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
[ 17, 8, 48, 8 ]
66
[ "17+48=65", "8/8=1", "65+1=66" ]
Current State: 66:[17, 8, 48, 8], Operations: [] Exploring Operation: 17+48=65, Resulting Numbers: [8, 8, 65] Generated Node #2: [8, 8, 65] from Operation: 17+48=65 Current State: 66:[8, 8, 65], Operations: ['17+48=65'] Exploring Operation: 8/8=1, Resulting Numbers: [65, 1] Generated Node #3: [65, 1] from Operation: 8/8=1 Current State: 66:[65, 1], Operations: ['17+48=65', '8/8=1'] Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[17, 8, 48, 8], Operations: [] Exploring Operation: 17+48=65, Resulting Numbers: [8, 8, 65] Generated Node #0,0: 66:[8, 8, 65] Operation: 17+48=65 Exploring Operation: 48-17=31, Resulting Numbers: [8, 8, 31] Generated Node #0,1: 66:[8, 8, 31] Operation: 48-17=31 Exploring Operation: 48/8=6, Resulting Numbers: [17, 8, 6] Generated Node #0,2: 66:[17, 8, 6] Operation: 48/8=6 Exploring Operation: 48/8=6, Resulting Numbers: [17, 8, 6] Generated Node #0,3: 66:[17, 8, 6] Operation: 48/8=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[8, 8, 65], Operations: ['17+48=65'] Exploring Operation: 8-8=0, Resulting Numbers: [65, 0] Generated Node #0,0,0: 66:[65, 0] Operation: 8-8=0 Exploring Operation: 8+8=16, Resulting Numbers: [65, 16] Generated Node #0,0,1: 66:[65, 16] Operation: 8+8=16 Exploring Operation: 8/8=1, Resulting Numbers: [65, 1] Generated Node #0,0,2: 66:[65, 1] Operation: 8/8=1 Exploring Operation: 8*8=64, Resulting Numbers: [65, 64] Generated Node #0,0,3: 66:[65, 64] Operation: 8*8=64 Moving to Node #0,0,2 Current State: 66:[65, 1], Operations: ['17+48=65', '8/8=1'] Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,66 unequal: No Solution Exploring Operation: 65*1=65, Resulting Numbers: [65] 65,66 unequal: No Solution Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,66 unequal: No Solution Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[17, 8, 48, 8], Operations: [] Exploring Operation: 17+48=65, Resulting Numbers: [8, 8, 65] Generated Node #0,0: 66:[8, 8, 65] Operation: 17+48=65 Moving to Node #0,0 Current State: 66:[8, 8, 65], Operations: ['17+48=65'] Exploring Operation: 8/8=1, Resulting Numbers: [65, 1] Generated Node #0,0,2: 66:[65, 1] Operation: 8/8=1 Moving to Node #0,0,2 Current State: 66:[65, 1], Operations: ['17+48=65', '8/8=1'] Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 51, 96, 14, 2 ]
20
[ "51*2=102", "96-14=82", "102-82=20" ]
Current State: 20:[51, 96, 14, 2], Operations: [] Exploring Operation: 51*2=102, Resulting Numbers: [96, 14, 102] Generated Node #2: [96, 14, 102] from Operation: 51*2=102 Current State: 20:[96, 14, 102], Operations: ['51*2=102'] Exploring Operation: 96-14=82, Resulting Numbers: [102, 82] Generated Node #3: [102, 82] from Operation: 96-14=82 Current State: 20:[102, 82], Operations: ['51*2=102', '96-14=82'] Exploring Operation: 102-82=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[51, 96, 14, 2], Operations: [] Exploring Operation: 96-14=82, Resulting Numbers: [51, 2, 82] Generated Node #0,0: 20:[51, 2, 82] Operation: 96-14=82 Exploring Operation: 51-14=37, Resulting Numbers: [96, 2, 37] Generated Node #0,1: 20:[96, 2, 37] Operation: 51-14=37 Exploring Operation: 96/2=48, Resulting Numbers: [51, 14, 48] Generated Node #0,2: 20:[51, 14, 48] Operation: 96/2=48 Exploring Operation: 96-51=45, Resulting Numbers: [14, 2, 45] Generated Node #0,3: 20:[14, 2, 45] Operation: 96-51=45 Start Sub Search at level 1: Moving to Node #0,3 Current State: 20:[14, 2, 45], Operations: ['96-51=45'] Exploring Operation: 14/2=7, Resulting Numbers: [45, 7] Generated Node #0,3,0: 20:[45, 7] Operation: 14/2=7 Exploring Operation: 14-2=12, Resulting Numbers: [45, 12] Generated Node #0,3,1: 20:[45, 12] Operation: 14-2=12 Exploring Operation: 45-14=31, Resulting Numbers: [2, 31] Generated Node #0,3,2: 20:[2, 31] Operation: 45-14=31 Exploring Operation: 45-2=43, Resulting Numbers: [14, 43] Generated Node #0,3,3: 20:[14, 43] Operation: 45-2=43 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 20:[2, 31], Operations: ['96-51=45', '45-14=31'] Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,20 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,20 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 20:[45, 7], Operations: ['96-51=45', '14/2=7'] Exploring Operation: 45+7=52, Resulting Numbers: [52] 52,20 unequal: No Solution Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,20 unequal: No Solution Exploring Operation: 45*7=315, Resulting Numbers: [315] 315,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 20:[45, 12], Operations: ['96-51=45', '14-2=12'] Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,20 unequal: No Solution Exploring Operation: 45+12=57, Resulting Numbers: [57] 57,20 unequal: No Solution Exploring Operation: 45*12=540, Resulting Numbers: [540] 540,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 20:[14, 43], Operations: ['96-51=45', '45-2=43'] Exploring Operation: 14+43=57, Resulting Numbers: [57] 57,20 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,20 unequal: No Solution Exploring Operation: 14*43=602, Resulting Numbers: [602] 602,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 20:[51, 14, 48], Operations: ['96/2=48'] Exploring Operation: 51-48=3, Resulting Numbers: [14, 3] Generated Node #0,2,0: 20:[14, 3] Operation: 51-48=3 Exploring Operation: 48-14=34, Resulting Numbers: [51, 34] Generated Node #0,2,1: 20:[51, 34] Operation: 48-14=34 Exploring Operation: 51+14=65, Resulting Numbers: [48, 65] Generated Node #0,2,2: 20:[48, 65] Operation: 51+14=65 Exploring Operation: 51-14=37, Resulting Numbers: [48, 37] Generated Node #0,2,3: 20:[48, 37] Operation: 51-14=37 Moving to Node #0,2,0 Current State: 20:[14, 3], Operations: ['96/2=48', '51-48=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,20 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,20 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,20 unequal: No Solution Moving to Node #0,2,3 Current State: 20:[48, 37], Operations: ['96/2=48', '51-14=37'] Exploring Operation: 48-37=11, Resulting Numbers: [11] 11,20 unequal: No Solution Exploring Operation: 48*37=1776, Resulting Numbers: [1776] 1776,20 unequal: No Solution Exploring Operation: 48+37=85, Resulting Numbers: [85] 85,20 unequal: No Solution Moving to Node #0,2,1 Current State: 20:[51, 34], Operations: ['96/2=48', '48-14=34'] Exploring Operation: 51-34=17, Resulting Numbers: [17] 17,20 unequal: No Solution Exploring Operation: 51+34=85, Resulting Numbers: [85] 85,20 unequal: No Solution Exploring Operation: 51*34=1734, Resulting Numbers: [1734] 1734,20 unequal: No Solution Moving to Node #0,2,2 Current State: 20:[48, 65], Operations: ['96/2=48', '51+14=65'] Exploring Operation: 65-48=17, Resulting Numbers: [17] 17,20 unequal: No Solution Exploring Operation: 48+65=113, Resulting Numbers: [113] 113,20 unequal: No Solution Exploring Operation: 48*65=3120, Resulting Numbers: [3120] 3120,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[51, 2, 82], Operations: ['96-14=82'] Exploring Operation: 51-2=49, Resulting Numbers: [82, 49] Generated Node #0,0,0: 20:[82, 49] Operation: 51-2=49 Exploring Operation: 82-2=80, Resulting Numbers: [51, 80] Generated Node #0,0,1: 20:[51, 80] Operation: 82-2=80 Exploring Operation: 82-51=31, Resulting Numbers: [2, 31] Generated Node #0,0,2: 20:[2, 31] Operation: 82-51=31 Exploring Operation: 82/2=41, Resulting Numbers: [51, 41] Generated Node #0,0,3: 20:[51, 41] Operation: 82/2=41 Moving to Node #0,0,2 Current State: 20:[2, 31], Operations: ['96-14=82', '82-51=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,20 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,20 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,20 unequal: No Solution Moving to Node #0,0,3 Current State: 20:[51, 41], Operations: ['96-14=82', '82/2=41'] Exploring Operation: 51+41=92, Resulting Numbers: [92] 92,20 unequal: No Solution Exploring Operation: 51-41=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 51*41=2091, Resulting Numbers: [2091] 2091,20 unequal: No Solution Moving to Node #0,0,1 Current State: 20:[51, 80], Operations: ['96-14=82', '82-2=80'] Exploring Operation: 51*80=4080, Resulting Numbers: [4080] 4080,20 unequal: No Solution Exploring Operation: 80-51=29, Resulting Numbers: [29] 29,20 unequal: No Solution Exploring Operation: 51+80=131, Resulting Numbers: [131] 131,20 unequal: No Solution Moving to Node #0,0,0 Current State: 20:[82, 49], Operations: ['96-14=82', '51-2=49'] Exploring Operation: 82*49=4018, Resulting Numbers: [4018] 4018,20 unequal: No Solution Exploring Operation: 82+49=131, Resulting Numbers: [131] 131,20 unequal: No Solution Exploring Operation: 82-49=33, Resulting Numbers: [33] 33,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[96, 2, 37], Operations: ['51-14=37'] Exploring Operation: 37-2=35, Resulting Numbers: [96, 35] Generated Node #0,1,0: 20:[96, 35] Operation: 37-2=35 Exploring Operation: 96/2=48, Resulting Numbers: [37, 48] Generated Node #0,1,1: 20:[37, 48] Operation: 96/2=48 Exploring Operation: 96-2=94, Resulting Numbers: [37, 94] Generated Node #0,1,2: 20:[37, 94] Operation: 96-2=94 Exploring Operation: 96-37=59, Resulting Numbers: [2, 59] Generated Node #0,1,3: 20:[2, 59] Operation: 96-37=59 Moving to Node #0,1,3 Current State: 20:[2, 59], Operations: ['51-14=37', '96-37=59'] Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,20 unequal: No Solution Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[37, 48], Operations: ['51-14=37', '96/2=48'] Exploring Operation: 37+48=85, Resulting Numbers: [85] 85,20 unequal: No Solution Exploring Operation: 48-37=11, Resulting Numbers: [11] 11,20 unequal: No Solution Exploring Operation: 37*48=1776, Resulting Numbers: [1776] 1776,20 unequal: No Solution Moving to Node #0,1,2 Current State: 20:[37, 94], Operations: ['51-14=37', '96-2=94'] Exploring Operation: 37+94=131, Resulting Numbers: [131] 131,20 unequal: No Solution Exploring Operation: 94-37=57, Resulting Numbers: [57] 57,20 unequal: No Solution Exploring Operation: 37*94=3478, Resulting Numbers: [3478] 3478,20 unequal: No Solution Moving to Node #0,1,0 Current State: 20:[96, 35], Operations: ['51-14=37', '37-2=35'] Exploring Operation: 96*35=3360, Resulting Numbers: [3360] 3360,20 unequal: No Solution Exploring Operation: 96-35=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 96+35=131, Resulting Numbers: [131] 131,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 27, 69, 33, 20 ]
83
[ "27+69=96", "33-20=13", "96-13=83" ]
Current State: 83:[27, 69, 33, 20], Operations: [] Exploring Operation: 27+69=96, Resulting Numbers: [33, 20, 96] Generated Node #2: [33, 20, 96] from Operation: 27+69=96 Current State: 83:[33, 20, 96], Operations: ['27+69=96'] Exploring Operation: 33-20=13, Resulting Numbers: [96, 13] Generated Node #3: [96, 13] from Operation: 33-20=13 Current State: 83:[96, 13], Operations: ['27+69=96', '33-20=13'] Exploring Operation: 96-13=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[27, 69, 33, 20], Operations: [] Exploring Operation: 27+33=60, Resulting Numbers: [69, 20, 60] Generated Node #0,0: 83:[69, 20, 60] Operation: 27+33=60 Moving to Node #0,0 Current State: 83:[69, 20, 60], Operations: ['27+33=60'] Exploring Operation: 20+60=80, Resulting Numbers: [69, 80] Generated Node #0,0,0: 83:[69, 80] Operation: 20+60=80 Moving to Node #0,0,0 Current State: 83:[69, 80], Operations: ['27+33=60', '20+60=80'] Exploring Operation: 69+80=149, Resulting Numbers: [149] 149,83 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 9, 7, 83, 54 ]
99
[ "9*83=747", "747-54=693", "693/7=99" ]
Current State: 99:[9, 7, 83, 54], Operations: [] Exploring Operation: 9*83=747, Resulting Numbers: [7, 54, 747] Generated Node #2: [7, 54, 747] from Operation: 9*83=747 Current State: 99:[7, 54, 747], Operations: ['9*83=747'] Exploring Operation: 747-54=693, Resulting Numbers: [7, 693] Generated Node #3: [7, 693] from Operation: 747-54=693 Current State: 99:[7, 693], Operations: ['9*83=747', '747-54=693'] Exploring Operation: 693/7=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[9, 7, 83, 54], Operations: [] Exploring Operation: 54/9=6, Resulting Numbers: [7, 83, 6] Generated Node #0,0: 99:[7, 83, 6] Operation: 54/9=6 Exploring Operation: 83-54=29, Resulting Numbers: [9, 7, 29] Generated Node #0,1: 99:[9, 7, 29] Operation: 83-54=29 Exploring Operation: 54-9=45, Resulting Numbers: [7, 83, 45] Generated Node #0,2: 99:[7, 83, 45] Operation: 54-9=45 Exploring Operation: 9+83=92, Resulting Numbers: [7, 54, 92] Generated Node #0,3: 99:[7, 54, 92] Operation: 9+83=92 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[9, 7, 29], Operations: ['83-54=29'] Exploring Operation: 9+7=16, Resulting Numbers: [29, 16] Generated Node #0,1,0: 99:[29, 16] Operation: 9+7=16 Exploring Operation: 9-7=2, Resulting Numbers: [29, 2] Generated Node #0,1,1: 99:[29, 2] Operation: 9-7=2 Exploring Operation: 7+29=36, Resulting Numbers: [9, 36] Generated Node #0,1,2: 99:[9, 36] Operation: 7+29=36 Exploring Operation: 9+29=38, Resulting Numbers: [7, 38] Generated Node #0,1,3: 99:[7, 38] Operation: 9+29=38 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 99:[9, 36], Operations: ['83-54=29', '7+29=36'] Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,99 unequal: No Solution Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,99 unequal: No Solution Exploring Operation: 9+36=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 9*36=324, Resulting Numbers: [324] 324,99 unequal: No Solution No 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: 99:[29, 2], Operations: ['83-54=29', '9-7=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,99 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,99 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,99 unequal: No Solution No 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: 99:[7, 38], Operations: ['83-54=29', '9+29=38'] Exploring Operation: 7+38=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 7*38=266, Resulting Numbers: [266] 266,99 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,99 unequal: No Solution No 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: 99:[29, 16], Operations: ['83-54=29', '9+7=16'] Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,99 unequal: No Solution Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,99 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[7, 83, 6], Operations: ['54/9=6'] Exploring Operation: 7+83=90, Resulting Numbers: [6, 90] Generated Node #0,0,0: 99:[6, 90] Operation: 7+83=90 Exploring Operation: 7+6=13, Resulting Numbers: [83, 13] Generated Node #0,0,1: 99:[83, 13] Operation: 7+6=13 Exploring Operation: 7-6=1, Resulting Numbers: [83, 1] Generated Node #0,0,2: 99:[83, 1] Operation: 7-6=1 Exploring Operation: 83+6=89, Resulting Numbers: [7, 89] Generated Node #0,0,3: 99:[7, 89] Operation: 83+6=89 Moving to Node #0,0,0 Current State: 99:[6, 90], Operations: ['54/9=6', '7+83=90'] Exploring Operation: 90-6=84, Resulting Numbers: [84] 84,99 unequal: No Solution Exploring Operation: 6*90=540, Resulting Numbers: [540] 540,99 unequal: No Solution Exploring Operation: 90/6=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 6+90=96, Resulting Numbers: [96] 96,99 unequal: No Solution Moving to Node #0,0,3 Current State: 99:[7, 89], Operations: ['54/9=6', '83+6=89'] Exploring Operation: 89-7=82, Resulting Numbers: [82] 82,99 unequal: No Solution Exploring Operation: 7*89=623, Resulting Numbers: [623] 623,99 unequal: No Solution Exploring Operation: 7+89=96, Resulting Numbers: [96] 96,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[83, 1], Operations: ['54/9=6', '7-6=1'] Exploring Operation: 83/1=83, Resulting Numbers: [83] 83,99 unequal: No Solution Exploring Operation: 83*1=83, Resulting Numbers: [83] 83,99 unequal: No Solution Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,99 unequal: No Solution Exploring Operation: 83+1=84, Resulting Numbers: [84] 84,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[83, 13], Operations: ['54/9=6', '7+6=13'] Exploring Operation: 83+13=96, Resulting Numbers: [96] 96,99 unequal: No Solution Exploring Operation: 83-13=70, Resulting Numbers: [70] 70,99 unequal: No Solution Exploring Operation: 83*13=1079, Resulting Numbers: [1079] 1079,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[7, 83, 45], Operations: ['54-9=45'] Exploring Operation: 83+45=128, Resulting Numbers: [7, 128] Generated Node #0,2,0: 99:[7, 128] Operation: 83+45=128 Exploring Operation: 45-7=38, Resulting Numbers: [83, 38] Generated Node #0,2,1: 99:[83, 38] Operation: 45-7=38 Exploring Operation: 7+83=90, Resulting Numbers: [45, 90] Generated Node #0,2,2: 99:[45, 90] Operation: 7+83=90 Exploring Operation: 83-45=38, Resulting Numbers: [7, 38] Generated Node #0,2,3: 99:[7, 38] Operation: 83-45=38 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 99:[7, 38], Operations: ['54-9=45', '83-45=38'] Exploring Operation: 7*38=266, Resulting Numbers: [266] 266,99 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,99 unequal: No Solution Exploring Operation: 7+38=45, Resulting Numbers: [45] 45,99 unequal: No Solution No 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: 99:[83, 38], Operations: ['54-9=45', '45-7=38'] Exploring Operation: 83*38=3154, Resulting Numbers: [3154] 3154,99 unequal: No Solution Exploring Operation: 83+38=121, Resulting Numbers: [121] 121,99 unequal: No Solution Exploring Operation: 83-38=45, Resulting Numbers: [45] 45,99 unequal: No Solution No 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: 99:[45, 90], Operations: ['54-9=45', '7+83=90'] Exploring Operation: 45+90=135, Resulting Numbers: [135] 135,99 unequal: No Solution Exploring Operation: 90-45=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 45*90=4050, Resulting Numbers: [4050] 4050,99 unequal: No Solution Exploring Operation: 90/45=2, Resulting Numbers: [2] 2,99 unequal: No Solution No 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: 99:[7, 128], Operations: ['54-9=45', '83+45=128'] Exploring Operation: 128-7=121, Resulting Numbers: [121] 121,99 unequal: No Solution Exploring Operation: 7*128=896, Resulting Numbers: [896] 896,99 unequal: No Solution Exploring Operation: 7+128=135, Resulting Numbers: [135] 135,99 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 Start Sub Search at level 1: Moving to Node #0,3 Current State: 99:[7, 54, 92], Operations: ['9+83=92'] Exploring Operation: 7+92=99, Resulting Numbers: [54, 99] Generated Node #0,3,0: 99:[54, 99] Operation: 7+92=99 Exploring Operation: 54-7=47, Resulting Numbers: [92, 47] Generated Node #0,3,1: 99:[92, 47] Operation: 54-7=47 Exploring Operation: 7+54=61, Resulting Numbers: [92, 61] Generated Node #0,3,2: 99:[92, 61] Operation: 7+54=61 Exploring Operation: 92-54=38, Resulting Numbers: [7, 38] Generated Node #0,3,3: 99:[7, 38] Operation: 92-54=38 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 99:[7, 38], Operations: ['9+83=92', '92-54=38'] Exploring Operation: 7*38=266, Resulting Numbers: [266] 266,99 unequal: No Solution Exploring Operation: 7+38=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,99 unequal: No Solution No 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: 99:[54, 99], Operations: ['9+83=92', '7+92=99'] Exploring Operation: 99-54=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 54*99=5346, Resulting Numbers: [5346] 5346,99 unequal: No Solution Exploring Operation: 54+99=153, Resulting Numbers: [153] 153,99 unequal: No Solution No 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: 99:[92, 47], Operations: ['9+83=92', '54-7=47'] Exploring Operation: 92-47=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 92+47=139, Resulting Numbers: [139] 139,99 unequal: No Solution Exploring Operation: 92*47=4324, Resulting Numbers: [4324] 4324,99 unequal: No Solution No 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: 99:[92, 61], Operations: ['9+83=92', '7+54=61'] Exploring Operation: 92-61=31, Resulting Numbers: [31] 31,99 unequal: No Solution Exploring Operation: 92*61=5612, Resulting Numbers: [5612] 5612,99 unequal: No Solution Exploring Operation: 92+61=153, Resulting Numbers: [153] 153,99 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_4
sum_heuristic
[ 20, 12, 60, 68 ]
83
[ "60/20=3", "12+68=80", "3+80=83" ]
Current State: 83:[20, 12, 60, 68], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [12, 68, 3] Generated Node #2: [12, 68, 3] from Operation: 60/20=3 Current State: 83:[12, 68, 3], Operations: ['60/20=3'] Exploring Operation: 12+68=80, Resulting Numbers: [3, 80] Generated Node #3: [3, 80] from Operation: 12+68=80 Current State: 83:[3, 80], Operations: ['60/20=3', '12+68=80'] Exploring Operation: 3+80=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[20, 12, 60, 68], Operations: [] Exploring Operation: 20+12=32, Resulting Numbers: [60, 68, 32] Generated Node #0,0: 83:[60, 68, 32] Operation: 20+12=32 Moving to Node #0,0 Current State: 83:[60, 68, 32], Operations: ['20+12=32'] Exploring Operation: 60+32=92, Resulting Numbers: [68, 92] Generated Node #0,0,0: 83:[68, 92] Operation: 60+32=92 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[68, 92], Operations: ['20+12=32', '60+32=92'] Exploring Operation: 92-68=24, Resulting Numbers: [24] 24,83 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
[ 39, 85, 3, 18 ]
83
[ "39-3=36", "36/18=2", "85-2=83" ]
Current State: 83:[39, 85, 3, 18], Operations: [] Exploring Operation: 39-3=36, Resulting Numbers: [85, 18, 36] Generated Node #2: [85, 18, 36] from Operation: 39-3=36 Current State: 83:[85, 18, 36], Operations: ['39-3=36'] Exploring Operation: 36/18=2, Resulting Numbers: [85, 2] Generated Node #3: [85, 2] from Operation: 36/18=2 Current State: 83:[85, 2], Operations: ['39-3=36', '36/18=2'] Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[39, 85, 3, 18], Operations: [] Exploring Operation: 39*3=117, Resulting Numbers: [85, 18, 117] Generated Node #0,0: 83:[85, 18, 117] Operation: 39*3=117 Exploring Operation: 39+3=42, Resulting Numbers: [85, 18, 42] Generated Node #0,1: 83:[85, 18, 42] Operation: 39+3=42 Exploring Operation: 3*18=54, Resulting Numbers: [39, 85, 54] Generated Node #0,2: 83:[39, 85, 54] Operation: 3*18=54 Moving to Node #0,2 Current State: 83:[39, 85, 54], Operations: ['3*18=54'] Exploring Operation: 85-39=46, Resulting Numbers: [54, 46] Generated Node #0,2,0: 83:[54, 46] Operation: 85-39=46 Exploring Operation: 39+54=93, Resulting Numbers: [85, 93] Generated Node #0,2,1: 83:[85, 93] Operation: 39+54=93 Exploring Operation: 39+85=124, Resulting Numbers: [54, 124] Generated Node #0,2,2: 83:[54, 124] Operation: 39+85=124 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 83:[85, 93], Operations: ['3*18=54', '39+54=93'] Exploring Operation: 85*93=7905, Resulting Numbers: [7905] 7905,83 unequal: No Solution Exploring Operation: 93-85=8, Resulting Numbers: [8] 8,83 unequal: No Solution Exploring Operation: 85+93=178, Resulting Numbers: [178] 178,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 83:[54, 46], Operations: ['3*18=54', '85-39=46'] Exploring Operation: 54*46=2484, Resulting Numbers: [2484] 2484,83 unequal: No Solution Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,83 unequal: No Solution Exploring Operation: 54+46=100, Resulting Numbers: [100] 100,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 83:[54, 124], Operations: ['3*18=54', '39+85=124'] Exploring Operation: 54+124=178, Resulting Numbers: [178] 178,83 unequal: No Solution Exploring Operation: 54*124=6696, Resulting Numbers: [6696] 6696,83 unequal: No Solution Exploring Operation: 124-54=70, Resulting Numbers: [70] 70,83 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: 83:[85, 18, 117], Operations: ['39*3=117'] Exploring Operation: 117-18=99, Resulting Numbers: [85, 99] Generated Node #0,0,0: 83:[85, 99] Operation: 117-18=99 Exploring Operation: 85-18=67, Resulting Numbers: [117, 67] Generated Node #0,0,1: 83:[117, 67] Operation: 85-18=67 Exploring Operation: 85+18=103, Resulting Numbers: [117, 103] Generated Node #0,0,2: 83:[117, 103] Operation: 85+18=103 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[85, 99], Operations: ['39*3=117', '117-18=99'] Exploring Operation: 85+99=184, Resulting Numbers: [184] 184,83 unequal: No Solution Exploring Operation: 85*99=8415, Resulting Numbers: [8415] 8415,83 unequal: No Solution Exploring Operation: 99-85=14, Resulting Numbers: [14] 14,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[117, 67], Operations: ['39*3=117', '85-18=67'] Exploring Operation: 117*67=7839, Resulting Numbers: [7839] 7839,83 unequal: No Solution Exploring Operation: 117+67=184, Resulting Numbers: [184] 184,83 unequal: No Solution Exploring Operation: 117-67=50, Resulting Numbers: [50] 50,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[117, 103], Operations: ['39*3=117', '85+18=103'] Exploring Operation: 117+103=220, Resulting Numbers: [220] 220,83 unequal: No Solution Exploring Operation: 117*103=12051, Resulting Numbers: [12051] 12051,83 unequal: No Solution Exploring Operation: 117-103=14, Resulting Numbers: [14] 14,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 83:[85, 18, 42], Operations: ['39+3=42'] Exploring Operation: 85+18=103, Resulting Numbers: [42, 103] Generated Node #0,1,0: 83:[42, 103] Operation: 85+18=103 Exploring Operation: 18+42=60, Resulting Numbers: [85, 60] Generated Node #0,1,1: 83:[85, 60] Operation: 18+42=60 Exploring Operation: 85-18=67, Resulting Numbers: [42, 67] Generated Node #0,1,2: 83:[42, 67] Operation: 85-18=67 Moving to Node #0,1,1 Current State: 83:[85, 60], Operations: ['39+3=42', '18+42=60'] Exploring Operation: 85*60=5100, Resulting Numbers: [5100] 5100,83 unequal: No Solution Exploring Operation: 85-60=25, Resulting Numbers: [25] 25,83 unequal: No Solution Exploring Operation: 85+60=145, Resulting Numbers: [145] 145,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[42, 67], Operations: ['39+3=42', '85-18=67'] Exploring Operation: 42*67=2814, Resulting Numbers: [2814] 2814,83 unequal: No Solution Exploring Operation: 67-42=25, Resulting Numbers: [25] 25,83 unequal: No Solution Exploring Operation: 42+67=109, Resulting Numbers: [109] 109,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[42, 103], Operations: ['39+3=42', '85+18=103'] Exploring Operation: 103-42=61, Resulting Numbers: [61] 61,83 unequal: No Solution Exploring Operation: 42+103=145, Resulting Numbers: [145] 145,83 unequal: No Solution Exploring Operation: 42*103=4326, Resulting Numbers: [4326] 4326,83 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 60, 51, 49, 62 ]
98
[ "60+51=111", "62-49=13", "111-13=98" ]
Current State: 98:[60, 51, 49, 62], Operations: [] Exploring Operation: 60+51=111, Resulting Numbers: [49, 62, 111] Generated Node #2: [49, 62, 111] from Operation: 60+51=111 Current State: 98:[49, 62, 111], Operations: ['60+51=111'] Exploring Operation: 62-49=13, Resulting Numbers: [111, 13] Generated Node #3: [111, 13] from Operation: 62-49=13 Current State: 98:[111, 13], Operations: ['60+51=111', '62-49=13'] Exploring Operation: 111-13=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[60, 51, 49, 62], Operations: [] Exploring Operation: 60-49=11, Resulting Numbers: [51, 62, 11] Generated Node #0,0: 98:[51, 62, 11] Operation: 60-49=11 Exploring Operation: 60-51=9, Resulting Numbers: [49, 62, 9] Generated Node #0,1: 98:[49, 62, 9] Operation: 60-51=9 Exploring Operation: 62-51=11, Resulting Numbers: [60, 49, 11] Generated Node #0,2: 98:[60, 49, 11] Operation: 62-51=11 Exploring Operation: 62-49=13, Resulting Numbers: [60, 51, 13] Generated Node #0,3: 98:[60, 51, 13] Operation: 62-49=13 Exploring Operation: 62-60=2, Resulting Numbers: [51, 49, 2] Generated Node #0,4: 98:[51, 49, 2] Operation: 62-60=2 Start Sub Search at level 1: Moving to Node #0,4 Current State: 98:[51, 49, 2], Operations: ['62-60=2'] Exploring Operation: 51-49=2, Resulting Numbers: [2, 2] Generated Node #0,4,0: 98:[2, 2] Operation: 51-49=2 Exploring Operation: 51+2=53, Resulting Numbers: [49, 53] Generated Node #0,4,1: 98:[49, 53] Operation: 51+2=53 Exploring Operation: 51+49=100, Resulting Numbers: [2, 100] Generated Node #0,4,2: 98:[2, 100] Operation: 51+49=100 Exploring Operation: 51-2=49, Resulting Numbers: [49, 49] Generated Node #0,4,3: 98:[49, 49] Operation: 51-2=49 Exploring Operation: 49*2=98, Resulting Numbers: [51, 98] Generated Node #0,4,4: 98:[51, 98] Operation: 49*2=98 Moving to Node #0,4,0 Current State: 98:[2, 2], Operations: ['62-60=2', '51-49=2'] Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,98 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,98 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,98 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,98 unequal: No Solution Moving to Node #0,4,3 Current State: 98:[49, 49], Operations: ['62-60=2', '51-2=49'] Exploring Operation: 49+49=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[60, 51, 49, 62], Operations: [] Exploring Operation: 62-60=2, Resulting Numbers: [51, 49, 2] Generated Node #0,4: 98:[51, 49, 2] Operation: 62-60=2 Moving to Node #0,4 Current State: 98:[51, 49, 2], Operations: ['62-60=2'] Exploring Operation: 51-2=49, Resulting Numbers: [49, 49] Generated Node #0,4,3: 98:[49, 49] Operation: 51-2=49 Moving to Node #0,4,3 Current State: 98:[49, 49], Operations: ['62-60=2', '51-2=49'] Exploring Operation: 49+49=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 16, 40, 2, 39 ]
11
[ "16+40=56", "56/2=28", "39-28=11" ]
Current State: 11:[16, 40, 2, 39], Operations: [] Exploring Operation: 16+40=56, Resulting Numbers: [2, 39, 56] Generated Node #2: [2, 39, 56] from Operation: 16+40=56 Current State: 11:[2, 39, 56], Operations: ['16+40=56'] Exploring Operation: 56/2=28, Resulting Numbers: [39, 28] Generated Node #3: [39, 28] from Operation: 56/2=28 Current State: 11:[39, 28], Operations: ['16+40=56', '56/2=28'] Exploring Operation: 39-28=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[16, 40, 2, 39], Operations: [] Exploring Operation: 40/2=20, Resulting Numbers: [16, 39, 20] Generated Node #0,0: 11:[16, 39, 20] Operation: 40/2=20 Exploring Operation: 40-16=24, Resulting Numbers: [2, 39, 24] Generated Node #0,1: 11:[2, 39, 24] Operation: 40-16=24 Exploring Operation: 16-2=14, Resulting Numbers: [40, 39, 14] Generated Node #0,2: 11:[40, 39, 14] Operation: 16-2=14 Exploring Operation: 39-16=23, Resulting Numbers: [40, 2, 23] Generated Node #0,3: 11:[40, 2, 23] Operation: 39-16=23 Exploring Operation: 40-39=1, Resulting Numbers: [16, 2, 1] Generated Node #0,4: 11:[16, 2, 1] Operation: 40-39=1 Moving to Node #0,4 Current State: 11:[16, 2, 1], Operations: ['40-39=1'] Exploring Operation: 2+1=3, Resulting Numbers: [16, 3] Generated Node #0,4,0: 11:[16, 3] Operation: 2+1=3 Exploring Operation: 16/2=8, Resulting Numbers: [1, 8] Generated Node #0,4,1: 11:[1, 8] Operation: 16/2=8 Exploring Operation: 16-2=14, Resulting Numbers: [1, 14] Generated Node #0,4,2: 11:[1, 14] Operation: 16-2=14 Exploring Operation: 16*1=16, Resulting Numbers: [2, 16] Generated Node #0,4,3: 11:[2, 16] Operation: 16*1=16 Exploring Operation: 16-1=15, Resulting Numbers: [2, 15] Generated Node #0,4,4: 11:[2, 15] Operation: 16-1=15 Moving to Node #0,0 Current State: 11:[16, 39, 20], Operations: ['40/2=20'] Exploring Operation: 16+20=36, Resulting Numbers: [39, 36] Generated Node #0,0,0: 11:[39, 36] Operation: 16+20=36 Exploring Operation: 20-16=4, Resulting Numbers: [39, 4] Generated Node #0,0,1: 11:[39, 4] Operation: 20-16=4 Exploring Operation: 16+39=55, Resulting Numbers: [20, 55] Generated Node #0,0,2: 11:[20, 55] Operation: 16+39=55 Exploring Operation: 39-16=23, Resulting Numbers: [20, 23] Generated Node #0,0,3: 11:[20, 23] Operation: 39-16=23 Exploring Operation: 39-20=19, Resulting Numbers: [16, 19] Generated Node #0,0,4: 11:[16, 19] Operation: 39-20=19 Moving to Node #0,1 Current State: 11:[2, 39, 24], Operations: ['40-16=24'] Exploring Operation: 24/2=12, Resulting Numbers: [39, 12] Generated Node #0,1,0: 11:[39, 12] Operation: 24/2=12 Exploring Operation: 2+39=41, Resulting Numbers: [24, 41] Generated Node #0,1,1: 11:[24, 41] Operation: 2+39=41 Exploring Operation: 39-2=37, Resulting Numbers: [24, 37] Generated Node #0,1,2: 11:[24, 37] Operation: 39-2=37 Exploring Operation: 39-24=15, Resulting Numbers: [2, 15] Generated Node #0,1,3: 11:[2, 15] Operation: 39-24=15 Exploring Operation: 24-2=22, Resulting Numbers: [39, 22] Generated Node #0,1,4: 11:[39, 22] Operation: 24-2=22 Moving to Node #0,3 Current State: 11:[40, 2, 23], Operations: ['39-16=23'] Exploring Operation: 40+2=42, Resulting Numbers: [23, 42] Generated Node #0,3,0: 11:[23, 42] Operation: 40+2=42 Exploring Operation: 23-2=21, Resulting Numbers: [40, 21] Generated Node #0,3,1: 11:[40, 21] Operation: 23-2=21 Exploring Operation: 40/2=20, Resulting Numbers: [23, 20] Generated Node #0,3,2: 11:[23, 20] Operation: 40/2=20 Exploring Operation: 40-2=38, Resulting Numbers: [23, 38] Generated Node #0,3,3: 11:[23, 38] Operation: 40-2=38 Exploring Operation: 40-23=17, Resulting Numbers: [2, 17] Generated Node #0,3,4: 11:[2, 17] Operation: 40-23=17 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 11:[2, 17], Operations: ['39-16=23', '40-23=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 11:[23, 20], Operations: ['39-16=23', '40/2=20'] Exploring Operation: 23*20=460, Resulting Numbers: [460] 460,11 unequal: No Solution Exploring Operation: 23+20=43, Resulting Numbers: [43] 43,11 unequal: No Solution Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 11:[40, 21], Operations: ['39-16=23', '23-2=21'] Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 40*21=840, Resulting Numbers: [840] 840,11 unequal: No Solution Exploring Operation: 40+21=61, Resulting Numbers: [61] 61,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 11:[23, 38], Operations: ['39-16=23', '40-2=38'] Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 23+38=61, Resulting Numbers: [61] 61,11 unequal: No Solution Exploring Operation: 23*38=874, Resulting Numbers: [874] 874,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 11:[23, 42], Operations: ['39-16=23', '40+2=42'] Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 23*42=966, Resulting Numbers: [966] 966,11 unequal: No Solution Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,11 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: 11:[40, 39, 14], Operations: ['16-2=14'] Exploring Operation: 40+39=79, Resulting Numbers: [14, 79] Generated Node #0,2,0: 11:[14, 79] Operation: 40+39=79 Exploring Operation: 39-14=25, Resulting Numbers: [40, 25] Generated Node #0,2,1: 11:[40, 25] Operation: 39-14=25 Exploring Operation: 40+14=54, Resulting Numbers: [39, 54] Generated Node #0,2,2: 11:[39, 54] Operation: 40+14=54 Exploring Operation: 40-39=1, Resulting Numbers: [14, 1] Generated Node #0,2,3: 11:[14, 1] Operation: 40-39=1 Exploring Operation: 40-14=26, Resulting Numbers: [39, 26] Generated Node #0,2,4: 11:[39, 26] Operation: 40-14=26 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 11:[14, 1], Operations: ['16-2=14', '40-39=1'] Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 11:[40, 25], Operations: ['16-2=14', '39-14=25'] Exploring Operation: 40*25=1000, Resulting Numbers: [1000] 1000,11 unequal: No Solution Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 40+25=65, Resulting Numbers: [65] 65,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 11:[39, 26], Operations: ['16-2=14', '40-14=26'] Exploring Operation: 39*26=1014, Resulting Numbers: [1014] 1014,11 unequal: No Solution Exploring Operation: 39+26=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 39-26=13, Resulting Numbers: [13] 13,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[14, 79], Operations: ['16-2=14', '40+39=79'] Exploring Operation: 14+79=93, Resulting Numbers: [93] 93,11 unequal: No Solution Exploring Operation: 14*79=1106, Resulting Numbers: [1106] 1106,11 unequal: No Solution Exploring Operation: 79-14=65, Resulting Numbers: [65] 65,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 11:[39, 54], Operations: ['16-2=14', '40+14=54'] Exploring Operation: 54-39=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 39*54=2106, Resulting Numbers: [2106] 2106,11 unequal: No Solution Exploring Operation: 39+54=93, Resulting Numbers: [93] 93,11 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: 11:[16, 3], Operations: ['40-39=1', '2+1=3'] Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,11 unequal: No Solution Moving to Node #0,4,2 Current State: 11:[1, 14], Operations: ['40-39=1', '16-2=14'] Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,11 unequal: No Solution Moving to Node #0,0,4 Current State: 11:[16, 19], Operations: ['40/2=20', '39-20=19'] Exploring Operation: 16*19=304, Resulting Numbers: [304] 304,11 unequal: No Solution Exploring Operation: 16+19=35, Resulting Numbers: [35] 35,11 unequal: No Solution Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,11 unequal: No Solution Moving to Node #0,4,1 Current State: 11:[1, 8], Operations: ['40-39=1', '16/2=8'] Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 1+8=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 1*8=8, Resulting Numbers: [8] 8,11 unequal: No Solution Moving to Node #0,1,3 Current State: 11:[2, 15], Operations: ['40-16=24', '39-24=15'] Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,11 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,11 unequal: No Solution Moving to Node #0,4,4 Current State: 11:[2, 15], Operations: ['40-39=1', '16-1=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,11 unequal: No Solution Moving to Node #0,4,3 Current State: 11:[2, 16], Operations: ['40-39=1', '16*1=16'] Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,11 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,11 unequal: No Solution Moving to Node #0,0,3 Current State: 11:[20, 23], Operations: ['40/2=20', '39-16=23'] Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 20+23=43, Resulting Numbers: [43] 43,11 unequal: No Solution Exploring Operation: 20*23=460, Resulting Numbers: [460] 460,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[39, 12], Operations: ['40-16=24', '24/2=12'] Exploring Operation: 39-12=27, Resulting Numbers: [27] 27,11 unequal: No Solution Exploring Operation: 39*12=468, Resulting Numbers: [468] 468,11 unequal: No Solution Exploring Operation: 39+12=51, Resulting Numbers: [51] 51,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[39, 4], Operations: ['40/2=20', '20-16=4'] Exploring Operation: 39*4=156, Resulting Numbers: [156] 156,11 unequal: No Solution Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,11 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,11 unequal: No Solution Moving to Node #0,1,4 Current State: 11:[39, 22], Operations: ['40-16=24', '24-2=22'] Exploring Operation: 39*22=858, Resulting Numbers: [858] 858,11 unequal: No Solution Exploring Operation: 39-22=17, Resulting Numbers: [17] 17,11 unequal: No Solution Exploring Operation: 39+22=61, Resulting Numbers: [61] 61,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[24, 37], Operations: ['40-16=24', '39-2=37'] Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 24*37=888, Resulting Numbers: [888] 888,11 unequal: No Solution Exploring Operation: 24+37=61, Resulting Numbers: [61] 61,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[24, 41], Operations: ['40-16=24', '2+39=41'] Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,11 unequal: No Solution Exploring Operation: 24+41=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 24*41=984, Resulting Numbers: [984] 984,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[20, 55], Operations: ['40/2=20', '16+39=55'] Exploring Operation: 20*55=1100, Resulting Numbers: [1100] 1100,11 unequal: No Solution Exploring Operation: 20+55=75, Resulting Numbers: [75] 75,11 unequal: No Solution Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,11 unequal: No Solution Moving to Node #0,0,0 Current State: 11:[39, 36], Operations: ['40/2=20', '16+20=36'] Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 39+36=75, Resulting Numbers: [75] 75,11 unequal: No Solution Exploring Operation: 39*36=1404, Resulting Numbers: [1404] 1404,11 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 61, 21, 9, 18 ]
73
[ "61+21=82", "18-9=9", "82-9=73" ]
Current State: 73:[61, 21, 9, 18], Operations: [] Exploring Operation: 61+21=82, Resulting Numbers: [9, 18, 82] Generated Node #2: [9, 18, 82] from Operation: 61+21=82 Current State: 73:[9, 18, 82], Operations: ['61+21=82'] Exploring Operation: 18-9=9, Resulting Numbers: [82, 9] Generated Node #3: [82, 9] from Operation: 18-9=9 Current State: 73:[82, 9], Operations: ['61+21=82', '18-9=9'] Exploring Operation: 82-9=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[61, 21, 9, 18], Operations: [] Exploring Operation: 21+9=30, Resulting Numbers: [61, 18, 30] Generated Node #0,0: 73:[61, 18, 30] Operation: 21+9=30 Exploring Operation: 61+9=70, Resulting Numbers: [21, 18, 70] Generated Node #0,1: 73:[21, 18, 70] Operation: 61+9=70 Exploring Operation: 9+18=27, Resulting Numbers: [61, 21, 27] Generated Node #0,2: 73:[61, 21, 27] Operation: 9+18=27 Exploring Operation: 21+18=39, Resulting Numbers: [61, 9, 39] Generated Node #0,3: 73:[61, 9, 39] Operation: 21+18=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[61, 18, 30], Operations: ['21+9=30'] Exploring Operation: 61-18=43, Resulting Numbers: [30, 43] Generated Node #0,0,0: 73:[30, 43] Operation: 61-18=43 Exploring Operation: 61+18=79, Resulting Numbers: [30, 79] Generated Node #0,0,1: 73:[30, 79] Operation: 61+18=79 Exploring Operation: 18+30=48, Resulting Numbers: [61, 48] Generated Node #0,0,2: 73:[61, 48] Operation: 18+30=48 Exploring Operation: 61+30=91, Resulting Numbers: [18, 91] Generated Node #0,0,3: 73:[18, 91] Operation: 61+30=91 Moving to Node #0,0,2 Current State: 73:[61, 48], Operations: ['21+9=30', '18+30=48'] Exploring Operation: 61*48=2928, Resulting Numbers: [2928] 2928,73 unequal: No Solution Exploring Operation: 61-48=13, Resulting Numbers: [13] 13,73 unequal: No Solution Exploring Operation: 61+48=109, Resulting Numbers: [109] 109,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[30, 79], Operations: ['21+9=30', '61+18=79'] Exploring Operation: 30+79=109, Resulting Numbers: [109] 109,73 unequal: No Solution Exploring Operation: 79-30=49, Resulting Numbers: [49] 49,73 unequal: No Solution Exploring Operation: 30*79=2370, Resulting Numbers: [2370] 2370,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[18, 91], Operations: ['21+9=30', '61+30=91'] Exploring Operation: 18*91=1638, Resulting Numbers: [1638] 1638,73 unequal: No Solution Exploring Operation: 91-18=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[61, 21, 9, 18], Operations: [] Exploring Operation: 21+9=30, Resulting Numbers: [61, 18, 30] Generated Node #0,0: 73:[61, 18, 30] Operation: 21+9=30 Moving to Node #0,0 Current State: 73:[61, 18, 30], Operations: ['21+9=30'] Exploring Operation: 61+30=91, Resulting Numbers: [18, 91] Generated Node #0,0,3: 73:[18, 91] Operation: 61+30=91 Moving to Node #0,0,3 Current State: 73:[18, 91], Operations: ['21+9=30', '61+30=91'] Exploring Operation: 91-18=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 62, 44, 81, 85 ]
51
[ "85-81=4", "44/4=11", "62-11=51" ]
Current State: 51:[62, 44, 81, 85], Operations: [] Exploring Operation: 85-81=4, Resulting Numbers: [62, 44, 4] Generated Node #2: [62, 44, 4] from Operation: 85-81=4 Current State: 51:[62, 44, 4], Operations: ['85-81=4'] Exploring Operation: 44/4=11, Resulting Numbers: [62, 11] Generated Node #3: [62, 11] from Operation: 44/4=11 Current State: 51:[62, 11], Operations: ['85-81=4', '44/4=11'] Exploring Operation: 62-11=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[62, 44, 81, 85], Operations: [] Exploring Operation: 85-62=23, Resulting Numbers: [44, 81, 23] Generated Node #0,0: 51:[44, 81, 23] Operation: 85-62=23 Exploring Operation: 85-44=41, Resulting Numbers: [62, 81, 41] Generated Node #0,1: 51:[62, 81, 41] Operation: 85-44=41 Exploring Operation: 85-81=4, Resulting Numbers: [62, 44, 4] Generated Node #0,2: 51:[62, 44, 4] Operation: 85-81=4 Exploring Operation: 81-44=37, Resulting Numbers: [62, 85, 37] Generated Node #0,3: 51:[62, 85, 37] Operation: 81-44=37 Exploring Operation: 81-62=19, Resulting Numbers: [44, 85, 19] Generated Node #0,4: 51:[44, 85, 19] Operation: 81-62=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[62, 44, 4], Operations: ['85-81=4'] Exploring Operation: 62-4=58, Resulting Numbers: [44, 58] Generated Node #0,2,0: 51:[44, 58] Operation: 62-4=58 Exploring Operation: 62-44=18, Resulting Numbers: [4, 18] Generated Node #0,2,1: 51:[4, 18] Operation: 62-44=18 Exploring Operation: 44/4=11, Resulting Numbers: [62, 11] Generated Node #0,2,2: 51:[62, 11] Operation: 44/4=11 Exploring Operation: 62+4=66, Resulting Numbers: [44, 66] Generated Node #0,2,3: 51:[44, 66] Operation: 62+4=66 Exploring Operation: 44+4=48, Resulting Numbers: [62, 48] Generated Node #0,2,4: 51:[62, 48] Operation: 44+4=48 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 51:[4, 18], Operations: ['85-81=4', '62-44=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,51 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,51 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,51 unequal: No Solution No 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: 51:[44, 58], Operations: ['85-81=4', '62-4=58'] Exploring Operation: 44*58=2552, Resulting Numbers: [2552] 2552,51 unequal: No Solution Exploring Operation: 44+58=102, Resulting Numbers: [102] 102,51 unequal: No Solution Exploring Operation: 58-44=14, Resulting Numbers: [14] 14,51 unequal: No Solution No 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: 51:[62, 48], Operations: ['85-81=4', '44+4=48'] Exploring Operation: 62-48=14, Resulting Numbers: [14] 14,51 unequal: No Solution Exploring Operation: 62+48=110, Resulting Numbers: [110] 110,51 unequal: No Solution Exploring Operation: 62*48=2976, Resulting Numbers: [2976] 2976,51 unequal: No Solution No 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: 51:[62, 11], Operations: ['85-81=4', '44/4=11'] Exploring Operation: 62*11=682, Resulting Numbers: [682] 682,51 unequal: No Solution Exploring Operation: 62-11=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[62, 44, 81, 85], Operations: [] Exploring Operation: 85-81=4, Resulting Numbers: [62, 44, 4] Generated Node #0,2: 51:[62, 44, 4] Operation: 85-81=4 Moving to Node #0,2 Current State: 51:[62, 44, 4], Operations: ['85-81=4'] Exploring Operation: 44/4=11, Resulting Numbers: [62, 11] Generated Node #0,2,2: 51:[62, 11] Operation: 44/4=11 Moving to Node #0,2,2 Current State: 51:[62, 11], Operations: ['85-81=4', '44/4=11'] Exploring Operation: 62-11=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_5
mult_heuristic
[ 29, 6, 13, 32 ]
68
[ "29-6=23", "13+32=45", "23+45=68" ]
Current State: 68:[29, 6, 13, 32], Operations: [] Exploring Operation: 29-6=23, Resulting Numbers: [13, 32, 23] Generated Node #2: [13, 32, 23] from Operation: 29-6=23 Current State: 68:[13, 32, 23], Operations: ['29-6=23'] Exploring Operation: 13+32=45, Resulting Numbers: [23, 45] Generated Node #3: [23, 45] from Operation: 13+32=45 Current State: 68:[23, 45], Operations: ['29-6=23', '13+32=45'] Exploring Operation: 23+45=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[29, 6, 13, 32], Operations: [] Exploring Operation: 29-13=16, Resulting Numbers: [6, 32, 16] Generated Node #0,0: 68:[6, 32, 16] Operation: 29-13=16 Exploring Operation: 29+6=35, Resulting Numbers: [13, 32, 35] Generated Node #0,1: 68:[13, 32, 35] Operation: 29+6=35 Exploring Operation: 6+13=19, Resulting Numbers: [29, 32, 19] Generated Node #0,2: 68:[29, 32, 19] Operation: 6+13=19 Exploring Operation: 32-29=3, Resulting Numbers: [6, 13, 3] Generated Node #0,3: 68:[6, 13, 3] Operation: 32-29=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[6, 32, 16], Operations: ['29-13=16'] Exploring Operation: 6+16=22, Resulting Numbers: [32, 22] Generated Node #0,0,0: 68:[32, 22] Operation: 6+16=22 Exploring Operation: 32-16=16, Resulting Numbers: [6, 16] Generated Node #0,0,1: 68:[6, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [6, 2] Generated Node #0,0,2: 68:[6, 2] Operation: 32/16=2 Exploring Operation: 6+32=38, Resulting Numbers: [16, 38] Generated Node #0,0,3: 68:[16, 38] Operation: 6+32=38 Moving to Node #0,0,2 Current State: 68:[6, 2], Operations: ['29-13=16', '32/16=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,68 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,68 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,68 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[6, 16], Operations: ['29-13=16', '32-16=16'] Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,68 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,68 unequal: No Solution Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,68 unequal: No Solution Moving to Node #0,0,3 Current State: 68:[16, 38], Operations: ['29-13=16', '6+32=38'] Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,68 unequal: No Solution Exploring Operation: 16*38=608, Resulting Numbers: [608] 608,68 unequal: No Solution Exploring Operation: 16+38=54, Resulting Numbers: [54] 54,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[32, 22], Operations: ['29-13=16', '6+16=22'] Exploring Operation: 32+22=54, Resulting Numbers: [54] 54,68 unequal: No Solution Exploring Operation: 32*22=704, Resulting Numbers: [704] 704,68 unequal: No Solution Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[13, 32, 35], Operations: ['29+6=35'] Exploring Operation: 35-13=22, Resulting Numbers: [32, 22] Generated Node #0,1,0: 68:[32, 22] Operation: 35-13=22 Exploring Operation: 32+35=67, Resulting Numbers: [13, 67] Generated Node #0,1,1: 68:[13, 67] Operation: 32+35=67 Exploring Operation: 35-32=3, Resulting Numbers: [13, 3] Generated Node #0,1,2: 68:[13, 3] Operation: 35-32=3 Exploring Operation: 32-13=19, Resulting Numbers: [35, 19] Generated Node #0,1,3: 68:[35, 19] Operation: 32-13=19 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 68:[35, 19], Operations: ['29+6=35', '32-13=19'] Exploring Operation: 35*19=665, Resulting Numbers: [665] 665,68 unequal: No Solution Exploring Operation: 35+19=54, Resulting Numbers: [54] 54,68 unequal: No Solution Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,68 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:[13, 67], Operations: ['29+6=35', '32+35=67'] Exploring Operation: 67-13=54, Resulting Numbers: [54] 54,68 unequal: No Solution Exploring Operation: 13+67=80, Resulting Numbers: [80] 80,68 unequal: No Solution Exploring Operation: 13*67=871, Resulting Numbers: [871] 871,68 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 #0,1,2 Current State: 68:[13, 3], Operations: ['29+6=35', '35-32=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,68 unequal: No Solution Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,68 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,68 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 #0,1,0 Current State: 68:[32, 22], Operations: ['29+6=35', '35-13=22'] Exploring Operation: 32*22=704, Resulting Numbers: [704] 704,68 unequal: No Solution Exploring Operation: 32+22=54, Resulting Numbers: [54] 54,68 unequal: No Solution Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,68 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 #0,3 Current State: 68:[6, 13, 3], Operations: ['32-29=3'] Exploring Operation: 13+3=16, Resulting Numbers: [6, 16] Generated Node #0,3,0: 68:[6, 16] Operation: 13+3=16 Exploring Operation: 13-6=7, Resulting Numbers: [3, 7] Generated Node #0,3,1: 68:[3, 7] Operation: 13-6=7 Exploring Operation: 6+13=19, Resulting Numbers: [3, 19] Generated Node #0,3,2: 68:[3, 19] Operation: 6+13=19 Exploring Operation: 6/3=2, Resulting Numbers: [13, 2] Generated Node #0,3,3: 68:[13, 2] Operation: 6/3=2 Moving to Node #0,3,0 Current State: 68:[6, 16], Operations: ['32-29=3', '13+3=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,68 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,68 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,68 unequal: No Solution Moving to Node #0,3,2 Current State: 68:[3, 19], Operations: ['32-29=3', '6+13=19'] Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,68 unequal: No Solution Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,68 unequal: No Solution Moving to Node #0,3,3 Current State: 68:[13, 2], Operations: ['32-29=3', '6/3=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,68 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,68 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,68 unequal: No Solution Moving to Node #0,3,1 Current State: 68:[3, 7], Operations: ['32-29=3', '13-6=7'] Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,68 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,68 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[29, 32, 19], Operations: ['6+13=19'] Exploring Operation: 29+32=61, Resulting Numbers: [19, 61] Generated Node #0,2,0: 68:[19, 61] Operation: 29+32=61 Exploring Operation: 29-19=10, Resulting Numbers: [32, 10] Generated Node #0,2,1: 68:[32, 10] Operation: 29-19=10 Exploring Operation: 32-29=3, Resulting Numbers: [19, 3] Generated Node #0,2,2: 68:[19, 3] Operation: 32-29=3 Exploring Operation: 32-19=13, Resulting Numbers: [29, 13] Generated Node #0,2,3: 68:[29, 13] Operation: 32-19=13 Moving to Node #0,2,2 Current State: 68:[19, 3], Operations: ['6+13=19', '32-29=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,68 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,68 unequal: No Solution Moving to Node #0,2,1 Current State: 68:[32, 10], Operations: ['6+13=19', '29-19=10'] Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,68 unequal: No Solution Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,68 unequal: No Solution Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,68 unequal: No Solution Moving to Node #0,2,3 Current State: 68:[29, 13], Operations: ['6+13=19', '32-19=13'] Exploring Operation: 29*13=377, Resulting Numbers: [377] 377,68 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,68 unequal: No Solution Exploring Operation: 29+13=42, Resulting Numbers: [42] 42,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[19, 61], Operations: ['6+13=19', '29+32=61'] Exploring Operation: 19+61=80, Resulting Numbers: [80] 80,68 unequal: No Solution Exploring Operation: 19*61=1159, Resulting Numbers: [1159] 1159,68 unequal: No Solution Exploring Operation: 61-19=42, Resulting Numbers: [42] 42,68 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
[ 3, 95, 17, 40 ]
35
[ "95-3=92", "17+40=57", "92-57=35" ]
Current State: 35:[3, 95, 17, 40], Operations: [] Exploring Operation: 95-3=92, Resulting Numbers: [17, 40, 92] Generated Node #2: [17, 40, 92] from Operation: 95-3=92 Current State: 35:[17, 40, 92], Operations: ['95-3=92'] Exploring Operation: 17+40=57, Resulting Numbers: [92, 57] Generated Node #3: [92, 57] from Operation: 17+40=57 Current State: 35:[92, 57], Operations: ['95-3=92', '17+40=57'] Exploring Operation: 92-57=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[3, 95, 17, 40], Operations: [] Exploring Operation: 95-40=55, Resulting Numbers: [3, 17, 55] Generated Node #0,0: 35:[3, 17, 55] Operation: 95-40=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[3, 17, 55], Operations: ['95-40=55'] Exploring Operation: 55-17=38, Resulting Numbers: [3, 38] Generated Node #0,0,0: 35:[3, 38] Operation: 55-17=38 Moving to Node #0,0,0 Current State: 35:[3, 38], Operations: ['95-40=55', '55-17=38'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[3, 95, 17, 40], Operations: [] Exploring Operation: 95-40=55, Resulting Numbers: [3, 17, 55] Generated Node #0,0: 35:[3, 17, 55] Operation: 95-40=55 Moving to Node #0,0 Current State: 35:[3, 17, 55], Operations: ['95-40=55'] Exploring Operation: 55-17=38, Resulting Numbers: [3, 38] Generated Node #0,0,0: 35:[3, 38] Operation: 55-17=38 Moving to Node #0,0,0 Current State: 35:[3, 38], Operations: ['95-40=55', '55-17=38'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 43, 70, 12, 46 ]
41
[ "70-46=24", "24/12=2", "43-2=41" ]
Current State: 41:[43, 70, 12, 46], Operations: [] Exploring Operation: 70-46=24, Resulting Numbers: [43, 12, 24] Generated Node #2: [43, 12, 24] from Operation: 70-46=24 Current State: 41:[43, 12, 24], Operations: ['70-46=24'] Exploring Operation: 24/12=2, Resulting Numbers: [43, 2] Generated Node #3: [43, 2] from Operation: 24/12=2 Current State: 41:[43, 2], Operations: ['70-46=24', '24/12=2'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[43, 70, 12, 46], Operations: [] Exploring Operation: 46-12=34, Resulting Numbers: [43, 70, 34] Generated Node #0,0: 41:[43, 70, 34] Operation: 46-12=34 Exploring Operation: 70-12=58, Resulting Numbers: [43, 46, 58] Generated Node #0,1: 41:[43, 46, 58] Operation: 70-12=58 Exploring Operation: 70-43=27, Resulting Numbers: [12, 46, 27] Generated Node #0,2: 41:[12, 46, 27] Operation: 70-43=27 Exploring Operation: 43-12=31, Resulting Numbers: [70, 46, 31] Generated Node #0,3: 41:[70, 46, 31] Operation: 43-12=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[43, 46, 58], Operations: ['70-12=58'] Exploring Operation: 43+46=89, Resulting Numbers: [58, 89] Generated Node #0,1,0: 41:[58, 89] Operation: 43+46=89 Exploring Operation: 58-43=15, Resulting Numbers: [46, 15] Generated Node #0,1,1: 41:[46, 15] Operation: 58-43=15 Exploring Operation: 46-43=3, Resulting Numbers: [58, 3] Generated Node #0,1,2: 41:[58, 3] Operation: 46-43=3 Exploring Operation: 58-46=12, Resulting Numbers: [43, 12] Generated Node #0,1,3: 41:[43, 12] Operation: 58-46=12 Moving to Node #0,1,1 Current State: 41:[46, 15], Operations: ['70-12=58', '58-43=15'] Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 46*15=690, Resulting Numbers: [690] 690,41 unequal: No Solution Exploring Operation: 46+15=61, Resulting Numbers: [61] 61,41 unequal: No Solution Moving to Node #0,1,3 Current State: 41:[43, 12], Operations: ['70-12=58', '58-46=12'] Exploring Operation: 43*12=516, Resulting Numbers: [516] 516,41 unequal: No Solution Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[58, 3], Operations: ['70-12=58', '46-43=3'] Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,41 unequal: No Solution Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,41 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[58, 89], Operations: ['70-12=58', '43+46=89'] Exploring Operation: 89-58=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 58*89=5162, Resulting Numbers: [5162] 5162,41 unequal: No Solution Exploring Operation: 58+89=147, Resulting Numbers: [147] 147,41 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 Current State: 41:[43, 70, 34], Operations: ['46-12=34'] Exploring Operation: 43+34=77, Resulting Numbers: [70, 77] Generated Node #0,0,0: 41:[70, 77] Operation: 43+34=77 Exploring Operation: 70-43=27, Resulting Numbers: [34, 27] Generated Node #0,0,1: 41:[34, 27] Operation: 70-43=27 Exploring Operation: 43-34=9, Resulting Numbers: [70, 9] Generated Node #0,0,2: 41:[70, 9] Operation: 43-34=9 Exploring Operation: 70-34=36, Resulting Numbers: [43, 36] Generated Node #0,0,3: 41:[43, 36] Operation: 70-34=36 Moving to Node #0,0,3 Current State: 41:[43, 36], Operations: ['46-12=34', '70-34=36'] Exploring Operation: 43-36=7, Resulting Numbers: [7] 7,41 unequal: No Solution Exploring Operation: 43*36=1548, Resulting Numbers: [1548] 1548,41 unequal: No Solution Exploring Operation: 43+36=79, Resulting Numbers: [79] 79,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[34, 27], Operations: ['46-12=34', '70-43=27'] Exploring Operation: 34*27=918, Resulting Numbers: [918] 918,41 unequal: No Solution Exploring Operation: 34-27=7, Resulting Numbers: [7] 7,41 unequal: No Solution Exploring Operation: 34+27=61, Resulting Numbers: [61] 61,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[70, 9], Operations: ['46-12=34', '43-34=9'] Exploring Operation: 70+9=79, Resulting Numbers: [79] 79,41 unequal: No Solution Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,41 unequal: No Solution Exploring Operation: 70*9=630, Resulting Numbers: [630] 630,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[70, 77], Operations: ['46-12=34', '43+34=77'] Exploring Operation: 70*77=5390, Resulting Numbers: [5390] 5390,41 unequal: No Solution Exploring Operation: 70+77=147, Resulting Numbers: [147] 147,41 unequal: No Solution Exploring Operation: 77-70=7, Resulting Numbers: [7] 7,41 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 #0,3 Current State: 41:[70, 46, 31], Operations: ['43-12=31'] Exploring Operation: 70-46=24, Resulting Numbers: [31, 24] Generated Node #0,3,0: 41:[31, 24] Operation: 70-46=24 Exploring Operation: 70-31=39, Resulting Numbers: [46, 39] Generated Node #0,3,1: 41:[46, 39] Operation: 70-31=39 Exploring Operation: 70+31=101, Resulting Numbers: [46, 101] Generated Node #0,3,2: 41:[46, 101] Operation: 70+31=101 Exploring Operation: 46-31=15, Resulting Numbers: [70, 15] Generated Node #0,3,3: 41:[70, 15] Operation: 46-31=15 Moving to Node #0,3,1 Current State: 41:[46, 39], Operations: ['43-12=31', '70-31=39'] Exploring Operation: 46+39=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 46*39=1794, Resulting Numbers: [1794] 1794,41 unequal: No Solution Exploring Operation: 46-39=7, Resulting Numbers: [7] 7,41 unequal: No Solution Moving to Node #0,3,0 Current State: 41:[31, 24], Operations: ['43-12=31', '70-46=24'] Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,41 unequal: No Solution Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,41 unequal: No Solution Moving to Node #0,3,3 Current State: 41:[70, 15], Operations: ['43-12=31', '46-31=15'] Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 70+15=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 70*15=1050, Resulting Numbers: [1050] 1050,41 unequal: No Solution Moving to Node #0,3,2 Current State: 41:[46, 101], Operations: ['43-12=31', '70+31=101'] Exploring Operation: 46+101=147, Resulting Numbers: [147] 147,41 unequal: No Solution Exploring Operation: 46*101=4646, Resulting Numbers: [4646] 4646,41 unequal: No Solution Exploring Operation: 101-46=55, Resulting Numbers: [55] 55,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[12, 46, 27], Operations: ['70-43=27'] Exploring Operation: 27-12=15, Resulting Numbers: [46, 15] Generated Node #0,2,0: 41:[46, 15] Operation: 27-12=15 Exploring Operation: 12+27=39, Resulting Numbers: [46, 39] Generated Node #0,2,1: 41:[46, 39] Operation: 12+27=39 Exploring Operation: 46-12=34, Resulting Numbers: [27, 34] Generated Node #0,2,2: 41:[27, 34] Operation: 46-12=34 Exploring Operation: 12+46=58, Resulting Numbers: [27, 58] Generated Node #0,2,3: 41:[27, 58] Operation: 12+46=58 Moving to Node #0,2,1 Current State: 41:[46, 39], Operations: ['70-43=27', '12+27=39'] Exploring Operation: 46*39=1794, Resulting Numbers: [1794] 1794,41 unequal: No Solution Exploring Operation: 46+39=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 46-39=7, Resulting Numbers: [7] 7,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[27, 34], Operations: ['70-43=27', '46-12=34'] Exploring Operation: 27*34=918, Resulting Numbers: [918] 918,41 unequal: No Solution Exploring Operation: 34-27=7, Resulting Numbers: [7] 7,41 unequal: No Solution Exploring Operation: 27+34=61, Resulting Numbers: [61] 61,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[27, 58], Operations: ['70-43=27', '12+46=58'] Exploring Operation: 27*58=1566, Resulting Numbers: [1566] 1566,41 unequal: No Solution Exploring Operation: 58-27=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 27+58=85, Resulting Numbers: [85] 85,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[46, 15], Operations: ['70-43=27', '27-12=15'] Exploring Operation: 46*15=690, Resulting Numbers: [690] 690,41 unequal: No Solution Exploring Operation: 46+15=61, Resulting Numbers: [61] 61,41 unequal: No Solution Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 80, 42, 41, 41 ]
39
[ "80-42=38", "41/41=1", "38+1=39" ]
Current State: 39:[80, 42, 41, 41], Operations: [] Exploring Operation: 80-42=38, Resulting Numbers: [41, 41, 38] Generated Node #2: [41, 41, 38] from Operation: 80-42=38 Current State: 39:[41, 41, 38], Operations: ['80-42=38'] Exploring Operation: 41/41=1, Resulting Numbers: [38, 1] Generated Node #3: [38, 1] from Operation: 41/41=1 Current State: 39:[38, 1], Operations: ['80-42=38', '41/41=1'] Exploring Operation: 38+1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[80, 42, 41, 41], Operations: [] Exploring Operation: 80-41=39, Resulting Numbers: [42, 41, 39] Generated Node #0,0: 39:[42, 41, 39] Operation: 80-41=39 Exploring Operation: 80-42=38, Resulting Numbers: [41, 41, 38] Generated Node #0,1: 39:[41, 41, 38] Operation: 80-42=38 Moving to Node #0,0 Current State: 39:[42, 41, 39], Operations: ['80-41=39'] Exploring Operation: 42-41=1, Resulting Numbers: [39, 1] Generated Node #0,0,0: 39:[39, 1] Operation: 42-41=1 Exploring Operation: 42-39=3, Resulting Numbers: [41, 3] Generated Node #0,0,1: 39:[41, 3] Operation: 42-39=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[39, 1], Operations: ['80-41=39', '42-41=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[80, 42, 41, 41], Operations: [] Exploring Operation: 80-41=39, Resulting Numbers: [42, 41, 39] Generated Node #0,0: 39:[42, 41, 39] Operation: 80-41=39 Moving to Node #0,0 Current State: 39:[42, 41, 39], Operations: ['80-41=39'] Exploring Operation: 42-41=1, Resulting Numbers: [39, 1] Generated Node #0,0,0: 39:[39, 1] Operation: 42-41=1 Moving to Node #0,0,0 Current State: 39:[39, 1], Operations: ['80-41=39', '42-41=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 6, 66, 51, 3 ]
45
[ "6-3=3", "66-51=15", "3*15=45" ]
Current State: 45:[6, 66, 51, 3], Operations: [] Exploring Operation: 6-3=3, Resulting Numbers: [66, 51, 3] Generated Node #2: [66, 51, 3] from Operation: 6-3=3 Current State: 45:[66, 51, 3], Operations: ['6-3=3'] Exploring Operation: 66-51=15, Resulting Numbers: [3, 15] Generated Node #3: [3, 15] from Operation: 66-51=15 Current State: 45:[3, 15], Operations: ['6-3=3', '66-51=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[6, 66, 51, 3], Operations: [] Exploring Operation: 66-51=15, Resulting Numbers: [6, 3, 15] Generated Node #0,0: 45:[6, 3, 15] Operation: 66-51=15 Exploring Operation: 66/6=11, Resulting Numbers: [51, 3, 11] Generated Node #0,1: 45:[51, 3, 11] Operation: 66/6=11 Moving to Node #0,0 Current State: 45:[6, 3, 15], Operations: ['66-51=15'] Exploring Operation: 6+3=9, Resulting Numbers: [15, 9] Generated Node #0,0,0: 45:[15, 9] Operation: 6+3=9 Exploring Operation: 6-3=3, Resulting Numbers: [15, 3] Generated Node #0,0,1: 45:[15, 3] Operation: 6-3=3 Moving to Node #0,1 Current State: 45:[51, 3, 11], Operations: ['66/6=11'] Exploring Operation: 51-3=48, Resulting Numbers: [11, 48] Generated Node #0,1,0: 45:[11, 48] Operation: 51-3=48 Exploring Operation: 51/3=17, Resulting Numbers: [11, 17] Generated Node #0,1,1: 45:[11, 17] Operation: 51/3=17 Moving to Node #0,0,0 Current State: 45:[15, 9], Operations: ['66-51=15', '6+3=9'] Exploring Operation: 15+9=24, Resulting Numbers: [24] 24,45 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[15, 3], Operations: ['66-51=15', '6-3=3'] Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[6, 66, 51, 3], Operations: [] Exploring Operation: 66-51=15, Resulting Numbers: [6, 3, 15] Generated Node #0,0: 45:[6, 3, 15] Operation: 66-51=15 Moving to Node #0,0 Current State: 45:[6, 3, 15], Operations: ['66-51=15'] Exploring Operation: 6-3=3, Resulting Numbers: [15, 3] Generated Node #0,0,1: 45:[15, 3] Operation: 6-3=3 Moving to Node #0,0,1 Current State: 45:[15, 3], Operations: ['66-51=15', '6-3=3'] Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
0.988715
hs_2
mult_heuristic
[ 25, 98, 25, 7 ]
91
[ "25+98=123", "25+7=32", "123-32=91" ]
Current State: 91:[25, 98, 25, 7], Operations: [] Exploring Operation: 25+98=123, Resulting Numbers: [7, 123] Generated Node #2: [7, 123] from Operation: 25+98=123 Current State: 91:[7, 123], Operations: ['25+98=123'] Exploring Operation: 25+7=32, Resulting Numbers: [123, 32] Generated Node #3: [123, 32] from Operation: 25+7=32 Current State: 91:[123, 32], Operations: ['25+98=123', '25+7=32'] Exploring Operation: 123-32=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[25, 98, 25, 7], Operations: [] Exploring Operation: 25-25=0, Resulting Numbers: [98, 7, 0] Generated Node #0,0: 91:[98, 7, 0] Operation: 25-25=0 Exploring Operation: 25/25=1, Resulting Numbers: [98, 7, 1] Generated Node #0,1: 91:[98, 7, 1] Operation: 25/25=1 Exploring Operation: 98-7=91, Resulting Numbers: [25, 25, 91] Generated Node #0,2: 91:[25, 25, 91] Operation: 98-7=91 Exploring Operation: 25-7=18, Resulting Numbers: [98, 25, 18] Generated Node #0,3: 91:[98, 25, 18] Operation: 25-7=18 Moving to Node #0,1 Current State: 91:[98, 7, 1], Operations: ['25/25=1'] Exploring Operation: 98-1=97, Resulting Numbers: [7, 97] Generated Node #0,1,0: 91:[7, 97] Operation: 98-1=97 Exploring Operation: 98-7=91, Resulting Numbers: [1, 91] Generated Node #0,1,1: 91:[1, 91] Operation: 98-7=91 Exploring Operation: 98*1=98, Resulting Numbers: [7, 98] Generated Node #0,1,2: 91:[7, 98] Operation: 98*1=98 Exploring Operation: 98/7=14, Resulting Numbers: [1, 14] Generated Node #0,1,3: 91:[1, 14] Operation: 98/7=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 91:[7, 97], Operations: ['25/25=1', '98-1=97'] Exploring Operation: 97-7=90, Resulting Numbers: [90] 90,91 unequal: No Solution Exploring Operation: 7+97=104, Resulting Numbers: [104] 104,91 unequal: No Solution Exploring Operation: 7*97=679, Resulting Numbers: [679] 679,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 91:[1, 91], Operations: ['25/25=1', '98-7=91'] Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,91 unequal: No Solution Exploring Operation: 1+91=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 1*91=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[25, 98, 25, 7], Operations: [] Exploring Operation: 25/25=1, Resulting Numbers: [98, 7, 1] Generated Node #0,1: 91:[98, 7, 1] Operation: 25/25=1 Moving to Node #0,1 Current State: 91:[98, 7, 1], Operations: ['25/25=1'] Exploring Operation: 98-7=91, Resulting Numbers: [1, 91] Generated Node #0,1,1: 91:[1, 91] Operation: 98-7=91 Moving to Node #0,1,1 Current State: 91:[1, 91], Operations: ['25/25=1', '98-7=91'] Exploring Operation: 1*91=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 42, 2, 89, 53 ]
98
[ "42+2=44", "89+53=142", "142-44=98" ]
Current State: 98:[42, 2, 89, 53], Operations: [] Exploring Operation: 42+2=44, Resulting Numbers: [89, 53, 44] Generated Node #2: [89, 53, 44] from Operation: 42+2=44 Current State: 98:[89, 53, 44], Operations: ['42+2=44'] Exploring Operation: 89+53=142, Resulting Numbers: [44, 142] Generated Node #3: [44, 142] from Operation: 89+53=142 Current State: 98:[44, 142], Operations: ['42+2=44', '89+53=142'] Exploring Operation: 142-44=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[42, 2, 89, 53], Operations: [] Exploring Operation: 53-42=11, Resulting Numbers: [2, 89, 11] Generated Node #0,0: 98:[2, 89, 11] Operation: 53-42=11 Exploring Operation: 89-42=47, Resulting Numbers: [2, 53, 47] Generated Node #0,1: 98:[2, 53, 47] Operation: 89-42=47 Exploring Operation: 42+53=95, Resulting Numbers: [2, 89, 95] Generated Node #0,2: 98:[2, 89, 95] Operation: 42+53=95 Exploring Operation: 2+89=91, Resulting Numbers: [42, 53, 91] Generated Node #0,3: 98:[42, 53, 91] Operation: 2+89=91 Exploring Operation: 42+2=44, Resulting Numbers: [89, 53, 44] Generated Node #0,4: 98:[89, 53, 44] Operation: 42+2=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[2, 53, 47], Operations: ['89-42=47'] Exploring Operation: 2+53=55, Resulting Numbers: [47, 55] Generated Node #0,1,0: 98:[47, 55] Operation: 2+53=55 Exploring Operation: 53+47=100, Resulting Numbers: [2, 100] Generated Node #0,1,1: 98:[2, 100] Operation: 53+47=100 Exploring Operation: 53-47=6, Resulting Numbers: [2, 6] Generated Node #0,1,2: 98:[2, 6] Operation: 53-47=6 Exploring Operation: 2+47=49, Resulting Numbers: [53, 49] Generated Node #0,1,3: 98:[53, 49] Operation: 2+47=49 Exploring Operation: 53-2=51, Resulting Numbers: [47, 51] Generated Node #0,1,4: 98:[47, 51] Operation: 53-2=51 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 98:[2, 6], Operations: ['89-42=47', '53-47=6'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,98 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,98 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,98 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,98 unequal: No Solution No 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: 98:[2, 100], Operations: ['89-42=47', '53+47=100'] Exploring Operation: 2+100=102, Resulting Numbers: [102] 102,98 unequal: No Solution Exploring Operation: 2*100=200, Resulting Numbers: [200] 200,98 unequal: No Solution Exploring Operation: 100/2=50, Resulting Numbers: [50] 50,98 unequal: No Solution Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[42, 2, 89, 53], Operations: [] Exploring Operation: 89-42=47, Resulting Numbers: [2, 53, 47] Generated Node #0,1: 98:[2, 53, 47] Operation: 89-42=47 Moving to Node #0,1 Current State: 98:[2, 53, 47], Operations: ['89-42=47'] Exploring Operation: 53+47=100, Resulting Numbers: [2, 100] Generated Node #0,1,1: 98:[2, 100] Operation: 53+47=100 Moving to Node #0,1,1 Current State: 98:[2, 100], Operations: ['89-42=47', '53+47=100'] Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 9, 19, 66, 42 ]
44
[ "9+19=28", "66*28=1848", "1848/42=44" ]
Current State: 44:[9, 19, 66, 42], Operations: [] Exploring Operation: 9+19=28, Resulting Numbers: [66, 42, 28] Generated Node #2: [66, 42, 28] from Operation: 9+19=28 Current State: 44:[66, 42, 28], Operations: ['9+19=28'] Exploring Operation: 66*28=1848, Resulting Numbers: [42, 1848] Generated Node #3: [42, 1848] from Operation: 66*28=1848 Current State: 44:[42, 1848], Operations: ['9+19=28', '66*28=1848'] Exploring Operation: 1848/42=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[9, 19, 66, 42], Operations: [] Exploring Operation: 66-9=57, Resulting Numbers: [19, 42, 57] Generated Node #0,0: 44:[19, 42, 57] Operation: 66-9=57 Exploring Operation: 66-42=24, Resulting Numbers: [9, 19, 24] Generated Node #0,1: 44:[9, 19, 24] Operation: 66-42=24 Exploring Operation: 66-19=47, Resulting Numbers: [9, 42, 47] Generated Node #0,2: 44:[9, 42, 47] Operation: 66-19=47 Exploring Operation: 19-9=10, Resulting Numbers: [66, 42, 10] Generated Node #0,3: 44:[66, 42, 10] Operation: 19-9=10 Moving to Node #0,1 Current State: 44:[9, 19, 24], Operations: ['66-42=24'] Exploring Operation: 24-9=15, Resulting Numbers: [19, 15] Generated Node #0,1,0: 44:[19, 15] Operation: 24-9=15 Exploring Operation: 19+24=43, Resulting Numbers: [9, 43] Generated Node #0,1,1: 44:[9, 43] Operation: 19+24=43 Exploring Operation: 24-19=5, Resulting Numbers: [9, 5] Generated Node #0,1,2: 44:[9, 5] Operation: 24-19=5 Exploring Operation: 19-9=10, Resulting Numbers: [24, 10] Generated Node #0,1,3: 44:[24, 10] Operation: 19-9=10 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 44:[9, 43], Operations: ['66-42=24', '19+24=43'] Exploring Operation: 9*43=387, Resulting Numbers: [387] 387,44 unequal: No Solution Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 9+43=52, Resulting Numbers: [52] 52,44 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:[9, 5], Operations: ['66-42=24', '24-19=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,44 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,44 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 #0,1,3 Current State: 44:[24, 10], Operations: ['66-42=24', '19-9=10'] Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 24*10=240, Resulting Numbers: [240] 240,44 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 #0,1,0 Current State: 44:[19, 15], Operations: ['66-42=24', '24-9=15'] Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 19*15=285, Resulting Numbers: [285] 285,44 unequal: No Solution Exploring Operation: 19+15=34, Resulting Numbers: [34] 34,44 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: 44:[9, 42, 47], Operations: ['66-19=47'] Exploring Operation: 9+42=51, Resulting Numbers: [47, 51] Generated Node #0,2,0: 44:[47, 51] Operation: 9+42=51 Exploring Operation: 47-42=5, Resulting Numbers: [9, 5] Generated Node #0,2,1: 44:[9, 5] Operation: 47-42=5 Exploring Operation: 42-9=33, Resulting Numbers: [47, 33] Generated Node #0,2,2: 44:[47, 33] Operation: 42-9=33 Exploring Operation: 47-9=38, Resulting Numbers: [42, 38] Generated Node #0,2,3: 44:[42, 38] Operation: 47-9=38 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 44:[9, 5], Operations: ['66-19=47', '47-42=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,44 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,44 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:[42, 38], Operations: ['66-19=47', '47-9=38'] Exploring Operation: 42*38=1596, Resulting Numbers: [1596] 1596,44 unequal: No Solution Exploring Operation: 42-38=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 42+38=80, Resulting Numbers: [80] 80,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 44:[47, 51], Operations: ['66-19=47', '9+42=51'] Exploring Operation: 47+51=98, Resulting Numbers: [98] 98,44 unequal: No Solution Exploring Operation: 47*51=2397, Resulting Numbers: [2397] 2397,44 unequal: No Solution Exploring Operation: 51-47=4, Resulting Numbers: [4] 4,44 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:[47, 33], Operations: ['66-19=47', '42-9=33'] Exploring Operation: 47*33=1551, Resulting Numbers: [1551] 1551,44 unequal: No Solution Exploring Operation: 47+33=80, Resulting Numbers: [80] 80,44 unequal: No Solution Exploring Operation: 47-33=14, Resulting Numbers: [14] 14,44 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:[19, 42, 57], Operations: ['66-9=57'] Exploring Operation: 57-42=15, Resulting Numbers: [19, 15] Generated Node #0,0,0: 44:[19, 15] Operation: 57-42=15 Exploring Operation: 42-19=23, Resulting Numbers: [57, 23] Generated Node #0,0,1: 44:[57, 23] Operation: 42-19=23 Exploring Operation: 57-19=38, Resulting Numbers: [42, 38] Generated Node #0,0,2: 44:[42, 38] Operation: 57-19=38 Exploring Operation: 57/19=3, Resulting Numbers: [42, 3] Generated Node #0,0,3: 44:[42, 3] Operation: 57/19=3 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 44:[42, 3], Operations: ['66-9=57', '57/19=3'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,44 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 42*3=126, Resulting Numbers: [126] 126,44 unequal: No Solution Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,44 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 #0,0,0 Current State: 44:[19, 15], Operations: ['66-9=57', '57-42=15'] Exploring Operation: 19+15=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 19*15=285, Resulting Numbers: [285] 285,44 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 #0,0,2 Current State: 44:[42, 38], Operations: ['66-9=57', '57-19=38'] Exploring Operation: 42+38=80, Resulting Numbers: [80] 80,44 unequal: No Solution Exploring Operation: 42*38=1596, Resulting Numbers: [1596] 1596,44 unequal: No Solution Exploring Operation: 42-38=4, Resulting Numbers: [4] 4,44 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 #0,0,1 Current State: 44:[57, 23], Operations: ['66-9=57', '42-19=23'] Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 57+23=80, Resulting Numbers: [80] 80,44 unequal: No Solution Exploring Operation: 57*23=1311, Resulting Numbers: [1311] 1311,44 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: 44:[66, 42, 10], Operations: ['19-9=10'] Exploring Operation: 66-10=56, Resulting Numbers: [42, 56] Generated Node #0,3,0: 44:[42, 56] Operation: 66-10=56 Exploring Operation: 42-10=32, Resulting Numbers: [66, 32] Generated Node #0,3,1: 44:[66, 32] Operation: 42-10=32 Exploring Operation: 42+10=52, Resulting Numbers: [66, 52] Generated Node #0,3,2: 44:[66, 52] Operation: 42+10=52 Exploring Operation: 66-42=24, Resulting Numbers: [10, 24] Generated Node #0,3,3: 44:[10, 24] Operation: 66-42=24 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 44:[10, 24], Operations: ['19-9=10', '66-42=24'] Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 10*24=240, Resulting Numbers: [240] 240,44 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 44:[42, 56], Operations: ['19-9=10', '66-10=56'] Exploring Operation: 42+56=98, Resulting Numbers: [98] 98,44 unequal: No Solution Exploring Operation: 56-42=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 42*56=2352, Resulting Numbers: [2352] 2352,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 44:[66, 52], Operations: ['19-9=10', '42+10=52'] Exploring Operation: 66+52=118, Resulting Numbers: [118] 118,44 unequal: No Solution Exploring Operation: 66-52=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 66*52=3432, Resulting Numbers: [3432] 3432,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 44:[66, 32], Operations: ['19-9=10', '42-10=32'] Exploring Operation: 66-32=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 66*32=2112, Resulting Numbers: [2112] 2112,44 unequal: No Solution Exploring Operation: 66+32=98, Resulting Numbers: [98] 98,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 26, 92, 91, 58 ]
31
[ "26+92=118", "91+58=149", "149-118=31" ]
Current State: 31:[26, 92, 91, 58], Operations: [] Exploring Operation: 26+92=118, Resulting Numbers: [91, 58, 118] Generated Node #2: [91, 58, 118] from Operation: 26+92=118 Current State: 31:[91, 58, 118], Operations: ['26+92=118'] Exploring Operation: 91+58=149, Resulting Numbers: [118, 149] Generated Node #3: [118, 149] from Operation: 91+58=149 Current State: 31:[118, 149], Operations: ['26+92=118', '91+58=149'] Exploring Operation: 149-118=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[26, 92, 91, 58], Operations: [] Exploring Operation: 92-58=34, Resulting Numbers: [26, 91, 34] Generated Node #0,0: 31:[26, 91, 34] Operation: 92-58=34 Exploring Operation: 92-26=66, Resulting Numbers: [91, 58, 66] Generated Node #0,1: 31:[91, 58, 66] Operation: 92-26=66 Exploring Operation: 91-58=33, Resulting Numbers: [26, 92, 33] Generated Node #0,2: 31:[26, 92, 33] Operation: 91-58=33 Exploring Operation: 92-91=1, Resulting Numbers: [26, 58, 1] Generated Node #0,3: 31:[26, 58, 1] Operation: 92-91=1 Moving to Node #0,3 Current State: 31:[26, 58, 1], Operations: ['92-91=1'] Exploring Operation: 26*1=26, Resulting Numbers: [58, 26] Generated Node #0,3,0: 31:[58, 26] Operation: 26*1=26 Exploring Operation: 58-26=32, Resulting Numbers: [1, 32] Generated Node #0,3,1: 31:[1, 32] Operation: 58-26=32 Exploring Operation: 26+1=27, Resulting Numbers: [58, 27] Generated Node #0,3,2: 31:[58, 27] Operation: 26+1=27 Exploring Operation: 58-1=57, Resulting Numbers: [26, 57] Generated Node #0,3,3: 31:[26, 57] Operation: 58-1=57 Moving to Node #0,2 Current State: 31:[26, 92, 33], Operations: ['91-58=33'] Exploring Operation: 92-26=66, Resulting Numbers: [33, 66] Generated Node #0,2,0: 31:[33, 66] Operation: 92-26=66 Exploring Operation: 33-26=7, Resulting Numbers: [92, 7] Generated Node #0,2,1: 31:[92, 7] Operation: 33-26=7 Exploring Operation: 26+92=118, Resulting Numbers: [33, 118] Generated Node #0,2,2: 31:[33, 118] Operation: 26+92=118 Exploring Operation: 92-33=59, Resulting Numbers: [26, 59] Generated Node #0,2,3: 31:[26, 59] Operation: 92-33=59 Moving to Node #0,0 Current State: 31:[26, 91, 34], Operations: ['92-58=34'] Exploring Operation: 91-26=65, Resulting Numbers: [34, 65] Generated Node #0,0,0: 31:[34, 65] Operation: 91-26=65 Exploring Operation: 91-34=57, Resulting Numbers: [26, 57] Generated Node #0,0,1: 31:[26, 57] Operation: 91-34=57 Exploring Operation: 34-26=8, Resulting Numbers: [91, 8] Generated Node #0,0,2: 31:[91, 8] Operation: 34-26=8 Exploring Operation: 26+91=117, Resulting Numbers: [34, 117] Generated Node #0,0,3: 31:[34, 117] Operation: 26+91=117 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[26, 57], Operations: ['92-58=34', '91-34=57'] Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[26, 92, 91, 58], Operations: [] Exploring Operation: 92-58=34, Resulting Numbers: [26, 91, 34] Generated Node #0,0: 31:[26, 91, 34] Operation: 92-58=34 Moving to Node #0,0 Current State: 31:[26, 91, 34], Operations: ['92-58=34'] Exploring Operation: 91-34=57, Resulting Numbers: [26, 57] Generated Node #0,0,1: 31:[26, 57] Operation: 91-34=57 Moving to Node #0,0,1 Current State: 31:[26, 57], Operations: ['92-58=34', '91-34=57'] Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 96, 9, 7, 96 ]
72
[ "96/96=1", "7+1=8", "9*8=72" ]
Current State: 72:[96, 9, 7, 96], Operations: [] Exploring Operation: 96/96=1, Resulting Numbers: [9, 7, 1] Generated Node #2: [9, 7, 1] from Operation: 96/96=1 Current State: 72:[9, 7, 1], Operations: ['96/96=1'] Exploring Operation: 7+1=8, Resulting Numbers: [9, 8] Generated Node #3: [9, 8] from Operation: 7+1=8 Current State: 72:[9, 8], Operations: ['96/96=1', '7+1=8'] Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[96, 9, 7, 96], Operations: [] Exploring Operation: 96/96=1, Resulting Numbers: [9, 7, 1] Generated Node #0,0: 72:[9, 7, 1] Operation: 96/96=1 Exploring Operation: 96-9=87, Resulting Numbers: [7, 96, 87] Generated Node #0,1: 72:[7, 96, 87] Operation: 96-9=87 Exploring Operation: 96-96=0, Resulting Numbers: [9, 7, 0] Generated Node #0,2: 72:[9, 7, 0] Operation: 96-96=0 Moving to Node #0,0 Current State: 72:[9, 7, 1], Operations: ['96/96=1'] Exploring Operation: 7-1=6, Resulting Numbers: [9, 6] Generated Node #0,0,0: 72:[9, 6] Operation: 7-1=6 Exploring Operation: 7+1=8, Resulting Numbers: [9, 8] Generated Node #0,0,1: 72:[9, 8] Operation: 7+1=8 Exploring Operation: 9-7=2, Resulting Numbers: [1, 2] Generated Node #0,0,2: 72:[1, 2] Operation: 9-7=2 Moving to Node #0,2 Current State: 72:[9, 7, 0], Operations: ['96-96=0'] Exploring Operation: 7+0=7, Resulting Numbers: [9, 7] Generated Node #0,2,0: 72:[9, 7] Operation: 7+0=7 Exploring Operation: 9+0=9, Resulting Numbers: [7, 9] Generated Node #0,2,1: 72:[7, 9] Operation: 9+0=9 Exploring Operation: 9-0=9, Resulting Numbers: [7, 9] Generated Node #0,2,2: 72:[7, 9] Operation: 9-0=9 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 72:[9, 7], Operations: ['96-96=0', '7+0=7'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 72:[7, 9], Operations: ['96-96=0', '9+0=9'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 72:[7, 9], Operations: ['96-96=0', '9-0=9'] Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 72:[7, 96, 87], Operations: ['96-9=87'] Exploring Operation: 87-7=80, Resulting Numbers: [96, 80] Generated Node #0,1,0: 72:[96, 80] Operation: 87-7=80 Exploring Operation: 96-7=89, Resulting Numbers: [87, 89] Generated Node #0,1,1: 72:[87, 89] Operation: 96-7=89 Exploring Operation: 96-87=9, Resulting Numbers: [7, 9] Generated Node #0,1,2: 72:[7, 9] Operation: 96-87=9 Moving to Node #0,0,0 Current State: 72:[9, 6], Operations: ['96/96=1', '7-1=6'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,72 unequal: No Solution Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,72 unequal: No Solution Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[9, 8], Operations: ['96/96=1', '7+1=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,72 unequal: No Solution Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[96, 9, 7, 96], Operations: [] Exploring Operation: 96/96=1, Resulting Numbers: [9, 7, 1] Generated Node #0,0: 72:[9, 7, 1] Operation: 96/96=1 Moving to Node #0,0 Current State: 72:[9, 7, 1], Operations: ['96/96=1'] Exploring Operation: 7+1=8, Resulting Numbers: [9, 8] Generated Node #0,0,1: 72:[9, 8] Operation: 7+1=8 Moving to Node #0,0,1 Current State: 72:[9, 8], Operations: ['96/96=1', '7+1=8'] Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.973958
hs_3
sum_heuristic
[ 25, 5, 64, 35 ]
46
[ "64-25=39", "35/5=7", "39+7=46" ]
Current State: 46:[25, 5, 64, 35], Operations: [] Exploring Operation: 64-25=39, Resulting Numbers: [5, 35, 39] Generated Node #2: [5, 35, 39] from Operation: 64-25=39 Current State: 46:[5, 35, 39], Operations: ['64-25=39'] Exploring Operation: 35/5=7, Resulting Numbers: [39, 7] Generated Node #3: [39, 7] from Operation: 35/5=7 Current State: 46:[39, 7], Operations: ['64-25=39', '35/5=7'] Exploring Operation: 39+7=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[25, 5, 64, 35], Operations: [] Exploring Operation: 64-5=59, Resulting Numbers: [25, 35, 59] Generated Node #0,0: 46:[25, 35, 59] Operation: 64-5=59 Exploring Operation: 64-35=29, Resulting Numbers: [25, 5, 29] Generated Node #0,1: 46:[25, 5, 29] Operation: 64-35=29 Exploring Operation: 64-25=39, Resulting Numbers: [5, 35, 39] Generated Node #0,2: 46:[5, 35, 39] Operation: 64-25=39 Exploring Operation: 35/5=7, Resulting Numbers: [25, 64, 7] Generated Node #0,3: 46:[25, 64, 7] Operation: 35/5=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[25, 5, 29], Operations: ['64-35=29'] Exploring Operation: 29-25=4, Resulting Numbers: [5, 4] Generated Node #0,1,0: 46:[5, 4] Operation: 29-25=4 Exploring Operation: 29-5=24, Resulting Numbers: [25, 24] Generated Node #0,1,1: 46:[25, 24] Operation: 29-5=24 Exploring Operation: 25/5=5, Resulting Numbers: [29, 5] Generated Node #0,1,2: 46:[29, 5] Operation: 25/5=5 Exploring Operation: 25-5=20, Resulting Numbers: [29, 20] Generated Node #0,1,3: 46:[29, 20] Operation: 25-5=20 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 46:[25, 24], Operations: ['64-35=29', '29-5=24'] Exploring Operation: 25*24=600, Resulting Numbers: [600] 600,46 unequal: No Solution Exploring Operation: 25+24=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 25-24=1, Resulting Numbers: [1] 1,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[5, 4], Operations: ['64-35=29', '29-25=4'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,46 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 46:[29, 5], Operations: ['64-35=29', '25/5=5'] Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,46 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,46 unequal: No Solution Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 46:[29, 20], Operations: ['64-35=29', '25-5=20'] Exploring Operation: 29*20=580, Resulting Numbers: [580] 580,46 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,46 unequal: No Solution Exploring Operation: 29+20=49, Resulting Numbers: [49] 49,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[5, 35, 39], Operations: ['64-25=39'] Exploring Operation: 35/5=7, Resulting Numbers: [39, 7] Generated Node #0,2,0: 46:[39, 7] Operation: 35/5=7 Exploring Operation: 5+39=44, Resulting Numbers: [35, 44] Generated Node #0,2,1: 46:[35, 44] Operation: 5+39=44 Exploring Operation: 5+35=40, Resulting Numbers: [39, 40] Generated Node #0,2,2: 46:[39, 40] Operation: 5+35=40 Exploring Operation: 39-35=4, Resulting Numbers: [5, 4] Generated Node #0,2,3: 46:[5, 4] Operation: 39-35=4 Moving to Node #0,2,3 Current State: 46:[5, 4], Operations: ['64-25=39', '39-35=4'] Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,46 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[39, 7], Operations: ['64-25=39', '35/5=7'] Exploring Operation: 39+7=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[25, 5, 64, 35], Operations: [] Exploring Operation: 64-25=39, Resulting Numbers: [5, 35, 39] Generated Node #0,2: 46:[5, 35, 39] Operation: 64-25=39 Moving to Node #0,2 Current State: 46:[5, 35, 39], Operations: ['64-25=39'] Exploring Operation: 35/5=7, Resulting Numbers: [39, 7] Generated Node #0,2,0: 46:[39, 7] Operation: 35/5=7 Moving to Node #0,2,0 Current State: 46:[39, 7], Operations: ['64-25=39', '35/5=7'] Exploring Operation: 39+7=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 98, 87, 51, 26 ]
66
[ "98-87=11", "51+26=77", "77-11=66" ]
Current State: 66:[98, 87, 51, 26], Operations: [] Exploring Operation: 98-87=11, Resulting Numbers: [51, 26, 11] Generated Node #2: [51, 26, 11] from Operation: 98-87=11 Current State: 66:[51, 26, 11], Operations: ['98-87=11'] Exploring Operation: 51+26=77, Resulting Numbers: [11, 77] Generated Node #3: [11, 77] from Operation: 51+26=77 Current State: 66:[11, 77], Operations: ['98-87=11', '51+26=77'] Exploring Operation: 77-11=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[98, 87, 51, 26], Operations: [] Exploring Operation: 98-87=11, Resulting Numbers: [51, 26, 11] Generated Node #0,0: 66:[51, 26, 11] Operation: 98-87=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[51, 26, 11], Operations: ['98-87=11'] Exploring Operation: 51-26=25, Resulting Numbers: [11, 25] Generated Node #0,0,0: 66:[11, 25] Operation: 51-26=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 66:[11, 25], Operations: ['98-87=11', '51-26=25'] Exploring Operation: 11+25=36, Resulting Numbers: [36] 36,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 55, 13, 6, 2 ]
40
[ "55+13=68", "68/2=34", "6+34=40" ]
Current State: 40:[55, 13, 6, 2], Operations: [] Exploring Operation: 55+13=68, Resulting Numbers: [6, 2, 68] Generated Node #2: [6, 2, 68] from Operation: 55+13=68 Current State: 40:[6, 2, 68], Operations: ['55+13=68'] Exploring Operation: 68/2=34, Resulting Numbers: [6, 34] Generated Node #3: [6, 34] from Operation: 68/2=34 Current State: 40:[6, 34], Operations: ['55+13=68', '68/2=34'] Exploring Operation: 6+34=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[55, 13, 6, 2], Operations: [] Exploring Operation: 55-6=49, Resulting Numbers: [13, 2, 49] Generated Node #0,0: 40:[13, 2, 49] Operation: 55-6=49 Exploring Operation: 13+6=19, Resulting Numbers: [55, 2, 19] Generated Node #0,1: 40:[55, 2, 19] Operation: 13+6=19 Exploring Operation: 55-13=42, Resulting Numbers: [6, 2, 42] Generated Node #0,2: 40:[6, 2, 42] Operation: 55-13=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[6, 2, 42], Operations: ['55-13=42'] Exploring Operation: 6+2=8, Resulting Numbers: [42, 8] Generated Node #0,2,0: 40:[42, 8] Operation: 6+2=8 Exploring Operation: 42/6=7, Resulting Numbers: [2, 7] Generated Node #0,2,1: 40:[2, 7] Operation: 42/6=7 Exploring Operation: 42-2=40, Resulting Numbers: [6, 40] Generated Node #0,2,2: 40:[6, 40] Operation: 42-2=40 Moving to Node #0,2,1 Current State: 40:[2, 7], Operations: ['55-13=42', '42/6=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,40 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,40 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,40 unequal: No Solution Moving to Node #0,2,2 Current State: 40:[6, 40], Operations: ['55-13=42', '42-2=40'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,40 unequal: No Solution Exploring Operation: 6*40=240, Resulting Numbers: [240] 240,40 unequal: No Solution Exploring Operation: 6+40=46, Resulting Numbers: [46] 46,40 unequal: No Solution Moving to Node #0,2,0 Current State: 40:[42, 8], Operations: ['55-13=42', '6+2=8'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,40 unequal: No Solution Exploring Operation: 42+8=50, Resulting Numbers: [50] 50,40 unequal: No Solution Exploring Operation: 42*8=336, Resulting Numbers: [336] 336,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[13, 2, 49], Operations: ['55-6=49'] Exploring Operation: 13-2=11, Resulting Numbers: [49, 11] Generated Node #0,0,0: 40:[49, 11] Operation: 13-2=11 Exploring Operation: 49-13=36, Resulting Numbers: [2, 36] Generated Node #0,0,1: 40:[2, 36] Operation: 49-13=36 Exploring Operation: 49-2=47, Resulting Numbers: [13, 47] Generated Node #0,0,2: 40:[13, 47] Operation: 49-2=47 Moving to Node #0,0,1 Current State: 40:[2, 36], Operations: ['55-6=49', '49-13=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,40 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,40 unequal: No Solution Moving to Node #0,0,0 Current State: 40:[49, 11], Operations: ['55-6=49', '13-2=11'] Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,40 unequal: No Solution Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,40 unequal: No Solution Exploring Operation: 49*11=539, Resulting Numbers: [539] 539,40 unequal: No Solution Moving to Node #0,0,2 Current State: 40:[13, 47], Operations: ['55-6=49', '49-2=47'] Exploring Operation: 13*47=611, Resulting Numbers: [611] 611,40 unequal: No Solution Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,40 unequal: No Solution Exploring Operation: 13+47=60, Resulting Numbers: [60] 60,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[55, 2, 19], Operations: ['13+6=19'] Exploring Operation: 55-19=36, Resulting Numbers: [2, 36] Generated Node #0,1,0: 40:[2, 36] Operation: 55-19=36 Exploring Operation: 55-2=53, Resulting Numbers: [19, 53] Generated Node #0,1,1: 40:[19, 53] Operation: 55-2=53 Exploring Operation: 2+19=21, Resulting Numbers: [55, 21] Generated Node #0,1,2: 40:[55, 21] Operation: 2+19=21 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 40:[2, 36], Operations: ['13+6=19', '55-19=36'] Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,40 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,40 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:[19, 53], Operations: ['13+6=19', '55-2=53'] Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,40 unequal: No Solution Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,40 unequal: No Solution Exploring Operation: 19*53=1007, Resulting Numbers: [1007] 1007,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 40:[55, 21], Operations: ['13+6=19', '2+19=21'] Exploring Operation: 55-21=34, Resulting Numbers: [34] 34,40 unequal: No Solution Exploring Operation: 55*21=1155, Resulting Numbers: [1155] 1155,40 unequal: No Solution Exploring Operation: 55+21=76, Resulting Numbers: [76] 76,40 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
mult_heuristic
[ 46, 7, 78, 8 ]
68
[ "46+78=124", "7*8=56", "124-56=68" ]
Current State: 68:[46, 7, 78, 8], Operations: [] Exploring Operation: 46+78=124, Resulting Numbers: [7, 8, 124] Generated Node #2: [7, 8, 124] from Operation: 46+78=124 Current State: 68:[7, 8, 124], Operations: ['46+78=124'] Exploring Operation: 7*8=56, Resulting Numbers: [124, 56] Generated Node #3: [124, 56] from Operation: 7*8=56 Current State: 68:[124, 56], Operations: ['46+78=124', '7*8=56'] Exploring Operation: 124-56=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[46, 7, 78, 8], Operations: [] Exploring Operation: 46-8=38, Resulting Numbers: [7, 78, 38] Generated Node #0,0: 68:[7, 78, 38] Operation: 46-8=38 Exploring Operation: 78-46=32, Resulting Numbers: [7, 8, 32] Generated Node #0,1: 68:[7, 8, 32] Operation: 78-46=32 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[7, 8, 32], Operations: ['78-46=32'] Exploring Operation: 8-7=1, Resulting Numbers: [32, 1] Generated Node #0,1,0: 68:[32, 1] Operation: 8-7=1 Exploring Operation: 32/8=4, Resulting Numbers: [7, 4] Generated Node #0,1,1: 68:[7, 4] Operation: 32/8=4 Moving to Node #0,1,0 Current State: 68:[32, 1], Operations: ['78-46=32', '8-7=1'] Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,68 unequal: No Solution Exploring Operation: 32*1=32, Resulting Numbers: [32] 32,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[7, 4], Operations: ['78-46=32', '32/8=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,68 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[7, 78, 38], Operations: ['46-8=38'] Exploring Operation: 78-7=71, Resulting Numbers: [38, 71] Generated Node #0,0,0: 68:[38, 71] Operation: 78-7=71 Exploring Operation: 78-38=40, Resulting Numbers: [7, 40] Generated Node #0,0,1: 68:[7, 40] Operation: 78-38=40 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[38, 71], Operations: ['46-8=38', '78-7=71'] Exploring Operation: 71-38=33, Resulting Numbers: [33] 33,68 unequal: No Solution Exploring Operation: 38+71=109, Resulting Numbers: [109] 109,68 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:[7, 40], Operations: ['46-8=38', '78-38=40'] Exploring Operation: 7+40=47, Resulting Numbers: [47] 47,68 unequal: No Solution Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,68 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
[ 3, 33, 21, 67 ]
57
[ "33/3=11", "67-21=46", "11+46=57" ]
Current State: 57:[3, 33, 21, 67], Operations: [] Exploring Operation: 33/3=11, Resulting Numbers: [21, 67, 11] Generated Node #2: [21, 67, 11] from Operation: 33/3=11 Current State: 57:[21, 67, 11], Operations: ['33/3=11'] Exploring Operation: 67-21=46, Resulting Numbers: [11, 46] Generated Node #3: [11, 46] from Operation: 67-21=46 Current State: 57:[11, 46], Operations: ['33/3=11', '67-21=46'] Exploring Operation: 11+46=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[3, 33, 21, 67], Operations: [] Exploring Operation: 33+21=54, Resulting Numbers: [3, 67, 54] Generated Node #0,0: 57:[3, 67, 54] Operation: 33+21=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[3, 67, 54], Operations: ['33+21=54'] Exploring Operation: 67-54=13, Resulting Numbers: [3, 13] Generated Node #0,0,0: 57:[3, 13] Operation: 67-54=13 Moving to Node #0,0,0 Current State: 57:[3, 13], Operations: ['33+21=54', '67-54=13'] Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 2, 10, 60, 1 ]
68
[ "10-2=8", "60*1=60", "8+60=68" ]
Current State: 68:[2, 10, 60, 1], Operations: [] Exploring Operation: 10-2=8, Resulting Numbers: [60, 1, 8] Generated Node #2: [60, 1, 8] from Operation: 10-2=8 Current State: 68:[60, 1, 8], Operations: ['10-2=8'] Exploring Operation: 60*1=60, Resulting Numbers: [8, 60] Generated Node #3: [8, 60] from Operation: 60*1=60 Current State: 68:[8, 60], Operations: ['10-2=8', '60*1=60'] Exploring Operation: 8+60=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[2, 10, 60, 1], Operations: [] Exploring Operation: 10+60=70, Resulting Numbers: [2, 1, 70] Generated Node #0,0: 68:[2, 1, 70] Operation: 10+60=70 Exploring Operation: 60/10=6, Resulting Numbers: [2, 1, 6] Generated Node #0,1: 68:[2, 1, 6] Operation: 60/10=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[2, 1, 70], Operations: ['10+60=70'] Exploring Operation: 70-2=68, Resulting Numbers: [1, 68] Generated Node #0,0,0: 68:[1, 68] Operation: 70-2=68 Exploring Operation: 70-1=69, Resulting Numbers: [2, 69] Generated Node #0,0,1: 68:[2, 69] Operation: 70-1=69 Moving to Node #0,0,0 Current State: 68:[1, 68], Operations: ['10+60=70', '70-2=68'] Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[2, 10, 60, 1], Operations: [] Exploring Operation: 10+60=70, Resulting Numbers: [2, 1, 70] Generated Node #0,0: 68:[2, 1, 70] Operation: 10+60=70 Moving to Node #0,0 Current State: 68:[2, 1, 70], Operations: ['10+60=70'] Exploring Operation: 70-2=68, Resulting Numbers: [1, 68] Generated Node #0,0,0: 68:[1, 68] Operation: 70-2=68 Moving to Node #0,0,0 Current State: 68:[1, 68], Operations: ['10+60=70', '70-2=68'] Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 34, 53, 84, 6 ]
97
[ "53-34=19", "84-6=78", "19+78=97" ]
Current State: 97:[34, 53, 84, 6], Operations: [] Exploring Operation: 53-34=19, Resulting Numbers: [84, 6, 19] Generated Node #2: [84, 6, 19] from Operation: 53-34=19 Current State: 97:[84, 6, 19], Operations: ['53-34=19'] Exploring Operation: 84-6=78, Resulting Numbers: [19, 78] Generated Node #3: [19, 78] from Operation: 84-6=78 Current State: 97:[19, 78], Operations: ['53-34=19', '84-6=78'] Exploring Operation: 19+78=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[34, 53, 84, 6], Operations: [] Exploring Operation: 34+53=87, Resulting Numbers: [84, 6, 87] Generated Node #0,0: 97:[84, 6, 87] Operation: 34+53=87 Exploring Operation: 34-6=28, Resulting Numbers: [53, 84, 28] Generated Node #0,1: 97:[53, 84, 28] Operation: 34-6=28 Exploring Operation: 53+6=59, Resulting Numbers: [34, 84, 59] Generated Node #0,2: 97:[34, 84, 59] Operation: 53+6=59 Exploring Operation: 84+6=90, Resulting Numbers: [34, 53, 90] Generated Node #0,3: 97:[34, 53, 90] Operation: 84+6=90 Exploring Operation: 34+6=40, Resulting Numbers: [53, 84, 40] Generated Node #0,4: 97:[53, 84, 40] Operation: 34+6=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[84, 6, 87], Operations: ['34+53=87'] Exploring Operation: 87-6=81, Resulting Numbers: [84, 81] Generated Node #0,0,0: 97:[84, 81] Operation: 87-6=81 Exploring Operation: 84-6=78, Resulting Numbers: [87, 78] Generated Node #0,0,1: 97:[87, 78] Operation: 84-6=78 Exploring Operation: 6+87=93, Resulting Numbers: [84, 93] Generated Node #0,0,2: 97:[84, 93] Operation: 6+87=93 Exploring Operation: 84/6=14, Resulting Numbers: [87, 14] Generated Node #0,0,3: 97:[87, 14] Operation: 84/6=14 Exploring Operation: 84+6=90, Resulting Numbers: [87, 90] Generated Node #0,0,4: 97:[87, 90] Operation: 84+6=90 Moving to Node #0,0,2 Current State: 97:[84, 93], Operations: ['34+53=87', '6+87=93'] Exploring Operation: 84*93=7812, Resulting Numbers: [7812] 7812,97 unequal: No Solution Exploring Operation: 84+93=177, Resulting Numbers: [177] 177,97 unequal: No Solution Exploring Operation: 93-84=9, Resulting Numbers: [9] 9,97 unequal: No Solution Moving to Node #0,0,4 Current State: 97:[87, 90], Operations: ['34+53=87', '84+6=90'] Exploring Operation: 87+90=177, Resulting Numbers: [177] 177,97 unequal: No Solution Exploring Operation: 90-87=3, Resulting Numbers: [3] 3,97 unequal: No Solution Exploring Operation: 87*90=7830, Resulting Numbers: [7830] 7830,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[84, 81], Operations: ['34+53=87', '87-6=81'] Exploring Operation: 84*81=6804, Resulting Numbers: [6804] 6804,97 unequal: No Solution Exploring Operation: 84-81=3, Resulting Numbers: [3] 3,97 unequal: No Solution Exploring Operation: 84+81=165, Resulting Numbers: [165] 165,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[87, 78], Operations: ['34+53=87', '84-6=78'] Exploring Operation: 87*78=6786, Resulting Numbers: [6786] 6786,97 unequal: No Solution Exploring Operation: 87+78=165, Resulting Numbers: [165] 165,97 unequal: No Solution Exploring Operation: 87-78=9, Resulting Numbers: [9] 9,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[87, 14], Operations: ['34+53=87', '84/6=14'] Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,97 unequal: No Solution Exploring Operation: 87*14=1218, Resulting Numbers: [1218] 1218,97 unequal: No Solution Exploring Operation: 87+14=101, Resulting Numbers: [101] 101,97 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 #0,2 Current State: 97:[34, 84, 59], Operations: ['53+6=59'] Exploring Operation: 84-34=50, Resulting Numbers: [59, 50] Generated Node #0,2,0: 97:[59, 50] Operation: 84-34=50 Exploring Operation: 34+84=118, Resulting Numbers: [59, 118] Generated Node #0,2,1: 97:[59, 118] Operation: 34+84=118 Exploring Operation: 84+59=143, Resulting Numbers: [34, 143] Generated Node #0,2,2: 97:[34, 143] Operation: 84+59=143 Exploring Operation: 34+59=93, Resulting Numbers: [84, 93] Generated Node #0,2,3: 97:[84, 93] Operation: 34+59=93 Exploring Operation: 59-34=25, Resulting Numbers: [84, 25] Generated Node #0,2,4: 97:[84, 25] Operation: 59-34=25 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 97:[84, 93], Operations: ['53+6=59', '34+59=93'] Exploring Operation: 84*93=7812, Resulting Numbers: [7812] 7812,97 unequal: No Solution Exploring Operation: 84+93=177, Resulting Numbers: [177] 177,97 unequal: No Solution Exploring Operation: 93-84=9, Resulting Numbers: [9] 9,97 unequal: No Solution No 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: 97:[59, 118], Operations: ['53+6=59', '34+84=118'] Exploring Operation: 118/59=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 59+118=177, Resulting Numbers: [177] 177,97 unequal: No Solution Exploring Operation: 59*118=6962, Resulting Numbers: [6962] 6962,97 unequal: No Solution Exploring Operation: 118-59=59, Resulting Numbers: [59] 59,97 unequal: No Solution No 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: 97:[59, 50], Operations: ['53+6=59', '84-34=50'] Exploring Operation: 59*50=2950, Resulting Numbers: [2950] 2950,97 unequal: No Solution Exploring Operation: 59-50=9, Resulting Numbers: [9] 9,97 unequal: No Solution Exploring Operation: 59+50=109, Resulting Numbers: [109] 109,97 unequal: No Solution No 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: 97:[84, 25], Operations: ['53+6=59', '59-34=25'] Exploring Operation: 84-25=59, Resulting Numbers: [59] 59,97 unequal: No Solution Exploring Operation: 84+25=109, Resulting Numbers: [109] 109,97 unequal: No Solution Exploring Operation: 84*25=2100, Resulting Numbers: [2100] 2100,97 unequal: No Solution No 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: 97:[34, 143], Operations: ['53+6=59', '84+59=143'] Exploring Operation: 34*143=4862, Resulting Numbers: [4862] 4862,97 unequal: No Solution Exploring Operation: 143-34=109, Resulting Numbers: [109] 109,97 unequal: No Solution Exploring Operation: 34+143=177, Resulting Numbers: [177] 177,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 97:[34, 53, 90], Operations: ['84+6=90'] Exploring Operation: 53+90=143, Resulting Numbers: [34, 143] Generated Node #0,3,0: 97:[34, 143] Operation: 53+90=143 Exploring Operation: 34+90=124, Resulting Numbers: [53, 124] Generated Node #0,3,1: 97:[53, 124] Operation: 34+90=124 Exploring Operation: 90-34=56, Resulting Numbers: [53, 56] Generated Node #0,3,2: 97:[53, 56] Operation: 90-34=56 Exploring Operation: 53-34=19, Resulting Numbers: [90, 19] Generated Node #0,3,3: 97:[90, 19] Operation: 53-34=19 Exploring Operation: 34+53=87, Resulting Numbers: [90, 87] Generated Node #0,3,4: 97:[90, 87] Operation: 34+53=87 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 97:[90, 87], Operations: ['84+6=90', '34+53=87'] Exploring Operation: 90-87=3, Resulting Numbers: [3] 3,97 unequal: No Solution Exploring Operation: 90*87=7830, Resulting Numbers: [7830] 7830,97 unequal: No Solution Exploring Operation: 90+87=177, Resulting Numbers: [177] 177,97 unequal: No Solution No 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: 97:[53, 124], Operations: ['84+6=90', '34+90=124'] Exploring Operation: 53*124=6572, Resulting Numbers: [6572] 6572,97 unequal: No Solution Exploring Operation: 53+124=177, Resulting Numbers: [177] 177,97 unequal: No Solution Exploring Operation: 124-53=71, Resulting Numbers: [71] 71,97 unequal: No Solution No 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: 97:[53, 56], Operations: ['84+6=90', '90-34=56'] Exploring Operation: 56-53=3, Resulting Numbers: [3] 3,97 unequal: No Solution Exploring Operation: 53+56=109, Resulting Numbers: [109] 109,97 unequal: No Solution Exploring Operation: 53*56=2968, Resulting Numbers: [2968] 2968,97 unequal: No Solution No 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: 97:[90, 19], Operations: ['84+6=90', '53-34=19'] Exploring Operation: 90*19=1710, Resulting Numbers: [1710] 1710,97 unequal: No Solution Exploring Operation: 90-19=71, Resulting Numbers: [71] 71,97 unequal: No Solution Exploring Operation: 90+19=109, Resulting Numbers: [109] 109,97 unequal: No Solution No 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: 97:[34, 143], Operations: ['84+6=90', '53+90=143'] Exploring Operation: 143-34=109, Resulting Numbers: [109] 109,97 unequal: No Solution Exploring Operation: 34+143=177, Resulting Numbers: [177] 177,97 unequal: No Solution Exploring Operation: 34*143=4862, Resulting Numbers: [4862] 4862,97 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: 97:[53, 84, 40], Operations: ['34+6=40'] Exploring Operation: 53+84=137, Resulting Numbers: [40, 137] Generated Node #0,4,0: 97:[40, 137] Operation: 53+84=137 Exploring Operation: 84+40=124, Resulting Numbers: [53, 124] Generated Node #0,4,1: 97:[53, 124] Operation: 84+40=124 Exploring Operation: 84-40=44, Resulting Numbers: [53, 44] Generated Node #0,4,2: 97:[53, 44] Operation: 84-40=44 Exploring Operation: 53+40=93, Resulting Numbers: [84, 93] Generated Node #0,4,3: 97:[84, 93] Operation: 53+40=93 Exploring Operation: 53-40=13, Resulting Numbers: [84, 13] Generated Node #0,4,4: 97:[84, 13] Operation: 53-40=13 Moving to Node #0,4,3 Current State: 97:[84, 93], Operations: ['34+6=40', '53+40=93'] Exploring Operation: 84*93=7812, Resulting Numbers: [7812] 7812,97 unequal: No Solution Exploring Operation: 84+93=177, Resulting Numbers: [177] 177,97 unequal: No Solution Exploring Operation: 93-84=9, Resulting Numbers: [9] 9,97 unequal: No Solution Moving to Node #0,4,1 Current State: 97:[53, 124], Operations: ['34+6=40', '84+40=124'] Exploring Operation: 53+124=177, Resulting Numbers: [177] 177,97 unequal: No Solution Exploring Operation: 124-53=71, Resulting Numbers: [71] 71,97 unequal: No Solution Exploring Operation: 53*124=6572, Resulting Numbers: [6572] 6572,97 unequal: No Solution Moving to Node #0,4,0 Current State: 97:[40, 137], Operations: ['34+6=40', '53+84=137'] Exploring Operation: 40*137=5480, Resulting Numbers: [5480] 5480,97 unequal: No Solution Exploring Operation: 40+137=177, Resulting Numbers: [177] 177,97 unequal: No Solution Exploring Operation: 137-40=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[34, 53, 84, 6], Operations: [] Exploring Operation: 34+6=40, Resulting Numbers: [53, 84, 40] Generated Node #0,4: 97:[53, 84, 40] Operation: 34+6=40 Moving to Node #0,4 Current State: 97:[53, 84, 40], Operations: ['34+6=40'] Exploring Operation: 53+84=137, Resulting Numbers: [40, 137] Generated Node #0,4,0: 97:[40, 137] Operation: 53+84=137 Moving to Node #0,4,0 Current State: 97:[40, 137], Operations: ['34+6=40', '53+84=137'] Exploring Operation: 137-40=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.927083
hs_5
mult_heuristic
[ 49, 72, 8, 5 ]
35
[ "49-5=44", "72/8=9", "44-9=35" ]
Current State: 35:[49, 72, 8, 5], Operations: [] Exploring Operation: 49-5=44, Resulting Numbers: [72, 8, 44] Generated Node #2: [72, 8, 44] from Operation: 49-5=44 Current State: 35:[72, 8, 44], Operations: ['49-5=44'] Exploring Operation: 72/8=9, Resulting Numbers: [44, 9] Generated Node #3: [44, 9] from Operation: 72/8=9 Current State: 35:[44, 9], Operations: ['49-5=44', '72/8=9'] Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[49, 72, 8, 5], Operations: [] Exploring Operation: 72-49=23, Resulting Numbers: [8, 5, 23] Generated Node #0,0: 35:[8, 5, 23] Operation: 72-49=23 Exploring Operation: 72/8=9, Resulting Numbers: [49, 5, 9] Generated Node #0,1: 35:[49, 5, 9] Operation: 72/8=9 Exploring Operation: 49-8=41, Resulting Numbers: [72, 5, 41] Generated Node #0,2: 35:[72, 5, 41] Operation: 49-8=41 Exploring Operation: 72-8=64, Resulting Numbers: [49, 5, 64] Generated Node #0,3: 35:[49, 5, 64] Operation: 72-8=64 Moving to Node #0,0 Current State: 35:[8, 5, 23], Operations: ['72-49=23'] Exploring Operation: 23-5=18, Resulting Numbers: [8, 18] Generated Node #0,0,0: 35:[8, 18] Operation: 23-5=18 Exploring Operation: 5+23=28, Resulting Numbers: [8, 28] Generated Node #0,0,1: 35:[8, 28] Operation: 5+23=28 Exploring Operation: 8+23=31, Resulting Numbers: [5, 31] Generated Node #0,0,2: 35:[5, 31] Operation: 8+23=31 Exploring Operation: 23-8=15, Resulting Numbers: [5, 15] Generated Node #0,0,3: 35:[5, 15] Operation: 23-8=15 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 35:[5, 31], Operations: ['72-49=23', '8+23=31'] Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,35 unequal: No Solution Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,35 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 35:[8, 28], Operations: ['72-49=23', '5+23=28'] Exploring Operation: 8*28=224, Resulting Numbers: [224] 224,35 unequal: No Solution Exploring Operation: 8+28=36, Resulting Numbers: [36] 36,35 unequal: No Solution Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 35:[5, 15], Operations: ['72-49=23', '23-8=15'] Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,35 unequal: No Solution Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,35 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[8, 18], Operations: ['72-49=23', '23-5=18'] Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,35 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,35 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: 35:[49, 5, 9], Operations: ['72/8=9'] Exploring Operation: 49-5=44, Resulting Numbers: [9, 44] Generated Node #0,1,0: 35:[9, 44] Operation: 49-5=44 Exploring Operation: 49-9=40, Resulting Numbers: [5, 40] Generated Node #0,1,1: 35:[5, 40] Operation: 49-9=40 Exploring Operation: 49+5=54, Resulting Numbers: [9, 54] Generated Node #0,1,2: 35:[9, 54] Operation: 49+5=54 Exploring Operation: 9-5=4, Resulting Numbers: [49, 4] Generated Node #0,1,3: 35:[49, 4] Operation: 9-5=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[5, 40], Operations: ['72/8=9', '49-9=40'] Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[49, 72, 8, 5], Operations: [] Exploring Operation: 72/8=9, Resulting Numbers: [49, 5, 9] Generated Node #0,1: 35:[49, 5, 9] Operation: 72/8=9 Moving to Node #0,1 Current State: 35:[49, 5, 9], Operations: ['72/8=9'] Exploring Operation: 49-9=40, Resulting Numbers: [5, 40] Generated Node #0,1,1: 35:[5, 40] Operation: 49-9=40 Moving to Node #0,1,1 Current State: 35:[5, 40], Operations: ['72/8=9', '49-9=40'] Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 43, 15, 3, 88 ]
33
[ "43+15=58", "3+88=91", "91-58=33" ]
Current State: 33:[43, 15, 3, 88], Operations: [] Exploring Operation: 43+15=58, Resulting Numbers: [3, 88, 58] Generated Node #2: [3, 88, 58] from Operation: 43+15=58 Current State: 33:[3, 88, 58], Operations: ['43+15=58'] Exploring Operation: 3+88=91, Resulting Numbers: [58, 91] Generated Node #3: [58, 91] from Operation: 3+88=91 Current State: 33:[58, 91], Operations: ['43+15=58', '3+88=91'] Exploring Operation: 91-58=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[43, 15, 3, 88], Operations: [] Exploring Operation: 43-15=28, Resulting Numbers: [3, 88, 28] Generated Node #0,0: 33:[3, 88, 28] Operation: 43-15=28 Exploring Operation: 88-15=73, Resulting Numbers: [43, 3, 73] Generated Node #0,1: 33:[43, 3, 73] Operation: 88-15=73 Exploring Operation: 43-3=40, Resulting Numbers: [15, 88, 40] Generated Node #0,2: 33:[15, 88, 40] Operation: 43-3=40 Exploring Operation: 15-3=12, Resulting Numbers: [43, 88, 12] Generated Node #0,3: 33:[43, 88, 12] Operation: 15-3=12 Exploring Operation: 88-43=45, Resulting Numbers: [15, 3, 45] Generated Node #0,4: 33:[15, 3, 45] Operation: 88-43=45 Start Sub Search at level 1: Moving to Node #0,4 Current State: 33:[15, 3, 45], Operations: ['88-43=45'] Exploring Operation: 45-15=30, Resulting Numbers: [3, 30] Generated Node #0,4,0: 33:[3, 30] Operation: 45-15=30 Exploring Operation: 45/3=15, Resulting Numbers: [15, 15] Generated Node #0,4,1: 33:[15, 15] Operation: 45/3=15 Exploring Operation: 45-3=42, Resulting Numbers: [15, 42] Generated Node #0,4,2: 33:[15, 42] Operation: 45-3=42 Exploring Operation: 45/15=3, Resulting Numbers: [3, 3] Generated Node #0,4,3: 33:[3, 3] Operation: 45/15=3 Exploring Operation: 15-3=12, Resulting Numbers: [45, 12] Generated Node #0,4,4: 33:[45, 12] Operation: 15-3=12 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 33:[3, 3], Operations: ['88-43=45', '45/15=3'] Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,33 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 33:[3, 30], Operations: ['88-43=45', '45-15=30'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,33 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[43, 15, 3, 88], Operations: [] Exploring Operation: 88-43=45, Resulting Numbers: [15, 3, 45] Generated Node #0,4: 33:[15, 3, 45] Operation: 88-43=45 Moving to Node #0,4 Current State: 33:[15, 3, 45], Operations: ['88-43=45'] Exploring Operation: 45-15=30, Resulting Numbers: [3, 30] Generated Node #0,4,0: 33:[3, 30] Operation: 45-15=30 Moving to Node #0,4,0 Current State: 33:[3, 30], Operations: ['88-43=45', '45-15=30'] Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 95, 63, 94, 17 ]
45
[ "95-63=32", "94-17=77", "77-32=45" ]
Current State: 45:[95, 63, 94, 17], Operations: [] Exploring Operation: 95-63=32, Resulting Numbers: [94, 17, 32] Generated Node #2: [94, 17, 32] from Operation: 95-63=32 Current State: 45:[94, 17, 32], Operations: ['95-63=32'] Exploring Operation: 94-17=77, Resulting Numbers: [32, 77] Generated Node #3: [32, 77] from Operation: 94-17=77 Current State: 45:[32, 77], Operations: ['95-63=32', '94-17=77'] Exploring Operation: 77-32=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[95, 63, 94, 17], Operations: [] Exploring Operation: 95-63=32, Resulting Numbers: [94, 17, 32] Generated Node #0,0: 45:[94, 17, 32] Operation: 95-63=32 Exploring Operation: 95-94=1, Resulting Numbers: [63, 17, 1] Generated Node #0,1: 45:[63, 17, 1] Operation: 95-94=1 Moving to Node #0,1 Current State: 45:[63, 17, 1], Operations: ['95-94=1'] Exploring Operation: 63-1=62, Resulting Numbers: [17, 62] Generated Node #0,1,0: 45:[17, 62] Operation: 63-1=62 Exploring Operation: 63-17=46, Resulting Numbers: [1, 46] Generated Node #0,1,1: 45:[1, 46] Operation: 63-17=46 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[1, 46], Operations: ['95-94=1', '63-17=46'] Exploring Operation: 1*46=46, Resulting Numbers: [46] 46,45 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[95, 63, 94, 17], Operations: [] Exploring Operation: 95-94=1, Resulting Numbers: [63, 17, 1] Generated Node #0,1: 45:[63, 17, 1] Operation: 95-94=1 Moving to Node #0,1 Current State: 45:[63, 17, 1], Operations: ['95-94=1'] Exploring Operation: 63-17=46, Resulting Numbers: [1, 46] Generated Node #0,1,1: 45:[1, 46] Operation: 63-17=46 Moving to Node #0,1,1 Current State: 45:[1, 46], Operations: ['95-94=1', '63-17=46'] Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 19, 40, 50, 84 ]
25
[ "19+40=59", "84-50=34", "59-34=25" ]
Current State: 25:[19, 40, 50, 84], Operations: [] Exploring Operation: 19+40=59, Resulting Numbers: [50, 84, 59] Generated Node #2: [50, 84, 59] from Operation: 19+40=59 Current State: 25:[50, 84, 59], Operations: ['19+40=59'] Exploring Operation: 84-50=34, Resulting Numbers: [59, 34] Generated Node #3: [59, 34] from Operation: 84-50=34 Current State: 25:[59, 34], Operations: ['19+40=59', '84-50=34'] Exploring Operation: 59-34=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[19, 40, 50, 84], Operations: [] Exploring Operation: 84-19=65, Resulting Numbers: [40, 50, 65] Generated Node #0,0: 25:[40, 50, 65] Operation: 84-19=65 Exploring Operation: 50-19=31, Resulting Numbers: [40, 84, 31] Generated Node #0,1: 25:[40, 84, 31] Operation: 50-19=31 Exploring Operation: 84-40=44, Resulting Numbers: [19, 50, 44] Generated Node #0,2: 25:[19, 50, 44] Operation: 84-40=44 Exploring Operation: 50-40=10, Resulting Numbers: [19, 84, 10] Generated Node #0,3: 25:[19, 84, 10] Operation: 50-40=10 Exploring Operation: 84-50=34, Resulting Numbers: [19, 40, 34] Generated Node #0,4: 25:[19, 40, 34] Operation: 84-50=34 Start Sub Search at level 1: Moving to Node #0,4 Current State: 25:[19, 40, 34], Operations: ['84-50=34'] Exploring Operation: 19+34=53, Resulting Numbers: [40, 53] Generated Node #0,4,0: 25:[40, 53] Operation: 19+34=53 Exploring Operation: 19+40=59, Resulting Numbers: [34, 59] Generated Node #0,4,1: 25:[34, 59] Operation: 19+40=59 Exploring Operation: 34-19=15, Resulting Numbers: [40, 15] Generated Node #0,4,2: 25:[40, 15] Operation: 34-19=15 Exploring Operation: 40-34=6, Resulting Numbers: [19, 6] Generated Node #0,4,3: 25:[19, 6] Operation: 40-34=6 Exploring Operation: 40-19=21, Resulting Numbers: [34, 21] Generated Node #0,4,4: 25:[34, 21] Operation: 40-19=21 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 25:[19, 6], Operations: ['84-50=34', '40-34=6'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[19, 40, 50, 84], Operations: [] Exploring Operation: 84-50=34, Resulting Numbers: [19, 40, 34] Generated Node #0,4: 25:[19, 40, 34] Operation: 84-50=34 Moving to Node #0,4 Current State: 25:[19, 40, 34], Operations: ['84-50=34'] Exploring Operation: 40-34=6, Resulting Numbers: [19, 6] Generated Node #0,4,3: 25:[19, 6] Operation: 40-34=6 Moving to Node #0,4,3 Current State: 25:[19, 6], Operations: ['84-50=34', '40-34=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 26, 90, 96, 81 ]
63
[ "96-26=70", "81*70=5670", "5670/90=63" ]
Current State: 63:[26, 90, 96, 81], Operations: [] Exploring Operation: 96-26=70, Resulting Numbers: [90, 81, 70] Generated Node #2: [90, 81, 70] from Operation: 96-26=70 Current State: 63:[90, 81, 70], Operations: ['96-26=70'] Exploring Operation: 81*70=5670, Resulting Numbers: [90, 5670] Generated Node #3: [90, 5670] from Operation: 81*70=5670 Current State: 63:[90, 5670], Operations: ['96-26=70', '81*70=5670'] Exploring Operation: 5670/90=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[26, 90, 96, 81], Operations: [] Exploring Operation: 96-81=15, Resulting Numbers: [26, 90, 15] Generated Node #0,0: 63:[26, 90, 15] Operation: 96-81=15 Exploring Operation: 96-90=6, Resulting Numbers: [26, 81, 6] Generated Node #0,1: 63:[26, 81, 6] Operation: 96-90=6 Exploring Operation: 90-81=9, Resulting Numbers: [26, 96, 9] Generated Node #0,2: 63:[26, 96, 9] Operation: 90-81=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[26, 81, 6], Operations: ['96-90=6'] Exploring Operation: 26-6=20, Resulting Numbers: [81, 20] Generated Node #0,1,0: 63:[81, 20] Operation: 26-6=20 Exploring Operation: 81-26=55, Resulting Numbers: [6, 55] Generated Node #0,1,1: 63:[6, 55] Operation: 81-26=55 Exploring Operation: 81-6=75, Resulting Numbers: [26, 75] Generated Node #0,1,2: 63:[26, 75] Operation: 81-6=75 Moving to Node #0,1,1 Current State: 63:[6, 55], Operations: ['96-90=6', '81-26=55'] Exploring Operation: 55-6=49, Resulting Numbers: [49] 49,63 unequal: No Solution Exploring Operation: 6+55=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 6*55=330, Resulting Numbers: [330] 330,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[26, 75], Operations: ['96-90=6', '81-6=75'] Exploring Operation: 26*75=1950, Resulting Numbers: [1950] 1950,63 unequal: No Solution Exploring Operation: 26+75=101, Resulting Numbers: [101] 101,63 unequal: No Solution Exploring Operation: 75-26=49, Resulting Numbers: [49] 49,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[81, 20], Operations: ['96-90=6', '26-6=20'] Exploring Operation: 81+20=101, Resulting Numbers: [101] 101,63 unequal: No Solution Exploring Operation: 81*20=1620, Resulting Numbers: [1620] 1620,63 unequal: No Solution Exploring Operation: 81-20=61, Resulting Numbers: [61] 61,63 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 Current State: 63:[26, 90, 15], Operations: ['96-81=15'] Exploring Operation: 90-15=75, Resulting Numbers: [26, 75] Generated Node #0,0,0: 63:[26, 75] Operation: 90-15=75 Exploring Operation: 90-26=64, Resulting Numbers: [15, 64] Generated Node #0,0,1: 63:[15, 64] Operation: 90-26=64 Exploring Operation: 90/15=6, Resulting Numbers: [26, 6] Generated Node #0,0,2: 63:[26, 6] Operation: 90/15=6 Moving to Node #0,0,2 Current State: 63:[26, 6], Operations: ['96-81=15', '90/15=6'] Exploring Operation: 26*6=156, Resulting Numbers: [156] 156,63 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[15, 64], Operations: ['96-81=15', '90-26=64'] Exploring Operation: 15*64=960, Resulting Numbers: [960] 960,63 unequal: No Solution Exploring Operation: 64-15=49, Resulting Numbers: [49] 49,63 unequal: No Solution Exploring Operation: 15+64=79, Resulting Numbers: [79] 79,63 unequal: No Solution Moving to Node #0,0,0 Current State: 63:[26, 75], Operations: ['96-81=15', '90-15=75'] Exploring Operation: 26+75=101, Resulting Numbers: [101] 101,63 unequal: No Solution Exploring Operation: 26*75=1950, Resulting Numbers: [1950] 1950,63 unequal: No Solution Exploring Operation: 75-26=49, Resulting Numbers: [49] 49,63 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 #0,2 Current State: 63:[26, 96, 9], Operations: ['90-81=9'] Exploring Operation: 26-9=17, Resulting Numbers: [96, 17] Generated Node #0,2,0: 63:[96, 17] Operation: 26-9=17 Exploring Operation: 96-9=87, Resulting Numbers: [26, 87] Generated Node #0,2,1: 63:[26, 87] Operation: 96-9=87 Exploring Operation: 96-26=70, Resulting Numbers: [9, 70] Generated Node #0,2,2: 63:[9, 70] Operation: 96-26=70 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 63:[9, 70], Operations: ['90-81=9', '96-26=70'] Exploring Operation: 9*70=630, Resulting Numbers: [630] 630,63 unequal: No Solution Exploring Operation: 9+70=79, Resulting Numbers: [79] 79,63 unequal: No Solution Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,63 unequal: No Solution No 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: 63:[26, 87], Operations: ['90-81=9', '96-9=87'] Exploring Operation: 26*87=2262, Resulting Numbers: [2262] 2262,63 unequal: No Solution Exploring Operation: 87-26=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 26+87=113, Resulting Numbers: [113] 113,63 unequal: No Solution No 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: 63:[96, 17], Operations: ['90-81=9', '26-9=17'] Exploring Operation: 96*17=1632, Resulting Numbers: [1632] 1632,63 unequal: No Solution Exploring Operation: 96-17=79, Resulting Numbers: [79] 79,63 unequal: No Solution Exploring Operation: 96+17=113, Resulting Numbers: [113] 113,63 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
[ 71, 13, 26, 6 ]
88
[ "71*6=426", "13*26=338", "426-338=88" ]
Current State: 88:[71, 13, 26, 6], Operations: [] Exploring Operation: 71*6=426, Resulting Numbers: [13, 26, 426] Generated Node #2: [13, 26, 426] from Operation: 71*6=426 Current State: 88:[13, 26, 426], Operations: ['71*6=426'] Exploring Operation: 13*26=338, Resulting Numbers: [426, 338] Generated Node #3: [426, 338] from Operation: 13*26=338 Current State: 88:[426, 338], Operations: ['71*6=426', '13*26=338'] Exploring Operation: 426-338=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[71, 13, 26, 6], Operations: [] Exploring Operation: 71+13=84, Resulting Numbers: [26, 6, 84] Generated Node #0,0: 88:[26, 6, 84] Operation: 71+13=84 Exploring Operation: 71+26=97, Resulting Numbers: [13, 6, 97] Generated Node #0,1: 88:[13, 6, 97] Operation: 71+26=97 Exploring Operation: 71-26=45, Resulting Numbers: [13, 6, 45] Generated Node #0,2: 88:[13, 6, 45] Operation: 71-26=45 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[13, 6, 45], Operations: ['71-26=45'] Exploring Operation: 13+6=19, Resulting Numbers: [45, 19] Generated Node #0,2,0: 88:[45, 19] Operation: 13+6=19 Exploring Operation: 45-6=39, Resulting Numbers: [13, 39] Generated Node #0,2,1: 88:[13, 39] Operation: 45-6=39 Exploring Operation: 13-6=7, Resulting Numbers: [45, 7] Generated Node #0,2,2: 88:[45, 7] Operation: 13-6=7 Moving to Node #0,2,2 Current State: 88:[45, 7], Operations: ['71-26=45', '13-6=7'] Exploring Operation: 45+7=52, Resulting Numbers: [52] 52,88 unequal: No Solution Exploring Operation: 45*7=315, Resulting Numbers: [315] 315,88 unequal: No Solution Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,88 unequal: No Solution Moving to Node #0,2,0 Current State: 88:[45, 19], Operations: ['71-26=45', '13+6=19'] Exploring Operation: 45+19=64, Resulting Numbers: [64] 64,88 unequal: No Solution Exploring Operation: 45*19=855, Resulting Numbers: [855] 855,88 unequal: No Solution Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[13, 39], Operations: ['71-26=45', '45-6=39'] Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 13+39=52, Resulting Numbers: [52] 52,88 unequal: No Solution Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[26, 6, 84], Operations: ['71+13=84'] Exploring Operation: 6+84=90, Resulting Numbers: [26, 90] Generated Node #0,0,0: 88:[26, 90] Operation: 6+84=90 Exploring Operation: 26-6=20, Resulting Numbers: [84, 20] Generated Node #0,0,1: 88:[84, 20] Operation: 26-6=20 Exploring Operation: 84/6=14, Resulting Numbers: [26, 14] Generated Node #0,0,2: 88:[26, 14] Operation: 84/6=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[26, 90], Operations: ['71+13=84', '6+84=90'] Exploring Operation: 90-26=64, Resulting Numbers: [64] 64,88 unequal: No Solution Exploring Operation: 26+90=116, Resulting Numbers: [116] 116,88 unequal: No Solution Exploring Operation: 26*90=2340, Resulting Numbers: [2340] 2340,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[84, 20], Operations: ['71+13=84', '26-6=20'] Exploring Operation: 84*20=1680, Resulting Numbers: [1680] 1680,88 unequal: No Solution Exploring Operation: 84+20=104, Resulting Numbers: [104] 104,88 unequal: No Solution Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 88:[26, 14], Operations: ['71+13=84', '84/6=14'] Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,88 unequal: No Solution Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[13, 6, 97], Operations: ['71+26=97'] Exploring Operation: 13-6=7, Resulting Numbers: [97, 7] Generated Node #0,1,0: 88:[97, 7] Operation: 13-6=7 Exploring Operation: 97-13=84, Resulting Numbers: [6, 84] Generated Node #0,1,1: 88:[6, 84] Operation: 97-13=84 Exploring Operation: 97-6=91, Resulting Numbers: [13, 91] Generated Node #0,1,2: 88:[13, 91] Operation: 97-6=91 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 88:[13, 91], Operations: ['71+26=97', '97-6=91'] Exploring Operation: 13+91=104, Resulting Numbers: [104] 104,88 unequal: No Solution Exploring Operation: 91-13=78, Resulting Numbers: [78] 78,88 unequal: No Solution Exploring Operation: 91/13=7, Resulting Numbers: [7] 7,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 88:[6, 84], Operations: ['71+26=97', '97-13=84'] Exploring Operation: 6+84=90, Resulting Numbers: [90] 90,88 unequal: No Solution Exploring Operation: 84-6=78, Resulting Numbers: [78] 78,88 unequal: No Solution Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 88:[97, 7], Operations: ['71+26=97', '13-6=7'] Exploring Operation: 97+7=104, Resulting Numbers: [104] 104,88 unequal: No Solution Exploring Operation: 97-7=90, Resulting Numbers: [90] 90,88 unequal: No Solution Exploring Operation: 97*7=679, Resulting Numbers: [679] 679,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 52, 33, 22, 2 ]
75
[ "52-2=50", "33*50=1650", "1650/22=75" ]
Current State: 75:[52, 33, 22, 2], Operations: [] Exploring Operation: 52-2=50, Resulting Numbers: [33, 22, 50] Generated Node #2: [33, 22, 50] from Operation: 52-2=50 Current State: 75:[33, 22, 50], Operations: ['52-2=50'] Exploring Operation: 33*50=1650, Resulting Numbers: [22, 1650] Generated Node #3: [22, 1650] from Operation: 33*50=1650 Current State: 75:[22, 1650], Operations: ['52-2=50', '33*50=1650'] Exploring Operation: 1650/22=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[52, 33, 22, 2], Operations: [] Exploring Operation: 52+22=74, Resulting Numbers: [33, 2, 74] Generated Node #0,0: 75:[33, 2, 74] Operation: 52+22=74 Exploring Operation: 52-33=19, Resulting Numbers: [22, 2, 19] Generated Node #0,1: 75:[22, 2, 19] Operation: 52-33=19 Moving to Node #0,1 Current State: 75:[22, 2, 19], Operations: ['52-33=19'] Exploring Operation: 22-19=3, Resulting Numbers: [2, 3] Generated Node #0,1,0: 75:[2, 3] Operation: 22-19=3 Exploring Operation: 22+2=24, Resulting Numbers: [19, 24] Generated Node #0,1,1: 75:[19, 24] Operation: 22+2=24 Moving to Node #0,0 Current State: 75:[33, 2, 74], Operations: ['52+22=74'] Exploring Operation: 33-2=31, Resulting Numbers: [74, 31] Generated Node #0,0,0: 75:[74, 31] Operation: 33-2=31 Exploring Operation: 2+74=76, Resulting Numbers: [33, 76] Generated Node #0,0,1: 75:[33, 76] Operation: 2+74=76 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[74, 31], Operations: ['52+22=74', '33-2=31'] Exploring Operation: 74-31=43, Resulting Numbers: [43] 43,75 unequal: No Solution Exploring Operation: 74+31=105, Resulting Numbers: [105] 105,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 75:[33, 76], Operations: ['52+22=74', '2+74=76'] Exploring Operation: 33+76=109, Resulting Numbers: [109] 109,75 unequal: No Solution Exploring Operation: 76-33=43, Resulting Numbers: [43] 43,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 75:[2, 3], Operations: ['52-33=19', '22-19=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,75 unequal: No Solution Moving to Node #0,1,1 Current State: 75:[19, 24], Operations: ['52-33=19', '22+2=24'] Exploring Operation: 24-19=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 19+24=43, Resulting Numbers: [43] 43,75 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 69, 92, 9, 82 ]
68
[ "92-69=23", "9+82=91", "91-23=68" ]
Current State: 68:[69, 92, 9, 82], Operations: [] Exploring Operation: 92-69=23, Resulting Numbers: [9, 82, 23] Generated Node #2: [9, 82, 23] from Operation: 92-69=23 Current State: 68:[9, 82, 23], Operations: ['92-69=23'] Exploring Operation: 9+82=91, Resulting Numbers: [23, 91] Generated Node #3: [23, 91] from Operation: 9+82=91 Current State: 68:[23, 91], Operations: ['92-69=23', '9+82=91'] Exploring Operation: 91-23=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[69, 92, 9, 82], Operations: [] Exploring Operation: 92-69=23, Resulting Numbers: [9, 82, 23] Generated Node #0,0: 68:[9, 82, 23] Operation: 92-69=23 Exploring Operation: 92-82=10, Resulting Numbers: [69, 9, 10] Generated Node #0,1: 68:[69, 9, 10] Operation: 92-82=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[69, 9, 10], Operations: ['92-82=10'] Exploring Operation: 9+10=19, Resulting Numbers: [69, 19] Generated Node #0,1,0: 68:[69, 19] Operation: 9+10=19 Exploring Operation: 10-9=1, Resulting Numbers: [69, 1] Generated Node #0,1,1: 68:[69, 1] Operation: 10-9=1 Moving to Node #0,1,1 Current State: 68:[69, 1], Operations: ['92-82=10', '10-9=1'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[69, 92, 9, 82], Operations: [] Exploring Operation: 92-82=10, Resulting Numbers: [69, 9, 10] Generated Node #0,1: 68:[69, 9, 10] Operation: 92-82=10 Moving to Node #0,1 Current State: 68:[69, 9, 10], Operations: ['92-82=10'] Exploring Operation: 10-9=1, Resulting Numbers: [69, 1] Generated Node #0,1,1: 68:[69, 1] Operation: 10-9=1 Moving to Node #0,1,1 Current State: 68:[69, 1], Operations: ['92-82=10', '10-9=1'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 46, 2, 49, 96 ]
23
[ "46*49=2254", "2+96=98", "2254/98=23" ]
Current State: 23:[46, 2, 49, 96], Operations: [] Exploring Operation: 46*49=2254, Resulting Numbers: [2, 96, 2254] Generated Node #2: [2, 96, 2254] from Operation: 46*49=2254 Current State: 23:[2, 96, 2254], Operations: ['46*49=2254'] Exploring Operation: 2+96=98, Resulting Numbers: [2254, 98] Generated Node #3: [2254, 98] from Operation: 2+96=98 Current State: 23:[2254, 98], Operations: ['46*49=2254', '2+96=98'] Exploring Operation: 2254/98=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[46, 2, 49, 96], Operations: [] Exploring Operation: 49-46=3, Resulting Numbers: [2, 96, 3] Generated Node #0,0: 23:[2, 96, 3] Operation: 49-46=3 Exploring Operation: 96-46=50, Resulting Numbers: [2, 49, 50] Generated Node #0,1: 23:[2, 49, 50] Operation: 96-46=50 Exploring Operation: 96-49=47, Resulting Numbers: [46, 2, 47] Generated Node #0,2: 23:[46, 2, 47] Operation: 96-49=47 Exploring Operation: 46/2=23, Resulting Numbers: [49, 96, 23] Generated Node #0,3: 23:[49, 96, 23] Operation: 46/2=23 Exploring Operation: 96/2=48, Resulting Numbers: [46, 49, 48] Generated Node #0,4: 23:[46, 49, 48] Operation: 96/2=48 Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[46, 2, 47], Operations: ['96-49=47'] Exploring Operation: 46+2=48, Resulting Numbers: [47, 48] Generated Node #0,2,0: 23:[47, 48] Operation: 46+2=48 Exploring Operation: 47-46=1, Resulting Numbers: [2, 1] Generated Node #0,2,1: 23:[2, 1] Operation: 47-46=1 Exploring Operation: 47-2=45, Resulting Numbers: [46, 45] Generated Node #0,2,2: 23:[46, 45] Operation: 47-2=45 Exploring Operation: 46/2=23, Resulting Numbers: [47, 23] Generated Node #0,2,3: 23:[47, 23] Operation: 46/2=23 Exploring Operation: 46-2=44, Resulting Numbers: [47, 44] Generated Node #0,2,4: 23:[47, 44] Operation: 46-2=44 Moving to Node #0,2,3 Current State: 23:[47, 23], Operations: ['96-49=47', '46/2=23'] Exploring Operation: 47-23=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 47+23=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 47*23=1081, Resulting Numbers: [1081] 1081,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[2, 1], Operations: ['96-49=47', '47-46=1'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[46, 45], Operations: ['96-49=47', '47-2=45'] Exploring Operation: 46+45=91, Resulting Numbers: [91] 91,23 unequal: No Solution Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 46*45=2070, Resulting Numbers: [2070] 2070,23 unequal: No Solution Moving to Node #0,2,4 Current State: 23:[47, 44], Operations: ['96-49=47', '46-2=44'] Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 47+44=91, Resulting Numbers: [91] 91,23 unequal: No Solution Exploring Operation: 47*44=2068, Resulting Numbers: [2068] 2068,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[47, 48], Operations: ['96-49=47', '46+2=48'] Exploring Operation: 47+48=95, Resulting Numbers: [95] 95,23 unequal: No Solution Exploring Operation: 47*48=2256, Resulting Numbers: [2256] 2256,23 unequal: No Solution Exploring Operation: 48-47=1, Resulting Numbers: [1] 1,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[2, 49, 50], Operations: ['96-46=50'] Exploring Operation: 50/2=25, Resulting Numbers: [49, 25] Generated Node #0,1,0: 23:[49, 25] Operation: 50/2=25 Exploring Operation: 2+49=51, Resulting Numbers: [50, 51] Generated Node #0,1,1: 23:[50, 51] Operation: 2+49=51 Exploring Operation: 49-2=47, Resulting Numbers: [50, 47] Generated Node #0,1,2: 23:[50, 47] Operation: 49-2=47 Exploring Operation: 50-49=1, Resulting Numbers: [2, 1] Generated Node #0,1,3: 23:[2, 1] Operation: 50-49=1 Exploring Operation: 50-2=48, Resulting Numbers: [49, 48] Generated Node #0,1,4: 23:[49, 48] Operation: 50-2=48 Moving to Node #0,1,0 Current State: 23:[49, 25], Operations: ['96-46=50', '50/2=25'] Exploring Operation: 49*25=1225, Resulting Numbers: [1225] 1225,23 unequal: No Solution Exploring Operation: 49+25=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,23 unequal: No Solution Moving to Node #0,1,3 Current State: 23:[2, 1], Operations: ['96-46=50', '50-49=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[50, 47], Operations: ['96-46=50', '49-2=47'] Exploring Operation: 50+47=97, Resulting Numbers: [97] 97,23 unequal: No Solution Exploring Operation: 50*47=2350, Resulting Numbers: [2350] 2350,23 unequal: No Solution Exploring Operation: 50-47=3, Resulting Numbers: [3] 3,23 unequal: No Solution Moving to Node #0,1,4 Current State: 23:[49, 48], Operations: ['96-46=50', '50-2=48'] Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,23 unequal: No Solution Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,23 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[50, 51], Operations: ['96-46=50', '2+49=51'] Exploring Operation: 50+51=101, Resulting Numbers: [101] 101,23 unequal: No Solution Exploring Operation: 51-50=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 50*51=2550, Resulting Numbers: [2550] 2550,23 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 #0,4 Current State: 23:[46, 49, 48], Operations: ['96/2=48'] Exploring Operation: 49-48=1, Resulting Numbers: [46, 1] Generated Node #0,4,0: 23:[46, 1] Operation: 49-48=1 Exploring Operation: 46+49=95, Resulting Numbers: [48, 95] Generated Node #0,4,1: 23:[48, 95] Operation: 46+49=95 Exploring Operation: 48-46=2, Resulting Numbers: [49, 2] Generated Node #0,4,2: 23:[49, 2] Operation: 48-46=2 Exploring Operation: 46+48=94, Resulting Numbers: [49, 94] Generated Node #0,4,3: 23:[49, 94] Operation: 46+48=94 Exploring Operation: 49-46=3, Resulting Numbers: [48, 3] Generated Node #0,4,4: 23:[48, 3] Operation: 49-46=3 Moving to Node #0,4,0 Current State: 23:[46, 1], Operations: ['96/2=48', '49-48=1'] Exploring Operation: 46+1=47, Resulting Numbers: [47] 47,23 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,23 unequal: No Solution Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,23 unequal: No Solution Moving to Node #0,4,4 Current State: 23:[48, 3], Operations: ['96/2=48', '49-46=3'] Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,23 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,23 unequal: No Solution Exploring Operation: 48*3=144, Resulting Numbers: [144] 144,23 unequal: No Solution Moving to Node #0,4,2 Current State: 23:[49, 2], Operations: ['96/2=48', '48-46=2'] Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,23 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,23 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,23 unequal: No Solution Moving to Node #0,4,1 Current State: 23:[48, 95], Operations: ['96/2=48', '46+49=95'] Exploring Operation: 48*95=4560, Resulting Numbers: [4560] 4560,23 unequal: No Solution Exploring Operation: 95-48=47, Resulting Numbers: [47] 47,23 unequal: No Solution Exploring Operation: 48+95=143, Resulting Numbers: [143] 143,23 unequal: No Solution Moving to Node #0,4,3 Current State: 23:[49, 94], Operations: ['96/2=48', '46+48=94'] Exploring Operation: 94-49=45, Resulting Numbers: [45] 45,23 unequal: No Solution Exploring Operation: 49*94=4606, Resulting Numbers: [4606] 4606,23 unequal: No Solution Exploring Operation: 49+94=143, Resulting Numbers: [143] 143,23 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:[49, 96, 23], Operations: ['46/2=23'] Exploring Operation: 49+23=72, Resulting Numbers: [96, 72] Generated Node #0,3,0: 23:[96, 72] Operation: 49+23=72 Exploring Operation: 96-23=73, Resulting Numbers: [49, 73] Generated Node #0,3,1: 23:[49, 73] Operation: 96-23=73 Exploring Operation: 49+96=145, Resulting Numbers: [23, 145] Generated Node #0,3,2: 23:[23, 145] Operation: 49+96=145 Exploring Operation: 49-23=26, Resulting Numbers: [96, 26] Generated Node #0,3,3: 23:[96, 26] Operation: 49-23=26 Exploring Operation: 96-49=47, Resulting Numbers: [23, 47] Generated Node #0,3,4: 23:[23, 47] Operation: 96-49=47 Moving to Node #0,3,4 Current State: 23:[23, 47], Operations: ['46/2=23', '96-49=47'] Exploring Operation: 23*47=1081, Resulting Numbers: [1081] 1081,23 unequal: No Solution Exploring Operation: 23+47=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 47-23=24, Resulting Numbers: [24] 24,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[96, 26], Operations: ['46/2=23', '49-23=26'] Exploring Operation: 96-26=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 96*26=2496, Resulting Numbers: [2496] 2496,23 unequal: No Solution Exploring Operation: 96+26=122, Resulting Numbers: [122] 122,23 unequal: No Solution Moving to Node #0,3,1 Current State: 23:[49, 73], Operations: ['46/2=23', '96-23=73'] Exploring Operation: 49+73=122, Resulting Numbers: [122] 122,23 unequal: No Solution Exploring Operation: 49*73=3577, Resulting Numbers: [3577] 3577,23 unequal: No Solution Exploring Operation: 73-49=24, Resulting Numbers: [24] 24,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[96, 72], Operations: ['46/2=23', '49+23=72'] Exploring Operation: 96+72=168, Resulting Numbers: [168] 168,23 unequal: No Solution Exploring Operation: 96-72=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 96*72=6912, Resulting Numbers: [6912] 6912,23 unequal: No Solution Moving to Node #0,3,2 Current State: 23:[23, 145], Operations: ['46/2=23', '49+96=145'] Exploring Operation: 23*145=3335, Resulting Numbers: [3335] 3335,23 unequal: No Solution Exploring Operation: 23+145=168, Resulting Numbers: [168] 168,23 unequal: No Solution Exploring Operation: 145-23=122, Resulting Numbers: [122] 122,23 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 #0,0 Current State: 23:[2, 96, 3], Operations: ['49-46=3'] Exploring Operation: 2+3=5, Resulting Numbers: [96, 5] Generated Node #0,0,0: 23:[96, 5] Operation: 2+3=5 Exploring Operation: 96-2=94, Resulting Numbers: [3, 94] Generated Node #0,0,1: 23:[3, 94] Operation: 96-2=94 Exploring Operation: 96/2=48, Resulting Numbers: [3, 48] Generated Node #0,0,2: 23:[3, 48] Operation: 96/2=48 Exploring Operation: 96/3=32, Resulting Numbers: [2, 32] Generated Node #0,0,3: 23:[2, 32] Operation: 96/3=32 Exploring Operation: 2*3=6, Resulting Numbers: [96, 6] Generated Node #0,0,4: 23:[96, 6] Operation: 2*3=6 Moving to Node #0,0,3 Current State: 23:[2, 32], Operations: ['49-46=3', '96/3=32'] Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,23 unequal: No Solution Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[3, 48], Operations: ['49-46=3', '96/2=48'] Exploring Operation: 3*48=144, Resulting Numbers: [144] 144,23 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,23 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,23 unequal: No Solution Moving to Node #0,0,4 Current State: 23:[96, 6], Operations: ['49-46=3', '2*3=6'] Exploring Operation: 96-6=90, Resulting Numbers: [90] 90,23 unequal: No Solution Exploring Operation: 96/6=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 96+6=102, Resulting Numbers: [102] 102,23 unequal: No Solution Exploring Operation: 96*6=576, Resulting Numbers: [576] 576,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[96, 5], Operations: ['49-46=3', '2+3=5'] Exploring Operation: 96*5=480, Resulting Numbers: [480] 480,23 unequal: No Solution Exploring Operation: 96+5=101, Resulting Numbers: [101] 101,23 unequal: No Solution Exploring Operation: 96-5=91, Resulting Numbers: [91] 91,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[3, 94], Operations: ['49-46=3', '96-2=94'] Exploring Operation: 3*94=282, Resulting Numbers: [282] 282,23 unequal: No Solution Exploring Operation: 3+94=97, Resulting Numbers: [97] 97,23 unequal: No Solution Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,23 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
[ 8, 88, 14, 11 ]
14
[ "88/8=11", "14+11=25", "25-11=14" ]
Current State: 14:[8, 88, 14, 11], Operations: [] Exploring Operation: 88/8=11, Resulting Numbers: [14, 11, 11] Generated Node #2: [14, 11, 11] from Operation: 88/8=11 Current State: 14:[14, 11, 11], Operations: ['88/8=11'] Exploring Operation: 14+11=25, Resulting Numbers: [25] 25,14 equal: Goal Reached Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[8, 88, 14, 11], Operations: [] Exploring Operation: 88/8=11, Resulting Numbers: [14, 11, 11] Generated Node #0,0: 14:[14, 11, 11] Operation: 88/8=11 Exploring Operation: 88/11=8, Resulting Numbers: [8, 14, 8] Generated Node #0,1: 14:[8, 14, 8] Operation: 88/11=8 Moving to Node #0,1 Current State: 14:[8, 14, 8], Operations: ['88/11=8'] Exploring Operation: 8/8=1, Resulting Numbers: [14, 1] Generated Node #0,1,0: 14:[14, 1] Operation: 8/8=1 Exploring Operation: 14-8=6, Resulting Numbers: [8, 6] Generated Node #0,1,1: 14:[8, 6] Operation: 14-8=6 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[14, 1], Operations: ['88/11=8', '8/8=1'] Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[8, 88, 14, 11], Operations: [] Exploring Operation: 88/11=8, Resulting Numbers: [8, 14, 8] Generated Node #0,1: 14:[8, 14, 8] Operation: 88/11=8 Moving to Node #0,1 Current State: 14:[8, 14, 8], Operations: ['88/11=8'] Exploring Operation: 8/8=1, Resulting Numbers: [14, 1] Generated Node #0,1,0: 14:[14, 1] Operation: 8/8=1 Moving to Node #0,1,0 Current State: 14:[14, 1], Operations: ['88/11=8', '8/8=1'] Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 5, 23, 17, 55 ]
55
[ "23-5=18", "18-17=1", "55*1=55" ]
Current State: 55:[5, 23, 17, 55], Operations: [] Exploring Operation: 23-5=18, Resulting Numbers: [17, 55, 18] Generated Node #2: [17, 55, 18] from Operation: 23-5=18 Current State: 55:[17, 55, 18], Operations: ['23-5=18'] Exploring Operation: 18-17=1, Resulting Numbers: [55, 1] Generated Node #3: [55, 1] from Operation: 18-17=1 Current State: 55:[55, 1], Operations: ['23-5=18', '18-17=1'] Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[5, 23, 17, 55], Operations: [] Exploring Operation: 17-5=12, Resulting Numbers: [23, 55, 12] Generated Node #0,0: 55:[23, 55, 12] Operation: 17-5=12 Exploring Operation: 23-17=6, Resulting Numbers: [5, 55, 6] Generated Node #0,1: 55:[5, 55, 6] Operation: 23-17=6 Exploring Operation: 23-5=18, Resulting Numbers: [17, 55, 18] Generated Node #0,2: 55:[17, 55, 18] Operation: 23-5=18 Exploring Operation: 23+17=40, Resulting Numbers: [5, 55, 40] Generated Node #0,3: 55:[5, 55, 40] Operation: 23+17=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[5, 55, 6], Operations: ['23-17=6'] Exploring Operation: 5+6=11, Resulting Numbers: [55, 11] Generated Node #0,1,0: 55:[55, 11] Operation: 5+6=11 Exploring Operation: 6-5=1, Resulting Numbers: [55, 1] Generated Node #0,1,1: 55:[55, 1] Operation: 6-5=1 Exploring Operation: 5+55=60, Resulting Numbers: [6, 60] Generated Node #0,1,2: 55:[6, 60] Operation: 5+55=60 Exploring Operation: 55/5=11, Resulting Numbers: [6, 11] Generated Node #0,1,3: 55:[6, 11] Operation: 55/5=11 Moving to Node #0,1,0 Current State: 55:[55, 11], Operations: ['23-17=6', '5+6=11'] Exploring Operation: 55*11=605, Resulting Numbers: [605] 605,55 unequal: No Solution Exploring Operation: 55+11=66, Resulting Numbers: [66] 66,55 unequal: No Solution Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,55 unequal: No Solution Moving to Node #0,1,3 Current State: 55:[6, 11], Operations: ['23-17=6', '55/5=11'] Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,55 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[55, 1], Operations: ['23-17=6', '6-5=1'] Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[5, 23, 17, 55], Operations: [] Exploring Operation: 23-17=6, Resulting Numbers: [5, 55, 6] Generated Node #0,1: 55:[5, 55, 6] Operation: 23-17=6 Moving to Node #0,1 Current State: 55:[5, 55, 6], Operations: ['23-17=6'] Exploring Operation: 6-5=1, Resulting Numbers: [55, 1] Generated Node #0,1,1: 55:[55, 1] Operation: 6-5=1 Moving to Node #0,1,1 Current State: 55:[55, 1], Operations: ['23-17=6', '6-5=1'] Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 50, 29, 25, 73 ]
42
[ "50/25=2", "73-29=44", "44-2=42" ]
Current State: 42:[50, 29, 25, 73], Operations: [] Exploring Operation: 50/25=2, Resulting Numbers: [29, 73, 2] Generated Node #2: [29, 73, 2] from Operation: 50/25=2 Current State: 42:[29, 73, 2], Operations: ['50/25=2'] Exploring Operation: 73-29=44, Resulting Numbers: [2, 44] Generated Node #3: [2, 44] from Operation: 73-29=44 Current State: 42:[2, 44], Operations: ['50/25=2', '73-29=44'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[50, 29, 25, 73], Operations: [] Exploring Operation: 73-50=23, Resulting Numbers: [29, 25, 23] Generated Node #0,0: 42:[29, 25, 23] Operation: 73-50=23 Exploring Operation: 73-29=44, Resulting Numbers: [50, 25, 44] Generated Node #0,1: 42:[50, 25, 44] Operation: 73-29=44 Exploring Operation: 73-25=48, Resulting Numbers: [50, 29, 48] Generated Node #0,2: 42:[50, 29, 48] Operation: 73-25=48 Exploring Operation: 50/25=2, Resulting Numbers: [29, 73, 2] Generated Node #0,3: 42:[29, 73, 2] Operation: 50/25=2 Exploring Operation: 50-29=21, Resulting Numbers: [25, 73, 21] Generated Node #0,4: 42:[25, 73, 21] Operation: 50-29=21 Moving to Node #0,0 Current State: 42:[29, 25, 23], Operations: ['73-50=23'] Exploring Operation: 29+23=52, Resulting Numbers: [25, 52] Generated Node #0,0,0: 42:[25, 52] Operation: 29+23=52 Exploring Operation: 29-25=4, Resulting Numbers: [23, 4] Generated Node #0,0,1: 42:[23, 4] Operation: 29-25=4 Exploring Operation: 25-23=2, Resulting Numbers: [29, 2] Generated Node #0,0,2: 42:[29, 2] Operation: 25-23=2 Exploring Operation: 29-23=6, Resulting Numbers: [25, 6] Generated Node #0,0,3: 42:[25, 6] Operation: 29-23=6 Exploring Operation: 29+25=54, Resulting Numbers: [23, 54] Generated Node #0,0,4: 42:[23, 54] Operation: 29+25=54 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 42:[23, 4], Operations: ['73-50=23', '29-25=4'] Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,42 unequal: No Solution Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,42 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 42:[25, 6], Operations: ['73-50=23', '29-23=6'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,42 unequal: No Solution Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 42:[29, 2], Operations: ['73-50=23', '25-23=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,42 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,42 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[25, 52], Operations: ['73-50=23', '29+23=52'] Exploring Operation: 52-25=27, Resulting Numbers: [27] 27,42 unequal: No Solution Exploring Operation: 25*52=1300, Resulting Numbers: [1300] 1300,42 unequal: No Solution Exploring Operation: 25+52=77, Resulting Numbers: [77] 77,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 42:[23, 54], Operations: ['73-50=23', '29+25=54'] Exploring Operation: 23+54=77, Resulting Numbers: [77] 77,42 unequal: No Solution Exploring Operation: 23*54=1242, Resulting Numbers: [1242] 1242,42 unequal: No Solution Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,42 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: 42:[50, 25, 44], Operations: ['73-29=44'] Exploring Operation: 50-25=25, Resulting Numbers: [44, 25] Generated Node #0,1,0: 42:[44, 25] Operation: 50-25=25 Exploring Operation: 44-25=19, Resulting Numbers: [50, 19] Generated Node #0,1,1: 42:[50, 19] Operation: 44-25=19 Exploring Operation: 50/25=2, Resulting Numbers: [44, 2] Generated Node #0,1,2: 42:[44, 2] Operation: 50/25=2 Exploring Operation: 50-44=6, Resulting Numbers: [25, 6] Generated Node #0,1,3: 42:[25, 6] Operation: 50-44=6 Exploring Operation: 50+25=75, Resulting Numbers: [44, 75] Generated Node #0,1,4: 42:[44, 75] Operation: 50+25=75 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 42:[44, 2], Operations: ['73-29=44', '50/25=2'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[50, 29, 25, 73], Operations: [] Exploring Operation: 73-29=44, Resulting Numbers: [50, 25, 44] Generated Node #0,1: 42:[50, 25, 44] Operation: 73-29=44 Moving to Node #0,1 Current State: 42:[50, 25, 44], Operations: ['73-29=44'] Exploring Operation: 50/25=2, Resulting Numbers: [44, 2] Generated Node #0,1,2: 42:[44, 2] Operation: 50/25=2 Moving to Node #0,1,2 Current State: 42:[44, 2], Operations: ['73-29=44', '50/25=2'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
sum_heuristic
[ 30, 14, 90, 8 ]
34
[ "90/30=3", "14*3=42", "42-8=34" ]
Current State: 34:[30, 14, 90, 8], Operations: [] Exploring Operation: 90/30=3, Resulting Numbers: [14, 8, 3] Generated Node #2: [14, 8, 3] from Operation: 90/30=3 Current State: 34:[14, 8, 3], Operations: ['90/30=3'] Exploring Operation: 14*3=42, Resulting Numbers: [8, 42] Generated Node #3: [8, 42] from Operation: 14*3=42 Current State: 34:[8, 42], Operations: ['90/30=3', '14*3=42'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[30, 14, 90, 8], Operations: [] Exploring Operation: 90-30=60, Resulting Numbers: [14, 8, 60] Generated Node #0,0: 34:[14, 8, 60] Operation: 90-30=60 Exploring Operation: 90/30=3, Resulting Numbers: [14, 8, 3] Generated Node #0,1: 34:[14, 8, 3] Operation: 90/30=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[14, 8, 3], Operations: ['90/30=3'] Exploring Operation: 14+8=22, Resulting Numbers: [3, 22] Generated Node #0,1,0: 34:[3, 22] Operation: 14+8=22 Exploring Operation: 14-8=6, Resulting Numbers: [3, 6] Generated Node #0,1,1: 34:[3, 6] Operation: 14-8=6 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 34:[3, 6], Operations: ['90/30=3', '14-8=6'] Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,34 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,34 unequal: No Solution No 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: 34:[3, 22], Operations: ['90/30=3', '14+8=22'] Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,34 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,34 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: 34:[14, 8, 60], Operations: ['90-30=60'] Exploring Operation: 60-14=46, Resulting Numbers: [8, 46] Generated Node #0,0,0: 34:[8, 46] Operation: 60-14=46 Exploring Operation: 60-8=52, Resulting Numbers: [14, 52] Generated Node #0,0,1: 34:[14, 52] Operation: 60-8=52 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[8, 46], Operations: ['90-30=60', '60-14=46'] Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,34 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,34 unequal: No Solution No 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: 34:[14, 52], Operations: ['90-30=60', '60-8=52'] Exploring Operation: 14+52=66, Resulting Numbers: [66] 66,34 unequal: No Solution Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,34 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
[ 60, 11, 84, 70 ]
85
[ "60+11=71", "84-70=14", "71+14=85" ]
Current State: 85:[60, 11, 84, 70], Operations: [] Exploring Operation: 60+11=71, Resulting Numbers: [84, 70, 71] Generated Node #2: [84, 70, 71] from Operation: 60+11=71 Current State: 85:[84, 70, 71], Operations: ['60+11=71'] Exploring Operation: 84-70=14, Resulting Numbers: [71, 14] Generated Node #3: [71, 14] from Operation: 84-70=14 Current State: 85:[71, 14], Operations: ['60+11=71', '84-70=14'] Exploring Operation: 71+14=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[60, 11, 84, 70], Operations: [] Exploring Operation: 70-60=10, Resulting Numbers: [11, 84, 10] Generated Node #0,0: 85:[11, 84, 10] Operation: 70-60=10 Exploring Operation: 84-60=24, Resulting Numbers: [11, 70, 24] Generated Node #0,1: 85:[11, 70, 24] Operation: 84-60=24 Moving to Node #0,0 Current State: 85:[11, 84, 10], Operations: ['70-60=10'] Exploring Operation: 11+10=21, Resulting Numbers: [84, 21] Generated Node #0,0,0: 85:[84, 21] Operation: 11+10=21 Exploring Operation: 11-10=1, Resulting Numbers: [84, 1] Generated Node #0,0,1: 85:[84, 1] Operation: 11-10=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[84, 21], Operations: ['70-60=10', '11+10=21'] Exploring Operation: 84+21=105, Resulting Numbers: [105] 105,85 unequal: No Solution Exploring Operation: 84/21=4, Resulting Numbers: [4] 4,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[84, 1], Operations: ['70-60=10', '11-10=1'] Exploring Operation: 84+1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[60, 11, 84, 70], Operations: [] Exploring Operation: 70-60=10, Resulting Numbers: [11, 84, 10] Generated Node #0,0: 85:[11, 84, 10] Operation: 70-60=10 Moving to Node #0,0 Current State: 85:[11, 84, 10], Operations: ['70-60=10'] Exploring Operation: 11-10=1, Resulting Numbers: [84, 1] Generated Node #0,0,1: 85:[84, 1] Operation: 11-10=1 Moving to Node #0,0,1 Current State: 85:[84, 1], Operations: ['70-60=10', '11-10=1'] Exploring Operation: 84+1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 18, 46, 62, 76 ]
74
[ "18+46=64", "62+76=138", "138-64=74" ]
Current State: 74:[18, 46, 62, 76], Operations: [] Exploring Operation: 18+46=64, Resulting Numbers: [62, 76, 64] Generated Node #2: [62, 76, 64] from Operation: 18+46=64 Current State: 74:[62, 76, 64], Operations: ['18+46=64'] Exploring Operation: 62+76=138, Resulting Numbers: [64, 138] Generated Node #3: [64, 138] from Operation: 62+76=138 Current State: 74:[64, 138], Operations: ['18+46=64', '62+76=138'] Exploring Operation: 138-64=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[18, 46, 62, 76], Operations: [] Exploring Operation: 62-18=44, Resulting Numbers: [46, 76, 44] Generated Node #0,0: 74:[46, 76, 44] Operation: 62-18=44 Exploring Operation: 18+46=64, Resulting Numbers: [62, 76, 64] Generated Node #0,1: 74:[62, 76, 64] Operation: 18+46=64 Exploring Operation: 18+62=80, Resulting Numbers: [46, 76, 80] Generated Node #0,2: 74:[46, 76, 80] Operation: 18+62=80 Exploring Operation: 46-18=28, Resulting Numbers: [62, 76, 28] Generated Node #0,3: 74:[62, 76, 28] Operation: 46-18=28 Moving to Node #0,2 Current State: 74:[46, 76, 80], Operations: ['18+62=80'] Exploring Operation: 80-76=4, Resulting Numbers: [46, 4] Generated Node #0,2,0: 74:[46, 4] Operation: 80-76=4 Exploring Operation: 76-46=30, Resulting Numbers: [80, 30] Generated Node #0,2,1: 74:[80, 30] Operation: 76-46=30 Exploring Operation: 80-46=34, Resulting Numbers: [76, 34] Generated Node #0,2,2: 74:[76, 34] Operation: 80-46=34 Exploring Operation: 46+76=122, Resulting Numbers: [80, 122] Generated Node #0,2,3: 74:[80, 122] Operation: 46+76=122 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 74:[76, 34], Operations: ['18+62=80', '80-46=34'] Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,74 unequal: No Solution Exploring Operation: 76*34=2584, Resulting Numbers: [2584] 2584,74 unequal: No Solution Exploring Operation: 76+34=110, Resulting Numbers: [110] 110,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 74:[46, 4], Operations: ['18+62=80', '80-76=4'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,74 unequal: No Solution Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,74 unequal: No Solution Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 74:[80, 30], Operations: ['18+62=80', '76-46=30'] Exploring Operation: 80+30=110, Resulting Numbers: [110] 110,74 unequal: No Solution Exploring Operation: 80*30=2400, Resulting Numbers: [2400] 2400,74 unequal: No Solution Exploring Operation: 80-30=50, Resulting Numbers: [50] 50,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 74:[80, 122], Operations: ['18+62=80', '46+76=122'] Exploring Operation: 80*122=9760, Resulting Numbers: [9760] 9760,74 unequal: No Solution Exploring Operation: 80+122=202, Resulting Numbers: [202] 202,74 unequal: No Solution Exploring Operation: 122-80=42, Resulting Numbers: [42] 42,74 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: 74:[46, 76, 44], Operations: ['62-18=44'] Exploring Operation: 76-44=32, Resulting Numbers: [46, 32] Generated Node #0,0,0: 74:[46, 32] Operation: 76-44=32 Exploring Operation: 76-46=30, Resulting Numbers: [44, 30] Generated Node #0,0,1: 74:[44, 30] Operation: 76-46=30 Exploring Operation: 46+44=90, Resulting Numbers: [76, 90] Generated Node #0,0,2: 74:[76, 90] Operation: 46+44=90 Exploring Operation: 46-44=2, Resulting Numbers: [76, 2] Generated Node #0,0,3: 74:[76, 2] Operation: 46-44=2 Moving to Node #0,3 Current State: 74:[62, 76, 28], Operations: ['46-18=28'] Exploring Operation: 76-62=14, Resulting Numbers: [28, 14] Generated Node #0,3,0: 74:[28, 14] Operation: 76-62=14 Exploring Operation: 62+28=90, Resulting Numbers: [76, 90] Generated Node #0,3,1: 74:[76, 90] Operation: 62+28=90 Exploring Operation: 76-28=48, Resulting Numbers: [62, 48] Generated Node #0,3,2: 74:[62, 48] Operation: 76-28=48 Exploring Operation: 62-28=34, Resulting Numbers: [76, 34] Generated Node #0,3,3: 74:[76, 34] Operation: 62-28=34 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 74:[76, 34], Operations: ['46-18=28', '62-28=34'] Exploring Operation: 76*34=2584, Resulting Numbers: [2584] 2584,74 unequal: No Solution Exploring Operation: 76+34=110, Resulting Numbers: [110] 110,74 unequal: No Solution Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 74:[76, 90], Operations: ['46-18=28', '62+28=90'] Exploring Operation: 90-76=14, Resulting Numbers: [14] 14,74 unequal: No Solution Exploring Operation: 76+90=166, Resulting Numbers: [166] 166,74 unequal: No Solution Exploring Operation: 76*90=6840, Resulting Numbers: [6840] 6840,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 74:[28, 14], Operations: ['46-18=28', '76-62=14'] Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,74 unequal: No Solution Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,74 unequal: No Solution Exploring Operation: 28*14=392, Resulting Numbers: [392] 392,74 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 74:[62, 48], Operations: ['46-18=28', '76-28=48'] Exploring Operation: 62+48=110, Resulting Numbers: [110] 110,74 unequal: No Solution Exploring Operation: 62-48=14, Resulting Numbers: [14] 14,74 unequal: No Solution Exploring Operation: 62*48=2976, Resulting Numbers: [2976] 2976,74 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: 74:[62, 76, 64], Operations: ['18+46=64'] Exploring Operation: 76-62=14, Resulting Numbers: [64, 14] Generated Node #0,1,0: 74:[64, 14] Operation: 76-62=14 Exploring Operation: 76-64=12, Resulting Numbers: [62, 12] Generated Node #0,1,1: 74:[62, 12] Operation: 76-64=12 Exploring Operation: 64-62=2, Resulting Numbers: [76, 2] Generated Node #0,1,2: 74:[76, 2] Operation: 64-62=2 Exploring Operation: 62+64=126, Resulting Numbers: [76, 126] Generated Node #0,1,3: 74:[76, 126] Operation: 62+64=126 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 74:[76, 2], Operations: ['18+46=64', '64-62=2'] Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[18, 46, 62, 76], Operations: [] Exploring Operation: 18+46=64, Resulting Numbers: [62, 76, 64] Generated Node #0,1: 74:[62, 76, 64] Operation: 18+46=64 Moving to Node #0,1 Current State: 74:[62, 76, 64], Operations: ['18+46=64'] Exploring Operation: 64-62=2, Resulting Numbers: [76, 2] Generated Node #0,1,2: 74:[76, 2] Operation: 64-62=2 Moving to Node #0,1,2 Current State: 74:[76, 2], Operations: ['18+46=64', '64-62=2'] Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.956597
hs_4
sum_heuristic
[ 38, 76, 31, 22 ]
42
[ "76/38=2", "22/2=11", "31+11=42" ]
Current State: 42:[38, 76, 31, 22], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [31, 22, 2] Generated Node #2: [31, 22, 2] from Operation: 76/38=2 Current State: 42:[31, 22, 2], Operations: ['76/38=2'] Exploring Operation: 22/2=11, Resulting Numbers: [31, 11] Generated Node #3: [31, 11] from Operation: 22/2=11 Current State: 42:[31, 11], Operations: ['76/38=2', '22/2=11'] Exploring Operation: 31+11=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[38, 76, 31, 22], Operations: [] Exploring Operation: 76-38=38, Resulting Numbers: [31, 22, 38] Generated Node #0,0: 42:[31, 22, 38] Operation: 76-38=38 Exploring Operation: 76-31=45, Resulting Numbers: [38, 22, 45] Generated Node #0,1: 42:[38, 22, 45] Operation: 76-31=45 Exploring Operation: 76/38=2, Resulting Numbers: [31, 22, 2] Generated Node #0,2: 42:[31, 22, 2] Operation: 76/38=2 Exploring Operation: 76-22=54, Resulting Numbers: [38, 31, 54] Generated Node #0,3: 42:[38, 31, 54] Operation: 76-22=54 Moving to Node #0,1 Current State: 42:[38, 22, 45], Operations: ['76-31=45'] Exploring Operation: 38+22=60, Resulting Numbers: [45, 60] Generated Node #0,1,0: 42:[45, 60] Operation: 38+22=60 Exploring Operation: 38-22=16, Resulting Numbers: [45, 16] Generated Node #0,1,1: 42:[45, 16] Operation: 38-22=16 Exploring Operation: 45-22=23, Resulting Numbers: [38, 23] Generated Node #0,1,2: 42:[38, 23] Operation: 45-22=23 Exploring Operation: 45-38=7, Resulting Numbers: [22, 7] Generated Node #0,1,3: 42:[22, 7] Operation: 45-38=7 Moving to Node #0,2 Current State: 42:[31, 22, 2], Operations: ['76/38=2'] Exploring Operation: 31-22=9, Resulting Numbers: [2, 9] Generated Node #0,2,0: 42:[2, 9] Operation: 31-22=9 Exploring Operation: 31+2=33, Resulting Numbers: [22, 33] Generated Node #0,2,1: 42:[22, 33] Operation: 31+2=33 Exploring Operation: 31+22=53, Resulting Numbers: [2, 53] Generated Node #0,2,2: 42:[2, 53] Operation: 31+22=53 Exploring Operation: 31-2=29, Resulting Numbers: [22, 29] Generated Node #0,2,3: 42:[22, 29] Operation: 31-2=29 Moving to Node #0,0 Current State: 42:[31, 22, 38], Operations: ['76-38=38'] Exploring Operation: 38-22=16, Resulting Numbers: [31, 16] Generated Node #0,0,0: 42:[31, 16] Operation: 38-22=16 Exploring Operation: 31-22=9, Resulting Numbers: [38, 9] Generated Node #0,0,1: 42:[38, 9] Operation: 31-22=9 Exploring Operation: 31+22=53, Resulting Numbers: [38, 53] Generated Node #0,0,2: 42:[38, 53] Operation: 31+22=53 Exploring Operation: 38-31=7, Resulting Numbers: [22, 7] Generated Node #0,0,3: 42:[22, 7] Operation: 38-31=7 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 42:[22, 7], Operations: ['76-38=38', '38-31=7'] Exploring Operation: 22+7=29, Resulting Numbers: [29] 29,42 unequal: No Solution Exploring Operation: 22*7=154, Resulting Numbers: [154] 154,42 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 42:[38, 9], Operations: ['76-38=38', '31-22=9'] Exploring Operation: 38*9=342, Resulting Numbers: [342] 342,42 unequal: No Solution Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,42 unequal: No Solution Exploring Operation: 38+9=47, Resulting Numbers: [47] 47,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[31, 16], Operations: ['76-38=38', '38-22=16'] Exploring Operation: 31+16=47, Resulting Numbers: [47] 47,42 unequal: No Solution Exploring Operation: 31-16=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 31*16=496, Resulting Numbers: [496] 496,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 42:[38, 53], Operations: ['76-38=38', '31+22=53'] Exploring Operation: 38*53=2014, Resulting Numbers: [2014] 2014,42 unequal: No Solution Exploring Operation: 38+53=91, Resulting Numbers: [91] 91,42 unequal: No Solution Exploring Operation: 53-38=15, Resulting Numbers: [15] 15,42 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: 42:[38, 31, 54], Operations: ['76-22=54'] Exploring Operation: 54-31=23, Resulting Numbers: [38, 23] Generated Node #0,3,0: 42:[38, 23] Operation: 54-31=23 Exploring Operation: 38-31=7, Resulting Numbers: [54, 7] Generated Node #0,3,1: 42:[54, 7] Operation: 38-31=7 Exploring Operation: 54-38=16, Resulting Numbers: [31, 16] Generated Node #0,3,2: 42:[31, 16] Operation: 54-38=16 Exploring Operation: 38+31=69, Resulting Numbers: [54, 69] Generated Node #0,3,3: 42:[54, 69] Operation: 38+31=69 Moving to Node #0,1,3 Current State: 42:[22, 7], Operations: ['76-31=45', '45-38=7'] Exploring Operation: 22+7=29, Resulting Numbers: [29] 29,42 unequal: No Solution Exploring Operation: 22*7=154, Resulting Numbers: [154] 154,42 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,42 unequal: No Solution Moving to Node #0,2,0 Current State: 42:[2, 9], Operations: ['76/38=2', '31-22=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,42 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,42 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[45, 16], Operations: ['76-31=45', '38-22=16'] Exploring Operation: 45+16=61, Resulting Numbers: [61] 61,42 unequal: No Solution Exploring Operation: 45*16=720, Resulting Numbers: [720] 720,42 unequal: No Solution Exploring Operation: 45-16=29, Resulting Numbers: [29] 29,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[38, 23], Operations: ['76-31=45', '45-22=23'] Exploring Operation: 38+23=61, Resulting Numbers: [61] 61,42 unequal: No Solution Exploring Operation: 38*23=874, Resulting Numbers: [874] 874,42 unequal: No Solution Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,42 unequal: No Solution Moving to Node #0,3,0 Current State: 42:[38, 23], Operations: ['76-22=54', '54-31=23'] Exploring Operation: 38*23=874, Resulting Numbers: [874] 874,42 unequal: No Solution Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 38+23=61, Resulting Numbers: [61] 61,42 unequal: No Solution Moving to Node #0,2,3 Current State: 42:[22, 29], Operations: ['76/38=2', '31-2=29'] Exploring Operation: 29-22=7, Resulting Numbers: [7] 7,42 unequal: No Solution Exploring Operation: 22*29=638, Resulting Numbers: [638] 638,42 unequal: No Solution Exploring Operation: 22+29=51, Resulting Numbers: [51] 51,42 unequal: No Solution Moving to Node #0,2,1 Current State: 42:[22, 33], Operations: ['76/38=2', '31+2=33'] Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,42 unequal: No Solution Exploring Operation: 22*33=726, Resulting Numbers: [726] 726,42 unequal: No Solution Exploring Operation: 22+33=55, Resulting Numbers: [55] 55,42 unequal: No Solution Moving to Node #0,2,2 Current State: 42:[2, 53], Operations: ['76/38=2', '31+22=53'] Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,42 unequal: No Solution Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,42 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,42 unequal: No Solution Moving to Node #0,3,1 Current State: 42:[54, 7], Operations: ['76-22=54', '38-31=7'] Exploring Operation: 54-7=47, Resulting Numbers: [47] 47,42 unequal: No Solution Exploring Operation: 54*7=378, Resulting Numbers: [378] 378,42 unequal: No Solution Exploring Operation: 54+7=61, Resulting Numbers: [61] 61,42 unequal: No Solution Moving to Node #0,3,2 Current State: 42:[31, 16], Operations: ['76-22=54', '54-38=16'] Exploring Operation: 31-16=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 31*16=496, Resulting Numbers: [496] 496,42 unequal: No Solution Exploring Operation: 31+16=47, Resulting Numbers: [47] 47,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[45, 60], Operations: ['76-31=45', '38+22=60'] Exploring Operation: 60-45=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 45*60=2700, Resulting Numbers: [2700] 2700,42 unequal: No Solution Exploring Operation: 45+60=105, Resulting Numbers: [105] 105,42 unequal: No Solution Moving to Node #0,3,3 Current State: 42:[54, 69], Operations: ['76-22=54', '38+31=69'] Exploring Operation: 54+69=123, Resulting Numbers: [123] 123,42 unequal: No Solution Exploring Operation: 54*69=3726, Resulting Numbers: [3726] 3726,42 unequal: No Solution Exploring Operation: 69-54=15, Resulting Numbers: [15] 15,42 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 28, 64, 20, 31 ]
81
[ "28+64=92", "31-20=11", "92-11=81" ]
Current State: 81:[28, 64, 20, 31], Operations: [] Exploring Operation: 28+64=92, Resulting Numbers: [20, 31, 92] Generated Node #2: [20, 31, 92] from Operation: 28+64=92 Current State: 81:[20, 31, 92], Operations: ['28+64=92'] Exploring Operation: 31-20=11, Resulting Numbers: [92, 11] Generated Node #3: [92, 11] from Operation: 31-20=11 Current State: 81:[92, 11], Operations: ['28+64=92', '31-20=11'] Exploring Operation: 92-11=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[28, 64, 20, 31], Operations: [] Exploring Operation: 64-28=36, Resulting Numbers: [20, 31, 36] Generated Node #0,0: 81:[20, 31, 36] Operation: 64-28=36 Exploring Operation: 31-20=11, Resulting Numbers: [28, 64, 11] Generated Node #0,1: 81:[28, 64, 11] Operation: 31-20=11 Exploring Operation: 64-31=33, Resulting Numbers: [28, 20, 33] Generated Node #0,2: 81:[28, 20, 33] Operation: 64-31=33 Exploring Operation: 64+20=84, Resulting Numbers: [28, 31, 84] Generated Node #0,3: 81:[28, 31, 84] Operation: 64+20=84 Start Sub Search at level 1: Moving to Node #0,3 Current State: 81:[28, 31, 84], Operations: ['64+20=84'] Exploring Operation: 84-31=53, Resulting Numbers: [28, 53] Generated Node #0,3,0: 81:[28, 53] Operation: 84-31=53 Exploring Operation: 28+31=59, Resulting Numbers: [84, 59] Generated Node #0,3,1: 81:[84, 59] Operation: 28+31=59 Exploring Operation: 31-28=3, Resulting Numbers: [84, 3] Generated Node #0,3,2: 81:[84, 3] Operation: 31-28=3 Exploring Operation: 84/28=3, Resulting Numbers: [31, 3] Generated Node #0,3,3: 81:[31, 3] Operation: 84/28=3 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 81:[84, 3], Operations: ['64+20=84', '31-28=3'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[28, 64, 20, 31], Operations: [] Exploring Operation: 64+20=84, Resulting Numbers: [28, 31, 84] Generated Node #0,3: 81:[28, 31, 84] Operation: 64+20=84 Moving to Node #0,3 Current State: 81:[28, 31, 84], Operations: ['64+20=84'] Exploring Operation: 31-28=3, Resulting Numbers: [84, 3] Generated Node #0,3,2: 81:[84, 3] Operation: 31-28=3 Moving to Node #0,3,2 Current State: 81:[84, 3], Operations: ['64+20=84', '31-28=3'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 68, 5, 47, 93 ]
78
[ "93-68=25", "5*25=125", "125-47=78" ]
Current State: 78:[68, 5, 47, 93], Operations: [] Exploring Operation: 93-68=25, Resulting Numbers: [5, 47, 25] Generated Node #2: [5, 47, 25] from Operation: 93-68=25 Current State: 78:[5, 47, 25], Operations: ['93-68=25'] Exploring Operation: 5*25=125, Resulting Numbers: [47, 125] Generated Node #3: [47, 125] from Operation: 5*25=125 Current State: 78:[47, 125], Operations: ['93-68=25', '5*25=125'] Exploring Operation: 125-47=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[68, 5, 47, 93], Operations: [] Exploring Operation: 68-47=21, Resulting Numbers: [5, 93, 21] Generated Node #0,0: 78:[5, 93, 21] Operation: 68-47=21 Exploring Operation: 93-47=46, Resulting Numbers: [68, 5, 46] Generated Node #0,1: 78:[68, 5, 46] Operation: 93-47=46 Exploring Operation: 68+5=73, Resulting Numbers: [47, 93, 73] Generated Node #0,2: 78:[47, 93, 73] Operation: 68+5=73 Exploring Operation: 93-68=25, Resulting Numbers: [5, 47, 25] Generated Node #0,3: 78:[5, 47, 25] Operation: 93-68=25 Moving to Node #0,3 Current State: 78:[5, 47, 25], Operations: ['93-68=25'] Exploring Operation: 47-25=22, Resulting Numbers: [5, 22] Generated Node #0,3,0: 78:[5, 22] Operation: 47-25=22 Exploring Operation: 47+25=72, Resulting Numbers: [5, 72] Generated Node #0,3,1: 78:[5, 72] Operation: 47+25=72 Exploring Operation: 25/5=5, Resulting Numbers: [47, 5] Generated Node #0,3,2: 78:[47, 5] Operation: 25/5=5 Exploring Operation: 47-5=42, Resulting Numbers: [25, 42] Generated Node #0,3,3: 78:[25, 42] Operation: 47-5=42 Moving to Node #0,1 Current State: 78:[68, 5, 46], Operations: ['93-47=46'] Exploring Operation: 68+5=73, Resulting Numbers: [46, 73] Generated Node #0,1,0: 78:[46, 73] Operation: 68+5=73 Exploring Operation: 68-5=63, Resulting Numbers: [46, 63] Generated Node #0,1,1: 78:[46, 63] Operation: 68-5=63 Exploring Operation: 68-46=22, Resulting Numbers: [5, 22] Generated Node #0,1,2: 78:[5, 22] Operation: 68-46=22 Exploring Operation: 46-5=41, Resulting Numbers: [68, 41] Generated Node #0,1,3: 78:[68, 41] Operation: 46-5=41 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 78:[5, 22], Operations: ['93-47=46', '68-46=22'] Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,78 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[46, 73], Operations: ['93-47=46', '68+5=73'] Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 46+73=119, Resulting Numbers: [119] 119,78 unequal: No Solution Exploring Operation: 46*73=3358, Resulting Numbers: [3358] 3358,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 78:[68, 41], Operations: ['93-47=46', '46-5=41'] Exploring Operation: 68*41=2788, Resulting Numbers: [2788] 2788,78 unequal: No Solution Exploring Operation: 68-41=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 68+41=109, Resulting Numbers: [109] 109,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[46, 63], Operations: ['93-47=46', '68-5=63'] Exploring Operation: 46*63=2898, Resulting Numbers: [2898] 2898,78 unequal: No Solution Exploring Operation: 63-46=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 46+63=109, Resulting Numbers: [109] 109,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 78:[5, 93, 21], Operations: ['68-47=21'] Exploring Operation: 5+21=26, Resulting Numbers: [93, 26] Generated Node #0,0,0: 78:[93, 26] Operation: 5+21=26 Exploring Operation: 93-5=88, Resulting Numbers: [21, 88] Generated Node #0,0,1: 78:[21, 88] Operation: 93-5=88 Exploring Operation: 93-21=72, Resulting Numbers: [5, 72] Generated Node #0,0,2: 78:[5, 72] Operation: 93-21=72 Exploring Operation: 21-5=16, Resulting Numbers: [93, 16] Generated Node #0,0,3: 78:[93, 16] Operation: 21-5=16 Moving to Node #0,2 Current State: 78:[47, 93, 73], Operations: ['68+5=73'] Exploring Operation: 93-73=20, Resulting Numbers: [47, 20] Generated Node #0,2,0: 78:[47, 20] Operation: 93-73=20 Exploring Operation: 73-47=26, Resulting Numbers: [93, 26] Generated Node #0,2,1: 78:[93, 26] Operation: 73-47=26 Exploring Operation: 93-47=46, Resulting Numbers: [73, 46] Generated Node #0,2,2: 78:[73, 46] Operation: 93-47=46 Exploring Operation: 47+73=120, Resulting Numbers: [93, 120] Generated Node #0,2,3: 78:[93, 120] Operation: 47+73=120 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 78:[73, 46], Operations: ['68+5=73', '93-47=46'] Exploring Operation: 73+46=119, Resulting Numbers: [119] 119,78 unequal: No Solution Exploring Operation: 73*46=3358, Resulting Numbers: [3358] 3358,78 unequal: No Solution Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,78 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 #0,2,0 Current State: 78:[47, 20], Operations: ['68+5=73', '93-73=20'] Exploring Operation: 47+20=67, Resulting Numbers: [67] 67,78 unequal: No Solution Exploring Operation: 47*20=940, Resulting Numbers: [940] 940,78 unequal: No Solution Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,78 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 #0,2,1 Current State: 78:[93, 26], Operations: ['68+5=73', '73-47=26'] Exploring Operation: 93*26=2418, Resulting Numbers: [2418] 2418,78 unequal: No Solution Exploring Operation: 93+26=119, Resulting Numbers: [119] 119,78 unequal: No Solution Exploring Operation: 93-26=67, Resulting Numbers: [67] 67,78 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 #0,2,3 Current State: 78:[93, 120], Operations: ['68+5=73', '47+73=120'] Exploring Operation: 120-93=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 93*120=11160, Resulting Numbers: [11160] 11160,78 unequal: No Solution Exploring Operation: 93+120=213, Resulting Numbers: [213] 213,78 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: 78:[25, 42], Operations: ['93-68=25', '47-5=42'] Exploring Operation: 42-25=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 25+42=67, Resulting Numbers: [67] 67,78 unequal: No Solution Exploring Operation: 25*42=1050, Resulting Numbers: [1050] 1050,78 unequal: No Solution Moving to Node #0,3,0 Current State: 78:[5, 22], Operations: ['93-68=25', '47-25=22'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,78 unequal: No Solution Moving to Node #0,3,1 Current State: 78:[5, 72], Operations: ['93-68=25', '47+25=72'] Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,78 unequal: No Solution Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,78 unequal: No Solution Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,78 unequal: No Solution Moving to Node #0,0,2 Current State: 78:[5, 72], Operations: ['68-47=21', '93-21=72'] Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,78 unequal: No Solution Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,78 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,78 unequal: No Solution Moving to Node #0,3,2 Current State: 78:[47, 5], Operations: ['93-68=25', '25/5=5'] Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,78 unequal: No Solution Exploring Operation: 47+5=52, Resulting Numbers: [52] 52,78 unequal: No Solution Exploring Operation: 47*5=235, Resulting Numbers: [235] 235,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[93, 26], Operations: ['68-47=21', '5+21=26'] Exploring Operation: 93+26=119, Resulting Numbers: [119] 119,78 unequal: No Solution Exploring Operation: 93*26=2418, Resulting Numbers: [2418] 2418,78 unequal: No Solution Exploring Operation: 93-26=67, Resulting Numbers: [67] 67,78 unequal: No Solution Moving to Node #0,0,1 Current State: 78:[21, 88], Operations: ['68-47=21', '93-5=88'] Exploring Operation: 88-21=67, Resulting Numbers: [67] 67,78 unequal: No Solution Exploring Operation: 21+88=109, Resulting Numbers: [109] 109,78 unequal: No Solution Exploring Operation: 21*88=1848, Resulting Numbers: [1848] 1848,78 unequal: No Solution Moving to Node #0,0,3 Current State: 78:[93, 16], Operations: ['68-47=21', '21-5=16'] Exploring Operation: 93-16=77, Resulting Numbers: [77] 77,78 unequal: No Solution Exploring Operation: 93*16=1488, Resulting Numbers: [1488] 1488,78 unequal: No Solution Exploring Operation: 93+16=109, Resulting Numbers: [109] 109,78 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 50, 95, 92, 3 ]
50
[ "50+95=145", "92+3=95", "145-95=50" ]
Current State: 50:[50, 95, 92, 3], Operations: [] Exploring Operation: 50+95=145, Resulting Numbers: [92, 3, 145] Generated Node #2: [92, 3, 145] from Operation: 50+95=145 Current State: 50:[92, 3, 145], Operations: ['50+95=145'] Exploring Operation: 92+3=95, Resulting Numbers: [145, 95] Generated Node #3: [145, 95] from Operation: 92+3=95 Current State: 50:[145, 95], Operations: ['50+95=145', '92+3=95'] Exploring Operation: 145-95=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[50, 95, 92, 3], Operations: [] Exploring Operation: 95-50=45, Resulting Numbers: [92, 3, 45] Generated Node #0,0: 50:[92, 3, 45] Operation: 95-50=45 Exploring Operation: 95-92=3, Resulting Numbers: [50, 3, 3] Generated Node #0,1: 50:[50, 3, 3] Operation: 95-92=3 Exploring Operation: 92-50=42, Resulting Numbers: [95, 3, 42] Generated Node #0,2: 50:[95, 3, 42] Operation: 92-50=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[50, 3, 3], Operations: ['95-92=3'] Exploring Operation: 3/3=1, Resulting Numbers: [50, 1] Generated Node #0,1,0: 50:[50, 1] Operation: 3/3=1 Exploring Operation: 3*3=9, Resulting Numbers: [50, 9] Generated Node #0,1,1: 50:[50, 9] Operation: 3*3=9 Exploring Operation: 3+3=6, Resulting Numbers: [50, 6] Generated Node #0,1,2: 50:[50, 6] Operation: 3+3=6 Moving to Node #0,1,0 Current State: 50:[50, 1], Operations: ['95-92=3', '3/3=1'] Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,50 unequal: No Solution Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[50, 95, 92, 3], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [50, 3, 3] Generated Node #0,1: 50:[50, 3, 3] Operation: 95-92=3 Moving to Node #0,1 Current State: 50:[50, 3, 3], Operations: ['95-92=3'] Exploring Operation: 3/3=1, Resulting Numbers: [50, 1] Generated Node #0,1,0: 50:[50, 1] Operation: 3/3=1 Moving to Node #0,1,0 Current State: 50:[50, 1], Operations: ['95-92=3', '3/3=1'] Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 9, 39, 80, 53 ]
85
[ "9+39=48", "80+53=133", "133-48=85" ]
Current State: 85:[9, 39, 80, 53], Operations: [] Exploring Operation: 9+39=48, Resulting Numbers: [80, 53, 48] Generated Node #2: [80, 53, 48] from Operation: 9+39=48 Current State: 85:[80, 53, 48], Operations: ['9+39=48'] Exploring Operation: 80+53=133, Resulting Numbers: [48, 133] Generated Node #3: [48, 133] from Operation: 80+53=133 Current State: 85:[48, 133], Operations: ['9+39=48', '80+53=133'] Exploring Operation: 133-48=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[9, 39, 80, 53], Operations: [] Exploring Operation: 53-39=14, Resulting Numbers: [9, 80, 14] Generated Node #0,0: 85:[9, 80, 14] Operation: 53-39=14 Exploring Operation: 39+53=92, Resulting Numbers: [9, 80, 92] Generated Node #0,1: 85:[9, 80, 92] Operation: 39+53=92 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[9, 80, 14], Operations: ['53-39=14'] Exploring Operation: 9+80=89, Resulting Numbers: [14, 89] Generated Node #0,0,0: 85:[14, 89] Operation: 9+80=89 Exploring Operation: 14-9=5, Resulting Numbers: [80, 5] Generated Node #0,0,1: 85:[80, 5] Operation: 14-9=5 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 85:[80, 5], Operations: ['53-39=14', '14-9=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[9, 39, 80, 53], Operations: [] Exploring Operation: 53-39=14, Resulting Numbers: [9, 80, 14] Generated Node #0,0: 85:[9, 80, 14] Operation: 53-39=14 Moving to Node #0,0 Current State: 85:[9, 80, 14], Operations: ['53-39=14'] Exploring Operation: 14-9=5, Resulting Numbers: [80, 5] Generated Node #0,0,1: 85:[80, 5] Operation: 14-9=5 Moving to Node #0,0,1 Current State: 85:[80, 5], Operations: ['53-39=14', '14-9=5'] Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 17, 39, 6, 78 ]
94
[ "39-17=22", "78-6=72", "22+72=94" ]
Current State: 94:[17, 39, 6, 78], Operations: [] Exploring Operation: 39-17=22, Resulting Numbers: [6, 78, 22] Generated Node #2: [6, 78, 22] from Operation: 39-17=22 Current State: 94:[6, 78, 22], Operations: ['39-17=22'] Exploring Operation: 78-6=72, Resulting Numbers: [22, 72] Generated Node #3: [22, 72] from Operation: 78-6=72 Current State: 94:[22, 72], Operations: ['39-17=22', '78-6=72'] Exploring Operation: 22+72=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[17, 39, 6, 78], Operations: [] Exploring Operation: 78-17=61, Resulting Numbers: [39, 6, 61] Generated Node #0,0: 94:[39, 6, 61] Operation: 78-17=61 Exploring Operation: 78/39=2, Resulting Numbers: [17, 6, 2] Generated Node #0,1: 94:[17, 6, 2] Operation: 78/39=2 Exploring Operation: 17+78=95, Resulting Numbers: [39, 6, 95] Generated Node #0,2: 94:[39, 6, 95] Operation: 17+78=95 Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[39, 6, 95], Operations: ['17+78=95'] Exploring Operation: 39+6=45, Resulting Numbers: [95, 45] Generated Node #0,2,0: 94:[95, 45] Operation: 39+6=45 Exploring Operation: 95-39=56, Resulting Numbers: [6, 56] Generated Node #0,2,1: 94:[6, 56] Operation: 95-39=56 Exploring Operation: 95-6=89, Resulting Numbers: [39, 89] Generated Node #0,2,2: 94:[39, 89] Operation: 95-6=89 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 94:[95, 45], Operations: ['17+78=95', '39+6=45'] Exploring Operation: 95-45=50, Resulting Numbers: [50] 50,94 unequal: No Solution Exploring Operation: 95+45=140, Resulting Numbers: [140] 140,94 unequal: No Solution Exploring Operation: 95*45=4275, Resulting Numbers: [4275] 4275,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 94:[6, 56], Operations: ['17+78=95', '95-39=56'] Exploring Operation: 6*56=336, Resulting Numbers: [336] 336,94 unequal: No Solution Exploring Operation: 6+56=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 94:[39, 89], Operations: ['17+78=95', '95-6=89'] Exploring Operation: 89-39=50, Resulting Numbers: [50] 50,94 unequal: No Solution Exploring Operation: 39*89=3471, Resulting Numbers: [3471] 3471,94 unequal: No Solution Exploring Operation: 39+89=128, Resulting Numbers: [128] 128,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[17, 6, 2], Operations: ['78/39=2'] Exploring Operation: 17*6=102, Resulting Numbers: [2, 102] Generated Node #0,1,0: 94:[2, 102] Operation: 17*6=102 Exploring Operation: 17-6=11, Resulting Numbers: [2, 11] Generated Node #0,1,1: 94:[2, 11] Operation: 17-6=11 Exploring Operation: 6/2=3, Resulting Numbers: [17, 3] Generated Node #0,1,2: 94:[17, 3] Operation: 6/2=3 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[2, 102], Operations: ['78/39=2', '17*6=102'] Exploring Operation: 102/2=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 2+102=104, Resulting Numbers: [104] 104,94 unequal: No Solution Exploring Operation: 102-2=100, Resulting Numbers: [100] 100,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[2, 11], Operations: ['78/39=2', '17-6=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,94 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,94 unequal: No Solution Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 94:[17, 3], Operations: ['78/39=2', '6/2=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,94 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[39, 6, 61], Operations: ['78-17=61'] Exploring Operation: 39+6=45, Resulting Numbers: [61, 45] Generated Node #0,0,0: 94:[61, 45] Operation: 39+6=45 Exploring Operation: 61-6=55, Resulting Numbers: [39, 55] Generated Node #0,0,1: 94:[39, 55] Operation: 61-6=55 Exploring Operation: 39+61=100, Resulting Numbers: [6, 100] Generated Node #0,0,2: 94:[6, 100] Operation: 39+61=100 Moving to Node #0,0,2 Current State: 94:[6, 100], Operations: ['78-17=61', '39+61=100'] Exploring Operation: 100-6=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[17, 39, 6, 78], Operations: [] Exploring Operation: 78-17=61, Resulting Numbers: [39, 6, 61] Generated Node #0,0: 94:[39, 6, 61] Operation: 78-17=61 Moving to Node #0,0 Current State: 94:[39, 6, 61], Operations: ['78-17=61'] Exploring Operation: 39+61=100, Resulting Numbers: [6, 100] Generated Node #0,0,2: 94:[6, 100] Operation: 39+61=100 Moving to Node #0,0,2 Current State: 94:[6, 100], Operations: ['78-17=61', '39+61=100'] Exploring Operation: 100-6=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_3
mult_heuristic
[ 8, 81, 55, 41 ]
60
[ "81-41=40", "40/8=5", "55+5=60" ]
Current State: 60:[8, 81, 55, 41], Operations: [] Exploring Operation: 81-41=40, Resulting Numbers: [8, 55, 40] Generated Node #2: [8, 55, 40] from Operation: 81-41=40 Current State: 60:[8, 55, 40], Operations: ['81-41=40'] Exploring Operation: 40/8=5, Resulting Numbers: [55, 5] Generated Node #3: [55, 5] from Operation: 40/8=5 Current State: 60:[55, 5], Operations: ['81-41=40', '40/8=5'] Exploring Operation: 55+5=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[8, 81, 55, 41], Operations: [] Exploring Operation: 81-55=26, Resulting Numbers: [8, 41, 26] Generated Node #0,0: 60:[8, 41, 26] Operation: 81-55=26 Exploring Operation: 81-41=40, Resulting Numbers: [8, 55, 40] Generated Node #0,1: 60:[8, 55, 40] Operation: 81-41=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[8, 41, 26], Operations: ['81-55=26'] Exploring Operation: 41-8=33, Resulting Numbers: [26, 33] Generated Node #0,0,0: 60:[26, 33] Operation: 41-8=33 Exploring Operation: 41-26=15, Resulting Numbers: [8, 15] Generated Node #0,0,1: 60:[8, 15] Operation: 41-26=15 Moving to Node #0,0,1 Current State: 60:[8, 15], Operations: ['81-55=26', '41-26=15'] Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,0,0 Current State: 60:[26, 33], Operations: ['81-55=26', '41-8=33'] Exploring Operation: 33-26=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 26+33=59, Resulting Numbers: [59] 59,60 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:[8, 55, 40], Operations: ['81-41=40'] Exploring Operation: 40/8=5, Resulting Numbers: [55, 5] Generated Node #0,1,0: 60:[55, 5] Operation: 40/8=5 Exploring Operation: 55-40=15, Resulting Numbers: [8, 15] Generated Node #0,1,1: 60:[8, 15] Operation: 55-40=15 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 60:[8, 15], Operations: ['81-41=40', '55-40=15'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,60 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 #0,1,0 Current State: 60:[55, 5], Operations: ['81-41=40', '40/8=5'] Exploring Operation: 55+5=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[8, 81, 55, 41], Operations: [] Exploring Operation: 81-41=40, Resulting Numbers: [8, 55, 40] Generated Node #0,1: 60:[8, 55, 40] Operation: 81-41=40 Moving to Node #0,1 Current State: 60:[8, 55, 40], Operations: ['81-41=40'] Exploring Operation: 40/8=5, Resulting Numbers: [55, 5] Generated Node #0,1,0: 60:[55, 5] Operation: 40/8=5 Moving to Node #0,1,0 Current State: 60:[55, 5], Operations: ['81-41=40', '40/8=5'] Exploring Operation: 55+5=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_2
sum_heuristic
[ 17, 31, 55, 85 ]
78
[ "17+31=48", "85-55=30", "48+30=78" ]
Current State: 78:[17, 31, 55, 85], Operations: [] Exploring Operation: 17+31=48, Resulting Numbers: [55, 85, 48] Generated Node #2: [55, 85, 48] from Operation: 17+31=48 Current State: 78:[55, 85, 48], Operations: ['17+31=48'] Exploring Operation: 85-55=30, Resulting Numbers: [48, 30] Generated Node #3: [48, 30] from Operation: 85-55=30 Current State: 78:[48, 30], Operations: ['17+31=48', '85-55=30'] Exploring Operation: 48+30=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[17, 31, 55, 85], Operations: [] Exploring Operation: 55-17=38, Resulting Numbers: [31, 85, 38] Generated Node #0,0: 78:[31, 85, 38] Operation: 55-17=38 Exploring Operation: 17+55=72, Resulting Numbers: [31, 85, 72] Generated Node #0,1: 78:[31, 85, 72] Operation: 17+55=72 Exploring Operation: 31+55=86, Resulting Numbers: [17, 85, 86] Generated Node #0,2: 78:[17, 85, 86] Operation: 31+55=86 Exploring Operation: 85-55=30, Resulting Numbers: [17, 31, 30] Generated Node #0,3: 78:[17, 31, 30] Operation: 85-55=30 Exploring Operation: 55-31=24, Resulting Numbers: [17, 85, 24] Generated Node #0,4: 78:[17, 85, 24] Operation: 55-31=24 Moving to Node #0,0 Current State: 78:[31, 85, 38], Operations: ['55-17=38'] Exploring Operation: 85-31=54, Resulting Numbers: [38, 54] Generated Node #0,0,0: 78:[38, 54] Operation: 85-31=54 Exploring Operation: 85-38=47, Resulting Numbers: [31, 47] Generated Node #0,0,1: 78:[31, 47] Operation: 85-38=47 Exploring Operation: 31+85=116, Resulting Numbers: [38, 116] Generated Node #0,0,2: 78:[38, 116] Operation: 31+85=116 Exploring Operation: 31+38=69, Resulting Numbers: [85, 69] Generated Node #0,0,3: 78:[85, 69] Operation: 31+38=69 Exploring Operation: 38-31=7, Resulting Numbers: [85, 7] Generated Node #0,0,4: 78:[85, 7] Operation: 38-31=7 Moving to Node #0,4 Current State: 78:[17, 85, 24], Operations: ['55-31=24'] Exploring Operation: 85-17=68, Resulting Numbers: [24, 68] Generated Node #0,4,0: 78:[24, 68] Operation: 85-17=68 Exploring Operation: 85-24=61, Resulting Numbers: [17, 61] Generated Node #0,4,1: 78:[17, 61] Operation: 85-24=61 Exploring Operation: 24-17=7, Resulting Numbers: [85, 7] Generated Node #0,4,2: 78:[85, 7] Operation: 24-17=7 Exploring Operation: 85/17=5, Resulting Numbers: [24, 5] Generated Node #0,4,3: 78:[24, 5] Operation: 85/17=5 Exploring Operation: 17+24=41, Resulting Numbers: [85, 41] Generated Node #0,4,4: 78:[85, 41] Operation: 17+24=41 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 78:[24, 5], Operations: ['55-31=24', '85/17=5'] Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,78 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,78 unequal: No Solution Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,78 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 #0,4,2 Current State: 78:[85, 7], Operations: ['55-31=24', '24-17=7'] Exploring Operation: 85-7=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[17, 31, 55, 85], Operations: [] Exploring Operation: 55-31=24, Resulting Numbers: [17, 85, 24] Generated Node #0,4: 78:[17, 85, 24] Operation: 55-31=24 Moving to Node #0,4 Current State: 78:[17, 85, 24], Operations: ['55-31=24'] Exploring Operation: 24-17=7, Resulting Numbers: [85, 7] Generated Node #0,4,2: 78:[85, 7] Operation: 24-17=7 Moving to Node #0,4,2 Current State: 78:[85, 7], Operations: ['55-31=24', '24-17=7'] Exploring Operation: 85-7=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 72, 3, 21, 48 ]
47
[ "72+21=93", "48+93=141", "141/3=47" ]
Current State: 47:[72, 3, 21, 48], Operations: [] Exploring Operation: 72+21=93, Resulting Numbers: [3, 48, 93] Generated Node #2: [3, 48, 93] from Operation: 72+21=93 Current State: 47:[3, 48, 93], Operations: ['72+21=93'] Exploring Operation: 48+93=141, Resulting Numbers: [3, 141] Generated Node #3: [3, 141] from Operation: 48+93=141 Current State: 47:[3, 141], Operations: ['72+21=93', '48+93=141'] Exploring Operation: 141/3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[72, 3, 21, 48], Operations: [] Exploring Operation: 3*21=63, Resulting Numbers: [72, 48, 63] Generated Node #0,0: 47:[72, 48, 63] Operation: 3*21=63 Exploring Operation: 72-3=69, Resulting Numbers: [21, 48, 69] Generated Node #0,1: 47:[21, 48, 69] Operation: 72-3=69 Exploring Operation: 72-21=51, Resulting Numbers: [3, 48, 51] Generated Node #0,2: 47:[3, 48, 51] Operation: 72-21=51 Exploring Operation: 3+21=24, Resulting Numbers: [72, 48, 24] Generated Node #0,3: 47:[72, 48, 24] Operation: 3+21=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[72, 48, 63], Operations: ['3*21=63'] Exploring Operation: 72+48=120, Resulting Numbers: [63, 120] Generated Node #0,0,0: 47:[63, 120] Operation: 72+48=120 Exploring Operation: 63-48=15, Resulting Numbers: [72, 15] Generated Node #0,0,1: 47:[72, 15] Operation: 63-48=15 Exploring Operation: 72-48=24, Resulting Numbers: [63, 24] Generated Node #0,0,2: 47:[63, 24] Operation: 72-48=24 Exploring Operation: 72-63=9, Resulting Numbers: [48, 9] Generated Node #0,0,3: 47:[48, 9] Operation: 72-63=9 Moving to Node #0,0,2 Current State: 47:[63, 24], Operations: ['3*21=63', '72-48=24'] Exploring Operation: 63*24=1512, Resulting Numbers: [1512] 1512,47 unequal: No Solution Exploring Operation: 63-24=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 63+24=87, Resulting Numbers: [87] 87,47 unequal: No Solution Moving to Node #0,0,3 Current State: 47:[48, 9], Operations: ['3*21=63', '72-63=9'] Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 48+9=57, Resulting Numbers: [57] 57,47 unequal: No Solution Exploring Operation: 48*9=432, Resulting Numbers: [432] 432,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[72, 15], Operations: ['3*21=63', '63-48=15'] Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,47 unequal: No Solution Exploring Operation: 72*15=1080, Resulting Numbers: [1080] 1080,47 unequal: No Solution Exploring Operation: 72+15=87, Resulting Numbers: [87] 87,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[63, 120], Operations: ['3*21=63', '72+48=120'] Exploring Operation: 63*120=7560, Resulting Numbers: [7560] 7560,47 unequal: No Solution Exploring Operation: 63+120=183, Resulting Numbers: [183] 183,47 unequal: No Solution Exploring Operation: 120-63=57, Resulting Numbers: [57] 57,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[21, 48, 69], Operations: ['72-3=69'] Exploring Operation: 69-21=48, Resulting Numbers: [48, 48] Generated Node #0,1,0: 47:[48, 48] Operation: 69-21=48 Exploring Operation: 21+48=69, Resulting Numbers: [69, 69] Generated Node #0,1,1: 47:[69, 69] Operation: 21+48=69 Exploring Operation: 48-21=27, Resulting Numbers: [69, 27] Generated Node #0,1,2: 47:[69, 27] Operation: 48-21=27 Exploring Operation: 21+69=90, Resulting Numbers: [48, 90] Generated Node #0,1,3: 47:[48, 90] Operation: 21+69=90 Moving to Node #0,1,0 Current State: 47:[48, 48], Operations: ['72-3=69', '69-21=48'] Exploring Operation: 48+48=96, Resulting Numbers: [96] 96,47 unequal: No Solution Exploring Operation: 48/48=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 48*48=2304, Resulting Numbers: [2304] 2304,47 unequal: No Solution Exploring Operation: 48-48=0, Resulting Numbers: [0] 0,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[69, 27], Operations: ['72-3=69', '48-21=27'] Exploring Operation: 69*27=1863, Resulting Numbers: [1863] 1863,47 unequal: No Solution Exploring Operation: 69+27=96, Resulting Numbers: [96] 96,47 unequal: No Solution Exploring Operation: 69-27=42, Resulting Numbers: [42] 42,47 unequal: No Solution Moving to Node #0,1,3 Current State: 47:[48, 90], Operations: ['72-3=69', '21+69=90'] Exploring Operation: 48*90=4320, Resulting Numbers: [4320] 4320,47 unequal: No Solution Exploring Operation: 48+90=138, Resulting Numbers: [138] 138,47 unequal: No Solution Exploring Operation: 90-48=42, Resulting Numbers: [42] 42,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[69, 69], Operations: ['72-3=69', '21+48=69'] Exploring Operation: 69/69=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 69+69=138, Resulting Numbers: [138] 138,47 unequal: No Solution Exploring Operation: 69*69=4761, Resulting Numbers: [4761] 4761,47 unequal: No Solution Exploring Operation: 69-69=0, Resulting Numbers: [0] 0,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 47:[3, 48, 51], Operations: ['72-21=51'] Exploring Operation: 3+48=51, Resulting Numbers: [51, 51] Generated Node #0,2,0: 47:[51, 51] Operation: 3+48=51 Exploring Operation: 51-3=48, Resulting Numbers: [48, 48] Generated Node #0,2,1: 47:[48, 48] Operation: 51-3=48 Exploring Operation: 3+51=54, Resulting Numbers: [48, 54] Generated Node #0,2,2: 47:[48, 54] Operation: 3+51=54 Exploring Operation: 48-3=45, Resulting Numbers: [51, 45] Generated Node #0,2,3: 47:[51, 45] Operation: 48-3=45 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 47:[48, 48], Operations: ['72-21=51', '51-3=48'] Exploring Operation: 48-48=0, Resulting Numbers: [0] 0,47 unequal: No Solution Exploring Operation: 48*48=2304, Resulting Numbers: [2304] 2304,47 unequal: No Solution Exploring Operation: 48/48=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 48+48=96, Resulting Numbers: [96] 96,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 47:[51, 45], Operations: ['72-21=51', '48-3=45'] Exploring Operation: 51-45=6, Resulting Numbers: [6] 6,47 unequal: No Solution Exploring Operation: 51*45=2295, Resulting Numbers: [2295] 2295,47 unequal: No Solution Exploring Operation: 51+45=96, Resulting Numbers: [96] 96,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 47:[51, 51], Operations: ['72-21=51', '3+48=51'] Exploring Operation: 51*51=2601, Resulting Numbers: [2601] 2601,47 unequal: No Solution Exploring Operation: 51+51=102, Resulting Numbers: [102] 102,47 unequal: No Solution Exploring Operation: 51-51=0, Resulting Numbers: [0] 0,47 unequal: No Solution Exploring Operation: 51/51=1, Resulting Numbers: [1] 1,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 47:[48, 54], Operations: ['72-21=51', '3+51=54'] Exploring Operation: 48*54=2592, Resulting Numbers: [2592] 2592,47 unequal: No Solution Exploring Operation: 54-48=6, Resulting Numbers: [6] 6,47 unequal: No Solution Exploring Operation: 48+54=102, Resulting Numbers: [102] 102,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 47:[72, 48, 24], Operations: ['3+21=24'] Exploring Operation: 48-24=24, Resulting Numbers: [72, 24] Generated Node #0,3,0: 47:[72, 24] Operation: 48-24=24 Exploring Operation: 72-24=48, Resulting Numbers: [48, 48] Generated Node #0,3,1: 47:[48, 48] Operation: 72-24=48 Exploring Operation: 72/24=3, Resulting Numbers: [48, 3] Generated Node #0,3,2: 47:[48, 3] Operation: 72/24=3 Exploring Operation: 72-48=24, Resulting Numbers: [24, 24] Generated Node #0,3,3: 47:[24, 24] Operation: 72-48=24 Moving to Node #0,3,1 Current State: 47:[48, 48], Operations: ['3+21=24', '72-24=48'] Exploring Operation: 48/48=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 48*48=2304, Resulting Numbers: [2304] 2304,47 unequal: No Solution Exploring Operation: 48+48=96, Resulting Numbers: [96] 96,47 unequal: No Solution Exploring Operation: 48-48=0, Resulting Numbers: [0] 0,47 unequal: No Solution Moving to Node #0,3,2 Current State: 47:[48, 3], Operations: ['3+21=24', '72/24=3'] Exploring Operation: 48*3=144, Resulting Numbers: [144] 144,47 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,47 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,47 unequal: No Solution Moving to Node #0,3,3 Current State: 47:[24, 24], Operations: ['3+21=24', '72-48=24'] Exploring Operation: 24*24=576, Resulting Numbers: [576] 576,47 unequal: No Solution Exploring Operation: 24-24=0, Resulting Numbers: [0] 0,47 unequal: No Solution Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,47 unequal: No Solution Moving to Node #0,3,0 Current State: 47:[72, 24], Operations: ['3+21=24', '48-24=24'] Exploring Operation: 72-24=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 72*24=1728, Resulting Numbers: [1728] 1728,47 unequal: No Solution Exploring Operation: 72/24=3, Resulting Numbers: [3] 3,47 unequal: No Solution Exploring Operation: 72+24=96, Resulting Numbers: [96] 96,47 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
[ 7, 38, 59, 66 ]
38
[ "7+38=45", "66-59=7", "45-7=38" ]
Current State: 38:[7, 38, 59, 66], Operations: [] Exploring Operation: 7+38=45, Resulting Numbers: [59, 66, 45] Generated Node #2: [59, 66, 45] from Operation: 7+38=45 Current State: 38:[59, 66, 45], Operations: ['7+38=45'] Exploring Operation: 66-59=7, Resulting Numbers: [45, 7] Generated Node #3: [45, 7] from Operation: 66-59=7 Current State: 38:[45, 7], Operations: ['7+38=45', '66-59=7'] Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[7, 38, 59, 66], Operations: [] Exploring Operation: 66-59=7, Resulting Numbers: [7, 38, 7] Generated Node #0,0: 38:[7, 38, 7] Operation: 66-59=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[7, 38, 7], Operations: ['66-59=7'] Exploring Operation: 7/7=1, Resulting Numbers: [38, 1] Generated Node #0,0,0: 38:[38, 1] Operation: 7/7=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 38:[38, 1], Operations: ['66-59=7', '7/7=1'] Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[7, 38, 59, 66], Operations: [] Exploring Operation: 66-59=7, Resulting Numbers: [7, 38, 7] Generated Node #0,0: 38:[7, 38, 7] Operation: 66-59=7 Moving to Node #0,0 Current State: 38:[7, 38, 7], Operations: ['66-59=7'] Exploring Operation: 7/7=1, Resulting Numbers: [38, 1] Generated Node #0,0,0: 38:[38, 1] Operation: 7/7=1 Moving to Node #0,0,0 Current State: 38:[38, 1], Operations: ['66-59=7', '7/7=1'] Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 21, 33, 13, 10 ]
57
[ "21+33=54", "13-10=3", "54+3=57" ]
Current State: 57:[21, 33, 13, 10], Operations: [] Exploring Operation: 21+33=54, Resulting Numbers: [13, 10, 54] Generated Node #2: [13, 10, 54] from Operation: 21+33=54 Current State: 57:[13, 10, 54], Operations: ['21+33=54'] Exploring Operation: 13-10=3, Resulting Numbers: [54, 3] Generated Node #3: [54, 3] from Operation: 13-10=3 Current State: 57:[54, 3], Operations: ['21+33=54', '13-10=3'] Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[21, 33, 13, 10], Operations: [] Exploring Operation: 13-10=3, Resulting Numbers: [21, 33, 3] Generated Node #0,0: 57:[21, 33, 3] Operation: 13-10=3 Exploring Operation: 33-21=12, Resulting Numbers: [13, 10, 12] Generated Node #0,1: 57:[13, 10, 12] Operation: 33-21=12 Exploring Operation: 33-13=20, Resulting Numbers: [21, 10, 20] Generated Node #0,2: 57:[21, 10, 20] Operation: 33-13=20 Exploring Operation: 33-10=23, Resulting Numbers: [21, 13, 23] Generated Node #0,3: 57:[21, 13, 23] Operation: 33-10=23 Exploring Operation: 21+33=54, Resulting Numbers: [13, 10, 54] Generated Node #0,4: 57:[13, 10, 54] Operation: 21+33=54 Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[21, 10, 20], Operations: ['33-13=20'] Exploring Operation: 20-10=10, Resulting Numbers: [21, 10] Generated Node #0,2,0: 57:[21, 10] Operation: 20-10=10 Exploring Operation: 21-10=11, Resulting Numbers: [20, 11] Generated Node #0,2,1: 57:[20, 11] Operation: 21-10=11 Exploring Operation: 21+10=31, Resulting Numbers: [20, 31] Generated Node #0,2,2: 57:[20, 31] Operation: 21+10=31 Exploring Operation: 21-20=1, Resulting Numbers: [10, 1] Generated Node #0,2,3: 57:[10, 1] Operation: 21-20=1 Exploring Operation: 20/10=2, Resulting Numbers: [21, 2] Generated Node #0,2,4: 57:[21, 2] Operation: 20/10=2 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 57:[21, 2], Operations: ['33-13=20', '20/10=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,57 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,57 unequal: No Solution No 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: 57:[21, 10], Operations: ['33-13=20', '20-10=10'] Exploring Operation: 21*10=210, Resulting Numbers: [210] 210,57 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,57 unequal: No Solution No 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: 57:[20, 11], Operations: ['33-13=20', '21-10=11'] Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,57 unequal: No Solution Exploring Operation: 20*11=220, Resulting Numbers: [220] 220,57 unequal: No Solution No 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: 57:[10, 1], Operations: ['33-13=20', '21-20=1'] Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,57 unequal: No Solution Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,57 unequal: No Solution No 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: 57:[20, 31], Operations: ['33-13=20', '21+10=31'] Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,57 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 20*31=620, Resulting Numbers: [620] 620,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 57:[21, 13, 23], Operations: ['33-10=23'] Exploring Operation: 21+13=34, Resulting Numbers: [23, 34] Generated Node #0,3,0: 57:[23, 34] Operation: 21+13=34 Exploring Operation: 23-13=10, Resulting Numbers: [21, 10] Generated Node #0,3,1: 57:[21, 10] Operation: 23-13=10 Exploring Operation: 21+23=44, Resulting Numbers: [13, 44] Generated Node #0,3,2: 57:[13, 44] Operation: 21+23=44 Exploring Operation: 21-13=8, Resulting Numbers: [23, 8] Generated Node #0,3,3: 57:[23, 8] Operation: 21-13=8 Exploring Operation: 23-21=2, Resulting Numbers: [13, 2] Generated Node #0,3,4: 57:[13, 2] Operation: 23-21=2 Moving to Node #0,3,4 Current State: 57:[13, 2], Operations: ['33-10=23', '23-21=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,57 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,57 unequal: No Solution Moving to Node #0,3,3 Current State: 57:[23, 8], Operations: ['33-10=23', '21-13=8'] Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,57 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,57 unequal: No Solution Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,57 unequal: No Solution Moving to Node #0,3,1 Current State: 57:[21, 10], Operations: ['33-10=23', '23-13=10'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 21*10=210, Resulting Numbers: [210] 210,57 unequal: No Solution Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,57 unequal: No Solution Moving to Node #0,3,0 Current State: 57:[23, 34], Operations: ['33-10=23', '21+13=34'] Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[21, 33, 13, 10], Operations: [] Exploring Operation: 33-10=23, Resulting Numbers: [21, 13, 23] Generated Node #0,3: 57:[21, 13, 23] Operation: 33-10=23 Moving to Node #0,3 Current State: 57:[21, 13, 23], Operations: ['33-10=23'] Exploring Operation: 21+13=34, Resulting Numbers: [23, 34] Generated Node #0,3,0: 57:[23, 34] Operation: 21+13=34 Moving to Node #0,3,0 Current State: 57:[23, 34], Operations: ['33-10=23', '21+13=34'] Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.960069
hs_5
sum_heuristic
[ 91, 3, 84, 63 ]
98
[ "91+63=154", "3*84=252", "252-154=98" ]
Current State: 98:[91, 3, 84, 63], Operations: [] Exploring Operation: 91+63=154, Resulting Numbers: [3, 84, 154] Generated Node #2: [3, 84, 154] from Operation: 91+63=154 Current State: 98:[3, 84, 154], Operations: ['91+63=154'] Exploring Operation: 3*84=252, Resulting Numbers: [154, 252] Generated Node #3: [154, 252] from Operation: 3*84=252 Current State: 98:[154, 252], Operations: ['91+63=154', '3*84=252'] Exploring Operation: 252-154=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[91, 3, 84, 63], Operations: [] Exploring Operation: 84-63=21, Resulting Numbers: [91, 3, 21] Generated Node #0,0: 98:[91, 3, 21] Operation: 84-63=21 Exploring Operation: 91-84=7, Resulting Numbers: [3, 63, 7] Generated Node #0,1: 98:[3, 63, 7] Operation: 91-84=7 Exploring Operation: 63/3=21, Resulting Numbers: [91, 84, 21] Generated Node #0,2: 98:[91, 84, 21] Operation: 63/3=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[91, 3, 21], Operations: ['84-63=21'] Exploring Operation: 91+3=94, Resulting Numbers: [21, 94] Generated Node #0,0,0: 98:[21, 94] Operation: 91+3=94 Exploring Operation: 21-3=18, Resulting Numbers: [91, 18] Generated Node #0,0,1: 98:[91, 18] Operation: 21-3=18 Exploring Operation: 21/3=7, Resulting Numbers: [91, 7] Generated Node #0,0,2: 98:[91, 7] Operation: 21/3=7 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 98:[91, 7], Operations: ['84-63=21', '21/3=7'] Exploring Operation: 91/7=13, Resulting Numbers: [13] 13,98 unequal: No Solution Exploring Operation: 91+7=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[91, 3, 84, 63], Operations: [] Exploring Operation: 84-63=21, Resulting Numbers: [91, 3, 21] Generated Node #0,0: 98:[91, 3, 21] Operation: 84-63=21 Moving to Node #0,0 Current State: 98:[91, 3, 21], Operations: ['84-63=21'] Exploring Operation: 21/3=7, Resulting Numbers: [91, 7] Generated Node #0,0,2: 98:[91, 7] Operation: 21/3=7 Moving to Node #0,0,2 Current State: 98:[91, 7], Operations: ['84-63=21', '21/3=7'] Exploring Operation: 91+7=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 4, 71, 97, 84 ]
88
[ "4+71=75", "97-84=13", "75+13=88" ]
Current State: 88:[4, 71, 97, 84], Operations: [] Exploring Operation: 4+71=75, Resulting Numbers: [97, 84, 75] Generated Node #2: [97, 84, 75] from Operation: 4+71=75 Current State: 88:[97, 84, 75], Operations: ['4+71=75'] Exploring Operation: 97-84=13, Resulting Numbers: [75, 13] Generated Node #3: [75, 13] from Operation: 97-84=13 Current State: 88:[75, 13], Operations: ['4+71=75', '97-84=13'] Exploring Operation: 75+13=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[4, 71, 97, 84], Operations: [] Exploring Operation: 97-71=26, Resulting Numbers: [4, 84, 26] Generated Node #0,0: 88:[4, 84, 26] Operation: 97-71=26 Exploring Operation: 84-71=13, Resulting Numbers: [4, 97, 13] Generated Node #0,1: 88:[4, 97, 13] Operation: 84-71=13 Moving to Node #0,0 Current State: 88:[4, 84, 26], Operations: ['97-71=26'] Exploring Operation: 4+84=88, Resulting Numbers: [26, 88] Generated Node #0,0,0: 88:[26, 88] Operation: 4+84=88 Exploring Operation: 26-4=22, Resulting Numbers: [84, 22] Generated Node #0,0,1: 88:[84, 22] Operation: 26-4=22 Moving to Node #0,1 Current State: 88:[4, 97, 13], Operations: ['84-71=13'] Exploring Operation: 97-4=93, Resulting Numbers: [13, 93] Generated Node #0,1,0: 88:[13, 93] Operation: 97-4=93 Exploring Operation: 97-13=84, Resulting Numbers: [4, 84] Generated Node #0,1,1: 88:[4, 84] Operation: 97-13=84 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 88:[4, 84], Operations: ['84-71=13', '97-13=84'] Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 4+84=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[4, 71, 97, 84], Operations: [] Exploring Operation: 84-71=13, Resulting Numbers: [4, 97, 13] Generated Node #0,1: 88:[4, 97, 13] Operation: 84-71=13 Moving to Node #0,1 Current State: 88:[4, 97, 13], Operations: ['84-71=13'] Exploring Operation: 97-13=84, Resulting Numbers: [4, 84] Generated Node #0,1,1: 88:[4, 84] Operation: 97-13=84 Moving to Node #0,1,1 Current State: 88:[4, 84], Operations: ['84-71=13', '97-13=84'] Exploring Operation: 4+84=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 52, 82, 3, 69 ]
42
[ "82-52=30", "3+69=72", "72-30=42" ]
Current State: 42:[52, 82, 3, 69], Operations: [] Exploring Operation: 82-52=30, Resulting Numbers: [3, 69, 30] Generated Node #2: [3, 69, 30] from Operation: 82-52=30 Current State: 42:[3, 69, 30], Operations: ['82-52=30'] Exploring Operation: 3+69=72, Resulting Numbers: [30, 72] Generated Node #3: [30, 72] from Operation: 3+69=72 Current State: 42:[30, 72], Operations: ['82-52=30', '3+69=72'] Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[52, 82, 3, 69], Operations: [] Exploring Operation: 82-69=13, Resulting Numbers: [52, 3, 13] Generated Node #0,0: 42:[52, 3, 13] Operation: 82-69=13 Exploring Operation: 82-52=30, Resulting Numbers: [3, 69, 30] Generated Node #0,1: 42:[3, 69, 30] Operation: 82-52=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[52, 3, 13], Operations: ['82-69=13'] Exploring Operation: 52/13=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 42:[3, 4] Operation: 52/13=4 Exploring Operation: 52-13=39, Resulting Numbers: [3, 39] Generated Node #0,0,1: 42:[3, 39] Operation: 52-13=39 Moving to Node #0,0,0 Current State: 42:[3, 4], Operations: ['82-69=13', '52/13=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,42 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[3, 39], Operations: ['82-69=13', '52-13=39'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[52, 82, 3, 69], Operations: [] Exploring Operation: 82-69=13, Resulting Numbers: [52, 3, 13] Generated Node #0,0: 42:[52, 3, 13] Operation: 82-69=13 Moving to Node #0,0 Current State: 42:[52, 3, 13], Operations: ['82-69=13'] Exploring Operation: 52-13=39, Resulting Numbers: [3, 39] Generated Node #0,0,1: 42:[3, 39] Operation: 52-13=39 Moving to Node #0,0,1 Current State: 42:[3, 39], Operations: ['82-69=13', '52-13=39'] Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 43, 34, 2, 1 ]
77
[ "43+34=77", "2-1=1", "77*1=77" ]
Current State: 77:[43, 34, 2, 1], Operations: [] Exploring Operation: 43+34=77, Resulting Numbers: [2, 1, 77] Generated Node #2: [2, 1, 77] from Operation: 43+34=77 Current State: 77:[2, 1, 77], Operations: ['43+34=77'] Exploring Operation: 2-1=1, Resulting Numbers: [77, 1] Generated Node #3: [77, 1] from Operation: 2-1=1 Current State: 77:[77, 1], Operations: ['43+34=77', '2-1=1'] Exploring Operation: 77*1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[43, 34, 2, 1], Operations: [] Exploring Operation: 43+34=77, Resulting Numbers: [2, 1, 77] Generated Node #0,0: 77:[2, 1, 77] Operation: 43+34=77 Exploring Operation: 43-34=9, Resulting Numbers: [2, 1, 9] Generated Node #0,1: 77:[2, 1, 9] Operation: 43-34=9 Moving to Node #0,0 Current State: 77:[2, 1, 77], Operations: ['43+34=77'] Exploring Operation: 2*1=2, Resulting Numbers: [77, 2] Generated Node #0,0,0: 77:[77, 2] Operation: 2*1=2 Exploring Operation: 2+1=3, Resulting Numbers: [77, 3] Generated Node #0,0,1: 77:[77, 3] Operation: 2+1=3 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[77, 3], Operations: ['43+34=77', '2+1=3'] Exploring Operation: 77+3=80, Resulting Numbers: [80] 80,77 unequal: No Solution Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[77, 2], Operations: ['43+34=77', '2*1=2'] Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,77 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,77 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: 77:[2, 1, 9], Operations: ['43-34=9'] Exploring Operation: 2+1=3, Resulting Numbers: [9, 3] Generated Node #0,1,0: 77:[9, 3] Operation: 2+1=3 Exploring Operation: 2+9=11, Resulting Numbers: [1, 11] Generated Node #0,1,1: 77:[1, 11] Operation: 2+9=11 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 77:[9, 3], Operations: ['43-34=9', '2+1=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,77 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 77:[1, 11], Operations: ['43-34=9', '2+9=11'] Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,77 unequal: No Solution Exploring Operation: 1*11=11, Resulting Numbers: [11] 11,77 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
[ 3, 28, 81, 94 ]
94
[ "81/3=27", "28-27=1", "94*1=94" ]
Current State: 94:[3, 28, 81, 94], Operations: [] Exploring Operation: 81/3=27, Resulting Numbers: [28, 94, 27] Generated Node #2: [28, 94, 27] from Operation: 81/3=27 Current State: 94:[28, 94, 27], Operations: ['81/3=27'] Exploring Operation: 28-27=1, Resulting Numbers: [94, 1] Generated Node #3: [94, 1] from Operation: 28-27=1 Current State: 94:[94, 1], Operations: ['81/3=27', '28-27=1'] Exploring Operation: 94*1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[3, 28, 81, 94], Operations: [] Exploring Operation: 3+81=84, Resulting Numbers: [28, 94, 84] Generated Node #0,0: 94:[28, 94, 84] Operation: 3+81=84 Exploring Operation: 81-28=53, Resulting Numbers: [3, 94, 53] Generated Node #0,1: 94:[3, 94, 53] Operation: 81-28=53 Exploring Operation: 3+28=31, Resulting Numbers: [81, 94, 31] Generated Node #0,2: 94:[81, 94, 31] Operation: 3+28=31 Exploring Operation: 3*28=84, Resulting Numbers: [81, 94, 84] Generated Node #0,3: 94:[81, 94, 84] Operation: 3*28=84 Exploring Operation: 28+81=109, Resulting Numbers: [3, 94, 109] Generated Node #0,4: 94:[3, 94, 109] Operation: 28+81=109 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[3, 94, 53], Operations: ['81-28=53'] Exploring Operation: 94-53=41, Resulting Numbers: [3, 41] Generated Node #0,1,0: 94:[3, 41] Operation: 94-53=41 Exploring Operation: 53-3=50, Resulting Numbers: [94, 50] Generated Node #0,1,1: 94:[94, 50] Operation: 53-3=50 Exploring Operation: 94-3=91, Resulting Numbers: [53, 91] Generated Node #0,1,2: 94:[53, 91] Operation: 94-3=91 Exploring Operation: 3+94=97, Resulting Numbers: [53, 97] Generated Node #0,1,3: 94:[53, 97] Operation: 3+94=97 Exploring Operation: 3+53=56, Resulting Numbers: [94, 56] Generated Node #0,1,4: 94:[94, 56] Operation: 3+53=56 Moving to Node #0,1,1 Current State: 94:[94, 50], Operations: ['81-28=53', '53-3=50'] Exploring Operation: 94-50=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 94+50=144, Resulting Numbers: [144] 144,94 unequal: No Solution Exploring Operation: 94*50=4700, Resulting Numbers: [4700] 4700,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[3, 41], Operations: ['81-28=53', '94-53=41'] Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,94 unequal: No Solution Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[53, 91], Operations: ['81-28=53', '94-3=91'] Exploring Operation: 53+91=144, Resulting Numbers: [144] 144,94 unequal: No Solution Exploring Operation: 91-53=38, Resulting Numbers: [38] 38,94 unequal: No Solution Exploring Operation: 53*91=4823, Resulting Numbers: [4823] 4823,94 unequal: No Solution Moving to Node #0,1,3 Current State: 94:[53, 97], Operations: ['81-28=53', '3+94=97'] Exploring Operation: 53*97=5141, Resulting Numbers: [5141] 5141,94 unequal: No Solution Exploring Operation: 53+97=150, Resulting Numbers: [150] 150,94 unequal: No Solution Exploring Operation: 97-53=44, Resulting Numbers: [44] 44,94 unequal: No Solution Moving to Node #0,1,4 Current State: 94:[94, 56], Operations: ['81-28=53', '3+53=56'] Exploring Operation: 94*56=5264, Resulting Numbers: [5264] 5264,94 unequal: No Solution Exploring Operation: 94+56=150, Resulting Numbers: [150] 150,94 unequal: No Solution Exploring Operation: 94-56=38, Resulting Numbers: [38] 38,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 94:[3, 94, 109], Operations: ['28+81=109'] Exploring Operation: 3+109=112, Resulting Numbers: [94, 112] Generated Node #0,4,0: 94:[94, 112] Operation: 3+109=112 Exploring Operation: 94-3=91, Resulting Numbers: [109, 91] Generated Node #0,4,1: 94:[109, 91] Operation: 94-3=91 Exploring Operation: 109-94=15, Resulting Numbers: [3, 15] Generated Node #0,4,2: 94:[3, 15] Operation: 109-94=15 Exploring Operation: 3+94=97, Resulting Numbers: [109, 97] Generated Node #0,4,3: 94:[109, 97] Operation: 3+94=97 Exploring Operation: 109-3=106, Resulting Numbers: [94, 106] Generated Node #0,4,4: 94:[94, 106] Operation: 109-3=106 Moving to Node #0,4,4 Current State: 94:[94, 106], Operations: ['28+81=109', '109-3=106'] Exploring Operation: 94+106=200, Resulting Numbers: [200] 200,94 unequal: No Solution Exploring Operation: 106-94=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 94*106=9964, Resulting Numbers: [9964] 9964,94 unequal: No Solution Moving to Node #0,4,2 Current State: 94:[3, 15], Operations: ['28+81=109', '109-94=15'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,94 unequal: No Solution Moving to Node #0,4,0 Current State: 94:[94, 112], Operations: ['28+81=109', '3+109=112'] Exploring Operation: 94+112=206, Resulting Numbers: [206] 206,94 unequal: No Solution Exploring Operation: 94*112=10528, Resulting Numbers: [10528] 10528,94 unequal: No Solution Exploring Operation: 112-94=18, Resulting Numbers: [18] 18,94 unequal: No Solution Moving to Node #0,4,1 Current State: 94:[109, 91], Operations: ['28+81=109', '94-3=91'] Exploring Operation: 109-91=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 109+91=200, Resulting Numbers: [200] 200,94 unequal: No Solution Exploring Operation: 109*91=9919, Resulting Numbers: [9919] 9919,94 unequal: No Solution Moving to Node #0,4,3 Current State: 94:[109, 97], Operations: ['28+81=109', '3+94=97'] Exploring Operation: 109+97=206, Resulting Numbers: [206] 206,94 unequal: No Solution Exploring Operation: 109-97=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 109*97=10573, Resulting Numbers: [10573] 10573,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[81, 94, 84], Operations: ['3*28=84'] Exploring Operation: 81+84=165, Resulting Numbers: [94, 165] Generated Node #0,3,0: 94:[94, 165] Operation: 81+84=165 Exploring Operation: 94-84=10, Resulting Numbers: [81, 10] Generated Node #0,3,1: 94:[81, 10] Operation: 94-84=10 Exploring Operation: 84-81=3, Resulting Numbers: [94, 3] Generated Node #0,3,2: 94:[94, 3] Operation: 84-81=3 Exploring Operation: 81+94=175, Resulting Numbers: [84, 175] Generated Node #0,3,3: 94:[84, 175] Operation: 81+94=175 Exploring Operation: 94-81=13, Resulting Numbers: [84, 13] Generated Node #0,3,4: 94:[84, 13] Operation: 94-81=13 Moving to Node #0,3,2 Current State: 94:[94, 3], Operations: ['3*28=84', '84-81=3'] Exploring Operation: 94+3=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 94*3=282, Resulting Numbers: [282] 282,94 unequal: No Solution Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,94 unequal: No Solution Moving to Node #0,3,4 Current State: 94:[84, 13], Operations: ['3*28=84', '94-81=13'] Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,94 unequal: No Solution Exploring Operation: 84*13=1092, Resulting Numbers: [1092] 1092,94 unequal: No Solution Exploring Operation: 84+13=97, Resulting Numbers: [97] 97,94 unequal: No Solution Moving to Node #0,3,1 Current State: 94:[81, 10], Operations: ['3*28=84', '94-84=10'] Exploring Operation: 81*10=810, Resulting Numbers: [810] 810,94 unequal: No Solution Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,94 unequal: No Solution Exploring Operation: 81+10=91, Resulting Numbers: [91] 91,94 unequal: No Solution Moving to Node #0,3,0 Current State: 94:[94, 165], Operations: ['3*28=84', '81+84=165'] Exploring Operation: 94+165=259, Resulting Numbers: [259] 259,94 unequal: No Solution Exploring Operation: 165-94=71, Resulting Numbers: [71] 71,94 unequal: No Solution Exploring Operation: 94*165=15510, Resulting Numbers: [15510] 15510,94 unequal: No Solution Moving to Node #0,3,3 Current State: 94:[84, 175], Operations: ['3*28=84', '81+94=175'] Exploring Operation: 84+175=259, Resulting Numbers: [259] 259,94 unequal: No Solution Exploring Operation: 175-84=91, Resulting Numbers: [91] 91,94 unequal: No Solution Exploring Operation: 84*175=14700, Resulting Numbers: [14700] 14700,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[28, 94, 84], Operations: ['3+81=84'] Exploring Operation: 84-28=56, Resulting Numbers: [94, 56] Generated Node #0,0,0: 94:[94, 56] Operation: 84-28=56 Exploring Operation: 28+84=112, Resulting Numbers: [94, 112] Generated Node #0,0,1: 94:[94, 112] Operation: 28+84=112 Exploring Operation: 84/28=3, Resulting Numbers: [94, 3] Generated Node #0,0,2: 94:[94, 3] Operation: 84/28=3 Exploring Operation: 94-84=10, Resulting Numbers: [28, 10] Generated Node #0,0,3: 94:[28, 10] Operation: 94-84=10 Exploring Operation: 94-28=66, Resulting Numbers: [84, 66] Generated Node #0,0,4: 94:[84, 66] Operation: 94-28=66 Moving to Node #0,0,2 Current State: 94:[94, 3], Operations: ['3+81=84', '84/28=3'] Exploring Operation: 94*3=282, Resulting Numbers: [282] 282,94 unequal: No Solution Exploring Operation: 94+3=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[94, 56], Operations: ['3+81=84', '84-28=56'] Exploring Operation: 94+56=150, Resulting Numbers: [150] 150,94 unequal: No Solution Exploring Operation: 94*56=5264, Resulting Numbers: [5264] 5264,94 unequal: No Solution Exploring Operation: 94-56=38, Resulting Numbers: [38] 38,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[94, 112], Operations: ['3+81=84', '28+84=112'] Exploring Operation: 94*112=10528, Resulting Numbers: [10528] 10528,94 unequal: No Solution Exploring Operation: 112-94=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 94+112=206, Resulting Numbers: [206] 206,94 unequal: No Solution Moving to Node #0,0,3 Current State: 94:[28, 10], Operations: ['3+81=84', '94-84=10'] Exploring Operation: 28+10=38, Resulting Numbers: [38] 38,94 unequal: No Solution Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 28*10=280, Resulting Numbers: [280] 280,94 unequal: No Solution Moving to Node #0,0,4 Current State: 94:[84, 66], Operations: ['3+81=84', '94-28=66'] Exploring Operation: 84+66=150, Resulting Numbers: [150] 150,94 unequal: No Solution Exploring Operation: 84*66=5544, Resulting Numbers: [5544] 5544,94 unequal: No Solution Exploring Operation: 84-66=18, Resulting Numbers: [18] 18,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[81, 94, 31], Operations: ['3+28=31'] Exploring Operation: 81+31=112, Resulting Numbers: [94, 112] Generated Node #0,2,0: 94:[94, 112] Operation: 81+31=112 Exploring Operation: 94-31=63, Resulting Numbers: [81, 63] Generated Node #0,2,1: 94:[81, 63] Operation: 94-31=63 Exploring Operation: 94-81=13, Resulting Numbers: [31, 13] Generated Node #0,2,2: 94:[31, 13] Operation: 94-81=13 Exploring Operation: 81-31=50, Resulting Numbers: [94, 50] Generated Node #0,2,3: 94:[94, 50] Operation: 81-31=50 Exploring Operation: 94+31=125, Resulting Numbers: [81, 125] Generated Node #0,2,4: 94:[81, 125] Operation: 94+31=125 Moving to Node #0,2,3 Current State: 94:[94, 50], Operations: ['3+28=31', '81-31=50'] Exploring Operation: 94*50=4700, Resulting Numbers: [4700] 4700,94 unequal: No Solution Exploring Operation: 94+50=144, Resulting Numbers: [144] 144,94 unequal: No Solution Exploring Operation: 94-50=44, Resulting Numbers: [44] 44,94 unequal: No Solution Moving to Node #0,2,0 Current State: 94:[94, 112], Operations: ['3+28=31', '81+31=112'] Exploring Operation: 94*112=10528, Resulting Numbers: [10528] 10528,94 unequal: No Solution Exploring Operation: 112-94=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 94+112=206, Resulting Numbers: [206] 206,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[31, 13], Operations: ['3+28=31', '94-81=13'] Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 31*13=403, Resulting Numbers: [403] 403,94 unequal: No Solution Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,94 unequal: No Solution Moving to Node #0,2,1 Current State: 94:[81, 63], Operations: ['3+28=31', '94-31=63'] Exploring Operation: 81+63=144, Resulting Numbers: [144] 144,94 unequal: No Solution Exploring Operation: 81-63=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 81*63=5103, Resulting Numbers: [5103] 5103,94 unequal: No Solution Moving to Node #0,2,4 Current State: 94:[81, 125], Operations: ['3+28=31', '94+31=125'] Exploring Operation: 125-81=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 81*125=10125, Resulting Numbers: [10125] 10125,94 unequal: No Solution Exploring Operation: 81+125=206, Resulting Numbers: [206] 206,94 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
[ 5, 71, 3, 89 ]
93
[ "89-71=18", "5*18=90", "3+90=93" ]
Current State: 93:[5, 71, 3, 89], Operations: [] Exploring Operation: 89-71=18, Resulting Numbers: [5, 3, 18] Generated Node #2: [5, 3, 18] from Operation: 89-71=18 Current State: 93:[5, 3, 18], Operations: ['89-71=18'] Exploring Operation: 5*18=90, Resulting Numbers: [3, 90] Generated Node #3: [3, 90] from Operation: 5*18=90 Current State: 93:[3, 90], Operations: ['89-71=18', '5*18=90'] Exploring Operation: 3+90=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[5, 71, 3, 89], Operations: [] Exploring Operation: 5+71=76, Resulting Numbers: [3, 89, 76] Generated Node #0,0: 93:[3, 89, 76] Operation: 5+71=76 Exploring Operation: 89-71=18, Resulting Numbers: [5, 3, 18] Generated Node #0,1: 93:[5, 3, 18] Operation: 89-71=18 Moving to Node #0,1 Current State: 93:[5, 3, 18], Operations: ['89-71=18'] Exploring Operation: 18/3=6, Resulting Numbers: [5, 6] Generated Node #0,1,0: 93:[5, 6] Operation: 18/3=6 Exploring Operation: 5*18=90, Resulting Numbers: [3, 90] Generated Node #0,1,1: 93:[3, 90] Operation: 5*18=90 Moving to Node #0,0 Current State: 93:[3, 89, 76], Operations: ['5+71=76'] Exploring Operation: 3+89=92, Resulting Numbers: [76, 92] Generated Node #0,0,0: 93:[76, 92] Operation: 3+89=92 Exploring Operation: 89-76=13, Resulting Numbers: [3, 13] Generated Node #0,0,1: 93:[3, 13] Operation: 89-76=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 93:[3, 13], Operations: ['5+71=76', '89-76=13'] Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,93 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,93 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 #0,0,0 Current State: 93:[76, 92], Operations: ['5+71=76', '3+89=92'] Exploring Operation: 92-76=16, Resulting Numbers: [16] 16,93 unequal: No Solution Exploring Operation: 76+92=168, Resulting Numbers: [168] 168,93 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: 93:[3, 90], Operations: ['89-71=18', '5*18=90'] Exploring Operation: 90/3=30, Resulting Numbers: [30] 30,93 unequal: No Solution Exploring Operation: 3+90=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[5, 71, 3, 89], Operations: [] Exploring Operation: 89-71=18, Resulting Numbers: [5, 3, 18] Generated Node #0,1: 93:[5, 3, 18] Operation: 89-71=18 Moving to Node #0,1 Current State: 93:[5, 3, 18], Operations: ['89-71=18'] Exploring Operation: 5*18=90, Resulting Numbers: [3, 90] Generated Node #0,1,1: 93:[3, 90] Operation: 5*18=90 Moving to Node #0,1,1 Current State: 93:[3, 90], Operations: ['89-71=18', '5*18=90'] Exploring Operation: 3+90=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 20, 51, 20, 46 ]
57
[ "51-20=31", "46-20=26", "31+26=57" ]
Current State: 57:[20, 51, 20, 46], Operations: [] Exploring Operation: 51-20=31, Resulting Numbers: [46, 31] Generated Node #2: [46, 31] from Operation: 51-20=31 Current State: 57:[46, 31], Operations: ['51-20=31'] Exploring Operation: 46-20=26, Resulting Numbers: [31, 26] Generated Node #3: [31, 26] from Operation: 46-20=26 Current State: 57:[31, 26], Operations: ['51-20=31', '46-20=26'] Exploring Operation: 31+26=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[20, 51, 20, 46], Operations: [] Exploring Operation: 46-20=26, Resulting Numbers: [51, 20, 26] Generated Node #0,0: 57:[51, 20, 26] Operation: 46-20=26 Exploring Operation: 51-46=5, Resulting Numbers: [20, 20, 5] Generated Node #0,1: 57:[20, 20, 5] Operation: 51-46=5 Moving to Node #0,1 Current State: 57:[20, 20, 5], Operations: ['51-46=5'] Exploring Operation: 20/5=4, Resulting Numbers: [20, 4] Generated Node #0,1,0: 57:[20, 4] Operation: 20/5=4 Exploring Operation: 20/5=4, Resulting Numbers: [20, 4] Generated Node #0,1,1: 57:[20, 4] Operation: 20/5=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[20, 4], Operations: ['51-46=5', '20/5=4'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,57 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 57:[20, 4], Operations: ['51-46=5', '20/5=4'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,57 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,57 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: 57:[51, 20, 26], Operations: ['46-20=26'] Exploring Operation: 26-20=6, Resulting Numbers: [51, 6] Generated Node #0,0,0: 57:[51, 6] Operation: 26-20=6 Exploring Operation: 51-26=25, Resulting Numbers: [20, 25] Generated Node #0,0,1: 57:[20, 25] Operation: 51-26=25 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 57:[20, 25], Operations: ['46-20=26', '51-26=25'] Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,57 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[51, 6], Operations: ['46-20=26', '26-20=6'] Exploring Operation: 51+6=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[20, 51, 20, 46], Operations: [] Exploring Operation: 46-20=26, Resulting Numbers: [51, 20, 26] Generated Node #0,0: 57:[51, 20, 26] Operation: 46-20=26 Moving to Node #0,0 Current State: 57:[51, 20, 26], Operations: ['46-20=26'] Exploring Operation: 26-20=6, Resulting Numbers: [51, 6] Generated Node #0,0,0: 57:[51, 6] Operation: 26-20=6 Moving to Node #0,0,0 Current State: 57:[51, 6], Operations: ['46-20=26', '26-20=6'] Exploring Operation: 51+6=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_2
mult_heuristic
[ 14, 42, 52, 88 ]
32
[ "52+88=140", "140/14=10", "42-10=32" ]
Current State: 32:[14, 42, 52, 88], Operations: [] Exploring Operation: 52+88=140, Resulting Numbers: [14, 42, 140] Generated Node #2: [14, 42, 140] from Operation: 52+88=140 Current State: 32:[14, 42, 140], Operations: ['52+88=140'] Exploring Operation: 140/14=10, Resulting Numbers: [42, 10] Generated Node #3: [42, 10] from Operation: 140/14=10 Current State: 32:[42, 10], Operations: ['52+88=140', '140/14=10'] Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[14, 42, 52, 88], Operations: [] Exploring Operation: 88-42=46, Resulting Numbers: [14, 52, 46] Generated Node #0,0: 32:[14, 52, 46] Operation: 88-42=46 Exploring Operation: 88-52=36, Resulting Numbers: [14, 42, 36] Generated Node #0,1: 32:[14, 42, 36] Operation: 88-52=36 Moving to Node #0,1 Current State: 32:[14, 42, 36], Operations: ['88-52=36'] Exploring Operation: 42/14=3, Resulting Numbers: [36, 3] Generated Node #0,1,0: 32:[36, 3] Operation: 42/14=3 Exploring Operation: 42-36=6, Resulting Numbers: [14, 6] Generated Node #0,1,1: 32:[14, 6] Operation: 42-36=6 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[14, 6], Operations: ['88-52=36', '42-36=6'] Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,32 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,32 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:[36, 3], Operations: ['88-52=36', '42/14=3'] Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,32 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,32 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: 32:[14, 52, 46], Operations: ['88-42=46'] Exploring Operation: 52-14=38, Resulting Numbers: [46, 38] Generated Node #0,0,0: 32:[46, 38] Operation: 52-14=38 Exploring Operation: 52-46=6, Resulting Numbers: [14, 6] Generated Node #0,0,1: 32:[14, 6] Operation: 52-46=6 Moving to Node #0,0,1 Current State: 32:[14, 6], Operations: ['88-42=46', '52-46=6'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,32 unequal: No Solution Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,32 unequal: No Solution Moving to Node #0,0,0 Current State: 32:[46, 38], Operations: ['88-42=46', '52-14=38'] Exploring Operation: 46-38=8, Resulting Numbers: [8] 8,32 unequal: No Solution Exploring Operation: 46+38=84, Resulting Numbers: [84] 84,32 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 62, 5, 88, 63 ]
92
[ "62+5=67", "88-63=25", "67+25=92" ]
Current State: 92:[62, 5, 88, 63], Operations: [] Exploring Operation: 62+5=67, Resulting Numbers: [88, 63, 67] Generated Node #2: [88, 63, 67] from Operation: 62+5=67 Current State: 92:[88, 63, 67], Operations: ['62+5=67'] Exploring Operation: 88-63=25, Resulting Numbers: [67, 25] Generated Node #3: [67, 25] from Operation: 88-63=25 Current State: 92:[67, 25], Operations: ['62+5=67', '88-63=25'] Exploring Operation: 67+25=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[62, 5, 88, 63], Operations: [] Exploring Operation: 63-62=1, Resulting Numbers: [5, 88, 1] Generated Node #0,0: 92:[5, 88, 1] Operation: 63-62=1 Exploring Operation: 88-63=25, Resulting Numbers: [62, 5, 25] Generated Node #0,1: 92:[62, 5, 25] Operation: 88-63=25 Moving to Node #0,0 Current State: 92:[5, 88, 1], Operations: ['63-62=1'] Exploring Operation: 5-1=4, Resulting Numbers: [88, 4] Generated Node #0,0,0: 92:[88, 4] Operation: 5-1=4 Exploring Operation: 5+88=93, Resulting Numbers: [1, 93] Generated Node #0,0,1: 92:[1, 93] Operation: 5+88=93 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[1, 93], Operations: ['63-62=1', '5+88=93'] Exploring Operation: 1*93=93, Resulting Numbers: [93] 93,92 unequal: No Solution Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[62, 5, 88, 63], Operations: [] Exploring Operation: 63-62=1, Resulting Numbers: [5, 88, 1] Generated Node #0,0: 92:[5, 88, 1] Operation: 63-62=1 Moving to Node #0,0 Current State: 92:[5, 88, 1], Operations: ['63-62=1'] Exploring Operation: 5+88=93, Resulting Numbers: [1, 93] Generated Node #0,0,1: 92:[1, 93] Operation: 5+88=93 Moving to Node #0,0,1 Current State: 92:[1, 93], Operations: ['63-62=1', '5+88=93'] Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 19, 22, 35, 52 ]
55
[ "22+35=57", "57/19=3", "52+3=55" ]
Current State: 55:[19, 22, 35, 52], Operations: [] Exploring Operation: 22+35=57, Resulting Numbers: [19, 52, 57] Generated Node #2: [19, 52, 57] from Operation: 22+35=57 Current State: 55:[19, 52, 57], Operations: ['22+35=57'] Exploring Operation: 57/19=3, Resulting Numbers: [52, 3] Generated Node #3: [52, 3] from Operation: 57/19=3 Current State: 55:[52, 3], Operations: ['22+35=57', '57/19=3'] Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[19, 22, 35, 52], Operations: [] Exploring Operation: 22+35=57, Resulting Numbers: [19, 52, 57] Generated Node #0,0: 55:[19, 52, 57] Operation: 22+35=57 Exploring Operation: 35-22=13, Resulting Numbers: [19, 52, 13] Generated Node #0,1: 55:[19, 52, 13] Operation: 35-22=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[19, 52, 57], Operations: ['22+35=57'] Exploring Operation: 57/19=3, Resulting Numbers: [52, 3] Generated Node #0,0,0: 55:[52, 3] Operation: 57/19=3 Exploring Operation: 57-52=5, Resulting Numbers: [19, 5] Generated Node #0,0,1: 55:[19, 5] Operation: 57-52=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[52, 3], Operations: ['22+35=57', '57/19=3'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,55 unequal: No Solution Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[19, 22, 35, 52], Operations: [] Exploring Operation: 22+35=57, Resulting Numbers: [19, 52, 57] Generated Node #0,0: 55:[19, 52, 57] Operation: 22+35=57 Moving to Node #0,0 Current State: 55:[19, 52, 57], Operations: ['22+35=57'] Exploring Operation: 57/19=3, Resulting Numbers: [52, 3] Generated Node #0,0,0: 55:[52, 3] Operation: 57/19=3 Moving to Node #0,0,0 Current State: 55:[52, 3], Operations: ['22+35=57', '57/19=3'] Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 78, 27, 76, 31 ]
23
[ "78-76=2", "27*2=54", "54-31=23" ]
Current State: 23:[78, 27, 76, 31], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [27, 31, 2] Generated Node #2: [27, 31, 2] from Operation: 78-76=2 Current State: 23:[27, 31, 2], Operations: ['78-76=2'] Exploring Operation: 27*2=54, Resulting Numbers: [31, 54] Generated Node #3: [31, 54] from Operation: 27*2=54 Current State: 23:[31, 54], Operations: ['78-76=2', '27*2=54'] Exploring Operation: 54-31=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[78, 27, 76, 31], Operations: [] Exploring Operation: 78-31=47, Resulting Numbers: [27, 76, 47] Generated Node #0,0: 23:[27, 76, 47] Operation: 78-31=47 Exploring Operation: 78-27=51, Resulting Numbers: [76, 31, 51] Generated Node #0,1: 23:[76, 31, 51] Operation: 78-27=51 Exploring Operation: 76-31=45, Resulting Numbers: [78, 27, 45] Generated Node #0,2: 23:[78, 27, 45] Operation: 76-31=45 Exploring Operation: 76-27=49, Resulting Numbers: [78, 31, 49] Generated Node #0,3: 23:[78, 31, 49] Operation: 76-27=49 Exploring Operation: 78-76=2, Resulting Numbers: [27, 31, 2] Generated Node #0,4: 23:[27, 31, 2] Operation: 78-76=2 Start Sub Search at level 1: Moving to Node #0,4 Current State: 23:[27, 31, 2], Operations: ['78-76=2'] Exploring Operation: 31-2=29, Resulting Numbers: [27, 29] Generated Node #0,4,0: 23:[27, 29] Operation: 31-2=29 Exploring Operation: 27-2=25, Resulting Numbers: [31, 25] Generated Node #0,4,1: 23:[31, 25] Operation: 27-2=25 Exploring Operation: 27*2=54, Resulting Numbers: [31, 54] Generated Node #0,4,2: 23:[31, 54] Operation: 27*2=54 Exploring Operation: 31+2=33, Resulting Numbers: [27, 33] Generated Node #0,4,3: 23:[27, 33] Operation: 31+2=33 Exploring Operation: 27+2=29, Resulting Numbers: [31, 29] Generated Node #0,4,4: 23:[31, 29] Operation: 27+2=29 Moving to Node #0,4,0 Current State: 23:[27, 29], Operations: ['78-76=2', '31-2=29'] Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,23 unequal: No Solution Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,23 unequal: No Solution Moving to Node #0,4,1 Current State: 23:[31, 25], Operations: ['78-76=2', '27-2=25'] Exploring Operation: 31*25=775, Resulting Numbers: [775] 775,23 unequal: No Solution Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 31+25=56, Resulting Numbers: [56] 56,23 unequal: No Solution Moving to Node #0,4,3 Current State: 23:[27, 33], Operations: ['78-76=2', '31+2=33'] Exploring Operation: 27+33=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 27*33=891, Resulting Numbers: [891] 891,23 unequal: No Solution Moving to Node #0,4,4 Current State: 23:[31, 29], Operations: ['78-76=2', '27+2=29'] Exploring Operation: 31*29=899, Resulting Numbers: [899] 899,23 unequal: No Solution Exploring Operation: 31+29=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 31-29=2, Resulting Numbers: [2] 2,23 unequal: No Solution Moving to Node #0,4,2 Current State: 23:[31, 54], Operations: ['78-76=2', '27*2=54'] Exploring Operation: 54-31=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[78, 27, 76, 31], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [27, 31, 2] Generated Node #0,4: 23:[27, 31, 2] Operation: 78-76=2 Moving to Node #0,4 Current State: 23:[27, 31, 2], Operations: ['78-76=2'] Exploring Operation: 27*2=54, Resulting Numbers: [31, 54] Generated Node #0,4,2: 23:[31, 54] Operation: 27*2=54 Moving to Node #0,4,2 Current State: 23:[31, 54], Operations: ['78-76=2', '27*2=54'] Exploring Operation: 54-31=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_5
sum_heuristic
[ 26, 6, 15, 45 ]
21
[ "26-15=11", "6*11=66", "66-45=21" ]
Current State: 21:[26, 6, 15, 45], Operations: [] Exploring Operation: 26-15=11, Resulting Numbers: [6, 45, 11] Generated Node #2: [6, 45, 11] from Operation: 26-15=11 Current State: 21:[6, 45, 11], Operations: ['26-15=11'] Exploring Operation: 6*11=66, Resulting Numbers: [45, 66] Generated Node #3: [45, 66] from Operation: 6*11=66 Current State: 21:[45, 66], Operations: ['26-15=11', '6*11=66'] Exploring Operation: 66-45=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[26, 6, 15, 45], Operations: [] Exploring Operation: 26-15=11, Resulting Numbers: [6, 45, 11] Generated Node #0,0: 21:[6, 45, 11] Operation: 26-15=11 Exploring Operation: 45-15=30, Resulting Numbers: [26, 6, 30] Generated Node #0,1: 21:[26, 6, 30] Operation: 45-15=30 Exploring Operation: 45/15=3, Resulting Numbers: [26, 6, 3] Generated Node #0,2: 21:[26, 6, 3] Operation: 45/15=3 Exploring Operation: 6+15=21, Resulting Numbers: [26, 45, 21] Generated Node #0,3: 21:[26, 45, 21] Operation: 6+15=21 Exploring Operation: 45-26=19, Resulting Numbers: [6, 15, 19] Generated Node #0,4: 21:[6, 15, 19] Operation: 45-26=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[26, 6, 3], Operations: ['45/15=3'] Exploring Operation: 6+3=9, Resulting Numbers: [26, 9] Generated Node #0,2,0: 21:[26, 9] Operation: 6+3=9 Exploring Operation: 26-3=23, Resulting Numbers: [6, 23] Generated Node #0,2,1: 21:[6, 23] Operation: 26-3=23 Exploring Operation: 6-3=3, Resulting Numbers: [26, 3] Generated Node #0,2,2: 21:[26, 3] Operation: 6-3=3 Exploring Operation: 26-6=20, Resulting Numbers: [3, 20] Generated Node #0,2,3: 21:[3, 20] Operation: 26-6=20 Exploring Operation: 6/3=2, Resulting Numbers: [26, 2] Generated Node #0,2,4: 21:[26, 2] Operation: 6/3=2 Moving to Node #0,2,3 Current State: 21:[3, 20], Operations: ['45/15=3', '26-6=20'] Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,21 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,21 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,21 unequal: No Solution Moving to Node #0,2,1 Current State: 21:[6, 23], Operations: ['45/15=3', '26-3=23'] Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,21 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,21 unequal: No Solution Exploring Operation: 6*23=138, Resulting Numbers: [138] 138,21 unequal: No Solution Moving to Node #0,2,2 Current State: 21:[26, 3], Operations: ['45/15=3', '6-3=3'] Exploring Operation: 26*3=78, Resulting Numbers: [78] 78,21 unequal: No Solution Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,21 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,21 unequal: No Solution Moving to Node #0,2,4 Current State: 21:[26, 2], Operations: ['45/15=3', '6/3=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,21 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,21 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,21 unequal: No Solution Moving to Node #0,2,0 Current State: 21:[26, 9], Operations: ['45/15=3', '6+3=9'] Exploring Operation: 26+9=35, Resulting Numbers: [35] 35,21 unequal: No Solution Exploring Operation: 26*9=234, Resulting Numbers: [234] 234,21 unequal: No Solution Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,21 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 #0,4 Current State: 21:[6, 15, 19], Operations: ['45-26=19'] Exploring Operation: 15-6=9, Resulting Numbers: [19, 9] Generated Node #0,4,0: 21:[19, 9] Operation: 15-6=9 Exploring Operation: 6+19=25, Resulting Numbers: [15, 25] Generated Node #0,4,1: 21:[15, 25] Operation: 6+19=25 Exploring Operation: 6+15=21, Resulting Numbers: [19, 21] Generated Node #0,4,2: 21:[19, 21] Operation: 6+15=21 Exploring Operation: 19-15=4, Resulting Numbers: [6, 4] Generated Node #0,4,3: 21:[6, 4] Operation: 19-15=4 Exploring Operation: 19-6=13, Resulting Numbers: [15, 13] Generated Node #0,4,4: 21:[15, 13] Operation: 19-6=13 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 21:[19, 21], Operations: ['45-26=19', '6+15=21'] Exploring Operation: 19*21=399, Resulting Numbers: [399] 399,21 unequal: No Solution Exploring Operation: 19+21=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 21-19=2, Resulting Numbers: [2] 2,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 21:[6, 4], Operations: ['45-26=19', '19-15=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 21:[19, 9], Operations: ['45-26=19', '15-6=9'] Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,21 unequal: No Solution Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 21:[15, 25], Operations: ['45-26=19', '6+19=25'] Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 15*25=375, Resulting Numbers: [375] 375,21 unequal: No Solution Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 21:[15, 13], Operations: ['45-26=19', '19-6=13'] Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 15*13=195, Resulting Numbers: [195] 195,21 unequal: No Solution Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[26, 6, 30], Operations: ['45-15=30'] Exploring Operation: 30-26=4, Resulting Numbers: [6, 4] Generated Node #0,1,0: 21:[6, 4] Operation: 30-26=4 Exploring Operation: 26+6=32, Resulting Numbers: [30, 32] Generated Node #0,1,1: 21:[30, 32] Operation: 26+6=32 Exploring Operation: 30-6=24, Resulting Numbers: [26, 24] Generated Node #0,1,2: 21:[26, 24] Operation: 30-6=24 Exploring Operation: 30/6=5, Resulting Numbers: [26, 5] Generated Node #0,1,3: 21:[26, 5] Operation: 30/6=5 Exploring Operation: 26-6=20, Resulting Numbers: [30, 20] Generated Node #0,1,4: 21:[30, 20] Operation: 26-6=20 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 21:[6, 4], Operations: ['45-15=30', '30-26=4'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 21:[26, 5], Operations: ['45-15=30', '30/6=5'] Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,21 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[26, 6, 15, 45], Operations: [] Exploring Operation: 45-15=30, Resulting Numbers: [26, 6, 30] Generated Node #0,1: 21:[26, 6, 30] Operation: 45-15=30 Moving to Node #0,1 Current State: 21:[26, 6, 30], Operations: ['45-15=30'] Exploring Operation: 30/6=5, Resulting Numbers: [26, 5] Generated Node #0,1,3: 21:[26, 5] Operation: 30/6=5 Moving to Node #0,1,3 Current State: 21:[26, 5], Operations: ['45-15=30', '30/6=5'] Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.947917
hs_5
sum_heuristic
[ 97, 95, 27, 71 ]
49
[ "97-95=2", "27+71=98", "98/2=49" ]
Current State: 49:[97, 95, 27, 71], Operations: [] Exploring Operation: 97-95=2, Resulting Numbers: [27, 71, 2] Generated Node #2: [27, 71, 2] from Operation: 97-95=2 Current State: 49:[27, 71, 2], Operations: ['97-95=2'] Exploring Operation: 27+71=98, Resulting Numbers: [2, 98] Generated Node #3: [2, 98] from Operation: 27+71=98 Current State: 49:[2, 98], Operations: ['97-95=2', '27+71=98'] Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[97, 95, 27, 71], Operations: [] Exploring Operation: 97-95=2, Resulting Numbers: [27, 71, 2] Generated Node #0,0: 49:[27, 71, 2] Operation: 97-95=2 Exploring Operation: 97-71=26, Resulting Numbers: [95, 27, 26] Generated Node #0,1: 49:[95, 27, 26] Operation: 97-71=26 Moving to Node #0,0 Current State: 49:[27, 71, 2], Operations: ['97-95=2'] Exploring Operation: 27*2=54, Resulting Numbers: [71, 54] Generated Node #0,0,0: 49:[71, 54] Operation: 27*2=54 Exploring Operation: 71-27=44, Resulting Numbers: [2, 44] Generated Node #0,0,1: 49:[2, 44] Operation: 71-27=44 Moving to Node #0,1 Current State: 49:[95, 27, 26], Operations: ['97-71=26'] Exploring Operation: 95-27=68, Resulting Numbers: [26, 68] Generated Node #0,1,0: 49:[26, 68] Operation: 95-27=68 Exploring Operation: 95-26=69, Resulting Numbers: [27, 69] Generated Node #0,1,1: 49:[27, 69] Operation: 95-26=69 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 49:[26, 68], Operations: ['97-71=26', '95-27=68'] Exploring Operation: 26+68=94, Resulting Numbers: [94] 94,49 unequal: No Solution Exploring Operation: 68-26=42, Resulting Numbers: [42] 42,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 49:[27, 69], Operations: ['97-71=26', '95-26=69'] Exploring Operation: 27+69=96, Resulting Numbers: [96] 96,49 unequal: No Solution Exploring Operation: 69-27=42, Resulting Numbers: [42] 42,49 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: 49:[2, 44], Operations: ['97-95=2', '71-27=44'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,49 unequal: No Solution Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,49 unequal: No Solution Moving to Node #0,0,0 Current State: 49:[71, 54], Operations: ['97-95=2', '27*2=54'] Exploring Operation: 71+54=125, Resulting Numbers: [125] 125,49 unequal: No Solution Exploring Operation: 71-54=17, Resulting Numbers: [17] 17,49 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 2, 2, 33, 30 ]
30
[ "2-2=0", "33*0=0", "30+0=30" ]
Current State: 30:[2, 2, 33, 30], Operations: [] Exploring Operation: 2-2=0, Resulting Numbers: [33, 30, 0] Generated Node #2: [33, 30, 0] from Operation: 2-2=0 Current State: 30:[33, 30, 0], Operations: ['2-2=0'] Exploring Operation: 33*0=0, Resulting Numbers: [30, 0] Generated Node #3: [30, 0] from Operation: 33*0=0 Current State: 30:[30, 0], Operations: ['2-2=0', '33*0=0'] Exploring Operation: 30+0=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[2, 2, 33, 30], Operations: [] Exploring Operation: 33-2=31, Resulting Numbers: [2, 30, 31] Generated Node #0,0: 30:[2, 30, 31] Operation: 33-2=31 Exploring Operation: 33-2=31, Resulting Numbers: [2, 30, 31] Generated Node #0,1: 30:[2, 30, 31] Operation: 33-2=31 Exploring Operation: 30/2=15, Resulting Numbers: [2, 33, 15] Generated Node #0,2: 30:[2, 33, 15] Operation: 30/2=15 Exploring Operation: 33-30=3, Resulting Numbers: [2, 2, 3] Generated Node #0,3: 30:[2, 2, 3] Operation: 33-30=3 Exploring Operation: 30/2=15, Resulting Numbers: [2, 33, 15] Generated Node #0,4: 30:[2, 33, 15] Operation: 30/2=15 Moving to Node #0,3 Current State: 30:[2, 2, 3], Operations: ['33-30=3'] Exploring Operation: 2+3=5, Resulting Numbers: [2, 5] Generated Node #0,3,0: 30:[2, 5] Operation: 2+3=5 Exploring Operation: 2*3=6, Resulting Numbers: [2, 6] Generated Node #0,3,1: 30:[2, 6] Operation: 2*3=6 Exploring Operation: 2*3=6, Resulting Numbers: [2, 6] Generated Node #0,3,2: 30:[2, 6] Operation: 2*3=6 Exploring Operation: 2+3=5, Resulting Numbers: [2, 5] Generated Node #0,3,3: 30:[2, 5] Operation: 2+3=5 Exploring Operation: 2+2=4, Resulting Numbers: [3, 4] Generated Node #0,3,4: 30:[3, 4] Operation: 2+2=4 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 30:[2, 5], Operations: ['33-30=3', '2+3=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,30 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 30:[2, 6], Operations: ['33-30=3', '2*3=6'] Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,30 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 30:[2, 6], Operations: ['33-30=3', '2*3=6'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 30:[2, 5], Operations: ['33-30=3', '2+3=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 30:[3, 4], Operations: ['33-30=3', '2+2=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,30 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:[2, 30, 31], Operations: ['33-2=31'] Exploring Operation: 30-2=28, Resulting Numbers: [31, 28] Generated Node #0,1,0: 30:[31, 28] Operation: 30-2=28 Exploring Operation: 30/2=15, Resulting Numbers: [31, 15] Generated Node #0,1,1: 30:[31, 15] Operation: 30/2=15 Exploring Operation: 31-30=1, Resulting Numbers: [2, 1] Generated Node #0,1,2: 30:[2, 1] Operation: 31-30=1 Exploring Operation: 31-2=29, Resulting Numbers: [30, 29] Generated Node #0,1,3: 30:[30, 29] Operation: 31-2=29 Exploring Operation: 2+30=32, Resulting Numbers: [31, 32] Generated Node #0,1,4: 30:[31, 32] Operation: 2+30=32 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 30:[31, 15], Operations: ['33-2=31', '30/2=15'] Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,30 unequal: No Solution Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,30 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 30:[2, 1], Operations: ['33-2=31', '31-30=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 30:[30, 29], Operations: ['33-2=31', '31-2=29'] Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 30+29=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 30*29=870, Resulting Numbers: [870] 870,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 30:[31, 28], Operations: ['33-2=31', '30-2=28'] Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 30:[31, 32], Operations: ['33-2=31', '2+30=32'] Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,30 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 31*32=992, Resulting Numbers: [992] 992,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 30:[2, 30, 31], Operations: ['33-2=31'] Exploring Operation: 30-2=28, Resulting Numbers: [31, 28] Generated Node #0,0,0: 30:[31, 28] Operation: 30-2=28 Exploring Operation: 2+30=32, Resulting Numbers: [31, 32] Generated Node #0,0,1: 30:[31, 32] Operation: 2+30=32 Exploring Operation: 31-2=29, Resulting Numbers: [30, 29] Generated Node #0,0,2: 30:[30, 29] Operation: 31-2=29 Exploring Operation: 31-30=1, Resulting Numbers: [2, 1] Generated Node #0,0,3: 30:[2, 1] Operation: 31-30=1 Exploring Operation: 30/2=15, Resulting Numbers: [31, 15] Generated Node #0,0,4: 30:[31, 15] Operation: 30/2=15 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 30:[30, 29], Operations: ['33-2=31', '31-2=29'] Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 30*29=870, Resulting Numbers: [870] 870,30 unequal: No Solution Exploring Operation: 30+29=59, Resulting Numbers: [59] 59,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 30:[2, 1], Operations: ['33-2=31', '31-30=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 30:[31, 15], Operations: ['33-2=31', '30/2=15'] Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,30 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,30 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:[31, 28], Operations: ['33-2=31', '30-2=28'] Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,30 unequal: No Solution Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,30 unequal: No Solution Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,30 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:[31, 32], Operations: ['33-2=31', '2+30=32'] Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,30 unequal: No Solution Exploring Operation: 31*32=992, Resulting Numbers: [992] 992,30 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:[2, 33, 15], Operations: ['30/2=15'] Exploring Operation: 33-2=31, Resulting Numbers: [15, 31] Generated Node #0,2,0: 30:[15, 31] Operation: 33-2=31 Exploring Operation: 2+33=35, Resulting Numbers: [15, 35] Generated Node #0,2,1: 30:[15, 35] Operation: 2+33=35 Exploring Operation: 2*15=30, Resulting Numbers: [33, 30] Generated Node #0,2,2: 30:[33, 30] Operation: 2*15=30 Exploring Operation: 2+15=17, Resulting Numbers: [33, 17] Generated Node #0,2,3: 30:[33, 17] Operation: 2+15=17 Exploring Operation: 33-15=18, Resulting Numbers: [2, 18] Generated Node #0,2,4: 30:[2, 18] Operation: 33-15=18 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 30:[15, 31], Operations: ['30/2=15', '33-2=31'] Exploring Operation: 15*31=465, Resulting Numbers: [465] 465,30 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,30 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 #0,2,2 Current State: 30:[33, 30], Operations: ['30/2=15', '2*15=30'] Exploring Operation: 33*30=990, Resulting Numbers: [990] 990,30 unequal: No Solution Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,30 unequal: No Solution Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 30:[2, 18], Operations: ['30/2=15', '33-15=18'] Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,30 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 30:[15, 35], Operations: ['30/2=15', '2+33=35'] Exploring Operation: 15+35=50, Resulting Numbers: [50] 50,30 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 15*35=525, Resulting Numbers: [525] 525,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 30:[33, 17], Operations: ['30/2=15', '2+15=17'] Exploring Operation: 33+17=50, Resulting Numbers: [50] 50,30 unequal: No Solution Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 33*17=561, Resulting Numbers: [561] 561,30 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: 30:[2, 33, 15], Operations: ['30/2=15'] Exploring Operation: 2+15=17, Resulting Numbers: [33, 17] Generated Node #0,4,0: 30:[33, 17] Operation: 2+15=17 Exploring Operation: 33-2=31, Resulting Numbers: [15, 31] Generated Node #0,4,1: 30:[15, 31] Operation: 33-2=31 Exploring Operation: 2*15=30, Resulting Numbers: [33, 30] Generated Node #0,4,2: 30:[33, 30] Operation: 2*15=30 Exploring Operation: 2+33=35, Resulting Numbers: [15, 35] Generated Node #0,4,3: 30:[15, 35] Operation: 2+33=35 Exploring Operation: 33-15=18, Resulting Numbers: [2, 18] Generated Node #0,4,4: 30:[2, 18] Operation: 33-15=18 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 30:[15, 31], Operations: ['30/2=15', '33-2=31'] Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,30 unequal: No Solution Exploring Operation: 15*31=465, Resulting Numbers: [465] 465,30 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 #0,4,2 Current State: 30:[33, 30], Operations: ['30/2=15', '2*15=30'] Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,30 unequal: No Solution Exploring Operation: 33*30=990, Resulting Numbers: [990] 990,30 unequal: No Solution Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,30 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 #0,4,4 Current State: 30:[2, 18], Operations: ['30/2=15', '33-15=18'] Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,30 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 30:[33, 17], Operations: ['30/2=15', '2+15=17'] Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 33+17=50, Resulting Numbers: [50] 50,30 unequal: No Solution Exploring Operation: 33*17=561, Resulting Numbers: [561] 561,30 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 #0,4,3 Current State: 30:[15, 35], Operations: ['30/2=15', '2+33=35'] Exploring Operation: 15+35=50, Resulting Numbers: [50] 50,30 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 15*35=525, Resulting Numbers: [525] 525,30 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
[ 13, 5, 84, 82 ]
63
[ "13*5=65", "84-82=2", "65-2=63" ]
Current State: 63:[13, 5, 84, 82], Operations: [] Exploring Operation: 13*5=65, Resulting Numbers: [84, 82, 65] Generated Node #2: [84, 82, 65] from Operation: 13*5=65 Current State: 63:[84, 82, 65], Operations: ['13*5=65'] Exploring Operation: 84-82=2, Resulting Numbers: [65, 2] Generated Node #3: [65, 2] from Operation: 84-82=2 Current State: 63:[65, 2], Operations: ['13*5=65', '84-82=2'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[13, 5, 84, 82], Operations: [] Exploring Operation: 84-13=71, Resulting Numbers: [5, 82, 71] Generated Node #0,0: 63:[5, 82, 71] Operation: 84-13=71 Exploring Operation: 84-82=2, Resulting Numbers: [13, 5, 2] Generated Node #0,1: 63:[13, 5, 2] Operation: 84-82=2 Moving to Node #0,1 Current State: 63:[13, 5, 2], Operations: ['84-82=2'] Exploring Operation: 13*5=65, Resulting Numbers: [2, 65] Generated Node #0,1,0: 63:[2, 65] Operation: 13*5=65 Exploring Operation: 13-5=8, Resulting Numbers: [2, 8] Generated Node #0,1,1: 63:[2, 8] Operation: 13-5=8 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 63:[2, 8], Operations: ['84-82=2', '13-5=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,63 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 63:[2, 65], Operations: ['84-82=2', '13*5=65'] Exploring Operation: 2+65=67, Resulting Numbers: [67] 67,63 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[13, 5, 84, 82], Operations: [] Exploring Operation: 84-82=2, Resulting Numbers: [13, 5, 2] Generated Node #0,1: 63:[13, 5, 2] Operation: 84-82=2 Moving to Node #0,1 Current State: 63:[13, 5, 2], Operations: ['84-82=2'] Exploring Operation: 13*5=65, Resulting Numbers: [2, 65] Generated Node #0,1,0: 63:[2, 65] Operation: 13*5=65 Moving to Node #0,1,0 Current State: 63:[2, 65], Operations: ['84-82=2', '13*5=65'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 99, 17, 98, 67 ]
85
[ "99+17=116", "98-67=31", "116-31=85" ]
Current State: 85:[99, 17, 98, 67], Operations: [] Exploring Operation: 99+17=116, Resulting Numbers: [98, 67, 116] Generated Node #2: [98, 67, 116] from Operation: 99+17=116 Current State: 85:[98, 67, 116], Operations: ['99+17=116'] Exploring Operation: 98-67=31, Resulting Numbers: [116, 31] Generated Node #3: [116, 31] from Operation: 98-67=31 Current State: 85:[116, 31], Operations: ['99+17=116', '98-67=31'] Exploring Operation: 116-31=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[99, 17, 98, 67], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [17, 67, 1] Generated Node #0,0: 85:[17, 67, 1] Operation: 99-98=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[17, 67, 1], Operations: ['99-98=1'] Exploring Operation: 17+67=84, Resulting Numbers: [1, 84] Generated Node #0,0,0: 85:[1, 84] Operation: 17+67=84 Moving to Node #0,0,0 Current State: 85:[1, 84], Operations: ['99-98=1', '17+67=84'] Exploring Operation: 1+84=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[99, 17, 98, 67], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [17, 67, 1] Generated Node #0,0: 85:[17, 67, 1] Operation: 99-98=1 Moving to Node #0,0 Current State: 85:[17, 67, 1], Operations: ['99-98=1'] Exploring Operation: 17+67=84, Resulting Numbers: [1, 84] Generated Node #0,0,0: 85:[1, 84] Operation: 17+67=84 Moving to Node #0,0,0 Current State: 85:[1, 84], Operations: ['99-98=1', '17+67=84'] Exploring Operation: 1+84=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 76, 82, 15, 71 ]
89
[ "82-71=11", "15*11=165", "165-76=89" ]
Current State: 89:[76, 82, 15, 71], Operations: [] Exploring Operation: 82-71=11, Resulting Numbers: [76, 15, 11] Generated Node #2: [76, 15, 11] from Operation: 82-71=11 Current State: 89:[76, 15, 11], Operations: ['82-71=11'] Exploring Operation: 15*11=165, Resulting Numbers: [76, 165] Generated Node #3: [76, 165] from Operation: 15*11=165 Current State: 89:[76, 165], Operations: ['82-71=11', '15*11=165'] Exploring Operation: 165-76=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[76, 82, 15, 71], Operations: [] Exploring Operation: 15+71=86, Resulting Numbers: [76, 82, 86] Generated Node #0,0: 89:[76, 82, 86] Operation: 15+71=86 Exploring Operation: 76+15=91, Resulting Numbers: [82, 71, 91] Generated Node #0,1: 89:[82, 71, 91] Operation: 76+15=91 Exploring Operation: 82+15=97, Resulting Numbers: [76, 71, 97] Generated Node #0,2: 89:[76, 71, 97] Operation: 82+15=97 Moving to Node #0,0 Current State: 89:[76, 82, 86], Operations: ['15+71=86'] Exploring Operation: 76+82=158, Resulting Numbers: [86, 158] Generated Node #0,0,0: 89:[86, 158] Operation: 76+82=158 Exploring Operation: 82-76=6, Resulting Numbers: [86, 6] Generated Node #0,0,1: 89:[86, 6] Operation: 82-76=6 Exploring Operation: 76+86=162, Resulting Numbers: [82, 162] Generated Node #0,0,2: 89:[82, 162] Operation: 76+86=162 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[86, 158], Operations: ['15+71=86', '76+82=158'] Exploring Operation: 86*158=13588, Resulting Numbers: [13588] 13588,89 unequal: No Solution Exploring Operation: 158-86=72, Resulting Numbers: [72] 72,89 unequal: No Solution Exploring Operation: 86+158=244, Resulting Numbers: [244] 244,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 89:[82, 162], Operations: ['15+71=86', '76+86=162'] Exploring Operation: 82*162=13284, Resulting Numbers: [13284] 13284,89 unequal: No Solution Exploring Operation: 82+162=244, Resulting Numbers: [244] 244,89 unequal: No Solution Exploring Operation: 162-82=80, Resulting Numbers: [80] 80,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[86, 6], Operations: ['15+71=86', '82-76=6'] Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,89 unequal: No Solution Exploring Operation: 86*6=516, Resulting Numbers: [516] 516,89 unequal: No Solution Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,89 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: 89:[82, 71, 91], Operations: ['76+15=91'] Exploring Operation: 82+71=153, Resulting Numbers: [91, 153] Generated Node #0,1,0: 89:[91, 153] Operation: 82+71=153 Exploring Operation: 82-71=11, Resulting Numbers: [91, 11] Generated Node #0,1,1: 89:[91, 11] Operation: 82-71=11 Exploring Operation: 91-71=20, Resulting Numbers: [82, 20] Generated Node #0,1,2: 89:[82, 20] Operation: 91-71=20 Moving to Node #0,2 Current State: 89:[76, 71, 97], Operations: ['82+15=97'] Exploring Operation: 76+71=147, Resulting Numbers: [97, 147] Generated Node #0,2,0: 89:[97, 147] Operation: 76+71=147 Exploring Operation: 97-76=21, Resulting Numbers: [71, 21] Generated Node #0,2,1: 89:[71, 21] Operation: 97-76=21 Exploring Operation: 97-71=26, Resulting Numbers: [76, 26] Generated Node #0,2,2: 89:[76, 26] Operation: 97-71=26 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 89:[97, 147], Operations: ['82+15=97', '76+71=147'] Exploring Operation: 97+147=244, Resulting Numbers: [244] 244,89 unequal: No Solution Exploring Operation: 97*147=14259, Resulting Numbers: [14259] 14259,89 unequal: No Solution Exploring Operation: 147-97=50, Resulting Numbers: [50] 50,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[76, 26], Operations: ['82+15=97', '97-71=26'] Exploring Operation: 76+26=102, Resulting Numbers: [102] 102,89 unequal: No Solution Exploring Operation: 76-26=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 76*26=1976, Resulting Numbers: [1976] 1976,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 89:[71, 21], Operations: ['82+15=97', '97-76=21'] Exploring Operation: 71+21=92, Resulting Numbers: [92] 92,89 unequal: No Solution Exploring Operation: 71-21=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 71*21=1491, Resulting Numbers: [1491] 1491,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 89:[91, 153], Operations: ['76+15=91', '82+71=153'] Exploring Operation: 91*153=13923, Resulting Numbers: [13923] 13923,89 unequal: No Solution Exploring Operation: 91+153=244, Resulting Numbers: [244] 244,89 unequal: No Solution Exploring Operation: 153-91=62, Resulting Numbers: [62] 62,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[82, 20], Operations: ['76+15=91', '91-71=20'] Exploring Operation: 82*20=1640, Resulting Numbers: [1640] 1640,89 unequal: No Solution Exploring Operation: 82-20=62, Resulting Numbers: [62] 62,89 unequal: No Solution Exploring Operation: 82+20=102, Resulting Numbers: [102] 102,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[91, 11], Operations: ['76+15=91', '82-71=11'] Exploring Operation: 91-11=80, Resulting Numbers: [80] 80,89 unequal: No Solution Exploring Operation: 91+11=102, Resulting Numbers: [102] 102,89 unequal: No Solution Exploring Operation: 91*11=1001, Resulting Numbers: [1001] 1001,89 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 18, 53, 78, 29 ]
14
[ "53-18=35", "78-29=49", "49-35=14" ]
Current State: 14:[18, 53, 78, 29], Operations: [] Exploring Operation: 53-18=35, Resulting Numbers: [78, 29, 35] Generated Node #2: [78, 29, 35] from Operation: 53-18=35 Current State: 14:[78, 29, 35], Operations: ['53-18=35'] Exploring Operation: 78-29=49, Resulting Numbers: [35, 49] Generated Node #3: [35, 49] from Operation: 78-29=49 Current State: 14:[35, 49], Operations: ['53-18=35', '78-29=49'] Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[18, 53, 78, 29], Operations: [] Exploring Operation: 78-53=25, Resulting Numbers: [18, 29, 25] Generated Node #0,0: 14:[18, 29, 25] Operation: 78-53=25 Exploring Operation: 53-29=24, Resulting Numbers: [18, 78, 24] Generated Node #0,1: 14:[18, 78, 24] Operation: 53-29=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[18, 29, 25], Operations: ['78-53=25'] Exploring Operation: 29-25=4, Resulting Numbers: [18, 4] Generated Node #0,0,0: 14:[18, 4] Operation: 29-25=4 Exploring Operation: 29-18=11, Resulting Numbers: [25, 11] Generated Node #0,0,1: 14:[25, 11] Operation: 29-18=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 14:[18, 4], Operations: ['78-53=25', '29-25=4'] Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[18, 53, 78, 29], Operations: [] Exploring Operation: 78-53=25, Resulting Numbers: [18, 29, 25] Generated Node #0,0: 14:[18, 29, 25] Operation: 78-53=25 Moving to Node #0,0 Current State: 14:[18, 29, 25], Operations: ['78-53=25'] Exploring Operation: 29-25=4, Resulting Numbers: [18, 4] Generated Node #0,0,0: 14:[18, 4] Operation: 29-25=4 Moving to Node #0,0,0 Current State: 14:[18, 4], Operations: ['78-53=25', '29-25=4'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 97, 49, 95, 67 ]
58
[ "97-95=2", "49+67=116", "116/2=58" ]
Current State: 58:[97, 49, 95, 67], Operations: [] Exploring Operation: 97-95=2, Resulting Numbers: [49, 67, 2] Generated Node #2: [49, 67, 2] from Operation: 97-95=2 Current State: 58:[49, 67, 2], Operations: ['97-95=2'] Exploring Operation: 49+67=116, Resulting Numbers: [2, 116] Generated Node #3: [2, 116] from Operation: 49+67=116 Current State: 58:[2, 116], Operations: ['97-95=2', '49+67=116'] Exploring Operation: 116/2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[97, 49, 95, 67], Operations: [] Exploring Operation: 95-67=28, Resulting Numbers: [97, 49, 28] Generated Node #0,0: 58:[97, 49, 28] Operation: 95-67=28 Exploring Operation: 97-67=30, Resulting Numbers: [49, 95, 30] Generated Node #0,1: 58:[49, 95, 30] Operation: 97-67=30 Exploring Operation: 97-95=2, Resulting Numbers: [49, 67, 2] Generated Node #0,2: 58:[49, 67, 2] Operation: 97-95=2 Moving to Node #0,2 Current State: 58:[49, 67, 2], Operations: ['97-95=2'] Exploring Operation: 49+2=51, Resulting Numbers: [67, 51] Generated Node #0,2,0: 58:[67, 51] Operation: 49+2=51 Exploring Operation: 67-49=18, Resulting Numbers: [2, 18] Generated Node #0,2,1: 58:[2, 18] Operation: 67-49=18 Exploring Operation: 67-2=65, Resulting Numbers: [49, 65] Generated Node #0,2,2: 58:[49, 65] Operation: 67-2=65 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 58:[2, 18], Operations: ['97-95=2', '67-49=18'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,58 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,58 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,58 unequal: No Solution No 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: 58:[67, 51], Operations: ['97-95=2', '49+2=51'] Exploring Operation: 67*51=3417, Resulting Numbers: [3417] 3417,58 unequal: No Solution Exploring Operation: 67-51=16, Resulting Numbers: [16] 16,58 unequal: No Solution Exploring Operation: 67+51=118, Resulting Numbers: [118] 118,58 unequal: No Solution No 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: 58:[49, 65], Operations: ['97-95=2', '67-2=65'] Exploring Operation: 49*65=3185, Resulting Numbers: [3185] 3185,58 unequal: No Solution Exploring Operation: 49+65=114, Resulting Numbers: [114] 114,58 unequal: No Solution Exploring Operation: 65-49=16, Resulting Numbers: [16] 16,58 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: 58:[49, 95, 30], Operations: ['97-67=30'] Exploring Operation: 95-30=65, Resulting Numbers: [49, 65] Generated Node #0,1,0: 58:[49, 65] Operation: 95-30=65 Exploring Operation: 95-49=46, Resulting Numbers: [30, 46] Generated Node #0,1,1: 58:[30, 46] Operation: 95-49=46 Exploring Operation: 49-30=19, Resulting Numbers: [95, 19] Generated Node #0,1,2: 58:[95, 19] Operation: 49-30=19 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 58:[30, 46], Operations: ['97-67=30', '95-49=46'] Exploring Operation: 30+46=76, Resulting Numbers: [76] 76,58 unequal: No Solution Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,58 unequal: No Solution Exploring Operation: 30*46=1380, Resulting Numbers: [1380] 1380,58 unequal: No Solution No 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: 58:[49, 65], Operations: ['97-67=30', '95-30=65'] Exploring Operation: 49+65=114, Resulting Numbers: [114] 114,58 unequal: No Solution Exploring Operation: 65-49=16, Resulting Numbers: [16] 16,58 unequal: No Solution Exploring Operation: 49*65=3185, Resulting Numbers: [3185] 3185,58 unequal: No Solution No 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: 58:[95, 19], Operations: ['97-67=30', '49-30=19'] Exploring Operation: 95-19=76, Resulting Numbers: [76] 76,58 unequal: No Solution Exploring Operation: 95+19=114, Resulting Numbers: [114] 114,58 unequal: No Solution Exploring Operation: 95/19=5, Resulting Numbers: [5] 5,58 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: 58:[97, 49, 28], Operations: ['95-67=28'] Exploring Operation: 97-49=48, Resulting Numbers: [28, 48] Generated Node #0,0,0: 58:[28, 48] Operation: 97-49=48 Exploring Operation: 49-28=21, Resulting Numbers: [97, 21] Generated Node #0,0,1: 58:[97, 21] Operation: 49-28=21 Exploring Operation: 97-28=69, Resulting Numbers: [49, 69] Generated Node #0,0,2: 58:[49, 69] Operation: 97-28=69 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[28, 48], Operations: ['95-67=28', '97-49=48'] Exploring Operation: 28+48=76, Resulting Numbers: [76] 76,58 unequal: No Solution Exploring Operation: 28*48=1344, Resulting Numbers: [1344] 1344,58 unequal: No Solution Exploring Operation: 48-28=20, Resulting Numbers: [20] 20,58 unequal: No Solution No 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: 58:[49, 69], Operations: ['95-67=28', '97-28=69'] Exploring Operation: 69-49=20, Resulting Numbers: [20] 20,58 unequal: No Solution Exploring Operation: 49+69=118, Resulting Numbers: [118] 118,58 unequal: No Solution Exploring Operation: 49*69=3381, Resulting Numbers: [3381] 3381,58 unequal: No Solution No 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: 58:[97, 21], Operations: ['95-67=28', '49-28=21'] Exploring Operation: 97-21=76, Resulting Numbers: [76] 76,58 unequal: No Solution Exploring Operation: 97+21=118, Resulting Numbers: [118] 118,58 unequal: No Solution Exploring Operation: 97*21=2037, Resulting Numbers: [2037] 2037,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 42, 23, 46, 16 ]
37
[ "42*23=966", "966/46=21", "16+21=37" ]
Current State: 37:[42, 23, 46, 16], Operations: [] Exploring Operation: 42*23=966, Resulting Numbers: [46, 16, 966] Generated Node #2: [46, 16, 966] from Operation: 42*23=966 Current State: 37:[46, 16, 966], Operations: ['42*23=966'] Exploring Operation: 966/46=21, Resulting Numbers: [16, 21] Generated Node #3: [16, 21] from Operation: 966/46=21 Current State: 37:[16, 21], Operations: ['42*23=966', '966/46=21'] Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[42, 23, 46, 16], Operations: [] Exploring Operation: 23+16=39, Resulting Numbers: [42, 46, 39] Generated Node #0,0: 37:[42, 46, 39] Operation: 23+16=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[42, 46, 39], Operations: ['23+16=39'] Exploring Operation: 46-42=4, Resulting Numbers: [39, 4] Generated Node #0,0,0: 37:[39, 4] Operation: 46-42=4 Moving to Node #0,0,0 Current State: 37:[39, 4], Operations: ['23+16=39', '46-42=4'] Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,37 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
[ 28, 33, 18, 8 ]
87
[ "28+33=61", "18+8=26", "61+26=87" ]
Current State: 87:[28, 33, 18, 8], Operations: [] Exploring Operation: 28+33=61, Resulting Numbers: [18, 8, 61] Generated Node #2: [18, 8, 61] from Operation: 28+33=61 Current State: 87:[18, 8, 61], Operations: ['28+33=61'] Exploring Operation: 18+8=26, Resulting Numbers: [61, 26] Generated Node #3: [61, 26] from Operation: 18+8=26 Current State: 87:[61, 26], Operations: ['28+33=61', '18+8=26'] Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[28, 33, 18, 8], Operations: [] Exploring Operation: 18+8=26, Resulting Numbers: [28, 33, 26] Generated Node #0,0: 87:[28, 33, 26] Operation: 18+8=26 Exploring Operation: 28-18=10, Resulting Numbers: [33, 8, 10] Generated Node #0,1: 87:[33, 8, 10] Operation: 28-18=10 Exploring Operation: 18-8=10, Resulting Numbers: [28, 33, 10] Generated Node #0,2: 87:[28, 33, 10] Operation: 18-8=10 Exploring Operation: 33-8=25, Resulting Numbers: [28, 18, 25] Generated Node #0,3: 87:[28, 18, 25] Operation: 33-8=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[28, 33, 26], Operations: ['18+8=26'] Exploring Operation: 28-26=2, Resulting Numbers: [33, 2] Generated Node #0,0,0: 87:[33, 2] Operation: 28-26=2 Exploring Operation: 28+33=61, Resulting Numbers: [26, 61] Generated Node #0,0,1: 87:[26, 61] Operation: 28+33=61 Exploring Operation: 33-26=7, Resulting Numbers: [28, 7] Generated Node #0,0,2: 87:[28, 7] Operation: 33-26=7 Exploring Operation: 33-28=5, Resulting Numbers: [26, 5] Generated Node #0,0,3: 87:[26, 5] Operation: 33-28=5 Moving to Node #0,0,0 Current State: 87:[33, 2], Operations: ['18+8=26', '28-26=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,87 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,87 unequal: No Solution Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,87 unequal: No Solution Moving to Node #0,0,3 Current State: 87:[26, 5], Operations: ['18+8=26', '33-28=5'] Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,87 unequal: No Solution Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,87 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,87 unequal: No Solution Moving to Node #0,0,2 Current State: 87:[28, 7], Operations: ['18+8=26', '33-26=7'] Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,87 unequal: No Solution Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,87 unequal: No Solution Exploring Operation: 28+7=35, Resulting Numbers: [35] 35,87 unequal: No Solution Exploring Operation: 28*7=196, Resulting Numbers: [196] 196,87 unequal: No Solution Moving to Node #0,0,1 Current State: 87:[26, 61], Operations: ['18+8=26', '28+33=61'] Exploring Operation: 26+61=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[28, 33, 18, 8], Operations: [] Exploring Operation: 18+8=26, Resulting Numbers: [28, 33, 26] Generated Node #0,0: 87:[28, 33, 26] Operation: 18+8=26 Moving to Node #0,0 Current State: 87:[28, 33, 26], Operations: ['18+8=26'] Exploring Operation: 28+33=61, Resulting Numbers: [26, 61] Generated Node #0,0,1: 87:[26, 61] Operation: 28+33=61 Moving to Node #0,0,1 Current State: 87:[26, 61], Operations: ['18+8=26', '28+33=61'] Exploring Operation: 26+61=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
mult_heuristic
[ 64, 8, 76, 13 ]
92
[ "76-64=12", "8*13=104", "104-12=92" ]
Current State: 92:[64, 8, 76, 13], Operations: [] Exploring Operation: 76-64=12, Resulting Numbers: [8, 13, 12] Generated Node #2: [8, 13, 12] from Operation: 76-64=12 Current State: 92:[8, 13, 12], Operations: ['76-64=12'] Exploring Operation: 8*13=104, Resulting Numbers: [12, 104] Generated Node #3: [12, 104] from Operation: 8*13=104 Current State: 92:[12, 104], Operations: ['76-64=12', '8*13=104'] Exploring Operation: 104-12=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[64, 8, 76, 13], Operations: [] Exploring Operation: 76-64=12, Resulting Numbers: [8, 13, 12] Generated Node #0,0: 92:[8, 13, 12] Operation: 76-64=12 Exploring Operation: 64-13=51, Resulting Numbers: [8, 76, 51] Generated Node #0,1: 92:[8, 76, 51] Operation: 64-13=51 Exploring Operation: 76+13=89, Resulting Numbers: [64, 8, 89] Generated Node #0,2: 92:[64, 8, 89] Operation: 76+13=89 Moving to Node #0,0 Current State: 92:[8, 13, 12], Operations: ['76-64=12'] Exploring Operation: 13-12=1, Resulting Numbers: [8, 1] Generated Node #0,0,0: 92:[8, 1] Operation: 13-12=1 Exploring Operation: 13-8=5, Resulting Numbers: [12, 5] Generated Node #0,0,1: 92:[12, 5] Operation: 13-8=5 Exploring Operation: 13+12=25, Resulting Numbers: [8, 25] Generated Node #0,0,2: 92:[8, 25] Operation: 13+12=25 Moving to Node #0,1 Current State: 92:[8, 76, 51], Operations: ['64-13=51'] Exploring Operation: 8+76=84, Resulting Numbers: [51, 84] Generated Node #0,1,0: 92:[51, 84] Operation: 8+76=84 Exploring Operation: 51-8=43, Resulting Numbers: [76, 43] Generated Node #0,1,1: 92:[76, 43] Operation: 51-8=43 Exploring Operation: 76-51=25, Resulting Numbers: [8, 25] Generated Node #0,1,2: 92:[8, 25] Operation: 76-51=25 Moving to Node #0,2 Current State: 92:[64, 8, 89], Operations: ['76+13=89'] Exploring Operation: 64-8=56, Resulting Numbers: [89, 56] Generated Node #0,2,0: 92:[89, 56] Operation: 64-8=56 Exploring Operation: 64/8=8, Resulting Numbers: [89, 8] Generated Node #0,2,1: 92:[89, 8] Operation: 64/8=8 Exploring Operation: 89-64=25, Resulting Numbers: [8, 25] Generated Node #0,2,2: 92:[8, 25] Operation: 89-64=25 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 92:[8, 25], Operations: ['76+13=89', '89-64=25'] Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,92 unequal: No Solution Exploring Operation: 8+25=33, Resulting Numbers: [33] 33,92 unequal: No Solution Exploring Operation: 8*25=200, Resulting Numbers: [200] 200,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 92:[89, 8], Operations: ['76+13=89', '64/8=8'] Exploring Operation: 89+8=97, Resulting Numbers: [97] 97,92 unequal: No Solution Exploring Operation: 89*8=712, Resulting Numbers: [712] 712,92 unequal: No Solution Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 92:[89, 56], Operations: ['76+13=89', '64-8=56'] Exploring Operation: 89-56=33, Resulting Numbers: [33] 33,92 unequal: No Solution Exploring Operation: 89*56=4984, Resulting Numbers: [4984] 4984,92 unequal: No Solution Exploring Operation: 89+56=145, Resulting Numbers: [145] 145,92 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: 92:[8, 1], Operations: ['76-64=12', '13-12=1'] Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,92 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,92 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,92 unequal: No Solution Moving to Node #0,0,2 Current State: 92:[8, 25], Operations: ['76-64=12', '13+12=25'] Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,92 unequal: No Solution Exploring Operation: 8+25=33, Resulting Numbers: [33] 33,92 unequal: No Solution Exploring Operation: 8*25=200, Resulting Numbers: [200] 200,92 unequal: No Solution Moving to Node #0,1,2 Current State: 92:[8, 25], Operations: ['64-13=51', '76-51=25'] Exploring Operation: 8+25=33, Resulting Numbers: [33] 33,92 unequal: No Solution Exploring Operation: 8*25=200, Resulting Numbers: [200] 200,92 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[12, 5], Operations: ['76-64=12', '13-8=5'] Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,92 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,92 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[51, 84], Operations: ['64-13=51', '8+76=84'] Exploring Operation: 84-51=33, Resulting Numbers: [33] 33,92 unequal: No Solution Exploring Operation: 51*84=4284, Resulting Numbers: [4284] 4284,92 unequal: No Solution Exploring Operation: 51+84=135, Resulting Numbers: [135] 135,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[76, 43], Operations: ['64-13=51', '51-8=43'] Exploring Operation: 76*43=3268, Resulting Numbers: [3268] 3268,92 unequal: No Solution Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,92 unequal: No Solution Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,92 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 8, 31, 27, 11 ]
52
[ "31-27=4", "11*4=44", "8+44=52" ]
Current State: 52:[8, 31, 27, 11], Operations: [] Exploring Operation: 31-27=4, Resulting Numbers: [8, 11, 4] Generated Node #2: [8, 11, 4] from Operation: 31-27=4 Current State: 52:[8, 11, 4], Operations: ['31-27=4'] Exploring Operation: 11*4=44, Resulting Numbers: [8, 44] Generated Node #3: [8, 44] from Operation: 11*4=44 Current State: 52:[8, 44], Operations: ['31-27=4', '11*4=44'] Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[8, 31, 27, 11], Operations: [] Exploring Operation: 31-8=23, Resulting Numbers: [27, 11, 23] Generated Node #0,0: 52:[27, 11, 23] Operation: 31-8=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[27, 11, 23], Operations: ['31-8=23'] Exploring Operation: 27-23=4, Resulting Numbers: [11, 4] Generated Node #0,0,0: 52:[11, 4] Operation: 27-23=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[11, 4], Operations: ['31-8=23', '27-23=4'] Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 13, 87, 13, 50 ]
63
[ "13+87=100", "50-13=37", "100-37=63" ]
Current State: 63:[13, 87, 13, 50], Operations: [] Exploring Operation: 13+87=100, Resulting Numbers: [50, 100] Generated Node #2: [50, 100] from Operation: 13+87=100 Current State: 63:[50, 100], Operations: ['13+87=100'] Exploring Operation: 50-13=37, Resulting Numbers: [100, 37] Generated Node #3: [100, 37] from Operation: 50-13=37 Current State: 63:[100, 37], Operations: ['13+87=100', '50-13=37'] Exploring Operation: 100-37=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[13, 87, 13, 50], Operations: [] Exploring Operation: 87-13=74, Resulting Numbers: [13, 50, 74] Generated Node #0,0: 63:[13, 50, 74] Operation: 87-13=74 Exploring Operation: 87-50=37, Resulting Numbers: [13, 13, 37] Generated Node #0,1: 63:[13, 13, 37] Operation: 87-50=37 Exploring Operation: 13+50=63, Resulting Numbers: [87, 13, 63] Generated Node #0,2: 63:[87, 13, 63] Operation: 13+50=63 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[13, 13, 37], Operations: ['87-50=37'] Exploring Operation: 13+37=50, Resulting Numbers: [13, 50] Generated Node #0,1,0: 63:[13, 50] Operation: 13+37=50 Exploring Operation: 37-13=24, Resulting Numbers: [13, 24] Generated Node #0,1,1: 63:[13, 24] Operation: 37-13=24 Exploring Operation: 37-13=24, Resulting Numbers: [13, 24] Generated Node #0,1,2: 63:[13, 24] Operation: 37-13=24 Moving to Node #0,1,1 Current State: 63:[13, 24], Operations: ['87-50=37', '37-13=24'] Exploring Operation: 13*24=312, Resulting Numbers: [312] 312,63 unequal: No Solution Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,63 unequal: No Solution Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[13, 24], Operations: ['87-50=37', '37-13=24'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,63 unequal: No Solution Exploring Operation: 13*24=312, Resulting Numbers: [312] 312,63 unequal: No Solution Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[13, 50], Operations: ['87-50=37', '13+37=50'] Exploring Operation: 13+50=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[13, 87, 13, 50], Operations: [] Exploring Operation: 87-50=37, Resulting Numbers: [13, 13, 37] Generated Node #0,1: 63:[13, 13, 37] Operation: 87-50=37 Moving to Node #0,1 Current State: 63:[13, 13, 37], Operations: ['87-50=37'] Exploring Operation: 13+37=50, Resulting Numbers: [13, 50] Generated Node #0,1,0: 63:[13, 50] Operation: 13+37=50 Moving to Node #0,1,0 Current State: 63:[13, 50], Operations: ['87-50=37', '13+37=50'] Exploring Operation: 13+50=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 55, 24, 17, 51 ]
47
[ "24*17=408", "408/51=8", "55-8=47" ]
Current State: 47:[55, 24, 17, 51], Operations: [] Exploring Operation: 24*17=408, Resulting Numbers: [55, 51, 408] Generated Node #2: [55, 51, 408] from Operation: 24*17=408 Current State: 47:[55, 51, 408], Operations: ['24*17=408'] Exploring Operation: 408/51=8, Resulting Numbers: [55, 8] Generated Node #3: [55, 8] from Operation: 408/51=8 Current State: 47:[55, 8], Operations: ['24*17=408', '408/51=8'] Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[55, 24, 17, 51], Operations: [] Exploring Operation: 24+17=41, Resulting Numbers: [55, 51, 41] Generated Node #0,0: 47:[55, 51, 41] Operation: 24+17=41 Exploring Operation: 55-17=38, Resulting Numbers: [24, 51, 38] Generated Node #0,1: 47:[24, 51, 38] Operation: 55-17=38 Moving to Node #0,0 Current State: 47:[55, 51, 41], Operations: ['24+17=41'] Exploring Operation: 51-41=10, Resulting Numbers: [55, 10] Generated Node #0,0,0: 47:[55, 10] Operation: 51-41=10 Exploring Operation: 55-41=14, Resulting Numbers: [51, 14] Generated Node #0,0,1: 47:[51, 14] Operation: 55-41=14 Moving to Node #0,1 Current State: 47:[24, 51, 38], Operations: ['55-17=38'] Exploring Operation: 51-24=27, Resulting Numbers: [38, 27] Generated Node #0,1,0: 47:[38, 27] Operation: 51-24=27 Exploring Operation: 24+38=62, Resulting Numbers: [51, 62] Generated Node #0,1,1: 47:[51, 62] Operation: 24+38=62 Moving to Node #0,1,1 Current State: 47:[51, 62], Operations: ['55-17=38', '24+38=62'] Exploring Operation: 62-51=11, Resulting Numbers: [11] 11,47 unequal: No Solution Exploring Operation: 51+62=113, Resulting Numbers: [113] 113,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[38, 27], Operations: ['55-17=38', '51-24=27'] Exploring Operation: 38+27=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[51, 14], Operations: ['24+17=41', '55-41=14'] Exploring Operation: 51+14=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[55, 10], Operations: ['24+17=41', '51-41=10'] Exploring Operation: 55-10=45, Resulting Numbers: [45] 45,47 unequal: No Solution Exploring Operation: 55+10=65, Resulting Numbers: [65] 65,47 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 11, 1, 18, 53 ]
59
[ "11+1=12", "18+53=71", "71-12=59" ]
Current State: 59:[11, 1, 18, 53], Operations: [] Exploring Operation: 11+1=12, Resulting Numbers: [18, 53, 12] Generated Node #2: [18, 53, 12] from Operation: 11+1=12 Current State: 59:[18, 53, 12], Operations: ['11+1=12'] Exploring Operation: 18+53=71, Resulting Numbers: [12, 71] Generated Node #3: [12, 71] from Operation: 18+53=71 Current State: 59:[12, 71], Operations: ['11+1=12', '18+53=71'] Exploring Operation: 71-12=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[11, 1, 18, 53], Operations: [] Exploring Operation: 11+1=12, Resulting Numbers: [18, 53, 12] Generated Node #0,0: 59:[18, 53, 12] Operation: 11+1=12 Exploring Operation: 11+18=29, Resulting Numbers: [1, 53, 29] Generated Node #0,1: 59:[1, 53, 29] Operation: 11+18=29 Exploring Operation: 1+18=19, Resulting Numbers: [11, 53, 19] Generated Node #0,2: 59:[11, 53, 19] Operation: 1+18=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[18, 53, 12], Operations: ['11+1=12'] Exploring Operation: 18+12=30, Resulting Numbers: [53, 30] Generated Node #0,0,0: 59:[53, 30] Operation: 18+12=30 Exploring Operation: 18+53=71, Resulting Numbers: [12, 71] Generated Node #0,0,1: 59:[12, 71] Operation: 18+53=71 Exploring Operation: 53+12=65, Resulting Numbers: [18, 65] Generated Node #0,0,2: 59:[18, 65] Operation: 53+12=65 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[53, 30], Operations: ['11+1=12', '18+12=30'] Exploring Operation: 53+30=83, Resulting Numbers: [83] 83,59 unequal: No Solution Exploring Operation: 53*30=1590, Resulting Numbers: [1590] 1590,59 unequal: No Solution Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 59:[18, 65], Operations: ['11+1=12', '53+12=65'] Exploring Operation: 18+65=83, Resulting Numbers: [83] 83,59 unequal: No Solution Exploring Operation: 18*65=1170, Resulting Numbers: [1170] 1170,59 unequal: No Solution Exploring Operation: 65-18=47, Resulting Numbers: [47] 47,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 59:[12, 71], Operations: ['11+1=12', '18+53=71'] Exploring Operation: 71-12=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[11, 1, 18, 53], Operations: [] Exploring Operation: 11+1=12, Resulting Numbers: [18, 53, 12] Generated Node #0,0: 59:[18, 53, 12] Operation: 11+1=12 Moving to Node #0,0 Current State: 59:[18, 53, 12], Operations: ['11+1=12'] Exploring Operation: 18+53=71, Resulting Numbers: [12, 71] Generated Node #0,0,1: 59:[12, 71] Operation: 18+53=71 Moving to Node #0,0,1 Current State: 59:[12, 71], Operations: ['11+1=12', '18+53=71'] Exploring Operation: 71-12=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 4, 63, 39, 43 ]
37
[ "63-39=24", "24/4=6", "43-6=37" ]
Current State: 37:[4, 63, 39, 43], Operations: [] Exploring Operation: 63-39=24, Resulting Numbers: [4, 43, 24] Generated Node #2: [4, 43, 24] from Operation: 63-39=24 Current State: 37:[4, 43, 24], Operations: ['63-39=24'] Exploring Operation: 24/4=6, Resulting Numbers: [43, 6] Generated Node #3: [43, 6] from Operation: 24/4=6 Current State: 37:[43, 6], Operations: ['63-39=24', '24/4=6'] Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[4, 63, 39, 43], Operations: [] Exploring Operation: 63-4=59, Resulting Numbers: [39, 43, 59] Generated Node #0,0: 37:[39, 43, 59] Operation: 63-4=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[39, 43, 59], Operations: ['63-4=59'] Exploring Operation: 59-39=20, Resulting Numbers: [43, 20] Generated Node #0,0,0: 37:[43, 20] Operation: 59-39=20 Moving to Node #0,0,0 Current State: 37:[43, 20], Operations: ['63-4=59', '59-39=20'] Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 2, 15, 14, 22 ]
80
[ "15+14=29", "2*29=58", "22+58=80" ]
Current State: 80:[2, 15, 14, 22], Operations: [] Exploring Operation: 15+14=29, Resulting Numbers: [2, 22, 29] Generated Node #2: [2, 22, 29] from Operation: 15+14=29 Current State: 80:[2, 22, 29], Operations: ['15+14=29'] Exploring Operation: 2*29=58, Resulting Numbers: [22, 58] Generated Node #3: [22, 58] from Operation: 2*29=58 Current State: 80:[22, 58], Operations: ['15+14=29', '2*29=58'] Exploring Operation: 22+58=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[2, 15, 14, 22], Operations: [] Exploring Operation: 2+14=16, Resulting Numbers: [15, 22, 16] Generated Node #0,0: 80:[15, 22, 16] Operation: 2+14=16 Exploring Operation: 22-2=20, Resulting Numbers: [15, 14, 20] Generated Node #0,1: 80:[15, 14, 20] Operation: 22-2=20 Exploring Operation: 22-14=8, Resulting Numbers: [2, 15, 8] Generated Node #0,2: 80:[2, 15, 8] Operation: 22-14=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[2, 15, 8], Operations: ['22-14=8'] Exploring Operation: 2*8=16, Resulting Numbers: [15, 16] Generated Node #0,2,0: 80:[15, 16] Operation: 2*8=16 Exploring Operation: 2+15=17, Resulting Numbers: [8, 17] Generated Node #0,2,1: 80:[8, 17] Operation: 2+15=17 Exploring Operation: 2+8=10, Resulting Numbers: [15, 10] Generated Node #0,2,2: 80:[15, 10] Operation: 2+8=10 Moving to Node #0,2,0 Current State: 80:[15, 16], Operations: ['22-14=8', '2*8=16'] Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,80 unequal: No Solution Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,80 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[8, 17], Operations: ['22-14=8', '2+15=17'] Exploring Operation: 8+17=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 8*17=136, Resulting Numbers: [136] 136,80 unequal: No Solution Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[15, 10], Operations: ['22-14=8', '2+8=10'] Exploring Operation: 15*10=150, Resulting Numbers: [150] 150,80 unequal: No Solution Exploring Operation: 15+10=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[15, 22, 16], Operations: ['2+14=16'] Exploring Operation: 22-15=7, Resulting Numbers: [16, 7] Generated Node #0,0,0: 80:[16, 7] Operation: 22-15=7 Exploring Operation: 22-16=6, Resulting Numbers: [15, 6] Generated Node #0,0,1: 80:[15, 6] Operation: 22-16=6 Exploring Operation: 15+22=37, Resulting Numbers: [16, 37] Generated Node #0,0,2: 80:[16, 37] Operation: 15+22=37 Moving to Node #0,0,0 Current State: 80:[16, 7], Operations: ['2+14=16', '22-15=7'] Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 16*7=112, Resulting Numbers: [112] 112,80 unequal: No Solution Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[15, 6], Operations: ['2+14=16', '22-16=6'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,80 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[16, 37], Operations: ['2+14=16', '15+22=37'] Exploring Operation: 16+37=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 16*37=592, Resulting Numbers: [592] 592,80 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 #0,1 Current State: 80:[15, 14, 20], Operations: ['22-2=20'] Exploring Operation: 20-14=6, Resulting Numbers: [15, 6] Generated Node #0,1,0: 80:[15, 6] Operation: 20-14=6 Exploring Operation: 20-15=5, Resulting Numbers: [14, 5] Generated Node #0,1,1: 80:[14, 5] Operation: 20-15=5 Exploring Operation: 15-14=1, Resulting Numbers: [20, 1] Generated Node #0,1,2: 80:[20, 1] Operation: 15-14=1 Moving to Node #0,1,2 Current State: 80:[20, 1], Operations: ['22-2=20', '15-14=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 Moving to Node #0,1,0 Current State: 80:[15, 6], Operations: ['22-2=20', '20-14=6'] Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,80 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[14, 5], Operations: ['22-2=20', '20-15=5'] Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,80 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
[ 12, 17, 27, 24 ]
56
[ "17-12=5", "27+24=51", "5+51=56" ]
Current State: 56:[12, 17, 27, 24], Operations: [] Exploring Operation: 17-12=5, Resulting Numbers: [27, 24, 5] Generated Node #2: [27, 24, 5] from Operation: 17-12=5 Current State: 56:[27, 24, 5], Operations: ['17-12=5'] Exploring Operation: 27+24=51, Resulting Numbers: [5, 51] Generated Node #3: [5, 51] from Operation: 27+24=51 Current State: 56:[5, 51], Operations: ['17-12=5', '27+24=51'] Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[12, 17, 27, 24], Operations: [] Exploring Operation: 24-17=7, Resulting Numbers: [12, 27, 7] Generated Node #0,0: 56:[12, 27, 7] Operation: 24-17=7 Exploring Operation: 24/12=2, Resulting Numbers: [17, 27, 2] Generated Node #0,1: 56:[17, 27, 2] Operation: 24/12=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[12, 27, 7], Operations: ['24-17=7'] Exploring Operation: 27-12=15, Resulting Numbers: [7, 15] Generated Node #0,0,0: 56:[7, 15] Operation: 27-12=15 Exploring Operation: 12-7=5, Resulting Numbers: [27, 5] Generated Node #0,0,1: 56:[27, 5] Operation: 12-7=5 Moving to Node #0,0,0 Current State: 56:[7, 15], Operations: ['24-17=7', '27-12=15'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,56 unequal: No Solution Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[27, 5], Operations: ['24-17=7', '12-7=5'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[17, 27, 2], Operations: ['24/12=2'] Exploring Operation: 27-17=10, Resulting Numbers: [2, 10] Generated Node #0,1,0: 56:[2, 10] Operation: 27-17=10 Exploring Operation: 17-2=15, Resulting Numbers: [27, 15] Generated Node #0,1,1: 56:[27, 15] Operation: 17-2=15 Moving to Node #0,1,0 Current State: 56:[2, 10], Operations: ['24/12=2', '27-17=10'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,56 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[27, 15], Operations: ['24/12=2', '17-2=15'] Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,56 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
[ 92, 43, 56, 27 ]
51
[ "92+43=135", "135/27=5", "56-5=51" ]
Current State: 51:[92, 43, 56, 27], Operations: [] Exploring Operation: 92+43=135, Resulting Numbers: [56, 27, 135] Generated Node #2: [56, 27, 135] from Operation: 92+43=135 Current State: 51:[56, 27, 135], Operations: ['92+43=135'] Exploring Operation: 135/27=5, Resulting Numbers: [56, 5] Generated Node #3: [56, 5] from Operation: 135/27=5 Current State: 51:[56, 5], Operations: ['92+43=135', '135/27=5'] Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[92, 43, 56, 27], Operations: [] Exploring Operation: 92-27=65, Resulting Numbers: [43, 56, 65] Generated Node #0,0: 51:[43, 56, 65] Operation: 92-27=65 Exploring Operation: 92-43=49, Resulting Numbers: [56, 27, 49] Generated Node #0,1: 51:[56, 27, 49] Operation: 92-43=49 Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[56, 27, 49], Operations: ['92-43=49'] Exploring Operation: 49-27=22, Resulting Numbers: [56, 22] Generated Node #0,1,0: 51:[56, 22] Operation: 49-27=22 Exploring Operation: 56-27=29, Resulting Numbers: [49, 29] Generated Node #0,1,1: 51:[49, 29] Operation: 56-27=29 Moving to Node #0,1,0 Current State: 51:[56, 22], Operations: ['92-43=49', '49-27=22'] Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,51 unequal: No Solution Exploring Operation: 56+22=78, Resulting Numbers: [78] 78,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[49, 29], Operations: ['92-43=49', '56-27=29'] Exploring Operation: 49-29=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 49+29=78, Resulting Numbers: [78] 78,51 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 #0,0 Current State: 51:[43, 56, 65], Operations: ['92-27=65'] Exploring Operation: 65-56=9, Resulting Numbers: [43, 9] Generated Node #0,0,0: 51:[43, 9] Operation: 65-56=9 Exploring Operation: 65-43=22, Resulting Numbers: [56, 22] Generated Node #0,0,1: 51:[56, 22] Operation: 65-43=22 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 51:[56, 22], Operations: ['92-27=65', '65-43=22'] Exploring Operation: 56+22=78, Resulting Numbers: [78] 78,51 unequal: No Solution Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,51 unequal: No Solution No 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: 51:[43, 9], Operations: ['92-27=65', '65-56=9'] Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,51 unequal: No Solution Exploring Operation: 43+9=52, Resulting Numbers: [52] 52,51 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
[ 99, 75, 10, 15 ]
84
[ "99-10=89", "75/15=5", "89-5=84" ]
Current State: 84:[99, 75, 10, 15], Operations: [] Exploring Operation: 99-10=89, Resulting Numbers: [75, 15, 89] Generated Node #2: [75, 15, 89] from Operation: 99-10=89 Current State: 84:[75, 15, 89], Operations: ['99-10=89'] Exploring Operation: 75/15=5, Resulting Numbers: [89, 5] Generated Node #3: [89, 5] from Operation: 75/15=5 Current State: 84:[89, 5], Operations: ['99-10=89', '75/15=5'] Exploring Operation: 89-5=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[99, 75, 10, 15], Operations: [] Exploring Operation: 75+10=85, Resulting Numbers: [99, 15, 85] Generated Node #0,0: 84:[99, 15, 85] Operation: 75+10=85 Exploring Operation: 99-75=24, Resulting Numbers: [10, 15, 24] Generated Node #0,1: 84:[10, 15, 24] Operation: 99-75=24 Exploring Operation: 75/15=5, Resulting Numbers: [99, 10, 5] Generated Node #0,2: 84:[99, 10, 5] Operation: 75/15=5 Exploring Operation: 99-15=84, Resulting Numbers: [75, 10, 84] Generated Node #0,3: 84:[75, 10, 84] Operation: 99-15=84 Exploring Operation: 99-10=89, Resulting Numbers: [75, 15, 89] Generated Node #0,4: 84:[75, 15, 89] Operation: 99-10=89 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[10, 15, 24], Operations: ['99-75=24'] Exploring Operation: 15-10=5, Resulting Numbers: [24, 5] Generated Node #0,1,0: 84:[24, 5] Operation: 15-10=5 Exploring Operation: 24-10=14, Resulting Numbers: [15, 14] Generated Node #0,1,1: 84:[15, 14] Operation: 24-10=14 Exploring Operation: 10+15=25, Resulting Numbers: [24, 25] Generated Node #0,1,2: 84:[24, 25] Operation: 10+15=25 Exploring Operation: 15+24=39, Resulting Numbers: [10, 39] Generated Node #0,1,3: 84:[10, 39] Operation: 15+24=39 Exploring Operation: 24-15=9, Resulting Numbers: [10, 9] Generated Node #0,1,4: 84:[10, 9] Operation: 24-15=9 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 84:[15, 14], Operations: ['99-75=24', '24-10=14'] Exploring Operation: 15*14=210, Resulting Numbers: [210] 210,84 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,84 unequal: No Solution Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,84 unequal: No Solution No 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: 84:[24, 5], Operations: ['99-75=24', '15-10=5'] Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,84 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 84:[10, 9], Operations: ['99-75=24', '24-15=9'] Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,84 unequal: No Solution Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,84 unequal: No Solution No 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: 84:[10, 39], Operations: ['99-75=24', '15+24=39'] Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,84 unequal: No Solution Exploring Operation: 10*39=390, Resulting Numbers: [390] 390,84 unequal: No Solution Exploring Operation: 10+39=49, Resulting Numbers: [49] 49,84 unequal: No Solution No 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: 84:[24, 25], Operations: ['99-75=24', '10+15=25'] Exploring Operation: 24*25=600, Resulting Numbers: [600] 600,84 unequal: No Solution Exploring Operation: 24+25=49, Resulting Numbers: [49] 49,84 unequal: No Solution Exploring Operation: 25-24=1, Resulting Numbers: [1] 1,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 84:[75, 10, 84], Operations: ['99-15=84'] Exploring Operation: 75-10=65, Resulting Numbers: [84, 65] Generated Node #0,3,0: 84:[84, 65] Operation: 75-10=65 Exploring Operation: 10+84=94, Resulting Numbers: [75, 94] Generated Node #0,3,1: 84:[75, 94] Operation: 10+84=94 Exploring Operation: 84-10=74, Resulting Numbers: [75, 74] Generated Node #0,3,2: 84:[75, 74] Operation: 84-10=74 Exploring Operation: 75+10=85, Resulting Numbers: [84, 85] Generated Node #0,3,3: 84:[84, 85] Operation: 75+10=85 Exploring Operation: 84-75=9, Resulting Numbers: [10, 9] Generated Node #0,3,4: 84:[10, 9] Operation: 84-75=9 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 84:[84, 85], Operations: ['99-15=84', '75+10=85'] Exploring Operation: 85-84=1, Resulting Numbers: [1] 1,84 unequal: No Solution Exploring Operation: 84+85=169, Resulting Numbers: [169] 169,84 unequal: No Solution Exploring Operation: 84*85=7140, Resulting Numbers: [7140] 7140,84 unequal: No Solution No 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: 84:[10, 9], Operations: ['99-15=84', '84-75=9'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,84 unequal: No Solution Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,84 unequal: No Solution No 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: 84:[84, 65], Operations: ['99-15=84', '75-10=65'] Exploring Operation: 84*65=5460, Resulting Numbers: [5460] 5460,84 unequal: No Solution Exploring Operation: 84-65=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 84+65=149, Resulting Numbers: [149] 149,84 unequal: No Solution No 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: 84:[75, 94], Operations: ['99-15=84', '10+84=94'] Exploring Operation: 94-75=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 75+94=169, Resulting Numbers: [169] 169,84 unequal: No Solution Exploring Operation: 75*94=7050, Resulting Numbers: [7050] 7050,84 unequal: No Solution No 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: 84:[75, 74], Operations: ['99-15=84', '84-10=74'] Exploring Operation: 75-74=1, Resulting Numbers: [1] 1,84 unequal: No Solution Exploring Operation: 75+74=149, Resulting Numbers: [149] 149,84 unequal: No Solution Exploring Operation: 75*74=5550, Resulting Numbers: [5550] 5550,84 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: 84:[75, 15, 89], Operations: ['99-10=89'] Exploring Operation: 89-75=14, Resulting Numbers: [15, 14] Generated Node #0,4,0: 84:[15, 14] Operation: 89-75=14 Exploring Operation: 75+15=90, Resulting Numbers: [89, 90] Generated Node #0,4,1: 84:[89, 90] Operation: 75+15=90 Exploring Operation: 89-15=74, Resulting Numbers: [75, 74] Generated Node #0,4,2: 84:[75, 74] Operation: 89-15=74 Exploring Operation: 75/15=5, Resulting Numbers: [89, 5] Generated Node #0,4,3: 84:[89, 5] Operation: 75/15=5 Exploring Operation: 75-15=60, Resulting Numbers: [89, 60] Generated Node #0,4,4: 84:[89, 60] Operation: 75-15=60 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 84:[15, 14], Operations: ['99-10=89', '89-75=14'] Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,84 unequal: No Solution Exploring Operation: 15*14=210, Resulting Numbers: [210] 210,84 unequal: No Solution Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 84:[89, 5], Operations: ['99-10=89', '75/15=5'] Exploring Operation: 89-5=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[99, 75, 10, 15], Operations: [] Exploring Operation: 99-10=89, Resulting Numbers: [75, 15, 89] Generated Node #0,4: 84:[75, 15, 89] Operation: 99-10=89 Moving to Node #0,4 Current State: 84:[75, 15, 89], Operations: ['99-10=89'] Exploring Operation: 75/15=5, Resulting Numbers: [89, 5] Generated Node #0,4,3: 84:[89, 5] Operation: 75/15=5 Moving to Node #0,4,3 Current State: 84:[89, 5], Operations: ['99-10=89', '75/15=5'] Exploring Operation: 89-5=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.949653
hs_5
sum_heuristic
[ 19, 34, 83, 63 ]
34
[ "83-19=64", "64-63=1", "34*1=34" ]
Current State: 34:[19, 34, 83, 63], Operations: [] Exploring Operation: 83-19=64, Resulting Numbers: [34, 63, 64] Generated Node #2: [34, 63, 64] from Operation: 83-19=64 Current State: 34:[34, 63, 64], Operations: ['83-19=64'] Exploring Operation: 64-63=1, Resulting Numbers: [34, 1] Generated Node #3: [34, 1] from Operation: 64-63=1 Current State: 34:[34, 1], Operations: ['83-19=64', '64-63=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[19, 34, 83, 63], Operations: [] Exploring Operation: 83-34=49, Resulting Numbers: [19, 63, 49] Generated Node #0,0: 34:[19, 63, 49] Operation: 83-34=49 Exploring Operation: 83-63=20, Resulting Numbers: [19, 34, 20] Generated Node #0,1: 34:[19, 34, 20] Operation: 83-63=20 Exploring Operation: 63-19=44, Resulting Numbers: [34, 83, 44] Generated Node #0,2: 34:[34, 83, 44] Operation: 63-19=44 Exploring Operation: 63-34=29, Resulting Numbers: [19, 83, 29] Generated Node #0,3: 34:[19, 83, 29] Operation: 63-34=29 Exploring Operation: 83-19=64, Resulting Numbers: [34, 63, 64] Generated Node #0,4: 34:[34, 63, 64] Operation: 83-19=64 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[19, 34, 20], Operations: ['83-63=20'] Exploring Operation: 19+20=39, Resulting Numbers: [34, 39] Generated Node #0,1,0: 34:[34, 39] Operation: 19+20=39 Exploring Operation: 19+34=53, Resulting Numbers: [20, 53] Generated Node #0,1,1: 34:[20, 53] Operation: 19+34=53 Exploring Operation: 34-20=14, Resulting Numbers: [19, 14] Generated Node #0,1,2: 34:[19, 14] Operation: 34-20=14 Exploring Operation: 20-19=1, Resulting Numbers: [34, 1] Generated Node #0,1,3: 34:[34, 1] Operation: 20-19=1 Exploring Operation: 34-19=15, Resulting Numbers: [20, 15] Generated Node #0,1,4: 34:[20, 15] Operation: 34-19=15 Moving to Node #0,1,3 Current State: 34:[34, 1], Operations: ['83-63=20', '20-19=1'] Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,34 unequal: No Solution Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,34 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[19, 34, 83, 63], Operations: [] Exploring Operation: 83-63=20, Resulting Numbers: [19, 34, 20] Generated Node #0,1: 34:[19, 34, 20] Operation: 83-63=20 Moving to Node #0,1 Current State: 34:[19, 34, 20], Operations: ['83-63=20'] Exploring Operation: 20-19=1, Resulting Numbers: [34, 1] Generated Node #0,1,3: 34:[34, 1] Operation: 20-19=1 Moving to Node #0,1,3 Current State: 34:[34, 1], Operations: ['83-63=20', '20-19=1'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 40, 57, 85, 17 ]
84
[ "57-40=17", "17/17=1", "85-1=84" ]
Current State: 84:[40, 57, 85, 17], Operations: [] Exploring Operation: 57-40=17, Resulting Numbers: [85, 17, 17] Generated Node #2: [85, 17, 17] from Operation: 57-40=17 Current State: 84:[85, 17, 17], Operations: ['57-40=17'] Exploring Operation: 17/17=1, Resulting Numbers: [85, 1] Generated Node #3: [85, 1] from Operation: 17/17=1 Current State: 84:[85, 1], Operations: ['57-40=17', '17/17=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[40, 57, 85, 17], Operations: [] Exploring Operation: 85-57=28, Resulting Numbers: [40, 17, 28] Generated Node #0,0: 84:[40, 17, 28] Operation: 85-57=28 Exploring Operation: 57-17=40, Resulting Numbers: [40, 85, 40] Generated Node #0,1: 84:[40, 85, 40] Operation: 57-17=40 Exploring Operation: 57+17=74, Resulting Numbers: [40, 85, 74] Generated Node #0,2: 84:[40, 85, 74] Operation: 57+17=74 Exploring Operation: 57-40=17, Resulting Numbers: [85, 17, 17] Generated Node #0,3: 84:[85, 17, 17] Operation: 57-40=17 Exploring Operation: 40+57=97, Resulting Numbers: [85, 17, 97] Generated Node #0,4: 84:[85, 17, 97] Operation: 40+57=97 Moving to Node #0,0 Current State: 84:[40, 17, 28], Operations: ['85-57=28'] Exploring Operation: 40-28=12, Resulting Numbers: [17, 12] Generated Node #0,0,0: 84:[17, 12] Operation: 40-28=12 Exploring Operation: 40-17=23, Resulting Numbers: [28, 23] Generated Node #0,0,1: 84:[28, 23] Operation: 40-17=23 Exploring Operation: 17+28=45, Resulting Numbers: [40, 45] Generated Node #0,0,2: 84:[40, 45] Operation: 17+28=45 Exploring Operation: 40+17=57, Resulting Numbers: [28, 57] Generated Node #0,0,3: 84:[28, 57] Operation: 40+17=57 Exploring Operation: 28-17=11, Resulting Numbers: [40, 11] Generated Node #0,0,4: 84:[40, 11] Operation: 28-17=11 Moving to Node #0,1 Current State: 84:[40, 85, 40], Operations: ['57-17=40'] Exploring Operation: 40-40=0, Resulting Numbers: [85, 0] Generated Node #0,1,0: 84:[85, 0] Operation: 40-40=0 Exploring Operation: 85-40=45, Resulting Numbers: [40, 45] Generated Node #0,1,1: 84:[40, 45] Operation: 85-40=45 Exploring Operation: 40/40=1, Resulting Numbers: [85, 1] Generated Node #0,1,2: 84:[85, 1] Operation: 40/40=1 Exploring Operation: 40+40=80, Resulting Numbers: [85, 80] Generated Node #0,1,3: 84:[85, 80] Operation: 40+40=80 Exploring Operation: 85-40=45, Resulting Numbers: [40, 45] Generated Node #0,1,4: 84:[40, 45] Operation: 85-40=45 Moving to Node #0,3 Current State: 84:[85, 17, 17], Operations: ['57-40=17'] Exploring Operation: 17-17=0, Resulting Numbers: [85, 0] Generated Node #0,3,0: 84:[85, 0] Operation: 17-17=0 Exploring Operation: 17/17=1, Resulting Numbers: [85, 1] Generated Node #0,3,1: 84:[85, 1] Operation: 17/17=1 Exploring Operation: 85/17=5, Resulting Numbers: [17, 5] Generated Node #0,3,2: 84:[17, 5] Operation: 85/17=5 Exploring Operation: 17+17=34, Resulting Numbers: [85, 34] Generated Node #0,3,3: 84:[85, 34] Operation: 17+17=34 Exploring Operation: 85/17=5, Resulting Numbers: [17, 5] Generated Node #0,3,4: 84:[17, 5] Operation: 85/17=5 Moving to Node #0,2 Current State: 84:[40, 85, 74], Operations: ['57+17=74'] Exploring Operation: 85-40=45, Resulting Numbers: [74, 45] Generated Node #0,2,0: 84:[74, 45] Operation: 85-40=45 Exploring Operation: 85-74=11, Resulting Numbers: [40, 11] Generated Node #0,2,1: 84:[40, 11] Operation: 85-74=11 Exploring Operation: 40+74=114, Resulting Numbers: [85, 114] Generated Node #0,2,2: 84:[85, 114] Operation: 40+74=114 Exploring Operation: 74-40=34, Resulting Numbers: [85, 34] Generated Node #0,2,3: 84:[85, 34] Operation: 74-40=34 Exploring Operation: 40+85=125, Resulting Numbers: [74, 125] Generated Node #0,2,4: 84:[74, 125] Operation: 40+85=125 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 84:[40, 11], Operations: ['57+17=74', '85-74=11'] Exploring Operation: 40+11=51, Resulting Numbers: [51] 51,84 unequal: No Solution Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,84 unequal: No Solution Exploring Operation: 40*11=440, Resulting Numbers: [440] 440,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 84:[85, 34], Operations: ['57+17=74', '74-40=34'] Exploring Operation: 85*34=2890, Resulting Numbers: [2890] 2890,84 unequal: No Solution Exploring Operation: 85-34=51, Resulting Numbers: [51] 51,84 unequal: No Solution Exploring Operation: 85+34=119, Resulting Numbers: [119] 119,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[74, 45], Operations: ['57+17=74', '85-40=45'] Exploring Operation: 74+45=119, Resulting Numbers: [119] 119,84 unequal: No Solution Exploring Operation: 74-45=29, Resulting Numbers: [29] 29,84 unequal: No Solution Exploring Operation: 74*45=3330, Resulting Numbers: [3330] 3330,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 84:[85, 114], Operations: ['57+17=74', '40+74=114'] Exploring Operation: 85+114=199, Resulting Numbers: [199] 199,84 unequal: No Solution Exploring Operation: 114-85=29, Resulting Numbers: [29] 29,84 unequal: No Solution Exploring Operation: 85*114=9690, Resulting Numbers: [9690] 9690,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 84:[74, 125], Operations: ['57+17=74', '40+85=125'] Exploring Operation: 74*125=9250, Resulting Numbers: [9250] 9250,84 unequal: No Solution Exploring Operation: 74+125=199, Resulting Numbers: [199] 199,84 unequal: No Solution Exploring Operation: 125-74=51, Resulting Numbers: [51] 51,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 84:[85, 17, 97], Operations: ['40+57=97'] Exploring Operation: 85+17=102, Resulting Numbers: [97, 102] Generated Node #0,4,0: 84:[97, 102] Operation: 85+17=102 Exploring Operation: 85-17=68, Resulting Numbers: [97, 68] Generated Node #0,4,1: 84:[97, 68] Operation: 85-17=68 Exploring Operation: 85/17=5, Resulting Numbers: [97, 5] Generated Node #0,4,2: 84:[97, 5] Operation: 85/17=5 Exploring Operation: 97-17=80, Resulting Numbers: [85, 80] Generated Node #0,4,3: 84:[85, 80] Operation: 97-17=80 Exploring Operation: 97-85=12, Resulting Numbers: [17, 12] Generated Node #0,4,4: 84:[17, 12] Operation: 97-85=12 Moving to Node #0,0,1 Current State: 84:[28, 23], Operations: ['85-57=28', '40-17=23'] Exploring Operation: 28*23=644, Resulting Numbers: [644] 644,84 unequal: No Solution Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 28+23=51, Resulting Numbers: [51] 51,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[85, 1], Operations: ['57-17=40', '40/40=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[40, 57, 85, 17], Operations: [] Exploring Operation: 57-17=40, Resulting Numbers: [40, 85, 40] Generated Node #0,1: 84:[40, 85, 40] Operation: 57-17=40 Moving to Node #0,1 Current State: 84:[40, 85, 40], Operations: ['57-17=40'] Exploring Operation: 40/40=1, Resulting Numbers: [85, 1] Generated Node #0,1,2: 84:[85, 1] Operation: 40/40=1 Moving to Node #0,1,2 Current State: 84:[85, 1], Operations: ['57-17=40', '40/40=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.953993
hs_5
mult_heuristic
[ 40, 2, 35, 29 ]
48
[ "40+2=42", "35-29=6", "42+6=48" ]
Current State: 48:[40, 2, 35, 29], Operations: [] Exploring Operation: 40+2=42, Resulting Numbers: [35, 29, 42] Generated Node #2: [35, 29, 42] from Operation: 40+2=42 Current State: 48:[35, 29, 42], Operations: ['40+2=42'] Exploring Operation: 35-29=6, Resulting Numbers: [42, 6] Generated Node #3: [42, 6] from Operation: 35-29=6 Current State: 48:[42, 6], Operations: ['40+2=42', '35-29=6'] Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[40, 2, 35, 29], Operations: [] Exploring Operation: 35-29=6, Resulting Numbers: [40, 2, 6] Generated Node #0,0: 48:[40, 2, 6] Operation: 35-29=6 Exploring Operation: 40-29=11, Resulting Numbers: [2, 35, 11] Generated Node #0,1: 48:[2, 35, 11] Operation: 40-29=11 Exploring Operation: 40-35=5, Resulting Numbers: [2, 29, 5] Generated Node #0,2: 48:[2, 29, 5] Operation: 40-35=5 Moving to Node #0,2 Current State: 48:[2, 29, 5], Operations: ['40-35=5'] Exploring Operation: 5-2=3, Resulting Numbers: [29, 3] Generated Node #0,2,0: 48:[29, 3] Operation: 5-2=3 Exploring Operation: 29-2=27, Resulting Numbers: [5, 27] Generated Node #0,2,1: 48:[5, 27] Operation: 29-2=27 Exploring Operation: 29-5=24, Resulting Numbers: [2, 24] Generated Node #0,2,2: 48:[2, 24] Operation: 29-5=24 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 48:[2, 24], Operations: ['40-35=5', '29-5=24'] Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[40, 2, 35, 29], Operations: [] Exploring Operation: 40-35=5, Resulting Numbers: [2, 29, 5] Generated Node #0,2: 48:[2, 29, 5] Operation: 40-35=5 Moving to Node #0,2 Current State: 48:[2, 29, 5], Operations: ['40-35=5'] Exploring Operation: 29-5=24, Resulting Numbers: [2, 24] Generated Node #0,2,2: 48:[2, 24] Operation: 29-5=24 Moving to Node #0,2,2 Current State: 48:[2, 24], Operations: ['40-35=5', '29-5=24'] Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 42, 62, 65, 30 ]
16
[ "65-62=3", "42/3=14", "30-14=16" ]
Current State: 16:[42, 62, 65, 30], Operations: [] Exploring Operation: 65-62=3, Resulting Numbers: [42, 30, 3] Generated Node #2: [42, 30, 3] from Operation: 65-62=3 Current State: 16:[42, 30, 3], Operations: ['65-62=3'] Exploring Operation: 42/3=14, Resulting Numbers: [30, 14] Generated Node #3: [30, 14] from Operation: 42/3=14 Current State: 16:[30, 14], Operations: ['65-62=3', '42/3=14'] Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[42, 62, 65, 30], Operations: [] Exploring Operation: 65-42=23, Resulting Numbers: [62, 30, 23] Generated Node #0,0: 16:[62, 30, 23] Operation: 65-42=23 Exploring Operation: 65-62=3, Resulting Numbers: [42, 30, 3] Generated Node #0,1: 16:[42, 30, 3] Operation: 65-62=3 Exploring Operation: 62-30=32, Resulting Numbers: [42, 65, 32] Generated Node #0,2: 16:[42, 65, 32] Operation: 62-30=32 Exploring Operation: 62-42=20, Resulting Numbers: [65, 30, 20] Generated Node #0,3: 16:[65, 30, 20] Operation: 62-42=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[42, 30, 3], Operations: ['65-62=3'] Exploring Operation: 42-3=39, Resulting Numbers: [30, 39] Generated Node #0,1,0: 16:[30, 39] Operation: 42-3=39 Exploring Operation: 42-30=12, Resulting Numbers: [3, 12] Generated Node #0,1,1: 16:[3, 12] Operation: 42-30=12 Exploring Operation: 30/3=10, Resulting Numbers: [42, 10] Generated Node #0,1,2: 16:[42, 10] Operation: 30/3=10 Exploring Operation: 42/3=14, Resulting Numbers: [30, 14] Generated Node #0,1,3: 16:[30, 14] Operation: 42/3=14 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[3, 12], Operations: ['65-62=3', '42-30=12'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,16 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,16 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,16 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 16:[30, 14], Operations: ['65-62=3', '42/3=14'] Exploring Operation: 30*14=420, Resulting Numbers: [420] 420,16 unequal: No Solution Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[42, 62, 65, 30], Operations: [] Exploring Operation: 65-62=3, Resulting Numbers: [42, 30, 3] Generated Node #0,1: 16:[42, 30, 3] Operation: 65-62=3 Moving to Node #0,1 Current State: 16:[42, 30, 3], Operations: ['65-62=3'] Exploring Operation: 42/3=14, Resulting Numbers: [30, 14] Generated Node #0,1,3: 16:[30, 14] Operation: 42/3=14 Moving to Node #0,1,3 Current State: 16:[30, 14], Operations: ['65-62=3', '42/3=14'] Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 18, 77, 29, 68 ]
61
[ "29-18=11", "77/11=7", "68-7=61" ]
Current State: 61:[18, 77, 29, 68], Operations: [] Exploring Operation: 29-18=11, Resulting Numbers: [77, 68, 11] Generated Node #2: [77, 68, 11] from Operation: 29-18=11 Current State: 61:[77, 68, 11], Operations: ['29-18=11'] Exploring Operation: 77/11=7, Resulting Numbers: [68, 7] Generated Node #3: [68, 7] from Operation: 77/11=7 Current State: 61:[68, 7], Operations: ['29-18=11', '77/11=7'] Exploring Operation: 68-7=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[18, 77, 29, 68], Operations: [] Exploring Operation: 18+29=47, Resulting Numbers: [77, 68, 47] Generated Node #0,0: 61:[77, 68, 47] Operation: 18+29=47 Exploring Operation: 77-18=59, Resulting Numbers: [29, 68, 59] Generated Node #0,1: 61:[29, 68, 59] Operation: 77-18=59 Exploring Operation: 77-29=48, Resulting Numbers: [18, 68, 48] Generated Node #0,2: 61:[18, 68, 48] Operation: 77-29=48 Exploring Operation: 68-18=50, Resulting Numbers: [77, 29, 50] Generated Node #0,3: 61:[77, 29, 50] Operation: 68-18=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[77, 68, 47], Operations: ['18+29=47'] Exploring Operation: 77+47=124, Resulting Numbers: [68, 124] Generated Node #0,0,0: 61:[68, 124] Operation: 77+47=124 Exploring Operation: 68-47=21, Resulting Numbers: [77, 21] Generated Node #0,0,1: 61:[77, 21] Operation: 68-47=21 Exploring Operation: 77-47=30, Resulting Numbers: [68, 30] Generated Node #0,0,2: 61:[68, 30] Operation: 77-47=30 Exploring Operation: 77-68=9, Resulting Numbers: [47, 9] Generated Node #0,0,3: 61:[47, 9] Operation: 77-68=9 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 61:[68, 30], Operations: ['18+29=47', '77-47=30'] Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,61 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,61 unequal: No Solution Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 61:[77, 21], Operations: ['18+29=47', '68-47=21'] Exploring Operation: 77*21=1617, Resulting Numbers: [1617] 1617,61 unequal: No Solution Exploring Operation: 77-21=56, Resulting Numbers: [56] 56,61 unequal: No Solution Exploring Operation: 77+21=98, Resulting Numbers: [98] 98,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 61:[47, 9], Operations: ['18+29=47', '77-68=9'] Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,61 unequal: No Solution Exploring Operation: 47*9=423, Resulting Numbers: [423] 423,61 unequal: No Solution Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[68, 124], Operations: ['18+29=47', '77+47=124'] Exploring Operation: 124-68=56, Resulting Numbers: [56] 56,61 unequal: No Solution Exploring Operation: 68+124=192, Resulting Numbers: [192] 192,61 unequal: No Solution Exploring Operation: 68*124=8432, Resulting Numbers: [8432] 8432,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[29, 68, 59], Operations: ['77-18=59'] Exploring Operation: 68-29=39, Resulting Numbers: [59, 39] Generated Node #0,1,0: 61:[59, 39] Operation: 68-29=39 Exploring Operation: 29+59=88, Resulting Numbers: [68, 88] Generated Node #0,1,1: 61:[68, 88] Operation: 29+59=88 Exploring Operation: 59-29=30, Resulting Numbers: [68, 30] Generated Node #0,1,2: 61:[68, 30] Operation: 59-29=30 Exploring Operation: 29+68=97, Resulting Numbers: [59, 97] Generated Node #0,1,3: 61:[59, 97] Operation: 29+68=97 Moving to Node #0,1,0 Current State: 61:[59, 39], Operations: ['77-18=59', '68-29=39'] Exploring Operation: 59-39=20, Resulting Numbers: [20] 20,61 unequal: No Solution Exploring Operation: 59+39=98, Resulting Numbers: [98] 98,61 unequal: No Solution Exploring Operation: 59*39=2301, Resulting Numbers: [2301] 2301,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[68, 88], Operations: ['77-18=59', '29+59=88'] Exploring Operation: 88-68=20, Resulting Numbers: [20] 20,61 unequal: No Solution Exploring Operation: 68+88=156, Resulting Numbers: [156] 156,61 unequal: No Solution Exploring Operation: 68*88=5984, Resulting Numbers: [5984] 5984,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[59, 97], Operations: ['77-18=59', '29+68=97'] Exploring Operation: 59*97=5723, Resulting Numbers: [5723] 5723,61 unequal: No Solution Exploring Operation: 59+97=156, Resulting Numbers: [156] 156,61 unequal: No Solution Exploring Operation: 97-59=38, Resulting Numbers: [38] 38,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[68, 30], Operations: ['77-18=59', '59-29=30'] Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,61 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,61 unequal: No Solution Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,61 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 #0,3 Current State: 61:[77, 29, 50], Operations: ['68-18=50'] Exploring Operation: 77-29=48, Resulting Numbers: [50, 48] Generated Node #0,3,0: 61:[50, 48] Operation: 77-29=48 Exploring Operation: 29+50=79, Resulting Numbers: [77, 79] Generated Node #0,3,1: 61:[77, 79] Operation: 29+50=79 Exploring Operation: 77+29=106, Resulting Numbers: [50, 106] Generated Node #0,3,2: 61:[50, 106] Operation: 77+29=106 Exploring Operation: 50-29=21, Resulting Numbers: [77, 21] Generated Node #0,3,3: 61:[77, 21] Operation: 50-29=21 Moving to Node #0,3,0 Current State: 61:[50, 48], Operations: ['68-18=50', '77-29=48'] Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,61 unequal: No Solution Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,61 unequal: No Solution Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[77, 79], Operations: ['68-18=50', '29+50=79'] Exploring Operation: 77*79=6083, Resulting Numbers: [6083] 6083,61 unequal: No Solution Exploring Operation: 79-77=2, Resulting Numbers: [2] 2,61 unequal: No Solution Exploring Operation: 77+79=156, Resulting Numbers: [156] 156,61 unequal: No Solution Moving to Node #0,3,3 Current State: 61:[77, 21], Operations: ['68-18=50', '50-29=21'] Exploring Operation: 77*21=1617, Resulting Numbers: [1617] 1617,61 unequal: No Solution Exploring Operation: 77-21=56, Resulting Numbers: [56] 56,61 unequal: No Solution Exploring Operation: 77+21=98, Resulting Numbers: [98] 98,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[50, 106], Operations: ['68-18=50', '77+29=106'] Exploring Operation: 106-50=56, Resulting Numbers: [56] 56,61 unequal: No Solution Exploring Operation: 50+106=156, Resulting Numbers: [156] 156,61 unequal: No Solution Exploring Operation: 50*106=5300, Resulting Numbers: [5300] 5300,61 unequal: No Solution No solution found. 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: 61:[18, 68, 48], Operations: ['77-29=48'] Exploring Operation: 18+68=86, Resulting Numbers: [48, 86] Generated Node #0,2,0: 61:[48, 86] Operation: 18+68=86 Exploring Operation: 18+48=66, Resulting Numbers: [68, 66] Generated Node #0,2,1: 61:[68, 66] Operation: 18+48=66 Exploring Operation: 68-18=50, Resulting Numbers: [48, 50] Generated Node #0,2,2: 61:[48, 50] Operation: 68-18=50 Exploring Operation: 48-18=30, Resulting Numbers: [68, 30] Generated Node #0,2,3: 61:[68, 30] Operation: 48-18=30 Moving to Node #0,2,1 Current State: 61:[68, 66], Operations: ['77-29=48', '18+48=66'] Exploring Operation: 68*66=4488, Resulting Numbers: [4488] 4488,61 unequal: No Solution Exploring Operation: 68+66=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 68-66=2, Resulting Numbers: [2] 2,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[48, 50], Operations: ['77-29=48', '68-18=50'] Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,61 unequal: No Solution Exploring Operation: 48*50=2400, Resulting Numbers: [2400] 2400,61 unequal: No Solution Exploring Operation: 48+50=98, Resulting Numbers: [98] 98,61 unequal: No Solution Moving to Node #0,2,3 Current State: 61:[68, 30], Operations: ['77-29=48', '48-18=30'] Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,61 unequal: No Solution Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,61 unequal: No Solution Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[48, 86], Operations: ['77-29=48', '18+68=86'] Exploring Operation: 86-48=38, Resulting Numbers: [38] 38,61 unequal: No Solution Exploring Operation: 48+86=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 48*86=4128, Resulting Numbers: [4128] 4128,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 12, 87, 73, 54 ]
52
[ "87-12=75", "73+54=127", "127-75=52" ]
Current State: 52:[12, 87, 73, 54], Operations: [] Exploring Operation: 87-12=75, Resulting Numbers: [73, 54, 75] Generated Node #2: [73, 54, 75] from Operation: 87-12=75 Current State: 52:[73, 54, 75], Operations: ['87-12=75'] Exploring Operation: 73+54=127, Resulting Numbers: [75, 127] Generated Node #3: [75, 127] from Operation: 73+54=127 Current State: 52:[75, 127], Operations: ['87-12=75', '73+54=127'] Exploring Operation: 127-75=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[12, 87, 73, 54], Operations: [] Exploring Operation: 73-54=19, Resulting Numbers: [12, 87, 19] Generated Node #0,0: 52:[12, 87, 19] Operation: 73-54=19 Exploring Operation: 87-54=33, Resulting Numbers: [12, 73, 33] Generated Node #0,1: 52:[12, 73, 33] Operation: 87-54=33 Exploring Operation: 87-73=14, Resulting Numbers: [12, 54, 14] Generated Node #0,2: 52:[12, 54, 14] Operation: 87-73=14 Moving to Node #0,2 Current State: 52:[12, 54, 14], Operations: ['87-73=14'] Exploring Operation: 12+14=26, Resulting Numbers: [54, 26] Generated Node #0,2,0: 52:[54, 26] Operation: 12+14=26 Exploring Operation: 54-12=42, Resulting Numbers: [14, 42] Generated Node #0,2,1: 52:[14, 42] Operation: 54-12=42 Exploring Operation: 14-12=2, Resulting Numbers: [54, 2] Generated Node #0,2,2: 52:[54, 2] Operation: 14-12=2 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 52:[54, 26], Operations: ['87-73=14', '12+14=26'] Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,52 unequal: No Solution Exploring Operation: 54*26=1404, Resulting Numbers: [1404] 1404,52 unequal: No Solution Exploring Operation: 54+26=80, Resulting Numbers: [80] 80,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 52:[54, 2], Operations: ['87-73=14', '14-12=2'] Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,52 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[12, 87, 73, 54], Operations: [] Exploring Operation: 87-73=14, Resulting Numbers: [12, 54, 14] Generated Node #0,2: 52:[12, 54, 14] Operation: 87-73=14 Moving to Node #0,2 Current State: 52:[12, 54, 14], Operations: ['87-73=14'] Exploring Operation: 14-12=2, Resulting Numbers: [54, 2] Generated Node #0,2,2: 52:[54, 2] Operation: 14-12=2 Moving to Node #0,2,2 Current State: 52:[54, 2], Operations: ['87-73=14', '14-12=2'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 47, 77, 2, 9 ]
89
[ "77-9=68", "2*68=136", "136-47=89" ]
Current State: 89:[47, 77, 2, 9], Operations: [] Exploring Operation: 77-9=68, Resulting Numbers: [47, 2, 68] Generated Node #2: [47, 2, 68] from Operation: 77-9=68 Current State: 89:[47, 2, 68], Operations: ['77-9=68'] Exploring Operation: 2*68=136, Resulting Numbers: [47, 136] Generated Node #3: [47, 136] from Operation: 2*68=136 Current State: 89:[47, 136], Operations: ['77-9=68', '2*68=136'] Exploring Operation: 136-47=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[47, 77, 2, 9], Operations: [] Exploring Operation: 47*2=94, Resulting Numbers: [77, 9, 94] Generated Node #0,0: 89:[77, 9, 94] Operation: 47*2=94 Exploring Operation: 2*9=18, Resulting Numbers: [47, 77, 18] Generated Node #0,1: 89:[47, 77, 18] Operation: 2*9=18 Moving to Node #0,0 Current State: 89:[77, 9, 94], Operations: ['47*2=94'] Exploring Operation: 77+9=86, Resulting Numbers: [94, 86] Generated Node #0,0,0: 89:[94, 86] Operation: 77+9=86 Exploring Operation: 94-9=85, Resulting Numbers: [77, 85] Generated Node #0,0,1: 89:[77, 85] Operation: 94-9=85 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[94, 86], Operations: ['47*2=94', '77+9=86'] Exploring Operation: 94-86=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 94+86=180, Resulting Numbers: [180] 180,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[77, 85], Operations: ['47*2=94', '94-9=85'] Exploring Operation: 77+85=162, Resulting Numbers: [162] 162,89 unequal: No Solution Exploring Operation: 85-77=8, Resulting Numbers: [8] 8,89 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: 89:[47, 77, 18], Operations: ['2*9=18'] Exploring Operation: 47+18=65, Resulting Numbers: [77, 65] Generated Node #0,1,0: 89:[77, 65] Operation: 47+18=65 Exploring Operation: 77+18=95, Resulting Numbers: [47, 95] Generated Node #0,1,1: 89:[47, 95] Operation: 77+18=95 Moving to Node #0,1,0 Current State: 89:[77, 65], Operations: ['2*9=18', '47+18=65'] Exploring Operation: 77-65=12, Resulting Numbers: [12] 12,89 unequal: No Solution Exploring Operation: 77+65=142, Resulting Numbers: [142] 142,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[47, 95], Operations: ['2*9=18', '77+18=95'] Exploring Operation: 95-47=48, Resulting Numbers: [48] 48,89 unequal: No Solution Exploring Operation: 47+95=142, Resulting Numbers: [142] 142,89 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 17, 15, 44, 28 ]
15
[ "44-17=27", "28-27=1", "15*1=15" ]
Current State: 15:[17, 15, 44, 28], Operations: [] Exploring Operation: 44-17=27, Resulting Numbers: [15, 28, 27] Generated Node #2: [15, 28, 27] from Operation: 44-17=27 Current State: 15:[15, 28, 27], Operations: ['44-17=27'] Exploring Operation: 28-27=1, Resulting Numbers: [15, 1] Generated Node #3: [15, 1] from Operation: 28-27=1 Current State: 15:[15, 1], Operations: ['44-17=27', '28-27=1'] Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[17, 15, 44, 28], Operations: [] Exploring Operation: 44-28=16, Resulting Numbers: [17, 15, 16] Generated Node #0,0: 15:[17, 15, 16] Operation: 44-28=16 Moving to Node #0,0 Current State: 15:[17, 15, 16], Operations: ['44-28=16'] Exploring Operation: 17-15=2, Resulting Numbers: [16, 2] Generated Node #0,0,0: 15:[16, 2] Operation: 17-15=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[16, 2], Operations: ['44-28=16', '17-15=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,15 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
[ 87, 5, 77, 66 ]
68
[ "87-77=10", "10/5=2", "66+2=68" ]
Current State: 68:[87, 5, 77, 66], Operations: [] Exploring Operation: 87-77=10, Resulting Numbers: [5, 66, 10] Generated Node #2: [5, 66, 10] from Operation: 87-77=10 Current State: 68:[5, 66, 10], Operations: ['87-77=10'] Exploring Operation: 10/5=2, Resulting Numbers: [66, 2] Generated Node #3: [66, 2] from Operation: 10/5=2 Current State: 68:[66, 2], Operations: ['87-77=10', '10/5=2'] Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[87, 5, 77, 66], Operations: [] Exploring Operation: 87-66=21, Resulting Numbers: [5, 77, 21] Generated Node #0,0: 68:[5, 77, 21] Operation: 87-66=21 Exploring Operation: 87-5=82, Resulting Numbers: [77, 66, 82] Generated Node #0,1: 68:[77, 66, 82] Operation: 87-5=82 Exploring Operation: 87-77=10, Resulting Numbers: [5, 66, 10] Generated Node #0,2: 68:[5, 66, 10] Operation: 87-77=10 Moving to Node #0,2 Current State: 68:[5, 66, 10], Operations: ['87-77=10'] Exploring Operation: 10-5=5, Resulting Numbers: [66, 5] Generated Node #0,2,0: 68:[66, 5] Operation: 10-5=5 Exploring Operation: 10/5=2, Resulting Numbers: [66, 2] Generated Node #0,2,1: 68:[66, 2] Operation: 10/5=2 Exploring Operation: 5+10=15, Resulting Numbers: [66, 15] Generated Node #0,2,2: 68:[66, 15] Operation: 5+10=15 Moving to Node #0,0 Current State: 68:[5, 77, 21], Operations: ['87-66=21'] Exploring Operation: 77-5=72, Resulting Numbers: [21, 72] Generated Node #0,0,0: 68:[21, 72] Operation: 77-5=72 Exploring Operation: 21-5=16, Resulting Numbers: [77, 16] Generated Node #0,0,1: 68:[77, 16] Operation: 21-5=16 Exploring Operation: 77-21=56, Resulting Numbers: [5, 56] Generated Node #0,0,2: 68:[5, 56] Operation: 77-21=56 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[21, 72], Operations: ['87-66=21', '77-5=72'] Exploring Operation: 21+72=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 21*72=1512, Resulting Numbers: [1512] 1512,68 unequal: No Solution Exploring Operation: 72-21=51, Resulting Numbers: [51] 51,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 68:[77, 16], Operations: ['87-66=21', '21-5=16'] Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,68 unequal: No Solution Exploring Operation: 77*16=1232, Resulting Numbers: [1232] 1232,68 unequal: No Solution Exploring Operation: 77+16=93, Resulting Numbers: [93] 93,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 68:[5, 56], Operations: ['87-66=21', '77-21=56'] Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,68 unequal: No Solution Exploring Operation: 5*56=280, Resulting Numbers: [280] 280,68 unequal: No Solution Exploring Operation: 5+56=61, Resulting Numbers: [61] 61,68 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: 68:[77, 66, 82], Operations: ['87-5=82'] Exploring Operation: 77-66=11, Resulting Numbers: [82, 11] Generated Node #0,1,0: 68:[82, 11] Operation: 77-66=11 Exploring Operation: 82-66=16, Resulting Numbers: [77, 16] Generated Node #0,1,1: 68:[77, 16] Operation: 82-66=16 Exploring Operation: 82-77=5, Resulting Numbers: [66, 5] Generated Node #0,1,2: 68:[66, 5] Operation: 82-77=5 Moving to Node #0,2,1 Current State: 68:[66, 2], Operations: ['87-77=10', '10/5=2'] Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[87, 5, 77, 66], Operations: [] Exploring Operation: 87-77=10, Resulting Numbers: [5, 66, 10] Generated Node #0,2: 68:[5, 66, 10] Operation: 87-77=10 Moving to Node #0,2 Current State: 68:[5, 66, 10], Operations: ['87-77=10'] Exploring Operation: 10/5=2, Resulting Numbers: [66, 2] Generated Node #0,2,1: 68:[66, 2] Operation: 10/5=2 Moving to Node #0,2,1 Current State: 68:[66, 2], Operations: ['87-77=10', '10/5=2'] Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
0.977431
hs_3
sum_heuristic
[ 48, 49, 72, 89 ]
60
[ "89-49=40", "72*40=2880", "2880/48=60" ]
Current State: 60:[48, 49, 72, 89], Operations: [] Exploring Operation: 89-49=40, Resulting Numbers: [48, 72, 40] Generated Node #2: [48, 72, 40] from Operation: 89-49=40 Current State: 60:[48, 72, 40], Operations: ['89-49=40'] Exploring Operation: 72*40=2880, Resulting Numbers: [48, 2880] Generated Node #3: [48, 2880] from Operation: 72*40=2880 Current State: 60:[48, 2880], Operations: ['89-49=40', '72*40=2880'] Exploring Operation: 2880/48=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[48, 49, 72, 89], Operations: [] Exploring Operation: 49-48=1, Resulting Numbers: [72, 89, 1] Generated Node #0,0: 60:[72, 89, 1] Operation: 49-48=1 Exploring Operation: 89-72=17, Resulting Numbers: [48, 49, 17] Generated Node #0,1: 60:[48, 49, 17] Operation: 89-72=17 Exploring Operation: 89-49=40, Resulting Numbers: [48, 72, 40] Generated Node #0,2: 60:[48, 72, 40] Operation: 89-49=40 Exploring Operation: 72-48=24, Resulting Numbers: [49, 89, 24] Generated Node #0,3: 60:[49, 89, 24] Operation: 72-48=24 Exploring Operation: 89-48=41, Resulting Numbers: [49, 72, 41] Generated Node #0,4: 60:[49, 72, 41] Operation: 89-48=41 Moving to Node #0,1 Current State: 60:[48, 49, 17], Operations: ['89-72=17'] Exploring Operation: 48-17=31, Resulting Numbers: [49, 31] Generated Node #0,1,0: 60:[49, 31] Operation: 48-17=31 Exploring Operation: 49-48=1, Resulting Numbers: [17, 1] Generated Node #0,1,1: 60:[17, 1] Operation: 49-48=1 Exploring Operation: 49-17=32, Resulting Numbers: [48, 32] Generated Node #0,1,2: 60:[48, 32] Operation: 49-17=32 Exploring Operation: 48+17=65, Resulting Numbers: [49, 65] Generated Node #0,1,3: 60:[49, 65] Operation: 48+17=65 Exploring Operation: 49+17=66, Resulting Numbers: [48, 66] Generated Node #0,1,4: 60:[48, 66] Operation: 49+17=66 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[17, 1], Operations: ['89-72=17', '49-48=1'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,60 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 #0,1,0 Current State: 60:[49, 31], Operations: ['89-72=17', '48-17=31'] Exploring Operation: 49+31=80, Resulting Numbers: [80] 80,60 unequal: No Solution Exploring Operation: 49-31=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 49*31=1519, Resulting Numbers: [1519] 1519,60 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 #0,1,2 Current State: 60:[48, 32], Operations: ['89-72=17', '49-17=32'] Exploring Operation: 48+32=80, Resulting Numbers: [80] 80,60 unequal: No Solution Exploring Operation: 48-32=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 48*32=1536, Resulting Numbers: [1536] 1536,60 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 #0,1,3 Current State: 60:[49, 65], Operations: ['89-72=17', '48+17=65'] Exploring Operation: 65-49=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 49+65=114, Resulting Numbers: [114] 114,60 unequal: No Solution Exploring Operation: 49*65=3185, Resulting Numbers: [3185] 3185,60 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 #0,1,4 Current State: 60:[48, 66], Operations: ['89-72=17', '49+17=66'] Exploring Operation: 66-48=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 48*66=3168, Resulting Numbers: [3168] 3168,60 unequal: No Solution Exploring Operation: 48+66=114, Resulting Numbers: [114] 114,60 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: 60:[49, 72, 41], Operations: ['89-48=41'] Exploring Operation: 72-41=31, Resulting Numbers: [49, 31] Generated Node #0,4,0: 60:[49, 31] Operation: 72-41=31 Exploring Operation: 49-41=8, Resulting Numbers: [72, 8] Generated Node #0,4,1: 60:[72, 8] Operation: 49-41=8 Exploring Operation: 49+41=90, Resulting Numbers: [72, 90] Generated Node #0,4,2: 60:[72, 90] Operation: 49+41=90 Exploring Operation: 72-49=23, Resulting Numbers: [41, 23] Generated Node #0,4,3: 60:[41, 23] Operation: 72-49=23 Exploring Operation: 72+41=113, Resulting Numbers: [49, 113] Generated Node #0,4,4: 60:[49, 113] Operation: 72+41=113 Moving to Node #0,2 Current State: 60:[48, 72, 40], Operations: ['89-49=40'] Exploring Operation: 72-40=32, Resulting Numbers: [48, 32] Generated Node #0,2,0: 60:[48, 32] Operation: 72-40=32 Exploring Operation: 48-40=8, Resulting Numbers: [72, 8] Generated Node #0,2,1: 60:[72, 8] Operation: 48-40=8 Exploring Operation: 72+40=112, Resulting Numbers: [48, 112] Generated Node #0,2,2: 60:[48, 112] Operation: 72+40=112 Exploring Operation: 48+40=88, Resulting Numbers: [72, 88] Generated Node #0,2,3: 60:[72, 88] Operation: 48+40=88 Exploring Operation: 72-48=24, Resulting Numbers: [40, 24] Generated Node #0,2,4: 60:[40, 24] Operation: 72-48=24 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 60:[48, 32], Operations: ['89-49=40', '72-40=32'] Exploring Operation: 48+32=80, Resulting Numbers: [80] 80,60 unequal: No Solution Exploring Operation: 48-32=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 48*32=1536, Resulting Numbers: [1536] 1536,60 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 #0,2,1 Current State: 60:[72, 8], Operations: ['89-49=40', '48-40=8'] Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,60 unequal: No Solution Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,60 unequal: No Solution Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,60 unequal: No Solution Exploring Operation: 72*8=576, Resulting Numbers: [576] 576,60 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 #0,2,4 Current State: 60:[40, 24], Operations: ['89-49=40', '72-48=24'] Exploring Operation: 40*24=960, Resulting Numbers: [960] 960,60 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 40+24=64, Resulting Numbers: [64] 64,60 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 #0,2,3 Current State: 60:[72, 88], Operations: ['89-49=40', '48+40=88'] Exploring Operation: 88-72=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 72+88=160, Resulting Numbers: [160] 160,60 unequal: No Solution Exploring Operation: 72*88=6336, Resulting Numbers: [6336] 6336,60 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 #0,2,2 Current State: 60:[48, 112], Operations: ['89-49=40', '72+40=112'] Exploring Operation: 112-48=64, Resulting Numbers: [64] 64,60 unequal: No Solution Exploring Operation: 48+112=160, Resulting Numbers: [160] 160,60 unequal: No Solution Exploring Operation: 48*112=5376, Resulting Numbers: [5376] 5376,60 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:[72, 89, 1], Operations: ['49-48=1'] Exploring Operation: 89-72=17, Resulting Numbers: [1, 17] Generated Node #0,0,0: 60:[1, 17] Operation: 89-72=17 Exploring Operation: 89-1=88, Resulting Numbers: [72, 88] Generated Node #0,0,1: 60:[72, 88] Operation: 89-1=88 Exploring Operation: 72-1=71, Resulting Numbers: [89, 71] Generated Node #0,0,2: 60:[89, 71] Operation: 72-1=71 Exploring Operation: 72*1=72, Resulting Numbers: [89, 72] Generated Node #0,0,3: 60:[89, 72] Operation: 72*1=72 Exploring Operation: 72/1=72, Resulting Numbers: [89, 72] Generated Node #0,0,4: 60:[89, 72] Operation: 72/1=72 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[1, 17], Operations: ['49-48=1', '89-72=17'] Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 1*17=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 1+17=18, Resulting Numbers: [18] 18,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[72, 88], Operations: ['49-48=1', '89-1=88'] Exploring Operation: 72+88=160, Resulting Numbers: [160] 160,60 unequal: No Solution Exploring Operation: 88-72=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 72*88=6336, Resulting Numbers: [6336] 6336,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[89, 71], Operations: ['49-48=1', '72-1=71'] Exploring Operation: 89*71=6319, Resulting Numbers: [6319] 6319,60 unequal: No Solution Exploring Operation: 89+71=160, Resulting Numbers: [160] 160,60 unequal: No Solution Exploring Operation: 89-71=18, Resulting Numbers: [18] 18,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 60:[89, 72], Operations: ['49-48=1', '72*1=72'] Exploring Operation: 89-72=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 89*72=6408, Resulting Numbers: [6408] 6408,60 unequal: No Solution Exploring Operation: 89+72=161, Resulting Numbers: [161] 161,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 60:[89, 72], Operations: ['49-48=1', '72/1=72'] Exploring Operation: 89*72=6408, Resulting Numbers: [6408] 6408,60 unequal: No Solution Exploring Operation: 89-72=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 89+72=161, Resulting Numbers: [161] 161,60 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: 60:[49, 89, 24], Operations: ['72-48=24'] Exploring Operation: 49+24=73, Resulting Numbers: [89, 73] Generated Node #0,3,0: 60:[89, 73] Operation: 49+24=73 Exploring Operation: 89-49=40, Resulting Numbers: [24, 40] Generated Node #0,3,1: 60:[24, 40] Operation: 89-49=40 Exploring Operation: 89+24=113, Resulting Numbers: [49, 113] Generated Node #0,3,2: 60:[49, 113] Operation: 89+24=113 Exploring Operation: 49-24=25, Resulting Numbers: [89, 25] Generated Node #0,3,3: 60:[89, 25] Operation: 49-24=25 Exploring Operation: 89-24=65, Resulting Numbers: [49, 65] Generated Node #0,3,4: 60:[49, 65] Operation: 89-24=65 Moving to Node #0,4,0 Current State: 60:[49, 31], Operations: ['89-48=41', '72-41=31'] Exploring Operation: 49*31=1519, Resulting Numbers: [1519] 1519,60 unequal: No Solution Exploring Operation: 49+31=80, Resulting Numbers: [80] 80,60 unequal: No Solution Exploring Operation: 49-31=18, Resulting Numbers: [18] 18,60 unequal: No Solution Moving to Node #0,4,3 Current State: 60:[41, 23], Operations: ['89-48=41', '72-49=23'] Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,60 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,60 unequal: No Solution Moving to Node #0,3,1 Current State: 60:[24, 40], Operations: ['72-48=24', '89-49=40'] Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 24*40=960, Resulting Numbers: [960] 960,60 unequal: No Solution Exploring Operation: 24+40=64, Resulting Numbers: [64] 64,60 unequal: No Solution Moving to Node #0,4,1 Current State: 60:[72, 8], Operations: ['89-48=41', '49-41=8'] Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,60 unequal: No Solution Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,60 unequal: No Solution Exploring Operation: 72*8=576, Resulting Numbers: [576] 576,60 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,60 unequal: No Solution Moving to Node #0,3,4 Current State: 60:[49, 65], Operations: ['72-48=24', '89-24=65'] Exploring Operation: 49+65=114, Resulting Numbers: [114] 114,60 unequal: No Solution Exploring Operation: 65-49=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 49*65=3185, Resulting Numbers: [3185] 3185,60 unequal: No Solution Moving to Node #0,3,3 Current State: 60:[89, 25], Operations: ['72-48=24', '49-24=25'] Exploring Operation: 89-25=64, Resulting Numbers: [64] 64,60 unequal: No Solution Exploring Operation: 89+25=114, Resulting Numbers: [114] 114,60 unequal: No Solution Exploring Operation: 89*25=2225, Resulting Numbers: [2225] 2225,60 unequal: No Solution Moving to Node #0,3,0 Current State: 60:[89, 73], Operations: ['72-48=24', '49+24=73'] Exploring Operation: 89+73=162, Resulting Numbers: [162] 162,60 unequal: No Solution Exploring Operation: 89*73=6497, Resulting Numbers: [6497] 6497,60 unequal: No Solution Exploring Operation: 89-73=16, Resulting Numbers: [16] 16,60 unequal: No Solution Moving to Node #0,4,2 Current State: 60:[72, 90], Operations: ['89-48=41', '49+41=90'] Exploring Operation: 72*90=6480, Resulting Numbers: [6480] 6480,60 unequal: No Solution Exploring Operation: 90-72=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 72+90=162, Resulting Numbers: [162] 162,60 unequal: No Solution Moving to Node #0,3,2 Current State: 60:[49, 113], Operations: ['72-48=24', '89+24=113'] Exploring Operation: 49+113=162, Resulting Numbers: [162] 162,60 unequal: No Solution Exploring Operation: 49*113=5537, Resulting Numbers: [5537] 5537,60 unequal: No Solution Exploring Operation: 113-49=64, Resulting Numbers: [64] 64,60 unequal: No Solution Moving to Node #0,4,4 Current State: 60:[49, 113], Operations: ['89-48=41', '72+41=113'] Exploring Operation: 113-49=64, Resulting Numbers: [64] 64,60 unequal: No Solution Exploring Operation: 49+113=162, Resulting Numbers: [162] 162,60 unequal: No Solution Exploring Operation: 49*113=5537, Resulting Numbers: [5537] 5537,60 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 63, 2, 9, 34 ]
25
[ "63/9=7", "34-2=32", "32-7=25" ]
Current State: 25:[63, 2, 9, 34], Operations: [] Exploring Operation: 63/9=7, Resulting Numbers: [2, 34, 7] Generated Node #2: [2, 34, 7] from Operation: 63/9=7 Current State: 25:[2, 34, 7], Operations: ['63/9=7'] Exploring Operation: 34-2=32, Resulting Numbers: [7, 32] Generated Node #3: [7, 32] from Operation: 34-2=32 Current State: 25:[7, 32], Operations: ['63/9=7', '34-2=32'] Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[63, 2, 9, 34], Operations: [] Exploring Operation: 63-34=29, Resulting Numbers: [2, 9, 29] Generated Node #0,0: 25:[2, 9, 29] Operation: 63-34=29 Exploring Operation: 63/9=7, Resulting Numbers: [2, 34, 7] Generated Node #0,1: 25:[2, 34, 7] Operation: 63/9=7 Moving to Node #0,0 Current State: 25:[2, 9, 29], Operations: ['63-34=29'] Exploring Operation: 9-2=7, Resulting Numbers: [29, 7] Generated Node #0,0,0: 25:[29, 7] Operation: 9-2=7 Exploring Operation: 29-2=27, Resulting Numbers: [9, 27] Generated Node #0,0,1: 25:[9, 27] Operation: 29-2=27 Moving to Node #0,1 Current State: 25:[2, 34, 7], Operations: ['63/9=7'] Exploring Operation: 34-2=32, Resulting Numbers: [7, 32] Generated Node #0,1,0: 25:[7, 32] Operation: 34-2=32 Exploring Operation: 34-7=27, Resulting Numbers: [2, 27] Generated Node #0,1,1: 25:[2, 27] Operation: 34-7=27 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 25:[2, 27], Operations: ['63/9=7', '34-7=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,25 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[63, 2, 9, 34], Operations: [] Exploring Operation: 63/9=7, Resulting Numbers: [2, 34, 7] Generated Node #0,1: 25:[2, 34, 7] Operation: 63/9=7 Moving to Node #0,1 Current State: 25:[2, 34, 7], Operations: ['63/9=7'] Exploring Operation: 34-7=27, Resulting Numbers: [2, 27] Generated Node #0,1,1: 25:[2, 27] Operation: 34-7=27 Moving to Node #0,1,1 Current State: 25:[2, 27], Operations: ['63/9=7', '34-7=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 98, 37, 99, 63 ]
98
[ "99-37=62", "63-62=1", "98*1=98" ]
Current State: 98:[98, 37, 99, 63], Operations: [] Exploring Operation: 99-37=62, Resulting Numbers: [98, 63, 62] Generated Node #2: [98, 63, 62] from Operation: 99-37=62 Current State: 98:[98, 63, 62], Operations: ['99-37=62'] Exploring Operation: 63-62=1, Resulting Numbers: [98, 1] Generated Node #3: [98, 1] from Operation: 63-62=1 Current State: 98:[98, 1], Operations: ['99-37=62', '63-62=1'] Exploring Operation: 98*1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[98, 37, 99, 63], Operations: [] Exploring Operation: 37+63=100, Resulting Numbers: [98, 99, 100] Generated Node #0,0: 98:[98, 99, 100] Operation: 37+63=100 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[98, 99, 100], Operations: ['37+63=100'] Exploring Operation: 100-98=2, Resulting Numbers: [99, 2] Generated Node #0,0,0: 98:[99, 2] Operation: 100-98=2 Moving to Node #0,0,0 Current State: 98:[99, 2], Operations: ['37+63=100', '100-98=2'] Exploring Operation: 99-2=97, Resulting Numbers: [97] 97,98 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
[ 29, 84, 10, 71 ]
87
[ "84-10=74", "74-71=3", "29*3=87" ]
Current State: 87:[29, 84, 10, 71], Operations: [] Exploring Operation: 84-10=74, Resulting Numbers: [29, 71, 74] Generated Node #2: [29, 71, 74] from Operation: 84-10=74 Current State: 87:[29, 71, 74], Operations: ['84-10=74'] Exploring Operation: 74-71=3, Resulting Numbers: [29, 3] Generated Node #3: [29, 3] from Operation: 74-71=3 Current State: 87:[29, 3], Operations: ['84-10=74', '74-71=3'] Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[29, 84, 10, 71], Operations: [] Exploring Operation: 84+10=94, Resulting Numbers: [29, 71, 94] Generated Node #0,0: 87:[29, 71, 94] Operation: 84+10=94 Exploring Operation: 84-71=13, Resulting Numbers: [29, 10, 13] Generated Node #0,1: 87:[29, 10, 13] Operation: 84-71=13 Exploring Operation: 29+71=100, Resulting Numbers: [84, 10, 100] Generated Node #0,2: 87:[84, 10, 100] Operation: 29+71=100 Exploring Operation: 10+71=81, Resulting Numbers: [29, 84, 81] Generated Node #0,3: 87:[29, 84, 81] Operation: 10+71=81 Exploring Operation: 71-29=42, Resulting Numbers: [84, 10, 42] Generated Node #0,4: 87:[84, 10, 42] Operation: 71-29=42 Start Sub Search at level 1: Moving to Node #0,3 Current State: 87:[29, 84, 81], Operations: ['10+71=81'] Exploring Operation: 29+81=110, Resulting Numbers: [84, 110] Generated Node #0,3,0: 87:[84, 110] Operation: 29+81=110 Exploring Operation: 84-29=55, Resulting Numbers: [81, 55] Generated Node #0,3,1: 87:[81, 55] Operation: 84-29=55 Exploring Operation: 29+84=113, Resulting Numbers: [81, 113] Generated Node #0,3,2: 87:[81, 113] Operation: 29+84=113 Exploring Operation: 84-81=3, Resulting Numbers: [29, 3] Generated Node #0,3,3: 87:[29, 3] Operation: 84-81=3 Exploring Operation: 81-29=52, Resulting Numbers: [84, 52] Generated Node #0,3,4: 87:[84, 52] Operation: 81-29=52 Moving to Node #0,3,3 Current State: 87:[29, 3], Operations: ['10+71=81', '84-81=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,87 unequal: No Solution Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[29, 84, 10, 71], Operations: [] Exploring Operation: 10+71=81, Resulting Numbers: [29, 84, 81] Generated Node #0,3: 87:[29, 84, 81] Operation: 10+71=81 Moving to Node #0,3 Current State: 87:[29, 84, 81], Operations: ['10+71=81'] Exploring Operation: 84-81=3, Resulting Numbers: [29, 3] Generated Node #0,3,3: 87:[29, 3] Operation: 84-81=3 Moving to Node #0,3,3 Current State: 87:[29, 3], Operations: ['10+71=81', '84-81=3'] Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 13, 82, 97, 53 ]
51
[ "13+82=95", "97-53=44", "95-44=51" ]
Current State: 51:[13, 82, 97, 53], Operations: [] Exploring Operation: 13+82=95, Resulting Numbers: [97, 53, 95] Generated Node #2: [97, 53, 95] from Operation: 13+82=95 Current State: 51:[97, 53, 95], Operations: ['13+82=95'] Exploring Operation: 97-53=44, Resulting Numbers: [95, 44] Generated Node #3: [95, 44] from Operation: 97-53=44 Current State: 51:[95, 44], Operations: ['13+82=95', '97-53=44'] Exploring Operation: 95-44=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[13, 82, 97, 53], Operations: [] Exploring Operation: 82-53=29, Resulting Numbers: [13, 97, 29] Generated Node #0,0: 51:[13, 97, 29] Operation: 82-53=29 Exploring Operation: 97-53=44, Resulting Numbers: [13, 82, 44] Generated Node #0,1: 51:[13, 82, 44] Operation: 97-53=44 Exploring Operation: 97-82=15, Resulting Numbers: [13, 53, 15] Generated Node #0,2: 51:[13, 53, 15] Operation: 97-82=15 Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[13, 53, 15], Operations: ['97-82=15'] Exploring Operation: 15-13=2, Resulting Numbers: [53, 2] Generated Node #0,2,0: 51:[53, 2] Operation: 15-13=2 Exploring Operation: 13+15=28, Resulting Numbers: [53, 28] Generated Node #0,2,1: 51:[53, 28] Operation: 13+15=28 Exploring Operation: 53-13=40, Resulting Numbers: [15, 40] Generated Node #0,2,2: 51:[15, 40] Operation: 53-13=40 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 51:[53, 2], Operations: ['97-82=15', '15-13=2'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[13, 82, 97, 53], Operations: [] Exploring Operation: 97-82=15, Resulting Numbers: [13, 53, 15] Generated Node #0,2: 51:[13, 53, 15] Operation: 97-82=15 Moving to Node #0,2 Current State: 51:[13, 53, 15], Operations: ['97-82=15'] Exploring Operation: 15-13=2, Resulting Numbers: [53, 2] Generated Node #0,2,0: 51:[53, 2] Operation: 15-13=2 Moving to Node #0,2,0 Current State: 51:[53, 2], Operations: ['97-82=15', '15-13=2'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 88, 48, 33, 30 ]
23
[ "88-48=40", "33+30=63", "63-40=23" ]
Current State: 23:[88, 48, 33, 30], Operations: [] Exploring Operation: 88-48=40, Resulting Numbers: [33, 30, 40] Generated Node #2: [33, 30, 40] from Operation: 88-48=40 Current State: 23:[33, 30, 40], Operations: ['88-48=40'] Exploring Operation: 33+30=63, Resulting Numbers: [40, 63] Generated Node #3: [40, 63] from Operation: 33+30=63 Current State: 23:[40, 63], Operations: ['88-48=40', '33+30=63'] Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[88, 48, 33, 30], Operations: [] Exploring Operation: 88-48=40, Resulting Numbers: [33, 30, 40] Generated Node #0,0: 23:[33, 30, 40] Operation: 88-48=40 Exploring Operation: 88-33=55, Resulting Numbers: [48, 30, 55] Generated Node #0,1: 23:[48, 30, 55] Operation: 88-33=55 Exploring Operation: 88-30=58, Resulting Numbers: [48, 33, 58] Generated Node #0,2: 23:[48, 33, 58] Operation: 88-30=58 Moving to Node #0,0 Current State: 23:[33, 30, 40], Operations: ['88-48=40'] Exploring Operation: 40-33=7, Resulting Numbers: [30, 7] Generated Node #0,0,0: 23:[30, 7] Operation: 40-33=7 Exploring Operation: 40-30=10, Resulting Numbers: [33, 10] Generated Node #0,0,1: 23:[33, 10] Operation: 40-30=10 Exploring Operation: 33-30=3, Resulting Numbers: [40, 3] Generated Node #0,0,2: 23:[40, 3] Operation: 33-30=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 23:[30, 7], Operations: ['88-48=40', '40-33=7'] Exploring Operation: 30*7=210, Resulting Numbers: [210] 210,23 unequal: No Solution Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[88, 48, 33, 30], Operations: [] Exploring Operation: 88-48=40, Resulting Numbers: [33, 30, 40] Generated Node #0,0: 23:[33, 30, 40] Operation: 88-48=40 Moving to Node #0,0 Current State: 23:[33, 30, 40], Operations: ['88-48=40'] Exploring Operation: 40-33=7, Resulting Numbers: [30, 7] Generated Node #0,0,0: 23:[30, 7] Operation: 40-33=7 Moving to Node #0,0,0 Current State: 23:[30, 7], Operations: ['88-48=40', '40-33=7'] Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 92, 84, 90, 61 ]
46
[ "92-90=2", "84-61=23", "2*23=46" ]
Current State: 46:[92, 84, 90, 61], Operations: [] Exploring Operation: 92-90=2, Resulting Numbers: [84, 61, 2] Generated Node #2: [84, 61, 2] from Operation: 92-90=2 Current State: 46:[84, 61, 2], Operations: ['92-90=2'] Exploring Operation: 84-61=23, Resulting Numbers: [2, 23] Generated Node #3: [2, 23] from Operation: 84-61=23 Current State: 46:[2, 23], Operations: ['92-90=2', '84-61=23'] Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[92, 84, 90, 61], Operations: [] Exploring Operation: 92-90=2, Resulting Numbers: [84, 61, 2] Generated Node #0,0: 46:[84, 61, 2] Operation: 92-90=2 Exploring Operation: 92-84=8, Resulting Numbers: [90, 61, 8] Generated Node #0,1: 46:[90, 61, 8] Operation: 92-84=8 Exploring Operation: 92-61=31, Resulting Numbers: [84, 90, 31] Generated Node #0,2: 46:[84, 90, 31] Operation: 92-61=31 Exploring Operation: 90-84=6, Resulting Numbers: [92, 61, 6] Generated Node #0,3: 46:[92, 61, 6] Operation: 90-84=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[84, 61, 2], Operations: ['92-90=2'] Exploring Operation: 84-2=82, Resulting Numbers: [61, 82] Generated Node #0,0,0: 46:[61, 82] Operation: 84-2=82 Exploring Operation: 84/2=42, Resulting Numbers: [61, 42] Generated Node #0,0,1: 46:[61, 42] Operation: 84/2=42 Exploring Operation: 61-2=59, Resulting Numbers: [84, 59] Generated Node #0,0,2: 46:[84, 59] Operation: 61-2=59 Exploring Operation: 84-61=23, Resulting Numbers: [2, 23] Generated Node #0,0,3: 46:[2, 23] Operation: 84-61=23 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 46:[2, 23], Operations: ['92-90=2', '84-61=23'] Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[92, 84, 90, 61], Operations: [] Exploring Operation: 92-90=2, Resulting Numbers: [84, 61, 2] Generated Node #0,0: 46:[84, 61, 2] Operation: 92-90=2 Moving to Node #0,0 Current State: 46:[84, 61, 2], Operations: ['92-90=2'] Exploring Operation: 84-61=23, Resulting Numbers: [2, 23] Generated Node #0,0,3: 46:[2, 23] Operation: 84-61=23 Moving to Node #0,0,3 Current State: 46:[2, 23], Operations: ['92-90=2', '84-61=23'] Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic