbers: [84, 15, 92] Generated Node #2: [84, 15, 92] from Operation: 2*46=92 Current State: 23:[84, 15, 92], Operations: ['2*46=92'] Exploring Operation: 84-15=69, Resulting Numbers: [92, 69] Generated Node #3: [92, 69] from Operation: 84-15=69 Current State: 23:[92, 69], Operations: ['2*46=92', '84-15=69'] Exploring Operation: 92-69=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[2, 84, 15, 46], Operations: [] Exploring Operation: 84/2=42, Resulting Numbers: [15, 46, 42] Generated Node #0,0: 23:[15, 46, 42] Operation: 84/2=42 Exploring Operation: 84-46=38, Resulting Numbers: [2, 15, 38] Generated Node #0,1: 23:[2, 15, 38] Operation: 84-46=38 Exploring Operation: 46/2=23, Resulting Numbers: [84, 15, 23] Generated Node #0,2: 23:[84, 15, 23] Operation: 46/2=23 Exploring Operation: 84-2=82, Resulting Numbers: [15, 46, 82] Generated Node #0,3: 23:[15, 46, 82] Operation: 84-2=82 Moving to Node #0,1 Current State: 23:[2, 15, 38], Operations: ['84-46=38'] Exploring Operation: 38/2=19, Resulting Numbers: [15, 19] Generated Node #0,1,0: 23:[15, 19] Operation: 38/2=19 Exploring Operation: 38-15=23, Resulting Numbers: [2, 23] Generated Node #0,1,1: 23:[2, 23] Operation: 38-15=23 Exploring Operation: 2+15=17, Resulting Numbers: [38, 17] Generated Node #0,1,2: 23:[38, 17] Operation: 2+15=17 Exploring Operation: 38-2=36, Resulting Numbers: [15, 36] Generated Node #0,1,3: 23:[15, 36] Operation: 38-2=36 Moving to Node #0,0 Current State: 23:[15, 46, 42], Operations: ['84/2=42'] Exploring Operation: 46-42=4, Resulting Numbers: [15, 4] Generated Node #0,0,0: 23:[15, 4] Operation: 46-42=4 Exploring Operation: 42-15=27, Resulting Numbers: [46, 27] Generated Node #0,0,1: 23:[46, 27] Operation: 42-15=27 Exploring Operation: 15+46=61, Resulting Numbers: [42, 61] Generated Node #0,0,2: 23:[42, 61] Operation: 15+46=61 Exploring Operation: 46-15=31, Resulting Numbers: [42, 31] Generated Node #0,0,3: 23:[42, 31] Operation: 46-15=31 Moving to Node #0,2 Current State: 23:[84, 15, 23], Operations: ['46/2=23'] Exploring Operation: 84-23=61, Resulting Numbers: [15, 61] Generated Node #0,2,0: 23:[15, 61] Operation: 84-23=61 Exploring Operation: 15+23=38, Resulting Numbers: [84, 38] Generated Node #0,2,1: 23:[84, 38] Operation: 15+23=38 Exploring Operation: 84+15=99, Resulting Numbers: [23, 99] Generated Node #0,2,2: 23:[23, 99] Operation: 84+15=99 Exploring Operation: 84-15=69, Resulting Numbers: [23, 69] Generated Node #0,2,3: 23:[23, 69] Operation: 84-15=69 Moving to Node #0,3 Current State: 23:[15, 46, 82], Operations: ['84-2=82'] Exploring Operation: 82-46=36, Resulting Numbers: [15, 36] Generated Node #0,3,0: 23:[15, 36] Operation: 82-46=36 Exploring Operation: 15+46=61, Resulting Numbers: [82, 61] Generated Node #0,3,1: 23:[82, 61] Operation: 15+46=61 Exploring Operation: 46-15=31, Resulting Numbers: [82, 31] Generated Node #0,3,2: 23:[82, 31] Operation: 46-15=31 Exploring Operation: 82-15=67, Resulting Numbers: [46, 67] Generated Node #0,3,3: 23:[46, 67] Operation: 82-15=67 Moving to Node #0,1,0 Current State: 23:[15, 19], Operations: ['84-46=38', '38/2=19'] Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,23 unequal: No Solution Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[38, 17], Operations: ['84-46=38', '2+15=17'] Exploring Operation: 38*17=646, Resulting Numbers: [646] 646,23 unequal: No Solution Exploring Operation: 38+17=55, Resulting Numbers: [55] 55,23 unequal: No Solution Exploring Operation: 38-17=21, Resulting Numbers: [21] 21,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[15, 36], Operations: ['84-2=82', '82-46=36'] Exploring Operation: 15*36=540, Resulting Numbers: [540] 540,23 unequal: No Solution Exploring Operation: 15+36=51, Resulting Numbers: [51] 51,23 unequal: No Solution Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[2, 23], Operations: ['84-46=38', '38-15=23'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,23 unequal: No Solution Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,23 unequal: No Solution Moving to Node #0,1,3 Current State: 23:[15, 36], Operations: ['84-46=38', '38-2=36'] Exploring Operation: 15*36=540, Resulting Numbers: [540] 540,23 unequal: No Solution Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 15+36=51, Resulting Numbers: [51] 51,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[42, 31], Operations: ['84/2=42', '46-15=31'] Exploring Operation: 42*31=1302, Resulting Numbers: [1302] 1302,23 unequal: No Solution Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 42+31=73, Resulting Numbers: [73] 73,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[46, 27], Operations: ['84/2=42', '42-15=27'] Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 46+27=73, Resulting Numbers: [73] 73,23 unequal: No Solution Exploring Operation: 46*27=1242, Resulting Numbers: [1242] 1242,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[15, 4], Operations: ['84/2=42', '46-42=4'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[23, 69], Operations: ['46/2=23', '84-15=69'] Exploring Operation: 23*69=1587, Resulting Numbers: [1587] 1587,23 unequal: No Solution Exploring Operation: 23+69=92, Resulting Numbers: [92] 92,23 unequal: No Solution Exploring Operation: 69/23=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 69-23=46, Resulting Numbers: [46] 46,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[15, 61], Operations: ['46/2=23', '84-23=61'] Exploring Operation: 15*61=915, Resulting Numbers: [915] 915,23 unequal: No Solution Exploring Operation: 61-15=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 15+61=76, Resulting Numbers: [76] 76,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[42, 61], Operations: ['84/2=42', '15+46=61'] Exploring Operation: 42+61=103, Resulting Numbers: [103] 103,23 unequal: No Solution Exploring Operation: 42*61=2562, Resulting Numbers: [2562] 2562,23 unequal: No Solution Exploring Operation: 61-42=19, Resulting Numbers: [19] 19,23 unequal: No Solution Moving to Node #0,3,2 Current State: 23:[82, 31], Operations: ['84-2=82', '46-15=31'] Exploring Operation: 82*31=2542, Resulting Numbers: [2542] 2542,23 unequal: No Solution Exploring Operation: 82+31=113, Resulting Numbers: [113] 113,23 unequal: No Solution Exploring Operation: 82-31=51, Resulting Numbers: [51] 51,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[46, 67], Operations: ['84-2=82', '82-15=67'] Exploring Operation: 46*67=3082, Resulting Numbers: [3082] 3082,23 unequal: No Solution Exploring Operation: 67-46=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 46+67=113, Resulting Numbers: [113] 113,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[23, 99], Operations: ['46/2=23', '84+15=99'] Exploring Operation: 23*99=2277, Resulting Numbers: [2277] 2277,23 unequal: No Solution Exploring Operation: 99-23=76, Resulting Numbers: [76] 76,23 unequal: No Solution Exploring Operation: 23+99=122, Resulting Numbers: [122] 122,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[84, 38], Operations: ['46/2=23', '15+23=38'] Exploring Operation: 84-38=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 84*38=3192, Resulting Numbers: [3192] 3192,23 unequal: No Solution Exploring Operation: 84+38=122, Resulting Numbers: [122] 122,23 unequal: No Solution Moving to Node #0,3,1 Current State: 23:[82, 61], Operations: ['84-2=82', '15+46=61'] Exploring Operation: 82*61=5002, Resulting Numbers: [5002] 5002,23 unequal: No Solution Exploring Operation: 82+61=143, Resulting Numbers: [143] 143,23 unequal: No Solution Exploring Operation: 82-61=21, Resulting Numbers: [21] 21,23 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 19, 55, 3, 13 ]
37
[ "19-13=6", "3*6=18", "55-18=37" ]
Current State: 37:[19, 55, 3, 13], Operations: [] Exploring Operation: 19-13=6, Resulting Numbers: [55, 3, 6] Generated Node #2: [55, 3, 6] from Operation: 19-13=6 Current State: 37:[55, 3, 6], Operations: ['19-13=6'] Exploring Operation: 3*6=18, Resulting Numbers: [55, 18] Generated Node #3: [55, 18] from Operation: 3*6=18 Current State: 37:[55, 18], Operations: ['19-13=6', '3*6=18'] Exploring Operation: 55-18=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[19, 55, 3, 13], Operations: [] Exploring Operation: 55-3=52, Resulting Numbers: [19, 13, 52] Generated Node #0,0: 37:[19, 13, 52] Operation: 55-3=52 Exploring Operation: 19+3=22, Resulting Numbers: [55, 13, 22] Generated Node #0,1: 37:[55, 13, 22] Operation: 19+3=22 Exploring Operation: 19+13=32, Resulting Numbers: [55, 3, 32] Generated Node #0,2: 37:[55, 3, 32] Operation: 19+13=32 Exploring Operation: 3*13=39, Resulting Numbers: [19, 55, 39] Generated Node #0,3: 37:[19, 55, 39] Operation: 3*13=39 Start Sub Search at level 1: Moving to Node #0,3 Current State: 37:[19, 55, 39], Operations: ['3*13=39'] Exploring Operation: 19+55=74, Resulting Numbers: [39, 74] Generated Node #0,3,0: 37:[39, 74] Operation: 19+55=74 Exploring Operation: 55-19=36, Resulting Numbers: [39, 36] Generated Node #0,3,1: 37:[39, 36] Operation: 55-19=36 Exploring Operation: 39-19=20, Resulting Numbers: [55, 20] Generated Node #0,3,2: 37:[55, 20] Operation: 39-19=20 Exploring Operation: 19+39=58, Resulting Numbers: [55, 58] Generated Node #0,3,3: 37:[55, 58] Operation: 19+39=58 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 37:[39, 36], Operations: ['3*13=39', '55-19=36'] Exploring Operation: 39*36=1404, Resulting Numbers: [1404] 1404,37 unequal: No Solution Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,37 unequal: No Solution Exploring Operation: 39+36=75, Resulting Numbers: [75] 75,37 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:[55, 20], Operations: ['3*13=39', '39-19=20'] Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,37 unequal: No Solution Exploring Operation: 55*20=1100, Resulting Numbers: [1100] 1100,37 unequal: No Solution Exploring Operation: 55+20=75, Resulting Numbers: [75] 75,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 37:[39, 74], Operations: ['3*13=39', '19+55=74'] Exploring Operation: 74-39=35, Resulting Numbers: [35] 35,37 unequal: No Solution Exploring Operation: 39*74=2886, Resulting Numbers: [2886] 2886,37 unequal: No Solution Exploring Operation: 39+74=113, Resulting Numbers: [113] 113,37 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:[55, 58], Operations: ['3*13=39', '19+39=58'] Exploring Operation: 55+58=113, Resulting Numbers: [113] 113,37 unequal: No Solution Exploring Operation: 55*58=3190, Resulting Numbers: [3190] 3190,37 unequal: No Solution Exploring Operation: 58-55=3, Resulting Numbers: [3] 3,37 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:[19, 13, 52], Operations: ['55-3=52'] Exploring Operation: 19+13=32, Resulting Numbers: [52, 32] Generated Node #0,0,0: 37:[52, 32] Operation: 19+13=32 Exploring Operation: 52-13=39, Resulting Numbers: [19, 39] Generated Node #0,0,1: 37:[19, 39] Operation: 52-13=39 Exploring Operation: 52-19=33, Resulting Numbers: [13, 33] Generated Node #0,0,2: 37:[13, 33] Operation: 52-19=33 Exploring Operation: 19-13=6, Resulting Numbers: [52, 6] Generated Node #0,0,3: 37:[52, 6] Operation: 19-13=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[52, 32], Operations: ['55-3=52', '19+13=32'] Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,37 unequal: No Solution Exploring Operation: 52*32=1664, Resulting Numbers: [1664] 1664,37 unequal: No Solution Exploring Operation: 52+32=84, Resulting Numbers: [84] 84,37 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 #0,0,1 Current State: 37:[19, 39], Operations: ['55-3=52', '52-13=39'] Exploring Operation: 19*39=741, Resulting Numbers: [741] 741,37 unequal: No Solution Exploring Operation: 19+39=58, Resulting Numbers: [58] 58,37 unequal: No Solution Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,37 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 #0,0,2 Current State: 37:[13, 33], Operations: ['55-3=52', '52-19=33'] Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,37 unequal: No Solution Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,37 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,37 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 #0,0,3 Current State: 37:[52, 6], Operations: ['55-3=52', '19-13=6'] Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,37 unequal: No Solution Exploring Operation: 52*6=312, Resulting Numbers: [312] 312,37 unequal: No Solution Exploring Operation: 52+6=58, Resulting Numbers: [58] 58,37 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 #0,1 Current State: 37:[55, 13, 22], Operations: ['19+3=22'] Exploring Operation: 55+13=68, Resulting Numbers: [22, 68] Generated Node #0,1,0: 37:[22, 68] Operation: 55+13=68 Exploring Operation: 55-22=33, Resulting Numbers: [13, 33] Generated Node #0,1,1: 37:[13, 33] Operation: 55-22=33 Exploring Operation: 13+22=35, Resulting Numbers: [55, 35] Generated Node #0,1,2: 37:[55, 35] Operation: 13+22=35 Exploring Operation: 55-13=42, Resulting Numbers: [22, 42] Generated Node #0,1,3: 37:[22, 42] Operation: 55-13=42 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 37:[55, 35], Operations: ['19+3=22', '13+22=35'] Exploring Operation: 55*35=1925, Resulting Numbers: [1925] 1925,37 unequal: No Solution Exploring Operation: 55+35=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,37 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 #0,1,3 Current State: 37:[22, 42], Operations: ['19+3=22', '55-13=42'] Exploring Operation: 22*42=924, Resulting Numbers: [924] 924,37 unequal: No Solution Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,37 unequal: No Solution Exploring Operation: 22+42=64, Resulting Numbers: [64] 64,37 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 #0,1,1 Current State: 37:[13, 33], Operations: ['19+3=22', '55-22=33'] Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,37 unequal: No Solution Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,37 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,37 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 #0,1,0 Current State: 37:[22, 68], Operations: ['19+3=22', '55+13=68'] Exploring Operation: 22*68=1496, Resulting Numbers: [1496] 1496,37 unequal: No Solution Exploring Operation: 22+68=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 68-22=46, Resulting Numbers: [46] 46,37 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 #0,2 Current State: 37:[55, 3, 32], Operations: ['19+13=32'] Exploring Operation: 3+32=35, Resulting Numbers: [55, 35] Generated Node #0,2,0: 37:[55, 35] Operation: 3+32=35 Exploring Operation: 55+3=58, Resulting Numbers: [32, 58] Generated Node #0,2,1: 37:[32, 58] Operation: 55+3=58 Exploring Operation: 32-3=29, Resulting Numbers: [55, 29] Generated Node #0,2,2: 37:[55, 29] Operation: 32-3=29 Exploring Operation: 55-3=52, Resulting Numbers: [32, 52] Generated Node #0,2,3: 37:[32, 52] Operation: 55-3=52 Moving to Node #0,2,0 Current State: 37:[55, 35], Operations: ['19+13=32', '3+32=35'] Exploring Operation: 55+35=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,37 unequal: No Solution Exploring Operation: 55*35=1925, Resulting Numbers: [1925] 1925,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[32, 52], Operations: ['19+13=32', '55-3=52'] Exploring Operation: 32+52=84, Resulting Numbers: [84] 84,37 unequal: No Solution Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,37 unequal: No Solution Exploring Operation: 32*52=1664, Resulting Numbers: [1664] 1664,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[55, 29], Operations: ['19+13=32', '32-3=29'] Exploring Operation: 55+29=84, Resulting Numbers: [84] 84,37 unequal: No Solution Exploring Operation: 55*29=1595, Resulting Numbers: [1595] 1595,37 unequal: No Solution Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[32, 58], Operations: ['19+13=32', '55+3=58'] Exploring Operation: 58-32=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 32+58=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 32*58=1856, Resulting Numbers: [1856] 1856,37 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, 53, 59, 85 ]
18
[ "61-53=8", "59+85=144", "144/8=18" ]
Current State: 18:[61, 53, 59, 85], Operations: [] Exploring Operation: 61-53=8, Resulting Numbers: [59, 85, 8] Generated Node #2: [59, 85, 8] from Operation: 61-53=8 Current State: 18:[59, 85, 8], Operations: ['61-53=8'] Exploring Operation: 59+85=144, Resulting Numbers: [8, 144] Generated Node #3: [8, 144] from Operation: 59+85=144 Current State: 18:[8, 144], Operations: ['61-53=8', '59+85=144'] Exploring Operation: 144/8=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[61, 53, 59, 85], Operations: [] Exploring Operation: 85-59=26, Resulting Numbers: [61, 53, 26] Generated Node #0,0: 18:[61, 53, 26] Operation: 85-59=26 Exploring Operation: 85-61=24, Resulting Numbers: [53, 59, 24] Generated Node #0,1: 18:[53, 59, 24] Operation: 85-61=24 Moving to Node #0,1 Current State: 18:[53, 59, 24], Operations: ['85-61=24'] Exploring Operation: 59-53=6, Resulting Numbers: [24, 6] Generated Node #0,1,0: 18:[24, 6] Operation: 59-53=6 Exploring Operation: 53-24=29, Resulting Numbers: [59, 29] Generated Node #0,1,1: 18:[59, 29] Operation: 53-24=29 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[24, 6], Operations: ['85-61=24', '59-53=6'] Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[61, 53, 59, 85], Operations: [] Exploring Operation: 85-61=24, Resulting Numbers: [53, 59, 24] Generated Node #0,1: 18:[53, 59, 24] Operation: 85-61=24 Moving to Node #0,1 Current State: 18:[53, 59, 24], Operations: ['85-61=24'] Exploring Operation: 59-53=6, Resulting Numbers: [24, 6] Generated Node #0,1,0: 18:[24, 6] Operation: 59-53=6 Moving to Node #0,1,0 Current State: 18:[24, 6], Operations: ['85-61=24', '59-53=6'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 33, 78, 1, 35 ]
15
[ "33*35=1155", "78-1=77", "1155/77=15" ]
Current State: 15:[33, 78, 1, 35], Operations: [] Exploring Operation: 33*35=1155, Resulting Numbers: [78, 1, 1155] Generated Node #2: [78, 1, 1155] from Operation: 33*35=1155 Current State: 15:[78, 1, 1155], Operations: ['33*35=1155'] Exploring Operation: 78-1=77, Resulting Numbers: [1155, 77] Generated Node #3: [1155, 77] from Operation: 78-1=77 Current State: 15:[1155, 77], Operations: ['33*35=1155', '78-1=77'] Exploring Operation: 1155/77=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[33, 78, 1, 35], Operations: [] Exploring Operation: 78-33=45, Resulting Numbers: [1, 35, 45] Generated Node #0,0: 15:[1, 35, 45] Operation: 78-33=45 Exploring Operation: 78-35=43, Resulting Numbers: [33, 1, 43] Generated Node #0,1: 15:[33, 1, 43] Operation: 78-35=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[33, 1, 43], Operations: ['78-35=43'] Exploring Operation: 43-33=10, Resulting Numbers: [1, 10] Generated Node #0,1,0: 15:[1, 10] Operation: 43-33=10 Exploring Operation: 33-1=32, Resulting Numbers: [43, 32] Generated Node #0,1,1: 15:[43, 32] Operation: 33-1=32 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 15:[1, 10], Operations: ['78-35=43', '43-33=10'] Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,15 unequal: No Solution Exploring Operation: 1+10=11, Resulting Numbers: [11] 11,15 unequal: No Solution No 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: 15:[43, 32], Operations: ['78-35=43', '33-1=32'] Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,15 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,15 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: 15:[1, 35, 45], Operations: ['78-33=45'] Exploring Operation: 45-35=10, Resulting Numbers: [1, 10] Generated Node #0,0,0: 15:[1, 10] Operation: 45-35=10 Exploring Operation: 35-1=34, Resulting Numbers: [45, 34] Generated Node #0,0,1: 15:[45, 34] Operation: 35-1=34 Moving to Node #0,0,0 Current State: 15:[1, 10], Operations: ['78-33=45', '45-35=10'] Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,15 unequal: No Solution Exploring Operation: 1+10=11, Resulting Numbers: [11] 11,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[45, 34], Operations: ['78-33=45', '35-1=34'] Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,15 unequal: No Solution Exploring Operation: 45+34=79, Resulting Numbers: [79] 79,15 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
[ 60, 27, 88, 86 ]
93
[ "88-86=2", "60*2=120", "120-27=93" ]
Current State: 93:[60, 27, 88, 86], Operations: [] Exploring Operation: 88-86=2, Resulting Numbers: [60, 27, 2] Generated Node #2: [60, 27, 2] from Operation: 88-86=2 Current State: 93:[60, 27, 2], Operations: ['88-86=2'] Exploring Operation: 60*2=120, Resulting Numbers: [27, 120] Generated Node #3: [27, 120] from Operation: 60*2=120 Current State: 93:[27, 120], Operations: ['88-86=2', '60*2=120'] Exploring Operation: 120-27=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[60, 27, 88, 86], Operations: [] Exploring Operation: 88-60=28, Resulting Numbers: [27, 86, 28] Generated Node #0,0: 93:[27, 86, 28] Operation: 88-60=28 Exploring Operation: 60-27=33, Resulting Numbers: [88, 86, 33] Generated Node #0,1: 93:[88, 86, 33] Operation: 60-27=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[27, 86, 28], Operations: ['88-60=28'] Exploring Operation: 28-27=1, Resulting Numbers: [86, 1] Generated Node #0,0,0: 93:[86, 1] Operation: 28-27=1 Exploring Operation: 27+86=113, Resulting Numbers: [28, 113] Generated Node #0,0,1: 93:[28, 113] Operation: 27+86=113 Moving to Node #0,0,0 Current State: 93:[86, 1], Operations: ['88-60=28', '28-27=1'] Exploring Operation: 86+1=87, Resulting Numbers: [87] 87,93 unequal: No Solution Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[28, 113], Operations: ['88-60=28', '27+86=113'] Exploring Operation: 113-28=85, Resulting Numbers: [85] 85,93 unequal: No Solution Exploring Operation: 28+113=141, Resulting Numbers: [141] 141,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[88, 86, 33], Operations: ['60-27=33'] Exploring Operation: 88-86=2, Resulting Numbers: [33, 2] Generated Node #0,1,0: 93:[33, 2] Operation: 88-86=2 Exploring Operation: 86-33=53, Resulting Numbers: [88, 53] Generated Node #0,1,1: 93:[88, 53] Operation: 86-33=53 Moving to Node #0,1,0 Current State: 93:[33, 2], Operations: ['60-27=33', '88-86=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,93 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,93 unequal: No Solution Moving to Node #0,1,1 Current State: 93:[88, 53], Operations: ['60-27=33', '86-33=53'] Exploring Operation: 88-53=35, Resulting Numbers: [35] 35,93 unequal: No Solution Exploring Operation: 88+53=141, Resulting Numbers: [141] 141,93 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
[ 35, 31, 28, 61 ]
24
[ "61-31=30", "28*30=840", "840/35=24" ]
Current State: 24:[35, 31, 28, 61], Operations: [] Exploring Operation: 61-31=30, Resulting Numbers: [35, 28, 30] Generated Node #2: [35, 28, 30] from Operation: 61-31=30 Current State: 24:[35, 28, 30], Operations: ['61-31=30'] Exploring Operation: 28*30=840, Resulting Numbers: [35, 840] Generated Node #3: [35, 840] from Operation: 28*30=840 Current State: 24:[35, 840], Operations: ['61-31=30', '28*30=840'] Exploring Operation: 840/35=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[35, 31, 28, 61], Operations: [] Exploring Operation: 61-35=26, Resulting Numbers: [31, 28, 26] Generated Node #0,0: 24:[31, 28, 26] Operation: 61-35=26 Moving to Node #0,0 Current State: 24:[31, 28, 26], Operations: ['61-35=26'] Exploring Operation: 31-28=3, Resulting Numbers: [26, 3] Generated Node #0,0,0: 24:[26, 3] Operation: 31-28=3 Moving to Node #0,0,0 Current State: 24:[26, 3], Operations: ['61-35=26', '31-28=3'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,24 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 96, 36, 93, 84 ]
100
[ "93-84=9", "36/9=4", "96+4=100" ]
Current State: 100:[96, 36, 93, 84], Operations: [] Exploring Operation: 93-84=9, Resulting Numbers: [96, 36, 9] Generated Node #2: [96, 36, 9] from Operation: 93-84=9 Current State: 100:[96, 36, 9], Operations: ['93-84=9'] Exploring Operation: 36/9=4, Resulting Numbers: [96, 4] Generated Node #3: [96, 4] from Operation: 36/9=4 Current State: 100:[96, 4], Operations: ['93-84=9', '36/9=4'] Exploring Operation: 96+4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[96, 36, 93, 84], Operations: [] Exploring Operation: 84-36=48, Resulting Numbers: [96, 93, 48] Generated Node #0,0: 100:[96, 93, 48] Operation: 84-36=48 Exploring Operation: 96-84=12, Resulting Numbers: [36, 93, 12] Generated Node #0,1: 100:[36, 93, 12] Operation: 96-84=12 Exploring Operation: 93-84=9, Resulting Numbers: [96, 36, 9] Generated Node #0,2: 100:[96, 36, 9] Operation: 93-84=9 Moving to Node #0,0 Current State: 100:[96, 93, 48], Operations: ['84-36=48'] Exploring Operation: 96-93=3, Resulting Numbers: [48, 3] Generated Node #0,0,0: 100:[48, 3] Operation: 96-93=3 Exploring Operation: 96/48=2, Resulting Numbers: [93, 2] Generated Node #0,0,1: 100:[93, 2] Operation: 96/48=2 Exploring Operation: 96-48=48, Resulting Numbers: [93, 48] Generated Node #0,0,2: 100:[93, 48] Operation: 96-48=48 Moving to Node #0,2 Current State: 100:[96, 36, 9], Operations: ['93-84=9'] Exploring Operation: 36-9=27, Resulting Numbers: [96, 27] Generated Node #0,2,0: 100:[96, 27] Operation: 36-9=27 Exploring Operation: 36+9=45, Resulting Numbers: [96, 45] Generated Node #0,2,1: 100:[96, 45] Operation: 36+9=45 Exploring Operation: 36/9=4, Resulting Numbers: [96, 4] Generated Node #0,2,2: 100:[96, 4] Operation: 36/9=4 Moving to Node #0,1 Current State: 100:[36, 93, 12], Operations: ['96-84=12'] Exploring Operation: 36/12=3, Resulting Numbers: [93, 3] Generated Node #0,1,0: 100:[93, 3] Operation: 36/12=3 Exploring Operation: 93-36=57, Resulting Numbers: [12, 57] Generated Node #0,1,1: 100:[12, 57] Operation: 93-36=57 Exploring Operation: 36-12=24, Resulting Numbers: [93, 24] Generated Node #0,1,2: 100:[93, 24] Operation: 36-12=24 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 100:[93, 3], Operations: ['96-84=12', '36/12=3'] Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,100 unequal: No Solution Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,100 unequal: No Solution Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 100:[93, 24], Operations: ['96-84=12', '36-12=24'] Exploring Operation: 93-24=69, Resulting Numbers: [69] 69,100 unequal: No Solution Exploring Operation: 93+24=117, Resulting Numbers: [117] 117,100 unequal: No Solution Exploring Operation: 93*24=2232, Resulting Numbers: [2232] 2232,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 100:[12, 57], Operations: ['96-84=12', '93-36=57'] Exploring Operation: 57-12=45, Resulting Numbers: [45] 45,100 unequal: No Solution Exploring Operation: 12*57=684, Resulting Numbers: [684] 684,100 unequal: No Solution Exploring Operation: 12+57=69, Resulting Numbers: [69] 69,100 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: 100:[48, 3], Operations: ['84-36=48', '96-93=3'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,100 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,100 unequal: No Solution Moving to Node #0,2,2 Current State: 100:[96, 4], Operations: ['93-84=9', '36/9=4'] Exploring Operation: 96-4=92, Resulting Numbers: [92] 92,100 unequal: No Solution Exploring Operation: 96/4=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 96+4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[96, 36, 93, 84], Operations: [] Exploring Operation: 93-84=9, Resulting Numbers: [96, 36, 9] Generated Node #0,2: 100:[96, 36, 9] Operation: 93-84=9 Moving to Node #0,2 Current State: 100:[96, 36, 9], Operations: ['93-84=9'] Exploring Operation: 36/9=4, Resulting Numbers: [96, 4] Generated Node #0,2,2: 100:[96, 4] Operation: 36/9=4 Moving to Node #0,2,2 Current State: 100:[96, 4], Operations: ['93-84=9', '36/9=4'] Exploring Operation: 96+4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.97309
hs_3
mult_heuristic
[ 72, 99, 6, 46 ]
67
[ "99-72=27", "46-6=40", "27+40=67" ]
Current State: 67:[72, 99, 6, 46], Operations: [] Exploring Operation: 99-72=27, Resulting Numbers: [6, 46, 27] Generated Node #2: [6, 46, 27] from Operation: 99-72=27 Current State: 67:[6, 46, 27], Operations: ['99-72=27'] Exploring Operation: 46-6=40, Resulting Numbers: [27, 40] Generated Node #3: [27, 40] from Operation: 46-6=40 Current State: 67:[27, 40], Operations: ['99-72=27', '46-6=40'] Exploring Operation: 27+40=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[72, 99, 6, 46], Operations: [] Exploring Operation: 6+46=52, Resulting Numbers: [72, 99, 52] Generated Node #0,0: 67:[72, 99, 52] Operation: 6+46=52 Exploring Operation: 99-6=93, Resulting Numbers: [72, 46, 93] Generated Node #0,1: 67:[72, 46, 93] Operation: 99-6=93 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[72, 99, 52], Operations: ['6+46=52'] Exploring Operation: 99-52=47, Resulting Numbers: [72, 47] Generated Node #0,0,0: 67:[72, 47] Operation: 99-52=47 Exploring Operation: 99-72=27, Resulting Numbers: [52, 27] Generated Node #0,0,1: 67:[52, 27] Operation: 99-72=27 Moving to Node #0,0,0 Current State: 67:[72, 47], Operations: ['6+46=52', '99-52=47'] Exploring Operation: 72+47=119, Resulting Numbers: [119] 119,67 unequal: No Solution Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[52, 27], Operations: ['6+46=52', '99-72=27'] Exploring Operation: 52+27=79, Resulting Numbers: [79] 79,67 unequal: No Solution Exploring Operation: 52-27=25, Resulting Numbers: [25] 25,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[72, 46, 93], Operations: ['99-6=93'] Exploring Operation: 72-46=26, Resulting Numbers: [93, 26] Generated Node #0,1,0: 67:[93, 26] Operation: 72-46=26 Exploring Operation: 93-46=47, Resulting Numbers: [72, 47] Generated Node #0,1,1: 67:[72, 47] Operation: 93-46=47 Moving to Node #0,1,1 Current State: 67:[72, 47], Operations: ['99-6=93', '93-46=47'] Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,67 unequal: No Solution Exploring Operation: 72+47=119, Resulting Numbers: [119] 119,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[93, 26], Operations: ['99-6=93', '72-46=26'] Exploring Operation: 93-26=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[72, 99, 6, 46], Operations: [] Exploring Operation: 99-6=93, Resulting Numbers: [72, 46, 93] Generated Node #0,1: 67:[72, 46, 93] Operation: 99-6=93 Moving to Node #0,1 Current State: 67:[72, 46, 93], Operations: ['99-6=93'] Exploring Operation: 72-46=26, Resulting Numbers: [93, 26] Generated Node #0,1,0: 67:[93, 26] Operation: 72-46=26 Moving to Node #0,1,0 Current State: 67:[93, 26], Operations: ['99-6=93', '72-46=26'] Exploring Operation: 93-26=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_2
mult_heuristic
[ 61, 30, 70, 92 ]
69
[ "61+30=91", "92-70=22", "91-22=69" ]
Current State: 69:[61, 30, 70, 92], Operations: [] Exploring Operation: 61+30=91, Resulting Numbers: [70, 92, 91] Generated Node #2: [70, 92, 91] from Operation: 61+30=91 Current State: 69:[70, 92, 91], Operations: ['61+30=91'] Exploring Operation: 92-70=22, Resulting Numbers: [91, 22] Generated Node #3: [91, 22] from Operation: 92-70=22 Current State: 69:[91, 22], Operations: ['61+30=91', '92-70=22'] Exploring Operation: 91-22=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[61, 30, 70, 92], Operations: [] Exploring Operation: 92-61=31, Resulting Numbers: [30, 70, 31] Generated Node #0,0: 69:[30, 70, 31] Operation: 92-61=31 Exploring Operation: 92-30=62, Resulting Numbers: [61, 70, 62] Generated Node #0,1: 69:[61, 70, 62] Operation: 92-30=62 Moving to Node #0,0 Current State: 69:[30, 70, 31], Operations: ['92-61=31'] Exploring Operation: 31-30=1, Resulting Numbers: [70, 1] Generated Node #0,0,0: 69:[70, 1] Operation: 31-30=1 Exploring Operation: 30+31=61, Resulting Numbers: [70, 61] Generated Node #0,0,1: 69:[70, 61] Operation: 30+31=61 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[70, 1], Operations: ['92-61=31', '31-30=1'] Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[61, 30, 70, 92], Operations: [] Exploring Operation: 92-61=31, Resulting Numbers: [30, 70, 31] Generated Node #0,0: 69:[30, 70, 31] Operation: 92-61=31 Moving to Node #0,0 Current State: 69:[30, 70, 31], Operations: ['92-61=31'] Exploring Operation: 31-30=1, Resulting Numbers: [70, 1] Generated Node #0,0,0: 69:[70, 1] Operation: 31-30=1 Moving to Node #0,0,0 Current State: 69:[70, 1], Operations: ['92-61=31', '31-30=1'] Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 84, 6, 90, 12 ]
67
[ "90+12=102", "102/6=17", "84-17=67" ]
Current State: 67:[84, 6, 90, 12], Operations: [] Exploring Operation: 90+12=102, Resulting Numbers: [84, 6, 102] Generated Node #2: [84, 6, 102] from Operation: 90+12=102 Current State: 67:[84, 6, 102], Operations: ['90+12=102'] Exploring Operation: 102/6=17, Resulting Numbers: [84, 17] Generated Node #3: [84, 17] from Operation: 102/6=17 Current State: 67:[84, 17], Operations: ['90+12=102', '102/6=17'] Exploring Operation: 84-17=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[84, 6, 90, 12], Operations: [] Exploring Operation: 6*12=72, Resulting Numbers: [84, 90, 72] Generated Node #0,0: 67:[84, 90, 72] Operation: 6*12=72 Exploring Operation: 84-6=78, Resulting Numbers: [90, 12, 78] Generated Node #0,1: 67:[90, 12, 78] Operation: 84-6=78 Moving to Node #0,0 Current State: 67:[84, 90, 72], Operations: ['6*12=72'] Exploring Operation: 90-72=18, Resulting Numbers: [84, 18] Generated Node #0,0,0: 67:[84, 18] Operation: 90-72=18 Exploring Operation: 90-84=6, Resulting Numbers: [72, 6] Generated Node #0,0,1: 67:[72, 6] Operation: 90-84=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[84, 18], Operations: ['6*12=72', '90-72=18'] Exploring Operation: 84+18=102, Resulting Numbers: [102] 102,67 unequal: No Solution Exploring Operation: 84-18=66, Resulting Numbers: [66] 66,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[72, 6], Operations: ['6*12=72', '90-84=6'] Exploring Operation: 72+6=78, Resulting Numbers: [78] 78,67 unequal: No Solution Exploring Operation: 72-6=66, Resulting Numbers: [66] 66,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 67:[90, 12, 78], Operations: ['84-6=78'] Exploring Operation: 90-12=78, Resulting Numbers: [78, 78] Generated Node #0,1,0: 67:[78, 78] Operation: 90-12=78 Exploring Operation: 78-12=66, Resulting Numbers: [90, 66] Generated Node #0,1,1: 67:[90, 66] Operation: 78-12=66 Moving to Node #0,1,0 Current State: 67:[78, 78], Operations: ['84-6=78', '90-12=78'] Exploring Operation: 78/78=1, Resulting Numbers: [1] 1,67 unequal: No Solution Exploring Operation: 78-78=0, Resulting Numbers: [0] 0,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[90, 66], Operations: ['84-6=78', '78-12=66'] Exploring Operation: 90+66=156, Resulting Numbers: [156] 156,67 unequal: No Solution Exploring Operation: 90-66=24, Resulting Numbers: [24] 24,67 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 28, 30, 28, 4 ]
64
[ "30-28=2", "28+4=32", "2*32=64" ]
Current State: 64:[28, 30, 28, 4], Operations: [] Exploring Operation: 30-28=2, Resulting Numbers: [4, 2] Generated Node #2: [4, 2] from Operation: 30-28=2 Current State: 64:[4, 2], Operations: ['30-28=2'] Exploring Operation: 28+4=32, Resulting Numbers: [2, 32] Generated Node #3: [2, 32] from Operation: 28+4=32 Current State: 64:[2, 32], Operations: ['30-28=2', '28+4=32'] Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[28, 30, 28, 4], Operations: [] Exploring Operation: 28-28=0, Resulting Numbers: [30, 4, 0] Generated Node #0,0: 64:[30, 4, 0] Operation: 28-28=0 Exploring Operation: 30-28=2, Resulting Numbers: [28, 4, 2] Generated Node #0,1: 64:[28, 4, 2] Operation: 30-28=2 Exploring Operation: 28/28=1, Resulting Numbers: [30, 4, 1] Generated Node #0,2: 64:[30, 4, 1] Operation: 28/28=1 Exploring Operation: 30-28=2, Resulting Numbers: [28, 4, 2] Generated Node #0,3: 64:[28, 4, 2] Operation: 30-28=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[30, 4, 1], Operations: ['28/28=1'] Exploring Operation: 30*1=30, Resulting Numbers: [4, 30] Generated Node #0,2,0: 64:[4, 30] Operation: 30*1=30 Exploring Operation: 30+1=31, Resulting Numbers: [4, 31] Generated Node #0,2,1: 64:[4, 31] Operation: 30+1=31 Exploring Operation: 4*1=4, Resulting Numbers: [30, 4] Generated Node #0,2,2: 64:[30, 4] Operation: 4*1=4 Exploring Operation: 30/1=30, Resulting Numbers: [4, 30] Generated Node #0,2,3: 64:[4, 30] Operation: 30/1=30 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 64:[4, 31], Operations: ['28/28=1', '30+1=31'] Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,64 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,64 unequal: No Solution Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,64 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 #0,2,0 Current State: 64:[4, 30], Operations: ['28/28=1', '30*1=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,64 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,64 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 #0,2,2 Current State: 64:[30, 4], Operations: ['28/28=1', '4*1=4'] Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,64 unequal: No Solution Exploring Operation: 30*4=120, Resulting Numbers: [120] 120,64 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 #0,2,3 Current State: 64:[4, 30], Operations: ['28/28=1', '30/1=30'] Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,64 unequal: No Solution Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,64 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:[30, 4, 0], Operations: ['28-28=0'] Exploring Operation: 4+0=4, Resulting Numbers: [30, 4] Generated Node #0,0,0: 64:[30, 4] Operation: 4+0=4 Exploring Operation: 30*0=0, Resulting Numbers: [4, 0] Generated Node #0,0,1: 64:[4, 0] Operation: 30*0=0 Exploring Operation: 30-0=30, Resulting Numbers: [4, 30] Generated Node #0,0,2: 64:[4, 30] Operation: 30-0=30 Exploring Operation: 30+0=30, Resulting Numbers: [4, 30] Generated Node #0,0,3: 64:[4, 30] Operation: 30+0=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 64:[30, 4], Operations: ['28-28=0', '4+0=4'] Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,64 unequal: No Solution Exploring Operation: 30*4=120, Resulting Numbers: [120] 120,64 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:[4, 0], Operations: ['28-28=0', '30*0=0'] Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 4*0=0, Resulting Numbers: [0] 0,64 unequal: No Solution Exploring Operation: 4+0=4, Resulting Numbers: [4] 4,64 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 #0,0,2 Current State: 64:[4, 30], Operations: ['28-28=0', '30-0=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,64 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,64 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 #0,0,3 Current State: 64:[4, 30], Operations: ['28-28=0', '30+0=30'] Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,64 unequal: No Solution Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,64 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,64 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 #0,1 Current State: 64:[28, 4, 2], Operations: ['30-28=2'] Exploring Operation: 28/2=14, Resulting Numbers: [4, 14] Generated Node #0,1,0: 64:[4, 14] Operation: 28/2=14 Exploring Operation: 28/4=7, Resulting Numbers: [2, 7] Generated Node #0,1,1: 64:[2, 7] Operation: 28/4=7 Exploring Operation: 28+4=32, Resulting Numbers: [2, 32] Generated Node #0,1,2: 64:[2, 32] Operation: 28+4=32 Exploring Operation: 28+2=30, Resulting Numbers: [4, 30] Generated Node #0,1,3: 64:[4, 30] Operation: 28+2=30 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 64:[2, 32], Operations: ['30-28=2', '28+4=32'] Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[28, 30, 28, 4], Operations: [] Exploring Operation: 30-28=2, Resulting Numbers: [28, 4, 2] Generated Node #0,1: 64:[28, 4, 2] Operation: 30-28=2 Moving to Node #0,1 Current State: 64:[28, 4, 2], Operations: ['30-28=2'] Exploring Operation: 28+4=32, Resulting Numbers: [2, 32] Generated Node #0,1,2: 64:[2, 32] Operation: 28+4=32 Moving to Node #0,1,2 Current State: 64:[2, 32], Operations: ['30-28=2', '28+4=32'] Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.960938
hs_4
mult_heuristic
[ 39, 18, 13, 61 ]
40
[ "39/13=3", "61-18=43", "43-3=40" ]
Current State: 40:[39, 18, 13, 61], Operations: [] Exploring Operation: 39/13=3, Resulting Numbers: [18, 61, 3] Generated Node #2: [18, 61, 3] from Operation: 39/13=3 Current State: 40:[18, 61, 3], Operations: ['39/13=3'] Exploring Operation: 61-18=43, Resulting Numbers: [3, 43] Generated Node #3: [3, 43] from Operation: 61-18=43 Current State: 40:[3, 43], Operations: ['39/13=3', '61-18=43'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[39, 18, 13, 61], Operations: [] Exploring Operation: 18-13=5, Resulting Numbers: [39, 61, 5] Generated Node #0,0: 40:[39, 61, 5] Operation: 18-13=5 Exploring Operation: 39/13=3, Resulting Numbers: [18, 61, 3] Generated Node #0,1: 40:[18, 61, 3] Operation: 39/13=3 Exploring Operation: 61-39=22, Resulting Numbers: [18, 13, 22] Generated Node #0,2: 40:[18, 13, 22] Operation: 61-39=22 Exploring Operation: 61-13=48, Resulting Numbers: [39, 18, 48] Generated Node #0,3: 40:[39, 18, 48] Operation: 61-13=48 Exploring Operation: 61-18=43, Resulting Numbers: [39, 13, 43] Generated Node #0,4: 40:[39, 13, 43] Operation: 61-18=43 Moving to Node #0,2 Current State: 40:[18, 13, 22], Operations: ['61-39=22'] Exploring Operation: 18-13=5, Resulting Numbers: [22, 5] Generated Node #0,2,0: 40:[22, 5] Operation: 18-13=5 Exploring Operation: 22-13=9, Resulting Numbers: [18, 9] Generated Node #0,2,1: 40:[18, 9] Operation: 22-13=9 Exploring Operation: 18+22=40, Resulting Numbers: [13, 40] Generated Node #0,2,2: 40:[13, 40] Operation: 18+22=40 Exploring Operation: 13+22=35, Resulting Numbers: [18, 35] Generated Node #0,2,3: 40:[18, 35] Operation: 13+22=35 Exploring Operation: 22-18=4, Resulting Numbers: [13, 4] Generated Node #0,2,4: 40:[13, 4] Operation: 22-18=4 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 40:[22, 5], Operations: ['61-39=22', '18-13=5'] Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,40 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,40 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 #0,2,1 Current State: 40:[18, 9], Operations: ['61-39=22', '22-13=9'] Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 18*9=162, Resulting Numbers: [162] 162,40 unequal: No Solution Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,40 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,40 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 #0,2,2 Current State: 40:[13, 40], Operations: ['61-39=22', '18+22=40'] Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,40 unequal: No Solution Exploring Operation: 13+40=53, Resulting Numbers: [53] 53,40 unequal: No Solution Exploring Operation: 13*40=520, Resulting Numbers: [520] 520,40 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 #0,2,4 Current State: 40:[13, 4], Operations: ['61-39=22', '22-18=4'] Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,40 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,40 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 #0,2,3 Current State: 40:[18, 35], Operations: ['61-39=22', '13+22=35'] Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,40 unequal: No Solution Exploring Operation: 18*35=630, Resulting Numbers: [630] 630,40 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,40 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: 40:[39, 13, 43], Operations: ['61-18=43'] Exploring Operation: 43-13=30, Resulting Numbers: [39, 30] Generated Node #0,4,0: 40:[39, 30] Operation: 43-13=30 Exploring Operation: 39/13=3, Resulting Numbers: [43, 3] Generated Node #0,4,1: 40:[43, 3] Operation: 39/13=3 Exploring Operation: 39+13=52, Resulting Numbers: [43, 52] Generated Node #0,4,2: 40:[43, 52] Operation: 39+13=52 Exploring Operation: 39-13=26, Resulting Numbers: [43, 26] Generated Node #0,4,3: 40:[43, 26] Operation: 39-13=26 Exploring Operation: 43-39=4, Resulting Numbers: [13, 4] Generated Node #0,4,4: 40:[13, 4] Operation: 43-39=4 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 40:[13, 4], Operations: ['61-18=43', '43-39=4'] Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,40 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,40 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 #0,4,1 Current State: 40:[43, 3], Operations: ['61-18=43', '39/13=3'] Exploring Operation: 43*3=129, Resulting Numbers: [129] 129,40 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[39, 18, 13, 61], Operations: [] Exploring Operation: 61-18=43, Resulting Numbers: [39, 13, 43] Generated Node #0,4: 40:[39, 13, 43] Operation: 61-18=43 Moving to Node #0,4 Current State: 40:[39, 13, 43], Operations: ['61-18=43'] Exploring Operation: 39/13=3, Resulting Numbers: [43, 3] Generated Node #0,4,1: 40:[43, 3] Operation: 39/13=3 Moving to Node #0,4,1 Current State: 40:[43, 3], Operations: ['61-18=43', '39/13=3'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_5
sum_heuristic
[ 40, 83, 9, 82 ]
31
[ "40-9=31", "83-82=1", "31*1=31" ]
Current State: 31:[40, 83, 9, 82], Operations: [] Exploring Operation: 40-9=31, Resulting Numbers: [83, 82, 31] Generated Node #2: [83, 82, 31] from Operation: 40-9=31 Current State: 31:[83, 82, 31], Operations: ['40-9=31'] Exploring Operation: 83-82=1, Resulting Numbers: [31, 1] Generated Node #3: [31, 1] from Operation: 83-82=1 Current State: 31:[31, 1], Operations: ['40-9=31', '83-82=1'] Exploring Operation: 31*1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[40, 83, 9, 82], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [40, 9, 1] Generated Node #0,0: 31:[40, 9, 1] Operation: 83-82=1 Exploring Operation: 83-40=43, Resulting Numbers: [9, 82, 43] Generated Node #0,1: 31:[9, 82, 43] Operation: 83-40=43 Moving to Node #0,0 Current State: 31:[40, 9, 1], Operations: ['83-82=1'] Exploring Operation: 40-9=31, Resulting Numbers: [1, 31] Generated Node #0,0,0: 31:[1, 31] Operation: 40-9=31 Exploring Operation: 40-1=39, Resulting Numbers: [9, 39] Generated Node #0,0,1: 31:[9, 39] Operation: 40-1=39 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[1, 31], Operations: ['83-82=1', '40-9=31'] Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[40, 83, 9, 82], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [40, 9, 1] Generated Node #0,0: 31:[40, 9, 1] Operation: 83-82=1 Moving to Node #0,0 Current State: 31:[40, 9, 1], Operations: ['83-82=1'] Exploring Operation: 40-9=31, Resulting Numbers: [1, 31] Generated Node #0,0,0: 31:[1, 31] Operation: 40-9=31 Moving to Node #0,0,0 Current State: 31:[1, 31], Operations: ['83-82=1', '40-9=31'] Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 3, 61, 65, 21 ]
18
[ "21/3=7", "61+65=126", "126/7=18" ]
Current State: 18:[3, 61, 65, 21], Operations: [] Exploring Operation: 21/3=7, Resulting Numbers: [61, 65, 7] Generated Node #2: [61, 65, 7] from Operation: 21/3=7 Current State: 18:[61, 65, 7], Operations: ['21/3=7'] Exploring Operation: 61+65=126, Resulting Numbers: [7, 126] Generated Node #3: [7, 126] from Operation: 61+65=126 Current State: 18:[7, 126], Operations: ['21/3=7', '61+65=126'] Exploring Operation: 126/7=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[3, 61, 65, 21], Operations: [] Exploring Operation: 65-21=44, Resulting Numbers: [3, 61, 44] Generated Node #0,0: 18:[3, 61, 44] Operation: 65-21=44 Exploring Operation: 61-21=40, Resulting Numbers: [3, 65, 40] Generated Node #0,1: 18:[3, 65, 40] Operation: 61-21=40 Exploring Operation: 65-61=4, Resulting Numbers: [3, 21, 4] Generated Node #0,2: 18:[3, 21, 4] Operation: 65-61=4 Exploring Operation: 61-3=58, Resulting Numbers: [65, 21, 58] Generated Node #0,3: 18:[65, 21, 58] Operation: 61-3=58 Moving to Node #0,2 Current State: 18:[3, 21, 4], Operations: ['65-61=4'] Exploring Operation: 21-3=18, Resulting Numbers: [4, 18] Generated Node #0,2,0: 18:[4, 18] Operation: 21-3=18 Exploring Operation: 21-4=17, Resulting Numbers: [3, 17] Generated Node #0,2,1: 18:[3, 17] Operation: 21-4=17 Exploring Operation: 3+4=7, Resulting Numbers: [21, 7] Generated Node #0,2,2: 18:[21, 7] Operation: 3+4=7 Exploring Operation: 21/3=7, Resulting Numbers: [4, 7] Generated Node #0,2,3: 18:[4, 7] Operation: 21/3=7 Moving to Node #0,1 Current State: 18:[3, 65, 40], Operations: ['61-21=40'] Exploring Operation: 65-40=25, Resulting Numbers: [3, 25] Generated Node #0,1,0: 18:[3, 25] Operation: 65-40=25 Exploring Operation: 3+65=68, Resulting Numbers: [40, 68] Generated Node #0,1,1: 18:[40, 68] Operation: 3+65=68 Exploring Operation: 40-3=37, Resulting Numbers: [65, 37] Generated Node #0,1,2: 18:[65, 37] Operation: 40-3=37 Exploring Operation: 65-3=62, Resulting Numbers: [40, 62] Generated Node #0,1,3: 18:[40, 62] Operation: 65-3=62 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[3, 25], Operations: ['61-21=40', '65-40=25'] Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,18 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[65, 37], Operations: ['61-21=40', '40-3=37'] Exploring Operation: 65-37=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 65+37=102, Resulting Numbers: [102] 102,18 unequal: No Solution Exploring Operation: 65*37=2405, Resulting Numbers: [2405] 2405,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[40, 62], Operations: ['61-21=40', '65-3=62'] Exploring Operation: 40*62=2480, Resulting Numbers: [2480] 2480,18 unequal: No Solution Exploring Operation: 40+62=102, Resulting Numbers: [102] 102,18 unequal: No Solution Exploring Operation: 62-40=22, Resulting Numbers: [22] 22,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[40, 68], Operations: ['61-21=40', '3+65=68'] Exploring Operation: 68-40=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 40*68=2720, Resulting Numbers: [2720] 2720,18 unequal: No Solution Exploring Operation: 40+68=108, Resulting Numbers: [108] 108,18 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: 18:[3, 61, 44], Operations: ['65-21=44'] Exploring Operation: 61-3=58, Resulting Numbers: [44, 58] Generated Node #0,0,0: 18:[44, 58] Operation: 61-3=58 Exploring Operation: 3+61=64, Resulting Numbers: [44, 64] Generated Node #0,0,1: 18:[44, 64] Operation: 3+61=64 Exploring Operation: 44-3=41, Resulting Numbers: [61, 41] Generated Node #0,0,2: 18:[61, 41] Operation: 44-3=41 Exploring Operation: 61-44=17, Resulting Numbers: [3, 17] Generated Node #0,0,3: 18:[3, 17] Operation: 61-44=17 Moving to Node #0,3 Current State: 18:[65, 21, 58], Operations: ['61-3=58'] Exploring Operation: 58-21=37, Resulting Numbers: [65, 37] Generated Node #0,3,0: 18:[65, 37] Operation: 58-21=37 Exploring Operation: 65-58=7, Resulting Numbers: [21, 7] Generated Node #0,3,1: 18:[21, 7] Operation: 65-58=7 Exploring Operation: 65-21=44, Resulting Numbers: [58, 44] Generated Node #0,3,2: 18:[58, 44] Operation: 65-21=44 Exploring Operation: 65+21=86, Resulting Numbers: [58, 86] Generated Node #0,3,3: 18:[58, 86] Operation: 65+21=86 Moving to Node #0,2,0 Current State: 18:[4, 18], Operations: ['65-61=4', '21-3=18'] Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,18 unequal: No Solution Moving to Node #0,2,1 Current State: 18:[3, 17], Operations: ['65-61=4', '21-4=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[3, 17], Operations: ['65-21=44', '61-44=17'] Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,18 unequal: No Solution Moving to Node #0,2,3 Current State: 18:[4, 7], Operations: ['65-61=4', '21/3=7'] Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[21, 7], Operations: ['65-61=4', '3+4=7'] Exploring Operation: 21+7=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 21*7=147, Resulting Numbers: [147] 147,18 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,18 unequal: No Solution Moving to Node #0,3,1 Current State: 18:[21, 7], Operations: ['61-3=58', '65-58=7'] Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 21+7=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 21*7=147, Resulting Numbers: [147] 147,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[61, 41], Operations: ['65-21=44', '44-3=41'] Exploring Operation: 61+41=102, Resulting Numbers: [102] 102,18 unequal: No Solution Exploring Operation: 61-41=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 61*41=2501, Resulting Numbers: [2501] 2501,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[44, 58], Operations: ['65-21=44', '61-3=58'] Exploring Operation: 58-44=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 44*58=2552, Resulting Numbers: [2552] 2552,18 unequal: No Solution Exploring Operation: 44+58=102, Resulting Numbers: [102] 102,18 unequal: No Solution Moving to Node #0,3,0 Current State: 18:[65, 37], Operations: ['61-3=58', '58-21=37'] Exploring Operation: 65*37=2405, Resulting Numbers: [2405] 2405,18 unequal: No Solution Exploring Operation: 65+37=102, Resulting Numbers: [102] 102,18 unequal: No Solution Exploring Operation: 65-37=28, Resulting Numbers: [28] 28,18 unequal: No Solution Moving to Node #0,3,2 Current State: 18:[58, 44], Operations: ['61-3=58', '65-21=44'] Exploring Operation: 58+44=102, Resulting Numbers: [102] 102,18 unequal: No Solution Exploring Operation: 58-44=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 58*44=2552, Resulting Numbers: [2552] 2552,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[44, 64], Operations: ['65-21=44', '3+61=64'] Exploring Operation: 64-44=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 44+64=108, Resulting Numbers: [108] 108,18 unequal: No Solution Exploring Operation: 44*64=2816, Resulting Numbers: [2816] 2816,18 unequal: No Solution Moving to Node #0,3,3 Current State: 18:[58, 86], Operations: ['61-3=58', '65+21=86'] Exploring Operation: 86-58=28, Resulting Numbers: [28] 28,18 unequal: No Solution Exploring Operation: 58+86=144, Resulting Numbers: [144] 144,18 unequal: No Solution Exploring Operation: 58*86=4988, Resulting Numbers: [4988] 4988,18 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 52, 40, 12, 49 ]
56
[ "49-40=9", "12*9=108", "108-52=56" ]
Current State: 56:[52, 40, 12, 49], Operations: [] Exploring Operation: 49-40=9, Resulting Numbers: [52, 12, 9] Generated Node #2: [52, 12, 9] from Operation: 49-40=9 Current State: 56:[52, 12, 9], Operations: ['49-40=9'] Exploring Operation: 12*9=108, Resulting Numbers: [52, 108] Generated Node #3: [52, 108] from Operation: 12*9=108 Current State: 56:[52, 108], Operations: ['49-40=9', '12*9=108'] Exploring Operation: 108-52=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[52, 40, 12, 49], Operations: [] Exploring Operation: 52-40=12, Resulting Numbers: [12, 49, 12] Generated Node #0,0: 56:[12, 49, 12] Operation: 52-40=12 Exploring Operation: 40+12=52, Resulting Numbers: [52, 49, 52] Generated Node #0,1: 56:[52, 49, 52] Operation: 40+12=52 Exploring Operation: 49-40=9, Resulting Numbers: [52, 12, 9] Generated Node #0,2: 56:[52, 12, 9] Operation: 49-40=9 Exploring Operation: 52-49=3, Resulting Numbers: [40, 12, 3] Generated Node #0,3: 56:[40, 12, 3] Operation: 52-49=3 Exploring Operation: 40-12=28, Resulting Numbers: [52, 49, 28] Generated Node #0,4: 56:[52, 49, 28] Operation: 40-12=28 Moving to Node #0,2 Current State: 56:[52, 12, 9], Operations: ['49-40=9'] Exploring Operation: 52+9=61, Resulting Numbers: [12, 61] Generated Node #0,2,0: 56:[12, 61] Operation: 52+9=61 Exploring Operation: 52+12=64, Resulting Numbers: [9, 64] Generated Node #0,2,1: 56:[9, 64] Operation: 52+12=64 Exploring Operation: 12-9=3, Resulting Numbers: [52, 3] Generated Node #0,2,2: 56:[52, 3] Operation: 12-9=3 Exploring Operation: 12+9=21, Resulting Numbers: [52, 21] Generated Node #0,2,3: 56:[52, 21] Operation: 12+9=21 Exploring Operation: 52-12=40, Resulting Numbers: [9, 40] Generated Node #0,2,4: 56:[9, 40] Operation: 52-12=40 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 56:[52, 3], Operations: ['49-40=9', '12-9=3'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,56 unequal: No Solution Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 52*3=156, Resulting Numbers: [156] 156,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 56:[12, 61], Operations: ['49-40=9', '52+9=61'] Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,56 unequal: No Solution Exploring Operation: 12*61=732, Resulting Numbers: [732] 732,56 unequal: No Solution Exploring Operation: 12+61=73, Resulting Numbers: [73] 73,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 56:[9, 64], Operations: ['49-40=9', '52+12=64'] Exploring Operation: 9+64=73, Resulting Numbers: [73] 73,56 unequal: No Solution Exploring Operation: 9*64=576, Resulting Numbers: [576] 576,56 unequal: No Solution Exploring Operation: 64-9=55, Resulting Numbers: [55] 55,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 56:[52, 21], Operations: ['49-40=9', '12+9=21'] Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,56 unequal: No Solution Exploring Operation: 52*21=1092, Resulting Numbers: [1092] 1092,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 56:[9, 40], Operations: ['49-40=9', '52-12=40'] Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 9*40=360, Resulting Numbers: [360] 360,56 unequal: No Solution Exploring Operation: 9+40=49, Resulting Numbers: [49] 49,56 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: 56:[52, 49, 28], Operations: ['40-12=28'] Exploring Operation: 52-49=3, Resulting Numbers: [28, 3] Generated Node #0,4,0: 56:[28, 3] Operation: 52-49=3 Exploring Operation: 49-28=21, Resulting Numbers: [52, 21] Generated Node #0,4,1: 56:[52, 21] Operation: 49-28=21 Exploring Operation: 52-28=24, Resulting Numbers: [49, 24] Generated Node #0,4,2: 56:[49, 24] Operation: 52-28=24 Exploring Operation: 49+28=77, Resulting Numbers: [52, 77] Generated Node #0,4,3: 56:[52, 77] Operation: 49+28=77 Exploring Operation: 52+28=80, Resulting Numbers: [49, 80] Generated Node #0,4,4: 56:[49, 80] Operation: 52+28=80 Moving to Node #0,0 Current State: 56:[12, 49, 12], Operations: ['52-40=12'] Exploring Operation: 12/12=1, Resulting Numbers: [49, 1] Generated Node #0,0,0: 56:[49, 1] Operation: 12/12=1 Exploring Operation: 49-12=37, Resulting Numbers: [12, 37] Generated Node #0,0,1: 56:[12, 37] Operation: 49-12=37 Exploring Operation: 49+12=61, Resulting Numbers: [12, 61] Generated Node #0,0,2: 56:[12, 61] Operation: 49+12=61 Exploring Operation: 12-12=0, Resulting Numbers: [49, 0] Generated Node #0,0,3: 56:[49, 0] Operation: 12-12=0 Exploring Operation: 12+49=61, Resulting Numbers: [12, 61] Generated Node #0,0,4: 56:[12, 61] Operation: 12+49=61 Moving to Node #0,1 Current State: 56:[52, 49, 52], Operations: ['40+12=52'] Exploring Operation: 52-52=0, Resulting Numbers: [49, 0] Generated Node #0,1,0: 56:[49, 0] Operation: 52-52=0 Exploring Operation: 52+49=101, Resulting Numbers: [52, 101] Generated Node #0,1,1: 56:[52, 101] Operation: 52+49=101 Exploring Operation: 52/52=1, Resulting Numbers: [49, 1] Generated Node #0,1,2: 56:[49, 1] Operation: 52/52=1 Exploring Operation: 52-49=3, Resulting Numbers: [52, 3] Generated Node #0,1,3: 56:[52, 3] Operation: 52-49=3 Exploring Operation: 52-49=3, Resulting Numbers: [52, 3] Generated Node #0,1,4: 56:[52, 3] Operation: 52-49=3 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 56:[52, 3], Operations: ['40+12=52', '52-49=3'] Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 52*3=156, Resulting Numbers: [156] 156,56 unequal: No Solution Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 56:[52, 3], Operations: ['40+12=52', '52-49=3'] Exploring Operation: 52*3=156, Resulting Numbers: [156] 156,56 unequal: No Solution Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,56 unequal: No Solution Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 56:[49, 1], Operations: ['40+12=52', '52/52=1'] Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,56 unequal: No Solution Exploring Operation: 49+1=50, Resulting Numbers: [50] 50,56 unequal: No Solution Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,56 unequal: No Solution Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 56:[49, 0], Operations: ['40+12=52', '52-52=0'] Exploring Operation: 49-0=49, Resulting Numbers: [49] 49,56 unequal: No Solution Exploring Operation: 49*0=0, Resulting Numbers: [0] 0,56 unequal: No Solution Exploring Operation: 49+0=49, Resulting Numbers: [49] 49,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 56:[52, 101], Operations: ['40+12=52', '52+49=101'] Exploring Operation: 52*101=5252, Resulting Numbers: [5252] 5252,56 unequal: No Solution Exploring Operation: 52+101=153, Resulting Numbers: [153] 153,56 unequal: No Solution Exploring Operation: 101-52=49, Resulting Numbers: [49] 49,56 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: 56:[40, 12, 3], Operations: ['52-49=3'] Exploring Operation: 12/3=4, Resulting Numbers: [40, 4] Generated Node #0,3,0: 56:[40, 4] Operation: 12/3=4 Exploring Operation: 40+12=52, Resulting Numbers: [3, 52] Generated Node #0,3,1: 56:[3, 52] Operation: 40+12=52 Exploring Operation: 12+3=15, Resulting Numbers: [40, 15] Generated Node #0,3,2: 56:[40, 15] Operation: 12+3=15 Exploring Operation: 40-12=28, Resulting Numbers: [3, 28] Generated Node #0,3,3: 56:[3, 28] Operation: 40-12=28 Exploring Operation: 40-3=37, Resulting Numbers: [12, 37] Generated Node #0,3,4: 56:[12, 37] Operation: 40-3=37 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 56:[3, 28], Operations: ['52-49=3', '40-12=28'] Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 56:[3, 52], Operations: ['52-49=3', '40+12=52'] Exploring Operation: 3*52=156, Resulting Numbers: [156] 156,56 unequal: No Solution Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 56:[12, 37], Operations: ['52-49=3', '40-3=37'] Exploring Operation: 12*37=444, Resulting Numbers: [444] 444,56 unequal: No Solution Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 12+37=49, Resulting Numbers: [49] 49,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 56:[40, 4], Operations: ['52-49=3', '12/3=4'] Exploring Operation: 40*4=160, Resulting Numbers: [160] 160,56 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,56 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,56 unequal: No Solution Exploring Operation: 40+4=44, Resulting Numbers: [44] 44,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 56:[40, 15], Operations: ['52-49=3', '12+3=15'] Exploring Operation: 40*15=600, Resulting Numbers: [600] 600,56 unequal: No Solution Exploring Operation: 40-15=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 40+15=55, Resulting Numbers: [55] 55,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,0 Current State: 56:[28, 3], Operations: ['40-12=28', '52-49=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,56 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,56 unequal: No Solution Moving to Node #0,0,2 Current State: 56:[12, 61], Operations: ['52-40=12', '49+12=61'] Exploring Operation: 12*61=732, Resulting Numbers: [732] 732,56 unequal: No Solution Exploring Operation: 12+61=73, Resulting Numbers: [73] 73,56 unequal: No Solution Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,56 unequal: No Solution Moving to Node #0,0,4 Current State: 56:[12, 61], Operations: ['52-40=12', '12+49=61'] Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,56 unequal: No Solution Exploring Operation: 12+61=73, Resulting Numbers: [73] 73,56 unequal: No Solution Exploring Operation: 12*61=732, Resulting Numbers: [732] 732,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[49, 1], Operations: ['52-40=12', '12/12=1'] Exploring Operation: 49+1=50, Resulting Numbers: [50] 50,56 unequal: No Solution Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,56 unequal: No Solution Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,56 unequal: No Solution Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,56 unequal: No Solution Moving to Node #0,0,3 Current State: 56:[49, 0], Operations: ['52-40=12', '12-12=0'] Exploring Operation: 49+0=49, Resulting Numbers: [49] 49,56 unequal: No Solution Exploring Operation: 49*0=0, Resulting Numbers: [0] 0,56 unequal: No Solution Exploring Operation: 49-0=49, Resulting Numbers: [49] 49,56 unequal: No Solution Moving to Node #0,4,2 Current State: 56:[49, 24], Operations: ['40-12=28', '52-28=24'] Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,56 unequal: No Solution Exploring Operation: 49*24=1176, Resulting Numbers: [1176] 1176,56 unequal: No Solution Moving to Node #0,4,1 Current State: 56:[52, 21], Operations: ['40-12=28', '49-28=21'] Exploring Operation: 52*21=1092, Resulting Numbers: [1092] 1092,56 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[12, 37], Operations: ['52-40=12', '49-12=37'] Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 12*37=444, Resulting Numbers: [444] 444,56 unequal: No Solution Exploring Operation: 12+37=49, Resulting Numbers: [49] 49,56 unequal: No Solution Moving to Node #0,4,3 Current State: 56:[52, 77], Operations: ['40-12=28', '49+28=77'] Exploring Operation: 77-52=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 52*77=4004, Resulting Numbers: [4004] 4004,56 unequal: No Solution Exploring Operation: 52+77=129, Resulting Numbers: [129] 129,56 unequal: No Solution Moving to Node #0,4,4 Current State: 56:[49, 80], Operations: ['40-12=28', '52+28=80'] Exploring Operation: 80-49=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 49+80=129, Resulting Numbers: [129] 129,56 unequal: No Solution Exploring Operation: 49*80=3920, Resulting Numbers: [3920] 3920,56 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 46, 93, 19, 73 ]
40
[ "93*19=1767", "73+1767=1840", "1840/46=40" ]
Current State: 40:[46, 93, 19, 73], Operations: [] Exploring Operation: 93*19=1767, Resulting Numbers: [46, 73, 1767] Generated Node #2: [46, 73, 1767] from Operation: 93*19=1767 Current State: 40:[46, 73, 1767], Operations: ['93*19=1767'] Exploring Operation: 73+1767=1840, Resulting Numbers: [46, 1840] Generated Node #3: [46, 1840] from Operation: 73+1767=1840 Current State: 40:[46, 1840], Operations: ['93*19=1767', '73+1767=1840'] Exploring Operation: 1840/46=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[46, 93, 19, 73], Operations: [] Exploring Operation: 93-46=47, Resulting Numbers: [19, 73, 47] Generated Node #0,0: 40:[19, 73, 47] Operation: 93-46=47 Exploring Operation: 73-46=27, Resulting Numbers: [93, 19, 27] Generated Node #0,1: 40:[93, 19, 27] Operation: 73-46=27 Exploring Operation: 93-73=20, Resulting Numbers: [46, 19, 20] Generated Node #0,2: 40:[46, 19, 20] Operation: 93-73=20 Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[46, 19, 20], Operations: ['93-73=20'] Exploring Operation: 46-19=27, Resulting Numbers: [20, 27] Generated Node #0,2,0: 40:[20, 27] Operation: 46-19=27 Exploring Operation: 19+20=39, Resulting Numbers: [46, 39] Generated Node #0,2,1: 40:[46, 39] Operation: 19+20=39 Exploring Operation: 46-20=26, Resulting Numbers: [19, 26] Generated Node #0,2,2: 40:[19, 26] Operation: 46-20=26 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 40:[20, 27], Operations: ['93-73=20', '46-19=27'] Exploring Operation: 20*27=540, Resulting Numbers: [540] 540,40 unequal: No Solution Exploring Operation: 20+27=47, Resulting Numbers: [47] 47,40 unequal: No Solution Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 40:[46, 39], Operations: ['93-73=20', '19+20=39'] Exploring Operation: 46+39=85, Resulting Numbers: [85] 85,40 unequal: No Solution Exploring Operation: 46-39=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 46*39=1794, Resulting Numbers: [1794] 1794,40 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 #0,2,2 Current State: 40:[19, 26], Operations: ['93-73=20', '46-20=26'] Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,40 unequal: No Solution Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,40 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[19, 73, 47], Operations: ['93-46=47'] Exploring Operation: 47-19=28, Resulting Numbers: [73, 28] Generated Node #0,0,0: 40:[73, 28] Operation: 47-19=28 Exploring Operation: 73-19=54, Resulting Numbers: [47, 54] Generated Node #0,0,1: 40:[47, 54] Operation: 73-19=54 Exploring Operation: 73-47=26, Resulting Numbers: [19, 26] Generated Node #0,0,2: 40:[19, 26] Operation: 73-47=26 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 40:[19, 26], Operations: ['93-46=47', '73-47=26'] Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,40 unequal: No Solution Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,40 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 40:[47, 54], Operations: ['93-46=47', '73-19=54'] Exploring Operation: 47*54=2538, Resulting Numbers: [2538] 2538,40 unequal: No Solution Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 47+54=101, Resulting Numbers: [101] 101,40 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 #0,0,0 Current State: 40:[73, 28], Operations: ['93-46=47', '47-19=28'] Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,40 unequal: No Solution Exploring Operation: 73*28=2044, Resulting Numbers: [2044] 2044,40 unequal: No Solution Exploring Operation: 73+28=101, Resulting Numbers: [101] 101,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[93, 19, 27], Operations: ['73-46=27'] Exploring Operation: 27-19=8, Resulting Numbers: [93, 8] Generated Node #0,1,0: 40:[93, 8] Operation: 27-19=8 Exploring Operation: 93-19=74, Resulting Numbers: [27, 74] Generated Node #0,1,1: 40:[27, 74] Operation: 93-19=74 Exploring Operation: 93-27=66, Resulting Numbers: [19, 66] Generated Node #0,1,2: 40:[19, 66] Operation: 93-27=66 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 40:[19, 66], Operations: ['73-46=27', '93-27=66'] Exploring Operation: 66-19=47, Resulting Numbers: [47] 47,40 unequal: No Solution Exploring Operation: 19*66=1254, Resulting Numbers: [1254] 1254,40 unequal: No Solution Exploring Operation: 19+66=85, Resulting Numbers: [85] 85,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 40:[27, 74], Operations: ['73-46=27', '93-19=74'] Exploring Operation: 27*74=1998, Resulting Numbers: [1998] 1998,40 unequal: No Solution Exploring Operation: 27+74=101, Resulting Numbers: [101] 101,40 unequal: No Solution Exploring Operation: 74-27=47, Resulting Numbers: [47] 47,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 40:[93, 8], Operations: ['73-46=27', '27-19=8'] Exploring Operation: 93+8=101, Resulting Numbers: [101] 101,40 unequal: No Solution Exploring Operation: 93*8=744, Resulting Numbers: [744] 744,40 unequal: No Solution Exploring Operation: 93-8=85, Resulting Numbers: [85] 85,40 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
[ 14, 48, 35, 42 ]
58
[ "48*42=2016", "14+2016=2030", "2030/35=58" ]
Current State: 58:[14, 48, 35, 42], Operations: [] Exploring Operation: 48*42=2016, Resulting Numbers: [14, 35, 2016] Generated Node #2: [14, 35, 2016] from Operation: 48*42=2016 Current State: 58:[14, 35, 2016], Operations: ['48*42=2016'] Exploring Operation: 14+2016=2030, Resulting Numbers: [35, 2030] Generated Node #3: [35, 2030] from Operation: 14+2016=2030 Current State: 58:[35, 2030], Operations: ['48*42=2016', '14+2016=2030'] Exploring Operation: 2030/35=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[14, 48, 35, 42], Operations: [] Exploring Operation: 42-14=28, Resulting Numbers: [48, 35, 28] Generated Node #0,0: 58:[48, 35, 28] Operation: 42-14=28 Moving to Node #0,0 Current State: 58:[48, 35, 28], Operations: ['42-14=28'] Exploring Operation: 48-35=13, Resulting Numbers: [28, 13] Generated Node #0,0,0: 58:[28, 13] Operation: 48-35=13 Moving to Node #0,0,0 Current State: 58:[28, 13], Operations: ['42-14=28', '48-35=13'] Exploring Operation: 28+13=41, Resulting Numbers: [41] 41,58 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 8, 10, 38, 30 ]
11
[ "10-8=2", "38/2=19", "30-19=11" ]
Current State: 11:[8, 10, 38, 30], Operations: [] Exploring Operation: 10-8=2, Resulting Numbers: [38, 30, 2] Generated Node #2: [38, 30, 2] from Operation: 10-8=2 Current State: 11:[38, 30, 2], Operations: ['10-8=2'] Exploring Operation: 38/2=19, Resulting Numbers: [30, 19] Generated Node #3: [30, 19] from Operation: 38/2=19 Current State: 11:[30, 19], Operations: ['10-8=2', '38/2=19'] Exploring Operation: 30-19=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[8, 10, 38, 30], Operations: [] Exploring Operation: 38-30=8, Resulting Numbers: [8, 10, 8] Generated Node #0,0: 11:[8, 10, 8] Operation: 38-30=8 Moving to Node #0,0 Current State: 11:[8, 10, 8], Operations: ['38-30=8'] Exploring Operation: 8+8=16, Resulting Numbers: [10, 16] Generated Node #0,0,0: 11:[10, 16] Operation: 8+8=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[10, 16], Operations: ['38-30=8', '8+8=16'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 37, 93, 3, 50 ]
32
[ "37*3=111", "93+50=143", "143-111=32" ]
Current State: 32:[37, 93, 3, 50], Operations: [] Exploring Operation: 37*3=111, Resulting Numbers: [93, 50, 111] Generated Node #2: [93, 50, 111] from Operation: 37*3=111 Current State: 32:[93, 50, 111], Operations: ['37*3=111'] Exploring Operation: 93+50=143, Resulting Numbers: [111, 143] Generated Node #3: [111, 143] from Operation: 93+50=143 Current State: 32:[111, 143], Operations: ['37*3=111', '93+50=143'] Exploring Operation: 143-111=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[37, 93, 3, 50], Operations: [] Exploring Operation: 93-50=43, Resulting Numbers: [37, 3, 43] Generated Node #0,0: 32:[37, 3, 43] Operation: 93-50=43 Exploring Operation: 93/3=31, Resulting Numbers: [37, 50, 31] Generated Node #0,1: 32:[37, 50, 31] Operation: 93/3=31 Moving to Node #0,0 Current State: 32:[37, 3, 43], Operations: ['93-50=43'] Exploring Operation: 43-37=6, Resulting Numbers: [3, 6] Generated Node #0,0,0: 32:[3, 6] Operation: 43-37=6 Exploring Operation: 37-3=34, Resulting Numbers: [43, 34] Generated Node #0,0,1: 32:[43, 34] Operation: 37-3=34 Moving to Node #0,1 Current State: 32:[37, 50, 31], Operations: ['93/3=31'] Exploring Operation: 50-31=19, Resulting Numbers: [37, 19] Generated Node #0,1,0: 32:[37, 19] Operation: 50-31=19 Exploring Operation: 50-37=13, Resulting Numbers: [31, 13] Generated Node #0,1,1: 32:[31, 13] Operation: 50-37=13 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[31, 13], Operations: ['93/3=31', '50-37=13'] Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,32 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[37, 19], Operations: ['93/3=31', '50-31=19'] Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 37+19=56, Resulting Numbers: [56] 56,32 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: 32:[3, 6], Operations: ['93-50=43', '43-37=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,32 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,32 unequal: No Solution Moving to Node #0,0,1 Current State: 32:[43, 34], Operations: ['93-50=43', '37-3=34'] Exploring Operation: 43+34=77, Resulting Numbers: [77] 77,32 unequal: No Solution Exploring Operation: 43-34=9, Resulting Numbers: [9] 9,32 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 47, 6, 18, 92 ]
69
[ "47-6=41", "18+92=110", "110-41=69" ]
Current State: 69:[47, 6, 18, 92], Operations: [] Exploring Operation: 47-6=41, Resulting Numbers: [18, 92, 41] Generated Node #2: [18, 92, 41] from Operation: 47-6=41 Current State: 69:[18, 92, 41], Operations: ['47-6=41'] Exploring Operation: 18+92=110, Resulting Numbers: [41, 110] Generated Node #3: [41, 110] from Operation: 18+92=110 Current State: 69:[41, 110], Operations: ['47-6=41', '18+92=110'] Exploring Operation: 110-41=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[47, 6, 18, 92], Operations: [] Exploring Operation: 92-47=45, Resulting Numbers: [6, 18, 45] Generated Node #0,0: 69:[6, 18, 45] Operation: 92-47=45 Exploring Operation: 47+18=65, Resulting Numbers: [6, 92, 65] Generated Node #0,1: 69:[6, 92, 65] Operation: 47+18=65 Exploring Operation: 92-18=74, Resulting Numbers: [47, 6, 74] Generated Node #0,2: 69:[47, 6, 74] Operation: 92-18=74 Exploring Operation: 47-18=29, Resulting Numbers: [6, 92, 29] Generated Node #0,3: 69:[6, 92, 29] Operation: 47-18=29 Exploring Operation: 47+6=53, Resulting Numbers: [18, 92, 53] Generated Node #0,4: 69:[18, 92, 53] Operation: 47+6=53 Moving to Node #0,0 Current State: 69:[6, 18, 45], Operations: ['92-47=45'] Exploring Operation: 45-18=27, Resulting Numbers: [6, 27] Generated Node #0,0,0: 69:[6, 27] Operation: 45-18=27 Exploring Operation: 6+18=24, Resulting Numbers: [45, 24] Generated Node #0,0,1: 69:[45, 24] Operation: 6+18=24 Exploring Operation: 18/6=3, Resulting Numbers: [45, 3] Generated Node #0,0,2: 69:[45, 3] Operation: 18/6=3 Exploring Operation: 18+45=63, Resulting Numbers: [6, 63] Generated Node #0,0,3: 69:[6, 63] Operation: 18+45=63 Exploring Operation: 45-6=39, Resulting Numbers: [18, 39] Generated Node #0,0,4: 69:[18, 39] Operation: 45-6=39 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[6, 27], Operations: ['92-47=45', '45-18=27'] Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,69 unequal: No Solution Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 6*27=162, Resulting Numbers: [162] 162,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 69:[6, 63], Operations: ['92-47=45', '18+45=63'] Exploring Operation: 6*63=378, Resulting Numbers: [378] 378,69 unequal: No Solution Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,69 unequal: No Solution Exploring Operation: 6+63=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[47, 6, 18, 92], Operations: [] Exploring Operation: 92-47=45, Resulting Numbers: [6, 18, 45] Generated Node #0,0: 69:[6, 18, 45] Operation: 92-47=45 Moving to Node #0,0 Current State: 69:[6, 18, 45], Operations: ['92-47=45'] Exploring Operation: 18+45=63, Resulting Numbers: [6, 63] Generated Node #0,0,3: 69:[6, 63] Operation: 18+45=63 Moving to Node #0,0,3 Current State: 69:[6, 63], Operations: ['92-47=45', '18+45=63'] Exploring Operation: 6+63=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 99, 92, 22, 88 ]
59
[ "99-92=7", "88-22=66", "66-7=59" ]
Current State: 59:[99, 92, 22, 88], Operations: [] Exploring Operation: 99-92=7, Resulting Numbers: [22, 88, 7] Generated Node #2: [22, 88, 7] from Operation: 99-92=7 Current State: 59:[22, 88, 7], Operations: ['99-92=7'] Exploring Operation: 88-22=66, Resulting Numbers: [7, 66] Generated Node #3: [7, 66] from Operation: 88-22=66 Current State: 59:[7, 66], Operations: ['99-92=7', '88-22=66'] Exploring Operation: 66-7=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[99, 92, 22, 88], Operations: [] Exploring Operation: 99-22=77, Resulting Numbers: [92, 88, 77] Generated Node #0,0: 59:[92, 88, 77] Operation: 99-22=77 Exploring Operation: 92-22=70, Resulting Numbers: [99, 88, 70] Generated Node #0,1: 59:[99, 88, 70] Operation: 92-22=70 Moving to Node #0,0 Current State: 59:[92, 88, 77], Operations: ['99-22=77'] Exploring Operation: 92-88=4, Resulting Numbers: [77, 4] Generated Node #0,0,0: 59:[77, 4] Operation: 92-88=4 Exploring Operation: 92-77=15, Resulting Numbers: [88, 15] Generated Node #0,0,1: 59:[88, 15] Operation: 92-77=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[77, 4], Operations: ['99-22=77', '92-88=4'] Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 77-4=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 #0,0,1 Current State: 59:[88, 15], Operations: ['99-22=77', '92-77=15'] Exploring Operation: 88+15=103, Resulting Numbers: [103] 103,59 unequal: No Solution Exploring Operation: 88-15=73, Resulting Numbers: [73] 73,59 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:[99, 88, 70], Operations: ['92-22=70'] Exploring Operation: 99-70=29, Resulting Numbers: [88, 29] Generated Node #0,1,0: 59:[88, 29] Operation: 99-70=29 Exploring Operation: 99-88=11, Resulting Numbers: [70, 11] Generated Node #0,1,1: 59:[70, 11] Operation: 99-88=11 Moving to Node #0,1,0 Current State: 59:[88, 29], Operations: ['92-22=70', '99-70=29'] Exploring Operation: 88+29=117, Resulting Numbers: [117] 117,59 unequal: No Solution Exploring Operation: 88-29=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[99, 92, 22, 88], Operations: [] Exploring Operation: 92-22=70, Resulting Numbers: [99, 88, 70] Generated Node #0,1: 59:[99, 88, 70] Operation: 92-22=70 Moving to Node #0,1 Current State: 59:[99, 88, 70], Operations: ['92-22=70'] Exploring Operation: 99-70=29, Resulting Numbers: [88, 29] Generated Node #0,1,0: 59:[88, 29] Operation: 99-70=29 Moving to Node #0,1,0 Current State: 59:[88, 29], Operations: ['92-22=70', '99-70=29'] Exploring Operation: 88-29=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 81, 29, 72, 38 ]
86
[ "81-29=52", "72-38=34", "52+34=86" ]
Current State: 86:[81, 29, 72, 38], Operations: [] Exploring Operation: 81-29=52, Resulting Numbers: [72, 38, 52] Generated Node #2: [72, 38, 52] from Operation: 81-29=52 Current State: 86:[72, 38, 52], Operations: ['81-29=52'] Exploring Operation: 72-38=34, Resulting Numbers: [52, 34] Generated Node #3: [52, 34] from Operation: 72-38=34 Current State: 86:[52, 34], Operations: ['81-29=52', '72-38=34'] Exploring Operation: 52+34=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[81, 29, 72, 38], Operations: [] Exploring Operation: 29+72=101, Resulting Numbers: [81, 38, 101] Generated Node #0,0: 86:[81, 38, 101] Operation: 29+72=101 Exploring Operation: 72-29=43, Resulting Numbers: [81, 38, 43] Generated Node #0,1: 86:[81, 38, 43] Operation: 72-29=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[81, 38, 43], Operations: ['72-29=43'] Exploring Operation: 81-38=43, Resulting Numbers: [43, 43] Generated Node #0,1,0: 86:[43, 43] Operation: 81-38=43 Exploring Operation: 43-38=5, Resulting Numbers: [81, 5] Generated Node #0,1,1: 86:[81, 5] Operation: 43-38=5 Moving to Node #0,1,0 Current State: 86:[43, 43], Operations: ['72-29=43', '81-38=43'] Exploring Operation: 43+43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[81, 29, 72, 38], Operations: [] Exploring Operation: 72-29=43, Resulting Numbers: [81, 38, 43] Generated Node #0,1: 86:[81, 38, 43] Operation: 72-29=43 Moving to Node #0,1 Current State: 86:[81, 38, 43], Operations: ['72-29=43'] Exploring Operation: 81-38=43, Resulting Numbers: [43, 43] Generated Node #0,1,0: 86:[43, 43] Operation: 81-38=43 Moving to Node #0,1,0 Current State: 86:[43, 43], Operations: ['72-29=43', '81-38=43'] Exploring Operation: 43+43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 51, 89, 9, 55 ]
84
[ "89-51=38", "55-9=46", "38+46=84" ]
Current State: 84:[51, 89, 9, 55], Operations: [] Exploring Operation: 89-51=38, Resulting Numbers: [9, 55, 38] Generated Node #2: [9, 55, 38] from Operation: 89-51=38 Current State: 84:[9, 55, 38], Operations: ['89-51=38'] Exploring Operation: 55-9=46, Resulting Numbers: [38, 46] Generated Node #3: [38, 46] from Operation: 55-9=46 Current State: 84:[38, 46], Operations: ['89-51=38', '55-9=46'] Exploring Operation: 38+46=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[51, 89, 9, 55], Operations: [] Exploring Operation: 89-55=34, Resulting Numbers: [51, 9, 34] Generated Node #0,0: 84:[51, 9, 34] Operation: 89-55=34 Exploring Operation: 51-9=42, Resulting Numbers: [89, 55, 42] Generated Node #0,1: 84:[89, 55, 42] Operation: 51-9=42 Exploring Operation: 55-9=46, Resulting Numbers: [51, 89, 46] Generated Node #0,2: 84:[51, 89, 46] Operation: 55-9=46 Exploring Operation: 55-51=4, Resulting Numbers: [89, 9, 4] Generated Node #0,3: 84:[89, 9, 4] Operation: 55-51=4 Moving to Node #0,3 Current State: 84:[89, 9, 4], Operations: ['55-51=4'] Exploring Operation: 89-9=80, Resulting Numbers: [4, 80] Generated Node #0,3,0: 84:[4, 80] Operation: 89-9=80 Exploring Operation: 9-4=5, Resulting Numbers: [89, 5] Generated Node #0,3,1: 84:[89, 5] Operation: 9-4=5 Exploring Operation: 89-4=85, Resulting Numbers: [9, 85] Generated Node #0,3,2: 84:[9, 85] Operation: 89-4=85 Exploring Operation: 9+4=13, Resulting Numbers: [89, 13] Generated Node #0,3,3: 84:[89, 13] Operation: 9+4=13 Moving to Node #0,0 Current State: 84:[51, 9, 34], Operations: ['89-55=34'] Exploring Operation: 51-34=17, Resulting Numbers: [9, 17] Generated Node #0,0,0: 84:[9, 17] Operation: 51-34=17 Exploring Operation: 51+34=85, Resulting Numbers: [9, 85] Generated Node #0,0,1: 84:[9, 85] Operation: 51+34=85 Exploring Operation: 51-9=42, Resulting Numbers: [34, 42] Generated Node #0,0,2: 84:[34, 42] Operation: 51-9=42 Exploring Operation: 9+34=43, Resulting Numbers: [51, 43] Generated Node #0,0,3: 84:[51, 43] Operation: 9+34=43 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[9, 85], Operations: ['89-55=34', '51+34=85'] Exploring Operation: 9+85=94, Resulting Numbers: [94] 94,84 unequal: No Solution Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,84 unequal: No Solution Exploring Operation: 9*85=765, Resulting Numbers: [765] 765,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[9, 17], Operations: ['89-55=34', '51-34=17'] Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,84 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,84 unequal: No Solution Exploring Operation: 9*17=153, Resulting Numbers: [153] 153,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 84:[34, 42], Operations: ['89-55=34', '51-9=42'] Exploring Operation: 34*42=1428, Resulting Numbers: [1428] 1428,84 unequal: No Solution Exploring Operation: 34+42=76, Resulting Numbers: [76] 76,84 unequal: No Solution Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 84:[51, 43], Operations: ['89-55=34', '9+34=43'] Exploring Operation: 51-43=8, Resulting Numbers: [8] 8,84 unequal: No Solution Exploring Operation: 51+43=94, Resulting Numbers: [94] 94,84 unequal: No Solution Exploring Operation: 51*43=2193, Resulting Numbers: [2193] 2193,84 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: 84:[51, 89, 46], Operations: ['55-9=46'] Exploring Operation: 51-46=5, Resulting Numbers: [89, 5] Generated Node #0,2,0: 84:[89, 5] Operation: 51-46=5 Exploring Operation: 89-51=38, Resulting Numbers: [46, 38] Generated Node #0,2,1: 84:[46, 38] Operation: 89-51=38 Exploring Operation: 51+46=97, Resulting Numbers: [89, 97] Generated Node #0,2,2: 84:[89, 97] Operation: 51+46=97 Exploring Operation: 89-46=43, Resulting Numbers: [51, 43] Generated Node #0,2,3: 84:[51, 43] Operation: 89-46=43 Moving to Node #0,1 Current State: 84:[89, 55, 42], Operations: ['51-9=42'] Exploring Operation: 89-42=47, Resulting Numbers: [55, 47] Generated Node #0,1,0: 84:[55, 47] Operation: 89-42=47 Exploring Operation: 55-42=13, Resulting Numbers: [89, 13] Generated Node #0,1,1: 84:[89, 13] Operation: 55-42=13 Exploring Operation: 89-55=34, Resulting Numbers: [42, 34] Generated Node #0,1,2: 84:[42, 34] Operation: 89-55=34 Exploring Operation: 55+42=97, Resulting Numbers: [89, 97] Generated Node #0,1,3: 84:[89, 97] Operation: 55+42=97 Moving to Node #0,3,2 Current State: 84:[9, 85], Operations: ['55-51=4', '89-4=85'] Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,84 unequal: No Solution Exploring Operation: 9*85=765, Resulting Numbers: [765] 765,84 unequal: No Solution Exploring Operation: 9+85=94, Resulting Numbers: [94] 94,84 unequal: No Solution Moving to Node #0,3,0 Current State: 84:[4, 80], Operations: ['55-51=4', '89-9=80'] Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 4*80=320, Resulting Numbers: [320] 320,84 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,84 unequal: No Solution Exploring Operation: 4+80=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[51, 89, 9, 55], Operations: [] Exploring Operation: 55-51=4, Resulting Numbers: [89, 9, 4] Generated Node #0,3: 84:[89, 9, 4] Operation: 55-51=4 Moving to Node #0,3 Current State: 84:[89, 9, 4], Operations: ['55-51=4'] Exploring Operation: 89-9=80, Resulting Numbers: [4, 80] Generated Node #0,3,0: 84:[4, 80] Operation: 89-9=80 Moving to Node #0,3,0 Current State: 84:[4, 80], Operations: ['55-51=4', '89-9=80'] Exploring Operation: 4+80=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.962674
hs_4
mult_heuristic
[ 28, 60, 22, 16 ]
26
[ "60-28=32", "22-16=6", "32-6=26" ]
Current State: 26:[28, 60, 22, 16], Operations: [] Exploring Operation: 60-28=32, Resulting Numbers: [22, 16, 32] Generated Node #2: [22, 16, 32] from Operation: 60-28=32 Current State: 26:[22, 16, 32], Operations: ['60-28=32'] Exploring Operation: 22-16=6, Resulting Numbers: [32, 6] Generated Node #3: [32, 6] from Operation: 22-16=6 Current State: 26:[32, 6], Operations: ['60-28=32', '22-16=6'] Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[28, 60, 22, 16], Operations: [] Exploring Operation: 60-16=44, Resulting Numbers: [28, 22, 44] Generated Node #0,0: 26:[28, 22, 44] Operation: 60-16=44 Exploring Operation: 60-28=32, Resulting Numbers: [22, 16, 32] Generated Node #0,1: 26:[22, 16, 32] Operation: 60-28=32 Exploring Operation: 60-22=38, Resulting Numbers: [28, 16, 38] Generated Node #0,2: 26:[28, 16, 38] Operation: 60-22=38 Exploring Operation: 28-16=12, Resulting Numbers: [60, 22, 12] Generated Node #0,3: 26:[60, 22, 12] Operation: 28-16=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[22, 16, 32], Operations: ['60-28=32'] Exploring Operation: 32-16=16, Resulting Numbers: [22, 16] Generated Node #0,1,0: 26:[22, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [22, 2] Generated Node #0,1,1: 26:[22, 2] Operation: 32/16=2 Exploring Operation: 22-16=6, Resulting Numbers: [32, 6] Generated Node #0,1,2: 26:[32, 6] Operation: 22-16=6 Exploring Operation: 32-22=10, Resulting Numbers: [16, 10] Generated Node #0,1,3: 26:[16, 10] Operation: 32-22=10 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 26:[22, 2], Operations: ['60-28=32', '32/16=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,26 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,26 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,26 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 26:[16, 10], Operations: ['60-28=32', '32-22=10'] Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,26 unequal: No Solution Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[28, 60, 22, 16], Operations: [] Exploring Operation: 60-28=32, Resulting Numbers: [22, 16, 32] Generated Node #0,1: 26:[22, 16, 32] Operation: 60-28=32 Moving to Node #0,1 Current State: 26:[22, 16, 32], Operations: ['60-28=32'] Exploring Operation: 32-22=10, Resulting Numbers: [16, 10] Generated Node #0,1,3: 26:[16, 10] Operation: 32-22=10 Moving to Node #0,1,3 Current State: 26:[16, 10], Operations: ['60-28=32', '32-22=10'] Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 80, 15, 77, 34 ]
39
[ "80-77=3", "15/3=5", "34+5=39" ]
Current State: 39:[80, 15, 77, 34], Operations: [] Exploring Operation: 80-77=3, Resulting Numbers: [15, 34, 3] Generated Node #2: [15, 34, 3] from Operation: 80-77=3 Current State: 39:[15, 34, 3], Operations: ['80-77=3'] Exploring Operation: 15/3=5, Resulting Numbers: [34, 5] Generated Node #3: [34, 5] from Operation: 15/3=5 Current State: 39:[34, 5], Operations: ['80-77=3', '15/3=5'] Exploring Operation: 34+5=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[80, 15, 77, 34], Operations: [] Exploring Operation: 80-77=3, Resulting Numbers: [15, 34, 3] Generated Node #0,0: 39:[15, 34, 3] Operation: 80-77=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[15, 34, 3], Operations: ['80-77=3'] Exploring Operation: 34+3=37, Resulting Numbers: [15, 37] Generated Node #0,0,0: 39:[15, 37] Operation: 34+3=37 Moving to Node #0,0,0 Current State: 39:[15, 37], Operations: ['80-77=3', '34+3=37'] Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 21, 18, 12, 4 ]
51
[ "21-18=3", "12*4=48", "3+48=51" ]
Current State: 51:[21, 18, 12, 4], Operations: [] Exploring Operation: 21-18=3, Resulting Numbers: [12, 4, 3] Generated Node #2: [12, 4, 3] from Operation: 21-18=3 Current State: 51:[12, 4, 3], Operations: ['21-18=3'] Exploring Operation: 12*4=48, Resulting Numbers: [3, 48] Generated Node #3: [3, 48] from Operation: 12*4=48 Current State: 51:[3, 48], Operations: ['21-18=3', '12*4=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[21, 18, 12, 4], Operations: [] Exploring Operation: 12/4=3, Resulting Numbers: [21, 18, 3] Generated Node #0,0: 51:[21, 18, 3] Operation: 12/4=3 Exploring Operation: 21-18=3, Resulting Numbers: [12, 4, 3] Generated Node #0,1: 51:[12, 4, 3] Operation: 21-18=3 Moving to Node #0,0 Current State: 51:[21, 18, 3], Operations: ['12/4=3'] Exploring Operation: 21-18=3, Resulting Numbers: [3, 3] Generated Node #0,0,0: 51:[3, 3] Operation: 21-18=3 Exploring Operation: 21-3=18, Resulting Numbers: [18, 18] Generated Node #0,0,1: 51:[18, 18] Operation: 21-3=18 Moving to Node #0,1 Current State: 51:[12, 4, 3], Operations: ['21-18=3'] Exploring Operation: 12/4=3, Resulting Numbers: [3, 3] Generated Node #0,1,0: 51:[3, 3] Operation: 12/4=3 Exploring Operation: 12+4=16, Resulting Numbers: [3, 16] Generated Node #0,1,1: 51:[3, 16] Operation: 12+4=16 Moving to Node #0,0,0 Current State: 51:[3, 3], Operations: ['12/4=3', '21-18=3'] Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,51 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[3, 3], Operations: ['21-18=3', '12/4=3'] Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[3, 16], Operations: ['21-18=3', '12+4=16'] Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,51 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[18, 18], Operations: ['12/4=3', '21-3=18'] Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 18-18=0, Resulting Numbers: [0] 0,51 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 50, 16, 10, 2 ]
68
[ "50+10=60", "16/2=8", "60+8=68" ]
Current State: 68:[50, 16, 10, 2], Operations: [] Exploring Operation: 50+10=60, Resulting Numbers: [16, 2, 60] Generated Node #2: [16, 2, 60] from Operation: 50+10=60 Current State: 68:[16, 2, 60], Operations: ['50+10=60'] Exploring Operation: 16/2=8, Resulting Numbers: [60, 8] Generated Node #3: [60, 8] from Operation: 16/2=8 Current State: 68:[60, 8], Operations: ['50+10=60', '16/2=8'] Exploring Operation: 60+8=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[50, 16, 10, 2], Operations: [] Exploring Operation: 50/10=5, Resulting Numbers: [16, 2, 5] Generated Node #0,0: 68:[16, 2, 5] Operation: 50/10=5 Exploring Operation: 50-16=34, Resulting Numbers: [10, 2, 34] Generated Node #0,1: 68:[10, 2, 34] Operation: 50-16=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[16, 2, 5], Operations: ['50/10=5'] Exploring Operation: 5-2=3, Resulting Numbers: [16, 3] Generated Node #0,0,0: 68:[16, 3] Operation: 5-2=3 Exploring Operation: 16+2=18, Resulting Numbers: [5, 18] Generated Node #0,0,1: 68:[5, 18] Operation: 16+2=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[16, 3], Operations: ['50/10=5', '5-2=3'] Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,68 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 68:[5, 18], Operations: ['50/10=5', '16+2=18'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[10, 2, 34], Operations: ['50-16=34'] Exploring Operation: 10/2=5, Resulting Numbers: [34, 5] Generated Node #0,1,0: 68:[34, 5] Operation: 10/2=5 Exploring Operation: 10*2=20, Resulting Numbers: [34, 20] Generated Node #0,1,1: 68:[34, 20] Operation: 10*2=20 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 68:[34, 5], Operations: ['50-16=34', '10/2=5'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,68 unequal: No Solution Exploring Operation: 34+5=39, Resulting Numbers: [39] 39,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 68:[34, 20], Operations: ['50-16=34', '10*2=20'] Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,68 unequal: No Solution Exploring Operation: 34+20=54, Resulting Numbers: [54] 54,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 80, 52, 3, 40 ]
46
[ "80*3=240", "240/40=6", "52-6=46" ]
Current State: 46:[80, 52, 3, 40], Operations: [] Exploring Operation: 80*3=240, Resulting Numbers: [52, 40, 240] Generated Node #2: [52, 40, 240] from Operation: 80*3=240 Current State: 46:[52, 40, 240], Operations: ['80*3=240'] Exploring Operation: 240/40=6, Resulting Numbers: [52, 6] Generated Node #3: [52, 6] from Operation: 240/40=6 Current State: 46:[52, 6], Operations: ['80*3=240', '240/40=6'] Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[80, 52, 3, 40], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [52, 3, 2] Generated Node #0,0: 46:[52, 3, 2] Operation: 80/40=2 Moving to Node #0,0 Current State: 46:[52, 3, 2], Operations: ['80/40=2'] Exploring Operation: 52-3=49, Resulting Numbers: [2, 49] Generated Node #0,0,0: 46:[2, 49] Operation: 52-3=49 Moving to Node #0,0,0 Current State: 46:[2, 49], Operations: ['80/40=2', '52-3=49'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,46 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 12, 14, 3, 28 ]
38
[ "12*3=36", "28/14=2", "36+2=38" ]
Current State: 38:[12, 14, 3, 28], Operations: [] Exploring Operation: 12*3=36, Resulting Numbers: [14, 28, 36] Generated Node #2: [14, 28, 36] from Operation: 12*3=36 Current State: 38:[14, 28, 36], Operations: ['12*3=36'] Exploring Operation: 28/14=2, Resulting Numbers: [36, 2] Generated Node #3: [36, 2] from Operation: 28/14=2 Current State: 38:[36, 2], Operations: ['12*3=36', '28/14=2'] Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[12, 14, 3, 28], Operations: [] Exploring Operation: 14-12=2, Resulting Numbers: [3, 28, 2] Generated Node #0,0: 38:[3, 28, 2] Operation: 14-12=2 Exploring Operation: 28-12=16, Resulting Numbers: [14, 3, 16] Generated Node #0,1: 38:[14, 3, 16] Operation: 28-12=16 Exploring Operation: 28/14=2, Resulting Numbers: [12, 3, 2] Generated Node #0,2: 38:[12, 3, 2] Operation: 28/14=2 Exploring Operation: 14+28=42, Resulting Numbers: [12, 3, 42] Generated Node #0,3: 38:[12, 3, 42] Operation: 14+28=42 Exploring Operation: 12+28=40, Resulting Numbers: [14, 3, 40] Generated Node #0,4: 38:[14, 3, 40] Operation: 12+28=40 Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[12, 3, 2], Operations: ['28/14=2'] Exploring Operation: 12/3=4, Resulting Numbers: [2, 4] Generated Node #0,2,0: 38:[2, 4] Operation: 12/3=4 Exploring Operation: 12*3=36, Resulting Numbers: [2, 36] Generated Node #0,2,1: 38:[2, 36] Operation: 12*3=36 Exploring Operation: 12/2=6, Resulting Numbers: [3, 6] Generated Node #0,2,2: 38:[3, 6] Operation: 12/2=6 Exploring Operation: 12+2=14, Resulting Numbers: [3, 14] Generated Node #0,2,3: 38:[3, 14] Operation: 12+2=14 Exploring Operation: 12+3=15, Resulting Numbers: [2, 15] Generated Node #0,2,4: 38:[2, 15] Operation: 12+3=15 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 38:[2, 4], Operations: ['28/14=2', '12/3=4'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,38 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:[2, 36], Operations: ['28/14=2', '12*3=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,38 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[12, 14, 3, 28], Operations: [] Exploring Operation: 28/14=2, Resulting Numbers: [12, 3, 2] Generated Node #0,2: 38:[12, 3, 2] Operation: 28/14=2 Moving to Node #0,2 Current State: 38:[12, 3, 2], Operations: ['28/14=2'] Exploring Operation: 12*3=36, Resulting Numbers: [2, 36] Generated Node #0,2,1: 38:[2, 36] Operation: 12*3=36 Moving to Node #0,2,1 Current State: 38:[2, 36], Operations: ['28/14=2', '12*3=36'] Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 64, 46, 6, 69 ]
90
[ "64*69=4416", "4416/46=96", "96-6=90" ]
Current State: 90:[64, 46, 6, 69], Operations: [] Exploring Operation: 64*69=4416, Resulting Numbers: [46, 6, 4416] Generated Node #2: [46, 6, 4416] from Operation: 64*69=4416 Current State: 90:[46, 6, 4416], Operations: ['64*69=4416'] Exploring Operation: 4416/46=96, Resulting Numbers: [6, 96] Generated Node #3: [6, 96] from Operation: 4416/46=96 Current State: 90:[6, 96], Operations: ['64*69=4416', '4416/46=96'] Exploring Operation: 96-6=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[64, 46, 6, 69], Operations: [] Exploring Operation: 69-64=5, Resulting Numbers: [46, 6, 5] Generated Node #0,0: 90:[46, 6, 5] Operation: 69-64=5 Exploring Operation: 64-6=58, Resulting Numbers: [46, 69, 58] Generated Node #0,1: 90:[46, 69, 58] Operation: 64-6=58 Exploring Operation: 64-46=18, Resulting Numbers: [6, 69, 18] Generated Node #0,2: 90:[6, 69, 18] Operation: 64-46=18 Exploring Operation: 69-46=23, Resulting Numbers: [64, 6, 23] Generated Node #0,3: 90:[64, 6, 23] Operation: 69-46=23 Moving to Node #0,0 Current State: 90:[46, 6, 5], Operations: ['69-64=5'] Exploring Operation: 6+5=11, Resulting Numbers: [46, 11] Generated Node #0,0,0: 90:[46, 11] Operation: 6+5=11 Exploring Operation: 46-5=41, Resulting Numbers: [6, 41] Generated Node #0,0,1: 90:[6, 41] Operation: 46-5=41 Exploring Operation: 6-5=1, Resulting Numbers: [46, 1] Generated Node #0,0,2: 90:[46, 1] Operation: 6-5=1 Exploring Operation: 6*5=30, Resulting Numbers: [46, 30] Generated Node #0,0,3: 90:[46, 30] Operation: 6*5=30 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 90:[46, 30], Operations: ['69-64=5', '6*5=30'] Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,90 unequal: No Solution Exploring Operation: 46+30=76, Resulting Numbers: [76] 76,90 unequal: No Solution Exploring Operation: 46*30=1380, Resulting Numbers: [1380] 1380,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[46, 11], Operations: ['69-64=5', '6+5=11'] Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 46+11=57, Resulting Numbers: [57] 57,90 unequal: No Solution Exploring Operation: 46*11=506, Resulting Numbers: [506] 506,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[46, 1], Operations: ['69-64=5', '6-5=1'] Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,90 unequal: No Solution Exploring Operation: 46+1=47, Resulting Numbers: [47] 47,90 unequal: No Solution Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[6, 41], Operations: ['69-64=5', '46-5=41'] Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 6+41=47, Resulting Numbers: [47] 47,90 unequal: No Solution Exploring Operation: 6*41=246, Resulting Numbers: [246] 246,90 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: 90:[6, 69, 18], Operations: ['64-46=18'] Exploring Operation: 69+18=87, Resulting Numbers: [6, 87] Generated Node #0,2,0: 90:[6, 87] Operation: 69+18=87 Exploring Operation: 69-18=51, Resulting Numbers: [6, 51] Generated Node #0,2,1: 90:[6, 51] Operation: 69-18=51 Exploring Operation: 69-6=63, Resulting Numbers: [18, 63] Generated Node #0,2,2: 90:[18, 63] Operation: 69-6=63 Exploring Operation: 6+69=75, Resulting Numbers: [18, 75] Generated Node #0,2,3: 90:[18, 75] Operation: 6+69=75 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 90:[6, 87], Operations: ['64-46=18', '69+18=87'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,90 unequal: No Solution Exploring Operation: 6*87=522, Resulting Numbers: [522] 522,90 unequal: No Solution Exploring Operation: 6+87=93, Resulting Numbers: [93] 93,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 90:[6, 51], Operations: ['64-46=18', '69-18=51'] Exploring Operation: 6*51=306, Resulting Numbers: [306] 306,90 unequal: No Solution Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 6+51=57, Resulting Numbers: [57] 57,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 90:[18, 75], Operations: ['64-46=18', '6+69=75'] Exploring Operation: 18+75=93, Resulting Numbers: [93] 93,90 unequal: No Solution Exploring Operation: 75-18=57, Resulting Numbers: [57] 57,90 unequal: No Solution Exploring Operation: 18*75=1350, Resulting Numbers: [1350] 1350,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 90:[18, 63], Operations: ['64-46=18', '69-6=63'] Exploring Operation: 18+63=81, Resulting Numbers: [81] 81,90 unequal: No Solution Exploring Operation: 63-18=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 18*63=1134, Resulting Numbers: [1134] 1134,90 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: 90:[64, 6, 23], Operations: ['69-46=23'] Exploring Operation: 6+23=29, Resulting Numbers: [64, 29] Generated Node #0,3,0: 90:[64, 29] Operation: 6+23=29 Exploring Operation: 64-6=58, Resulting Numbers: [23, 58] Generated Node #0,3,1: 90:[23, 58] Operation: 64-6=58 Exploring Operation: 64-23=41, Resulting Numbers: [6, 41] Generated Node #0,3,2: 90:[6, 41] Operation: 64-23=41 Exploring Operation: 64+23=87, Resulting Numbers: [6, 87] Generated Node #0,3,3: 90:[6, 87] Operation: 64+23=87 Moving to Node #0,1 Current State: 90:[46, 69, 58], Operations: ['64-6=58'] Exploring Operation: 46+58=104, Resulting Numbers: [69, 104] Generated Node #0,1,0: 90:[69, 104] Operation: 46+58=104 Exploring Operation: 58-46=12, Resulting Numbers: [69, 12] Generated Node #0,1,1: 90:[69, 12] Operation: 58-46=12 Exploring Operation: 69-58=11, Resulting Numbers: [46, 11] Generated Node #0,1,2: 90:[46, 11] Operation: 69-58=11 Exploring Operation: 69-46=23, Resulting Numbers: [58, 23] Generated Node #0,1,3: 90:[58, 23] Operation: 69-46=23 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 90:[46, 11], Operations: ['64-6=58', '69-58=11'] Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 46*11=506, Resulting Numbers: [506] 506,90 unequal: No Solution Exploring Operation: 46+11=57, Resulting Numbers: [57] 57,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 90:[58, 23], Operations: ['64-6=58', '69-46=23'] Exploring Operation: 58-23=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 58+23=81, Resulting Numbers: [81] 81,90 unequal: No Solution Exploring Operation: 58*23=1334, Resulting Numbers: [1334] 1334,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[69, 12], Operations: ['64-6=58', '58-46=12'] Exploring Operation: 69-12=57, Resulting Numbers: [57] 57,90 unequal: No Solution Exploring Operation: 69*12=828, Resulting Numbers: [828] 828,90 unequal: No Solution Exploring Operation: 69+12=81, Resulting Numbers: [81] 81,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[69, 104], Operations: ['64-6=58', '46+58=104'] Exploring Operation: 69+104=173, Resulting Numbers: [173] 173,90 unequal: No Solution Exploring Operation: 104-69=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 69*104=7176, Resulting Numbers: [7176] 7176,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,3 Current State: 90:[6, 87], Operations: ['69-46=23', '64+23=87'] Exploring Operation: 6+87=93, Resulting Numbers: [93] 93,90 unequal: No Solution Exploring Operation: 6*87=522, Resulting Numbers: [522] 522,90 unequal: No Solution Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,90 unequal: No Solution Moving to Node #0,3,2 Current State: 90:[6, 41], Operations: ['69-46=23', '64-23=41'] Exploring Operation: 6+41=47, Resulting Numbers: [47] 47,90 unequal: No Solution Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 6*41=246, Resulting Numbers: [246] 246,90 unequal: No Solution Moving to Node #0,3,1 Current State: 90:[23, 58], Operations: ['69-46=23', '64-6=58'] Exploring Operation: 58-23=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 23*58=1334, Resulting Numbers: [1334] 1334,90 unequal: No Solution Exploring Operation: 23+58=81, Resulting Numbers: [81] 81,90 unequal: No Solution Moving to Node #0,3,0 Current State: 90:[64, 29], Operations: ['69-46=23', '6+23=29'] Exploring Operation: 64-29=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 64+29=93, Resulting Numbers: [93] 93,90 unequal: No Solution Exploring Operation: 64*29=1856, Resulting Numbers: [1856] 1856,90 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 54, 11, 6, 52 ]
64
[ "54-52=2", "11*6=66", "66-2=64" ]
Current State: 64:[54, 11, 6, 52], Operations: [] Exploring Operation: 54-52=2, Resulting Numbers: [11, 6, 2] Generated Node #2: [11, 6, 2] from Operation: 54-52=2 Current State: 64:[11, 6, 2], Operations: ['54-52=2'] Exploring Operation: 11*6=66, Resulting Numbers: [2, 66] Generated Node #3: [2, 66] from Operation: 11*6=66 Current State: 64:[2, 66], Operations: ['54-52=2', '11*6=66'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[54, 11, 6, 52], Operations: [] Exploring Operation: 54-52=2, Resulting Numbers: [11, 6, 2] Generated Node #0,0: 64:[11, 6, 2] Operation: 54-52=2 Exploring Operation: 54+11=65, Resulting Numbers: [6, 52, 65] Generated Node #0,1: 64:[6, 52, 65] Operation: 54+11=65 Exploring Operation: 11+52=63, Resulting Numbers: [54, 6, 63] Generated Node #0,2: 64:[54, 6, 63] Operation: 11+52=63 Exploring Operation: 54+6=60, Resulting Numbers: [11, 52, 60] Generated Node #0,3: 64:[11, 52, 60] Operation: 54+6=60 Exploring Operation: 54/6=9, Resulting Numbers: [11, 52, 9] Generated Node #0,4: 64:[11, 52, 9] Operation: 54/6=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[11, 6, 2], Operations: ['54-52=2'] Exploring Operation: 11-6=5, Resulting Numbers: [2, 5] Generated Node #0,0,0: 64:[2, 5] Operation: 11-6=5 Exploring Operation: 11+6=17, Resulting Numbers: [2, 17] Generated Node #0,0,1: 64:[2, 17] Operation: 11+6=17 Exploring Operation: 11-2=9, Resulting Numbers: [6, 9] Generated Node #0,0,2: 64:[6, 9] Operation: 11-2=9 Exploring Operation: 11*6=66, Resulting Numbers: [2, 66] Generated Node #0,0,3: 64:[2, 66] Operation: 11*6=66 Exploring Operation: 6+2=8, Resulting Numbers: [11, 8] Generated Node #0,0,4: 64:[11, 8] Operation: 6+2=8 Moving to Node #0,0,0 Current State: 64:[2, 5], Operations: ['54-52=2', '11-6=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,64 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[2, 17], Operations: ['54-52=2', '11+6=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,64 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,64 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,64 unequal: No Solution Moving to Node #0,0,3 Current State: 64:[2, 66], Operations: ['54-52=2', '11*6=66'] Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,64 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,64 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[54, 11, 6, 52], Operations: [] Exploring Operation: 54-52=2, Resulting Numbers: [11, 6, 2] Generated Node #0,0: 64:[11, 6, 2] Operation: 54-52=2 Moving to Node #0,0 Current State: 64:[11, 6, 2], Operations: ['54-52=2'] Exploring Operation: 11*6=66, Resulting Numbers: [2, 66] Generated Node #0,0,3: 64:[2, 66] Operation: 11*6=66 Moving to Node #0,0,3 Current State: 64:[2, 66], Operations: ['54-52=2', '11*6=66'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 69, 86, 85, 42 ]
60
[ "86-69=17", "85-42=43", "17+43=60" ]
Current State: 60:[69, 86, 85, 42], Operations: [] Exploring Operation: 86-69=17, Resulting Numbers: [85, 42, 17] Generated Node #2: [85, 42, 17] from Operation: 86-69=17 Current State: 60:[85, 42, 17], Operations: ['86-69=17'] Exploring Operation: 85-42=43, Resulting Numbers: [17, 43] Generated Node #3: [17, 43] from Operation: 85-42=43 Current State: 60:[17, 43], Operations: ['86-69=17', '85-42=43'] Exploring Operation: 17+43=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[69, 86, 85, 42], Operations: [] Exploring Operation: 86-85=1, Resulting Numbers: [69, 42, 1] Generated Node #0,0: 60:[69, 42, 1] Operation: 86-85=1 Exploring Operation: 86-69=17, Resulting Numbers: [85, 42, 17] Generated Node #0,1: 60:[85, 42, 17] Operation: 86-69=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[69, 42, 1], Operations: ['86-85=1'] Exploring Operation: 69-1=68, Resulting Numbers: [42, 68] Generated Node #0,0,0: 60:[42, 68] Operation: 69-1=68 Exploring Operation: 69-42=27, Resulting Numbers: [1, 27] Generated Node #0,0,1: 60:[1, 27] Operation: 69-42=27 Moving to Node #0,0,1 Current State: 60:[1, 27], Operations: ['86-85=1', '69-42=27'] Exploring Operation: 1+27=28, Resulting Numbers: [28] 28,60 unequal: No Solution Exploring Operation: 1*27=27, Resulting Numbers: [27] 27,60 unequal: No Solution Moving to Node #0,0,0 Current State: 60:[42, 68], Operations: ['86-85=1', '69-1=68'] Exploring Operation: 68-42=26, Resulting Numbers: [26] 26,60 unequal: No Solution Exploring Operation: 42+68=110, Resulting Numbers: [110] 110,60 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 #0,1 Current State: 60:[85, 42, 17], Operations: ['86-69=17'] Exploring Operation: 85/17=5, Resulting Numbers: [42, 5] Generated Node #0,1,0: 60:[42, 5] Operation: 85/17=5 Exploring Operation: 85-42=43, Resulting Numbers: [17, 43] Generated Node #0,1,1: 60:[17, 43] Operation: 85-42=43 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 60:[42, 5], Operations: ['86-69=17', '85/17=5'] Exploring Operation: 42+5=47, Resulting Numbers: [47] 47,60 unequal: No Solution Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,60 unequal: No Solution No 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: 60:[17, 43], Operations: ['86-69=17', '85-42=43'] Exploring Operation: 43-17=26, Resulting Numbers: [26] 26,60 unequal: No Solution Exploring Operation: 17+43=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[69, 86, 85, 42], Operations: [] Exploring Operation: 86-69=17, Resulting Numbers: [85, 42, 17] Generated Node #0,1: 60:[85, 42, 17] Operation: 86-69=17 Moving to Node #0,1 Current State: 60:[85, 42, 17], Operations: ['86-69=17'] Exploring Operation: 85-42=43, Resulting Numbers: [17, 43] Generated Node #0,1,1: 60:[17, 43] Operation: 85-42=43 Moving to Node #0,1,1 Current State: 60:[17, 43], Operations: ['86-69=17', '85-42=43'] Exploring Operation: 17+43=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
sum_heuristic
[ 41, 20, 70, 9 ]
28
[ "41+9=50", "20*70=1400", "1400/50=28" ]
Current State: 28:[41, 20, 70, 9], Operations: [] Exploring Operation: 41+9=50, Resulting Numbers: [20, 70, 50] Generated Node #2: [20, 70, 50] from Operation: 41+9=50 Current State: 28:[20, 70, 50], Operations: ['41+9=50'] Exploring Operation: 20*70=1400, Resulting Numbers: [50, 1400] Generated Node #3: [50, 1400] from Operation: 20*70=1400 Current State: 28:[50, 1400], Operations: ['41+9=50', '20*70=1400'] Exploring Operation: 1400/50=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[41, 20, 70, 9], Operations: [] Exploring Operation: 41-20=21, Resulting Numbers: [70, 9, 21] Generated Node #0,0: 28:[70, 9, 21] Operation: 41-20=21 Exploring Operation: 70-20=50, Resulting Numbers: [41, 9, 50] Generated Node #0,1: 28:[41, 9, 50] Operation: 70-20=50 Exploring Operation: 70-41=29, Resulting Numbers: [20, 9, 29] Generated Node #0,2: 28:[20, 9, 29] Operation: 70-41=29 Moving to Node #0,2 Current State: 28:[20, 9, 29], Operations: ['70-41=29'] Exploring Operation: 29-20=9, Resulting Numbers: [9, 9] Generated Node #0,2,0: 28:[9, 9] Operation: 29-20=9 Exploring Operation: 20-9=11, Resulting Numbers: [29, 11] Generated Node #0,2,1: 28:[29, 11] Operation: 20-9=11 Exploring Operation: 20+9=29, Resulting Numbers: [29, 29] Generated Node #0,2,2: 28:[29, 29] Operation: 20+9=29 Moving to Node #0,1 Current State: 28:[41, 9, 50], Operations: ['70-20=50'] Exploring Operation: 50-41=9, Resulting Numbers: [9, 9] Generated Node #0,1,0: 28:[9, 9] Operation: 50-41=9 Exploring Operation: 50-9=41, Resulting Numbers: [41, 41] Generated Node #0,1,1: 28:[41, 41] Operation: 50-9=41 Exploring Operation: 41-9=32, Resulting Numbers: [50, 32] Generated Node #0,1,2: 28:[50, 32] Operation: 41-9=32 Moving to Node #0,0 Current State: 28:[70, 9, 21], Operations: ['41-20=21'] Exploring Operation: 70-21=49, Resulting Numbers: [9, 49] Generated Node #0,0,0: 28:[9, 49] Operation: 70-21=49 Exploring Operation: 9+21=30, Resulting Numbers: [70, 30] Generated Node #0,0,1: 28:[70, 30] Operation: 9+21=30 Exploring Operation: 70-9=61, Resulting Numbers: [21, 61] Generated Node #0,0,2: 28:[21, 61] Operation: 70-9=61 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 28:[9, 49], Operations: ['41-20=21', '70-21=49'] Exploring Operation: 9+49=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 49-9=40, Resulting Numbers: [40] 40,28 unequal: No Solution Exploring Operation: 9*49=441, Resulting Numbers: [441] 441,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 28:[21, 61], Operations: ['41-20=21', '70-9=61'] Exploring Operation: 21+61=82, Resulting Numbers: [82] 82,28 unequal: No Solution Exploring Operation: 21*61=1281, Resulting Numbers: [1281] 1281,28 unequal: No Solution Exploring Operation: 61-21=40, Resulting Numbers: [40] 40,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 28:[70, 30], Operations: ['41-20=21', '9+21=30'] Exploring Operation: 70*30=2100, Resulting Numbers: [2100] 2100,28 unequal: No Solution Exploring Operation: 70+30=100, Resulting Numbers: [100] 100,28 unequal: No Solution Exploring Operation: 70-30=40, Resulting Numbers: [40] 40,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 28:[29, 29], Operations: ['70-41=29', '20+9=29'] Exploring Operation: 29/29=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 29-29=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 29+29=58, Resulting Numbers: [58] 58,28 unequal: No Solution Moving to Node #0,2,1 Current State: 28:[29, 11], Operations: ['70-41=29', '20-9=11'] Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,28 unequal: No Solution Exploring Operation: 29+11=40, Resulting Numbers: [40] 40,28 unequal: No Solution Exploring Operation: 29*11=319, Resulting Numbers: [319] 319,28 unequal: No Solution Moving to Node #0,2,0 Current State: 28:[9, 9], Operations: ['70-41=29', '29-20=9'] Exploring Operation: 9/9=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,28 unequal: No Solution Exploring Operation: 9-9=0, Resulting Numbers: [0] 0,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[9, 9], Operations: ['70-20=50', '50-41=9'] Exploring Operation: 9-9=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,28 unequal: No Solution Exploring Operation: 9/9=1, Resulting Numbers: [1] 1,28 unequal: No Solution Moving to Node #0,1,1 Current State: 28:[41, 41], Operations: ['70-20=50', '50-9=41'] Exploring Operation: 41-41=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,28 unequal: No Solution Exploring Operation: 41/41=1, Resulting Numbers: [1] 1,28 unequal: No Solution Moving to Node #0,1,2 Current State: 28:[50, 32], Operations: ['70-20=50', '41-9=32'] Exploring Operation: 50*32=1600, Resulting Numbers: [1600] 1600,28 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,28 unequal: No Solution Exploring Operation: 50+32=82, Resulting Numbers: [82] 82,28 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 30, 19, 49, 56 ]
42
[ "30+19=49", "56-49=7", "49-7=42" ]
Current State: 42:[30, 19, 49, 56], Operations: [] Exploring Operation: 30+19=49, Resulting Numbers: [49, 56, 49] Generated Node #2: [49, 56, 49] from Operation: 30+19=49 Current State: 42:[49, 56, 49], Operations: ['30+19=49'] Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,42 equal: Goal Reached Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[30, 19, 49, 56], Operations: [] Exploring Operation: 56-19=37, Resulting Numbers: [30, 49, 37] Generated Node #0,0: 42:[30, 49, 37] Operation: 56-19=37 Exploring Operation: 56-30=26, Resulting Numbers: [19, 49, 26] Generated Node #0,1: 42:[19, 49, 26] Operation: 56-30=26 Exploring Operation: 49-30=19, Resulting Numbers: [19, 56, 19] Generated Node #0,2: 42:[19, 56, 19] Operation: 49-30=19 Exploring Operation: 56-49=7, Resulting Numbers: [30, 19, 7] Generated Node #0,3: 42:[30, 19, 7] Operation: 56-49=7 Start Sub Search at level 1: Moving to Node #0,3 Current State: 42:[30, 19, 7], Operations: ['56-49=7'] Exploring Operation: 30-19=11, Resulting Numbers: [7, 11] Generated Node #0,3,0: 42:[7, 11] Operation: 30-19=11 Exploring Operation: 30-7=23, Resulting Numbers: [19, 23] Generated Node #0,3,1: 42:[19, 23] Operation: 30-7=23 Exploring Operation: 30+7=37, Resulting Numbers: [19, 37] Generated Node #0,3,2: 42:[19, 37] Operation: 30+7=37 Exploring Operation: 30+19=49, Resulting Numbers: [7, 49] Generated Node #0,3,3: 42:[7, 49] Operation: 30+19=49 Moving to Node #0,3,0 Current State: 42:[7, 11], Operations: ['56-49=7', '30-19=11'] Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,42 unequal: No Solution Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,42 unequal: No Solution Moving to Node #0,3,1 Current State: 42:[19, 23], Operations: ['56-49=7', '30-7=23'] Exploring Operation: 19*23=437, Resulting Numbers: [437] 437,42 unequal: No Solution Exploring Operation: 19+23=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[30, 19, 49, 56], Operations: [] Exploring Operation: 56-49=7, Resulting Numbers: [30, 19, 7] Generated Node #0,3: 42:[30, 19, 7] Operation: 56-49=7 Moving to Node #0,3 Current State: 42:[30, 19, 7], Operations: ['56-49=7'] Exploring Operation: 30-7=23, Resulting Numbers: [19, 23] Generated Node #0,3,1: 42:[19, 23] Operation: 30-7=23 Moving to Node #0,3,1 Current State: 42:[19, 23], Operations: ['56-49=7', '30-7=23'] Exploring Operation: 19+23=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 89, 92, 77, 99 ]
25
[ "92-89=3", "99-77=22", "3+22=25" ]
Current State: 25:[89, 92, 77, 99], Operations: [] Exploring Operation: 92-89=3, Resulting Numbers: [77, 99, 3] Generated Node #2: [77, 99, 3] from Operation: 92-89=3 Current State: 25:[77, 99, 3], Operations: ['92-89=3'] Exploring Operation: 99-77=22, Resulting Numbers: [3, 22] Generated Node #3: [3, 22] from Operation: 99-77=22 Current State: 25:[3, 22], Operations: ['92-89=3', '99-77=22'] Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[89, 92, 77, 99], Operations: [] Exploring Operation: 99-92=7, Resulting Numbers: [89, 77, 7] Generated Node #0,0: 25:[89, 77, 7] Operation: 99-92=7 Exploring Operation: 92-89=3, Resulting Numbers: [77, 99, 3] Generated Node #0,1: 25:[77, 99, 3] Operation: 92-89=3 Exploring Operation: 99-89=10, Resulting Numbers: [92, 77, 10] Generated Node #0,2: 25:[92, 77, 10] Operation: 99-89=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[89, 77, 7], Operations: ['99-92=7'] Exploring Operation: 77/7=11, Resulting Numbers: [89, 11] Generated Node #0,0,0: 25:[89, 11] Operation: 77/7=11 Exploring Operation: 89-7=82, Resulting Numbers: [77, 82] Generated Node #0,0,1: 25:[77, 82] Operation: 89-7=82 Exploring Operation: 89-77=12, Resulting Numbers: [7, 12] Generated Node #0,0,2: 25:[7, 12] Operation: 89-77=12 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 25:[7, 12], Operations: ['99-92=7', '89-77=12'] Exploring Operation: 7+12=19, Resulting Numbers: [19] 19,25 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[89, 11], Operations: ['99-92=7', '77/7=11'] Exploring Operation: 89+11=100, Resulting Numbers: [100] 100,25 unequal: No Solution Exploring Operation: 89-11=78, Resulting Numbers: [78] 78,25 unequal: No Solution Exploring Operation: 89*11=979, Resulting Numbers: [979] 979,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 25:[77, 82], Operations: ['99-92=7', '89-7=82'] Exploring Operation: 77+82=159, Resulting Numbers: [159] 159,25 unequal: No Solution Exploring Operation: 77*82=6314, Resulting Numbers: [6314] 6314,25 unequal: No Solution Exploring Operation: 82-77=5, Resulting Numbers: [5] 5,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[92, 77, 10], Operations: ['99-89=10'] Exploring Operation: 92-77=15, Resulting Numbers: [10, 15] Generated Node #0,2,0: 25:[10, 15] Operation: 92-77=15 Exploring Operation: 77-10=67, Resulting Numbers: [92, 67] Generated Node #0,2,1: 25:[92, 67] Operation: 77-10=67 Exploring Operation: 92-10=82, Resulting Numbers: [77, 82] Generated Node #0,2,2: 25:[77, 82] Operation: 92-10=82 Moving to Node #0,2,0 Current State: 25:[10, 15], Operations: ['99-89=10', '92-77=15'] Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 10+15=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[89, 92, 77, 99], Operations: [] Exploring Operation: 99-89=10, Resulting Numbers: [92, 77, 10] Generated Node #0,2: 25:[92, 77, 10] Operation: 99-89=10 Moving to Node #0,2 Current State: 25:[92, 77, 10], Operations: ['99-89=10'] Exploring Operation: 92-77=15, Resulting Numbers: [10, 15] Generated Node #0,2,0: 25:[10, 15] Operation: 92-77=15 Moving to Node #0,2,0 Current State: 25:[10, 15], Operations: ['99-89=10', '92-77=15'] Exploring Operation: 10+15=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 68, 15, 41, 43 ]
31
[ "68-15=53", "41+43=84", "84-53=31" ]
Current State: 31:[68, 15, 41, 43], Operations: [] Exploring Operation: 68-15=53, Resulting Numbers: [41, 43, 53] Generated Node #2: [41, 43, 53] from Operation: 68-15=53 Current State: 31:[41, 43, 53], Operations: ['68-15=53'] Exploring Operation: 41+43=84, Resulting Numbers: [53, 84] Generated Node #3: [53, 84] from Operation: 41+43=84 Current State: 31:[53, 84], Operations: ['68-15=53', '41+43=84'] Exploring Operation: 84-53=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[68, 15, 41, 43], Operations: [] Exploring Operation: 68-15=53, Resulting Numbers: [41, 43, 53] Generated Node #0,0: 31:[41, 43, 53] Operation: 68-15=53 Exploring Operation: 68-41=27, Resulting Numbers: [15, 43, 27] Generated Node #0,1: 31:[15, 43, 27] Operation: 68-41=27 Exploring Operation: 43-15=28, Resulting Numbers: [68, 41, 28] Generated Node #0,2: 31:[68, 41, 28] Operation: 43-15=28 Exploring Operation: 41-15=26, Resulting Numbers: [68, 43, 26] Generated Node #0,3: 31:[68, 43, 26] Operation: 41-15=26 Exploring Operation: 68-43=25, Resulting Numbers: [15, 41, 25] Generated Node #0,4: 31:[15, 41, 25] Operation: 68-43=25 Moving to Node #0,1 Current State: 31:[15, 43, 27], Operations: ['68-41=27'] Exploring Operation: 27-15=12, Resulting Numbers: [43, 12] Generated Node #0,1,0: 31:[43, 12] Operation: 27-15=12 Exploring Operation: 15+43=58, Resulting Numbers: [27, 58] Generated Node #0,1,1: 31:[27, 58] Operation: 15+43=58 Exploring Operation: 43-15=28, Resulting Numbers: [27, 28] Generated Node #0,1,2: 31:[27, 28] Operation: 43-15=28 Exploring Operation: 43-27=16, Resulting Numbers: [15, 16] Generated Node #0,1,3: 31:[15, 16] Operation: 43-27=16 Exploring Operation: 15+27=42, Resulting Numbers: [43, 42] Generated Node #0,1,4: 31:[43, 42] Operation: 15+27=42 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[27, 28], Operations: ['68-41=27', '43-15=28'] Exploring Operation: 27*28=756, Resulting Numbers: [756] 756,31 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 31:[43, 42], Operations: ['68-41=27', '15+27=42'] Exploring Operation: 43-42=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 43+42=85, Resulting Numbers: [85] 85,31 unequal: No Solution Exploring Operation: 43*42=1806, Resulting Numbers: [1806] 1806,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[43, 12], Operations: ['68-41=27', '27-15=12'] Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,31 unequal: No Solution Exploring Operation: 43*12=516, Resulting Numbers: [516] 516,31 unequal: No Solution Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[68, 15, 41, 43], Operations: [] Exploring Operation: 68-41=27, Resulting Numbers: [15, 43, 27] Generated Node #0,1: 31:[15, 43, 27] Operation: 68-41=27 Moving to Node #0,1 Current State: 31:[15, 43, 27], Operations: ['68-41=27'] Exploring Operation: 27-15=12, Resulting Numbers: [43, 12] Generated Node #0,1,0: 31:[43, 12] Operation: 27-15=12 Moving to Node #0,1,0 Current State: 31:[43, 12], Operations: ['68-41=27', '27-15=12'] Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 22, 79, 34, 44 ]
91
[ "22+79=101", "44-34=10", "101-10=91" ]
Current State: 91:[22, 79, 34, 44], Operations: [] Exploring Operation: 22+79=101, Resulting Numbers: [34, 44, 101] Generated Node #2: [34, 44, 101] from Operation: 22+79=101 Current State: 91:[34, 44, 101], Operations: ['22+79=101'] Exploring Operation: 44-34=10, Resulting Numbers: [101, 10] Generated Node #3: [101, 10] from Operation: 44-34=10 Current State: 91:[101, 10], Operations: ['22+79=101', '44-34=10'] Exploring Operation: 101-10=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[22, 79, 34, 44], Operations: [] Exploring Operation: 34+44=78, Resulting Numbers: [22, 79, 78] Generated Node #0,0: 91:[22, 79, 78] Operation: 34+44=78 Exploring Operation: 44-34=10, Resulting Numbers: [22, 79, 10] Generated Node #0,1: 91:[22, 79, 10] Operation: 44-34=10 Exploring Operation: 44/22=2, Resulting Numbers: [79, 34, 2] Generated Node #0,2: 91:[79, 34, 2] Operation: 44/22=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[22, 79, 10], Operations: ['44-34=10'] Exploring Operation: 22+79=101, Resulting Numbers: [10, 101] Generated Node #0,1,0: 91:[10, 101] Operation: 22+79=101 Exploring Operation: 79+10=89, Resulting Numbers: [22, 89] Generated Node #0,1,1: 91:[22, 89] Operation: 79+10=89 Exploring Operation: 22-10=12, Resulting Numbers: [79, 12] Generated Node #0,1,2: 91:[79, 12] Operation: 22-10=12 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[22, 89], Operations: ['44-34=10', '79+10=89'] Exploring Operation: 89-22=67, Resulting Numbers: [67] 67,91 unequal: No Solution Exploring Operation: 22+89=111, Resulting Numbers: [111] 111,91 unequal: No Solution Exploring Operation: 22*89=1958, Resulting Numbers: [1958] 1958,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[10, 101], Operations: ['44-34=10', '22+79=101'] Exploring Operation: 10+101=111, Resulting Numbers: [111] 111,91 unequal: No Solution Exploring Operation: 10*101=1010, Resulting Numbers: [1010] 1010,91 unequal: No Solution Exploring Operation: 101-10=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[22, 79, 34, 44], Operations: [] Exploring Operation: 44-34=10, Resulting Numbers: [22, 79, 10] Generated Node #0,1: 91:[22, 79, 10] Operation: 44-34=10 Moving to Node #0,1 Current State: 91:[22, 79, 10], Operations: ['44-34=10'] Exploring Operation: 22+79=101, Resulting Numbers: [10, 101] Generated Node #0,1,0: 91:[10, 101] Operation: 22+79=101 Moving to Node #0,1,0 Current State: 91:[10, 101], Operations: ['44-34=10', '22+79=101'] Exploring Operation: 101-10=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 6, 93, 63, 33 ]
87
[ "63-33=30", "6*30=180", "180-93=87" ]
Current State: 87:[6, 93, 63, 33], Operations: [] Exploring Operation: 63-33=30, Resulting Numbers: [6, 93, 30] Generated Node #2: [6, 93, 30] from Operation: 63-33=30 Current State: 87:[6, 93, 30], Operations: ['63-33=30'] Exploring Operation: 6*30=180, Resulting Numbers: [93, 180] Generated Node #3: [93, 180] from Operation: 6*30=180 Current State: 87:[93, 180], Operations: ['63-33=30', '6*30=180'] Exploring Operation: 180-93=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[6, 93, 63, 33], Operations: [] Exploring Operation: 93-63=30, Resulting Numbers: [6, 33, 30] Generated Node #0,0: 87:[6, 33, 30] Operation: 93-63=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[6, 33, 30], Operations: ['93-63=30'] Exploring Operation: 33-6=27, Resulting Numbers: [30, 27] Generated Node #0,0,0: 87:[30, 27] Operation: 33-6=27 Moving to Node #0,0,0 Current State: 87:[30, 27], Operations: ['93-63=30', '33-6=27'] Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,87 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
[ 45, 32, 66, 48 ]
54
[ "48-45=3", "66/3=22", "32+22=54" ]
Current State: 54:[45, 32, 66, 48], Operations: [] Exploring Operation: 48-45=3, Resulting Numbers: [32, 66, 3] Generated Node #2: [32, 66, 3] from Operation: 48-45=3 Current State: 54:[32, 66, 3], Operations: ['48-45=3'] Exploring Operation: 66/3=22, Resulting Numbers: [32, 22] Generated Node #3: [32, 22] from Operation: 66/3=22 Current State: 54:[32, 22], Operations: ['48-45=3', '66/3=22'] Exploring Operation: 32+22=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[45, 32, 66, 48], Operations: [] Exploring Operation: 66-32=34, Resulting Numbers: [45, 48, 34] Generated Node #0,0: 54:[45, 48, 34] Operation: 66-32=34 Exploring Operation: 48-45=3, Resulting Numbers: [32, 66, 3] Generated Node #0,1: 54:[32, 66, 3] Operation: 48-45=3 Exploring Operation: 66-48=18, Resulting Numbers: [45, 32, 18] Generated Node #0,2: 54:[45, 32, 18] Operation: 66-48=18 Exploring Operation: 45-32=13, Resulting Numbers: [66, 48, 13] Generated Node #0,3: 54:[66, 48, 13] Operation: 45-32=13 Exploring Operation: 66-45=21, Resulting Numbers: [32, 48, 21] Generated Node #0,4: 54:[32, 48, 21] Operation: 66-45=21 Moving to Node #0,2 Current State: 54:[45, 32, 18], Operations: ['66-48=18'] Exploring Operation: 45-32=13, Resulting Numbers: [18, 13] Generated Node #0,2,0: 54:[18, 13] Operation: 45-32=13 Exploring Operation: 32+18=50, Resulting Numbers: [45, 50] Generated Node #0,2,1: 54:[45, 50] Operation: 32+18=50 Exploring Operation: 45-18=27, Resulting Numbers: [32, 27] Generated Node #0,2,2: 54:[32, 27] Operation: 45-18=27 Exploring Operation: 32-18=14, Resulting Numbers: [45, 14] Generated Node #0,2,3: 54:[45, 14] Operation: 32-18=14 Exploring Operation: 45+18=63, Resulting Numbers: [32, 63] Generated Node #0,2,4: 54:[32, 63] Operation: 45+18=63 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 54:[18, 13], Operations: ['66-48=18', '45-32=13'] Exploring Operation: 18-13=5, Resulting Numbers: [5] 5,54 unequal: No Solution Exploring Operation: 18+13=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 18*13=234, Resulting Numbers: [234] 234,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 54:[32, 27], Operations: ['66-48=18', '45-18=27'] Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,54 unequal: No Solution Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,54 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 54:[45, 50], Operations: ['66-48=18', '32+18=50'] Exploring Operation: 45*50=2250, Resulting Numbers: [2250] 2250,54 unequal: No Solution Exploring Operation: 45+50=95, Resulting Numbers: [95] 95,54 unequal: No Solution Exploring Operation: 50-45=5, Resulting Numbers: [5] 5,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 54:[45, 14], Operations: ['66-48=18', '32-18=14'] Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 45*14=630, Resulting Numbers: [630] 630,54 unequal: No Solution Exploring Operation: 45+14=59, Resulting Numbers: [59] 59,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 54:[32, 63], Operations: ['66-48=18', '45+18=63'] Exploring Operation: 32*63=2016, Resulting Numbers: [2016] 2016,54 unequal: No Solution Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 32+63=95, Resulting Numbers: [95] 95,54 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: 54:[32, 48, 21], Operations: ['66-45=21'] Exploring Operation: 48-21=27, Resulting Numbers: [32, 27] Generated Node #0,4,0: 54:[32, 27] Operation: 48-21=27 Exploring Operation: 32-21=11, Resulting Numbers: [48, 11] Generated Node #0,4,1: 54:[48, 11] Operation: 32-21=11 Exploring Operation: 48-32=16, Resulting Numbers: [21, 16] Generated Node #0,4,2: 54:[21, 16] Operation: 48-32=16 Exploring Operation: 32+21=53, Resulting Numbers: [48, 53] Generated Node #0,4,3: 54:[48, 53] Operation: 32+21=53 Exploring Operation: 48+21=69, Resulting Numbers: [32, 69] Generated Node #0,4,4: 54:[32, 69] Operation: 48+21=69 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 54:[32, 27], Operations: ['66-45=21', '48-21=27'] Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,54 unequal: No Solution Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,54 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 54:[21, 16], Operations: ['66-45=21', '48-32=16'] Exploring Operation: 21*16=336, Resulting Numbers: [336] 336,54 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,54 unequal: No Solution Exploring Operation: 21+16=37, Resulting Numbers: [37] 37,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 54:[48, 53], Operations: ['66-45=21', '32+21=53'] Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,54 unequal: No Solution Exploring Operation: 48+53=101, Resulting Numbers: [101] 101,54 unequal: No Solution Exploring Operation: 48*53=2544, Resulting Numbers: [2544] 2544,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 54:[48, 11], Operations: ['66-45=21', '32-21=11'] Exploring Operation: 48+11=59, Resulting Numbers: [59] 59,54 unequal: No Solution Exploring Operation: 48*11=528, Resulting Numbers: [528] 528,54 unequal: No Solution Exploring Operation: 48-11=37, Resulting Numbers: [37] 37,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 54:[32, 69], Operations: ['66-45=21', '48+21=69'] Exploring Operation: 32*69=2208, Resulting Numbers: [2208] 2208,54 unequal: No Solution Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,54 unequal: No Solution Exploring Operation: 32+69=101, Resulting Numbers: [101] 101,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 54:[32, 66, 3], Operations: ['48-45=3'] Exploring Operation: 66-3=63, Resulting Numbers: [32, 63] Generated Node #0,1,0: 54:[32, 63] Operation: 66-3=63 Exploring Operation: 32-3=29, Resulting Numbers: [66, 29] Generated Node #0,1,1: 54:[66, 29] Operation: 32-3=29 Exploring Operation: 66/3=22, Resulting Numbers: [32, 22] Generated Node #0,1,2: 54:[32, 22] Operation: 66/3=22 Exploring Operation: 66-32=34, Resulting Numbers: [3, 34] Generated Node #0,1,3: 54:[3, 34] Operation: 66-32=34 Exploring Operation: 32+3=35, Resulting Numbers: [66, 35] Generated Node #0,1,4: 54:[66, 35] Operation: 32+3=35 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 54:[3, 34], Operations: ['48-45=3', '66-32=34'] Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,54 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,54 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 54:[32, 22], Operations: ['48-45=3', '66/3=22'] Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 32+22=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[45, 32, 66, 48], Operations: [] Exploring Operation: 48-45=3, Resulting Numbers: [32, 66, 3] Generated Node #0,1: 54:[32, 66, 3] Operation: 48-45=3 Moving to Node #0,1 Current State: 54:[32, 66, 3], Operations: ['48-45=3'] Exploring Operation: 66/3=22, Resulting Numbers: [32, 22] Generated Node #0,1,2: 54:[32, 22] Operation: 66/3=22 Moving to Node #0,1,2 Current State: 54:[32, 22], Operations: ['48-45=3', '66/3=22'] Exploring Operation: 32+22=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.948785
hs_5
sum_heuristic
[ 5, 48, 92, 14 ]
70
[ "5*14=70", "48+92=140", "140-70=70" ]
Current State: 70:[5, 48, 92, 14], Operations: [] Exploring Operation: 5*14=70, Resulting Numbers: [48, 92, 70] Generated Node #2: [48, 92, 70] from Operation: 5*14=70 Current State: 70:[48, 92, 70], Operations: ['5*14=70'] Exploring Operation: 48+92=140, Resulting Numbers: [70, 140] Generated Node #3: [70, 140] from Operation: 48+92=140 Current State: 70:[70, 140], Operations: ['5*14=70', '48+92=140'] Exploring Operation: 140-70=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[5, 48, 92, 14], Operations: [] Exploring Operation: 92-14=78, Resulting Numbers: [5, 48, 78] Generated Node #0,0: 70:[5, 48, 78] Operation: 92-14=78 Exploring Operation: 92-48=44, Resulting Numbers: [5, 14, 44] Generated Node #0,1: 70:[5, 14, 44] Operation: 92-48=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[5, 14, 44], Operations: ['92-48=44'] Exploring Operation: 44-5=39, Resulting Numbers: [14, 39] Generated Node #0,1,0: 70:[14, 39] Operation: 44-5=39 Exploring Operation: 44-14=30, Resulting Numbers: [5, 30] Generated Node #0,1,1: 70:[5, 30] Operation: 44-14=30 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 70:[14, 39], Operations: ['92-48=44', '44-5=39'] Exploring Operation: 14+39=53, Resulting Numbers: [53] 53,70 unequal: No Solution Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 70:[5, 30], Operations: ['92-48=44', '44-14=30'] Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 5+30=35, Resulting Numbers: [35] 35,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[5, 48, 78], Operations: ['92-14=78'] Exploring Operation: 78-48=30, Resulting Numbers: [5, 30] Generated Node #0,0,0: 70:[5, 30] Operation: 78-48=30 Exploring Operation: 48-5=43, Resulting Numbers: [78, 43] Generated Node #0,0,1: 70:[78, 43] Operation: 48-5=43 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 70:[5, 30], Operations: ['92-14=78', '78-48=30'] Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 5+30=35, Resulting Numbers: [35] 35,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 70:[78, 43], Operations: ['92-14=78', '48-5=43'] Exploring Operation: 78-43=35, Resulting Numbers: [35] 35,70 unequal: No Solution Exploring Operation: 78+43=121, Resulting Numbers: [121] 121,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 13, 25, 41, 75 ]
80
[ "13*75=975", "975/25=39", "41+39=80" ]
Current State: 80:[13, 25, 41, 75], Operations: [] Exploring Operation: 13*75=975, Resulting Numbers: [25, 41, 975] Generated Node #2: [25, 41, 975] from Operation: 13*75=975 Current State: 80:[25, 41, 975], Operations: ['13*75=975'] Exploring Operation: 975/25=39, Resulting Numbers: [41, 39] Generated Node #3: [41, 39] from Operation: 975/25=39 Current State: 80:[41, 39], Operations: ['13*75=975', '975/25=39'] Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[13, 25, 41, 75], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [13, 41, 3] Generated Node #0,0: 80:[13, 41, 3] Operation: 75/25=3 Exploring Operation: 13+25=38, Resulting Numbers: [41, 75, 38] Generated Node #0,1: 80:[41, 75, 38] Operation: 13+25=38 Exploring Operation: 41-25=16, Resulting Numbers: [13, 75, 16] Generated Node #0,2: 80:[13, 75, 16] Operation: 41-25=16 Exploring Operation: 25-13=12, Resulting Numbers: [41, 75, 12] Generated Node #0,3: 80:[41, 75, 12] Operation: 25-13=12 Exploring Operation: 13+75=88, Resulting Numbers: [25, 41, 88] Generated Node #0,4: 80:[25, 41, 88] Operation: 13+75=88 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[13, 41, 3], Operations: ['75/25=3'] Exploring Operation: 13+3=16, Resulting Numbers: [41, 16] Generated Node #0,0,0: 80:[41, 16] Operation: 13+3=16 Exploring Operation: 13*3=39, Resulting Numbers: [41, 39] Generated Node #0,0,1: 80:[41, 39] Operation: 13*3=39 Exploring Operation: 41-3=38, Resulting Numbers: [13, 38] Generated Node #0,0,2: 80:[13, 38] Operation: 41-3=38 Exploring Operation: 13-3=10, Resulting Numbers: [41, 10] Generated Node #0,0,3: 80:[41, 10] Operation: 13-3=10 Exploring Operation: 41+3=44, Resulting Numbers: [13, 44] Generated Node #0,0,4: 80:[13, 44] Operation: 41+3=44 Moving to Node #0,0,0 Current State: 80:[41, 16], Operations: ['75/25=3', '13+3=16'] Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 41+16=57, Resulting Numbers: [57] 57,80 unequal: No Solution Exploring Operation: 41*16=656, Resulting Numbers: [656] 656,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[41, 10], Operations: ['75/25=3', '13-3=10'] Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,80 unequal: No Solution Exploring Operation: 41+10=51, Resulting Numbers: [51] 51,80 unequal: No Solution Exploring Operation: 41*10=410, Resulting Numbers: [410] 410,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[41, 39], Operations: ['75/25=3', '13*3=39'] Exploring Operation: 41*39=1599, Resulting Numbers: [1599] 1599,80 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[13, 25, 41, 75], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [13, 41, 3] Generated Node #0,0: 80:[13, 41, 3] Operation: 75/25=3 Moving to Node #0,0 Current State: 80:[13, 41, 3], Operations: ['75/25=3'] Exploring Operation: 13*3=39, Resulting Numbers: [41, 39] Generated Node #0,0,1: 80:[41, 39] Operation: 13*3=39 Moving to Node #0,0,1 Current State: 80:[41, 39], Operations: ['75/25=3', '13*3=39'] Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 90, 26, 87, 70 ]
10
[ "87-26=61", "70-61=9", "90/9=10" ]
Current State: 10:[90, 26, 87, 70], Operations: [] Exploring Operation: 87-26=61, Resulting Numbers: [90, 70, 61] Generated Node #2: [90, 70, 61] from Operation: 87-26=61 Current State: 10:[90, 70, 61], Operations: ['87-26=61'] Exploring Operation: 70-61=9, Resulting Numbers: [90, 9] Generated Node #3: [90, 9] from Operation: 70-61=9 Current State: 10:[90, 9], Operations: ['87-26=61', '70-61=9'] Exploring Operation: 90/9=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[90, 26, 87, 70], Operations: [] Exploring Operation: 90-87=3, Resulting Numbers: [26, 70, 3] Generated Node #0,0: 10:[26, 70, 3] Operation: 90-87=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[26, 70, 3], Operations: ['90-87=3'] Exploring Operation: 70-26=44, Resulting Numbers: [3, 44] Generated Node #0,0,0: 10:[3, 44] Operation: 70-26=44 Moving to Node #0,0,0 Current State: 10:[3, 44], Operations: ['90-87=3', '70-26=44'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 98, 94, 43, 28 ]
60
[ "98-94=4", "43-28=15", "4*15=60" ]
Current State: 60:[98, 94, 43, 28], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [43, 28, 4] Generated Node #2: [43, 28, 4] from Operation: 98-94=4 Current State: 60:[43, 28, 4], Operations: ['98-94=4'] Exploring Operation: 43-28=15, Resulting Numbers: [4, 15] Generated Node #3: [4, 15] from Operation: 43-28=15 Current State: 60:[4, 15], Operations: ['98-94=4', '43-28=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[98, 94, 43, 28], Operations: [] Exploring Operation: 94-43=51, Resulting Numbers: [98, 28, 51] Generated Node #0,0: 60:[98, 28, 51] Operation: 94-43=51 Exploring Operation: 98-28=70, Resulting Numbers: [94, 43, 70] Generated Node #0,1: 60:[94, 43, 70] Operation: 98-28=70 Exploring Operation: 98-94=4, Resulting Numbers: [43, 28, 4] Generated Node #0,2: 60:[43, 28, 4] Operation: 98-94=4 Exploring Operation: 94-28=66, Resulting Numbers: [98, 43, 66] Generated Node #0,3: 60:[98, 43, 66] Operation: 94-28=66 Exploring Operation: 98-43=55, Resulting Numbers: [94, 28, 55] Generated Node #0,4: 60:[94, 28, 55] Operation: 98-43=55 Moving to Node #0,2 Current State: 60:[43, 28, 4], Operations: ['98-94=4'] Exploring Operation: 43-28=15, Resulting Numbers: [4, 15] Generated Node #0,2,0: 60:[4, 15] Operation: 43-28=15 Exploring Operation: 43-4=39, Resulting Numbers: [28, 39] Generated Node #0,2,1: 60:[28, 39] Operation: 43-4=39 Exploring Operation: 43+28=71, Resulting Numbers: [4, 71] Generated Node #0,2,2: 60:[4, 71] Operation: 43+28=71 Exploring Operation: 43+4=47, Resulting Numbers: [28, 47] Generated Node #0,2,3: 60:[28, 47] Operation: 43+4=47 Exploring Operation: 28/4=7, Resulting Numbers: [43, 7] Generated Node #0,2,4: 60:[43, 7] Operation: 28/4=7 Moving to Node #0,4 Current State: 60:[94, 28, 55], Operations: ['98-43=55'] Exploring Operation: 28+55=83, Resulting Numbers: [94, 83] Generated Node #0,4,0: 60:[94, 83] Operation: 28+55=83 Exploring Operation: 94-55=39, Resulting Numbers: [28, 39] Generated Node #0,4,1: 60:[28, 39] Operation: 94-55=39 Exploring Operation: 55-28=27, Resulting Numbers: [94, 27] Generated Node #0,4,2: 60:[94, 27] Operation: 55-28=27 Exploring Operation: 94-28=66, Resulting Numbers: [55, 66] Generated Node #0,4,3: 60:[55, 66] Operation: 94-28=66 Exploring Operation: 94+28=122, Resulting Numbers: [55, 122] Generated Node #0,4,4: 60:[55, 122] Operation: 94+28=122 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 60:[28, 39], Operations: ['98-43=55', '94-55=39'] Exploring Operation: 28+39=67, Resulting Numbers: [67] 67,60 unequal: No Solution Exploring Operation: 39-28=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 28*39=1092, Resulting Numbers: [1092] 1092,60 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 #0,4,3 Current State: 60:[55, 66], Operations: ['98-43=55', '94-28=66'] Exploring Operation: 55+66=121, Resulting Numbers: [121] 121,60 unequal: No Solution Exploring Operation: 66-55=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 55*66=3630, Resulting Numbers: [3630] 3630,60 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 #0,4,2 Current State: 60:[94, 27], Operations: ['98-43=55', '55-28=27'] Exploring Operation: 94*27=2538, Resulting Numbers: [2538] 2538,60 unequal: No Solution Exploring Operation: 94-27=67, Resulting Numbers: [67] 67,60 unequal: No Solution Exploring Operation: 94+27=121, Resulting Numbers: [121] 121,60 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 #0,4,0 Current State: 60:[94, 83], Operations: ['98-43=55', '28+55=83'] Exploring Operation: 94-83=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 94+83=177, Resulting Numbers: [177] 177,60 unequal: No Solution Exploring Operation: 94*83=7802, Resulting Numbers: [7802] 7802,60 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 #0,4,4 Current State: 60:[55, 122], Operations: ['98-43=55', '94+28=122'] Exploring Operation: 55+122=177, Resulting Numbers: [177] 177,60 unequal: No Solution Exploring Operation: 55*122=6710, Resulting Numbers: [6710] 6710,60 unequal: No Solution Exploring Operation: 122-55=67, Resulting Numbers: [67] 67,60 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: 60:[98, 28, 51], Operations: ['94-43=51'] Exploring Operation: 98-28=70, Resulting Numbers: [51, 70] Generated Node #0,0,0: 60:[51, 70] Operation: 98-28=70 Exploring Operation: 51-28=23, Resulting Numbers: [98, 23] Generated Node #0,0,1: 60:[98, 23] Operation: 51-28=23 Exploring Operation: 28+51=79, Resulting Numbers: [98, 79] Generated Node #0,0,2: 60:[98, 79] Operation: 28+51=79 Exploring Operation: 98-51=47, Resulting Numbers: [28, 47] Generated Node #0,0,3: 60:[28, 47] Operation: 98-51=47 Exploring Operation: 98+28=126, Resulting Numbers: [51, 126] Generated Node #0,0,4: 60:[51, 126] Operation: 98+28=126 Moving to Node #0,1 Current State: 60:[94, 43, 70], Operations: ['98-28=70'] Exploring Operation: 94-43=51, Resulting Numbers: [70, 51] Generated Node #0,1,0: 60:[70, 51] Operation: 94-43=51 Exploring Operation: 70-43=27, Resulting Numbers: [94, 27] Generated Node #0,1,1: 60:[94, 27] Operation: 70-43=27 Exploring Operation: 43+70=113, Resulting Numbers: [94, 113] Generated Node #0,1,2: 60:[94, 113] Operation: 43+70=113 Exploring Operation: 94-70=24, Resulting Numbers: [43, 24] Generated Node #0,1,3: 60:[43, 24] Operation: 94-70=24 Exploring Operation: 94+43=137, Resulting Numbers: [70, 137] Generated Node #0,1,4: 60:[70, 137] Operation: 94+43=137 Moving to Node #0,3 Current State: 60:[98, 43, 66], Operations: ['94-28=66'] Exploring Operation: 98-66=32, Resulting Numbers: [43, 32] Generated Node #0,3,0: 60:[43, 32] Operation: 98-66=32 Exploring Operation: 98-43=55, Resulting Numbers: [66, 55] Generated Node #0,3,1: 60:[66, 55] Operation: 98-43=55 Exploring Operation: 43+66=109, Resulting Numbers: [98, 109] Generated Node #0,3,2: 60:[98, 109] Operation: 43+66=109 Exploring Operation: 66-43=23, Resulting Numbers: [98, 23] Generated Node #0,3,3: 60:[98, 23] Operation: 66-43=23 Exploring Operation: 98+43=141, Resulting Numbers: [66, 141] Generated Node #0,3,4: 60:[66, 141] Operation: 98+43=141 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 60:[66, 55], Operations: ['94-28=66', '98-43=55'] Exploring Operation: 66*55=3630, Resulting Numbers: [3630] 3630,60 unequal: No Solution Exploring Operation: 66-55=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 66+55=121, Resulting Numbers: [121] 121,60 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 #0,3,0 Current State: 60:[43, 32], Operations: ['94-28=66', '98-66=32'] Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,60 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,60 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 #0,3,3 Current State: 60:[98, 23], Operations: ['94-28=66', '66-43=23'] Exploring Operation: 98-23=75, Resulting Numbers: [75] 75,60 unequal: No Solution Exploring Operation: 98+23=121, Resulting Numbers: [121] 121,60 unequal: No Solution Exploring Operation: 98*23=2254, Resulting Numbers: [2254] 2254,60 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 #0,3,2 Current State: 60:[98, 109], Operations: ['94-28=66', '43+66=109'] Exploring Operation: 98*109=10682, Resulting Numbers: [10682] 10682,60 unequal: No Solution Exploring Operation: 98+109=207, Resulting Numbers: [207] 207,60 unequal: No Solution Exploring Operation: 109-98=11, Resulting Numbers: [11] 11,60 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 #0,3,4 Current State: 60:[66, 141], Operations: ['94-28=66', '98+43=141'] Exploring Operation: 66*141=9306, Resulting Numbers: [9306] 9306,60 unequal: No Solution Exploring Operation: 66+141=207, Resulting Numbers: [207] 207,60 unequal: No Solution Exploring Operation: 141-66=75, Resulting Numbers: [75] 75,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 60:[4, 15], Operations: ['98-94=4', '43-28=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[98, 94, 43, 28], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [43, 28, 4] Generated Node #0,2: 60:[43, 28, 4] Operation: 98-94=4 Moving to Node #0,2 Current State: 60:[43, 28, 4], Operations: ['98-94=4'] Exploring Operation: 43-28=15, Resulting Numbers: [4, 15] Generated Node #0,2,0: 60:[4, 15] Operation: 43-28=15 Moving to Node #0,2,0 Current State: 60:[4, 15], Operations: ['98-94=4', '43-28=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
0.943576
hs_5
mult_heuristic
[ 11, 5, 64, 86 ]
71
[ "11+64=75", "75/5=15", "86-15=71" ]
Current State: 71:[11, 5, 64, 86], Operations: [] Exploring Operation: 11+64=75, Resulting Numbers: [5, 86, 75] Generated Node #2: [5, 86, 75] from Operation: 11+64=75 Current State: 71:[5, 86, 75], Operations: ['11+64=75'] Exploring Operation: 75/5=15, Resulting Numbers: [86, 15] Generated Node #3: [86, 15] from Operation: 75/5=15 Current State: 71:[86, 15], Operations: ['11+64=75', '75/5=15'] Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[11, 5, 64, 86], Operations: [] Exploring Operation: 11*5=55, Resulting Numbers: [64, 86, 55] Generated Node #0,0: 71:[64, 86, 55] Operation: 11*5=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[64, 86, 55], Operations: ['11*5=55'] Exploring Operation: 86-55=31, Resulting Numbers: [64, 31] Generated Node #0,0,0: 71:[64, 31] Operation: 86-55=31 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[64, 31], Operations: ['11*5=55', '86-55=31'] Exploring Operation: 64+31=95, Resulting Numbers: [95] 95,71 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
[ 28, 96, 70, 56 ]
22
[ "28*96=2688", "2688/56=48", "70-48=22" ]
Current State: 22:[28, 96, 70, 56], Operations: [] Exploring Operation: 28*96=2688, Resulting Numbers: [70, 56, 2688] Generated Node #2: [70, 56, 2688] from Operation: 28*96=2688 Current State: 22:[70, 56, 2688], Operations: ['28*96=2688'] Exploring Operation: 2688/56=48, Resulting Numbers: [70, 48] Generated Node #3: [70, 48] from Operation: 2688/56=48 Current State: 22:[70, 48], Operations: ['28*96=2688', '2688/56=48'] Exploring Operation: 70-48=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[28, 96, 70, 56], Operations: [] Exploring Operation: 96-70=26, Resulting Numbers: [28, 56, 26] Generated Node #0,0: 22:[28, 56, 26] Operation: 96-70=26 Exploring Operation: 96-56=40, Resulting Numbers: [28, 70, 40] Generated Node #0,1: 22:[28, 70, 40] Operation: 96-56=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[28, 56, 26], Operations: ['96-70=26'] Exploring Operation: 56-28=28, Resulting Numbers: [26, 28] Generated Node #0,0,0: 22:[26, 28] Operation: 56-28=28 Exploring Operation: 56/28=2, Resulting Numbers: [26, 2] Generated Node #0,0,1: 22:[26, 2] Operation: 56/28=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 22:[26, 2], Operations: ['96-70=26', '56/28=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,22 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,22 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 #0,0,0 Current State: 22:[26, 28], Operations: ['96-70=26', '56-28=28'] Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,22 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,22 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:[28, 70, 40], Operations: ['96-56=40'] Exploring Operation: 70-28=42, Resulting Numbers: [40, 42] Generated Node #0,1,0: 22:[40, 42] Operation: 70-28=42 Exploring Operation: 70-40=30, Resulting Numbers: [28, 30] Generated Node #0,1,1: 22:[28, 30] Operation: 70-40=30 Moving to Node #0,1,1 Current State: 22:[28, 30], Operations: ['96-56=40', '70-40=30'] Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,22 unequal: No Solution Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,22 unequal: No Solution Moving to Node #0,1,0 Current State: 22:[40, 42], Operations: ['96-56=40', '70-28=42'] Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 40+42=82, Resulting Numbers: [82] 82,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 11, 1, 5, 4 ]
21
[ "11+1=12", "5+4=9", "12+9=21" ]
Current State: 21:[11, 1, 5, 4], Operations: [] Exploring Operation: 11+1=12, Resulting Numbers: [5, 4, 12] Generated Node #2: [5, 4, 12] from Operation: 11+1=12 Current State: 21:[5, 4, 12], Operations: ['11+1=12'] Exploring Operation: 5+4=9, Resulting Numbers: [12, 9] Generated Node #3: [12, 9] from Operation: 5+4=9 Current State: 21:[12, 9], Operations: ['11+1=12', '5+4=9'] Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[11, 1, 5, 4], Operations: [] Exploring Operation: 11-5=6, Resulting Numbers: [1, 4, 6] Generated Node #0,0: 21:[1, 4, 6] Operation: 11-5=6 Moving to Node #0,0 Current State: 21:[1, 4, 6], Operations: ['11-5=6'] Exploring Operation: 4-1=3, Resulting Numbers: [6, 3] Generated Node #0,0,0: 21:[6, 3] Operation: 4-1=3 Moving to Node #0,0,0 Current State: 21:[6, 3], Operations: ['11-5=6', '4-1=3'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,21 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 68, 3, 39, 30 ]
18
[ "68-3=65", "39*30=1170", "1170/65=18" ]
Current State: 18:[68, 3, 39, 30], Operations: [] Exploring Operation: 68-3=65, Resulting Numbers: [39, 30, 65] Generated Node #2: [39, 30, 65] from Operation: 68-3=65 Current State: 18:[39, 30, 65], Operations: ['68-3=65'] Exploring Operation: 39*30=1170, Resulting Numbers: [65, 1170] Generated Node #3: [65, 1170] from Operation: 39*30=1170 Current State: 18:[65, 1170], Operations: ['68-3=65', '39*30=1170'] Exploring Operation: 1170/65=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[68, 3, 39, 30], Operations: [] Exploring Operation: 68-30=38, Resulting Numbers: [3, 39, 38] Generated Node #0,0: 18:[3, 39, 38] Operation: 68-30=38 Exploring Operation: 39/3=13, Resulting Numbers: [68, 30, 13] Generated Node #0,1: 18:[68, 30, 13] Operation: 39/3=13 Exploring Operation: 68-39=29, Resulting Numbers: [3, 30, 29] Generated Node #0,2: 18:[3, 30, 29] Operation: 68-39=29 Exploring Operation: 39-30=9, Resulting Numbers: [68, 3, 9] Generated Node #0,3: 18:[68, 3, 9] Operation: 39-30=9 Exploring Operation: 30/3=10, Resulting Numbers: [68, 39, 10] Generated Node #0,4: 18:[68, 39, 10] Operation: 30/3=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[3, 30, 29], Operations: ['68-39=29'] Exploring Operation: 3+30=33, Resulting Numbers: [29, 33] Generated Node #0,2,0: 18:[29, 33] Operation: 3+30=33 Exploring Operation: 30-3=27, Resulting Numbers: [29, 27] Generated Node #0,2,1: 18:[29, 27] Operation: 30-3=27 Exploring Operation: 29-3=26, Resulting Numbers: [30, 26] Generated Node #0,2,2: 18:[30, 26] Operation: 29-3=26 Exploring Operation: 30-29=1, Resulting Numbers: [3, 1] Generated Node #0,2,3: 18:[3, 1] Operation: 30-29=1 Exploring Operation: 30/3=10, Resulting Numbers: [29, 10] Generated Node #0,2,4: 18:[29, 10] Operation: 30/3=10 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 18:[3, 1], Operations: ['68-39=29', '30-29=1'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,18 unequal: No Solution No 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: 18:[29, 10], Operations: ['68-39=29', '30/3=10'] Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 29*10=290, Resulting Numbers: [290] 290,18 unequal: No Solution No 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: 18:[29, 27], Operations: ['68-39=29', '30-3=27'] Exploring Operation: 29+27=56, Resulting Numbers: [56] 56,18 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 29*27=783, Resulting Numbers: [783] 783,18 unequal: No Solution No 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: 18:[30, 26], Operations: ['68-39=29', '29-3=26'] Exploring Operation: 30-26=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 30*26=780, Resulting Numbers: [780] 780,18 unequal: No Solution Exploring Operation: 30+26=56, Resulting Numbers: [56] 56,18 unequal: No Solution No 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: 18:[29, 33], Operations: ['68-39=29', '3+30=33'] Exploring Operation: 29+33=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 33-29=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 29*33=957, Resulting Numbers: [957] 957,18 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: 18:[3, 39, 38], Operations: ['68-30=38'] Exploring Operation: 38-3=35, Resulting Numbers: [39, 35] Generated Node #0,0,0: 18:[39, 35] Operation: 38-3=35 Exploring Operation: 39/3=13, Resulting Numbers: [38, 13] Generated Node #0,0,1: 18:[38, 13] Operation: 39/3=13 Exploring Operation: 39-38=1, Resulting Numbers: [3, 1] Generated Node #0,0,2: 18:[3, 1] Operation: 39-38=1 Exploring Operation: 3+39=42, Resulting Numbers: [38, 42] Generated Node #0,0,3: 18:[38, 42] Operation: 3+39=42 Exploring Operation: 39-3=36, Resulting Numbers: [38, 36] Generated Node #0,0,4: 18:[38, 36] Operation: 39-3=36 Moving to Node #0,0,2 Current State: 18:[3, 1], Operations: ['68-30=38', '39-38=1'] Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[38, 13], Operations: ['68-30=38', '39/3=13'] Exploring Operation: 38*13=494, Resulting Numbers: [494] 494,18 unequal: No Solution Exploring Operation: 38+13=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 38-13=25, Resulting Numbers: [25] 25,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[39, 35], Operations: ['68-30=38', '38-3=35'] Exploring Operation: 39+35=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 39*35=1365, Resulting Numbers: [1365] 1365,18 unequal: No Solution Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,18 unequal: No Solution Moving to Node #0,0,4 Current State: 18:[38, 36], Operations: ['68-30=38', '39-3=36'] Exploring Operation: 38+36=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 38*36=1368, Resulting Numbers: [1368] 1368,18 unequal: No Solution Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[38, 42], Operations: ['68-30=38', '3+39=42'] Exploring Operation: 38+42=80, Resulting Numbers: [80] 80,18 unequal: No Solution Exploring Operation: 42-38=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 38*42=1596, Resulting Numbers: [1596] 1596,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 18:[68, 3, 9], Operations: ['39-30=9'] Exploring Operation: 9-3=6, Resulting Numbers: [68, 6] Generated Node #0,3,0: 18:[68, 6] Operation: 9-3=6 Exploring Operation: 68-9=59, Resulting Numbers: [3, 59] Generated Node #0,3,1: 18:[3, 59] Operation: 68-9=59 Exploring Operation: 68+3=71, Resulting Numbers: [9, 71] Generated Node #0,3,2: 18:[9, 71] Operation: 68+3=71 Exploring Operation: 9/3=3, Resulting Numbers: [68, 3] Generated Node #0,3,3: 18:[68, 3] Operation: 9/3=3 Exploring Operation: 68-3=65, Resulting Numbers: [9, 65] Generated Node #0,3,4: 18:[9, 65] Operation: 68-3=65 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 18:[3, 59], Operations: ['39-30=9', '68-9=59'] Exploring Operation: 3*59=177, Resulting Numbers: [177] 177,18 unequal: No Solution Exploring Operation: 3+59=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,18 unequal: No Solution No 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: 18:[9, 65], Operations: ['39-30=9', '68-3=65'] Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,18 unequal: No Solution Exploring Operation: 9+65=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 9*65=585, Resulting Numbers: [585] 585,18 unequal: No Solution No 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: 18:[68, 6], Operations: ['39-30=9', '9-3=6'] Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 68+6=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 68*6=408, Resulting Numbers: [408] 408,18 unequal: No Solution No 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: 18:[68, 3], Operations: ['39-30=9', '9/3=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,18 unequal: No Solution Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,18 unequal: No Solution Exploring Operation: 68*3=204, Resulting Numbers: [204] 204,18 unequal: No Solution No 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: 18:[9, 71], Operations: ['39-30=9', '68+3=71'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 9*71=639, Resulting Numbers: [639] 639,18 unequal: No Solution Exploring Operation: 9+71=80, Resulting Numbers: [80] 80,18 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: 18:[68, 30, 13], Operations: ['39/3=13'] Exploring Operation: 30+13=43, Resulting Numbers: [68, 43] Generated Node #0,1,0: 18:[68, 43] Operation: 30+13=43 Exploring Operation: 30-13=17, Resulting Numbers: [68, 17] Generated Node #0,1,1: 18:[68, 17] Operation: 30-13=17 Exploring Operation: 68+13=81, Resulting Numbers: [30, 81] Generated Node #0,1,2: 18:[30, 81] Operation: 68+13=81 Exploring Operation: 68-13=55, Resulting Numbers: [30, 55] Generated Node #0,1,3: 18:[30, 55] Operation: 68-13=55 Exploring Operation: 68-30=38, Resulting Numbers: [13, 38] Generated Node #0,1,4: 18:[13, 38] Operation: 68-30=38 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 18:[13, 38], Operations: ['39/3=13', '68-30=38'] Exploring Operation: 13*38=494, Resulting Numbers: [494] 494,18 unequal: No Solution Exploring Operation: 38-13=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 13+38=51, Resulting Numbers: [51] 51,18 unequal: No Solution No 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: 18:[30, 55], Operations: ['39/3=13', '68-13=55'] Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 30*55=1650, Resulting Numbers: [1650] 1650,18 unequal: No Solution Exploring Operation: 30+55=85, Resulting Numbers: [85] 85,18 unequal: No Solution No 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: 18:[68, 17], Operations: ['39/3=13', '30-13=17'] Exploring Operation: 68*17=1156, Resulting Numbers: [1156] 1156,18 unequal: No Solution Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 68+17=85, Resulting Numbers: [85] 85,18 unequal: No Solution Exploring Operation: 68-17=51, Resulting Numbers: [51] 51,18 unequal: No Solution No 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: 18:[68, 43], Operations: ['39/3=13', '30+13=43'] Exploring Operation: 68+43=111, Resulting Numbers: [111] 111,18 unequal: No Solution Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 68*43=2924, Resulting Numbers: [2924] 2924,18 unequal: No Solution No 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: 18:[30, 81], Operations: ['39/3=13', '68+13=81'] Exploring Operation: 81-30=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 30*81=2430, Resulting Numbers: [2430] 2430,18 unequal: No Solution Exploring Operation: 30+81=111, Resulting Numbers: [111] 111,18 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: 18:[68, 39, 10], Operations: ['30/3=10'] Exploring Operation: 39-10=29, Resulting Numbers: [68, 29] Generated Node #0,4,0: 18:[68, 29] Operation: 39-10=29 Exploring Operation: 68+10=78, Resulting Numbers: [39, 78] Generated Node #0,4,1: 18:[39, 78] Operation: 68+10=78 Exploring Operation: 68-39=29, Resulting Numbers: [10, 29] Generated Node #0,4,2: 18:[10, 29] Operation: 68-39=29 Exploring Operation: 68-10=58, Resulting Numbers: [39, 58] Generated Node #0,4,3: 18:[39, 58] Operation: 68-10=58 Exploring Operation: 39+10=49, Resulting Numbers: [68, 49] Generated Node #0,4,4: 18:[68, 49] Operation: 39+10=49 Moving to Node #0,4,2 Current State: 18:[10, 29], Operations: ['30/3=10', '68-39=29'] Exploring Operation: 10+29=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 10*29=290, Resulting Numbers: [290] 290,18 unequal: No Solution Moving to Node #0,4,3 Current State: 18:[39, 58], Operations: ['30/3=10', '68-10=58'] Exploring Operation: 39*58=2262, Resulting Numbers: [2262] 2262,18 unequal: No Solution Exploring Operation: 58-39=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 39+58=97, Resulting Numbers: [97] 97,18 unequal: No Solution Moving to Node #0,4,0 Current State: 18:[68, 29], Operations: ['30/3=10', '39-10=29'] Exploring Operation: 68*29=1972, Resulting Numbers: [1972] 1972,18 unequal: No Solution Exploring Operation: 68+29=97, Resulting Numbers: [97] 97,18 unequal: No Solution Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,18 unequal: No Solution Moving to Node #0,4,1 Current State: 18:[39, 78], Operations: ['30/3=10', '68+10=78'] Exploring Operation: 39*78=3042, Resulting Numbers: [3042] 3042,18 unequal: No Solution Exploring Operation: 39+78=117, Resulting Numbers: [117] 117,18 unequal: No Solution Exploring Operation: 78/39=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 78-39=39, Resulting Numbers: [39] 39,18 unequal: No Solution Moving to Node #0,4,4 Current State: 18:[68, 49], Operations: ['30/3=10', '39+10=49'] Exploring Operation: 68*49=3332, Resulting Numbers: [3332] 3332,18 unequal: No Solution Exploring Operation: 68+49=117, Resulting Numbers: [117] 117,18 unequal: No Solution Exploring Operation: 68-49=19, Resulting Numbers: [19] 19,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 28, 99, 64, 65 ]
72
[ "99-28=71", "65-64=1", "71+1=72" ]
Current State: 72:[28, 99, 64, 65], Operations: [] Exploring Operation: 99-28=71, Resulting Numbers: [64, 65, 71] Generated Node #2: [64, 65, 71] from Operation: 99-28=71 Current State: 72:[64, 65, 71], Operations: ['99-28=71'] Exploring Operation: 65-64=1, Resulting Numbers: [71, 1] Generated Node #3: [71, 1] from Operation: 65-64=1 Current State: 72:[71, 1], Operations: ['99-28=71', '65-64=1'] Exploring Operation: 71+1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[28, 99, 64, 65], Operations: [] Exploring Operation: 99-64=35, Resulting Numbers: [28, 65, 35] Generated Node #0,0: 72:[28, 65, 35] Operation: 99-64=35 Exploring Operation: 99-65=34, Resulting Numbers: [28, 64, 34] Generated Node #0,1: 72:[28, 64, 34] Operation: 99-65=34 Exploring Operation: 99-28=71, Resulting Numbers: [64, 65, 71] Generated Node #0,2: 72:[64, 65, 71] Operation: 99-28=71 Exploring Operation: 65-64=1, Resulting Numbers: [28, 99, 1] Generated Node #0,3: 72:[28, 99, 1] Operation: 65-64=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[28, 65, 35], Operations: ['99-64=35'] Exploring Operation: 35-28=7, Resulting Numbers: [65, 7] Generated Node #0,0,0: 72:[65, 7] Operation: 35-28=7 Exploring Operation: 65-28=37, Resulting Numbers: [35, 37] Generated Node #0,0,1: 72:[35, 37] Operation: 65-28=37 Exploring Operation: 28+35=63, Resulting Numbers: [65, 63] Generated Node #0,0,2: 72:[65, 63] Operation: 28+35=63 Exploring Operation: 65-35=30, Resulting Numbers: [28, 30] Generated Node #0,0,3: 72:[28, 30] Operation: 65-35=30 Moving to Node #0,0,1 Current State: 72:[35, 37], Operations: ['99-64=35', '65-28=37'] Exploring Operation: 35+37=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[28, 99, 64, 65], Operations: [] Exploring Operation: 99-64=35, Resulting Numbers: [28, 65, 35] Generated Node #0,0: 72:[28, 65, 35] Operation: 99-64=35 Moving to Node #0,0 Current State: 72:[28, 65, 35], Operations: ['99-64=35'] Exploring Operation: 65-28=37, Resulting Numbers: [35, 37] Generated Node #0,0,1: 72:[35, 37] Operation: 65-28=37 Moving to Node #0,0,1 Current State: 72:[35, 37], Operations: ['99-64=35', '65-28=37'] Exploring Operation: 35+37=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 82, 69, 45, 2 ]
73
[ "82/2=41", "69+45=114", "114-41=73" ]
Current State: 73:[82, 69, 45, 2], Operations: [] Exploring Operation: 82/2=41, Resulting Numbers: [69, 45, 41] Generated Node #2: [69, 45, 41] from Operation: 82/2=41 Current State: 73:[69, 45, 41], Operations: ['82/2=41'] Exploring Operation: 69+45=114, Resulting Numbers: [41, 114] Generated Node #3: [41, 114] from Operation: 69+45=114 Current State: 73:[41, 114], Operations: ['82/2=41', '69+45=114'] Exploring Operation: 114-41=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[82, 69, 45, 2], Operations: [] Exploring Operation: 69+2=71, Resulting Numbers: [82, 45, 71] Generated Node #0,0: 73:[82, 45, 71] Operation: 69+2=71 Exploring Operation: 82-2=80, Resulting Numbers: [69, 45, 80] Generated Node #0,1: 73:[69, 45, 80] Operation: 82-2=80 Exploring Operation: 45*2=90, Resulting Numbers: [82, 69, 90] Generated Node #0,2: 73:[82, 69, 90] Operation: 45*2=90 Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[82, 69, 90], Operations: ['45*2=90'] Exploring Operation: 82-69=13, Resulting Numbers: [90, 13] Generated Node #0,2,0: 73:[90, 13] Operation: 82-69=13 Exploring Operation: 90-69=21, Resulting Numbers: [82, 21] Generated Node #0,2,1: 73:[82, 21] Operation: 90-69=21 Exploring Operation: 90-82=8, Resulting Numbers: [69, 8] Generated Node #0,2,2: 73:[69, 8] Operation: 90-82=8 Moving to Node #0,2,1 Current State: 73:[82, 21], Operations: ['45*2=90', '90-69=21'] Exploring Operation: 82*21=1722, Resulting Numbers: [1722] 1722,73 unequal: No Solution Exploring Operation: 82+21=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 82-21=61, Resulting Numbers: [61] 61,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[69, 8], Operations: ['45*2=90', '90-82=8'] Exploring Operation: 69*8=552, Resulting Numbers: [552] 552,73 unequal: No Solution Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,73 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[90, 13], Operations: ['45*2=90', '82-69=13'] Exploring Operation: 90*13=1170, Resulting Numbers: [1170] 1170,73 unequal: No Solution Exploring Operation: 90-13=77, Resulting Numbers: [77] 77,73 unequal: No Solution Exploring Operation: 90+13=103, Resulting Numbers: [103] 103,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[82, 45, 71], Operations: ['69+2=71'] Exploring Operation: 82-45=37, Resulting Numbers: [71, 37] Generated Node #0,0,0: 73:[71, 37] Operation: 82-45=37 Exploring Operation: 45+71=116, Resulting Numbers: [82, 116] Generated Node #0,0,1: 73:[82, 116] Operation: 45+71=116 Exploring Operation: 82+45=127, Resulting Numbers: [71, 127] Generated Node #0,0,2: 73:[71, 127] Operation: 82+45=127 Moving to Node #0,0,0 Current State: 73:[71, 37], Operations: ['69+2=71', '82-45=37'] Exploring Operation: 71+37=108, Resulting Numbers: [108] 108,73 unequal: No Solution Exploring Operation: 71*37=2627, Resulting Numbers: [2627] 2627,73 unequal: No Solution Exploring Operation: 71-37=34, Resulting Numbers: [34] 34,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[82, 116], Operations: ['69+2=71', '45+71=116'] Exploring Operation: 82+116=198, Resulting Numbers: [198] 198,73 unequal: No Solution Exploring Operation: 116-82=34, Resulting Numbers: [34] 34,73 unequal: No Solution Exploring Operation: 82*116=9512, Resulting Numbers: [9512] 9512,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[71, 127], Operations: ['69+2=71', '82+45=127'] Exploring Operation: 71*127=9017, Resulting Numbers: [9017] 9017,73 unequal: No Solution Exploring Operation: 71+127=198, Resulting Numbers: [198] 198,73 unequal: No Solution Exploring Operation: 127-71=56, Resulting Numbers: [56] 56,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[69, 45, 80], Operations: ['82-2=80'] Exploring Operation: 69+45=114, Resulting Numbers: [80, 114] Generated Node #0,1,0: 73:[80, 114] Operation: 69+45=114 Exploring Operation: 69-45=24, Resulting Numbers: [80, 24] Generated Node #0,1,1: 73:[80, 24] Operation: 69-45=24 Exploring Operation: 80-45=35, Resulting Numbers: [69, 35] Generated Node #0,1,2: 73:[69, 35] Operation: 80-45=35 Moving to Node #0,1,2 Current State: 73:[69, 35], Operations: ['82-2=80', '80-45=35'] Exploring Operation: 69+35=104, Resulting Numbers: [104] 104,73 unequal: No Solution Exploring Operation: 69*35=2415, Resulting Numbers: [2415] 2415,73 unequal: No Solution Exploring Operation: 69-35=34, Resulting Numbers: [34] 34,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[80, 114], Operations: ['82-2=80', '69+45=114'] Exploring Operation: 114-80=34, Resulting Numbers: [34] 34,73 unequal: No Solution Exploring Operation: 80*114=9120, Resulting Numbers: [9120] 9120,73 unequal: No Solution Exploring Operation: 80+114=194, Resulting Numbers: [194] 194,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[80, 24], Operations: ['82-2=80', '69-45=24'] Exploring Operation: 80+24=104, Resulting Numbers: [104] 104,73 unequal: No Solution Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,73 unequal: No Solution Exploring Operation: 80*24=1920, Resulting Numbers: [1920] 1920,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 5, 56, 64, 39 ]
21
[ "56-39=17", "5*17=85", "85-64=21" ]
Current State: 21:[5, 56, 64, 39], Operations: [] Exploring Operation: 56-39=17, Resulting Numbers: [5, 64, 17] Generated Node #2: [5, 64, 17] from Operation: 56-39=17 Current State: 21:[5, 64, 17], Operations: ['56-39=17'] Exploring Operation: 5*17=85, Resulting Numbers: [64, 85] Generated Node #3: [64, 85] from Operation: 5*17=85 Current State: 21:[64, 85], Operations: ['56-39=17', '5*17=85'] Exploring Operation: 85-64=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[5, 56, 64, 39], Operations: [] Exploring Operation: 64-39=25, Resulting Numbers: [5, 56, 25] Generated Node #0,0: 21:[5, 56, 25] Operation: 64-39=25 Exploring Operation: 56-39=17, Resulting Numbers: [5, 64, 17] Generated Node #0,1: 21:[5, 64, 17] Operation: 56-39=17 Exploring Operation: 64-56=8, Resulting Numbers: [5, 39, 8] Generated Node #0,2: 21:[5, 39, 8] Operation: 64-56=8 Moving to Node #0,2 Current State: 21:[5, 39, 8], Operations: ['64-56=8'] Exploring Operation: 8-5=3, Resulting Numbers: [39, 3] Generated Node #0,2,0: 21:[39, 3] Operation: 8-5=3 Exploring Operation: 39-5=34, Resulting Numbers: [8, 34] Generated Node #0,2,1: 21:[8, 34] Operation: 39-5=34 Exploring Operation: 39-8=31, Resulting Numbers: [5, 31] Generated Node #0,2,2: 21:[5, 31] Operation: 39-8=31 Moving to Node #0,0 Current State: 21:[5, 56, 25], Operations: ['64-39=25'] Exploring Operation: 25-5=20, Resulting Numbers: [56, 20] Generated Node #0,0,0: 21:[56, 20] Operation: 25-5=20 Exploring Operation: 56-5=51, Resulting Numbers: [25, 51] Generated Node #0,0,1: 21:[25, 51] Operation: 56-5=51 Exploring Operation: 56-25=31, Resulting Numbers: [5, 31] Generated Node #0,0,2: 21:[5, 31] Operation: 56-25=31 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 21:[5, 31], Operations: ['64-39=25', '56-25=31'] Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,21 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[25, 51], Operations: ['64-39=25', '56-5=51'] Exploring Operation: 25+51=76, Resulting Numbers: [76] 76,21 unequal: No Solution Exploring Operation: 51-25=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 25*51=1275, Resulting Numbers: [1275] 1275,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[56, 20], Operations: ['64-39=25', '25-5=20'] Exploring Operation: 56-20=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 56+20=76, Resulting Numbers: [76] 76,21 unequal: No Solution Exploring Operation: 56*20=1120, Resulting Numbers: [1120] 1120,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 21:[5, 64, 17], Operations: ['56-39=17'] Exploring Operation: 64-17=47, Resulting Numbers: [5, 47] Generated Node #0,1,0: 21:[5, 47] Operation: 64-17=47 Exploring Operation: 5+17=22, Resulting Numbers: [64, 22] Generated Node #0,1,1: 21:[64, 22] Operation: 5+17=22 Exploring Operation: 64-5=59, Resulting Numbers: [17, 59] Generated Node #0,1,2: 21:[17, 59] Operation: 64-5=59 Moving to Node #0,2,2 Current State: 21:[5, 31], Operations: ['64-56=8', '39-8=31'] Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,21 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,21 unequal: No Solution Moving to Node #0,2,1 Current State: 21:[8, 34], Operations: ['64-56=8', '39-5=34'] Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,21 unequal: No Solution Exploring Operation: 8*34=272, Resulting Numbers: [272] 272,21 unequal: No Solution Moving to Node #0,2,0 Current State: 21:[39, 3], Operations: ['64-56=8', '8-5=3'] Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,21 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,21 unequal: No Solution Moving to Node #0,1,0 Current State: 21:[5, 47], Operations: ['56-39=17', '64-17=47'] Exploring Operation: 5*47=235, Resulting Numbers: [235] 235,21 unequal: No Solution Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,21 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[17, 59], Operations: ['56-39=17', '64-5=59'] Exploring Operation: 59-17=42, Resulting Numbers: [42] 42,21 unequal: No Solution Exploring Operation: 17*59=1003, Resulting Numbers: [1003] 1003,21 unequal: No Solution Exploring Operation: 17+59=76, Resulting Numbers: [76] 76,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[64, 22], Operations: ['56-39=17', '5+17=22'] Exploring Operation: 64+22=86, Resulting Numbers: [86] 86,21 unequal: No Solution Exploring Operation: 64*22=1408, Resulting Numbers: [1408] 1408,21 unequal: No Solution Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,21 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 93, 26, 75, 17 ]
61
[ "93+26=119", "75-17=58", "119-58=61" ]
Current State: 61:[93, 26, 75, 17], Operations: [] Exploring Operation: 93+26=119, Resulting Numbers: [75, 17, 119] Generated Node #2: [75, 17, 119] from Operation: 93+26=119 Current State: 61:[75, 17, 119], Operations: ['93+26=119'] Exploring Operation: 75-17=58, Resulting Numbers: [119, 58] Generated Node #3: [119, 58] from Operation: 75-17=58 Current State: 61:[119, 58], Operations: ['93+26=119', '75-17=58'] Exploring Operation: 119-58=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[93, 26, 75, 17], Operations: [] Exploring Operation: 75-26=49, Resulting Numbers: [93, 17, 49] Generated Node #0,0: 61:[93, 17, 49] Operation: 75-26=49 Exploring Operation: 26+17=43, Resulting Numbers: [93, 75, 43] Generated Node #0,1: 61:[93, 75, 43] Operation: 26+17=43 Exploring Operation: 75-17=58, Resulting Numbers: [93, 26, 58] Generated Node #0,2: 61:[93, 26, 58] Operation: 75-17=58 Exploring Operation: 93-26=67, Resulting Numbers: [75, 17, 67] Generated Node #0,3: 61:[75, 17, 67] Operation: 93-26=67 Exploring Operation: 93-17=76, Resulting Numbers: [26, 75, 76] Generated Node #0,4: 61:[26, 75, 76] Operation: 93-17=76 Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[93, 75, 43], Operations: ['26+17=43'] Exploring Operation: 93-43=50, Resulting Numbers: [75, 50] Generated Node #0,1,0: 61:[75, 50] Operation: 93-43=50 Exploring Operation: 75-43=32, Resulting Numbers: [93, 32] Generated Node #0,1,1: 61:[93, 32] Operation: 75-43=32 Exploring Operation: 93-75=18, Resulting Numbers: [43, 18] Generated Node #0,1,2: 61:[43, 18] Operation: 93-75=18 Exploring Operation: 75+43=118, Resulting Numbers: [93, 118] Generated Node #0,1,3: 61:[93, 118] Operation: 75+43=118 Exploring Operation: 93+43=136, Resulting Numbers: [75, 136] Generated Node #0,1,4: 61:[75, 136] Operation: 93+43=136 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[75, 50], Operations: ['26+17=43', '93-43=50'] Exploring Operation: 75+50=125, Resulting Numbers: [125] 125,61 unequal: No Solution Exploring Operation: 75*50=3750, Resulting Numbers: [3750] 3750,61 unequal: No Solution Exploring Operation: 75-50=25, Resulting Numbers: [25] 25,61 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:[93, 32], Operations: ['26+17=43', '75-43=32'] Exploring Operation: 93-32=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[93, 26, 75, 17], Operations: [] Exploring Operation: 26+17=43, Resulting Numbers: [93, 75, 43] Generated Node #0,1: 61:[93, 75, 43] Operation: 26+17=43 Moving to Node #0,1 Current State: 61:[93, 75, 43], Operations: ['26+17=43'] Exploring Operation: 75-43=32, Resulting Numbers: [93, 32] Generated Node #0,1,1: 61:[93, 32] Operation: 75-43=32 Moving to Node #0,1,1 Current State: 61:[93, 32], Operations: ['26+17=43', '75-43=32'] Exploring Operation: 93-32=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 6, 10, 92, 20 ]
23
[ "6+10=16", "20-16=4", "92/4=23" ]
Current State: 23:[6, 10, 92, 20], Operations: [] Exploring Operation: 6+10=16, Resulting Numbers: [92, 20, 16] Generated Node #2: [92, 20, 16] from Operation: 6+10=16 Current State: 23:[92, 20, 16], Operations: ['6+10=16'] Exploring Operation: 20-16=4, Resulting Numbers: [92, 4] Generated Node #3: [92, 4] from Operation: 20-16=4 Current State: 23:[92, 4], Operations: ['6+10=16', '20-16=4'] Exploring Operation: 92/4=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[6, 10, 92, 20], Operations: [] Exploring Operation: 92-10=82, Resulting Numbers: [6, 20, 82] Generated Node #0,0: 23:[6, 20, 82] Operation: 92-10=82 Exploring Operation: 6+10=16, Resulting Numbers: [92, 20, 16] Generated Node #0,1: 23:[92, 20, 16] Operation: 6+10=16 Exploring Operation: 92-6=86, Resulting Numbers: [10, 20, 86] Generated Node #0,2: 23:[10, 20, 86] Operation: 92-6=86 Exploring Operation: 92-20=72, Resulting Numbers: [6, 10, 72] Generated Node #0,3: 23:[6, 10, 72] Operation: 92-20=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[6, 20, 82], Operations: ['92-10=82'] Exploring Operation: 20-6=14, Resulting Numbers: [82, 14] Generated Node #0,0,0: 23:[82, 14] Operation: 20-6=14 Exploring Operation: 82-6=76, Resulting Numbers: [20, 76] Generated Node #0,0,1: 23:[20, 76] Operation: 82-6=76 Exploring Operation: 6+20=26, Resulting Numbers: [82, 26] Generated Node #0,0,2: 23:[82, 26] Operation: 6+20=26 Exploring Operation: 82-20=62, Resulting Numbers: [6, 62] Generated Node #0,0,3: 23:[6, 62] Operation: 82-20=62 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 23:[20, 76], Operations: ['92-10=82', '82-6=76'] Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 20*76=1520, Resulting Numbers: [1520] 1520,23 unequal: No Solution Exploring Operation: 20+76=96, Resulting Numbers: [96] 96,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 23:[6, 62], Operations: ['92-10=82', '82-20=62'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,23 unequal: No Solution Exploring Operation: 6*62=372, Resulting Numbers: [372] 372,23 unequal: No Solution No 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: 23:[82, 26], Operations: ['92-10=82', '6+20=26'] Exploring Operation: 82+26=108, Resulting Numbers: [108] 108,23 unequal: No Solution Exploring Operation: 82*26=2132, Resulting Numbers: [2132] 2132,23 unequal: No Solution Exploring Operation: 82-26=56, Resulting Numbers: [56] 56,23 unequal: No Solution No 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: 23:[82, 14], Operations: ['92-10=82', '20-6=14'] Exploring Operation: 82+14=96, Resulting Numbers: [96] 96,23 unequal: No Solution Exploring Operation: 82-14=68, Resulting Numbers: [68] 68,23 unequal: No Solution Exploring Operation: 82*14=1148, Resulting Numbers: [1148] 1148,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[92, 20, 16], Operations: ['6+10=16'] Exploring Operation: 20+16=36, Resulting Numbers: [92, 36] Generated Node #0,1,0: 23:[92, 36] Operation: 20+16=36 Exploring Operation: 92-16=76, Resulting Numbers: [20, 76] Generated Node #0,1,1: 23:[20, 76] Operation: 92-16=76 Exploring Operation: 92-20=72, Resulting Numbers: [16, 72] Generated Node #0,1,2: 23:[16, 72] Operation: 92-20=72 Exploring Operation: 92+16=108, Resulting Numbers: [20, 108] Generated Node #0,1,3: 23:[20, 108] Operation: 92+16=108 Moving to Node #0,1,1 Current State: 23:[20, 76], Operations: ['6+10=16', '92-16=76'] Exploring Operation: 20*76=1520, Resulting Numbers: [1520] 1520,23 unequal: No Solution Exploring Operation: 20+76=96, Resulting Numbers: [96] 96,23 unequal: No Solution Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[16, 72], Operations: ['6+10=16', '92-20=72'] Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 16+72=88, Resulting Numbers: [88] 88,23 unequal: No Solution Exploring Operation: 16*72=1152, Resulting Numbers: [1152] 1152,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[92, 36], Operations: ['6+10=16', '20+16=36'] Exploring Operation: 92-36=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 92+36=128, Resulting Numbers: [128] 128,23 unequal: No Solution Exploring Operation: 92*36=3312, Resulting Numbers: [3312] 3312,23 unequal: No Solution Moving to Node #0,1,3 Current State: 23:[20, 108], Operations: ['6+10=16', '92+16=108'] Exploring Operation: 108-20=88, Resulting Numbers: [88] 88,23 unequal: No Solution Exploring Operation: 20*108=2160, Resulting Numbers: [2160] 2160,23 unequal: No Solution Exploring Operation: 20+108=128, Resulting Numbers: [128] 128,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[10, 20, 86], Operations: ['92-6=86'] Exploring Operation: 86-20=66, Resulting Numbers: [10, 66] Generated Node #0,2,0: 23:[10, 66] Operation: 86-20=66 Exploring Operation: 20-10=10, Resulting Numbers: [86, 10] Generated Node #0,2,1: 23:[86, 10] Operation: 20-10=10 Exploring Operation: 10+20=30, Resulting Numbers: [86, 30] Generated Node #0,2,2: 23:[86, 30] Operation: 10+20=30 Exploring Operation: 86-10=76, Resulting Numbers: [20, 76] Generated Node #0,2,3: 23:[20, 76] Operation: 86-10=76 Moving to Node #0,2,0 Current State: 23:[10, 66], Operations: ['92-6=86', '86-20=66'] Exploring Operation: 10*66=660, Resulting Numbers: [660] 660,23 unequal: No Solution Exploring Operation: 10+66=76, Resulting Numbers: [76] 76,23 unequal: No Solution Exploring Operation: 66-10=56, Resulting Numbers: [56] 56,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[20, 76], Operations: ['92-6=86', '86-10=76'] Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 20+76=96, Resulting Numbers: [96] 96,23 unequal: No Solution Exploring Operation: 20*76=1520, Resulting Numbers: [1520] 1520,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[86, 30], Operations: ['92-6=86', '10+20=30'] Exploring Operation: 86+30=116, Resulting Numbers: [116] 116,23 unequal: No Solution Exploring Operation: 86-30=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 86*30=2580, Resulting Numbers: [2580] 2580,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[86, 10], Operations: ['92-6=86', '20-10=10'] Exploring Operation: 86*10=860, Resulting Numbers: [860] 860,23 unequal: No Solution Exploring Operation: 86-10=76, Resulting Numbers: [76] 76,23 unequal: No Solution Exploring Operation: 86+10=96, Resulting Numbers: [96] 96,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 23:[6, 10, 72], Operations: ['92-20=72'] Exploring Operation: 72/6=12, Resulting Numbers: [10, 12] Generated Node #0,3,0: 23:[10, 12] Operation: 72/6=12 Exploring Operation: 6+10=16, Resulting Numbers: [72, 16] Generated Node #0,3,1: 23:[72, 16] Operation: 6+10=16 Exploring Operation: 72-10=62, Resulting Numbers: [6, 62] Generated Node #0,3,2: 23:[6, 62] Operation: 72-10=62 Exploring Operation: 72-6=66, Resulting Numbers: [10, 66] Generated Node #0,3,3: 23:[10, 66] Operation: 72-6=66 Moving to Node #0,3,0 Current State: 23:[10, 12], Operations: ['92-20=72', '72/6=12'] Exploring Operation: 10*12=120, Resulting Numbers: [120] 120,23 unequal: No Solution Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,23 unequal: No Solution Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,23 unequal: No Solution Moving to Node #0,3,2 Current State: 23:[6, 62], Operations: ['92-20=72', '72-10=62'] Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,23 unequal: No Solution Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 6*62=372, Resulting Numbers: [372] 372,23 unequal: No Solution Moving to Node #0,3,1 Current State: 23:[72, 16], Operations: ['92-20=72', '6+10=16'] Exploring Operation: 72+16=88, Resulting Numbers: [88] 88,23 unequal: No Solution Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 72*16=1152, Resulting Numbers: [1152] 1152,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[10, 66], Operations: ['92-20=72', '72-6=66'] Exploring Operation: 10*66=660, Resulting Numbers: [660] 660,23 unequal: No Solution Exploring Operation: 10+66=76, Resulting Numbers: [76] 76,23 unequal: No Solution Exploring Operation: 66-10=56, Resulting Numbers: [56] 56,23 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
[ 2, 6, 32, 51 ]
78
[ "2*32=64", "64-51=13", "6*13=78" ]
Current State: 78:[2, 6, 32, 51], Operations: [] Exploring Operation: 2*32=64, Resulting Numbers: [6, 51, 64] Generated Node #2: [6, 51, 64] from Operation: 2*32=64 Current State: 78:[6, 51, 64], Operations: ['2*32=64'] Exploring Operation: 64-51=13, Resulting Numbers: [6, 13] Generated Node #3: [6, 13] from Operation: 64-51=13 Current State: 78:[6, 13], Operations: ['2*32=64', '64-51=13'] Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[2, 6, 32, 51], Operations: [] Exploring Operation: 32+51=83, Resulting Numbers: [2, 6, 83] Generated Node #0,0: 78:[2, 6, 83] Operation: 32+51=83 Moving to Node #0,0 Current State: 78:[2, 6, 83], Operations: ['32+51=83'] Exploring Operation: 83-6=77, Resulting Numbers: [2, 77] Generated Node #0,0,0: 78:[2, 77] Operation: 83-6=77 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[2, 77], Operations: ['32+51=83', '83-6=77'] Exploring Operation: 2+77=79, Resulting Numbers: [79] 79,78 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
[ 86, 85, 8, 24 ]
17
[ "86-85=1", "24-8=16", "1+16=17" ]
Current State: 17:[86, 85, 8, 24], Operations: [] Exploring Operation: 86-85=1, Resulting Numbers: [8, 24, 1] Generated Node #2: [8, 24, 1] from Operation: 86-85=1 Current State: 17:[8, 24, 1], Operations: ['86-85=1'] Exploring Operation: 24-8=16, Resulting Numbers: [1, 16] Generated Node #3: [1, 16] from Operation: 24-8=16 Current State: 17:[1, 16], Operations: ['86-85=1', '24-8=16'] Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[86, 85, 8, 24], Operations: [] Exploring Operation: 86-85=1, Resulting Numbers: [8, 24, 1] Generated Node #0,0: 17:[8, 24, 1] Operation: 86-85=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[8, 24, 1], Operations: ['86-85=1'] Exploring Operation: 8+1=9, Resulting Numbers: [24, 9] Generated Node #0,0,0: 17:[24, 9] Operation: 8+1=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[24, 9], Operations: ['86-85=1', '8+1=9'] Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,17 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
[ 18, 78, 30, 40 ]
50
[ "78-18=60", "40-30=10", "60-10=50" ]
Current State: 50:[18, 78, 30, 40], Operations: [] Exploring Operation: 78-18=60, Resulting Numbers: [30, 40, 60] Generated Node #2: [30, 40, 60] from Operation: 78-18=60 Current State: 50:[30, 40, 60], Operations: ['78-18=60'] Exploring Operation: 40-30=10, Resulting Numbers: [60, 10] Generated Node #3: [60, 10] from Operation: 40-30=10 Current State: 50:[60, 10], Operations: ['78-18=60', '40-30=10'] Exploring Operation: 60-10=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[18, 78, 30, 40], Operations: [] Exploring Operation: 78-18=60, Resulting Numbers: [30, 40, 60] Generated Node #0,0: 50:[30, 40, 60] Operation: 78-18=60 Exploring Operation: 78-40=38, Resulting Numbers: [18, 30, 38] Generated Node #0,1: 50:[18, 30, 38] Operation: 78-40=38 Exploring Operation: 78-30=48, Resulting Numbers: [18, 40, 48] Generated Node #0,2: 50:[18, 40, 48] Operation: 78-30=48 Exploring Operation: 40-30=10, Resulting Numbers: [18, 78, 10] Generated Node #0,3: 50:[18, 78, 10] Operation: 40-30=10 Exploring Operation: 40-18=22, Resulting Numbers: [78, 30, 22] Generated Node #0,4: 50:[78, 30, 22] Operation: 40-18=22 Start Sub Search at level 1: Moving to Node #0,2 Current State: 50:[18, 40, 48], Operations: ['78-30=48'] Exploring Operation: 48-18=30, Resulting Numbers: [40, 30] Generated Node #0,2,0: 50:[40, 30] Operation: 48-18=30 Exploring Operation: 48-40=8, Resulting Numbers: [18, 8] Generated Node #0,2,1: 50:[18, 8] Operation: 48-40=8 Exploring Operation: 40-18=22, Resulting Numbers: [48, 22] Generated Node #0,2,2: 50:[48, 22] Operation: 40-18=22 Exploring Operation: 18+40=58, Resulting Numbers: [48, 58] Generated Node #0,2,3: 50:[48, 58] Operation: 18+40=58 Exploring Operation: 18+48=66, Resulting Numbers: [40, 66] Generated Node #0,2,4: 50:[40, 66] Operation: 18+48=66 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 50:[48, 22], Operations: ['78-30=48', '40-18=22'] Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 48*22=1056, Resulting Numbers: [1056] 1056,50 unequal: No Solution Exploring Operation: 48+22=70, Resulting Numbers: [70] 70,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 50:[18, 8], Operations: ['78-30=48', '48-40=8'] Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,50 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 50:[48, 58], Operations: ['78-30=48', '18+40=58'] Exploring Operation: 58-48=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 48*58=2784, Resulting Numbers: [2784] 2784,50 unequal: No Solution Exploring Operation: 48+58=106, Resulting Numbers: [106] 106,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 50:[40, 30], Operations: ['78-30=48', '48-18=30'] Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 40*30=1200, Resulting Numbers: [1200] 1200,50 unequal: No Solution Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 50:[40, 66], Operations: ['78-30=48', '18+48=66'] Exploring Operation: 40*66=2640, Resulting Numbers: [2640] 2640,50 unequal: No Solution Exploring Operation: 66-40=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 40+66=106, Resulting Numbers: [106] 106,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[18, 30, 38], Operations: ['78-40=38'] Exploring Operation: 18+30=48, Resulting Numbers: [38, 48] Generated Node #0,1,0: 50:[38, 48] Operation: 18+30=48 Exploring Operation: 30-18=12, Resulting Numbers: [38, 12] Generated Node #0,1,1: 50:[38, 12] Operation: 30-18=12 Exploring Operation: 38-30=8, Resulting Numbers: [18, 8] Generated Node #0,1,2: 50:[18, 8] Operation: 38-30=8 Exploring Operation: 38-18=20, Resulting Numbers: [30, 20] Generated Node #0,1,3: 50:[30, 20] Operation: 38-18=20 Exploring Operation: 18+38=56, Resulting Numbers: [30, 56] Generated Node #0,1,4: 50:[30, 56] Operation: 18+38=56 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 50:[18, 8], Operations: ['78-40=38', '38-30=8'] Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,50 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 50:[30, 20], Operations: ['78-40=38', '38-18=20'] Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[18, 78, 30, 40], Operations: [] Exploring Operation: 78-40=38, Resulting Numbers: [18, 30, 38] Generated Node #0,1: 50:[18, 30, 38] Operation: 78-40=38 Moving to Node #0,1 Current State: 50:[18, 30, 38], Operations: ['78-40=38'] Exploring Operation: 38-18=20, Resulting Numbers: [30, 20] Generated Node #0,1,3: 50:[30, 20] Operation: 38-18=20 Moving to Node #0,1,3 Current State: 50:[30, 20], Operations: ['78-40=38', '38-18=20'] Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_5
mult_heuristic
[ 48, 34, 36, 3 ]
99
[ "36-34=2", "48*2=96", "3+96=99" ]
Current State: 99:[48, 34, 36, 3], Operations: [] Exploring Operation: 36-34=2, Resulting Numbers: [48, 3, 2] Generated Node #2: [48, 3, 2] from Operation: 36-34=2 Current State: 99:[48, 3, 2], Operations: ['36-34=2'] Exploring Operation: 48*2=96, Resulting Numbers: [3, 96] Generated Node #3: [3, 96] from Operation: 48*2=96 Current State: 99:[3, 96], Operations: ['36-34=2', '48*2=96'] Exploring Operation: 3+96=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[48, 34, 36, 3], Operations: [] Exploring Operation: 48-36=12, Resulting Numbers: [34, 3, 12] Generated Node #0,0: 99:[34, 3, 12] Operation: 48-36=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[34, 3, 12], Operations: ['48-36=12'] Exploring Operation: 12-3=9, Resulting Numbers: [34, 9] Generated Node #0,0,0: 99:[34, 9] Operation: 12-3=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[34, 9], Operations: ['48-36=12', '12-3=9'] Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,99 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
[ 67, 38, 78, 86 ]
97
[ "67+38=105", "86-78=8", "105-8=97" ]
Current State: 97:[67, 38, 78, 86], Operations: [] Exploring Operation: 67+38=105, Resulting Numbers: [78, 86, 105] Generated Node #2: [78, 86, 105] from Operation: 67+38=105 Current State: 97:[78, 86, 105], Operations: ['67+38=105'] Exploring Operation: 86-78=8, Resulting Numbers: [105, 8] Generated Node #3: [105, 8] from Operation: 86-78=8 Current State: 97:[105, 8], Operations: ['67+38=105', '86-78=8'] Exploring Operation: 105-8=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[67, 38, 78, 86], Operations: [] Exploring Operation: 38+86=124, Resulting Numbers: [67, 78, 124] Generated Node #0,0: 97:[67, 78, 124] Operation: 38+86=124 Exploring Operation: 67+38=105, Resulting Numbers: [78, 86, 105] Generated Node #0,1: 97:[78, 86, 105] Operation: 67+38=105 Exploring Operation: 38+78=116, Resulting Numbers: [67, 86, 116] Generated Node #0,2: 97:[67, 86, 116] Operation: 38+78=116 Exploring Operation: 67-38=29, Resulting Numbers: [78, 86, 29] Generated Node #0,3: 97:[78, 86, 29] Operation: 67-38=29 Moving to Node #0,1 Current State: 97:[78, 86, 105], Operations: ['67+38=105'] Exploring Operation: 105-78=27, Resulting Numbers: [86, 27] Generated Node #0,1,0: 97:[86, 27] Operation: 105-78=27 Exploring Operation: 86-78=8, Resulting Numbers: [105, 8] Generated Node #0,1,1: 97:[105, 8] Operation: 86-78=8 Exploring Operation: 78+105=183, Resulting Numbers: [86, 183] Generated Node #0,1,2: 97:[86, 183] Operation: 78+105=183 Exploring Operation: 78+86=164, Resulting Numbers: [105, 164] Generated Node #0,1,3: 97:[105, 164] Operation: 78+86=164 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 97:[105, 164], Operations: ['67+38=105', '78+86=164'] Exploring Operation: 105+164=269, Resulting Numbers: [269] 269,97 unequal: No Solution Exploring Operation: 105*164=17220, Resulting Numbers: [17220] 17220,97 unequal: No Solution Exploring Operation: 164-105=59, Resulting Numbers: [59] 59,97 unequal: No Solution No 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: 97:[86, 27], Operations: ['67+38=105', '105-78=27'] Exploring Operation: 86+27=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 86-27=59, Resulting Numbers: [59] 59,97 unequal: No Solution Exploring Operation: 86*27=2322, Resulting Numbers: [2322] 2322,97 unequal: No Solution No 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: 97:[105, 8], Operations: ['67+38=105', '86-78=8'] Exploring Operation: 105-8=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[67, 38, 78, 86], Operations: [] Exploring Operation: 67+38=105, Resulting Numbers: [78, 86, 105] Generated Node #0,1: 97:[78, 86, 105] Operation: 67+38=105 Moving to Node #0,1 Current State: 97:[78, 86, 105], Operations: ['67+38=105'] Exploring Operation: 86-78=8, Resulting Numbers: [105, 8] Generated Node #0,1,1: 97:[105, 8] Operation: 86-78=8 Moving to Node #0,1,1 Current State: 97:[105, 8], Operations: ['67+38=105', '86-78=8'] Exploring Operation: 105-8=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 68, 85, 1, 73 ]
90
[ "85-68=17", "1*73=73", "17+73=90" ]
Current State: 90:[68, 85, 1, 73], Operations: [] Exploring Operation: 85-68=17, Resulting Numbers: [1, 73, 17] Generated Node #2: [1, 73, 17] from Operation: 85-68=17 Current State: 90:[1, 73, 17], Operations: ['85-68=17'] Exploring Operation: 1*73=73, Resulting Numbers: [17, 73] Generated Node #3: [17, 73] from Operation: 1*73=73 Current State: 90:[17, 73], Operations: ['85-68=17', '1*73=73'] Exploring Operation: 17+73=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[68, 85, 1, 73], Operations: [] Exploring Operation: 73-68=5, Resulting Numbers: [85, 1, 5] Generated Node #0,0: 90:[85, 1, 5] Operation: 73-68=5 Exploring Operation: 85-68=17, Resulting Numbers: [1, 73, 17] Generated Node #0,1: 90:[1, 73, 17] Operation: 85-68=17 Moving to Node #0,0 Current State: 90:[85, 1, 5], Operations: ['73-68=5'] Exploring Operation: 85+5=90, Resulting Numbers: [1, 90] Generated Node #0,0,0: 90:[1, 90] Operation: 85+5=90 Exploring Operation: 85/5=17, Resulting Numbers: [1, 17] Generated Node #0,0,1: 90:[1, 17] Operation: 85/5=17 Moving to Node #0,1 Current State: 90:[1, 73, 17], Operations: ['85-68=17'] Exploring Operation: 73+17=90, Resulting Numbers: [1, 90] Generated Node #0,1,0: 90:[1, 90] Operation: 73+17=90 Exploring Operation: 73-17=56, Resulting Numbers: [1, 56] Generated Node #0,1,1: 90:[1, 56] Operation: 73-17=56 Moving to Node #0,0,0 Current State: 90:[1, 90], Operations: ['73-68=5', '85+5=90'] Exploring Operation: 1*90=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[68, 85, 1, 73], Operations: [] Exploring Operation: 73-68=5, Resulting Numbers: [85, 1, 5] Generated Node #0,0: 90:[85, 1, 5] Operation: 73-68=5 Moving to Node #0,0 Current State: 90:[85, 1, 5], Operations: ['73-68=5'] Exploring Operation: 85+5=90, Resulting Numbers: [1, 90] Generated Node #0,0,0: 90:[1, 90] Operation: 85+5=90 Moving to Node #0,0,0 Current State: 90:[1, 90], Operations: ['73-68=5', '85+5=90'] Exploring Operation: 1*90=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 24, 65, 75, 60 ]
40
[ "65+60=125", "24*125=3000", "3000/75=40" ]
Current State: 40:[24, 65, 75, 60], Operations: [] Exploring Operation: 65+60=125, Resulting Numbers: [24, 75, 125] Generated Node #2: [24, 75, 125] from Operation: 65+60=125 Current State: 40:[24, 75, 125], Operations: ['65+60=125'] Exploring Operation: 24*125=3000, Resulting Numbers: [75, 3000] Generated Node #3: [75, 3000] from Operation: 24*125=3000 Current State: 40:[75, 3000], Operations: ['65+60=125', '24*125=3000'] Exploring Operation: 3000/75=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[24, 65, 75, 60], Operations: [] Exploring Operation: 65-24=41, Resulting Numbers: [75, 60, 41] Generated Node #0,0: 40:[75, 60, 41] Operation: 65-24=41 Exploring Operation: 75-60=15, Resulting Numbers: [24, 65, 15] Generated Node #0,1: 40:[24, 65, 15] Operation: 75-60=15 Exploring Operation: 65-60=5, Resulting Numbers: [24, 75, 5] Generated Node #0,2: 40:[24, 75, 5] Operation: 65-60=5 Exploring Operation: 75-65=10, Resulting Numbers: [24, 60, 10] Generated Node #0,3: 40:[24, 60, 10] Operation: 75-65=10 Exploring Operation: 75-24=51, Resulting Numbers: [65, 60, 51] Generated Node #0,4: 40:[65, 60, 51] Operation: 75-24=51 Moving to Node #0,3 Current State: 40:[24, 60, 10], Operations: ['75-65=10'] Exploring Operation: 24+10=34, Resulting Numbers: [60, 34] Generated Node #0,3,0: 40:[60, 34] Operation: 24+10=34 Exploring Operation: 60-24=36, Resulting Numbers: [10, 36] Generated Node #0,3,1: 40:[10, 36] Operation: 60-24=36 Exploring Operation: 60/10=6, Resulting Numbers: [24, 6] Generated Node #0,3,2: 40:[24, 6] Operation: 60/10=6 Exploring Operation: 24-10=14, Resulting Numbers: [60, 14] Generated Node #0,3,3: 40:[60, 14] Operation: 24-10=14 Exploring Operation: 60-10=50, Resulting Numbers: [24, 50] Generated Node #0,3,4: 40:[24, 50] Operation: 60-10=50 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 40:[10, 36], Operations: ['75-65=10', '60-24=36'] Exploring Operation: 10+36=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,40 unequal: No Solution Exploring Operation: 10*36=360, Resulting Numbers: [360] 360,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 40:[24, 6], Operations: ['75-65=10', '60/10=6'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 24+6=30, Resulting Numbers: [30] 30,40 unequal: No Solution Exploring Operation: 24*6=144, Resulting Numbers: [144] 144,40 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 40:[24, 50], Operations: ['75-65=10', '60-10=50'] Exploring Operation: 24+50=74, Resulting Numbers: [74] 74,40 unequal: No Solution Exploring Operation: 24*50=1200, Resulting Numbers: [1200] 1200,40 unequal: No Solution Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 40:[60, 14], Operations: ['75-65=10', '24-10=14'] Exploring Operation: 60*14=840, Resulting Numbers: [840] 840,40 unequal: No Solution Exploring Operation: 60-14=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 60+14=74, Resulting Numbers: [74] 74,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 40:[60, 34], Operations: ['75-65=10', '24+10=34'] Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,40 unequal: No Solution Exploring Operation: 60+34=94, Resulting Numbers: [94] 94,40 unequal: No Solution Exploring Operation: 60*34=2040, Resulting Numbers: [2040] 2040,40 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: 40:[24, 65, 15], Operations: ['75-60=15'] Exploring Operation: 65-15=50, Resulting Numbers: [24, 50] Generated Node #0,1,0: 40:[24, 50] Operation: 65-15=50 Exploring Operation: 24+15=39, Resulting Numbers: [65, 39] Generated Node #0,1,1: 40:[65, 39] Operation: 24+15=39 Exploring Operation: 24-15=9, Resulting Numbers: [65, 9] Generated Node #0,1,2: 40:[65, 9] Operation: 24-15=9 Exploring Operation: 65+15=80, Resulting Numbers: [24, 80] Generated Node #0,1,3: 40:[24, 80] Operation: 65+15=80 Exploring Operation: 65-24=41, Resulting Numbers: [15, 41] Generated Node #0,1,4: 40:[15, 41] Operation: 65-24=41 Moving to Node #0,2 Current State: 40:[24, 75, 5], Operations: ['65-60=5'] Exploring Operation: 24-5=19, Resulting Numbers: [75, 19] Generated Node #0,2,0: 40:[75, 19] Operation: 24-5=19 Exploring Operation: 75-5=70, Resulting Numbers: [24, 70] Generated Node #0,2,1: 40:[24, 70] Operation: 75-5=70 Exploring Operation: 75-24=51, Resulting Numbers: [5, 51] Generated Node #0,2,2: 40:[5, 51] Operation: 75-24=51 Exploring Operation: 24+5=29, Resulting Numbers: [75, 29] Generated Node #0,2,3: 40:[75, 29] Operation: 24+5=29 Exploring Operation: 75/5=15, Resulting Numbers: [24, 15] Generated Node #0,2,4: 40:[24, 15] Operation: 75/5=15 Moving to Node #0,0 Current State: 40:[75, 60, 41], Operations: ['65-24=41'] Exploring Operation: 75+60=135, Resulting Numbers: [41, 135] Generated Node #0,0,0: 40:[41, 135] Operation: 75+60=135 Exploring Operation: 75-41=34, Resulting Numbers: [60, 34] Generated Node #0,0,1: 40:[60, 34] Operation: 75-41=34 Exploring Operation: 75-60=15, Resulting Numbers: [41, 15] Generated Node #0,0,2: 40:[41, 15] Operation: 75-60=15 Exploring Operation: 75+41=116, Resulting Numbers: [60, 116] Generated Node #0,0,3: 40:[60, 116] Operation: 75+41=116 Exploring Operation: 60-41=19, Resulting Numbers: [75, 19] Generated Node #0,0,4: 40:[75, 19] Operation: 60-41=19 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 40:[41, 15], Operations: ['65-24=41', '75-60=15'] Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,40 unequal: No Solution Exploring Operation: 41+15=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 41*15=615, Resulting Numbers: [615] 615,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[60, 34], Operations: ['65-24=41', '75-41=34'] Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,40 unequal: No Solution Exploring Operation: 60+34=94, Resulting Numbers: [94] 94,40 unequal: No Solution Exploring Operation: 60*34=2040, Resulting Numbers: [2040] 2040,40 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 #0,0,4 Current State: 40:[75, 19], Operations: ['65-24=41', '60-41=19'] Exploring Operation: 75-19=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 75+19=94, Resulting Numbers: [94] 94,40 unequal: No Solution Exploring Operation: 75*19=1425, Resulting Numbers: [1425] 1425,40 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 #0,0,0 Current State: 40:[41, 135], Operations: ['65-24=41', '75+60=135'] Exploring Operation: 41*135=5535, Resulting Numbers: [5535] 5535,40 unequal: No Solution Exploring Operation: 135-41=94, Resulting Numbers: [94] 94,40 unequal: No Solution Exploring Operation: 41+135=176, Resulting Numbers: [176] 176,40 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 #0,0,3 Current State: 40:[60, 116], Operations: ['65-24=41', '75+41=116'] Exploring Operation: 60+116=176, Resulting Numbers: [176] 176,40 unequal: No Solution Exploring Operation: 116-60=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 60*116=6960, Resulting Numbers: [6960] 6960,40 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: 40:[65, 60, 51], Operations: ['75-24=51'] Exploring Operation: 65-60=5, Resulting Numbers: [51, 5] Generated Node #0,4,0: 40:[51, 5] Operation: 65-60=5 Exploring Operation: 60-51=9, Resulting Numbers: [65, 9] Generated Node #0,4,1: 40:[65, 9] Operation: 60-51=9 Exploring Operation: 65-51=14, Resulting Numbers: [60, 14] Generated Node #0,4,2: 40:[60, 14] Operation: 65-51=14 Exploring Operation: 65+60=125, Resulting Numbers: [51, 125] Generated Node #0,4,3: 40:[51, 125] Operation: 65+60=125 Exploring Operation: 65+51=116, Resulting Numbers: [60, 116] Generated Node #0,4,4: 40:[60, 116] Operation: 65+51=116 Moving to Node #0,1,4 Current State: 40:[15, 41], Operations: ['75-60=15', '65-24=41'] Exploring Operation: 15+41=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 15*41=615, Resulting Numbers: [615] 615,40 unequal: No Solution Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,40 unequal: No Solution Moving to Node #0,2,4 Current State: 40:[24, 15], Operations: ['65-60=5', '75/5=15'] Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,40 unequal: No Solution Exploring Operation: 24*15=360, Resulting Numbers: [360] 360,40 unequal: No Solution Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,40 unequal: No Solution Moving to Node #0,2,2 Current State: 40:[5, 51], Operations: ['65-60=5', '75-24=51'] Exploring Operation: 5*51=255, Resulting Numbers: [255] 255,40 unequal: No Solution Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,40 unequal: No Solution Moving to Node #0,4,0 Current State: 40:[51, 5], Operations: ['75-24=51', '65-60=5'] Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,40 unequal: No Solution Moving to Node #0,1,0 Current State: 40:[24, 50], Operations: ['75-60=15', '65-15=50'] Exploring Operation: 24+50=74, Resulting Numbers: [74] 74,40 unequal: No Solution Exploring Operation: 24*50=1200, Resulting Numbers: [1200] 1200,40 unequal: No Solution Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,40 unequal: No Solution Moving to Node #0,4,2 Current State: 40:[60, 14], Operations: ['75-24=51', '65-51=14'] Exploring Operation: 60+14=74, Resulting Numbers: [74] 74,40 unequal: No Solution Exploring Operation: 60-14=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 60*14=840, Resulting Numbers: [840] 840,40 unequal: No Solution Moving to Node #0,4,1 Current State: 40:[65, 9], Operations: ['75-24=51', '60-51=9'] Exploring Operation: 65*9=585, Resulting Numbers: [585] 585,40 unequal: No Solution Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,40 unequal: No Solution Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,40 unequal: No Solution Moving to Node #0,1,2 Current State: 40:[65, 9], Operations: ['75-60=15', '24-15=9'] Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,40 unequal: No Solution Exploring Operation: 65*9=585, Resulting Numbers: [585] 585,40 unequal: No Solution Moving to Node #0,1,1 Current State: 40:[65, 39], Operations: ['75-60=15', '24+15=39'] Exploring Operation: 65*39=2535, Resulting Numbers: [2535] 2535,40 unequal: No Solution Exploring Operation: 65+39=104, Resulting Numbers: [104] 104,40 unequal: No Solution Exploring Operation: 65-39=26, Resulting Numbers: [26] 26,40 unequal: No Solution Moving to Node #0,2,1 Current State: 40:[24, 70], Operations: ['65-60=5', '75-5=70'] Exploring Operation: 70-24=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 24*70=1680, Resulting Numbers: [1680] 1680,40 unequal: No Solution Exploring Operation: 24+70=94, Resulting Numbers: [94] 94,40 unequal: No Solution Moving to Node #0,2,0 Current State: 40:[75, 19], Operations: ['65-60=5', '24-5=19'] Exploring Operation: 75-19=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 75+19=94, Resulting Numbers: [94] 94,40 unequal: No Solution Exploring Operation: 75*19=1425, Resulting Numbers: [1425] 1425,40 unequal: No Solution Moving to Node #0,2,3 Current State: 40:[75, 29], Operations: ['65-60=5', '24+5=29'] Exploring Operation: 75*29=2175, Resulting Numbers: [2175] 2175,40 unequal: No Solution Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 75+29=104, Resulting Numbers: [104] 104,40 unequal: No Solution Moving to Node #0,1,3 Current State: 40:[24, 80], Operations: ['75-60=15', '65+15=80'] Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 24*80=1920, Resulting Numbers: [1920] 1920,40 unequal: No Solution Exploring Operation: 24+80=104, Resulting Numbers: [104] 104,40 unequal: No Solution Moving to Node #0,4,3 Current State: 40:[51, 125], Operations: ['75-24=51', '65+60=125'] Exploring Operation: 51*125=6375, Resulting Numbers: [6375] 6375,40 unequal: No Solution Exploring Operation: 51+125=176, Resulting Numbers: [176] 176,40 unequal: No Solution Exploring Operation: 125-51=74, Resulting Numbers: [74] 74,40 unequal: No Solution Moving to Node #0,4,4 Current State: 40:[60, 116], Operations: ['75-24=51', '65+51=116'] Exploring Operation: 60+116=176, Resulting Numbers: [176] 176,40 unequal: No Solution Exploring Operation: 116-60=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 60*116=6960, Resulting Numbers: [6960] 6960,40 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 25, 5, 47, 9 ]
36
[ "25-5=20", "47+9=56", "56-20=36" ]
Current State: 36:[25, 5, 47, 9], Operations: [] Exploring Operation: 25-5=20, Resulting Numbers: [47, 9, 20] Generated Node #2: [47, 9, 20] from Operation: 25-5=20 Current State: 36:[47, 9, 20], Operations: ['25-5=20'] Exploring Operation: 47+9=56, Resulting Numbers: [20, 56] Generated Node #3: [20, 56] from Operation: 47+9=56 Current State: 36:[20, 56], Operations: ['25-5=20', '47+9=56'] Exploring Operation: 56-20=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[25, 5, 47, 9], Operations: [] Exploring Operation: 47-9=38, Resulting Numbers: [25, 5, 38] Generated Node #0,0: 36:[25, 5, 38] Operation: 47-9=38 Exploring Operation: 47-25=22, Resulting Numbers: [5, 9, 22] Generated Node #0,1: 36:[5, 9, 22] Operation: 47-25=22 Moving to Node #0,1 Current State: 36:[5, 9, 22], Operations: ['47-25=22'] Exploring Operation: 22-9=13, Resulting Numbers: [5, 13] Generated Node #0,1,0: 36:[5, 13] Operation: 22-9=13 Exploring Operation: 22-5=17, Resulting Numbers: [9, 17] Generated Node #0,1,1: 36:[9, 17] Operation: 22-5=17 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 36:[9, 17], Operations: ['47-25=22', '22-5=17'] Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,36 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 36:[5, 13], Operations: ['47-25=22', '22-9=13'] Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 36:[25, 5, 38], Operations: ['47-9=38'] Exploring Operation: 38-25=13, Resulting Numbers: [5, 13] Generated Node #0,0,0: 36:[5, 13] Operation: 38-25=13 Exploring Operation: 25/5=5, Resulting Numbers: [38, 5] Generated Node #0,0,1: 36:[38, 5] Operation: 25/5=5 Moving to Node #0,0,0 Current State: 36:[5, 13], Operations: ['47-9=38', '38-25=13'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,36 unequal: No Solution Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,36 unequal: No Solution Moving to Node #0,0,1 Current State: 36:[38, 5], Operations: ['47-9=38', '25/5=5'] Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,36 unequal: No Solution Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,36 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 81, 10, 49, 27 ]
13
[ "81/27=3", "49-10=39", "39/3=13" ]
Current State: 13:[81, 10, 49, 27], Operations: [] Exploring Operation: 81/27=3, Resulting Numbers: [10, 49, 3] Generated Node #2: [10, 49, 3] from Operation: 81/27=3 Current State: 13:[10, 49, 3], Operations: ['81/27=3'] Exploring Operation: 49-10=39, Resulting Numbers: [3, 39] Generated Node #3: [3, 39] from Operation: 49-10=39 Current State: 13:[3, 39], Operations: ['81/27=3', '49-10=39'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[81, 10, 49, 27], Operations: [] Exploring Operation: 81-10=71, Resulting Numbers: [49, 27, 71] Generated Node #0,0: 13:[49, 27, 71] Operation: 81-10=71 Exploring Operation: 81/27=3, Resulting Numbers: [10, 49, 3] Generated Node #0,1: 13:[10, 49, 3] Operation: 81/27=3 Exploring Operation: 49-27=22, Resulting Numbers: [81, 10, 22] Generated Node #0,2: 13:[81, 10, 22] Operation: 49-27=22 Exploring Operation: 81-49=32, Resulting Numbers: [10, 27, 32] Generated Node #0,3: 13:[10, 27, 32] Operation: 81-49=32 Exploring Operation: 81-27=54, Resulting Numbers: [10, 49, 54] Generated Node #0,4: 13:[10, 49, 54] Operation: 81-27=54 Moving to Node #0,3 Current State: 13:[10, 27, 32], Operations: ['81-49=32'] Exploring Operation: 27-10=17, Resulting Numbers: [32, 17] Generated Node #0,3,0: 13:[32, 17] Operation: 27-10=17 Exploring Operation: 32-27=5, Resulting Numbers: [10, 5] Generated Node #0,3,1: 13:[10, 5] Operation: 32-27=5 Exploring Operation: 32-10=22, Resulting Numbers: [27, 22] Generated Node #0,3,2: 13:[27, 22] Operation: 32-10=22 Exploring Operation: 10+27=37, Resulting Numbers: [32, 37] Generated Node #0,3,3: 13:[32, 37] Operation: 10+27=37 Exploring Operation: 10+32=42, Resulting Numbers: [27, 42] Generated Node #0,3,4: 13:[27, 42] Operation: 10+32=42 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 13:[10, 5], Operations: ['81-49=32', '32-27=5'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 10*5=50, Resulting Numbers: [50] 50,13 unequal: No Solution Exploring Operation: 10+5=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 13:[32, 17], Operations: ['81-49=32', '27-10=17'] Exploring Operation: 32*17=544, Resulting Numbers: [544] 544,13 unequal: No Solution Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 32+17=49, Resulting Numbers: [49] 49,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 13:[27, 22], Operations: ['81-49=32', '32-10=22'] Exploring Operation: 27+22=49, Resulting Numbers: [49] 49,13 unequal: No Solution Exploring Operation: 27*22=594, Resulting Numbers: [594] 594,13 unequal: No Solution Exploring Operation: 27-22=5, Resulting Numbers: [5] 5,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 13:[32, 37], Operations: ['81-49=32', '10+27=37'] Exploring Operation: 32*37=1184, Resulting Numbers: [1184] 1184,13 unequal: No Solution Exploring Operation: 32+37=69, Resulting Numbers: [69] 69,13 unequal: No Solution Exploring Operation: 37-32=5, Resulting Numbers: [5] 5,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 13:[27, 42], Operations: ['81-49=32', '10+32=42'] Exploring Operation: 27+42=69, Resulting Numbers: [69] 69,13 unequal: No Solution Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 27*42=1134, Resulting Numbers: [1134] 1134,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 13:[10, 49, 3], Operations: ['81/27=3'] Exploring Operation: 10+3=13, Resulting Numbers: [49, 13] Generated Node #0,1,0: 13:[49, 13] Operation: 10+3=13 Exploring Operation: 49-3=46, Resulting Numbers: [10, 46] Generated Node #0,1,1: 13:[10, 46] Operation: 49-3=46 Exploring Operation: 10-3=7, Resulting Numbers: [49, 7] Generated Node #0,1,2: 13:[49, 7] Operation: 10-3=7 Exploring Operation: 49-10=39, Resulting Numbers: [3, 39] Generated Node #0,1,3: 13:[3, 39] Operation: 49-10=39 Exploring Operation: 49+3=52, Resulting Numbers: [10, 52] Generated Node #0,1,4: 13:[10, 52] Operation: 49+3=52 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 13:[49, 13], Operations: ['81/27=3', '10+3=13'] Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 49+13=62, Resulting Numbers: [62] 62,13 unequal: No Solution Exploring Operation: 49*13=637, Resulting Numbers: [637] 637,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 13:[10, 46], Operations: ['81/27=3', '49-3=46'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 10+46=56, Resulting Numbers: [56] 56,13 unequal: No Solution Exploring Operation: 10*46=460, Resulting Numbers: [460] 460,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 13:[3, 39], Operations: ['81/27=3', '49-10=39'] Exploring Operation: 3*39=117, Resulting Numbers: [117] 117,13 unequal: No Solution Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,13 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[81, 10, 49, 27], Operations: [] Exploring Operation: 81/27=3, Resulting Numbers: [10, 49, 3] Generated Node #0,1: 13:[10, 49, 3] Operation: 81/27=3 Moving to Node #0,1 Current State: 13:[10, 49, 3], Operations: ['81/27=3'] Exploring Operation: 49-10=39, Resulting Numbers: [3, 39] Generated Node #0,1,3: 13:[3, 39] Operation: 49-10=39 Moving to Node #0,1,3 Current State: 13:[3, 39], Operations: ['81/27=3', '49-10=39'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.961806
hs_5
sum_heuristic
[ 70, 31, 99, 88 ]
44
[ "70+31=101", "101-99=2", "88/2=44" ]
Current State: 44:[70, 31, 99, 88], Operations: [] Exploring Operation: 70+31=101, Resulting Numbers: [99, 88, 101] Generated Node #2: [99, 88, 101] from Operation: 70+31=101 Current State: 44:[99, 88, 101], Operations: ['70+31=101'] Exploring Operation: 101-99=2, Resulting Numbers: [88, 2] Generated Node #3: [88, 2] from Operation: 101-99=2 Current State: 44:[88, 2], Operations: ['70+31=101', '101-99=2'] Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[70, 31, 99, 88], Operations: [] Exploring Operation: 88-31=57, Resulting Numbers: [70, 99, 57] Generated Node #0,0: 44:[70, 99, 57] Operation: 88-31=57 Exploring Operation: 99-31=68, Resulting Numbers: [70, 88, 68] Generated Node #0,1: 44:[70, 88, 68] Operation: 99-31=68 Exploring Operation: 88-70=18, Resulting Numbers: [31, 99, 18] Generated Node #0,2: 44:[31, 99, 18] Operation: 88-70=18 Exploring Operation: 99-88=11, Resulting Numbers: [70, 31, 11] Generated Node #0,3: 44:[70, 31, 11] Operation: 99-88=11 Exploring Operation: 99-70=29, Resulting Numbers: [31, 88, 29] Generated Node #0,4: 44:[31, 88, 29] Operation: 99-70=29 Moving to Node #0,3 Current State: 44:[70, 31, 11], Operations: ['99-88=11'] Exploring Operation: 31+11=42, Resulting Numbers: [70, 42] Generated Node #0,3,0: 44:[70, 42] Operation: 31+11=42 Exploring Operation: 70-11=59, Resulting Numbers: [31, 59] Generated Node #0,3,1: 44:[31, 59] Operation: 70-11=59 Exploring Operation: 70-31=39, Resulting Numbers: [11, 39] Generated Node #0,3,2: 44:[11, 39] Operation: 70-31=39 Exploring Operation: 70+11=81, Resulting Numbers: [31, 81] Generated Node #0,3,3: 44:[31, 81] Operation: 70+11=81 Exploring Operation: 31-11=20, Resulting Numbers: [70, 20] Generated Node #0,3,4: 44:[70, 20] Operation: 31-11=20 Moving to Node #0,4 Current State: 44:[31, 88, 29], Operations: ['99-70=29'] Exploring Operation: 31+29=60, Resulting Numbers: [88, 60] Generated Node #0,4,0: 44:[88, 60] Operation: 31+29=60 Exploring Operation: 31-29=2, Resulting Numbers: [88, 2] Generated Node #0,4,1: 44:[88, 2] Operation: 31-29=2 Exploring Operation: 31+88=119, Resulting Numbers: [29, 119] Generated Node #0,4,2: 44:[29, 119] Operation: 31+88=119 Exploring Operation: 88-31=57, Resulting Numbers: [29, 57] Generated Node #0,4,3: 44:[29, 57] Operation: 88-31=57 Exploring Operation: 88-29=59, Resulting Numbers: [31, 59] Generated Node #0,4,4: 44:[31, 59] Operation: 88-29=59 Moving to Node #0,2 Current State: 44:[31, 99, 18], Operations: ['88-70=18'] Exploring Operation: 99-18=81, Resulting Numbers: [31, 81] Generated Node #0,2,0: 44:[31, 81] Operation: 99-18=81 Exploring Operation: 99-31=68, Resulting Numbers: [18, 68] Generated Node #0,2,1: 44:[18, 68] Operation: 99-31=68 Exploring Operation: 31+18=49, Resulting Numbers: [99, 49] Generated Node #0,2,2: 44:[99, 49] Operation: 31+18=49 Exploring Operation: 99+18=117, Resulting Numbers: [31, 117] Generated Node #0,2,3: 44:[31, 117] Operation: 99+18=117 Exploring Operation: 31-18=13, Resulting Numbers: [99, 13] Generated Node #0,2,4: 44:[99, 13] Operation: 31-18=13 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 44:[18, 68], Operations: ['88-70=18', '99-31=68'] Exploring Operation: 68-18=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 18+68=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 18*68=1224, Resulting Numbers: [1224] 1224,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 44:[31, 81], Operations: ['88-70=18', '99-18=81'] Exploring Operation: 81-31=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 31+81=112, Resulting Numbers: [112] 112,44 unequal: No Solution Exploring Operation: 31*81=2511, Resulting Numbers: [2511] 2511,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 44:[99, 13], Operations: ['88-70=18', '31-18=13'] Exploring Operation: 99-13=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 99+13=112, Resulting Numbers: [112] 112,44 unequal: No Solution Exploring Operation: 99*13=1287, Resulting Numbers: [1287] 1287,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 44:[99, 49], Operations: ['88-70=18', '31+18=49'] Exploring Operation: 99-49=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 99*49=4851, Resulting Numbers: [4851] 4851,44 unequal: No Solution Exploring Operation: 99+49=148, Resulting Numbers: [148] 148,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 44:[31, 117], Operations: ['88-70=18', '99+18=117'] Exploring Operation: 117-31=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 31+117=148, Resulting Numbers: [148] 148,44 unequal: No Solution Exploring Operation: 31*117=3627, Resulting Numbers: [3627] 3627,44 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: 44:[70, 99, 57], Operations: ['88-31=57'] Exploring Operation: 99-70=29, Resulting Numbers: [57, 29] Generated Node #0,0,0: 44:[57, 29] Operation: 99-70=29 Exploring Operation: 70-57=13, Resulting Numbers: [99, 13] Generated Node #0,0,1: 44:[99, 13] Operation: 70-57=13 Exploring Operation: 70+57=127, Resulting Numbers: [99, 127] Generated Node #0,0,2: 44:[99, 127] Operation: 70+57=127 Exploring Operation: 70+99=169, Resulting Numbers: [57, 169] Generated Node #0,0,3: 44:[57, 169] Operation: 70+99=169 Exploring Operation: 99-57=42, Resulting Numbers: [70, 42] Generated Node #0,0,4: 44:[70, 42] Operation: 99-57=42 Moving to Node #0,1 Current State: 44:[70, 88, 68], Operations: ['99-31=68'] Exploring Operation: 88-68=20, Resulting Numbers: [70, 20] Generated Node #0,1,0: 44:[70, 20] Operation: 88-68=20 Exploring Operation: 70+68=138, Resulting Numbers: [88, 138] Generated Node #0,1,1: 44:[88, 138] Operation: 70+68=138 Exploring Operation: 70-68=2, Resulting Numbers: [88, 2] Generated Node #0,1,2: 44:[88, 2] Operation: 70-68=2 Exploring Operation: 70+88=158, Resulting Numbers: [68, 158] Generated Node #0,1,3: 44:[68, 158] Operation: 70+88=158 Exploring Operation: 88-70=18, Resulting Numbers: [68, 18] Generated Node #0,1,4: 44:[68, 18] Operation: 88-70=18 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 44:[70, 20], Operations: ['99-31=68', '88-68=20'] Exploring Operation: 70-20=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 70*20=1400, Resulting Numbers: [1400] 1400,44 unequal: No Solution Exploring Operation: 70+20=90, Resulting Numbers: [90] 90,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 44:[68, 18], Operations: ['99-31=68', '88-70=18'] Exploring Operation: 68-18=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 68+18=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 68*18=1224, Resulting Numbers: [1224] 1224,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 44:[88, 2], Operations: ['99-31=68', '70-68=2'] Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[70, 31, 99, 88], Operations: [] Exploring Operation: 99-31=68, Resulting Numbers: [70, 88, 68] Generated Node #0,1: 44:[70, 88, 68] Operation: 99-31=68 Moving to Node #0,1 Current State: 44:[70, 88, 68], Operations: ['99-31=68'] Exploring Operation: 70-68=2, Resulting Numbers: [88, 2] Generated Node #0,1,2: 44:[88, 2] Operation: 70-68=2 Moving to Node #0,1,2 Current State: 44:[88, 2], Operations: ['99-31=68', '70-68=2'] Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.951389
hs_5
mult_heuristic
[ 53, 10, 2, 19 ]
48
[ "53-10=43", "43-19=24", "2*24=48" ]
Current State: 48:[53, 10, 2, 19], Operations: [] Exploring Operation: 53-10=43, Resulting Numbers: [2, 19, 43] Generated Node #2: [2, 19, 43] from Operation: 53-10=43 Current State: 48:[2, 19, 43], Operations: ['53-10=43'] Exploring Operation: 43-19=24, Resulting Numbers: [2, 24] Generated Node #3: [2, 24] from Operation: 43-19=24 Current State: 48:[2, 24], Operations: ['53-10=43', '43-19=24'] Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[53, 10, 2, 19], Operations: [] Exploring Operation: 53-2=51, Resulting Numbers: [10, 19, 51] Generated Node #0,0: 48:[10, 19, 51] Operation: 53-2=51 Exploring Operation: 19-10=9, Resulting Numbers: [53, 2, 9] Generated Node #0,1: 48:[53, 2, 9] Operation: 19-10=9 Exploring Operation: 53-10=43, Resulting Numbers: [2, 19, 43] Generated Node #0,2: 48:[2, 19, 43] Operation: 53-10=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[53, 2, 9], Operations: ['19-10=9'] Exploring Operation: 2+9=11, Resulting Numbers: [53, 11] Generated Node #0,1,0: 48:[53, 11] Operation: 2+9=11 Exploring Operation: 53-9=44, Resulting Numbers: [2, 44] Generated Node #0,1,1: 48:[2, 44] Operation: 53-9=44 Exploring Operation: 53-2=51, Resulting Numbers: [9, 51] Generated Node #0,1,2: 48:[9, 51] Operation: 53-2=51 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 48:[2, 44], Operations: ['19-10=9', '53-9=44'] Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,48 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 48:[9, 51], Operations: ['19-10=9', '53-2=51'] Exploring Operation: 9*51=459, Resulting Numbers: [459] 459,48 unequal: No Solution Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 9+51=60, Resulting Numbers: [60] 60,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 48:[53, 11], Operations: ['19-10=9', '2+9=11'] Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 53*11=583, Resulting Numbers: [583] 583,48 unequal: No Solution Exploring Operation: 53+11=64, Resulting Numbers: [64] 64,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[10, 19, 51], Operations: ['53-2=51'] Exploring Operation: 19-10=9, Resulting Numbers: [51, 9] Generated Node #0,0,0: 48:[51, 9] Operation: 19-10=9 Exploring Operation: 51-10=41, Resulting Numbers: [19, 41] Generated Node #0,0,1: 48:[19, 41] Operation: 51-10=41 Exploring Operation: 10+19=29, Resulting Numbers: [51, 29] Generated Node #0,0,2: 48:[51, 29] Operation: 10+19=29 Moving to Node #0,0,0 Current State: 48:[51, 9], Operations: ['53-2=51', '19-10=9'] Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 51*9=459, Resulting Numbers: [459] 459,48 unequal: No Solution Exploring Operation: 51+9=60, Resulting Numbers: [60] 60,48 unequal: No Solution Moving to Node #0,0,2 Current State: 48:[51, 29], Operations: ['53-2=51', '10+19=29'] Exploring Operation: 51+29=80, Resulting Numbers: [80] 80,48 unequal: No Solution Exploring Operation: 51*29=1479, Resulting Numbers: [1479] 1479,48 unequal: No Solution Exploring Operation: 51-29=22, Resulting Numbers: [22] 22,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[19, 41], Operations: ['53-2=51', '51-10=41'] Exploring Operation: 19+41=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 41-19=22, Resulting Numbers: [22] 22,48 unequal: No Solution Exploring Operation: 19*41=779, Resulting Numbers: [779] 779,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[2, 19, 43], Operations: ['53-10=43'] Exploring Operation: 43-19=24, Resulting Numbers: [2, 24] Generated Node #0,2,0: 48:[2, 24] Operation: 43-19=24 Exploring Operation: 19-2=17, Resulting Numbers: [43, 17] Generated Node #0,2,1: 48:[43, 17] Operation: 19-2=17 Exploring Operation: 2+43=45, Resulting Numbers: [19, 45] Generated Node #0,2,2: 48:[19, 45] Operation: 2+43=45 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 48:[2, 24], Operations: ['53-10=43', '43-19=24'] Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[53, 10, 2, 19], Operations: [] Exploring Operation: 53-10=43, Resulting Numbers: [2, 19, 43] Generated Node #0,2: 48:[2, 19, 43] Operation: 53-10=43 Moving to Node #0,2 Current State: 48:[2, 19, 43], Operations: ['53-10=43'] Exploring Operation: 43-19=24, Resulting Numbers: [2, 24] Generated Node #0,2,0: 48:[2, 24] Operation: 43-19=24 Moving to Node #0,2,0 Current State: 48:[2, 24], Operations: ['53-10=43', '43-19=24'] Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 79, 73, 2, 35 ]
51
[ "79-35=44", "44/2=22", "73-22=51" ]
Current State: 51:[79, 73, 2, 35], Operations: [] Exploring Operation: 79-35=44, Resulting Numbers: [73, 2, 44] Generated Node #2: [73, 2, 44] from Operation: 79-35=44 Current State: 51:[73, 2, 44], Operations: ['79-35=44'] Exploring Operation: 44/2=22, Resulting Numbers: [73, 22] Generated Node #3: [73, 22] from Operation: 44/2=22 Current State: 51:[73, 22], Operations: ['79-35=44', '44/2=22'] Exploring Operation: 73-22=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[79, 73, 2, 35], Operations: [] Exploring Operation: 73-35=38, Resulting Numbers: [79, 2, 38] Generated Node #0,0: 51:[79, 2, 38] Operation: 73-35=38 Exploring Operation: 79-73=6, Resulting Numbers: [2, 35, 6] Generated Node #0,1: 51:[2, 35, 6] Operation: 79-73=6 Exploring Operation: 79-2=77, Resulting Numbers: [73, 35, 77] Generated Node #0,2: 51:[73, 35, 77] Operation: 79-2=77 Exploring Operation: 79-35=44, Resulting Numbers: [73, 2, 44] Generated Node #0,3: 51:[73, 2, 44] Operation: 79-35=44 Moving to Node #0,1 Current State: 51:[2, 35, 6], Operations: ['79-73=6'] Exploring Operation: 35+6=41, Resulting Numbers: [2, 41] Generated Node #0,1,0: 51:[2, 41] Operation: 35+6=41 Exploring Operation: 2+35=37, Resulting Numbers: [6, 37] Generated Node #0,1,1: 51:[6, 37] Operation: 2+35=37 Exploring Operation: 35-6=29, Resulting Numbers: [2, 29] Generated Node #0,1,2: 51:[2, 29] Operation: 35-6=29 Exploring Operation: 6/2=3, Resulting Numbers: [35, 3] Generated Node #0,1,3: 51:[35, 3] Operation: 6/2=3 Moving to Node #0,3 Current State: 51:[73, 2, 44], Operations: ['79-35=44'] Exploring Operation: 73-44=29, Resulting Numbers: [2, 29] Generated Node #0,3,0: 51:[2, 29] Operation: 73-44=29 Exploring Operation: 44/2=22, Resulting Numbers: [73, 22] Generated Node #0,3,1: 51:[73, 22] Operation: 44/2=22 Exploring Operation: 2+44=46, Resulting Numbers: [73, 46] Generated Node #0,3,2: 51:[73, 46] Operation: 2+44=46 Exploring Operation: 73-2=71, Resulting Numbers: [44, 71] Generated Node #0,3,3: 51:[44, 71] Operation: 73-2=71 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 51:[2, 29], Operations: ['79-35=44', '73-44=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,51 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 51:[73, 22], Operations: ['79-35=44', '44/2=22'] Exploring Operation: 73*22=1606, Resulting Numbers: [1606] 1606,51 unequal: No Solution Exploring Operation: 73+22=95, Resulting Numbers: [95] 95,51 unequal: No Solution Exploring Operation: 73-22=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[79, 73, 2, 35], Operations: [] Exploring Operation: 79-35=44, Resulting Numbers: [73, 2, 44] Generated Node #0,3: 51:[73, 2, 44] Operation: 79-35=44 Moving to Node #0,3 Current State: 51:[73, 2, 44], Operations: ['79-35=44'] Exploring Operation: 44/2=22, Resulting Numbers: [73, 22] Generated Node #0,3,1: 51:[73, 22] Operation: 44/2=22 Moving to Node #0,3,1 Current State: 51:[73, 22], Operations: ['79-35=44', '44/2=22'] Exploring Operation: 73-22=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
mult_heuristic
[ 31, 96, 1, 44 ]
41
[ "31+1=32", "96/32=3", "44-3=41" ]
Current State: 41:[31, 96, 1, 44], Operations: [] Exploring Operation: 31+1=32, Resulting Numbers: [96, 44, 32] Generated Node #2: [96, 44, 32] from Operation: 31+1=32 Current State: 41:[96, 44, 32], Operations: ['31+1=32'] Exploring Operation: 96/32=3, Resulting Numbers: [44, 3] Generated Node #3: [44, 3] from Operation: 96/32=3 Current State: 41:[44, 3], Operations: ['31+1=32', '96/32=3'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[31, 96, 1, 44], Operations: [] Exploring Operation: 96-44=52, Resulting Numbers: [31, 1, 52] Generated Node #0,0: 41:[31, 1, 52] Operation: 96-44=52 Exploring Operation: 31+1=32, Resulting Numbers: [96, 44, 32] Generated Node #0,1: 41:[96, 44, 32] Operation: 31+1=32 Exploring Operation: 96-31=65, Resulting Numbers: [1, 44, 65] Generated Node #0,2: 41:[1, 44, 65] Operation: 96-31=65 Moving to Node #0,0 Current State: 41:[31, 1, 52], Operations: ['96-44=52'] Exploring Operation: 31+1=32, Resulting Numbers: [52, 32] Generated Node #0,0,0: 41:[52, 32] Operation: 31+1=32 Exploring Operation: 31*1=31, Resulting Numbers: [52, 31] Generated Node #0,0,1: 41:[52, 31] Operation: 31*1=31 Exploring Operation: 52-1=51, Resulting Numbers: [31, 51] Generated Node #0,0,2: 41:[31, 51] Operation: 52-1=51 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[52, 32], Operations: ['96-44=52', '31+1=32'] Exploring Operation: 52+32=84, Resulting Numbers: [84] 84,41 unequal: No Solution Exploring Operation: 52*32=1664, Resulting Numbers: [1664] 1664,41 unequal: No Solution Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,41 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:[31, 51], Operations: ['96-44=52', '52-1=51'] Exploring Operation: 31+51=82, Resulting Numbers: [82] 82,41 unequal: No Solution Exploring Operation: 51-31=20, Resulting Numbers: [20] 20,41 unequal: No Solution Exploring Operation: 31*51=1581, Resulting Numbers: [1581] 1581,41 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:[52, 31], Operations: ['96-44=52', '31*1=31'] Exploring Operation: 52+31=83, Resulting Numbers: [83] 83,41 unequal: No Solution Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 52*31=1612, Resulting Numbers: [1612] 1612,41 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:[96, 44, 32], Operations: ['31+1=32'] Exploring Operation: 96/32=3, Resulting Numbers: [44, 3] Generated Node #0,1,0: 41:[44, 3] Operation: 96/32=3 Exploring Operation: 96-44=52, Resulting Numbers: [32, 52] Generated Node #0,1,1: 41:[32, 52] Operation: 96-44=52 Exploring Operation: 96-32=64, Resulting Numbers: [44, 64] Generated Node #0,1,2: 41:[44, 64] Operation: 96-32=64 Moving to Node #0,2 Current State: 41:[1, 44, 65], Operations: ['96-31=65'] Exploring Operation: 44-1=43, Resulting Numbers: [65, 43] Generated Node #0,2,0: 41:[65, 43] Operation: 44-1=43 Exploring Operation: 1*44=44, Resulting Numbers: [65, 44] Generated Node #0,2,1: 41:[65, 44] Operation: 1*44=44 Exploring Operation: 65-1=64, Resulting Numbers: [44, 64] Generated Node #0,2,2: 41:[44, 64] Operation: 65-1=64 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 41:[65, 43], Operations: ['96-31=65', '44-1=43'] Exploring Operation: 65-43=22, Resulting Numbers: [22] 22,41 unequal: No Solution Exploring Operation: 65*43=2795, Resulting Numbers: [2795] 2795,41 unequal: No Solution Exploring Operation: 65+43=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 #0,2,2 Current State: 41:[44, 64], Operations: ['96-31=65', '65-1=64'] Exploring Operation: 44+64=108, Resulting Numbers: [108] 108,41 unequal: No Solution Exploring Operation: 44*64=2816, Resulting Numbers: [2816] 2816,41 unequal: No Solution Exploring Operation: 64-44=20, Resulting Numbers: [20] 20,41 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:[65, 44], Operations: ['96-31=65', '1*44=44'] Exploring Operation: 65-44=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 65*44=2860, Resulting Numbers: [2860] 2860,41 unequal: No Solution Exploring Operation: 65+44=109, Resulting Numbers: [109] 109,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 41:[32, 52], Operations: ['31+1=32', '96-44=52'] Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,41 unequal: No Solution Exploring Operation: 32+52=84, Resulting Numbers: [84] 84,41 unequal: No Solution Exploring Operation: 32*52=1664, Resulting Numbers: [1664] 1664,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[44, 64], Operations: ['31+1=32', '96-32=64'] Exploring Operation: 64-44=20, Resulting Numbers: [20] 20,41 unequal: No Solution Exploring Operation: 44*64=2816, Resulting Numbers: [2816] 2816,41 unequal: No Solution Exploring Operation: 44+64=108, Resulting Numbers: [108] 108,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[44, 3], Operations: ['31+1=32', '96/32=3'] Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,41 unequal: No Solution Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[31, 96, 1, 44], Operations: [] Exploring Operation: 31+1=32, Resulting Numbers: [96, 44, 32] Generated Node #0,1: 41:[96, 44, 32] Operation: 31+1=32 Moving to Node #0,1 Current State: 41:[96, 44, 32], Operations: ['31+1=32'] Exploring Operation: 96/32=3, Resulting Numbers: [44, 3] Generated Node #0,1,0: 41:[44, 3] Operation: 96/32=3 Moving to Node #0,1,0 Current State: 41:[44, 3], Operations: ['31+1=32', '96/32=3'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
0.963542
hs_3
sum_heuristic
[ 47, 8, 89, 27 ]
44
[ "47+89=136", "136/8=17", "27+17=44" ]
Current State: 44:[47, 8, 89, 27], Operations: [] Exploring Operation: 47+89=136, Resulting Numbers: [8, 27, 136] Generated Node #2: [8, 27, 136] from Operation: 47+89=136 Current State: 44:[8, 27, 136], Operations: ['47+89=136'] Exploring Operation: 136/8=17, Resulting Numbers: [27, 17] Generated Node #3: [27, 17] from Operation: 136/8=17 Current State: 44:[27, 17], Operations: ['47+89=136', '136/8=17'] Exploring Operation: 27+17=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[47, 8, 89, 27], Operations: [] Exploring Operation: 89-47=42, Resulting Numbers: [8, 27, 42] Generated Node #0,0: 44:[8, 27, 42] Operation: 89-47=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[8, 27, 42], Operations: ['89-47=42'] Exploring Operation: 27-8=19, Resulting Numbers: [42, 19] Generated Node #0,0,0: 44:[42, 19] Operation: 27-8=19 Moving to Node #0,0,0 Current State: 44:[42, 19], Operations: ['89-47=42', '27-8=19'] Exploring Operation: 42-19=23, Resulting Numbers: [23] 23,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 35, 22, 41, 54 ]
78
[ "41-35=6", "22*6=132", "132-54=78" ]
Current State: 78:[35, 22, 41, 54], Operations: [] Exploring Operation: 41-35=6, Resulting Numbers: [22, 54, 6] Generated Node #2: [22, 54, 6] from Operation: 41-35=6 Current State: 78:[22, 54, 6], Operations: ['41-35=6'] Exploring Operation: 22*6=132, Resulting Numbers: [54, 132] Generated Node #3: [54, 132] from Operation: 22*6=132 Current State: 78:[54, 132], Operations: ['41-35=6', '22*6=132'] Exploring Operation: 132-54=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[35, 22, 41, 54], Operations: [] Exploring Operation: 22+54=76, Resulting Numbers: [35, 41, 76] Generated Node #0,0: 78:[35, 41, 76] Operation: 22+54=76 Exploring Operation: 54-41=13, Resulting Numbers: [35, 22, 13] Generated Node #0,1: 78:[35, 22, 13] Operation: 54-41=13 Exploring Operation: 54-35=19, Resulting Numbers: [22, 41, 19] Generated Node #0,2: 78:[22, 41, 19] Operation: 54-35=19 Moving to Node #0,0 Current State: 78:[35, 41, 76], Operations: ['22+54=76'] Exploring Operation: 76-35=41, Resulting Numbers: [41, 41] Generated Node #0,0,0: 78:[41, 41] Operation: 76-35=41 Exploring Operation: 41-35=6, Resulting Numbers: [76, 6] Generated Node #0,0,1: 78:[76, 6] Operation: 41-35=6 Exploring Operation: 35+41=76, Resulting Numbers: [76, 76] Generated Node #0,0,2: 78:[76, 76] Operation: 35+41=76 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[76, 6], Operations: ['22+54=76', '41-35=6'] Exploring Operation: 76*6=456, Resulting Numbers: [456] 456,78 unequal: No Solution Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,78 unequal: No Solution Exploring Operation: 76+6=82, Resulting Numbers: [82] 82,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[41, 41], Operations: ['22+54=76', '76-35=41'] Exploring Operation: 41-41=0, Resulting Numbers: [0] 0,78 unequal: No Solution Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,78 unequal: No Solution Exploring Operation: 41/41=1, Resulting Numbers: [1] 1,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 78:[76, 76], Operations: ['22+54=76', '35+41=76'] Exploring Operation: 76/76=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 76-76=0, Resulting Numbers: [0] 0,78 unequal: No Solution Exploring Operation: 76+76=152, Resulting Numbers: [152] 152,78 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: 78:[35, 22, 13], Operations: ['54-41=13'] Exploring Operation: 35-13=22, Resulting Numbers: [22, 22] Generated Node #0,1,0: 78:[22, 22] Operation: 35-13=22 Exploring Operation: 35-22=13, Resulting Numbers: [13, 13] Generated Node #0,1,1: 78:[13, 13] Operation: 35-22=13 Exploring Operation: 22-13=9, Resulting Numbers: [35, 9] Generated Node #0,1,2: 78:[35, 9] Operation: 22-13=9 Moving to Node #0,2 Current State: 78:[22, 41, 19], Operations: ['54-35=19'] Exploring Operation: 22-19=3, Resulting Numbers: [41, 3] Generated Node #0,2,0: 78:[41, 3] Operation: 22-19=3 Exploring Operation: 41-19=22, Resulting Numbers: [22, 22] Generated Node #0,2,1: 78:[22, 22] Operation: 41-19=22 Exploring Operation: 22+19=41, Resulting Numbers: [41, 41] Generated Node #0,2,2: 78:[41, 41] Operation: 22+19=41 Moving to Node #0,1,1 Current State: 78:[13, 13], Operations: ['54-41=13', '35-22=13'] Exploring Operation: 13/13=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 13-13=0, Resulting Numbers: [0] 0,78 unequal: No Solution Exploring Operation: 13+13=26, Resulting Numbers: [26] 26,78 unequal: No Solution Moving to Node #0,2,0 Current State: 78:[41, 3], Operations: ['54-35=19', '22-19=3'] Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,78 unequal: No Solution Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,78 unequal: No Solution Exploring Operation: 41*3=123, Resulting Numbers: [123] 123,78 unequal: No Solution Moving to Node #0,2,2 Current State: 78:[41, 41], Operations: ['54-35=19', '22+19=41'] Exploring Operation: 41-41=0, Resulting Numbers: [0] 0,78 unequal: No Solution Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,78 unequal: No Solution Exploring Operation: 41/41=1, Resulting Numbers: [1] 1,78 unequal: No Solution Moving to Node #0,1,2 Current State: 78:[35, 9], Operations: ['54-41=13', '22-13=9'] Exploring Operation: 35*9=315, Resulting Numbers: [315] 315,78 unequal: No Solution Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,78 unequal: No Solution Moving to Node #0,2,1 Current State: 78:[22, 22], Operations: ['54-35=19', '41-19=22'] Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,78 unequal: No Solution Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[22, 22], Operations: ['54-41=13', '35-13=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,78 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,78 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 74, 21, 97, 74 ]
75
[ "74/74=1", "97-21=76", "76-1=75" ]
Current State: 75:[74, 21, 97, 74], Operations: [] Exploring Operation: 74/74=1, Resulting Numbers: [21, 97, 1] Generated Node #2: [21, 97, 1] from Operation: 74/74=1 Current State: 75:[21, 97, 1], Operations: ['74/74=1'] Exploring Operation: 97-21=76, Resulting Numbers: [1, 76] Generated Node #3: [1, 76] from Operation: 97-21=76 Current State: 75:[1, 76], Operations: ['74/74=1', '97-21=76'] Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[74, 21, 97, 74], Operations: [] Exploring Operation: 74/74=1, Resulting Numbers: [21, 97, 1] Generated Node #0,0: 75:[21, 97, 1] Operation: 74/74=1 Exploring Operation: 97-74=23, Resulting Numbers: [74, 21, 23] Generated Node #0,1: 75:[74, 21, 23] Operation: 97-74=23 Exploring Operation: 97-21=76, Resulting Numbers: [74, 74, 76] Generated Node #0,2: 75:[74, 74, 76] Operation: 97-21=76 Exploring Operation: 97-74=23, Resulting Numbers: [21, 74, 23] Generated Node #0,3: 75:[21, 74, 23] Operation: 97-74=23 Moving to Node #0,2 Current State: 75:[74, 74, 76], Operations: ['97-21=76'] Exploring Operation: 74-74=0, Resulting Numbers: [76, 0] Generated Node #0,2,0: 75:[76, 0] Operation: 74-74=0 Exploring Operation: 76-74=2, Resulting Numbers: [74, 2] Generated Node #0,2,1: 75:[74, 2] Operation: 76-74=2 Exploring Operation: 74/74=1, Resulting Numbers: [76, 1] Generated Node #0,2,2: 75:[76, 1] Operation: 74/74=1 Exploring Operation: 76-74=2, Resulting Numbers: [74, 2] Generated Node #0,2,3: 75:[74, 2] Operation: 76-74=2 Moving to Node #0,3 Current State: 75:[21, 74, 23], Operations: ['97-74=23'] Exploring Operation: 21+23=44, Resulting Numbers: [74, 44] Generated Node #0,3,0: 75:[74, 44] Operation: 21+23=44 Exploring Operation: 21+74=95, Resulting Numbers: [23, 95] Generated Node #0,3,1: 75:[23, 95] Operation: 21+74=95 Exploring Operation: 74-21=53, Resulting Numbers: [23, 53] Generated Node #0,3,2: 75:[23, 53] Operation: 74-21=53 Exploring Operation: 23-21=2, Resulting Numbers: [74, 2] Generated Node #0,3,3: 75:[74, 2] Operation: 23-21=2 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 75:[74, 2], Operations: ['97-74=23', '23-21=2'] Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,75 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,75 unequal: No Solution Exploring Operation: 74*2=148, Resulting Numbers: [148] 148,75 unequal: No Solution Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,75 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 #0,3,0 Current State: 75:[74, 44], Operations: ['97-74=23', '21+23=44'] Exploring Operation: 74-44=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 74*44=3256, Resulting Numbers: [3256] 3256,75 unequal: No Solution Exploring Operation: 74+44=118, Resulting Numbers: [118] 118,75 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 #0,3,1 Current State: 75:[23, 95], Operations: ['97-74=23', '21+74=95'] Exploring Operation: 23+95=118, Resulting Numbers: [118] 118,75 unequal: No Solution Exploring Operation: 95-23=72, Resulting Numbers: [72] 72,75 unequal: No Solution Exploring Operation: 23*95=2185, Resulting Numbers: [2185] 2185,75 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 #0,3,2 Current State: 75:[23, 53], Operations: ['97-74=23', '74-21=53'] Exploring Operation: 53-23=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 23+53=76, Resulting Numbers: [76] 76,75 unequal: No Solution Exploring Operation: 23*53=1219, Resulting Numbers: [1219] 1219,75 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: 75:[74, 21, 23], Operations: ['97-74=23'] Exploring Operation: 23-21=2, Resulting Numbers: [74, 2] Generated Node #0,1,0: 75:[74, 2] Operation: 23-21=2 Exploring Operation: 74-21=53, Resulting Numbers: [23, 53] Generated Node #0,1,1: 75:[23, 53] Operation: 74-21=53 Exploring Operation: 74+21=95, Resulting Numbers: [23, 95] Generated Node #0,1,2: 75:[23, 95] Operation: 74+21=95 Exploring Operation: 21+23=44, Resulting Numbers: [74, 44] Generated Node #0,1,3: 75:[74, 44] Operation: 21+23=44 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 75:[74, 2], Operations: ['97-74=23', '23-21=2'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,75 unequal: No Solution Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,75 unequal: No Solution Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 74*2=148, Resulting Numbers: [148] 148,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 75:[74, 44], Operations: ['97-74=23', '21+23=44'] Exploring Operation: 74*44=3256, Resulting Numbers: [3256] 3256,75 unequal: No Solution Exploring Operation: 74+44=118, Resulting Numbers: [118] 118,75 unequal: No Solution Exploring Operation: 74-44=30, Resulting Numbers: [30] 30,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 75:[23, 95], Operations: ['97-74=23', '74+21=95'] Exploring Operation: 95-23=72, Resulting Numbers: [72] 72,75 unequal: No Solution Exploring Operation: 23*95=2185, Resulting Numbers: [2185] 2185,75 unequal: No Solution Exploring Operation: 23+95=118, Resulting Numbers: [118] 118,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 75:[23, 53], Operations: ['97-74=23', '74-21=53'] Exploring Operation: 23+53=76, Resulting Numbers: [76] 76,75 unequal: No Solution Exploring Operation: 53-23=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 23*53=1219, Resulting Numbers: [1219] 1219,75 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: 75:[21, 97, 1], Operations: ['74/74=1'] Exploring Operation: 97-1=96, Resulting Numbers: [21, 96] Generated Node #0,0,0: 75:[21, 96] Operation: 97-1=96 Exploring Operation: 21+1=22, Resulting Numbers: [97, 22] Generated Node #0,0,1: 75:[97, 22] Operation: 21+1=22 Exploring Operation: 97-21=76, Resulting Numbers: [1, 76] Generated Node #0,0,2: 75:[1, 76] Operation: 97-21=76 Exploring Operation: 21*1=21, Resulting Numbers: [97, 21] Generated Node #0,0,3: 75:[97, 21] Operation: 21*1=21 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 75:[1, 76], Operations: ['74/74=1', '97-21=76'] Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[74, 21, 97, 74], Operations: [] Exploring Operation: 74/74=1, Resulting Numbers: [21, 97, 1] Generated Node #0,0: 75:[21, 97, 1] Operation: 74/74=1 Moving to Node #0,0 Current State: 75:[21, 97, 1], Operations: ['74/74=1'] Exploring Operation: 97-21=76, Resulting Numbers: [1, 76] Generated Node #0,0,2: 75:[1, 76] Operation: 97-21=76 Moving to Node #0,0,2 Current State: 75:[1, 76], Operations: ['74/74=1', '97-21=76'] Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.955729
hs_4
sum_heuristic
[ 86, 82, 67, 82 ]
19
[ "86+82=168", "67+82=149", "168-149=19" ]
Current State: 19:[86, 82, 67, 82], Operations: [] Exploring Operation: 86+82=168, Resulting Numbers: [67, 168] Generated Node #2: [67, 168] from Operation: 86+82=168 Current State: 19:[67, 168], Operations: ['86+82=168'] Exploring Operation: 67+82=149, Resulting Numbers: [168, 149] Generated Node #3: [168, 149] from Operation: 67+82=149 Current State: 19:[168, 149], Operations: ['86+82=168', '67+82=149'] Exploring Operation: 168-149=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[86, 82, 67, 82], Operations: [] Exploring Operation: 86-82=4, Resulting Numbers: [67, 82, 4] Generated Node #0,0: 19:[67, 82, 4] Operation: 86-82=4 Exploring Operation: 86-82=4, Resulting Numbers: [82, 67, 4] Generated Node #0,1: 19:[82, 67, 4] Operation: 86-82=4 Exploring Operation: 86-67=19, Resulting Numbers: [82, 82, 19] Generated Node #0,2: 19:[82, 82, 19] Operation: 86-67=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[67, 82, 4], Operations: ['86-82=4'] Exploring Operation: 82-4=78, Resulting Numbers: [67, 78] Generated Node #0,0,0: 19:[67, 78] Operation: 82-4=78 Exploring Operation: 82-67=15, Resulting Numbers: [4, 15] Generated Node #0,0,1: 19:[4, 15] Operation: 82-67=15 Exploring Operation: 67-4=63, Resulting Numbers: [82, 63] Generated Node #0,0,2: 19:[82, 63] Operation: 67-4=63 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 19:[4, 15], Operations: ['86-82=4', '82-67=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,19 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,19 unequal: No Solution Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[86, 82, 67, 82], Operations: [] Exploring Operation: 86-82=4, Resulting Numbers: [67, 82, 4] Generated Node #0,0: 19:[67, 82, 4] Operation: 86-82=4 Moving to Node #0,0 Current State: 19:[67, 82, 4], Operations: ['86-82=4'] Exploring Operation: 82-67=15, Resulting Numbers: [4, 15] Generated Node #0,0,1: 19:[4, 15] Operation: 82-67=15 Moving to Node #0,0,1 Current State: 19:[4, 15], Operations: ['86-82=4', '82-67=15'] Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 74, 11, 57, 92 ]
50
[ "74+11=85", "92-57=35", "85-35=50" ]
Current State: 50:[74, 11, 57, 92], Operations: [] Exploring Operation: 74+11=85, Resulting Numbers: [57, 92, 85] Generated Node #2: [57, 92, 85] from Operation: 74+11=85 Current State: 50:[57, 92, 85], Operations: ['74+11=85'] Exploring Operation: 92-57=35, Resulting Numbers: [85, 35] Generated Node #3: [85, 35] from Operation: 92-57=35 Current State: 50:[85, 35], Operations: ['74+11=85', '92-57=35'] Exploring Operation: 85-35=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[74, 11, 57, 92], Operations: [] Exploring Operation: 74-57=17, Resulting Numbers: [11, 92, 17] Generated Node #0,0: 50:[11, 92, 17] Operation: 74-57=17 Exploring Operation: 74-11=63, Resulting Numbers: [57, 92, 63] Generated Node #0,1: 50:[57, 92, 63] Operation: 74-11=63 Exploring Operation: 92-57=35, Resulting Numbers: [74, 11, 35] Generated Node #0,2: 50:[74, 11, 35] Operation: 92-57=35 Exploring Operation: 92-74=18, Resulting Numbers: [11, 57, 18] Generated Node #0,3: 50:[11, 57, 18] Operation: 92-74=18 Start Sub Search at level 1: Moving to Node #0,3 Current State: 50:[11, 57, 18], Operations: ['92-74=18'] Exploring Operation: 57-18=39, Resulting Numbers: [11, 39] Generated Node #0,3,0: 50:[11, 39] Operation: 57-18=39 Exploring Operation: 57-11=46, Resulting Numbers: [18, 46] Generated Node #0,3,1: 50:[18, 46] Operation: 57-11=46 Exploring Operation: 18-11=7, Resulting Numbers: [57, 7] Generated Node #0,3,2: 50:[57, 7] Operation: 18-11=7 Exploring Operation: 11+18=29, Resulting Numbers: [57, 29] Generated Node #0,3,3: 50:[57, 29] Operation: 11+18=29 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 50:[57, 7], Operations: ['92-74=18', '18-11=7'] Exploring Operation: 57+7=64, Resulting Numbers: [64] 64,50 unequal: No Solution Exploring Operation: 57*7=399, Resulting Numbers: [399] 399,50 unequal: No Solution Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[74, 11, 57, 92], Operations: [] Exploring Operation: 92-74=18, Resulting Numbers: [11, 57, 18] Generated Node #0,3: 50:[11, 57, 18] Operation: 92-74=18 Moving to Node #0,3 Current State: 50:[11, 57, 18], Operations: ['92-74=18'] Exploring Operation: 18-11=7, Resulting Numbers: [57, 7] Generated Node #0,3,2: 50:[57, 7] Operation: 18-11=7 Moving to Node #0,3,2 Current State: 50:[57, 7], Operations: ['92-74=18', '18-11=7'] Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 42, 64, 93, 18 ]
97
[ "64-42=22", "93-18=75", "22+75=97" ]
Current State: 97:[42, 64, 93, 18], Operations: [] Exploring Operation: 64-42=22, Resulting Numbers: [93, 18, 22] Generated Node #2: [93, 18, 22] from Operation: 64-42=22 Current State: 97:[93, 18, 22], Operations: ['64-42=22'] Exploring Operation: 93-18=75, Resulting Numbers: [22, 75] Generated Node #3: [22, 75] from Operation: 93-18=75 Current State: 97:[22, 75], Operations: ['64-42=22', '93-18=75'] Exploring Operation: 22+75=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[42, 64, 93, 18], Operations: [] Exploring Operation: 64+18=82, Resulting Numbers: [42, 93, 82] Generated Node #0,0: 97:[42, 93, 82] Operation: 64+18=82 Exploring Operation: 42+64=106, Resulting Numbers: [93, 18, 106] Generated Node #0,1: 97:[93, 18, 106] Operation: 42+64=106 Exploring Operation: 42+18=60, Resulting Numbers: [64, 93, 60] Generated Node #0,2: 97:[64, 93, 60] Operation: 42+18=60 Moving to Node #0,0 Current State: 97:[42, 93, 82], Operations: ['64+18=82'] Exploring Operation: 42+93=135, Resulting Numbers: [82, 135] Generated Node #0,0,0: 97:[82, 135] Operation: 42+93=135 Exploring Operation: 42+82=124, Resulting Numbers: [93, 124] Generated Node #0,0,1: 97:[93, 124] Operation: 42+82=124 Exploring Operation: 93-42=51, Resulting Numbers: [82, 51] Generated Node #0,0,2: 97:[82, 51] Operation: 93-42=51 Moving to Node #0,2 Current State: 97:[64, 93, 60], Operations: ['42+18=60'] Exploring Operation: 93+60=153, Resulting Numbers: [64, 153] Generated Node #0,2,0: 97:[64, 153] Operation: 93+60=153 Exploring Operation: 64+93=157, Resulting Numbers: [60, 157] Generated Node #0,2,1: 97:[60, 157] Operation: 64+93=157 Exploring Operation: 64+60=124, Resulting Numbers: [93, 124] Generated Node #0,2,2: 97:[93, 124] Operation: 64+60=124 Moving to Node #0,1 Current State: 97:[93, 18, 106], Operations: ['42+64=106'] Exploring Operation: 93-18=75, Resulting Numbers: [106, 75] Generated Node #0,1,0: 97:[106, 75] Operation: 93-18=75 Exploring Operation: 93+18=111, Resulting Numbers: [106, 111] Generated Node #0,1,1: 97:[106, 111] Operation: 93+18=111 Exploring Operation: 106-18=88, Resulting Numbers: [93, 88] Generated Node #0,1,2: 97:[93, 88] Operation: 106-18=88 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 97:[93, 88], Operations: ['42+64=106', '106-18=88'] Exploring Operation: 93+88=181, Resulting Numbers: [181] 181,97 unequal: No Solution Exploring Operation: 93*88=8184, Resulting Numbers: [8184] 8184,97 unequal: No Solution Exploring Operation: 93-88=5, Resulting Numbers: [5] 5,97 unequal: No Solution No 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: 97:[106, 111], Operations: ['42+64=106', '93+18=111'] Exploring Operation: 106+111=217, Resulting Numbers: [217] 217,97 unequal: No Solution Exploring Operation: 106*111=11766, Resulting Numbers: [11766] 11766,97 unequal: No Solution Exploring Operation: 111-106=5, Resulting Numbers: [5] 5,97 unequal: No Solution No 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: 97:[106, 75], Operations: ['42+64=106', '93-18=75'] Exploring Operation: 106-75=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 106+75=181, Resulting Numbers: [181] 181,97 unequal: No Solution Exploring Operation: 106*75=7950, Resulting Numbers: [7950] 7950,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 97:[93, 124], Operations: ['64+18=82', '42+82=124'] Exploring Operation: 93*124=11532, Resulting Numbers: [11532] 11532,97 unequal: No Solution Exploring Operation: 93+124=217, Resulting Numbers: [217] 217,97 unequal: No Solution Exploring Operation: 124-93=31, Resulting Numbers: [31] 31,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[93, 124], Operations: ['42+18=60', '64+60=124'] Exploring Operation: 93+124=217, Resulting Numbers: [217] 217,97 unequal: No Solution Exploring Operation: 93*124=11532, Resulting Numbers: [11532] 11532,97 unequal: No Solution Exploring Operation: 124-93=31, Resulting Numbers: [31] 31,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[82, 135], Operations: ['64+18=82', '42+93=135'] Exploring Operation: 82+135=217, Resulting Numbers: [217] 217,97 unequal: No Solution Exploring Operation: 135-82=53, Resulting Numbers: [53] 53,97 unequal: No Solution Exploring Operation: 82*135=11070, Resulting Numbers: [11070] 11070,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[82, 51], Operations: ['64+18=82', '93-42=51'] Exploring Operation: 82+51=133, Resulting Numbers: [133] 133,97 unequal: No Solution Exploring Operation: 82-51=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 82*51=4182, Resulting Numbers: [4182] 4182,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[64, 153], Operations: ['42+18=60', '93+60=153'] Exploring Operation: 64+153=217, Resulting Numbers: [217] 217,97 unequal: No Solution Exploring Operation: 64*153=9792, Resulting Numbers: [9792] 9792,97 unequal: No Solution Exploring Operation: 153-64=89, Resulting Numbers: [89] 89,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[60, 157], Operations: ['42+18=60', '64+93=157'] Exploring Operation: 60+157=217, Resulting Numbers: [217] 217,97 unequal: No Solution Exploring Operation: 60*157=9420, Resulting Numbers: [9420] 9420,97 unequal: No Solution Exploring Operation: 157-60=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[42, 64, 93, 18], Operations: [] Exploring Operation: 42+18=60, Resulting Numbers: [64, 93, 60] Generated Node #0,2: 97:[64, 93, 60] Operation: 42+18=60 Moving to Node #0,2 Current State: 97:[64, 93, 60], Operations: ['42+18=60'] Exploring Operation: 64+93=157, Resulting Numbers: [60, 157] Generated Node #0,2,1: 97:[60, 157] Operation: 64+93=157 Moving to Node #0,2,1 Current State: 97:[60, 157], Operations: ['42+18=60', '64+93=157'] Exploring Operation: 157-60=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
0.962674
hs_3
mult_heuristic
[ 47, 47, 60, 48 ]
12
[ "47-47=0", "60-48=12", "0+12=12" ]
Current State: 12:[47, 47, 60, 48], Operations: [] Exploring Operation: 47-47=0, Resulting Numbers: [60, 48, 0] Generated Node #2: [60, 48, 0] from Operation: 47-47=0 Current State: 12:[60, 48, 0], Operations: ['47-47=0'] Exploring Operation: 60-48=12, Resulting Numbers: [0, 12] Generated Node #3: [0, 12] from Operation: 60-48=12 Current State: 12:[0, 12], Operations: ['47-47=0', '60-48=12'] Exploring Operation: 0+12=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[47, 47, 60, 48], Operations: [] Exploring Operation: 60-47=13, Resulting Numbers: [47, 48, 13] Generated Node #0,0: 12:[47, 48, 13] Operation: 60-47=13 Exploring Operation: 60-47=13, Resulting Numbers: [47, 48, 13] Generated Node #0,1: 12:[47, 48, 13] Operation: 60-47=13 Exploring Operation: 60-48=12, Resulting Numbers: [47, 47, 12] Generated Node #0,2: 12:[47, 47, 12] Operation: 60-48=12 Moving to Node #0,2 Current State: 12:[47, 47, 12], Operations: ['60-48=12'] Exploring Operation: 47-12=35, Resulting Numbers: [47, 35] Generated Node #0,2,0: 12:[47, 35] Operation: 47-12=35 Exploring Operation: 47/47=1, Resulting Numbers: [12, 1] Generated Node #0,2,1: 12:[12, 1] Operation: 47/47=1 Exploring Operation: 47-47=0, Resulting Numbers: [12, 0] Generated Node #0,2,2: 12:[12, 0] Operation: 47-47=0 Moving to Node #0,0 Current State: 12:[47, 48, 13], Operations: ['60-47=13'] Exploring Operation: 47-13=34, Resulting Numbers: [48, 34] Generated Node #0,0,0: 12:[48, 34] Operation: 47-13=34 Exploring Operation: 48-47=1, Resulting Numbers: [13, 1] Generated Node #0,0,1: 12:[13, 1] Operation: 48-47=1 Exploring Operation: 48-13=35, Resulting Numbers: [47, 35] Generated Node #0,0,2: 12:[47, 35] Operation: 48-13=35 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[13, 1], Operations: ['60-47=13', '48-47=1'] Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,12 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[47, 47, 60, 48], Operations: [] Exploring Operation: 60-47=13, Resulting Numbers: [47, 48, 13] Generated Node #0,0: 12:[47, 48, 13] Operation: 60-47=13 Moving to Node #0,0 Current State: 12:[47, 48, 13], Operations: ['60-47=13'] Exploring Operation: 48-47=1, Resulting Numbers: [13, 1] Generated Node #0,0,1: 12:[13, 1] Operation: 48-47=1 Moving to Node #0,0,1 Current State: 12:[13, 1], Operations: ['60-47=13', '48-47=1'] Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 41, 2, 34, 58 ]
82
[ "41+58=99", "34/2=17", "99-17=82" ]
Current State: 82:[41, 2, 34, 58], Operations: [] Exploring Operation: 41+58=99, Resulting Numbers: [2, 34, 99] Generated Node #2: [2, 34, 99] from Operation: 41+58=99 Current State: 82:[2, 34, 99], Operations: ['41+58=99'] Exploring Operation: 34/2=17, Resulting Numbers: [99, 17] Generated Node #3: [99, 17] from Operation: 34/2=17 Current State: 82:[99, 17], Operations: ['41+58=99', '34/2=17'] Exploring Operation: 99-17=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[41, 2, 34, 58], Operations: [] Exploring Operation: 58-34=24, Resulting Numbers: [41, 2, 24] Generated Node #0,0: 82:[41, 2, 24] Operation: 58-34=24 Exploring Operation: 34+58=92, Resulting Numbers: [41, 2, 92] Generated Node #0,1: 82:[41, 2, 92] Operation: 34+58=92 Moving to Node #0,1 Current State: 82:[41, 2, 92], Operations: ['34+58=92'] Exploring Operation: 92/2=46, Resulting Numbers: [41, 46] Generated Node #0,1,0: 82:[41, 46] Operation: 92/2=46 Exploring Operation: 92-2=90, Resulting Numbers: [41, 90] Generated Node #0,1,1: 82:[41, 90] Operation: 92-2=90 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 82:[41, 46], Operations: ['34+58=92', '92/2=46'] Exploring Operation: 41+46=87, Resulting Numbers: [87] 87,82 unequal: No Solution Exploring Operation: 46-41=5, Resulting Numbers: [5] 5,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 82:[41, 90], Operations: ['34+58=92', '92-2=90'] Exploring Operation: 41+90=131, Resulting Numbers: [131] 131,82 unequal: No Solution Exploring Operation: 90-41=49, Resulting Numbers: [49] 49,82 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: 82:[41, 2, 24], Operations: ['58-34=24'] Exploring Operation: 24/2=12, Resulting Numbers: [41, 12] Generated Node #0,0,0: 82:[41, 12] Operation: 24/2=12 Exploring Operation: 2*24=48, Resulting Numbers: [41, 48] Generated Node #0,0,1: 82:[41, 48] Operation: 2*24=48 Moving to Node #0,0,1 Current State: 82:[41, 48], Operations: ['58-34=24', '2*24=48'] Exploring Operation: 48-41=7, Resulting Numbers: [7] 7,82 unequal: No Solution Exploring Operation: 41+48=89, Resulting Numbers: [89] 89,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[41, 12], Operations: ['58-34=24', '24/2=12'] Exploring Operation: 41-12=29, Resulting Numbers: [29] 29,82 unequal: No Solution Exploring Operation: 41+12=53, Resulting Numbers: [53] 53,82 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 1, 38, 11, 89 ]
62
[ "1*38=38", "11+89=100", "100-38=62" ]
Current State: 62:[1, 38, 11, 89], Operations: [] Exploring Operation: 1*38=38, Resulting Numbers: [11, 89, 38] Generated Node #2: [11, 89, 38] from Operation: 1*38=38 Current State: 62:[11, 89, 38], Operations: ['1*38=38'] Exploring Operation: 11+89=100, Resulting Numbers: [38, 100] Generated Node #3: [38, 100] from Operation: 11+89=100 Current State: 62:[38, 100], Operations: ['1*38=38', '11+89=100'] Exploring Operation: 100-38=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[1, 38, 11, 89], Operations: [] Exploring Operation: 89-11=78, Resulting Numbers: [1, 38, 78] Generated Node #0,0: 62:[1, 38, 78] Operation: 89-11=78 Exploring Operation: 89-38=51, Resulting Numbers: [1, 11, 51] Generated Node #0,1: 62:[1, 11, 51] Operation: 89-38=51 Exploring Operation: 38-11=27, Resulting Numbers: [1, 89, 27] Generated Node #0,2: 62:[1, 89, 27] Operation: 38-11=27 Moving to Node #0,1 Current State: 62:[1, 11, 51], Operations: ['89-38=51'] Exploring Operation: 11+51=62, Resulting Numbers: [1, 62] Generated Node #0,1,0: 62:[1, 62] Operation: 11+51=62 Exploring Operation: 51-11=40, Resulting Numbers: [1, 40] Generated Node #0,1,1: 62:[1, 40] Operation: 51-11=40 Exploring Operation: 11-1=10, Resulting Numbers: [51, 10] Generated Node #0,1,2: 62:[51, 10] Operation: 11-1=10 Moving to Node #0,0 Current State: 62:[1, 38, 78], Operations: ['89-11=78'] Exploring Operation: 78-38=40, Resulting Numbers: [1, 40] Generated Node #0,0,0: 62:[1, 40] Operation: 78-38=40 Exploring Operation: 78-1=77, Resulting Numbers: [38, 77] Generated Node #0,0,1: 62:[38, 77] Operation: 78-1=77 Exploring Operation: 38-1=37, Resulting Numbers: [78, 37] Generated Node #0,0,2: 62:[78, 37] Operation: 38-1=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[1, 40], Operations: ['89-11=78', '78-38=40'] Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,62 unequal: No Solution Exploring Operation: 1*40=40, Resulting Numbers: [40] 40,62 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 62:[38, 77], Operations: ['89-11=78', '78-1=77'] Exploring Operation: 38+77=115, Resulting Numbers: [115] 115,62 unequal: No Solution Exploring Operation: 38*77=2926, Resulting Numbers: [2926] 2926,62 unequal: No Solution Exploring Operation: 77-38=39, Resulting Numbers: [39] 39,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 62:[78, 37], Operations: ['89-11=78', '38-1=37'] Exploring Operation: 78-37=41, Resulting Numbers: [41] 41,62 unequal: No Solution Exploring Operation: 78*37=2886, Resulting Numbers: [2886] 2886,62 unequal: No Solution Exploring Operation: 78+37=115, Resulting Numbers: [115] 115,62 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: 62:[1, 89, 27], Operations: ['38-11=27'] Exploring Operation: 89-27=62, Resulting Numbers: [1, 62] Generated Node #0,2,0: 62:[1, 62] Operation: 89-27=62 Exploring Operation: 1+27=28, Resulting Numbers: [89, 28] Generated Node #0,2,1: 62:[89, 28] Operation: 1+27=28 Exploring Operation: 89-1=88, Resulting Numbers: [27, 88] Generated Node #0,2,2: 62:[27, 88] Operation: 89-1=88 Moving to Node #0,1,0 Current State: 62:[1, 62], Operations: ['89-38=51', '11+51=62'] Exploring Operation: 1*62=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[1, 38, 11, 89], Operations: [] Exploring Operation: 89-38=51, Resulting Numbers: [1, 11, 51] Generated Node #0,1: 62:[1, 11, 51] Operation: 89-38=51 Moving to Node #0,1 Current State: 62:[1, 11, 51], Operations: ['89-38=51'] Exploring Operation: 11+51=62, Resulting Numbers: [1, 62] Generated Node #0,1,0: 62:[1, 62] Operation: 11+51=62 Moving to Node #0,1,0 Current State: 62:[1, 62], Operations: ['89-38=51', '11+51=62'] Exploring Operation: 1*62=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.977431
hs_3
sum_heuristic
[ 85, 33, 59, 89 ]
82
[ "85-33=52", "89-59=30", "52+30=82" ]
Current State: 82:[85, 33, 59, 89], Operations: [] Exploring Operation: 85-33=52, Resulting Numbers: [59, 89, 52] Generated Node #2: [59, 89, 52] from Operation: 85-33=52 Current State: 82:[59, 89, 52], Operations: ['85-33=52'] Exploring Operation: 89-59=30, Resulting Numbers: [52, 30] Generated Node #3: [52, 30] from Operation: 89-59=30 Current State: 82:[52, 30], Operations: ['85-33=52', '89-59=30'] Exploring Operation: 52+30=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[85, 33, 59, 89], Operations: [] Exploring Operation: 59-33=26, Resulting Numbers: [85, 89, 26] Generated Node #0,0: 82:[85, 89, 26] Operation: 59-33=26 Exploring Operation: 33+59=92, Resulting Numbers: [85, 89, 92] Generated Node #0,1: 82:[85, 89, 92] Operation: 33+59=92 Exploring Operation: 89-59=30, Resulting Numbers: [85, 33, 30] Generated Node #0,2: 82:[85, 33, 30] Operation: 89-59=30 Moving to Node #0,1 Current State: 82:[85, 89, 92], Operations: ['33+59=92'] Exploring Operation: 89-85=4, Resulting Numbers: [92, 4] Generated Node #0,1,0: 82:[92, 4] Operation: 89-85=4 Exploring Operation: 92-89=3, Resulting Numbers: [85, 3] Generated Node #0,1,1: 82:[85, 3] Operation: 92-89=3 Exploring Operation: 92-85=7, Resulting Numbers: [89, 7] Generated Node #0,1,2: 82:[89, 7] Operation: 92-85=7 Moving to Node #0,2 Current State: 82:[85, 33, 30], Operations: ['89-59=30'] Exploring Operation: 85-33=52, Resulting Numbers: [30, 52] Generated Node #0,2,0: 82:[30, 52] Operation: 85-33=52 Exploring Operation: 33-30=3, Resulting Numbers: [85, 3] Generated Node #0,2,1: 82:[85, 3] Operation: 33-30=3 Exploring Operation: 85-30=55, Resulting Numbers: [33, 55] Generated Node #0,2,2: 82:[33, 55] Operation: 85-30=55 Moving to Node #0,0 Current State: 82:[85, 89, 26], Operations: ['59-33=26'] Exploring Operation: 89-26=63, Resulting Numbers: [85, 63] Generated Node #0,0,0: 82:[85, 63] Operation: 89-26=63 Exploring Operation: 85-26=59, Resulting Numbers: [89, 59] Generated Node #0,0,1: 82:[89, 59] Operation: 85-26=59 Exploring Operation: 89-85=4, Resulting Numbers: [26, 4] Generated Node #0,0,2: 82:[26, 4] Operation: 89-85=4 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 82:[26, 4], Operations: ['59-33=26', '89-85=4'] Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,82 unequal: No Solution Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 82:[85, 63], Operations: ['59-33=26', '89-26=63'] Exploring Operation: 85-63=22, Resulting Numbers: [22] 22,82 unequal: No Solution Exploring Operation: 85+63=148, Resulting Numbers: [148] 148,82 unequal: No Solution Exploring Operation: 85*63=5355, Resulting Numbers: [5355] 5355,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 82:[89, 59], Operations: ['59-33=26', '85-26=59'] Exploring Operation: 89-59=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 89*59=5251, Resulting Numbers: [5251] 5251,82 unequal: No Solution Exploring Operation: 89+59=148, Resulting Numbers: [148] 148,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 82:[85, 3], Operations: ['33+59=92', '92-89=3'] Exploring Operation: 85+3=88, Resulting Numbers: [88] 88,82 unequal: No Solution Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[85, 33, 59, 89], Operations: [] Exploring Operation: 33+59=92, Resulting Numbers: [85, 89, 92] Generated Node #0,1: 82:[85, 89, 92] Operation: 33+59=92 Moving to Node #0,1 Current State: 82:[85, 89, 92], Operations: ['33+59=92'] Exploring Operation: 92-89=3, Resulting Numbers: [85, 3] Generated Node #0,1,1: 82:[85, 3] Operation: 92-89=3 Moving to Node #0,1,1 Current State: 82:[85, 3], Operations: ['33+59=92', '92-89=3'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.976563
hs_3
sum_heuristic
[ 37, 34, 6, 98 ]
33
[ "37+34=71", "6+98=104", "104-71=33" ]
Current State: 33:[37, 34, 6, 98], Operations: [] Exploring Operation: 37+34=71, Resulting Numbers: [6, 98, 71] Generated Node #2: [6, 98, 71] from Operation: 37+34=71 Current State: 33:[6, 98, 71], Operations: ['37+34=71'] Exploring Operation: 6+98=104, Resulting Numbers: [71, 104] Generated Node #3: [71, 104] from Operation: 6+98=104 Current State: 33:[71, 104], Operations: ['37+34=71', '6+98=104'] Exploring Operation: 104-71=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[37, 34, 6, 98], Operations: [] Exploring Operation: 98-6=92, Resulting Numbers: [37, 34, 92] Generated Node #0,0: 33:[37, 34, 92] Operation: 98-6=92 Exploring Operation: 98-34=64, Resulting Numbers: [37, 6, 64] Generated Node #0,1: 33:[37, 6, 64] Operation: 98-34=64 Exploring Operation: 37-34=3, Resulting Numbers: [6, 98, 3] Generated Node #0,2: 33:[6, 98, 3] Operation: 37-34=3 Exploring Operation: 37-6=31, Resulting Numbers: [34, 98, 31] Generated Node #0,3: 33:[34, 98, 31] Operation: 37-6=31 Exploring Operation: 98-37=61, Resulting Numbers: [34, 6, 61] Generated Node #0,4: 33:[34, 6, 61] Operation: 98-37=61 Start Sub Search at level 1: Moving to Node #0,4 Current State: 33:[34, 6, 61], Operations: ['98-37=61'] Exploring Operation: 34+6=40, Resulting Numbers: [61, 40] Generated Node #0,4,0: 33:[61, 40] Operation: 34+6=40 Exploring Operation: 61-34=27, Resulting Numbers: [6, 27] Generated Node #0,4,1: 33:[6, 27] Operation: 61-34=27 Exploring Operation: 6+61=67, Resulting Numbers: [34, 67] Generated Node #0,4,2: 33:[34, 67] Operation: 6+61=67 Exploring Operation: 34-6=28, Resulting Numbers: [61, 28] Generated Node #0,4,3: 33:[61, 28] Operation: 34-6=28 Exploring Operation: 61-6=55, Resulting Numbers: [34, 55] Generated Node #0,4,4: 33:[34, 55] Operation: 61-6=55 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 33:[6, 27], Operations: ['98-37=61', '61-34=27'] Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[37, 34, 6, 98], Operations: [] Exploring Operation: 98-37=61, Resulting Numbers: [34, 6, 61] Generated Node #0,4: 33:[34, 6, 61] Operation: 98-37=61 Moving to Node #0,4 Current State: 33:[34, 6, 61], Operations: ['98-37=61'] Exploring Operation: 61-34=27, Resulting Numbers: [6, 27] Generated Node #0,4,1: 33:[6, 27] Operation: 61-34=27 Moving to Node #0,4,1 Current State: 33:[6, 27], Operations: ['98-37=61', '61-34=27'] Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 83, 7, 35, 3 ]
58
[ "83+7=90", "35-3=32", "90-32=58" ]
Current State: 58:[83, 7, 35, 3], Operations: [] Exploring Operation: 83+7=90, Resulting Numbers: [35, 3, 90] Generated Node #2: [35, 3, 90] from Operation: 83+7=90 Current State: 58:[35, 3, 90], Operations: ['83+7=90'] Exploring Operation: 35-3=32, Resulting Numbers: [90, 32] Generated Node #3: [90, 32] from Operation: 35-3=32 Current State: 58:[90, 32], Operations: ['83+7=90', '35-3=32'] Exploring Operation: 90-32=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[83, 7, 35, 3], Operations: [] Exploring Operation: 83-35=48, Resulting Numbers: [7, 3, 48] Generated Node #0,0: 58:[7, 3, 48] Operation: 83-35=48 Exploring Operation: 83-7=76, Resulting Numbers: [35, 3, 76] Generated Node #0,1: 58:[35, 3, 76] Operation: 83-7=76 Exploring Operation: 35/7=5, Resulting Numbers: [83, 3, 5] Generated Node #0,2: 58:[83, 3, 5] Operation: 35/7=5 Exploring Operation: 35-7=28, Resulting Numbers: [83, 3, 28] Generated Node #0,3: 58:[83, 3, 28] Operation: 35-7=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[7, 3, 48], Operations: ['83-35=48'] Exploring Operation: 7-3=4, Resulting Numbers: [48, 4] Generated Node #0,0,0: 58:[48, 4] Operation: 7-3=4 Exploring Operation: 7+48=55, Resulting Numbers: [3, 55] Generated Node #0,0,1: 58:[3, 55] Operation: 7+48=55 Exploring Operation: 48-7=41, Resulting Numbers: [3, 41] Generated Node #0,0,2: 58:[3, 41] Operation: 48-7=41 Exploring Operation: 3+48=51, Resulting Numbers: [7, 51] Generated Node #0,0,3: 58:[7, 51] Operation: 3+48=51 Moving to Node #0,0,1 Current State: 58:[3, 55], Operations: ['83-35=48', '7+48=55'] Exploring Operation: 3+55=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[83, 7, 35, 3], Operations: [] Exploring Operation: 83-35=48, Resulting Numbers: [7, 3, 48] Generated Node #0,0: 58:[7, 3, 48] Operation: 83-35=48 Moving to Node #0,0 Current State: 58:[7, 3, 48], Operations: ['83-35=48'] Exploring Operation: 7+48=55, Resulting Numbers: [3, 55] Generated Node #0,0,1: 58:[3, 55] Operation: 7+48=55 Moving to Node #0,0,1 Current State: 58:[3, 55], Operations: ['83-35=48', '7+48=55'] Exploring Operation: 3+55=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 79, 80, 37, 5 ]
78
[ "79-5=74", "74/37=2", "80-2=78" ]
Current State: 78:[79, 80, 37, 5], Operations: [] Exploring Operation: 79-5=74, Resulting Numbers: [80, 37, 74] Generated Node #2: [80, 37, 74] from Operation: 79-5=74 Current State: 78:[80, 37, 74], Operations: ['79-5=74'] Exploring Operation: 74/37=2, Resulting Numbers: [80, 2] Generated Node #3: [80, 2] from Operation: 74/37=2 Current State: 78:[80, 2], Operations: ['79-5=74', '74/37=2'] Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[79, 80, 37, 5], Operations: [] Exploring Operation: 80-79=1, Resulting Numbers: [37, 5, 1] Generated Node #0,0: 78:[37, 5, 1] Operation: 80-79=1 Moving to Node #0,0 Current State: 78:[37, 5, 1], Operations: ['80-79=1'] Exploring Operation: 37+1=38, Resulting Numbers: [5, 38] Generated Node #0,0,0: 78:[5, 38] Operation: 37+1=38 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[5, 38], Operations: ['80-79=1', '37+1=38'] Exploring Operation: 5+38=43, Resulting Numbers: [43] 43,78 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
[ 45, 46, 20, 99 ]
79
[ "46-45=1", "99-20=79", "1*79=79" ]
Current State: 79:[45, 46, 20, 99], Operations: [] Exploring Operation: 46-45=1, Resulting Numbers: [20, 99, 1] Generated Node #2: [20, 99, 1] from Operation: 46-45=1 Current State: 79:[20, 99, 1], Operations: ['46-45=1'] Exploring Operation: 99-20=79, Resulting Numbers: [1, 79] Generated Node #3: [1, 79] from Operation: 99-20=79 Current State: 79:[1, 79], Operations: ['46-45=1', '99-20=79'] Exploring Operation: 1*79=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[45, 46, 20, 99], Operations: [] Exploring Operation: 99-20=79, Resulting Numbers: [45, 46, 79] Generated Node #0,0: 79:[45, 46, 79] Operation: 99-20=79 Exploring Operation: 45+20=65, Resulting Numbers: [46, 99, 65] Generated Node #0,1: 79:[46, 99, 65] Operation: 45+20=65 Exploring Operation: 46+20=66, Resulting Numbers: [45, 99, 66] Generated Node #0,2: 79:[45, 99, 66] Operation: 46+20=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[45, 46, 79], Operations: ['99-20=79'] Exploring Operation: 45+46=91, Resulting Numbers: [79, 91] Generated Node #0,0,0: 79:[79, 91] Operation: 45+46=91 Exploring Operation: 46-45=1, Resulting Numbers: [79, 1] Generated Node #0,0,1: 79:[79, 1] Operation: 46-45=1 Exploring Operation: 45+79=124, Resulting Numbers: [46, 124] Generated Node #0,0,2: 79:[46, 124] Operation: 45+79=124 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[79, 91], Operations: ['99-20=79', '45+46=91'] Exploring Operation: 79+91=170, Resulting Numbers: [170] 170,79 unequal: No Solution Exploring Operation: 91-79=12, Resulting Numbers: [12] 12,79 unequal: No Solution Exploring Operation: 79*91=7189, Resulting Numbers: [7189] 7189,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 79:[79, 1], Operations: ['99-20=79', '46-45=1'] Exploring Operation: 79*1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[45, 46, 20, 99], Operations: [] Exploring Operation: 99-20=79, Resulting Numbers: [45, 46, 79] Generated Node #0,0: 79:[45, 46, 79] Operation: 99-20=79 Moving to Node #0,0 Current State: 79:[45, 46, 79], Operations: ['99-20=79'] Exploring Operation: 46-45=1, Resulting Numbers: [79, 1] Generated Node #0,0,1: 79:[79, 1] Operation: 46-45=1 Moving to Node #0,0,1 Current State: 79:[79, 1], Operations: ['99-20=79', '46-45=1'] Exploring Operation: 79*1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 9, 60, 6, 49 ]
49
[ "60/6=10", "10-9=1", "49*1=49" ]
Current State: 49:[9, 60, 6, 49], Operations: [] Exploring Operation: 60/6=10, Resulting Numbers: [9, 49, 10] Generated Node #2: [9, 49, 10] from Operation: 60/6=10 Current State: 49:[9, 49, 10], Operations: ['60/6=10'] Exploring Operation: 10-9=1, Resulting Numbers: [49, 1] Generated Node #3: [49, 1] from Operation: 10-9=1 Current State: 49:[49, 1], Operations: ['60/6=10', '10-9=1'] Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[9, 60, 6, 49], Operations: [] Exploring Operation: 60-9=51, Resulting Numbers: [6, 49, 51] Generated Node #0,0: 49:[6, 49, 51] Operation: 60-9=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[6, 49, 51], Operations: ['60-9=51'] Exploring Operation: 51-6=45, Resulting Numbers: [49, 45] Generated Node #0,0,0: 49:[49, 45] Operation: 51-6=45 Moving to Node #0,0,0 Current State: 49:[49, 45], Operations: ['60-9=51', '51-6=45'] Exploring Operation: 49-45=4, Resulting Numbers: [4] 4,49 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
[ 9, 10, 6, 2 ]
46
[ "9*6=54", "10-2=8", "54-8=46" ]
Current State: 46:[9, 10, 6, 2], Operations: [] Exploring Operation: 9*6=54, Resulting Numbers: [10, 2, 54] Generated Node #2: [10, 2, 54] from Operation: 9*6=54 Current State: 46:[10, 2, 54], Operations: ['9*6=54'] Exploring Operation: 10-2=8, Resulting Numbers: [54, 8] Generated Node #3: [54, 8] from Operation: 10-2=8 Current State: 46:[54, 8], Operations: ['9*6=54', '10-2=8'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[9, 10, 6, 2], Operations: [] Exploring Operation: 10-9=1, Resulting Numbers: [6, 2, 1] Generated Node #0,0: 46:[6, 2, 1] Operation: 10-9=1 Moving to Node #0,0 Current State: 46:[6, 2, 1], Operations: ['10-9=1'] Exploring Operation: 6/2=3, Resulting Numbers: [1, 3] Generated Node #0,0,0: 46:[1, 3] Operation: 6/2=3 Moving to Node #0,0,0 Current State: 46:[1, 3], Operations: ['10-9=1', '6/2=3'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,46 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 95, 22, 9, 52 ]
44
[ "95+9=104", "22*104=2288", "2288/52=44" ]
Current State: 44:[95, 22, 9, 52], Operations: [] Exploring Operation: 95+9=104, Resulting Numbers: [22, 52, 104] Generated Node #2: [22, 52, 104] from Operation: 95+9=104 Current State: 44:[22, 52, 104], Operations: ['95+9=104'] Exploring Operation: 22*104=2288, Resulting Numbers: [52, 2288] Generated Node #3: [52, 2288] from Operation: 22*104=2288 Current State: 44:[52, 2288], Operations: ['95+9=104', '22*104=2288'] Exploring Operation: 2288/52=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[95, 22, 9, 52], Operations: [] Exploring Operation: 95-52=43, Resulting Numbers: [22, 9, 43] Generated Node #0,0: 44:[22, 9, 43] Operation: 95-52=43 Exploring Operation: 52-9=43, Resulting Numbers: [95, 22, 43] Generated Node #0,1: 44:[95, 22, 43] Operation: 52-9=43 Exploring Operation: 95-9=86, Resulting Numbers: [22, 52, 86] Generated Node #0,2: 44:[22, 52, 86] Operation: 95-9=86 Exploring Operation: 95-22=73, Resulting Numbers: [9, 52, 73] Generated Node #0,3: 44:[9, 52, 73] Operation: 95-22=73 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[22, 9, 43], Operations: ['95-52=43'] Exploring Operation: 22+9=31, Resulting Numbers: [43, 31] Generated Node #0,0,0: 44:[43, 31] Operation: 22+9=31 Exploring Operation: 22-9=13, Resulting Numbers: [43, 13] Generated Node #0,0,1: 44:[43, 13] Operation: 22-9=13 Exploring Operation: 9+43=52, Resulting Numbers: [22, 52] Generated Node #0,0,2: 44:[22, 52] Operation: 9+43=52 Exploring Operation: 43-22=21, Resulting Numbers: [9, 21] Generated Node #0,0,3: 44:[9, 21] Operation: 43-22=21 Moving to Node #0,0,1 Current State: 44:[43, 13], Operations: ['95-52=43', '22-9=13'] Exploring Operation: 43*13=559, Resulting Numbers: [559] 559,44 unequal: No Solution Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,44 unequal: No Solution Exploring Operation: 43+13=56, Resulting Numbers: [56] 56,44 unequal: No Solution Moving to Node #0,0,3 Current State: 44:[9, 21], Operations: ['95-52=43', '43-22=21'] Exploring Operation: 9*21=189, Resulting Numbers: [189] 189,44 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,44 unequal: No Solution Moving to Node #0,0,2 Current State: 44:[22, 52], Operations: ['95-52=43', '9+43=52'] Exploring Operation: 22+52=74, Resulting Numbers: [74] 74,44 unequal: No Solution Exploring Operation: 22*52=1144, Resulting Numbers: [1144] 1144,44 unequal: No Solution Exploring Operation: 52-22=30, Resulting Numbers: [30] 30,44 unequal: No Solution Moving to Node #0,0,0 Current State: 44:[43, 31], Operations: ['95-52=43', '22+9=31'] Exploring Operation: 43-31=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 43*31=1333, Resulting Numbers: [1333] 1333,44 unequal: No Solution Exploring Operation: 43+31=74, Resulting Numbers: [74] 74,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[9, 52, 73], Operations: ['95-22=73'] Exploring Operation: 52-9=43, Resulting Numbers: [73, 43] Generated Node #0,3,0: 44:[73, 43] Operation: 52-9=43 Exploring Operation: 73-9=64, Resulting Numbers: [52, 64] Generated Node #0,3,1: 44:[52, 64] Operation: 73-9=64 Exploring Operation: 9+52=61, Resulting Numbers: [73, 61] Generated Node #0,3,2: 44:[73, 61] Operation: 9+52=61 Exploring Operation: 73-52=21, Resulting Numbers: [9, 21] Generated Node #0,3,3: 44:[9, 21] Operation: 73-52=21 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 44:[9, 21], Operations: ['95-22=73', '73-52=21'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 9*21=189, Resulting Numbers: [189] 189,44 unequal: No Solution Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,44 unequal: No Solution No 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: 44:[52, 64], Operations: ['95-22=73', '73-9=64'] Exploring Operation: 64-52=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 52+64=116, Resulting Numbers: [116] 116,44 unequal: No Solution Exploring Operation: 52*64=3328, Resulting Numbers: [3328] 3328,44 unequal: No Solution No 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: 44:[73, 43], Operations: ['95-22=73', '52-9=43'] Exploring Operation: 73+43=116, Resulting Numbers: [116] 116,44 unequal: No Solution Exploring Operation: 73-43=30, Resulting Numbers: [30] 30,44 unequal: No Solution Exploring Operation: 73*43=3139, Resulting Numbers: [3139] 3139,44 unequal: No Solution No 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: 44:[73, 61], Operations: ['95-22=73', '9+52=61'] Exploring Operation: 73*61=4453, Resulting Numbers: [4453] 4453,44 unequal: No Solution Exploring Operation: 73+61=134, Resulting Numbers: [134] 134,44 unequal: No Solution Exploring Operation: 73-61=12, Resulting Numbers: [12] 12,44 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: 44:[22, 52, 86], Operations: ['95-9=86'] Exploring Operation: 22+52=74, Resulting Numbers: [86, 74] Generated Node #0,2,0: 44:[86, 74] Operation: 22+52=74 Exploring Operation: 52-22=30, Resulting Numbers: [86, 30] Generated Node #0,2,1: 44:[86, 30] Operation: 52-22=30 Exploring Operation: 86-22=64, Resulting Numbers: [52, 64] Generated Node #0,2,2: 44:[52, 64] Operation: 86-22=64 Exploring Operation: 86-52=34, Resulting Numbers: [22, 34] Generated Node #0,2,3: 44:[22, 34] Operation: 86-52=34 Moving to Node #0,2,3 Current State: 44:[22, 34], Operations: ['95-9=86', '86-52=34'] Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 22+34=56, Resulting Numbers: [56] 56,44 unequal: No Solution Exploring Operation: 22*34=748, Resulting Numbers: [748] 748,44 unequal: No Solution Moving to Node #0,2,2 Current State: 44:[52, 64], Operations: ['95-9=86', '86-22=64'] Exploring Operation: 64-52=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 52*64=3328, Resulting Numbers: [3328] 3328,44 unequal: No Solution Exploring Operation: 52+64=116, Resulting Numbers: [116] 116,44 unequal: No Solution Moving to Node #0,2,1 Current State: 44:[86, 30], Operations: ['95-9=86', '52-22=30'] Exploring Operation: 86+30=116, Resulting Numbers: [116] 116,44 unequal: No Solution Exploring Operation: 86*30=2580, Resulting Numbers: [2580] 2580,44 unequal: No Solution Exploring Operation: 86-30=56, Resulting Numbers: [56] 56,44 unequal: No Solution Moving to Node #0,2,0 Current State: 44:[86, 74], Operations: ['95-9=86', '22+52=74'] Exploring Operation: 86+74=160, Resulting Numbers: [160] 160,44 unequal: No Solution Exploring Operation: 86*74=6364, Resulting Numbers: [6364] 6364,44 unequal: No Solution Exploring Operation: 86-74=12, Resulting Numbers: [12] 12,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[95, 22, 43], Operations: ['52-9=43'] Exploring Operation: 43-22=21, Resulting Numbers: [95, 21] Generated Node #0,1,0: 44:[95, 21] Operation: 43-22=21 Exploring Operation: 95-22=73, Resulting Numbers: [43, 73] Generated Node #0,1,1: 44:[43, 73] Operation: 95-22=73 Exploring Operation: 22+43=65, Resulting Numbers: [95, 65] Generated Node #0,1,2: 44:[95, 65] Operation: 22+43=65 Exploring Operation: 95-43=52, Resulting Numbers: [22, 52] Generated Node #0,1,3: 44:[22, 52] Operation: 95-43=52 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 44:[22, 52], Operations: ['52-9=43', '95-43=52'] Exploring Operation: 52-22=30, Resulting Numbers: [30] 30,44 unequal: No Solution Exploring Operation: 22+52=74, Resulting Numbers: [74] 74,44 unequal: No Solution Exploring Operation: 22*52=1144, Resulting Numbers: [1144] 1144,44 unequal: No Solution No 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: 44:[43, 73], Operations: ['52-9=43', '95-22=73'] Exploring Operation: 43*73=3139, Resulting Numbers: [3139] 3139,44 unequal: No Solution Exploring Operation: 73-43=30, Resulting Numbers: [30] 30,44 unequal: No Solution Exploring Operation: 43+73=116, Resulting Numbers: [116] 116,44 unequal: No Solution No 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: 44:[95, 21], Operations: ['52-9=43', '43-22=21'] Exploring Operation: 95-21=74, Resulting Numbers: [74] 74,44 unequal: No Solution Exploring Operation: 95*21=1995, Resulting Numbers: [1995] 1995,44 unequal: No Solution Exploring Operation: 95+21=116, Resulting Numbers: [116] 116,44 unequal: No Solution No 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: 44:[95, 65], Operations: ['52-9=43', '22+43=65'] Exploring Operation: 95*65=6175, Resulting Numbers: [6175] 6175,44 unequal: No Solution Exploring Operation: 95-65=30, Resulting Numbers: [30] 30,44 unequal: No Solution Exploring Operation: 95+65=160, Resulting Numbers: [160] 160,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 8, 59, 7, 56 ]
18
[ "8+59=67", "56-7=49", "67-49=18" ]
Current State: 18:[8, 59, 7, 56], Operations: [] Exploring Operation: 8+59=67, Resulting Numbers: [7, 56, 67] Generated Node #2: [7, 56, 67] from Operation: 8+59=67 Current State: 18:[7, 56, 67], Operations: ['8+59=67'] Exploring Operation: 56-7=49, Resulting Numbers: [67, 49] Generated Node #3: [67, 49] from Operation: 56-7=49 Current State: 18:[67, 49], Operations: ['8+59=67', '56-7=49'] Exploring Operation: 67-49=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[8, 59, 7, 56], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [59, 7, 7] Generated Node #0,0: 18:[59, 7, 7] Operation: 56/8=7 Exploring Operation: 56/7=8, Resulting Numbers: [8, 59, 8] Generated Node #0,1: 18:[8, 59, 8] Operation: 56/7=8 Exploring Operation: 59-8=51, Resulting Numbers: [7, 56, 51] Generated Node #0,2: 18:[7, 56, 51] Operation: 59-8=51 Exploring Operation: 59-56=3, Resulting Numbers: [8, 7, 3] Generated Node #0,3: 18:[8, 7, 3] Operation: 59-56=3 Moving to Node #0,3 Current State: 18:[8, 7, 3], Operations: ['59-56=3'] Exploring Operation: 8-3=5, Resulting Numbers: [7, 5] Generated Node #0,3,0: 18:[7, 5] Operation: 8-3=5 Exploring Operation: 7-3=4, Resulting Numbers: [8, 4] Generated Node #0,3,1: 18:[8, 4] Operation: 7-3=4 Exploring Operation: 8-7=1, Resulting Numbers: [3, 1] Generated Node #0,3,2: 18:[3, 1] Operation: 8-7=1 Exploring Operation: 7+3=10, Resulting Numbers: [8, 10] Generated Node #0,3,3: 18:[8, 10] Operation: 7+3=10 Moving to Node #0,1 Current State: 18:[8, 59, 8], Operations: ['56/7=8'] Exploring Operation: 8/8=1, Resulting Numbers: [59, 1] Generated Node #0,1,0: 18:[59, 1] Operation: 8/8=1 Exploring Operation: 8+8=16, Resulting Numbers: [59, 16] Generated Node #0,1,1: 18:[59, 16] Operation: 8+8=16 Exploring Operation: 59-8=51, Resulting Numbers: [8, 51] Generated Node #0,1,2: 18:[8, 51] Operation: 59-8=51 Exploring Operation: 59-8=51, Resulting Numbers: [8, 51] Generated Node #0,1,3: 18:[8, 51] Operation: 59-8=51 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[8, 51], Operations: ['56/7=8', '59-8=51'] Exploring Operation: 8+51=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 8*51=408, Resulting Numbers: [408] 408,18 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[8, 51], Operations: ['56/7=8', '59-8=51'] Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,18 unequal: No Solution Exploring Operation: 8+51=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 8*51=408, Resulting Numbers: [408] 408,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[59, 1], Operations: ['56/7=8', '8/8=1'] Exploring Operation: 59+1=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 59*1=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 59-1=58, Resulting Numbers: [58] 58,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[59, 16], Operations: ['56/7=8', '8+8=16'] Exploring Operation: 59*16=944, Resulting Numbers: [944] 944,18 unequal: No Solution Exploring Operation: 59-16=43, Resulting Numbers: [43] 43,18 unequal: No Solution Exploring Operation: 59+16=75, Resulting Numbers: [75] 75,18 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: 18:[59, 7, 7], Operations: ['56/8=7'] Exploring Operation: 59-7=52, Resulting Numbers: [7, 52] Generated Node #0,0,0: 18:[7, 52] Operation: 59-7=52 Exploring Operation: 7/7=1, Resulting Numbers: [59, 1] Generated Node #0,0,1: 18:[59, 1] Operation: 7/7=1 Exploring Operation: 59-7=52, Resulting Numbers: [7, 52] Generated Node #0,0,2: 18:[7, 52] Operation: 59-7=52 Exploring Operation: 7-7=0, Resulting Numbers: [59, 0] Generated Node #0,0,3: 18:[59, 0] Operation: 7-7=0 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[7, 52], Operations: ['56/8=7', '59-7=52'] Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 7*52=364, Resulting Numbers: [364] 364,18 unequal: No Solution Exploring Operation: 7+52=59, Resulting Numbers: [59] 59,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[7, 52], Operations: ['56/8=7', '59-7=52'] Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 7*52=364, Resulting Numbers: [364] 364,18 unequal: No Solution Exploring Operation: 7+52=59, Resulting Numbers: [59] 59,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[59, 1], Operations: ['56/8=7', '7/7=1'] Exploring Operation: 59*1=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 59+1=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 59-1=58, Resulting Numbers: [58] 58,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 18:[59, 0], Operations: ['56/8=7', '7-7=0'] Exploring Operation: 59-0=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 59+0=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 59*0=0, Resulting Numbers: [0] 0,18 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: 18:[7, 56, 51], Operations: ['59-8=51'] Exploring Operation: 56-7=49, Resulting Numbers: [51, 49] Generated Node #0,2,0: 18:[51, 49] Operation: 56-7=49 Exploring Operation: 51-7=44, Resulting Numbers: [56, 44] Generated Node #0,2,1: 18:[56, 44] Operation: 51-7=44 Exploring Operation: 56-51=5, Resulting Numbers: [7, 5] Generated Node #0,2,2: 18:[7, 5] Operation: 56-51=5 Exploring Operation: 56/7=8, Resulting Numbers: [51, 8] Generated Node #0,2,3: 18:[51, 8] Operation: 56/7=8 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[7, 5], Operations: ['59-8=51', '56-51=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 18:[51, 8], Operations: ['59-8=51', '56/7=8'] Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,18 unequal: No Solution Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[51, 49], Operations: ['59-8=51', '56-7=49'] Exploring Operation: 51-49=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 51+49=100, Resulting Numbers: [100] 100,18 unequal: No Solution Exploring Operation: 51*49=2499, Resulting Numbers: [2499] 2499,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[56, 44], Operations: ['59-8=51', '51-7=44'] Exploring Operation: 56+44=100, Resulting Numbers: [100] 100,18 unequal: No Solution Exploring Operation: 56-44=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 56*44=2464, Resulting Numbers: [2464] 2464,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 18:[3, 1], Operations: ['59-56=3', '8-7=1'] Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,18 unequal: No Solution Moving to Node #0,3,1 Current State: 18:[8, 4], Operations: ['59-56=3', '7-3=4'] Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,18 unequal: No Solution Moving to Node #0,3,0 Current State: 18:[7, 5], Operations: ['59-56=3', '8-3=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,18 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,18 unequal: No Solution Moving to Node #0,3,3 Current State: 18:[8, 10], Operations: ['59-56=3', '7+3=10'] Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,18 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[8, 59, 7, 56], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [8, 7, 3] Generated Node #0,3: 18:[8, 7, 3] Operation: 59-56=3 Moving to Node #0,3 Current State: 18:[8, 7, 3], Operations: ['59-56=3'] Exploring Operation: 7+3=10, Resulting Numbers: [8, 10] Generated Node #0,3,3: 18:[8, 10] Operation: 7+3=10 Moving to Node #0,3,3 Current State: 18:[8, 10], Operations: ['59-56=3', '7+3=10'] Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.934028
hs_4
sum_heuristic
[ 25, 8, 18, 17 ]
63
[ "25-18=7", "17-8=9", "7*9=63" ]
Current State: 63:[25, 8, 18, 17], Operations: [] Exploring Operation: 25-18=7, Resulting Numbers: [8, 17, 7] Generated Node #2: [8, 17, 7] from Operation: 25-18=7 Current State: 63:[8, 17, 7], Operations: ['25-18=7'] Exploring Operation: 17-8=9, Resulting Numbers: [7, 9] Generated Node #3: [7, 9] from Operation: 17-8=9 Current State: 63:[7, 9], Operations: ['25-18=7', '17-8=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[25, 8, 18, 17], Operations: [] Exploring Operation: 25-17=8, Resulting Numbers: [8, 18, 8] Generated Node #0,0: 63:[8, 18, 8] Operation: 25-17=8 Exploring Operation: 25-18=7, Resulting Numbers: [8, 17, 7] Generated Node #0,1: 63:[8, 17, 7] Operation: 25-18=7 Exploring Operation: 17-8=9, Resulting Numbers: [25, 18, 9] Generated Node #0,2: 63:[25, 18, 9] Operation: 17-8=9 Moving to Node #0,0 Current State: 63:[8, 18, 8], Operations: ['25-17=8'] Exploring Operation: 18-8=10, Resulting Numbers: [8, 10] Generated Node #0,0,0: 63:[8, 10] Operation: 18-8=10 Exploring Operation: 18-8=10, Resulting Numbers: [8, 10] Generated Node #0,0,1: 63:[8, 10] Operation: 18-8=10 Exploring Operation: 8*8=64, Resulting Numbers: [18, 64] Generated Node #0,0,2: 63:[18, 64] Operation: 8*8=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[8, 10], Operations: ['25-17=8', '18-8=10'] Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,63 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,63 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[8, 10], Operations: ['25-17=8', '18-8=10'] Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,63 unequal: No Solution Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,63 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 63:[18, 64], Operations: ['25-17=8', '8*8=64'] Exploring Operation: 64-18=46, Resulting Numbers: [46] 46,63 unequal: No Solution Exploring Operation: 18+64=82, Resulting Numbers: [82] 82,63 unequal: No Solution Exploring Operation: 18*64=1152, Resulting Numbers: [1152] 1152,63 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: 63:[8, 17, 7], Operations: ['25-18=7'] Exploring Operation: 17-7=10, Resulting Numbers: [8, 10] Generated Node #0,1,0: 63:[8, 10] Operation: 17-7=10 Exploring Operation: 17-8=9, Resulting Numbers: [7, 9] Generated Node #0,1,1: 63:[7, 9] Operation: 17-8=9 Exploring Operation: 8+17=25, Resulting Numbers: [7, 25] Generated Node #0,1,2: 63:[7, 25] Operation: 8+17=25 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 63:[7, 9], Operations: ['25-18=7', '17-8=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[25, 8, 18, 17], Operations: [] Exploring Operation: 25-18=7, Resulting Numbers: [8, 17, 7] Generated Node #0,1: 63:[8, 17, 7] Operation: 25-18=7 Moving to Node #0,1 Current State: 63:[8, 17, 7], Operations: ['25-18=7'] Exploring Operation: 17-8=9, Resulting Numbers: [7, 9] Generated Node #0,1,1: 63:[7, 9] Operation: 17-8=9 Moving to Node #0,1,1 Current State: 63:[7, 9], Operations: ['25-18=7', '17-8=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 16, 1, 11, 88 ]
24
[ "16*1=16", "88/11=8", "16+8=24" ]
Current State: 24:[16, 1, 11, 88], Operations: [] Exploring Operation: 16*1=16, Resulting Numbers: [11, 88, 16] Generated Node #2: [11, 88, 16] from Operation: 16*1=16 Current State: 24:[11, 88, 16], Operations: ['16*1=16'] Exploring Operation: 88/11=8, Resulting Numbers: [16, 8] Generated Node #3: [16, 8] from Operation: 88/11=8 Current State: 24:[16, 8], Operations: ['16*1=16', '88/11=8'] Exploring Operation: 16+8=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[16, 1, 11, 88], Operations: [] Exploring Operation: 88/11=8, Resulting Numbers: [16, 1, 8] Generated Node #0,0: 24:[16, 1, 8] Operation: 88/11=8 Exploring Operation: 88-16=72, Resulting Numbers: [1, 11, 72] Generated Node #0,1: 24:[1, 11, 72] Operation: 88-16=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[16, 1, 8], Operations: ['88/11=8'] Exploring Operation: 16-8=8, Resulting Numbers: [1, 8] Generated Node #0,0,0: 24:[1, 8] Operation: 16-8=8 Exploring Operation: 16+8=24, Resulting Numbers: [1, 24] Generated Node #0,0,1: 24:[1, 24] Operation: 16+8=24 Moving to Node #0,0,0 Current State: 24:[1, 8], Operations: ['88/11=8', '16-8=8'] Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,24 unequal: No Solution Exploring Operation: 1*8=8, Resulting Numbers: [8] 8,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[1, 24], Operations: ['88/11=8', '16+8=24'] Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[16, 1, 11, 88], Operations: [] Exploring Operation: 88/11=8, Resulting Numbers: [16, 1, 8] Generated Node #0,0: 24:[16, 1, 8] Operation: 88/11=8 Moving to Node #0,0 Current State: 24:[16, 1, 8], Operations: ['88/11=8'] Exploring Operation: 16+8=24, Resulting Numbers: [1, 24] Generated Node #0,0,1: 24:[1, 24] Operation: 16+8=24 Moving to Node #0,0,1 Current State: 24:[1, 24], Operations: ['88/11=8', '16+8=24'] Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 32, 10, 92, 9 ]
61
[ "32-10=22", "92-9=83", "83-22=61" ]
Current State: 61:[32, 10, 92, 9], Operations: [] Exploring Operation: 32-10=22, Resulting Numbers: [92, 9, 22] Generated Node #2: [92, 9, 22] from Operation: 32-10=22 Current State: 61:[92, 9, 22], Operations: ['32-10=22'] Exploring Operation: 92-9=83, Resulting Numbers: [22, 83] Generated Node #3: [22, 83] from Operation: 92-9=83 Current State: 61:[22, 83], Operations: ['32-10=22', '92-9=83'] Exploring Operation: 83-22=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[32, 10, 92, 9], Operations: [] Exploring Operation: 32+10=42, Resulting Numbers: [92, 9, 42] Generated Node #0,0: 61:[92, 9, 42] Operation: 32+10=42 Exploring Operation: 10*9=90, Resulting Numbers: [32, 92, 90] Generated Node #0,1: 61:[32, 92, 90] Operation: 10*9=90 Exploring Operation: 32+9=41, Resulting Numbers: [10, 92, 41] Generated Node #0,2: 61:[10, 92, 41] Operation: 32+9=41 Moving to Node #0,1 Current State: 61:[32, 92, 90], Operations: ['10*9=90'] Exploring Operation: 92-90=2, Resulting Numbers: [32, 2] Generated Node #0,1,0: 61:[32, 2] Operation: 92-90=2 Exploring Operation: 92-32=60, Resulting Numbers: [90, 60] Generated Node #0,1,1: 61:[90, 60] Operation: 92-32=60 Exploring Operation: 90-32=58, Resulting Numbers: [92, 58] Generated Node #0,1,2: 61:[92, 58] Operation: 90-32=58 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[90, 60], Operations: ['10*9=90', '92-32=60'] Exploring Operation: 90*60=5400, Resulting Numbers: [5400] 5400,61 unequal: No Solution Exploring Operation: 90-60=30, Resulting Numbers: [30] 30,61 unequal: No Solution Exploring Operation: 90+60=150, Resulting Numbers: [150] 150,61 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:[92, 58], Operations: ['10*9=90', '90-32=58'] Exploring Operation: 92+58=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 92-58=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 92*58=5336, Resulting Numbers: [5336] 5336,61 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 #0,1,0 Current State: 61:[32, 2], Operations: ['10*9=90', '92-90=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,61 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,61 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: 61:[92, 9, 42], Operations: ['32+10=42'] Exploring Operation: 9+42=51, Resulting Numbers: [92, 51] Generated Node #0,0,0: 61:[92, 51] Operation: 9+42=51 Exploring Operation: 92-9=83, Resulting Numbers: [42, 83] Generated Node #0,0,1: 61:[42, 83] Operation: 92-9=83 Exploring Operation: 92+9=101, Resulting Numbers: [42, 101] Generated Node #0,0,2: 61:[42, 101] Operation: 92+9=101 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[92, 51], Operations: ['32+10=42', '9+42=51'] Exploring Operation: 92+51=143, Resulting Numbers: [143] 143,61 unequal: No Solution Exploring Operation: 92*51=4692, Resulting Numbers: [4692] 4692,61 unequal: No Solution Exploring Operation: 92-51=41, Resulting Numbers: [41] 41,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[42, 83], Operations: ['32+10=42', '92-9=83'] Exploring Operation: 42*83=3486, Resulting Numbers: [3486] 3486,61 unequal: No Solution Exploring Operation: 42+83=125, Resulting Numbers: [125] 125,61 unequal: No Solution Exploring Operation: 83-42=41, Resulting Numbers: [41] 41,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 61:[42, 101], Operations: ['32+10=42', '92+9=101'] Exploring Operation: 101-42=59, Resulting Numbers: [59] 59,61 unequal: No Solution Exploring Operation: 42+101=143, Resulting Numbers: [143] 143,61 unequal: No Solution Exploring Operation: 42*101=4242, Resulting Numbers: [4242] 4242,61 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: 61:[10, 92, 41], Operations: ['32+9=41'] Exploring Operation: 10+92=102, Resulting Numbers: [41, 102] Generated Node #0,2,0: 61:[41, 102] Operation: 10+92=102 Exploring Operation: 92-10=82, Resulting Numbers: [41, 82] Generated Node #0,2,1: 61:[41, 82] Operation: 92-10=82 Exploring Operation: 10+41=51, Resulting Numbers: [92, 51] Generated Node #0,2,2: 61:[92, 51] Operation: 10+41=51 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 61:[41, 82], Operations: ['32+9=41', '92-10=82'] Exploring Operation: 41+82=123, Resulting Numbers: [123] 123,61 unequal: No Solution Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,61 unequal: No Solution Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 61:[92, 51], Operations: ['32+9=41', '10+41=51'] Exploring Operation: 92*51=4692, Resulting Numbers: [4692] 4692,61 unequal: No Solution Exploring Operation: 92-51=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 92+51=143, Resulting Numbers: [143] 143,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[41, 102], Operations: ['32+9=41', '10+92=102'] Exploring Operation: 41+102=143, Resulting Numbers: [143] 143,61 unequal: No Solution Exploring Operation: 102-41=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[32, 10, 92, 9], Operations: [] Exploring Operation: 32+9=41, Resulting Numbers: [10, 92, 41] Generated Node #0,2: 61:[10, 92, 41] Operation: 32+9=41 Moving to Node #0,2 Current State: 61:[10, 92, 41], Operations: ['32+9=41'] Exploring Operation: 10+92=102, Resulting Numbers: [41, 102] Generated Node #0,2,0: 61:[41, 102] Operation: 10+92=102 Moving to Node #0,2,0 Current State: 61:[41, 102], Operations: ['32+9=41', '10+92=102'] Exploring Operation: 102-41=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_3
mult_heuristic
[ 20, 72, 30, 42 ]
80
[ "20+72=92", "42-30=12", "92-12=80" ]
Current State: 80:[20, 72, 30, 42], Operations: [] Exploring Operation: 20+72=92, Resulting Numbers: [30, 42, 92] Generated Node #2: [30, 42, 92] from Operation: 20+72=92 Current State: 80:[30, 42, 92], Operations: ['20+72=92'] Exploring Operation: 42-30=12, Resulting Numbers: [92, 12] Generated Node #3: [92, 12] from Operation: 42-30=12 Current State: 80:[92, 12], Operations: ['20+72=92', '42-30=12'] Exploring Operation: 92-12=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[20, 72, 30, 42], Operations: [] Exploring Operation: 30-20=10, Resulting Numbers: [72, 42, 10] Generated Node #0,0: 80:[72, 42, 10] Operation: 30-20=10 Exploring Operation: 72-30=42, Resulting Numbers: [20, 42, 42] Generated Node #0,1: 80:[20, 42, 42] Operation: 72-30=42 Exploring Operation: 42-30=12, Resulting Numbers: [20, 72, 12] Generated Node #0,2: 80:[20, 72, 12] Operation: 42-30=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[20, 42, 42], Operations: ['72-30=42'] Exploring Operation: 42-20=22, Resulting Numbers: [42, 22] Generated Node #0,1,0: 80:[42, 22] Operation: 42-20=22 Exploring Operation: 42/42=1, Resulting Numbers: [20, 1] Generated Node #0,1,1: 80:[20, 1] Operation: 42/42=1 Exploring Operation: 42-42=0, Resulting Numbers: [20, 0] Generated Node #0,1,2: 80:[20, 0] Operation: 42-42=0 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 80:[20, 1], Operations: ['72-30=42', '42/42=1'] Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 80:[20, 0], Operations: ['72-30=42', '42-42=0'] Exploring Operation: 20-0=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 20*0=0, Resulting Numbers: [0] 0,80 unequal: No Solution Exploring Operation: 20+0=20, Resulting Numbers: [20] 20,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 80:[42, 22], Operations: ['72-30=42', '42-20=22'] Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 42+22=64, Resulting Numbers: [64] 64,80 unequal: No Solution Exploring Operation: 42*22=924, Resulting Numbers: [924] 924,80 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: 80:[72, 42, 10], Operations: ['30-20=10'] Exploring Operation: 72+10=82, Resulting Numbers: [42, 82] Generated Node #0,0,0: 80:[42, 82] Operation: 72+10=82 Exploring Operation: 72-42=30, Resulting Numbers: [10, 30] Generated Node #0,0,1: 80:[10, 30] Operation: 72-42=30 Exploring Operation: 42-10=32, Resulting Numbers: [72, 32] Generated Node #0,0,2: 80:[72, 32] Operation: 42-10=32 Moving to Node #0,0,0 Current State: 80:[42, 82], Operations: ['30-20=10', '72+10=82'] Exploring Operation: 82-42=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 42+82=124, Resulting Numbers: [124] 124,80 unequal: No Solution Exploring Operation: 42*82=3444, Resulting Numbers: [3444] 3444,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[10, 30], Operations: ['30-20=10', '72-42=30'] Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[72, 32], Operations: ['30-20=10', '42-10=32'] Exploring Operation: 72*32=2304, Resulting Numbers: [2304] 2304,80 unequal: No Solution Exploring Operation: 72+32=104, Resulting Numbers: [104] 104,80 unequal: No Solution Exploring Operation: 72-32=40, Resulting Numbers: [40] 40,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[20, 72, 12], Operations: ['42-30=12'] Exploring Operation: 72/12=6, Resulting Numbers: [20, 6] Generated Node #0,2,0: 80:[20, 6] Operation: 72/12=6 Exploring Operation: 72+12=84, Resulting Numbers: [20, 84] Generated Node #0,2,1: 80:[20, 84] Operation: 72+12=84 Exploring Operation: 20-12=8, Resulting Numbers: [72, 8] Generated Node #0,2,2: 80:[72, 8] Operation: 20-12=8 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 80:[20, 6], Operations: ['42-30=12', '72/12=6'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,80 unequal: No Solution Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,80 unequal: No Solution Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 80:[20, 84], Operations: ['42-30=12', '72+12=84'] Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,80 unequal: No Solution Exploring Operation: 20+84=104, Resulting Numbers: [104] 104,80 unequal: No Solution Exploring Operation: 20*84=1680, Resulting Numbers: [1680] 1680,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 80:[72, 8], Operations: ['42-30=12', '20-12=8'] Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,80 unequal: No Solution Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[20, 72, 30, 42], Operations: [] Exploring Operation: 42-30=12, Resulting Numbers: [20, 72, 12] Generated Node #0,2: 80:[20, 72, 12] Operation: 42-30=12 Moving to Node #0,2 Current State: 80:[20, 72, 12], Operations: ['42-30=12'] Exploring Operation: 20-12=8, Resulting Numbers: [72, 8] Generated Node #0,2,2: 80:[72, 8] Operation: 20-12=8 Moving to Node #0,2,2 Current State: 80:[72, 8], Operations: ['42-30=12', '20-12=8'] Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.963542
hs_3
mult_heuristic
[ 61, 2, 3, 77 ]
86
[ "77-2=75", "75/3=25", "61+25=86" ]
Current State: 86:[61, 2, 3, 77], Operations: [] Exploring Operation: 77-2=75, Resulting Numbers: [61, 3, 75] Generated Node #2: [61, 3, 75] from Operation: 77-2=75 Current State: 86:[61, 3, 75], Operations: ['77-2=75'] Exploring Operation: 75/3=25, Resulting Numbers: [61, 25] Generated Node #3: [61, 25] from Operation: 75/3=25 Current State: 86:[61, 25], Operations: ['77-2=75', '75/3=25'] Exploring Operation: 61+25=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[61, 2, 3, 77], Operations: [] Exploring Operation: 77-61=16, Resulting Numbers: [2, 3, 16] Generated Node #0,0: 86:[2, 3, 16] Operation: 77-61=16 Exploring Operation: 61-3=58, Resulting Numbers: [2, 77, 58] Generated Node #0,1: 86:[2, 77, 58] Operation: 61-3=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[2, 3, 16], Operations: ['77-61=16'] Exploring Operation: 3*16=48, Resulting Numbers: [2, 48] Generated Node #0,0,0: 86:[2, 48] Operation: 3*16=48 Exploring Operation: 16/2=8, Resulting Numbers: [3, 8] Generated Node #0,0,1: 86:[3, 8] Operation: 16/2=8 Moving to Node #0,0,0 Current State: 86:[2, 48], Operations: ['77-61=16', '3*16=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,86 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[3, 8], Operations: ['77-61=16', '16/2=8'] Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[2, 77, 58], Operations: ['61-3=58'] Exploring Operation: 77-58=19, Resulting Numbers: [2, 19] Generated Node #0,1,0: 86:[2, 19] Operation: 77-58=19 Exploring Operation: 2+77=79, Resulting Numbers: [58, 79] Generated Node #0,1,1: 86:[58, 79] Operation: 2+77=79 Moving to Node #0,1,0 Current State: 86:[2, 19], Operations: ['61-3=58', '77-58=19'] Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[58, 79], Operations: ['61-3=58', '2+77=79'] Exploring Operation: 58+79=137, Resulting Numbers: [137] 137,86 unequal: No Solution Exploring Operation: 79-58=21, Resulting Numbers: [21] 21,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 8, 50, 14, 29 ]
85
[ "50-8=42", "14+29=43", "42+43=85" ]
Current State: 85:[8, 50, 14, 29], Operations: [] Exploring Operation: 50-8=42, Resulting Numbers: [14, 29, 42] Generated Node #2: [14, 29, 42] from Operation: 50-8=42 Current State: 85:[14, 29, 42], Operations: ['50-8=42'] Exploring Operation: 14+29=43, Resulting Numbers: [42, 43] Generated Node #3: [42, 43] from Operation: 14+29=43 Current State: 85:[42, 43], Operations: ['50-8=42', '14+29=43'] Exploring Operation: 42+43=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[8, 50, 14, 29], Operations: [] Exploring Operation: 50-29=21, Resulting Numbers: [8, 14, 21] Generated Node #0,0: 85:[8, 14, 21] Operation: 50-29=21 Exploring Operation: 29-14=15, Resulting Numbers: [8, 50, 15] Generated Node #0,1: 85:[8, 50, 15] Operation: 29-14=15 Exploring Operation: 50+14=64, Resulting Numbers: [8, 29, 64] Generated Node #0,2: 85:[8, 29, 64] Operation: 50+14=64 Exploring Operation: 50-14=36, Resulting Numbers: [8, 29, 36] Generated Node #0,3: 85:[8, 29, 36] Operation: 50-14=36 Exploring Operation: 50+29=79, Resulting Numbers: [8, 14, 79] Generated Node #0,4: 85:[8, 14, 79] Operation: 50+29=79 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[8, 14, 21], Operations: ['50-29=21'] Exploring Operation: 14-8=6, Resulting Numbers: [21, 6] Generated Node #0,0,0: 85:[21, 6] Operation: 14-8=6 Exploring Operation: 21-8=13, Resulting Numbers: [14, 13] Generated Node #0,0,1: 85:[14, 13] Operation: 21-8=13 Exploring Operation: 8+21=29, Resulting Numbers: [14, 29] Generated Node #0,0,2: 85:[14, 29] Operation: 8+21=29 Exploring Operation: 8+14=22, Resulting Numbers: [21, 22] Generated Node #0,0,3: 85:[21, 22] Operation: 8+14=22 Exploring Operation: 21-14=7, Resulting Numbers: [8, 7] Generated Node #0,0,4: 85:[8, 7] Operation: 21-14=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[21, 6], Operations: ['50-29=21', '14-8=6'] Exploring Operation: 21*6=126, Resulting Numbers: [126] 126,85 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 21+6=27, Resulting Numbers: [27] 27,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 85:[8, 7], Operations: ['50-29=21', '21-14=7'] Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,85 unequal: No Solution Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 85:[14, 13], Operations: ['50-29=21', '21-8=13'] Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,85 unequal: No Solution Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 85:[21, 22], Operations: ['50-29=21', '8+14=22'] Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 21*22=462, Resulting Numbers: [462] 462,85 unequal: No Solution Exploring Operation: 21+22=43, Resulting Numbers: [43] 43,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 85:[14, 29], Operations: ['50-29=21', '8+21=29'] Exploring Operation: 14+29=43, Resulting Numbers: [43] 43,85 unequal: No Solution Exploring Operation: 14*29=406, Resulting Numbers: [406] 406,85 unequal: No Solution Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,85 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: 85:[8, 14, 79], Operations: ['50+29=79'] Exploring Operation: 79-8=71, Resulting Numbers: [14, 71] Generated Node #0,4,0: 85:[14, 71] Operation: 79-8=71 Exploring Operation: 8+79=87, Resulting Numbers: [14, 87] Generated Node #0,4,1: 85:[14, 87] Operation: 8+79=87 Exploring Operation: 14-8=6, Resulting Numbers: [79, 6] Generated Node #0,4,2: 85:[79, 6] Operation: 14-8=6 Exploring Operation: 8+14=22, Resulting Numbers: [79, 22] Generated Node #0,4,3: 85:[79, 22] Operation: 8+14=22 Exploring Operation: 14+79=93, Resulting Numbers: [8, 93] Generated Node #0,4,4: 85:[8, 93] Operation: 14+79=93 Moving to Node #0,4,1 Current State: 85:[14, 87], Operations: ['50+29=79', '8+79=87'] Exploring Operation: 14+87=101, Resulting Numbers: [101] 101,85 unequal: No Solution Exploring Operation: 14*87=1218, Resulting Numbers: [1218] 1218,85 unequal: No Solution Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,85 unequal: No Solution Moving to Node #0,4,2 Current State: 85:[79, 6], Operations: ['50+29=79', '14-8=6'] Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,85 unequal: No Solution Exploring Operation: 79+6=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[8, 50, 14, 29], Operations: [] Exploring Operation: 50+29=79, Resulting Numbers: [8, 14, 79] Generated Node #0,4: 85:[8, 14, 79] Operation: 50+29=79 Moving to Node #0,4 Current State: 85:[8, 14, 79], Operations: ['50+29=79'] Exploring Operation: 14-8=6, Resulting Numbers: [79, 6] Generated Node #0,4,2: 85:[79, 6] Operation: 14-8=6 Moving to Node #0,4,2 Current State: 85:[79, 6], Operations: ['50+29=79', '14-8=6'] Exploring Operation: 79+6=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_5
sum_heuristic
[ 34, 18, 46, 27 ]
71
[ "34+18=52", "46-27=19", "52+19=71" ]
Current State: 71:[34, 18, 46, 27], Operations: [] Exploring Operation: 34+18=52, Resulting Numbers: [46, 27, 52] Generated Node #2: [46, 27, 52] from Operation: 34+18=52 Current State: 71:[46, 27, 52], Operations: ['34+18=52'] Exploring Operation: 46-27=19, Resulting Numbers: [52, 19] Generated Node #3: [52, 19] from Operation: 46-27=19 Current State: 71:[52, 19], Operations: ['34+18=52', '46-27=19'] Exploring Operation: 52+19=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[34, 18, 46, 27], Operations: [] Exploring Operation: 34+27=61, Resulting Numbers: [18, 46, 61] Generated Node #0,0: 71:[18, 46, 61] Operation: 34+27=61 Exploring Operation: 18+27=45, Resulting Numbers: [34, 46, 45] Generated Node #0,1: 71:[34, 46, 45] Operation: 18+27=45 Exploring Operation: 18+46=64, Resulting Numbers: [34, 27, 64] Generated Node #0,2: 71:[34, 27, 64] Operation: 18+46=64 Exploring Operation: 34+18=52, Resulting Numbers: [46, 27, 52] Generated Node #0,3: 71:[46, 27, 52] Operation: 34+18=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[18, 46, 61], Operations: ['34+27=61'] Exploring Operation: 46-18=28, Resulting Numbers: [61, 28] Generated Node #0,0,0: 71:[61, 28] Operation: 46-18=28 Exploring Operation: 61-18=43, Resulting Numbers: [46, 43] Generated Node #0,0,1: 71:[46, 43] Operation: 61-18=43 Exploring Operation: 18+46=64, Resulting Numbers: [61, 64] Generated Node #0,0,2: 71:[61, 64] Operation: 18+46=64 Exploring Operation: 18+61=79, Resulting Numbers: [46, 79] Generated Node #0,0,3: 71:[46, 79] Operation: 18+61=79 Moving to Node #0,0,2 Current State: 71:[61, 64], Operations: ['34+27=61', '18+46=64'] Exploring Operation: 64-61=3, Resulting Numbers: [3] 3,71 unequal: No Solution Exploring Operation: 61*64=3904, Resulting Numbers: [3904] 3904,71 unequal: No Solution Exploring Operation: 61+64=125, Resulting Numbers: [125] 125,71 unequal: No Solution Moving to Node #0,0,3 Current State: 71:[46, 79], Operations: ['34+27=61', '18+61=79'] Exploring Operation: 46*79=3634, Resulting Numbers: [3634] 3634,71 unequal: No Solution Exploring Operation: 79-46=33, Resulting Numbers: [33] 33,71 unequal: No Solution Exploring Operation: 46+79=125, Resulting Numbers: [125] 125,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[46, 43], Operations: ['34+27=61', '61-18=43'] Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,71 unequal: No Solution Exploring Operation: 46*43=1978, Resulting Numbers: [1978] 1978,71 unequal: No Solution Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[61, 28], Operations: ['34+27=61', '46-18=28'] Exploring Operation: 61+28=89, Resulting Numbers: [89] 89,71 unequal: No Solution Exploring Operation: 61*28=1708, Resulting Numbers: [1708] 1708,71 unequal: No Solution Exploring Operation: 61-28=33, Resulting Numbers: [33] 33,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[34, 46, 45], Operations: ['18+27=45'] Exploring Operation: 34+46=80, Resulting Numbers: [45, 80] Generated Node #0,1,0: 71:[45, 80] Operation: 34+46=80 Exploring Operation: 46-34=12, Resulting Numbers: [45, 12] Generated Node #0,1,1: 71:[45, 12] Operation: 46-34=12 Exploring Operation: 34+45=79, Resulting Numbers: [46, 79] Generated Node #0,1,2: 71:[46, 79] Operation: 34+45=79 Exploring Operation: 46+45=91, Resulting Numbers: [34, 91] Generated Node #0,1,3: 71:[34, 91] Operation: 46+45=91 Moving to Node #0,1,2 Current State: 71:[46, 79], Operations: ['18+27=45', '34+45=79'] Exploring Operation: 46+79=125, Resulting Numbers: [125] 125,71 unequal: No Solution Exploring Operation: 79-46=33, Resulting Numbers: [33] 33,71 unequal: No Solution Exploring Operation: 46*79=3634, Resulting Numbers: [3634] 3634,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[45, 80], Operations: ['18+27=45', '34+46=80'] Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,71 unequal: No Solution Exploring Operation: 45+80=125, Resulting Numbers: [125] 125,71 unequal: No Solution Exploring Operation: 45*80=3600, Resulting Numbers: [3600] 3600,71 unequal: No Solution Moving to Node #0,1,3 Current State: 71:[34, 91], Operations: ['18+27=45', '46+45=91'] Exploring Operation: 91-34=57, Resulting Numbers: [57] 57,71 unequal: No Solution Exploring Operation: 34+91=125, Resulting Numbers: [125] 125,71 unequal: No Solution Exploring Operation: 34*91=3094, Resulting Numbers: [3094] 3094,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[45, 12], Operations: ['18+27=45', '46-34=12'] Exploring Operation: 45*12=540, Resulting Numbers: [540] 540,71 unequal: No Solution Exploring Operation: 45+12=57, Resulting Numbers: [57] 57,71 unequal: No Solution Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[34, 27, 64], Operations: ['18+46=64'] Exploring Operation: 34-27=7, Resulting Numbers: [64, 7] Generated Node #0,2,0: 71:[64, 7] Operation: 34-27=7 Exploring Operation: 34+64=98, Resulting Numbers: [27, 98] Generated Node #0,2,1: 71:[27, 98] Operation: 34+64=98 Exploring Operation: 27+64=91, Resulting Numbers: [34, 91] Generated Node #0,2,2: 71:[34, 91] Operation: 27+64=91 Exploring Operation: 34+27=61, Resulting Numbers: [64, 61] Generated Node #0,2,3: 71:[64, 61] Operation: 34+27=61 Moving to Node #0,2,3 Current State: 71:[64, 61], Operations: ['18+46=64', '34+27=61'] Exploring Operation: 64+61=125, Resulting Numbers: [125] 125,71 unequal: No Solution Exploring Operation: 64*61=3904, Resulting Numbers: [3904] 3904,71 unequal: No Solution Exploring Operation: 64-61=3, Resulting Numbers: [3] 3,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[34, 91], Operations: ['18+46=64', '27+64=91'] Exploring Operation: 34*91=3094, Resulting Numbers: [3094] 3094,71 unequal: No Solution Exploring Operation: 34+91=125, Resulting Numbers: [125] 125,71 unequal: No Solution Exploring Operation: 91-34=57, Resulting Numbers: [57] 57,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[27, 98], Operations: ['18+46=64', '34+64=98'] Exploring Operation: 27+98=125, Resulting Numbers: [125] 125,71 unequal: No Solution Exploring Operation: 27*98=2646, Resulting Numbers: [2646] 2646,71 unequal: No Solution Exploring Operation: 98-27=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[34, 18, 46, 27], Operations: [] Exploring Operation: 18+46=64, Resulting Numbers: [34, 27, 64] Generated Node #0,2: 71:[34, 27, 64] Operation: 18+46=64 Moving to Node #0,2 Current State: 71:[34, 27, 64], Operations: ['18+46=64'] Exploring Operation: 34+64=98, Resulting Numbers: [27, 98] Generated Node #0,2,1: 71:[27, 98] Operation: 34+64=98 Moving to Node #0,2,1 Current State: 71:[27, 98], Operations: ['18+46=64', '34+64=98'] Exploring Operation: 98-27=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.953993
hs_4
mult_heuristic
[ 77, 79, 87, 84 ]
56
[ "84-77=7", "87-79=8", "7*8=56" ]
Current State: 56:[77, 79, 87, 84], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [79, 87, 7] Generated Node #2: [79, 87, 7] from Operation: 84-77=7 Current State: 56:[79, 87, 7], Operations: ['84-77=7'] Exploring Operation: 87-79=8, Resulting Numbers: [7, 8] Generated Node #3: [7, 8] from Operation: 87-79=8 Current State: 56:[7, 8], Operations: ['84-77=7', '87-79=8'] Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[77, 79, 87, 84], Operations: [] Exploring Operation: 87-84=3, Resulting Numbers: [77, 79, 3] Generated Node #0,0: 56:[77, 79, 3] Operation: 87-84=3 Exploring Operation: 87-79=8, Resulting Numbers: [77, 84, 8] Generated Node #0,1: 56:[77, 84, 8] Operation: 87-79=8 Exploring Operation: 87-77=10, Resulting Numbers: [79, 84, 10] Generated Node #0,2: 56:[79, 84, 10] Operation: 87-77=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[77, 79, 3], Operations: ['87-84=3'] Exploring Operation: 79-77=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 56:[3, 2] Operation: 79-77=2 Exploring Operation: 77-3=74, Resulting Numbers: [79, 74] Generated Node #0,0,1: 56:[79, 74] Operation: 77-3=74 Exploring Operation: 79-3=76, Resulting Numbers: [77, 76] Generated Node #0,0,2: 56:[77, 76] Operation: 79-3=76 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[3, 2], Operations: ['87-84=3', '79-77=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,56 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 56:[79, 74], Operations: ['87-84=3', '77-3=74'] Exploring Operation: 79+74=153, Resulting Numbers: [153] 153,56 unequal: No Solution Exploring Operation: 79-74=5, Resulting Numbers: [5] 5,56 unequal: No Solution Exploring Operation: 79*74=5846, Resulting Numbers: [5846] 5846,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 56:[77, 76], Operations: ['87-84=3', '79-3=76'] Exploring Operation: 77*76=5852, Resulting Numbers: [5852] 5852,56 unequal: No Solution Exploring Operation: 77-76=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 77+76=153, Resulting Numbers: [153] 153,56 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: 56:[77, 84, 8], Operations: ['87-79=8'] Exploring Operation: 84-77=7, Resulting Numbers: [8, 7] Generated Node #0,1,0: 56:[8, 7] Operation: 84-77=7 Exploring Operation: 84-8=76, Resulting Numbers: [77, 76] Generated Node #0,1,1: 56:[77, 76] Operation: 84-8=76 Exploring Operation: 77-8=69, Resulting Numbers: [84, 69] Generated Node #0,1,2: 56:[84, 69] Operation: 77-8=69 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 56:[8, 7], Operations: ['87-79=8', '84-77=7'] Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,56 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[77, 79, 87, 84], Operations: [] Exploring Operation: 87-79=8, Resulting Numbers: [77, 84, 8] Generated Node #0,1: 56:[77, 84, 8] Operation: 87-79=8 Moving to Node #0,1 Current State: 56:[77, 84, 8], Operations: ['87-79=8'] Exploring Operation: 84-77=7, Resulting Numbers: [8, 7] Generated Node #0,1,0: 56:[8, 7] Operation: 84-77=7 Moving to Node #0,1,0 Current State: 56:[8, 7], Operations: ['87-79=8', '84-77=7'] Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 50, 4, 19, 99 ]
82
[ "50*4=200", "19+99=118", "200-118=82" ]
Current State: 82:[50, 4, 19, 99], Operations: [] Exploring Operation: 50*4=200, Resulting Numbers: [19, 99, 200] Generated Node #2: [19, 99, 200] from Operation: 50*4=200 Current State: 82:[19, 99, 200], Operations: ['50*4=200'] Exploring Operation: 19+99=118, Resulting Numbers: [200, 118] Generated Node #3: [200, 118] from Operation: 19+99=118 Current State: 82:[200, 118], Operations: ['50*4=200', '19+99=118'] Exploring Operation: 200-118=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[50, 4, 19, 99], Operations: [] Exploring Operation: 4*19=76, Resulting Numbers: [50, 99, 76] Generated Node #0,0: 82:[50, 99, 76] Operation: 4*19=76 Exploring Operation: 50+19=69, Resulting Numbers: [4, 99, 69] Generated Node #0,1: 82:[4, 99, 69] Operation: 50+19=69 Exploring Operation: 99-19=80, Resulting Numbers: [50, 4, 80] Generated Node #0,2: 82:[50, 4, 80] Operation: 99-19=80 Exploring Operation: 99-50=49, Resulting Numbers: [4, 19, 49] Generated Node #0,3: 82:[4, 19, 49] Operation: 99-50=49 Exploring Operation: 50-19=31, Resulting Numbers: [4, 99, 31] Generated Node #0,4: 82:[4, 99, 31] Operation: 50-19=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[50, 4, 80], Operations: ['99-19=80'] Exploring Operation: 80-50=30, Resulting Numbers: [4, 30] Generated Node #0,2,0: 82:[4, 30] Operation: 80-50=30 Exploring Operation: 80-4=76, Resulting Numbers: [50, 76] Generated Node #0,2,1: 82:[50, 76] Operation: 80-4=76 Exploring Operation: 50+4=54, Resulting Numbers: [80, 54] Generated Node #0,2,2: 82:[80, 54] Operation: 50+4=54 Exploring Operation: 4+80=84, Resulting Numbers: [50, 84] Generated Node #0,2,3: 82:[50, 84] Operation: 4+80=84 Exploring Operation: 50-4=46, Resulting Numbers: [80, 46] Generated Node #0,2,4: 82:[80, 46] Operation: 50-4=46 Moving to Node #0,2,4 Current State: 82:[80, 46], Operations: ['99-19=80', '50-4=46'] Exploring Operation: 80+46=126, Resulting Numbers: [126] 126,82 unequal: No Solution Exploring Operation: 80-46=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 80*46=3680, Resulting Numbers: [3680] 3680,82 unequal: No Solution Moving to Node #0,2,3 Current State: 82:[50, 84], Operations: ['99-19=80', '4+80=84'] Exploring Operation: 50*84=4200, Resulting Numbers: [4200] 4200,82 unequal: No Solution Exploring Operation: 84-50=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 50+84=134, Resulting Numbers: [134] 134,82 unequal: No Solution Moving to Node #0,2,0 Current State: 82:[4, 30], Operations: ['99-19=80', '80-50=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,82 unequal: No Solution Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,82 unequal: No Solution Moving to Node #0,2,1 Current State: 82:[50, 76], Operations: ['99-19=80', '80-4=76'] Exploring Operation: 50*76=3800, Resulting Numbers: [3800] 3800,82 unequal: No Solution Exploring Operation: 50+76=126, Resulting Numbers: [126] 126,82 unequal: No Solution Exploring Operation: 76-50=26, Resulting Numbers: [26] 26,82 unequal: No Solution Moving to Node #0,2,2 Current State: 82:[80, 54], Operations: ['99-19=80', '50+4=54'] Exploring Operation: 80*54=4320, Resulting Numbers: [4320] 4320,82 unequal: No Solution Exploring Operation: 80-54=26, Resulting Numbers: [26] 26,82 unequal: No Solution Exploring Operation: 80+54=134, Resulting Numbers: [134] 134,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[4, 19, 49], Operations: ['99-50=49'] Exploring Operation: 49-19=30, Resulting Numbers: [4, 30] Generated Node #0,3,0: 82:[4, 30] Operation: 49-19=30 Exploring Operation: 19+49=68, Resulting Numbers: [4, 68] Generated Node #0,3,1: 82:[4, 68] Operation: 19+49=68 Exploring Operation: 49-4=45, Resulting Numbers: [19, 45] Generated Node #0,3,2: 82:[19, 45] Operation: 49-4=45 Exploring Operation: 19-4=15, Resulting Numbers: [49, 15] Generated Node #0,3,3: 82:[49, 15] Operation: 19-4=15 Exploring Operation: 4*19=76, Resulting Numbers: [49, 76] Generated Node #0,3,4: 82:[49, 76] Operation: 4*19=76 Moving to Node #0,3,0 Current State: 82:[4, 30], Operations: ['99-50=49', '49-19=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,82 unequal: No Solution Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,82 unequal: No Solution Moving to Node #0,3,4 Current State: 82:[49, 76], Operations: ['99-50=49', '4*19=76'] Exploring Operation: 49+76=125, Resulting Numbers: [125] 125,82 unequal: No Solution Exploring Operation: 76-49=27, Resulting Numbers: [27] 27,82 unequal: No Solution Exploring Operation: 49*76=3724, Resulting Numbers: [3724] 3724,82 unequal: No Solution Moving to Node #0,3,1 Current State: 82:[4, 68], Operations: ['99-50=49', '19+49=68'] Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,82 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,82 unequal: No Solution Moving to Node #0,3,2 Current State: 82:[19, 45], Operations: ['99-50=49', '49-4=45'] Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,82 unequal: No Solution Exploring Operation: 19*45=855, Resulting Numbers: [855] 855,82 unequal: No Solution Exploring Operation: 19+45=64, Resulting Numbers: [64] 64,82 unequal: No Solution Moving to Node #0,3,3 Current State: 82:[49, 15], Operations: ['99-50=49', '19-4=15'] Exploring Operation: 49+15=64, Resulting Numbers: [64] 64,82 unequal: No Solution Exploring Operation: 49-15=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 49*15=735, Resulting Numbers: [735] 735,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 82:[4, 99, 31], Operations: ['50-19=31'] Exploring Operation: 4+99=103, Resulting Numbers: [31, 103] Generated Node #0,4,0: 82:[31, 103] Operation: 4+99=103 Exploring Operation: 4+31=35, Resulting Numbers: [99, 35] Generated Node #0,4,1: 82:[99, 35] Operation: 4+31=35 Exploring Operation: 99-31=68, Resulting Numbers: [4, 68] Generated Node #0,4,2: 82:[4, 68] Operation: 99-31=68 Exploring Operation: 99-4=95, Resulting Numbers: [31, 95] Generated Node #0,4,3: 82:[31, 95] Operation: 99-4=95 Exploring Operation: 31-4=27, Resulting Numbers: [99, 27] Generated Node #0,4,4: 82:[99, 27] Operation: 31-4=27 Moving to Node #0,4,2 Current State: 82:[4, 68], Operations: ['50-19=31', '99-31=68'] Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,82 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,82 unequal: No Solution Moving to Node #0,4,3 Current State: 82:[31, 95], Operations: ['50-19=31', '99-4=95'] Exploring Operation: 31+95=126, Resulting Numbers: [126] 126,82 unequal: No Solution Exploring Operation: 95-31=64, Resulting Numbers: [64] 64,82 unequal: No Solution Exploring Operation: 31*95=2945, Resulting Numbers: [2945] 2945,82 unequal: No Solution Moving to Node #0,4,1 Current State: 82:[99, 35], Operations: ['50-19=31', '4+31=35'] Exploring Operation: 99*35=3465, Resulting Numbers: [3465] 3465,82 unequal: No Solution Exploring Operation: 99-35=64, Resulting Numbers: [64] 64,82 unequal: No Solution Exploring Operation: 99+35=134, Resulting Numbers: [134] 134,82 unequal: No Solution Moving to Node #0,4,0 Current State: 82:[31, 103], Operations: ['50-19=31', '4+99=103'] Exploring Operation: 103-31=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 31*103=3193, Resulting Numbers: [3193] 3193,82 unequal: No Solution Exploring Operation: 31+103=134, Resulting Numbers: [134] 134,82 unequal: No Solution Moving to Node #0,4,4 Current State: 82:[99, 27], Operations: ['50-19=31', '31-4=27'] Exploring Operation: 99-27=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 99+27=126, Resulting Numbers: [126] 126,82 unequal: No Solution Exploring Operation: 99*27=2673, Resulting Numbers: [2673] 2673,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[50, 99, 76], Operations: ['4*19=76'] Exploring Operation: 99-76=23, Resulting Numbers: [50, 23] Generated Node #0,0,0: 82:[50, 23] Operation: 99-76=23 Exploring Operation: 50+76=126, Resulting Numbers: [99, 126] Generated Node #0,0,1: 82:[99, 126] Operation: 50+76=126 Exploring Operation: 76-50=26, Resulting Numbers: [99, 26] Generated Node #0,0,2: 82:[99, 26] Operation: 76-50=26 Exploring Operation: 50+99=149, Resulting Numbers: [76, 149] Generated Node #0,0,3: 82:[76, 149] Operation: 50+99=149 Exploring Operation: 99-50=49, Resulting Numbers: [76, 49] Generated Node #0,0,4: 82:[76, 49] Operation: 99-50=49 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 82:[76, 49], Operations: ['4*19=76', '99-50=49'] Exploring Operation: 76*49=3724, Resulting Numbers: [3724] 3724,82 unequal: No Solution Exploring Operation: 76-49=27, Resulting Numbers: [27] 27,82 unequal: No Solution Exploring Operation: 76+49=125, Resulting Numbers: [125] 125,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[50, 23], Operations: ['4*19=76', '99-76=23'] Exploring Operation: 50*23=1150, Resulting Numbers: [1150] 1150,82 unequal: No Solution Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,82 unequal: No Solution Exploring Operation: 50+23=73, Resulting Numbers: [73] 73,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[99, 26], Operations: ['4*19=76', '76-50=26'] Exploring Operation: 99+26=125, Resulting Numbers: [125] 125,82 unequal: No Solution Exploring Operation: 99-26=73, Resulting Numbers: [73] 73,82 unequal: No Solution Exploring Operation: 99*26=2574, Resulting Numbers: [2574] 2574,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[99, 126], Operations: ['4*19=76', '50+76=126'] Exploring Operation: 99*126=12474, Resulting Numbers: [12474] 12474,82 unequal: No Solution Exploring Operation: 126-99=27, Resulting Numbers: [27] 27,82 unequal: No Solution Exploring Operation: 99+126=225, Resulting Numbers: [225] 225,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 82:[76, 149], Operations: ['4*19=76', '50+99=149'] Exploring Operation: 76*149=11324, Resulting Numbers: [11324] 11324,82 unequal: No Solution Exploring Operation: 149-76=73, Resulting Numbers: [73] 73,82 unequal: No Solution Exploring Operation: 76+149=225, Resulting Numbers: [225] 225,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[4, 99, 69], Operations: ['50+19=69'] Exploring Operation: 4+69=73, Resulting Numbers: [99, 73] Generated Node #0,1,0: 82:[99, 73] Operation: 4+69=73 Exploring Operation: 4+99=103, Resulting Numbers: [69, 103] Generated Node #0,1,1: 82:[69, 103] Operation: 4+99=103 Exploring Operation: 99-4=95, Resulting Numbers: [69, 95] Generated Node #0,1,2: 82:[69, 95] Operation: 99-4=95 Exploring Operation: 99-69=30, Resulting Numbers: [4, 30] Generated Node #0,1,3: 82:[4, 30] Operation: 99-69=30 Exploring Operation: 69-4=65, Resulting Numbers: [99, 65] Generated Node #0,1,4: 82:[99, 65] Operation: 69-4=65 Moving to Node #0,1,3 Current State: 82:[4, 30], Operations: ['50+19=69', '99-69=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,82 unequal: No Solution Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[69, 95], Operations: ['50+19=69', '99-4=95'] Exploring Operation: 69+95=164, Resulting Numbers: [164] 164,82 unequal: No Solution Exploring Operation: 95-69=26, Resulting Numbers: [26] 26,82 unequal: No Solution Exploring Operation: 69*95=6555, Resulting Numbers: [6555] 6555,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[99, 73], Operations: ['50+19=69', '4+69=73'] Exploring Operation: 99*73=7227, Resulting Numbers: [7227] 7227,82 unequal: No Solution Exploring Operation: 99+73=172, Resulting Numbers: [172] 172,82 unequal: No Solution Exploring Operation: 99-73=26, Resulting Numbers: [26] 26,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[69, 103], Operations: ['50+19=69', '4+99=103'] Exploring Operation: 69+103=172, Resulting Numbers: [172] 172,82 unequal: No Solution Exploring Operation: 103-69=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 69*103=7107, Resulting Numbers: [7107] 7107,82 unequal: No Solution Moving to Node #0,1,4 Current State: 82:[99, 65], Operations: ['50+19=69', '69-4=65'] Exploring Operation: 99*65=6435, Resulting Numbers: [6435] 6435,82 unequal: No Solution Exploring Operation: 99-65=34, Resulting Numbers: [34] 34,82 unequal: No Solution Exploring Operation: 99+65=164, Resulting Numbers: [164] 164,82 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
[ 31, 55, 22, 25 ]
89
[ "31+55=86", "25-22=3", "86+3=89" ]
Current State: 89:[31, 55, 22, 25], Operations: [] Exploring Operation: 31+55=86, Resulting Numbers: [22, 25, 86] Generated Node #2: [22, 25, 86] from Operation: 31+55=86 Current State: 89:[22, 25, 86], Operations: ['31+55=86'] Exploring Operation: 25-22=3, Resulting Numbers: [86, 3] Generated Node #3: [86, 3] from Operation: 25-22=3 Current State: 89:[86, 3], Operations: ['31+55=86', '25-22=3'] Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[31, 55, 22, 25], Operations: [] Exploring Operation: 31+55=86, Resulting Numbers: [22, 25, 86] Generated Node #0,0: 89:[22, 25, 86] Operation: 31+55=86 Exploring Operation: 31+22=53, Resulting Numbers: [55, 25, 53] Generated Node #0,1: 89:[55, 25, 53] Operation: 31+22=53 Exploring Operation: 31+25=56, Resulting Numbers: [55, 22, 56] Generated Node #0,2: 89:[55, 22, 56] Operation: 31+25=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[22, 25, 86], Operations: ['31+55=86'] Exploring Operation: 22+25=47, Resulting Numbers: [86, 47] Generated Node #0,0,0: 89:[86, 47] Operation: 22+25=47 Exploring Operation: 22+86=108, Resulting Numbers: [25, 108] Generated Node #0,0,1: 89:[25, 108] Operation: 22+86=108 Exploring Operation: 25-22=3, Resulting Numbers: [86, 3] Generated Node #0,0,2: 89:[86, 3] Operation: 25-22=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[86, 47], Operations: ['31+55=86', '22+25=47'] Exploring Operation: 86*47=4042, Resulting Numbers: [4042] 4042,89 unequal: No Solution Exploring Operation: 86+47=133, Resulting Numbers: [133] 133,89 unequal: No Solution Exploring Operation: 86-47=39, Resulting Numbers: [39] 39,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[25, 108], Operations: ['31+55=86', '22+86=108'] Exploring Operation: 25+108=133, Resulting Numbers: [133] 133,89 unequal: No Solution Exploring Operation: 25*108=2700, Resulting Numbers: [2700] 2700,89 unequal: No Solution Exploring Operation: 108-25=83, Resulting Numbers: [83] 83,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[86, 3], Operations: ['31+55=86', '25-22=3'] Exploring Operation: 86*3=258, Resulting Numbers: [258] 258,89 unequal: No Solution Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,89 unequal: No Solution Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[31, 55, 22, 25], Operations: [] Exploring Operation: 31+55=86, Resulting Numbers: [22, 25, 86] Generated Node #0,0: 89:[22, 25, 86] Operation: 31+55=86 Moving to Node #0,0 Current State: 89:[22, 25, 86], Operations: ['31+55=86'] Exploring Operation: 25-22=3, Resulting Numbers: [86, 3] Generated Node #0,0,2: 89:[86, 3] Operation: 25-22=3 Moving to Node #0,0,2 Current State: 89:[86, 3], Operations: ['31+55=86', '25-22=3'] Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 86, 68, 36, 73 ]
75
[ "86-68=18", "36/18=2", "73+2=75" ]
Current State: 75:[86, 68, 36, 73], Operations: [] Exploring Operation: 86-68=18, Resulting Numbers: [36, 73, 18] Generated Node #2: [36, 73, 18] from Operation: 86-68=18 Current State: 75:[36, 73, 18], Operations: ['86-68=18'] Exploring Operation: 36/18=2, Resulting Numbers: [73, 2] Generated Node #3: [73, 2] from Operation: 36/18=2 Current State: 75:[73, 2], Operations: ['86-68=18', '36/18=2'] Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[86, 68, 36, 73], Operations: [] Exploring Operation: 86-68=18, Resulting Numbers: [36, 73, 18] Generated Node #0,0: 75:[36, 73, 18] Operation: 86-68=18 Moving to Node #0,0 Current State: 75:[36, 73, 18], Operations: ['86-68=18'] Exploring Operation: 36/18=2, Resulting Numbers: [73, 2] Generated Node #0,0,0: 75:[73, 2] Operation: 36/18=2 Moving to Node #0,0,0 Current State: 75:[73, 2], Operations: ['86-68=18', '36/18=2'] Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[86, 68, 36, 73], Operations: [] Exploring Operation: 86-68=18, Resulting Numbers: [36, 73, 18] Generated Node #0,0: 75:[36, 73, 18] Operation: 86-68=18 Moving to Node #0,0 Current State: 75:[36, 73, 18], Operations: ['86-68=18'] Exploring Operation: 36/18=2, Resulting Numbers: [73, 2] Generated Node #0,0,0: 75:[73, 2] Operation: 36/18=2 Moving to Node #0,0,0 Current State: 75:[73, 2], Operations: ['86-68=18', '36/18=2'] Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 27, 17, 8, 47 ]
65
[ "27-17=10", "8+47=55", "10+55=65" ]
Current State: 65:[27, 17, 8, 47], Operations: [] Exploring Operation: 27-17=10, Resulting Numbers: [8, 47, 10] Generated Node #2: [8, 47, 10] from Operation: 27-17=10 Current State: 65:[8, 47, 10], Operations: ['27-17=10'] Exploring Operation: 8+47=55, Resulting Numbers: [10, 55] Generated Node #3: [10, 55] from Operation: 8+47=55 Current State: 65:[10, 55], Operations: ['27-17=10', '8+47=55'] Exploring Operation: 10+55=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[27, 17, 8, 47], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [17, 8, 20] Generated Node #0,0: 65:[17, 8, 20] Operation: 47-27=20 Moving to Node #0,0 Current State: 65:[17, 8, 20], Operations: ['47-27=20'] Exploring Operation: 20-17=3, Resulting Numbers: [8, 3] Generated Node #0,0,0: 65:[8, 3] Operation: 20-17=3 Moving to Node #0,0,0 Current State: 65:[8, 3], Operations: ['47-27=20', '20-17=3'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,65 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 93, 96, 31, 26 ]
15
[ "96-93=3", "31-26=5", "3*5=15" ]
Current State: 15:[93, 96, 31, 26], Operations: [] Exploring Operation: 96-93=3, Resulting Numbers: [31, 26, 3] Generated Node #2: [31, 26, 3] from Operation: 96-93=3 Current State: 15:[31, 26, 3], Operations: ['96-93=3'] Exploring Operation: 31-26=5, Resulting Numbers: [3, 5] Generated Node #3: [3, 5] from Operation: 31-26=5 Current State: 15:[3, 5], Operations: ['96-93=3', '31-26=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[93, 96, 31, 26], Operations: [] Exploring Operation: 93/31=3, Resulting Numbers: [96, 26, 3] Generated Node #0,0: 15:[96, 26, 3] Operation: 93/31=3 Exploring Operation: 93-31=62, Resulting Numbers: [96, 26, 62] Generated Node #0,1: 15:[96, 26, 62] Operation: 93-31=62 Exploring Operation: 96-93=3, Resulting Numbers: [31, 26, 3] Generated Node #0,2: 15:[31, 26, 3] Operation: 96-93=3 Moving to Node #0,2 Current State: 15:[31, 26, 3], Operations: ['96-93=3'] Exploring Operation: 31-3=28, Resulting Numbers: [26, 28] Generated Node #0,2,0: 15:[26, 28] Operation: 31-3=28 Exploring Operation: 31-26=5, Resulting Numbers: [3, 5] Generated Node #0,2,1: 15:[3, 5] Operation: 31-26=5 Exploring Operation: 26-3=23, Resulting Numbers: [31, 23] Generated Node #0,2,2: 15:[31, 23] Operation: 26-3=23 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 15:[3, 5], Operations: ['96-93=3', '31-26=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[93, 96, 31, 26], Operations: [] Exploring Operation: 96-93=3, Resulting Numbers: [31, 26, 3] Generated Node #0,2: 15:[31, 26, 3] Operation: 96-93=3 Moving to Node #0,2 Current State: 15:[31, 26, 3], Operations: ['96-93=3'] Exploring Operation: 31-26=5, Resulting Numbers: [3, 5] Generated Node #0,2,1: 15:[3, 5] Operation: 31-26=5 Moving to Node #0,2,1 Current State: 15:[3, 5], Operations: ['96-93=3', '31-26=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 26, 85, 23, 49 ]
86
[ "26+23=49", "49/49=1", "85+1=86" ]
Current State: 86:[26, 85, 23, 49], Operations: [] Exploring Operation: 26+23=49, Resulting Numbers: [85, 49, 49] Generated Node #2: [85, 49, 49] from Operation: 26+23=49 Current State: 86:[85, 49, 49], Operations: ['26+23=49'] Exploring Operation: 49/49=1, Resulting Numbers: [85, 1] Generated Node #3: [85, 1] from Operation: 49/49=1 Current State: 86:[85, 1], Operations: ['26+23=49', '49/49=1'] Exploring Operation: 85+1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[26, 85, 23, 49], Operations: [] Exploring Operation: 26-23=3, Resulting Numbers: [85, 49, 3] Generated Node #0,0: 86:[85, 49, 3] Operation: 26-23=3 Exploring Operation: 26+49=75, Resulting Numbers: [85, 23, 75] Generated Node #0,1: 86:[85, 23, 75] Operation: 26+49=75 Exploring Operation: 26+23=49, Resulting Numbers: [85, 49, 49] Generated Node #0,2: 86:[85, 49, 49] Operation: 26+23=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[85, 49, 3], Operations: ['26-23=3'] Exploring Operation: 49-3=46, Resulting Numbers: [85, 46] Generated Node #0,0,0: 86:[85, 46] Operation: 49-3=46 Exploring Operation: 85+3=88, Resulting Numbers: [49, 88] Generated Node #0,0,1: 86:[49, 88] Operation: 85+3=88 Exploring Operation: 85-49=36, Resulting Numbers: [3, 36] Generated Node #0,0,2: 86:[3, 36] Operation: 85-49=36 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[85, 46], Operations: ['26-23=3', '49-3=46'] Exploring Operation: 85-46=39, Resulting Numbers: [39] 39,86 unequal: No Solution Exploring Operation: 85*46=3910, Resulting Numbers: [3910] 3910,86 unequal: No Solution Exploring Operation: 85+46=131, Resulting Numbers: [131] 131,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[49, 88], Operations: ['26-23=3', '85+3=88'] Exploring Operation: 88-49=39, Resulting Numbers: [39] 39,86 unequal: No Solution Exploring Operation: 49+88=137, Resulting Numbers: [137] 137,86 unequal: No Solution Exploring Operation: 49*88=4312, Resulting Numbers: [4312] 4312,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 86:[3, 36], Operations: ['26-23=3', '85-49=36'] Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,86 unequal: No Solution Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,86 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,86 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:[85, 49, 49], Operations: ['26+23=49'] Exploring Operation: 85-49=36, Resulting Numbers: [49, 36] Generated Node #0,2,0: 86:[49, 36] Operation: 85-49=36 Exploring Operation: 49-49=0, Resulting Numbers: [85, 0] Generated Node #0,2,1: 86:[85, 0] Operation: 49-49=0 Exploring Operation: 49/49=1, Resulting Numbers: [85, 1] Generated Node #0,2,2: 86:[85, 1] Operation: 49/49=1 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 86:[85, 1], Operations: ['26+23=49', '49/49=1'] Exploring Operation: 85+1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[26, 85, 23, 49], Operations: [] Exploring Operation: 26+23=49, Resulting Numbers: [85, 49, 49] Generated Node #0,2: 86:[85, 49, 49] Operation: 26+23=49 Moving to Node #0,2 Current State: 86:[85, 49, 49], Operations: ['26+23=49'] Exploring Operation: 49/49=1, Resulting Numbers: [85, 1] Generated Node #0,2,2: 86:[85, 1] Operation: 49/49=1 Moving to Node #0,2,2 Current State: 86:[85, 1], Operations: ['26+23=49', '49/49=1'] Exploring Operation: 85+1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 36, 39, 61, 49 ]
64
[ "49-36=13", "39/13=3", "61+3=64" ]
Current State: 64:[36, 39, 61, 49], Operations: [] Exploring Operation: 49-36=13, Resulting Numbers: [39, 61, 13] Generated Node #2: [39, 61, 13] from Operation: 49-36=13 Current State: 64:[39, 61, 13], Operations: ['49-36=13'] Exploring Operation: 39/13=3, Resulting Numbers: [61, 3] Generated Node #3: [61, 3] from Operation: 39/13=3 Current State: 64:[61, 3], Operations: ['49-36=13', '39/13=3'] Exploring Operation: 61+3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[36, 39, 61, 49], Operations: [] Exploring Operation: 61-49=12, Resulting Numbers: [36, 39, 12] Generated Node #0,0: 64:[36, 39, 12] Operation: 61-49=12 Exploring Operation: 49-39=10, Resulting Numbers: [36, 61, 10] Generated Node #0,1: 64:[36, 61, 10] Operation: 49-39=10 Exploring Operation: 49-36=13, Resulting Numbers: [39, 61, 13] Generated Node #0,2: 64:[39, 61, 13] Operation: 49-36=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[36, 61, 10], Operations: ['49-39=10'] Exploring Operation: 61+10=71, Resulting Numbers: [36, 71] Generated Node #0,1,0: 64:[36, 71] Operation: 61+10=71 Exploring Operation: 61-36=25, Resulting Numbers: [10, 25] Generated Node #0,1,1: 64:[10, 25] Operation: 61-36=25 Exploring Operation: 36-10=26, Resulting Numbers: [61, 26] Generated Node #0,1,2: 64:[61, 26] Operation: 36-10=26 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 64:[10, 25], Operations: ['49-39=10', '61-36=25'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,64 unequal: No Solution Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,64 unequal: No Solution Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,64 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 #0,1,2 Current State: 64:[61, 26], Operations: ['49-39=10', '36-10=26'] Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,64 unequal: No Solution Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,64 unequal: No Solution Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,64 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 #0,1,0 Current State: 64:[36, 71], Operations: ['49-39=10', '61+10=71'] Exploring Operation: 36+71=107, Resulting Numbers: [107] 107,64 unequal: No Solution Exploring Operation: 36*71=2556, Resulting Numbers: [2556] 2556,64 unequal: No Solution Exploring Operation: 71-36=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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[39, 61, 13], Operations: ['49-36=13'] Exploring Operation: 39/13=3, Resulting Numbers: [61, 3] Generated Node #0,2,0: 64:[61, 3] Operation: 39/13=3 Exploring Operation: 39-13=26, Resulting Numbers: [61, 26] Generated Node #0,2,1: 64:[61, 26] Operation: 39-13=26 Exploring Operation: 61-39=22, Resulting Numbers: [13, 22] Generated Node #0,2,2: 64:[13, 22] Operation: 61-39=22 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 64:[61, 3], Operations: ['49-36=13', '39/13=3'] Exploring Operation: 61*3=183, Resulting Numbers: [183] 183,64 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,64 unequal: No Solution Exploring Operation: 61+3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[36, 39, 61, 49], Operations: [] Exploring Operation: 49-36=13, Resulting Numbers: [39, 61, 13] Generated Node #0,2: 64:[39, 61, 13] Operation: 49-36=13 Moving to Node #0,2 Current State: 64:[39, 61, 13], Operations: ['49-36=13'] Exploring Operation: 39/13=3, Resulting Numbers: [61, 3] Generated Node #0,2,0: 64:[61, 3] Operation: 39/13=3 Moving to Node #0,2,0 Current State: 64:[61, 3], Operations: ['49-36=13', '39/13=3'] Exploring Operation: 61+3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_3
sum_heuristic
[ 22, 45, 39, 44 ]
17
[ "39-22=17", "45-44=1", "17*1=17" ]
Current State: 17:[22, 45, 39, 44], Operations: [] Exploring Operation: 39-22=17, Resulting Numbers: [45, 44, 17] Generated Node #2: [45, 44, 17] from Operation: 39-22=17 Current State: 17:[45, 44, 17], Operations: ['39-22=17'] Exploring Operation: 45-44=1, Resulting Numbers: [17, 1] Generated Node #3: [17, 1] from Operation: 45-44=1 Current State: 17:[17, 1], Operations: ['39-22=17', '45-44=1'] Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[22, 45, 39, 44], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [22, 39, 1] Generated Node #0,0: 17:[22, 39, 1] Operation: 45-44=1 Exploring Operation: 45-39=6, Resulting Numbers: [22, 44, 6] Generated Node #0,1: 17:[22, 44, 6] Operation: 45-39=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[22, 39, 1], Operations: ['45-44=1'] Exploring Operation: 39-22=17, Resulting Numbers: [1, 17] Generated Node #0,0,0: 17:[1, 17] Operation: 39-22=17 Exploring Operation: 22-1=21, Resulting Numbers: [39, 21] Generated Node #0,0,1: 17:[39, 21] Operation: 22-1=21 Moving to Node #0,0,0 Current State: 17:[1, 17], Operations: ['45-44=1', '39-22=17'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[22, 45, 39, 44], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [22, 39, 1] Generated Node #0,0: 17:[22, 39, 1] Operation: 45-44=1 Moving to Node #0,0 Current State: 17:[22, 39, 1], Operations: ['45-44=1'] Exploring Operation: 39-22=17, Resulting Numbers: [1, 17] Generated Node #0,0,0: 17:[1, 17] Operation: 39-22=17 Moving to Node #0,0,0 Current State: 17:[1, 17], Operations: ['45-44=1', '39-22=17'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic