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
[ 10, 78, 95, 75 ]
88
[ "78-10=68", "95-75=20", "68+20=88" ]
Current State: 88:[10, 78, 95, 75], Operations: [] Exploring Operation: 78-10=68, Resulting Numbers: [95, 75, 68] Generated Node #2: [95, 75, 68] from Operation: 78-10=68 Current State: 88:[95, 75, 68], Operations: ['78-10=68'] Exploring Operation: 95-75=20, Resulting Numbers: [68, 20] Generated Node #3: [68, 20] from Operation: 95-75=20 Current State: 88:[68, 20], Operations: ['78-10=68', '95-75=20'] Exploring Operation: 68+20=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[10, 78, 95, 75], Operations: [] Exploring Operation: 78-75=3, Resulting Numbers: [10, 95, 3] Generated Node #0,0: 88:[10, 95, 3] Operation: 78-75=3 Moving to Node #0,0 Current State: 88:[10, 95, 3], Operations: ['78-75=3'] Exploring Operation: 95-10=85, Resulting Numbers: [3, 85] Generated Node #0,0,0: 88:[3, 85] Operation: 95-10=85 Moving to Node #0,0,0 Current State: 88:[3, 85], Operations: ['78-75=3', '95-10=85'] Exploring Operation: 3+85=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[10, 78, 95, 75], Operations: [] Exploring Operation: 78-75=3, Resulting Numbers: [10, 95, 3] Generated Node #0,0: 88:[10, 95, 3] Operation: 78-75=3 Moving to Node #0,0 Current State: 88:[10, 95, 3], Operations: ['78-75=3'] Exploring Operation: 95-10=85, Resulting Numbers: [3, 85] Generated Node #0,0,0: 88:[3, 85] Operation: 95-10=85 Moving to Node #0,0,0 Current State: 88:[3, 85], Operations: ['78-75=3', '95-10=85'] Exploring Operation: 3+85=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 28, 8, 14, 93 ]
83
[ "28/14=2", "93-8=85", "85-2=83" ]
Current State: 83:[28, 8, 14, 93], Operations: [] Exploring Operation: 28/14=2, Resulting Numbers: [8, 93, 2] Generated Node #2: [8, 93, 2] from Operation: 28/14=2 Current State: 83:[8, 93, 2], Operations: ['28/14=2'] Exploring Operation: 93-8=85, Resulting Numbers: [2, 85] Generated Node #3: [2, 85] from Operation: 93-8=85 Current State: 83:[2, 85], Operations: ['28/14=2', '93-8=85'] Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[28, 8, 14, 93], Operations: [] Exploring Operation: 8*14=112, Resulting Numbers: [28, 93, 112] Generated Node #0,0: 83:[28, 93, 112] Operation: 8*14=112 Exploring Operation: 28+14=42, Resulting Numbers: [8, 93, 42] Generated Node #0,1: 83:[8, 93, 42] Operation: 28+14=42 Exploring Operation: 28+8=36, Resulting Numbers: [14, 93, 36] Generated Node #0,2: 83:[14, 93, 36] Operation: 28+8=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[28, 93, 112], Operations: ['8*14=112'] Exploring Operation: 112-28=84, Resulting Numbers: [93, 84] Generated Node #0,0,0: 83:[93, 84] Operation: 112-28=84 Exploring Operation: 28+93=121, Resulting Numbers: [112, 121] Generated Node #0,0,1: 83:[112, 121] Operation: 28+93=121 Exploring Operation: 93-28=65, Resulting Numbers: [112, 65] Generated Node #0,0,2: 83:[112, 65] Operation: 93-28=65 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[93, 84], Operations: ['8*14=112', '112-28=84'] Exploring Operation: 93-84=9, Resulting Numbers: [9] 9,83 unequal: No Solution Exploring Operation: 93+84=177, Resulting Numbers: [177] 177,83 unequal: No Solution Exploring Operation: 93*84=7812, Resulting Numbers: [7812] 7812,83 unequal: No Solution No 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: 83:[112, 65], Operations: ['8*14=112', '93-28=65'] Exploring Operation: 112*65=7280, Resulting Numbers: [7280] 7280,83 unequal: No Solution Exploring Operation: 112-65=47, Resulting Numbers: [47] 47,83 unequal: No Solution Exploring Operation: 112+65=177, Resulting Numbers: [177] 177,83 unequal: No Solution No 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: 83:[112, 121], Operations: ['8*14=112', '28+93=121'] Exploring Operation: 112*121=13552, Resulting Numbers: [13552] 13552,83 unequal: No Solution Exploring Operation: 112+121=233, Resulting Numbers: [233] 233,83 unequal: No Solution Exploring Operation: 121-112=9, Resulting Numbers: [9] 9,83 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: 83:[8, 93, 42], Operations: ['28+14=42'] Exploring Operation: 8+93=101, Resulting Numbers: [42, 101] Generated Node #0,1,0: 83:[42, 101] Operation: 8+93=101 Exploring Operation: 93-8=85, Resulting Numbers: [42, 85] Generated Node #0,1,1: 83:[42, 85] Operation: 93-8=85 Exploring Operation: 8+42=50, Resulting Numbers: [93, 50] Generated Node #0,1,2: 83:[93, 50] Operation: 8+42=50 Moving to Node #0,1,1 Current State: 83:[42, 85], Operations: ['28+14=42', '93-8=85'] Exploring Operation: 42*85=3570, Resulting Numbers: [3570] 3570,83 unequal: No Solution Exploring Operation: 85-42=43, Resulting Numbers: [43] 43,83 unequal: No Solution Exploring Operation: 42+85=127, Resulting Numbers: [127] 127,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[93, 50], Operations: ['28+14=42', '8+42=50'] Exploring Operation: 93*50=4650, Resulting Numbers: [4650] 4650,83 unequal: No Solution Exploring Operation: 93-50=43, Resulting Numbers: [43] 43,83 unequal: No Solution Exploring Operation: 93+50=143, Resulting Numbers: [143] 143,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[42, 101], Operations: ['28+14=42', '8+93=101'] Exploring Operation: 42*101=4242, Resulting Numbers: [4242] 4242,83 unequal: No Solution Exploring Operation: 101-42=59, Resulting Numbers: [59] 59,83 unequal: No Solution Exploring Operation: 42+101=143, Resulting Numbers: [143] 143,83 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 Current State: 83:[14, 93, 36], Operations: ['28+8=36'] Exploring Operation: 93-14=79, Resulting Numbers: [36, 79] Generated Node #0,2,0: 83:[36, 79] Operation: 93-14=79 Exploring Operation: 14+93=107, Resulting Numbers: [36, 107] Generated Node #0,2,1: 83:[36, 107] Operation: 14+93=107 Exploring Operation: 14+36=50, Resulting Numbers: [93, 50] Generated Node #0,2,2: 83:[93, 50] Operation: 14+36=50 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 83:[93, 50], Operations: ['28+8=36', '14+36=50'] Exploring Operation: 93-50=43, Resulting Numbers: [43] 43,83 unequal: No Solution Exploring Operation: 93+50=143, Resulting Numbers: [143] 143,83 unequal: No Solution Exploring Operation: 93*50=4650, Resulting Numbers: [4650] 4650,83 unequal: No Solution No 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: 83:[36, 79], Operations: ['28+8=36', '93-14=79'] Exploring Operation: 36*79=2844, Resulting Numbers: [2844] 2844,83 unequal: No Solution Exploring Operation: 36+79=115, Resulting Numbers: [115] 115,83 unequal: No Solution Exploring Operation: 79-36=43, Resulting Numbers: [43] 43,83 unequal: No Solution No 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: 83:[36, 107], Operations: ['28+8=36', '14+93=107'] Exploring Operation: 36*107=3852, Resulting Numbers: [3852] 3852,83 unequal: No Solution Exploring Operation: 36+107=143, Resulting Numbers: [143] 143,83 unequal: No Solution Exploring Operation: 107-36=71, Resulting Numbers: [71] 71,83 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
[ 96, 84, 4, 95 ]
98
[ "96-84=12", "12/4=3", "95+3=98" ]
Current State: 98:[96, 84, 4, 95], Operations: [] Exploring Operation: 96-84=12, Resulting Numbers: [4, 95, 12] Generated Node #2: [4, 95, 12] from Operation: 96-84=12 Current State: 98:[4, 95, 12], Operations: ['96-84=12'] Exploring Operation: 12/4=3, Resulting Numbers: [95, 3] Generated Node #3: [95, 3] from Operation: 12/4=3 Current State: 98:[95, 3], Operations: ['96-84=12', '12/4=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[96, 84, 4, 95], Operations: [] Exploring Operation: 96-84=12, Resulting Numbers: [4, 95, 12] Generated Node #0,0: 98:[4, 95, 12] Operation: 96-84=12 Exploring Operation: 84+4=88, Resulting Numbers: [96, 95, 88] Generated Node #0,1: 98:[96, 95, 88] Operation: 84+4=88 Exploring Operation: 84/4=21, Resulting Numbers: [96, 95, 21] Generated Node #0,2: 98:[96, 95, 21] Operation: 84/4=21 Exploring Operation: 95-84=11, Resulting Numbers: [96, 4, 11] Generated Node #0,3: 98:[96, 4, 11] Operation: 95-84=11 Exploring Operation: 96-95=1, Resulting Numbers: [84, 4, 1] Generated Node #0,4: 98:[84, 4, 1] Operation: 96-95=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[4, 95, 12], Operations: ['96-84=12'] Exploring Operation: 4*12=48, Resulting Numbers: [95, 48] Generated Node #0,0,0: 98:[95, 48] Operation: 4*12=48 Exploring Operation: 4+12=16, Resulting Numbers: [95, 16] Generated Node #0,0,1: 98:[95, 16] Operation: 4+12=16 Exploring Operation: 12/4=3, Resulting Numbers: [95, 3] Generated Node #0,0,2: 98:[95, 3] Operation: 12/4=3 Exploring Operation: 12-4=8, Resulting Numbers: [95, 8] Generated Node #0,0,3: 98:[95, 8] Operation: 12-4=8 Exploring Operation: 4+95=99, Resulting Numbers: [12, 99] Generated Node #0,0,4: 98:[12, 99] Operation: 4+95=99 Moving to Node #0,0,4 Current State: 98:[12, 99], Operations: ['96-84=12', '4+95=99'] Exploring Operation: 12+99=111, Resulting Numbers: [111] 111,98 unequal: No Solution Exploring Operation: 99-12=87, Resulting Numbers: [87] 87,98 unequal: No Solution Exploring Operation: 12*99=1188, Resulting Numbers: [1188] 1188,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[95, 3], Operations: ['96-84=12', '12/4=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[96, 84, 4, 95], Operations: [] Exploring Operation: 96-84=12, Resulting Numbers: [4, 95, 12] Generated Node #0,0: 98:[4, 95, 12] Operation: 96-84=12 Moving to Node #0,0 Current State: 98:[4, 95, 12], Operations: ['96-84=12'] Exploring Operation: 12/4=3, Resulting Numbers: [95, 3] Generated Node #0,0,2: 98:[95, 3] Operation: 12/4=3 Moving to Node #0,0,2 Current State: 98:[95, 3], Operations: ['96-84=12', '12/4=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 78, 55, 15, 60 ]
81
[ "60-55=5", "15/5=3", "78+3=81" ]
Current State: 81:[78, 55, 15, 60], Operations: [] Exploring Operation: 60-55=5, Resulting Numbers: [78, 15, 5] Generated Node #2: [78, 15, 5] from Operation: 60-55=5 Current State: 81:[78, 15, 5], Operations: ['60-55=5'] Exploring Operation: 15/5=3, Resulting Numbers: [78, 3] Generated Node #3: [78, 3] from Operation: 15/5=3 Current State: 81:[78, 3], Operations: ['60-55=5', '15/5=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[78, 55, 15, 60], Operations: [] Exploring Operation: 78-55=23, Resulting Numbers: [15, 60, 23] Generated Node #0,0: 81:[15, 60, 23] Operation: 78-55=23 Exploring Operation: 55+15=70, Resulting Numbers: [78, 60, 70] Generated Node #0,1: 81:[78, 60, 70] Operation: 55+15=70 Exploring Operation: 60/15=4, Resulting Numbers: [78, 55, 4] Generated Node #0,2: 81:[78, 55, 4] Operation: 60/15=4 Exploring Operation: 60-55=5, Resulting Numbers: [78, 15, 5] Generated Node #0,3: 81:[78, 15, 5] Operation: 60-55=5 Exploring Operation: 15+60=75, Resulting Numbers: [78, 55, 75] Generated Node #0,4: 81:[78, 55, 75] Operation: 15+60=75 Start Sub Search at level 1: Moving to Node #0,3 Current State: 81:[78, 15, 5], Operations: ['60-55=5'] Exploring Operation: 15*5=75, Resulting Numbers: [78, 75] Generated Node #0,3,0: 81:[78, 75] Operation: 15*5=75 Exploring Operation: 15-5=10, Resulting Numbers: [78, 10] Generated Node #0,3,1: 81:[78, 10] Operation: 15-5=10 Exploring Operation: 78+5=83, Resulting Numbers: [15, 83] Generated Node #0,3,2: 81:[15, 83] Operation: 78+5=83 Exploring Operation: 15+5=20, Resulting Numbers: [78, 20] Generated Node #0,3,3: 81:[78, 20] Operation: 15+5=20 Exploring Operation: 15/5=3, Resulting Numbers: [78, 3] Generated Node #0,3,4: 81:[78, 3] Operation: 15/5=3 Moving to Node #0,3,4 Current State: 81:[78, 3], Operations: ['60-55=5', '15/5=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[78, 55, 15, 60], Operations: [] Exploring Operation: 60-55=5, Resulting Numbers: [78, 15, 5] Generated Node #0,3: 81:[78, 15, 5] Operation: 60-55=5 Moving to Node #0,3 Current State: 81:[78, 15, 5], Operations: ['60-55=5'] Exploring Operation: 15/5=3, Resulting Numbers: [78, 3] Generated Node #0,3,4: 81:[78, 3] Operation: 15/5=3 Moving to Node #0,3,4 Current State: 81:[78, 3], Operations: ['60-55=5', '15/5=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 40, 52, 79, 5 ]
35
[ "40/5=8", "79-52=27", "8+27=35" ]
Current State: 35:[40, 52, 79, 5], Operations: [] Exploring Operation: 40/5=8, Resulting Numbers: [52, 79, 8] Generated Node #2: [52, 79, 8] from Operation: 40/5=8 Current State: 35:[52, 79, 8], Operations: ['40/5=8'] Exploring Operation: 79-52=27, Resulting Numbers: [8, 27] Generated Node #3: [8, 27] from Operation: 79-52=27 Current State: 35:[8, 27], Operations: ['40/5=8', '79-52=27'] Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[40, 52, 79, 5], Operations: [] Exploring Operation: 79-52=27, Resulting Numbers: [40, 5, 27] Generated Node #0,0: 35:[40, 5, 27] Operation: 79-52=27 Exploring Operation: 79-40=39, Resulting Numbers: [52, 5, 39] Generated Node #0,1: 35:[52, 5, 39] Operation: 79-40=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[40, 5, 27], Operations: ['79-52=27'] Exploring Operation: 40-27=13, Resulting Numbers: [5, 13] Generated Node #0,0,0: 35:[5, 13] Operation: 40-27=13 Exploring Operation: 40-5=35, Resulting Numbers: [27, 35] Generated Node #0,0,1: 35:[27, 35] Operation: 40-5=35 Moving to Node #0,0,0 Current State: 35:[5, 13], Operations: ['79-52=27', '40-27=13'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[27, 35], Operations: ['79-52=27', '40-5=35'] Exploring Operation: 27+35=62, Resulting Numbers: [62] 62,35 unequal: No Solution Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[52, 5, 39], Operations: ['79-40=39'] Exploring Operation: 52-5=47, Resulting Numbers: [39, 47] Generated Node #0,1,0: 35:[39, 47] Operation: 52-5=47 Exploring Operation: 52-39=13, Resulting Numbers: [5, 13] Generated Node #0,1,1: 35:[5, 13] Operation: 52-39=13 Moving to Node #0,1,1 Current State: 35:[5, 13], Operations: ['79-40=39', '52-39=13'] Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,35 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[39, 47], Operations: ['79-40=39', '52-5=47'] Exploring Operation: 39+47=86, Resulting Numbers: [86] 86,35 unequal: No Solution Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 30, 37, 4, 34 ]
97
[ "30+37=67", "34-4=30", "67+30=97" ]
Current State: 97:[30, 37, 4, 34], Operations: [] Exploring Operation: 30+37=67, Resulting Numbers: [4, 34, 67] Generated Node #2: [4, 34, 67] from Operation: 30+37=67 Current State: 97:[4, 34, 67], Operations: ['30+37=67'] Exploring Operation: 34-4=30, Resulting Numbers: [67, 30] Generated Node #3: [67, 30] from Operation: 34-4=30 Current State: 97:[67, 30], Operations: ['30+37=67', '34-4=30'] Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[30, 37, 4, 34], Operations: [] Exploring Operation: 30+37=67, Resulting Numbers: [4, 34, 67] Generated Node #0,0: 97:[4, 34, 67] Operation: 30+37=67 Exploring Operation: 30*4=120, Resulting Numbers: [37, 34, 120] Generated Node #0,1: 97:[37, 34, 120] Operation: 30*4=120 Exploring Operation: 4*34=136, Resulting Numbers: [30, 37, 136] Generated Node #0,2: 97:[30, 37, 136] Operation: 4*34=136 Exploring Operation: 37*4=148, Resulting Numbers: [30, 34, 148] Generated Node #0,3: 97:[30, 34, 148] Operation: 37*4=148 Moving to Node #0,1 Current State: 97:[37, 34, 120], Operations: ['30*4=120'] Exploring Operation: 37-34=3, Resulting Numbers: [120, 3] Generated Node #0,1,0: 97:[120, 3] Operation: 37-34=3 Exploring Operation: 120-34=86, Resulting Numbers: [37, 86] Generated Node #0,1,1: 97:[37, 86] Operation: 120-34=86 Exploring Operation: 37+34=71, Resulting Numbers: [120, 71] Generated Node #0,1,2: 97:[120, 71] Operation: 37+34=71 Exploring Operation: 120-37=83, Resulting Numbers: [34, 83] Generated Node #0,1,3: 97:[34, 83] Operation: 120-37=83 Moving to Node #0,2 Current State: 97:[30, 37, 136], Operations: ['4*34=136'] Exploring Operation: 37-30=7, Resulting Numbers: [136, 7] Generated Node #0,2,0: 97:[136, 7] Operation: 37-30=7 Exploring Operation: 136-37=99, Resulting Numbers: [30, 99] Generated Node #0,2,1: 97:[30, 99] Operation: 136-37=99 Exploring Operation: 30+37=67, Resulting Numbers: [136, 67] Generated Node #0,2,2: 97:[136, 67] Operation: 30+37=67 Exploring Operation: 136-30=106, Resulting Numbers: [37, 106] Generated Node #0,2,3: 97:[37, 106] Operation: 136-30=106 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[30, 99], Operations: ['4*34=136', '136-37=99'] Exploring Operation: 30*99=2970, Resulting Numbers: [2970] 2970,97 unequal: No Solution Exploring Operation: 99-30=69, Resulting Numbers: [69] 69,97 unequal: No Solution Exploring Operation: 30+99=129, Resulting Numbers: [129] 129,97 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 #0,2,2 Current State: 97:[136, 67], Operations: ['4*34=136', '30+37=67'] Exploring Operation: 136*67=9112, Resulting Numbers: [9112] 9112,97 unequal: No Solution Exploring Operation: 136-67=69, Resulting Numbers: [69] 69,97 unequal: No Solution Exploring Operation: 136+67=203, Resulting Numbers: [203] 203,97 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 #0,2,3 Current State: 97:[37, 106], Operations: ['4*34=136', '136-30=106'] Exploring Operation: 106-37=69, Resulting Numbers: [69] 69,97 unequal: No Solution Exploring Operation: 37+106=143, Resulting Numbers: [143] 143,97 unequal: No Solution Exploring Operation: 37*106=3922, Resulting Numbers: [3922] 3922,97 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 #0,2,0 Current State: 97:[136, 7], Operations: ['4*34=136', '37-30=7'] Exploring Operation: 136+7=143, Resulting Numbers: [143] 143,97 unequal: No Solution Exploring Operation: 136-7=129, Resulting Numbers: [129] 129,97 unequal: No Solution Exploring Operation: 136*7=952, Resulting Numbers: [952] 952,97 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: 97:[30, 34, 148], Operations: ['37*4=148'] Exploring Operation: 148-34=114, Resulting Numbers: [30, 114] Generated Node #0,3,0: 97:[30, 114] Operation: 148-34=114 Exploring Operation: 30+34=64, Resulting Numbers: [148, 64] Generated Node #0,3,1: 97:[148, 64] Operation: 30+34=64 Exploring Operation: 34-30=4, Resulting Numbers: [148, 4] Generated Node #0,3,2: 97:[148, 4] Operation: 34-30=4 Exploring Operation: 148-30=118, Resulting Numbers: [34, 118] Generated Node #0,3,3: 97:[34, 118] Operation: 148-30=118 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 97:[30, 114], Operations: ['37*4=148', '148-34=114'] Exploring Operation: 30*114=3420, Resulting Numbers: [3420] 3420,97 unequal: No Solution Exploring Operation: 30+114=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 114-30=84, Resulting Numbers: [84] 84,97 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 #0,3,1 Current State: 97:[148, 64], Operations: ['37*4=148', '30+34=64'] Exploring Operation: 148+64=212, Resulting Numbers: [212] 212,97 unequal: No Solution Exploring Operation: 148-64=84, Resulting Numbers: [84] 84,97 unequal: No Solution Exploring Operation: 148*64=9472, Resulting Numbers: [9472] 9472,97 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 #0,3,3 Current State: 97:[34, 118], Operations: ['37*4=148', '148-30=118'] Exploring Operation: 34*118=4012, Resulting Numbers: [4012] 4012,97 unequal: No Solution Exploring Operation: 118-34=84, Resulting Numbers: [84] 84,97 unequal: No Solution Exploring Operation: 34+118=152, Resulting Numbers: [152] 152,97 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 #0,3,2 Current State: 97:[148, 4], Operations: ['37*4=148', '34-30=4'] Exploring Operation: 148+4=152, Resulting Numbers: [152] 152,97 unequal: No Solution Exploring Operation: 148*4=592, Resulting Numbers: [592] 592,97 unequal: No Solution Exploring Operation: 148-4=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 148/4=37, Resulting Numbers: [37] 37,97 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: 97:[4, 34, 67], Operations: ['30+37=67'] Exploring Operation: 34-4=30, Resulting Numbers: [67, 30] Generated Node #0,0,0: 97:[67, 30] Operation: 34-4=30 Exploring Operation: 4+34=38, Resulting Numbers: [67, 38] Generated Node #0,0,1: 97:[67, 38] Operation: 4+34=38 Exploring Operation: 4*34=136, Resulting Numbers: [67, 136] Generated Node #0,0,2: 97:[67, 136] Operation: 4*34=136 Exploring Operation: 4+67=71, Resulting Numbers: [34, 71] Generated Node #0,0,3: 97:[34, 71] Operation: 4+67=71 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 97:[67, 136], Operations: ['30+37=67', '4*34=136'] Exploring Operation: 67*136=9112, Resulting Numbers: [9112] 9112,97 unequal: No Solution Exploring Operation: 67+136=203, Resulting Numbers: [203] 203,97 unequal: No Solution Exploring Operation: 136-67=69, Resulting Numbers: [69] 69,97 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 #0,0,1 Current State: 97:[67, 38], Operations: ['30+37=67', '4+34=38'] Exploring Operation: 67+38=105, Resulting Numbers: [105] 105,97 unequal: No Solution Exploring Operation: 67*38=2546, Resulting Numbers: [2546] 2546,97 unequal: No Solution Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,97 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 #0,0,3 Current State: 97:[34, 71], Operations: ['30+37=67', '4+67=71'] Exploring Operation: 34*71=2414, Resulting Numbers: [2414] 2414,97 unequal: No Solution Exploring Operation: 71-34=37, Resulting Numbers: [37] 37,97 unequal: No Solution Exploring Operation: 34+71=105, Resulting Numbers: [105] 105,97 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 #0,0,0 Current State: 97:[67, 30], Operations: ['30+37=67', '34-4=30'] Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[30, 37, 4, 34], Operations: [] Exploring Operation: 30+37=67, Resulting Numbers: [4, 34, 67] Generated Node #0,0: 97:[4, 34, 67] Operation: 30+37=67 Moving to Node #0,0 Current State: 97:[4, 34, 67], Operations: ['30+37=67'] Exploring Operation: 34-4=30, Resulting Numbers: [67, 30] Generated Node #0,0,0: 97:[67, 30] Operation: 34-4=30 Moving to Node #0,0,0 Current State: 97:[67, 30], Operations: ['30+37=67', '34-4=30'] Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.948785
hs_4
sum_heuristic
[ 12, 14, 98, 8 ]
76
[ "12*98=1176", "1176/14=84", "84-8=76" ]
Current State: 76:[12, 14, 98, 8], Operations: [] Exploring Operation: 12*98=1176, Resulting Numbers: [14, 8, 1176] Generated Node #2: [14, 8, 1176] from Operation: 12*98=1176 Current State: 76:[14, 8, 1176], Operations: ['12*98=1176'] Exploring Operation: 1176/14=84, Resulting Numbers: [8, 84] Generated Node #3: [8, 84] from Operation: 1176/14=84 Current State: 76:[8, 84], Operations: ['12*98=1176', '1176/14=84'] Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[12, 14, 98, 8], Operations: [] Exploring Operation: 98-12=86, Resulting Numbers: [14, 8, 86] Generated Node #0,0: 76:[14, 8, 86] Operation: 98-12=86 Exploring Operation: 98-8=90, Resulting Numbers: [12, 14, 90] Generated Node #0,1: 76:[12, 14, 90] Operation: 98-8=90 Exploring Operation: 14-12=2, Resulting Numbers: [98, 8, 2] Generated Node #0,2: 76:[98, 8, 2] Operation: 14-12=2 Exploring Operation: 98-14=84, Resulting Numbers: [12, 8, 84] Generated Node #0,3: 76:[12, 8, 84] Operation: 98-14=84 Exploring Operation: 98/14=7, Resulting Numbers: [12, 8, 7] Generated Node #0,4: 76:[12, 8, 7] Operation: 98/14=7 Moving to Node #0,4 Current State: 76:[12, 8, 7], Operations: ['98/14=7'] Exploring Operation: 12+8=20, Resulting Numbers: [7, 20] Generated Node #0,4,0: 76:[7, 20] Operation: 12+8=20 Exploring Operation: 8-7=1, Resulting Numbers: [12, 1] Generated Node #0,4,1: 76:[12, 1] Operation: 8-7=1 Exploring Operation: 12+7=19, Resulting Numbers: [8, 19] Generated Node #0,4,2: 76:[8, 19] Operation: 12+7=19 Exploring Operation: 12-8=4, Resulting Numbers: [7, 4] Generated Node #0,4,3: 76:[7, 4] Operation: 12-8=4 Exploring Operation: 12-7=5, Resulting Numbers: [8, 5] Generated Node #0,4,4: 76:[8, 5] Operation: 12-7=5 Moving to Node #0,3 Current State: 76:[12, 8, 84], Operations: ['98-14=84'] Exploring Operation: 84-12=72, Resulting Numbers: [8, 72] Generated Node #0,3,0: 76:[8, 72] Operation: 84-12=72 Exploring Operation: 12-8=4, Resulting Numbers: [84, 4] Generated Node #0,3,1: 76:[84, 4] Operation: 12-8=4 Exploring Operation: 84-8=76, Resulting Numbers: [12, 76] Generated Node #0,3,2: 76:[12, 76] Operation: 84-8=76 Exploring Operation: 12+8=20, Resulting Numbers: [84, 20] Generated Node #0,3,3: 76:[84, 20] Operation: 12+8=20 Exploring Operation: 84/12=7, Resulting Numbers: [8, 7] Generated Node #0,3,4: 76:[8, 7] Operation: 84/12=7 Moving to Node #0,0 Current State: 76:[14, 8, 86], Operations: ['98-12=86'] Exploring Operation: 86-8=78, Resulting Numbers: [14, 78] Generated Node #0,0,0: 76:[14, 78] Operation: 86-8=78 Exploring Operation: 8+86=94, Resulting Numbers: [14, 94] Generated Node #0,0,1: 76:[14, 94] Operation: 8+86=94 Exploring Operation: 14+8=22, Resulting Numbers: [86, 22] Generated Node #0,0,2: 76:[86, 22] Operation: 14+8=22 Exploring Operation: 86-14=72, Resulting Numbers: [8, 72] Generated Node #0,0,3: 76:[8, 72] Operation: 86-14=72 Exploring Operation: 14-8=6, Resulting Numbers: [86, 6] Generated Node #0,0,4: 76:[86, 6] Operation: 14-8=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[14, 78], Operations: ['98-12=86', '86-8=78'] Exploring Operation: 14*78=1092, Resulting Numbers: [1092] 1092,76 unequal: No Solution Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 14+78=92, Resulting Numbers: [92] 92,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 76:[8, 72], Operations: ['98-12=86', '86-14=72'] Exploring Operation: 8+72=80, Resulting Numbers: [80] 80,76 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 8*72=576, Resulting Numbers: [576] 576,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 76:[86, 6], Operations: ['98-12=86', '14-8=6'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,76 unequal: No Solution Exploring Operation: 86*6=516, Resulting Numbers: [516] 516,76 unequal: No Solution Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 76:[86, 22], Operations: ['98-12=86', '14+8=22'] Exploring Operation: 86*22=1892, Resulting Numbers: [1892] 1892,76 unequal: No Solution Exploring Operation: 86-22=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 86+22=108, Resulting Numbers: [108] 108,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 76:[14, 94], Operations: ['98-12=86', '8+86=94'] Exploring Operation: 14*94=1316, Resulting Numbers: [1316] 1316,76 unequal: No Solution Exploring Operation: 14+94=108, Resulting Numbers: [108] 108,76 unequal: No Solution Exploring Operation: 94-14=80, Resulting Numbers: [80] 80,76 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: 76:[12, 14, 90], Operations: ['98-8=90'] Exploring Operation: 90-12=78, Resulting Numbers: [14, 78] Generated Node #0,1,0: 76:[14, 78] Operation: 90-12=78 Exploring Operation: 12+14=26, Resulting Numbers: [90, 26] Generated Node #0,1,1: 76:[90, 26] Operation: 12+14=26 Exploring Operation: 12+90=102, Resulting Numbers: [14, 102] Generated Node #0,1,2: 76:[14, 102] Operation: 12+90=102 Exploring Operation: 14-12=2, Resulting Numbers: [90, 2] Generated Node #0,1,3: 76:[90, 2] Operation: 14-12=2 Exploring Operation: 90-14=76, Resulting Numbers: [12, 76] Generated Node #0,1,4: 76:[12, 76] Operation: 90-14=76 Moving to Node #0,2 Current State: 76:[98, 8, 2], Operations: ['14-12=2'] Exploring Operation: 98-8=90, Resulting Numbers: [2, 90] Generated Node #0,2,0: 76:[2, 90] Operation: 98-8=90 Exploring Operation: 8-2=6, Resulting Numbers: [98, 6] Generated Node #0,2,1: 76:[98, 6] Operation: 8-2=6 Exploring Operation: 98/2=49, Resulting Numbers: [8, 49] Generated Node #0,2,2: 76:[8, 49] Operation: 98/2=49 Exploring Operation: 98-2=96, Resulting Numbers: [8, 96] Generated Node #0,2,3: 76:[8, 96] Operation: 98-2=96 Exploring Operation: 8/2=4, Resulting Numbers: [98, 4] Generated Node #0,2,4: 76:[98, 4] Operation: 8/2=4 Moving to Node #0,4,3 Current State: 76:[7, 4], Operations: ['98/14=7', '12-8=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,76 unequal: No Solution Moving to Node #0,4,2 Current State: 76:[8, 19], Operations: ['98/14=7', '12+7=19'] Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,76 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,76 unequal: No Solution Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,76 unequal: No Solution Moving to Node #0,4,0 Current State: 76:[7, 20], Operations: ['98/14=7', '12+8=20'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,76 unequal: No Solution Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,76 unequal: No Solution Moving to Node #0,4,4 Current State: 76:[8, 5], Operations: ['98/14=7', '12-7=5'] Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,76 unequal: No Solution Moving to Node #0,3,4 Current State: 76:[8, 7], Operations: ['98-14=84', '84/12=7'] Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,76 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[12, 76], Operations: ['98-14=84', '84-8=76'] Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 12+76=88, Resulting Numbers: [88] 88,76 unequal: No Solution Exploring Operation: 12*76=912, Resulting Numbers: [912] 912,76 unequal: No Solution Moving to Node #0,1,4 Current State: 76:[12, 76], Operations: ['98-8=90', '90-14=76'] Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 12*76=912, Resulting Numbers: [912] 912,76 unequal: No Solution Exploring Operation: 12+76=88, Resulting Numbers: [88] 88,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[14, 78], Operations: ['98-8=90', '90-12=78'] Exploring Operation: 14*78=1092, Resulting Numbers: [1092] 1092,76 unequal: No Solution Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 14+78=92, Resulting Numbers: [92] 92,76 unequal: No Solution Moving to Node #0,4,1 Current State: 76:[12, 1], Operations: ['98/14=7', '8-7=1'] Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 12*1=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,76 unequal: No Solution Exploring Operation: 12+1=13, Resulting Numbers: [13] 13,76 unequal: No Solution Moving to Node #0,3,1 Current State: 76:[84, 4], Operations: ['98-14=84', '12-8=4'] Exploring Operation: 84+4=88, Resulting Numbers: [88] 88,76 unequal: No Solution Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,76 unequal: No Solution Exploring Operation: 84*4=336, Resulting Numbers: [336] 336,76 unequal: No Solution Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[8, 72], Operations: ['98-14=84', '84-12=72'] Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 8*72=576, Resulting Numbers: [576] 576,76 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 8+72=80, Resulting Numbers: [80] 80,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[84, 20], Operations: ['98-14=84', '12+8=20'] Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 84*20=1680, Resulting Numbers: [1680] 1680,76 unequal: No Solution Exploring Operation: 84+20=104, Resulting Numbers: [104] 104,76 unequal: No Solution Moving to Node #0,1,3 Current State: 76:[90, 2], Operations: ['98-8=90', '14-12=2'] Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,76 unequal: No Solution Exploring Operation: 90*2=180, Resulting Numbers: [180] 180,76 unequal: No Solution Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,76 unequal: No Solution Exploring Operation: 90+2=92, Resulting Numbers: [92] 92,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[2, 90], Operations: ['14-12=2', '98-8=90'] Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,76 unequal: No Solution Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,76 unequal: No Solution Exploring Operation: 2+90=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 2*90=180, Resulting Numbers: [180] 180,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[8, 49], Operations: ['14-12=2', '98/2=49'] Exploring Operation: 8+49=57, Resulting Numbers: [57] 57,76 unequal: No Solution Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,76 unequal: No Solution Exploring Operation: 8*49=392, Resulting Numbers: [392] 392,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[90, 26], Operations: ['98-8=90', '12+14=26'] Exploring Operation: 90-26=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 90*26=2340, Resulting Numbers: [2340] 2340,76 unequal: No Solution Exploring Operation: 90+26=116, Resulting Numbers: [116] 116,76 unequal: No Solution Moving to Node #0,2,4 Current State: 76:[98, 4], Operations: ['14-12=2', '8/2=4'] Exploring Operation: 98*4=392, Resulting Numbers: [392] 392,76 unequal: No Solution Exploring Operation: 98-4=94, Resulting Numbers: [94] 94,76 unequal: No Solution Exploring Operation: 98+4=102, Resulting Numbers: [102] 102,76 unequal: No Solution Moving to Node #0,2,1 Current State: 76:[98, 6], Operations: ['14-12=2', '8-2=6'] Exploring Operation: 98+6=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 98-6=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 98*6=588, Resulting Numbers: [588] 588,76 unequal: No Solution Moving to Node #0,2,3 Current State: 76:[8, 96], Operations: ['14-12=2', '98-2=96'] Exploring Operation: 96/8=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 96-8=88, Resulting Numbers: [88] 88,76 unequal: No Solution Exploring Operation: 8+96=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 8*96=768, Resulting Numbers: [768] 768,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[14, 102], Operations: ['98-8=90', '12+90=102'] Exploring Operation: 102-14=88, Resulting Numbers: [88] 88,76 unequal: No Solution Exploring Operation: 14+102=116, Resulting Numbers: [116] 116,76 unequal: No Solution Exploring Operation: 14*102=1428, Resulting Numbers: [1428] 1428,76 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 51, 8, 51, 13 ]
91
[ "51/51=1", "8-1=7", "13*7=91" ]
Current State: 91:[51, 8, 51, 13], Operations: [] Exploring Operation: 51/51=1, Resulting Numbers: [8, 13, 1] Generated Node #2: [8, 13, 1] from Operation: 51/51=1 Current State: 91:[8, 13, 1], Operations: ['51/51=1'] Exploring Operation: 8-1=7, Resulting Numbers: [13, 7] Generated Node #3: [13, 7] from Operation: 8-1=7 Current State: 91:[13, 7], Operations: ['51/51=1', '8-1=7'] Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[51, 8, 51, 13], Operations: [] Exploring Operation: 51/51=1, Resulting Numbers: [8, 13, 1] Generated Node #0,0: 91:[8, 13, 1] Operation: 51/51=1 Exploring Operation: 51+51=102, Resulting Numbers: [8, 13, 102] Generated Node #0,1: 91:[8, 13, 102] Operation: 51+51=102 Exploring Operation: 51-13=38, Resulting Numbers: [8, 51, 38] Generated Node #0,2: 91:[8, 51, 38] Operation: 51-13=38 Exploring Operation: 51-51=0, Resulting Numbers: [8, 13, 0] Generated Node #0,3: 91:[8, 13, 0] Operation: 51-51=0 Exploring Operation: 51-13=38, Resulting Numbers: [51, 8, 38] Generated Node #0,4: 91:[51, 8, 38] Operation: 51-13=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[8, 13, 1], Operations: ['51/51=1'] Exploring Operation: 8/1=8, Resulting Numbers: [13, 8] Generated Node #0,0,0: 91:[13, 8] Operation: 8/1=8 Exploring Operation: 13*1=13, Resulting Numbers: [8, 13] Generated Node #0,0,1: 91:[8, 13] Operation: 13*1=13 Exploring Operation: 8*1=8, Resulting Numbers: [13, 8] Generated Node #0,0,2: 91:[13, 8] Operation: 8*1=8 Exploring Operation: 13/1=13, Resulting Numbers: [8, 13] Generated Node #0,0,3: 91:[8, 13] Operation: 13/1=13 Exploring Operation: 8-1=7, Resulting Numbers: [13, 7] Generated Node #0,0,4: 91:[13, 7] Operation: 8-1=7 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 91:[13, 7], Operations: ['51/51=1', '8-1=7'] Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[51, 8, 51, 13], Operations: [] Exploring Operation: 51/51=1, Resulting Numbers: [8, 13, 1] Generated Node #0,0: 91:[8, 13, 1] Operation: 51/51=1 Moving to Node #0,0 Current State: 91:[8, 13, 1], Operations: ['51/51=1'] Exploring Operation: 8-1=7, Resulting Numbers: [13, 7] Generated Node #0,0,4: 91:[13, 7] Operation: 8-1=7 Moving to Node #0,0,4 Current State: 91:[13, 7], Operations: ['51/51=1', '8-1=7'] Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 69, 78, 26, 93 ]
76
[ "78-69=9", "93-26=67", "9+67=76" ]
Current State: 76:[69, 78, 26, 93], Operations: [] Exploring Operation: 78-69=9, Resulting Numbers: [26, 93, 9] Generated Node #2: [26, 93, 9] from Operation: 78-69=9 Current State: 76:[26, 93, 9], Operations: ['78-69=9'] Exploring Operation: 93-26=67, Resulting Numbers: [9, 67] Generated Node #3: [9, 67] from Operation: 93-26=67 Current State: 76:[9, 67], Operations: ['78-69=9', '93-26=67'] Exploring Operation: 9+67=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[69, 78, 26, 93], Operations: [] Exploring Operation: 93-69=24, Resulting Numbers: [78, 26, 24] Generated Node #0,0: 76:[78, 26, 24] Operation: 93-69=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[78, 26, 24], Operations: ['93-69=24'] Exploring Operation: 26-24=2, Resulting Numbers: [78, 2] Generated Node #0,0,0: 76:[78, 2] Operation: 26-24=2 Moving to Node #0,0,0 Current State: 76:[78, 2], Operations: ['93-69=24', '26-24=2'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[69, 78, 26, 93], Operations: [] Exploring Operation: 93-69=24, Resulting Numbers: [78, 26, 24] Generated Node #0,0: 76:[78, 26, 24] Operation: 93-69=24 Moving to Node #0,0 Current State: 76:[78, 26, 24], Operations: ['93-69=24'] Exploring Operation: 26-24=2, Resulting Numbers: [78, 2] Generated Node #0,0,0: 76:[78, 2] Operation: 26-24=2 Moving to Node #0,0,0 Current State: 76:[78, 2], Operations: ['93-69=24', '26-24=2'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 45, 3, 34, 78 ]
37
[ "45-34=11", "78/3=26", "11+26=37" ]
Current State: 37:[45, 3, 34, 78], Operations: [] Exploring Operation: 45-34=11, Resulting Numbers: [3, 78, 11] Generated Node #2: [3, 78, 11] from Operation: 45-34=11 Current State: 37:[3, 78, 11], Operations: ['45-34=11'] Exploring Operation: 78/3=26, Resulting Numbers: [11, 26] Generated Node #3: [11, 26] from Operation: 78/3=26 Current State: 37:[11, 26], Operations: ['45-34=11', '78/3=26'] Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[45, 3, 34, 78], Operations: [] Exploring Operation: 78-45=33, Resulting Numbers: [3, 34, 33] Generated Node #0,0: 37:[3, 34, 33] Operation: 78-45=33 Exploring Operation: 78/3=26, Resulting Numbers: [45, 34, 26] Generated Node #0,1: 37:[45, 34, 26] Operation: 78/3=26 Exploring Operation: 45-3=42, Resulting Numbers: [34, 78, 42] Generated Node #0,2: 37:[34, 78, 42] Operation: 45-3=42 Moving to Node #0,1 Current State: 37:[45, 34, 26], Operations: ['78/3=26'] Exploring Operation: 45-34=11, Resulting Numbers: [26, 11] Generated Node #0,1,0: 37:[26, 11] Operation: 45-34=11 Exploring Operation: 45-26=19, Resulting Numbers: [34, 19] Generated Node #0,1,1: 37:[34, 19] Operation: 45-26=19 Exploring Operation: 34+26=60, Resulting Numbers: [45, 60] Generated Node #0,1,2: 37:[45, 60] Operation: 34+26=60 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 37:[34, 19], Operations: ['78/3=26', '45-26=19'] Exploring Operation: 34-19=15, Resulting Numbers: [15] 15,37 unequal: No Solution Exploring Operation: 34*19=646, Resulting Numbers: [646] 646,37 unequal: No Solution Exploring Operation: 34+19=53, Resulting Numbers: [53] 53,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 37:[45, 60], Operations: ['78/3=26', '34+26=60'] Exploring Operation: 45*60=2700, Resulting Numbers: [2700] 2700,37 unequal: No Solution Exploring Operation: 60-45=15, Resulting Numbers: [15] 15,37 unequal: No Solution Exploring Operation: 45+60=105, Resulting Numbers: [105] 105,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[26, 11], Operations: ['78/3=26', '45-34=11'] Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[45, 3, 34, 78], Operations: [] Exploring Operation: 78/3=26, Resulting Numbers: [45, 34, 26] Generated Node #0,1: 37:[45, 34, 26] Operation: 78/3=26 Moving to Node #0,1 Current State: 37:[45, 34, 26], Operations: ['78/3=26'] Exploring Operation: 45-34=11, Resulting Numbers: [26, 11] Generated Node #0,1,0: 37:[26, 11] Operation: 45-34=11 Moving to Node #0,1,0 Current State: 37:[26, 11], Operations: ['78/3=26', '45-34=11'] Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 47, 75, 38, 25 ]
91
[ "75-47=28", "38+25=63", "28+63=91" ]
Current State: 91:[47, 75, 38, 25], Operations: [] Exploring Operation: 75-47=28, Resulting Numbers: [38, 25, 28] Generated Node #2: [38, 25, 28] from Operation: 75-47=28 Current State: 91:[38, 25, 28], Operations: ['75-47=28'] Exploring Operation: 38+25=63, Resulting Numbers: [28, 63] Generated Node #3: [28, 63] from Operation: 38+25=63 Current State: 91:[28, 63], Operations: ['75-47=28', '38+25=63'] Exploring Operation: 28+63=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[47, 75, 38, 25], Operations: [] Exploring Operation: 47+38=85, Resulting Numbers: [75, 25, 85] Generated Node #0,0: 91:[75, 25, 85] Operation: 47+38=85 Exploring Operation: 38-25=13, Resulting Numbers: [47, 75, 13] Generated Node #0,1: 91:[47, 75, 13] Operation: 38-25=13 Exploring Operation: 47-38=9, Resulting Numbers: [75, 25, 9] Generated Node #0,2: 91:[75, 25, 9] Operation: 47-38=9 Exploring Operation: 47-25=22, Resulting Numbers: [75, 38, 22] Generated Node #0,3: 91:[75, 38, 22] Operation: 47-25=22 Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[75, 25, 9], Operations: ['47-38=9'] Exploring Operation: 75+9=84, Resulting Numbers: [25, 84] Generated Node #0,2,0: 91:[25, 84] Operation: 75+9=84 Exploring Operation: 75/25=3, Resulting Numbers: [9, 3] Generated Node #0,2,1: 91:[9, 3] Operation: 75/25=3 Exploring Operation: 75+25=100, Resulting Numbers: [9, 100] Generated Node #0,2,2: 91:[9, 100] Operation: 75+25=100 Exploring Operation: 25-9=16, Resulting Numbers: [75, 16] Generated Node #0,2,3: 91:[75, 16] Operation: 25-9=16 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 91:[9, 3], Operations: ['47-38=9', '75/25=3'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,91 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,91 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,91 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 91:[9, 100], Operations: ['47-38=9', '75+25=100'] Exploring Operation: 9*100=900, Resulting Numbers: [900] 900,91 unequal: No Solution Exploring Operation: 9+100=109, Resulting Numbers: [109] 109,91 unequal: No Solution Exploring Operation: 100-9=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[47, 75, 38, 25], Operations: [] Exploring Operation: 47-38=9, Resulting Numbers: [75, 25, 9] Generated Node #0,2: 91:[75, 25, 9] Operation: 47-38=9 Moving to Node #0,2 Current State: 91:[75, 25, 9], Operations: ['47-38=9'] Exploring Operation: 75+25=100, Resulting Numbers: [9, 100] Generated Node #0,2,2: 91:[9, 100] Operation: 75+25=100 Moving to Node #0,2,2 Current State: 91:[9, 100], Operations: ['47-38=9', '75+25=100'] Exploring Operation: 100-9=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 86, 75, 99, 60 ]
69
[ "86-75=11", "99/11=9", "60+9=69" ]
Current State: 69:[86, 75, 99, 60], Operations: [] Exploring Operation: 86-75=11, Resulting Numbers: [99, 60, 11] Generated Node #2: [99, 60, 11] from Operation: 86-75=11 Current State: 69:[99, 60, 11], Operations: ['86-75=11'] Exploring Operation: 99/11=9, Resulting Numbers: [60, 9] Generated Node #3: [60, 9] from Operation: 99/11=9 Current State: 69:[60, 9], Operations: ['86-75=11', '99/11=9'] Exploring Operation: 60+9=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[86, 75, 99, 60], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [86, 60, 24] Generated Node #0,0: 69:[86, 60, 24] Operation: 99-75=24 Exploring Operation: 86-60=26, Resulting Numbers: [75, 99, 26] Generated Node #0,1: 69:[75, 99, 26] Operation: 86-60=26 Exploring Operation: 99-86=13, Resulting Numbers: [75, 60, 13] Generated Node #0,2: 69:[75, 60, 13] Operation: 99-86=13 Moving to Node #0,2 Current State: 69:[75, 60, 13], Operations: ['99-86=13'] Exploring Operation: 60+13=73, Resulting Numbers: [75, 73] Generated Node #0,2,0: 69:[75, 73] Operation: 60+13=73 Exploring Operation: 75-60=15, Resulting Numbers: [13, 15] Generated Node #0,2,1: 69:[13, 15] Operation: 75-60=15 Exploring Operation: 75-13=62, Resulting Numbers: [60, 62] Generated Node #0,2,2: 69:[60, 62] Operation: 75-13=62 Moving to Node #0,0 Current State: 69:[86, 60, 24], Operations: ['99-75=24'] Exploring Operation: 86-24=62, Resulting Numbers: [60, 62] Generated Node #0,0,0: 69:[60, 62] Operation: 86-24=62 Exploring Operation: 60-24=36, Resulting Numbers: [86, 36] Generated Node #0,0,1: 69:[86, 36] Operation: 60-24=36 Exploring Operation: 86-60=26, Resulting Numbers: [24, 26] Generated Node #0,0,2: 69:[24, 26] Operation: 86-60=26 Moving to Node #0,1 Current State: 69:[75, 99, 26], Operations: ['86-60=26'] Exploring Operation: 75-26=49, Resulting Numbers: [99, 49] Generated Node #0,1,0: 69:[99, 49] Operation: 75-26=49 Exploring Operation: 99-26=73, Resulting Numbers: [75, 73] Generated Node #0,1,1: 69:[75, 73] Operation: 99-26=73 Exploring Operation: 99-75=24, Resulting Numbers: [26, 24] Generated Node #0,1,2: 69:[26, 24] Operation: 99-75=24 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[26, 24], Operations: ['86-60=26', '99-75=24'] Exploring Operation: 26*24=624, Resulting Numbers: [624] 624,69 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 26+24=50, Resulting Numbers: [50] 50,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[75, 73], Operations: ['86-60=26', '99-26=73'] Exploring Operation: 75-73=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 75*73=5475, Resulting Numbers: [5475] 5475,69 unequal: No Solution Exploring Operation: 75+73=148, Resulting Numbers: [148] 148,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[99, 49], Operations: ['86-60=26', '75-26=49'] Exploring Operation: 99*49=4851, Resulting Numbers: [4851] 4851,69 unequal: No Solution Exploring Operation: 99+49=148, Resulting Numbers: [148] 148,69 unequal: No Solution Exploring Operation: 99-49=50, Resulting Numbers: [50] 50,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 69:[24, 26], Operations: ['99-75=24', '86-60=26'] Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 24*26=624, Resulting Numbers: [624] 624,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[75, 73], Operations: ['99-86=13', '60+13=73'] Exploring Operation: 75-73=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 75+73=148, Resulting Numbers: [148] 148,69 unequal: No Solution Exploring Operation: 75*73=5475, Resulting Numbers: [5475] 5475,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[60, 62], Operations: ['99-75=24', '86-24=62'] Exploring Operation: 60*62=3720, Resulting Numbers: [3720] 3720,69 unequal: No Solution Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 60+62=122, Resulting Numbers: [122] 122,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[60, 62], Operations: ['99-86=13', '75-13=62'] Exploring Operation: 60+62=122, Resulting Numbers: [122] 122,69 unequal: No Solution Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 60*62=3720, Resulting Numbers: [3720] 3720,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[13, 15], Operations: ['99-86=13', '75-60=15'] Exploring Operation: 13+15=28, Resulting Numbers: [28] 28,69 unequal: No Solution Exploring Operation: 13*15=195, Resulting Numbers: [195] 195,69 unequal: No Solution Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,69 unequal: No Solution Moving to Node #0,0,1 Current State: 69:[86, 36], Operations: ['99-75=24', '60-24=36'] Exploring Operation: 86*36=3096, Resulting Numbers: [3096] 3096,69 unequal: No Solution Exploring Operation: 86+36=122, Resulting Numbers: [122] 122,69 unequal: No Solution Exploring Operation: 86-36=50, Resulting Numbers: [50] 50,69 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 13, 33, 53, 61 ]
38
[ "13+33=46", "61-53=8", "46-8=38" ]
Current State: 38:[13, 33, 53, 61], Operations: [] Exploring Operation: 13+33=46, Resulting Numbers: [53, 61, 46] Generated Node #2: [53, 61, 46] from Operation: 13+33=46 Current State: 38:[53, 61, 46], Operations: ['13+33=46'] Exploring Operation: 61-53=8, Resulting Numbers: [46, 8] Generated Node #3: [46, 8] from Operation: 61-53=8 Current State: 38:[46, 8], Operations: ['13+33=46', '61-53=8'] Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[13, 33, 53, 61], Operations: [] Exploring Operation: 61-53=8, Resulting Numbers: [13, 33, 8] Generated Node #0,0: 38:[13, 33, 8] Operation: 61-53=8 Exploring Operation: 61-13=48, Resulting Numbers: [33, 53, 48] Generated Node #0,1: 38:[33, 53, 48] Operation: 61-13=48 Exploring Operation: 53-13=40, Resulting Numbers: [33, 61, 40] Generated Node #0,2: 38:[33, 61, 40] Operation: 53-13=40 Exploring Operation: 53-33=20, Resulting Numbers: [13, 61, 20] Generated Node #0,3: 38:[13, 61, 20] Operation: 53-33=20 Moving to Node #0,0 Current State: 38:[13, 33, 8], Operations: ['61-53=8'] Exploring Operation: 13-8=5, Resulting Numbers: [33, 5] Generated Node #0,0,0: 38:[33, 5] Operation: 13-8=5 Exploring Operation: 13+8=21, Resulting Numbers: [33, 21] Generated Node #0,0,1: 38:[33, 21] Operation: 13+8=21 Exploring Operation: 33-13=20, Resulting Numbers: [8, 20] Generated Node #0,0,2: 38:[8, 20] Operation: 33-13=20 Exploring Operation: 33+8=41, Resulting Numbers: [13, 41] Generated Node #0,0,3: 38:[13, 41] Operation: 33+8=41 Moving to Node #0,2 Current State: 38:[33, 61, 40], Operations: ['53-13=40'] Exploring Operation: 61-40=21, Resulting Numbers: [33, 21] Generated Node #0,2,0: 38:[33, 21] Operation: 61-40=21 Exploring Operation: 61-33=28, Resulting Numbers: [40, 28] Generated Node #0,2,1: 38:[40, 28] Operation: 61-33=28 Exploring Operation: 40-33=7, Resulting Numbers: [61, 7] Generated Node #0,2,2: 38:[61, 7] Operation: 40-33=7 Exploring Operation: 33+61=94, Resulting Numbers: [40, 94] Generated Node #0,2,3: 38:[40, 94] Operation: 33+61=94 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 38:[33, 21], Operations: ['53-13=40', '61-40=21'] Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,38 unequal: No Solution Exploring Operation: 33*21=693, Resulting Numbers: [693] 693,38 unequal: No Solution Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 38:[40, 28], Operations: ['53-13=40', '61-33=28'] Exploring Operation: 40+28=68, Resulting Numbers: [68] 68,38 unequal: No Solution Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,38 unequal: No Solution Exploring Operation: 40*28=1120, Resulting Numbers: [1120] 1120,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 38:[61, 7], Operations: ['53-13=40', '40-33=7'] Exploring Operation: 61+7=68, Resulting Numbers: [68] 68,38 unequal: No Solution Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,38 unequal: No Solution Exploring Operation: 61*7=427, Resulting Numbers: [427] 427,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 38:[40, 94], Operations: ['53-13=40', '33+61=94'] Exploring Operation: 94-40=54, Resulting Numbers: [54] 54,38 unequal: No Solution Exploring Operation: 40+94=134, Resulting Numbers: [134] 134,38 unequal: No Solution Exploring Operation: 40*94=3760, Resulting Numbers: [3760] 3760,38 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: 38:[33, 53, 48], Operations: ['61-13=48'] Exploring Operation: 48-33=15, Resulting Numbers: [53, 15] Generated Node #0,1,0: 38:[53, 15] Operation: 48-33=15 Exploring Operation: 33+53=86, Resulting Numbers: [48, 86] Generated Node #0,1,1: 38:[48, 86] Operation: 33+53=86 Exploring Operation: 53-48=5, Resulting Numbers: [33, 5] Generated Node #0,1,2: 38:[33, 5] Operation: 53-48=5 Exploring Operation: 53-33=20, Resulting Numbers: [48, 20] Generated Node #0,1,3: 38:[48, 20] Operation: 53-33=20 Moving to Node #0,3 Current State: 38:[13, 61, 20], Operations: ['53-33=20'] Exploring Operation: 20-13=7, Resulting Numbers: [61, 7] Generated Node #0,3,0: 38:[61, 7] Operation: 20-13=7 Exploring Operation: 61-20=41, Resulting Numbers: [13, 41] Generated Node #0,3,1: 38:[13, 41] Operation: 61-20=41 Exploring Operation: 13+20=33, Resulting Numbers: [61, 33] Generated Node #0,3,2: 38:[61, 33] Operation: 13+20=33 Exploring Operation: 61-13=48, Resulting Numbers: [20, 48] Generated Node #0,3,3: 38:[20, 48] Operation: 61-13=48 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 38:[13, 41], Operations: ['53-33=20', '61-20=41'] Exploring Operation: 13*41=533, Resulting Numbers: [533] 533,38 unequal: No Solution Exploring Operation: 13+41=54, Resulting Numbers: [54] 54,38 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 38:[20, 48], Operations: ['53-33=20', '61-13=48'] Exploring Operation: 20+48=68, Resulting Numbers: [68] 68,38 unequal: No Solution Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,38 unequal: No Solution Exploring Operation: 20*48=960, Resulting Numbers: [960] 960,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 38:[61, 7], Operations: ['53-33=20', '20-13=7'] Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,38 unequal: No Solution Exploring Operation: 61*7=427, Resulting Numbers: [427] 427,38 unequal: No Solution Exploring Operation: 61+7=68, Resulting Numbers: [68] 68,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 38:[61, 33], Operations: ['53-33=20', '13+20=33'] Exploring Operation: 61-33=28, Resulting Numbers: [28] 28,38 unequal: No Solution Exploring Operation: 61+33=94, Resulting Numbers: [94] 94,38 unequal: No Solution Exploring Operation: 61*33=2013, Resulting Numbers: [2013] 2013,38 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: 38:[33, 21], Operations: ['61-53=8', '13+8=21'] Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,38 unequal: No Solution Exploring Operation: 33*21=693, Resulting Numbers: [693] 693,38 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[8, 20], Operations: ['61-53=8', '33-13=20'] Exploring Operation: 8*20=160, Resulting Numbers: [160] 160,38 unequal: No Solution Exploring Operation: 8+20=28, Resulting Numbers: [28] 28,38 unequal: No Solution Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[33, 5], Operations: ['61-53=8', '13-8=5'] Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,38 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,38 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[13, 33, 53, 61], Operations: [] Exploring Operation: 61-53=8, Resulting Numbers: [13, 33, 8] Generated Node #0,0: 38:[13, 33, 8] Operation: 61-53=8 Moving to Node #0,0 Current State: 38:[13, 33, 8], Operations: ['61-53=8'] Exploring Operation: 13-8=5, Resulting Numbers: [33, 5] Generated Node #0,0,0: 38:[33, 5] Operation: 13-8=5 Moving to Node #0,0,0 Current State: 38:[33, 5], Operations: ['61-53=8', '13-8=5'] Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
0.950521
hs_4
sum_heuristic
[ 7, 32, 12, 8 ]
43
[ "7+32=39", "12-8=4", "39+4=43" ]
Current State: 43:[7, 32, 12, 8], Operations: [] Exploring Operation: 7+32=39, Resulting Numbers: [12, 8, 39] Generated Node #2: [12, 8, 39] from Operation: 7+32=39 Current State: 43:[12, 8, 39], Operations: ['7+32=39'] Exploring Operation: 12-8=4, Resulting Numbers: [39, 4] Generated Node #3: [39, 4] from Operation: 12-8=4 Current State: 43:[39, 4], Operations: ['7+32=39', '12-8=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[7, 32, 12, 8], Operations: [] Exploring Operation: 7*8=56, Resulting Numbers: [32, 12, 56] Generated Node #0,0: 43:[32, 12, 56] Operation: 7*8=56 Moving to Node #0,0 Current State: 43:[32, 12, 56], Operations: ['7*8=56'] Exploring Operation: 56-12=44, Resulting Numbers: [32, 44] Generated Node #0,0,0: 43:[32, 44] Operation: 56-12=44 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[32, 44], Operations: ['7*8=56', '56-12=44'] Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 4, 55, 6, 40 ]
70
[ "6-4=2", "55*2=110", "110-40=70" ]
Current State: 70:[4, 55, 6, 40], Operations: [] Exploring Operation: 6-4=2, Resulting Numbers: [55, 40, 2] Generated Node #2: [55, 40, 2] from Operation: 6-4=2 Current State: 70:[55, 40, 2], Operations: ['6-4=2'] Exploring Operation: 55*2=110, Resulting Numbers: [40, 110] Generated Node #3: [40, 110] from Operation: 55*2=110 Current State: 70:[40, 110], Operations: ['6-4=2', '55*2=110'] Exploring Operation: 110-40=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[4, 55, 6, 40], Operations: [] Exploring Operation: 55-40=15, Resulting Numbers: [4, 6, 15] Generated Node #0,0: 70:[4, 6, 15] Operation: 55-40=15 Moving to Node #0,0 Current State: 70:[4, 6, 15], Operations: ['55-40=15'] Exploring Operation: 4+6=10, Resulting Numbers: [15, 10] Generated Node #0,0,0: 70:[15, 10] Operation: 4+6=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[15, 10], Operations: ['55-40=15', '4+6=10'] Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 41, 39, 46, 77 ]
52
[ "46-39=7", "77/7=11", "41+11=52" ]
Current State: 52:[41, 39, 46, 77], Operations: [] Exploring Operation: 46-39=7, Resulting Numbers: [41, 77, 7] Generated Node #2: [41, 77, 7] from Operation: 46-39=7 Current State: 52:[41, 77, 7], Operations: ['46-39=7'] Exploring Operation: 77/7=11, Resulting Numbers: [41, 11] Generated Node #3: [41, 11] from Operation: 77/7=11 Current State: 52:[41, 11], Operations: ['46-39=7', '77/7=11'] Exploring Operation: 41+11=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[41, 39, 46, 77], Operations: [] Exploring Operation: 77-46=31, Resulting Numbers: [41, 39, 31] Generated Node #0,0: 52:[41, 39, 31] Operation: 77-46=31 Exploring Operation: 77-41=36, Resulting Numbers: [39, 46, 36] Generated Node #0,1: 52:[39, 46, 36] Operation: 77-41=36 Exploring Operation: 46-41=5, Resulting Numbers: [39, 77, 5] Generated Node #0,2: 52:[39, 77, 5] Operation: 46-41=5 Exploring Operation: 77-39=38, Resulting Numbers: [41, 46, 38] Generated Node #0,3: 52:[41, 46, 38] Operation: 77-39=38 Exploring Operation: 41-39=2, Resulting Numbers: [46, 77, 2] Generated Node #0,4: 52:[46, 77, 2] Operation: 41-39=2 Moving to Node #0,0 Current State: 52:[41, 39, 31], Operations: ['77-46=31'] Exploring Operation: 39+31=70, Resulting Numbers: [41, 70] Generated Node #0,0,0: 52:[41, 70] Operation: 39+31=70 Exploring Operation: 41+39=80, Resulting Numbers: [31, 80] Generated Node #0,0,1: 52:[31, 80] Operation: 41+39=80 Exploring Operation: 41-31=10, Resulting Numbers: [39, 10] Generated Node #0,0,2: 52:[39, 10] Operation: 41-31=10 Exploring Operation: 41-39=2, Resulting Numbers: [31, 2] Generated Node #0,0,3: 52:[31, 2] Operation: 41-39=2 Exploring Operation: 39-31=8, Resulting Numbers: [41, 8] Generated Node #0,0,4: 52:[41, 8] Operation: 39-31=8 Moving to Node #0,3 Current State: 52:[41, 46, 38], Operations: ['77-39=38'] Exploring Operation: 41-38=3, Resulting Numbers: [46, 3] Generated Node #0,3,0: 52:[46, 3] Operation: 41-38=3 Exploring Operation: 46+38=84, Resulting Numbers: [41, 84] Generated Node #0,3,1: 52:[41, 84] Operation: 46+38=84 Exploring Operation: 41+38=79, Resulting Numbers: [46, 79] Generated Node #0,3,2: 52:[46, 79] Operation: 41+38=79 Exploring Operation: 46-38=8, Resulting Numbers: [41, 8] Generated Node #0,3,3: 52:[41, 8] Operation: 46-38=8 Exploring Operation: 46-41=5, Resulting Numbers: [38, 5] Generated Node #0,3,4: 52:[38, 5] Operation: 46-41=5 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 52:[46, 3], Operations: ['77-39=38', '41-38=3'] Exploring Operation: 46+3=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 46*3=138, Resulting Numbers: [138] 138,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 52:[38, 5], Operations: ['77-39=38', '46-41=5'] Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,52 unequal: No Solution Exploring Operation: 38*5=190, Resulting Numbers: [190] 190,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 52:[41, 8], Operations: ['77-39=38', '46-38=8'] Exploring Operation: 41*8=328, Resulting Numbers: [328] 328,52 unequal: No Solution Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,52 unequal: No Solution Exploring Operation: 41+8=49, Resulting Numbers: [49] 49,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 52:[46, 79], Operations: ['77-39=38', '41+38=79'] Exploring Operation: 46+79=125, Resulting Numbers: [125] 125,52 unequal: No Solution Exploring Operation: 46*79=3634, Resulting Numbers: [3634] 3634,52 unequal: No Solution Exploring Operation: 79-46=33, Resulting Numbers: [33] 33,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 52:[41, 84], Operations: ['77-39=38', '46+38=84'] Exploring Operation: 84-41=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 41*84=3444, Resulting Numbers: [3444] 3444,52 unequal: No Solution Exploring Operation: 41+84=125, Resulting Numbers: [125] 125,52 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: 52:[39, 46, 36], Operations: ['77-41=36'] Exploring Operation: 46-39=7, Resulting Numbers: [36, 7] Generated Node #0,1,0: 52:[36, 7] Operation: 46-39=7 Exploring Operation: 46-36=10, Resulting Numbers: [39, 10] Generated Node #0,1,1: 52:[39, 10] Operation: 46-36=10 Exploring Operation: 39+36=75, Resulting Numbers: [46, 75] Generated Node #0,1,2: 52:[46, 75] Operation: 39+36=75 Exploring Operation: 39+46=85, Resulting Numbers: [36, 85] Generated Node #0,1,3: 52:[36, 85] Operation: 39+46=85 Exploring Operation: 39-36=3, Resulting Numbers: [46, 3] Generated Node #0,1,4: 52:[46, 3] Operation: 39-36=3 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 52:[46, 3], Operations: ['77-41=36', '39-36=3'] Exploring Operation: 46+3=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 46*3=138, Resulting Numbers: [138] 138,52 unequal: No Solution Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 52:[36, 7], Operations: ['77-41=36', '46-39=7'] Exploring Operation: 36-7=29, Resulting Numbers: [29] 29,52 unequal: No Solution Exploring Operation: 36+7=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 36*7=252, Resulting Numbers: [252] 252,52 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 #0,1,1 Current State: 52:[39, 10], Operations: ['77-41=36', '46-36=10'] Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,52 unequal: No Solution Exploring Operation: 39*10=390, Resulting Numbers: [390] 390,52 unequal: No Solution Exploring Operation: 39+10=49, Resulting Numbers: [49] 49,52 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 #0,1,2 Current State: 52:[46, 75], Operations: ['77-41=36', '39+36=75'] Exploring Operation: 46*75=3450, Resulting Numbers: [3450] 3450,52 unequal: No Solution Exploring Operation: 46+75=121, Resulting Numbers: [121] 121,52 unequal: No Solution Exploring Operation: 75-46=29, Resulting Numbers: [29] 29,52 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 #0,1,3 Current State: 52:[36, 85], Operations: ['77-41=36', '39+46=85'] Exploring Operation: 85-36=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 36*85=3060, Resulting Numbers: [3060] 3060,52 unequal: No Solution Exploring Operation: 36+85=121, Resulting Numbers: [121] 121,52 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: 52:[46, 77, 2], Operations: ['41-39=2'] Exploring Operation: 77-2=75, Resulting Numbers: [46, 75] Generated Node #0,4,0: 52:[46, 75] Operation: 77-2=75 Exploring Operation: 77-46=31, Resulting Numbers: [2, 31] Generated Node #0,4,1: 52:[2, 31] Operation: 77-46=31 Exploring Operation: 46-2=44, Resulting Numbers: [77, 44] Generated Node #0,4,2: 52:[77, 44] Operation: 46-2=44 Exploring Operation: 46+2=48, Resulting Numbers: [77, 48] Generated Node #0,4,3: 52:[77, 48] Operation: 46+2=48 Exploring Operation: 46/2=23, Resulting Numbers: [77, 23] Generated Node #0,4,4: 52:[77, 23] Operation: 46/2=23 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 52:[2, 31], Operations: ['41-39=2', '77-46=31'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,52 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,52 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,52 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 #0,4,4 Current State: 52:[77, 23], Operations: ['41-39=2', '46/2=23'] Exploring Operation: 77-23=54, Resulting Numbers: [54] 54,52 unequal: No Solution Exploring Operation: 77*23=1771, Resulting Numbers: [1771] 1771,52 unequal: No Solution Exploring Operation: 77+23=100, Resulting Numbers: [100] 100,52 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 #0,4,0 Current State: 52:[46, 75], Operations: ['41-39=2', '77-2=75'] Exploring Operation: 75-46=29, Resulting Numbers: [29] 29,52 unequal: No Solution Exploring Operation: 46+75=121, Resulting Numbers: [121] 121,52 unequal: No Solution Exploring Operation: 46*75=3450, Resulting Numbers: [3450] 3450,52 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 #0,4,3 Current State: 52:[77, 48], Operations: ['41-39=2', '46+2=48'] Exploring Operation: 77*48=3696, Resulting Numbers: [3696] 3696,52 unequal: No Solution Exploring Operation: 77-48=29, Resulting Numbers: [29] 29,52 unequal: No Solution Exploring Operation: 77+48=125, Resulting Numbers: [125] 125,52 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 #0,4,2 Current State: 52:[77, 44], Operations: ['41-39=2', '46-2=44'] Exploring Operation: 77*44=3388, Resulting Numbers: [3388] 3388,52 unequal: No Solution Exploring Operation: 77+44=121, Resulting Numbers: [121] 121,52 unequal: No Solution Exploring Operation: 77-44=33, Resulting Numbers: [33] 33,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 52:[39, 77, 5], Operations: ['46-41=5'] Exploring Operation: 39+5=44, Resulting Numbers: [77, 44] Generated Node #0,2,0: 52:[77, 44] Operation: 39+5=44 Exploring Operation: 39-5=34, Resulting Numbers: [77, 34] Generated Node #0,2,1: 52:[77, 34] Operation: 39-5=34 Exploring Operation: 77-5=72, Resulting Numbers: [39, 72] Generated Node #0,2,2: 52:[39, 72] Operation: 77-5=72 Exploring Operation: 77+5=82, Resulting Numbers: [39, 82] Generated Node #0,2,3: 52:[39, 82] Operation: 77+5=82 Exploring Operation: 77-39=38, Resulting Numbers: [5, 38] Generated Node #0,2,4: 52:[5, 38] Operation: 77-39=38 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 52:[5, 38], Operations: ['46-41=5', '77-39=38'] Exploring Operation: 5+38=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 5*38=190, Resulting Numbers: [190] 190,52 unequal: No Solution Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,52 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 #0,2,0 Current State: 52:[77, 44], Operations: ['46-41=5', '39+5=44'] Exploring Operation: 77+44=121, Resulting Numbers: [121] 121,52 unequal: No Solution Exploring Operation: 77*44=3388, Resulting Numbers: [3388] 3388,52 unequal: No Solution Exploring Operation: 77-44=33, Resulting Numbers: [33] 33,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 52:[77, 34], Operations: ['46-41=5', '39-5=34'] Exploring Operation: 77+34=111, Resulting Numbers: [111] 111,52 unequal: No Solution Exploring Operation: 77-34=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 77*34=2618, Resulting Numbers: [2618] 2618,52 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:[39, 72], Operations: ['46-41=5', '77-5=72'] Exploring Operation: 39*72=2808, Resulting Numbers: [2808] 2808,52 unequal: No Solution Exploring Operation: 72-39=33, Resulting Numbers: [33] 33,52 unequal: No Solution Exploring Operation: 39+72=111, Resulting Numbers: [111] 111,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 52:[39, 82], Operations: ['46-41=5', '77+5=82'] Exploring Operation: 39*82=3198, Resulting Numbers: [3198] 3198,52 unequal: No Solution Exploring Operation: 82-39=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 39+82=121, Resulting Numbers: [121] 121,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 52:[31, 2], Operations: ['77-46=31', '41-39=2'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,52 unequal: No Solution Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,52 unequal: No Solution Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,52 unequal: No Solution Moving to Node #0,0,4 Current State: 52:[41, 8], Operations: ['77-46=31', '39-31=8'] Exploring Operation: 41+8=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 41*8=328, Resulting Numbers: [328] 328,52 unequal: No Solution Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[39, 10], Operations: ['77-46=31', '41-31=10'] Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,52 unequal: No Solution Exploring Operation: 39*10=390, Resulting Numbers: [390] 390,52 unequal: No Solution Exploring Operation: 39+10=49, Resulting Numbers: [49] 49,52 unequal: No Solution Moving to Node #0,0,0 Current State: 52:[41, 70], Operations: ['77-46=31', '39+31=70'] Exploring Operation: 41*70=2870, Resulting Numbers: [2870] 2870,52 unequal: No Solution Exploring Operation: 70-41=29, Resulting Numbers: [29] 29,52 unequal: No Solution Exploring Operation: 41+70=111, Resulting Numbers: [111] 111,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[31, 80], Operations: ['77-46=31', '41+39=80'] Exploring Operation: 31*80=2480, Resulting Numbers: [2480] 2480,52 unequal: No Solution Exploring Operation: 80-31=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 31+80=111, Resulting Numbers: [111] 111,52 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 97, 90, 10, 25 ]
95
[ "97-90=7", "10*7=70", "25+70=95" ]
Current State: 95:[97, 90, 10, 25], Operations: [] Exploring Operation: 97-90=7, Resulting Numbers: [10, 25, 7] Generated Node #2: [10, 25, 7] from Operation: 97-90=7 Current State: 95:[10, 25, 7], Operations: ['97-90=7'] Exploring Operation: 10*7=70, Resulting Numbers: [25, 70] Generated Node #3: [25, 70] from Operation: 10*7=70 Current State: 95:[25, 70], Operations: ['97-90=7', '10*7=70'] Exploring Operation: 25+70=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[97, 90, 10, 25], Operations: [] Exploring Operation: 90/10=9, Resulting Numbers: [97, 25, 9] Generated Node #0,0: 95:[97, 25, 9] Operation: 90/10=9 Exploring Operation: 25-10=15, Resulting Numbers: [97, 90, 15] Generated Node #0,1: 95:[97, 90, 15] Operation: 25-10=15 Exploring Operation: 97-10=87, Resulting Numbers: [90, 25, 87] Generated Node #0,2: 95:[90, 25, 87] Operation: 97-10=87 Exploring Operation: 97-90=7, Resulting Numbers: [10, 25, 7] Generated Node #0,3: 95:[10, 25, 7] Operation: 97-90=7 Exploring Operation: 90+10=100, Resulting Numbers: [97, 25, 100] Generated Node #0,4: 95:[97, 25, 100] Operation: 90+10=100 Moving to Node #0,1 Current State: 95:[97, 90, 15], Operations: ['25-10=15'] Exploring Operation: 90/15=6, Resulting Numbers: [97, 6] Generated Node #0,1,0: 95:[97, 6] Operation: 90/15=6 Exploring Operation: 97-15=82, Resulting Numbers: [90, 82] Generated Node #0,1,1: 95:[90, 82] Operation: 97-15=82 Exploring Operation: 97+15=112, Resulting Numbers: [90, 112] Generated Node #0,1,2: 95:[90, 112] Operation: 97+15=112 Exploring Operation: 90+15=105, Resulting Numbers: [97, 105] Generated Node #0,1,3: 95:[97, 105] Operation: 90+15=105 Exploring Operation: 97-90=7, Resulting Numbers: [15, 7] Generated Node #0,1,4: 95:[15, 7] Operation: 97-90=7 Moving to Node #0,0 Current State: 95:[97, 25, 9], Operations: ['90/10=9'] Exploring Operation: 97-25=72, Resulting Numbers: [9, 72] Generated Node #0,0,0: 95:[9, 72] Operation: 97-25=72 Exploring Operation: 25+9=34, Resulting Numbers: [97, 34] Generated Node #0,0,1: 95:[97, 34] Operation: 25+9=34 Exploring Operation: 25-9=16, Resulting Numbers: [97, 16] Generated Node #0,0,2: 95:[97, 16] Operation: 25-9=16 Exploring Operation: 97-9=88, Resulting Numbers: [25, 88] Generated Node #0,0,3: 95:[25, 88] Operation: 97-9=88 Exploring Operation: 97+9=106, Resulting Numbers: [25, 106] Generated Node #0,0,4: 95:[25, 106] Operation: 97+9=106 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 95:[97, 16], Operations: ['90/10=9', '25-9=16'] Exploring Operation: 97-16=81, Resulting Numbers: [81] 81,95 unequal: No Solution Exploring Operation: 97+16=113, Resulting Numbers: [113] 113,95 unequal: No Solution Exploring Operation: 97*16=1552, Resulting Numbers: [1552] 1552,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 95:[25, 88], Operations: ['90/10=9', '97-9=88'] Exploring Operation: 25+88=113, Resulting Numbers: [113] 113,95 unequal: No Solution Exploring Operation: 25*88=2200, Resulting Numbers: [2200] 2200,95 unequal: No Solution Exploring Operation: 88-25=63, Resulting Numbers: [63] 63,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 95:[97, 34], Operations: ['90/10=9', '25+9=34'] Exploring Operation: 97*34=3298, Resulting Numbers: [3298] 3298,95 unequal: No Solution Exploring Operation: 97-34=63, Resulting Numbers: [63] 63,95 unequal: No Solution Exploring Operation: 97+34=131, Resulting Numbers: [131] 131,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 95:[25, 106], Operations: ['90/10=9', '97+9=106'] Exploring Operation: 25*106=2650, Resulting Numbers: [2650] 2650,95 unequal: No Solution Exploring Operation: 25+106=131, Resulting Numbers: [131] 131,95 unequal: No Solution Exploring Operation: 106-25=81, Resulting Numbers: [81] 81,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[9, 72], Operations: ['90/10=9', '97-25=72'] Exploring Operation: 72/9=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 9+72=81, Resulting Numbers: [81] 81,95 unequal: No Solution Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,95 unequal: No Solution Exploring Operation: 9*72=648, Resulting Numbers: [648] 648,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 95:[10, 25, 7], Operations: ['97-90=7'] Exploring Operation: 10+25=35, Resulting Numbers: [7, 35] Generated Node #0,3,0: 95:[7, 35] Operation: 10+25=35 Exploring Operation: 25-10=15, Resulting Numbers: [7, 15] Generated Node #0,3,1: 95:[7, 15] Operation: 25-10=15 Exploring Operation: 10-7=3, Resulting Numbers: [25, 3] Generated Node #0,3,2: 95:[25, 3] Operation: 10-7=3 Exploring Operation: 10+7=17, Resulting Numbers: [25, 17] Generated Node #0,3,3: 95:[25, 17] Operation: 10+7=17 Exploring Operation: 25-7=18, Resulting Numbers: [10, 18] Generated Node #0,3,4: 95:[10, 18] Operation: 25-7=18 Moving to Node #0,4 Current State: 95:[97, 25, 100], Operations: ['90+10=100'] Exploring Operation: 100-25=75, Resulting Numbers: [97, 75] Generated Node #0,4,0: 95:[97, 75] Operation: 100-25=75 Exploring Operation: 97+25=122, Resulting Numbers: [100, 122] Generated Node #0,4,1: 95:[100, 122] Operation: 97+25=122 Exploring Operation: 100/25=4, Resulting Numbers: [97, 4] Generated Node #0,4,2: 95:[97, 4] Operation: 100/25=4 Exploring Operation: 97-25=72, Resulting Numbers: [100, 72] Generated Node #0,4,3: 95:[100, 72] Operation: 97-25=72 Exploring Operation: 100-97=3, Resulting Numbers: [25, 3] Generated Node #0,4,4: 95:[25, 3] Operation: 100-97=3 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 95:[97, 4], Operations: ['90+10=100', '100/25=4'] Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,95 unequal: No Solution Exploring Operation: 97+4=101, Resulting Numbers: [101] 101,95 unequal: No Solution Exploring Operation: 97*4=388, Resulting Numbers: [388] 388,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 95:[25, 3], Operations: ['90+10=100', '100-97=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,95 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 95:[97, 75], Operations: ['90+10=100', '100-25=75'] Exploring Operation: 97+75=172, Resulting Numbers: [172] 172,95 unequal: No Solution Exploring Operation: 97*75=7275, Resulting Numbers: [7275] 7275,95 unequal: No Solution Exploring Operation: 97-75=22, Resulting Numbers: [22] 22,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 95:[100, 72], Operations: ['90+10=100', '97-25=72'] Exploring Operation: 100+72=172, Resulting Numbers: [172] 172,95 unequal: No Solution Exploring Operation: 100*72=7200, Resulting Numbers: [7200] 7200,95 unequal: No Solution Exploring Operation: 100-72=28, Resulting Numbers: [28] 28,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 95:[100, 122], Operations: ['90+10=100', '97+25=122'] Exploring Operation: 100*122=12200, Resulting Numbers: [12200] 12200,95 unequal: No Solution Exploring Operation: 122-100=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 100+122=222, Resulting Numbers: [222] 222,95 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: 95:[90, 25, 87], Operations: ['97-10=87'] Exploring Operation: 90+25=115, Resulting Numbers: [87, 115] Generated Node #0,2,0: 95:[87, 115] Operation: 90+25=115 Exploring Operation: 90-87=3, Resulting Numbers: [25, 3] Generated Node #0,2,1: 95:[25, 3] Operation: 90-87=3 Exploring Operation: 90-25=65, Resulting Numbers: [87, 65] Generated Node #0,2,2: 95:[87, 65] Operation: 90-25=65 Exploring Operation: 25+87=112, Resulting Numbers: [90, 112] Generated Node #0,2,3: 95:[90, 112] Operation: 25+87=112 Exploring Operation: 87-25=62, Resulting Numbers: [90, 62] Generated Node #0,2,4: 95:[90, 62] Operation: 87-25=62 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 95:[25, 3], Operations: ['97-10=87', '90-87=3'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,95 unequal: No Solution Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 95:[90, 112], Operations: ['97-10=87', '25+87=112'] Exploring Operation: 112-90=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 90+112=202, Resulting Numbers: [202] 202,95 unequal: No Solution Exploring Operation: 90*112=10080, Resulting Numbers: [10080] 10080,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 95:[87, 115], Operations: ['97-10=87', '90+25=115'] Exploring Operation: 87+115=202, Resulting Numbers: [202] 202,95 unequal: No Solution Exploring Operation: 87*115=10005, Resulting Numbers: [10005] 10005,95 unequal: No Solution Exploring Operation: 115-87=28, Resulting Numbers: [28] 28,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 95:[87, 65], Operations: ['97-10=87', '90-25=65'] Exploring Operation: 87*65=5655, Resulting Numbers: [5655] 5655,95 unequal: No Solution Exploring Operation: 87-65=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 87+65=152, Resulting Numbers: [152] 152,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 95:[90, 62], Operations: ['97-10=87', '87-25=62'] Exploring Operation: 90-62=28, Resulting Numbers: [28] 28,95 unequal: No Solution Exploring Operation: 90+62=152, Resulting Numbers: [152] 152,95 unequal: No Solution Exploring Operation: 90*62=5580, Resulting Numbers: [5580] 5580,95 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: 95:[97, 6], Operations: ['25-10=15', '90/15=6'] Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,95 unequal: No Solution Exploring Operation: 97*6=582, Resulting Numbers: [582] 582,95 unequal: No Solution Exploring Operation: 97+6=103, Resulting Numbers: [103] 103,95 unequal: No Solution Moving to Node #0,3,1 Current State: 95:[7, 15], Operations: ['97-90=7', '25-10=15'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 7*15=105, Resulting Numbers: [105] 105,95 unequal: No Solution Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,95 unequal: No Solution Moving to Node #0,3,4 Current State: 95:[10, 18], Operations: ['97-90=7', '25-7=18'] Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,95 unequal: No Solution Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,95 unequal: No Solution Moving to Node #0,1,4 Current State: 95:[15, 7], Operations: ['25-10=15', '97-90=7'] Exploring Operation: 15*7=105, Resulting Numbers: [105] 105,95 unequal: No Solution Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,95 unequal: No Solution Moving to Node #0,3,3 Current State: 95:[25, 17], Operations: ['97-90=7', '10+7=17'] Exploring Operation: 25+17=42, Resulting Numbers: [42] 42,95 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 25*17=425, Resulting Numbers: [425] 425,95 unequal: No Solution Moving to Node #0,3,2 Current State: 95:[25, 3], Operations: ['97-90=7', '10-7=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,95 unequal: No Solution Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,95 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,95 unequal: No Solution Moving to Node #0,1,3 Current State: 95:[97, 105], Operations: ['25-10=15', '90+15=105'] Exploring Operation: 97+105=202, Resulting Numbers: [202] 202,95 unequal: No Solution Exploring Operation: 97*105=10185, Resulting Numbers: [10185] 10185,95 unequal: No Solution Exploring Operation: 105-97=8, Resulting Numbers: [8] 8,95 unequal: No Solution Moving to Node #0,3,0 Current State: 95:[7, 35], Operations: ['97-90=7', '10+25=35'] Exploring Operation: 7*35=245, Resulting Numbers: [245] 245,95 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,95 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[90, 82], Operations: ['25-10=15', '97-15=82'] Exploring Operation: 90-82=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 90+82=172, Resulting Numbers: [172] 172,95 unequal: No Solution Exploring Operation: 90*82=7380, Resulting Numbers: [7380] 7380,95 unequal: No Solution Moving to Node #0,1,2 Current State: 95:[90, 112], Operations: ['25-10=15', '97+15=112'] Exploring Operation: 112-90=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 90+112=202, Resulting Numbers: [202] 202,95 unequal: No Solution Exploring Operation: 90*112=10080, Resulting Numbers: [10080] 10080,95 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 74, 86, 32, 29 ]
49
[ "86-74=12", "32+29=61", "61-12=49" ]
Current State: 49:[74, 86, 32, 29], Operations: [] Exploring Operation: 86-74=12, Resulting Numbers: [32, 29, 12] Generated Node #2: [32, 29, 12] from Operation: 86-74=12 Current State: 49:[32, 29, 12], Operations: ['86-74=12'] Exploring Operation: 32+29=61, Resulting Numbers: [12, 61] Generated Node #3: [12, 61] from Operation: 32+29=61 Current State: 49:[12, 61], Operations: ['86-74=12', '32+29=61'] Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[74, 86, 32, 29], Operations: [] Exploring Operation: 86-74=12, Resulting Numbers: [32, 29, 12] Generated Node #0,0: 49:[32, 29, 12] Operation: 86-74=12 Exploring Operation: 86-32=54, Resulting Numbers: [74, 29, 54] Generated Node #0,1: 49:[74, 29, 54] Operation: 86-32=54 Exploring Operation: 86-29=57, Resulting Numbers: [74, 32, 57] Generated Node #0,2: 49:[74, 32, 57] Operation: 86-29=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[32, 29, 12], Operations: ['86-74=12'] Exploring Operation: 32+12=44, Resulting Numbers: [29, 44] Generated Node #0,0,0: 49:[29, 44] Operation: 32+12=44 Exploring Operation: 32+29=61, Resulting Numbers: [12, 61] Generated Node #0,0,1: 49:[12, 61] Operation: 32+29=61 Exploring Operation: 32-29=3, Resulting Numbers: [12, 3] Generated Node #0,0,2: 49:[12, 3] Operation: 32-29=3 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 49:[12, 3], Operations: ['86-74=12', '32-29=3'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,49 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,49 unequal: No Solution No 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: 49:[12, 61], Operations: ['86-74=12', '32+29=61'] Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[74, 86, 32, 29], Operations: [] Exploring Operation: 86-74=12, Resulting Numbers: [32, 29, 12] Generated Node #0,0: 49:[32, 29, 12] Operation: 86-74=12 Moving to Node #0,0 Current State: 49:[32, 29, 12], Operations: ['86-74=12'] Exploring Operation: 32+29=61, Resulting Numbers: [12, 61] Generated Node #0,0,1: 49:[12, 61] Operation: 32+29=61 Moving to Node #0,0,1 Current State: 49:[12, 61], Operations: ['86-74=12', '32+29=61'] Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 66, 5, 83, 54 ]
31
[ "83-66=17", "5*17=85", "85-54=31" ]
Current State: 31:[66, 5, 83, 54], Operations: [] Exploring Operation: 83-66=17, Resulting Numbers: [5, 54, 17] Generated Node #2: [5, 54, 17] from Operation: 83-66=17 Current State: 31:[5, 54, 17], Operations: ['83-66=17'] Exploring Operation: 5*17=85, Resulting Numbers: [54, 85] Generated Node #3: [54, 85] from Operation: 5*17=85 Current State: 31:[54, 85], Operations: ['83-66=17', '5*17=85'] Exploring Operation: 85-54=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[66, 5, 83, 54], Operations: [] Exploring Operation: 83-54=29, Resulting Numbers: [66, 5, 29] Generated Node #0,0: 31:[66, 5, 29] Operation: 83-54=29 Exploring Operation: 83-66=17, Resulting Numbers: [5, 54, 17] Generated Node #0,1: 31:[5, 54, 17] Operation: 83-66=17 Moving to Node #0,0 Current State: 31:[66, 5, 29], Operations: ['83-54=29'] Exploring Operation: 66-5=61, Resulting Numbers: [29, 61] Generated Node #0,0,0: 31:[29, 61] Operation: 66-5=61 Exploring Operation: 66-29=37, Resulting Numbers: [5, 37] Generated Node #0,0,1: 31:[5, 37] Operation: 66-29=37 Moving to Node #0,1 Current State: 31:[5, 54, 17], Operations: ['83-66=17'] Exploring Operation: 54-5=49, Resulting Numbers: [17, 49] Generated Node #0,1,0: 31:[17, 49] Operation: 54-5=49 Exploring Operation: 5+17=22, Resulting Numbers: [54, 22] Generated Node #0,1,1: 31:[54, 22] Operation: 5+17=22 Moving to Node #0,0,0 Current State: 31:[29, 61], Operations: ['83-54=29', '66-5=61'] Exploring Operation: 29+61=90, Resulting Numbers: [90] 90,31 unequal: No Solution Exploring Operation: 61-29=32, Resulting Numbers: [32] 32,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[17, 49], Operations: ['83-66=17', '54-5=49'] Exploring Operation: 49-17=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 17+49=66, Resulting Numbers: [66] 66,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[5, 37], Operations: ['83-54=29', '66-29=37'] Exploring Operation: 5+37=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[54, 22], Operations: ['83-66=17', '5+17=22'] Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 54+22=76, Resulting Numbers: [76] 76,31 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 1, 37, 5, 85 ]
43
[ "1*37=37", "85-5=80", "80-37=43" ]
Current State: 43:[1, 37, 5, 85], Operations: [] Exploring Operation: 1*37=37, Resulting Numbers: [5, 85, 37] Generated Node #2: [5, 85, 37] from Operation: 1*37=37 Current State: 43:[5, 85, 37], Operations: ['1*37=37'] Exploring Operation: 85-5=80, Resulting Numbers: [37, 80] Generated Node #3: [37, 80] from Operation: 85-5=80 Current State: 43:[37, 80], Operations: ['1*37=37', '85-5=80'] Exploring Operation: 80-37=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[1, 37, 5, 85], Operations: [] Exploring Operation: 85/5=17, Resulting Numbers: [1, 37, 17] Generated Node #0,0: 43:[1, 37, 17] Operation: 85/5=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[1, 37, 17], Operations: ['85/5=17'] Exploring Operation: 1+37=38, Resulting Numbers: [17, 38] Generated Node #0,0,0: 43:[17, 38] Operation: 1+37=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[17, 38], Operations: ['85/5=17', '1+37=38'] Exploring Operation: 17+38=55, Resulting Numbers: [55] 55,43 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
[ 32, 36, 32, 66 ]
58
[ "36-32=4", "32/4=8", "66-8=58" ]
Current State: 58:[32, 36, 32, 66], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [66, 4] Generated Node #2: [66, 4] from Operation: 36-32=4 Current State: 58:[66, 4], Operations: ['36-32=4'] Exploring Operation: 32/4=8, Resulting Numbers: [66, 8] Generated Node #3: [66, 8] from Operation: 32/4=8 Current State: 58:[66, 8], Operations: ['36-32=4', '32/4=8'] Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[32, 36, 32, 66], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [32, 66, 4] Generated Node #0,0: 58:[32, 66, 4] Operation: 36-32=4 Exploring Operation: 66-36=30, Resulting Numbers: [32, 32, 30] Generated Node #0,1: 58:[32, 32, 30] Operation: 66-36=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[32, 32, 30], Operations: ['66-36=30'] Exploring Operation: 32/32=1, Resulting Numbers: [30, 1] Generated Node #0,1,0: 58:[30, 1] Operation: 32/32=1 Exploring Operation: 32-32=0, Resulting Numbers: [30, 0] Generated Node #0,1,1: 58:[30, 0] Operation: 32-32=0 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 58:[30, 1], Operations: ['66-36=30', '32/32=1'] Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,58 unequal: No Solution Exploring Operation: 30*1=30, Resulting Numbers: [30] 30,58 unequal: No Solution No 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: 58:[30, 0], Operations: ['66-36=30', '32-32=0'] Exploring Operation: 30-0=30, Resulting Numbers: [30] 30,58 unequal: No Solution Exploring Operation: 30+0=30, Resulting Numbers: [30] 30,58 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: 58:[32, 66, 4], Operations: ['36-32=4'] Exploring Operation: 66-32=34, Resulting Numbers: [4, 34] Generated Node #0,0,0: 58:[4, 34] Operation: 66-32=34 Exploring Operation: 66-4=62, Resulting Numbers: [32, 62] Generated Node #0,0,1: 58:[32, 62] Operation: 66-4=62 Moving to Node #0,0,0 Current State: 58:[4, 34], Operations: ['36-32=4', '66-32=34'] Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,58 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,58 unequal: No Solution Moving to Node #0,0,1 Current State: 58:[32, 62], Operations: ['36-32=4', '66-4=62'] Exploring Operation: 32+62=94, Resulting Numbers: [94] 94,58 unequal: No Solution Exploring Operation: 62-32=30, Resulting Numbers: [30] 30,58 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
[ 61, 48, 20, 11 ]
22
[ "61-48=13", "20-11=9", "13+9=22" ]
Current State: 22:[61, 48, 20, 11], Operations: [] Exploring Operation: 61-48=13, Resulting Numbers: [20, 11, 13] Generated Node #2: [20, 11, 13] from Operation: 61-48=13 Current State: 22:[20, 11, 13], Operations: ['61-48=13'] Exploring Operation: 20-11=9, Resulting Numbers: [13, 9] Generated Node #3: [13, 9] from Operation: 20-11=9 Current State: 22:[13, 9], Operations: ['61-48=13', '20-11=9'] Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[61, 48, 20, 11], Operations: [] Exploring Operation: 61-20=41, Resulting Numbers: [48, 11, 41] Generated Node #0,0: 22:[48, 11, 41] Operation: 61-20=41 Exploring Operation: 61-48=13, Resulting Numbers: [20, 11, 13] Generated Node #0,1: 22:[20, 11, 13] Operation: 61-48=13 Exploring Operation: 61-11=50, Resulting Numbers: [48, 20, 50] Generated Node #0,2: 22:[48, 20, 50] Operation: 61-11=50 Exploring Operation: 48-11=37, Resulting Numbers: [61, 20, 37] Generated Node #0,3: 22:[61, 20, 37] Operation: 48-11=37 Exploring Operation: 48-20=28, Resulting Numbers: [61, 11, 28] Generated Node #0,4: 22:[61, 11, 28] Operation: 48-20=28 Moving to Node #0,1 Current State: 22:[20, 11, 13], Operations: ['61-48=13'] Exploring Operation: 20+11=31, Resulting Numbers: [13, 31] Generated Node #0,1,0: 22:[13, 31] Operation: 20+11=31 Exploring Operation: 13-11=2, Resulting Numbers: [20, 2] Generated Node #0,1,1: 22:[20, 2] Operation: 13-11=2 Exploring Operation: 11+13=24, Resulting Numbers: [20, 24] Generated Node #0,1,2: 22:[20, 24] Operation: 11+13=24 Exploring Operation: 20-11=9, Resulting Numbers: [13, 9] Generated Node #0,1,3: 22:[13, 9] Operation: 20-11=9 Exploring Operation: 20-13=7, Resulting Numbers: [11, 7] Generated Node #0,1,4: 22:[11, 7] Operation: 20-13=7 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[20, 2], Operations: ['61-48=13', '13-11=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[61, 48, 20, 11], Operations: [] Exploring Operation: 61-48=13, Resulting Numbers: [20, 11, 13] Generated Node #0,1: 22:[20, 11, 13] Operation: 61-48=13 Moving to Node #0,1 Current State: 22:[20, 11, 13], Operations: ['61-48=13'] Exploring Operation: 13-11=2, Resulting Numbers: [20, 2] Generated Node #0,1,1: 22:[20, 2] Operation: 13-11=2 Moving to Node #0,1,1 Current State: 22:[20, 2], Operations: ['61-48=13', '13-11=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 36, 3, 79, 13 ]
59
[ "36-3=33", "79+13=92", "92-33=59" ]
Current State: 59:[36, 3, 79, 13], Operations: [] Exploring Operation: 36-3=33, Resulting Numbers: [79, 13, 33] Generated Node #2: [79, 13, 33] from Operation: 36-3=33 Current State: 59:[79, 13, 33], Operations: ['36-3=33'] Exploring Operation: 79+13=92, Resulting Numbers: [33, 92] Generated Node #3: [33, 92] from Operation: 79+13=92 Current State: 59:[33, 92], Operations: ['36-3=33', '79+13=92'] Exploring Operation: 92-33=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[36, 3, 79, 13], Operations: [] Exploring Operation: 3+13=16, Resulting Numbers: [36, 79, 16] Generated Node #0,0: 59:[36, 79, 16] Operation: 3+13=16 Exploring Operation: 36+3=39, Resulting Numbers: [79, 13, 39] Generated Node #0,1: 59:[79, 13, 39] Operation: 36+3=39 Exploring Operation: 3*13=39, Resulting Numbers: [36, 79, 39] Generated Node #0,2: 59:[36, 79, 39] Operation: 3*13=39 Exploring Operation: 79-3=76, Resulting Numbers: [36, 13, 76] Generated Node #0,3: 59:[36, 13, 76] Operation: 79-3=76 Exploring Operation: 36+13=49, Resulting Numbers: [3, 79, 49] Generated Node #0,4: 59:[3, 79, 49] Operation: 36+13=49 Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[36, 79, 39], Operations: ['3*13=39'] Exploring Operation: 39-36=3, Resulting Numbers: [79, 3] Generated Node #0,2,0: 59:[79, 3] Operation: 39-36=3 Exploring Operation: 36+39=75, Resulting Numbers: [79, 75] Generated Node #0,2,1: 59:[79, 75] Operation: 36+39=75 Exploring Operation: 79-39=40, Resulting Numbers: [36, 40] Generated Node #0,2,2: 59:[36, 40] Operation: 79-39=40 Exploring Operation: 36+79=115, Resulting Numbers: [39, 115] Generated Node #0,2,3: 59:[39, 115] Operation: 36+79=115 Exploring Operation: 79-36=43, Resulting Numbers: [39, 43] Generated Node #0,2,4: 59:[39, 43] Operation: 79-36=43 Moving to Node #0,2,1 Current State: 59:[79, 75], Operations: ['3*13=39', '36+39=75'] Exploring Operation: 79*75=5925, Resulting Numbers: [5925] 5925,59 unequal: No Solution Exploring Operation: 79-75=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 79+75=154, Resulting Numbers: [154] 154,59 unequal: No Solution Moving to Node #0,2,4 Current State: 59:[39, 43], Operations: ['3*13=39', '79-36=43'] Exploring Operation: 43-39=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 39+43=82, Resulting Numbers: [82] 82,59 unequal: No Solution Exploring Operation: 39*43=1677, Resulting Numbers: [1677] 1677,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[36, 40], Operations: ['3*13=39', '79-39=40'] Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,59 unequal: No Solution Exploring Operation: 36*40=1440, Resulting Numbers: [1440] 1440,59 unequal: No Solution Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[79, 3], Operations: ['3*13=39', '39-36=3'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,59 unequal: No Solution Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,59 unequal: No Solution Exploring Operation: 79*3=237, Resulting Numbers: [237] 237,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[39, 115], Operations: ['3*13=39', '36+79=115'] Exploring Operation: 115-39=76, Resulting Numbers: [76] 76,59 unequal: No Solution Exploring Operation: 39+115=154, Resulting Numbers: [154] 154,59 unequal: No Solution Exploring Operation: 39*115=4485, Resulting Numbers: [4485] 4485,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[36, 79, 16], Operations: ['3+13=16'] Exploring Operation: 36+16=52, Resulting Numbers: [79, 52] Generated Node #0,0,0: 59:[79, 52] Operation: 36+16=52 Exploring Operation: 36-16=20, Resulting Numbers: [79, 20] Generated Node #0,0,1: 59:[79, 20] Operation: 36-16=20 Exploring Operation: 79-16=63, Resulting Numbers: [36, 63] Generated Node #0,0,2: 59:[36, 63] Operation: 79-16=63 Exploring Operation: 79+16=95, Resulting Numbers: [36, 95] Generated Node #0,0,3: 59:[36, 95] Operation: 79+16=95 Exploring Operation: 79-36=43, Resulting Numbers: [16, 43] Generated Node #0,0,4: 59:[16, 43] Operation: 79-36=43 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[79, 52], Operations: ['3+13=16', '36+16=52'] Exploring Operation: 79-52=27, Resulting Numbers: [27] 27,59 unequal: No Solution Exploring Operation: 79+52=131, Resulting Numbers: [131] 131,59 unequal: No Solution Exploring Operation: 79*52=4108, Resulting Numbers: [4108] 4108,59 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:[36, 63], Operations: ['3+13=16', '79-16=63'] Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,59 unequal: No Solution Exploring Operation: 36+63=99, Resulting Numbers: [99] 99,59 unequal: No Solution Exploring Operation: 36*63=2268, Resulting Numbers: [2268] 2268,59 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:[79, 20], Operations: ['3+13=16', '36-16=20'] Exploring Operation: 79-20=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[36, 3, 79, 13], Operations: [] Exploring Operation: 3+13=16, Resulting Numbers: [36, 79, 16] Generated Node #0,0: 59:[36, 79, 16] Operation: 3+13=16 Moving to Node #0,0 Current State: 59:[36, 79, 16], Operations: ['3+13=16'] Exploring Operation: 36-16=20, Resulting Numbers: [79, 20] Generated Node #0,0,1: 59:[79, 20] Operation: 36-16=20 Moving to Node #0,0,1 Current State: 59:[79, 20], Operations: ['3+13=16', '36-16=20'] Exploring Operation: 79-20=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_5
sum_heuristic
[ 82, 48, 24, 2 ]
86
[ "82+2=84", "48/24=2", "84+2=86" ]
Current State: 86:[82, 48, 24, 2], Operations: [] Exploring Operation: 82+2=84, Resulting Numbers: [48, 24, 84] Generated Node #2: [48, 24, 84] from Operation: 82+2=84 Current State: 86:[48, 24, 84], Operations: ['82+2=84'] Exploring Operation: 48/24=2, Resulting Numbers: [84, 2] Generated Node #3: [84, 2] from Operation: 48/24=2 Current State: 86:[84, 2], Operations: ['82+2=84', '48/24=2'] Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[82, 48, 24, 2], Operations: [] Exploring Operation: 24*2=48, Resulting Numbers: [82, 48, 48] Generated Node #0,0: 86:[82, 48, 48] Operation: 24*2=48 Exploring Operation: 48/24=2, Resulting Numbers: [82, 2, 2] Generated Node #0,1: 86:[82, 2, 2] Operation: 48/24=2 Moving to Node #0,1 Current State: 86:[82, 2, 2], Operations: ['48/24=2'] Exploring Operation: 82/2=41, Resulting Numbers: [2, 41] Generated Node #0,1,0: 86:[2, 41] Operation: 82/2=41 Exploring Operation: 82+2=84, Resulting Numbers: [2, 84] Generated Node #0,1,1: 86:[2, 84] Operation: 82+2=84 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[2, 41], Operations: ['48/24=2', '82/2=41'] Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[2, 84], Operations: ['48/24=2', '82+2=84'] Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[82, 48, 24, 2], Operations: [] Exploring Operation: 48/24=2, Resulting Numbers: [82, 2, 2] Generated Node #0,1: 86:[82, 2, 2] Operation: 48/24=2 Moving to Node #0,1 Current State: 86:[82, 2, 2], Operations: ['48/24=2'] Exploring Operation: 82+2=84, Resulting Numbers: [2, 84] Generated Node #0,1,1: 86:[2, 84] Operation: 82+2=84 Moving to Node #0,1,1 Current State: 86:[2, 84], Operations: ['48/24=2', '82+2=84'] Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 97, 41, 21, 1 ]
99
[ "41+1=42", "42/21=2", "97+2=99" ]
Current State: 99:[97, 41, 21, 1], Operations: [] Exploring Operation: 41+1=42, Resulting Numbers: [97, 21, 42] Generated Node #2: [97, 21, 42] from Operation: 41+1=42 Current State: 99:[97, 21, 42], Operations: ['41+1=42'] Exploring Operation: 42/21=2, Resulting Numbers: [97, 2] Generated Node #3: [97, 2] from Operation: 42/21=2 Current State: 99:[97, 2], Operations: ['41+1=42', '42/21=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[97, 41, 21, 1], Operations: [] Exploring Operation: 41-21=20, Resulting Numbers: [97, 1, 20] Generated Node #0,0: 99:[97, 1, 20] Operation: 41-21=20 Exploring Operation: 97+1=98, Resulting Numbers: [41, 21, 98] Generated Node #0,1: 99:[41, 21, 98] Operation: 97+1=98 Moving to Node #0,0 Current State: 99:[97, 1, 20], Operations: ['41-21=20'] Exploring Operation: 20-1=19, Resulting Numbers: [97, 19] Generated Node #0,0,0: 99:[97, 19] Operation: 20-1=19 Exploring Operation: 97+1=98, Resulting Numbers: [20, 98] Generated Node #0,0,1: 99:[20, 98] Operation: 97+1=98 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[97, 19], Operations: ['41-21=20', '20-1=19'] Exploring Operation: 97+19=116, Resulting Numbers: [116] 116,99 unequal: No Solution Exploring Operation: 97-19=78, Resulting Numbers: [78] 78,99 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 #0,0,1 Current State: 99:[20, 98], Operations: ['41-21=20', '97+1=98'] Exploring Operation: 98-20=78, Resulting Numbers: [78] 78,99 unequal: No Solution Exploring Operation: 20+98=118, Resulting Numbers: [118] 118,99 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: 99:[41, 21, 98], Operations: ['97+1=98'] Exploring Operation: 41-21=20, Resulting Numbers: [98, 20] Generated Node #0,1,0: 99:[98, 20] Operation: 41-21=20 Exploring Operation: 21+98=119, Resulting Numbers: [41, 119] Generated Node #0,1,1: 99:[41, 119] Operation: 21+98=119 Moving to Node #0,1,0 Current State: 99:[98, 20], Operations: ['97+1=98', '41-21=20'] Exploring Operation: 98-20=78, Resulting Numbers: [78] 78,99 unequal: No Solution Exploring Operation: 98+20=118, Resulting Numbers: [118] 118,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[41, 119], Operations: ['97+1=98', '21+98=119'] Exploring Operation: 41+119=160, Resulting Numbers: [160] 160,99 unequal: No Solution Exploring Operation: 119-41=78, Resulting Numbers: [78] 78,99 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 12, 7, 1, 18 ]
48
[ "18-12=6", "7+1=8", "6*8=48" ]
Current State: 48:[12, 7, 1, 18], Operations: [] Exploring Operation: 18-12=6, Resulting Numbers: [7, 1, 6] Generated Node #2: [7, 1, 6] from Operation: 18-12=6 Current State: 48:[7, 1, 6], Operations: ['18-12=6'] Exploring Operation: 7+1=8, Resulting Numbers: [6, 8] Generated Node #3: [6, 8] from Operation: 7+1=8 Current State: 48:[6, 8], Operations: ['18-12=6', '7+1=8'] Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[12, 7, 1, 18], Operations: [] Exploring Operation: 18-12=6, Resulting Numbers: [7, 1, 6] Generated Node #0,0: 48:[7, 1, 6] Operation: 18-12=6 Exploring Operation: 7-1=6, Resulting Numbers: [12, 18, 6] Generated Node #0,1: 48:[12, 18, 6] Operation: 7-1=6 Exploring Operation: 7+1=8, Resulting Numbers: [12, 18, 8] Generated Node #0,2: 48:[12, 18, 8] Operation: 7+1=8 Exploring Operation: 7+18=25, Resulting Numbers: [12, 1, 25] Generated Node #0,3: 48:[12, 1, 25] Operation: 7+18=25 Exploring Operation: 18-7=11, Resulting Numbers: [12, 1, 11] Generated Node #0,4: 48:[12, 1, 11] Operation: 18-7=11 Moving to Node #0,0 Current State: 48:[7, 1, 6], Operations: ['18-12=6'] Exploring Operation: 7+1=8, Resulting Numbers: [6, 8] Generated Node #0,0,0: 48:[6, 8] Operation: 7+1=8 Exploring Operation: 7-1=6, Resulting Numbers: [6, 6] Generated Node #0,0,1: 48:[6, 6] Operation: 7-1=6 Exploring Operation: 7*1=7, Resulting Numbers: [6, 7] Generated Node #0,0,2: 48:[6, 7] Operation: 7*1=7 Exploring Operation: 7/1=7, Resulting Numbers: [6, 7] Generated Node #0,0,3: 48:[6, 7] Operation: 7/1=7 Exploring Operation: 1*6=6, Resulting Numbers: [7, 6] Generated Node #0,0,4: 48:[7, 6] Operation: 1*6=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[6, 8], Operations: ['18-12=6', '7+1=8'] Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[12, 7, 1, 18], Operations: [] Exploring Operation: 18-12=6, Resulting Numbers: [7, 1, 6] Generated Node #0,0: 48:[7, 1, 6] Operation: 18-12=6 Moving to Node #0,0 Current State: 48:[7, 1, 6], Operations: ['18-12=6'] Exploring Operation: 7+1=8, Resulting Numbers: [6, 8] Generated Node #0,0,0: 48:[6, 8] Operation: 7+1=8 Moving to Node #0,0,0 Current State: 48:[6, 8], Operations: ['18-12=6', '7+1=8'] Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 20, 15, 54, 17 ]
49
[ "20-17=3", "15/3=5", "54-5=49" ]
Current State: 49:[20, 15, 54, 17], Operations: [] Exploring Operation: 20-17=3, Resulting Numbers: [15, 54, 3] Generated Node #2: [15, 54, 3] from Operation: 20-17=3 Current State: 49:[15, 54, 3], Operations: ['20-17=3'] Exploring Operation: 15/3=5, Resulting Numbers: [54, 5] Generated Node #3: [54, 5] from Operation: 15/3=5 Current State: 49:[54, 5], Operations: ['20-17=3', '15/3=5'] Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[20, 15, 54, 17], Operations: [] Exploring Operation: 20-15=5, Resulting Numbers: [54, 17, 5] Generated Node #0,0: 49:[54, 17, 5] Operation: 20-15=5 Exploring Operation: 20+15=35, Resulting Numbers: [54, 17, 35] Generated Node #0,1: 49:[54, 17, 35] Operation: 20+15=35 Exploring Operation: 20+17=37, Resulting Numbers: [15, 54, 37] Generated Node #0,2: 49:[15, 54, 37] Operation: 20+17=37 Exploring Operation: 20-17=3, Resulting Numbers: [15, 54, 3] Generated Node #0,3: 49:[15, 54, 3] Operation: 20-17=3 Exploring Operation: 17-15=2, Resulting Numbers: [20, 54, 2] Generated Node #0,4: 49:[20, 54, 2] Operation: 17-15=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[54, 17, 5], Operations: ['20-15=5'] Exploring Operation: 17+5=22, Resulting Numbers: [54, 22] Generated Node #0,0,0: 49:[54, 22] Operation: 17+5=22 Exploring Operation: 17-5=12, Resulting Numbers: [54, 12] Generated Node #0,0,1: 49:[54, 12] Operation: 17-5=12 Exploring Operation: 54-17=37, Resulting Numbers: [5, 37] Generated Node #0,0,2: 49:[5, 37] Operation: 54-17=37 Exploring Operation: 54-5=49, Resulting Numbers: [17, 49] Generated Node #0,0,3: 49:[17, 49] Operation: 54-5=49 Exploring Operation: 54+5=59, Resulting Numbers: [17, 59] Generated Node #0,0,4: 49:[17, 59] Operation: 54+5=59 Moving to Node #0,0,1 Current State: 49:[54, 12], Operations: ['20-15=5', '17-5=12'] Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,49 unequal: No Solution Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,49 unequal: No Solution Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,49 unequal: No Solution Moving to Node #0,0,3 Current State: 49:[17, 49], Operations: ['20-15=5', '54-5=49'] Exploring Operation: 17*49=833, Resulting Numbers: [833] 833,49 unequal: No Solution Exploring Operation: 17+49=66, Resulting Numbers: [66] 66,49 unequal: No Solution Exploring Operation: 49-17=32, Resulting Numbers: [32] 32,49 unequal: No Solution Moving to Node #0,0,2 Current State: 49:[5, 37], Operations: ['20-15=5', '54-17=37'] Exploring Operation: 5*37=185, Resulting Numbers: [185] 185,49 unequal: No Solution Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,49 unequal: No Solution Exploring Operation: 5+37=42, Resulting Numbers: [42] 42,49 unequal: No Solution Moving to Node #0,0,0 Current State: 49:[54, 22], Operations: ['20-15=5', '17+5=22'] Exploring Operation: 54*22=1188, Resulting Numbers: [1188] 1188,49 unequal: No Solution Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,49 unequal: No Solution Exploring Operation: 54+22=76, Resulting Numbers: [76] 76,49 unequal: No Solution Moving to Node #0,0,4 Current State: 49:[17, 59], Operations: ['20-15=5', '54+5=59'] Exploring Operation: 59-17=42, Resulting Numbers: [42] 42,49 unequal: No Solution Exploring Operation: 17*59=1003, Resulting Numbers: [1003] 1003,49 unequal: No Solution Exploring Operation: 17+59=76, Resulting Numbers: [76] 76,49 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 #0,3 Current State: 49:[15, 54, 3], Operations: ['20-17=3'] Exploring Operation: 54-15=39, Resulting Numbers: [3, 39] Generated Node #0,3,0: 49:[3, 39] Operation: 54-15=39 Exploring Operation: 15*3=45, Resulting Numbers: [54, 45] Generated Node #0,3,1: 49:[54, 45] Operation: 15*3=45 Exploring Operation: 15-3=12, Resulting Numbers: [54, 12] Generated Node #0,3,2: 49:[54, 12] Operation: 15-3=12 Exploring Operation: 15/3=5, Resulting Numbers: [54, 5] Generated Node #0,3,3: 49:[54, 5] Operation: 15/3=5 Exploring Operation: 54-3=51, Resulting Numbers: [15, 51] Generated Node #0,3,4: 49:[15, 51] Operation: 54-3=51 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 49:[54, 5], Operations: ['20-17=3', '15/3=5'] Exploring Operation: 54*5=270, Resulting Numbers: [270] 270,49 unequal: No Solution Exploring Operation: 54+5=59, Resulting Numbers: [59] 59,49 unequal: No Solution Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[20, 15, 54, 17], Operations: [] Exploring Operation: 20-17=3, Resulting Numbers: [15, 54, 3] Generated Node #0,3: 49:[15, 54, 3] Operation: 20-17=3 Moving to Node #0,3 Current State: 49:[15, 54, 3], Operations: ['20-17=3'] Exploring Operation: 15/3=5, Resulting Numbers: [54, 5] Generated Node #0,3,3: 49:[54, 5] Operation: 15/3=5 Moving to Node #0,3,3 Current State: 49:[54, 5], Operations: ['20-17=3', '15/3=5'] Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_5
mult_heuristic
[ 34, 90, 4, 18 ]
70
[ "90-34=56", "18-4=14", "56+14=70" ]
Current State: 70:[34, 90, 4, 18], Operations: [] Exploring Operation: 90-34=56, Resulting Numbers: [4, 18, 56] Generated Node #2: [4, 18, 56] from Operation: 90-34=56 Current State: 70:[4, 18, 56], Operations: ['90-34=56'] Exploring Operation: 18-4=14, Resulting Numbers: [56, 14] Generated Node #3: [56, 14] from Operation: 18-4=14 Current State: 70:[56, 14], Operations: ['90-34=56', '18-4=14'] Exploring Operation: 56+14=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[34, 90, 4, 18], Operations: [] Exploring Operation: 90/18=5, Resulting Numbers: [34, 4, 5] Generated Node #0,0: 70:[34, 4, 5] Operation: 90/18=5 Moving to Node #0,0 Current State: 70:[34, 4, 5], Operations: ['90/18=5'] Exploring Operation: 4+5=9, Resulting Numbers: [34, 9] Generated Node #0,0,0: 70:[34, 9] Operation: 4+5=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[34, 9], Operations: ['90/18=5', '4+5=9'] Exploring Operation: 34+9=43, Resulting Numbers: [43] 43,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 15, 46, 21, 49 ]
66
[ "49-46=3", "15*3=45", "21+45=66" ]
Current State: 66:[15, 46, 21, 49], Operations: [] Exploring Operation: 49-46=3, Resulting Numbers: [15, 21, 3] Generated Node #2: [15, 21, 3] from Operation: 49-46=3 Current State: 66:[15, 21, 3], Operations: ['49-46=3'] Exploring Operation: 15*3=45, Resulting Numbers: [21, 45] Generated Node #3: [21, 45] from Operation: 15*3=45 Current State: 66:[21, 45], Operations: ['49-46=3', '15*3=45'] Exploring Operation: 21+45=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[15, 46, 21, 49], Operations: [] Exploring Operation: 49-46=3, Resulting Numbers: [15, 21, 3] Generated Node #0,0: 66:[15, 21, 3] Operation: 49-46=3 Moving to Node #0,0 Current State: 66:[15, 21, 3], Operations: ['49-46=3'] Exploring Operation: 21-15=6, Resulting Numbers: [3, 6] Generated Node #0,0,0: 66:[3, 6] Operation: 21-15=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 66:[3, 6], Operations: ['49-46=3', '21-15=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,66 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
[ 24, 54, 56, 29 ]
97
[ "54*56=3024", "3024/24=126", "126-29=97" ]
Current State: 97:[24, 54, 56, 29], Operations: [] Exploring Operation: 54*56=3024, Resulting Numbers: [24, 29, 3024] Generated Node #2: [24, 29, 3024] from Operation: 54*56=3024 Current State: 97:[24, 29, 3024], Operations: ['54*56=3024'] Exploring Operation: 3024/24=126, Resulting Numbers: [29, 126] Generated Node #3: [29, 126] from Operation: 3024/24=126 Current State: 97:[29, 126], Operations: ['54*56=3024', '3024/24=126'] Exploring Operation: 126-29=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[24, 54, 56, 29], Operations: [] Exploring Operation: 24+56=80, Resulting Numbers: [54, 29, 80] Generated Node #0,0: 97:[54, 29, 80] Operation: 24+56=80 Exploring Operation: 24+54=78, Resulting Numbers: [56, 29, 78] Generated Node #0,1: 97:[56, 29, 78] Operation: 24+54=78 Moving to Node #0,0 Current State: 97:[54, 29, 80], Operations: ['24+56=80'] Exploring Operation: 29+80=109, Resulting Numbers: [54, 109] Generated Node #0,0,0: 97:[54, 109] Operation: 29+80=109 Exploring Operation: 54+29=83, Resulting Numbers: [80, 83] Generated Node #0,0,1: 97:[80, 83] Operation: 54+29=83 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 97:[80, 83], Operations: ['24+56=80', '54+29=83'] Exploring Operation: 83-80=3, Resulting Numbers: [3] 3,97 unequal: No Solution Exploring Operation: 80+83=163, Resulting Numbers: [163] 163,97 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 #0,0,0 Current State: 97:[54, 109], Operations: ['24+56=80', '29+80=109'] Exploring Operation: 109-54=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 54+109=163, Resulting Numbers: [163] 163,97 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: 97:[56, 29, 78], Operations: ['24+54=78'] Exploring Operation: 56+29=85, Resulting Numbers: [78, 85] Generated Node #0,1,0: 97:[78, 85] Operation: 56+29=85 Exploring Operation: 29+78=107, Resulting Numbers: [56, 107] Generated Node #0,1,1: 97:[56, 107] Operation: 29+78=107 Moving to Node #0,1,0 Current State: 97:[78, 85], Operations: ['24+54=78', '56+29=85'] Exploring Operation: 85-78=7, Resulting Numbers: [7] 7,97 unequal: No Solution Exploring Operation: 78+85=163, Resulting Numbers: [163] 163,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[56, 107], Operations: ['24+54=78', '29+78=107'] Exploring Operation: 56+107=163, Resulting Numbers: [163] 163,97 unequal: No Solution Exploring Operation: 107-56=51, Resulting Numbers: [51] 51,97 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 32, 59, 30, 37 ]
11
[ "32-30=2", "59-37=22", "22/2=11" ]
Current State: 11:[32, 59, 30, 37], Operations: [] Exploring Operation: 32-30=2, Resulting Numbers: [59, 37, 2] Generated Node #2: [59, 37, 2] from Operation: 32-30=2 Current State: 11:[59, 37, 2], Operations: ['32-30=2'] Exploring Operation: 59-37=22, Resulting Numbers: [2, 22] Generated Node #3: [2, 22] from Operation: 59-37=22 Current State: 11:[2, 22], Operations: ['32-30=2', '59-37=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[32, 59, 30, 37], Operations: [] Exploring Operation: 59-30=29, Resulting Numbers: [32, 37, 29] Generated Node #0,0: 11:[32, 37, 29] Operation: 59-30=29 Exploring Operation: 37-30=7, Resulting Numbers: [32, 59, 7] Generated Node #0,1: 11:[32, 59, 7] Operation: 37-30=7 Exploring Operation: 59-37=22, Resulting Numbers: [32, 30, 22] Generated Node #0,2: 11:[32, 30, 22] Operation: 59-37=22 Exploring Operation: 37-32=5, Resulting Numbers: [59, 30, 5] Generated Node #0,3: 11:[59, 30, 5] Operation: 37-32=5 Exploring Operation: 59-32=27, Resulting Numbers: [30, 37, 27] Generated Node #0,4: 11:[30, 37, 27] Operation: 59-32=27 Moving to Node #0,2 Current State: 11:[32, 30, 22], Operations: ['59-37=22'] Exploring Operation: 32+30=62, Resulting Numbers: [22, 62] Generated Node #0,2,0: 11:[22, 62] Operation: 32+30=62 Exploring Operation: 32-30=2, Resulting Numbers: [22, 2] Generated Node #0,2,1: 11:[22, 2] Operation: 32-30=2 Exploring Operation: 32-22=10, Resulting Numbers: [30, 10] Generated Node #0,2,2: 11:[30, 10] Operation: 32-22=10 Exploring Operation: 32+22=54, Resulting Numbers: [30, 54] Generated Node #0,2,3: 11:[30, 54] Operation: 32+22=54 Exploring Operation: 30-22=8, Resulting Numbers: [32, 8] Generated Node #0,2,4: 11:[32, 8] Operation: 30-22=8 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 11:[22, 2], Operations: ['59-37=22', '32-30=2'] Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,11 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[32, 59, 30, 37], Operations: [] Exploring Operation: 59-37=22, Resulting Numbers: [32, 30, 22] Generated Node #0,2: 11:[32, 30, 22] Operation: 59-37=22 Moving to Node #0,2 Current State: 11:[32, 30, 22], Operations: ['59-37=22'] Exploring Operation: 32-30=2, Resulting Numbers: [22, 2] Generated Node #0,2,1: 11:[22, 2] Operation: 32-30=2 Moving to Node #0,2,1 Current State: 11:[22, 2], Operations: ['59-37=22', '32-30=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 6, 48, 20, 78 ]
50
[ "48/6=8", "78-20=58", "58-8=50" ]
Current State: 50:[6, 48, 20, 78], Operations: [] Exploring Operation: 48/6=8, Resulting Numbers: [20, 78, 8] Generated Node #2: [20, 78, 8] from Operation: 48/6=8 Current State: 50:[20, 78, 8], Operations: ['48/6=8'] Exploring Operation: 78-20=58, Resulting Numbers: [8, 58] Generated Node #3: [8, 58] from Operation: 78-20=58 Current State: 50:[8, 58], Operations: ['48/6=8', '78-20=58'] Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[6, 48, 20, 78], Operations: [] Exploring Operation: 78-48=30, Resulting Numbers: [6, 20, 30] Generated Node #0,0: 50:[6, 20, 30] Operation: 78-48=30 Exploring Operation: 78/6=13, Resulting Numbers: [48, 20, 13] Generated Node #0,1: 50:[48, 20, 13] Operation: 78/6=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[48, 20, 13], Operations: ['78/6=13'] Exploring Operation: 48-20=28, Resulting Numbers: [13, 28] Generated Node #0,1,0: 50:[13, 28] Operation: 48-20=28 Exploring Operation: 20-13=7, Resulting Numbers: [48, 7] Generated Node #0,1,1: 50:[48, 7] Operation: 20-13=7 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 50:[48, 7], Operations: ['78/6=13', '20-13=7'] Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,50 unequal: No Solution Exploring Operation: 48+7=55, Resulting Numbers: [55] 55,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 50:[13, 28], Operations: ['78/6=13', '48-20=28'] Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,50 unequal: No Solution Exploring Operation: 13+28=41, Resulting Numbers: [41] 41,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[6, 20, 30], Operations: ['78-48=30'] Exploring Operation: 20+30=50, Resulting Numbers: [6, 50] Generated Node #0,0,0: 50:[6, 50] Operation: 20+30=50 Exploring Operation: 30-20=10, Resulting Numbers: [6, 10] Generated Node #0,0,1: 50:[6, 10] Operation: 30-20=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 50:[6, 50], Operations: ['78-48=30', '20+30=50'] Exploring Operation: 6+50=56, Resulting Numbers: [56] 56,50 unequal: No Solution Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 50:[6, 10], Operations: ['78-48=30', '30-20=10'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 35, 61, 79, 52 ]
77
[ "61-35=26", "52/26=2", "79-2=77" ]
Current State: 77:[35, 61, 79, 52], Operations: [] Exploring Operation: 61-35=26, Resulting Numbers: [79, 52, 26] Generated Node #2: [79, 52, 26] from Operation: 61-35=26 Current State: 77:[79, 52, 26], Operations: ['61-35=26'] Exploring Operation: 52/26=2, Resulting Numbers: [79, 2] Generated Node #3: [79, 2] from Operation: 52/26=2 Current State: 77:[79, 2], Operations: ['61-35=26', '52/26=2'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[35, 61, 79, 52], Operations: [] Exploring Operation: 61-52=9, Resulting Numbers: [35, 79, 9] Generated Node #0,0: 77:[35, 79, 9] Operation: 61-52=9 Exploring Operation: 52-35=17, Resulting Numbers: [61, 79, 17] Generated Node #0,1: 77:[61, 79, 17] Operation: 52-35=17 Exploring Operation: 35+52=87, Resulting Numbers: [61, 79, 87] Generated Node #0,2: 77:[61, 79, 87] Operation: 35+52=87 Exploring Operation: 35+61=96, Resulting Numbers: [79, 52, 96] Generated Node #0,3: 77:[79, 52, 96] Operation: 35+61=96 Exploring Operation: 61-35=26, Resulting Numbers: [79, 52, 26] Generated Node #0,4: 77:[79, 52, 26] Operation: 61-35=26 Moving to Node #0,1 Current State: 77:[61, 79, 17], Operations: ['52-35=17'] Exploring Operation: 79-17=62, Resulting Numbers: [61, 62] Generated Node #0,1,0: 77:[61, 62] Operation: 79-17=62 Exploring Operation: 61+17=78, Resulting Numbers: [79, 78] Generated Node #0,1,1: 77:[79, 78] Operation: 61+17=78 Exploring Operation: 79+17=96, Resulting Numbers: [61, 96] Generated Node #0,1,2: 77:[61, 96] Operation: 79+17=96 Exploring Operation: 79-61=18, Resulting Numbers: [17, 18] Generated Node #0,1,3: 77:[17, 18] Operation: 79-61=18 Exploring Operation: 61-17=44, Resulting Numbers: [79, 44] Generated Node #0,1,4: 77:[79, 44] Operation: 61-17=44 Moving to Node #0,2 Current State: 77:[61, 79, 87], Operations: ['35+52=87'] Exploring Operation: 61+79=140, Resulting Numbers: [87, 140] Generated Node #0,2,0: 77:[87, 140] Operation: 61+79=140 Exploring Operation: 61+87=148, Resulting Numbers: [79, 148] Generated Node #0,2,1: 77:[79, 148] Operation: 61+87=148 Exploring Operation: 87-61=26, Resulting Numbers: [79, 26] Generated Node #0,2,2: 77:[79, 26] Operation: 87-61=26 Exploring Operation: 79-61=18, Resulting Numbers: [87, 18] Generated Node #0,2,3: 77:[87, 18] Operation: 79-61=18 Exploring Operation: 87-79=8, Resulting Numbers: [61, 8] Generated Node #0,2,4: 77:[61, 8] Operation: 87-79=8 Moving to Node #0,0 Current State: 77:[35, 79, 9], Operations: ['61-52=9'] Exploring Operation: 35+9=44, Resulting Numbers: [79, 44] Generated Node #0,0,0: 77:[79, 44] Operation: 35+9=44 Exploring Operation: 79+9=88, Resulting Numbers: [35, 88] Generated Node #0,0,1: 77:[35, 88] Operation: 79+9=88 Exploring Operation: 79-35=44, Resulting Numbers: [9, 44] Generated Node #0,0,2: 77:[9, 44] Operation: 79-35=44 Exploring Operation: 35-9=26, Resulting Numbers: [79, 26] Generated Node #0,0,3: 77:[79, 26] Operation: 35-9=26 Exploring Operation: 79-9=70, Resulting Numbers: [35, 70] Generated Node #0,0,4: 77:[35, 70] Operation: 79-9=70 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 77:[79, 26], Operations: ['61-52=9', '35-9=26'] Exploring Operation: 79+26=105, Resulting Numbers: [105] 105,77 unequal: No Solution Exploring Operation: 79*26=2054, Resulting Numbers: [2054] 2054,77 unequal: No Solution Exploring Operation: 79-26=53, Resulting Numbers: [53] 53,77 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 #0,0,4 Current State: 77:[35, 70], Operations: ['61-52=9', '79-9=70'] Exploring Operation: 70/35=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 35*70=2450, Resulting Numbers: [2450] 2450,77 unequal: No Solution Exploring Operation: 70-35=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 35+70=105, Resulting Numbers: [105] 105,77 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:[79, 44], Operations: ['61-52=9', '35+9=44'] Exploring Operation: 79*44=3476, Resulting Numbers: [3476] 3476,77 unequal: No Solution Exploring Operation: 79-44=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 79+44=123, Resulting Numbers: [123] 123,77 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 #0,0,1 Current State: 77:[35, 88], Operations: ['61-52=9', '79+9=88'] Exploring Operation: 88-35=53, Resulting Numbers: [53] 53,77 unequal: No Solution Exploring Operation: 35*88=3080, Resulting Numbers: [3080] 3080,77 unequal: No Solution Exploring Operation: 35+88=123, Resulting Numbers: [123] 123,77 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 #0,0,2 Current State: 77:[9, 44], Operations: ['61-52=9', '79-35=44'] Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 9+44=53, Resulting Numbers: [53] 53,77 unequal: No Solution Exploring Operation: 9*44=396, Resulting Numbers: [396] 396,77 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: 77:[79, 52, 26], Operations: ['61-35=26'] Exploring Operation: 52-26=26, Resulting Numbers: [79, 26] Generated Node #0,4,0: 77:[79, 26] Operation: 52-26=26 Exploring Operation: 52/26=2, Resulting Numbers: [79, 2] Generated Node #0,4,1: 77:[79, 2] Operation: 52/26=2 Exploring Operation: 79-52=27, Resulting Numbers: [26, 27] Generated Node #0,4,2: 77:[26, 27] Operation: 79-52=27 Exploring Operation: 52+26=78, Resulting Numbers: [79, 78] Generated Node #0,4,3: 77:[79, 78] Operation: 52+26=78 Exploring Operation: 79-26=53, Resulting Numbers: [52, 53] Generated Node #0,4,4: 77:[52, 53] Operation: 79-26=53 Moving to Node #0,3 Current State: 77:[79, 52, 96], Operations: ['35+61=96'] Exploring Operation: 96-79=17, Resulting Numbers: [52, 17] Generated Node #0,3,0: 77:[52, 17] Operation: 96-79=17 Exploring Operation: 79-52=27, Resulting Numbers: [96, 27] Generated Node #0,3,1: 77:[96, 27] Operation: 79-52=27 Exploring Operation: 96-52=44, Resulting Numbers: [79, 44] Generated Node #0,3,2: 77:[79, 44] Operation: 96-52=44 Exploring Operation: 79+52=131, Resulting Numbers: [96, 131] Generated Node #0,3,3: 77:[96, 131] Operation: 79+52=131 Exploring Operation: 52+96=148, Resulting Numbers: [79, 148] Generated Node #0,3,4: 77:[79, 148] Operation: 52+96=148 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 77:[52, 17], Operations: ['35+61=96', '96-79=17'] Exploring Operation: 52*17=884, Resulting Numbers: [884] 884,77 unequal: No Solution Exploring Operation: 52+17=69, Resulting Numbers: [69] 69,77 unequal: No Solution Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 77:[96, 27], Operations: ['35+61=96', '79-52=27'] Exploring Operation: 96+27=123, Resulting Numbers: [123] 123,77 unequal: No Solution Exploring Operation: 96-27=69, Resulting Numbers: [69] 69,77 unequal: No Solution Exploring Operation: 96*27=2592, Resulting Numbers: [2592] 2592,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 77:[79, 44], Operations: ['35+61=96', '96-52=44'] Exploring Operation: 79*44=3476, Resulting Numbers: [3476] 3476,77 unequal: No Solution Exploring Operation: 79-44=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 79+44=123, Resulting Numbers: [123] 123,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 77:[96, 131], Operations: ['35+61=96', '79+52=131'] Exploring Operation: 96+131=227, Resulting Numbers: [227] 227,77 unequal: No Solution Exploring Operation: 131-96=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 96*131=12576, Resulting Numbers: [12576] 12576,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 77:[79, 148], Operations: ['35+61=96', '52+96=148'] Exploring Operation: 79+148=227, Resulting Numbers: [227] 227,77 unequal: No Solution Exploring Operation: 79*148=11692, Resulting Numbers: [11692] 11692,77 unequal: No Solution Exploring Operation: 148-79=69, Resulting Numbers: [69] 69,77 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: 77:[79, 78], Operations: ['52-35=17', '61+17=78'] Exploring Operation: 79+78=157, Resulting Numbers: [157] 157,77 unequal: No Solution Exploring Operation: 79*78=6162, Resulting Numbers: [6162] 6162,77 unequal: No Solution Exploring Operation: 79-78=1, Resulting Numbers: [1] 1,77 unequal: No Solution Moving to Node #0,4,3 Current State: 77:[79, 78], Operations: ['61-35=26', '52+26=78'] Exploring Operation: 79-78=1, Resulting Numbers: [1] 1,77 unequal: No Solution Exploring Operation: 79+78=157, Resulting Numbers: [157] 157,77 unequal: No Solution Exploring Operation: 79*78=6162, Resulting Numbers: [6162] 6162,77 unequal: No Solution Moving to Node #0,4,1 Current State: 77:[79, 2], Operations: ['61-35=26', '52/26=2'] Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,77 unequal: No Solution Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,77 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[35, 61, 79, 52], Operations: [] Exploring Operation: 61-35=26, Resulting Numbers: [79, 52, 26] Generated Node #0,4: 77:[79, 52, 26] Operation: 61-35=26 Moving to Node #0,4 Current State: 77:[79, 52, 26], Operations: ['61-35=26'] Exploring Operation: 52/26=2, Resulting Numbers: [79, 2] Generated Node #0,4,1: 77:[79, 2] Operation: 52/26=2 Moving to Node #0,4,1 Current State: 77:[79, 2], Operations: ['61-35=26', '52/26=2'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
0.935764
hs_5
mult_heuristic
[ 38, 66, 88, 63 ]
53
[ "66-38=28", "88-63=25", "28+25=53" ]
Current State: 53:[38, 66, 88, 63], Operations: [] Exploring Operation: 66-38=28, Resulting Numbers: [88, 63, 28] Generated Node #2: [88, 63, 28] from Operation: 66-38=28 Current State: 53:[88, 63, 28], Operations: ['66-38=28'] Exploring Operation: 88-63=25, Resulting Numbers: [28, 25] Generated Node #3: [28, 25] from Operation: 88-63=25 Current State: 53:[28, 25], Operations: ['66-38=28', '88-63=25'] Exploring Operation: 28+25=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[38, 66, 88, 63], Operations: [] Exploring Operation: 88-63=25, Resulting Numbers: [38, 66, 25] Generated Node #0,0: 53:[38, 66, 25] Operation: 88-63=25 Exploring Operation: 88-38=50, Resulting Numbers: [66, 63, 50] Generated Node #0,1: 53:[66, 63, 50] Operation: 88-38=50 Exploring Operation: 88-66=22, Resulting Numbers: [38, 63, 22] Generated Node #0,2: 53:[38, 63, 22] Operation: 88-66=22 Moving to Node #0,1 Current State: 53:[66, 63, 50], Operations: ['88-38=50'] Exploring Operation: 66-63=3, Resulting Numbers: [50, 3] Generated Node #0,1,0: 53:[50, 3] Operation: 66-63=3 Exploring Operation: 66-50=16, Resulting Numbers: [63, 16] Generated Node #0,1,1: 53:[63, 16] Operation: 66-50=16 Exploring Operation: 63-50=13, Resulting Numbers: [66, 13] Generated Node #0,1,2: 53:[66, 13] Operation: 63-50=13 Moving to Node #0,0 Current State: 53:[38, 66, 25], Operations: ['88-63=25'] Exploring Operation: 66-38=28, Resulting Numbers: [25, 28] Generated Node #0,0,0: 53:[25, 28] Operation: 66-38=28 Exploring Operation: 38+25=63, Resulting Numbers: [66, 63] Generated Node #0,0,1: 53:[66, 63] Operation: 38+25=63 Exploring Operation: 66-25=41, Resulting Numbers: [38, 41] Generated Node #0,0,2: 53:[38, 41] Operation: 66-25=41 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[66, 63], Operations: ['88-63=25', '38+25=63'] Exploring Operation: 66-63=3, Resulting Numbers: [3] 3,53 unequal: No Solution Exploring Operation: 66+63=129, Resulting Numbers: [129] 129,53 unequal: No Solution Exploring Operation: 66*63=4158, Resulting Numbers: [4158] 4158,53 unequal: No Solution No 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: 53:[38, 41], Operations: ['88-63=25', '66-25=41'] Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,53 unequal: No Solution Exploring Operation: 38*41=1558, Resulting Numbers: [1558] 1558,53 unequal: No Solution Exploring Operation: 38+41=79, Resulting Numbers: [79] 79,53 unequal: No Solution No 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: 53:[25, 28], Operations: ['88-63=25', '66-38=28'] Exploring Operation: 25*28=700, Resulting Numbers: [700] 700,53 unequal: No Solution Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,53 unequal: No Solution Exploring Operation: 25+28=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[38, 66, 88, 63], Operations: [] Exploring Operation: 88-63=25, Resulting Numbers: [38, 66, 25] Generated Node #0,0: 53:[38, 66, 25] Operation: 88-63=25 Moving to Node #0,0 Current State: 53:[38, 66, 25], Operations: ['88-63=25'] Exploring Operation: 66-38=28, Resulting Numbers: [25, 28] Generated Node #0,0,0: 53:[25, 28] Operation: 66-38=28 Moving to Node #0,0,0 Current State: 53:[25, 28], Operations: ['88-63=25', '66-38=28'] Exploring Operation: 25+28=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_3
mult_heuristic
[ 10, 10, 32, 63 ]
51
[ "10+10=20", "63-32=31", "20+31=51" ]
Current State: 51:[10, 10, 32, 63], Operations: [] Exploring Operation: 10+10=20, Resulting Numbers: [32, 63, 20] Generated Node #2: [32, 63, 20] from Operation: 10+10=20 Current State: 51:[32, 63, 20], Operations: ['10+10=20'] Exploring Operation: 63-32=31, Resulting Numbers: [20, 31] Generated Node #3: [20, 31] from Operation: 63-32=31 Current State: 51:[20, 31], Operations: ['10+10=20', '63-32=31'] Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[10, 10, 32, 63], Operations: [] Exploring Operation: 32-10=22, Resulting Numbers: [10, 63, 22] Generated Node #0,0: 51:[10, 63, 22] Operation: 32-10=22 Exploring Operation: 63-10=53, Resulting Numbers: [10, 32, 53] Generated Node #0,1: 51:[10, 32, 53] Operation: 63-10=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[10, 63, 22], Operations: ['32-10=22'] Exploring Operation: 63-10=53, Resulting Numbers: [22, 53] Generated Node #0,0,0: 51:[22, 53] Operation: 63-10=53 Exploring Operation: 22-10=12, Resulting Numbers: [63, 12] Generated Node #0,0,1: 51:[63, 12] Operation: 22-10=12 Moving to Node #0,0,0 Current State: 51:[22, 53], Operations: ['32-10=22', '63-10=53'] Exploring Operation: 53-22=31, Resulting Numbers: [31] 31,51 unequal: No Solution Exploring Operation: 22+53=75, Resulting Numbers: [75] 75,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[63, 12], Operations: ['32-10=22', '22-10=12'] Exploring Operation: 63+12=75, Resulting Numbers: [75] 75,51 unequal: No Solution Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[10, 10, 32, 63], Operations: [] Exploring Operation: 32-10=22, Resulting Numbers: [10, 63, 22] Generated Node #0,0: 51:[10, 63, 22] Operation: 32-10=22 Moving to Node #0,0 Current State: 51:[10, 63, 22], Operations: ['32-10=22'] Exploring Operation: 22-10=12, Resulting Numbers: [63, 12] Generated Node #0,0,1: 51:[63, 12] Operation: 22-10=12 Moving to Node #0,0,1 Current State: 51:[63, 12], Operations: ['32-10=22', '22-10=12'] Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 4, 3, 77, 32 ]
72
[ "32/4=8", "3+77=80", "80-8=72" ]
Current State: 72:[4, 3, 77, 32], Operations: [] Exploring Operation: 32/4=8, Resulting Numbers: [3, 77, 8] Generated Node #2: [3, 77, 8] from Operation: 32/4=8 Current State: 72:[3, 77, 8], Operations: ['32/4=8'] Exploring Operation: 3+77=80, Resulting Numbers: [8, 80] Generated Node #3: [8, 80] from Operation: 3+77=80 Current State: 72:[8, 80], Operations: ['32/4=8', '3+77=80'] Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[4, 3, 77, 32], Operations: [] Exploring Operation: 77-3=74, Resulting Numbers: [4, 32, 74] Generated Node #0,0: 72:[4, 32, 74] Operation: 77-3=74 Exploring Operation: 32/4=8, Resulting Numbers: [3, 77, 8] Generated Node #0,1: 72:[3, 77, 8] Operation: 32/4=8 Exploring Operation: 77-4=73, Resulting Numbers: [3, 32, 73] Generated Node #0,2: 72:[3, 32, 73] Operation: 77-4=73 Exploring Operation: 4+32=36, Resulting Numbers: [3, 77, 36] Generated Node #0,3: 72:[3, 77, 36] Operation: 4+32=36 Exploring Operation: 3+32=35, Resulting Numbers: [4, 77, 35] Generated Node #0,4: 72:[4, 77, 35] Operation: 3+32=35 Moving to Node #0,1 Current State: 72:[3, 77, 8], Operations: ['32/4=8'] Exploring Operation: 77-8=69, Resulting Numbers: [3, 69] Generated Node #0,1,0: 72:[3, 69] Operation: 77-8=69 Exploring Operation: 3*8=24, Resulting Numbers: [77, 24] Generated Node #0,1,1: 72:[77, 24] Operation: 3*8=24 Exploring Operation: 3+8=11, Resulting Numbers: [77, 11] Generated Node #0,1,2: 72:[77, 11] Operation: 3+8=11 Exploring Operation: 8-3=5, Resulting Numbers: [77, 5] Generated Node #0,1,3: 72:[77, 5] Operation: 8-3=5 Exploring Operation: 77-3=74, Resulting Numbers: [8, 74] Generated Node #0,1,4: 72:[8, 74] Operation: 77-3=74 Moving to Node #0,3 Current State: 72:[3, 77, 36], Operations: ['4+32=36'] Exploring Operation: 77-36=41, Resulting Numbers: [3, 41] Generated Node #0,3,0: 72:[3, 41] Operation: 77-36=41 Exploring Operation: 36/3=12, Resulting Numbers: [77, 12] Generated Node #0,3,1: 72:[77, 12] Operation: 36/3=12 Exploring Operation: 3+77=80, Resulting Numbers: [36, 80] Generated Node #0,3,2: 72:[36, 80] Operation: 3+77=80 Exploring Operation: 3+36=39, Resulting Numbers: [77, 39] Generated Node #0,3,3: 72:[77, 39] Operation: 3+36=39 Exploring Operation: 77-3=74, Resulting Numbers: [36, 74] Generated Node #0,3,4: 72:[36, 74] Operation: 77-3=74 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 72:[36, 74], Operations: ['4+32=36', '77-3=74'] Exploring Operation: 74-36=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 36*74=2664, Resulting Numbers: [2664] 2664,72 unequal: No Solution Exploring Operation: 36+74=110, Resulting Numbers: [110] 110,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 72:[3, 41], Operations: ['4+32=36', '77-36=41'] Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,72 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 72:[77, 12], Operations: ['4+32=36', '36/3=12'] Exploring Operation: 77-12=65, Resulting Numbers: [65] 65,72 unequal: No Solution Exploring Operation: 77*12=924, Resulting Numbers: [924] 924,72 unequal: No Solution Exploring Operation: 77+12=89, Resulting Numbers: [89] 89,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 72:[36, 80], Operations: ['4+32=36', '3+77=80'] Exploring Operation: 36*80=2880, Resulting Numbers: [2880] 2880,72 unequal: No Solution Exploring Operation: 36+80=116, Resulting Numbers: [116] 116,72 unequal: No Solution Exploring Operation: 80-36=44, Resulting Numbers: [44] 44,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 72:[77, 39], Operations: ['4+32=36', '3+36=39'] Exploring Operation: 77*39=3003, Resulting Numbers: [3003] 3003,72 unequal: No Solution Exploring Operation: 77+39=116, Resulting Numbers: [116] 116,72 unequal: No Solution Exploring Operation: 77-39=38, Resulting Numbers: [38] 38,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 72:[3, 32, 73], Operations: ['77-4=73'] Exploring Operation: 73-32=41, Resulting Numbers: [3, 41] Generated Node #0,2,0: 72:[3, 41] Operation: 73-32=41 Exploring Operation: 73-3=70, Resulting Numbers: [32, 70] Generated Node #0,2,1: 72:[32, 70] Operation: 73-3=70 Exploring Operation: 32-3=29, Resulting Numbers: [73, 29] Generated Node #0,2,2: 72:[73, 29] Operation: 32-3=29 Exploring Operation: 3+73=76, Resulting Numbers: [32, 76] Generated Node #0,2,3: 72:[32, 76] Operation: 3+73=76 Exploring Operation: 3+32=35, Resulting Numbers: [73, 35] Generated Node #0,2,4: 72:[73, 35] Operation: 3+32=35 Moving to Node #0,0 Current State: 72:[4, 32, 74], Operations: ['77-3=74'] Exploring Operation: 32-4=28, Resulting Numbers: [74, 28] Generated Node #0,0,0: 72:[74, 28] Operation: 32-4=28 Exploring Operation: 32/4=8, Resulting Numbers: [74, 8] Generated Node #0,0,1: 72:[74, 8] Operation: 32/4=8 Exploring Operation: 74-4=70, Resulting Numbers: [32, 70] Generated Node #0,0,2: 72:[32, 70] Operation: 74-4=70 Exploring Operation: 74-32=42, Resulting Numbers: [4, 42] Generated Node #0,0,3: 72:[4, 42] Operation: 74-32=42 Exploring Operation: 4+32=36, Resulting Numbers: [74, 36] Generated Node #0,0,4: 72:[74, 36] Operation: 4+32=36 Moving to Node #0,4 Current State: 72:[4, 77, 35], Operations: ['3+32=35'] Exploring Operation: 77-4=73, Resulting Numbers: [35, 73] Generated Node #0,4,0: 72:[35, 73] Operation: 77-4=73 Exploring Operation: 35-4=31, Resulting Numbers: [77, 31] Generated Node #0,4,1: 72:[77, 31] Operation: 35-4=31 Exploring Operation: 4+35=39, Resulting Numbers: [77, 39] Generated Node #0,4,2: 72:[77, 39] Operation: 4+35=39 Exploring Operation: 77-35=42, Resulting Numbers: [4, 42] Generated Node #0,4,3: 72:[4, 42] Operation: 77-35=42 Exploring Operation: 4+77=81, Resulting Numbers: [35, 81] Generated Node #0,4,4: 72:[35, 81] Operation: 4+77=81 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 72:[35, 73], Operations: ['3+32=35', '77-4=73'] Exploring Operation: 35*73=2555, Resulting Numbers: [2555] 2555,72 unequal: No Solution Exploring Operation: 73-35=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 35+73=108, Resulting Numbers: [108] 108,72 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 #0,4,3 Current State: 72:[4, 42], Operations: ['3+32=35', '77-35=42'] Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,72 unequal: No Solution Exploring Operation: 4*42=168, Resulting Numbers: [168] 168,72 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 #0,4,2 Current State: 72:[77, 39], Operations: ['3+32=35', '4+35=39'] Exploring Operation: 77+39=116, Resulting Numbers: [116] 116,72 unequal: No Solution Exploring Operation: 77*39=3003, Resulting Numbers: [3003] 3003,72 unequal: No Solution Exploring Operation: 77-39=38, Resulting Numbers: [38] 38,72 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 #0,4,1 Current State: 72:[77, 31], Operations: ['3+32=35', '35-4=31'] Exploring Operation: 77*31=2387, Resulting Numbers: [2387] 2387,72 unequal: No Solution Exploring Operation: 77+31=108, Resulting Numbers: [108] 108,72 unequal: No Solution Exploring Operation: 77-31=46, Resulting Numbers: [46] 46,72 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 #0,4,4 Current State: 72:[35, 81], Operations: ['3+32=35', '4+77=81'] Exploring Operation: 35*81=2835, Resulting Numbers: [2835] 2835,72 unequal: No Solution Exploring Operation: 35+81=116, Resulting Numbers: [116] 116,72 unequal: No Solution Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,4 Current State: 72:[8, 74], Operations: ['32/4=8', '77-3=74'] Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,72 unequal: No Solution Exploring Operation: 8+74=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 8*74=592, Resulting Numbers: [592] 592,72 unequal: No Solution Moving to Node #0,2,4 Current State: 72:[73, 35], Operations: ['77-4=73', '3+32=35'] Exploring Operation: 73-35=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 73*35=2555, Resulting Numbers: [2555] 2555,72 unequal: No Solution Exploring Operation: 73+35=108, Resulting Numbers: [108] 108,72 unequal: No Solution Moving to Node #0,0,4 Current State: 72:[74, 36], Operations: ['77-3=74', '4+32=36'] Exploring Operation: 74*36=2664, Resulting Numbers: [2664] 2664,72 unequal: No Solution Exploring Operation: 74+36=110, Resulting Numbers: [110] 110,72 unequal: No Solution Exploring Operation: 74-36=38, Resulting Numbers: [38] 38,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[74, 8], Operations: ['77-3=74', '32/4=8'] Exploring Operation: 74+8=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 74*8=592, Resulting Numbers: [592] 592,72 unequal: No Solution Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[3, 69], Operations: ['32/4=8', '77-8=69'] Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 3+69=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[4, 3, 77, 32], Operations: [] Exploring Operation: 32/4=8, Resulting Numbers: [3, 77, 8] Generated Node #0,1: 72:[3, 77, 8] Operation: 32/4=8 Moving to Node #0,1 Current State: 72:[3, 77, 8], Operations: ['32/4=8'] Exploring Operation: 77-8=69, Resulting Numbers: [3, 69] Generated Node #0,1,0: 72:[3, 69] Operation: 77-8=69 Moving to Node #0,1,0 Current State: 72:[3, 69], Operations: ['32/4=8', '77-8=69'] Exploring Operation: 3+69=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.932292
hs_5
mult_heuristic
[ 23, 86, 21, 6 ]
90
[ "86-23=63", "21+6=27", "63+27=90" ]
Current State: 90:[23, 86, 21, 6], Operations: [] Exploring Operation: 86-23=63, Resulting Numbers: [21, 6, 63] Generated Node #2: [21, 6, 63] from Operation: 86-23=63 Current State: 90:[21, 6, 63], Operations: ['86-23=63'] Exploring Operation: 21+6=27, Resulting Numbers: [63, 27] Generated Node #3: [63, 27] from Operation: 21+6=27 Current State: 90:[63, 27], Operations: ['86-23=63', '21+6=27'] Exploring Operation: 63+27=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[23, 86, 21, 6], Operations: [] Exploring Operation: 23+21=44, Resulting Numbers: [86, 6, 44] Generated Node #0,0: 90:[86, 6, 44] Operation: 23+21=44 Exploring Operation: 23-21=2, Resulting Numbers: [86, 6, 2] Generated Node #0,1: 90:[86, 6, 2] Operation: 23-21=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[86, 6, 2], Operations: ['23-21=2'] Exploring Operation: 86+2=88, Resulting Numbers: [6, 88] Generated Node #0,1,0: 90:[6, 88] Operation: 86+2=88 Exploring Operation: 86+6=92, Resulting Numbers: [2, 92] Generated Node #0,1,1: 90:[2, 92] Operation: 86+6=92 Moving to Node #0,1,0 Current State: 90:[6, 88], Operations: ['23-21=2', '86+2=88'] Exploring Operation: 6+88=94, Resulting Numbers: [94] 94,90 unequal: No Solution Exploring Operation: 88-6=82, Resulting Numbers: [82] 82,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[2, 92], Operations: ['23-21=2', '86+6=92'] Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[23, 86, 21, 6], Operations: [] Exploring Operation: 23-21=2, Resulting Numbers: [86, 6, 2] Generated Node #0,1: 90:[86, 6, 2] Operation: 23-21=2 Moving to Node #0,1 Current State: 90:[86, 6, 2], Operations: ['23-21=2'] Exploring Operation: 86+6=92, Resulting Numbers: [2, 92] Generated Node #0,1,1: 90:[2, 92] Operation: 86+6=92 Moving to Node #0,1,1 Current State: 90:[2, 92], Operations: ['23-21=2', '86+6=92'] Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 14, 66, 20, 65 ]
16
[ "66-14=52", "20*52=1040", "1040/65=16" ]
Current State: 16:[14, 66, 20, 65], Operations: [] Exploring Operation: 66-14=52, Resulting Numbers: [20, 65, 52] Generated Node #2: [20, 65, 52] from Operation: 66-14=52 Current State: 16:[20, 65, 52], Operations: ['66-14=52'] Exploring Operation: 20*52=1040, Resulting Numbers: [65, 1040] Generated Node #3: [65, 1040] from Operation: 20*52=1040 Current State: 16:[65, 1040], Operations: ['66-14=52', '20*52=1040'] Exploring Operation: 1040/65=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[14, 66, 20, 65], Operations: [] Exploring Operation: 66-20=46, Resulting Numbers: [14, 65, 46] Generated Node #0,0: 16:[14, 65, 46] Operation: 66-20=46 Exploring Operation: 66-65=1, Resulting Numbers: [14, 20, 1] Generated Node #0,1: 16:[14, 20, 1] Operation: 66-65=1 Moving to Node #0,1 Current State: 16:[14, 20, 1], Operations: ['66-65=1'] Exploring Operation: 20-14=6, Resulting Numbers: [1, 6] Generated Node #0,1,0: 16:[1, 6] Operation: 20-14=6 Exploring Operation: 14+1=15, Resulting Numbers: [20, 15] Generated Node #0,1,1: 16:[20, 15] Operation: 14+1=15 Moving to Node #0,0 Current State: 16:[14, 65, 46], Operations: ['66-20=46'] Exploring Operation: 65-14=51, Resulting Numbers: [46, 51] Generated Node #0,0,0: 16:[46, 51] Operation: 65-14=51 Exploring Operation: 65-46=19, Resulting Numbers: [14, 19] Generated Node #0,0,1: 16:[14, 19] Operation: 65-46=19 Moving to Node #0,1,0 Current State: 16:[1, 6], Operations: ['66-65=1', '20-14=6'] Exploring Operation: 1+6=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[14, 19], Operations: ['66-20=46', '65-46=19'] Exploring Operation: 14+19=33, Resulting Numbers: [33] 33,16 unequal: No Solution Exploring Operation: 19-14=5, Resulting Numbers: [5] 5,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[20, 15], Operations: ['66-65=1', '14+1=15'] Exploring Operation: 20+15=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[46, 51], Operations: ['66-20=46', '65-14=51'] Exploring Operation: 51-46=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 46+51=97, Resulting Numbers: [97] 97,16 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 11, 64, 98, 75 ]
97
[ "11+64=75", "75/75=1", "98-1=97" ]
Current State: 97:[11, 64, 98, 75], Operations: [] Exploring Operation: 11+64=75, Resulting Numbers: [98, 75, 75] Generated Node #2: [98, 75, 75] from Operation: 11+64=75 Current State: 97:[98, 75, 75], Operations: ['11+64=75'] Exploring Operation: 75/75=1, Resulting Numbers: [98, 1] Generated Node #3: [98, 1] from Operation: 75/75=1 Current State: 97:[98, 1], Operations: ['11+64=75', '75/75=1'] Exploring Operation: 98-1=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[11, 64, 98, 75], Operations: [] Exploring Operation: 11+64=75, Resulting Numbers: [98, 75, 75] Generated Node #0,0: 97:[98, 75, 75] Operation: 11+64=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[98, 75, 75], Operations: ['11+64=75'] Exploring Operation: 75+75=150, Resulting Numbers: [98, 150] Generated Node #0,0,0: 97:[98, 150] Operation: 75+75=150 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[98, 150], Operations: ['11+64=75', '75+75=150'] Exploring Operation: 150-98=52, Resulting Numbers: [52] 52,97 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 No solution found.
0
hs_1
sum_heuristic
[ 60, 54, 11, 2 ]
55
[ "60*2=120", "54+11=65", "120-65=55" ]
Current State: 55:[60, 54, 11, 2], Operations: [] Exploring Operation: 60*2=120, Resulting Numbers: [54, 11, 120] Generated Node #2: [54, 11, 120] from Operation: 60*2=120 Current State: 55:[54, 11, 120], Operations: ['60*2=120'] Exploring Operation: 54+11=65, Resulting Numbers: [120, 65] Generated Node #3: [120, 65] from Operation: 54+11=65 Current State: 55:[120, 65], Operations: ['60*2=120', '54+11=65'] Exploring Operation: 120-65=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[60, 54, 11, 2], Operations: [] Exploring Operation: 60-2=58, Resulting Numbers: [54, 11, 58] Generated Node #0,0: 55:[54, 11, 58] Operation: 60-2=58 Exploring Operation: 54+2=56, Resulting Numbers: [60, 11, 56] Generated Node #0,1: 55:[60, 11, 56] Operation: 54+2=56 Exploring Operation: 60-54=6, Resulting Numbers: [11, 2, 6] Generated Node #0,2: 55:[11, 2, 6] Operation: 60-54=6 Moving to Node #0,0 Current State: 55:[54, 11, 58], Operations: ['60-2=58'] Exploring Operation: 58-11=47, Resulting Numbers: [54, 47] Generated Node #0,0,0: 55:[54, 47] Operation: 58-11=47 Exploring Operation: 54+11=65, Resulting Numbers: [58, 65] Generated Node #0,0,1: 55:[58, 65] Operation: 54+11=65 Exploring Operation: 58-54=4, Resulting Numbers: [11, 4] Generated Node #0,0,2: 55:[11, 4] Operation: 58-54=4 Moving to Node #0,2 Current State: 55:[11, 2, 6], Operations: ['60-54=6'] Exploring Operation: 2*6=12, Resulting Numbers: [11, 12] Generated Node #0,2,0: 55:[11, 12] Operation: 2*6=12 Exploring Operation: 6-2=4, Resulting Numbers: [11, 4] Generated Node #0,2,1: 55:[11, 4] Operation: 6-2=4 Exploring Operation: 6/2=3, Resulting Numbers: [11, 3] Generated Node #0,2,2: 55:[11, 3] Operation: 6/2=3 Moving to Node #0,1 Current State: 55:[60, 11, 56], Operations: ['54+2=56'] Exploring Operation: 56-11=45, Resulting Numbers: [60, 45] Generated Node #0,1,0: 55:[60, 45] Operation: 56-11=45 Exploring Operation: 60-56=4, Resulting Numbers: [11, 4] Generated Node #0,1,1: 55:[11, 4] Operation: 60-56=4 Exploring Operation: 60-11=49, Resulting Numbers: [56, 49] Generated Node #0,1,2: 55:[56, 49] Operation: 60-11=49 Moving to Node #0,0,2 Current State: 55:[11, 4], Operations: ['60-2=58', '58-54=4'] Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,55 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[11, 4], Operations: ['54+2=56', '60-56=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,55 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,55 unequal: No Solution Moving to Node #0,2,0 Current State: 55:[11, 12], Operations: ['60-54=6', '2*6=12'] Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,55 unequal: No Solution Exploring Operation: 11*12=132, Resulting Numbers: [132] 132,55 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,55 unequal: No Solution Moving to Node #0,2,1 Current State: 55:[11, 4], Operations: ['60-54=6', '6-2=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[11, 3], Operations: ['60-54=6', '6/2=3'] Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,55 unequal: No Solution Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,55 unequal: No Solution Moving to Node #0,1,2 Current State: 55:[56, 49], Operations: ['54+2=56', '60-11=49'] Exploring Operation: 56*49=2744, Resulting Numbers: [2744] 2744,55 unequal: No Solution Exploring Operation: 56+49=105, Resulting Numbers: [105] 105,55 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[54, 47], Operations: ['60-2=58', '58-11=47'] Exploring Operation: 54*47=2538, Resulting Numbers: [2538] 2538,55 unequal: No Solution Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 54+47=101, Resulting Numbers: [101] 101,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[58, 65], Operations: ['60-2=58', '54+11=65'] Exploring Operation: 58*65=3770, Resulting Numbers: [3770] 3770,55 unequal: No Solution Exploring Operation: 58+65=123, Resulting Numbers: [123] 123,55 unequal: No Solution Exploring Operation: 65-58=7, Resulting Numbers: [7] 7,55 unequal: No Solution Moving to Node #0,1,0 Current State: 55:[60, 45], Operations: ['54+2=56', '56-11=45'] Exploring Operation: 60-45=15, Resulting Numbers: [15] 15,55 unequal: No Solution Exploring Operation: 60+45=105, Resulting Numbers: [105] 105,55 unequal: No Solution Exploring Operation: 60*45=2700, Resulting Numbers: [2700] 2700,55 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 4, 47, 27, 24 ]
16
[ "47-27=20", "24-20=4", "4*4=16" ]
Current State: 16:[4, 47, 27, 24], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [4, 24, 20] Generated Node #2: [4, 24, 20] from Operation: 47-27=20 Current State: 16:[4, 24, 20], Operations: ['47-27=20'] Exploring Operation: 24-20=4, Resulting Numbers: [4, 4] Generated Node #3: [4, 4] from Operation: 24-20=4 Current State: 16:[4, 4], Operations: ['47-27=20', '24-20=4'] Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[4, 47, 27, 24], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [4, 24, 20] Generated Node #0,0: 16:[4, 24, 20] Operation: 47-27=20 Exploring Operation: 47-24=23, Resulting Numbers: [4, 27, 23] Generated Node #0,1: 16:[4, 27, 23] Operation: 47-24=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[4, 24, 20], Operations: ['47-27=20'] Exploring Operation: 24-20=4, Resulting Numbers: [4, 4] Generated Node #0,0,0: 16:[4, 4] Operation: 24-20=4 Exploring Operation: 24/4=6, Resulting Numbers: [20, 6] Generated Node #0,0,1: 16:[20, 6] Operation: 24/4=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 16:[4, 4], Operations: ['47-27=20', '24-20=4'] Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[4, 47, 27, 24], Operations: [] Exploring Operation: 47-27=20, Resulting Numbers: [4, 24, 20] Generated Node #0,0: 16:[4, 24, 20] Operation: 47-27=20 Moving to Node #0,0 Current State: 16:[4, 24, 20], Operations: ['47-27=20'] Exploring Operation: 24-20=4, Resulting Numbers: [4, 4] Generated Node #0,0,0: 16:[4, 4] Operation: 24-20=4 Moving to Node #0,0,0 Current State: 16:[4, 4], Operations: ['47-27=20', '24-20=4'] Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 98, 91, 70, 50 ]
33
[ "91*50=4550", "4550/70=65", "98-65=33" ]
Current State: 33:[98, 91, 70, 50], Operations: [] Exploring Operation: 91*50=4550, Resulting Numbers: [98, 70, 4550] Generated Node #2: [98, 70, 4550] from Operation: 91*50=4550 Current State: 33:[98, 70, 4550], Operations: ['91*50=4550'] Exploring Operation: 4550/70=65, Resulting Numbers: [98, 65] Generated Node #3: [98, 65] from Operation: 4550/70=65 Current State: 33:[98, 65], Operations: ['91*50=4550', '4550/70=65'] Exploring Operation: 98-65=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[98, 91, 70, 50], Operations: [] Exploring Operation: 98-91=7, Resulting Numbers: [70, 50, 7] Generated Node #0,0: 33:[70, 50, 7] Operation: 98-91=7 Moving to Node #0,0 Current State: 33:[70, 50, 7], Operations: ['98-91=7'] Exploring Operation: 70-50=20, Resulting Numbers: [7, 20] Generated Node #0,0,0: 33:[7, 20] Operation: 70-50=20 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[7, 20], Operations: ['98-91=7', '70-50=20'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,33 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
[ 88, 5, 32, 38 ]
62
[ "88+32=120", "120/5=24", "38+24=62" ]
Current State: 62:[88, 5, 32, 38], Operations: [] Exploring Operation: 88+32=120, Resulting Numbers: [5, 38, 120] Generated Node #2: [5, 38, 120] from Operation: 88+32=120 Current State: 62:[5, 38, 120], Operations: ['88+32=120'] Exploring Operation: 120/5=24, Resulting Numbers: [38, 24] Generated Node #3: [38, 24] from Operation: 120/5=24 Current State: 62:[38, 24], Operations: ['88+32=120', '120/5=24'] Exploring Operation: 38+24=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[88, 5, 32, 38], Operations: [] Exploring Operation: 88-32=56, Resulting Numbers: [5, 38, 56] Generated Node #0,0: 62:[5, 38, 56] Operation: 88-32=56 Moving to Node #0,0 Current State: 62:[5, 38, 56], Operations: ['88-32=56'] Exploring Operation: 38-5=33, Resulting Numbers: [56, 33] Generated Node #0,0,0: 62:[56, 33] Operation: 38-5=33 Moving to Node #0,0,0 Current State: 62:[56, 33], Operations: ['88-32=56', '38-5=33'] Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,62 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 45, 84, 44, 27 ]
22
[ "84-45=39", "44-27=17", "39-17=22" ]
Current State: 22:[45, 84, 44, 27], Operations: [] Exploring Operation: 84-45=39, Resulting Numbers: [44, 27, 39] Generated Node #2: [44, 27, 39] from Operation: 84-45=39 Current State: 22:[44, 27, 39], Operations: ['84-45=39'] Exploring Operation: 44-27=17, Resulting Numbers: [39, 17] Generated Node #3: [39, 17] from Operation: 44-27=17 Current State: 22:[39, 17], Operations: ['84-45=39', '44-27=17'] Exploring Operation: 39-17=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[45, 84, 44, 27], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [84, 27, 1] Generated Node #0,0: 22:[84, 27, 1] Operation: 45-44=1 Exploring Operation: 84-44=40, Resulting Numbers: [45, 27, 40] Generated Node #0,1: 22:[45, 27, 40] Operation: 84-44=40 Exploring Operation: 84-45=39, Resulting Numbers: [44, 27, 39] Generated Node #0,2: 22:[44, 27, 39] Operation: 84-45=39 Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[44, 27, 39], Operations: ['84-45=39'] Exploring Operation: 44-39=5, Resulting Numbers: [27, 5] Generated Node #0,2,0: 22:[27, 5] Operation: 44-39=5 Exploring Operation: 39-27=12, Resulting Numbers: [44, 12] Generated Node #0,2,1: 22:[44, 12] Operation: 39-27=12 Exploring Operation: 44-27=17, Resulting Numbers: [39, 17] Generated Node #0,2,2: 22:[39, 17] Operation: 44-27=17 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 22:[27, 5], Operations: ['84-45=39', '44-39=5'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[45, 84, 44, 27], Operations: [] Exploring Operation: 84-45=39, Resulting Numbers: [44, 27, 39] Generated Node #0,2: 22:[44, 27, 39] Operation: 84-45=39 Moving to Node #0,2 Current State: 22:[44, 27, 39], Operations: ['84-45=39'] Exploring Operation: 44-39=5, Resulting Numbers: [27, 5] Generated Node #0,2,0: 22:[27, 5] Operation: 44-39=5 Moving to Node #0,2,0 Current State: 22:[27, 5], Operations: ['84-45=39', '44-39=5'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 79, 52, 85, 32 ]
26
[ "79-52=27", "85-32=53", "53-27=26" ]
Current State: 26:[79, 52, 85, 32], Operations: [] Exploring Operation: 79-52=27, Resulting Numbers: [85, 32, 27] Generated Node #2: [85, 32, 27] from Operation: 79-52=27 Current State: 26:[85, 32, 27], Operations: ['79-52=27'] Exploring Operation: 85-32=53, Resulting Numbers: [27, 53] Generated Node #3: [27, 53] from Operation: 85-32=53 Current State: 26:[27, 53], Operations: ['79-52=27', '85-32=53'] Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[79, 52, 85, 32], Operations: [] Exploring Operation: 85-32=53, Resulting Numbers: [79, 52, 53] Generated Node #0,0: 26:[79, 52, 53] Operation: 85-32=53 Exploring Operation: 79-52=27, Resulting Numbers: [85, 32, 27] Generated Node #0,1: 26:[85, 32, 27] Operation: 79-52=27 Exploring Operation: 85-52=33, Resulting Numbers: [79, 32, 33] Generated Node #0,2: 26:[79, 32, 33] Operation: 85-52=33 Exploring Operation: 85-79=6, Resulting Numbers: [52, 32, 6] Generated Node #0,3: 26:[52, 32, 6] Operation: 85-79=6 Exploring Operation: 79-32=47, Resulting Numbers: [52, 85, 47] Generated Node #0,4: 26:[52, 85, 47] Operation: 79-32=47 Start Sub Search at level 1: Moving to Node #0,3 Current State: 26:[52, 32, 6], Operations: ['85-79=6'] Exploring Operation: 52-32=20, Resulting Numbers: [6, 20] Generated Node #0,3,0: 26:[6, 20] Operation: 52-32=20 Exploring Operation: 52+6=58, Resulting Numbers: [32, 58] Generated Node #0,3,1: 26:[32, 58] Operation: 52+6=58 Exploring Operation: 32+6=38, Resulting Numbers: [52, 38] Generated Node #0,3,2: 26:[52, 38] Operation: 32+6=38 Exploring Operation: 52-6=46, Resulting Numbers: [32, 46] Generated Node #0,3,3: 26:[32, 46] Operation: 52-6=46 Exploring Operation: 32-6=26, Resulting Numbers: [52, 26] Generated Node #0,3,4: 26:[52, 26] Operation: 32-6=26 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 26:[6, 20], Operations: ['85-79=6', '52-32=20'] Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[79, 52, 85, 32], Operations: [] Exploring Operation: 85-79=6, Resulting Numbers: [52, 32, 6] Generated Node #0,3: 26:[52, 32, 6] Operation: 85-79=6 Moving to Node #0,3 Current State: 26:[52, 32, 6], Operations: ['85-79=6'] Exploring Operation: 52-32=20, Resulting Numbers: [6, 20] Generated Node #0,3,0: 26:[6, 20] Operation: 52-32=20 Moving to Node #0,3,0 Current State: 26:[6, 20], Operations: ['85-79=6', '52-32=20'] Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 34, 38, 3, 59 ]
29
[ "59-38=21", "3*21=63", "63-34=29" ]
Current State: 29:[34, 38, 3, 59], Operations: [] Exploring Operation: 59-38=21, Resulting Numbers: [34, 3, 21] Generated Node #2: [34, 3, 21] from Operation: 59-38=21 Current State: 29:[34, 3, 21], Operations: ['59-38=21'] Exploring Operation: 3*21=63, Resulting Numbers: [34, 63] Generated Node #3: [34, 63] from Operation: 3*21=63 Current State: 29:[34, 63], Operations: ['59-38=21', '3*21=63'] Exploring Operation: 63-34=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[34, 38, 3, 59], Operations: [] Exploring Operation: 59-34=25, Resulting Numbers: [38, 3, 25] Generated Node #0,0: 29:[38, 3, 25] Operation: 59-34=25 Exploring Operation: 59-38=21, Resulting Numbers: [34, 3, 21] Generated Node #0,1: 29:[34, 3, 21] Operation: 59-38=21 Moving to Node #0,0 Current State: 29:[38, 3, 25], Operations: ['59-34=25'] Exploring Operation: 38-3=35, Resulting Numbers: [25, 35] Generated Node #0,0,0: 29:[25, 35] Operation: 38-3=35 Exploring Operation: 3+25=28, Resulting Numbers: [38, 28] Generated Node #0,0,1: 29:[38, 28] Operation: 3+25=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[25, 35], Operations: ['59-34=25', '38-3=35'] Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,29 unequal: No Solution No 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: 29:[38, 28], Operations: ['59-34=25', '3+25=28'] Exploring Operation: 38-28=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 38+28=66, Resulting Numbers: [66] 66,29 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: 29:[34, 3, 21], Operations: ['59-38=21'] Exploring Operation: 3+21=24, Resulting Numbers: [34, 24] Generated Node #0,1,0: 29:[34, 24] Operation: 3+21=24 Exploring Operation: 34-3=31, Resulting Numbers: [21, 31] Generated Node #0,1,1: 29:[21, 31] Operation: 34-3=31 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 29:[34, 24], Operations: ['59-38=21', '3+21=24'] Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,29 unequal: No Solution No 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: 29:[21, 31], Operations: ['59-38=21', '34-3=31'] Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,29 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 30, 34, 12, 67 ]
15
[ "30+34=64", "12+67=79", "79-64=15" ]
Current State: 15:[30, 34, 12, 67], Operations: [] Exploring Operation: 30+34=64, Resulting Numbers: [12, 67, 64] Generated Node #2: [12, 67, 64] from Operation: 30+34=64 Current State: 15:[12, 67, 64], Operations: ['30+34=64'] Exploring Operation: 12+67=79, Resulting Numbers: [64, 79] Generated Node #3: [64, 79] from Operation: 12+67=79 Current State: 15:[64, 79], Operations: ['30+34=64', '12+67=79'] Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[30, 34, 12, 67], Operations: [] Exploring Operation: 34-30=4, Resulting Numbers: [12, 67, 4] Generated Node #0,0: 15:[12, 67, 4] Operation: 34-30=4 Exploring Operation: 30-12=18, Resulting Numbers: [34, 67, 18] Generated Node #0,1: 15:[34, 67, 18] Operation: 30-12=18 Exploring Operation: 67-30=37, Resulting Numbers: [34, 12, 37] Generated Node #0,2: 15:[34, 12, 37] Operation: 67-30=37 Exploring Operation: 67-34=33, Resulting Numbers: [30, 12, 33] Generated Node #0,3: 15:[30, 12, 33] Operation: 67-34=33 Start Sub Search at level 1: Moving to Node #0,3 Current State: 15:[30, 12, 33], Operations: ['67-34=33'] Exploring Operation: 33-12=21, Resulting Numbers: [30, 21] Generated Node #0,3,0: 15:[30, 21] Operation: 33-12=21 Exploring Operation: 30-12=18, Resulting Numbers: [33, 18] Generated Node #0,3,1: 15:[33, 18] Operation: 30-12=18 Exploring Operation: 30+12=42, Resulting Numbers: [33, 42] Generated Node #0,3,2: 15:[33, 42] Operation: 30+12=42 Exploring Operation: 33-30=3, Resulting Numbers: [12, 3] Generated Node #0,3,3: 15:[12, 3] Operation: 33-30=3 Moving to Node #0,3,3 Current State: 15:[12, 3], Operations: ['67-34=33', '33-30=3'] Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[30, 34, 12, 67], Operations: [] Exploring Operation: 67-34=33, Resulting Numbers: [30, 12, 33] Generated Node #0,3: 15:[30, 12, 33] Operation: 67-34=33 Moving to Node #0,3 Current State: 15:[30, 12, 33], Operations: ['67-34=33'] Exploring Operation: 33-30=3, Resulting Numbers: [12, 3] Generated Node #0,3,3: 15:[12, 3] Operation: 33-30=3 Moving to Node #0,3,3 Current State: 15:[12, 3], Operations: ['67-34=33', '33-30=3'] Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 62, 71, 80, 30 ]
83
[ "62+71=133", "80-30=50", "133-50=83" ]
Current State: 83:[62, 71, 80, 30], Operations: [] Exploring Operation: 62+71=133, Resulting Numbers: [80, 30, 133] Generated Node #2: [80, 30, 133] from Operation: 62+71=133 Current State: 83:[80, 30, 133], Operations: ['62+71=133'] Exploring Operation: 80-30=50, Resulting Numbers: [133, 50] Generated Node #3: [133, 50] from Operation: 80-30=50 Current State: 83:[133, 50], Operations: ['62+71=133', '80-30=50'] Exploring Operation: 133-50=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[62, 71, 80, 30], Operations: [] Exploring Operation: 62+30=92, Resulting Numbers: [71, 80, 92] Generated Node #0,0: 83:[71, 80, 92] Operation: 62+30=92 Exploring Operation: 71+30=101, Resulting Numbers: [62, 80, 101] Generated Node #0,1: 83:[62, 80, 101] Operation: 71+30=101 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[71, 80, 92], Operations: ['62+30=92'] Exploring Operation: 71+80=151, Resulting Numbers: [92, 151] Generated Node #0,0,0: 83:[92, 151] Operation: 71+80=151 Exploring Operation: 92-71=21, Resulting Numbers: [80, 21] Generated Node #0,0,1: 83:[80, 21] Operation: 92-71=21 Moving to Node #0,0,1 Current State: 83:[80, 21], Operations: ['62+30=92', '92-71=21'] Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,83 unequal: No Solution Exploring Operation: 80+21=101, Resulting Numbers: [101] 101,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[92, 151], Operations: ['62+30=92', '71+80=151'] Exploring Operation: 92+151=243, Resulting Numbers: [243] 243,83 unequal: No Solution Exploring Operation: 151-92=59, Resulting Numbers: [59] 59,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[62, 80, 101], Operations: ['71+30=101'] Exploring Operation: 101-62=39, Resulting Numbers: [80, 39] Generated Node #0,1,0: 83:[80, 39] Operation: 101-62=39 Exploring Operation: 62+80=142, Resulting Numbers: [101, 142] Generated Node #0,1,1: 83:[101, 142] Operation: 62+80=142 Moving to Node #0,1,0 Current State: 83:[80, 39], Operations: ['71+30=101', '101-62=39'] Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 80+39=119, Resulting Numbers: [119] 119,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[101, 142], Operations: ['71+30=101', '62+80=142'] Exploring Operation: 142-101=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 101+142=243, Resulting Numbers: [243] 243,83 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
[ 70, 28, 92, 97 ]
93
[ "70+28=98", "97-92=5", "98-5=93" ]
Current State: 93:[70, 28, 92, 97], Operations: [] Exploring Operation: 70+28=98, Resulting Numbers: [92, 97, 98] Generated Node #2: [92, 97, 98] from Operation: 70+28=98 Current State: 93:[92, 97, 98], Operations: ['70+28=98'] Exploring Operation: 97-92=5, Resulting Numbers: [98, 5] Generated Node #3: [98, 5] from Operation: 97-92=5 Current State: 93:[98, 5], Operations: ['70+28=98', '97-92=5'] Exploring Operation: 98-5=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[70, 28, 92, 97], Operations: [] Exploring Operation: 70-28=42, Resulting Numbers: [92, 97, 42] Generated Node #0,0: 93:[92, 97, 42] Operation: 70-28=42 Exploring Operation: 70+28=98, Resulting Numbers: [92, 97, 98] Generated Node #0,1: 93:[92, 97, 98] Operation: 70+28=98 Exploring Operation: 97-70=27, Resulting Numbers: [28, 92, 27] Generated Node #0,2: 93:[28, 92, 27] Operation: 97-70=27 Moving to Node #0,2 Current State: 93:[28, 92, 27], Operations: ['97-70=27'] Exploring Operation: 92+27=119, Resulting Numbers: [28, 119] Generated Node #0,2,0: 93:[28, 119] Operation: 92+27=119 Exploring Operation: 28+27=55, Resulting Numbers: [92, 55] Generated Node #0,2,1: 93:[92, 55] Operation: 28+27=55 Exploring Operation: 28-27=1, Resulting Numbers: [92, 1] Generated Node #0,2,2: 93:[92, 1] Operation: 28-27=1 Moving to Node #0,1 Current State: 93:[92, 97, 98], Operations: ['70+28=98'] Exploring Operation: 98-92=6, Resulting Numbers: [97, 6] Generated Node #0,1,0: 93:[97, 6] Operation: 98-92=6 Exploring Operation: 98-97=1, Resulting Numbers: [92, 1] Generated Node #0,1,1: 93:[92, 1] Operation: 98-97=1 Exploring Operation: 97-92=5, Resulting Numbers: [98, 5] Generated Node #0,1,2: 93:[98, 5] Operation: 97-92=5 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 93:[92, 1], Operations: ['70+28=98', '98-97=1'] Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[70, 28, 92, 97], Operations: [] Exploring Operation: 70+28=98, Resulting Numbers: [92, 97, 98] Generated Node #0,1: 93:[92, 97, 98] Operation: 70+28=98 Moving to Node #0,1 Current State: 93:[92, 97, 98], Operations: ['70+28=98'] Exploring Operation: 98-97=1, Resulting Numbers: [92, 1] Generated Node #0,1,1: 93:[92, 1] Operation: 98-97=1 Moving to Node #0,1,1 Current State: 93:[92, 1], Operations: ['70+28=98', '98-97=1'] Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 22, 11, 60, 11 ]
20
[ "22+11=33", "60*11=660", "660/33=20" ]
Current State: 20:[22, 11, 60, 11], Operations: [] Exploring Operation: 22+11=33, Resulting Numbers: [60, 33] Generated Node #2: [60, 33] from Operation: 22+11=33 Current State: 20:[60, 33], Operations: ['22+11=33'] Exploring Operation: 60*11=660, Resulting Numbers: [33, 660] Generated Node #3: [33, 660] from Operation: 60*11=660 Current State: 20:[33, 660], Operations: ['22+11=33', '60*11=660'] Exploring Operation: 660/33=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[22, 11, 60, 11], Operations: [] Exploring Operation: 60-11=49, Resulting Numbers: [22, 11, 49] Generated Node #0,0: 20:[22, 11, 49] Operation: 60-11=49 Exploring Operation: 60-22=38, Resulting Numbers: [11, 11, 38] Generated Node #0,1: 20:[11, 11, 38] Operation: 60-22=38 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[11, 11, 38], Operations: ['60-22=38'] Exploring Operation: 38-11=27, Resulting Numbers: [11, 27] Generated Node #0,1,0: 20:[11, 27] Operation: 38-11=27 Exploring Operation: 38-11=27, Resulting Numbers: [11, 27] Generated Node #0,1,1: 20:[11, 27] Operation: 38-11=27 Moving to Node #0,1,0 Current State: 20:[11, 27], Operations: ['60-22=38', '38-11=27'] Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,20 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[11, 27], Operations: ['60-22=38', '38-11=27'] Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,20 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,20 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:[22, 11, 49], Operations: ['60-11=49'] Exploring Operation: 49-22=27, Resulting Numbers: [11, 27] Generated Node #0,0,0: 20:[11, 27] Operation: 49-22=27 Exploring Operation: 49-11=38, Resulting Numbers: [22, 38] Generated Node #0,0,1: 20:[22, 38] Operation: 49-11=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 20:[11, 27], Operations: ['60-11=49', '49-22=27'] Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,20 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 20:[22, 38], Operations: ['60-11=49', '49-11=38'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 22+38=60, Resulting Numbers: [60] 60,20 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 No solution found.
0
hs_2
mult_heuristic
[ 72, 59, 6, 51 ]
96
[ "72/6=12", "59-51=8", "12*8=96" ]
Current State: 96:[72, 59, 6, 51], Operations: [] Exploring Operation: 72/6=12, Resulting Numbers: [59, 51, 12] Generated Node #2: [59, 51, 12] from Operation: 72/6=12 Current State: 96:[59, 51, 12], Operations: ['72/6=12'] Exploring Operation: 59-51=8, Resulting Numbers: [12, 8] Generated Node #3: [12, 8] from Operation: 59-51=8 Current State: 96:[12, 8], Operations: ['72/6=12', '59-51=8'] Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[72, 59, 6, 51], Operations: [] Exploring Operation: 72-59=13, Resulting Numbers: [6, 51, 13] Generated Node #0,0: 96:[6, 51, 13] Operation: 72-59=13 Exploring Operation: 72-51=21, Resulting Numbers: [59, 6, 21] Generated Node #0,1: 96:[59, 6, 21] Operation: 72-51=21 Exploring Operation: 59-51=8, Resulting Numbers: [72, 6, 8] Generated Node #0,2: 96:[72, 6, 8] Operation: 59-51=8 Exploring Operation: 72/6=12, Resulting Numbers: [59, 51, 12] Generated Node #0,3: 96:[59, 51, 12] Operation: 72/6=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[6, 51, 13], Operations: ['72-59=13'] Exploring Operation: 13-6=7, Resulting Numbers: [51, 7] Generated Node #0,0,0: 96:[51, 7] Operation: 13-6=7 Exploring Operation: 6+13=19, Resulting Numbers: [51, 19] Generated Node #0,0,1: 96:[51, 19] Operation: 6+13=19 Exploring Operation: 51-13=38, Resulting Numbers: [6, 38] Generated Node #0,0,2: 96:[6, 38] Operation: 51-13=38 Exploring Operation: 51-6=45, Resulting Numbers: [13, 45] Generated Node #0,0,3: 96:[13, 45] Operation: 51-6=45 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[51, 7], Operations: ['72-59=13', '13-6=7'] Exploring Operation: 51-7=44, Resulting Numbers: [44] 44,96 unequal: No Solution Exploring Operation: 51+7=58, Resulting Numbers: [58] 58,96 unequal: No Solution Exploring Operation: 51*7=357, Resulting Numbers: [357] 357,96 unequal: No Solution No 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: 96:[13, 45], Operations: ['72-59=13', '51-6=45'] Exploring Operation: 13*45=585, Resulting Numbers: [585] 585,96 unequal: No Solution Exploring Operation: 45-13=32, Resulting Numbers: [32] 32,96 unequal: No Solution Exploring Operation: 13+45=58, Resulting Numbers: [58] 58,96 unequal: No Solution No 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: 96:[51, 19], Operations: ['72-59=13', '6+13=19'] Exploring Operation: 51+19=70, Resulting Numbers: [70] 70,96 unequal: No Solution Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,96 unequal: No Solution Exploring Operation: 51*19=969, Resulting Numbers: [969] 969,96 unequal: No Solution No 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: 96:[6, 38], Operations: ['72-59=13', '51-13=38'] Exploring Operation: 6*38=228, Resulting Numbers: [228] 228,96 unequal: No Solution Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,96 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,96 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: 96:[59, 6, 21], Operations: ['72-51=21'] Exploring Operation: 6+21=27, Resulting Numbers: [59, 27] Generated Node #0,1,0: 96:[59, 27] Operation: 6+21=27 Exploring Operation: 59-6=53, Resulting Numbers: [21, 53] Generated Node #0,1,1: 96:[21, 53] Operation: 59-6=53 Exploring Operation: 21-6=15, Resulting Numbers: [59, 15] Generated Node #0,1,2: 96:[59, 15] Operation: 21-6=15 Exploring Operation: 59-21=38, Resulting Numbers: [6, 38] Generated Node #0,1,3: 96:[6, 38] Operation: 59-21=38 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 96:[6, 38], Operations: ['72-51=21', '59-21=38'] Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,96 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,96 unequal: No Solution Exploring Operation: 6*38=228, Resulting Numbers: [228] 228,96 unequal: No Solution No 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: 96:[21, 53], Operations: ['72-51=21', '59-6=53'] Exploring Operation: 53-21=32, Resulting Numbers: [32] 32,96 unequal: No Solution Exploring Operation: 21+53=74, Resulting Numbers: [74] 74,96 unequal: No Solution Exploring Operation: 21*53=1113, Resulting Numbers: [1113] 1113,96 unequal: No Solution No 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: 96:[59, 15], Operations: ['72-51=21', '21-6=15'] Exploring Operation: 59*15=885, Resulting Numbers: [885] 885,96 unequal: No Solution Exploring Operation: 59-15=44, Resulting Numbers: [44] 44,96 unequal: No Solution Exploring Operation: 59+15=74, Resulting Numbers: [74] 74,96 unequal: No Solution No 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: 96:[59, 27], Operations: ['72-51=21', '6+21=27'] Exploring Operation: 59+27=86, Resulting Numbers: [86] 86,96 unequal: No Solution Exploring Operation: 59*27=1593, Resulting Numbers: [1593] 1593,96 unequal: No Solution Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,96 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: 96:[59, 51, 12], Operations: ['72/6=12'] Exploring Operation: 59+51=110, Resulting Numbers: [12, 110] Generated Node #0,3,0: 96:[12, 110] Operation: 59+51=110 Exploring Operation: 51-12=39, Resulting Numbers: [59, 39] Generated Node #0,3,1: 96:[59, 39] Operation: 51-12=39 Exploring Operation: 59-51=8, Resulting Numbers: [12, 8] Generated Node #0,3,2: 96:[12, 8] Operation: 59-51=8 Exploring Operation: 59-12=47, Resulting Numbers: [51, 47] Generated Node #0,3,3: 96:[51, 47] Operation: 59-12=47 Moving to Node #0,3,2 Current State: 96:[12, 8], Operations: ['72/6=12', '59-51=8'] Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[72, 59, 6, 51], Operations: [] Exploring Operation: 72/6=12, Resulting Numbers: [59, 51, 12] Generated Node #0,3: 96:[59, 51, 12] Operation: 72/6=12 Moving to Node #0,3 Current State: 96:[59, 51, 12], Operations: ['72/6=12'] Exploring Operation: 59-51=8, Resulting Numbers: [12, 8] Generated Node #0,3,2: 96:[12, 8] Operation: 59-51=8 Moving to Node #0,3,2 Current State: 96:[12, 8], Operations: ['72/6=12', '59-51=8'] Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.960069
hs_4
sum_heuristic
[ 82, 36, 19, 74 ]
25
[ "82+36=118", "19+74=93", "118-93=25" ]
Current State: 25:[82, 36, 19, 74], Operations: [] Exploring Operation: 82+36=118, Resulting Numbers: [19, 74, 118] Generated Node #2: [19, 74, 118] from Operation: 82+36=118 Current State: 25:[19, 74, 118], Operations: ['82+36=118'] Exploring Operation: 19+74=93, Resulting Numbers: [118, 93] Generated Node #3: [118, 93] from Operation: 19+74=93 Current State: 25:[118, 93], Operations: ['82+36=118', '19+74=93'] Exploring Operation: 118-93=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[82, 36, 19, 74], Operations: [] Exploring Operation: 82-36=46, Resulting Numbers: [19, 74, 46] Generated Node #0,0: 25:[19, 74, 46] Operation: 82-36=46 Exploring Operation: 74-36=38, Resulting Numbers: [82, 19, 38] Generated Node #0,1: 25:[82, 19, 38] Operation: 74-36=38 Exploring Operation: 82-74=8, Resulting Numbers: [36, 19, 8] Generated Node #0,2: 25:[36, 19, 8] Operation: 82-74=8 Moving to Node #0,2 Current State: 25:[36, 19, 8], Operations: ['82-74=8'] Exploring Operation: 36-19=17, Resulting Numbers: [8, 17] Generated Node #0,2,0: 25:[8, 17] Operation: 36-19=17 Exploring Operation: 36-8=28, Resulting Numbers: [19, 28] Generated Node #0,2,1: 25:[19, 28] Operation: 36-8=28 Exploring Operation: 19+8=27, Resulting Numbers: [36, 27] Generated Node #0,2,2: 25:[36, 27] Operation: 19+8=27 Moving to Node #0,0 Current State: 25:[19, 74, 46], Operations: ['82-36=46'] Exploring Operation: 46-19=27, Resulting Numbers: [74, 27] Generated Node #0,0,0: 25:[74, 27] Operation: 46-19=27 Exploring Operation: 74-46=28, Resulting Numbers: [19, 28] Generated Node #0,0,1: 25:[19, 28] Operation: 74-46=28 Exploring Operation: 74-19=55, Resulting Numbers: [46, 55] Generated Node #0,0,2: 25:[46, 55] Operation: 74-19=55 Moving to Node #0,1 Current State: 25:[82, 19, 38], Operations: ['74-36=38'] Exploring Operation: 82-19=63, Resulting Numbers: [38, 63] Generated Node #0,1,0: 25:[38, 63] Operation: 82-19=63 Exploring Operation: 82-38=44, Resulting Numbers: [19, 44] Generated Node #0,1,1: 25:[19, 44] Operation: 82-38=44 Exploring Operation: 38/19=2, Resulting Numbers: [82, 2] Generated Node #0,1,2: 25:[82, 2] Operation: 38/19=2 Moving to Node #0,2,1 Current State: 25:[19, 28], Operations: ['82-74=8', '36-8=28'] Exploring Operation: 19*28=532, Resulting Numbers: [532] 532,25 unequal: No Solution Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 19+28=47, Resulting Numbers: [47] 47,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[19, 28], Operations: ['82-36=46', '74-46=28'] Exploring Operation: 19+28=47, Resulting Numbers: [47] 47,25 unequal: No Solution Exploring Operation: 19*28=532, Resulting Numbers: [532] 532,25 unequal: No Solution Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,25 unequal: No Solution Moving to Node #0,2,0 Current State: 25:[8, 17], Operations: ['82-74=8', '36-19=17'] Exploring Operation: 8+17=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[82, 36, 19, 74], Operations: [] Exploring Operation: 82-74=8, Resulting Numbers: [36, 19, 8] Generated Node #0,2: 25:[36, 19, 8] Operation: 82-74=8 Moving to Node #0,2 Current State: 25:[36, 19, 8], Operations: ['82-74=8'] Exploring Operation: 36-19=17, Resulting Numbers: [8, 17] Generated Node #0,2,0: 25:[8, 17] Operation: 36-19=17 Moving to Node #0,2,0 Current State: 25:[8, 17], Operations: ['82-74=8', '36-19=17'] Exploring Operation: 8+17=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
0.980035
hs_3
mult_heuristic
[ 27, 56, 72, 69 ]
42
[ "27+69=96", "56*72=4032", "4032/96=42" ]
Current State: 42:[27, 56, 72, 69], Operations: [] Exploring Operation: 27+69=96, Resulting Numbers: [56, 72, 96] Generated Node #2: [56, 72, 96] from Operation: 27+69=96 Current State: 42:[56, 72, 96], Operations: ['27+69=96'] Exploring Operation: 56*72=4032, Resulting Numbers: [96, 4032] Generated Node #3: [96, 4032] from Operation: 56*72=4032 Current State: 42:[96, 4032], Operations: ['27+69=96', '56*72=4032'] Exploring Operation: 4032/96=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[27, 56, 72, 69], Operations: [] Exploring Operation: 72-56=16, Resulting Numbers: [27, 69, 16] Generated Node #0,0: 42:[27, 69, 16] Operation: 72-56=16 Exploring Operation: 72-69=3, Resulting Numbers: [27, 56, 3] Generated Node #0,1: 42:[27, 56, 3] Operation: 72-69=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[27, 56, 3], Operations: ['72-69=3'] Exploring Operation: 27/3=9, Resulting Numbers: [56, 9] Generated Node #0,1,0: 42:[56, 9] Operation: 27/3=9 Exploring Operation: 56-27=29, Resulting Numbers: [3, 29] Generated Node #0,1,1: 42:[3, 29] Operation: 56-27=29 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 42:[3, 29], Operations: ['72-69=3', '56-27=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,42 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,42 unequal: No Solution No 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: 42:[56, 9], Operations: ['72-69=3', '27/3=9'] Exploring Operation: 56-9=47, Resulting Numbers: [47] 47,42 unequal: No Solution Exploring Operation: 56+9=65, Resulting Numbers: [65] 65,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[27, 69, 16], Operations: ['72-56=16'] Exploring Operation: 69-27=42, Resulting Numbers: [16, 42] Generated Node #0,0,0: 42:[16, 42] Operation: 69-27=42 Exploring Operation: 69-16=53, Resulting Numbers: [27, 53] Generated Node #0,0,1: 42:[27, 53] Operation: 69-16=53 Moving to Node #0,0,0 Current State: 42:[16, 42], Operations: ['72-56=16', '69-27=42'] Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,42 unequal: No Solution Exploring Operation: 16+42=58, Resulting Numbers: [58] 58,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[27, 53], Operations: ['72-56=16', '69-16=53'] Exploring Operation: 27+53=80, Resulting Numbers: [80] 80,42 unequal: No Solution Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 49, 8, 15, 6 ]
32
[ "49-8=41", "15-6=9", "41-9=32" ]
Current State: 32:[49, 8, 15, 6], Operations: [] Exploring Operation: 49-8=41, Resulting Numbers: [15, 6, 41] Generated Node #2: [15, 6, 41] from Operation: 49-8=41 Current State: 32:[15, 6, 41], Operations: ['49-8=41'] Exploring Operation: 15-6=9, Resulting Numbers: [41, 9] Generated Node #3: [41, 9] from Operation: 15-6=9 Current State: 32:[41, 9], Operations: ['49-8=41', '15-6=9'] Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[49, 8, 15, 6], Operations: [] Exploring Operation: 8-6=2, Resulting Numbers: [49, 15, 2] Generated Node #0,0: 32:[49, 15, 2] Operation: 8-6=2 Exploring Operation: 49-8=41, Resulting Numbers: [15, 6, 41] Generated Node #0,1: 32:[15, 6, 41] Operation: 49-8=41 Exploring Operation: 49-6=43, Resulting Numbers: [8, 15, 43] Generated Node #0,2: 32:[8, 15, 43] Operation: 49-6=43 Exploring Operation: 49-15=34, Resulting Numbers: [8, 6, 34] Generated Node #0,3: 32:[8, 6, 34] Operation: 49-15=34 Moving to Node #0,3 Current State: 32:[8, 6, 34], Operations: ['49-15=34'] Exploring Operation: 34-6=28, Resulting Numbers: [8, 28] Generated Node #0,3,0: 32:[8, 28] Operation: 34-6=28 Exploring Operation: 8-6=2, Resulting Numbers: [34, 2] Generated Node #0,3,1: 32:[34, 2] Operation: 8-6=2 Exploring Operation: 8+6=14, Resulting Numbers: [34, 14] Generated Node #0,3,2: 32:[34, 14] Operation: 8+6=14 Exploring Operation: 34-8=26, Resulting Numbers: [6, 26] Generated Node #0,3,3: 32:[6, 26] Operation: 34-8=26 Moving to Node #0,2 Current State: 32:[8, 15, 43], Operations: ['49-6=43'] Exploring Operation: 43-15=28, Resulting Numbers: [8, 28] Generated Node #0,2,0: 32:[8, 28] Operation: 43-15=28 Exploring Operation: 43-8=35, Resulting Numbers: [15, 35] Generated Node #0,2,1: 32:[15, 35] Operation: 43-8=35 Exploring Operation: 8+15=23, Resulting Numbers: [43, 23] Generated Node #0,2,2: 32:[43, 23] Operation: 8+15=23 Exploring Operation: 15-8=7, Resulting Numbers: [43, 7] Generated Node #0,2,3: 32:[43, 7] Operation: 15-8=7 Moving to Node #0,1 Current State: 32:[15, 6, 41], Operations: ['49-8=41'] Exploring Operation: 41-6=35, Resulting Numbers: [15, 35] Generated Node #0,1,0: 32:[15, 35] Operation: 41-6=35 Exploring Operation: 15+6=21, Resulting Numbers: [41, 21] Generated Node #0,1,1: 32:[41, 21] Operation: 15+6=21 Exploring Operation: 15-6=9, Resulting Numbers: [41, 9] Generated Node #0,1,2: 32:[41, 9] Operation: 15-6=9 Exploring Operation: 41-15=26, Resulting Numbers: [6, 26] Generated Node #0,1,3: 32:[6, 26] Operation: 41-15=26 Moving to Node #0,0 Current State: 32:[49, 15, 2], Operations: ['8-6=2'] Exploring Operation: 15*2=30, Resulting Numbers: [49, 30] Generated Node #0,0,0: 32:[49, 30] Operation: 15*2=30 Exploring Operation: 15+2=17, Resulting Numbers: [49, 17] Generated Node #0,0,1: 32:[49, 17] Operation: 15+2=17 Exploring Operation: 49-15=34, Resulting Numbers: [2, 34] Generated Node #0,0,2: 32:[2, 34] Operation: 49-15=34 Exploring Operation: 49-2=47, Resulting Numbers: [15, 47] Generated Node #0,0,3: 32:[15, 47] Operation: 49-2=47 Moving to Node #0,3,1 Current State: 32:[34, 2], Operations: ['49-15=34', '8-6=2'] Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,32 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[49, 8, 15, 6], Operations: [] Exploring Operation: 49-15=34, Resulting Numbers: [8, 6, 34] Generated Node #0,3: 32:[8, 6, 34] Operation: 49-15=34 Moving to Node #0,3 Current State: 32:[8, 6, 34], Operations: ['49-15=34'] Exploring Operation: 8-6=2, Resulting Numbers: [34, 2] Generated Node #0,3,1: 32:[34, 2] Operation: 8-6=2 Moving to Node #0,3,1 Current State: 32:[34, 2], Operations: ['49-15=34', '8-6=2'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.976563
hs_4
sum_heuristic
[ 7, 84, 43, 5 ]
96
[ "43-7=36", "5*36=180", "180-84=96" ]
Current State: 96:[7, 84, 43, 5], Operations: [] Exploring Operation: 43-7=36, Resulting Numbers: [84, 5, 36] Generated Node #2: [84, 5, 36] from Operation: 43-7=36 Current State: 96:[84, 5, 36], Operations: ['43-7=36'] Exploring Operation: 5*36=180, Resulting Numbers: [84, 180] Generated Node #3: [84, 180] from Operation: 5*36=180 Current State: 96:[84, 180], Operations: ['43-7=36', '5*36=180'] Exploring Operation: 180-84=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[7, 84, 43, 5], Operations: [] Exploring Operation: 84/7=12, Resulting Numbers: [43, 5, 12] Generated Node #0,0: 96:[43, 5, 12] Operation: 84/7=12 Moving to Node #0,0 Current State: 96:[43, 5, 12], Operations: ['84/7=12'] Exploring Operation: 43+5=48, Resulting Numbers: [12, 48] Generated Node #0,0,0: 96:[12, 48] Operation: 43+5=48 Moving to Node #0,0,0 Current State: 96:[12, 48], Operations: ['84/7=12', '43+5=48'] Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,96 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 31, 27, 86, 7 ]
83
[ "31-27=4", "86-7=79", "4+79=83" ]
Current State: 83:[31, 27, 86, 7], Operations: [] Exploring Operation: 31-27=4, Resulting Numbers: [86, 7, 4] Generated Node #2: [86, 7, 4] from Operation: 31-27=4 Current State: 83:[86, 7, 4], Operations: ['31-27=4'] Exploring Operation: 86-7=79, Resulting Numbers: [4, 79] Generated Node #3: [4, 79] from Operation: 86-7=79 Current State: 83:[4, 79], Operations: ['31-27=4', '86-7=79'] Exploring Operation: 4+79=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[31, 27, 86, 7], Operations: [] Exploring Operation: 27+7=34, Resulting Numbers: [31, 86, 34] Generated Node #0,0: 83:[31, 86, 34] Operation: 27+7=34 Exploring Operation: 31+27=58, Resulting Numbers: [86, 7, 58] Generated Node #0,1: 83:[86, 7, 58] Operation: 31+27=58 Exploring Operation: 31+7=38, Resulting Numbers: [27, 86, 38] Generated Node #0,2: 83:[27, 86, 38] Operation: 31+7=38 Moving to Node #0,0 Current State: 83:[31, 86, 34], Operations: ['27+7=34'] Exploring Operation: 31+34=65, Resulting Numbers: [86, 65] Generated Node #0,0,0: 83:[86, 65] Operation: 31+34=65 Exploring Operation: 86-31=55, Resulting Numbers: [34, 55] Generated Node #0,0,1: 83:[34, 55] Operation: 86-31=55 Exploring Operation: 31+86=117, Resulting Numbers: [34, 117] Generated Node #0,0,2: 83:[34, 117] Operation: 31+86=117 Moving to Node #0,1 Current State: 83:[86, 7, 58], Operations: ['31+27=58'] Exploring Operation: 86+7=93, Resulting Numbers: [58, 93] Generated Node #0,1,0: 83:[58, 93] Operation: 86+7=93 Exploring Operation: 7+58=65, Resulting Numbers: [86, 65] Generated Node #0,1,1: 83:[86, 65] Operation: 7+58=65 Exploring Operation: 86-7=79, Resulting Numbers: [58, 79] Generated Node #0,1,2: 83:[58, 79] Operation: 86-7=79 Moving to Node #0,2 Current State: 83:[27, 86, 38], Operations: ['31+7=38'] Exploring Operation: 27+38=65, Resulting Numbers: [86, 65] Generated Node #0,2,0: 83:[86, 65] Operation: 27+38=65 Exploring Operation: 86-27=59, Resulting Numbers: [38, 59] Generated Node #0,2,1: 83:[38, 59] Operation: 86-27=59 Exploring Operation: 27+86=113, Resulting Numbers: [38, 113] Generated Node #0,2,2: 83:[38, 113] Operation: 27+86=113 Moving to Node #0,0,0 Current State: 83:[86, 65], Operations: ['27+7=34', '31+34=65'] Exploring Operation: 86*65=5590, Resulting Numbers: [5590] 5590,83 unequal: No Solution Exploring Operation: 86-65=21, Resulting Numbers: [21] 21,83 unequal: No Solution Exploring Operation: 86+65=151, Resulting Numbers: [151] 151,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[86, 65], Operations: ['31+7=38', '27+38=65'] Exploring Operation: 86-65=21, Resulting Numbers: [21] 21,83 unequal: No Solution Exploring Operation: 86+65=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 86*65=5590, Resulting Numbers: [5590] 5590,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[86, 65], Operations: ['31+27=58', '7+58=65'] Exploring Operation: 86-65=21, Resulting Numbers: [21] 21,83 unequal: No Solution Exploring Operation: 86+65=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 86*65=5590, Resulting Numbers: [5590] 5590,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[58, 79], Operations: ['31+27=58', '86-7=79'] Exploring Operation: 79-58=21, Resulting Numbers: [21] 21,83 unequal: No Solution Exploring Operation: 58+79=137, Resulting Numbers: [137] 137,83 unequal: No Solution Exploring Operation: 58*79=4582, Resulting Numbers: [4582] 4582,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[58, 93], Operations: ['31+27=58', '86+7=93'] Exploring Operation: 58*93=5394, Resulting Numbers: [5394] 5394,83 unequal: No Solution Exploring Operation: 93-58=35, Resulting Numbers: [35] 35,83 unequal: No Solution Exploring Operation: 58+93=151, Resulting Numbers: [151] 151,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[38, 59], Operations: ['31+7=38', '86-27=59'] Exploring Operation: 38+59=97, Resulting Numbers: [97] 97,83 unequal: No Solution Exploring Operation: 59-38=21, Resulting Numbers: [21] 21,83 unequal: No Solution Exploring Operation: 38*59=2242, Resulting Numbers: [2242] 2242,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[38, 113], Operations: ['31+7=38', '27+86=113'] Exploring Operation: 38*113=4294, Resulting Numbers: [4294] 4294,83 unequal: No Solution Exploring Operation: 113-38=75, Resulting Numbers: [75] 75,83 unequal: No Solution Exploring Operation: 38+113=151, Resulting Numbers: [151] 151,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[34, 55], Operations: ['27+7=34', '86-31=55'] Exploring Operation: 34*55=1870, Resulting Numbers: [1870] 1870,83 unequal: No Solution Exploring Operation: 34+55=89, Resulting Numbers: [89] 89,83 unequal: No Solution Exploring Operation: 55-34=21, Resulting Numbers: [21] 21,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[34, 117], Operations: ['27+7=34', '31+86=117'] Exploring Operation: 34*117=3978, Resulting Numbers: [3978] 3978,83 unequal: No Solution Exploring Operation: 34+117=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 117-34=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[31, 27, 86, 7], Operations: [] Exploring Operation: 27+7=34, Resulting Numbers: [31, 86, 34] Generated Node #0,0: 83:[31, 86, 34] Operation: 27+7=34 Moving to Node #0,0 Current State: 83:[31, 86, 34], Operations: ['27+7=34'] Exploring Operation: 31+86=117, Resulting Numbers: [34, 117] Generated Node #0,0,2: 83:[34, 117] Operation: 31+86=117 Moving to Node #0,0,2 Current State: 83:[34, 117], Operations: ['27+7=34', '31+86=117'] Exploring Operation: 117-34=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
0.962674
hs_3
mult_heuristic
[ 41, 43, 1, 20 ]
41
[ "43-41=2", "20*2=40", "1+40=41" ]
Current State: 41:[41, 43, 1, 20], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [1, 20, 2] Generated Node #2: [1, 20, 2] from Operation: 43-41=2 Current State: 41:[1, 20, 2], Operations: ['43-41=2'] Exploring Operation: 20*2=40, Resulting Numbers: [1, 40] Generated Node #3: [1, 40] from Operation: 20*2=40 Current State: 41:[1, 40], Operations: ['43-41=2', '20*2=40'] Exploring Operation: 1+40=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[41, 43, 1, 20], Operations: [] Exploring Operation: 41/1=41, Resulting Numbers: [43, 20, 41] Generated Node #0,0: 41:[43, 20, 41] Operation: 41/1=41 Exploring Operation: 1+20=21, Resulting Numbers: [41, 43, 21] Generated Node #0,1: 41:[41, 43, 21] Operation: 1+20=21 Exploring Operation: 43-1=42, Resulting Numbers: [41, 20, 42] Generated Node #0,2: 41:[41, 20, 42] Operation: 43-1=42 Exploring Operation: 41*1=41, Resulting Numbers: [43, 20, 41] Generated Node #0,3: 41:[43, 20, 41] Operation: 41*1=41 Exploring Operation: 43*1=43, Resulting Numbers: [41, 20, 43] Generated Node #0,4: 41:[41, 20, 43] Operation: 43*1=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[41, 43, 21], Operations: ['1+20=21'] Exploring Operation: 43-21=22, Resulting Numbers: [41, 22] Generated Node #0,1,0: 41:[41, 22] Operation: 43-21=22 Exploring Operation: 41-21=20, Resulting Numbers: [43, 20] Generated Node #0,1,1: 41:[43, 20] Operation: 41-21=20 Exploring Operation: 43+21=64, Resulting Numbers: [41, 64] Generated Node #0,1,2: 41:[41, 64] Operation: 43+21=64 Exploring Operation: 43-41=2, Resulting Numbers: [21, 2] Generated Node #0,1,3: 41:[21, 2] Operation: 43-41=2 Exploring Operation: 41+21=62, Resulting Numbers: [43, 62] Generated Node #0,1,4: 41:[43, 62] Operation: 41+21=62 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[41, 22], Operations: ['1+20=21', '43-21=22'] Exploring Operation: 41*22=902, Resulting Numbers: [902] 902,41 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 41+22=63, Resulting Numbers: [63] 63,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 41:[43, 20], Operations: ['1+20=21', '41-21=20'] Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 43+20=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 43*20=860, Resulting Numbers: [860] 860,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 41:[41, 64], Operations: ['1+20=21', '43+21=64'] Exploring Operation: 64-41=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 41*64=2624, Resulting Numbers: [2624] 2624,41 unequal: No Solution Exploring Operation: 41+64=105, Resulting Numbers: [105] 105,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 41:[43, 62], Operations: ['1+20=21', '41+21=62'] Exploring Operation: 43*62=2666, Resulting Numbers: [2666] 2666,41 unequal: No Solution Exploring Operation: 62-43=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 43+62=105, Resulting Numbers: [105] 105,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 41:[21, 2], Operations: ['1+20=21', '43-41=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[41, 20, 42], Operations: ['43-1=42'] Exploring Operation: 41-20=21, Resulting Numbers: [42, 21] Generated Node #0,2,0: 41:[42, 21] Operation: 41-20=21 Exploring Operation: 20+42=62, Resulting Numbers: [41, 62] Generated Node #0,2,1: 41:[41, 62] Operation: 20+42=62 Exploring Operation: 42-20=22, Resulting Numbers: [41, 22] Generated Node #0,2,2: 41:[41, 22] Operation: 42-20=22 Exploring Operation: 42-41=1, Resulting Numbers: [20, 1] Generated Node #0,2,3: 41:[20, 1] Operation: 42-41=1 Exploring Operation: 41+20=61, Resulting Numbers: [42, 61] Generated Node #0,2,4: 41:[42, 61] Operation: 41+20=61 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 41:[41, 22], Operations: ['43-1=42', '42-20=22'] Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 41+22=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 41*22=902, Resulting Numbers: [902] 902,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 41:[42, 21], Operations: ['43-1=42', '41-20=21'] Exploring Operation: 42+21=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 42*21=882, Resulting Numbers: [882] 882,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 41:[41, 62], Operations: ['43-1=42', '20+42=62'] Exploring Operation: 62-41=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 41*62=2542, Resulting Numbers: [2542] 2542,41 unequal: No Solution Exploring Operation: 41+62=103, Resulting Numbers: [103] 103,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 41:[42, 61], Operations: ['43-1=42', '41+20=61'] Exploring Operation: 42*61=2562, Resulting Numbers: [2562] 2562,41 unequal: No Solution Exploring Operation: 61-42=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 42+61=103, Resulting Numbers: [103] 103,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 41:[20, 1], Operations: ['43-1=42', '42-41=1'] Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,41 unequal: No Solution Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[43, 20, 41], Operations: ['41/1=41'] Exploring Operation: 43+20=63, Resulting Numbers: [41, 63] Generated Node #0,0,0: 41:[41, 63] Operation: 43+20=63 Exploring Operation: 43-41=2, Resulting Numbers: [20, 2] Generated Node #0,0,1: 41:[20, 2] Operation: 43-41=2 Exploring Operation: 41-20=21, Resulting Numbers: [43, 21] Generated Node #0,0,2: 41:[43, 21] Operation: 41-20=21 Exploring Operation: 20+41=61, Resulting Numbers: [43, 61] Generated Node #0,0,3: 41:[43, 61] Operation: 20+41=61 Exploring Operation: 43-20=23, Resulting Numbers: [41, 23] Generated Node #0,0,4: 41:[41, 23] Operation: 43-20=23 Moving to Node #0,0,4 Current State: 41:[41, 23], Operations: ['41/1=41', '43-20=23'] Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,41 unequal: No Solution Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,41 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[43, 21], Operations: ['41/1=41', '41-20=21'] Exploring Operation: 43*21=903, Resulting Numbers: [903] 903,41 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,41 unequal: No Solution Exploring Operation: 43+21=64, Resulting Numbers: [64] 64,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[41, 63], Operations: ['41/1=41', '43+20=63'] Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,41 unequal: No Solution Exploring Operation: 41*63=2583, Resulting Numbers: [2583] 2583,41 unequal: No Solution Exploring Operation: 41+63=104, Resulting Numbers: [104] 104,41 unequal: No Solution Moving to Node #0,0,3 Current State: 41:[43, 61], Operations: ['41/1=41', '20+41=61'] Exploring Operation: 43*61=2623, Resulting Numbers: [2623] 2623,41 unequal: No Solution Exploring Operation: 43+61=104, Resulting Numbers: [104] 104,41 unequal: No Solution Exploring Operation: 61-43=18, Resulting Numbers: [18] 18,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[20, 2], Operations: ['41/1=41', '43-41=2'] Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,41 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,41 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:[43, 20, 41], Operations: ['41*1=41'] Exploring Operation: 43-41=2, Resulting Numbers: [20, 2] Generated Node #0,3,0: 41:[20, 2] Operation: 43-41=2 Exploring Operation: 41-20=21, Resulting Numbers: [43, 21] Generated Node #0,3,1: 41:[43, 21] Operation: 41-20=21 Exploring Operation: 20+41=61, Resulting Numbers: [43, 61] Generated Node #0,3,2: 41:[43, 61] Operation: 20+41=61 Exploring Operation: 43+20=63, Resulting Numbers: [41, 63] Generated Node #0,3,3: 41:[41, 63] Operation: 43+20=63 Exploring Operation: 43-20=23, Resulting Numbers: [41, 23] Generated Node #0,3,4: 41:[41, 23] Operation: 43-20=23 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 41:[41, 23], Operations: ['41*1=41', '43-20=23'] Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,41 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 41:[43, 21], Operations: ['41*1=41', '41-20=21'] Exploring Operation: 43*21=903, Resulting Numbers: [903] 903,41 unequal: No Solution Exploring Operation: 43+21=64, Resulting Numbers: [64] 64,41 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 41:[43, 61], Operations: ['41*1=41', '20+41=61'] Exploring Operation: 43*61=2623, Resulting Numbers: [2623] 2623,41 unequal: No Solution Exploring Operation: 43+61=104, Resulting Numbers: [104] 104,41 unequal: No Solution Exploring Operation: 61-43=18, Resulting Numbers: [18] 18,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 41:[41, 63], Operations: ['41*1=41', '43+20=63'] Exploring Operation: 41*63=2583, Resulting Numbers: [2583] 2583,41 unequal: No Solution Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,41 unequal: No Solution Exploring Operation: 41+63=104, Resulting Numbers: [104] 104,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 41:[20, 2], Operations: ['41*1=41', '43-41=2'] Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,41 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,41 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 41:[41, 20, 43], Operations: ['43*1=43'] Exploring Operation: 43-41=2, Resulting Numbers: [20, 2] Generated Node #0,4,0: 41:[20, 2] Operation: 43-41=2 Exploring Operation: 20+43=63, Resulting Numbers: [41, 63] Generated Node #0,4,1: 41:[41, 63] Operation: 20+43=63 Exploring Operation: 41+20=61, Resulting Numbers: [43, 61] Generated Node #0,4,2: 41:[43, 61] Operation: 41+20=61 Exploring Operation: 43-20=23, Resulting Numbers: [41, 23] Generated Node #0,4,3: 41:[41, 23] Operation: 43-20=23 Exploring Operation: 41-20=21, Resulting Numbers: [43, 21] Generated Node #0,4,4: 41:[43, 21] Operation: 41-20=21 Moving to Node #0,4,3 Current State: 41:[41, 23], Operations: ['43*1=43', '43-20=23'] Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,41 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,41 unequal: No Solution Moving to Node #0,4,2 Current State: 41:[43, 61], Operations: ['43*1=43', '41+20=61'] Exploring Operation: 43+61=104, Resulting Numbers: [104] 104,41 unequal: No Solution Exploring Operation: 43*61=2623, Resulting Numbers: [2623] 2623,41 unequal: No Solution Exploring Operation: 61-43=18, Resulting Numbers: [18] 18,41 unequal: No Solution Moving to Node #0,4,1 Current State: 41:[41, 63], Operations: ['43*1=43', '20+43=63'] Exploring Operation: 41*63=2583, Resulting Numbers: [2583] 2583,41 unequal: No Solution Exploring Operation: 41+63=104, Resulting Numbers: [104] 104,41 unequal: No Solution Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,41 unequal: No Solution Moving to Node #0,4,4 Current State: 41:[43, 21], Operations: ['43*1=43', '41-20=21'] Exploring Operation: 43+21=64, Resulting Numbers: [64] 64,41 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,41 unequal: No Solution Exploring Operation: 43*21=903, Resulting Numbers: [903] 903,41 unequal: No Solution Moving to Node #0,4,0 Current State: 41:[20, 2], Operations: ['43*1=43', '43-41=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,41 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,41 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
[ 64, 48, 53, 27 ]
60
[ "53+27=80", "48*80=3840", "3840/64=60" ]
Current State: 60:[64, 48, 53, 27], Operations: [] Exploring Operation: 53+27=80, Resulting Numbers: [64, 48, 80] Generated Node #2: [64, 48, 80] from Operation: 53+27=80 Current State: 60:[64, 48, 80], Operations: ['53+27=80'] Exploring Operation: 48*80=3840, Resulting Numbers: [64, 3840] Generated Node #3: [64, 3840] from Operation: 48*80=3840 Current State: 60:[64, 3840], Operations: ['53+27=80', '48*80=3840'] Exploring Operation: 3840/64=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[64, 48, 53, 27], Operations: [] Exploring Operation: 64-48=16, Resulting Numbers: [53, 27, 16] Generated Node #0,0: 60:[53, 27, 16] Operation: 64-48=16 Exploring Operation: 48-27=21, Resulting Numbers: [64, 53, 21] Generated Node #0,1: 60:[64, 53, 21] Operation: 48-27=21 Exploring Operation: 53-48=5, Resulting Numbers: [64, 27, 5] Generated Node #0,2: 60:[64, 27, 5] Operation: 53-48=5 Moving to Node #0,2 Current State: 60:[64, 27, 5], Operations: ['53-48=5'] Exploring Operation: 64-5=59, Resulting Numbers: [27, 59] Generated Node #0,2,0: 60:[27, 59] Operation: 64-5=59 Exploring Operation: 27+5=32, Resulting Numbers: [64, 32] Generated Node #0,2,1: 60:[64, 32] Operation: 27+5=32 Exploring Operation: 27-5=22, Resulting Numbers: [64, 22] Generated Node #0,2,2: 60:[64, 22] Operation: 27-5=22 Moving to Node #0,0 Current State: 60:[53, 27, 16], Operations: ['64-48=16'] Exploring Operation: 53-27=26, Resulting Numbers: [16, 26] Generated Node #0,0,0: 60:[16, 26] Operation: 53-27=26 Exploring Operation: 27-16=11, Resulting Numbers: [53, 11] Generated Node #0,0,1: 60:[53, 11] Operation: 27-16=11 Exploring Operation: 53-16=37, Resulting Numbers: [27, 37] Generated Node #0,0,2: 60:[27, 37] Operation: 53-16=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[16, 26], Operations: ['64-48=16', '53-27=26'] Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,60 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,60 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:[53, 11], Operations: ['64-48=16', '27-16=11'] Exploring Operation: 53*11=583, Resulting Numbers: [583] 583,60 unequal: No Solution Exploring Operation: 53+11=64, Resulting Numbers: [64] 64,60 unequal: No Solution Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,60 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:[27, 37], Operations: ['64-48=16', '53-16=37'] Exploring Operation: 27+37=64, Resulting Numbers: [64] 64,60 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 27*37=999, Resulting Numbers: [999] 999,60 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: 60:[64, 53, 21], Operations: ['48-27=21'] Exploring Operation: 53+21=74, Resulting Numbers: [64, 74] Generated Node #0,1,0: 60:[64, 74] Operation: 53+21=74 Exploring Operation: 53-21=32, Resulting Numbers: [64, 32] Generated Node #0,1,1: 60:[64, 32] Operation: 53-21=32 Exploring Operation: 64-53=11, Resulting Numbers: [21, 11] Generated Node #0,1,2: 60:[21, 11] Operation: 64-53=11 Moving to Node #0,1,2 Current State: 60:[21, 11], Operations: ['48-27=21', '64-53=11'] Exploring Operation: 21+11=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 21*11=231, Resulting Numbers: [231] 231,60 unequal: No Solution Moving to Node #0,2,0 Current State: 60:[27, 59], Operations: ['53-48=5', '64-5=59'] Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 27*59=1593, Resulting Numbers: [1593] 1593,60 unequal: No Solution Exploring Operation: 27+59=86, Resulting Numbers: [86] 86,60 unequal: No Solution Moving to Node #0,2,2 Current State: 60:[64, 22], Operations: ['53-48=5', '27-5=22'] Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,60 unequal: No Solution Exploring Operation: 64+22=86, Resulting Numbers: [86] 86,60 unequal: No Solution Exploring Operation: 64*22=1408, Resulting Numbers: [1408] 1408,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[64, 32], Operations: ['48-27=21', '53-21=32'] Exploring Operation: 64/32=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 64-32=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 64+32=96, Resulting Numbers: [96] 96,60 unequal: No Solution Moving to Node #0,2,1 Current State: 60:[64, 32], Operations: ['53-48=5', '27+5=32'] Exploring Operation: 64/32=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 64-32=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 64+32=96, Resulting Numbers: [96] 96,60 unequal: No Solution Moving to Node #0,1,0 Current State: 60:[64, 74], Operations: ['48-27=21', '53+21=74'] Exploring Operation: 74-64=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 64*74=4736, Resulting Numbers: [4736] 4736,60 unequal: No Solution Exploring Operation: 64+74=138, Resulting Numbers: [138] 138,60 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 98, 66, 10, 74 ]
84
[ "66+74=140", "140/10=14", "98-14=84" ]
Current State: 84:[98, 66, 10, 74], Operations: [] Exploring Operation: 66+74=140, Resulting Numbers: [98, 10, 140] Generated Node #2: [98, 10, 140] from Operation: 66+74=140 Current State: 84:[98, 10, 140], Operations: ['66+74=140'] Exploring Operation: 140/10=14, Resulting Numbers: [98, 14] Generated Node #3: [98, 14] from Operation: 140/10=14 Current State: 84:[98, 14], Operations: ['66+74=140', '140/10=14'] Exploring Operation: 98-14=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[98, 66, 10, 74], Operations: [] Exploring Operation: 74-66=8, Resulting Numbers: [98, 10, 8] Generated Node #0,0: 84:[98, 10, 8] Operation: 74-66=8 Exploring Operation: 98-66=32, Resulting Numbers: [10, 74, 32] Generated Node #0,1: 84:[10, 74, 32] Operation: 98-66=32 Exploring Operation: 98-74=24, Resulting Numbers: [66, 10, 24] Generated Node #0,2: 84:[66, 10, 24] Operation: 98-74=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[10, 74, 32], Operations: ['98-66=32'] Exploring Operation: 74-32=42, Resulting Numbers: [10, 42] Generated Node #0,1,0: 84:[10, 42] Operation: 74-32=42 Exploring Operation: 10+74=84, Resulting Numbers: [32, 84] Generated Node #0,1,1: 84:[32, 84] Operation: 10+74=84 Exploring Operation: 10+32=42, Resulting Numbers: [74, 42] Generated Node #0,1,2: 84:[74, 42] Operation: 10+32=42 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 84:[10, 42], Operations: ['98-66=32', '74-32=42'] Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,84 unequal: No Solution Exploring Operation: 10+42=52, Resulting Numbers: [52] 52,84 unequal: No Solution Exploring Operation: 10*42=420, Resulting Numbers: [420] 420,84 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 #0,1,1 Current State: 84:[32, 84], Operations: ['98-66=32', '10+74=84'] Exploring Operation: 32+84=116, Resulting Numbers: [116] 116,84 unequal: No Solution Exploring Operation: 84-32=52, Resulting Numbers: [52] 52,84 unequal: No Solution Exploring Operation: 32*84=2688, Resulting Numbers: [2688] 2688,84 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:[74, 42], Operations: ['98-66=32', '10+32=42'] Exploring Operation: 74*42=3108, Resulting Numbers: [3108] 3108,84 unequal: No Solution Exploring Operation: 74-42=32, Resulting Numbers: [32] 32,84 unequal: No Solution Exploring Operation: 74+42=116, Resulting Numbers: [116] 116,84 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 #0,0 Current State: 84:[98, 10, 8], Operations: ['74-66=8'] Exploring Operation: 10-8=2, Resulting Numbers: [98, 2] Generated Node #0,0,0: 84:[98, 2] Operation: 10-8=2 Exploring Operation: 98-8=90, Resulting Numbers: [10, 90] Generated Node #0,0,1: 84:[10, 90] Operation: 98-8=90 Exploring Operation: 98-10=88, Resulting Numbers: [8, 88] Generated Node #0,0,2: 84:[8, 88] Operation: 98-10=88 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 84:[8, 88], Operations: ['74-66=8', '98-10=88'] Exploring Operation: 88-8=80, Resulting Numbers: [80] 80,84 unequal: No Solution Exploring Operation: 88/8=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 8+88=96, Resulting Numbers: [96] 96,84 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 #0,0,1 Current State: 84:[10, 90], Operations: ['74-66=8', '98-8=90'] Exploring Operation: 10+90=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,84 unequal: No Solution Exploring Operation: 90/10=9, Resulting Numbers: [9] 9,84 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 #0,0,0 Current State: 84:[98, 2], Operations: ['74-66=8', '10-8=2'] Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,84 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,84 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 #0,2 Current State: 84:[66, 10, 24], Operations: ['98-74=24'] Exploring Operation: 66-24=42, Resulting Numbers: [10, 42] Generated Node #0,2,0: 84:[10, 42] Operation: 66-24=42 Exploring Operation: 66+10=76, Resulting Numbers: [24, 76] Generated Node #0,2,1: 84:[24, 76] Operation: 66+10=76 Exploring Operation: 66+24=90, Resulting Numbers: [10, 90] Generated Node #0,2,2: 84:[10, 90] Operation: 66+24=90 Moving to Node #0,2,0 Current State: 84:[10, 42], Operations: ['98-74=24', '66-24=42'] Exploring Operation: 10*42=420, Resulting Numbers: [420] 420,84 unequal: No Solution Exploring Operation: 10+42=52, Resulting Numbers: [52] 52,84 unequal: No Solution Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[10, 90], Operations: ['98-74=24', '66+24=90'] Exploring Operation: 10+90=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 90/10=9, Resulting Numbers: [9] 9,84 unequal: No Solution Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,84 unequal: No Solution Moving to Node #0,2,1 Current State: 84:[24, 76], Operations: ['98-74=24', '66+10=76'] Exploring Operation: 24+76=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 24*76=1824, Resulting Numbers: [1824] 1824,84 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 51, 59, 27, 1 ]
83
[ "51+59=110", "27*1=27", "110-27=83" ]
Current State: 83:[51, 59, 27, 1], Operations: [] Exploring Operation: 51+59=110, Resulting Numbers: [27, 1, 110] Generated Node #2: [27, 1, 110] from Operation: 51+59=110 Current State: 83:[27, 1, 110], Operations: ['51+59=110'] Exploring Operation: 27*1=27, Resulting Numbers: [110, 27] Generated Node #3: [110, 27] from Operation: 27*1=27 Current State: 83:[110, 27], Operations: ['51+59=110', '27*1=27'] Exploring Operation: 110-27=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[51, 59, 27, 1], Operations: [] Exploring Operation: 51+27=78, Resulting Numbers: [59, 1, 78] Generated Node #0,0: 83:[59, 1, 78] Operation: 51+27=78 Exploring Operation: 59+1=60, Resulting Numbers: [51, 27, 60] Generated Node #0,1: 83:[51, 27, 60] Operation: 59+1=60 Exploring Operation: 51+1=52, Resulting Numbers: [59, 27, 52] Generated Node #0,2: 83:[59, 27, 52] Operation: 51+1=52 Moving to Node #0,0 Current State: 83:[59, 1, 78], Operations: ['51+27=78'] Exploring Operation: 59+1=60, Resulting Numbers: [78, 60] Generated Node #0,0,0: 83:[78, 60] Operation: 59+1=60 Exploring Operation: 1+78=79, Resulting Numbers: [59, 79] Generated Node #0,0,1: 83:[59, 79] Operation: 1+78=79 Exploring Operation: 59*1=59, Resulting Numbers: [78, 59] Generated Node #0,0,2: 83:[78, 59] Operation: 59*1=59 Moving to Node #0,1 Current State: 83:[51, 27, 60], Operations: ['59+1=60'] Exploring Operation: 27+60=87, Resulting Numbers: [51, 87] Generated Node #0,1,0: 83:[51, 87] Operation: 27+60=87 Exploring Operation: 51-27=24, Resulting Numbers: [60, 24] Generated Node #0,1,1: 83:[60, 24] Operation: 51-27=24 Exploring Operation: 51+27=78, Resulting Numbers: [60, 78] Generated Node #0,1,2: 83:[60, 78] Operation: 51+27=78 Moving to Node #0,2 Current State: 83:[59, 27, 52], Operations: ['51+1=52'] Exploring Operation: 59-27=32, Resulting Numbers: [52, 32] Generated Node #0,2,0: 83:[52, 32] Operation: 59-27=32 Exploring Operation: 59+27=86, Resulting Numbers: [52, 86] Generated Node #0,2,1: 83:[52, 86] Operation: 59+27=86 Exploring Operation: 27+52=79, Resulting Numbers: [59, 79] Generated Node #0,2,2: 83:[59, 79] Operation: 27+52=79 Moving to Node #0,0,0 Current State: 83:[78, 60], Operations: ['51+27=78', '59+1=60'] Exploring Operation: 78*60=4680, Resulting Numbers: [4680] 4680,83 unequal: No Solution Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,83 unequal: No Solution Exploring Operation: 78+60=138, Resulting Numbers: [138] 138,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[59, 79], Operations: ['51+1=52', '27+52=79'] Exploring Operation: 59*79=4661, Resulting Numbers: [4661] 4661,83 unequal: No Solution Exploring Operation: 59+79=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 79-59=20, Resulting Numbers: [20] 20,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[59, 79], Operations: ['51+27=78', '1+78=79'] Exploring Operation: 79-59=20, Resulting Numbers: [20] 20,83 unequal: No Solution Exploring Operation: 59+79=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 59*79=4661, Resulting Numbers: [4661] 4661,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[60, 78], Operations: ['59+1=60', '51+27=78'] Exploring Operation: 60*78=4680, Resulting Numbers: [4680] 4680,83 unequal: No Solution Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,83 unequal: No Solution Exploring Operation: 60+78=138, Resulting Numbers: [138] 138,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[78, 59], Operations: ['51+27=78', '59*1=59'] Exploring Operation: 78*59=4602, Resulting Numbers: [4602] 4602,83 unequal: No Solution Exploring Operation: 78+59=137, Resulting Numbers: [137] 137,83 unequal: No Solution Exploring Operation: 78-59=19, Resulting Numbers: [19] 19,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[52, 86], Operations: ['51+1=52', '59+27=86'] Exploring Operation: 52+86=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 52*86=4472, Resulting Numbers: [4472] 4472,83 unequal: No Solution Exploring Operation: 86-52=34, Resulting Numbers: [34] 34,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[51, 87], Operations: ['59+1=60', '27+60=87'] Exploring Operation: 51+87=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 87-51=36, Resulting Numbers: [36] 36,83 unequal: No Solution Exploring Operation: 51*87=4437, Resulting Numbers: [4437] 4437,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[52, 32], Operations: ['51+1=52', '59-27=32'] Exploring Operation: 52+32=84, Resulting Numbers: [84] 84,83 unequal: No Solution Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,83 unequal: No Solution Exploring Operation: 52*32=1664, Resulting Numbers: [1664] 1664,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[60, 24], Operations: ['59+1=60', '51-27=24'] Exploring Operation: 60+24=84, Resulting Numbers: [84] 84,83 unequal: No Solution Exploring Operation: 60-24=36, Resulting Numbers: [36] 36,83 unequal: No Solution Exploring Operation: 60*24=1440, Resulting Numbers: [1440] 1440,83 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 87, 89, 33, 77 ]
55
[ "89-87=2", "33+77=110", "110/2=55" ]
Current State: 55:[87, 89, 33, 77], Operations: [] Exploring Operation: 89-87=2, Resulting Numbers: [33, 77, 2] Generated Node #2: [33, 77, 2] from Operation: 89-87=2 Current State: 55:[33, 77, 2], Operations: ['89-87=2'] Exploring Operation: 33+77=110, Resulting Numbers: [2, 110] Generated Node #3: [2, 110] from Operation: 33+77=110 Current State: 55:[2, 110], Operations: ['89-87=2', '33+77=110'] Exploring Operation: 110/2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[87, 89, 33, 77], Operations: [] Exploring Operation: 89-33=56, Resulting Numbers: [87, 77, 56] Generated Node #0,0: 55:[87, 77, 56] Operation: 89-33=56 Exploring Operation: 89-87=2, Resulting Numbers: [33, 77, 2] Generated Node #0,1: 55:[33, 77, 2] Operation: 89-87=2 Exploring Operation: 89-77=12, Resulting Numbers: [87, 33, 12] Generated Node #0,2: 55:[87, 33, 12] Operation: 89-77=12 Exploring Operation: 87-33=54, Resulting Numbers: [89, 77, 54] Generated Node #0,3: 55:[89, 77, 54] Operation: 87-33=54 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[33, 77, 2], Operations: ['89-87=2'] Exploring Operation: 33+2=35, Resulting Numbers: [77, 35] Generated Node #0,1,0: 55:[77, 35] Operation: 33+2=35 Exploring Operation: 33-2=31, Resulting Numbers: [77, 31] Generated Node #0,1,1: 55:[77, 31] Operation: 33-2=31 Exploring Operation: 33*2=66, Resulting Numbers: [77, 66] Generated Node #0,1,2: 55:[77, 66] Operation: 33*2=66 Exploring Operation: 77-33=44, Resulting Numbers: [2, 44] Generated Node #0,1,3: 55:[2, 44] Operation: 77-33=44 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 55:[2, 44], Operations: ['89-87=2', '77-33=44'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,55 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,55 unequal: No Solution Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,55 unequal: No Solution No 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: 55:[77, 66], Operations: ['89-87=2', '33*2=66'] Exploring Operation: 77-66=11, Resulting Numbers: [11] 11,55 unequal: No Solution Exploring Operation: 77+66=143, Resulting Numbers: [143] 143,55 unequal: No Solution Exploring Operation: 77*66=5082, Resulting Numbers: [5082] 5082,55 unequal: No Solution No 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: 55:[77, 35], Operations: ['89-87=2', '33+2=35'] Exploring Operation: 77*35=2695, Resulting Numbers: [2695] 2695,55 unequal: No Solution Exploring Operation: 77+35=112, Resulting Numbers: [112] 112,55 unequal: No Solution Exploring Operation: 77-35=42, Resulting Numbers: [42] 42,55 unequal: No Solution No 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: 55:[77, 31], Operations: ['89-87=2', '33-2=31'] Exploring Operation: 77-31=46, Resulting Numbers: [46] 46,55 unequal: No Solution Exploring Operation: 77+31=108, Resulting Numbers: [108] 108,55 unequal: No Solution Exploring Operation: 77*31=2387, Resulting Numbers: [2387] 2387,55 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: 55:[87, 77, 56], Operations: ['89-33=56'] Exploring Operation: 87-56=31, Resulting Numbers: [77, 31] Generated Node #0,0,0: 55:[77, 31] Operation: 87-56=31 Exploring Operation: 87+77=164, Resulting Numbers: [56, 164] Generated Node #0,0,1: 55:[56, 164] Operation: 87+77=164 Exploring Operation: 77-56=21, Resulting Numbers: [87, 21] Generated Node #0,0,2: 55:[87, 21] Operation: 77-56=21 Exploring Operation: 87-77=10, Resulting Numbers: [56, 10] Generated Node #0,0,3: 55:[56, 10] Operation: 87-77=10 Moving to Node #0,0,3 Current State: 55:[56, 10], Operations: ['89-33=56', '87-77=10'] Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,55 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,55 unequal: No Solution Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[87, 21], Operations: ['89-33=56', '77-56=21'] Exploring Operation: 87*21=1827, Resulting Numbers: [1827] 1827,55 unequal: No Solution Exploring Operation: 87-21=66, Resulting Numbers: [66] 66,55 unequal: No Solution Exploring Operation: 87+21=108, Resulting Numbers: [108] 108,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[77, 31], Operations: ['89-33=56', '87-56=31'] Exploring Operation: 77-31=46, Resulting Numbers: [46] 46,55 unequal: No Solution Exploring Operation: 77+31=108, Resulting Numbers: [108] 108,55 unequal: No Solution Exploring Operation: 77*31=2387, Resulting Numbers: [2387] 2387,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[56, 164], Operations: ['89-33=56', '87+77=164'] Exploring Operation: 56+164=220, Resulting Numbers: [220] 220,55 unequal: No Solution Exploring Operation: 164-56=108, Resulting Numbers: [108] 108,55 unequal: No Solution Exploring Operation: 56*164=9184, Resulting Numbers: [9184] 9184,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[87, 33, 12], Operations: ['89-77=12'] Exploring Operation: 33-12=21, Resulting Numbers: [87, 21] Generated Node #0,2,0: 55:[87, 21] Operation: 33-12=21 Exploring Operation: 87-12=75, Resulting Numbers: [33, 75] Generated Node #0,2,1: 55:[33, 75] Operation: 87-12=75 Exploring Operation: 33+12=45, Resulting Numbers: [87, 45] Generated Node #0,2,2: 55:[87, 45] Operation: 33+12=45 Exploring Operation: 87-33=54, Resulting Numbers: [12, 54] Generated Node #0,2,3: 55:[12, 54] Operation: 87-33=54 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 55:[12, 54], Operations: ['89-77=12', '87-33=54'] Exploring Operation: 12+54=66, Resulting Numbers: [66] 66,55 unequal: No Solution Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 12*54=648, Resulting Numbers: [648] 648,55 unequal: No Solution No 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: 55:[87, 21], Operations: ['89-77=12', '33-12=21'] Exploring Operation: 87+21=108, Resulting Numbers: [108] 108,55 unequal: No Solution Exploring Operation: 87*21=1827, Resulting Numbers: [1827] 1827,55 unequal: No Solution Exploring Operation: 87-21=66, Resulting Numbers: [66] 66,55 unequal: No Solution No 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: 55:[33, 75], Operations: ['89-77=12', '87-12=75'] Exploring Operation: 33*75=2475, Resulting Numbers: [2475] 2475,55 unequal: No Solution Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 33+75=108, Resulting Numbers: [108] 108,55 unequal: No Solution No 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: 55:[87, 45], Operations: ['89-77=12', '33+12=45'] Exploring Operation: 87+45=132, Resulting Numbers: [132] 132,55 unequal: No Solution Exploring Operation: 87*45=3915, Resulting Numbers: [3915] 3915,55 unequal: No Solution Exploring Operation: 87-45=42, Resulting Numbers: [42] 42,55 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: 55:[89, 77, 54], Operations: ['87-33=54'] Exploring Operation: 89-54=35, Resulting Numbers: [77, 35] Generated Node #0,3,0: 55:[77, 35] Operation: 89-54=35 Exploring Operation: 89-77=12, Resulting Numbers: [54, 12] Generated Node #0,3,1: 55:[54, 12] Operation: 89-77=12 Exploring Operation: 89+54=143, Resulting Numbers: [77, 143] Generated Node #0,3,2: 55:[77, 143] Operation: 89+54=143 Exploring Operation: 77-54=23, Resulting Numbers: [89, 23] Generated Node #0,3,3: 55:[89, 23] Operation: 77-54=23 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 55:[54, 12], Operations: ['87-33=54', '89-77=12'] Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,55 unequal: No Solution Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,55 unequal: No Solution No 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: 55:[77, 35], Operations: ['87-33=54', '89-54=35'] Exploring Operation: 77*35=2695, Resulting Numbers: [2695] 2695,55 unequal: No Solution Exploring Operation: 77-35=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 77+35=112, Resulting Numbers: [112] 112,55 unequal: No Solution No 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: 55:[89, 23], Operations: ['87-33=54', '77-54=23'] Exploring Operation: 89-23=66, Resulting Numbers: [66] 66,55 unequal: No Solution Exploring Operation: 89+23=112, Resulting Numbers: [112] 112,55 unequal: No Solution Exploring Operation: 89*23=2047, Resulting Numbers: [2047] 2047,55 unequal: No Solution No 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: 55:[77, 143], Operations: ['87-33=54', '89+54=143'] Exploring Operation: 143-77=66, Resulting Numbers: [66] 66,55 unequal: No Solution Exploring Operation: 77*143=11011, Resulting Numbers: [11011] 11011,55 unequal: No Solution Exploring Operation: 77+143=220, Resulting Numbers: [220] 220,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 45, 46, 49, 5 ]
54
[ "46-45=1", "49+5=54", "1*54=54" ]
Current State: 54:[45, 46, 49, 5], Operations: [] Exploring Operation: 46-45=1, Resulting Numbers: [49, 5, 1] Generated Node #2: [49, 5, 1] from Operation: 46-45=1 Current State: 54:[49, 5, 1], Operations: ['46-45=1'] Exploring Operation: 49+5=54, Resulting Numbers: [1, 54] Generated Node #3: [1, 54] from Operation: 49+5=54 Current State: 54:[1, 54], Operations: ['46-45=1', '49+5=54'] Exploring Operation: 1*54=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[45, 46, 49, 5], Operations: [] Exploring Operation: 46-45=1, Resulting Numbers: [49, 5, 1] Generated Node #0,0: 54:[49, 5, 1] Operation: 46-45=1 Exploring Operation: 49-45=4, Resulting Numbers: [46, 5, 4] Generated Node #0,1: 54:[46, 5, 4] Operation: 49-45=4 Exploring Operation: 49-46=3, Resulting Numbers: [45, 5, 3] Generated Node #0,2: 54:[45, 5, 3] Operation: 49-46=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[49, 5, 1], Operations: ['46-45=1'] Exploring Operation: 49+5=54, Resulting Numbers: [1, 54] Generated Node #0,0,0: 54:[1, 54] Operation: 49+5=54 Exploring Operation: 5+1=6, Resulting Numbers: [49, 6] Generated Node #0,0,1: 54:[49, 6] Operation: 5+1=6 Exploring Operation: 49+1=50, Resulting Numbers: [5, 50] Generated Node #0,0,2: 54:[5, 50] Operation: 49+1=50 Moving to Node #0,0,0 Current State: 54:[1, 54], Operations: ['46-45=1', '49+5=54'] Exploring Operation: 1*54=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[45, 46, 49, 5], Operations: [] Exploring Operation: 46-45=1, Resulting Numbers: [49, 5, 1] Generated Node #0,0: 54:[49, 5, 1] Operation: 46-45=1 Moving to Node #0,0 Current State: 54:[49, 5, 1], Operations: ['46-45=1'] Exploring Operation: 49+5=54, Resulting Numbers: [1, 54] Generated Node #0,0,0: 54:[1, 54] Operation: 49+5=54 Moving to Node #0,0,0 Current State: 54:[1, 54], Operations: ['46-45=1', '49+5=54'] Exploring Operation: 1*54=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 39, 77, 47, 50 ]
64
[ "50-47=3", "39/3=13", "77-13=64" ]
Current State: 64:[39, 77, 47, 50], Operations: [] Exploring Operation: 50-47=3, Resulting Numbers: [39, 77, 3] Generated Node #2: [39, 77, 3] from Operation: 50-47=3 Current State: 64:[39, 77, 3], Operations: ['50-47=3'] Exploring Operation: 39/3=13, Resulting Numbers: [77, 13] Generated Node #3: [77, 13] from Operation: 39/3=13 Current State: 64:[77, 13], Operations: ['50-47=3', '39/3=13'] Exploring Operation: 77-13=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[39, 77, 47, 50], Operations: [] Exploring Operation: 50-47=3, Resulting Numbers: [39, 77, 3] Generated Node #0,0: 64:[39, 77, 3] Operation: 50-47=3 Moving to Node #0,0 Current State: 64:[39, 77, 3], Operations: ['50-47=3'] Exploring Operation: 77-39=38, Resulting Numbers: [3, 38] Generated Node #0,0,0: 64:[3, 38] Operation: 77-39=38 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[3, 38], Operations: ['50-47=3', '77-39=38'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,64 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
[ 73, 32, 4, 27 ]
18
[ "73-32=41", "27-4=23", "41-23=18" ]
Current State: 18:[73, 32, 4, 27], Operations: [] Exploring Operation: 73-32=41, Resulting Numbers: [4, 27, 41] Generated Node #2: [4, 27, 41] from Operation: 73-32=41 Current State: 18:[4, 27, 41], Operations: ['73-32=41'] Exploring Operation: 27-4=23, Resulting Numbers: [41, 23] Generated Node #3: [41, 23] from Operation: 27-4=23 Current State: 18:[41, 23], Operations: ['73-32=41', '27-4=23'] Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[73, 32, 4, 27], Operations: [] Exploring Operation: 73-27=46, Resulting Numbers: [32, 4, 46] Generated Node #0,0: 18:[32, 4, 46] Operation: 73-27=46 Exploring Operation: 73-32=41, Resulting Numbers: [4, 27, 41] Generated Node #0,1: 18:[4, 27, 41] Operation: 73-32=41 Moving to Node #0,1 Current State: 18:[4, 27, 41], Operations: ['73-32=41'] Exploring Operation: 41-27=14, Resulting Numbers: [4, 14] Generated Node #0,1,0: 18:[4, 14] Operation: 41-27=14 Exploring Operation: 27-4=23, Resulting Numbers: [41, 23] Generated Node #0,1,1: 18:[41, 23] Operation: 27-4=23 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[4, 14], Operations: ['73-32=41', '41-27=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[73, 32, 4, 27], Operations: [] Exploring Operation: 73-32=41, Resulting Numbers: [4, 27, 41] Generated Node #0,1: 18:[4, 27, 41] Operation: 73-32=41 Moving to Node #0,1 Current State: 18:[4, 27, 41], Operations: ['73-32=41'] Exploring Operation: 41-27=14, Resulting Numbers: [4, 14] Generated Node #0,1,0: 18:[4, 14] Operation: 41-27=14 Moving to Node #0,1,0 Current State: 18:[4, 14], Operations: ['73-32=41', '41-27=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 98, 89, 39, 45 ]
54
[ "98-89=9", "45-39=6", "9*6=54" ]
Current State: 54:[98, 89, 39, 45], Operations: [] Exploring Operation: 98-89=9, Resulting Numbers: [39, 45, 9] Generated Node #2: [39, 45, 9] from Operation: 98-89=9 Current State: 54:[39, 45, 9], Operations: ['98-89=9'] Exploring Operation: 45-39=6, Resulting Numbers: [9, 6] Generated Node #3: [9, 6] from Operation: 45-39=6 Current State: 54:[9, 6], Operations: ['98-89=9', '45-39=6'] Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[98, 89, 39, 45], Operations: [] Exploring Operation: 98-89=9, Resulting Numbers: [39, 45, 9] Generated Node #0,0: 54:[39, 45, 9] Operation: 98-89=9 Exploring Operation: 98-39=59, Resulting Numbers: [89, 45, 59] Generated Node #0,1: 54:[89, 45, 59] Operation: 98-39=59 Exploring Operation: 98-45=53, Resulting Numbers: [89, 39, 53] Generated Node #0,2: 54:[89, 39, 53] Operation: 98-45=53 Moving to Node #0,0 Current State: 54:[39, 45, 9], Operations: ['98-89=9'] Exploring Operation: 45+9=54, Resulting Numbers: [39, 54] Generated Node #0,0,0: 54:[39, 54] Operation: 45+9=54 Exploring Operation: 45-39=6, Resulting Numbers: [9, 6] Generated Node #0,0,1: 54:[9, 6] Operation: 45-39=6 Exploring Operation: 39-9=30, Resulting Numbers: [45, 30] Generated Node #0,0,2: 54:[45, 30] Operation: 39-9=30 Moving to Node #0,2 Current State: 54:[89, 39, 53], Operations: ['98-45=53'] Exploring Operation: 89-53=36, Resulting Numbers: [39, 36] Generated Node #0,2,0: 54:[39, 36] Operation: 89-53=36 Exploring Operation: 89-39=50, Resulting Numbers: [53, 50] Generated Node #0,2,1: 54:[53, 50] Operation: 89-39=50 Exploring Operation: 53-39=14, Resulting Numbers: [89, 14] Generated Node #0,2,2: 54:[89, 14] Operation: 53-39=14 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 54:[53, 50], Operations: ['98-45=53', '89-39=50'] Exploring Operation: 53*50=2650, Resulting Numbers: [2650] 2650,54 unequal: No Solution Exploring Operation: 53+50=103, Resulting Numbers: [103] 103,54 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 54:[39, 36], Operations: ['98-45=53', '89-53=36'] Exploring Operation: 39*36=1404, Resulting Numbers: [1404] 1404,54 unequal: No Solution Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 39+36=75, Resulting Numbers: [75] 75,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 54:[89, 14], Operations: ['98-45=53', '53-39=14'] Exploring Operation: 89-14=75, Resulting Numbers: [75] 75,54 unequal: No Solution Exploring Operation: 89+14=103, Resulting Numbers: [103] 103,54 unequal: No Solution Exploring Operation: 89*14=1246, Resulting Numbers: [1246] 1246,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 54:[89, 45, 59], Operations: ['98-39=59'] Exploring Operation: 89-59=30, Resulting Numbers: [45, 30] Generated Node #0,1,0: 54:[45, 30] Operation: 89-59=30 Exploring Operation: 89-45=44, Resulting Numbers: [59, 44] Generated Node #0,1,1: 54:[59, 44] Operation: 89-45=44 Exploring Operation: 59-45=14, Resulting Numbers: [89, 14] Generated Node #0,1,2: 54:[89, 14] Operation: 59-45=14 Moving to Node #0,0,1 Current State: 54:[9, 6], Operations: ['98-89=9', '45-39=6'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[98, 89, 39, 45], Operations: [] Exploring Operation: 98-89=9, Resulting Numbers: [39, 45, 9] Generated Node #0,0: 54:[39, 45, 9] Operation: 98-89=9 Moving to Node #0,0 Current State: 54:[39, 45, 9], Operations: ['98-89=9'] Exploring Operation: 45-39=6, Resulting Numbers: [9, 6] Generated Node #0,0,1: 54:[9, 6] Operation: 45-39=6 Moving to Node #0,0,1 Current State: 54:[9, 6], Operations: ['98-89=9', '45-39=6'] Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
0.976563
hs_3
sum_heuristic
[ 91, 37, 56, 33 ]
39
[ "91+37=128", "56+33=89", "128-89=39" ]
Current State: 39:[91, 37, 56, 33], Operations: [] Exploring Operation: 91+37=128, Resulting Numbers: [56, 33, 128] Generated Node #2: [56, 33, 128] from Operation: 91+37=128 Current State: 39:[56, 33, 128], Operations: ['91+37=128'] Exploring Operation: 56+33=89, Resulting Numbers: [128, 89] Generated Node #3: [128, 89] from Operation: 56+33=89 Current State: 39:[128, 89], Operations: ['91+37=128', '56+33=89'] Exploring Operation: 128-89=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[91, 37, 56, 33], Operations: [] Exploring Operation: 91-37=54, Resulting Numbers: [56, 33, 54] Generated Node #0,0: 39:[56, 33, 54] Operation: 91-37=54 Exploring Operation: 91-33=58, Resulting Numbers: [37, 56, 58] Generated Node #0,1: 39:[37, 56, 58] Operation: 91-33=58 Exploring Operation: 56-37=19, Resulting Numbers: [91, 33, 19] Generated Node #0,2: 39:[91, 33, 19] Operation: 56-37=19 Exploring Operation: 91-56=35, Resulting Numbers: [37, 33, 35] Generated Node #0,3: 39:[37, 33, 35] Operation: 91-56=35 Exploring Operation: 56-33=23, Resulting Numbers: [91, 37, 23] Generated Node #0,4: 39:[91, 37, 23] Operation: 56-33=23 Start Sub Search at level 1: Moving to Node #0,3 Current State: 39:[37, 33, 35], Operations: ['91-56=35'] Exploring Operation: 37+33=70, Resulting Numbers: [35, 70] Generated Node #0,3,0: 39:[35, 70] Operation: 37+33=70 Exploring Operation: 35-33=2, Resulting Numbers: [37, 2] Generated Node #0,3,1: 39:[37, 2] Operation: 35-33=2 Exploring Operation: 37-35=2, Resulting Numbers: [33, 2] Generated Node #0,3,2: 39:[33, 2] Operation: 37-35=2 Exploring Operation: 37-33=4, Resulting Numbers: [35, 4] Generated Node #0,3,3: 39:[35, 4] Operation: 37-33=4 Exploring Operation: 33+35=68, Resulting Numbers: [37, 68] Generated Node #0,3,4: 39:[37, 68] Operation: 33+35=68 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 39:[37, 2], Operations: ['91-56=35', '35-33=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[91, 37, 56, 33], Operations: [] Exploring Operation: 91-56=35, Resulting Numbers: [37, 33, 35] Generated Node #0,3: 39:[37, 33, 35] Operation: 91-56=35 Moving to Node #0,3 Current State: 39:[37, 33, 35], Operations: ['91-56=35'] Exploring Operation: 35-33=2, Resulting Numbers: [37, 2] Generated Node #0,3,1: 39:[37, 2] Operation: 35-33=2 Moving to Node #0,3,1 Current State: 39:[37, 2], Operations: ['91-56=35', '35-33=2'] Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 84, 42, 81, 69 ]
55
[ "84-81=3", "42/3=14", "69-14=55" ]
Current State: 55:[84, 42, 81, 69], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [42, 69, 3] Generated Node #2: [42, 69, 3] from Operation: 84-81=3 Current State: 55:[42, 69, 3], Operations: ['84-81=3'] Exploring Operation: 42/3=14, Resulting Numbers: [69, 14] Generated Node #3: [69, 14] from Operation: 42/3=14 Current State: 55:[69, 14], Operations: ['84-81=3', '42/3=14'] Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[84, 42, 81, 69], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [42, 69, 3] Generated Node #0,0: 55:[42, 69, 3] Operation: 84-81=3 Exploring Operation: 84/42=2, Resulting Numbers: [81, 69, 2] Generated Node #0,1: 55:[81, 69, 2] Operation: 84/42=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[42, 69, 3], Operations: ['84-81=3'] Exploring Operation: 42/3=14, Resulting Numbers: [69, 14] Generated Node #0,0,0: 55:[69, 14] Operation: 42/3=14 Exploring Operation: 69-42=27, Resulting Numbers: [3, 27] Generated Node #0,0,1: 55:[3, 27] Operation: 69-42=27 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[69, 14], Operations: ['84-81=3', '42/3=14'] Exploring Operation: 69+14=83, Resulting Numbers: [83] 83,55 unequal: No Solution Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[84, 42, 81, 69], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [42, 69, 3] Generated Node #0,0: 55:[42, 69, 3] Operation: 84-81=3 Moving to Node #0,0 Current State: 55:[42, 69, 3], Operations: ['84-81=3'] Exploring Operation: 42/3=14, Resulting Numbers: [69, 14] Generated Node #0,0,0: 55:[69, 14] Operation: 42/3=14 Moving to Node #0,0,0 Current State: 55:[69, 14], Operations: ['84-81=3', '42/3=14'] Exploring Operation: 69-14=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
[ 47, 15, 78, 31 ]
78
[ "47-15=32", "32-31=1", "78*1=78" ]
Current State: 78:[47, 15, 78, 31], Operations: [] Exploring Operation: 47-15=32, Resulting Numbers: [78, 31, 32] Generated Node #2: [78, 31, 32] from Operation: 47-15=32 Current State: 78:[78, 31, 32], Operations: ['47-15=32'] Exploring Operation: 32-31=1, Resulting Numbers: [78, 1] Generated Node #3: [78, 1] from Operation: 32-31=1 Current State: 78:[78, 1], Operations: ['47-15=32', '32-31=1'] Exploring Operation: 78*1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[47, 15, 78, 31], Operations: [] Exploring Operation: 47-31=16, Resulting Numbers: [15, 78, 16] Generated Node #0,0: 78:[15, 78, 16] Operation: 47-31=16 Exploring Operation: 47+31=78, Resulting Numbers: [15, 78, 78] Generated Node #0,1: 78:[15, 78, 78] Operation: 47+31=78 Moving to Node #0,1 Current State: 78:[15, 78, 78], Operations: ['47+31=78'] Exploring Operation: 78/78=1, Resulting Numbers: [15, 1] Generated Node #0,1,0: 78:[15, 1] Operation: 78/78=1 Exploring Operation: 78-78=0, Resulting Numbers: [15, 0] Generated Node #0,1,1: 78:[15, 0] Operation: 78-78=0 Moving to Node #0,0 Current State: 78:[15, 78, 16], Operations: ['47-31=16'] Exploring Operation: 16-15=1, Resulting Numbers: [78, 1] Generated Node #0,0,0: 78:[78, 1] Operation: 16-15=1 Exploring Operation: 15+16=31, Resulting Numbers: [78, 31] Generated Node #0,0,1: 78:[78, 31] Operation: 15+16=31 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[78, 1], Operations: ['47-31=16', '16-15=1'] Exploring Operation: 78*1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[47, 15, 78, 31], Operations: [] Exploring Operation: 47-31=16, Resulting Numbers: [15, 78, 16] Generated Node #0,0: 78:[15, 78, 16] Operation: 47-31=16 Moving to Node #0,0 Current State: 78:[15, 78, 16], Operations: ['47-31=16'] Exploring Operation: 16-15=1, Resulting Numbers: [78, 1] Generated Node #0,0,0: 78:[78, 1] Operation: 16-15=1 Moving to Node #0,0,0 Current State: 78:[78, 1], Operations: ['47-31=16', '16-15=1'] Exploring Operation: 78*1=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 2, 3, 7, 22 ]
96
[ "2+22=24", "7-3=4", "24*4=96" ]
Current State: 96:[2, 3, 7, 22], Operations: [] Exploring Operation: 2+22=24, Resulting Numbers: [3, 7, 24] Generated Node #2: [3, 7, 24] from Operation: 2+22=24 Current State: 96:[3, 7, 24], Operations: ['2+22=24'] Exploring Operation: 7-3=4, Resulting Numbers: [24, 4] Generated Node #3: [24, 4] from Operation: 7-3=4 Current State: 96:[24, 4], Operations: ['2+22=24', '7-3=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[2, 3, 7, 22], Operations: [] Exploring Operation: 22-7=15, Resulting Numbers: [2, 3, 15] Generated Node #0,0: 96:[2, 3, 15] Operation: 22-7=15 Exploring Operation: 2+22=24, Resulting Numbers: [3, 7, 24] Generated Node #0,1: 96:[3, 7, 24] Operation: 2+22=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[2, 3, 15], Operations: ['22-7=15'] Exploring Operation: 2*3=6, Resulting Numbers: [15, 6] Generated Node #0,0,0: 96:[15, 6] Operation: 2*3=6 Exploring Operation: 15-3=12, Resulting Numbers: [2, 12] Generated Node #0,0,1: 96:[2, 12] Operation: 15-3=12 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 96:[2, 12], Operations: ['22-7=15', '15-3=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,96 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,96 unequal: No Solution No 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: 96:[15, 6], Operations: ['22-7=15', '2*3=6'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,96 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,96 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: 96:[3, 7, 24], Operations: ['2+22=24'] Exploring Operation: 24/3=8, Resulting Numbers: [7, 8] Generated Node #0,1,0: 96:[7, 8] Operation: 24/3=8 Exploring Operation: 7-3=4, Resulting Numbers: [24, 4] Generated Node #0,1,1: 96:[24, 4] Operation: 7-3=4 Moving to Node #0,1,1 Current State: 96:[24, 4], Operations: ['2+22=24', '7-3=4'] Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,96 unequal: No Solution Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[2, 3, 7, 22], Operations: [] Exploring Operation: 2+22=24, Resulting Numbers: [3, 7, 24] Generated Node #0,1: 96:[3, 7, 24] Operation: 2+22=24 Moving to Node #0,1 Current State: 96:[3, 7, 24], Operations: ['2+22=24'] Exploring Operation: 7-3=4, Resulting Numbers: [24, 4] Generated Node #0,1,1: 96:[24, 4] Operation: 7-3=4 Moving to Node #0,1,1 Current State: 96:[24, 4], Operations: ['2+22=24', '7-3=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 78, 65, 70, 24 ]
59
[ "78-65=13", "70-24=46", "13+46=59" ]
Current State: 59:[78, 65, 70, 24], Operations: [] Exploring Operation: 78-65=13, Resulting Numbers: [70, 24, 13] Generated Node #2: [70, 24, 13] from Operation: 78-65=13 Current State: 59:[70, 24, 13], Operations: ['78-65=13'] Exploring Operation: 70-24=46, Resulting Numbers: [13, 46] Generated Node #3: [13, 46] from Operation: 70-24=46 Current State: 59:[13, 46], Operations: ['78-65=13', '70-24=46'] Exploring Operation: 13+46=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[78, 65, 70, 24], Operations: [] Exploring Operation: 65+24=89, Resulting Numbers: [78, 70, 89] Generated Node #0,0: 59:[78, 70, 89] Operation: 65+24=89 Exploring Operation: 78-24=54, Resulting Numbers: [65, 70, 54] Generated Node #0,1: 59:[65, 70, 54] Operation: 78-24=54 Exploring Operation: 78+24=102, Resulting Numbers: [65, 70, 102] Generated Node #0,2: 59:[65, 70, 102] Operation: 78+24=102 Exploring Operation: 70-24=46, Resulting Numbers: [78, 65, 46] Generated Node #0,3: 59:[78, 65, 46] Operation: 70-24=46 Exploring Operation: 65-24=41, Resulting Numbers: [78, 70, 41] Generated Node #0,4: 59:[78, 70, 41] Operation: 65-24=41 Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[65, 70, 54], Operations: ['78-24=54'] Exploring Operation: 65-54=11, Resulting Numbers: [70, 11] Generated Node #0,1,0: 59:[70, 11] Operation: 65-54=11 Exploring Operation: 70-65=5, Resulting Numbers: [54, 5] Generated Node #0,1,1: 59:[54, 5] Operation: 70-65=5 Exploring Operation: 70+54=124, Resulting Numbers: [65, 124] Generated Node #0,1,2: 59:[65, 124] Operation: 70+54=124 Exploring Operation: 65+54=119, Resulting Numbers: [70, 119] Generated Node #0,1,3: 59:[70, 119] Operation: 65+54=119 Exploring Operation: 70-54=16, Resulting Numbers: [65, 16] Generated Node #0,1,4: 59:[65, 16] Operation: 70-54=16 Moving to Node #0,1,4 Current State: 59:[65, 16], Operations: ['78-24=54', '70-54=16'] Exploring Operation: 65+16=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 65*16=1040, Resulting Numbers: [1040] 1040,59 unequal: No Solution Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[54, 5], Operations: ['78-24=54', '70-65=5'] Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,59 unequal: No Solution Exploring Operation: 54+5=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[78, 65, 70, 24], Operations: [] Exploring Operation: 78-24=54, Resulting Numbers: [65, 70, 54] Generated Node #0,1: 59:[65, 70, 54] Operation: 78-24=54 Moving to Node #0,1 Current State: 59:[65, 70, 54], Operations: ['78-24=54'] Exploring Operation: 70-65=5, Resulting Numbers: [54, 5] Generated Node #0,1,1: 59:[54, 5] Operation: 70-65=5 Moving to Node #0,1,1 Current State: 59:[54, 5], Operations: ['78-24=54', '70-65=5'] Exploring Operation: 54+5=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 36, 67, 21, 90 ]
61
[ "36-21=15", "90/15=6", "67-6=61" ]
Current State: 61:[36, 67, 21, 90], Operations: [] Exploring Operation: 36-21=15, Resulting Numbers: [67, 90, 15] Generated Node #2: [67, 90, 15] from Operation: 36-21=15 Current State: 61:[67, 90, 15], Operations: ['36-21=15'] Exploring Operation: 90/15=6, Resulting Numbers: [67, 6] Generated Node #3: [67, 6] from Operation: 90/15=6 Current State: 61:[67, 6], Operations: ['36-21=15', '90/15=6'] Exploring Operation: 67-6=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[36, 67, 21, 90], Operations: [] Exploring Operation: 36+21=57, Resulting Numbers: [67, 90, 57] Generated Node #0,0: 61:[67, 90, 57] Operation: 36+21=57 Exploring Operation: 67-21=46, Resulting Numbers: [36, 90, 46] Generated Node #0,1: 61:[36, 90, 46] Operation: 67-21=46 Exploring Operation: 90-36=54, Resulting Numbers: [67, 21, 54] Generated Node #0,2: 61:[67, 21, 54] Operation: 90-36=54 Exploring Operation: 90-21=69, Resulting Numbers: [36, 67, 69] Generated Node #0,3: 61:[36, 67, 69] Operation: 90-21=69 Exploring Operation: 36-21=15, Resulting Numbers: [67, 90, 15] Generated Node #0,4: 61:[67, 90, 15] Operation: 36-21=15 Moving to Node #0,0 Current State: 61:[67, 90, 57], Operations: ['36+21=57'] Exploring Operation: 67-57=10, Resulting Numbers: [90, 10] Generated Node #0,0,0: 61:[90, 10] Operation: 67-57=10 Exploring Operation: 90+57=147, Resulting Numbers: [67, 147] Generated Node #0,0,1: 61:[67, 147] Operation: 90+57=147 Exploring Operation: 90-57=33, Resulting Numbers: [67, 33] Generated Node #0,0,2: 61:[67, 33] Operation: 90-57=33 Exploring Operation: 90-67=23, Resulting Numbers: [57, 23] Generated Node #0,0,3: 61:[57, 23] Operation: 90-67=23 Exploring Operation: 67+57=124, Resulting Numbers: [90, 124] Generated Node #0,0,4: 61:[90, 124] Operation: 67+57=124 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 61:[67, 33], Operations: ['36+21=57', '90-57=33'] Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 67*33=2211, Resulting Numbers: [2211] 2211,61 unequal: No Solution Exploring Operation: 67+33=100, Resulting Numbers: [100] 100,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 61:[57, 23], Operations: ['36+21=57', '90-67=23'] Exploring Operation: 57+23=80, Resulting Numbers: [80] 80,61 unequal: No Solution Exploring Operation: 57*23=1311, Resulting Numbers: [1311] 1311,61 unequal: No Solution Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[90, 10], Operations: ['36+21=57', '67-57=10'] Exploring Operation: 90/10=9, Resulting Numbers: [9] 9,61 unequal: No Solution Exploring Operation: 90*10=900, Resulting Numbers: [900] 900,61 unequal: No Solution Exploring Operation: 90+10=100, Resulting Numbers: [100] 100,61 unequal: No Solution Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[67, 147], Operations: ['36+21=57', '90+57=147'] Exploring Operation: 67*147=9849, Resulting Numbers: [9849] 9849,61 unequal: No Solution Exploring Operation: 147-67=80, Resulting Numbers: [80] 80,61 unequal: No Solution Exploring Operation: 67+147=214, Resulting Numbers: [214] 214,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 61:[90, 124], Operations: ['36+21=57', '67+57=124'] Exploring Operation: 124-90=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 90+124=214, Resulting Numbers: [214] 214,61 unequal: No Solution Exploring Operation: 90*124=11160, Resulting Numbers: [11160] 11160,61 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: 61:[36, 67, 69], Operations: ['90-21=69'] Exploring Operation: 36+67=103, Resulting Numbers: [69, 103] Generated Node #0,3,0: 61:[69, 103] Operation: 36+67=103 Exploring Operation: 36+69=105, Resulting Numbers: [67, 105] Generated Node #0,3,1: 61:[67, 105] Operation: 36+69=105 Exploring Operation: 67-36=31, Resulting Numbers: [69, 31] Generated Node #0,3,2: 61:[69, 31] Operation: 67-36=31 Exploring Operation: 69-36=33, Resulting Numbers: [67, 33] Generated Node #0,3,3: 61:[67, 33] Operation: 69-36=33 Exploring Operation: 69-67=2, Resulting Numbers: [36, 2] Generated Node #0,3,4: 61:[36, 2] Operation: 69-67=2 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 61:[67, 33], Operations: ['90-21=69', '69-36=33'] Exploring Operation: 67*33=2211, Resulting Numbers: [2211] 2211,61 unequal: No Solution Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 67+33=100, Resulting Numbers: [100] 100,61 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 #0,3,2 Current State: 61:[69, 31], Operations: ['90-21=69', '67-36=31'] Exploring Operation: 69-31=38, Resulting Numbers: [38] 38,61 unequal: No Solution Exploring Operation: 69*31=2139, Resulting Numbers: [2139] 2139,61 unequal: No Solution Exploring Operation: 69+31=100, Resulting Numbers: [100] 100,61 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 #0,3,0 Current State: 61:[69, 103], Operations: ['90-21=69', '36+67=103'] Exploring Operation: 69+103=172, Resulting Numbers: [172] 172,61 unequal: No Solution Exploring Operation: 103-69=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 69*103=7107, Resulting Numbers: [7107] 7107,61 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 #0,3,1 Current State: 61:[67, 105], Operations: ['90-21=69', '36+69=105'] Exploring Operation: 105-67=38, Resulting Numbers: [38] 38,61 unequal: No Solution Exploring Operation: 67*105=7035, Resulting Numbers: [7035] 7035,61 unequal: No Solution Exploring Operation: 67+105=172, Resulting Numbers: [172] 172,61 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 #0,3,4 Current State: 61:[36, 2], Operations: ['90-21=69', '69-67=2'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 36*2=72, Resulting Numbers: [72] 72,61 unequal: No Solution Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,61 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 61:[67, 21, 54], Operations: ['90-36=54'] Exploring Operation: 67-21=46, Resulting Numbers: [54, 46] Generated Node #0,2,0: 61:[54, 46] Operation: 67-21=46 Exploring Operation: 67+21=88, Resulting Numbers: [54, 88] Generated Node #0,2,1: 61:[54, 88] Operation: 67+21=88 Exploring Operation: 67-54=13, Resulting Numbers: [21, 13] Generated Node #0,2,2: 61:[21, 13] Operation: 67-54=13 Exploring Operation: 21+54=75, Resulting Numbers: [67, 75] Generated Node #0,2,3: 61:[67, 75] Operation: 21+54=75 Exploring Operation: 54-21=33, Resulting Numbers: [67, 33] Generated Node #0,2,4: 61:[67, 33] Operation: 54-21=33 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 61:[67, 75], Operations: ['90-36=54', '21+54=75'] Exploring Operation: 75-67=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 67+75=142, Resulting Numbers: [142] 142,61 unequal: No Solution Exploring Operation: 67*75=5025, Resulting Numbers: [5025] 5025,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[54, 46], Operations: ['90-36=54', '67-21=46'] Exploring Operation: 54+46=100, Resulting Numbers: [100] 100,61 unequal: No Solution Exploring Operation: 54*46=2484, Resulting Numbers: [2484] 2484,61 unequal: No Solution Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,61 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 #0,2,1 Current State: 61:[54, 88], Operations: ['90-36=54', '67+21=88'] Exploring Operation: 54*88=4752, Resulting Numbers: [4752] 4752,61 unequal: No Solution Exploring Operation: 88-54=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 54+88=142, Resulting Numbers: [142] 142,61 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 #0,2,4 Current State: 61:[67, 33], Operations: ['90-36=54', '54-21=33'] Exploring Operation: 67+33=100, Resulting Numbers: [100] 100,61 unequal: No Solution Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 67*33=2211, Resulting Numbers: [2211] 2211,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 61:[21, 13], Operations: ['90-36=54', '67-54=13'] Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 21+13=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 21*13=273, Resulting Numbers: [273] 273,61 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: 61:[36, 90, 46], Operations: ['67-21=46'] Exploring Operation: 36+46=82, Resulting Numbers: [90, 82] Generated Node #0,1,0: 61:[90, 82] Operation: 36+46=82 Exploring Operation: 90-46=44, Resulting Numbers: [36, 44] Generated Node #0,1,1: 61:[36, 44] Operation: 90-46=44 Exploring Operation: 36+90=126, Resulting Numbers: [46, 126] Generated Node #0,1,2: 61:[46, 126] Operation: 36+90=126 Exploring Operation: 90-36=54, Resulting Numbers: [46, 54] Generated Node #0,1,3: 61:[46, 54] Operation: 90-36=54 Exploring Operation: 46-36=10, Resulting Numbers: [90, 10] Generated Node #0,1,4: 61:[90, 10] Operation: 46-36=10 Moving to Node #0,4 Current State: 61:[67, 90, 15], Operations: ['36-21=15'] Exploring Operation: 90/15=6, Resulting Numbers: [67, 6] Generated Node #0,4,0: 61:[67, 6] Operation: 90/15=6 Exploring Operation: 67+15=82, Resulting Numbers: [90, 82] Generated Node #0,4,1: 61:[90, 82] Operation: 67+15=82 Exploring Operation: 67-15=52, Resulting Numbers: [90, 52] Generated Node #0,4,2: 61:[90, 52] Operation: 67-15=52 Exploring Operation: 90-15=75, Resulting Numbers: [67, 75] Generated Node #0,4,3: 61:[67, 75] Operation: 90-15=75 Exploring Operation: 90+15=105, Resulting Numbers: [67, 105] Generated Node #0,4,4: 61:[67, 105] Operation: 90+15=105 Moving to Node #0,4,3 Current State: 61:[67, 75], Operations: ['36-21=15', '90-15=75'] Exploring Operation: 75-67=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 67+75=142, Resulting Numbers: [142] 142,61 unequal: No Solution Exploring Operation: 67*75=5025, Resulting Numbers: [5025] 5025,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[46, 54], Operations: ['67-21=46', '90-36=54'] Exploring Operation: 46+54=100, Resulting Numbers: [100] 100,61 unequal: No Solution Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 46*54=2484, Resulting Numbers: [2484] 2484,61 unequal: No Solution Moving to Node #0,4,2 Current State: 61:[90, 52], Operations: ['36-21=15', '67-15=52'] Exploring Operation: 90*52=4680, Resulting Numbers: [4680] 4680,61 unequal: No Solution Exploring Operation: 90+52=142, Resulting Numbers: [142] 142,61 unequal: No Solution Exploring Operation: 90-52=38, Resulting Numbers: [38] 38,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[36, 44], Operations: ['67-21=46', '90-46=44'] Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 36*44=1584, Resulting Numbers: [1584] 1584,61 unequal: No Solution Exploring Operation: 36+44=80, Resulting Numbers: [80] 80,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[90, 82], Operations: ['67-21=46', '36+46=82'] Exploring Operation: 90+82=172, Resulting Numbers: [172] 172,61 unequal: No Solution Exploring Operation: 90-82=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 90*82=7380, Resulting Numbers: [7380] 7380,61 unequal: No Solution Moving to Node #0,4,4 Current State: 61:[67, 105], Operations: ['36-21=15', '90+15=105'] Exploring Operation: 67+105=172, Resulting Numbers: [172] 172,61 unequal: No Solution Exploring Operation: 105-67=38, Resulting Numbers: [38] 38,61 unequal: No Solution Exploring Operation: 67*105=7035, Resulting Numbers: [7035] 7035,61 unequal: No Solution Moving to Node #0,4,1 Current State: 61:[90, 82], Operations: ['36-21=15', '67+15=82'] Exploring Operation: 90*82=7380, Resulting Numbers: [7380] 7380,61 unequal: No Solution Exploring Operation: 90+82=172, Resulting Numbers: [172] 172,61 unequal: No Solution Exploring Operation: 90-82=8, Resulting Numbers: [8] 8,61 unequal: No Solution Moving to Node #0,4,0 Current State: 61:[67, 6], Operations: ['36-21=15', '90/15=6'] Exploring Operation: 67*6=402, Resulting Numbers: [402] 402,61 unequal: No Solution Exploring Operation: 67+6=73, Resulting Numbers: [73] 73,61 unequal: No Solution Exploring Operation: 67-6=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[36, 67, 21, 90], Operations: [] Exploring Operation: 36-21=15, Resulting Numbers: [67, 90, 15] Generated Node #0,4: 61:[67, 90, 15] Operation: 36-21=15 Moving to Node #0,4 Current State: 61:[67, 90, 15], Operations: ['36-21=15'] Exploring Operation: 90/15=6, Resulting Numbers: [67, 6] Generated Node #0,4,0: 61:[67, 6] Operation: 90/15=6 Moving to Node #0,4,0 Current State: 61:[67, 6], Operations: ['36-21=15', '90/15=6'] Exploring Operation: 67-6=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
0.908854
hs_5
sum_heuristic
[ 34, 83, 60, 21 ]
17
[ "83-60=23", "23-21=2", "34/2=17" ]
Current State: 17:[34, 83, 60, 21], Operations: [] Exploring Operation: 83-60=23, Resulting Numbers: [34, 21, 23] Generated Node #2: [34, 21, 23] from Operation: 83-60=23 Current State: 17:[34, 21, 23], Operations: ['83-60=23'] Exploring Operation: 23-21=2, Resulting Numbers: [34, 2] Generated Node #3: [34, 2] from Operation: 23-21=2 Current State: 17:[34, 2], Operations: ['83-60=23', '23-21=2'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[34, 83, 60, 21], Operations: [] Exploring Operation: 83-21=62, Resulting Numbers: [34, 60, 62] Generated Node #0,0: 17:[34, 60, 62] Operation: 83-21=62 Exploring Operation: 60-34=26, Resulting Numbers: [83, 21, 26] Generated Node #0,1: 17:[83, 21, 26] Operation: 60-34=26 Exploring Operation: 83-60=23, Resulting Numbers: [34, 21, 23] Generated Node #0,2: 17:[34, 21, 23] Operation: 83-60=23 Exploring Operation: 83-34=49, Resulting Numbers: [60, 21, 49] Generated Node #0,3: 17:[60, 21, 49] Operation: 83-34=49 Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[34, 21, 23], Operations: ['83-60=23'] Exploring Operation: 34-23=11, Resulting Numbers: [21, 11] Generated Node #0,2,0: 17:[21, 11] Operation: 34-23=11 Exploring Operation: 34+21=55, Resulting Numbers: [23, 55] Generated Node #0,2,1: 17:[23, 55] Operation: 34+21=55 Exploring Operation: 23-21=2, Resulting Numbers: [34, 2] Generated Node #0,2,2: 17:[34, 2] Operation: 23-21=2 Exploring Operation: 34-21=13, Resulting Numbers: [23, 13] Generated Node #0,2,3: 17:[23, 13] Operation: 34-21=13 Moving to Node #0,2,0 Current State: 17:[21, 11], Operations: ['83-60=23', '34-23=11'] Exploring Operation: 21+11=32, Resulting Numbers: [32] 32,17 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,17 unequal: No Solution Exploring Operation: 21*11=231, Resulting Numbers: [231] 231,17 unequal: No Solution Moving to Node #0,2,3 Current State: 17:[23, 13], Operations: ['83-60=23', '34-21=13'] Exploring Operation: 23*13=299, Resulting Numbers: [299] 299,17 unequal: No Solution Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,17 unequal: No Solution Exploring Operation: 23+13=36, Resulting Numbers: [36] 36,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[34, 2], Operations: ['83-60=23', '23-21=2'] Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,17 unequal: No Solution Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,17 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[34, 83, 60, 21], Operations: [] Exploring Operation: 83-60=23, Resulting Numbers: [34, 21, 23] Generated Node #0,2: 17:[34, 21, 23] Operation: 83-60=23 Moving to Node #0,2 Current State: 17:[34, 21, 23], Operations: ['83-60=23'] Exploring Operation: 23-21=2, Resulting Numbers: [34, 2] Generated Node #0,2,2: 17:[34, 2] Operation: 23-21=2 Moving to Node #0,2,2 Current State: 17:[34, 2], Operations: ['83-60=23', '23-21=2'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 8, 58, 62, 88 ]
14
[ "62-58=4", "88/4=22", "22-8=14" ]
Current State: 14:[8, 58, 62, 88], Operations: [] Exploring Operation: 62-58=4, Resulting Numbers: [8, 88, 4] Generated Node #2: [8, 88, 4] from Operation: 62-58=4 Current State: 14:[8, 88, 4], Operations: ['62-58=4'] Exploring Operation: 88/4=22, Resulting Numbers: [8, 22] Generated Node #3: [8, 22] from Operation: 88/4=22 Current State: 14:[8, 22], Operations: ['62-58=4', '88/4=22'] Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[8, 58, 62, 88], Operations: [] Exploring Operation: 88-62=26, Resulting Numbers: [8, 58, 26] Generated Node #0,0: 14:[8, 58, 26] Operation: 88-62=26 Moving to Node #0,0 Current State: 14:[8, 58, 26], Operations: ['88-62=26'] Exploring Operation: 58-26=32, Resulting Numbers: [8, 32] Generated Node #0,0,0: 14:[8, 32] Operation: 58-26=32 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[8, 32], Operations: ['88-62=26', '58-26=32'] Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,14 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
[ 95, 23, 50, 24 ]
47
[ "95-23=72", "72/24=3", "50-3=47" ]
Current State: 47:[95, 23, 50, 24], Operations: [] Exploring Operation: 95-23=72, Resulting Numbers: [50, 24, 72] Generated Node #2: [50, 24, 72] from Operation: 95-23=72 Current State: 47:[50, 24, 72], Operations: ['95-23=72'] Exploring Operation: 72/24=3, Resulting Numbers: [50, 3] Generated Node #3: [50, 3] from Operation: 72/24=3 Current State: 47:[50, 3], Operations: ['95-23=72', '72/24=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[95, 23, 50, 24], Operations: [] Exploring Operation: 95-50=45, Resulting Numbers: [23, 24, 45] Generated Node #0,0: 47:[23, 24, 45] Operation: 95-50=45 Exploring Operation: 95-23=72, Resulting Numbers: [50, 24, 72] Generated Node #0,1: 47:[50, 24, 72] Operation: 95-23=72 Exploring Operation: 95-24=71, Resulting Numbers: [23, 50, 71] Generated Node #0,2: 47:[23, 50, 71] Operation: 95-24=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[23, 24, 45], Operations: ['95-50=45'] Exploring Operation: 24+45=69, Resulting Numbers: [23, 69] Generated Node #0,0,0: 47:[23, 69] Operation: 24+45=69 Exploring Operation: 23+45=68, Resulting Numbers: [24, 68] Generated Node #0,0,1: 47:[24, 68] Operation: 23+45=68 Exploring Operation: 23+24=47, Resulting Numbers: [45, 47] Generated Node #0,0,2: 47:[45, 47] Operation: 23+24=47 Moving to Node #0,0,2 Current State: 47:[45, 47], Operations: ['95-50=45', '23+24=47'] Exploring Operation: 45+47=92, Resulting Numbers: [92] 92,47 unequal: No Solution Exploring Operation: 45*47=2115, Resulting Numbers: [2115] 2115,47 unequal: No Solution Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[24, 68], Operations: ['95-50=45', '23+45=68'] Exploring Operation: 24*68=1632, Resulting Numbers: [1632] 1632,47 unequal: No Solution Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,47 unequal: No Solution Exploring Operation: 24+68=92, Resulting Numbers: [92] 92,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[23, 69], Operations: ['95-50=45', '24+45=69'] Exploring Operation: 69-23=46, Resulting Numbers: [46] 46,47 unequal: No Solution Exploring Operation: 23+69=92, Resulting Numbers: [92] 92,47 unequal: No Solution Exploring Operation: 69/23=3, Resulting Numbers: [3] 3,47 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:[50, 24, 72], Operations: ['95-23=72'] Exploring Operation: 72-24=48, Resulting Numbers: [50, 48] Generated Node #0,1,0: 47:[50, 48] Operation: 72-24=48 Exploring Operation: 72/24=3, Resulting Numbers: [50, 3] Generated Node #0,1,1: 47:[50, 3] Operation: 72/24=3 Exploring Operation: 50-24=26, Resulting Numbers: [72, 26] Generated Node #0,1,2: 47:[72, 26] Operation: 50-24=26 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 47:[50, 48], Operations: ['95-23=72', '72-24=48'] Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,47 unequal: No Solution Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,47 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 #0,1,2 Current State: 47:[72, 26], Operations: ['95-23=72', '50-24=26'] Exploring Operation: 72*26=1872, Resulting Numbers: [1872] 1872,47 unequal: No Solution Exploring Operation: 72+26=98, Resulting Numbers: [98] 98,47 unequal: No Solution Exploring Operation: 72-26=46, Resulting Numbers: [46] 46,47 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 #0,1,1 Current State: 47:[50, 3], Operations: ['95-23=72', '72/24=3'] Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,47 unequal: No Solution Exploring Operation: 50*3=150, Resulting Numbers: [150] 150,47 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[95, 23, 50, 24], Operations: [] Exploring Operation: 95-23=72, Resulting Numbers: [50, 24, 72] Generated Node #0,1: 47:[50, 24, 72] Operation: 95-23=72 Moving to Node #0,1 Current State: 47:[50, 24, 72], Operations: ['95-23=72'] Exploring Operation: 72/24=3, Resulting Numbers: [50, 3] Generated Node #0,1,1: 47:[50, 3] Operation: 72/24=3 Moving to Node #0,1,1 Current State: 47:[50, 3], Operations: ['95-23=72', '72/24=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_3
sum_heuristic
[ 45, 99, 30, 54 ]
10
[ "99*30=2970", "2970/54=55", "55-45=10" ]
Current State: 10:[45, 99, 30, 54], Operations: [] Exploring Operation: 99*30=2970, Resulting Numbers: [45, 54, 2970] Generated Node #2: [45, 54, 2970] from Operation: 99*30=2970 Current State: 10:[45, 54, 2970], Operations: ['99*30=2970'] Exploring Operation: 2970/54=55, Resulting Numbers: [45, 55] Generated Node #3: [45, 55] from Operation: 2970/54=55 Current State: 10:[45, 55], Operations: ['99*30=2970', '2970/54=55'] Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[45, 99, 30, 54], Operations: [] Exploring Operation: 99-54=45, Resulting Numbers: [45, 30, 45] Generated Node #0,0: 10:[45, 30, 45] Operation: 99-54=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[45, 30, 45], Operations: ['99-54=45'] Exploring Operation: 45/45=1, Resulting Numbers: [30, 1] Generated Node #0,0,0: 10:[30, 1] Operation: 45/45=1 Moving to Node #0,0,0 Current State: 10:[30, 1], Operations: ['99-54=45', '45/45=1'] Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 26, 16, 43, 67 ]
100
[ "26-16=10", "43+67=110", "110-10=100" ]
Current State: 100:[26, 16, 43, 67], Operations: [] Exploring Operation: 26-16=10, Resulting Numbers: [43, 67, 10] Generated Node #2: [43, 67, 10] from Operation: 26-16=10 Current State: 100:[43, 67, 10], Operations: ['26-16=10'] Exploring Operation: 43+67=110, Resulting Numbers: [10, 110] Generated Node #3: [10, 110] from Operation: 43+67=110 Current State: 100:[10, 110], Operations: ['26-16=10', '43+67=110'] Exploring Operation: 110-10=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[26, 16, 43, 67], Operations: [] Exploring Operation: 43+67=110, Resulting Numbers: [26, 16, 110] Generated Node #0,0: 100:[26, 16, 110] Operation: 43+67=110 Exploring Operation: 67-43=24, Resulting Numbers: [26, 16, 24] Generated Node #0,1: 100:[26, 16, 24] Operation: 67-43=24 Exploring Operation: 26+67=93, Resulting Numbers: [16, 43, 93] Generated Node #0,2: 100:[16, 43, 93] Operation: 26+67=93 Exploring Operation: 67-16=51, Resulting Numbers: [26, 43, 51] Generated Node #0,3: 100:[26, 43, 51] Operation: 67-16=51 Moving to Node #0,1 Current State: 100:[26, 16, 24], Operations: ['67-43=24'] Exploring Operation: 24-16=8, Resulting Numbers: [26, 8] Generated Node #0,1,0: 100:[26, 8] Operation: 24-16=8 Exploring Operation: 26+24=50, Resulting Numbers: [16, 50] Generated Node #0,1,1: 100:[16, 50] Operation: 26+24=50 Exploring Operation: 26-24=2, Resulting Numbers: [16, 2] Generated Node #0,1,2: 100:[16, 2] Operation: 26-24=2 Exploring Operation: 26-16=10, Resulting Numbers: [24, 10] Generated Node #0,1,3: 100:[24, 10] Operation: 26-16=10 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 100:[24, 10], Operations: ['67-43=24', '26-16=10'] Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,100 unequal: No Solution Exploring Operation: 24*10=240, Resulting Numbers: [240] 240,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 100:[26, 8], Operations: ['67-43=24', '24-16=8'] Exploring Operation: 26*8=208, Resulting Numbers: [208] 208,100 unequal: No Solution Exploring Operation: 26+8=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 100:[16, 50], Operations: ['67-43=24', '26+24=50'] Exploring Operation: 16*50=800, Resulting Numbers: [800] 800,100 unequal: No Solution Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 16+50=66, Resulting Numbers: [66] 66,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 100:[16, 2], Operations: ['67-43=24', '26-24=2'] Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,100 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,100 unequal: No Solution Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,100 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: 100:[26, 43, 51], Operations: ['67-16=51'] Exploring Operation: 43+51=94, Resulting Numbers: [26, 94] Generated Node #0,3,0: 100:[26, 94] Operation: 43+51=94 Exploring Operation: 51-26=25, Resulting Numbers: [43, 25] Generated Node #0,3,1: 100:[43, 25] Operation: 51-26=25 Exploring Operation: 43-26=17, Resulting Numbers: [51, 17] Generated Node #0,3,2: 100:[51, 17] Operation: 43-26=17 Exploring Operation: 51-43=8, Resulting Numbers: [26, 8] Generated Node #0,3,3: 100:[26, 8] Operation: 51-43=8 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 100:[26, 8], Operations: ['67-16=51', '51-43=8'] Exploring Operation: 26*8=208, Resulting Numbers: [208] 208,100 unequal: No Solution Exploring Operation: 26+8=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 100:[51, 17], Operations: ['67-16=51', '43-26=17'] Exploring Operation: 51/17=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 51-17=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 51*17=867, Resulting Numbers: [867] 867,100 unequal: No Solution Exploring Operation: 51+17=68, Resulting Numbers: [68] 68,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 100:[26, 94], Operations: ['67-16=51', '43+51=94'] Exploring Operation: 94-26=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 26*94=2444, Resulting Numbers: [2444] 2444,100 unequal: No Solution Exploring Operation: 26+94=120, Resulting Numbers: [120] 120,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 100:[43, 25], Operations: ['67-16=51', '51-26=25'] Exploring Operation: 43*25=1075, Resulting Numbers: [1075] 1075,100 unequal: No Solution Exploring Operation: 43-25=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 43+25=68, Resulting Numbers: [68] 68,100 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: 100:[26, 16, 110], Operations: ['43+67=110'] Exploring Operation: 110-16=94, Resulting Numbers: [26, 94] Generated Node #0,0,0: 100:[26, 94] Operation: 110-16=94 Exploring Operation: 26+16=42, Resulting Numbers: [110, 42] Generated Node #0,0,1: 100:[110, 42] Operation: 26+16=42 Exploring Operation: 110-26=84, Resulting Numbers: [16, 84] Generated Node #0,0,2: 100:[16, 84] Operation: 110-26=84 Exploring Operation: 26-16=10, Resulting Numbers: [110, 10] Generated Node #0,0,3: 100:[110, 10] Operation: 26-16=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[26, 94], Operations: ['43+67=110', '110-16=94'] Exploring Operation: 26*94=2444, Resulting Numbers: [2444] 2444,100 unequal: No Solution Exploring Operation: 94-26=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 26+94=120, Resulting Numbers: [120] 120,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 100:[110, 10], Operations: ['43+67=110', '26-16=10'] Exploring Operation: 110/10=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 110*10=1100, Resulting Numbers: [1100] 1100,100 unequal: No Solution Exploring Operation: 110-10=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[26, 16, 43, 67], Operations: [] Exploring Operation: 43+67=110, Resulting Numbers: [26, 16, 110] Generated Node #0,0: 100:[26, 16, 110] Operation: 43+67=110 Moving to Node #0,0 Current State: 100:[26, 16, 110], Operations: ['43+67=110'] Exploring Operation: 26-16=10, Resulting Numbers: [110, 10] Generated Node #0,0,3: 100:[110, 10] Operation: 26-16=10 Moving to Node #0,0,3 Current State: 100:[110, 10], Operations: ['43+67=110', '26-16=10'] Exploring Operation: 110-10=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.954861
hs_4
mult_heuristic
[ 30, 28, 40, 50 ]
29
[ "30*28=840", "840/40=21", "50-21=29" ]
Current State: 29:[30, 28, 40, 50], Operations: [] Exploring Operation: 30*28=840, Resulting Numbers: [40, 50, 840] Generated Node #2: [40, 50, 840] from Operation: 30*28=840 Current State: 29:[40, 50, 840], Operations: ['30*28=840'] Exploring Operation: 840/40=21, Resulting Numbers: [50, 21] Generated Node #3: [50, 21] from Operation: 840/40=21 Current State: 29:[50, 21], Operations: ['30*28=840', '840/40=21'] Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[30, 28, 40, 50], Operations: [] Exploring Operation: 50-30=20, Resulting Numbers: [28, 40, 20] Generated Node #0,0: 29:[28, 40, 20] Operation: 50-30=20 Exploring Operation: 50-28=22, Resulting Numbers: [30, 40, 22] Generated Node #0,1: 29:[30, 40, 22] Operation: 50-28=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[30, 40, 22], Operations: ['50-28=22'] Exploring Operation: 40-30=10, Resulting Numbers: [22, 10] Generated Node #0,1,0: 29:[22, 10] Operation: 40-30=10 Exploring Operation: 40-22=18, Resulting Numbers: [30, 18] Generated Node #0,1,1: 29:[30, 18] Operation: 40-22=18 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 29:[30, 18], Operations: ['50-28=22', '40-22=18'] Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 29:[22, 10], Operations: ['50-28=22', '40-30=10'] Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,29 unequal: No Solution Exploring Operation: 22+10=32, Resulting Numbers: [32] 32,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[28, 40, 20], Operations: ['50-30=20'] Exploring Operation: 40-28=12, Resulting Numbers: [20, 12] Generated Node #0,0,0: 29:[20, 12] Operation: 40-28=12 Exploring Operation: 40-20=20, Resulting Numbers: [28, 20] Generated Node #0,0,1: 29:[28, 20] Operation: 40-20=20 Moving to Node #0,0,1 Current State: 29:[28, 20], Operations: ['50-30=20', '40-20=20'] Exploring Operation: 28+20=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[20, 12], Operations: ['50-30=20', '40-28=12'] Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,29 unequal: No Solution Exploring Operation: 20+12=32, Resulting Numbers: [32] 32,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 42, 87, 15, 3 ]
30
[ "87-42=45", "45/3=15", "15+15=30" ]
Current State: 30:[42, 87, 15, 3], Operations: [] Exploring Operation: 87-42=45, Resulting Numbers: [15, 3, 45] Generated Node #2: [15, 3, 45] from Operation: 87-42=45 Current State: 30:[15, 3, 45], Operations: ['87-42=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15, 15] Generated Node #3: [15, 15] from Operation: 45/3=15 Current State: 30:[15, 15], Operations: ['87-42=45', '45/3=15'] Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[42, 87, 15, 3], Operations: [] Exploring Operation: 42/3=14, Resulting Numbers: [87, 15, 14] Generated Node #0,0: 30:[87, 15, 14] Operation: 42/3=14 Exploring Operation: 87/3=29, Resulting Numbers: [42, 15, 29] Generated Node #0,1: 30:[42, 15, 29] Operation: 87/3=29 Exploring Operation: 87-42=45, Resulting Numbers: [15, 3, 45] Generated Node #0,2: 30:[15, 3, 45] Operation: 87-42=45 Exploring Operation: 87-15=72, Resulting Numbers: [42, 3, 72] Generated Node #0,3: 30:[42, 3, 72] Operation: 87-15=72 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[42, 15, 29], Operations: ['87/3=29'] Exploring Operation: 29-15=14, Resulting Numbers: [42, 14] Generated Node #0,1,0: 30:[42, 14] Operation: 29-15=14 Exploring Operation: 15+29=44, Resulting Numbers: [42, 44] Generated Node #0,1,1: 30:[42, 44] Operation: 15+29=44 Exploring Operation: 42-15=27, Resulting Numbers: [29, 27] Generated Node #0,1,2: 30:[29, 27] Operation: 42-15=27 Exploring Operation: 42-29=13, Resulting Numbers: [15, 13] Generated Node #0,1,3: 30:[15, 13] Operation: 42-29=13 Moving to Node #0,1,3 Current State: 30:[15, 13], Operations: ['87/3=29', '42-29=13'] Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 15*13=195, Resulting Numbers: [195] 195,30 unequal: No Solution Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[29, 27], Operations: ['87/3=29', '42-15=27'] Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 29*27=783, Resulting Numbers: [783] 783,30 unequal: No Solution Exploring Operation: 29+27=56, Resulting Numbers: [56] 56,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[42, 14], Operations: ['87/3=29', '29-15=14'] Exploring Operation: 42+14=56, Resulting Numbers: [56] 56,30 unequal: No Solution Exploring Operation: 42-14=28, Resulting Numbers: [28] 28,30 unequal: No Solution Exploring Operation: 42*14=588, Resulting Numbers: [588] 588,30 unequal: No Solution Exploring Operation: 42/14=3, Resulting Numbers: [3] 3,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[42, 44], Operations: ['87/3=29', '15+29=44'] Exploring Operation: 42+44=86, Resulting Numbers: [86] 86,30 unequal: No Solution Exploring Operation: 42*44=1848, Resulting Numbers: [1848] 1848,30 unequal: No Solution Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,30 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 Current State: 30:[15, 3, 45], Operations: ['87-42=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15, 15] Generated Node #0,2,0: 30:[15, 15] Operation: 45/3=15 Exploring Operation: 45/15=3, Resulting Numbers: [3, 3] Generated Node #0,2,1: 30:[3, 3] Operation: 45/15=3 Exploring Operation: 45-3=42, Resulting Numbers: [15, 42] Generated Node #0,2,2: 30:[15, 42] Operation: 45-3=42 Exploring Operation: 45-15=30, Resulting Numbers: [3, 30] Generated Node #0,2,3: 30:[3, 30] Operation: 45-15=30 Moving to Node #0,2,0 Current State: 30:[15, 15], Operations: ['87-42=45', '45/3=15'] Exploring Operation: 15*15=225, Resulting Numbers: [225] 225,30 unequal: No Solution Exploring Operation: 15-15=0, Resulting Numbers: [0] 0,30 unequal: No Solution Exploring Operation: 15/15=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[42, 87, 15, 3], Operations: [] Exploring Operation: 87-42=45, Resulting Numbers: [15, 3, 45] Generated Node #0,2: 30:[15, 3, 45] Operation: 87-42=45 Moving to Node #0,2 Current State: 30:[15, 3, 45], Operations: ['87-42=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15, 15] Generated Node #0,2,0: 30:[15, 15] Operation: 45/3=15 Moving to Node #0,2,0 Current State: 30:[15, 15], Operations: ['87-42=45', '45/3=15'] Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
sum_heuristic
[ 10, 75, 21, 4 ]
60
[ "10+75=85", "21+4=25", "85-25=60" ]
Current State: 60:[10, 75, 21, 4], Operations: [] Exploring Operation: 10+75=85, Resulting Numbers: [21, 4, 85] Generated Node #2: [21, 4, 85] from Operation: 10+75=85 Current State: 60:[21, 4, 85], Operations: ['10+75=85'] Exploring Operation: 21+4=25, Resulting Numbers: [85, 25] Generated Node #3: [85, 25] from Operation: 21+4=25 Current State: 60:[85, 25], Operations: ['10+75=85', '21+4=25'] Exploring Operation: 85-25=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[10, 75, 21, 4], Operations: [] Exploring Operation: 75-10=65, Resulting Numbers: [21, 4, 65] Generated Node #0,0: 60:[21, 4, 65] Operation: 75-10=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[21, 4, 65], Operations: ['75-10=65'] Exploring Operation: 65-4=61, Resulting Numbers: [21, 61] Generated Node #0,0,0: 60:[21, 61] Operation: 65-4=61 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[21, 61], Operations: ['75-10=65', '65-4=61'] Exploring Operation: 61-21=40, Resulting Numbers: [40] 40,60 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
[ 44, 70, 53, 20 ]
47
[ "70-44=26", "53+20=73", "73-26=47" ]
Current State: 47:[44, 70, 53, 20], Operations: [] Exploring Operation: 70-44=26, Resulting Numbers: [53, 20, 26] Generated Node #2: [53, 20, 26] from Operation: 70-44=26 Current State: 47:[53, 20, 26], Operations: ['70-44=26'] Exploring Operation: 53+20=73, Resulting Numbers: [26, 73] Generated Node #3: [26, 73] from Operation: 53+20=73 Current State: 47:[26, 73], Operations: ['70-44=26', '53+20=73'] Exploring Operation: 73-26=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[44, 70, 53, 20], Operations: [] Exploring Operation: 53-20=33, Resulting Numbers: [44, 70, 33] Generated Node #0,0: 47:[44, 70, 33] Operation: 53-20=33 Exploring Operation: 70-20=50, Resulting Numbers: [44, 53, 50] Generated Node #0,1: 47:[44, 53, 50] Operation: 70-20=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[44, 53, 50], Operations: ['70-20=50'] Exploring Operation: 53-44=9, Resulting Numbers: [50, 9] Generated Node #0,1,0: 47:[50, 9] Operation: 53-44=9 Exploring Operation: 50-44=6, Resulting Numbers: [53, 6] Generated Node #0,1,1: 47:[53, 6] Operation: 50-44=6 Moving to Node #0,1,0 Current State: 47:[50, 9], Operations: ['70-20=50', '53-44=9'] Exploring Operation: 50+9=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 50-9=41, Resulting Numbers: [41] 41,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[53, 6], Operations: ['70-20=50', '50-44=6'] Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[44, 70, 53, 20], Operations: [] Exploring Operation: 70-20=50, Resulting Numbers: [44, 53, 50] Generated Node #0,1: 47:[44, 53, 50] Operation: 70-20=50 Moving to Node #0,1 Current State: 47:[44, 53, 50], Operations: ['70-20=50'] Exploring Operation: 50-44=6, Resulting Numbers: [53, 6] Generated Node #0,1,1: 47:[53, 6] Operation: 50-44=6 Moving to Node #0,1,1 Current State: 47:[53, 6], Operations: ['70-20=50', '50-44=6'] Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 3, 11, 10, 21 ]
62
[ "3*10=30", "11+21=32", "30+32=62" ]
Current State: 62:[3, 11, 10, 21], Operations: [] Exploring Operation: 3*10=30, Resulting Numbers: [11, 21, 30] Generated Node #2: [11, 21, 30] from Operation: 3*10=30 Current State: 62:[11, 21, 30], Operations: ['3*10=30'] Exploring Operation: 11+21=32, Resulting Numbers: [30, 32] Generated Node #3: [30, 32] from Operation: 11+21=32 Current State: 62:[30, 32], Operations: ['3*10=30', '11+21=32'] Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[3, 11, 10, 21], Operations: [] Exploring Operation: 11+21=32, Resulting Numbers: [3, 10, 32] Generated Node #0,0: 62:[3, 10, 32] Operation: 11+21=32 Exploring Operation: 10+21=31, Resulting Numbers: [3, 11, 31] Generated Node #0,1: 62:[3, 11, 31] Operation: 10+21=31 Moving to Node #0,0 Current State: 62:[3, 10, 32], Operations: ['11+21=32'] Exploring Operation: 10-3=7, Resulting Numbers: [32, 7] Generated Node #0,0,0: 62:[32, 7] Operation: 10-3=7 Exploring Operation: 3*10=30, Resulting Numbers: [32, 30] Generated Node #0,0,1: 62:[32, 30] Operation: 3*10=30 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 62:[32, 30], Operations: ['11+21=32', '3*10=30'] Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 32+30=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[3, 11, 10, 21], Operations: [] Exploring Operation: 11+21=32, Resulting Numbers: [3, 10, 32] Generated Node #0,0: 62:[3, 10, 32] Operation: 11+21=32 Moving to Node #0,0 Current State: 62:[3, 10, 32], Operations: ['11+21=32'] Exploring Operation: 3*10=30, Resulting Numbers: [32, 30] Generated Node #0,0,1: 62:[32, 30] Operation: 3*10=30 Moving to Node #0,0,1 Current State: 62:[32, 30], Operations: ['11+21=32', '3*10=30'] Exploring Operation: 32+30=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 13, 89, 23, 13 ]
57
[ "13*13=169", "89+23=112", "169-112=57" ]
Current State: 57:[13, 89, 23, 13], Operations: [] Exploring Operation: 13*13=169, Resulting Numbers: [89, 23, 169] Generated Node #2: [89, 23, 169] from Operation: 13*13=169 Current State: 57:[89, 23, 169], Operations: ['13*13=169'] Exploring Operation: 89+23=112, Resulting Numbers: [169, 112] Generated Node #3: [169, 112] from Operation: 89+23=112 Current State: 57:[169, 112], Operations: ['13*13=169', '89+23=112'] Exploring Operation: 169-112=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[13, 89, 23, 13], Operations: [] Exploring Operation: 89-23=66, Resulting Numbers: [13, 13, 66] Generated Node #0,0: 57:[13, 13, 66] Operation: 89-23=66 Exploring Operation: 13-13=0, Resulting Numbers: [89, 23, 0] Generated Node #0,1: 57:[89, 23, 0] Operation: 13-13=0 Exploring Operation: 89-13=76, Resulting Numbers: [23, 13, 76] Generated Node #0,2: 57:[23, 13, 76] Operation: 89-13=76 Exploring Operation: 89-13=76, Resulting Numbers: [13, 23, 76] Generated Node #0,3: 57:[13, 23, 76] Operation: 89-13=76 Exploring Operation: 13/13=1, Resulting Numbers: [89, 23, 1] Generated Node #0,4: 57:[89, 23, 1] Operation: 13/13=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[13, 13, 66], Operations: ['89-23=66'] Exploring Operation: 13/13=1, Resulting Numbers: [66, 1] Generated Node #0,0,0: 57:[66, 1] Operation: 13/13=1 Exploring Operation: 13+13=26, Resulting Numbers: [66, 26] Generated Node #0,0,1: 57:[66, 26] Operation: 13+13=26 Exploring Operation: 13-13=0, Resulting Numbers: [66, 0] Generated Node #0,0,2: 57:[66, 0] Operation: 13-13=0 Exploring Operation: 66-13=53, Resulting Numbers: [13, 53] Generated Node #0,0,3: 57:[13, 53] Operation: 66-13=53 Exploring Operation: 66-13=53, Resulting Numbers: [13, 53] Generated Node #0,0,4: 57:[13, 53] Operation: 66-13=53 Moving to Node #0,0,3 Current State: 57:[13, 53], Operations: ['89-23=66', '66-13=53'] Exploring Operation: 13+53=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 13*53=689, Resulting Numbers: [689] 689,57 unequal: No Solution Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,57 unequal: No Solution Moving to Node #0,0,4 Current State: 57:[13, 53], Operations: ['89-23=66', '66-13=53'] Exploring Operation: 13+53=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,57 unequal: No Solution Exploring Operation: 13*53=689, Resulting Numbers: [689] 689,57 unequal: No Solution Moving to Node #0,0,0 Current State: 57:[66, 1], Operations: ['89-23=66', '13/13=1'] Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,57 unequal: No Solution Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,57 unequal: No Solution Exploring Operation: 66*1=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,57 unequal: No Solution Moving to Node #0,0,2 Current State: 57:[66, 0], Operations: ['89-23=66', '13-13=0'] Exploring Operation: 66*0=0, Resulting Numbers: [0] 0,57 unequal: No Solution Exploring Operation: 66+0=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 66-0=66, Resulting Numbers: [66] 66,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[66, 26], Operations: ['89-23=66', '13+13=26'] Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,57 unequal: No Solution Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,57 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,57 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 #0,2 Current State: 57:[23, 13, 76], Operations: ['89-13=76'] Exploring Operation: 13+76=89, Resulting Numbers: [23, 89] Generated Node #0,2,0: 57:[23, 89] Operation: 13+76=89 Exploring Operation: 76-13=63, Resulting Numbers: [23, 63] Generated Node #0,2,1: 57:[23, 63] Operation: 76-13=63 Exploring Operation: 23-13=10, Resulting Numbers: [76, 10] Generated Node #0,2,2: 57:[76, 10] Operation: 23-13=10 Exploring Operation: 23+13=36, Resulting Numbers: [76, 36] Generated Node #0,2,3: 57:[76, 36] Operation: 23+13=36 Exploring Operation: 76-23=53, Resulting Numbers: [13, 53] Generated Node #0,2,4: 57:[13, 53] Operation: 76-23=53 Moving to Node #0,2,1 Current State: 57:[23, 63], Operations: ['89-13=76', '76-13=63'] Exploring Operation: 23*63=1449, Resulting Numbers: [1449] 1449,57 unequal: No Solution Exploring Operation: 23+63=86, Resulting Numbers: [86] 86,57 unequal: No Solution Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,57 unequal: No Solution Moving to Node #0,2,4 Current State: 57:[13, 53], Operations: ['89-13=76', '76-23=53'] Exploring Operation: 13+53=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,57 unequal: No Solution Exploring Operation: 13*53=689, Resulting Numbers: [689] 689,57 unequal: No Solution Moving to Node #0,2,2 Current State: 57:[76, 10], Operations: ['89-13=76', '23-13=10'] Exploring Operation: 76+10=86, Resulting Numbers: [86] 86,57 unequal: No Solution Exploring Operation: 76*10=760, Resulting Numbers: [760] 760,57 unequal: No Solution Exploring Operation: 76-10=66, Resulting Numbers: [66] 66,57 unequal: No Solution Moving to Node #0,2,0 Current State: 57:[23, 89], Operations: ['89-13=76', '13+76=89'] Exploring Operation: 23+89=112, Resulting Numbers: [112] 112,57 unequal: No Solution Exploring Operation: 23*89=2047, Resulting Numbers: [2047] 2047,57 unequal: No Solution Exploring Operation: 89-23=66, Resulting Numbers: [66] 66,57 unequal: No Solution Moving to Node #0,2,3 Current State: 57:[76, 36], Operations: ['89-13=76', '23+13=36'] Exploring Operation: 76*36=2736, Resulting Numbers: [2736] 2736,57 unequal: No Solution Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,57 unequal: No Solution Exploring Operation: 76+36=112, Resulting Numbers: [112] 112,57 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 #0,3 Current State: 57:[13, 23, 76], Operations: ['89-13=76'] Exploring Operation: 13+23=36, Resulting Numbers: [76, 36] Generated Node #0,3,0: 57:[76, 36] Operation: 13+23=36 Exploring Operation: 76-23=53, Resulting Numbers: [13, 53] Generated Node #0,3,1: 57:[13, 53] Operation: 76-23=53 Exploring Operation: 13+76=89, Resulting Numbers: [23, 89] Generated Node #0,3,2: 57:[23, 89] Operation: 13+76=89 Exploring Operation: 76-13=63, Resulting Numbers: [23, 63] Generated Node #0,3,3: 57:[23, 63] Operation: 76-13=63 Exploring Operation: 23-13=10, Resulting Numbers: [76, 10] Generated Node #0,3,4: 57:[76, 10] Operation: 23-13=10 Moving to Node #0,3,1 Current State: 57:[13, 53], Operations: ['89-13=76', '76-23=53'] Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,57 unequal: No Solution Exploring Operation: 13*53=689, Resulting Numbers: [689] 689,57 unequal: No Solution Exploring Operation: 13+53=66, Resulting Numbers: [66] 66,57 unequal: No Solution Moving to Node #0,3,3 Current State: 57:[23, 63], Operations: ['89-13=76', '76-13=63'] Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,57 unequal: No Solution Exploring Operation: 23+63=86, Resulting Numbers: [86] 86,57 unequal: No Solution Exploring Operation: 23*63=1449, Resulting Numbers: [1449] 1449,57 unequal: No Solution Moving to Node #0,3,4 Current State: 57:[76, 10], Operations: ['89-13=76', '23-13=10'] Exploring Operation: 76-10=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 76+10=86, Resulting Numbers: [86] 86,57 unequal: No Solution Exploring Operation: 76*10=760, Resulting Numbers: [760] 760,57 unequal: No Solution Moving to Node #0,3,0 Current State: 57:[76, 36], Operations: ['89-13=76', '13+23=36'] Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,57 unequal: No Solution Exploring Operation: 76*36=2736, Resulting Numbers: [2736] 2736,57 unequal: No Solution Exploring Operation: 76+36=112, Resulting Numbers: [112] 112,57 unequal: No Solution Moving to Node #0,3,2 Current State: 57:[23, 89], Operations: ['89-13=76', '13+76=89'] Exploring Operation: 23+89=112, Resulting Numbers: [112] 112,57 unequal: No Solution Exploring Operation: 23*89=2047, Resulting Numbers: [2047] 2047,57 unequal: No Solution Exploring Operation: 89-23=66, Resulting Numbers: [66] 66,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 57:[89, 23, 1], Operations: ['13/13=1'] Exploring Operation: 89-23=66, Resulting Numbers: [1, 66] Generated Node #0,4,0: 57:[1, 66] Operation: 89-23=66 Exploring Operation: 89*1=89, Resulting Numbers: [23, 89] Generated Node #0,4,1: 57:[23, 89] Operation: 89*1=89 Exploring Operation: 89-1=88, Resulting Numbers: [23, 88] Generated Node #0,4,2: 57:[23, 88] Operation: 89-1=88 Exploring Operation: 89/1=89, Resulting Numbers: [23, 89] Generated Node #0,4,3: 57:[23, 89] Operation: 89/1=89 Exploring Operation: 23-1=22, Resulting Numbers: [89, 22] Generated Node #0,4,4: 57:[89, 22] Operation: 23-1=22 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 57:[1, 66], Operations: ['13/13=1', '89-23=66'] Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,57 unequal: No Solution Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 1+66=67, Resulting Numbers: [67] 67,57 unequal: No Solution Exploring Operation: 1*66=66, Resulting Numbers: [66] 66,57 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 #0,4,2 Current State: 57:[23, 88], Operations: ['13/13=1', '89-1=88'] Exploring Operation: 88-23=65, Resulting Numbers: [65] 65,57 unequal: No Solution Exploring Operation: 23+88=111, Resulting Numbers: [111] 111,57 unequal: No Solution Exploring Operation: 23*88=2024, Resulting Numbers: [2024] 2024,57 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 #0,4,4 Current State: 57:[89, 22], Operations: ['13/13=1', '23-1=22'] Exploring Operation: 89*22=1958, Resulting Numbers: [1958] 1958,57 unequal: No Solution Exploring Operation: 89+22=111, Resulting Numbers: [111] 111,57 unequal: No Solution Exploring Operation: 89-22=67, Resulting Numbers: [67] 67,57 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 #0,4,1 Current State: 57:[23, 89], Operations: ['13/13=1', '89*1=89'] Exploring Operation: 23+89=112, Resulting Numbers: [112] 112,57 unequal: No Solution Exploring Operation: 89-23=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 23*89=2047, Resulting Numbers: [2047] 2047,57 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 #0,4,3 Current State: 57:[23, 89], Operations: ['13/13=1', '89/1=89'] Exploring Operation: 89-23=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 23*89=2047, Resulting Numbers: [2047] 2047,57 unequal: No Solution Exploring Operation: 23+89=112, Resulting Numbers: [112] 112,57 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 #0,1 Current State: 57:[89, 23, 0], Operations: ['13-13=0'] Exploring Operation: 89*0=0, Resulting Numbers: [23, 0] Generated Node #0,1,0: 57:[23, 0] Operation: 89*0=0 Exploring Operation: 89-23=66, Resulting Numbers: [0, 66] Generated Node #0,1,1: 57:[0, 66] Operation: 89-23=66 Exploring Operation: 89-0=89, Resulting Numbers: [23, 89] Generated Node #0,1,2: 57:[23, 89] Operation: 89-0=89 Exploring Operation: 89+0=89, Resulting Numbers: [23, 89] Generated Node #0,1,3: 57:[23, 89] Operation: 89+0=89 Exploring Operation: 23*0=0, Resulting Numbers: [89, 0] Generated Node #0,1,4: 57:[89, 0] Operation: 23*0=0 Moving to Node #0,1,0 Current State: 57:[23, 0], Operations: ['13-13=0', '89*0=0'] Exploring Operation: 23+0=23, Resulting Numbers: [23] 23,57 unequal: No Solution Exploring Operation: 23*0=0, Resulting Numbers: [0] 0,57 unequal: No Solution Exploring Operation: 23-0=23, Resulting Numbers: [23] 23,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[0, 66], Operations: ['13-13=0', '89-23=66'] Exploring Operation: 0*66=0, Resulting Numbers: [0] 0,57 unequal: No Solution Exploring Operation: 0+66=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 66-0=66, Resulting Numbers: [66] 66,57 unequal: No Solution Moving to Node #0,1,4 Current State: 57:[89, 0], Operations: ['13-13=0', '23*0=0'] Exploring Operation: 89-0=89, Resulting Numbers: [89] 89,57 unequal: No Solution Exploring Operation: 89*0=0, Resulting Numbers: [0] 0,57 unequal: No Solution Exploring Operation: 89+0=89, Resulting Numbers: [89] 89,57 unequal: No Solution Moving to Node #0,1,2 Current State: 57:[23, 89], Operations: ['13-13=0', '89-0=89'] Exploring Operation: 23+89=112, Resulting Numbers: [112] 112,57 unequal: No Solution Exploring Operation: 23*89=2047, Resulting Numbers: [2047] 2047,57 unequal: No Solution Exploring Operation: 89-23=66, Resulting Numbers: [66] 66,57 unequal: No Solution Moving to Node #0,1,3 Current State: 57:[23, 89], Operations: ['13-13=0', '89+0=89'] Exploring Operation: 23*89=2047, Resulting Numbers: [2047] 2047,57 unequal: No Solution Exploring Operation: 89-23=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 23+89=112, Resulting Numbers: [112] 112,57 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
[ 71, 36, 70, 22 ]
59
[ "71+36=107", "70-22=48", "107-48=59" ]
Current State: 59:[71, 36, 70, 22], Operations: [] Exploring Operation: 71+36=107, Resulting Numbers: [70, 22, 107] Generated Node #2: [70, 22, 107] from Operation: 71+36=107 Current State: 59:[70, 22, 107], Operations: ['71+36=107'] Exploring Operation: 70-22=48, Resulting Numbers: [107, 48] Generated Node #3: [107, 48] from Operation: 70-22=48 Current State: 59:[107, 48], Operations: ['71+36=107', '70-22=48'] Exploring Operation: 107-48=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[71, 36, 70, 22], Operations: [] Exploring Operation: 36+22=58, Resulting Numbers: [71, 70, 58] Generated Node #0,0: 59:[71, 70, 58] Operation: 36+22=58 Exploring Operation: 71-22=49, Resulting Numbers: [36, 70, 49] Generated Node #0,1: 59:[36, 70, 49] Operation: 71-22=49 Moving to Node #0,0 Current State: 59:[71, 70, 58], Operations: ['36+22=58'] Exploring Operation: 71-70=1, Resulting Numbers: [58, 1] Generated Node #0,0,0: 59:[58, 1] Operation: 71-70=1 Exploring Operation: 71-58=13, Resulting Numbers: [70, 13] Generated Node #0,0,1: 59:[70, 13] Operation: 71-58=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[70, 13], Operations: ['36+22=58', '71-58=13'] Exploring Operation: 70-13=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 70+13=83, Resulting Numbers: [83] 83,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[58, 1], Operations: ['36+22=58', '71-70=1'] Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,59 unequal: No Solution Exploring Operation: 58+1=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[71, 36, 70, 22], Operations: [] Exploring Operation: 36+22=58, Resulting Numbers: [71, 70, 58] Generated Node #0,0: 59:[71, 70, 58] Operation: 36+22=58 Moving to Node #0,0 Current State: 59:[71, 70, 58], Operations: ['36+22=58'] Exploring Operation: 71-70=1, Resulting Numbers: [58, 1] Generated Node #0,0,0: 59:[58, 1] Operation: 71-70=1 Moving to Node #0,0,0 Current State: 59:[58, 1], Operations: ['36+22=58', '71-70=1'] Exploring Operation: 58+1=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 75, 83, 36, 78 ]
34
[ "83-75=8", "78-36=42", "42-8=34" ]
Current State: 34:[75, 83, 36, 78], Operations: [] Exploring Operation: 83-75=8, Resulting Numbers: [36, 78, 8] Generated Node #2: [36, 78, 8] from Operation: 83-75=8 Current State: 34:[36, 78, 8], Operations: ['83-75=8'] Exploring Operation: 78-36=42, Resulting Numbers: [8, 42] Generated Node #3: [8, 42] from Operation: 78-36=42 Current State: 34:[8, 42], Operations: ['83-75=8', '78-36=42'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[75, 83, 36, 78], Operations: [] Exploring Operation: 78-75=3, Resulting Numbers: [83, 36, 3] Generated Node #0,0: 34:[83, 36, 3] Operation: 78-75=3 Exploring Operation: 83-75=8, Resulting Numbers: [36, 78, 8] Generated Node #0,1: 34:[36, 78, 8] Operation: 83-75=8 Exploring Operation: 83-78=5, Resulting Numbers: [75, 36, 5] Generated Node #0,2: 34:[75, 36, 5] Operation: 83-78=5 Moving to Node #0,2 Current State: 34:[75, 36, 5], Operations: ['83-78=5'] Exploring Operation: 75-36=39, Resulting Numbers: [5, 39] Generated Node #0,2,0: 34:[5, 39] Operation: 75-36=39 Exploring Operation: 75/5=15, Resulting Numbers: [36, 15] Generated Node #0,2,1: 34:[36, 15] Operation: 75/5=15 Exploring Operation: 75-5=70, Resulting Numbers: [36, 70] Generated Node #0,2,2: 34:[36, 70] Operation: 75-5=70 Moving to Node #0,0 Current State: 34:[83, 36, 3], Operations: ['78-75=3'] Exploring Operation: 36-3=33, Resulting Numbers: [83, 33] Generated Node #0,0,0: 34:[83, 33] Operation: 36-3=33 Exploring Operation: 83-36=47, Resulting Numbers: [3, 47] Generated Node #0,0,1: 34:[3, 47] Operation: 83-36=47 Exploring Operation: 83-3=80, Resulting Numbers: [36, 80] Generated Node #0,0,2: 34:[36, 80] Operation: 83-3=80 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 34:[3, 47], Operations: ['78-75=3', '83-36=47'] Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,34 unequal: No Solution Exploring Operation: 3*47=141, Resulting Numbers: [141] 141,34 unequal: No Solution Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,34 unequal: No Solution No 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: 34:[36, 80], Operations: ['78-75=3', '83-3=80'] Exploring Operation: 36*80=2880, Resulting Numbers: [2880] 2880,34 unequal: No Solution Exploring Operation: 80-36=44, Resulting Numbers: [44] 44,34 unequal: No Solution Exploring Operation: 36+80=116, Resulting Numbers: [116] 116,34 unequal: No Solution No 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: 34:[83, 33], Operations: ['78-75=3', '36-3=33'] Exploring Operation: 83+33=116, Resulting Numbers: [116] 116,34 unequal: No Solution Exploring Operation: 83*33=2739, Resulting Numbers: [2739] 2739,34 unequal: No Solution Exploring Operation: 83-33=50, Resulting Numbers: [50] 50,34 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: 34:[36, 78, 8], Operations: ['83-75=8'] Exploring Operation: 78-36=42, Resulting Numbers: [8, 42] Generated Node #0,1,0: 34:[8, 42] Operation: 78-36=42 Exploring Operation: 36-8=28, Resulting Numbers: [78, 28] Generated Node #0,1,1: 34:[78, 28] Operation: 36-8=28 Exploring Operation: 78-8=70, Resulting Numbers: [36, 70] Generated Node #0,1,2: 34:[36, 70] Operation: 78-8=70 Moving to Node #0,2,1 Current State: 34:[36, 15], Operations: ['83-78=5', '75/5=15'] Exploring Operation: 36+15=51, Resulting Numbers: [51] 51,34 unequal: No Solution Exploring Operation: 36*15=540, Resulting Numbers: [540] 540,34 unequal: No Solution Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[5, 39], Operations: ['83-78=5', '75-36=39'] Exploring Operation: 5*39=195, Resulting Numbers: [195] 195,34 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[75, 83, 36, 78], Operations: [] Exploring Operation: 83-78=5, Resulting Numbers: [75, 36, 5] Generated Node #0,2: 34:[75, 36, 5] Operation: 83-78=5 Moving to Node #0,2 Current State: 34:[75, 36, 5], Operations: ['83-78=5'] Exploring Operation: 75-36=39, Resulting Numbers: [5, 39] Generated Node #0,2,0: 34:[5, 39] Operation: 75-36=39 Moving to Node #0,2,0 Current State: 34:[5, 39], Operations: ['83-78=5', '75-36=39'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
0.973958
hs_3
sum_heuristic
[ 25, 36, 58, 49 ]
99
[ "36-25=11", "58-49=9", "11*9=99" ]
Current State: 99:[25, 36, 58, 49], Operations: [] Exploring Operation: 36-25=11, Resulting Numbers: [58, 49, 11] Generated Node #2: [58, 49, 11] from Operation: 36-25=11 Current State: 99:[58, 49, 11], Operations: ['36-25=11'] Exploring Operation: 58-49=9, Resulting Numbers: [11, 9] Generated Node #3: [11, 9] from Operation: 58-49=9 Current State: 99:[11, 9], Operations: ['36-25=11', '58-49=9'] Exploring Operation: 11*9=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[25, 36, 58, 49], Operations: [] Exploring Operation: 36+58=94, Resulting Numbers: [25, 49, 94] Generated Node #0,0: 99:[25, 49, 94] Operation: 36+58=94 Exploring Operation: 58-49=9, Resulting Numbers: [25, 36, 9] Generated Node #0,1: 99:[25, 36, 9] Operation: 58-49=9 Exploring Operation: 58+49=107, Resulting Numbers: [25, 36, 107] Generated Node #0,2: 99:[25, 36, 107] Operation: 58+49=107 Exploring Operation: 58-25=33, Resulting Numbers: [36, 49, 33] Generated Node #0,3: 99:[36, 49, 33] Operation: 58-25=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[25, 36, 9], Operations: ['58-49=9'] Exploring Operation: 25-9=16, Resulting Numbers: [36, 16] Generated Node #0,1,0: 99:[36, 16] Operation: 25-9=16 Exploring Operation: 36-25=11, Resulting Numbers: [9, 11] Generated Node #0,1,1: 99:[9, 11] Operation: 36-25=11 Exploring Operation: 25+9=34, Resulting Numbers: [36, 34] Generated Node #0,1,2: 99:[36, 34] Operation: 25+9=34 Exploring Operation: 36/9=4, Resulting Numbers: [25, 4] Generated Node #0,1,3: 99:[25, 4] Operation: 36/9=4 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 99:[9, 11], Operations: ['58-49=9', '36-25=11'] Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[25, 36, 58, 49], Operations: [] Exploring Operation: 58-49=9, Resulting Numbers: [25, 36, 9] Generated Node #0,1: 99:[25, 36, 9] Operation: 58-49=9 Moving to Node #0,1 Current State: 99:[25, 36, 9], Operations: ['58-49=9'] Exploring Operation: 36-25=11, Resulting Numbers: [9, 11] Generated Node #0,1,1: 99:[9, 11] Operation: 36-25=11 Moving to Node #0,1,1 Current State: 99:[9, 11], Operations: ['58-49=9', '36-25=11'] Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 57, 3, 6, 31 ]
70
[ "57+31=88", "3*6=18", "88-18=70" ]
Current State: 70:[57, 3, 6, 31], Operations: [] Exploring Operation: 57+31=88, Resulting Numbers: [3, 6, 88] Generated Node #2: [3, 6, 88] from Operation: 57+31=88 Current State: 70:[3, 6, 88], Operations: ['57+31=88'] Exploring Operation: 3*6=18, Resulting Numbers: [88, 18] Generated Node #3: [88, 18] from Operation: 3*6=18 Current State: 70:[88, 18], Operations: ['57+31=88', '3*6=18'] Exploring Operation: 88-18=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[57, 3, 6, 31], Operations: [] Exploring Operation: 57+3=60, Resulting Numbers: [6, 31, 60] Generated Node #0,0: 70:[6, 31, 60] Operation: 57+3=60 Exploring Operation: 57/3=19, Resulting Numbers: [6, 31, 19] Generated Node #0,1: 70:[6, 31, 19] Operation: 57/3=19 Exploring Operation: 57+6=63, Resulting Numbers: [3, 31, 63] Generated Node #0,2: 70:[3, 31, 63] Operation: 57+6=63 Exploring Operation: 57-31=26, Resulting Numbers: [3, 6, 26] Generated Node #0,3: 70:[3, 6, 26] Operation: 57-31=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[6, 31, 19], Operations: ['57/3=19'] Exploring Operation: 6+31=37, Resulting Numbers: [19, 37] Generated Node #0,1,0: 70:[19, 37] Operation: 6+31=37 Exploring Operation: 6+19=25, Resulting Numbers: [31, 25] Generated Node #0,1,1: 70:[31, 25] Operation: 6+19=25 Exploring Operation: 31-19=12, Resulting Numbers: [6, 12] Generated Node #0,1,2: 70:[6, 12] Operation: 31-19=12 Exploring Operation: 19-6=13, Resulting Numbers: [31, 13] Generated Node #0,1,3: 70:[31, 13] Operation: 19-6=13 Moving to Node #0,1,2 Current State: 70:[6, 12], Operations: ['57/3=19', '31-19=12'] Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,70 unequal: No Solution Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,70 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,70 unequal: No Solution Moving to Node #0,1,3 Current State: 70:[31, 13], Operations: ['57/3=19', '19-6=13'] Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,70 unequal: No Solution Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,70 unequal: No Solution Exploring Operation: 31*13=403, Resulting Numbers: [403] 403,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[19, 37], Operations: ['57/3=19', '6+31=37'] Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,70 unequal: No Solution Exploring Operation: 19+37=56, Resulting Numbers: [56] 56,70 unequal: No Solution Exploring Operation: 19*37=703, Resulting Numbers: [703] 703,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[31, 25], Operations: ['57/3=19', '6+19=25'] Exploring Operation: 31+25=56, Resulting Numbers: [56] 56,70 unequal: No Solution Exploring Operation: 31*25=775, Resulting Numbers: [775] 775,70 unequal: No Solution Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,70 unequal: No Solution No 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: 70:[3, 6, 26], Operations: ['57-31=26'] Exploring Operation: 6+26=32, Resulting Numbers: [3, 32] Generated Node #0,3,0: 70:[3, 32] Operation: 6+26=32 Exploring Operation: 26-6=20, Resulting Numbers: [3, 20] Generated Node #0,3,1: 70:[3, 20] Operation: 26-6=20 Exploring Operation: 3+26=29, Resulting Numbers: [6, 29] Generated Node #0,3,2: 70:[6, 29] Operation: 3+26=29 Exploring Operation: 6/3=2, Resulting Numbers: [26, 2] Generated Node #0,3,3: 70:[26, 2] Operation: 6/3=2 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 70:[3, 32], Operations: ['57-31=26', '6+26=32'] Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,70 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,70 unequal: No Solution Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 70:[3, 20], Operations: ['57-31=26', '26-6=20'] Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,70 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,70 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 70:[6, 29], Operations: ['57-31=26', '3+26=29'] Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,70 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 70:[26, 2], Operations: ['57-31=26', '6/3=2'] Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,70 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,70 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,70 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[3, 31, 63], Operations: ['57+6=63'] Exploring Operation: 3+63=66, Resulting Numbers: [31, 66] Generated Node #0,2,0: 70:[31, 66] Operation: 3+63=66 Exploring Operation: 3+31=34, Resulting Numbers: [63, 34] Generated Node #0,2,1: 70:[63, 34] Operation: 3+31=34 Exploring Operation: 63-31=32, Resulting Numbers: [3, 32] Generated Node #0,2,2: 70:[3, 32] Operation: 63-31=32 Exploring Operation: 63/3=21, Resulting Numbers: [31, 21] Generated Node #0,2,3: 70:[31, 21] Operation: 63/3=21 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 70:[3, 32], Operations: ['57+6=63', '63-31=32'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,70 unequal: No Solution Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,70 unequal: No Solution Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 70:[31, 66], Operations: ['57+6=63', '3+63=66'] Exploring Operation: 31*66=2046, Resulting Numbers: [2046] 2046,70 unequal: No Solution Exploring Operation: 31+66=97, Resulting Numbers: [97] 97,70 unequal: No Solution Exploring Operation: 66-31=35, Resulting Numbers: [35] 35,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 70:[63, 34], Operations: ['57+6=63', '3+31=34'] Exploring Operation: 63-34=29, Resulting Numbers: [29] 29,70 unequal: No Solution Exploring Operation: 63*34=2142, Resulting Numbers: [2142] 2142,70 unequal: No Solution Exploring Operation: 63+34=97, Resulting Numbers: [97] 97,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 70:[31, 21], Operations: ['57+6=63', '63/3=21'] Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,70 unequal: No Solution Exploring Operation: 31*21=651, Resulting Numbers: [651] 651,70 unequal: No Solution Exploring Operation: 31+21=52, Resulting Numbers: [52] 52,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[6, 31, 60], Operations: ['57+3=60'] Exploring Operation: 6+31=37, Resulting Numbers: [60, 37] Generated Node #0,0,0: 70:[60, 37] Operation: 6+31=37 Exploring Operation: 60-31=29, Resulting Numbers: [6, 29] Generated Node #0,0,1: 70:[6, 29] Operation: 60-31=29 Exploring Operation: 60/6=10, Resulting Numbers: [31, 10] Generated Node #0,0,2: 70:[31, 10] Operation: 60/6=10 Exploring Operation: 6+60=66, Resulting Numbers: [31, 66] Generated Node #0,0,3: 70:[31, 66] Operation: 6+60=66 Moving to Node #0,0,2 Current State: 70:[31, 10], Operations: ['57+3=60', '60/6=10'] Exploring Operation: 31+10=41, Resulting Numbers: [41] 41,70 unequal: No Solution Exploring Operation: 31*10=310, Resulting Numbers: [310] 310,70 unequal: No Solution Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[6, 29], Operations: ['57+3=60', '60-31=29'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,70 unequal: No Solution Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,70 unequal: No Solution Moving to Node #0,0,3 Current State: 70:[31, 66], Operations: ['57+3=60', '6+60=66'] Exploring Operation: 31+66=97, Resulting Numbers: [97] 97,70 unequal: No Solution Exploring Operation: 66-31=35, Resulting Numbers: [35] 35,70 unequal: No Solution Exploring Operation: 31*66=2046, Resulting Numbers: [2046] 2046,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[60, 37], Operations: ['57+3=60', '6+31=37'] Exploring Operation: 60*37=2220, Resulting Numbers: [2220] 2220,70 unequal: No Solution Exploring Operation: 60-37=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 60+37=97, Resulting Numbers: [97] 97,70 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
[ 60, 81, 39, 81 ]
98
[ "60+39=99", "81/81=1", "99-1=98" ]
Current State: 98:[60, 81, 39, 81], Operations: [] Exploring Operation: 60+39=99, Resulting Numbers: [81, 81, 99] Generated Node #2: [81, 81, 99] from Operation: 60+39=99 Current State: 98:[81, 81, 99], Operations: ['60+39=99'] Exploring Operation: 81/81=1, Resulting Numbers: [99, 1] Generated Node #3: [99, 1] from Operation: 81/81=1 Current State: 98:[99, 1], Operations: ['60+39=99', '81/81=1'] Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[60, 81, 39, 81], Operations: [] Exploring Operation: 81-60=21, Resulting Numbers: [39, 81, 21] Generated Node #0,0: 98:[39, 81, 21] Operation: 81-60=21 Exploring Operation: 81/81=1, Resulting Numbers: [60, 39, 1] Generated Node #0,1: 98:[60, 39, 1] Operation: 81/81=1 Exploring Operation: 81-81=0, Resulting Numbers: [60, 39, 0] Generated Node #0,2: 98:[60, 39, 0] Operation: 81-81=0 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[60, 39, 1], Operations: ['81/81=1'] Exploring Operation: 60+39=99, Resulting Numbers: [1, 99] Generated Node #0,1,0: 98:[1, 99] Operation: 60+39=99 Exploring Operation: 60-39=21, Resulting Numbers: [1, 21] Generated Node #0,1,1: 98:[1, 21] Operation: 60-39=21 Exploring Operation: 60-1=59, Resulting Numbers: [39, 59] Generated Node #0,1,2: 98:[39, 59] Operation: 60-1=59 Moving to Node #0,1,0 Current State: 98:[1, 99], Operations: ['81/81=1', '60+39=99'] Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[60, 81, 39, 81], Operations: [] Exploring Operation: 81/81=1, Resulting Numbers: [60, 39, 1] Generated Node #0,1: 98:[60, 39, 1] Operation: 81/81=1 Moving to Node #0,1 Current State: 98:[60, 39, 1], Operations: ['81/81=1'] Exploring Operation: 60+39=99, Resulting Numbers: [1, 99] Generated Node #0,1,0: 98:[1, 99] Operation: 60+39=99 Moving to Node #0,1,0 Current State: 98:[1, 99], Operations: ['81/81=1', '60+39=99'] Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 4, 20, 98, 14 ]
31
[ "4+20=24", "98/14=7", "24+7=31" ]
Current State: 31:[4, 20, 98, 14], Operations: [] Exploring Operation: 4+20=24, Resulting Numbers: [98, 14, 24] Generated Node #2: [98, 14, 24] from Operation: 4+20=24 Current State: 31:[98, 14, 24], Operations: ['4+20=24'] Exploring Operation: 98/14=7, Resulting Numbers: [24, 7] Generated Node #3: [24, 7] from Operation: 98/14=7 Current State: 31:[24, 7], Operations: ['4+20=24', '98/14=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[4, 20, 98, 14], Operations: [] Exploring Operation: 4+20=24, Resulting Numbers: [98, 14, 24] Generated Node #0,0: 31:[98, 14, 24] Operation: 4+20=24 Exploring Operation: 98/14=7, Resulting Numbers: [4, 20, 7] Generated Node #0,1: 31:[4, 20, 7] Operation: 98/14=7 Exploring Operation: 4+14=18, Resulting Numbers: [20, 98, 18] Generated Node #0,2: 31:[20, 98, 18] Operation: 4+14=18 Exploring Operation: 98-20=78, Resulting Numbers: [4, 14, 78] Generated Node #0,3: 31:[4, 14, 78] Operation: 98-20=78 Exploring Operation: 98-4=94, Resulting Numbers: [20, 14, 94] Generated Node #0,4: 31:[20, 14, 94] Operation: 98-4=94 Moving to Node #0,1 Current State: 31:[4, 20, 7], Operations: ['98/14=7'] Exploring Operation: 4+20=24, Resulting Numbers: [7, 24] Generated Node #0,1,0: 31:[7, 24] Operation: 4+20=24 Exploring Operation: 20-4=16, Resulting Numbers: [7, 16] Generated Node #0,1,1: 31:[7, 16] Operation: 20-4=16 Exploring Operation: 4+7=11, Resulting Numbers: [20, 11] Generated Node #0,1,2: 31:[20, 11] Operation: 4+7=11 Exploring Operation: 20+7=27, Resulting Numbers: [4, 27] Generated Node #0,1,3: 31:[4, 27] Operation: 20+7=27 Exploring Operation: 4*7=28, Resulting Numbers: [20, 28] Generated Node #0,1,4: 31:[20, 28] Operation: 4*7=28 Moving to Node #0,2 Current State: 31:[20, 98, 18], Operations: ['4+14=18'] Exploring Operation: 98-18=80, Resulting Numbers: [20, 80] Generated Node #0,2,0: 31:[20, 80] Operation: 98-18=80 Exploring Operation: 98+18=116, Resulting Numbers: [20, 116] Generated Node #0,2,1: 31:[20, 116] Operation: 98+18=116 Exploring Operation: 98-20=78, Resulting Numbers: [18, 78] Generated Node #0,2,2: 31:[18, 78] Operation: 98-20=78 Exploring Operation: 20-18=2, Resulting Numbers: [98, 2] Generated Node #0,2,3: 31:[98, 2] Operation: 20-18=2 Exploring Operation: 20+18=38, Resulting Numbers: [98, 38] Generated Node #0,2,4: 31:[98, 38] Operation: 20+18=38 Moving to Node #0,4 Current State: 31:[20, 14, 94], Operations: ['98-4=94'] Exploring Operation: 14+94=108, Resulting Numbers: [20, 108] Generated Node #0,4,0: 31:[20, 108] Operation: 14+94=108 Exploring Operation: 20-14=6, Resulting Numbers: [94, 6] Generated Node #0,4,1: 31:[94, 6] Operation: 20-14=6 Exploring Operation: 94-14=80, Resulting Numbers: [20, 80] Generated Node #0,4,2: 31:[20, 80] Operation: 94-14=80 Exploring Operation: 94-20=74, Resulting Numbers: [14, 74] Generated Node #0,4,3: 31:[14, 74] Operation: 94-20=74 Exploring Operation: 20+14=34, Resulting Numbers: [94, 34] Generated Node #0,4,4: 31:[94, 34] Operation: 20+14=34 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 31:[20, 80], Operations: ['98-4=94', '94-14=80'] Exploring Operation: 20+80=100, Resulting Numbers: [100] 100,31 unequal: No Solution Exploring Operation: 80/20=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 80-20=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 20*80=1600, Resulting Numbers: [1600] 1600,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 31:[14, 74], Operations: ['98-4=94', '94-20=74'] Exploring Operation: 74-14=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 14*74=1036, Resulting Numbers: [1036] 1036,31 unequal: No Solution Exploring Operation: 14+74=88, Resulting Numbers: [88] 88,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 31:[94, 34], Operations: ['98-4=94', '20+14=34'] Exploring Operation: 94-34=60, Resulting Numbers: [60] 60,31 unequal: No Solution Exploring Operation: 94+34=128, Resulting Numbers: [128] 128,31 unequal: No Solution Exploring Operation: 94*34=3196, Resulting Numbers: [3196] 3196,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 31:[20, 108], Operations: ['98-4=94', '14+94=108'] Exploring Operation: 20*108=2160, Resulting Numbers: [2160] 2160,31 unequal: No Solution Exploring Operation: 20+108=128, Resulting Numbers: [128] 128,31 unequal: No Solution Exploring Operation: 108-20=88, Resulting Numbers: [88] 88,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 31:[94, 6], Operations: ['98-4=94', '20-14=6'] Exploring Operation: 94-6=88, Resulting Numbers: [88] 88,31 unequal: No Solution Exploring Operation: 94+6=100, Resulting Numbers: [100] 100,31 unequal: No Solution Exploring Operation: 94*6=564, Resulting Numbers: [564] 564,31 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: 31:[98, 14, 24], Operations: ['4+20=24'] Exploring Operation: 98+14=112, Resulting Numbers: [24, 112] Generated Node #0,0,0: 31:[24, 112] Operation: 98+14=112 Exploring Operation: 14+24=38, Resulting Numbers: [98, 38] Generated Node #0,0,1: 31:[98, 38] Operation: 14+24=38 Exploring Operation: 98-24=74, Resulting Numbers: [14, 74] Generated Node #0,0,2: 31:[14, 74] Operation: 98-24=74 Exploring Operation: 98-14=84, Resulting Numbers: [24, 84] Generated Node #0,0,3: 31:[24, 84] Operation: 98-14=84 Exploring Operation: 98/14=7, Resulting Numbers: [24, 7] Generated Node #0,0,4: 31:[24, 7] Operation: 98/14=7 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 31:[24, 7], Operations: ['4+20=24', '98/14=7'] Exploring Operation: 24*7=168, Resulting Numbers: [168] 168,31 unequal: No Solution Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[4, 20, 98, 14], Operations: [] Exploring Operation: 4+20=24, Resulting Numbers: [98, 14, 24] Generated Node #0,0: 31:[98, 14, 24] Operation: 4+20=24 Moving to Node #0,0 Current State: 31:[98, 14, 24], Operations: ['4+20=24'] Exploring Operation: 98/14=7, Resulting Numbers: [24, 7] Generated Node #0,0,4: 31:[24, 7] Operation: 98/14=7 Moving to Node #0,0,4 Current State: 31:[24, 7], Operations: ['4+20=24', '98/14=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
mult_heuristic
[ 75, 40, 1, 80 ]
38
[ "75+1=76", "80/40=2", "76/2=38" ]
Current State: 38:[75, 40, 1, 80], Operations: [] Exploring Operation: 75+1=76, Resulting Numbers: [40, 80, 76] Generated Node #2: [40, 80, 76] from Operation: 75+1=76 Current State: 38:[40, 80, 76], Operations: ['75+1=76'] Exploring Operation: 80/40=2, Resulting Numbers: [76, 2] Generated Node #3: [76, 2] from Operation: 80/40=2 Current State: 38:[76, 2], Operations: ['75+1=76', '80/40=2'] Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[75, 40, 1, 80], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [75, 1, 2] Generated Node #0,0: 38:[75, 1, 2] Operation: 80/40=2 Exploring Operation: 80-75=5, Resulting Numbers: [40, 1, 5] Generated Node #0,1: 38:[40, 1, 5] Operation: 80-75=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[40, 1, 5], Operations: ['80-75=5'] Exploring Operation: 40-1=39, Resulting Numbers: [5, 39] Generated Node #0,1,0: 38:[5, 39] Operation: 40-1=39 Exploring Operation: 40-5=35, Resulting Numbers: [1, 35] Generated Node #0,1,1: 38:[1, 35] Operation: 40-5=35 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 38:[5, 39], Operations: ['80-75=5', '40-1=39'] Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,38 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 38:[1, 35], Operations: ['80-75=5', '40-5=35'] Exploring Operation: 1+35=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 1*35=35, Resulting Numbers: [35] 35,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[75, 1, 2], Operations: ['80/40=2'] Exploring Operation: 75-2=73, Resulting Numbers: [1, 73] Generated Node #0,0,0: 38:[1, 73] Operation: 75-2=73 Exploring Operation: 75-1=74, Resulting Numbers: [2, 74] Generated Node #0,0,1: 38:[2, 74] Operation: 75-1=74 Moving to Node #0,0,0 Current State: 38:[1, 73], Operations: ['80/40=2', '75-2=73'] Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,38 unequal: No Solution Exploring Operation: 1*73=73, Resulting Numbers: [73] 73,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[2, 74], Operations: ['80/40=2', '75-1=74'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,38 unequal: No Solution Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,38 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
[ 28, 22, 92, 90 ]
100
[ "28+22=50", "92-90=2", "50*2=100" ]
Current State: 100:[28, 22, 92, 90], Operations: [] Exploring Operation: 28+22=50, Resulting Numbers: [92, 90, 50] Generated Node #2: [92, 90, 50] from Operation: 28+22=50 Current State: 100:[92, 90, 50], Operations: ['28+22=50'] Exploring Operation: 92-90=2, Resulting Numbers: [50, 2] Generated Node #3: [50, 2] from Operation: 92-90=2 Current State: 100:[50, 2], Operations: ['28+22=50', '92-90=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[28, 22, 92, 90], Operations: [] Exploring Operation: 28+22=50, Resulting Numbers: [92, 90, 50] Generated Node #0,0: 100:[92, 90, 50] Operation: 28+22=50 Exploring Operation: 28-22=6, Resulting Numbers: [92, 90, 6] Generated Node #0,1: 100:[92, 90, 6] Operation: 28-22=6 Exploring Operation: 92-90=2, Resulting Numbers: [28, 22, 2] Generated Node #0,2: 100:[28, 22, 2] Operation: 92-90=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[28, 22, 2], Operations: ['92-90=2'] Exploring Operation: 28-22=6, Resulting Numbers: [2, 6] Generated Node #0,2,0: 100:[2, 6] Operation: 28-22=6 Exploring Operation: 28+22=50, Resulting Numbers: [2, 50] Generated Node #0,2,1: 100:[2, 50] Operation: 28+22=50 Exploring Operation: 28-2=26, Resulting Numbers: [22, 26] Generated Node #0,2,2: 100:[22, 26] Operation: 28-2=26 Moving to Node #0,2,1 Current State: 100:[2, 50], Operations: ['92-90=2', '28+22=50'] Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,100 unequal: No Solution Exploring Operation: 2*50=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[28, 22, 92, 90], Operations: [] Exploring Operation: 92-90=2, Resulting Numbers: [28, 22, 2] Generated Node #0,2: 100:[28, 22, 2] Operation: 92-90=2 Moving to Node #0,2 Current State: 100:[28, 22, 2], Operations: ['92-90=2'] Exploring Operation: 28+22=50, Resulting Numbers: [2, 50] Generated Node #0,2,1: 100:[2, 50] Operation: 28+22=50 Moving to Node #0,2,1 Current State: 100:[2, 50], Operations: ['92-90=2', '28+22=50'] Exploring Operation: 2*50=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 69, 96, 29, 81 ]
32
[ "96-69=27", "81/27=3", "29+3=32" ]
Current State: 32:[69, 96, 29, 81], Operations: [] Exploring Operation: 96-69=27, Resulting Numbers: [29, 81, 27] Generated Node #2: [29, 81, 27] from Operation: 96-69=27 Current State: 32:[29, 81, 27], Operations: ['96-69=27'] Exploring Operation: 81/27=3, Resulting Numbers: [29, 3] Generated Node #3: [29, 3] from Operation: 81/27=3 Current State: 32:[29, 3], Operations: ['96-69=27', '81/27=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[69, 96, 29, 81], Operations: [] Exploring Operation: 81-69=12, Resulting Numbers: [96, 29, 12] Generated Node #0,0: 32:[96, 29, 12] Operation: 81-69=12 Exploring Operation: 96-69=27, Resulting Numbers: [29, 81, 27] Generated Node #0,1: 32:[29, 81, 27] Operation: 96-69=27 Exploring Operation: 69-29=40, Resulting Numbers: [96, 81, 40] Generated Node #0,2: 32:[96, 81, 40] Operation: 69-29=40 Exploring Operation: 96-81=15, Resulting Numbers: [69, 29, 15] Generated Node #0,3: 32:[69, 29, 15] Operation: 96-81=15 Moving to Node #0,3 Current State: 32:[69, 29, 15], Operations: ['96-81=15'] Exploring Operation: 29-15=14, Resulting Numbers: [69, 14] Generated Node #0,3,0: 32:[69, 14] Operation: 29-15=14 Exploring Operation: 69-15=54, Resulting Numbers: [29, 54] Generated Node #0,3,1: 32:[29, 54] Operation: 69-15=54 Exploring Operation: 69-29=40, Resulting Numbers: [15, 40] Generated Node #0,3,2: 32:[15, 40] Operation: 69-29=40 Exploring Operation: 29+15=44, Resulting Numbers: [69, 44] Generated Node #0,3,3: 32:[69, 44] Operation: 29+15=44 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 32:[15, 40], Operations: ['96-81=15', '69-29=40'] Exploring Operation: 40-15=25, Resulting Numbers: [25] 25,32 unequal: No Solution Exploring Operation: 15*40=600, Resulting Numbers: [600] 600,32 unequal: No Solution Exploring Operation: 15+40=55, Resulting Numbers: [55] 55,32 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 #0,3,1 Current State: 32:[29, 54], Operations: ['96-81=15', '69-15=54'] Exploring Operation: 29*54=1566, Resulting Numbers: [1566] 1566,32 unequal: No Solution Exploring Operation: 54-29=25, Resulting Numbers: [25] 25,32 unequal: No Solution Exploring Operation: 29+54=83, Resulting Numbers: [83] 83,32 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 #0,3,0 Current State: 32:[69, 14], Operations: ['96-81=15', '29-15=14'] Exploring Operation: 69*14=966, Resulting Numbers: [966] 966,32 unequal: No Solution Exploring Operation: 69+14=83, Resulting Numbers: [83] 83,32 unequal: No Solution Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,32 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 #0,3,3 Current State: 32:[69, 44], Operations: ['96-81=15', '29+15=44'] Exploring Operation: 69*44=3036, Resulting Numbers: [3036] 3036,32 unequal: No Solution Exploring Operation: 69+44=113, Resulting Numbers: [113] 113,32 unequal: No Solution Exploring Operation: 69-44=25, Resulting Numbers: [25] 25,32 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: 32:[29, 81, 27], Operations: ['96-69=27'] Exploring Operation: 29-27=2, Resulting Numbers: [81, 2] Generated Node #0,1,0: 32:[81, 2] Operation: 29-27=2 Exploring Operation: 81-27=54, Resulting Numbers: [29, 54] Generated Node #0,1,1: 32:[29, 54] Operation: 81-27=54 Exploring Operation: 81/27=3, Resulting Numbers: [29, 3] Generated Node #0,1,2: 32:[29, 3] Operation: 81/27=3 Exploring Operation: 81-29=52, Resulting Numbers: [27, 52] Generated Node #0,1,3: 32:[27, 52] Operation: 81-29=52 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 32:[29, 3], Operations: ['96-69=27', '81/27=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[69, 96, 29, 81], Operations: [] Exploring Operation: 96-69=27, Resulting Numbers: [29, 81, 27] Generated Node #0,1: 32:[29, 81, 27] Operation: 96-69=27 Moving to Node #0,1 Current State: 32:[29, 81, 27], Operations: ['96-69=27'] Exploring Operation: 81/27=3, Resulting Numbers: [29, 3] Generated Node #0,1,2: 32:[29, 3] Operation: 81/27=3 Moving to Node #0,1,2 Current State: 32:[29, 3], Operations: ['96-69=27', '81/27=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 62, 53, 5, 22 ]
23
[ "62-53=9", "5*9=45", "45-22=23" ]
Current State: 23:[62, 53, 5, 22], Operations: [] Exploring Operation: 62-53=9, Resulting Numbers: [5, 22, 9] Generated Node #2: [5, 22, 9] from Operation: 62-53=9 Current State: 23:[5, 22, 9], Operations: ['62-53=9'] Exploring Operation: 5*9=45, Resulting Numbers: [22, 45] Generated Node #3: [22, 45] from Operation: 5*9=45 Current State: 23:[22, 45], Operations: ['62-53=9', '5*9=45'] Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[62, 53, 5, 22], Operations: [] Exploring Operation: 62-53=9, Resulting Numbers: [5, 22, 9] Generated Node #0,0: 23:[5, 22, 9] Operation: 62-53=9 Exploring Operation: 62-5=57, Resulting Numbers: [53, 22, 57] Generated Node #0,1: 23:[53, 22, 57] Operation: 62-5=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[5, 22, 9], Operations: ['62-53=9'] Exploring Operation: 5+22=27, Resulting Numbers: [9, 27] Generated Node #0,0,0: 23:[9, 27] Operation: 5+22=27 Exploring Operation: 5+9=14, Resulting Numbers: [22, 14] Generated Node #0,0,1: 23:[22, 14] Operation: 5+9=14 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 23:[22, 14], Operations: ['62-53=9', '5+9=14'] Exploring Operation: 22+14=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[9, 27], Operations: ['62-53=9', '5+22=27'] Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 9+27=36, Resulting Numbers: [36] 36,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[53, 22, 57], Operations: ['62-5=57'] Exploring Operation: 57-53=4, Resulting Numbers: [22, 4] Generated Node #0,1,0: 23:[22, 4] Operation: 57-53=4 Exploring Operation: 53-22=31, Resulting Numbers: [57, 31] Generated Node #0,1,1: 23:[57, 31] Operation: 53-22=31 Moving to Node #0,1,0 Current State: 23:[22, 4], Operations: ['62-5=57', '57-53=4'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[57, 31], Operations: ['62-5=57', '53-22=31'] Exploring Operation: 57-31=26, Resulting Numbers: [26] 26,23 unequal: No Solution Exploring Operation: 57+31=88, Resulting Numbers: [88] 88,23 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
[ 4, 9, 78, 8 ]
89
[ "8/4=2", "9+78=87", "2+87=89" ]
Current State: 89:[4, 9, 78, 8], Operations: [] Exploring Operation: 8/4=2, Resulting Numbers: [9, 78, 2] Generated Node #2: [9, 78, 2] from Operation: 8/4=2 Current State: 89:[9, 78, 2], Operations: ['8/4=2'] Exploring Operation: 9+78=87, Resulting Numbers: [2, 87] Generated Node #3: [2, 87] from Operation: 9+78=87 Current State: 89:[2, 87], Operations: ['8/4=2', '9+78=87'] Exploring Operation: 2+87=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[4, 9, 78, 8], Operations: [] Exploring Operation: 4*9=36, Resulting Numbers: [78, 8, 36] Generated Node #0,0: 89:[78, 8, 36] Operation: 4*9=36 Exploring Operation: 9*8=72, Resulting Numbers: [4, 78, 72] Generated Node #0,1: 89:[4, 78, 72] Operation: 9*8=72 Exploring Operation: 4*8=32, Resulting Numbers: [9, 78, 32] Generated Node #0,2: 89:[9, 78, 32] Operation: 4*8=32 Moving to Node #0,1 Current State: 89:[4, 78, 72], Operations: ['9*8=72'] Exploring Operation: 4+72=76, Resulting Numbers: [78, 76] Generated Node #0,1,0: 89:[78, 76] Operation: 4+72=76 Exploring Operation: 78-4=74, Resulting Numbers: [72, 74] Generated Node #0,1,1: 89:[72, 74] Operation: 78-4=74 Exploring Operation: 4+78=82, Resulting Numbers: [72, 82] Generated Node #0,1,2: 89:[72, 82] Operation: 4+78=82 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[78, 76], Operations: ['9*8=72', '4+72=76'] Exploring Operation: 78-76=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 78*76=5928, Resulting Numbers: [5928] 5928,89 unequal: No Solution Exploring Operation: 78+76=154, Resulting Numbers: [154] 154,89 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 #0,1,2 Current State: 89:[72, 82], Operations: ['9*8=72', '4+78=82'] Exploring Operation: 82-72=10, Resulting Numbers: [10] 10,89 unequal: No Solution Exploring Operation: 72+82=154, Resulting Numbers: [154] 154,89 unequal: No Solution Exploring Operation: 72*82=5904, Resulting Numbers: [5904] 5904,89 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 #0,1,1 Current State: 89:[72, 74], Operations: ['9*8=72', '78-4=74'] Exploring Operation: 72*74=5328, Resulting Numbers: [5328] 5328,89 unequal: No Solution Exploring Operation: 72+74=146, Resulting Numbers: [146] 146,89 unequal: No Solution Exploring Operation: 74-72=2, Resulting Numbers: [2] 2,89 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: 89:[78, 8, 36], Operations: ['4*9=36'] Exploring Operation: 78+8=86, Resulting Numbers: [36, 86] Generated Node #0,0,0: 89:[36, 86] Operation: 78+8=86 Exploring Operation: 78-8=70, Resulting Numbers: [36, 70] Generated Node #0,0,1: 89:[36, 70] Operation: 78-8=70 Exploring Operation: 8+36=44, Resulting Numbers: [78, 44] Generated Node #0,0,2: 89:[78, 44] Operation: 8+36=44 Moving to Node #0,2 Current State: 89:[9, 78, 32], Operations: ['4*8=32'] Exploring Operation: 9+32=41, Resulting Numbers: [78, 41] Generated Node #0,2,0: 89:[78, 41] Operation: 9+32=41 Exploring Operation: 9+78=87, Resulting Numbers: [32, 87] Generated Node #0,2,1: 89:[32, 87] Operation: 9+78=87 Exploring Operation: 78-9=69, Resulting Numbers: [32, 69] Generated Node #0,2,2: 89:[32, 69] Operation: 78-9=69 Moving to Node #0,0,0 Current State: 89:[36, 86], Operations: ['4*9=36', '78+8=86'] Exploring Operation: 86-36=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 36*86=3096, Resulting Numbers: [3096] 3096,89 unequal: No Solution Exploring Operation: 36+86=122, Resulting Numbers: [122] 122,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[78, 44], Operations: ['4*9=36', '8+36=44'] Exploring Operation: 78-44=34, Resulting Numbers: [34] 34,89 unequal: No Solution Exploring Operation: 78*44=3432, Resulting Numbers: [3432] 3432,89 unequal: No Solution Exploring Operation: 78+44=122, Resulting Numbers: [122] 122,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[32, 87], Operations: ['4*8=32', '9+78=87'] Exploring Operation: 32*87=2784, Resulting Numbers: [2784] 2784,89 unequal: No Solution Exploring Operation: 87-32=55, Resulting Numbers: [55] 55,89 unequal: No Solution Exploring Operation: 32+87=119, Resulting Numbers: [119] 119,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[78, 41], Operations: ['4*8=32', '9+32=41'] Exploring Operation: 78+41=119, Resulting Numbers: [119] 119,89 unequal: No Solution Exploring Operation: 78-41=37, Resulting Numbers: [37] 37,89 unequal: No Solution Exploring Operation: 78*41=3198, Resulting Numbers: [3198] 3198,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[36, 70], Operations: ['4*9=36', '78-8=70'] Exploring Operation: 36*70=2520, Resulting Numbers: [2520] 2520,89 unequal: No Solution Exploring Operation: 36+70=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[32, 69], Operations: ['4*8=32', '78-9=69'] Exploring Operation: 32+69=101, Resulting Numbers: [101] 101,89 unequal: No Solution Exploring Operation: 32*69=2208, Resulting Numbers: [2208] 2208,89 unequal: No Solution Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,89 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 1, 61, 13, 10 ]
58
[ "1*61=61", "13-10=3", "61-3=58" ]
Current State: 58:[1, 61, 13, 10], Operations: [] Exploring Operation: 1*61=61, Resulting Numbers: [13, 10, 61] Generated Node #2: [13, 10, 61] from Operation: 1*61=61 Current State: 58:[13, 10, 61], Operations: ['1*61=61'] Exploring Operation: 13-10=3, Resulting Numbers: [61, 3] Generated Node #3: [61, 3] from Operation: 13-10=3 Current State: 58:[61, 3], Operations: ['1*61=61', '13-10=3'] Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[1, 61, 13, 10], Operations: [] Exploring Operation: 13-10=3, Resulting Numbers: [1, 61, 3] Generated Node #0,0: 58:[1, 61, 3] Operation: 13-10=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[1, 61, 3], Operations: ['13-10=3'] Exploring Operation: 61-3=58, Resulting Numbers: [1, 58] Generated Node #0,0,0: 58:[1, 58] Operation: 61-3=58 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[1, 58], Operations: ['13-10=3', '61-3=58'] Exploring Operation: 1*58=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[1, 61, 13, 10], Operations: [] Exploring Operation: 13-10=3, Resulting Numbers: [1, 61, 3] Generated Node #0,0: 58:[1, 61, 3] Operation: 13-10=3 Moving to Node #0,0 Current State: 58:[1, 61, 3], Operations: ['13-10=3'] Exploring Operation: 61-3=58, Resulting Numbers: [1, 58] Generated Node #0,0,0: 58:[1, 58] Operation: 61-3=58 Moving to Node #0,0,0 Current State: 58:[1, 58], Operations: ['13-10=3', '61-3=58'] Exploring Operation: 1*58=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 56, 95, 53, 24 ]
87
[ "56-53=3", "24/3=8", "95-8=87" ]
Current State: 87:[56, 95, 53, 24], Operations: [] Exploring Operation: 56-53=3, Resulting Numbers: [95, 24, 3] Generated Node #2: [95, 24, 3] from Operation: 56-53=3 Current State: 87:[95, 24, 3], Operations: ['56-53=3'] Exploring Operation: 24/3=8, Resulting Numbers: [95, 8] Generated Node #3: [95, 8] from Operation: 24/3=8 Current State: 87:[95, 8], Operations: ['56-53=3', '24/3=8'] Exploring Operation: 95-8=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[56, 95, 53, 24], Operations: [] Exploring Operation: 56+53=109, Resulting Numbers: [95, 24, 109] Generated Node #0,0: 87:[95, 24, 109] Operation: 56+53=109 Exploring Operation: 56-53=3, Resulting Numbers: [95, 24, 3] Generated Node #0,1: 87:[95, 24, 3] Operation: 56-53=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[95, 24, 3], Operations: ['56-53=3'] Exploring Operation: 24+3=27, Resulting Numbers: [95, 27] Generated Node #0,1,0: 87:[95, 27] Operation: 24+3=27 Exploring Operation: 95-3=92, Resulting Numbers: [24, 92] Generated Node #0,1,1: 87:[24, 92] Operation: 95-3=92 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[95, 27], Operations: ['56-53=3', '24+3=27'] Exploring Operation: 95-27=68, Resulting Numbers: [68] 68,87 unequal: No Solution Exploring Operation: 95+27=122, Resulting Numbers: [122] 122,87 unequal: No Solution No 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: 87:[24, 92], Operations: ['56-53=3', '95-3=92'] Exploring Operation: 24+92=116, Resulting Numbers: [116] 116,87 unequal: No Solution Exploring Operation: 92-24=68, Resulting Numbers: [68] 68,87 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: 87:[95, 24, 109], Operations: ['56+53=109'] Exploring Operation: 109-95=14, Resulting Numbers: [24, 14] Generated Node #0,0,0: 87:[24, 14] Operation: 109-95=14 Exploring Operation: 109-24=85, Resulting Numbers: [95, 85] Generated Node #0,0,1: 87:[95, 85] Operation: 109-24=85 Moving to Node #0,0,1 Current State: 87:[95, 85], Operations: ['56+53=109', '109-24=85'] Exploring Operation: 95-85=10, Resulting Numbers: [10] 10,87 unequal: No Solution Exploring Operation: 95+85=180, Resulting Numbers: [180] 180,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[24, 14], Operations: ['56+53=109', '109-95=14'] Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,87 unequal: No Solution Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,87 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
[ 44, 45, 50, 30 ]
79
[ "45-44=1", "50+30=80", "80-1=79" ]
Current State: 79:[44, 45, 50, 30], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [50, 30, 1] Generated Node #2: [50, 30, 1] from Operation: 45-44=1 Current State: 79:[50, 30, 1], Operations: ['45-44=1'] Exploring Operation: 50+30=80, Resulting Numbers: [1, 80] Generated Node #3: [1, 80] from Operation: 50+30=80 Current State: 79:[1, 80], Operations: ['45-44=1', '50+30=80'] Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[44, 45, 50, 30], Operations: [] Exploring Operation: 44+30=74, Resulting Numbers: [45, 50, 74] Generated Node #0,0: 79:[45, 50, 74] Operation: 44+30=74 Exploring Operation: 50+30=80, Resulting Numbers: [44, 45, 80] Generated Node #0,1: 79:[44, 45, 80] Operation: 50+30=80 Exploring Operation: 45+30=75, Resulting Numbers: [44, 50, 75] Generated Node #0,2: 79:[44, 50, 75] Operation: 45+30=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[45, 50, 74], Operations: ['44+30=74'] Exploring Operation: 50-45=5, Resulting Numbers: [74, 5] Generated Node #0,0,0: 79:[74, 5] Operation: 50-45=5 Exploring Operation: 45+50=95, Resulting Numbers: [74, 95] Generated Node #0,0,1: 79:[74, 95] Operation: 45+50=95 Exploring Operation: 45+74=119, Resulting Numbers: [50, 119] Generated Node #0,0,2: 79:[50, 119] Operation: 45+74=119 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 79:[74, 95], Operations: ['44+30=74', '45+50=95'] Exploring Operation: 74*95=7030, Resulting Numbers: [7030] 7030,79 unequal: No Solution Exploring Operation: 74+95=169, Resulting Numbers: [169] 169,79 unequal: No Solution Exploring Operation: 95-74=21, Resulting Numbers: [21] 21,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 79:[50, 119], Operations: ['44+30=74', '45+74=119'] Exploring Operation: 50+119=169, Resulting Numbers: [169] 169,79 unequal: No Solution Exploring Operation: 50*119=5950, Resulting Numbers: [5950] 5950,79 unequal: No Solution Exploring Operation: 119-50=69, Resulting Numbers: [69] 69,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[74, 5], Operations: ['44+30=74', '50-45=5'] Exploring Operation: 74+5=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[44, 45, 50, 30], Operations: [] Exploring Operation: 44+30=74, Resulting Numbers: [45, 50, 74] Generated Node #0,0: 79:[45, 50, 74] Operation: 44+30=74 Moving to Node #0,0 Current State: 79:[45, 50, 74], Operations: ['44+30=74'] Exploring Operation: 50-45=5, Resulting Numbers: [74, 5] Generated Node #0,0,0: 79:[74, 5] Operation: 50-45=5 Moving to Node #0,0,0 Current State: 79:[74, 5], Operations: ['44+30=74', '50-45=5'] Exploring Operation: 74+5=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 43, 66, 18, 6 ]
57
[ "66+18=84", "84/6=14", "43+14=57" ]
Current State: 57:[43, 66, 18, 6], Operations: [] Exploring Operation: 66+18=84, Resulting Numbers: [43, 6, 84] Generated Node #2: [43, 6, 84] from Operation: 66+18=84 Current State: 57:[43, 6, 84], Operations: ['66+18=84'] Exploring Operation: 84/6=14, Resulting Numbers: [43, 14] Generated Node #3: [43, 14] from Operation: 84/6=14 Current State: 57:[43, 14], Operations: ['66+18=84', '84/6=14'] Exploring Operation: 43+14=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[43, 66, 18, 6], Operations: [] Exploring Operation: 66-6=60, Resulting Numbers: [43, 18, 60] Generated Node #0,0: 57:[43, 18, 60] Operation: 66-6=60 Exploring Operation: 43+6=49, Resulting Numbers: [66, 18, 49] Generated Node #0,1: 57:[66, 18, 49] Operation: 43+6=49 Exploring Operation: 43+18=61, Resulting Numbers: [66, 6, 61] Generated Node #0,2: 57:[66, 6, 61] Operation: 43+18=61 Exploring Operation: 66-43=23, Resulting Numbers: [18, 6, 23] Generated Node #0,3: 57:[18, 6, 23] Operation: 66-43=23 Exploring Operation: 43-18=25, Resulting Numbers: [66, 6, 25] Generated Node #0,4: 57:[66, 6, 25] Operation: 43-18=25 Moving to Node #0,3 Current State: 57:[18, 6, 23], Operations: ['66-43=23'] Exploring Operation: 23-18=5, Resulting Numbers: [6, 5] Generated Node #0,3,0: 57:[6, 5] Operation: 23-18=5 Exploring Operation: 23-6=17, Resulting Numbers: [18, 17] Generated Node #0,3,1: 57:[18, 17] Operation: 23-6=17 Exploring Operation: 18-6=12, Resulting Numbers: [23, 12] Generated Node #0,3,2: 57:[23, 12] Operation: 18-6=12 Exploring Operation: 18+6=24, Resulting Numbers: [23, 24] Generated Node #0,3,3: 57:[23, 24] Operation: 18+6=24 Exploring Operation: 18/6=3, Resulting Numbers: [23, 3] Generated Node #0,3,4: 57:[23, 3] Operation: 18/6=3 Moving to Node #0,2 Current State: 57:[66, 6, 61], Operations: ['43+18=61'] Exploring Operation: 66-61=5, Resulting Numbers: [6, 5] Generated Node #0,2,0: 57:[6, 5] Operation: 66-61=5 Exploring Operation: 61-6=55, Resulting Numbers: [66, 55] Generated Node #0,2,1: 57:[66, 55] Operation: 61-6=55 Exploring Operation: 66+6=72, Resulting Numbers: [61, 72] Generated Node #0,2,2: 57:[61, 72] Operation: 66+6=72 Exploring Operation: 66/6=11, Resulting Numbers: [61, 11] Generated Node #0,2,3: 57:[61, 11] Operation: 66/6=11 Exploring Operation: 66-6=60, Resulting Numbers: [61, 60] Generated Node #0,2,4: 57:[61, 60] Operation: 66-6=60 Moving to Node #0,0 Current State: 57:[43, 18, 60], Operations: ['66-6=60'] Exploring Operation: 60-18=42, Resulting Numbers: [43, 42] Generated Node #0,0,0: 57:[43, 42] Operation: 60-18=42 Exploring Operation: 43+18=61, Resulting Numbers: [60, 61] Generated Node #0,0,1: 57:[60, 61] Operation: 43+18=61 Exploring Operation: 60-43=17, Resulting Numbers: [18, 17] Generated Node #0,0,2: 57:[18, 17] Operation: 60-43=17 Exploring Operation: 18+60=78, Resulting Numbers: [43, 78] Generated Node #0,0,3: 57:[43, 78] Operation: 18+60=78 Exploring Operation: 43-18=25, Resulting Numbers: [60, 25] Generated Node #0,0,4: 57:[60, 25] Operation: 43-18=25 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 57:[18, 17], Operations: ['66-6=60', '60-43=17'] Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 18*17=306, Resulting Numbers: [306] 306,57 unequal: No Solution Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,57 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 #0,0,1 Current State: 57:[60, 61], Operations: ['66-6=60', '43+18=61'] Exploring Operation: 60+61=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 61-60=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 60*61=3660, Resulting Numbers: [3660] 3660,57 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 #0,0,4 Current State: 57:[60, 25], Operations: ['66-6=60', '43-18=25'] Exploring Operation: 60*25=1500, Resulting Numbers: [1500] 1500,57 unequal: No Solution Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 60+25=85, Resulting Numbers: [85] 85,57 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:[43, 42], Operations: ['66-6=60', '60-18=42'] Exploring Operation: 43-42=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 43+42=85, Resulting Numbers: [85] 85,57 unequal: No Solution Exploring Operation: 43*42=1806, Resulting Numbers: [1806] 1806,57 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 #0,0,3 Current State: 57:[43, 78], Operations: ['66-6=60', '18+60=78'] Exploring Operation: 43+78=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 43*78=3354, Resulting Numbers: [3354] 3354,57 unequal: No Solution Exploring Operation: 78-43=35, Resulting Numbers: [35] 35,57 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: 57:[66, 18, 49], Operations: ['43+6=49'] Exploring Operation: 66-49=17, Resulting Numbers: [18, 17] Generated Node #0,1,0: 57:[18, 17] Operation: 66-49=17 Exploring Operation: 49-18=31, Resulting Numbers: [66, 31] Generated Node #0,1,1: 57:[66, 31] Operation: 49-18=31 Exploring Operation: 18+49=67, Resulting Numbers: [66, 67] Generated Node #0,1,2: 57:[66, 67] Operation: 18+49=67 Exploring Operation: 66+18=84, Resulting Numbers: [49, 84] Generated Node #0,1,3: 57:[49, 84] Operation: 66+18=84 Exploring Operation: 66-18=48, Resulting Numbers: [49, 48] Generated Node #0,1,4: 57:[49, 48] Operation: 66-18=48 Moving to Node #0,4 Current State: 57:[66, 6, 25], Operations: ['43-18=25'] Exploring Operation: 66+6=72, Resulting Numbers: [25, 72] Generated Node #0,4,0: 57:[25, 72] Operation: 66+6=72 Exploring Operation: 66-25=41, Resulting Numbers: [6, 41] Generated Node #0,4,1: 57:[6, 41] Operation: 66-25=41 Exploring Operation: 25-6=19, Resulting Numbers: [66, 19] Generated Node #0,4,2: 57:[66, 19] Operation: 25-6=19 Exploring Operation: 66/6=11, Resulting Numbers: [25, 11] Generated Node #0,4,3: 57:[25, 11] Operation: 66/6=11 Exploring Operation: 66-6=60, Resulting Numbers: [25, 60] Generated Node #0,4,4: 57:[25, 60] Operation: 66-6=60 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 57:[66, 19], Operations: ['43-18=25', '25-6=19'] Exploring Operation: 66-19=47, Resulting Numbers: [47] 47,57 unequal: No Solution Exploring Operation: 66+19=85, Resulting Numbers: [85] 85,57 unequal: No Solution Exploring Operation: 66*19=1254, Resulting Numbers: [1254] 1254,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 57:[25, 60], Operations: ['43-18=25', '66-6=60'] Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 25*60=1500, Resulting Numbers: [1500] 1500,57 unequal: No Solution Exploring Operation: 25+60=85, Resulting Numbers: [85] 85,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 57:[25, 11], Operations: ['43-18=25', '66/6=11'] Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,57 unequal: No Solution Exploring Operation: 25*11=275, Resulting Numbers: [275] 275,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 57:[6, 41], Operations: ['43-18=25', '66-25=41'] Exploring Operation: 6+41=47, Resulting Numbers: [47] 47,57 unequal: No Solution Exploring Operation: 6*41=246, Resulting Numbers: [246] 246,57 unequal: No Solution Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 57:[25, 72], Operations: ['43-18=25', '66+6=72'] Exploring Operation: 25*72=1800, Resulting Numbers: [1800] 1800,57 unequal: No Solution Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,57 unequal: No Solution Exploring Operation: 25+72=97, Resulting Numbers: [97] 97,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 57:[18, 17], Operations: ['66-43=23', '23-6=17'] Exploring Operation: 18*17=306, Resulting Numbers: [306] 306,57 unequal: No Solution Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[18, 17], Operations: ['43+6=49', '66-49=17'] Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 18*17=306, Resulting Numbers: [306] 306,57 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,57 unequal: No Solution Moving to Node #0,3,4 Current State: 57:[23, 3], Operations: ['66-43=23', '18/6=3'] Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,57 unequal: No Solution Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,57 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,57 unequal: No Solution Moving to Node #0,3,0 Current State: 57:[6, 5], Operations: ['66-43=23', '23-18=5'] Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,57 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,57 unequal: No Solution Moving to Node #0,2,0 Current State: 57:[6, 5], Operations: ['43+18=61', '66-61=5'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,57 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,57 unequal: No Solution Moving to Node #0,2,4 Current State: 57:[61, 60], Operations: ['43+18=61', '66-6=60'] Exploring Operation: 61*60=3660, Resulting Numbers: [3660] 3660,57 unequal: No Solution Exploring Operation: 61-60=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 61+60=121, Resulting Numbers: [121] 121,57 unequal: No Solution Moving to Node #0,3,3 Current State: 57:[23, 24], Operations: ['66-43=23', '18+6=24'] Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,57 unequal: No Solution Exploring Operation: 23*24=552, Resulting Numbers: [552] 552,57 unequal: No Solution Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,57 unequal: No Solution Moving to Node #0,3,2 Current State: 57:[23, 12], Operations: ['66-43=23', '18-6=12'] Exploring Operation: 23*12=276, Resulting Numbers: [276] 276,57 unequal: No Solution Exploring Operation: 23+12=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[66, 55], Operations: ['43+18=61', '61-6=55'] Exploring Operation: 66*55=3630, Resulting Numbers: [3630] 3630,57 unequal: No Solution Exploring Operation: 66+55=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 66-55=11, Resulting Numbers: [11] 11,57 unequal: No Solution Moving to Node #0,2,3 Current State: 57:[61, 11], Operations: ['43+18=61', '66/6=11'] Exploring Operation: 61-11=50, Resulting Numbers: [50] 50,57 unequal: No Solution Exploring Operation: 61*11=671, Resulting Numbers: [671] 671,57 unequal: No Solution Exploring Operation: 61+11=72, Resulting Numbers: [72] 72,57 unequal: No Solution Moving to Node #0,1,4 Current State: 57:[49, 48], Operations: ['43+6=49', '66-18=48'] Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,57 unequal: No Solution Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,57 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,57 unequal: No Solution Moving to Node #0,2,2 Current State: 57:[61, 72], Operations: ['43+18=61', '66+6=72'] Exploring Operation: 61+72=133, Resulting Numbers: [133] 133,57 unequal: No Solution Exploring Operation: 61*72=4392, Resulting Numbers: [4392] 4392,57 unequal: No Solution Exploring Operation: 72-61=11, Resulting Numbers: [11] 11,57 unequal: No Solution Moving to Node #0,1,2 Current State: 57:[66, 67], Operations: ['43+6=49', '18+49=67'] Exploring Operation: 66*67=4422, Resulting Numbers: [4422] 4422,57 unequal: No Solution Exploring Operation: 67-66=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 66+67=133, Resulting Numbers: [133] 133,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[66, 31], Operations: ['43+6=49', '49-18=31'] Exploring Operation: 66+31=97, Resulting Numbers: [97] 97,57 unequal: No Solution Exploring Operation: 66*31=2046, Resulting Numbers: [2046] 2046,57 unequal: No Solution Exploring Operation: 66-31=35, Resulting Numbers: [35] 35,57 unequal: No Solution Moving to Node #0,1,3 Current State: 57:[49, 84], Operations: ['43+6=49', '66+18=84'] Exploring Operation: 84-49=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 49+84=133, Resulting Numbers: [133] 133,57 unequal: No Solution Exploring Operation: 49*84=4116, Resulting Numbers: [4116] 4116,57 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 4, 73, 5, 2 ]
45
[ "5+2=7", "4*7=28", "73-28=45" ]
Current State: 45:[4, 73, 5, 2], Operations: [] Exploring Operation: 5+2=7, Resulting Numbers: [4, 73, 7] Generated Node #2: [4, 73, 7] from Operation: 5+2=7 Current State: 45:[4, 73, 7], Operations: ['5+2=7'] Exploring Operation: 4*7=28, Resulting Numbers: [73, 28] Generated Node #3: [73, 28] from Operation: 4*7=28 Current State: 45:[73, 28], Operations: ['5+2=7', '4*7=28'] Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[4, 73, 5, 2], Operations: [] Exploring Operation: 73-2=71, Resulting Numbers: [4, 5, 71] Generated Node #0,0: 45:[4, 5, 71] Operation: 73-2=71 Exploring Operation: 73-5=68, Resulting Numbers: [4, 2, 68] Generated Node #0,1: 45:[4, 2, 68] Operation: 73-5=68 Exploring Operation: 4+5=9, Resulting Numbers: [73, 2, 9] Generated Node #0,2: 45:[73, 2, 9] Operation: 4+5=9 Exploring Operation: 73-4=69, Resulting Numbers: [5, 2, 69] Generated Node #0,3: 45:[5, 2, 69] Operation: 73-4=69 Moving to Node #0,1 Current State: 45:[4, 2, 68], Operations: ['73-5=68'] Exploring Operation: 68-2=66, Resulting Numbers: [4, 66] Generated Node #0,1,0: 45:[4, 66] Operation: 68-2=66 Exploring Operation: 68/4=17, Resulting Numbers: [2, 17] Generated Node #0,1,1: 45:[2, 17] Operation: 68/4=17 Exploring Operation: 68/2=34, Resulting Numbers: [4, 34] Generated Node #0,1,2: 45:[4, 34] Operation: 68/2=34 Exploring Operation: 68-4=64, Resulting Numbers: [2, 64] Generated Node #0,1,3: 45:[2, 64] Operation: 68-4=64 Moving to Node #0,3 Current State: 45:[5, 2, 69], Operations: ['73-4=69'] Exploring Operation: 5*2=10, Resulting Numbers: [69, 10] Generated Node #0,3,0: 45:[69, 10] Operation: 5*2=10 Exploring Operation: 69-5=64, Resulting Numbers: [2, 64] Generated Node #0,3,1: 45:[2, 64] Operation: 69-5=64 Exploring Operation: 5-2=3, Resulting Numbers: [69, 3] Generated Node #0,3,2: 45:[69, 3] Operation: 5-2=3 Exploring Operation: 69-2=67, Resulting Numbers: [5, 67] Generated Node #0,3,3: 45:[5, 67] Operation: 69-2=67 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 45:[2, 64], Operations: ['73-4=69', '69-5=64'] Exploring Operation: 2*64=128, Resulting Numbers: [128] 128,45 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,45 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,45 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,45 unequal: No Solution No 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: 45:[5, 67], Operations: ['73-4=69', '69-2=67'] Exploring Operation: 5+67=72, Resulting Numbers: [72] 72,45 unequal: No Solution Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 5*67=335, Resulting Numbers: [335] 335,45 unequal: No Solution No 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: 45:[69, 3], Operations: ['73-4=69', '5-2=3'] Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,45 unequal: No Solution Exploring Operation: 69*3=207, Resulting Numbers: [207] 207,45 unequal: No Solution Exploring Operation: 69+3=72, Resulting Numbers: [72] 72,45 unequal: No Solution Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,45 unequal: No Solution No 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: 45:[69, 10], Operations: ['73-4=69', '5*2=10'] Exploring Operation: 69*10=690, Resulting Numbers: [690] 690,45 unequal: No Solution Exploring Operation: 69-10=59, Resulting Numbers: [59] 59,45 unequal: No Solution Exploring Operation: 69+10=79, Resulting Numbers: [79] 79,45 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: 45:[4, 5, 71], Operations: ['73-2=71'] Exploring Operation: 71-4=67, Resulting Numbers: [5, 67] Generated Node #0,0,0: 45:[5, 67] Operation: 71-4=67 Exploring Operation: 71-5=66, Resulting Numbers: [4, 66] Generated Node #0,0,1: 45:[4, 66] Operation: 71-5=66 Exploring Operation: 5-4=1, Resulting Numbers: [71, 1] Generated Node #0,0,2: 45:[71, 1] Operation: 5-4=1 Exploring Operation: 4+5=9, Resulting Numbers: [71, 9] Generated Node #0,0,3: 45:[71, 9] Operation: 4+5=9 Moving to Node #0,2 Current State: 45:[73, 2, 9], Operations: ['4+5=9'] Exploring Operation: 73+2=75, Resulting Numbers: [9, 75] Generated Node #0,2,0: 45:[9, 75] Operation: 73+2=75 Exploring Operation: 73-9=64, Resulting Numbers: [2, 64] Generated Node #0,2,1: 45:[2, 64] Operation: 73-9=64 Exploring Operation: 2+9=11, Resulting Numbers: [73, 11] Generated Node #0,2,2: 45:[73, 11] Operation: 2+9=11 Exploring Operation: 73-2=71, Resulting Numbers: [9, 71] Generated Node #0,2,3: 45:[9, 71] Operation: 73-2=71 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 45:[2, 64], Operations: ['4+5=9', '73-9=64'] Exploring Operation: 2*64=128, Resulting Numbers: [128] 128,45 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,45 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,45 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,45 unequal: No Solution No 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: 45:[9, 71], Operations: ['4+5=9', '73-2=71'] Exploring Operation: 9+71=80, Resulting Numbers: [80] 80,45 unequal: No Solution Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 9*71=639, Resulting Numbers: [639] 639,45 unequal: No Solution No 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: 45:[9, 75], Operations: ['4+5=9', '73+2=75'] Exploring Operation: 9+75=84, Resulting Numbers: [84] 84,45 unequal: No Solution Exploring Operation: 75-9=66, Resulting Numbers: [66] 66,45 unequal: No Solution Exploring Operation: 9*75=675, Resulting Numbers: [675] 675,45 unequal: No Solution No 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: 45:[73, 11], Operations: ['4+5=9', '2+9=11'] Exploring Operation: 73*11=803, Resulting Numbers: [803] 803,45 unequal: No Solution Exploring Operation: 73+11=84, Resulting Numbers: [84] 84,45 unequal: No Solution Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,45 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: 45:[2, 17], Operations: ['73-5=68', '68/4=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,45 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,45 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,45 unequal: No Solution Moving to Node #0,1,2 Current State: 45:[4, 34], Operations: ['73-5=68', '68/2=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,45 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,45 unequal: No Solution Moving to Node #0,1,3 Current State: 45:[2, 64], Operations: ['73-5=68', '68-4=64'] Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,45 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,45 unequal: No Solution Exploring Operation: 2*64=128, Resulting Numbers: [128] 128,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[4, 66], Operations: ['73-2=71', '71-5=66'] Exploring Operation: 4+66=70, Resulting Numbers: [70] 70,45 unequal: No Solution Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 4*66=264, Resulting Numbers: [264] 264,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[5, 67], Operations: ['73-2=71', '71-4=67'] Exploring Operation: 5+67=72, Resulting Numbers: [72] 72,45 unequal: No Solution Exploring Operation: 5*67=335, Resulting Numbers: [335] 335,45 unequal: No Solution Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[4, 66], Operations: ['73-5=68', '68-2=66'] Exploring Operation: 4+66=70, Resulting Numbers: [70] 70,45 unequal: No Solution Exploring Operation: 4*66=264, Resulting Numbers: [264] 264,45 unequal: No Solution Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,45 unequal: No Solution Moving to Node #0,0,3 Current State: 45:[71, 9], Operations: ['73-2=71', '4+5=9'] Exploring Operation: 71+9=80, Resulting Numbers: [80] 80,45 unequal: No Solution Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 71*9=639, Resulting Numbers: [639] 639,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[71, 1], Operations: ['73-2=71', '5-4=1'] Exploring Operation: 71*1=71, Resulting Numbers: [71] 71,45 unequal: No Solution Exploring Operation: 71-1=70, Resulting Numbers: [70] 70,45 unequal: No Solution Exploring Operation: 71/1=71, Resulting Numbers: [71] 71,45 unequal: No Solution Exploring Operation: 71+1=72, Resulting Numbers: [72] 72,45 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 3, 51, 47, 16 ]
76
[ "3+16=19", "51-47=4", "19*4=76" ]
Current State: 76:[3, 51, 47, 16], Operations: [] Exploring Operation: 3+16=19, Resulting Numbers: [51, 47, 19] Generated Node #2: [51, 47, 19] from Operation: 3+16=19 Current State: 76:[51, 47, 19], Operations: ['3+16=19'] Exploring Operation: 51-47=4, Resulting Numbers: [19, 4] Generated Node #3: [19, 4] from Operation: 51-47=4 Current State: 76:[19, 4], Operations: ['3+16=19', '51-47=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[3, 51, 47, 16], Operations: [] Exploring Operation: 51-47=4, Resulting Numbers: [3, 16, 4] Generated Node #0,0: 76:[3, 16, 4] Operation: 51-47=4 Moving to Node #0,0 Current State: 76:[3, 16, 4], Operations: ['51-47=4'] Exploring Operation: 3+16=19, Resulting Numbers: [4, 19] Generated Node #0,0,0: 76:[4, 19] Operation: 3+16=19 Moving to Node #0,0,0 Current State: 76:[4, 19], Operations: ['51-47=4', '3+16=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[3, 51, 47, 16], Operations: [] Exploring Operation: 51-47=4, Resulting Numbers: [3, 16, 4] Generated Node #0,0: 76:[3, 16, 4] Operation: 51-47=4 Moving to Node #0,0 Current State: 76:[3, 16, 4], Operations: ['51-47=4'] Exploring Operation: 3+16=19, Resulting Numbers: [4, 19] Generated Node #0,0,0: 76:[4, 19] Operation: 3+16=19 Moving to Node #0,0,0 Current State: 76:[4, 19], Operations: ['51-47=4', '3+16=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 6, 63, 98, 11 ]
40
[ "6+63=69", "98+11=109", "109-69=40" ]
Current State: 40:[6, 63, 98, 11], Operations: [] Exploring Operation: 6+63=69, Resulting Numbers: [98, 11, 69] Generated Node #2: [98, 11, 69] from Operation: 6+63=69 Current State: 40:[98, 11, 69], Operations: ['6+63=69'] Exploring Operation: 98+11=109, Resulting Numbers: [69, 109] Generated Node #3: [69, 109] from Operation: 98+11=109 Current State: 40:[69, 109], Operations: ['6+63=69', '98+11=109'] Exploring Operation: 109-69=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[6, 63, 98, 11], Operations: [] Exploring Operation: 98-11=87, Resulting Numbers: [6, 63, 87] Generated Node #0,0: 40:[6, 63, 87] Operation: 98-11=87 Exploring Operation: 98-63=35, Resulting Numbers: [6, 11, 35] Generated Node #0,1: 40:[6, 11, 35] Operation: 98-63=35 Exploring Operation: 98-6=92, Resulting Numbers: [63, 11, 92] Generated Node #0,2: 40:[63, 11, 92] Operation: 98-6=92 Exploring Operation: 63-11=52, Resulting Numbers: [6, 98, 52] Generated Node #0,3: 40:[6, 98, 52] Operation: 63-11=52 Exploring Operation: 63-6=57, Resulting Numbers: [98, 11, 57] Generated Node #0,4: 40:[98, 11, 57] Operation: 63-6=57 Moving to Node #0,1 Current State: 40:[6, 11, 35], Operations: ['98-63=35'] Exploring Operation: 11-6=5, Resulting Numbers: [35, 5] Generated Node #0,1,0: 40:[35, 5] Operation: 11-6=5 Exploring Operation: 11+35=46, Resulting Numbers: [6, 46] Generated Node #0,1,1: 40:[6, 46] Operation: 11+35=46 Exploring Operation: 35-11=24, Resulting Numbers: [6, 24] Generated Node #0,1,2: 40:[6, 24] Operation: 35-11=24 Exploring Operation: 6+35=41, Resulting Numbers: [11, 41] Generated Node #0,1,3: 40:[11, 41] Operation: 6+35=41 Exploring Operation: 6+11=17, Resulting Numbers: [35, 17] Generated Node #0,1,4: 40:[35, 17] Operation: 6+11=17 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 40:[11, 41], Operations: ['98-63=35', '6+35=41'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,40 unequal: No Solution Exploring Operation: 11+41=52, Resulting Numbers: [52] 52,40 unequal: No Solution Exploring Operation: 11*41=451, Resulting Numbers: [451] 451,40 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 #0,1,0 Current State: 40:[35, 5], Operations: ['98-63=35', '11-6=5'] Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[6, 63, 98, 11], Operations: [] Exploring Operation: 98-63=35, Resulting Numbers: [6, 11, 35] Generated Node #0,1: 40:[6, 11, 35] Operation: 98-63=35 Moving to Node #0,1 Current State: 40:[6, 11, 35], Operations: ['98-63=35'] Exploring Operation: 11-6=5, Resulting Numbers: [35, 5] Generated Node #0,1,0: 40:[35, 5] Operation: 11-6=5 Moving to Node #0,1,0 Current State: 40:[35, 5], Operations: ['98-63=35', '11-6=5'] Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic