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
[ 7, 24, 74, 2 ]
79
[ "74-7=67", "24/2=12", "67+12=79" ]
Current State: 79:[7, 24, 74, 2], Operations: [] Exploring Operation: 74-7=67, Resulting Numbers: [24, 2, 67] Generated Node #2: [24, 2, 67] from Operation: 74-7=67 Current State: 79:[24, 2, 67], Operations: ['74-7=67'] Exploring Operation: 24/2=12, Resulting Numbers: [67, 12] Generated Node #3: [67, 12] from Operation: 24/2=12 Current State: 79:[67, 12], Operations: ['74-7=67', '24/2=12'] Exploring Operation: 67+12=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[7, 24, 74, 2], Operations: [] Exploring Operation: 24*2=48, Resulting Numbers: [7, 74, 48] Generated Node #0,0: 79:[7, 74, 48] Operation: 24*2=48 Exploring Operation: 7*2=14, Resulting Numbers: [24, 74, 14] Generated Node #0,1: 79:[24, 74, 14] Operation: 7*2=14 Exploring Operation: 24+2=26, Resulting Numbers: [7, 74, 26] Generated Node #0,2: 79:[7, 74, 26] Operation: 24+2=26 Exploring Operation: 7+2=9, Resulting Numbers: [24, 74, 9] Generated Node #0,3: 79:[24, 74, 9] Operation: 7+2=9 Exploring Operation: 7+24=31, Resulting Numbers: [74, 2, 31] Generated Node #0,4: 79:[74, 2, 31] Operation: 7+24=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[7, 74, 48], Operations: ['24*2=48'] Exploring Operation: 48-7=41, Resulting Numbers: [74, 41] Generated Node #0,0,0: 79:[74, 41] Operation: 48-7=41 Exploring Operation: 7+48=55, Resulting Numbers: [74, 55] Generated Node #0,0,1: 79:[74, 55] Operation: 7+48=55 Exploring Operation: 7+74=81, Resulting Numbers: [48, 81] Generated Node #0,0,2: 79:[48, 81] Operation: 7+74=81 Exploring Operation: 74+48=122, Resulting Numbers: [7, 122] Generated Node #0,0,3: 79:[7, 122] Operation: 74+48=122 Exploring Operation: 74-7=67, Resulting Numbers: [48, 67] Generated Node #0,0,4: 79:[48, 67] Operation: 74-7=67 Moving to Node #0,0,1 Current State: 79:[74, 55], Operations: ['24*2=48', '7+48=55'] Exploring Operation: 74-55=19, Resulting Numbers: [19] 19,79 unequal: No Solution Exploring Operation: 74*55=4070, Resulting Numbers: [4070] 4070,79 unequal: No Solution Exploring Operation: 74+55=129, Resulting Numbers: [129] 129,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[48, 81], Operations: ['24*2=48', '7+74=81'] Exploring Operation: 48+81=129, Resulting Numbers: [129] 129,79 unequal: No Solution Exploring Operation: 48*81=3888, Resulting Numbers: [3888] 3888,79 unequal: No Solution Exploring Operation: 81-48=33, Resulting Numbers: [33] 33,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[74, 41], Operations: ['24*2=48', '48-7=41'] Exploring Operation: 74-41=33, Resulting Numbers: [33] 33,79 unequal: No Solution Exploring Operation: 74+41=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 74*41=3034, Resulting Numbers: [3034] 3034,79 unequal: No Solution Moving to Node #0,0,4 Current State: 79:[48, 67], Operations: ['24*2=48', '74-7=67'] Exploring Operation: 48+67=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 48*67=3216, Resulting Numbers: [3216] 3216,79 unequal: No Solution Exploring Operation: 67-48=19, Resulting Numbers: [19] 19,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[7, 122], Operations: ['24*2=48', '74+48=122'] Exploring Operation: 122-7=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 7+122=129, Resulting Numbers: [129] 129,79 unequal: No Solution Exploring Operation: 7*122=854, Resulting Numbers: [854] 854,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[24, 74, 14], Operations: ['7*2=14'] Exploring Operation: 24+14=38, Resulting Numbers: [74, 38] Generated Node #0,1,0: 79:[74, 38] Operation: 24+14=38 Exploring Operation: 24-14=10, Resulting Numbers: [74, 10] Generated Node #0,1,1: 79:[74, 10] Operation: 24-14=10 Exploring Operation: 74+14=88, Resulting Numbers: [24, 88] Generated Node #0,1,2: 79:[24, 88] Operation: 74+14=88 Exploring Operation: 24+74=98, Resulting Numbers: [14, 98] Generated Node #0,1,3: 79:[14, 98] Operation: 24+74=98 Exploring Operation: 74-14=60, Resulting Numbers: [24, 60] Generated Node #0,1,4: 79:[24, 60] Operation: 74-14=60 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 79:[74, 38], Operations: ['7*2=14', '24+14=38'] Exploring Operation: 74+38=112, Resulting Numbers: [112] 112,79 unequal: No Solution Exploring Operation: 74-38=36, Resulting Numbers: [36] 36,79 unequal: No Solution Exploring Operation: 74*38=2812, Resulting Numbers: [2812] 2812,79 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 #0,1,2 Current State: 79:[24, 88], Operations: ['7*2=14', '74+14=88'] Exploring Operation: 88-24=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 24+88=112, Resulting Numbers: [112] 112,79 unequal: No Solution Exploring Operation: 24*88=2112, Resulting Numbers: [2112] 2112,79 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 #0,1,1 Current State: 79:[74, 10], Operations: ['7*2=14', '24-14=10'] Exploring Operation: 74+10=84, Resulting Numbers: [84] 84,79 unequal: No Solution Exploring Operation: 74*10=740, Resulting Numbers: [740] 740,79 unequal: No Solution Exploring Operation: 74-10=64, Resulting Numbers: [64] 64,79 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 #0,1,4 Current State: 79:[24, 60], Operations: ['7*2=14', '74-14=60'] Exploring Operation: 24+60=84, Resulting Numbers: [84] 84,79 unequal: No Solution Exploring Operation: 24*60=1440, Resulting Numbers: [1440] 1440,79 unequal: No Solution Exploring Operation: 60-24=36, Resulting Numbers: [36] 36,79 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 #0,1,3 Current State: 79:[14, 98], Operations: ['7*2=14', '24+74=98'] Exploring Operation: 14*98=1372, Resulting Numbers: [1372] 1372,79 unequal: No Solution Exploring Operation: 14+98=112, Resulting Numbers: [112] 112,79 unequal: No Solution Exploring Operation: 98-14=84, Resulting Numbers: [84] 84,79 unequal: No Solution Exploring Operation: 98/14=7, Resulting Numbers: [7] 7,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[7, 74, 26], Operations: ['24+2=26'] Exploring Operation: 26-7=19, Resulting Numbers: [74, 19] Generated Node #0,2,0: 79:[74, 19] Operation: 26-7=19 Exploring Operation: 74+26=100, Resulting Numbers: [7, 100] Generated Node #0,2,1: 79:[7, 100] Operation: 74+26=100 Exploring Operation: 7+26=33, Resulting Numbers: [74, 33] Generated Node #0,2,2: 79:[74, 33] Operation: 7+26=33 Exploring Operation: 7+74=81, Resulting Numbers: [26, 81] Generated Node #0,2,3: 79:[26, 81] Operation: 7+74=81 Exploring Operation: 74-7=67, Resulting Numbers: [26, 67] Generated Node #0,2,4: 79:[26, 67] Operation: 74-7=67 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 79:[74, 33], Operations: ['24+2=26', '7+26=33'] Exploring Operation: 74*33=2442, Resulting Numbers: [2442] 2442,79 unequal: No Solution Exploring Operation: 74+33=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 74-33=41, Resulting Numbers: [41] 41,79 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 #0,2,3 Current State: 79:[26, 81], Operations: ['24+2=26', '7+74=81'] Exploring Operation: 26*81=2106, Resulting Numbers: [2106] 2106,79 unequal: No Solution Exploring Operation: 26+81=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 81-26=55, Resulting Numbers: [55] 55,79 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 #0,2,0 Current State: 79:[74, 19], Operations: ['24+2=26', '26-7=19'] Exploring Operation: 74*19=1406, Resulting Numbers: [1406] 1406,79 unequal: No Solution Exploring Operation: 74+19=93, Resulting Numbers: [93] 93,79 unequal: No Solution Exploring Operation: 74-19=55, Resulting Numbers: [55] 55,79 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 #0,2,4 Current State: 79:[26, 67], Operations: ['24+2=26', '74-7=67'] Exploring Operation: 67-26=41, Resulting Numbers: [41] 41,79 unequal: No Solution Exploring Operation: 26*67=1742, Resulting Numbers: [1742] 1742,79 unequal: No Solution Exploring Operation: 26+67=93, Resulting Numbers: [93] 93,79 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 #0,2,1 Current State: 79:[7, 100], Operations: ['24+2=26', '74+26=100'] Exploring Operation: 100-7=93, Resulting Numbers: [93] 93,79 unequal: No Solution Exploring Operation: 7+100=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 7*100=700, Resulting Numbers: [700] 700,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 79:[24, 74, 9], Operations: ['7+2=9'] Exploring Operation: 24+9=33, Resulting Numbers: [74, 33] Generated Node #0,3,0: 79:[74, 33] Operation: 24+9=33 Exploring Operation: 24+74=98, Resulting Numbers: [9, 98] Generated Node #0,3,1: 79:[9, 98] Operation: 24+74=98 Exploring Operation: 74+9=83, Resulting Numbers: [24, 83] Generated Node #0,3,2: 79:[24, 83] Operation: 74+9=83 Exploring Operation: 74-9=65, Resulting Numbers: [24, 65] Generated Node #0,3,3: 79:[24, 65] Operation: 74-9=65 Exploring Operation: 24-9=15, Resulting Numbers: [74, 15] Generated Node #0,3,4: 79:[74, 15] Operation: 24-9=15 Moving to Node #0,3,0 Current State: 79:[74, 33], Operations: ['7+2=9', '24+9=33'] Exploring Operation: 74-33=41, Resulting Numbers: [41] 41,79 unequal: No Solution Exploring Operation: 74+33=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 74*33=2442, Resulting Numbers: [2442] 2442,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[24, 83], Operations: ['7+2=9', '74+9=83'] Exploring Operation: 83-24=59, Resulting Numbers: [59] 59,79 unequal: No Solution Exploring Operation: 24+83=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 24*83=1992, Resulting Numbers: [1992] 1992,79 unequal: No Solution Moving to Node #0,3,3 Current State: 79:[24, 65], Operations: ['7+2=9', '74-9=65'] Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,79 unequal: No Solution Exploring Operation: 24+65=89, Resulting Numbers: [89] 89,79 unequal: No Solution Exploring Operation: 24*65=1560, Resulting Numbers: [1560] 1560,79 unequal: No Solution Moving to Node #0,3,4 Current State: 79:[74, 15], Operations: ['7+2=9', '24-9=15'] Exploring Operation: 74-15=59, Resulting Numbers: [59] 59,79 unequal: No Solution Exploring Operation: 74*15=1110, Resulting Numbers: [1110] 1110,79 unequal: No Solution Exploring Operation: 74+15=89, Resulting Numbers: [89] 89,79 unequal: No Solution Moving to Node #0,3,1 Current State: 79:[9, 98], Operations: ['7+2=9', '24+74=98'] Exploring Operation: 9+98=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 98-9=89, Resulting Numbers: [89] 89,79 unequal: No Solution Exploring Operation: 9*98=882, Resulting Numbers: [882] 882,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 79:[74, 2, 31], Operations: ['7+24=31'] Exploring Operation: 74-2=72, Resulting Numbers: [31, 72] Generated Node #0,4,0: 79:[31, 72] Operation: 74-2=72 Exploring Operation: 74+2=76, Resulting Numbers: [31, 76] Generated Node #0,4,1: 79:[31, 76] Operation: 74+2=76 Exploring Operation: 2*31=62, Resulting Numbers: [74, 62] Generated Node #0,4,2: 79:[74, 62] Operation: 2*31=62 Exploring Operation: 31-2=29, Resulting Numbers: [74, 29] Generated Node #0,4,3: 79:[74, 29] Operation: 31-2=29 Exploring Operation: 2+31=33, Resulting Numbers: [74, 33] Generated Node #0,4,4: 79:[74, 33] Operation: 2+31=33 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 79:[74, 62], Operations: ['7+24=31', '2*31=62'] Exploring Operation: 74-62=12, Resulting Numbers: [12] 12,79 unequal: No Solution Exploring Operation: 74+62=136, Resulting Numbers: [136] 136,79 unequal: No Solution Exploring Operation: 74*62=4588, Resulting Numbers: [4588] 4588,79 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 #0,4,1 Current State: 79:[31, 76], Operations: ['7+24=31', '74+2=76'] Exploring Operation: 31*76=2356, Resulting Numbers: [2356] 2356,79 unequal: No Solution Exploring Operation: 76-31=45, Resulting Numbers: [45] 45,79 unequal: No Solution Exploring Operation: 31+76=107, Resulting Numbers: [107] 107,79 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 #0,4,4 Current State: 79:[74, 33], Operations: ['7+24=31', '2+31=33'] Exploring Operation: 74+33=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 74-33=41, Resulting Numbers: [41] 41,79 unequal: No Solution Exploring Operation: 74*33=2442, Resulting Numbers: [2442] 2442,79 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 #0,4,0 Current State: 79:[31, 72], Operations: ['7+24=31', '74-2=72'] Exploring Operation: 31+72=103, Resulting Numbers: [103] 103,79 unequal: No Solution Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,79 unequal: No Solution Exploring Operation: 31*72=2232, Resulting Numbers: [2232] 2232,79 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 #0,4,3 Current State: 79:[74, 29], Operations: ['7+24=31', '31-2=29'] Exploring Operation: 74*29=2146, Resulting Numbers: [2146] 2146,79 unequal: No Solution Exploring Operation: 74-29=45, Resulting Numbers: [45] 45,79 unequal: No Solution Exploring Operation: 74+29=103, Resulting Numbers: [103] 103,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 62, 33, 63, 66 ]
34
[ "62+33=95", "63+66=129", "129-95=34" ]
Current State: 34:[62, 33, 63, 66], Operations: [] Exploring Operation: 62+33=95, Resulting Numbers: [63, 66, 95] Generated Node #2: [63, 66, 95] from Operation: 62+33=95 Current State: 34:[63, 66, 95], Operations: ['62+33=95'] Exploring Operation: 63+66=129, Resulting Numbers: [95, 129] Generated Node #3: [95, 129] from Operation: 63+66=129 Current State: 34:[95, 129], Operations: ['62+33=95', '63+66=129'] Exploring Operation: 129-95=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[62, 33, 63, 66], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [33, 63, 4] Generated Node #0,0: 34:[33, 63, 4] Operation: 66-62=4 Exploring Operation: 63-62=1, Resulting Numbers: [33, 66, 1] Generated Node #0,1: 34:[33, 66, 1] Operation: 63-62=1 Exploring Operation: 66-33=33, Resulting Numbers: [62, 63, 33] Generated Node #0,2: 34:[62, 63, 33] Operation: 66-33=33 Exploring Operation: 66-63=3, Resulting Numbers: [62, 33, 3] Generated Node #0,3: 34:[62, 33, 3] Operation: 66-63=3 Exploring Operation: 66/33=2, Resulting Numbers: [62, 63, 2] Generated Node #0,4: 34:[62, 63, 2] Operation: 66/33=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 34:[62, 33, 3], Operations: ['66-63=3'] Exploring Operation: 62-33=29, Resulting Numbers: [3, 29] Generated Node #0,3,0: 34:[3, 29] Operation: 62-33=29 Exploring Operation: 62+3=65, Resulting Numbers: [33, 65] Generated Node #0,3,1: 34:[33, 65] Operation: 62+3=65 Exploring Operation: 62-3=59, Resulting Numbers: [33, 59] Generated Node #0,3,2: 34:[33, 59] Operation: 62-3=59 Exploring Operation: 33-3=30, Resulting Numbers: [62, 30] Generated Node #0,3,3: 34:[62, 30] Operation: 33-3=30 Exploring Operation: 33+3=36, Resulting Numbers: [62, 36] Generated Node #0,3,4: 34:[62, 36] Operation: 33+3=36 Moving to Node #0,3,0 Current State: 34:[3, 29], Operations: ['66-63=3', '62-33=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,34 unequal: No Solution Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,34 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,34 unequal: No Solution Moving to Node #0,3,2 Current State: 34:[33, 59], Operations: ['66-63=3', '62-3=59'] Exploring Operation: 33*59=1947, Resulting Numbers: [1947] 1947,34 unequal: No Solution Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,34 unequal: No Solution Exploring Operation: 33+59=92, Resulting Numbers: [92] 92,34 unequal: No Solution Moving to Node #0,3,4 Current State: 34:[62, 36], Operations: ['66-63=3', '33+3=36'] Exploring Operation: 62*36=2232, Resulting Numbers: [2232] 2232,34 unequal: No Solution Exploring Operation: 62+36=98, Resulting Numbers: [98] 98,34 unequal: No Solution Exploring Operation: 62-36=26, Resulting Numbers: [26] 26,34 unequal: No Solution Moving to Node #0,3,1 Current State: 34:[33, 65], Operations: ['66-63=3', '62+3=65'] Exploring Operation: 33*65=2145, Resulting Numbers: [2145] 2145,34 unequal: No Solution Exploring Operation: 65-33=32, Resulting Numbers: [32] 32,34 unequal: No Solution Exploring Operation: 33+65=98, Resulting Numbers: [98] 98,34 unequal: No Solution Moving to Node #0,3,3 Current State: 34:[62, 30], Operations: ['66-63=3', '33-3=30'] Exploring Operation: 62+30=92, Resulting Numbers: [92] 92,34 unequal: No Solution Exploring Operation: 62-30=32, Resulting Numbers: [32] 32,34 unequal: No Solution Exploring Operation: 62*30=1860, Resulting Numbers: [1860] 1860,34 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 Current State: 34:[33, 63, 4], Operations: ['66-62=4'] Exploring Operation: 63-4=59, Resulting Numbers: [33, 59] Generated Node #0,0,0: 34:[33, 59] Operation: 63-4=59 Exploring Operation: 33-4=29, Resulting Numbers: [63, 29] Generated Node #0,0,1: 34:[63, 29] Operation: 33-4=29 Exploring Operation: 33+4=37, Resulting Numbers: [63, 37] Generated Node #0,0,2: 34:[63, 37] Operation: 33+4=37 Exploring Operation: 63-33=30, Resulting Numbers: [4, 30] Generated Node #0,0,3: 34:[4, 30] Operation: 63-33=30 Exploring Operation: 63+4=67, Resulting Numbers: [33, 67] Generated Node #0,0,4: 34:[33, 67] Operation: 63+4=67 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 34:[4, 30], Operations: ['66-62=4', '63-33=30'] Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,34 unequal: No Solution Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[62, 33, 63, 66], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [33, 63, 4] Generated Node #0,0: 34:[33, 63, 4] Operation: 66-62=4 Moving to Node #0,0 Current State: 34:[33, 63, 4], Operations: ['66-62=4'] Exploring Operation: 63-33=30, Resulting Numbers: [4, 30] Generated Node #0,0,3: 34:[4, 30] Operation: 63-33=30 Moving to Node #0,0,3 Current State: 34:[4, 30], Operations: ['66-62=4', '63-33=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_5
sum_heuristic
[ 75, 45, 61, 3 ]
51
[ "75-45=30", "30/3=10", "61-10=51" ]
Current State: 51:[75, 45, 61, 3], Operations: [] Exploring Operation: 75-45=30, Resulting Numbers: [61, 3, 30] Generated Node #2: [61, 3, 30] from Operation: 75-45=30 Current State: 51:[61, 3, 30], Operations: ['75-45=30'] Exploring Operation: 30/3=10, Resulting Numbers: [61, 10] Generated Node #3: [61, 10] from Operation: 30/3=10 Current State: 51:[61, 10], Operations: ['75-45=30', '30/3=10'] Exploring Operation: 61-10=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[75, 45, 61, 3], Operations: [] Exploring Operation: 61-45=16, Resulting Numbers: [75, 3, 16] Generated Node #0,0: 51:[75, 3, 16] Operation: 61-45=16 Exploring Operation: 45/3=15, Resulting Numbers: [75, 61, 15] Generated Node #0,1: 51:[75, 61, 15] Operation: 45/3=15 Exploring Operation: 75-61=14, Resulting Numbers: [45, 3, 14] Generated Node #0,2: 51:[45, 3, 14] Operation: 75-61=14 Exploring Operation: 75-45=30, Resulting Numbers: [61, 3, 30] Generated Node #0,3: 51:[61, 3, 30] Operation: 75-45=30 Exploring Operation: 75/3=25, Resulting Numbers: [45, 61, 25] Generated Node #0,4: 51:[45, 61, 25] Operation: 75/3=25 Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[45, 3, 14], Operations: ['75-61=14'] Exploring Operation: 45/3=15, Resulting Numbers: [14, 15] Generated Node #0,2,0: 51:[14, 15] Operation: 45/3=15 Exploring Operation: 45-3=42, Resulting Numbers: [14, 42] Generated Node #0,2,1: 51:[14, 42] Operation: 45-3=42 Exploring Operation: 45+14=59, Resulting Numbers: [3, 59] Generated Node #0,2,2: 51:[3, 59] Operation: 45+14=59 Exploring Operation: 45+3=48, Resulting Numbers: [14, 48] Generated Node #0,2,3: 51:[14, 48] Operation: 45+3=48 Exploring Operation: 3+14=17, Resulting Numbers: [45, 17] Generated Node #0,2,4: 51:[45, 17] Operation: 3+14=17 Moving to Node #0,2,0 Current State: 51:[14, 15], Operations: ['75-61=14', '45/3=15'] Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,51 unequal: No Solution Exploring Operation: 14*15=210, Resulting Numbers: [210] 210,51 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,51 unequal: No Solution Moving to Node #0,2,4 Current State: 51:[45, 17], Operations: ['75-61=14', '3+14=17'] Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,51 unequal: No Solution Exploring Operation: 45*17=765, Resulting Numbers: [765] 765,51 unequal: No Solution Exploring Operation: 45+17=62, Resulting Numbers: [62] 62,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[14, 48], Operations: ['75-61=14', '45+3=48'] Exploring Operation: 14*48=672, Resulting Numbers: [672] 672,51 unequal: No Solution Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,51 unequal: No Solution Exploring Operation: 14+48=62, Resulting Numbers: [62] 62,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[3, 59], Operations: ['75-61=14', '45+14=59'] Exploring Operation: 3+59=62, Resulting Numbers: [62] 62,51 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 3*59=177, Resulting Numbers: [177] 177,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[14, 42], Operations: ['75-61=14', '45-3=42'] Exploring Operation: 14+42=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 42-14=28, Resulting Numbers: [28] 28,51 unequal: No Solution Exploring Operation: 14*42=588, Resulting Numbers: [588] 588,51 unequal: No Solution Exploring Operation: 42/14=3, Resulting Numbers: [3] 3,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[61, 3, 30], Operations: ['75-45=30'] Exploring Operation: 61-3=58, Resulting Numbers: [30, 58] Generated Node #0,3,0: 51:[30, 58] Operation: 61-3=58 Exploring Operation: 30/3=10, Resulting Numbers: [61, 10] Generated Node #0,3,1: 51:[61, 10] Operation: 30/3=10 Exploring Operation: 61+3=64, Resulting Numbers: [30, 64] Generated Node #0,3,2: 51:[30, 64] Operation: 61+3=64 Exploring Operation: 61-30=31, Resulting Numbers: [3, 31] Generated Node #0,3,3: 51:[3, 31] Operation: 61-30=31 Exploring Operation: 30-3=27, Resulting Numbers: [61, 27] Generated Node #0,3,4: 51:[61, 27] Operation: 30-3=27 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 51:[3, 31], Operations: ['75-45=30', '61-30=31'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,51 unequal: No Solution Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,51 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 51:[61, 10], Operations: ['75-45=30', '30/3=10'] Exploring Operation: 61+10=71, Resulting Numbers: [71] 71,51 unequal: No Solution Exploring Operation: 61-10=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[75, 45, 61, 3], Operations: [] Exploring Operation: 75-45=30, Resulting Numbers: [61, 3, 30] Generated Node #0,3: 51:[61, 3, 30] Operation: 75-45=30 Moving to Node #0,3 Current State: 51:[61, 3, 30], Operations: ['75-45=30'] Exploring Operation: 30/3=10, Resulting Numbers: [61, 10] Generated Node #0,3,1: 51:[61, 10] Operation: 30/3=10 Moving to Node #0,3,1 Current State: 51:[61, 10], Operations: ['75-45=30', '30/3=10'] Exploring Operation: 61-10=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_5
sum_heuristic
[ 54, 41, 1, 41 ]
28
[ "54-41=13", "1*41=41", "41-13=28" ]
Current State: 28:[54, 41, 1, 41], Operations: [] Exploring Operation: 54-41=13, Resulting Numbers: [1, 13] Generated Node #2: [1, 13] from Operation: 54-41=13 Current State: 28:[1, 13], Operations: ['54-41=13'] Exploring Operation: 1*41=41, Resulting Numbers: [13, 41] Generated Node #3: [13, 41] from Operation: 1*41=41 Current State: 28:[13, 41], Operations: ['54-41=13', '1*41=41'] Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[54, 41, 1, 41], Operations: [] Exploring Operation: 54-41=13, Resulting Numbers: [1, 41, 13] Generated Node #0,0: 28:[1, 41, 13] Operation: 54-41=13 Exploring Operation: 54-41=13, Resulting Numbers: [41, 1, 13] Generated Node #0,1: 28:[41, 1, 13] Operation: 54-41=13 Exploring Operation: 41-41=0, Resulting Numbers: [54, 1, 0] Generated Node #0,2: 28:[54, 1, 0] Operation: 41-41=0 Exploring Operation: 41/41=1, Resulting Numbers: [54, 1, 1] Generated Node #0,3: 28:[54, 1, 1] Operation: 41/41=1 Moving to Node #0,0 Current State: 28:[1, 41, 13], Operations: ['54-41=13'] Exploring Operation: 41-13=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 28:[1, 28] Operation: 41-13=28 Exploring Operation: 41-1=40, Resulting Numbers: [13, 40] Generated Node #0,0,1: 28:[13, 40] Operation: 41-1=40 Exploring Operation: 1*41=41, Resulting Numbers: [13, 41] Generated Node #0,0,2: 28:[13, 41] Operation: 1*41=41 Exploring Operation: 1+13=14, Resulting Numbers: [41, 14] Generated Node #0,0,3: 28:[41, 14] Operation: 1+13=14 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 28:[1, 28], Operations: ['54-41=13', '41-13=28'] Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[54, 41, 1, 41], Operations: [] Exploring Operation: 54-41=13, Resulting Numbers: [1, 41, 13] Generated Node #0,0: 28:[1, 41, 13] Operation: 54-41=13 Moving to Node #0,0 Current State: 28:[1, 41, 13], Operations: ['54-41=13'] Exploring Operation: 41-13=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 28:[1, 28] Operation: 41-13=28 Moving to Node #0,0,0 Current State: 28:[1, 28], Operations: ['54-41=13', '41-13=28'] Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 96, 51, 66, 62 ]
75
[ "66-62=4", "96/4=24", "51+24=75" ]
Current State: 75:[96, 51, 66, 62], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [96, 51, 4] Generated Node #2: [96, 51, 4] from Operation: 66-62=4 Current State: 75:[96, 51, 4], Operations: ['66-62=4'] Exploring Operation: 96/4=24, Resulting Numbers: [51, 24] Generated Node #3: [51, 24] from Operation: 96/4=24 Current State: 75:[51, 24], Operations: ['66-62=4', '96/4=24'] Exploring Operation: 51+24=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[96, 51, 66, 62], Operations: [] Exploring Operation: 66-51=15, Resulting Numbers: [96, 62, 15] Generated Node #0,0: 75:[96, 62, 15] Operation: 66-51=15 Moving to Node #0,0 Current State: 75:[96, 62, 15], Operations: ['66-51=15'] Exploring Operation: 96-62=34, Resulting Numbers: [15, 34] Generated Node #0,0,0: 75:[15, 34] Operation: 96-62=34 Moving to Node #0,0,0 Current State: 75:[15, 34], Operations: ['66-51=15', '96-62=34'] Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,75 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 82, 12, 71, 13 ]
89
[ "71+13=84", "84/12=7", "82+7=89" ]
Current State: 89:[82, 12, 71, 13], Operations: [] Exploring Operation: 71+13=84, Resulting Numbers: [82, 12, 84] Generated Node #2: [82, 12, 84] from Operation: 71+13=84 Current State: 89:[82, 12, 84], Operations: ['71+13=84'] Exploring Operation: 84/12=7, Resulting Numbers: [82, 7] Generated Node #3: [82, 7] from Operation: 84/12=7 Current State: 89:[82, 7], Operations: ['71+13=84', '84/12=7'] Exploring Operation: 82+7=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[82, 12, 71, 13], Operations: [] Exploring Operation: 12+71=83, Resulting Numbers: [82, 13, 83] Generated Node #0,0: 89:[82, 13, 83] Operation: 12+71=83 Moving to Node #0,0 Current State: 89:[82, 13, 83], Operations: ['12+71=83'] Exploring Operation: 82+13=95, Resulting Numbers: [83, 95] Generated Node #0,0,0: 89:[83, 95] Operation: 82+13=95 Moving to Node #0,0,0 Current State: 89:[83, 95], Operations: ['12+71=83', '82+13=95'] Exploring Operation: 95-83=12, Resulting Numbers: [12] 12,89 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 48, 96, 90, 91 ]
92
[ "96/48=2", "91*2=182", "182-90=92" ]
Current State: 92:[48, 96, 90, 91], Operations: [] Exploring Operation: 96/48=2, Resulting Numbers: [90, 91, 2] Generated Node #2: [90, 91, 2] from Operation: 96/48=2 Current State: 92:[90, 91, 2], Operations: ['96/48=2'] Exploring Operation: 91*2=182, Resulting Numbers: [90, 182] Generated Node #3: [90, 182] from Operation: 91*2=182 Current State: 92:[90, 182], Operations: ['96/48=2', '91*2=182'] Exploring Operation: 182-90=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[48, 96, 90, 91], Operations: [] Exploring Operation: 96/48=2, Resulting Numbers: [90, 91, 2] Generated Node #0,0: 92:[90, 91, 2] Operation: 96/48=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[90, 91, 2], Operations: ['96/48=2'] Exploring Operation: 91-90=1, Resulting Numbers: [2, 1] Generated Node #0,0,0: 92:[2, 1] Operation: 91-90=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[2, 1], Operations: ['96/48=2', '91-90=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,92 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
[ 6, 14, 6, 39 ]
51
[ "6*14=84", "39-6=33", "84-33=51" ]
Current State: 51:[6, 14, 6, 39], Operations: [] Exploring Operation: 6*14=84, Resulting Numbers: [39, 84] Generated Node #2: [39, 84] from Operation: 6*14=84 Current State: 51:[39, 84], Operations: ['6*14=84'] Exploring Operation: 39-6=33, Resulting Numbers: [84, 33] Generated Node #3: [84, 33] from Operation: 39-6=33 Current State: 51:[84, 33], Operations: ['6*14=84', '39-6=33'] Exploring Operation: 84-33=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[6, 14, 6, 39], Operations: [] Exploring Operation: 6+39=45, Resulting Numbers: [6, 14, 45] Generated Node #0,0: 51:[6, 14, 45] Operation: 6+39=45 Exploring Operation: 39-14=25, Resulting Numbers: [6, 6, 25] Generated Node #0,1: 51:[6, 6, 25] Operation: 39-14=25 Exploring Operation: 6+39=45, Resulting Numbers: [14, 6, 45] Generated Node #0,2: 51:[14, 6, 45] Operation: 6+39=45 Exploring Operation: 14+39=53, Resulting Numbers: [6, 6, 53] Generated Node #0,3: 51:[6, 6, 53] Operation: 14+39=53 Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[6, 6, 53], Operations: ['14+39=53'] Exploring Operation: 6-6=0, Resulting Numbers: [53, 0] Generated Node #0,3,0: 51:[53, 0] Operation: 6-6=0 Exploring Operation: 6+6=12, Resulting Numbers: [53, 12] Generated Node #0,3,1: 51:[53, 12] Operation: 6+6=12 Exploring Operation: 6/6=1, Resulting Numbers: [53, 1] Generated Node #0,3,2: 51:[53, 1] Operation: 6/6=1 Exploring Operation: 53-6=47, Resulting Numbers: [6, 47] Generated Node #0,3,3: 51:[6, 47] Operation: 53-6=47 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 51:[53, 1], Operations: ['14+39=53', '6/6=1'] Exploring Operation: 53*1=53, Resulting Numbers: [53] 53,51 unequal: No Solution Exploring Operation: 53+1=54, Resulting Numbers: [54] 54,51 unequal: No Solution Exploring Operation: 53/1=53, Resulting Numbers: [53] 53,51 unequal: No Solution Exploring Operation: 53-1=52, Resulting Numbers: [52] 52,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 51:[53, 0], Operations: ['14+39=53', '6-6=0'] Exploring Operation: 53+0=53, Resulting Numbers: [53] 53,51 unequal: No Solution Exploring Operation: 53*0=0, Resulting Numbers: [0] 0,51 unequal: No Solution Exploring Operation: 53-0=53, Resulting Numbers: [53] 53,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 51:[53, 12], Operations: ['14+39=53', '6+6=12'] Exploring Operation: 53+12=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 53-12=41, Resulting Numbers: [41] 41,51 unequal: No Solution Exploring Operation: 53*12=636, Resulting Numbers: [636] 636,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 51:[6, 47], Operations: ['14+39=53', '53-6=47'] Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,51 unequal: No Solution Exploring Operation: 6*47=282, Resulting Numbers: [282] 282,51 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[6, 14, 45], Operations: ['6+39=45'] Exploring Operation: 14-6=8, Resulting Numbers: [45, 8] Generated Node #0,0,0: 51:[45, 8] Operation: 14-6=8 Exploring Operation: 14+45=59, Resulting Numbers: [6, 59] Generated Node #0,0,1: 51:[6, 59] Operation: 14+45=59 Exploring Operation: 6+45=51, Resulting Numbers: [14, 51] Generated Node #0,0,2: 51:[14, 51] Operation: 6+45=51 Exploring Operation: 6+14=20, Resulting Numbers: [45, 20] Generated Node #0,0,3: 51:[45, 20] Operation: 6+14=20 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 51:[14, 51], Operations: ['6+39=45', '6+45=51'] Exploring Operation: 14*51=714, Resulting Numbers: [714] 714,51 unequal: No Solution Exploring Operation: 14+51=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 51:[45, 20], Operations: ['6+39=45', '6+14=20'] Exploring Operation: 45*20=900, Resulting Numbers: [900] 900,51 unequal: No Solution Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,51 unequal: No Solution Exploring Operation: 45+20=65, Resulting Numbers: [65] 65,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[45, 8], Operations: ['6+39=45', '14-6=8'] Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,51 unequal: No Solution Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,51 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 51:[6, 59], Operations: ['6+39=45', '14+45=59'] Exploring Operation: 6*59=354, Resulting Numbers: [354] 354,51 unequal: No Solution Exploring Operation: 6+59=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[14, 6, 45], Operations: ['6+39=45'] Exploring Operation: 14+6=20, Resulting Numbers: [45, 20] Generated Node #0,2,0: 51:[45, 20] Operation: 14+6=20 Exploring Operation: 6+45=51, Resulting Numbers: [14, 51] Generated Node #0,2,1: 51:[14, 51] Operation: 6+45=51 Exploring Operation: 14-6=8, Resulting Numbers: [45, 8] Generated Node #0,2,2: 51:[45, 8] Operation: 14-6=8 Exploring Operation: 14+45=59, Resulting Numbers: [6, 59] Generated Node #0,2,3: 51:[6, 59] Operation: 14+45=59 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 51:[14, 51], Operations: ['6+39=45', '6+45=51'] Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,51 unequal: No Solution Exploring Operation: 14+51=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 14*51=714, Resulting Numbers: [714] 714,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 51:[45, 20], Operations: ['6+39=45', '14+6=20'] Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,51 unequal: No Solution Exploring Operation: 45+20=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 45*20=900, Resulting Numbers: [900] 900,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 51:[45, 8], Operations: ['6+39=45', '14-6=8'] Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,51 unequal: No Solution Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,51 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 51:[6, 59], Operations: ['6+39=45', '14+45=59'] Exploring Operation: 6+59=65, Resulting Numbers: [65] 65,51 unequal: No Solution Exploring Operation: 6*59=354, Resulting Numbers: [354] 354,51 unequal: No Solution Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[6, 6, 25], Operations: ['39-14=25'] Exploring Operation: 6-6=0, Resulting Numbers: [25, 0] Generated Node #0,1,0: 51:[25, 0] Operation: 6-6=0 Exploring Operation: 25-6=19, Resulting Numbers: [6, 19] Generated Node #0,1,1: 51:[6, 19] Operation: 25-6=19 Exploring Operation: 6/6=1, Resulting Numbers: [25, 1] Generated Node #0,1,2: 51:[25, 1] Operation: 6/6=1 Exploring Operation: 25-6=19, Resulting Numbers: [6, 19] Generated Node #0,1,3: 51:[6, 19] Operation: 25-6=19 Moving to Node #0,1,1 Current State: 51:[6, 19], Operations: ['39-14=25', '25-6=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,51 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,51 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,51 unequal: No Solution Moving to Node #0,1,3 Current State: 51:[6, 19], Operations: ['39-14=25', '25-6=19'] Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,51 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,51 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,51 unequal: No Solution Moving to Node #0,1,2 Current State: 51:[25, 1], Operations: ['39-14=25', '6/6=1'] Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,51 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,51 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,51 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[25, 0], Operations: ['39-14=25', '6-6=0'] Exploring Operation: 25*0=0, Resulting Numbers: [0] 0,51 unequal: No Solution Exploring Operation: 25+0=25, Resulting Numbers: [25] 25,51 unequal: No Solution Exploring Operation: 25-0=25, Resulting Numbers: [25] 25,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 65, 16, 79, 44 ]
88
[ "65+16=81", "81-79=2", "44*2=88" ]
Current State: 88:[65, 16, 79, 44], Operations: [] Exploring Operation: 65+16=81, Resulting Numbers: [79, 44, 81] Generated Node #2: [79, 44, 81] from Operation: 65+16=81 Current State: 88:[79, 44, 81], Operations: ['65+16=81'] Exploring Operation: 81-79=2, Resulting Numbers: [44, 2] Generated Node #3: [44, 2] from Operation: 81-79=2 Current State: 88:[44, 2], Operations: ['65+16=81', '81-79=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[65, 16, 79, 44], Operations: [] Exploring Operation: 65-44=21, Resulting Numbers: [16, 79, 21] Generated Node #0,0: 88:[16, 79, 21] Operation: 65-44=21 Exploring Operation: 65+16=81, Resulting Numbers: [79, 44, 81] Generated Node #0,1: 88:[79, 44, 81] Operation: 65+16=81 Exploring Operation: 79-65=14, Resulting Numbers: [16, 44, 14] Generated Node #0,2: 88:[16, 44, 14] Operation: 79-65=14 Exploring Operation: 65-16=49, Resulting Numbers: [79, 44, 49] Generated Node #0,3: 88:[79, 44, 49] Operation: 65-16=49 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[16, 44, 14], Operations: ['79-65=14'] Exploring Operation: 44-14=30, Resulting Numbers: [16, 30] Generated Node #0,2,0: 88:[16, 30] Operation: 44-14=30 Exploring Operation: 16-14=2, Resulting Numbers: [44, 2] Generated Node #0,2,1: 88:[44, 2] Operation: 16-14=2 Exploring Operation: 44-16=28, Resulting Numbers: [14, 28] Generated Node #0,2,2: 88:[14, 28] Operation: 44-16=28 Exploring Operation: 16+14=30, Resulting Numbers: [44, 30] Generated Node #0,2,3: 88:[44, 30] Operation: 16+14=30 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 88:[44, 2], Operations: ['79-65=14', '16-14=2'] Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,88 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,88 unequal: No Solution Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[65, 16, 79, 44], Operations: [] Exploring Operation: 79-65=14, Resulting Numbers: [16, 44, 14] Generated Node #0,2: 88:[16, 44, 14] Operation: 79-65=14 Moving to Node #0,2 Current State: 88:[16, 44, 14], Operations: ['79-65=14'] Exploring Operation: 16-14=2, Resulting Numbers: [44, 2] Generated Node #0,2,1: 88:[44, 2] Operation: 16-14=2 Moving to Node #0,2,1 Current State: 88:[44, 2], Operations: ['79-65=14', '16-14=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 62, 38, 26, 62 ]
38
[ "62-62=0", "26*0=0", "38+0=38" ]
Current State: 38:[62, 38, 26, 62], Operations: [] Exploring Operation: 62-62=0, Resulting Numbers: [38, 26, 0] Generated Node #2: [38, 26, 0] from Operation: 62-62=0 Current State: 38:[38, 26, 0], Operations: ['62-62=0'] Exploring Operation: 26*0=0, Resulting Numbers: [38, 0] Generated Node #3: [38, 0] from Operation: 26*0=0 Current State: 38:[38, 0], Operations: ['62-62=0', '26*0=0'] Exploring Operation: 38+0=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[62, 38, 26, 62], Operations: [] Exploring Operation: 62-26=36, Resulting Numbers: [38, 62, 36] Generated Node #0,0: 38:[38, 62, 36] Operation: 62-26=36 Exploring Operation: 62-26=36, Resulting Numbers: [62, 38, 36] Generated Node #0,1: 38:[62, 38, 36] Operation: 62-26=36 Exploring Operation: 62/62=1, Resulting Numbers: [38, 26, 1] Generated Node #0,2: 38:[38, 26, 1] Operation: 62/62=1 Exploring Operation: 62-62=0, Resulting Numbers: [38, 26, 0] Generated Node #0,3: 38:[38, 26, 0] Operation: 62-62=0 Moving to Node #0,2 Current State: 38:[38, 26, 1], Operations: ['62/62=1'] Exploring Operation: 26-1=25, Resulting Numbers: [38, 25] Generated Node #0,2,0: 38:[38, 25] Operation: 26-1=25 Exploring Operation: 26*1=26, Resulting Numbers: [38, 26] Generated Node #0,2,1: 38:[38, 26] Operation: 26*1=26 Exploring Operation: 38*1=38, Resulting Numbers: [26, 38] Generated Node #0,2,2: 38:[26, 38] Operation: 38*1=38 Exploring Operation: 38/1=38, Resulting Numbers: [26, 38] Generated Node #0,2,3: 38:[26, 38] Operation: 38/1=38 Moving to Node #0,3 Current State: 38:[38, 26, 0], Operations: ['62-62=0'] Exploring Operation: 26*0=0, Resulting Numbers: [38, 0] Generated Node #0,3,0: 38:[38, 0] Operation: 26*0=0 Exploring Operation: 26+0=26, Resulting Numbers: [38, 26] Generated Node #0,3,1: 38:[38, 26] Operation: 26+0=26 Exploring Operation: 38+0=38, Resulting Numbers: [26, 38] Generated Node #0,3,2: 38:[26, 38] Operation: 38+0=38 Exploring Operation: 38-0=38, Resulting Numbers: [26, 38] Generated Node #0,3,3: 38:[26, 38] Operation: 38-0=38 Moving to Node #0,1 Current State: 38:[62, 38, 36], Operations: ['62-26=36'] Exploring Operation: 38-36=2, Resulting Numbers: [62, 2] Generated Node #0,1,0: 38:[62, 2] Operation: 38-36=2 Exploring Operation: 62-36=26, Resulting Numbers: [38, 26] Generated Node #0,1,1: 38:[38, 26] Operation: 62-36=26 Exploring Operation: 62+36=98, Resulting Numbers: [38, 98] Generated Node #0,1,2: 38:[38, 98] Operation: 62+36=98 Exploring Operation: 62-38=24, Resulting Numbers: [36, 24] Generated Node #0,1,3: 38:[36, 24] Operation: 62-38=24 Moving to Node #0,0 Current State: 38:[38, 62, 36], Operations: ['62-26=36'] Exploring Operation: 38-36=2, Resulting Numbers: [62, 2] Generated Node #0,0,0: 38:[62, 2] Operation: 38-36=2 Exploring Operation: 62-38=24, Resulting Numbers: [36, 24] Generated Node #0,0,1: 38:[36, 24] Operation: 62-38=24 Exploring Operation: 38+36=74, Resulting Numbers: [62, 74] Generated Node #0,0,2: 38:[62, 74] Operation: 38+36=74 Exploring Operation: 62-36=26, Resulting Numbers: [38, 26] Generated Node #0,0,3: 38:[38, 26] Operation: 62-36=26 Moving to Node #0,3,0 Current State: 38:[38, 0], Operations: ['62-62=0', '26*0=0'] Exploring Operation: 38-0=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[62, 38, 26, 62], Operations: [] Exploring Operation: 62-62=0, Resulting Numbers: [38, 26, 0] Generated Node #0,3: 38:[38, 26, 0] Operation: 62-62=0 Moving to Node #0,3 Current State: 38:[38, 26, 0], Operations: ['62-62=0'] Exploring Operation: 26*0=0, Resulting Numbers: [38, 0] Generated Node #0,3,0: 38:[38, 0] Operation: 26*0=0 Moving to Node #0,3,0 Current State: 38:[38, 0], Operations: ['62-62=0', '26*0=0'] Exploring Operation: 38-0=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
0.978299
hs_4
sum_heuristic
[ 30, 77, 28, 10 ]
70
[ "30*28=840", "77*10=770", "840-770=70" ]
Current State: 70:[30, 77, 28, 10], Operations: [] Exploring Operation: 30*28=840, Resulting Numbers: [77, 10, 840] Generated Node #2: [77, 10, 840] from Operation: 30*28=840 Current State: 70:[77, 10, 840], Operations: ['30*28=840'] Exploring Operation: 77*10=770, Resulting Numbers: [840, 770] Generated Node #3: [840, 770] from Operation: 77*10=770 Current State: 70:[840, 770], Operations: ['30*28=840', '77*10=770'] Exploring Operation: 840-770=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[30, 77, 28, 10], Operations: [] Exploring Operation: 30-28=2, Resulting Numbers: [77, 10, 2] Generated Node #0,0: 70:[77, 10, 2] Operation: 30-28=2 Exploring Operation: 30/10=3, Resulting Numbers: [77, 28, 3] Generated Node #0,1: 70:[77, 28, 3] Operation: 30/10=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[77, 10, 2], Operations: ['30-28=2'] Exploring Operation: 77-10=67, Resulting Numbers: [2, 67] Generated Node #0,0,0: 70:[2, 67] Operation: 77-10=67 Exploring Operation: 77-2=75, Resulting Numbers: [10, 75] Generated Node #0,0,1: 70:[10, 75] Operation: 77-2=75 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 70:[2, 67], Operations: ['30-28=2', '77-10=67'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,70 unequal: No Solution Exploring Operation: 2+67=69, Resulting Numbers: [69] 69,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 70:[10, 75], Operations: ['30-28=2', '77-2=75'] Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,70 unequal: No Solution Exploring Operation: 10+75=85, Resulting Numbers: [85] 85,70 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 #0,1 Current State: 70:[77, 28, 3], Operations: ['30/10=3'] Exploring Operation: 77-3=74, Resulting Numbers: [28, 74] Generated Node #0,1,0: 70:[28, 74] Operation: 77-3=74 Exploring Operation: 28+3=31, Resulting Numbers: [77, 31] Generated Node #0,1,1: 70:[77, 31] Operation: 28+3=31 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 70:[28, 74], Operations: ['30/10=3', '77-3=74'] Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,70 unequal: No Solution Exploring Operation: 28+74=102, Resulting Numbers: [102] 102,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 70:[77, 31], Operations: ['30/10=3', '28+3=31'] Exploring Operation: 77+31=108, Resulting Numbers: [108] 108,70 unequal: No Solution Exploring Operation: 77-31=46, Resulting Numbers: [46] 46,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 4, 2, 30, 55 ]
79
[ "4+2=6", "30+55=85", "85-6=79" ]
Current State: 79:[4, 2, 30, 55], Operations: [] Exploring Operation: 4+2=6, Resulting Numbers: [30, 55, 6] Generated Node #2: [30, 55, 6] from Operation: 4+2=6 Current State: 79:[30, 55, 6], Operations: ['4+2=6'] Exploring Operation: 30+55=85, Resulting Numbers: [6, 85] Generated Node #3: [6, 85] from Operation: 30+55=85 Current State: 79:[6, 85], Operations: ['4+2=6', '30+55=85'] Exploring Operation: 85-6=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[4, 2, 30, 55], Operations: [] Exploring Operation: 4*30=120, Resulting Numbers: [2, 55, 120] Generated Node #0,0: 79:[2, 55, 120] Operation: 4*30=120 Exploring Operation: 4*2=8, Resulting Numbers: [30, 55, 8] Generated Node #0,1: 79:[30, 55, 8] Operation: 4*2=8 Exploring Operation: 2*30=60, Resulting Numbers: [4, 55, 60] Generated Node #0,2: 79:[4, 55, 60] Operation: 2*30=60 Exploring Operation: 4+2=6, Resulting Numbers: [30, 55, 6] Generated Node #0,3: 79:[30, 55, 6] Operation: 4+2=6 Moving to Node #0,2 Current State: 79:[4, 55, 60], Operations: ['2*30=60'] Exploring Operation: 60-4=56, Resulting Numbers: [55, 56] Generated Node #0,2,0: 79:[55, 56] Operation: 60-4=56 Exploring Operation: 4+55=59, Resulting Numbers: [60, 59] Generated Node #0,2,1: 79:[60, 59] Operation: 4+55=59 Exploring Operation: 55-4=51, Resulting Numbers: [60, 51] Generated Node #0,2,2: 79:[60, 51] Operation: 55-4=51 Exploring Operation: 4+60=64, Resulting Numbers: [55, 64] Generated Node #0,2,3: 79:[55, 64] Operation: 4+60=64 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[60, 59], Operations: ['2*30=60', '4+55=59'] Exploring Operation: 60+59=119, Resulting Numbers: [119] 119,79 unequal: No Solution Exploring Operation: 60*59=3540, Resulting Numbers: [3540] 3540,79 unequal: No Solution Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 79:[55, 64], Operations: ['2*30=60', '4+60=64'] Exploring Operation: 55*64=3520, Resulting Numbers: [3520] 3520,79 unequal: No Solution Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,79 unequal: No Solution Exploring Operation: 55+64=119, Resulting Numbers: [119] 119,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[55, 56], Operations: ['2*30=60', '60-4=56'] Exploring Operation: 55*56=3080, Resulting Numbers: [3080] 3080,79 unequal: No Solution Exploring Operation: 55+56=111, Resulting Numbers: [111] 111,79 unequal: No Solution Exploring Operation: 56-55=1, Resulting Numbers: [1] 1,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[60, 51], Operations: ['2*30=60', '55-4=51'] Exploring Operation: 60*51=3060, Resulting Numbers: [3060] 3060,79 unequal: No Solution Exploring Operation: 60-51=9, Resulting Numbers: [9] 9,79 unequal: No Solution Exploring Operation: 60+51=111, Resulting Numbers: [111] 111,79 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: 79:[2, 55, 120], Operations: ['4*30=120'] Exploring Operation: 2+55=57, Resulting Numbers: [120, 57] Generated Node #0,0,0: 79:[120, 57] Operation: 2+55=57 Exploring Operation: 55-2=53, Resulting Numbers: [120, 53] Generated Node #0,0,1: 79:[120, 53] Operation: 55-2=53 Exploring Operation: 120-2=118, Resulting Numbers: [55, 118] Generated Node #0,0,2: 79:[55, 118] Operation: 120-2=118 Exploring Operation: 120/2=60, Resulting Numbers: [55, 60] Generated Node #0,0,3: 79:[55, 60] Operation: 120/2=60 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 79:[55, 60], Operations: ['4*30=120', '120/2=60'] Exploring Operation: 55+60=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,79 unequal: No Solution Exploring Operation: 55*60=3300, Resulting Numbers: [3300] 3300,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[120, 57], Operations: ['4*30=120', '2+55=57'] Exploring Operation: 120+57=177, Resulting Numbers: [177] 177,79 unequal: No Solution Exploring Operation: 120*57=6840, Resulting Numbers: [6840] 6840,79 unequal: No Solution Exploring Operation: 120-57=63, Resulting Numbers: [63] 63,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 79:[55, 118], Operations: ['4*30=120', '120-2=118'] Exploring Operation: 118-55=63, Resulting Numbers: [63] 63,79 unequal: No Solution Exploring Operation: 55+118=173, Resulting Numbers: [173] 173,79 unequal: No Solution Exploring Operation: 55*118=6490, Resulting Numbers: [6490] 6490,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[120, 53], Operations: ['4*30=120', '55-2=53'] Exploring Operation: 120-53=67, Resulting Numbers: [67] 67,79 unequal: No Solution Exploring Operation: 120+53=173, Resulting Numbers: [173] 173,79 unequal: No Solution Exploring Operation: 120*53=6360, Resulting Numbers: [6360] 6360,79 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: 79:[30, 55, 8], Operations: ['4*2=8'] Exploring Operation: 30+8=38, Resulting Numbers: [55, 38] Generated Node #0,1,0: 79:[55, 38] Operation: 30+8=38 Exploring Operation: 30-8=22, Resulting Numbers: [55, 22] Generated Node #0,1,1: 79:[55, 22] Operation: 30-8=22 Exploring Operation: 30+55=85, Resulting Numbers: [8, 85] Generated Node #0,1,2: 79:[8, 85] Operation: 30+55=85 Exploring Operation: 55+8=63, Resulting Numbers: [30, 63] Generated Node #0,1,3: 79:[30, 63] Operation: 55+8=63 Moving to Node #0,3 Current State: 79:[30, 55, 6], Operations: ['4+2=6'] Exploring Operation: 30-6=24, Resulting Numbers: [55, 24] Generated Node #0,3,0: 79:[55, 24] Operation: 30-6=24 Exploring Operation: 55+6=61, Resulting Numbers: [30, 61] Generated Node #0,3,1: 79:[30, 61] Operation: 55+6=61 Exploring Operation: 30+6=36, Resulting Numbers: [55, 36] Generated Node #0,3,2: 79:[55, 36] Operation: 30+6=36 Exploring Operation: 30+55=85, Resulting Numbers: [6, 85] Generated Node #0,3,3: 79:[6, 85] Operation: 30+55=85 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 79:[30, 61], Operations: ['4+2=6', '55+6=61'] Exploring Operation: 30+61=91, Resulting Numbers: [91] 91,79 unequal: No Solution Exploring Operation: 30*61=1830, Resulting Numbers: [1830] 1830,79 unequal: No Solution Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 79:[55, 36], Operations: ['4+2=6', '30+6=36'] Exploring Operation: 55+36=91, Resulting Numbers: [91] 91,79 unequal: No Solution Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,79 unequal: No Solution Exploring Operation: 55*36=1980, Resulting Numbers: [1980] 1980,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 79:[55, 24], Operations: ['4+2=6', '30-6=24'] Exploring Operation: 55+24=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[4, 2, 30, 55], Operations: [] Exploring Operation: 4+2=6, Resulting Numbers: [30, 55, 6] Generated Node #0,3: 79:[30, 55, 6] Operation: 4+2=6 Moving to Node #0,3 Current State: 79:[30, 55, 6], Operations: ['4+2=6'] Exploring Operation: 30-6=24, Resulting Numbers: [55, 24] Generated Node #0,3,0: 79:[55, 24] Operation: 30-6=24 Moving to Node #0,3,0 Current State: 79:[55, 24], Operations: ['4+2=6', '30-6=24'] Exploring Operation: 55+24=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.952257
hs_4
mult_heuristic
[ 8, 18, 91, 23 ]
78
[ "18-8=10", "91-23=68", "10+68=78" ]
Current State: 78:[8, 18, 91, 23], Operations: [] Exploring Operation: 18-8=10, Resulting Numbers: [91, 23, 10] Generated Node #2: [91, 23, 10] from Operation: 18-8=10 Current State: 78:[91, 23, 10], Operations: ['18-8=10'] Exploring Operation: 91-23=68, Resulting Numbers: [10, 68] Generated Node #3: [10, 68] from Operation: 91-23=68 Current State: 78:[10, 68], Operations: ['18-8=10', '91-23=68'] Exploring Operation: 10+68=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[8, 18, 91, 23], Operations: [] Exploring Operation: 91-18=73, Resulting Numbers: [8, 23, 73] Generated Node #0,0: 78:[8, 23, 73] Operation: 91-18=73 Exploring Operation: 91-8=83, Resulting Numbers: [18, 23, 83] Generated Node #0,1: 78:[18, 23, 83] Operation: 91-8=83 Moving to Node #0,0 Current State: 78:[8, 23, 73], Operations: ['91-18=73'] Exploring Operation: 8+73=81, Resulting Numbers: [23, 81] Generated Node #0,0,0: 78:[23, 81] Operation: 8+73=81 Exploring Operation: 23-8=15, Resulting Numbers: [73, 15] Generated Node #0,0,1: 78:[73, 15] Operation: 23-8=15 Moving to Node #0,1 Current State: 78:[18, 23, 83], Operations: ['91-8=83'] Exploring Operation: 18+23=41, Resulting Numbers: [83, 41] Generated Node #0,1,0: 78:[83, 41] Operation: 18+23=41 Exploring Operation: 23-18=5, Resulting Numbers: [83, 5] Generated Node #0,1,1: 78:[83, 5] Operation: 23-18=5 Moving to Node #0,0,0 Current State: 78:[23, 81], Operations: ['91-18=73', '8+73=81'] Exploring Operation: 23+81=104, Resulting Numbers: [104] 104,78 unequal: No Solution Exploring Operation: 81-23=58, Resulting Numbers: [58] 58,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[83, 5], Operations: ['91-8=83', '23-18=5'] Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[8, 18, 91, 23], Operations: [] Exploring Operation: 91-8=83, Resulting Numbers: [18, 23, 83] Generated Node #0,1: 78:[18, 23, 83] Operation: 91-8=83 Moving to Node #0,1 Current State: 78:[18, 23, 83], Operations: ['91-8=83'] Exploring Operation: 23-18=5, Resulting Numbers: [83, 5] Generated Node #0,1,1: 78:[83, 5] Operation: 23-18=5 Moving to Node #0,1,1 Current State: 78:[83, 5], Operations: ['91-8=83', '23-18=5'] Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
0.988715
hs_2
sum_heuristic
[ 10, 33, 44, 24 ]
43
[ "33-10=23", "44-24=20", "23+20=43" ]
Current State: 43:[10, 33, 44, 24], Operations: [] Exploring Operation: 33-10=23, Resulting Numbers: [44, 24, 23] Generated Node #2: [44, 24, 23] from Operation: 33-10=23 Current State: 43:[44, 24, 23], Operations: ['33-10=23'] Exploring Operation: 44-24=20, Resulting Numbers: [23, 20] Generated Node #3: [23, 20] from Operation: 44-24=20 Current State: 43:[23, 20], Operations: ['33-10=23', '44-24=20'] Exploring Operation: 23+20=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[10, 33, 44, 24], Operations: [] Exploring Operation: 10+24=34, Resulting Numbers: [33, 44, 34] Generated Node #0,0: 43:[33, 44, 34] Operation: 10+24=34 Exploring Operation: 33-10=23, Resulting Numbers: [44, 24, 23] Generated Node #0,1: 43:[44, 24, 23] Operation: 33-10=23 Exploring Operation: 10+33=43, Resulting Numbers: [44, 24, 43] Generated Node #0,2: 43:[44, 24, 43] Operation: 10+33=43 Exploring Operation: 44-10=34, Resulting Numbers: [33, 24, 34] Generated Node #0,3: 43:[33, 24, 34] Operation: 44-10=34 Moving to Node #0,0 Current State: 43:[33, 44, 34], Operations: ['10+24=34'] Exploring Operation: 44-33=11, Resulting Numbers: [34, 11] Generated Node #0,0,0: 43:[34, 11] Operation: 44-33=11 Exploring Operation: 34-33=1, Resulting Numbers: [44, 1] Generated Node #0,0,1: 43:[44, 1] Operation: 34-33=1 Exploring Operation: 33+34=67, Resulting Numbers: [44, 67] Generated Node #0,0,2: 43:[44, 67] Operation: 33+34=67 Exploring Operation: 33+44=77, Resulting Numbers: [34, 77] Generated Node #0,0,3: 43:[34, 77] Operation: 33+44=77 Moving to Node #0,2 Current State: 43:[44, 24, 43], Operations: ['10+33=43'] Exploring Operation: 43-24=19, Resulting Numbers: [44, 19] Generated Node #0,2,0: 43:[44, 19] Operation: 43-24=19 Exploring Operation: 44+24=68, Resulting Numbers: [43, 68] Generated Node #0,2,1: 43:[43, 68] Operation: 44+24=68 Exploring Operation: 24+43=67, Resulting Numbers: [44, 67] Generated Node #0,2,2: 43:[44, 67] Operation: 24+43=67 Exploring Operation: 44-24=20, Resulting Numbers: [43, 20] Generated Node #0,2,3: 43:[43, 20] Operation: 44-24=20 Moving to Node #0,3 Current State: 43:[33, 24, 34], Operations: ['44-10=34'] Exploring Operation: 33-24=9, Resulting Numbers: [34, 9] Generated Node #0,3,0: 43:[34, 9] Operation: 33-24=9 Exploring Operation: 24+34=58, Resulting Numbers: [33, 58] Generated Node #0,3,1: 43:[33, 58] Operation: 24+34=58 Exploring Operation: 33+34=67, Resulting Numbers: [24, 67] Generated Node #0,3,2: 43:[24, 67] Operation: 33+34=67 Exploring Operation: 33+24=57, Resulting Numbers: [34, 57] Generated Node #0,3,3: 43:[34, 57] Operation: 33+24=57 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 43:[34, 57], Operations: ['44-10=34', '33+24=57'] Exploring Operation: 34*57=1938, Resulting Numbers: [1938] 1938,43 unequal: No Solution Exploring Operation: 34+57=91, Resulting Numbers: [91] 91,43 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 43:[33, 58], Operations: ['44-10=34', '24+34=58'] Exploring Operation: 33*58=1914, Resulting Numbers: [1914] 1914,43 unequal: No Solution Exploring Operation: 58-33=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 33+58=91, Resulting Numbers: [91] 91,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 43:[34, 9], Operations: ['44-10=34', '33-24=9'] Exploring Operation: 34*9=306, Resulting Numbers: [306] 306,43 unequal: No Solution Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 34+9=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[10, 33, 44, 24], Operations: [] Exploring Operation: 44-10=34, Resulting Numbers: [33, 24, 34] Generated Node #0,3: 43:[33, 24, 34] Operation: 44-10=34 Moving to Node #0,3 Current State: 43:[33, 24, 34], Operations: ['44-10=34'] Exploring Operation: 33-24=9, Resulting Numbers: [34, 9] Generated Node #0,3,0: 43:[34, 9] Operation: 33-24=9 Moving to Node #0,3,0 Current State: 43:[34, 9], Operations: ['44-10=34', '33-24=9'] Exploring Operation: 34+9=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 53, 84, 1, 44 ]
94
[ "53+84=137", "44-1=43", "137-43=94" ]
Current State: 94:[53, 84, 1, 44], Operations: [] Exploring Operation: 53+84=137, Resulting Numbers: [1, 44, 137] Generated Node #2: [1, 44, 137] from Operation: 53+84=137 Current State: 94:[1, 44, 137], Operations: ['53+84=137'] Exploring Operation: 44-1=43, Resulting Numbers: [137, 43] Generated Node #3: [137, 43] from Operation: 44-1=43 Current State: 94:[137, 43], Operations: ['53+84=137', '44-1=43'] Exploring Operation: 137-43=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[53, 84, 1, 44], Operations: [] Exploring Operation: 53+44=97, Resulting Numbers: [84, 1, 97] Generated Node #0,0: 94:[84, 1, 97] Operation: 53+44=97 Exploring Operation: 84-44=40, Resulting Numbers: [53, 1, 40] Generated Node #0,1: 94:[53, 1, 40] Operation: 84-44=40 Exploring Operation: 53-1=52, Resulting Numbers: [84, 44, 52] Generated Node #0,2: 94:[84, 44, 52] Operation: 53-1=52 Exploring Operation: 53-44=9, Resulting Numbers: [84, 1, 9] Generated Node #0,3: 94:[84, 1, 9] Operation: 53-44=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[84, 1, 97], Operations: ['53+44=97'] Exploring Operation: 97-84=13, Resulting Numbers: [1, 13] Generated Node #0,0,0: 94:[1, 13] Operation: 97-84=13 Exploring Operation: 97-1=96, Resulting Numbers: [84, 96] Generated Node #0,0,1: 94:[84, 96] Operation: 97-1=96 Exploring Operation: 84*1=84, Resulting Numbers: [97, 84] Generated Node #0,0,2: 94:[97, 84] Operation: 84*1=84 Exploring Operation: 84+1=85, Resulting Numbers: [97, 85] Generated Node #0,0,3: 94:[97, 85] Operation: 84+1=85 Moving to Node #0,0,0 Current State: 94:[1, 13], Operations: ['53+44=97', '97-84=13'] Exploring Operation: 1*13=13, Resulting Numbers: [13] 13,94 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,94 unequal: No Solution Exploring Operation: 1+13=14, Resulting Numbers: [14] 14,94 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,94 unequal: No Solution Moving to Node #0,0,3 Current State: 94:[97, 85], Operations: ['53+44=97', '84+1=85'] Exploring Operation: 97-85=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 97*85=8245, Resulting Numbers: [8245] 8245,94 unequal: No Solution Exploring Operation: 97+85=182, Resulting Numbers: [182] 182,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[84, 96], Operations: ['53+44=97', '97-1=96'] Exploring Operation: 96-84=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 84*96=8064, Resulting Numbers: [8064] 8064,94 unequal: No Solution Exploring Operation: 84+96=180, Resulting Numbers: [180] 180,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[97, 84], Operations: ['53+44=97', '84*1=84'] Exploring Operation: 97-84=13, Resulting Numbers: [13] 13,94 unequal: No Solution Exploring Operation: 97*84=8148, Resulting Numbers: [8148] 8148,94 unequal: No Solution Exploring Operation: 97+84=181, Resulting Numbers: [181] 181,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[53, 1, 40], Operations: ['84-44=40'] Exploring Operation: 53+40=93, Resulting Numbers: [1, 93] Generated Node #0,1,0: 94:[1, 93] Operation: 53+40=93 Exploring Operation: 53-1=52, Resulting Numbers: [40, 52] Generated Node #0,1,1: 94:[40, 52] Operation: 53-1=52 Exploring Operation: 53-40=13, Resulting Numbers: [1, 13] Generated Node #0,1,2: 94:[1, 13] Operation: 53-40=13 Exploring Operation: 1+40=41, Resulting Numbers: [53, 41] Generated Node #0,1,3: 94:[53, 41] Operation: 1+40=41 Moving to Node #0,1,0 Current State: 94:[1, 93], Operations: ['84-44=40', '53+40=93'] Exploring Operation: 1+93=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[53, 84, 1, 44], Operations: [] Exploring Operation: 84-44=40, Resulting Numbers: [53, 1, 40] Generated Node #0,1: 94:[53, 1, 40] Operation: 84-44=40 Moving to Node #0,1 Current State: 94:[53, 1, 40], Operations: ['84-44=40'] Exploring Operation: 53+40=93, Resulting Numbers: [1, 93] Generated Node #0,1,0: 94:[1, 93] Operation: 53+40=93 Moving to Node #0,1,0 Current State: 94:[1, 93], Operations: ['84-44=40', '53+40=93'] Exploring Operation: 1+93=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 75, 79, 66, 7 ]
22
[ "79-75=4", "7-4=3", "66/3=22" ]
Current State: 22:[75, 79, 66, 7], Operations: [] Exploring Operation: 79-75=4, Resulting Numbers: [66, 7, 4] Generated Node #2: [66, 7, 4] from Operation: 79-75=4 Current State: 22:[66, 7, 4], Operations: ['79-75=4'] Exploring Operation: 7-4=3, Resulting Numbers: [66, 3] Generated Node #3: [66, 3] from Operation: 7-4=3 Current State: 22:[66, 3], Operations: ['79-75=4', '7-4=3'] Exploring Operation: 66/3=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[75, 79, 66, 7], Operations: [] Exploring Operation: 79-66=13, Resulting Numbers: [75, 7, 13] Generated Node #0,0: 22:[75, 7, 13] Operation: 79-66=13 Exploring Operation: 75-66=9, Resulting Numbers: [79, 7, 9] Generated Node #0,1: 22:[79, 7, 9] Operation: 75-66=9 Exploring Operation: 79-75=4, Resulting Numbers: [66, 7, 4] Generated Node #0,2: 22:[66, 7, 4] Operation: 79-75=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[66, 7, 4], Operations: ['79-75=4'] Exploring Operation: 66-4=62, Resulting Numbers: [7, 62] Generated Node #0,2,0: 22:[7, 62] Operation: 66-4=62 Exploring Operation: 66-7=59, Resulting Numbers: [4, 59] Generated Node #0,2,1: 22:[4, 59] Operation: 66-7=59 Exploring Operation: 7+4=11, Resulting Numbers: [66, 11] Generated Node #0,2,2: 22:[66, 11] Operation: 7+4=11 Moving to Node #0,2,1 Current State: 22:[4, 59], Operations: ['79-75=4', '66-7=59'] Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,22 unequal: No Solution Exploring Operation: 4*59=236, Resulting Numbers: [236] 236,22 unequal: No Solution Exploring Operation: 4+59=63, Resulting Numbers: [63] 63,22 unequal: No Solution Moving to Node #0,2,0 Current State: 22:[7, 62], Operations: ['79-75=4', '66-4=62'] Exploring Operation: 7+62=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 7*62=434, Resulting Numbers: [434] 434,22 unequal: No Solution Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[66, 11], Operations: ['79-75=4', '7+4=11'] Exploring Operation: 66+11=77, Resulting Numbers: [77] 77,22 unequal: No Solution Exploring Operation: 66-11=55, Resulting Numbers: [55] 55,22 unequal: No Solution Exploring Operation: 66/11=6, Resulting Numbers: [6] 6,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[75, 7, 13], Operations: ['79-66=13'] Exploring Operation: 75-13=62, Resulting Numbers: [7, 62] Generated Node #0,0,0: 22:[7, 62] Operation: 75-13=62 Exploring Operation: 7+13=20, Resulting Numbers: [75, 20] Generated Node #0,0,1: 22:[75, 20] Operation: 7+13=20 Exploring Operation: 75-7=68, Resulting Numbers: [13, 68] Generated Node #0,0,2: 22:[13, 68] Operation: 75-7=68 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 22:[7, 62], Operations: ['79-66=13', '75-13=62'] Exploring Operation: 7+62=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,22 unequal: No Solution Exploring Operation: 7*62=434, Resulting Numbers: [434] 434,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 22:[13, 68], Operations: ['79-66=13', '75-7=68'] Exploring Operation: 13+68=81, Resulting Numbers: [81] 81,22 unequal: No Solution Exploring Operation: 13*68=884, Resulting Numbers: [884] 884,22 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 22:[75, 20], Operations: ['79-66=13', '7+13=20'] Exploring Operation: 75-20=55, Resulting Numbers: [55] 55,22 unequal: No Solution Exploring Operation: 75+20=95, Resulting Numbers: [95] 95,22 unequal: No Solution Exploring Operation: 75*20=1500, Resulting Numbers: [1500] 1500,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[79, 7, 9], Operations: ['75-66=9'] Exploring Operation: 79-7=72, Resulting Numbers: [9, 72] Generated Node #0,1,0: 22:[9, 72] Operation: 79-7=72 Exploring Operation: 9-7=2, Resulting Numbers: [79, 2] Generated Node #0,1,1: 22:[79, 2] Operation: 9-7=2 Exploring Operation: 79-9=70, Resulting Numbers: [7, 70] Generated Node #0,1,2: 22:[7, 70] Operation: 79-9=70 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 22:[9, 72], Operations: ['75-66=9', '79-7=72'] Exploring Operation: 9+72=81, Resulting Numbers: [81] 81,22 unequal: No Solution Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 72/9=8, Resulting Numbers: [8] 8,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 22:[7, 70], Operations: ['75-66=9', '79-9=70'] Exploring Operation: 70-7=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 70/7=10, Resulting Numbers: [10] 10,22 unequal: No Solution Exploring Operation: 7+70=77, Resulting Numbers: [77] 77,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 22:[79, 2], Operations: ['75-66=9', '9-7=2'] Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,22 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,22 unequal: No Solution Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 58, 56, 2, 50 ]
70
[ "56-50=6", "2*6=12", "58+12=70" ]
Current State: 70:[58, 56, 2, 50], Operations: [] Exploring Operation: 56-50=6, Resulting Numbers: [58, 2, 6] Generated Node #2: [58, 2, 6] from Operation: 56-50=6 Current State: 70:[58, 2, 6], Operations: ['56-50=6'] Exploring Operation: 2*6=12, Resulting Numbers: [58, 12] Generated Node #3: [58, 12] from Operation: 2*6=12 Current State: 70:[58, 12], Operations: ['56-50=6', '2*6=12'] Exploring Operation: 58+12=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[58, 56, 2, 50], Operations: [] Exploring Operation: 56-50=6, Resulting Numbers: [58, 2, 6] Generated Node #0,0: 70:[58, 2, 6] Operation: 56-50=6 Exploring Operation: 58-56=2, Resulting Numbers: [2, 50, 2] Generated Node #0,1: 70:[2, 50, 2] Operation: 58-56=2 Moving to Node #0,0 Current State: 70:[58, 2, 6], Operations: ['56-50=6'] Exploring Operation: 58/2=29, Resulting Numbers: [6, 29] Generated Node #0,0,0: 70:[6, 29] Operation: 58/2=29 Exploring Operation: 58+6=64, Resulting Numbers: [2, 64] Generated Node #0,0,1: 70:[2, 64] Operation: 58+6=64 Moving to Node #0,1 Current State: 70:[2, 50, 2], Operations: ['58-56=2'] Exploring Operation: 50/2=25, Resulting Numbers: [2, 25] Generated Node #0,1,0: 70:[2, 25] Operation: 50/2=25 Exploring Operation: 50/2=25, Resulting Numbers: [2, 25] Generated Node #0,1,1: 70:[2, 25] Operation: 50/2=25 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 70:[2, 25], Operations: ['58-56=2', '50/2=25'] Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,70 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,70 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 #0,1,1 Current State: 70:[2, 25], Operations: ['58-56=2', '50/2=25'] Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,70 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,70 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: 70:[2, 64], Operations: ['56-50=6', '58+6=64'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,70 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[6, 29], Operations: ['56-50=6', '58/2=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 No solution found.
0
hs_2
mult_heuristic
[ 91, 39, 31, 26 ]
26
[ "91+39=130", "31-26=5", "130/5=26" ]
Current State: 26:[91, 39, 31, 26], Operations: [] Exploring Operation: 91+39=130, Resulting Numbers: [31, 26, 130] Generated Node #2: [31, 26, 130] from Operation: 91+39=130 Current State: 26:[31, 26, 130], Operations: ['91+39=130'] Exploring Operation: 31-26=5, Resulting Numbers: [130, 5] Generated Node #3: [130, 5] from Operation: 31-26=5 Current State: 26:[130, 5], Operations: ['91+39=130', '31-26=5'] Exploring Operation: 130/5=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[91, 39, 31, 26], Operations: [] Exploring Operation: 91-39=52, Resulting Numbers: [31, 26, 52] Generated Node #0,0: 26:[31, 26, 52] Operation: 91-39=52 Moving to Node #0,0 Current State: 26:[31, 26, 52], Operations: ['91-39=52'] Exploring Operation: 52-31=21, Resulting Numbers: [26, 21] Generated Node #0,0,0: 26:[26, 21] Operation: 52-31=21 Moving to Node #0,0,0 Current State: 26:[26, 21], Operations: ['91-39=52', '52-31=21'] Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,26 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 42, 46, 5, 93 ]
71
[ "42*5=210", "46+93=139", "210-139=71" ]
Current State: 71:[42, 46, 5, 93], Operations: [] Exploring Operation: 42*5=210, Resulting Numbers: [46, 93, 210] Generated Node #2: [46, 93, 210] from Operation: 42*5=210 Current State: 71:[46, 93, 210], Operations: ['42*5=210'] Exploring Operation: 46+93=139, Resulting Numbers: [210, 139] Generated Node #3: [210, 139] from Operation: 46+93=139 Current State: 71:[210, 139], Operations: ['42*5=210', '46+93=139'] Exploring Operation: 210-139=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[42, 46, 5, 93], Operations: [] Exploring Operation: 93-5=88, Resulting Numbers: [42, 46, 88] Generated Node #0,0: 71:[42, 46, 88] Operation: 93-5=88 Exploring Operation: 42-5=37, Resulting Numbers: [46, 93, 37] Generated Node #0,1: 71:[46, 93, 37] Operation: 42-5=37 Exploring Operation: 46-5=41, Resulting Numbers: [42, 93, 41] Generated Node #0,2: 71:[42, 93, 41] Operation: 46-5=41 Exploring Operation: 42+5=47, Resulting Numbers: [46, 93, 47] Generated Node #0,3: 71:[46, 93, 47] Operation: 42+5=47 Exploring Operation: 46+5=51, Resulting Numbers: [42, 93, 51] Generated Node #0,4: 71:[42, 93, 51] Operation: 46+5=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[42, 46, 88], Operations: ['93-5=88'] Exploring Operation: 88-46=42, Resulting Numbers: [42, 42] Generated Node #0,0,0: 71:[42, 42] Operation: 88-46=42 Exploring Operation: 46-42=4, Resulting Numbers: [88, 4] Generated Node #0,0,1: 71:[88, 4] Operation: 46-42=4 Exploring Operation: 42+88=130, Resulting Numbers: [46, 130] Generated Node #0,0,2: 71:[46, 130] Operation: 42+88=130 Exploring Operation: 88-42=46, Resulting Numbers: [46, 46] Generated Node #0,0,3: 71:[46, 46] Operation: 88-42=46 Exploring Operation: 42+46=88, Resulting Numbers: [88, 88] Generated Node #0,0,4: 71:[88, 88] Operation: 42+46=88 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 71:[88, 88], Operations: ['93-5=88', '42+46=88'] Exploring Operation: 88-88=0, Resulting Numbers: [0] 0,71 unequal: No Solution Exploring Operation: 88*88=7744, Resulting Numbers: [7744] 7744,71 unequal: No Solution Exploring Operation: 88+88=176, Resulting Numbers: [176] 176,71 unequal: No Solution Exploring Operation: 88/88=1, Resulting Numbers: [1] 1,71 unequal: No Solution No 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: 71:[46, 46], Operations: ['93-5=88', '88-42=46'] Exploring Operation: 46*46=2116, Resulting Numbers: [2116] 2116,71 unequal: No Solution Exploring Operation: 46-46=0, Resulting Numbers: [0] 0,71 unequal: No Solution Exploring Operation: 46/46=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 46+46=92, Resulting Numbers: [92] 92,71 unequal: No Solution No 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: 71:[42, 42], Operations: ['93-5=88', '88-46=42'] Exploring Operation: 42/42=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 42+42=84, Resulting Numbers: [84] 84,71 unequal: No Solution Exploring Operation: 42*42=1764, Resulting Numbers: [1764] 1764,71 unequal: No Solution Exploring Operation: 42-42=0, Resulting Numbers: [0] 0,71 unequal: No Solution No 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: 71:[88, 4], Operations: ['93-5=88', '46-42=4'] Exploring Operation: 88+4=92, Resulting Numbers: [92] 92,71 unequal: No Solution Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,71 unequal: No Solution Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,71 unequal: No Solution Exploring Operation: 88*4=352, Resulting Numbers: [352] 352,71 unequal: No Solution No 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: 71:[46, 130], Operations: ['93-5=88', '42+88=130'] Exploring Operation: 130-46=84, Resulting Numbers: [84] 84,71 unequal: No Solution Exploring Operation: 46+130=176, Resulting Numbers: [176] 176,71 unequal: No Solution Exploring Operation: 46*130=5980, Resulting Numbers: [5980] 5980,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 71:[46, 93, 47], Operations: ['42+5=47'] Exploring Operation: 93-46=47, Resulting Numbers: [47, 47] Generated Node #0,3,0: 71:[47, 47] Operation: 93-46=47 Exploring Operation: 47-46=1, Resulting Numbers: [93, 1] Generated Node #0,3,1: 71:[93, 1] Operation: 47-46=1 Exploring Operation: 46+47=93, Resulting Numbers: [93, 93] Generated Node #0,3,2: 71:[93, 93] Operation: 46+47=93 Exploring Operation: 46+93=139, Resulting Numbers: [47, 139] Generated Node #0,3,3: 71:[47, 139] Operation: 46+93=139 Exploring Operation: 93-47=46, Resulting Numbers: [46, 46] Generated Node #0,3,4: 71:[46, 46] Operation: 93-47=46 Moving to Node #0,3,2 Current State: 71:[93, 93], Operations: ['42+5=47', '46+47=93'] Exploring Operation: 93-93=0, Resulting Numbers: [0] 0,71 unequal: No Solution Exploring Operation: 93+93=186, Resulting Numbers: [186] 186,71 unequal: No Solution Exploring Operation: 93/93=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 93*93=8649, Resulting Numbers: [8649] 8649,71 unequal: No Solution Moving to Node #0,3,0 Current State: 71:[47, 47], Operations: ['42+5=47', '93-46=47'] Exploring Operation: 47-47=0, Resulting Numbers: [0] 0,71 unequal: No Solution Exploring Operation: 47*47=2209, Resulting Numbers: [2209] 2209,71 unequal: No Solution Exploring Operation: 47/47=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,71 unequal: No Solution Moving to Node #0,3,4 Current State: 71:[46, 46], Operations: ['42+5=47', '93-47=46'] Exploring Operation: 46*46=2116, Resulting Numbers: [2116] 2116,71 unequal: No Solution Exploring Operation: 46+46=92, Resulting Numbers: [92] 92,71 unequal: No Solution Exploring Operation: 46-46=0, Resulting Numbers: [0] 0,71 unequal: No Solution Exploring Operation: 46/46=1, Resulting Numbers: [1] 1,71 unequal: No Solution Moving to Node #0,3,1 Current State: 71:[93, 1], Operations: ['42+5=47', '47-46=1'] Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,71 unequal: No Solution Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,71 unequal: No Solution Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,71 unequal: No Solution Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,71 unequal: No Solution Moving to Node #0,3,3 Current State: 71:[47, 139], Operations: ['42+5=47', '46+93=139'] Exploring Operation: 139-47=92, Resulting Numbers: [92] 92,71 unequal: No Solution Exploring Operation: 47*139=6533, Resulting Numbers: [6533] 6533,71 unequal: No Solution Exploring Operation: 47+139=186, Resulting Numbers: [186] 186,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 71:[42, 93, 51], Operations: ['46+5=51'] Exploring Operation: 93-42=51, Resulting Numbers: [51, 51] Generated Node #0,4,0: 71:[51, 51] Operation: 93-42=51 Exploring Operation: 42+51=93, Resulting Numbers: [93, 93] Generated Node #0,4,1: 71:[93, 93] Operation: 42+51=93 Exploring Operation: 42+93=135, Resulting Numbers: [51, 135] Generated Node #0,4,2: 71:[51, 135] Operation: 42+93=135 Exploring Operation: 93-51=42, Resulting Numbers: [42, 42] Generated Node #0,4,3: 71:[42, 42] Operation: 93-51=42 Exploring Operation: 51-42=9, Resulting Numbers: [93, 9] Generated Node #0,4,4: 71:[93, 9] Operation: 51-42=9 Moving to Node #0,4,0 Current State: 71:[51, 51], Operations: ['46+5=51', '93-42=51'] Exploring Operation: 51-51=0, Resulting Numbers: [0] 0,71 unequal: No Solution Exploring Operation: 51/51=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 51+51=102, Resulting Numbers: [102] 102,71 unequal: No Solution Exploring Operation: 51*51=2601, Resulting Numbers: [2601] 2601,71 unequal: No Solution Moving to Node #0,4,1 Current State: 71:[93, 93], Operations: ['46+5=51', '42+51=93'] Exploring Operation: 93/93=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 93-93=0, Resulting Numbers: [0] 0,71 unequal: No Solution Exploring Operation: 93*93=8649, Resulting Numbers: [8649] 8649,71 unequal: No Solution Exploring Operation: 93+93=186, Resulting Numbers: [186] 186,71 unequal: No Solution Moving to Node #0,4,3 Current State: 71:[42, 42], Operations: ['46+5=51', '93-51=42'] Exploring Operation: 42*42=1764, Resulting Numbers: [1764] 1764,71 unequal: No Solution Exploring Operation: 42/42=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 42-42=0, Resulting Numbers: [0] 0,71 unequal: No Solution Exploring Operation: 42+42=84, Resulting Numbers: [84] 84,71 unequal: No Solution Moving to Node #0,4,2 Current State: 71:[51, 135], Operations: ['46+5=51', '42+93=135'] Exploring Operation: 51+135=186, Resulting Numbers: [186] 186,71 unequal: No Solution Exploring Operation: 51*135=6885, Resulting Numbers: [6885] 6885,71 unequal: No Solution Exploring Operation: 135-51=84, Resulting Numbers: [84] 84,71 unequal: No Solution Moving to Node #0,4,4 Current State: 71:[93, 9], Operations: ['46+5=51', '51-42=9'] Exploring Operation: 93-9=84, Resulting Numbers: [84] 84,71 unequal: No Solution Exploring Operation: 93+9=102, Resulting Numbers: [102] 102,71 unequal: No Solution Exploring Operation: 93*9=837, Resulting Numbers: [837] 837,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[46, 93, 37], Operations: ['42-5=37'] Exploring Operation: 93+37=130, Resulting Numbers: [46, 130] Generated Node #0,1,0: 71:[46, 130] Operation: 93+37=130 Exploring Operation: 93-37=56, Resulting Numbers: [46, 56] Generated Node #0,1,1: 71:[46, 56] Operation: 93-37=56 Exploring Operation: 46+37=83, Resulting Numbers: [93, 83] Generated Node #0,1,2: 71:[93, 83] Operation: 46+37=83 Exploring Operation: 93-46=47, Resulting Numbers: [37, 47] Generated Node #0,1,3: 71:[37, 47] Operation: 93-46=47 Exploring Operation: 46-37=9, Resulting Numbers: [93, 9] Generated Node #0,1,4: 71:[93, 9] Operation: 46-37=9 Moving to Node #0,1,2 Current State: 71:[93, 83], Operations: ['42-5=37', '46+37=83'] Exploring Operation: 93*83=7719, Resulting Numbers: [7719] 7719,71 unequal: No Solution Exploring Operation: 93+83=176, Resulting Numbers: [176] 176,71 unequal: No Solution Exploring Operation: 93-83=10, Resulting Numbers: [10] 10,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[46, 56], Operations: ['42-5=37', '93-37=56'] Exploring Operation: 56-46=10, Resulting Numbers: [10] 10,71 unequal: No Solution Exploring Operation: 46*56=2576, Resulting Numbers: [2576] 2576,71 unequal: No Solution Exploring Operation: 46+56=102, Resulting Numbers: [102] 102,71 unequal: No Solution Moving to Node #0,1,3 Current State: 71:[37, 47], Operations: ['42-5=37', '93-46=47'] Exploring Operation: 37*47=1739, Resulting Numbers: [1739] 1739,71 unequal: No Solution Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,71 unequal: No Solution Exploring Operation: 37+47=84, Resulting Numbers: [84] 84,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[46, 130], Operations: ['42-5=37', '93+37=130'] Exploring Operation: 46*130=5980, Resulting Numbers: [5980] 5980,71 unequal: No Solution Exploring Operation: 130-46=84, Resulting Numbers: [84] 84,71 unequal: No Solution Exploring Operation: 46+130=176, Resulting Numbers: [176] 176,71 unequal: No Solution Moving to Node #0,1,4 Current State: 71:[93, 9], Operations: ['42-5=37', '46-37=9'] Exploring Operation: 93-9=84, Resulting Numbers: [84] 84,71 unequal: No Solution Exploring Operation: 93*9=837, Resulting Numbers: [837] 837,71 unequal: No Solution Exploring Operation: 93+9=102, Resulting Numbers: [102] 102,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[42, 93, 41], Operations: ['46-5=41'] Exploring Operation: 93+41=134, Resulting Numbers: [42, 134] Generated Node #0,2,0: 71:[42, 134] Operation: 93+41=134 Exploring Operation: 93-42=51, Resulting Numbers: [41, 51] Generated Node #0,2,1: 71:[41, 51] Operation: 93-42=51 Exploring Operation: 93-41=52, Resulting Numbers: [42, 52] Generated Node #0,2,2: 71:[42, 52] Operation: 93-41=52 Exploring Operation: 42-41=1, Resulting Numbers: [93, 1] Generated Node #0,2,3: 71:[93, 1] Operation: 42-41=1 Exploring Operation: 42+41=83, Resulting Numbers: [93, 83] Generated Node #0,2,4: 71:[93, 83] Operation: 42+41=83 Moving to Node #0,2,4 Current State: 71:[93, 83], Operations: ['46-5=41', '42+41=83'] Exploring Operation: 93+83=176, Resulting Numbers: [176] 176,71 unequal: No Solution Exploring Operation: 93*83=7719, Resulting Numbers: [7719] 7719,71 unequal: No Solution Exploring Operation: 93-83=10, Resulting Numbers: [10] 10,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[42, 52], Operations: ['46-5=41', '93-41=52'] Exploring Operation: 42+52=94, Resulting Numbers: [94] 94,71 unequal: No Solution Exploring Operation: 42*52=2184, Resulting Numbers: [2184] 2184,71 unequal: No Solution Exploring Operation: 52-42=10, Resulting Numbers: [10] 10,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[41, 51], Operations: ['46-5=41', '93-42=51'] Exploring Operation: 41+51=92, Resulting Numbers: [92] 92,71 unequal: No Solution Exploring Operation: 51-41=10, Resulting Numbers: [10] 10,71 unequal: No Solution Exploring Operation: 41*51=2091, Resulting Numbers: [2091] 2091,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[42, 134], Operations: ['46-5=41', '93+41=134'] Exploring Operation: 134-42=92, Resulting Numbers: [92] 92,71 unequal: No Solution Exploring Operation: 42+134=176, Resulting Numbers: [176] 176,71 unequal: No Solution Exploring Operation: 42*134=5628, Resulting Numbers: [5628] 5628,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[93, 1], Operations: ['46-5=41', '42-41=1'] Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,71 unequal: No Solution Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,71 unequal: No Solution Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,71 unequal: No Solution Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,71 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
[ 1, 4, 60, 29 ]
43
[ "29-1=28", "60/4=15", "28+15=43" ]
Current State: 43:[1, 4, 60, 29], Operations: [] Exploring Operation: 29-1=28, Resulting Numbers: [4, 60, 28] Generated Node #2: [4, 60, 28] from Operation: 29-1=28 Current State: 43:[4, 60, 28], Operations: ['29-1=28'] Exploring Operation: 60/4=15, Resulting Numbers: [28, 15] Generated Node #3: [28, 15] from Operation: 60/4=15 Current State: 43:[28, 15], Operations: ['29-1=28', '60/4=15'] Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[1, 4, 60, 29], Operations: [] Exploring Operation: 1+4=5, Resulting Numbers: [60, 29, 5] Generated Node #0,0: 43:[60, 29, 5] Operation: 1+4=5 Exploring Operation: 60-1=59, Resulting Numbers: [4, 29, 59] Generated Node #0,1: 43:[4, 29, 59] Operation: 60-1=59 Moving to Node #0,0 Current State: 43:[60, 29, 5], Operations: ['1+4=5'] Exploring Operation: 60-5=55, Resulting Numbers: [29, 55] Generated Node #0,0,0: 43:[29, 55] Operation: 60-5=55 Exploring Operation: 29+5=34, Resulting Numbers: [60, 34] Generated Node #0,0,1: 43:[60, 34] Operation: 29+5=34 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[29, 55], Operations: ['1+4=5', '60-5=55'] Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,43 unequal: No Solution Exploring Operation: 29+55=84, Resulting Numbers: [84] 84,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 43:[60, 34], Operations: ['1+4=5', '29+5=34'] Exploring Operation: 60+34=94, Resulting Numbers: [94] 94,43 unequal: No Solution Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 43:[4, 29, 59], Operations: ['60-1=59'] Exploring Operation: 4+29=33, Resulting Numbers: [59, 33] Generated Node #0,1,0: 43:[59, 33] Operation: 4+29=33 Exploring Operation: 59-4=55, Resulting Numbers: [29, 55] Generated Node #0,1,1: 43:[29, 55] Operation: 59-4=55 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[59, 33], Operations: ['60-1=59', '4+29=33'] Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,43 unequal: No Solution Exploring Operation: 59+33=92, Resulting Numbers: [92] 92,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 43:[29, 55], Operations: ['60-1=59', '59-4=55'] Exploring Operation: 29+55=84, Resulting Numbers: [84] 84,43 unequal: No Solution Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,43 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
[ 58, 12, 7, 16 ]
66
[ "58-12=46", "7*16=112", "112-46=66" ]
Current State: 66:[58, 12, 7, 16], Operations: [] Exploring Operation: 58-12=46, Resulting Numbers: [7, 16, 46] Generated Node #2: [7, 16, 46] from Operation: 58-12=46 Current State: 66:[7, 16, 46], Operations: ['58-12=46'] Exploring Operation: 7*16=112, Resulting Numbers: [46, 112] Generated Node #3: [46, 112] from Operation: 7*16=112 Current State: 66:[46, 112], Operations: ['58-12=46', '7*16=112'] Exploring Operation: 112-46=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[58, 12, 7, 16], Operations: [] Exploring Operation: 58+7=65, Resulting Numbers: [12, 16, 65] Generated Node #0,0: 66:[12, 16, 65] Operation: 58+7=65 Exploring Operation: 58+12=70, Resulting Numbers: [7, 16, 70] Generated Node #0,1: 66:[7, 16, 70] Operation: 58+12=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[12, 16, 65], Operations: ['58+7=65'] Exploring Operation: 16-12=4, Resulting Numbers: [65, 4] Generated Node #0,0,0: 66:[65, 4] Operation: 16-12=4 Exploring Operation: 12+16=28, Resulting Numbers: [65, 28] Generated Node #0,0,1: 66:[65, 28] Operation: 12+16=28 Moving to Node #0,0,0 Current State: 66:[65, 4], Operations: ['58+7=65', '16-12=4'] Exploring Operation: 65-4=61, Resulting Numbers: [61] 61,66 unequal: No Solution Exploring Operation: 65+4=69, Resulting Numbers: [69] 69,66 unequal: No Solution Moving to Node #0,0,1 Current State: 66:[65, 28], Operations: ['58+7=65', '12+16=28'] Exploring Operation: 65+28=93, Resulting Numbers: [93] 93,66 unequal: No Solution Exploring Operation: 65-28=37, Resulting Numbers: [37] 37,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[7, 16, 70], Operations: ['58+12=70'] Exploring Operation: 16-7=9, Resulting Numbers: [70, 9] Generated Node #0,1,0: 66:[70, 9] Operation: 16-7=9 Exploring Operation: 7+16=23, Resulting Numbers: [70, 23] Generated Node #0,1,1: 66:[70, 23] Operation: 7+16=23 Moving to Node #0,1,1 Current State: 66:[70, 23], Operations: ['58+12=70', '7+16=23'] Exploring Operation: 70-23=47, Resulting Numbers: [47] 47,66 unequal: No Solution Exploring Operation: 70+23=93, Resulting Numbers: [93] 93,66 unequal: No Solution Moving to Node #0,1,0 Current State: 66:[70, 9], Operations: ['58+12=70', '16-7=9'] Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,66 unequal: No Solution Exploring Operation: 70+9=79, Resulting Numbers: [79] 79,66 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
[ 85, 43, 71, 39 ]
68
[ "85-43=42", "71+39=110", "110-42=68" ]
Current State: 68:[85, 43, 71, 39], Operations: [] Exploring Operation: 85-43=42, Resulting Numbers: [71, 39, 42] Generated Node #2: [71, 39, 42] from Operation: 85-43=42 Current State: 68:[71, 39, 42], Operations: ['85-43=42'] Exploring Operation: 71+39=110, Resulting Numbers: [42, 110] Generated Node #3: [42, 110] from Operation: 71+39=110 Current State: 68:[42, 110], Operations: ['85-43=42', '71+39=110'] Exploring Operation: 110-42=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[85, 43, 71, 39], Operations: [] Exploring Operation: 85-43=42, Resulting Numbers: [71, 39, 42] Generated Node #0,0: 68:[71, 39, 42] Operation: 85-43=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[71, 39, 42], Operations: ['85-43=42'] Exploring Operation: 42-39=3, Resulting Numbers: [71, 3] Generated Node #0,0,0: 68:[71, 3] Operation: 42-39=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[71, 3], Operations: ['85-43=42', '42-39=3'] Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[85, 43, 71, 39], Operations: [] Exploring Operation: 85-43=42, Resulting Numbers: [71, 39, 42] Generated Node #0,0: 68:[71, 39, 42] Operation: 85-43=42 Moving to Node #0,0 Current State: 68:[71, 39, 42], Operations: ['85-43=42'] Exploring Operation: 42-39=3, Resulting Numbers: [71, 3] Generated Node #0,0,0: 68:[71, 3] Operation: 42-39=3 Moving to Node #0,0,0 Current State: 68:[71, 3], Operations: ['85-43=42', '42-39=3'] Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 2, 18, 42, 36 ]
86
[ "2*42=84", "36/18=2", "84+2=86" ]
Current State: 86:[2, 18, 42, 36], Operations: [] Exploring Operation: 2*42=84, Resulting Numbers: [18, 36, 84] Generated Node #2: [18, 36, 84] from Operation: 2*42=84 Current State: 86:[18, 36, 84], Operations: ['2*42=84'] Exploring Operation: 36/18=2, Resulting Numbers: [84, 2] Generated Node #3: [84, 2] from Operation: 36/18=2 Current State: 86:[84, 2], Operations: ['2*42=84', '36/18=2'] Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[2, 18, 42, 36], Operations: [] Exploring Operation: 2*18=36, Resulting Numbers: [42, 36, 36] Generated Node #0,0: 86:[42, 36, 36] Operation: 2*18=36 Exploring Operation: 18/2=9, Resulting Numbers: [42, 36, 9] Generated Node #0,1: 86:[42, 36, 9] Operation: 18/2=9 Exploring Operation: 18+36=54, Resulting Numbers: [2, 42, 54] Generated Node #0,2: 86:[2, 42, 54] Operation: 18+36=54 Exploring Operation: 36/18=2, Resulting Numbers: [2, 42, 2] Generated Node #0,3: 86:[2, 42, 2] Operation: 36/18=2 Exploring Operation: 36-18=18, Resulting Numbers: [2, 42, 18] Generated Node #0,4: 86:[2, 42, 18] Operation: 36-18=18 Moving to Node #0,3 Current State: 86:[2, 42, 2], Operations: ['36/18=2'] Exploring Operation: 42+2=44, Resulting Numbers: [2, 44] Generated Node #0,3,0: 86:[2, 44] Operation: 42+2=44 Exploring Operation: 2+42=44, Resulting Numbers: [2, 44] Generated Node #0,3,1: 86:[2, 44] Operation: 2+42=44 Exploring Operation: 42*2=84, Resulting Numbers: [2, 84] Generated Node #0,3,2: 86:[2, 84] Operation: 42*2=84 Exploring Operation: 2*42=84, Resulting Numbers: [2, 84] Generated Node #0,3,3: 86:[2, 84] Operation: 2*42=84 Exploring Operation: 2/2=1, Resulting Numbers: [42, 1] Generated Node #0,3,4: 86:[42, 1] Operation: 2/2=1 Moving to Node #0,2 Current State: 86:[2, 42, 54], Operations: ['18+36=54'] Exploring Operation: 54-42=12, Resulting Numbers: [2, 12] Generated Node #0,2,0: 86:[2, 12] Operation: 54-42=12 Exploring Operation: 42+54=96, Resulting Numbers: [2, 96] Generated Node #0,2,1: 86:[2, 96] Operation: 42+54=96 Exploring Operation: 54-2=52, Resulting Numbers: [42, 52] Generated Node #0,2,2: 86:[42, 52] Operation: 54-2=52 Exploring Operation: 2+42=44, Resulting Numbers: [54, 44] Generated Node #0,2,3: 86:[54, 44] Operation: 2+42=44 Exploring Operation: 2*42=84, Resulting Numbers: [54, 84] Generated Node #0,2,4: 86:[54, 84] Operation: 2*42=84 Moving to Node #0,0 Current State: 86:[42, 36, 36], Operations: ['2*18=36'] Exploring Operation: 36-36=0, Resulting Numbers: [42, 0] Generated Node #0,0,0: 86:[42, 0] Operation: 36-36=0 Exploring Operation: 42-36=6, Resulting Numbers: [36, 6] Generated Node #0,0,1: 86:[36, 6] Operation: 42-36=6 Exploring Operation: 42+36=78, Resulting Numbers: [36, 78] Generated Node #0,0,2: 86:[36, 78] Operation: 42+36=78 Exploring Operation: 36/36=1, Resulting Numbers: [42, 1] Generated Node #0,0,3: 86:[42, 1] Operation: 36/36=1 Exploring Operation: 42-36=6, Resulting Numbers: [36, 6] Generated Node #0,0,4: 86:[36, 6] Operation: 42-36=6 Moving to Node #0,1 Current State: 86:[42, 36, 9], Operations: ['18/2=9'] Exploring Operation: 36/9=4, Resulting Numbers: [42, 4] Generated Node #0,1,0: 86:[42, 4] Operation: 36/9=4 Exploring Operation: 42-36=6, Resulting Numbers: [9, 6] Generated Node #0,1,1: 86:[9, 6] Operation: 42-36=6 Exploring Operation: 36+9=45, Resulting Numbers: [42, 45] Generated Node #0,1,2: 86:[42, 45] Operation: 36+9=45 Exploring Operation: 42+36=78, Resulting Numbers: [9, 78] Generated Node #0,1,3: 86:[9, 78] Operation: 42+36=78 Exploring Operation: 42+9=51, Resulting Numbers: [36, 51] Generated Node #0,1,4: 86:[36, 51] Operation: 42+9=51 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[42, 4], Operations: ['18/2=9', '36/9=4'] Exploring Operation: 42*4=168, Resulting Numbers: [168] 168,86 unequal: No Solution Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,86 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,86 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 #0,1,2 Current State: 86:[42, 45], Operations: ['18/2=9', '36+9=45'] Exploring Operation: 45-42=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 42+45=87, Resulting Numbers: [87] 87,86 unequal: No Solution Exploring Operation: 42*45=1890, Resulting Numbers: [1890] 1890,86 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:[9, 6], Operations: ['18/2=9', '42-36=6'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,86 unequal: No Solution Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,86 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 #0,1,3 Current State: 86:[9, 78], Operations: ['18/2=9', '42+36=78'] Exploring Operation: 9+78=87, Resulting Numbers: [87] 87,86 unequal: No Solution Exploring Operation: 9*78=702, Resulting Numbers: [702] 702,86 unequal: No Solution Exploring Operation: 78-9=69, Resulting Numbers: [69] 69,86 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 #0,1,4 Current State: 86:[36, 51], Operations: ['18/2=9', '42+9=51'] Exploring Operation: 36+51=87, Resulting Numbers: [87] 87,86 unequal: No Solution Exploring Operation: 51-36=15, Resulting Numbers: [15] 15,86 unequal: No Solution Exploring Operation: 36*51=1836, Resulting Numbers: [1836] 1836,86 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: 86:[2, 42, 18], Operations: ['36-18=18'] Exploring Operation: 42+18=60, Resulting Numbers: [2, 60] Generated Node #0,4,0: 86:[2, 60] Operation: 42+18=60 Exploring Operation: 2*18=36, Resulting Numbers: [42, 36] Generated Node #0,4,1: 86:[42, 36] Operation: 2*18=36 Exploring Operation: 18/2=9, Resulting Numbers: [42, 9] Generated Node #0,4,2: 86:[42, 9] Operation: 18/2=9 Exploring Operation: 2+42=44, Resulting Numbers: [18, 44] Generated Node #0,4,3: 86:[18, 44] Operation: 2+42=44 Exploring Operation: 18-2=16, Resulting Numbers: [42, 16] Generated Node #0,4,4: 86:[42, 16] Operation: 18-2=16 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 86:[42, 36], Operations: ['36-18=18', '2*18=36'] Exploring Operation: 42*36=1512, Resulting Numbers: [1512] 1512,86 unequal: No Solution Exploring Operation: 42+36=78, Resulting Numbers: [78] 78,86 unequal: No Solution Exploring Operation: 42-36=6, Resulting Numbers: [6] 6,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 86:[42, 9], Operations: ['36-18=18', '18/2=9'] Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,86 unequal: No Solution Exploring Operation: 42*9=378, Resulting Numbers: [378] 378,86 unequal: No Solution Exploring Operation: 42+9=51, Resulting Numbers: [51] 51,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 86:[42, 16], Operations: ['36-18=18', '18-2=16'] Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,86 unequal: No Solution Exploring Operation: 42*16=672, Resulting Numbers: [672] 672,86 unequal: No Solution Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 86:[2, 60], Operations: ['36-18=18', '42+18=60'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,86 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 2*60=120, Resulting Numbers: [120] 120,86 unequal: No Solution Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 86:[18, 44], Operations: ['36-18=18', '2+42=44'] Exploring Operation: 18+44=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 44-18=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 18*44=792, Resulting Numbers: [792] 792,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 86:[2, 44], Operations: ['36/18=2', '42+2=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,86 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,86 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,86 unequal: No Solution Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,86 unequal: No Solution Moving to Node #0,3,1 Current State: 86:[2, 44], Operations: ['36/18=2', '2+42=44'] Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,86 unequal: No Solution Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,86 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,86 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,86 unequal: No Solution Moving to Node #0,3,2 Current State: 86:[2, 84], Operations: ['36/18=2', '42*2=84'] Exploring Operation: 2*84=168, Resulting Numbers: [168] 168,86 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,86 unequal: No Solution Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[2, 18, 42, 36], Operations: [] Exploring Operation: 36/18=2, Resulting Numbers: [2, 42, 2] Generated Node #0,3: 86:[2, 42, 2] Operation: 36/18=2 Moving to Node #0,3 Current State: 86:[2, 42, 2], Operations: ['36/18=2'] Exploring Operation: 42*2=84, Resulting Numbers: [2, 84] Generated Node #0,3,2: 86:[2, 84] Operation: 42*2=84 Moving to Node #0,3,2 Current State: 86:[2, 84], Operations: ['36/18=2', '42*2=84'] Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
0.934028
hs_5
sum_heuristic
[ 7, 38, 10, 81 ]
46
[ "7+38=45", "10+81=91", "91-45=46" ]
Current State: 46:[7, 38, 10, 81], Operations: [] Exploring Operation: 7+38=45, Resulting Numbers: [10, 81, 45] Generated Node #2: [10, 81, 45] from Operation: 7+38=45 Current State: 46:[10, 81, 45], Operations: ['7+38=45'] Exploring Operation: 10+81=91, Resulting Numbers: [45, 91] Generated Node #3: [45, 91] from Operation: 10+81=91 Current State: 46:[45, 91], Operations: ['7+38=45', '10+81=91'] Exploring Operation: 91-45=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[7, 38, 10, 81], Operations: [] Exploring Operation: 81-38=43, Resulting Numbers: [7, 10, 43] Generated Node #0,0: 46:[7, 10, 43] Operation: 81-38=43 Exploring Operation: 81-10=71, Resulting Numbers: [7, 38, 71] Generated Node #0,1: 46:[7, 38, 71] Operation: 81-10=71 Exploring Operation: 38+10=48, Resulting Numbers: [7, 81, 48] Generated Node #0,2: 46:[7, 81, 48] Operation: 38+10=48 Exploring Operation: 10-7=3, Resulting Numbers: [38, 81, 3] Generated Node #0,3: 46:[38, 81, 3] Operation: 10-7=3 Exploring Operation: 7+38=45, Resulting Numbers: [10, 81, 45] Generated Node #0,4: 46:[10, 81, 45] Operation: 7+38=45 Moving to Node #0,0 Current State: 46:[7, 10, 43], Operations: ['81-38=43'] Exploring Operation: 7+43=50, Resulting Numbers: [10, 50] Generated Node #0,0,0: 46:[10, 50] Operation: 7+43=50 Exploring Operation: 7+10=17, Resulting Numbers: [43, 17] Generated Node #0,0,1: 46:[43, 17] Operation: 7+10=17 Exploring Operation: 10-7=3, Resulting Numbers: [43, 3] Generated Node #0,0,2: 46:[43, 3] Operation: 10-7=3 Exploring Operation: 43-10=33, Resulting Numbers: [7, 33] Generated Node #0,0,3: 46:[7, 33] Operation: 43-10=33 Exploring Operation: 10+43=53, Resulting Numbers: [7, 53] Generated Node #0,0,4: 46:[7, 53] Operation: 10+43=53 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 46:[43, 3], Operations: ['81-38=43', '10-7=3'] Exploring Operation: 43*3=129, Resulting Numbers: [129] 129,46 unequal: No Solution Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[7, 38, 10, 81], Operations: [] Exploring Operation: 81-38=43, Resulting Numbers: [7, 10, 43] Generated Node #0,0: 46:[7, 10, 43] Operation: 81-38=43 Moving to Node #0,0 Current State: 46:[7, 10, 43], Operations: ['81-38=43'] Exploring Operation: 10-7=3, Resulting Numbers: [43, 3] Generated Node #0,0,2: 46:[43, 3] Operation: 10-7=3 Moving to Node #0,0,2 Current State: 46:[43, 3], Operations: ['81-38=43', '10-7=3'] Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 42, 68, 59, 58 ]
25
[ "68-42=26", "59-58=1", "26-1=25" ]
Current State: 25:[42, 68, 59, 58], Operations: [] Exploring Operation: 68-42=26, Resulting Numbers: [59, 58, 26] Generated Node #2: [59, 58, 26] from Operation: 68-42=26 Current State: 25:[59, 58, 26], Operations: ['68-42=26'] Exploring Operation: 59-58=1, Resulting Numbers: [26, 1] Generated Node #3: [26, 1] from Operation: 59-58=1 Current State: 25:[26, 1], Operations: ['68-42=26', '59-58=1'] Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[42, 68, 59, 58], Operations: [] Exploring Operation: 68-59=9, Resulting Numbers: [42, 58, 9] Generated Node #0,0: 25:[42, 58, 9] Operation: 68-59=9 Exploring Operation: 68-58=10, Resulting Numbers: [42, 59, 10] Generated Node #0,1: 25:[42, 59, 10] Operation: 68-58=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[42, 58, 9], Operations: ['68-59=9'] Exploring Operation: 42-9=33, Resulting Numbers: [58, 33] Generated Node #0,0,0: 25:[58, 33] Operation: 42-9=33 Exploring Operation: 58-42=16, Resulting Numbers: [9, 16] Generated Node #0,0,1: 25:[9, 16] Operation: 58-42=16 Moving to Node #0,0,1 Current State: 25:[9, 16], Operations: ['68-59=9', '58-42=16'] Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[42, 68, 59, 58], Operations: [] Exploring Operation: 68-59=9, Resulting Numbers: [42, 58, 9] Generated Node #0,0: 25:[42, 58, 9] Operation: 68-59=9 Moving to Node #0,0 Current State: 25:[42, 58, 9], Operations: ['68-59=9'] Exploring Operation: 58-42=16, Resulting Numbers: [9, 16] Generated Node #0,0,1: 25:[9, 16] Operation: 58-42=16 Moving to Node #0,0,1 Current State: 25:[9, 16], Operations: ['68-59=9', '58-42=16'] Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 11, 2, 58, 11 ]
59
[ "11/11=1", "2+58=60", "60-1=59" ]
Current State: 59:[11, 2, 58, 11], Operations: [] Exploring Operation: 11/11=1, Resulting Numbers: [2, 58, 1] Generated Node #2: [2, 58, 1] from Operation: 11/11=1 Current State: 59:[2, 58, 1], Operations: ['11/11=1'] Exploring Operation: 2+58=60, Resulting Numbers: [1, 60] Generated Node #3: [1, 60] from Operation: 2+58=60 Current State: 59:[1, 60], Operations: ['11/11=1', '2+58=60'] Exploring Operation: 60-1=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[11, 2, 58, 11], Operations: [] Exploring Operation: 11*2=22, Resulting Numbers: [58, 11, 22] Generated Node #0,0: 59:[58, 11, 22] Operation: 11*2=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[58, 11, 22], Operations: ['11*2=22'] Exploring Operation: 11+22=33, Resulting Numbers: [58, 33] Generated Node #0,0,0: 59:[58, 33] Operation: 11+22=33 Moving to Node #0,0,0 Current State: 59:[58, 33], Operations: ['11*2=22', '11+22=33'] Exploring Operation: 58+33=91, Resulting Numbers: [91] 91,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 90, 45, 29, 15 ]
91
[ "90+45=135", "29+15=44", "135-44=91" ]
Current State: 91:[90, 45, 29, 15], Operations: [] Exploring Operation: 90+45=135, Resulting Numbers: [29, 15, 135] Generated Node #2: [29, 15, 135] from Operation: 90+45=135 Current State: 91:[29, 15, 135], Operations: ['90+45=135'] Exploring Operation: 29+15=44, Resulting Numbers: [135, 44] Generated Node #3: [135, 44] from Operation: 29+15=44 Current State: 91:[135, 44], Operations: ['90+45=135', '29+15=44'] Exploring Operation: 135-44=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[90, 45, 29, 15], Operations: [] Exploring Operation: 45+29=74, Resulting Numbers: [90, 15, 74] Generated Node #0,0: 91:[90, 15, 74] Operation: 45+29=74 Exploring Operation: 45-29=16, Resulting Numbers: [90, 15, 16] Generated Node #0,1: 91:[90, 15, 16] Operation: 45-29=16 Moving to Node #0,1 Current State: 91:[90, 15, 16], Operations: ['45-29=16'] Exploring Operation: 90/15=6, Resulting Numbers: [16, 6] Generated Node #0,1,0: 91:[16, 6] Operation: 90/15=6 Exploring Operation: 16-15=1, Resulting Numbers: [90, 1] Generated Node #0,1,1: 91:[90, 1] Operation: 16-15=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 91:[16, 6], Operations: ['45-29=16', '90/15=6'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,91 unequal: No Solution Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 91:[90, 1], Operations: ['45-29=16', '16-15=1'] Exploring Operation: 90*1=90, Resulting Numbers: [90] 90,91 unequal: No Solution Exploring Operation: 90+1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[90, 45, 29, 15], Operations: [] Exploring Operation: 45-29=16, Resulting Numbers: [90, 15, 16] Generated Node #0,1: 91:[90, 15, 16] Operation: 45-29=16 Moving to Node #0,1 Current State: 91:[90, 15, 16], Operations: ['45-29=16'] Exploring Operation: 16-15=1, Resulting Numbers: [90, 1] Generated Node #0,1,1: 91:[90, 1] Operation: 16-15=1 Moving to Node #0,1,1 Current State: 91:[90, 1], Operations: ['45-29=16', '16-15=1'] Exploring Operation: 90+1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 20, 19, 3, 61 ]
16
[ "61-20=41", "19*3=57", "57-41=16" ]
Current State: 16:[20, 19, 3, 61], Operations: [] Exploring Operation: 61-20=41, Resulting Numbers: [19, 3, 41] Generated Node #2: [19, 3, 41] from Operation: 61-20=41 Current State: 16:[19, 3, 41], Operations: ['61-20=41'] Exploring Operation: 19*3=57, Resulting Numbers: [41, 57] Generated Node #3: [41, 57] from Operation: 19*3=57 Current State: 16:[41, 57], Operations: ['61-20=41', '19*3=57'] Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[20, 19, 3, 61], Operations: [] Exploring Operation: 61-19=42, Resulting Numbers: [20, 3, 42] Generated Node #0,0: 16:[20, 3, 42] Operation: 61-19=42 Exploring Operation: 61-20=41, Resulting Numbers: [19, 3, 41] Generated Node #0,1: 16:[19, 3, 41] Operation: 61-20=41 Moving to Node #0,1 Current State: 16:[19, 3, 41], Operations: ['61-20=41'] Exploring Operation: 19-3=16, Resulting Numbers: [41, 16] Generated Node #0,1,0: 16:[41, 16] Operation: 19-3=16 Exploring Operation: 41-19=22, Resulting Numbers: [3, 22] Generated Node #0,1,1: 16:[3, 22] Operation: 41-19=22 Moving to Node #0,0 Current State: 16:[20, 3, 42], Operations: ['61-19=42'] Exploring Operation: 42/3=14, Resulting Numbers: [20, 14] Generated Node #0,0,0: 16:[20, 14] Operation: 42/3=14 Exploring Operation: 42-20=22, Resulting Numbers: [3, 22] Generated Node #0,0,1: 16:[3, 22] Operation: 42-20=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[20, 14], Operations: ['61-19=42', '42/3=14'] Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[3, 22], Operations: ['61-19=42', '42-20=22'] Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,16 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: 16:[3, 22], Operations: ['61-20=41', '41-19=22'] Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[41, 16], Operations: ['61-20=41', '19-3=16'] Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 41+16=57, Resulting Numbers: [57] 57,16 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 15, 54, 51, 32 ]
39
[ "54+51=105", "105/15=7", "32+7=39" ]
Current State: 39:[15, 54, 51, 32], Operations: [] Exploring Operation: 54+51=105, Resulting Numbers: [15, 32, 105] Generated Node #2: [15, 32, 105] from Operation: 54+51=105 Current State: 39:[15, 32, 105], Operations: ['54+51=105'] Exploring Operation: 105/15=7, Resulting Numbers: [32, 7] Generated Node #3: [32, 7] from Operation: 105/15=7 Current State: 39:[32, 7], Operations: ['54+51=105', '105/15=7'] Exploring Operation: 32+7=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[15, 54, 51, 32], Operations: [] Exploring Operation: 54-51=3, Resulting Numbers: [15, 32, 3] Generated Node #0,0: 39:[15, 32, 3] Operation: 54-51=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[15, 32, 3], Operations: ['54-51=3'] Exploring Operation: 32-15=17, Resulting Numbers: [3, 17] Generated Node #0,0,0: 39:[3, 17] Operation: 32-15=17 Moving to Node #0,0,0 Current State: 39:[3, 17], Operations: ['54-51=3', '32-15=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 42, 66, 6, 44 ]
29
[ "42/6=7", "66-44=22", "7+22=29" ]
Current State: 29:[42, 66, 6, 44], Operations: [] Exploring Operation: 42/6=7, Resulting Numbers: [66, 44, 7] Generated Node #2: [66, 44, 7] from Operation: 42/6=7 Current State: 29:[66, 44, 7], Operations: ['42/6=7'] Exploring Operation: 66-44=22, Resulting Numbers: [7, 22] Generated Node #3: [7, 22] from Operation: 66-44=22 Current State: 29:[7, 22], Operations: ['42/6=7', '66-44=22'] Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[42, 66, 6, 44], Operations: [] Exploring Operation: 66-42=24, Resulting Numbers: [6, 44, 24] Generated Node #0,0: 29:[6, 44, 24] Operation: 66-42=24 Exploring Operation: 66/6=11, Resulting Numbers: [42, 44, 11] Generated Node #0,1: 29:[42, 44, 11] Operation: 66/6=11 Exploring Operation: 66-44=22, Resulting Numbers: [42, 6, 22] Generated Node #0,2: 29:[42, 6, 22] Operation: 66-44=22 Exploring Operation: 42-6=36, Resulting Numbers: [66, 44, 36] Generated Node #0,3: 29:[66, 44, 36] Operation: 42-6=36 Exploring Operation: 66-6=60, Resulting Numbers: [42, 44, 60] Generated Node #0,4: 29:[42, 44, 60] Operation: 66-6=60 Moving to Node #0,0 Current State: 29:[6, 44, 24], Operations: ['66-42=24'] Exploring Operation: 44-6=38, Resulting Numbers: [24, 38] Generated Node #0,0,0: 29:[24, 38] Operation: 44-6=38 Exploring Operation: 6+24=30, Resulting Numbers: [44, 30] Generated Node #0,0,1: 29:[44, 30] Operation: 6+24=30 Exploring Operation: 44-24=20, Resulting Numbers: [6, 20] Generated Node #0,0,2: 29:[6, 20] Operation: 44-24=20 Exploring Operation: 24-6=18, Resulting Numbers: [44, 18] Generated Node #0,0,3: 29:[44, 18] Operation: 24-6=18 Exploring Operation: 6+44=50, Resulting Numbers: [24, 50] Generated Node #0,0,4: 29:[24, 50] Operation: 6+44=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[24, 38], Operations: ['66-42=24', '44-6=38'] Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,29 unequal: No Solution Exploring Operation: 24+38=62, Resulting Numbers: [62] 62,29 unequal: No Solution Exploring Operation: 24*38=912, Resulting Numbers: [912] 912,29 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:[44, 30], Operations: ['66-42=24', '6+24=30'] Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,29 unequal: No Solution Exploring Operation: 44*30=1320, Resulting Numbers: [1320] 1320,29 unequal: No Solution Exploring Operation: 44+30=74, Resulting Numbers: [74] 74,29 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 #0,0,3 Current State: 29:[44, 18], Operations: ['66-42=24', '24-6=18'] Exploring Operation: 44-18=26, Resulting Numbers: [26] 26,29 unequal: No Solution Exploring Operation: 44*18=792, Resulting Numbers: [792] 792,29 unequal: No Solution Exploring Operation: 44+18=62, Resulting Numbers: [62] 62,29 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 #0,0,4 Current State: 29:[24, 50], Operations: ['66-42=24', '6+44=50'] Exploring Operation: 24*50=1200, Resulting Numbers: [1200] 1200,29 unequal: No Solution Exploring Operation: 24+50=74, Resulting Numbers: [74] 74,29 unequal: No Solution Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,29 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 #0,0,2 Current State: 29:[6, 20], Operations: ['66-42=24', '44-24=20'] Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,29 unequal: No Solution Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,29 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,29 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: 29:[42, 6, 22], Operations: ['66-44=22'] Exploring Operation: 42/6=7, Resulting Numbers: [22, 7] Generated Node #0,2,0: 29:[22, 7] Operation: 42/6=7 Exploring Operation: 42+6=48, Resulting Numbers: [22, 48] Generated Node #0,2,1: 29:[22, 48] Operation: 42+6=48 Exploring Operation: 42-6=36, Resulting Numbers: [22, 36] Generated Node #0,2,2: 29:[22, 36] Operation: 42-6=36 Exploring Operation: 22-6=16, Resulting Numbers: [42, 16] Generated Node #0,2,3: 29:[42, 16] Operation: 22-6=16 Exploring Operation: 6+22=28, Resulting Numbers: [42, 28] Generated Node #0,2,4: 29:[42, 28] Operation: 6+22=28 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 29:[22, 36], Operations: ['66-44=22', '42-6=36'] Exploring Operation: 22+36=58, Resulting Numbers: [58] 58,29 unequal: No Solution Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,29 unequal: No Solution Exploring Operation: 22*36=792, Resulting Numbers: [792] 792,29 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 #0,2,4 Current State: 29:[42, 28], Operations: ['66-44=22', '6+22=28'] Exploring Operation: 42+28=70, Resulting Numbers: [70] 70,29 unequal: No Solution Exploring Operation: 42*28=1176, Resulting Numbers: [1176] 1176,29 unequal: No Solution Exploring Operation: 42-28=14, Resulting Numbers: [14] 14,29 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 #0,2,1 Current State: 29:[22, 48], Operations: ['66-44=22', '42+6=48'] Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,29 unequal: No Solution Exploring Operation: 22*48=1056, Resulting Numbers: [1056] 1056,29 unequal: No Solution Exploring Operation: 22+48=70, Resulting Numbers: [70] 70,29 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 #0,2,3 Current State: 29:[42, 16], Operations: ['66-44=22', '22-6=16'] Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,29 unequal: No Solution Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,29 unequal: No Solution Exploring Operation: 42*16=672, Resulting Numbers: [672] 672,29 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 #0,2,0 Current State: 29:[22, 7], Operations: ['66-44=22', '42/6=7'] Exploring Operation: 22+7=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[42, 66, 6, 44], Operations: [] Exploring Operation: 66-44=22, Resulting Numbers: [42, 6, 22] Generated Node #0,2: 29:[42, 6, 22] Operation: 66-44=22 Moving to Node #0,2 Current State: 29:[42, 6, 22], Operations: ['66-44=22'] Exploring Operation: 42/6=7, Resulting Numbers: [22, 7] Generated Node #0,2,0: 29:[22, 7] Operation: 42/6=7 Moving to Node #0,2,0 Current State: 29:[22, 7], Operations: ['66-44=22', '42/6=7'] Exploring Operation: 22+7=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
mult_heuristic
[ 43, 24, 44, 39 ]
38
[ "43-39=4", "24/4=6", "44-6=38" ]
Current State: 38:[43, 24, 44, 39], Operations: [] Exploring Operation: 43-39=4, Resulting Numbers: [24, 44, 4] Generated Node #2: [24, 44, 4] from Operation: 43-39=4 Current State: 38:[24, 44, 4], Operations: ['43-39=4'] Exploring Operation: 24/4=6, Resulting Numbers: [44, 6] Generated Node #3: [44, 6] from Operation: 24/4=6 Current State: 38:[44, 6], Operations: ['43-39=4', '24/4=6'] Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[43, 24, 44, 39], Operations: [] Exploring Operation: 44-24=20, Resulting Numbers: [43, 39, 20] Generated Node #0,0: 38:[43, 39, 20] Operation: 44-24=20 Exploring Operation: 44-43=1, Resulting Numbers: [24, 39, 1] Generated Node #0,1: 38:[24, 39, 1] Operation: 44-43=1 Exploring Operation: 43-24=19, Resulting Numbers: [44, 39, 19] Generated Node #0,2: 38:[44, 39, 19] Operation: 43-24=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[43, 39, 20], Operations: ['44-24=20'] Exploring Operation: 39-20=19, Resulting Numbers: [43, 19] Generated Node #0,0,0: 38:[43, 19] Operation: 39-20=19 Exploring Operation: 43-39=4, Resulting Numbers: [20, 4] Generated Node #0,0,1: 38:[20, 4] Operation: 43-39=4 Exploring Operation: 43-20=23, Resulting Numbers: [39, 23] Generated Node #0,0,2: 38:[39, 23] Operation: 43-20=23 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 38:[20, 4], Operations: ['44-24=20', '43-39=4'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,38 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 #0,0,0 Current State: 38:[43, 19], Operations: ['44-24=20', '39-20=19'] Exploring Operation: 43*19=817, Resulting Numbers: [817] 817,38 unequal: No Solution Exploring Operation: 43+19=62, Resulting Numbers: [62] 62,38 unequal: No Solution Exploring Operation: 43-19=24, Resulting Numbers: [24] 24,38 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 #0,0,2 Current State: 38:[39, 23], Operations: ['44-24=20', '43-20=23'] Exploring Operation: 39+23=62, Resulting Numbers: [62] 62,38 unequal: No Solution Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 39*23=897, Resulting Numbers: [897] 897,38 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 #0,1 Current State: 38:[24, 39, 1], Operations: ['44-43=1'] Exploring Operation: 24-1=23, Resulting Numbers: [39, 23] Generated Node #0,1,0: 38:[39, 23] Operation: 24-1=23 Exploring Operation: 39-24=15, Resulting Numbers: [1, 15] Generated Node #0,1,1: 38:[1, 15] Operation: 39-24=15 Exploring Operation: 39-1=38, Resulting Numbers: [24, 38] Generated Node #0,1,2: 38:[24, 38] Operation: 39-1=38 Moving to Node #0,1,0 Current State: 38:[39, 23], Operations: ['44-43=1', '24-1=23'] Exploring Operation: 39+23=62, Resulting Numbers: [62] 62,38 unequal: No Solution Exploring Operation: 39*23=897, Resulting Numbers: [897] 897,38 unequal: No Solution Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[1, 15], Operations: ['44-43=1', '39-24=15'] Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,38 unequal: No Solution Exploring Operation: 1*15=15, Resulting Numbers: [15] 15,38 unequal: No Solution Exploring Operation: 1+15=16, Resulting Numbers: [16] 16,38 unequal: No Solution Moving to Node #0,1,2 Current State: 38:[24, 38], Operations: ['44-43=1', '39-1=38'] Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,38 unequal: No Solution Exploring Operation: 24*38=912, Resulting Numbers: [912] 912,38 unequal: No Solution Exploring Operation: 24+38=62, Resulting Numbers: [62] 62,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[44, 39, 19], Operations: ['43-24=19'] Exploring Operation: 44-39=5, Resulting Numbers: [19, 5] Generated Node #0,2,0: 38:[19, 5] Operation: 44-39=5 Exploring Operation: 39-19=20, Resulting Numbers: [44, 20] Generated Node #0,2,1: 38:[44, 20] Operation: 39-19=20 Exploring Operation: 44-19=25, Resulting Numbers: [39, 25] Generated Node #0,2,2: 38:[39, 25] Operation: 44-19=25 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 38:[19, 5], Operations: ['43-24=19', '44-39=5'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,38 unequal: No Solution Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,38 unequal: No Solution Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 38:[44, 20], Operations: ['43-24=19', '39-19=20'] Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 44*20=880, Resulting Numbers: [880] 880,38 unequal: No Solution Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 38:[39, 25], Operations: ['43-24=19', '44-19=25'] Exploring Operation: 39*25=975, Resulting Numbers: [975] 975,38 unequal: No Solution Exploring Operation: 39+25=64, Resulting Numbers: [64] 64,38 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,38 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 No solution found.
0
hs_3
sum_heuristic
[ 91, 18, 53, 24 ]
24
[ "91+53=144", "24-18=6", "144/6=24" ]
Current State: 24:[91, 18, 53, 24], Operations: [] Exploring Operation: 91+53=144, Resulting Numbers: [18, 24, 144] Generated Node #2: [18, 24, 144] from Operation: 91+53=144 Current State: 24:[18, 24, 144], Operations: ['91+53=144'] Exploring Operation: 24-18=6, Resulting Numbers: [144, 6] Generated Node #3: [144, 6] from Operation: 24-18=6 Current State: 24:[144, 6], Operations: ['91+53=144', '24-18=6'] Exploring Operation: 144/6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[91, 18, 53, 24], Operations: [] Exploring Operation: 53-18=35, Resulting Numbers: [91, 24, 35] Generated Node #0,0: 24:[91, 24, 35] Operation: 53-18=35 Exploring Operation: 91-18=73, Resulting Numbers: [53, 24, 73] Generated Node #0,1: 24:[53, 24, 73] Operation: 91-18=73 Exploring Operation: 91-24=67, Resulting Numbers: [18, 53, 67] Generated Node #0,2: 24:[18, 53, 67] Operation: 91-24=67 Exploring Operation: 91-53=38, Resulting Numbers: [18, 24, 38] Generated Node #0,3: 24:[18, 24, 38] Operation: 91-53=38 Start Sub Search at level 1: Moving to Node #0,3 Current State: 24:[18, 24, 38], Operations: ['91-53=38'] Exploring Operation: 38-18=20, Resulting Numbers: [24, 20] Generated Node #0,3,0: 24:[24, 20] Operation: 38-18=20 Exploring Operation: 18+24=42, Resulting Numbers: [38, 42] Generated Node #0,3,1: 24:[38, 42] Operation: 18+24=42 Exploring Operation: 38-24=14, Resulting Numbers: [18, 14] Generated Node #0,3,2: 24:[18, 14] Operation: 38-24=14 Exploring Operation: 24-18=6, Resulting Numbers: [38, 6] Generated Node #0,3,3: 24:[38, 6] Operation: 24-18=6 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 24:[24, 20], Operations: ['91-53=38', '38-18=20'] Exploring Operation: 24*20=480, Resulting Numbers: [480] 480,24 unequal: No Solution Exploring Operation: 24+20=44, Resulting Numbers: [44] 44,24 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,24 unequal: No Solution No 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: 24:[18, 14], Operations: ['91-53=38', '38-24=14'] Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 18+14=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 18*14=252, Resulting Numbers: [252] 252,24 unequal: No Solution No 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: 24:[38, 6], Operations: ['91-53=38', '24-18=6'] Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,24 unequal: No Solution Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,24 unequal: No Solution No 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: 24:[38, 42], Operations: ['91-53=38', '18+24=42'] Exploring Operation: 42-38=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 38*42=1596, Resulting Numbers: [1596] 1596,24 unequal: No Solution Exploring Operation: 38+42=80, Resulting Numbers: [80] 80,24 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: 24:[91, 24, 35], Operations: ['53-18=35'] Exploring Operation: 91-35=56, Resulting Numbers: [24, 56] Generated Node #0,0,0: 24:[24, 56] Operation: 91-35=56 Exploring Operation: 35-24=11, Resulting Numbers: [91, 11] Generated Node #0,0,1: 24:[91, 11] Operation: 35-24=11 Exploring Operation: 91+24=115, Resulting Numbers: [35, 115] Generated Node #0,0,2: 24:[35, 115] Operation: 91+24=115 Exploring Operation: 91-24=67, Resulting Numbers: [35, 67] Generated Node #0,0,3: 24:[35, 67] Operation: 91-24=67 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[24, 56], Operations: ['53-18=35', '91-35=56'] Exploring Operation: 56-24=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 24*56=1344, Resulting Numbers: [1344] 1344,24 unequal: No Solution Exploring Operation: 24+56=80, Resulting Numbers: [80] 80,24 unequal: No Solution No 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: 24:[35, 67], Operations: ['53-18=35', '91-24=67'] Exploring Operation: 67-35=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 35*67=2345, Resulting Numbers: [2345] 2345,24 unequal: No Solution Exploring Operation: 35+67=102, Resulting Numbers: [102] 102,24 unequal: No Solution No 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: 24:[91, 11], Operations: ['53-18=35', '35-24=11'] Exploring Operation: 91*11=1001, Resulting Numbers: [1001] 1001,24 unequal: No Solution Exploring Operation: 91+11=102, Resulting Numbers: [102] 102,24 unequal: No Solution Exploring Operation: 91-11=80, Resulting Numbers: [80] 80,24 unequal: No Solution No 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: 24:[35, 115], Operations: ['53-18=35', '91+24=115'] Exploring Operation: 115-35=80, Resulting Numbers: [80] 80,24 unequal: No Solution Exploring Operation: 35+115=150, Resulting Numbers: [150] 150,24 unequal: No Solution Exploring Operation: 35*115=4025, Resulting Numbers: [4025] 4025,24 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: 24:[53, 24, 73], Operations: ['91-18=73'] Exploring Operation: 53+24=77, Resulting Numbers: [73, 77] Generated Node #0,1,0: 24:[73, 77] Operation: 53+24=77 Exploring Operation: 73-53=20, Resulting Numbers: [24, 20] Generated Node #0,1,1: 24:[24, 20] Operation: 73-53=20 Exploring Operation: 73-24=49, Resulting Numbers: [53, 49] Generated Node #0,1,2: 24:[53, 49] Operation: 73-24=49 Exploring Operation: 53-24=29, Resulting Numbers: [73, 29] Generated Node #0,1,3: 24:[73, 29] Operation: 53-24=29 Moving to Node #0,1,1 Current State: 24:[24, 20], Operations: ['91-18=73', '73-53=20'] Exploring Operation: 24+20=44, Resulting Numbers: [44] 44,24 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 24*20=480, Resulting Numbers: [480] 480,24 unequal: No Solution Moving to Node #0,1,3 Current State: 24:[73, 29], Operations: ['91-18=73', '53-24=29'] Exploring Operation: 73+29=102, Resulting Numbers: [102] 102,24 unequal: No Solution Exploring Operation: 73-29=44, Resulting Numbers: [44] 44,24 unequal: No Solution Exploring Operation: 73*29=2117, Resulting Numbers: [2117] 2117,24 unequal: No Solution Moving to Node #0,1,2 Current State: 24:[53, 49], Operations: ['91-18=73', '73-24=49'] Exploring Operation: 53+49=102, Resulting Numbers: [102] 102,24 unequal: No Solution Exploring Operation: 53*49=2597, Resulting Numbers: [2597] 2597,24 unequal: No Solution Exploring Operation: 53-49=4, Resulting Numbers: [4] 4,24 unequal: No Solution Moving to Node #0,1,0 Current State: 24:[73, 77], Operations: ['91-18=73', '53+24=77'] Exploring Operation: 73+77=150, Resulting Numbers: [150] 150,24 unequal: No Solution Exploring Operation: 73*77=5621, Resulting Numbers: [5621] 5621,24 unequal: No Solution Exploring Operation: 77-73=4, Resulting Numbers: [4] 4,24 unequal: No Solution No 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: 24:[18, 53, 67], Operations: ['91-24=67'] Exploring Operation: 67-18=49, Resulting Numbers: [53, 49] Generated Node #0,2,0: 24:[53, 49] Operation: 67-18=49 Exploring Operation: 18+53=71, Resulting Numbers: [67, 71] Generated Node #0,2,1: 24:[67, 71] Operation: 18+53=71 Exploring Operation: 67-53=14, Resulting Numbers: [18, 14] Generated Node #0,2,2: 24:[18, 14] Operation: 67-53=14 Exploring Operation: 53-18=35, Resulting Numbers: [67, 35] Generated Node #0,2,3: 24:[67, 35] Operation: 53-18=35 Moving to Node #0,2,2 Current State: 24:[18, 14], Operations: ['91-24=67', '67-53=14'] Exploring Operation: 18+14=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 18*14=252, Resulting Numbers: [252] 252,24 unequal: No Solution Moving to Node #0,2,3 Current State: 24:[67, 35], Operations: ['91-24=67', '53-18=35'] Exploring Operation: 67*35=2345, Resulting Numbers: [2345] 2345,24 unequal: No Solution Exploring Operation: 67+35=102, Resulting Numbers: [102] 102,24 unequal: No Solution Exploring Operation: 67-35=32, Resulting Numbers: [32] 32,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[53, 49], Operations: ['91-24=67', '67-18=49'] Exploring Operation: 53-49=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 53+49=102, Resulting Numbers: [102] 102,24 unequal: No Solution Exploring Operation: 53*49=2597, Resulting Numbers: [2597] 2597,24 unequal: No Solution Moving to Node #0,2,1 Current State: 24:[67, 71], Operations: ['91-24=67', '18+53=71'] Exploring Operation: 67*71=4757, Resulting Numbers: [4757] 4757,24 unequal: No Solution Exploring Operation: 71-67=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 67+71=138, Resulting Numbers: [138] 138,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 56, 52, 8, 76 ]
80
[ "56-52=4", "8+76=84", "84-4=80" ]
Current State: 80:[56, 52, 8, 76], Operations: [] Exploring Operation: 56-52=4, Resulting Numbers: [8, 76, 4] Generated Node #2: [8, 76, 4] from Operation: 56-52=4 Current State: 80:[8, 76, 4], Operations: ['56-52=4'] Exploring Operation: 8+76=84, Resulting Numbers: [4, 84] Generated Node #3: [4, 84] from Operation: 8+76=84 Current State: 80:[4, 84], Operations: ['56-52=4', '8+76=84'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[56, 52, 8, 76], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [52, 76, 7] Generated Node #0,0: 80:[52, 76, 7] Operation: 56/8=7 Exploring Operation: 76-52=24, Resulting Numbers: [56, 8, 24] Generated Node #0,1: 80:[56, 8, 24] Operation: 76-52=24 Exploring Operation: 76-56=20, Resulting Numbers: [52, 8, 20] Generated Node #0,2: 80:[52, 8, 20] Operation: 76-56=20 Exploring Operation: 56-52=4, Resulting Numbers: [8, 76, 4] Generated Node #0,3: 80:[8, 76, 4] Operation: 56-52=4 Moving to Node #0,3 Current State: 80:[8, 76, 4], Operations: ['56-52=4'] Exploring Operation: 76+4=80, Resulting Numbers: [8, 80] Generated Node #0,3,0: 80:[8, 80] Operation: 76+4=80 Exploring Operation: 8+76=84, Resulting Numbers: [4, 84] Generated Node #0,3,1: 80:[4, 84] Operation: 8+76=84 Exploring Operation: 8-4=4, Resulting Numbers: [76, 4] Generated Node #0,3,2: 80:[76, 4] Operation: 8-4=4 Exploring Operation: 76/4=19, Resulting Numbers: [8, 19] Generated Node #0,3,3: 80:[8, 19] Operation: 76/4=19 Moving to Node #0,2 Current State: 80:[52, 8, 20], Operations: ['76-56=20'] Exploring Operation: 52-20=32, Resulting Numbers: [8, 32] Generated Node #0,2,0: 80:[8, 32] Operation: 52-20=32 Exploring Operation: 52+20=72, Resulting Numbers: [8, 72] Generated Node #0,2,1: 80:[8, 72] Operation: 52+20=72 Exploring Operation: 20-8=12, Resulting Numbers: [52, 12] Generated Node #0,2,2: 80:[52, 12] Operation: 20-8=12 Exploring Operation: 52-8=44, Resulting Numbers: [20, 44] Generated Node #0,2,3: 80:[20, 44] Operation: 52-8=44 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 80:[20, 44], Operations: ['76-56=20', '52-8=44'] Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 20*44=880, Resulting Numbers: [880] 880,80 unequal: No Solution Exploring Operation: 20+44=64, Resulting Numbers: [64] 64,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[8, 32], Operations: ['76-56=20', '52-20=32'] Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 8*32=256, Resulting Numbers: [256] 256,80 unequal: No Solution Exploring Operation: 8+32=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 80:[8, 72], Operations: ['76-56=20', '52+20=72'] Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 8*72=576, Resulting Numbers: [576] 576,80 unequal: No Solution Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,80 unequal: No Solution Exploring Operation: 8+72=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[56, 52, 8, 76], Operations: [] Exploring Operation: 76-56=20, Resulting Numbers: [52, 8, 20] Generated Node #0,2: 80:[52, 8, 20] Operation: 76-56=20 Moving to Node #0,2 Current State: 80:[52, 8, 20], Operations: ['76-56=20'] Exploring Operation: 52+20=72, Resulting Numbers: [8, 72] Generated Node #0,2,1: 80:[8, 72] Operation: 52+20=72 Moving to Node #0,2,1 Current State: 80:[8, 72], Operations: ['76-56=20', '52+20=72'] Exploring Operation: 8+72=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_4
sum_heuristic
[ 77, 6, 87, 88 ]
84
[ "77+6=83", "88-87=1", "83+1=84" ]
Current State: 84:[77, 6, 87, 88], Operations: [] Exploring Operation: 77+6=83, Resulting Numbers: [87, 88, 83] Generated Node #2: [87, 88, 83] from Operation: 77+6=83 Current State: 84:[87, 88, 83], Operations: ['77+6=83'] Exploring Operation: 88-87=1, Resulting Numbers: [83, 1] Generated Node #3: [83, 1] from Operation: 88-87=1 Current State: 84:[83, 1], Operations: ['77+6=83', '88-87=1'] Exploring Operation: 83+1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[77, 6, 87, 88], Operations: [] Exploring Operation: 88-87=1, Resulting Numbers: [77, 6, 1] Generated Node #0,0: 84:[77, 6, 1] Operation: 88-87=1 Exploring Operation: 88-77=11, Resulting Numbers: [6, 87, 11] Generated Node #0,1: 84:[6, 87, 11] Operation: 88-77=11 Exploring Operation: 77+6=83, Resulting Numbers: [87, 88, 83] Generated Node #0,2: 84:[87, 88, 83] Operation: 77+6=83 Exploring Operation: 87-77=10, Resulting Numbers: [6, 88, 10] Generated Node #0,3: 84:[6, 88, 10] Operation: 87-77=10 Moving to Node #0,1 Current State: 84:[6, 87, 11], Operations: ['88-77=11'] Exploring Operation: 11-6=5, Resulting Numbers: [87, 5] Generated Node #0,1,0: 84:[87, 5] Operation: 11-6=5 Exploring Operation: 6+11=17, Resulting Numbers: [87, 17] Generated Node #0,1,1: 84:[87, 17] Operation: 6+11=17 Exploring Operation: 87-6=81, Resulting Numbers: [11, 81] Generated Node #0,1,2: 84:[11, 81] Operation: 87-6=81 Exploring Operation: 87-11=76, Resulting Numbers: [6, 76] Generated Node #0,1,3: 84:[6, 76] Operation: 87-11=76 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 84:[87, 5], Operations: ['88-77=11', '11-6=5'] Exploring Operation: 87*5=435, Resulting Numbers: [435] 435,84 unequal: No Solution Exploring Operation: 87-5=82, Resulting Numbers: [82] 82,84 unequal: No Solution Exploring Operation: 87+5=92, Resulting Numbers: [92] 92,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 84:[11, 81], Operations: ['88-77=11', '87-6=81'] Exploring Operation: 11*81=891, Resulting Numbers: [891] 891,84 unequal: No Solution Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 11+81=92, Resulting Numbers: [92] 92,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[87, 17], Operations: ['88-77=11', '6+11=17'] Exploring Operation: 87-17=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 87*17=1479, Resulting Numbers: [1479] 1479,84 unequal: No Solution Exploring Operation: 87+17=104, Resulting Numbers: [104] 104,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 84:[6, 76], Operations: ['88-77=11', '87-11=76'] Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 6+76=82, Resulting Numbers: [82] 82,84 unequal: No Solution Exploring Operation: 6*76=456, Resulting Numbers: [456] 456,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 84:[6, 88, 10], Operations: ['87-77=10'] Exploring Operation: 88-10=78, Resulting Numbers: [6, 78] Generated Node #0,3,0: 84:[6, 78] Operation: 88-10=78 Exploring Operation: 10-6=4, Resulting Numbers: [88, 4] Generated Node #0,3,1: 84:[88, 4] Operation: 10-6=4 Exploring Operation: 6+10=16, Resulting Numbers: [88, 16] Generated Node #0,3,2: 84:[88, 16] Operation: 6+10=16 Exploring Operation: 88-6=82, Resulting Numbers: [10, 82] Generated Node #0,3,3: 84:[10, 82] Operation: 88-6=82 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 84:[88, 4], Operations: ['87-77=10', '10-6=4'] Exploring Operation: 88*4=352, Resulting Numbers: [352] 352,84 unequal: No Solution Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 88+4=92, Resulting Numbers: [92] 92,84 unequal: No Solution Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[77, 6, 87, 88], Operations: [] Exploring Operation: 87-77=10, Resulting Numbers: [6, 88, 10] Generated Node #0,3: 84:[6, 88, 10] Operation: 87-77=10 Moving to Node #0,3 Current State: 84:[6, 88, 10], Operations: ['87-77=10'] Exploring Operation: 10-6=4, Resulting Numbers: [88, 4] Generated Node #0,3,1: 84:[88, 4] Operation: 10-6=4 Moving to Node #0,3,1 Current State: 84:[88, 4], Operations: ['87-77=10', '10-6=4'] Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 93, 64, 97, 17 ]
77
[ "93+64=157", "97-17=80", "157-80=77" ]
Current State: 77:[93, 64, 97, 17], Operations: [] Exploring Operation: 93+64=157, Resulting Numbers: [97, 17, 157] Generated Node #2: [97, 17, 157] from Operation: 93+64=157 Current State: 77:[97, 17, 157], Operations: ['93+64=157'] Exploring Operation: 97-17=80, Resulting Numbers: [157, 80] Generated Node #3: [157, 80] from Operation: 97-17=80 Current State: 77:[157, 80], Operations: ['93+64=157', '97-17=80'] Exploring Operation: 157-80=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[93, 64, 97, 17], Operations: [] Exploring Operation: 97-93=4, Resulting Numbers: [64, 17, 4] Generated Node #0,0: 77:[64, 17, 4] Operation: 97-93=4 Exploring Operation: 97-17=80, Resulting Numbers: [93, 64, 80] Generated Node #0,1: 77:[93, 64, 80] Operation: 97-17=80 Moving to Node #0,0 Current State: 77:[64, 17, 4], Operations: ['97-93=4'] Exploring Operation: 64/4=16, Resulting Numbers: [17, 16] Generated Node #0,0,0: 77:[17, 16] Operation: 64/4=16 Exploring Operation: 64+17=81, Resulting Numbers: [4, 81] Generated Node #0,0,1: 77:[4, 81] Operation: 64+17=81 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[4, 81], Operations: ['97-93=4', '64+17=81'] Exploring Operation: 4+81=85, Resulting Numbers: [85] 85,77 unequal: No Solution Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[93, 64, 97, 17], Operations: [] Exploring Operation: 97-93=4, Resulting Numbers: [64, 17, 4] Generated Node #0,0: 77:[64, 17, 4] Operation: 97-93=4 Moving to Node #0,0 Current State: 77:[64, 17, 4], Operations: ['97-93=4'] Exploring Operation: 64+17=81, Resulting Numbers: [4, 81] Generated Node #0,0,1: 77:[4, 81] Operation: 64+17=81 Moving to Node #0,0,1 Current State: 77:[4, 81], Operations: ['97-93=4', '64+17=81'] Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 47, 56, 2, 16 ]
70
[ "47+16=63", "2*63=126", "126-56=70" ]
Current State: 70:[47, 56, 2, 16], Operations: [] Exploring Operation: 47+16=63, Resulting Numbers: [56, 2, 63] Generated Node #2: [56, 2, 63] from Operation: 47+16=63 Current State: 70:[56, 2, 63], Operations: ['47+16=63'] Exploring Operation: 2*63=126, Resulting Numbers: [56, 126] Generated Node #3: [56, 126] from Operation: 2*63=126 Current State: 70:[56, 126], Operations: ['47+16=63', '2*63=126'] Exploring Operation: 126-56=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[47, 56, 2, 16], Operations: [] Exploring Operation: 56-47=9, Resulting Numbers: [2, 16, 9] Generated Node #0,0: 70:[2, 16, 9] Operation: 56-47=9 Exploring Operation: 56+16=72, Resulting Numbers: [47, 2, 72] Generated Node #0,1: 70:[47, 2, 72] Operation: 56+16=72 Exploring Operation: 56-16=40, Resulting Numbers: [47, 2, 40] Generated Node #0,2: 70:[47, 2, 40] Operation: 56-16=40 Moving to Node #0,0 Current State: 70:[2, 16, 9], Operations: ['56-47=9'] Exploring Operation: 16-9=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 70:[2, 7] Operation: 16-9=7 Exploring Operation: 16-2=14, Resulting Numbers: [9, 14] Generated Node #0,0,1: 70:[9, 14] Operation: 16-2=14 Exploring Operation: 16/2=8, Resulting Numbers: [9, 8] Generated Node #0,0,2: 70:[9, 8] Operation: 16/2=8 Moving to Node #0,1 Current State: 70:[47, 2, 72], Operations: ['56+16=72'] Exploring Operation: 72-47=25, Resulting Numbers: [2, 25] Generated Node #0,1,0: 70:[2, 25] Operation: 72-47=25 Exploring Operation: 72-2=70, Resulting Numbers: [47, 70] Generated Node #0,1,1: 70:[47, 70] Operation: 72-2=70 Exploring Operation: 47-2=45, Resulting Numbers: [72, 45] Generated Node #0,1,2: 70:[72, 45] Operation: 47-2=45 Moving to Node #0,2 Current State: 70:[47, 2, 40], Operations: ['56-16=40'] Exploring Operation: 47-2=45, Resulting Numbers: [40, 45] Generated Node #0,2,0: 70:[40, 45] Operation: 47-2=45 Exploring Operation: 47-40=7, Resulting Numbers: [2, 7] Generated Node #0,2,1: 70:[2, 7] Operation: 47-40=7 Exploring Operation: 40-2=38, Resulting Numbers: [47, 38] Generated Node #0,2,2: 70:[47, 38] Operation: 40-2=38 Moving to Node #0,0,0 Current State: 70:[2, 7], Operations: ['56-47=9', '16-9=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,70 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,70 unequal: No Solution Moving to Node #0,2,1 Current State: 70:[2, 7], Operations: ['56-16=40', '47-40=7'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,70 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[9, 14], Operations: ['56-47=9', '16-2=14'] Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,70 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[9, 8], Operations: ['56-47=9', '16/2=8'] Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,70 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,70 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[2, 25], Operations: ['56+16=72', '72-47=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,70 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,70 unequal: No Solution Moving to Node #0,1,2 Current State: 70:[72, 45], Operations: ['56+16=72', '47-2=45'] Exploring Operation: 72*45=3240, Resulting Numbers: [3240] 3240,70 unequal: No Solution Exploring Operation: 72+45=117, Resulting Numbers: [117] 117,70 unequal: No Solution Exploring Operation: 72-45=27, Resulting Numbers: [27] 27,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[47, 70], Operations: ['56+16=72', '72-2=70'] Exploring Operation: 47*70=3290, Resulting Numbers: [3290] 3290,70 unequal: No Solution Exploring Operation: 70-47=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 47+70=117, Resulting Numbers: [117] 117,70 unequal: No Solution Moving to Node #0,2,0 Current State: 70:[40, 45], Operations: ['56-16=40', '47-2=45'] Exploring Operation: 40+45=85, Resulting Numbers: [85] 85,70 unequal: No Solution Exploring Operation: 45-40=5, Resulting Numbers: [5] 5,70 unequal: No Solution Exploring Operation: 40*45=1800, Resulting Numbers: [1800] 1800,70 unequal: No Solution Moving to Node #0,2,2 Current State: 70:[47, 38], Operations: ['56-16=40', '40-2=38'] Exploring Operation: 47*38=1786, Resulting Numbers: [1786] 1786,70 unequal: No Solution Exploring Operation: 47-38=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 47+38=85, Resulting Numbers: [85] 85,70 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 92, 83, 87, 53 ]
43
[ "92-83=9", "87-53=34", "9+34=43" ]
Current State: 43:[92, 83, 87, 53], Operations: [] Exploring Operation: 92-83=9, Resulting Numbers: [87, 53, 9] Generated Node #2: [87, 53, 9] from Operation: 92-83=9 Current State: 43:[87, 53, 9], Operations: ['92-83=9'] Exploring Operation: 87-53=34, Resulting Numbers: [9, 34] Generated Node #3: [9, 34] from Operation: 87-53=34 Current State: 43:[9, 34], Operations: ['92-83=9', '87-53=34'] Exploring Operation: 9+34=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[92, 83, 87, 53], Operations: [] Exploring Operation: 87-83=4, Resulting Numbers: [92, 53, 4] Generated Node #0,0: 43:[92, 53, 4] Operation: 87-83=4 Exploring Operation: 92-53=39, Resulting Numbers: [83, 87, 39] Generated Node #0,1: 43:[83, 87, 39] Operation: 92-53=39 Exploring Operation: 92-83=9, Resulting Numbers: [87, 53, 9] Generated Node #0,2: 43:[87, 53, 9] Operation: 92-83=9 Exploring Operation: 87-53=34, Resulting Numbers: [92, 83, 34] Generated Node #0,3: 43:[92, 83, 34] Operation: 87-53=34 Exploring Operation: 92-87=5, Resulting Numbers: [83, 53, 5] Generated Node #0,4: 43:[83, 53, 5] Operation: 92-87=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[83, 87, 39], Operations: ['92-53=39'] Exploring Operation: 83+39=122, Resulting Numbers: [87, 122] Generated Node #0,1,0: 43:[87, 122] Operation: 83+39=122 Exploring Operation: 87-39=48, Resulting Numbers: [83, 48] Generated Node #0,1,1: 43:[83, 48] Operation: 87-39=48 Exploring Operation: 83-39=44, Resulting Numbers: [87, 44] Generated Node #0,1,2: 43:[87, 44] Operation: 83-39=44 Exploring Operation: 87-83=4, Resulting Numbers: [39, 4] Generated Node #0,1,3: 43:[39, 4] Operation: 87-83=4 Exploring Operation: 87+39=126, Resulting Numbers: [83, 126] Generated Node #0,1,4: 43:[83, 126] Operation: 87+39=126 Moving to Node #0,1,3 Current State: 43:[39, 4], Operations: ['92-53=39', '87-83=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[92, 83, 87, 53], Operations: [] Exploring Operation: 92-53=39, Resulting Numbers: [83, 87, 39] Generated Node #0,1: 43:[83, 87, 39] Operation: 92-53=39 Moving to Node #0,1 Current State: 43:[83, 87, 39], Operations: ['92-53=39'] Exploring Operation: 87-83=4, Resulting Numbers: [39, 4] Generated Node #0,1,3: 43:[39, 4] Operation: 87-83=4 Moving to Node #0,1,3 Current State: 43:[39, 4], Operations: ['92-53=39', '87-83=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 19, 40, 68, 16 ]
63
[ "40-19=21", "68+16=84", "84-21=63" ]
Current State: 63:[19, 40, 68, 16], Operations: [] Exploring Operation: 40-19=21, Resulting Numbers: [68, 16, 21] Generated Node #2: [68, 16, 21] from Operation: 40-19=21 Current State: 63:[68, 16, 21], Operations: ['40-19=21'] Exploring Operation: 68+16=84, Resulting Numbers: [21, 84] Generated Node #3: [21, 84] from Operation: 68+16=84 Current State: 63:[21, 84], Operations: ['40-19=21', '68+16=84'] Exploring Operation: 84-21=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[19, 40, 68, 16], Operations: [] Exploring Operation: 40-19=21, Resulting Numbers: [68, 16, 21] Generated Node #0,0: 63:[68, 16, 21] Operation: 40-19=21 Moving to Node #0,0 Current State: 63:[68, 16, 21], Operations: ['40-19=21'] Exploring Operation: 21-16=5, Resulting Numbers: [68, 5] Generated Node #0,0,0: 63:[68, 5] Operation: 21-16=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[68, 5], Operations: ['40-19=21', '21-16=5'] Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[19, 40, 68, 16], Operations: [] Exploring Operation: 40-19=21, Resulting Numbers: [68, 16, 21] Generated Node #0,0: 63:[68, 16, 21] Operation: 40-19=21 Moving to Node #0,0 Current State: 63:[68, 16, 21], Operations: ['40-19=21'] Exploring Operation: 21-16=5, Resulting Numbers: [68, 5] Generated Node #0,0,0: 63:[68, 5] Operation: 21-16=5 Moving to Node #0,0,0 Current State: 63:[68, 5], Operations: ['40-19=21', '21-16=5'] Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 87, 55, 5, 88 ]
79
[ "55/5=11", "88/11=8", "87-8=79" ]
Current State: 79:[87, 55, 5, 88], Operations: [] Exploring Operation: 55/5=11, Resulting Numbers: [87, 88, 11] Generated Node #2: [87, 88, 11] from Operation: 55/5=11 Current State: 79:[87, 88, 11], Operations: ['55/5=11'] Exploring Operation: 88/11=8, Resulting Numbers: [87, 8] Generated Node #3: [87, 8] from Operation: 88/11=8 Current State: 79:[87, 8], Operations: ['55/5=11', '88/11=8'] Exploring Operation: 87-8=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[87, 55, 5, 88], Operations: [] Exploring Operation: 88-5=83, Resulting Numbers: [87, 55, 83] Generated Node #0,0: 79:[87, 55, 83] Operation: 88-5=83 Exploring Operation: 55+5=60, Resulting Numbers: [87, 88, 60] Generated Node #0,1: 79:[87, 88, 60] Operation: 55+5=60 Exploring Operation: 87-5=82, Resulting Numbers: [55, 88, 82] Generated Node #0,2: 79:[55, 88, 82] Operation: 87-5=82 Moving to Node #0,0 Current State: 79:[87, 55, 83], Operations: ['88-5=83'] Exploring Operation: 87+55=142, Resulting Numbers: [83, 142] Generated Node #0,0,0: 79:[83, 142] Operation: 87+55=142 Exploring Operation: 87-55=32, Resulting Numbers: [83, 32] Generated Node #0,0,1: 79:[83, 32] Operation: 87-55=32 Exploring Operation: 83-55=28, Resulting Numbers: [87, 28] Generated Node #0,0,2: 79:[87, 28] Operation: 83-55=28 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[83, 32], Operations: ['88-5=83', '87-55=32'] Exploring Operation: 83+32=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 83*32=2656, Resulting Numbers: [2656] 2656,79 unequal: No Solution Exploring Operation: 83-32=51, Resulting Numbers: [51] 51,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 79:[87, 28], Operations: ['88-5=83', '83-55=28'] Exploring Operation: 87-28=59, Resulting Numbers: [59] 59,79 unequal: No Solution Exploring Operation: 87*28=2436, Resulting Numbers: [2436] 2436,79 unequal: No Solution Exploring Operation: 87+28=115, Resulting Numbers: [115] 115,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[83, 142], Operations: ['88-5=83', '87+55=142'] Exploring Operation: 83*142=11786, Resulting Numbers: [11786] 11786,79 unequal: No Solution Exploring Operation: 142-83=59, Resulting Numbers: [59] 59,79 unequal: No Solution Exploring Operation: 83+142=225, Resulting Numbers: [225] 225,79 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: 79:[87, 88, 60], Operations: ['55+5=60'] Exploring Operation: 88-60=28, Resulting Numbers: [87, 28] Generated Node #0,1,0: 79:[87, 28] Operation: 88-60=28 Exploring Operation: 87+60=147, Resulting Numbers: [88, 147] Generated Node #0,1,1: 79:[88, 147] Operation: 87+60=147 Exploring Operation: 87-60=27, Resulting Numbers: [88, 27] Generated Node #0,1,2: 79:[88, 27] Operation: 87-60=27 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[87, 28], Operations: ['55+5=60', '88-60=28'] Exploring Operation: 87-28=59, Resulting Numbers: [59] 59,79 unequal: No Solution Exploring Operation: 87+28=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 87*28=2436, Resulting Numbers: [2436] 2436,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[88, 27], Operations: ['55+5=60', '87-60=27'] Exploring Operation: 88*27=2376, Resulting Numbers: [2376] 2376,79 unequal: No Solution Exploring Operation: 88+27=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 88-27=61, Resulting Numbers: [61] 61,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[88, 147], Operations: ['55+5=60', '87+60=147'] Exploring Operation: 88*147=12936, Resulting Numbers: [12936] 12936,79 unequal: No Solution Exploring Operation: 147-88=59, Resulting Numbers: [59] 59,79 unequal: No Solution Exploring Operation: 88+147=235, Resulting Numbers: [235] 235,79 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: 79:[55, 88, 82], Operations: ['87-5=82'] Exploring Operation: 55+88=143, Resulting Numbers: [82, 143] Generated Node #0,2,0: 79:[82, 143] Operation: 55+88=143 Exploring Operation: 88-55=33, Resulting Numbers: [82, 33] Generated Node #0,2,1: 79:[82, 33] Operation: 88-55=33 Exploring Operation: 82-55=27, Resulting Numbers: [88, 27] Generated Node #0,2,2: 79:[88, 27] Operation: 82-55=27 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[82, 33], Operations: ['87-5=82', '88-55=33'] Exploring Operation: 82+33=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 82*33=2706, Resulting Numbers: [2706] 2706,79 unequal: No Solution Exploring Operation: 82-33=49, Resulting Numbers: [49] 49,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[88, 27], Operations: ['87-5=82', '82-55=27'] Exploring Operation: 88-27=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 88*27=2376, Resulting Numbers: [2376] 2376,79 unequal: No Solution Exploring Operation: 88+27=115, Resulting Numbers: [115] 115,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[82, 143], Operations: ['87-5=82', '55+88=143'] Exploring Operation: 82+143=225, Resulting Numbers: [225] 225,79 unequal: No Solution Exploring Operation: 143-82=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 82*143=11726, Resulting Numbers: [11726] 11726,79 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
[ 18, 47, 31, 70 ]
72
[ "47-18=29", "31+70=101", "101-29=72" ]
Current State: 72:[18, 47, 31, 70], Operations: [] Exploring Operation: 47-18=29, Resulting Numbers: [31, 70, 29] Generated Node #2: [31, 70, 29] from Operation: 47-18=29 Current State: 72:[31, 70, 29], Operations: ['47-18=29'] Exploring Operation: 31+70=101, Resulting Numbers: [29, 101] Generated Node #3: [29, 101] from Operation: 31+70=101 Current State: 72:[29, 101], Operations: ['47-18=29', '31+70=101'] Exploring Operation: 101-29=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[18, 47, 31, 70], Operations: [] Exploring Operation: 47-31=16, Resulting Numbers: [18, 70, 16] Generated Node #0,0: 72:[18, 70, 16] Operation: 47-31=16 Exploring Operation: 70-47=23, Resulting Numbers: [18, 31, 23] Generated Node #0,1: 72:[18, 31, 23] Operation: 70-47=23 Exploring Operation: 47+31=78, Resulting Numbers: [18, 70, 78] Generated Node #0,2: 72:[18, 70, 78] Operation: 47+31=78 Moving to Node #0,0 Current State: 72:[18, 70, 16], Operations: ['47-31=16'] Exploring Operation: 18+16=34, Resulting Numbers: [70, 34] Generated Node #0,0,0: 72:[70, 34] Operation: 18+16=34 Exploring Operation: 18-16=2, Resulting Numbers: [70, 2] Generated Node #0,0,1: 72:[70, 2] Operation: 18-16=2 Exploring Operation: 70+16=86, Resulting Numbers: [18, 86] Generated Node #0,0,2: 72:[18, 86] Operation: 70+16=86 Moving to Node #0,1 Current State: 72:[18, 31, 23], Operations: ['70-47=23'] Exploring Operation: 23-18=5, Resulting Numbers: [31, 5] Generated Node #0,1,0: 72:[31, 5] Operation: 23-18=5 Exploring Operation: 31-23=8, Resulting Numbers: [18, 8] Generated Node #0,1,1: 72:[18, 8] Operation: 31-23=8 Exploring Operation: 31-18=13, Resulting Numbers: [23, 13] Generated Node #0,1,2: 72:[23, 13] Operation: 31-18=13 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 72:[18, 8], Operations: ['70-47=23', '31-23=8'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,72 unequal: No Solution Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,72 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 72:[23, 13], Operations: ['70-47=23', '31-18=13'] Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,72 unequal: No Solution Exploring Operation: 23*13=299, Resulting Numbers: [299] 299,72 unequal: No Solution Exploring Operation: 23+13=36, Resulting Numbers: [36] 36,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 72:[31, 5], Operations: ['70-47=23', '23-18=5'] Exploring Operation: 31+5=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 31*5=155, Resulting Numbers: [155] 155,72 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,72 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:[18, 70, 78], Operations: ['47+31=78'] Exploring Operation: 18+70=88, Resulting Numbers: [78, 88] Generated Node #0,2,0: 72:[78, 88] Operation: 18+70=88 Exploring Operation: 78-70=8, Resulting Numbers: [18, 8] Generated Node #0,2,1: 72:[18, 8] Operation: 78-70=8 Exploring Operation: 78-18=60, Resulting Numbers: [70, 60] Generated Node #0,2,2: 72:[70, 60] Operation: 78-18=60 Moving to Node #0,2,1 Current State: 72:[18, 8], Operations: ['47+31=78', '78-70=8'] Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,72 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,72 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[70, 2], Operations: ['47-31=16', '18-16=2'] Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,72 unequal: No Solution Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[18, 47, 31, 70], Operations: [] Exploring Operation: 47-31=16, Resulting Numbers: [18, 70, 16] Generated Node #0,0: 72:[18, 70, 16] Operation: 47-31=16 Moving to Node #0,0 Current State: 72:[18, 70, 16], Operations: ['47-31=16'] Exploring Operation: 18-16=2, Resulting Numbers: [70, 2] Generated Node #0,0,1: 72:[70, 2] Operation: 18-16=2 Moving to Node #0,0,1 Current State: 72:[70, 2], Operations: ['47-31=16', '18-16=2'] Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.973958
hs_3
mult_heuristic
[ 97, 99, 69, 31 ]
97
[ "99-69=30", "31-30=1", "97*1=97" ]
Current State: 97:[97, 99, 69, 31], Operations: [] Exploring Operation: 99-69=30, Resulting Numbers: [97, 31, 30] Generated Node #2: [97, 31, 30] from Operation: 99-69=30 Current State: 97:[97, 31, 30], Operations: ['99-69=30'] Exploring Operation: 31-30=1, Resulting Numbers: [97, 1] Generated Node #3: [97, 1] from Operation: 31-30=1 Current State: 97:[97, 1], Operations: ['99-69=30', '31-30=1'] Exploring Operation: 97*1=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[97, 99, 69, 31], Operations: [] Exploring Operation: 69+31=100, Resulting Numbers: [97, 99, 100] Generated Node #0,0: 97:[97, 99, 100] Operation: 69+31=100 Moving to Node #0,0 Current State: 97:[97, 99, 100], Operations: ['69+31=100'] Exploring Operation: 100-97=3, Resulting Numbers: [99, 3] Generated Node #0,0,0: 97:[99, 3] Operation: 100-97=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[99, 3], Operations: ['69+31=100', '100-97=3'] Exploring Operation: 99-3=96, Resulting Numbers: [96] 96,97 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
[ 16, 26, 57, 20 ]
39
[ "26-20=6", "16*6=96", "96-57=39" ]
Current State: 39:[16, 26, 57, 20], Operations: [] Exploring Operation: 26-20=6, Resulting Numbers: [16, 57, 6] Generated Node #2: [16, 57, 6] from Operation: 26-20=6 Current State: 39:[16, 57, 6], Operations: ['26-20=6'] Exploring Operation: 16*6=96, Resulting Numbers: [57, 96] Generated Node #3: [57, 96] from Operation: 16*6=96 Current State: 39:[57, 96], Operations: ['26-20=6', '16*6=96'] Exploring Operation: 96-57=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[16, 26, 57, 20], Operations: [] Exploring Operation: 57-20=37, Resulting Numbers: [16, 26, 37] Generated Node #0,0: 39:[16, 26, 37] Operation: 57-20=37 Exploring Operation: 57-26=31, Resulting Numbers: [16, 20, 31] Generated Node #0,1: 39:[16, 20, 31] Operation: 57-26=31 Exploring Operation: 26-20=6, Resulting Numbers: [16, 57, 6] Generated Node #0,2: 39:[16, 57, 6] Operation: 26-20=6 Exploring Operation: 57-16=41, Resulting Numbers: [26, 20, 41] Generated Node #0,3: 39:[26, 20, 41] Operation: 57-16=41 Moving to Node #0,0 Current State: 39:[16, 26, 37], Operations: ['57-20=37'] Exploring Operation: 16+26=42, Resulting Numbers: [37, 42] Generated Node #0,0,0: 39:[37, 42] Operation: 16+26=42 Exploring Operation: 37-26=11, Resulting Numbers: [16, 11] Generated Node #0,0,1: 39:[16, 11] Operation: 37-26=11 Exploring Operation: 37-16=21, Resulting Numbers: [26, 21] Generated Node #0,0,2: 39:[26, 21] Operation: 37-16=21 Exploring Operation: 26-16=10, Resulting Numbers: [37, 10] Generated Node #0,0,3: 39:[37, 10] Operation: 26-16=10 Moving to Node #0,1 Current State: 39:[16, 20, 31], Operations: ['57-26=31'] Exploring Operation: 31-16=15, Resulting Numbers: [20, 15] Generated Node #0,1,0: 39:[20, 15] Operation: 31-16=15 Exploring Operation: 20-16=4, Resulting Numbers: [31, 4] Generated Node #0,1,1: 39:[31, 4] Operation: 20-16=4 Exploring Operation: 16+20=36, Resulting Numbers: [31, 36] Generated Node #0,1,2: 39:[31, 36] Operation: 16+20=36 Exploring Operation: 31-20=11, Resulting Numbers: [16, 11] Generated Node #0,1,3: 39:[16, 11] Operation: 31-20=11 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 39:[16, 11], Operations: ['57-26=31', '31-20=11'] Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 16+11=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 16*11=176, Resulting Numbers: [176] 176,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[20, 15], Operations: ['57-26=31', '31-16=15'] Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 20+15=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 20*15=300, Resulting Numbers: [300] 300,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[31, 4], Operations: ['57-26=31', '20-16=4'] Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 39:[31, 36], Operations: ['57-26=31', '16+20=36'] Exploring Operation: 31*36=1116, Resulting Numbers: [1116] 1116,39 unequal: No Solution Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 31+36=67, Resulting Numbers: [67] 67,39 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: 39:[26, 20, 41], Operations: ['57-16=41'] Exploring Operation: 26+20=46, Resulting Numbers: [41, 46] Generated Node #0,3,0: 39:[41, 46] Operation: 26+20=46 Exploring Operation: 41-20=21, Resulting Numbers: [26, 21] Generated Node #0,3,1: 39:[26, 21] Operation: 41-20=21 Exploring Operation: 26-20=6, Resulting Numbers: [41, 6] Generated Node #0,3,2: 39:[41, 6] Operation: 26-20=6 Exploring Operation: 41-26=15, Resulting Numbers: [20, 15] Generated Node #0,3,3: 39:[20, 15] Operation: 41-26=15 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 39:[41, 6], Operations: ['57-16=41', '26-20=6'] Exploring Operation: 41+6=47, Resulting Numbers: [47] 47,39 unequal: No Solution Exploring Operation: 41*6=246, Resulting Numbers: [246] 246,39 unequal: No Solution Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 39:[41, 46], Operations: ['57-16=41', '26+20=46'] Exploring Operation: 41+46=87, Resulting Numbers: [87] 87,39 unequal: No Solution Exploring Operation: 46-41=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 41*46=1886, Resulting Numbers: [1886] 1886,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 39:[20, 15], Operations: ['57-16=41', '41-26=15'] Exploring Operation: 20*15=300, Resulting Numbers: [300] 300,39 unequal: No Solution Exploring Operation: 20+15=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 39:[26, 21], Operations: ['57-16=41', '41-20=21'] Exploring Operation: 26+21=47, Resulting Numbers: [47] 47,39 unequal: No Solution Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 26*21=546, Resulting Numbers: [546] 546,39 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: 39:[16, 57, 6], Operations: ['26-20=6'] Exploring Operation: 16+6=22, Resulting Numbers: [57, 22] Generated Node #0,2,0: 39:[57, 22] Operation: 16+6=22 Exploring Operation: 16-6=10, Resulting Numbers: [57, 10] Generated Node #0,2,1: 39:[57, 10] Operation: 16-6=10 Exploring Operation: 57-16=41, Resulting Numbers: [6, 41] Generated Node #0,2,2: 39:[6, 41] Operation: 57-16=41 Exploring Operation: 57-6=51, Resulting Numbers: [16, 51] Generated Node #0,2,3: 39:[16, 51] Operation: 57-6=51 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 39:[6, 41], Operations: ['26-20=6', '57-16=41'] Exploring Operation: 6+41=47, Resulting Numbers: [47] 47,39 unequal: No Solution Exploring Operation: 6*41=246, Resulting Numbers: [246] 246,39 unequal: No Solution Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 39:[16, 51], Operations: ['26-20=6', '57-6=51'] Exploring Operation: 16+51=67, Resulting Numbers: [67] 67,39 unequal: No Solution Exploring Operation: 16*51=816, Resulting Numbers: [816] 816,39 unequal: No Solution Exploring Operation: 51-16=35, Resulting Numbers: [35] 35,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 39:[57, 10], Operations: ['26-20=6', '16-6=10'] Exploring Operation: 57+10=67, Resulting Numbers: [67] 67,39 unequal: No Solution Exploring Operation: 57*10=570, Resulting Numbers: [570] 570,39 unequal: No Solution Exploring Operation: 57-10=47, Resulting Numbers: [47] 47,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[57, 22], Operations: ['26-20=6', '16+6=22'] Exploring Operation: 57+22=79, Resulting Numbers: [79] 79,39 unequal: No Solution Exploring Operation: 57-22=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 57*22=1254, Resulting Numbers: [1254] 1254,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 39:[37, 42], Operations: ['57-20=37', '16+26=42'] Exploring Operation: 37+42=79, Resulting Numbers: [79] 79,39 unequal: No Solution Exploring Operation: 37*42=1554, Resulting Numbers: [1554] 1554,39 unequal: No Solution Exploring Operation: 42-37=5, Resulting Numbers: [5] 5,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[37, 10], Operations: ['57-20=37', '26-16=10'] Exploring Operation: 37*10=370, Resulting Numbers: [370] 370,39 unequal: No Solution Exploring Operation: 37-10=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 37+10=47, Resulting Numbers: [47] 47,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[16, 11], Operations: ['57-20=37', '37-26=11'] Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,39 unequal: No Solution Exploring Operation: 16*11=176, Resulting Numbers: [176] 176,39 unequal: No Solution Exploring Operation: 16+11=27, Resulting Numbers: [27] 27,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[26, 21], Operations: ['57-20=37', '37-16=21'] Exploring Operation: 26+21=47, Resulting Numbers: [47] 47,39 unequal: No Solution Exploring Operation: 26*21=546, Resulting Numbers: [546] 546,39 unequal: No Solution Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,39 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 65, 66, 72, 17 ]
56
[ "66-65=1", "72-17=55", "1+55=56" ]
Current State: 56:[65, 66, 72, 17], Operations: [] Exploring Operation: 66-65=1, Resulting Numbers: [72, 17, 1] Generated Node #2: [72, 17, 1] from Operation: 66-65=1 Current State: 56:[72, 17, 1], Operations: ['66-65=1'] Exploring Operation: 72-17=55, Resulting Numbers: [1, 55] Generated Node #3: [1, 55] from Operation: 72-17=55 Current State: 56:[1, 55], Operations: ['66-65=1', '72-17=55'] Exploring Operation: 1+55=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[65, 66, 72, 17], Operations: [] Exploring Operation: 66-65=1, Resulting Numbers: [72, 17, 1] Generated Node #0,0: 56:[72, 17, 1] Operation: 66-65=1 Exploring Operation: 72-17=55, Resulting Numbers: [65, 66, 55] Generated Node #0,1: 56:[65, 66, 55] Operation: 72-17=55 Exploring Operation: 66-17=49, Resulting Numbers: [65, 72, 49] Generated Node #0,2: 56:[65, 72, 49] Operation: 66-17=49 Exploring Operation: 72-66=6, Resulting Numbers: [65, 17, 6] Generated Node #0,3: 56:[65, 17, 6] Operation: 72-66=6 Exploring Operation: 72-65=7, Resulting Numbers: [66, 17, 7] Generated Node #0,4: 56:[66, 17, 7] Operation: 72-65=7 Moving to Node #0,3 Current State: 56:[65, 17, 6], Operations: ['72-66=6'] Exploring Operation: 65-6=59, Resulting Numbers: [17, 59] Generated Node #0,3,0: 56:[17, 59] Operation: 65-6=59 Exploring Operation: 65-17=48, Resulting Numbers: [6, 48] Generated Node #0,3,1: 56:[6, 48] Operation: 65-17=48 Exploring Operation: 17-6=11, Resulting Numbers: [65, 11] Generated Node #0,3,2: 56:[65, 11] Operation: 17-6=11 Exploring Operation: 65+6=71, Resulting Numbers: [17, 71] Generated Node #0,3,3: 56:[17, 71] Operation: 65+6=71 Exploring Operation: 17+6=23, Resulting Numbers: [65, 23] Generated Node #0,3,4: 56:[65, 23] Operation: 17+6=23 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 56:[17, 59], Operations: ['72-66=6', '65-6=59'] Exploring Operation: 17+59=76, Resulting Numbers: [76] 76,56 unequal: No Solution Exploring Operation: 59-17=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 17*59=1003, Resulting Numbers: [1003] 1003,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 56:[6, 48], Operations: ['72-66=6', '65-17=48'] Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,56 unequal: No Solution Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,56 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 6*48=288, Resulting Numbers: [288] 288,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 56:[65, 11], Operations: ['72-66=6', '17-6=11'] Exploring Operation: 65+11=76, Resulting Numbers: [76] 76,56 unequal: No Solution Exploring Operation: 65*11=715, Resulting Numbers: [715] 715,56 unequal: No Solution Exploring Operation: 65-11=54, Resulting Numbers: [54] 54,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 56:[65, 23], Operations: ['72-66=6', '17+6=23'] Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 65+23=88, Resulting Numbers: [88] 88,56 unequal: No Solution Exploring Operation: 65*23=1495, Resulting Numbers: [1495] 1495,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 56:[17, 71], Operations: ['72-66=6', '65+6=71'] Exploring Operation: 17+71=88, Resulting Numbers: [88] 88,56 unequal: No Solution Exploring Operation: 71-17=54, Resulting Numbers: [54] 54,56 unequal: No Solution Exploring Operation: 17*71=1207, Resulting Numbers: [1207] 1207,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 56:[66, 17, 7], Operations: ['72-65=7'] Exploring Operation: 66-17=49, Resulting Numbers: [7, 49] Generated Node #0,4,0: 56:[7, 49] Operation: 66-17=49 Exploring Operation: 17-7=10, Resulting Numbers: [66, 10] Generated Node #0,4,1: 56:[66, 10] Operation: 17-7=10 Exploring Operation: 17+7=24, Resulting Numbers: [66, 24] Generated Node #0,4,2: 56:[66, 24] Operation: 17+7=24 Exploring Operation: 66+7=73, Resulting Numbers: [17, 73] Generated Node #0,4,3: 56:[17, 73] Operation: 66+7=73 Exploring Operation: 66-7=59, Resulting Numbers: [17, 59] Generated Node #0,4,4: 56:[17, 59] Operation: 66-7=59 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 56:[17, 59], Operations: ['72-65=7', '66-7=59'] Exploring Operation: 17*59=1003, Resulting Numbers: [1003] 1003,56 unequal: No Solution Exploring Operation: 17+59=76, Resulting Numbers: [76] 76,56 unequal: No Solution Exploring Operation: 59-17=42, Resulting Numbers: [42] 42,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 56:[7, 49], Operations: ['72-65=7', '66-17=49'] Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 7*49=343, Resulting Numbers: [343] 343,56 unequal: No Solution Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[65, 66, 72, 17], Operations: [] Exploring Operation: 72-65=7, Resulting Numbers: [66, 17, 7] Generated Node #0,4: 56:[66, 17, 7] Operation: 72-65=7 Moving to Node #0,4 Current State: 56:[66, 17, 7], Operations: ['72-65=7'] Exploring Operation: 66-17=49, Resulting Numbers: [7, 49] Generated Node #0,4,0: 56:[7, 49] Operation: 66-17=49 Moving to Node #0,4,0 Current State: 56:[7, 49], Operations: ['72-65=7', '66-17=49'] Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_5
mult_heuristic
[ 99, 42, 57, 34 ]
35
[ "99-42=57", "57/57=1", "34+1=35" ]
Current State: 35:[99, 42, 57, 34], Operations: [] Exploring Operation: 99-42=57, Resulting Numbers: [57, 34, 57] Generated Node #2: [57, 34, 57] from Operation: 99-42=57 Current State: 35:[57, 34, 57], Operations: ['99-42=57'] Exploring Operation: 57/57=1, Resulting Numbers: [34, 1] Generated Node #3: [34, 1] from Operation: 57/57=1 Current State: 35:[34, 1], Operations: ['99-42=57', '57/57=1'] Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[99, 42, 57, 34], Operations: [] Exploring Operation: 99-57=42, Resulting Numbers: [42, 34, 42] Generated Node #0,0: 35:[42, 34, 42] Operation: 99-57=42 Moving to Node #0,0 Current State: 35:[42, 34, 42], Operations: ['99-57=42'] Exploring Operation: 42/42=1, Resulting Numbers: [34, 1] Generated Node #0,0,0: 35:[34, 1] Operation: 42/42=1 Moving to Node #0,0,0 Current State: 35:[34, 1], Operations: ['99-57=42', '42/42=1'] Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[99, 42, 57, 34], Operations: [] Exploring Operation: 99-57=42, Resulting Numbers: [42, 34, 42] Generated Node #0,0: 35:[42, 34, 42] Operation: 99-57=42 Moving to Node #0,0 Current State: 35:[42, 34, 42], Operations: ['99-57=42'] Exploring Operation: 42/42=1, Resulting Numbers: [34, 1] Generated Node #0,0,0: 35:[34, 1] Operation: 42/42=1 Moving to Node #0,0,0 Current State: 35:[34, 1], Operations: ['99-57=42', '42/42=1'] Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 88, 56, 64, 15 ]
65
[ "88+56=144", "64+15=79", "144-79=65" ]
Current State: 65:[88, 56, 64, 15], Operations: [] Exploring Operation: 88+56=144, Resulting Numbers: [64, 15, 144] Generated Node #2: [64, 15, 144] from Operation: 88+56=144 Current State: 65:[64, 15, 144], Operations: ['88+56=144'] Exploring Operation: 64+15=79, Resulting Numbers: [144, 79] Generated Node #3: [144, 79] from Operation: 64+15=79 Current State: 65:[144, 79], Operations: ['88+56=144', '64+15=79'] Exploring Operation: 144-79=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[88, 56, 64, 15], Operations: [] Exploring Operation: 88-64=24, Resulting Numbers: [56, 15, 24] Generated Node #0,0: 65:[56, 15, 24] Operation: 88-64=24 Exploring Operation: 64-56=8, Resulting Numbers: [88, 15, 8] Generated Node #0,1: 65:[88, 15, 8] Operation: 64-56=8 Exploring Operation: 88-15=73, Resulting Numbers: [56, 64, 73] Generated Node #0,2: 65:[56, 64, 73] Operation: 88-15=73 Exploring Operation: 88-56=32, Resulting Numbers: [64, 15, 32] Generated Node #0,3: 65:[64, 15, 32] Operation: 88-56=32 Moving to Node #0,2 Current State: 65:[56, 64, 73], Operations: ['88-15=73'] Exploring Operation: 56+64=120, Resulting Numbers: [73, 120] Generated Node #0,2,0: 65:[73, 120] Operation: 56+64=120 Exploring Operation: 73-56=17, Resulting Numbers: [64, 17] Generated Node #0,2,1: 65:[64, 17] Operation: 73-56=17 Exploring Operation: 73-64=9, Resulting Numbers: [56, 9] Generated Node #0,2,2: 65:[56, 9] Operation: 73-64=9 Exploring Operation: 64-56=8, Resulting Numbers: [73, 8] Generated Node #0,2,3: 65:[73, 8] Operation: 64-56=8 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 65:[64, 17], Operations: ['88-15=73', '73-56=17'] Exploring Operation: 64+17=81, Resulting Numbers: [81] 81,65 unequal: No Solution Exploring Operation: 64*17=1088, Resulting Numbers: [1088] 1088,65 unequal: No Solution Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 65:[73, 8], Operations: ['88-15=73', '64-56=8'] Exploring Operation: 73*8=584, Resulting Numbers: [584] 584,65 unequal: No Solution Exploring Operation: 73+8=81, Resulting Numbers: [81] 81,65 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[88, 56, 64, 15], Operations: [] Exploring Operation: 88-15=73, Resulting Numbers: [56, 64, 73] Generated Node #0,2: 65:[56, 64, 73] Operation: 88-15=73 Moving to Node #0,2 Current State: 65:[56, 64, 73], Operations: ['88-15=73'] Exploring Operation: 64-56=8, Resulting Numbers: [73, 8] Generated Node #0,2,3: 65:[73, 8] Operation: 64-56=8 Moving to Node #0,2,3 Current State: 65:[73, 8], Operations: ['88-15=73', '64-56=8'] Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 40, 91, 94, 57 ]
100
[ "91-40=51", "94+57=151", "151-51=100" ]
Current State: 100:[40, 91, 94, 57], Operations: [] Exploring Operation: 91-40=51, Resulting Numbers: [94, 57, 51] Generated Node #2: [94, 57, 51] from Operation: 91-40=51 Current State: 100:[94, 57, 51], Operations: ['91-40=51'] Exploring Operation: 94+57=151, Resulting Numbers: [51, 151] Generated Node #3: [51, 151] from Operation: 94+57=151 Current State: 100:[51, 151], Operations: ['91-40=51', '94+57=151'] Exploring Operation: 151-51=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[40, 91, 94, 57], Operations: [] Exploring Operation: 94-40=54, Resulting Numbers: [91, 57, 54] Generated Node #0,0: 100:[91, 57, 54] Operation: 94-40=54 Exploring Operation: 91-40=51, Resulting Numbers: [94, 57, 51] Generated Node #0,1: 100:[94, 57, 51] Operation: 91-40=51 Exploring Operation: 57-40=17, Resulting Numbers: [91, 94, 17] Generated Node #0,2: 100:[91, 94, 17] Operation: 57-40=17 Exploring Operation: 40+57=97, Resulting Numbers: [91, 94, 97] Generated Node #0,3: 100:[91, 94, 97] Operation: 40+57=97 Exploring Operation: 94-91=3, Resulting Numbers: [40, 57, 3] Generated Node #0,4: 100:[40, 57, 3] Operation: 94-91=3 Moving to Node #0,1 Current State: 100:[94, 57, 51], Operations: ['91-40=51'] Exploring Operation: 94-57=37, Resulting Numbers: [51, 37] Generated Node #0,1,0: 100:[51, 37] Operation: 94-57=37 Exploring Operation: 57-51=6, Resulting Numbers: [94, 6] Generated Node #0,1,1: 100:[94, 6] Operation: 57-51=6 Exploring Operation: 94+57=151, Resulting Numbers: [51, 151] Generated Node #0,1,2: 100:[51, 151] Operation: 94+57=151 Exploring Operation: 57+51=108, Resulting Numbers: [94, 108] Generated Node #0,1,3: 100:[94, 108] Operation: 57+51=108 Exploring Operation: 94-51=43, Resulting Numbers: [57, 43] Generated Node #0,1,4: 100:[57, 43] Operation: 94-51=43 Moving to Node #0,3 Current State: 100:[91, 94, 97], Operations: ['40+57=97'] Exploring Operation: 91+97=188, Resulting Numbers: [94, 188] Generated Node #0,3,0: 100:[94, 188] Operation: 91+97=188 Exploring Operation: 97-94=3, Resulting Numbers: [91, 3] Generated Node #0,3,1: 100:[91, 3] Operation: 97-94=3 Exploring Operation: 91+94=185, Resulting Numbers: [97, 185] Generated Node #0,3,2: 100:[97, 185] Operation: 91+94=185 Exploring Operation: 97-91=6, Resulting Numbers: [94, 6] Generated Node #0,3,3: 100:[94, 6] Operation: 97-91=6 Exploring Operation: 94-91=3, Resulting Numbers: [97, 3] Generated Node #0,3,4: 100:[97, 3] Operation: 94-91=3 Moving to Node #0,2 Current State: 100:[91, 94, 17], Operations: ['57-40=17'] Exploring Operation: 91+17=108, Resulting Numbers: [94, 108] Generated Node #0,2,0: 100:[94, 108] Operation: 91+17=108 Exploring Operation: 94-91=3, Resulting Numbers: [17, 3] Generated Node #0,2,1: 100:[17, 3] Operation: 94-91=3 Exploring Operation: 91-17=74, Resulting Numbers: [94, 74] Generated Node #0,2,2: 100:[94, 74] Operation: 91-17=74 Exploring Operation: 94-17=77, Resulting Numbers: [91, 77] Generated Node #0,2,3: 100:[91, 77] Operation: 94-17=77 Exploring Operation: 94+17=111, Resulting Numbers: [91, 111] Generated Node #0,2,4: 100:[91, 111] Operation: 94+17=111 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 100:[17, 3], Operations: ['57-40=17', '94-91=3'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,100 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,100 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 #0,2,0 Current State: 100:[94, 108], Operations: ['57-40=17', '91+17=108'] Exploring Operation: 94+108=202, Resulting Numbers: [202] 202,100 unequal: No Solution Exploring Operation: 108-94=14, Resulting Numbers: [14] 14,100 unequal: No Solution Exploring Operation: 94*108=10152, Resulting Numbers: [10152] 10152,100 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 #0,2,4 Current State: 100:[91, 111], Operations: ['57-40=17', '94+17=111'] Exploring Operation: 91*111=10101, Resulting Numbers: [10101] 10101,100 unequal: No Solution Exploring Operation: 111-91=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 91+111=202, Resulting Numbers: [202] 202,100 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 #0,2,2 Current State: 100:[94, 74], Operations: ['57-40=17', '91-17=74'] Exploring Operation: 94*74=6956, Resulting Numbers: [6956] 6956,100 unequal: No Solution Exploring Operation: 94+74=168, Resulting Numbers: [168] 168,100 unequal: No Solution Exploring Operation: 94-74=20, Resulting Numbers: [20] 20,100 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 #0,2,3 Current State: 100:[91, 77], Operations: ['57-40=17', '94-17=77'] Exploring Operation: 91*77=7007, Resulting Numbers: [7007] 7007,100 unequal: No Solution Exploring Operation: 91+77=168, Resulting Numbers: [168] 168,100 unequal: No Solution Exploring Operation: 91-77=14, Resulting Numbers: [14] 14,100 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: 100:[40, 57, 3], Operations: ['94-91=3'] Exploring Operation: 57/3=19, Resulting Numbers: [40, 19] Generated Node #0,4,0: 100:[40, 19] Operation: 57/3=19 Exploring Operation: 57-3=54, Resulting Numbers: [40, 54] Generated Node #0,4,1: 100:[40, 54] Operation: 57-3=54 Exploring Operation: 40+57=97, Resulting Numbers: [3, 97] Generated Node #0,4,2: 100:[3, 97] Operation: 40+57=97 Exploring Operation: 40+3=43, Resulting Numbers: [57, 43] Generated Node #0,4,3: 100:[57, 43] Operation: 40+3=43 Exploring Operation: 57-40=17, Resulting Numbers: [3, 17] Generated Node #0,4,4: 100:[3, 17] Operation: 57-40=17 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 100:[3, 97], Operations: ['94-91=3', '40+57=97'] Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,100 unequal: No Solution Exploring Operation: 3*97=291, Resulting Numbers: [291] 291,100 unequal: No Solution Exploring Operation: 3+97=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[40, 91, 94, 57], Operations: [] Exploring Operation: 94-91=3, Resulting Numbers: [40, 57, 3] Generated Node #0,4: 100:[40, 57, 3] Operation: 94-91=3 Moving to Node #0,4 Current State: 100:[40, 57, 3], Operations: ['94-91=3'] Exploring Operation: 40+57=97, Resulting Numbers: [3, 97] Generated Node #0,4,2: 100:[3, 97] Operation: 40+57=97 Moving to Node #0,4,2 Current State: 100:[3, 97], Operations: ['94-91=3', '40+57=97'] Exploring Operation: 3+97=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
sum_heuristic
[ 55, 3, 40, 60 ]
78
[ "55+3=58", "60-40=20", "58+20=78" ]
Current State: 78:[55, 3, 40, 60], Operations: [] Exploring Operation: 55+3=58, Resulting Numbers: [40, 60, 58] Generated Node #2: [40, 60, 58] from Operation: 55+3=58 Current State: 78:[40, 60, 58], Operations: ['55+3=58'] Exploring Operation: 60-40=20, Resulting Numbers: [58, 20] Generated Node #3: [58, 20] from Operation: 60-40=20 Current State: 78:[58, 20], Operations: ['55+3=58', '60-40=20'] Exploring Operation: 58+20=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[55, 3, 40, 60], Operations: [] Exploring Operation: 60/3=20, Resulting Numbers: [55, 40, 20] Generated Node #0,0: 78:[55, 40, 20] Operation: 60/3=20 Exploring Operation: 60-55=5, Resulting Numbers: [3, 40, 5] Generated Node #0,1: 78:[3, 40, 5] Operation: 60-55=5 Exploring Operation: 55-40=15, Resulting Numbers: [3, 60, 15] Generated Node #0,2: 78:[3, 60, 15] Operation: 55-40=15 Exploring Operation: 60-40=20, Resulting Numbers: [55, 3, 20] Generated Node #0,3: 78:[55, 3, 20] Operation: 60-40=20 Exploring Operation: 55-3=52, Resulting Numbers: [40, 60, 52] Generated Node #0,4: 78:[40, 60, 52] Operation: 55-3=52 Moving to Node #0,1 Current State: 78:[3, 40, 5], Operations: ['60-55=5'] Exploring Operation: 40/5=8, Resulting Numbers: [3, 8] Generated Node #0,1,0: 78:[3, 8] Operation: 40/5=8 Exploring Operation: 3*5=15, Resulting Numbers: [40, 15] Generated Node #0,1,1: 78:[40, 15] Operation: 3*5=15 Exploring Operation: 5-3=2, Resulting Numbers: [40, 2] Generated Node #0,1,2: 78:[40, 2] Operation: 5-3=2 Exploring Operation: 40-3=37, Resulting Numbers: [5, 37] Generated Node #0,1,3: 78:[5, 37] Operation: 40-3=37 Exploring Operation: 3+5=8, Resulting Numbers: [40, 8] Generated Node #0,1,4: 78:[40, 8] Operation: 3+5=8 Moving to Node #0,2 Current State: 78:[3, 60, 15], Operations: ['55-40=15'] Exploring Operation: 60+15=75, Resulting Numbers: [3, 75] Generated Node #0,2,0: 78:[3, 75] Operation: 60+15=75 Exploring Operation: 3+60=63, Resulting Numbers: [15, 63] Generated Node #0,2,1: 78:[15, 63] Operation: 3+60=63 Exploring Operation: 60/3=20, Resulting Numbers: [15, 20] Generated Node #0,2,2: 78:[15, 20] Operation: 60/3=20 Exploring Operation: 60-15=45, Resulting Numbers: [3, 45] Generated Node #0,2,3: 78:[3, 45] Operation: 60-15=45 Exploring Operation: 60/15=4, Resulting Numbers: [3, 4] Generated Node #0,2,4: 78:[3, 4] Operation: 60/15=4 Moving to Node #0,3 Current State: 78:[55, 3, 20], Operations: ['60-40=20'] Exploring Operation: 3+20=23, Resulting Numbers: [55, 23] Generated Node #0,3,0: 78:[55, 23] Operation: 3+20=23 Exploring Operation: 20-3=17, Resulting Numbers: [55, 17] Generated Node #0,3,1: 78:[55, 17] Operation: 20-3=17 Exploring Operation: 55-3=52, Resulting Numbers: [20, 52] Generated Node #0,3,2: 78:[20, 52] Operation: 55-3=52 Exploring Operation: 55+20=75, Resulting Numbers: [3, 75] Generated Node #0,3,3: 78:[3, 75] Operation: 55+20=75 Exploring Operation: 55-20=35, Resulting Numbers: [3, 35] Generated Node #0,3,4: 78:[3, 35] Operation: 55-20=35 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 78:[3, 75], Operations: ['60-40=20', '55+20=75'] Exploring Operation: 75-3=72, Resulting Numbers: [72] 72,78 unequal: No Solution Exploring Operation: 3*75=225, Resulting Numbers: [225] 225,78 unequal: No Solution Exploring Operation: 75/3=25, Resulting Numbers: [25] 25,78 unequal: No Solution Exploring Operation: 3+75=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[55, 3, 40, 60], Operations: [] Exploring Operation: 60-40=20, Resulting Numbers: [55, 3, 20] Generated Node #0,3: 78:[55, 3, 20] Operation: 60-40=20 Moving to Node #0,3 Current State: 78:[55, 3, 20], Operations: ['60-40=20'] Exploring Operation: 55+20=75, Resulting Numbers: [3, 75] Generated Node #0,3,3: 78:[3, 75] Operation: 55+20=75 Moving to Node #0,3,3 Current State: 78:[3, 75], Operations: ['60-40=20', '55+20=75'] Exploring Operation: 3+75=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_5
mult_heuristic
[ 4, 6, 12, 17 ]
90
[ "17-4=13", "6*13=78", "12+78=90" ]
Current State: 90:[4, 6, 12, 17], Operations: [] Exploring Operation: 17-4=13, Resulting Numbers: [6, 12, 13] Generated Node #2: [6, 12, 13] from Operation: 17-4=13 Current State: 90:[6, 12, 13], Operations: ['17-4=13'] Exploring Operation: 6*13=78, Resulting Numbers: [12, 78] Generated Node #3: [12, 78] from Operation: 6*13=78 Current State: 90:[12, 78], Operations: ['17-4=13', '6*13=78'] Exploring Operation: 12+78=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[4, 6, 12, 17], Operations: [] Exploring Operation: 12/4=3, Resulting Numbers: [6, 17, 3] Generated Node #0,0: 90:[6, 17, 3] Operation: 12/4=3 Exploring Operation: 12-4=8, Resulting Numbers: [6, 17, 8] Generated Node #0,1: 90:[6, 17, 8] Operation: 12-4=8 Exploring Operation: 4+12=16, Resulting Numbers: [6, 17, 16] Generated Node #0,2: 90:[6, 17, 16] Operation: 4+12=16 Exploring Operation: 17-12=5, Resulting Numbers: [4, 6, 5] Generated Node #0,3: 90:[4, 6, 5] Operation: 17-12=5 Exploring Operation: 6+12=18, Resulting Numbers: [4, 17, 18] Generated Node #0,4: 90:[4, 17, 18] Operation: 6+12=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[6, 17, 3], Operations: ['12/4=3'] Exploring Operation: 6*3=18, Resulting Numbers: [17, 18] Generated Node #0,0,0: 90:[17, 18] Operation: 6*3=18 Exploring Operation: 6+3=9, Resulting Numbers: [17, 9] Generated Node #0,0,1: 90:[17, 9] Operation: 6+3=9 Exploring Operation: 17-6=11, Resulting Numbers: [3, 11] Generated Node #0,0,2: 90:[3, 11] Operation: 17-6=11 Exploring Operation: 6/3=2, Resulting Numbers: [17, 2] Generated Node #0,0,3: 90:[17, 2] Operation: 6/3=2 Exploring Operation: 6-3=3, Resulting Numbers: [17, 3] Generated Node #0,0,4: 90:[17, 3] Operation: 6-3=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[17, 18], Operations: ['12/4=3', '6*3=18'] Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 17*18=306, Resulting Numbers: [306] 306,90 unequal: No Solution Exploring Operation: 17+18=35, Resulting Numbers: [35] 35,90 unequal: No Solution No 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: 90:[17, 9], Operations: ['12/4=3', '6+3=9'] Exploring Operation: 17*9=153, Resulting Numbers: [153] 153,90 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 17+9=26, Resulting Numbers: [26] 26,90 unequal: No Solution No 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: 90:[3, 11], Operations: ['12/4=3', '17-6=11'] Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,90 unequal: No Solution No 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: 90:[17, 2], Operations: ['12/4=3', '6/3=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,90 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 90:[17, 3], Operations: ['12/4=3', '6-3=3'] Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,90 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[4, 6, 5], Operations: ['17-12=5'] Exploring Operation: 4+5=9, Resulting Numbers: [6, 9] Generated Node #0,3,0: 90:[6, 9] Operation: 4+5=9 Exploring Operation: 5-4=1, Resulting Numbers: [6, 1] Generated Node #0,3,1: 90:[6, 1] Operation: 5-4=1 Exploring Operation: 6-4=2, Resulting Numbers: [5, 2] Generated Node #0,3,2: 90:[5, 2] Operation: 6-4=2 Exploring Operation: 4+6=10, Resulting Numbers: [5, 10] Generated Node #0,3,3: 90:[5, 10] Operation: 4+6=10 Exploring Operation: 6*5=30, Resulting Numbers: [4, 30] Generated Node #0,3,4: 90:[4, 30] Operation: 6*5=30 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 90:[6, 9], Operations: ['17-12=5', '4+5=9'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,90 unequal: No Solution Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,90 unequal: No Solution No 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: 90:[5, 2], Operations: ['17-12=5', '6-4=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,90 unequal: No Solution No 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: 90:[5, 10], Operations: ['17-12=5', '4+6=10'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,90 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,90 unequal: No Solution No 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: 90:[6, 1], Operations: ['17-12=5', '5-4=1'] Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 90:[4, 30], Operations: ['17-12=5', '6*5=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,90 unequal: No Solution Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,90 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[6, 17, 8], Operations: ['12-4=8'] Exploring Operation: 17-6=11, Resulting Numbers: [8, 11] Generated Node #0,1,0: 90:[8, 11] Operation: 17-6=11 Exploring Operation: 17-8=9, Resulting Numbers: [6, 9] Generated Node #0,1,1: 90:[6, 9] Operation: 17-8=9 Exploring Operation: 8-6=2, Resulting Numbers: [17, 2] Generated Node #0,1,2: 90:[17, 2] Operation: 8-6=2 Exploring Operation: 6+8=14, Resulting Numbers: [17, 14] Generated Node #0,1,3: 90:[17, 14] Operation: 6+8=14 Exploring Operation: 6*8=48, Resulting Numbers: [17, 48] Generated Node #0,1,4: 90:[17, 48] Operation: 6*8=48 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[6, 9], Operations: ['12-4=8', '17-8=9'] Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,90 unequal: No Solution No 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: 90:[17, 2], Operations: ['12-4=8', '8-6=2'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,90 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,90 unequal: No Solution No 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: 90:[8, 11], Operations: ['12-4=8', '17-6=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,90 unequal: No Solution No 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: 90:[17, 14], Operations: ['12-4=8', '6+8=14'] Exploring Operation: 17*14=238, Resulting Numbers: [238] 238,90 unequal: No Solution Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 17+14=31, Resulting Numbers: [31] 31,90 unequal: No Solution No 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: 90:[17, 48], Operations: ['12-4=8', '6*8=48'] Exploring Operation: 17+48=65, Resulting Numbers: [65] 65,90 unequal: No Solution Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 17*48=816, Resulting Numbers: [816] 816,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[6, 17, 16], Operations: ['4+12=16'] Exploring Operation: 17+16=33, Resulting Numbers: [6, 33] Generated Node #0,2,0: 90:[6, 33] Operation: 17+16=33 Exploring Operation: 17-6=11, Resulting Numbers: [16, 11] Generated Node #0,2,1: 90:[16, 11] Operation: 17-6=11 Exploring Operation: 17-16=1, Resulting Numbers: [6, 1] Generated Node #0,2,2: 90:[6, 1] Operation: 17-16=1 Exploring Operation: 16-6=10, Resulting Numbers: [17, 10] Generated Node #0,2,3: 90:[17, 10] Operation: 16-6=10 Exploring Operation: 6+16=22, Resulting Numbers: [17, 22] Generated Node #0,2,4: 90:[17, 22] Operation: 6+16=22 Moving to Node #0,2,2 Current State: 90:[6, 1], Operations: ['4+12=16', '17-16=1'] Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,90 unequal: No Solution Moving to Node #0,2,3 Current State: 90:[17, 10], Operations: ['4+12=16', '16-6=10'] Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,90 unequal: No Solution Moving to Node #0,2,1 Current State: 90:[16, 11], Operations: ['4+12=16', '17-6=11'] Exploring Operation: 16+11=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 16*11=176, Resulting Numbers: [176] 176,90 unequal: No Solution Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,90 unequal: No Solution Moving to Node #0,2,0 Current State: 90:[6, 33], Operations: ['4+12=16', '17+16=33'] Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 6*33=198, Resulting Numbers: [198] 198,90 unequal: No Solution Exploring Operation: 6+33=39, Resulting Numbers: [39] 39,90 unequal: No Solution Moving to Node #0,2,4 Current State: 90:[17, 22], Operations: ['4+12=16', '6+16=22'] Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 17*22=374, Resulting Numbers: [374] 374,90 unequal: No Solution Exploring Operation: 17+22=39, Resulting Numbers: [39] 39,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 90:[4, 17, 18], Operations: ['6+12=18'] Exploring Operation: 18-4=14, Resulting Numbers: [17, 14] Generated Node #0,4,0: 90:[17, 14] Operation: 18-4=14 Exploring Operation: 4+17=21, Resulting Numbers: [18, 21] Generated Node #0,4,1: 90:[18, 21] Operation: 4+17=21 Exploring Operation: 4+18=22, Resulting Numbers: [17, 22] Generated Node #0,4,2: 90:[17, 22] Operation: 4+18=22 Exploring Operation: 18-17=1, Resulting Numbers: [4, 1] Generated Node #0,4,3: 90:[4, 1] Operation: 18-17=1 Exploring Operation: 17-4=13, Resulting Numbers: [18, 13] Generated Node #0,4,4: 90:[18, 13] Operation: 17-4=13 Moving to Node #0,4,0 Current State: 90:[17, 14], Operations: ['6+12=18', '18-4=14'] Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 17+14=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 17*14=238, Resulting Numbers: [238] 238,90 unequal: No Solution Moving to Node #0,4,4 Current State: 90:[18, 13], Operations: ['6+12=18', '17-4=13'] Exploring Operation: 18*13=234, Resulting Numbers: [234] 234,90 unequal: No Solution Exploring Operation: 18-13=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 18+13=31, Resulting Numbers: [31] 31,90 unequal: No Solution Moving to Node #0,4,3 Current State: 90:[4, 1], Operations: ['6+12=18', '18-17=1'] Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,90 unequal: No Solution Moving to Node #0,4,1 Current State: 90:[18, 21], Operations: ['6+12=18', '4+17=21'] Exploring Operation: 18+21=39, Resulting Numbers: [39] 39,90 unequal: No Solution Exploring Operation: 18*21=378, Resulting Numbers: [378] 378,90 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,90 unequal: No Solution Moving to Node #0,4,2 Current State: 90:[17, 22], Operations: ['6+12=18', '4+18=22'] Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 17+22=39, Resulting Numbers: [39] 39,90 unequal: No Solution Exploring Operation: 17*22=374, Resulting Numbers: [374] 374,90 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
[ 42, 88, 66, 44 ]
25
[ "42*66=2772", "2772/44=63", "88-63=25" ]
Current State: 25:[42, 88, 66, 44], Operations: [] Exploring Operation: 42*66=2772, Resulting Numbers: [88, 44, 2772] Generated Node #2: [88, 44, 2772] from Operation: 42*66=2772 Current State: 25:[88, 44, 2772], Operations: ['42*66=2772'] Exploring Operation: 2772/44=63, Resulting Numbers: [88, 63] Generated Node #3: [88, 63] from Operation: 2772/44=63 Current State: 25:[88, 63], Operations: ['42*66=2772', '2772/44=63'] Exploring Operation: 88-63=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[42, 88, 66, 44], Operations: [] Exploring Operation: 66-42=24, Resulting Numbers: [88, 44, 24] Generated Node #0,0: 25:[88, 44, 24] Operation: 66-42=24 Exploring Operation: 88-44=44, Resulting Numbers: [42, 66, 44] Generated Node #0,1: 25:[42, 66, 44] Operation: 88-44=44 Exploring Operation: 88-42=46, Resulting Numbers: [66, 44, 46] Generated Node #0,2: 25:[66, 44, 46] Operation: 88-42=46 Exploring Operation: 88-66=22, Resulting Numbers: [42, 44, 22] Generated Node #0,3: 25:[42, 44, 22] Operation: 88-66=22 Exploring Operation: 88/44=2, Resulting Numbers: [42, 66, 2] Generated Node #0,4: 25:[42, 66, 2] Operation: 88/44=2 Moving to Node #0,3 Current State: 25:[42, 44, 22], Operations: ['88-66=22'] Exploring Operation: 42+22=64, Resulting Numbers: [44, 64] Generated Node #0,3,0: 25:[44, 64] Operation: 42+22=64 Exploring Operation: 44/22=2, Resulting Numbers: [42, 2] Generated Node #0,3,1: 25:[42, 2] Operation: 44/22=2 Exploring Operation: 42-22=20, Resulting Numbers: [44, 20] Generated Node #0,3,2: 25:[44, 20] Operation: 42-22=20 Exploring Operation: 44-42=2, Resulting Numbers: [22, 2] Generated Node #0,3,3: 25:[22, 2] Operation: 44-42=2 Exploring Operation: 44-22=22, Resulting Numbers: [42, 22] Generated Node #0,3,4: 25:[42, 22] Operation: 44-22=22 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 25:[22, 2], Operations: ['88-66=22', '44-42=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,25 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 25:[42, 2], Operations: ['88-66=22', '44/22=2'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,25 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,25 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 25:[42, 22], Operations: ['88-66=22', '44-22=22'] Exploring Operation: 42+22=64, Resulting Numbers: [64] 64,25 unequal: No Solution Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 42*22=924, Resulting Numbers: [924] 924,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 25:[44, 20], Operations: ['88-66=22', '42-22=20'] Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,25 unequal: No Solution Exploring Operation: 44*20=880, Resulting Numbers: [880] 880,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 25:[44, 64], Operations: ['88-66=22', '42+22=64'] Exploring Operation: 44*64=2816, Resulting Numbers: [2816] 2816,25 unequal: No Solution Exploring Operation: 44+64=108, Resulting Numbers: [108] 108,25 unequal: No Solution Exploring Operation: 64-44=20, Resulting Numbers: [20] 20,25 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: 25:[42, 66, 2], Operations: ['88/44=2'] Exploring Operation: 66-2=64, Resulting Numbers: [42, 64] Generated Node #0,4,0: 25:[42, 64] Operation: 66-2=64 Exploring Operation: 42-2=40, Resulting Numbers: [66, 40] Generated Node #0,4,1: 25:[66, 40] Operation: 42-2=40 Exploring Operation: 42/2=21, Resulting Numbers: [66, 21] Generated Node #0,4,2: 25:[66, 21] Operation: 42/2=21 Exploring Operation: 66-42=24, Resulting Numbers: [2, 24] Generated Node #0,4,3: 25:[2, 24] Operation: 66-42=24 Exploring Operation: 66/2=33, Resulting Numbers: [42, 33] Generated Node #0,4,4: 25:[42, 33] Operation: 66/2=33 Moving to Node #0,1 Current State: 25:[42, 66, 44], Operations: ['88-44=44'] Exploring Operation: 66-44=22, Resulting Numbers: [42, 22] Generated Node #0,1,0: 25:[42, 22] Operation: 66-44=22 Exploring Operation: 44-42=2, Resulting Numbers: [66, 2] Generated Node #0,1,1: 25:[66, 2] Operation: 44-42=2 Exploring Operation: 42+44=86, Resulting Numbers: [66, 86] Generated Node #0,1,2: 25:[66, 86] Operation: 42+44=86 Exploring Operation: 42+66=108, Resulting Numbers: [44, 108] Generated Node #0,1,3: 25:[44, 108] Operation: 42+66=108 Exploring Operation: 66-42=24, Resulting Numbers: [44, 24] Generated Node #0,1,4: 25:[44, 24] Operation: 66-42=24 Moving to Node #0,2 Current State: 25:[66, 44, 46], Operations: ['88-42=46'] Exploring Operation: 66-44=22, Resulting Numbers: [46, 22] Generated Node #0,2,0: 25:[46, 22] Operation: 66-44=22 Exploring Operation: 66+46=112, Resulting Numbers: [44, 112] Generated Node #0,2,1: 25:[44, 112] Operation: 66+46=112 Exploring Operation: 66+44=110, Resulting Numbers: [46, 110] Generated Node #0,2,2: 25:[46, 110] Operation: 66+44=110 Exploring Operation: 66-46=20, Resulting Numbers: [44, 20] Generated Node #0,2,3: 25:[44, 20] Operation: 66-46=20 Exploring Operation: 46-44=2, Resulting Numbers: [66, 2] Generated Node #0,2,4: 25:[66, 2] Operation: 46-44=2 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 25:[46, 22], Operations: ['88-42=46', '66-44=22'] Exploring Operation: 46*22=1012, Resulting Numbers: [1012] 1012,25 unequal: No Solution Exploring Operation: 46+22=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 46-22=24, Resulting Numbers: [24] 24,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 25:[44, 20], Operations: ['88-42=46', '66-46=20'] Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,25 unequal: No Solution Exploring Operation: 44*20=880, Resulting Numbers: [880] 880,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 25:[66, 2], Operations: ['88-42=46', '46-44=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,25 unequal: No Solution Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,25 unequal: No Solution Exploring Operation: 66*2=132, Resulting Numbers: [132] 132,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 25:[44, 112], Operations: ['88-42=46', '66+46=112'] Exploring Operation: 44+112=156, Resulting Numbers: [156] 156,25 unequal: No Solution Exploring Operation: 112-44=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 44*112=4928, Resulting Numbers: [4928] 4928,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 25:[46, 110], Operations: ['88-42=46', '66+44=110'] Exploring Operation: 46+110=156, Resulting Numbers: [156] 156,25 unequal: No Solution Exploring Operation: 46*110=5060, Resulting Numbers: [5060] 5060,25 unequal: No Solution Exploring Operation: 110-46=64, Resulting Numbers: [64] 64,25 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: 25:[88, 44, 24], Operations: ['66-42=24'] Exploring Operation: 44-24=20, Resulting Numbers: [88, 20] Generated Node #0,0,0: 25:[88, 20] Operation: 44-24=20 Exploring Operation: 88-24=64, Resulting Numbers: [44, 64] Generated Node #0,0,1: 25:[44, 64] Operation: 88-24=64 Exploring Operation: 88-44=44, Resulting Numbers: [24, 44] Generated Node #0,0,2: 25:[24, 44] Operation: 88-44=44 Exploring Operation: 88/44=2, Resulting Numbers: [24, 2] Generated Node #0,0,3: 25:[24, 2] Operation: 88/44=2 Exploring Operation: 88+24=112, Resulting Numbers: [44, 112] Generated Node #0,0,4: 25:[44, 112] Operation: 88+24=112 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 25:[24, 2], Operations: ['66-42=24', '88/44=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,25 unequal: No Solution Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,25 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 25:[24, 44], Operations: ['66-42=24', '88-44=44'] Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 24+44=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 24*44=1056, Resulting Numbers: [1056] 1056,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 25:[44, 64], Operations: ['66-42=24', '88-24=64'] Exploring Operation: 44*64=2816, Resulting Numbers: [2816] 2816,25 unequal: No Solution Exploring Operation: 44+64=108, Resulting Numbers: [108] 108,25 unequal: No Solution Exploring Operation: 64-44=20, Resulting Numbers: [20] 20,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[88, 20], Operations: ['66-42=24', '44-24=20'] Exploring Operation: 88-20=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 88*20=1760, Resulting Numbers: [1760] 1760,25 unequal: No Solution Exploring Operation: 88+20=108, Resulting Numbers: [108] 108,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 25:[44, 112], Operations: ['66-42=24', '88+24=112'] Exploring Operation: 112-44=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 44+112=156, Resulting Numbers: [156] 156,25 unequal: No Solution Exploring Operation: 44*112=4928, Resulting Numbers: [4928] 4928,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,3 Current State: 25:[2, 24], Operations: ['88/44=2', '66-42=24'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,25 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,25 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,25 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,25 unequal: No Solution Moving to Node #0,1,0 Current State: 25:[42, 22], Operations: ['88-44=44', '66-44=22'] Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 42*22=924, Resulting Numbers: [924] 924,25 unequal: No Solution Exploring Operation: 42+22=64, Resulting Numbers: [64] 64,25 unequal: No Solution Moving to Node #0,1,4 Current State: 25:[44, 24], Operations: ['88-44=44', '66-42=24'] Exploring Operation: 44*24=1056, Resulting Numbers: [1056] 1056,25 unequal: No Solution Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 44+24=68, Resulting Numbers: [68] 68,25 unequal: No Solution Moving to Node #0,4,4 Current State: 25:[42, 33], Operations: ['88/44=2', '66/2=33'] Exploring Operation: 42-33=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 42*33=1386, Resulting Numbers: [1386] 1386,25 unequal: No Solution Exploring Operation: 42+33=75, Resulting Numbers: [75] 75,25 unequal: No Solution Moving to Node #0,1,1 Current State: 25:[66, 2], Operations: ['88-44=44', '44-42=2'] Exploring Operation: 66*2=132, Resulting Numbers: [132] 132,25 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,25 unequal: No Solution Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,25 unequal: No Solution Moving to Node #0,4,2 Current State: 25:[66, 21], Operations: ['88/44=2', '42/2=21'] Exploring Operation: 66*21=1386, Resulting Numbers: [1386] 1386,25 unequal: No Solution Exploring Operation: 66-21=45, Resulting Numbers: [45] 45,25 unequal: No Solution Exploring Operation: 66+21=87, Resulting Numbers: [87] 87,25 unequal: No Solution Moving to Node #0,4,1 Current State: 25:[66, 40], Operations: ['88/44=2', '42-2=40'] Exploring Operation: 66+40=106, Resulting Numbers: [106] 106,25 unequal: No Solution Exploring Operation: 66*40=2640, Resulting Numbers: [2640] 2640,25 unequal: No Solution Exploring Operation: 66-40=26, Resulting Numbers: [26] 26,25 unequal: No Solution Moving to Node #0,4,0 Current State: 25:[42, 64], Operations: ['88/44=2', '66-2=64'] Exploring Operation: 42+64=106, Resulting Numbers: [106] 106,25 unequal: No Solution Exploring Operation: 42*64=2688, Resulting Numbers: [2688] 2688,25 unequal: No Solution Exploring Operation: 64-42=22, Resulting Numbers: [22] 22,25 unequal: No Solution Moving to Node #0,1,3 Current State: 25:[44, 108], Operations: ['88-44=44', '42+66=108'] Exploring Operation: 44*108=4752, Resulting Numbers: [4752] 4752,25 unequal: No Solution Exploring Operation: 44+108=152, Resulting Numbers: [152] 152,25 unequal: No Solution Exploring Operation: 108-44=64, Resulting Numbers: [64] 64,25 unequal: No Solution Moving to Node #0,1,2 Current State: 25:[66, 86], Operations: ['88-44=44', '42+44=86'] Exploring Operation: 66+86=152, Resulting Numbers: [152] 152,25 unequal: No Solution Exploring Operation: 86-66=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 66*86=5676, Resulting Numbers: [5676] 5676,25 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 57, 1, 51, 6 ]
35
[ "57-51=6", "6*6=36", "36-1=35" ]
Current State: 35:[57, 1, 51, 6], Operations: [] Exploring Operation: 57-51=6, Resulting Numbers: [1, 6, 6] Generated Node #2: [1, 6, 6] from Operation: 57-51=6 Current State: 35:[1, 6, 6], Operations: ['57-51=6'] Exploring Operation: 6*6=36, Resulting Numbers: [1, 36] Generated Node #3: [1, 36] from Operation: 6*6=36 Current State: 35:[1, 36], Operations: ['57-51=6', '6*6=36'] Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[57, 1, 51, 6], Operations: [] Exploring Operation: 57-51=6, Resulting Numbers: [1, 6, 6] Generated Node #0,0: 35:[1, 6, 6] Operation: 57-51=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[1, 6, 6], Operations: ['57-51=6'] Exploring Operation: 1+6=7, Resulting Numbers: [6, 7] Generated Node #0,0,0: 35:[6, 7] Operation: 1+6=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[6, 7], Operations: ['57-51=6', '1+6=7'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 93, 80, 26, 37 ]
24
[ "93-80=13", "37-26=11", "13+11=24" ]
Current State: 24:[93, 80, 26, 37], Operations: [] Exploring Operation: 93-80=13, Resulting Numbers: [26, 37, 13] Generated Node #2: [26, 37, 13] from Operation: 93-80=13 Current State: 24:[26, 37, 13], Operations: ['93-80=13'] Exploring Operation: 37-26=11, Resulting Numbers: [13, 11] Generated Node #3: [13, 11] from Operation: 37-26=11 Current State: 24:[13, 11], Operations: ['93-80=13', '37-26=11'] Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[93, 80, 26, 37], Operations: [] Exploring Operation: 93-37=56, Resulting Numbers: [80, 26, 56] Generated Node #0,0: 24:[80, 26, 56] Operation: 93-37=56 Exploring Operation: 93-80=13, Resulting Numbers: [26, 37, 13] Generated Node #0,1: 24:[26, 37, 13] Operation: 93-80=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[26, 37, 13], Operations: ['93-80=13'] Exploring Operation: 37-13=24, Resulting Numbers: [26, 24] Generated Node #0,1,0: 24:[26, 24] Operation: 37-13=24 Exploring Operation: 37-26=11, Resulting Numbers: [13, 11] Generated Node #0,1,1: 24:[13, 11] Operation: 37-26=11 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 24:[26, 24], Operations: ['93-80=13', '37-13=24'] Exploring Operation: 26+24=50, Resulting Numbers: [50] 50,24 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,24 unequal: No Solution No 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: 24:[13, 11], Operations: ['93-80=13', '37-26=11'] Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[93, 80, 26, 37], Operations: [] Exploring Operation: 93-80=13, Resulting Numbers: [26, 37, 13] Generated Node #0,1: 24:[26, 37, 13] Operation: 93-80=13 Moving to Node #0,1 Current State: 24:[26, 37, 13], Operations: ['93-80=13'] Exploring Operation: 37-26=11, Resulting Numbers: [13, 11] Generated Node #0,1,1: 24:[13, 11] Operation: 37-26=11 Moving to Node #0,1,1 Current State: 24:[13, 11], Operations: ['93-80=13', '37-26=11'] Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 84, 93, 65, 68 ]
71
[ "93-65=28", "84/28=3", "68+3=71" ]
Current State: 71:[84, 93, 65, 68], Operations: [] Exploring Operation: 93-65=28, Resulting Numbers: [84, 68, 28] Generated Node #2: [84, 68, 28] from Operation: 93-65=28 Current State: 71:[84, 68, 28], Operations: ['93-65=28'] Exploring Operation: 84/28=3, Resulting Numbers: [68, 3] Generated Node #3: [68, 3] from Operation: 84/28=3 Current State: 71:[68, 3], Operations: ['93-65=28', '84/28=3'] Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[84, 93, 65, 68], Operations: [] Exploring Operation: 93-84=9, Resulting Numbers: [65, 68, 9] Generated Node #0,0: 71:[65, 68, 9] Operation: 93-84=9 Exploring Operation: 93-68=25, Resulting Numbers: [84, 65, 25] Generated Node #0,1: 71:[84, 65, 25] Operation: 93-68=25 Exploring Operation: 93-65=28, Resulting Numbers: [84, 68, 28] Generated Node #0,2: 71:[84, 68, 28] Operation: 93-65=28 Moving to Node #0,2 Current State: 71:[84, 68, 28], Operations: ['93-65=28'] Exploring Operation: 84-28=56, Resulting Numbers: [68, 56] Generated Node #0,2,0: 71:[68, 56] Operation: 84-28=56 Exploring Operation: 68+28=96, Resulting Numbers: [84, 96] Generated Node #0,2,1: 71:[84, 96] Operation: 68+28=96 Exploring Operation: 84+28=112, Resulting Numbers: [68, 112] Generated Node #0,2,2: 71:[68, 112] Operation: 84+28=112 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 71:[68, 56], Operations: ['93-65=28', '84-28=56'] Exploring Operation: 68+56=124, Resulting Numbers: [124] 124,71 unequal: No Solution Exploring Operation: 68-56=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 68*56=3808, Resulting Numbers: [3808] 3808,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 71:[84, 96], Operations: ['93-65=28', '68+28=96'] Exploring Operation: 96-84=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 84+96=180, Resulting Numbers: [180] 180,71 unequal: No Solution Exploring Operation: 84*96=8064, Resulting Numbers: [8064] 8064,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 71:[68, 112], Operations: ['93-65=28', '84+28=112'] Exploring Operation: 112-68=44, Resulting Numbers: [44] 44,71 unequal: No Solution Exploring Operation: 68+112=180, Resulting Numbers: [180] 180,71 unequal: No Solution Exploring Operation: 68*112=7616, Resulting Numbers: [7616] 7616,71 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: 71:[84, 65, 25], Operations: ['93-68=25'] Exploring Operation: 84-25=59, Resulting Numbers: [65, 59] Generated Node #0,1,0: 71:[65, 59] Operation: 84-25=59 Exploring Operation: 84+25=109, Resulting Numbers: [65, 109] Generated Node #0,1,1: 71:[65, 109] Operation: 84+25=109 Exploring Operation: 65+25=90, Resulting Numbers: [84, 90] Generated Node #0,1,2: 71:[84, 90] Operation: 65+25=90 Moving to Node #0,0 Current State: 71:[65, 68, 9], Operations: ['93-84=9'] Exploring Operation: 65-9=56, Resulting Numbers: [68, 56] Generated Node #0,0,0: 71:[68, 56] Operation: 65-9=56 Exploring Operation: 65+9=74, Resulting Numbers: [68, 74] Generated Node #0,0,1: 71:[68, 74] Operation: 65+9=74 Exploring Operation: 68+9=77, Resulting Numbers: [65, 77] Generated Node #0,0,2: 71:[65, 77] Operation: 68+9=77 Moving to Node #0,0,1 Current State: 71:[68, 74], Operations: ['93-84=9', '65+9=74'] Exploring Operation: 68*74=5032, Resulting Numbers: [5032] 5032,71 unequal: No Solution Exploring Operation: 68+74=142, Resulting Numbers: [142] 142,71 unequal: No Solution Exploring Operation: 74-68=6, Resulting Numbers: [6] 6,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[65, 77], Operations: ['93-84=9', '68+9=77'] Exploring Operation: 77-65=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 65+77=142, Resulting Numbers: [142] 142,71 unequal: No Solution Exploring Operation: 65*77=5005, Resulting Numbers: [5005] 5005,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[68, 56], Operations: ['93-84=9', '65-9=56'] Exploring Operation: 68*56=3808, Resulting Numbers: [3808] 3808,71 unequal: No Solution Exploring Operation: 68-56=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 68+56=124, Resulting Numbers: [124] 124,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[65, 59], Operations: ['93-68=25', '84-25=59'] Exploring Operation: 65+59=124, Resulting Numbers: [124] 124,71 unequal: No Solution Exploring Operation: 65*59=3835, Resulting Numbers: [3835] 3835,71 unequal: No Solution Exploring Operation: 65-59=6, Resulting Numbers: [6] 6,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[84, 90], Operations: ['93-68=25', '65+25=90'] Exploring Operation: 84*90=7560, Resulting Numbers: [7560] 7560,71 unequal: No Solution Exploring Operation: 90-84=6, Resulting Numbers: [6] 6,71 unequal: No Solution Exploring Operation: 84+90=174, Resulting Numbers: [174] 174,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[65, 109], Operations: ['93-68=25', '84+25=109'] Exploring Operation: 65+109=174, Resulting Numbers: [174] 174,71 unequal: No Solution Exploring Operation: 65*109=7085, Resulting Numbers: [7085] 7085,71 unequal: No Solution Exploring Operation: 109-65=44, Resulting Numbers: [44] 44,71 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 8, 23, 94, 4 ]
73
[ "8/4=2", "94-23=71", "2+71=73" ]
Current State: 73:[8, 23, 94, 4], Operations: [] Exploring Operation: 8/4=2, Resulting Numbers: [23, 94, 2] Generated Node #2: [23, 94, 2] from Operation: 8/4=2 Current State: 73:[23, 94, 2], Operations: ['8/4=2'] Exploring Operation: 94-23=71, Resulting Numbers: [2, 71] Generated Node #3: [2, 71] from Operation: 94-23=71 Current State: 73:[2, 71], Operations: ['8/4=2', '94-23=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[8, 23, 94, 4], Operations: [] Exploring Operation: 8*4=32, Resulting Numbers: [23, 94, 32] Generated Node #0,0: 73:[23, 94, 32] Operation: 8*4=32 Exploring Operation: 8+23=31, Resulting Numbers: [94, 4, 31] Generated Node #0,1: 73:[94, 4, 31] Operation: 8+23=31 Exploring Operation: 23*4=92, Resulting Numbers: [8, 94, 92] Generated Node #0,2: 73:[8, 94, 92] Operation: 23*4=92 Exploring Operation: 94-8=86, Resulting Numbers: [23, 4, 86] Generated Node #0,3: 73:[23, 4, 86] Operation: 94-8=86 Moving to Node #0,2 Current State: 73:[8, 94, 92], Operations: ['23*4=92'] Exploring Operation: 92-8=84, Resulting Numbers: [94, 84] Generated Node #0,2,0: 73:[94, 84] Operation: 92-8=84 Exploring Operation: 8+94=102, Resulting Numbers: [92, 102] Generated Node #0,2,1: 73:[92, 102] Operation: 8+94=102 Exploring Operation: 8+92=100, Resulting Numbers: [94, 100] Generated Node #0,2,2: 73:[94, 100] Operation: 8+92=100 Exploring Operation: 94-8=86, Resulting Numbers: [92, 86] Generated Node #0,2,3: 73:[92, 86] Operation: 94-8=86 Moving to Node #0,0 Current State: 73:[23, 94, 32], Operations: ['8*4=32'] Exploring Operation: 94-32=62, Resulting Numbers: [23, 62] Generated Node #0,0,0: 73:[23, 62] Operation: 94-32=62 Exploring Operation: 94-23=71, Resulting Numbers: [32, 71] Generated Node #0,0,1: 73:[32, 71] Operation: 94-23=71 Exploring Operation: 23+94=117, Resulting Numbers: [32, 117] Generated Node #0,0,2: 73:[32, 117] Operation: 23+94=117 Exploring Operation: 23+32=55, Resulting Numbers: [94, 55] Generated Node #0,0,3: 73:[94, 55] Operation: 23+32=55 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 73:[94, 55], Operations: ['8*4=32', '23+32=55'] Exploring Operation: 94*55=5170, Resulting Numbers: [5170] 5170,73 unequal: No Solution Exploring Operation: 94+55=149, Resulting Numbers: [149] 149,73 unequal: No Solution Exploring Operation: 94-55=39, Resulting Numbers: [39] 39,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[32, 71], Operations: ['8*4=32', '94-23=71'] Exploring Operation: 71-32=39, Resulting Numbers: [39] 39,73 unequal: No Solution Exploring Operation: 32+71=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 32*71=2272, Resulting Numbers: [2272] 2272,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[23, 62], Operations: ['8*4=32', '94-32=62'] Exploring Operation: 23+62=85, Resulting Numbers: [85] 85,73 unequal: No Solution Exploring Operation: 23*62=1426, Resulting Numbers: [1426] 1426,73 unequal: No Solution Exploring Operation: 62-23=39, Resulting Numbers: [39] 39,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 73:[32, 117], Operations: ['8*4=32', '23+94=117'] Exploring Operation: 32+117=149, Resulting Numbers: [149] 149,73 unequal: No Solution Exploring Operation: 117-32=85, Resulting Numbers: [85] 85,73 unequal: No Solution Exploring Operation: 32*117=3744, Resulting Numbers: [3744] 3744,73 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: 73:[23, 4, 86], Operations: ['94-8=86'] Exploring Operation: 86-4=82, Resulting Numbers: [23, 82] Generated Node #0,3,0: 73:[23, 82] Operation: 86-4=82 Exploring Operation: 23+4=27, Resulting Numbers: [86, 27] Generated Node #0,3,1: 73:[86, 27] Operation: 23+4=27 Exploring Operation: 23*4=92, Resulting Numbers: [86, 92] Generated Node #0,3,2: 73:[86, 92] Operation: 23*4=92 Exploring Operation: 23-4=19, Resulting Numbers: [86, 19] Generated Node #0,3,3: 73:[86, 19] Operation: 23-4=19 Moving to Node #0,1 Current State: 73:[94, 4, 31], Operations: ['8+23=31'] Exploring Operation: 94+4=98, Resulting Numbers: [31, 98] Generated Node #0,1,0: 73:[31, 98] Operation: 94+4=98 Exploring Operation: 4+31=35, Resulting Numbers: [94, 35] Generated Node #0,1,1: 73:[94, 35] Operation: 4+31=35 Exploring Operation: 31-4=27, Resulting Numbers: [94, 27] Generated Node #0,1,2: 73:[94, 27] Operation: 31-4=27 Exploring Operation: 94-4=90, Resulting Numbers: [31, 90] Generated Node #0,1,3: 73:[31, 90] Operation: 94-4=90 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[94, 35], Operations: ['8+23=31', '4+31=35'] Exploring Operation: 94+35=129, Resulting Numbers: [129] 129,73 unequal: No Solution Exploring Operation: 94*35=3290, Resulting Numbers: [3290] 3290,73 unequal: No Solution Exploring Operation: 94-35=59, Resulting Numbers: [59] 59,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 73:[31, 90], Operations: ['8+23=31', '94-4=90'] Exploring Operation: 31*90=2790, Resulting Numbers: [2790] 2790,73 unequal: No Solution Exploring Operation: 90-31=59, Resulting Numbers: [59] 59,73 unequal: No Solution Exploring Operation: 31+90=121, Resulting Numbers: [121] 121,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[31, 98], Operations: ['8+23=31', '94+4=98'] Exploring Operation: 98-31=67, Resulting Numbers: [67] 67,73 unequal: No Solution Exploring Operation: 31+98=129, Resulting Numbers: [129] 129,73 unequal: No Solution Exploring Operation: 31*98=3038, Resulting Numbers: [3038] 3038,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 73:[94, 27], Operations: ['8+23=31', '31-4=27'] Exploring Operation: 94*27=2538, Resulting Numbers: [2538] 2538,73 unequal: No Solution Exploring Operation: 94-27=67, Resulting Numbers: [67] 67,73 unequal: No Solution Exploring Operation: 94+27=121, Resulting Numbers: [121] 121,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 73:[94, 84], Operations: ['23*4=92', '92-8=84'] Exploring Operation: 94+84=178, Resulting Numbers: [178] 178,73 unequal: No Solution Exploring Operation: 94-84=10, Resulting Numbers: [10] 10,73 unequal: No Solution Exploring Operation: 94*84=7896, Resulting Numbers: [7896] 7896,73 unequal: No Solution Moving to Node #0,2,3 Current State: 73:[92, 86], Operations: ['23*4=92', '94-8=86'] Exploring Operation: 92+86=178, Resulting Numbers: [178] 178,73 unequal: No Solution Exploring Operation: 92*86=7912, Resulting Numbers: [7912] 7912,73 unequal: No Solution Exploring Operation: 92-86=6, Resulting Numbers: [6] 6,73 unequal: No Solution Moving to Node #0,3,2 Current State: 73:[86, 92], Operations: ['94-8=86', '23*4=92'] Exploring Operation: 92-86=6, Resulting Numbers: [6] 6,73 unequal: No Solution Exploring Operation: 86+92=178, Resulting Numbers: [178] 178,73 unequal: No Solution Exploring Operation: 86*92=7912, Resulting Numbers: [7912] 7912,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[92, 102], Operations: ['23*4=92', '8+94=102'] Exploring Operation: 102-92=10, Resulting Numbers: [10] 10,73 unequal: No Solution Exploring Operation: 92+102=194, Resulting Numbers: [194] 194,73 unequal: No Solution Exploring Operation: 92*102=9384, Resulting Numbers: [9384] 9384,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[94, 100], Operations: ['23*4=92', '8+92=100'] Exploring Operation: 94+100=194, Resulting Numbers: [194] 194,73 unequal: No Solution Exploring Operation: 94*100=9400, Resulting Numbers: [9400] 9400,73 unequal: No Solution Exploring Operation: 100-94=6, Resulting Numbers: [6] 6,73 unequal: No Solution Moving to Node #0,3,0 Current State: 73:[23, 82], Operations: ['94-8=86', '86-4=82'] Exploring Operation: 23+82=105, Resulting Numbers: [105] 105,73 unequal: No Solution Exploring Operation: 82-23=59, Resulting Numbers: [59] 59,73 unequal: No Solution Exploring Operation: 23*82=1886, Resulting Numbers: [1886] 1886,73 unequal: No Solution Moving to Node #0,3,1 Current State: 73:[86, 27], Operations: ['94-8=86', '23+4=27'] Exploring Operation: 86+27=113, Resulting Numbers: [113] 113,73 unequal: No Solution Exploring Operation: 86*27=2322, Resulting Numbers: [2322] 2322,73 unequal: No Solution Exploring Operation: 86-27=59, Resulting Numbers: [59] 59,73 unequal: No Solution Moving to Node #0,3,3 Current State: 73:[86, 19], Operations: ['94-8=86', '23-4=19'] Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,73 unequal: No Solution Exploring Operation: 86*19=1634, Resulting Numbers: [1634] 1634,73 unequal: No Solution Exploring Operation: 86+19=105, Resulting Numbers: [105] 105,73 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 49, 24, 32, 58 ]
99
[ "49+24=73", "58-32=26", "73+26=99" ]
Current State: 99:[49, 24, 32, 58], Operations: [] Exploring Operation: 49+24=73, Resulting Numbers: [32, 58, 73] Generated Node #2: [32, 58, 73] from Operation: 49+24=73 Current State: 99:[32, 58, 73], Operations: ['49+24=73'] Exploring Operation: 58-32=26, Resulting Numbers: [73, 26] Generated Node #3: [73, 26] from Operation: 58-32=26 Current State: 99:[73, 26], Operations: ['49+24=73', '58-32=26'] Exploring Operation: 73+26=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[49, 24, 32, 58], Operations: [] Exploring Operation: 49+58=107, Resulting Numbers: [24, 32, 107] Generated Node #0,0: 99:[24, 32, 107] Operation: 49+58=107 Exploring Operation: 58-49=9, Resulting Numbers: [24, 32, 9] Generated Node #0,1: 99:[24, 32, 9] Operation: 58-49=9 Moving to Node #0,1 Current State: 99:[24, 32, 9], Operations: ['58-49=9'] Exploring Operation: 24+9=33, Resulting Numbers: [32, 33] Generated Node #0,1,0: 99:[32, 33] Operation: 24+9=33 Exploring Operation: 32-24=8, Resulting Numbers: [9, 8] Generated Node #0,1,1: 99:[9, 8] Operation: 32-24=8 Moving to Node #0,0 Current State: 99:[24, 32, 107], Operations: ['49+58=107'] Exploring Operation: 32-24=8, Resulting Numbers: [107, 8] Generated Node #0,0,0: 99:[107, 8] Operation: 32-24=8 Exploring Operation: 107-24=83, Resulting Numbers: [32, 83] Generated Node #0,0,1: 99:[32, 83] Operation: 107-24=83 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[107, 8], Operations: ['49+58=107', '32-24=8'] Exploring Operation: 107-8=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[49, 24, 32, 58], Operations: [] Exploring Operation: 49+58=107, Resulting Numbers: [24, 32, 107] Generated Node #0,0: 99:[24, 32, 107] Operation: 49+58=107 Moving to Node #0,0 Current State: 99:[24, 32, 107], Operations: ['49+58=107'] Exploring Operation: 32-24=8, Resulting Numbers: [107, 8] Generated Node #0,0,0: 99:[107, 8] Operation: 32-24=8 Moving to Node #0,0,0 Current State: 99:[107, 8], Operations: ['49+58=107', '32-24=8'] Exploring Operation: 107-8=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 99, 61, 27, 28 ]
30
[ "61-28=33", "99/33=3", "27+3=30" ]
Current State: 30:[99, 61, 27, 28], Operations: [] Exploring Operation: 61-28=33, Resulting Numbers: [99, 27, 33] Generated Node #2: [99, 27, 33] from Operation: 61-28=33 Current State: 30:[99, 27, 33], Operations: ['61-28=33'] Exploring Operation: 99/33=3, Resulting Numbers: [27, 3] Generated Node #3: [27, 3] from Operation: 99/33=3 Current State: 30:[27, 3], Operations: ['61-28=33', '99/33=3'] Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[99, 61, 27, 28], Operations: [] Exploring Operation: 99-27=72, Resulting Numbers: [61, 28, 72] Generated Node #0,0: 30:[61, 28, 72] Operation: 99-27=72 Exploring Operation: 99-61=38, Resulting Numbers: [27, 28, 38] Generated Node #0,1: 30:[27, 28, 38] Operation: 99-61=38 Exploring Operation: 99-28=71, Resulting Numbers: [61, 27, 71] Generated Node #0,2: 30:[61, 27, 71] Operation: 99-28=71 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[27, 28, 38], Operations: ['99-61=38'] Exploring Operation: 38-28=10, Resulting Numbers: [27, 10] Generated Node #0,1,0: 30:[27, 10] Operation: 38-28=10 Exploring Operation: 28-27=1, Resulting Numbers: [38, 1] Generated Node #0,1,1: 30:[38, 1] Operation: 28-27=1 Exploring Operation: 38-27=11, Resulting Numbers: [28, 11] Generated Node #0,1,2: 30:[28, 11] Operation: 38-27=11 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[27, 10], Operations: ['99-61=38', '38-28=10'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 27*10=270, Resulting Numbers: [270] 270,30 unequal: No Solution Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,30 unequal: No Solution No 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: 30:[28, 11], Operations: ['99-61=38', '38-27=11'] Exploring Operation: 28*11=308, Resulting Numbers: [308] 308,30 unequal: No Solution Exploring Operation: 28+11=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,30 unequal: No Solution No 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: 30:[38, 1], Operations: ['99-61=38', '28-27=1'] Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,30 unequal: No Solution Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,30 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: 30:[61, 28, 72], Operations: ['99-27=72'] Exploring Operation: 72-28=44, Resulting Numbers: [61, 44] Generated Node #0,0,0: 30:[61, 44] Operation: 72-28=44 Exploring Operation: 72-61=11, Resulting Numbers: [28, 11] Generated Node #0,0,1: 30:[28, 11] Operation: 72-61=11 Exploring Operation: 61-28=33, Resulting Numbers: [72, 33] Generated Node #0,0,2: 30:[72, 33] Operation: 61-28=33 Moving to Node #0,0,1 Current State: 30:[28, 11], Operations: ['99-27=72', '72-61=11'] Exploring Operation: 28+11=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 28*11=308, Resulting Numbers: [308] 308,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[61, 44], Operations: ['99-27=72', '72-28=44'] Exploring Operation: 61-44=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 61+44=105, Resulting Numbers: [105] 105,30 unequal: No Solution Exploring Operation: 61*44=2684, Resulting Numbers: [2684] 2684,30 unequal: No Solution Moving to Node #0,0,2 Current State: 30:[72, 33], Operations: ['99-27=72', '61-28=33'] Exploring Operation: 72+33=105, Resulting Numbers: [105] 105,30 unequal: No Solution Exploring Operation: 72*33=2376, Resulting Numbers: [2376] 2376,30 unequal: No Solution Exploring Operation: 72-33=39, Resulting Numbers: [39] 39,30 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:[61, 27, 71], Operations: ['99-28=71'] Exploring Operation: 71-27=44, Resulting Numbers: [61, 44] Generated Node #0,2,0: 30:[61, 44] Operation: 71-27=44 Exploring Operation: 61-27=34, Resulting Numbers: [71, 34] Generated Node #0,2,1: 30:[71, 34] Operation: 61-27=34 Exploring Operation: 71-61=10, Resulting Numbers: [27, 10] Generated Node #0,2,2: 30:[27, 10] Operation: 71-61=10 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 30:[27, 10], Operations: ['99-28=71', '71-61=10'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 27*10=270, Resulting Numbers: [270] 270,30 unequal: No Solution Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,30 unequal: No Solution No 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: 30:[61, 44], Operations: ['99-28=71', '71-27=44'] Exploring Operation: 61-44=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 61*44=2684, Resulting Numbers: [2684] 2684,30 unequal: No Solution Exploring Operation: 61+44=105, Resulting Numbers: [105] 105,30 unequal: No Solution No 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: 30:[71, 34], Operations: ['99-28=71', '61-27=34'] Exploring Operation: 71+34=105, Resulting Numbers: [105] 105,30 unequal: No Solution Exploring Operation: 71*34=2414, Resulting Numbers: [2414] 2414,30 unequal: No Solution Exploring Operation: 71-34=37, Resulting Numbers: [37] 37,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 78, 9, 89, 16 ]
14
[ "78+9=87", "89-16=73", "87-73=14" ]
Current State: 14:[78, 9, 89, 16], Operations: [] Exploring Operation: 78+9=87, Resulting Numbers: [89, 16, 87] Generated Node #2: [89, 16, 87] from Operation: 78+9=87 Current State: 14:[89, 16, 87], Operations: ['78+9=87'] Exploring Operation: 89-16=73, Resulting Numbers: [87, 73] Generated Node #3: [87, 73] from Operation: 89-16=73 Current State: 14:[87, 73], Operations: ['78+9=87', '89-16=73'] Exploring Operation: 87-73=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[78, 9, 89, 16], Operations: [] Exploring Operation: 89-78=11, Resulting Numbers: [9, 16, 11] Generated Node #0,0: 14:[9, 16, 11] Operation: 89-78=11 Exploring Operation: 89-16=73, Resulting Numbers: [78, 9, 73] Generated Node #0,1: 14:[78, 9, 73] Operation: 89-16=73 Exploring Operation: 78-16=62, Resulting Numbers: [9, 89, 62] Generated Node #0,2: 14:[9, 89, 62] Operation: 78-16=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[9, 16, 11], Operations: ['89-78=11'] Exploring Operation: 16-11=5, Resulting Numbers: [9, 5] Generated Node #0,0,0: 14:[9, 5] Operation: 16-11=5 Exploring Operation: 16-9=7, Resulting Numbers: [11, 7] Generated Node #0,0,1: 14:[11, 7] Operation: 16-9=7 Exploring Operation: 11-9=2, Resulting Numbers: [16, 2] Generated Node #0,0,2: 14:[16, 2] Operation: 11-9=2 Moving to Node #0,0,2 Current State: 14:[16, 2], Operations: ['89-78=11', '11-9=2'] Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[78, 9, 89, 16], Operations: [] Exploring Operation: 89-78=11, Resulting Numbers: [9, 16, 11] Generated Node #0,0: 14:[9, 16, 11] Operation: 89-78=11 Moving to Node #0,0 Current State: 14:[9, 16, 11], Operations: ['89-78=11'] Exploring Operation: 11-9=2, Resulting Numbers: [16, 2] Generated Node #0,0,2: 14:[16, 2] Operation: 11-9=2 Moving to Node #0,0,2 Current State: 14:[16, 2], Operations: ['89-78=11', '11-9=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 74, 26, 90, 19 ]
29
[ "74+26=100", "90-19=71", "100-71=29" ]
Current State: 29:[74, 26, 90, 19], Operations: [] Exploring Operation: 74+26=100, Resulting Numbers: [90, 19, 100] Generated Node #2: [90, 19, 100] from Operation: 74+26=100 Current State: 29:[90, 19, 100], Operations: ['74+26=100'] Exploring Operation: 90-19=71, Resulting Numbers: [100, 71] Generated Node #3: [100, 71] from Operation: 90-19=71 Current State: 29:[100, 71], Operations: ['74+26=100', '90-19=71'] Exploring Operation: 100-71=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[74, 26, 90, 19], Operations: [] Exploring Operation: 90-19=71, Resulting Numbers: [74, 26, 71] Generated Node #0,0: 29:[74, 26, 71] Operation: 90-19=71 Exploring Operation: 90-74=16, Resulting Numbers: [26, 19, 16] Generated Node #0,1: 29:[26, 19, 16] Operation: 90-74=16 Exploring Operation: 74-19=55, Resulting Numbers: [26, 90, 55] Generated Node #0,2: 29:[26, 90, 55] Operation: 74-19=55 Exploring Operation: 74-26=48, Resulting Numbers: [90, 19, 48] Generated Node #0,3: 29:[90, 19, 48] Operation: 74-26=48 Exploring Operation: 90-26=64, Resulting Numbers: [74, 19, 64] Generated Node #0,4: 29:[74, 19, 64] Operation: 90-26=64 Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[26, 19, 16], Operations: ['90-74=16'] Exploring Operation: 26+16=42, Resulting Numbers: [19, 42] Generated Node #0,1,0: 29:[19, 42] Operation: 26+16=42 Exploring Operation: 19+16=35, Resulting Numbers: [26, 35] Generated Node #0,1,1: 29:[26, 35] Operation: 19+16=35 Exploring Operation: 19-16=3, Resulting Numbers: [26, 3] Generated Node #0,1,2: 29:[26, 3] Operation: 19-16=3 Exploring Operation: 26+19=45, Resulting Numbers: [16, 45] Generated Node #0,1,3: 29:[16, 45] Operation: 26+19=45 Exploring Operation: 26-16=10, Resulting Numbers: [19, 10] Generated Node #0,1,4: 29:[19, 10] Operation: 26-16=10 Moving to Node #0,1,1 Current State: 29:[26, 35], Operations: ['90-74=16', '19+16=35'] Exploring Operation: 26*35=910, Resulting Numbers: [910] 910,29 unequal: No Solution Exploring Operation: 26+35=61, Resulting Numbers: [61] 61,29 unequal: No Solution Exploring Operation: 35-26=9, Resulting Numbers: [9] 9,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[19, 42], Operations: ['90-74=16', '26+16=42'] Exploring Operation: 42-19=23, Resulting Numbers: [23] 23,29 unequal: No Solution Exploring Operation: 19*42=798, Resulting Numbers: [798] 798,29 unequal: No Solution Exploring Operation: 19+42=61, Resulting Numbers: [61] 61,29 unequal: No Solution Moving to Node #0,1,2 Current State: 29:[26, 3], Operations: ['90-74=16', '19-16=3'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,29 unequal: No Solution Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[74, 26, 90, 19], Operations: [] Exploring Operation: 90-74=16, Resulting Numbers: [26, 19, 16] Generated Node #0,1: 29:[26, 19, 16] Operation: 90-74=16 Moving to Node #0,1 Current State: 29:[26, 19, 16], Operations: ['90-74=16'] Exploring Operation: 19-16=3, Resulting Numbers: [26, 3] Generated Node #0,1,2: 29:[26, 3] Operation: 19-16=3 Moving to Node #0,1,2 Current State: 29:[26, 3], Operations: ['90-74=16', '19-16=3'] Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 50, 25, 66, 90 ]
51
[ "50+25=75", "90-66=24", "75-24=51" ]
Current State: 51:[50, 25, 66, 90], Operations: [] Exploring Operation: 50+25=75, Resulting Numbers: [66, 90, 75] Generated Node #2: [66, 90, 75] from Operation: 50+25=75 Current State: 51:[66, 90, 75], Operations: ['50+25=75'] Exploring Operation: 90-66=24, Resulting Numbers: [75, 24] Generated Node #3: [75, 24] from Operation: 90-66=24 Current State: 51:[75, 24], Operations: ['50+25=75', '90-66=24'] Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[50, 25, 66, 90], Operations: [] Exploring Operation: 90-25=65, Resulting Numbers: [50, 66, 65] Generated Node #0,0: 51:[50, 66, 65] Operation: 90-25=65 Exploring Operation: 66-25=41, Resulting Numbers: [50, 90, 41] Generated Node #0,1: 51:[50, 90, 41] Operation: 66-25=41 Exploring Operation: 90-50=40, Resulting Numbers: [25, 66, 40] Generated Node #0,2: 51:[25, 66, 40] Operation: 90-50=40 Exploring Operation: 90-66=24, Resulting Numbers: [50, 25, 24] Generated Node #0,3: 51:[50, 25, 24] Operation: 90-66=24 Exploring Operation: 66-50=16, Resulting Numbers: [25, 90, 16] Generated Node #0,4: 51:[25, 90, 16] Operation: 66-50=16 Moving to Node #0,3 Current State: 51:[50, 25, 24], Operations: ['90-66=24'] Exploring Operation: 50-25=25, Resulting Numbers: [24, 25] Generated Node #0,3,0: 51:[24, 25] Operation: 50-25=25 Exploring Operation: 50/25=2, Resulting Numbers: [24, 2] Generated Node #0,3,1: 51:[24, 2] Operation: 50/25=2 Exploring Operation: 25+24=49, Resulting Numbers: [50, 49] Generated Node #0,3,2: 51:[50, 49] Operation: 25+24=49 Exploring Operation: 25-24=1, Resulting Numbers: [50, 1] Generated Node #0,3,3: 51:[50, 1] Operation: 25-24=1 Exploring Operation: 50-24=26, Resulting Numbers: [25, 26] Generated Node #0,3,4: 51:[25, 26] Operation: 50-24=26 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 51:[50, 49], Operations: ['90-66=24', '25+24=49'] Exploring Operation: 50*49=2450, Resulting Numbers: [2450] 2450,51 unequal: No Solution Exploring Operation: 50+49=99, Resulting Numbers: [99] 99,51 unequal: No Solution Exploring Operation: 50-49=1, Resulting Numbers: [1] 1,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 51:[50, 1], Operations: ['90-66=24', '25-24=1'] Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[50, 25, 66, 90], Operations: [] Exploring Operation: 90-66=24, Resulting Numbers: [50, 25, 24] Generated Node #0,3: 51:[50, 25, 24] Operation: 90-66=24 Moving to Node #0,3 Current State: 51:[50, 25, 24], Operations: ['90-66=24'] Exploring Operation: 25-24=1, Resulting Numbers: [50, 1] Generated Node #0,3,3: 51:[50, 1] Operation: 25-24=1 Moving to Node #0,3,3 Current State: 51:[50, 1], Operations: ['90-66=24', '25-24=1'] Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 42, 25, 7, 97 ]
87
[ "42-25=17", "7+97=104", "104-17=87" ]
Current State: 87:[42, 25, 7, 97], Operations: [] Exploring Operation: 42-25=17, Resulting Numbers: [7, 97, 17] Generated Node #2: [7, 97, 17] from Operation: 42-25=17 Current State: 87:[7, 97, 17], Operations: ['42-25=17'] Exploring Operation: 7+97=104, Resulting Numbers: [17, 104] Generated Node #3: [17, 104] from Operation: 7+97=104 Current State: 87:[17, 104], Operations: ['42-25=17', '7+97=104'] Exploring Operation: 104-17=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[42, 25, 7, 97], Operations: [] Exploring Operation: 42/7=6, Resulting Numbers: [25, 97, 6] Generated Node #0,0: 87:[25, 97, 6] Operation: 42/7=6 Exploring Operation: 97-7=90, Resulting Numbers: [42, 25, 90] Generated Node #0,1: 87:[42, 25, 90] Operation: 97-7=90 Exploring Operation: 42-7=35, Resulting Numbers: [25, 97, 35] Generated Node #0,2: 87:[25, 97, 35] Operation: 42-7=35 Moving to Node #0,0 Current State: 87:[25, 97, 6], Operations: ['42/7=6'] Exploring Operation: 97-6=91, Resulting Numbers: [25, 91] Generated Node #0,0,0: 87:[25, 91] Operation: 97-6=91 Exploring Operation: 25+6=31, Resulting Numbers: [97, 31] Generated Node #0,0,1: 87:[97, 31] Operation: 25+6=31 Exploring Operation: 97-25=72, Resulting Numbers: [6, 72] Generated Node #0,0,2: 87:[6, 72] Operation: 97-25=72 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[25, 91], Operations: ['42/7=6', '97-6=91'] Exploring Operation: 25+91=116, Resulting Numbers: [116] 116,87 unequal: No Solution Exploring Operation: 25*91=2275, Resulting Numbers: [2275] 2275,87 unequal: No Solution Exploring Operation: 91-25=66, Resulting Numbers: [66] 66,87 unequal: No Solution No 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: 87:[97, 31], Operations: ['42/7=6', '25+6=31'] Exploring Operation: 97+31=128, Resulting Numbers: [128] 128,87 unequal: No Solution Exploring Operation: 97*31=3007, Resulting Numbers: [3007] 3007,87 unequal: No Solution Exploring Operation: 97-31=66, Resulting Numbers: [66] 66,87 unequal: No Solution No 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: 87:[6, 72], Operations: ['42/7=6', '97-25=72'] Exploring Operation: 72-6=66, Resulting Numbers: [66] 66,87 unequal: No Solution Exploring Operation: 6+72=78, Resulting Numbers: [78] 78,87 unequal: No Solution Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,87 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: 87:[42, 25, 90], Operations: ['97-7=90'] Exploring Operation: 42+25=67, Resulting Numbers: [90, 67] Generated Node #0,1,0: 87:[90, 67] Operation: 42+25=67 Exploring Operation: 90-42=48, Resulting Numbers: [25, 48] Generated Node #0,1,1: 87:[25, 48] Operation: 90-42=48 Exploring Operation: 42-25=17, Resulting Numbers: [90, 17] Generated Node #0,1,2: 87:[90, 17] Operation: 42-25=17 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 87:[90, 17], Operations: ['97-7=90', '42-25=17'] Exploring Operation: 90*17=1530, Resulting Numbers: [1530] 1530,87 unequal: No Solution Exploring Operation: 90-17=73, Resulting Numbers: [73] 73,87 unequal: No Solution Exploring Operation: 90+17=107, Resulting Numbers: [107] 107,87 unequal: No Solution No 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: 87:[90, 67], Operations: ['97-7=90', '42+25=67'] Exploring Operation: 90-67=23, Resulting Numbers: [23] 23,87 unequal: No Solution Exploring Operation: 90*67=6030, Resulting Numbers: [6030] 6030,87 unequal: No Solution Exploring Operation: 90+67=157, Resulting Numbers: [157] 157,87 unequal: No Solution No 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: 87:[25, 48], Operations: ['97-7=90', '90-42=48'] Exploring Operation: 25*48=1200, Resulting Numbers: [1200] 1200,87 unequal: No Solution Exploring Operation: 25+48=73, Resulting Numbers: [73] 73,87 unequal: No Solution Exploring Operation: 48-25=23, Resulting Numbers: [23] 23,87 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: 87:[25, 97, 35], Operations: ['42-7=35'] Exploring Operation: 97-35=62, Resulting Numbers: [25, 62] Generated Node #0,2,0: 87:[25, 62] Operation: 97-35=62 Exploring Operation: 35-25=10, Resulting Numbers: [97, 10] Generated Node #0,2,1: 87:[97, 10] Operation: 35-25=10 Exploring Operation: 97-25=72, Resulting Numbers: [35, 72] Generated Node #0,2,2: 87:[35, 72] Operation: 97-25=72 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 87:[97, 10], Operations: ['42-7=35', '35-25=10'] Exploring Operation: 97+10=107, Resulting Numbers: [107] 107,87 unequal: No Solution Exploring Operation: 97*10=970, Resulting Numbers: [970] 970,87 unequal: No Solution Exploring Operation: 97-10=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[42, 25, 7, 97], Operations: [] Exploring Operation: 42-7=35, Resulting Numbers: [25, 97, 35] Generated Node #0,2: 87:[25, 97, 35] Operation: 42-7=35 Moving to Node #0,2 Current State: 87:[25, 97, 35], Operations: ['42-7=35'] Exploring Operation: 35-25=10, Resulting Numbers: [97, 10] Generated Node #0,2,1: 87:[97, 10] Operation: 35-25=10 Moving to Node #0,2,1 Current State: 87:[97, 10], Operations: ['42-7=35', '35-25=10'] Exploring Operation: 97-10=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_3
mult_heuristic
[ 11, 25, 20, 33 ]
72
[ "20-11=9", "33-25=8", "9*8=72" ]
Current State: 72:[11, 25, 20, 33], Operations: [] Exploring Operation: 20-11=9, Resulting Numbers: [25, 33, 9] Generated Node #2: [25, 33, 9] from Operation: 20-11=9 Current State: 72:[25, 33, 9], Operations: ['20-11=9'] Exploring Operation: 33-25=8, Resulting Numbers: [9, 8] Generated Node #3: [9, 8] from Operation: 33-25=8 Current State: 72:[9, 8], Operations: ['20-11=9', '33-25=8'] Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[11, 25, 20, 33], Operations: [] Exploring Operation: 33-25=8, Resulting Numbers: [11, 20, 8] Generated Node #0,0: 72:[11, 20, 8] Operation: 33-25=8 Exploring Operation: 33-20=13, Resulting Numbers: [11, 25, 13] Generated Node #0,1: 72:[11, 25, 13] Operation: 33-20=13 Exploring Operation: 33/11=3, Resulting Numbers: [25, 20, 3] Generated Node #0,2: 72:[25, 20, 3] Operation: 33/11=3 Moving to Node #0,0 Current State: 72:[11, 20, 8], Operations: ['33-25=8'] Exploring Operation: 11-8=3, Resulting Numbers: [20, 3] Generated Node #0,0,0: 72:[20, 3] Operation: 11-8=3 Exploring Operation: 20-8=12, Resulting Numbers: [11, 12] Generated Node #0,0,1: 72:[11, 12] Operation: 20-8=12 Exploring Operation: 20-11=9, Resulting Numbers: [8, 9] Generated Node #0,0,2: 72:[8, 9] Operation: 20-11=9 Moving to Node #0,1 Current State: 72:[11, 25, 13], Operations: ['33-20=13'] Exploring Operation: 11+13=24, Resulting Numbers: [25, 24] Generated Node #0,1,0: 72:[25, 24] Operation: 11+13=24 Exploring Operation: 13-11=2, Resulting Numbers: [25, 2] Generated Node #0,1,1: 72:[25, 2] Operation: 13-11=2 Exploring Operation: 11+25=36, Resulting Numbers: [13, 36] Generated Node #0,1,2: 72:[13, 36] Operation: 11+25=36 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 72:[25, 24], Operations: ['33-20=13', '11+13=24'] Exploring Operation: 25*24=600, Resulting Numbers: [600] 600,72 unequal: No Solution Exploring Operation: 25+24=49, Resulting Numbers: [49] 49,72 unequal: No Solution Exploring Operation: 25-24=1, Resulting Numbers: [1] 1,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 72:[25, 2], Operations: ['33-20=13', '13-11=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,72 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 72:[13, 36], Operations: ['33-20=13', '11+25=36'] Exploring Operation: 13*36=468, Resulting Numbers: [468] 468,72 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,72 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:[25, 20, 3], Operations: ['33/11=3'] Exploring Operation: 20+3=23, Resulting Numbers: [25, 23] Generated Node #0,2,0: 72:[25, 23] Operation: 20+3=23 Exploring Operation: 20-3=17, Resulting Numbers: [25, 17] Generated Node #0,2,1: 72:[25, 17] Operation: 20-3=17 Exploring Operation: 25-20=5, Resulting Numbers: [3, 5] Generated Node #0,2,2: 72:[3, 5] Operation: 25-20=5 Moving to Node #0,0,2 Current State: 72:[8, 9], Operations: ['33-25=8', '20-11=9'] Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[11, 25, 20, 33], Operations: [] Exploring Operation: 33-25=8, Resulting Numbers: [11, 20, 8] Generated Node #0,0: 72:[11, 20, 8] Operation: 33-25=8 Moving to Node #0,0 Current State: 72:[11, 20, 8], Operations: ['33-25=8'] Exploring Operation: 20-11=9, Resulting Numbers: [8, 9] Generated Node #0,0,2: 72:[8, 9] Operation: 20-11=9 Moving to Node #0,0,2 Current State: 72:[8, 9], Operations: ['33-25=8', '20-11=9'] Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.977431
hs_3
mult_heuristic
[ 59, 72, 58, 20 ]
52
[ "59-58=1", "72-20=52", "1*52=52" ]
Current State: 52:[59, 72, 58, 20], Operations: [] Exploring Operation: 59-58=1, Resulting Numbers: [72, 20, 1] Generated Node #2: [72, 20, 1] from Operation: 59-58=1 Current State: 52:[72, 20, 1], Operations: ['59-58=1'] Exploring Operation: 72-20=52, Resulting Numbers: [1, 52] Generated Node #3: [1, 52] from Operation: 72-20=52 Current State: 52:[1, 52], Operations: ['59-58=1', '72-20=52'] Exploring Operation: 1*52=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[59, 72, 58, 20], Operations: [] Exploring Operation: 72-58=14, Resulting Numbers: [59, 20, 14] Generated Node #0,0: 52:[59, 20, 14] Operation: 72-58=14 Exploring Operation: 72-20=52, Resulting Numbers: [59, 58, 52] Generated Node #0,1: 52:[59, 58, 52] Operation: 72-20=52 Exploring Operation: 59-58=1, Resulting Numbers: [72, 20, 1] Generated Node #0,2: 52:[72, 20, 1] Operation: 59-58=1 Exploring Operation: 72-59=13, Resulting Numbers: [58, 20, 13] Generated Node #0,3: 52:[58, 20, 13] Operation: 72-59=13 Moving to Node #0,3 Current State: 52:[58, 20, 13], Operations: ['72-59=13'] Exploring Operation: 58-13=45, Resulting Numbers: [20, 45] Generated Node #0,3,0: 52:[20, 45] Operation: 58-13=45 Exploring Operation: 20-13=7, Resulting Numbers: [58, 7] Generated Node #0,3,1: 52:[58, 7] Operation: 20-13=7 Exploring Operation: 20+13=33, Resulting Numbers: [58, 33] Generated Node #0,3,2: 52:[58, 33] Operation: 20+13=33 Exploring Operation: 58-20=38, Resulting Numbers: [13, 38] Generated Node #0,3,3: 52:[13, 38] Operation: 58-20=38 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 52:[58, 7], Operations: ['72-59=13', '20-13=7'] Exploring Operation: 58+7=65, Resulting Numbers: [65] 65,52 unequal: No Solution Exploring Operation: 58-7=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 58*7=406, Resulting Numbers: [406] 406,52 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:[13, 38], Operations: ['72-59=13', '58-20=38'] Exploring Operation: 13+38=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 13*38=494, Resulting Numbers: [494] 494,52 unequal: No Solution Exploring Operation: 38-13=25, Resulting Numbers: [25] 25,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 52:[20, 45], Operations: ['72-59=13', '58-13=45'] Exploring Operation: 20+45=65, Resulting Numbers: [65] 65,52 unequal: No Solution Exploring Operation: 20*45=900, Resulting Numbers: [900] 900,52 unequal: No Solution Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,52 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:[58, 33], Operations: ['72-59=13', '20+13=33'] Exploring Operation: 58-33=25, Resulting Numbers: [25] 25,52 unequal: No Solution Exploring Operation: 58+33=91, Resulting Numbers: [91] 91,52 unequal: No Solution Exploring Operation: 58*33=1914, Resulting Numbers: [1914] 1914,52 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:[59, 58, 52], Operations: ['72-20=52'] Exploring Operation: 59-52=7, Resulting Numbers: [58, 7] Generated Node #0,1,0: 52:[58, 7] Operation: 59-52=7 Exploring Operation: 59+58=117, Resulting Numbers: [52, 117] Generated Node #0,1,1: 52:[52, 117] Operation: 59+58=117 Exploring Operation: 58-52=6, Resulting Numbers: [59, 6] Generated Node #0,1,2: 52:[59, 6] Operation: 58-52=6 Exploring Operation: 59-58=1, Resulting Numbers: [52, 1] Generated Node #0,1,3: 52:[52, 1] Operation: 59-58=1 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 52:[52, 1], Operations: ['72-20=52', '59-58=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[59, 72, 58, 20], Operations: [] Exploring Operation: 72-20=52, Resulting Numbers: [59, 58, 52] Generated Node #0,1: 52:[59, 58, 52] Operation: 72-20=52 Moving to Node #0,1 Current State: 52:[59, 58, 52], Operations: ['72-20=52'] Exploring Operation: 59-58=1, Resulting Numbers: [52, 1] Generated Node #0,1,3: 52:[52, 1] Operation: 59-58=1 Moving to Node #0,1,3 Current State: 52:[52, 1], Operations: ['72-20=52', '59-58=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic
[ 52, 81, 4, 30 ]
98
[ "52/4=13", "81+30=111", "111-13=98" ]
Current State: 98:[52, 81, 4, 30], Operations: [] Exploring Operation: 52/4=13, Resulting Numbers: [81, 30, 13] Generated Node #2: [81, 30, 13] from Operation: 52/4=13 Current State: 98:[81, 30, 13], Operations: ['52/4=13'] Exploring Operation: 81+30=111, Resulting Numbers: [13, 111] Generated Node #3: [13, 111] from Operation: 81+30=111 Current State: 98:[13, 111], Operations: ['52/4=13', '81+30=111'] Exploring Operation: 111-13=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[52, 81, 4, 30], Operations: [] Exploring Operation: 81+30=111, Resulting Numbers: [52, 4, 111] Generated Node #0,0: 98:[52, 4, 111] Operation: 81+30=111 Exploring Operation: 81-30=51, Resulting Numbers: [52, 4, 51] Generated Node #0,1: 98:[52, 4, 51] Operation: 81-30=51 Exploring Operation: 52-30=22, Resulting Numbers: [81, 4, 22] Generated Node #0,2: 98:[81, 4, 22] Operation: 52-30=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[52, 4, 51], Operations: ['81-30=51'] Exploring Operation: 52/4=13, Resulting Numbers: [51, 13] Generated Node #0,1,0: 98:[51, 13] Operation: 52/4=13 Exploring Operation: 52-51=1, Resulting Numbers: [4, 1] Generated Node #0,1,1: 98:[4, 1] Operation: 52-51=1 Exploring Operation: 52-4=48, Resulting Numbers: [51, 48] Generated Node #0,1,2: 98:[51, 48] Operation: 52-4=48 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 98:[51, 13], Operations: ['81-30=51', '52/4=13'] Exploring Operation: 51-13=38, Resulting Numbers: [38] 38,98 unequal: No Solution Exploring Operation: 51*13=663, Resulting Numbers: [663] 663,98 unequal: No Solution Exploring Operation: 51+13=64, Resulting Numbers: [64] 64,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 98:[4, 1], Operations: ['81-30=51', '52-51=1'] Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,98 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 98:[51, 48], Operations: ['81-30=51', '52-4=48'] Exploring Operation: 51*48=2448, Resulting Numbers: [2448] 2448,98 unequal: No Solution Exploring Operation: 51+48=99, Resulting Numbers: [99] 99,98 unequal: No Solution Exploring Operation: 51-48=3, Resulting Numbers: [3] 3,98 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: 98:[52, 4, 111], Operations: ['81+30=111'] Exploring Operation: 111-4=107, Resulting Numbers: [52, 107] Generated Node #0,0,0: 98:[52, 107] Operation: 111-4=107 Exploring Operation: 52-4=48, Resulting Numbers: [111, 48] Generated Node #0,0,1: 98:[111, 48] Operation: 52-4=48 Exploring Operation: 111-52=59, Resulting Numbers: [4, 59] Generated Node #0,0,2: 98:[4, 59] Operation: 111-52=59 Moving to Node #0,0,0 Current State: 98:[52, 107], Operations: ['81+30=111', '111-4=107'] Exploring Operation: 52+107=159, Resulting Numbers: [159] 159,98 unequal: No Solution Exploring Operation: 52*107=5564, Resulting Numbers: [5564] 5564,98 unequal: No Solution Exploring Operation: 107-52=55, Resulting Numbers: [55] 55,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[4, 59], Operations: ['81+30=111', '111-52=59'] Exploring Operation: 4*59=236, Resulting Numbers: [236] 236,98 unequal: No Solution Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,98 unequal: No Solution Exploring Operation: 4+59=63, Resulting Numbers: [63] 63,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[111, 48], Operations: ['81+30=111', '52-4=48'] Exploring Operation: 111+48=159, Resulting Numbers: [159] 159,98 unequal: No Solution Exploring Operation: 111-48=63, Resulting Numbers: [63] 63,98 unequal: No Solution Exploring Operation: 111*48=5328, Resulting Numbers: [5328] 5328,98 unequal: No Solution No 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: 98:[81, 4, 22], Operations: ['52-30=22'] Exploring Operation: 81+22=103, Resulting Numbers: [4, 103] Generated Node #0,2,0: 98:[4, 103] Operation: 81+22=103 Exploring Operation: 81+4=85, Resulting Numbers: [22, 85] Generated Node #0,2,1: 98:[22, 85] Operation: 81+4=85 Exploring Operation: 81-22=59, Resulting Numbers: [4, 59] Generated Node #0,2,2: 98:[4, 59] Operation: 81-22=59 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 98:[4, 103], Operations: ['52-30=22', '81+22=103'] Exploring Operation: 103-4=99, Resulting Numbers: [99] 99,98 unequal: No Solution Exploring Operation: 4+103=107, Resulting Numbers: [107] 107,98 unequal: No Solution Exploring Operation: 4*103=412, Resulting Numbers: [412] 412,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 98:[4, 59], Operations: ['52-30=22', '81-22=59'] Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,98 unequal: No Solution Exploring Operation: 4*59=236, Resulting Numbers: [236] 236,98 unequal: No Solution Exploring Operation: 4+59=63, Resulting Numbers: [63] 63,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 98:[22, 85], Operations: ['52-30=22', '81+4=85'] Exploring Operation: 85-22=63, Resulting Numbers: [63] 63,98 unequal: No Solution Exploring Operation: 22*85=1870, Resulting Numbers: [1870] 1870,98 unequal: No Solution Exploring Operation: 22+85=107, Resulting Numbers: [107] 107,98 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
[ 1, 26, 55, 42 ]
72
[ "26-1=25", "55+42=97", "97-25=72" ]
Current State: 72:[1, 26, 55, 42], Operations: [] Exploring Operation: 26-1=25, Resulting Numbers: [55, 42, 25] Generated Node #2: [55, 42, 25] from Operation: 26-1=25 Current State: 72:[55, 42, 25], Operations: ['26-1=25'] Exploring Operation: 55+42=97, Resulting Numbers: [25, 97] Generated Node #3: [25, 97] from Operation: 55+42=97 Current State: 72:[25, 97], Operations: ['26-1=25', '55+42=97'] Exploring Operation: 97-25=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[1, 26, 55, 42], Operations: [] Exploring Operation: 55-26=29, Resulting Numbers: [1, 42, 29] Generated Node #0,0: 72:[1, 42, 29] Operation: 55-26=29 Exploring Operation: 26+55=81, Resulting Numbers: [1, 42, 81] Generated Node #0,1: 72:[1, 42, 81] Operation: 26+55=81 Exploring Operation: 55-42=13, Resulting Numbers: [1, 26, 13] Generated Node #0,2: 72:[1, 26, 13] Operation: 55-42=13 Exploring Operation: 42-26=16, Resulting Numbers: [1, 55, 16] Generated Node #0,3: 72:[1, 55, 16] Operation: 42-26=16 Moving to Node #0,2 Current State: 72:[1, 26, 13], Operations: ['55-42=13'] Exploring Operation: 26-13=13, Resulting Numbers: [1, 13] Generated Node #0,2,0: 72:[1, 13] Operation: 26-13=13 Exploring Operation: 13-1=12, Resulting Numbers: [26, 12] Generated Node #0,2,1: 72:[26, 12] Operation: 13-1=12 Exploring Operation: 26/13=2, Resulting Numbers: [1, 2] Generated Node #0,2,2: 72:[1, 2] Operation: 26/13=2 Exploring Operation: 26-1=25, Resulting Numbers: [13, 25] Generated Node #0,2,3: 72:[13, 25] Operation: 26-1=25 Moving to Node #0,0 Current State: 72:[1, 42, 29], Operations: ['55-26=29'] Exploring Operation: 29-1=28, Resulting Numbers: [42, 28] Generated Node #0,0,0: 72:[42, 28] Operation: 29-1=28 Exploring Operation: 42+29=71, Resulting Numbers: [1, 71] Generated Node #0,0,1: 72:[1, 71] Operation: 42+29=71 Exploring Operation: 42-29=13, Resulting Numbers: [1, 13] Generated Node #0,0,2: 72:[1, 13] Operation: 42-29=13 Exploring Operation: 42-1=41, Resulting Numbers: [29, 41] Generated Node #0,0,3: 72:[29, 41] Operation: 42-1=41 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[1, 71], Operations: ['55-26=29', '42+29=71'] Exploring Operation: 71-1=70, Resulting Numbers: [70] 70,72 unequal: No Solution Exploring Operation: 1*71=71, Resulting Numbers: [71] 71,72 unequal: No Solution Exploring Operation: 71/1=71, Resulting Numbers: [71] 71,72 unequal: No Solution Exploring Operation: 1+71=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[1, 26, 55, 42], Operations: [] Exploring Operation: 55-26=29, Resulting Numbers: [1, 42, 29] Generated Node #0,0: 72:[1, 42, 29] Operation: 55-26=29 Moving to Node #0,0 Current State: 72:[1, 42, 29], Operations: ['55-26=29'] Exploring Operation: 42+29=71, Resulting Numbers: [1, 71] Generated Node #0,0,1: 72:[1, 71] Operation: 42+29=71 Moving to Node #0,0,1 Current State: 72:[1, 71], Operations: ['55-26=29', '42+29=71'] Exploring Operation: 1+71=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 81, 98, 21, 41 ]
37
[ "98-81=17", "41-21=20", "17+20=37" ]
Current State: 37:[81, 98, 21, 41], Operations: [] Exploring Operation: 98-81=17, Resulting Numbers: [21, 41, 17] Generated Node #2: [21, 41, 17] from Operation: 98-81=17 Current State: 37:[21, 41, 17], Operations: ['98-81=17'] Exploring Operation: 41-21=20, Resulting Numbers: [17, 20] Generated Node #3: [17, 20] from Operation: 41-21=20 Current State: 37:[17, 20], Operations: ['98-81=17', '41-21=20'] Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[81, 98, 21, 41], Operations: [] Exploring Operation: 98-81=17, Resulting Numbers: [21, 41, 17] Generated Node #0,0: 37:[21, 41, 17] Operation: 98-81=17 Exploring Operation: 81-41=40, Resulting Numbers: [98, 21, 40] Generated Node #0,1: 37:[98, 21, 40] Operation: 81-41=40 Exploring Operation: 98-41=57, Resulting Numbers: [81, 21, 57] Generated Node #0,2: 37:[81, 21, 57] Operation: 98-41=57 Moving to Node #0,0 Current State: 37:[21, 41, 17], Operations: ['98-81=17'] Exploring Operation: 41-17=24, Resulting Numbers: [21, 24] Generated Node #0,0,0: 37:[21, 24] Operation: 41-17=24 Exploring Operation: 41-21=20, Resulting Numbers: [17, 20] Generated Node #0,0,1: 37:[17, 20] Operation: 41-21=20 Exploring Operation: 21+17=38, Resulting Numbers: [41, 38] Generated Node #0,0,2: 37:[41, 38] Operation: 21+17=38 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 37:[41, 38], Operations: ['98-81=17', '21+17=38'] Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,37 unequal: No Solution Exploring Operation: 41+38=79, Resulting Numbers: [79] 79,37 unequal: No Solution Exploring Operation: 41*38=1558, Resulting Numbers: [1558] 1558,37 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 #0,0,0 Current State: 37:[21, 24], Operations: ['98-81=17', '41-17=24'] Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,37 unequal: No Solution Exploring Operation: 21*24=504, Resulting Numbers: [504] 504,37 unequal: No Solution Exploring Operation: 21+24=45, Resulting Numbers: [45] 45,37 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 #0,0,1 Current State: 37:[17, 20], Operations: ['98-81=17', '41-21=20'] Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,37 unequal: No Solution Exploring Operation: 17*20=340, Resulting Numbers: [340] 340,37 unequal: No Solution Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[81, 98, 21, 41], Operations: [] Exploring Operation: 98-81=17, Resulting Numbers: [21, 41, 17] Generated Node #0,0: 37:[21, 41, 17] Operation: 98-81=17 Moving to Node #0,0 Current State: 37:[21, 41, 17], Operations: ['98-81=17'] Exploring Operation: 41-21=20, Resulting Numbers: [17, 20] Generated Node #0,0,1: 37:[17, 20] Operation: 41-21=20 Moving to Node #0,0,1 Current State: 37:[17, 20], Operations: ['98-81=17', '41-21=20'] Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
mult_heuristic
[ 46, 29, 22, 6 ]
59
[ "46+29=75", "22-6=16", "75-16=59" ]
Current State: 59:[46, 29, 22, 6], Operations: [] Exploring Operation: 46+29=75, Resulting Numbers: [22, 6, 75] Generated Node #2: [22, 6, 75] from Operation: 46+29=75 Current State: 59:[22, 6, 75], Operations: ['46+29=75'] Exploring Operation: 22-6=16, Resulting Numbers: [75, 16] Generated Node #3: [75, 16] from Operation: 22-6=16 Current State: 59:[75, 16], Operations: ['46+29=75', '22-6=16'] Exploring Operation: 75-16=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[46, 29, 22, 6], Operations: [] Exploring Operation: 46+6=52, Resulting Numbers: [29, 22, 52] Generated Node #0,0: 59:[29, 22, 52] Operation: 46+6=52 Exploring Operation: 29+22=51, Resulting Numbers: [46, 6, 51] Generated Node #0,1: 59:[46, 6, 51] Operation: 29+22=51 Exploring Operation: 29+6=35, Resulting Numbers: [46, 22, 35] Generated Node #0,2: 59:[46, 22, 35] Operation: 29+6=35 Moving to Node #0,0 Current State: 59:[29, 22, 52], Operations: ['46+6=52'] Exploring Operation: 22+52=74, Resulting Numbers: [29, 74] Generated Node #0,0,0: 59:[29, 74] Operation: 22+52=74 Exploring Operation: 29+22=51, Resulting Numbers: [52, 51] Generated Node #0,0,1: 59:[52, 51] Operation: 29+22=51 Exploring Operation: 29-22=7, Resulting Numbers: [52, 7] Generated Node #0,0,2: 59:[52, 7] Operation: 29-22=7 Moving to Node #0,1 Current State: 59:[46, 6, 51], Operations: ['29+22=51'] Exploring Operation: 6+51=57, Resulting Numbers: [46, 57] Generated Node #0,1,0: 59:[46, 57] Operation: 6+51=57 Exploring Operation: 46+6=52, Resulting Numbers: [51, 52] Generated Node #0,1,1: 59:[51, 52] Operation: 46+6=52 Exploring Operation: 46-6=40, Resulting Numbers: [51, 40] Generated Node #0,1,2: 59:[51, 40] Operation: 46-6=40 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[46, 57], Operations: ['29+22=51', '6+51=57'] Exploring Operation: 46+57=103, Resulting Numbers: [103] 103,59 unequal: No Solution Exploring Operation: 57-46=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 46*57=2622, Resulting Numbers: [2622] 2622,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[51, 52], Operations: ['29+22=51', '46+6=52'] Exploring Operation: 51*52=2652, Resulting Numbers: [2652] 2652,59 unequal: No Solution Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 51+52=103, Resulting Numbers: [103] 103,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[51, 40], Operations: ['29+22=51', '46-6=40'] Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 51+40=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 51*40=2040, Resulting Numbers: [2040] 2040,59 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: 59:[46, 22, 35], Operations: ['29+6=35'] Exploring Operation: 46+22=68, Resulting Numbers: [35, 68] Generated Node #0,2,0: 59:[35, 68] Operation: 46+22=68 Exploring Operation: 22+35=57, Resulting Numbers: [46, 57] Generated Node #0,2,1: 59:[46, 57] Operation: 22+35=57 Exploring Operation: 46-22=24, Resulting Numbers: [35, 24] Generated Node #0,2,2: 59:[35, 24] Operation: 46-22=24 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[46, 57], Operations: ['29+6=35', '22+35=57'] Exploring Operation: 46*57=2622, Resulting Numbers: [2622] 2622,59 unequal: No Solution Exploring Operation: 57-46=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 46+57=103, Resulting Numbers: [103] 103,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[35, 68], Operations: ['29+6=35', '46+22=68'] Exploring Operation: 35+68=103, Resulting Numbers: [103] 103,59 unequal: No Solution Exploring Operation: 68-35=33, Resulting Numbers: [33] 33,59 unequal: No Solution Exploring Operation: 35*68=2380, Resulting Numbers: [2380] 2380,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[35, 24], Operations: ['29+6=35', '46-22=24'] Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[46, 29, 22, 6], Operations: [] Exploring Operation: 29+6=35, Resulting Numbers: [46, 22, 35] Generated Node #0,2: 59:[46, 22, 35] Operation: 29+6=35 Moving to Node #0,2 Current State: 59:[46, 22, 35], Operations: ['29+6=35'] Exploring Operation: 46-22=24, Resulting Numbers: [35, 24] Generated Node #0,2,2: 59:[35, 24] Operation: 46-22=24 Moving to Node #0,2,2 Current State: 59:[35, 24], Operations: ['29+6=35', '46-22=24'] Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_3
mult_heuristic
[ 69, 72, 31, 60 ]
51
[ "72-69=3", "60/3=20", "31+20=51" ]
Current State: 51:[69, 72, 31, 60], Operations: [] Exploring Operation: 72-69=3, Resulting Numbers: [31, 60, 3] Generated Node #2: [31, 60, 3] from Operation: 72-69=3 Current State: 51:[31, 60, 3], Operations: ['72-69=3'] Exploring Operation: 60/3=20, Resulting Numbers: [31, 20] Generated Node #3: [31, 20] from Operation: 60/3=20 Current State: 51:[31, 20], Operations: ['72-69=3', '60/3=20'] Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[69, 72, 31, 60], Operations: [] Exploring Operation: 72-69=3, Resulting Numbers: [31, 60, 3] Generated Node #0,0: 51:[31, 60, 3] Operation: 72-69=3 Exploring Operation: 72-31=41, Resulting Numbers: [69, 60, 41] Generated Node #0,1: 51:[69, 60, 41] Operation: 72-31=41 Exploring Operation: 72-60=12, Resulting Numbers: [69, 31, 12] Generated Node #0,2: 51:[69, 31, 12] Operation: 72-60=12 Moving to Node #0,0 Current State: 51:[31, 60, 3], Operations: ['72-69=3'] Exploring Operation: 60/3=20, Resulting Numbers: [31, 20] Generated Node #0,0,0: 51:[31, 20] Operation: 60/3=20 Exploring Operation: 60-31=29, Resulting Numbers: [3, 29] Generated Node #0,0,1: 51:[3, 29] Operation: 60-31=29 Exploring Operation: 31-3=28, Resulting Numbers: [60, 28] Generated Node #0,0,2: 51:[60, 28] Operation: 31-3=28 Moving to Node #0,1 Current State: 51:[69, 60, 41], Operations: ['72-31=41'] Exploring Operation: 60-41=19, Resulting Numbers: [69, 19] Generated Node #0,1,0: 51:[69, 19] Operation: 60-41=19 Exploring Operation: 69-60=9, Resulting Numbers: [41, 9] Generated Node #0,1,1: 51:[41, 9] Operation: 69-60=9 Exploring Operation: 69-41=28, Resulting Numbers: [60, 28] Generated Node #0,1,2: 51:[60, 28] Operation: 69-41=28 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 51:[41, 9], Operations: ['72-31=41', '69-60=9'] Exploring Operation: 41*9=369, Resulting Numbers: [369] 369,51 unequal: No Solution Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,51 unequal: No Solution Exploring Operation: 41+9=50, Resulting Numbers: [50] 50,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 51:[69, 19], Operations: ['72-31=41', '60-41=19'] Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 69*19=1311, Resulting Numbers: [1311] 1311,51 unequal: No Solution Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 51:[60, 28], Operations: ['72-31=41', '69-41=28'] Exploring Operation: 60*28=1680, Resulting Numbers: [1680] 1680,51 unequal: No Solution Exploring Operation: 60+28=88, Resulting Numbers: [88] 88,51 unequal: No Solution Exploring Operation: 60-28=32, Resulting Numbers: [32] 32,51 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: 51:[69, 31, 12], Operations: ['72-60=12'] Exploring Operation: 69-31=38, Resulting Numbers: [12, 38] Generated Node #0,2,0: 51:[12, 38] Operation: 69-31=38 Exploring Operation: 31-12=19, Resulting Numbers: [69, 19] Generated Node #0,2,1: 51:[69, 19] Operation: 31-12=19 Exploring Operation: 69-12=57, Resulting Numbers: [31, 57] Generated Node #0,2,2: 51:[31, 57] Operation: 69-12=57 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 51:[12, 38], Operations: ['72-60=12', '69-31=38'] Exploring Operation: 38-12=26, Resulting Numbers: [26] 26,51 unequal: No Solution Exploring Operation: 12*38=456, Resulting Numbers: [456] 456,51 unequal: No Solution Exploring Operation: 12+38=50, Resulting Numbers: [50] 50,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 51:[69, 19], Operations: ['72-60=12', '31-12=19'] Exploring Operation: 69*19=1311, Resulting Numbers: [1311] 1311,51 unequal: No Solution Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 51:[31, 57], Operations: ['72-60=12', '69-12=57'] Exploring Operation: 57-31=26, Resulting Numbers: [26] 26,51 unequal: No Solution Exploring Operation: 31+57=88, Resulting Numbers: [88] 88,51 unequal: No Solution Exploring Operation: 31*57=1767, Resulting Numbers: [1767] 1767,51 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: 51:[3, 29], Operations: ['72-69=3', '60-31=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,51 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,51 unequal: No Solution Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[31, 20], Operations: ['72-69=3', '60/3=20'] Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[69, 72, 31, 60], Operations: [] Exploring Operation: 72-69=3, Resulting Numbers: [31, 60, 3] Generated Node #0,0: 51:[31, 60, 3] Operation: 72-69=3 Moving to Node #0,0 Current State: 51:[31, 60, 3], Operations: ['72-69=3'] Exploring Operation: 60/3=20, Resulting Numbers: [31, 20] Generated Node #0,0,0: 51:[31, 20] Operation: 60/3=20 Moving to Node #0,0,0 Current State: 51:[31, 20], Operations: ['72-69=3', '60/3=20'] Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
0.967014
hs_3
mult_heuristic
[ 68, 82, 18, 20 ]
71
[ "68*20=1360", "1360-82=1278", "1278/18=71" ]
Current State: 71:[68, 82, 18, 20], Operations: [] Exploring Operation: 68*20=1360, Resulting Numbers: [82, 18, 1360] Generated Node #2: [82, 18, 1360] from Operation: 68*20=1360 Current State: 71:[82, 18, 1360], Operations: ['68*20=1360'] Exploring Operation: 1360-82=1278, Resulting Numbers: [18, 1278] Generated Node #3: [18, 1278] from Operation: 1360-82=1278 Current State: 71:[18, 1278], Operations: ['68*20=1360', '1360-82=1278'] Exploring Operation: 1278/18=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[68, 82, 18, 20], Operations: [] Exploring Operation: 82-18=64, Resulting Numbers: [68, 20, 64] Generated Node #0,0: 71:[68, 20, 64] Operation: 82-18=64 Exploring Operation: 18+20=38, Resulting Numbers: [68, 82, 38] Generated Node #0,1: 71:[68, 82, 38] Operation: 18+20=38 Exploring Operation: 82-20=62, Resulting Numbers: [68, 18, 62] Generated Node #0,2: 71:[68, 18, 62] Operation: 82-20=62 Moving to Node #0,1 Current State: 71:[68, 82, 38], Operations: ['18+20=38'] Exploring Operation: 68+38=106, Resulting Numbers: [82, 106] Generated Node #0,1,0: 71:[82, 106] Operation: 68+38=106 Exploring Operation: 82-38=44, Resulting Numbers: [68, 44] Generated Node #0,1,1: 71:[68, 44] Operation: 82-38=44 Exploring Operation: 68-38=30, Resulting Numbers: [82, 30] Generated Node #0,1,2: 71:[82, 30] Operation: 68-38=30 Moving to Node #0,0 Current State: 71:[68, 20, 64], Operations: ['82-18=64'] Exploring Operation: 68+20=88, Resulting Numbers: [64, 88] Generated Node #0,0,0: 71:[64, 88] Operation: 68+20=88 Exploring Operation: 68-20=48, Resulting Numbers: [64, 48] Generated Node #0,0,1: 71:[64, 48] Operation: 68-20=48 Exploring Operation: 20+64=84, Resulting Numbers: [68, 84] Generated Node #0,0,2: 71:[68, 84] Operation: 20+64=84 Moving to Node #0,2 Current State: 71:[68, 18, 62], Operations: ['82-20=62'] Exploring Operation: 68+18=86, Resulting Numbers: [62, 86] Generated Node #0,2,0: 71:[62, 86] Operation: 68+18=86 Exploring Operation: 68-18=50, Resulting Numbers: [62, 50] Generated Node #0,2,1: 71:[62, 50] Operation: 68-18=50 Exploring Operation: 18+62=80, Resulting Numbers: [68, 80] Generated Node #0,2,2: 71:[68, 80] Operation: 18+62=80 Moving to Node #0,2,2 Current State: 71:[68, 80], Operations: ['82-20=62', '18+62=80'] Exploring Operation: 68*80=5440, Resulting Numbers: [5440] 5440,71 unequal: No Solution Exploring Operation: 68+80=148, Resulting Numbers: [148] 148,71 unequal: No Solution Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[68, 84], Operations: ['82-18=64', '20+64=84'] Exploring Operation: 68*84=5712, Resulting Numbers: [5712] 5712,71 unequal: No Solution Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,71 unequal: No Solution Exploring Operation: 68+84=152, Resulting Numbers: [152] 152,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[64, 88], Operations: ['82-18=64', '68+20=88'] Exploring Operation: 64*88=5632, Resulting Numbers: [5632] 5632,71 unequal: No Solution Exploring Operation: 88-64=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 64+88=152, Resulting Numbers: [152] 152,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[62, 86], Operations: ['82-20=62', '68+18=86'] Exploring Operation: 86-62=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 62*86=5332, Resulting Numbers: [5332] 5332,71 unequal: No Solution Exploring Operation: 62+86=148, Resulting Numbers: [148] 148,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[64, 48], Operations: ['82-18=64', '68-20=48'] Exploring Operation: 64-48=16, Resulting Numbers: [16] 16,71 unequal: No Solution Exploring Operation: 64*48=3072, Resulting Numbers: [3072] 3072,71 unequal: No Solution Exploring Operation: 64+48=112, Resulting Numbers: [112] 112,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[68, 44], Operations: ['18+20=38', '82-38=44'] Exploring Operation: 68+44=112, Resulting Numbers: [112] 112,71 unequal: No Solution Exploring Operation: 68-44=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 68*44=2992, Resulting Numbers: [2992] 2992,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[62, 50], Operations: ['82-20=62', '68-18=50'] Exploring Operation: 62-50=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 62+50=112, Resulting Numbers: [112] 112,71 unequal: No Solution Exploring Operation: 62*50=3100, Resulting Numbers: [3100] 3100,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[82, 106], Operations: ['18+20=38', '68+38=106'] Exploring Operation: 82+106=188, Resulting Numbers: [188] 188,71 unequal: No Solution Exploring Operation: 82*106=8692, Resulting Numbers: [8692] 8692,71 unequal: No Solution Exploring Operation: 106-82=24, Resulting Numbers: [24] 24,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[82, 30], Operations: ['18+20=38', '68-38=30'] Exploring Operation: 82+30=112, Resulting Numbers: [112] 112,71 unequal: No Solution Exploring Operation: 82-30=52, Resulting Numbers: [52] 52,71 unequal: No Solution Exploring Operation: 82*30=2460, Resulting Numbers: [2460] 2460,71 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 64, 69, 30, 3 ]
45
[ "69-64=5", "3*5=15", "30+15=45" ]
Current State: 45:[64, 69, 30, 3], Operations: [] Exploring Operation: 69-64=5, Resulting Numbers: [30, 3, 5] Generated Node #2: [30, 3, 5] from Operation: 69-64=5 Current State: 45:[30, 3, 5], Operations: ['69-64=5'] Exploring Operation: 3*5=15, Resulting Numbers: [30, 15] Generated Node #3: [30, 15] from Operation: 3*5=15 Current State: 45:[30, 15], Operations: ['69-64=5', '3*5=15'] Exploring Operation: 30+15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[64, 69, 30, 3], Operations: [] Exploring Operation: 69-64=5, Resulting Numbers: [30, 3, 5] Generated Node #0,0: 45:[30, 3, 5] Operation: 69-64=5 Exploring Operation: 64-30=34, Resulting Numbers: [69, 3, 34] Generated Node #0,1: 45:[69, 3, 34] Operation: 64-30=34 Exploring Operation: 69-30=39, Resulting Numbers: [64, 3, 39] Generated Node #0,2: 45:[64, 3, 39] Operation: 69-30=39 Exploring Operation: 69/3=23, Resulting Numbers: [64, 30, 23] Generated Node #0,3: 45:[64, 30, 23] Operation: 69/3=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[30, 3, 5], Operations: ['69-64=5'] Exploring Operation: 30+5=35, Resulting Numbers: [3, 35] Generated Node #0,0,0: 45:[3, 35] Operation: 30+5=35 Exploring Operation: 30/5=6, Resulting Numbers: [3, 6] Generated Node #0,0,1: 45:[3, 6] Operation: 30/5=6 Exploring Operation: 30-5=25, Resulting Numbers: [3, 25] Generated Node #0,0,2: 45:[3, 25] Operation: 30-5=25 Exploring Operation: 30/3=10, Resulting Numbers: [5, 10] Generated Node #0,0,3: 45:[5, 10] Operation: 30/3=10 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 45:[3, 6], Operations: ['69-64=5', '30/5=6'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,45 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,45 unequal: No Solution No 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: 45:[5, 10], Operations: ['69-64=5', '30/3=10'] Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,45 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,45 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,45 unequal: No Solution No 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: 45:[3, 35], Operations: ['69-64=5', '30+5=35'] Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,45 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,45 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,45 unequal: No Solution No 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: 45:[3, 25], Operations: ['69-64=5', '30-5=25'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,45 unequal: No Solution Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 45:[64, 3, 39], Operations: ['69-30=39'] Exploring Operation: 3+39=42, Resulting Numbers: [64, 42] Generated Node #0,2,0: 45:[64, 42] Operation: 3+39=42 Exploring Operation: 39/3=13, Resulting Numbers: [64, 13] Generated Node #0,2,1: 45:[64, 13] Operation: 39/3=13 Exploring Operation: 64-3=61, Resulting Numbers: [39, 61] Generated Node #0,2,2: 45:[39, 61] Operation: 64-3=61 Exploring Operation: 64-39=25, Resulting Numbers: [3, 25] Generated Node #0,2,3: 45:[3, 25] Operation: 64-39=25 Moving to Node #0,2,3 Current State: 45:[3, 25], Operations: ['69-30=39', '64-39=25'] Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,45 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,45 unequal: No Solution Moving to Node #0,2,1 Current State: 45:[64, 13], Operations: ['69-30=39', '39/3=13'] Exploring Operation: 64+13=77, Resulting Numbers: [77] 77,45 unequal: No Solution Exploring Operation: 64*13=832, Resulting Numbers: [832] 832,45 unequal: No Solution Exploring Operation: 64-13=51, Resulting Numbers: [51] 51,45 unequal: No Solution Moving to Node #0,2,2 Current State: 45:[39, 61], Operations: ['69-30=39', '64-3=61'] Exploring Operation: 61-39=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 39*61=2379, Resulting Numbers: [2379] 2379,45 unequal: No Solution Exploring Operation: 39+61=100, Resulting Numbers: [100] 100,45 unequal: No Solution Moving to Node #0,2,0 Current State: 45:[64, 42], Operations: ['69-30=39', '3+39=42'] Exploring Operation: 64+42=106, Resulting Numbers: [106] 106,45 unequal: No Solution Exploring Operation: 64*42=2688, Resulting Numbers: [2688] 2688,45 unequal: No Solution Exploring Operation: 64-42=22, Resulting Numbers: [22] 22,45 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 #0,1 Current State: 45:[69, 3, 34], Operations: ['64-30=34'] Exploring Operation: 69-34=35, Resulting Numbers: [3, 35] Generated Node #0,1,0: 45:[3, 35] Operation: 69-34=35 Exploring Operation: 69-3=66, Resulting Numbers: [34, 66] Generated Node #0,1,1: 45:[34, 66] Operation: 69-3=66 Exploring Operation: 69/3=23, Resulting Numbers: [34, 23] Generated Node #0,1,2: 45:[34, 23] Operation: 69/3=23 Exploring Operation: 3+34=37, Resulting Numbers: [69, 37] Generated Node #0,1,3: 45:[69, 37] Operation: 3+34=37 Moving to Node #0,1,0 Current State: 45:[3, 35], Operations: ['64-30=34', '69-34=35'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,45 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,45 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,45 unequal: No Solution Moving to Node #0,1,2 Current State: 45:[34, 23], Operations: ['64-30=34', '69/3=23'] Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,45 unequal: No Solution Exploring Operation: 34+23=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 34*23=782, Resulting Numbers: [782] 782,45 unequal: No Solution Moving to Node #0,1,3 Current State: 45:[69, 37], Operations: ['64-30=34', '3+34=37'] Exploring Operation: 69*37=2553, Resulting Numbers: [2553] 2553,45 unequal: No Solution Exploring Operation: 69+37=106, Resulting Numbers: [106] 106,45 unequal: No Solution Exploring Operation: 69-37=32, Resulting Numbers: [32] 32,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[34, 66], Operations: ['64-30=34', '69-3=66'] Exploring Operation: 34+66=100, Resulting Numbers: [100] 100,45 unequal: No Solution Exploring Operation: 66-34=32, Resulting Numbers: [32] 32,45 unequal: No Solution Exploring Operation: 34*66=2244, Resulting Numbers: [2244] 2244,45 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 Current State: 45:[64, 30, 23], Operations: ['69/3=23'] Exploring Operation: 30-23=7, Resulting Numbers: [64, 7] Generated Node #0,3,0: 45:[64, 7] Operation: 30-23=7 Exploring Operation: 64-30=34, Resulting Numbers: [23, 34] Generated Node #0,3,1: 45:[23, 34] Operation: 64-30=34 Exploring Operation: 30+23=53, Resulting Numbers: [64, 53] Generated Node #0,3,2: 45:[64, 53] Operation: 30+23=53 Exploring Operation: 64-23=41, Resulting Numbers: [30, 41] Generated Node #0,3,3: 45:[30, 41] Operation: 64-23=41 Moving to Node #0,3,1 Current State: 45:[23, 34], Operations: ['69/3=23', '64-30=34'] Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,45 unequal: No Solution Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 23*34=782, Resulting Numbers: [782] 782,45 unequal: No Solution Moving to Node #0,3,3 Current State: 45:[30, 41], Operations: ['69/3=23', '64-23=41'] Exploring Operation: 30+41=71, Resulting Numbers: [71] 71,45 unequal: No Solution Exploring Operation: 41-30=11, Resulting Numbers: [11] 11,45 unequal: No Solution Exploring Operation: 30*41=1230, Resulting Numbers: [1230] 1230,45 unequal: No Solution Moving to Node #0,3,0 Current State: 45:[64, 7], Operations: ['69/3=23', '30-23=7'] Exploring Operation: 64+7=71, Resulting Numbers: [71] 71,45 unequal: No Solution Exploring Operation: 64*7=448, Resulting Numbers: [448] 448,45 unequal: No Solution Exploring Operation: 64-7=57, Resulting Numbers: [57] 57,45 unequal: No Solution Moving to Node #0,3,2 Current State: 45:[64, 53], Operations: ['69/3=23', '30+23=53'] Exploring Operation: 64+53=117, Resulting Numbers: [117] 117,45 unequal: No Solution Exploring Operation: 64*53=3392, Resulting Numbers: [3392] 3392,45 unequal: No Solution Exploring Operation: 64-53=11, Resulting Numbers: [11] 11,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 23, 25, 22, 47 ]
91
[ "25-23=2", "22*2=44", "47+44=91" ]
Current State: 91:[23, 25, 22, 47], Operations: [] Exploring Operation: 25-23=2, Resulting Numbers: [22, 47, 2] Generated Node #2: [22, 47, 2] from Operation: 25-23=2 Current State: 91:[22, 47, 2], Operations: ['25-23=2'] Exploring Operation: 22*2=44, Resulting Numbers: [47, 44] Generated Node #3: [47, 44] from Operation: 22*2=44 Current State: 91:[47, 44], Operations: ['25-23=2', '22*2=44'] Exploring Operation: 47+44=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[23, 25, 22, 47], Operations: [] Exploring Operation: 47-22=25, Resulting Numbers: [23, 25, 25] Generated Node #0,0: 91:[23, 25, 25] Operation: 47-22=25 Exploring Operation: 47-25=22, Resulting Numbers: [23, 22, 22] Generated Node #0,1: 91:[23, 22, 22] Operation: 47-25=22 Exploring Operation: 47-23=24, Resulting Numbers: [25, 22, 24] Generated Node #0,2: 91:[25, 22, 24] Operation: 47-23=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[23, 22, 22], Operations: ['47-25=22'] Exploring Operation: 23-22=1, Resulting Numbers: [22, 1] Generated Node #0,1,0: 91:[22, 1] Operation: 23-22=1 Exploring Operation: 23-22=1, Resulting Numbers: [22, 1] Generated Node #0,1,1: 91:[22, 1] Operation: 23-22=1 Exploring Operation: 22/22=1, Resulting Numbers: [23, 1] Generated Node #0,1,2: 91:[23, 1] Operation: 22/22=1 Moving to Node #0,1,0 Current State: 91:[22, 1], Operations: ['47-25=22', '23-22=1'] Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[22, 1], Operations: ['47-25=22', '23-22=1'] Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,91 unequal: No Solution Moving to Node #0,1,2 Current State: 91:[23, 1], Operations: ['47-25=22', '22/22=1'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,91 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[25, 22, 24], Operations: ['47-23=24'] Exploring Operation: 25-24=1, Resulting Numbers: [22, 1] Generated Node #0,2,0: 91:[22, 1] Operation: 25-24=1 Exploring Operation: 24-22=2, Resulting Numbers: [25, 2] Generated Node #0,2,1: 91:[25, 2] Operation: 24-22=2 Exploring Operation: 25-22=3, Resulting Numbers: [24, 3] Generated Node #0,2,2: 91:[24, 3] Operation: 25-22=3 Moving to Node #0,2,0 Current State: 91:[22, 1], Operations: ['47-23=24', '25-24=1'] Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,91 unequal: No Solution Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[24, 3], Operations: ['47-23=24', '25-22=3'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,91 unequal: No Solution Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,91 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[25, 2], Operations: ['47-23=24', '24-22=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,91 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[23, 25, 25], Operations: ['47-22=25'] Exploring Operation: 25/25=1, Resulting Numbers: [23, 1] Generated Node #0,0,0: 91:[23, 1] Operation: 25/25=1 Exploring Operation: 25-23=2, Resulting Numbers: [25, 2] Generated Node #0,0,1: 91:[25, 2] Operation: 25-23=2 Exploring Operation: 25-23=2, Resulting Numbers: [25, 2] Generated Node #0,0,2: 91:[25, 2] Operation: 25-23=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[23, 1], Operations: ['47-22=25', '25/25=1'] Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,91 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,91 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,91 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 #0,0,1 Current State: 91:[25, 2], Operations: ['47-22=25', '25-23=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,91 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,91 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 #0,0,2 Current State: 91:[25, 2], Operations: ['47-22=25', '25-23=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,91 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 32, 46, 17, 33 ]
30
[ "46-32=14", "33-17=16", "14+16=30" ]
Current State: 30:[32, 46, 17, 33], Operations: [] Exploring Operation: 46-32=14, Resulting Numbers: [17, 33, 14] Generated Node #2: [17, 33, 14] from Operation: 46-32=14 Current State: 30:[17, 33, 14], Operations: ['46-32=14'] Exploring Operation: 33-17=16, Resulting Numbers: [14, 16] Generated Node #3: [14, 16] from Operation: 33-17=16 Current State: 30:[14, 16], Operations: ['46-32=14', '33-17=16'] Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[32, 46, 17, 33], Operations: [] Exploring Operation: 46-32=14, Resulting Numbers: [17, 33, 14] Generated Node #0,0: 30:[17, 33, 14] Operation: 46-32=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[17, 33, 14], Operations: ['46-32=14'] Exploring Operation: 33-17=16, Resulting Numbers: [14, 16] Generated Node #0,0,0: 30:[14, 16] Operation: 33-17=16 Moving to Node #0,0,0 Current State: 30:[14, 16], Operations: ['46-32=14', '33-17=16'] Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[32, 46, 17, 33], Operations: [] Exploring Operation: 46-32=14, Resulting Numbers: [17, 33, 14] Generated Node #0,0: 30:[17, 33, 14] Operation: 46-32=14 Moving to Node #0,0 Current State: 30:[17, 33, 14], Operations: ['46-32=14'] Exploring Operation: 33-17=16, Resulting Numbers: [14, 16] Generated Node #0,0,0: 30:[14, 16] Operation: 33-17=16 Moving to Node #0,0,0 Current State: 30:[14, 16], Operations: ['46-32=14', '33-17=16'] Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 43, 51, 67, 95 ]
36
[ "51-43=8", "95-67=28", "8+28=36" ]
Current State: 36:[43, 51, 67, 95], Operations: [] Exploring Operation: 51-43=8, Resulting Numbers: [67, 95, 8] Generated Node #2: [67, 95, 8] from Operation: 51-43=8 Current State: 36:[67, 95, 8], Operations: ['51-43=8'] Exploring Operation: 95-67=28, Resulting Numbers: [8, 28] Generated Node #3: [8, 28] from Operation: 95-67=28 Current State: 36:[8, 28], Operations: ['51-43=8', '95-67=28'] Exploring Operation: 8+28=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[43, 51, 67, 95], Operations: [] Exploring Operation: 95-51=44, Resulting Numbers: [43, 67, 44] Generated Node #0,0: 36:[43, 67, 44] Operation: 95-51=44 Exploring Operation: 95-67=28, Resulting Numbers: [43, 51, 28] Generated Node #0,1: 36:[43, 51, 28] Operation: 95-67=28 Moving to Node #0,1 Current State: 36:[43, 51, 28], Operations: ['95-67=28'] Exploring Operation: 51-43=8, Resulting Numbers: [28, 8] Generated Node #0,1,0: 36:[28, 8] Operation: 51-43=8 Exploring Operation: 51-28=23, Resulting Numbers: [43, 23] Generated Node #0,1,1: 36:[43, 23] Operation: 51-28=23 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 36:[28, 8], Operations: ['95-67=28', '51-43=8'] Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[43, 51, 67, 95], Operations: [] Exploring Operation: 95-67=28, Resulting Numbers: [43, 51, 28] Generated Node #0,1: 36:[43, 51, 28] Operation: 95-67=28 Moving to Node #0,1 Current State: 36:[43, 51, 28], Operations: ['95-67=28'] Exploring Operation: 51-43=8, Resulting Numbers: [28, 8] Generated Node #0,1,0: 36:[28, 8] Operation: 51-43=8 Moving to Node #0,1,0 Current State: 36:[28, 8], Operations: ['95-67=28', '51-43=8'] Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 26, 13, 25, 67 ]
84
[ "26/13=2", "67-25=42", "2*42=84" ]
Current State: 84:[26, 13, 25, 67], Operations: [] Exploring Operation: 26/13=2, Resulting Numbers: [25, 67, 2] Generated Node #2: [25, 67, 2] from Operation: 26/13=2 Current State: 84:[25, 67, 2], Operations: ['26/13=2'] Exploring Operation: 67-25=42, Resulting Numbers: [2, 42] Generated Node #3: [2, 42] from Operation: 67-25=42 Current State: 84:[2, 42], Operations: ['26/13=2', '67-25=42'] Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[26, 13, 25, 67], Operations: [] Exploring Operation: 13+67=80, Resulting Numbers: [26, 25, 80] Generated Node #0,0: 84:[26, 25, 80] Operation: 13+67=80 Exploring Operation: 26+67=93, Resulting Numbers: [13, 25, 93] Generated Node #0,1: 84:[13, 25, 93] Operation: 26+67=93 Exploring Operation: 67-26=41, Resulting Numbers: [13, 25, 41] Generated Node #0,2: 84:[13, 25, 41] Operation: 67-26=41 Exploring Operation: 25+67=92, Resulting Numbers: [26, 13, 92] Generated Node #0,3: 84:[26, 13, 92] Operation: 25+67=92 Exploring Operation: 67-25=42, Resulting Numbers: [26, 13, 42] Generated Node #0,4: 84:[26, 13, 42] Operation: 67-25=42 Start Sub Search at level 1: Moving to Node #0,4 Current State: 84:[26, 13, 42], Operations: ['67-25=42'] Exploring Operation: 26/13=2, Resulting Numbers: [42, 2] Generated Node #0,4,0: 84:[42, 2] Operation: 26/13=2 Exploring Operation: 42-13=29, Resulting Numbers: [26, 29] Generated Node #0,4,1: 84:[26, 29] Operation: 42-13=29 Exploring Operation: 26+13=39, Resulting Numbers: [42, 39] Generated Node #0,4,2: 84:[42, 39] Operation: 26+13=39 Exploring Operation: 42-26=16, Resulting Numbers: [13, 16] Generated Node #0,4,3: 84:[13, 16] Operation: 42-26=16 Exploring Operation: 26-13=13, Resulting Numbers: [42, 13] Generated Node #0,4,4: 84:[42, 13] Operation: 26-13=13 Moving to Node #0,4,0 Current State: 84:[42, 2], Operations: ['67-25=42', '26/13=2'] Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,84 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[26, 13, 25, 67], Operations: [] Exploring Operation: 67-25=42, Resulting Numbers: [26, 13, 42] Generated Node #0,4: 84:[26, 13, 42] Operation: 67-25=42 Moving to Node #0,4 Current State: 84:[26, 13, 42], Operations: ['67-25=42'] Exploring Operation: 26/13=2, Resulting Numbers: [42, 2] Generated Node #0,4,0: 84:[42, 2] Operation: 26/13=2 Moving to Node #0,4,0 Current State: 84:[42, 2], Operations: ['67-25=42', '26/13=2'] Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 34, 90, 3, 47 ]
57
[ "34+90=124", "47+124=171", "171/3=57" ]
Current State: 57:[34, 90, 3, 47], Operations: [] Exploring Operation: 34+90=124, Resulting Numbers: [3, 47, 124] Generated Node #2: [3, 47, 124] from Operation: 34+90=124 Current State: 57:[3, 47, 124], Operations: ['34+90=124'] Exploring Operation: 47+124=171, Resulting Numbers: [3, 171] Generated Node #3: [3, 171] from Operation: 47+124=171 Current State: 57:[3, 171], Operations: ['34+90=124', '47+124=171'] Exploring Operation: 171/3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[34, 90, 3, 47], Operations: [] Exploring Operation: 90-34=56, Resulting Numbers: [3, 47, 56] Generated Node #0,0: 57:[3, 47, 56] Operation: 90-34=56 Exploring Operation: 90-47=43, Resulting Numbers: [34, 3, 43] Generated Node #0,1: 57:[34, 3, 43] Operation: 90-47=43 Moving to Node #0,0 Current State: 57:[3, 47, 56], Operations: ['90-34=56'] Exploring Operation: 56-47=9, Resulting Numbers: [3, 9] Generated Node #0,0,0: 57:[3, 9] Operation: 56-47=9 Exploring Operation: 3+47=50, Resulting Numbers: [56, 50] Generated Node #0,0,1: 57:[56, 50] Operation: 3+47=50 Moving to Node #0,1 Current State: 57:[34, 3, 43], Operations: ['90-47=43'] Exploring Operation: 43-34=9, Resulting Numbers: [3, 9] Generated Node #0,1,0: 57:[3, 9] Operation: 43-34=9 Exploring Operation: 34+43=77, Resulting Numbers: [3, 77] Generated Node #0,1,1: 57:[3, 77] Operation: 34+43=77 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[3, 9], Operations: ['90-47=43', '43-34=9'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 57:[3, 77], Operations: ['90-47=43', '34+43=77'] Exploring Operation: 3+77=80, Resulting Numbers: [80] 80,57 unequal: No Solution Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 57:[3, 9], Operations: ['90-34=56', '56-47=9'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[56, 50], Operations: ['90-34=56', '3+47=50'] Exploring Operation: 56+50=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 56-50=6, Resulting Numbers: [6] 6,57 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 10, 10, 38, 34 ]
92
[ "10+10=20", "38+34=72", "20+72=92" ]
Current State: 92:[10, 10, 38, 34], Operations: [] Exploring Operation: 10+10=20, Resulting Numbers: [38, 34, 20] Generated Node #2: [38, 34, 20] from Operation: 10+10=20 Current State: 92:[38, 34, 20], Operations: ['10+10=20'] Exploring Operation: 38+34=72, Resulting Numbers: [20, 72] Generated Node #3: [20, 72] from Operation: 38+34=72 Current State: 92:[20, 72], Operations: ['10+10=20', '38+34=72'] Exploring Operation: 20+72=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[10, 10, 38, 34], Operations: [] Exploring Operation: 34-10=24, Resulting Numbers: [10, 38, 24] Generated Node #0,0: 92:[10, 38, 24] Operation: 34-10=24 Exploring Operation: 38-34=4, Resulting Numbers: [10, 10, 4] Generated Node #0,1: 92:[10, 10, 4] Operation: 38-34=4 Exploring Operation: 10+34=44, Resulting Numbers: [10, 38, 44] Generated Node #0,2: 92:[10, 38, 44] Operation: 10+34=44 Exploring Operation: 34-10=24, Resulting Numbers: [10, 38, 24] Generated Node #0,3: 92:[10, 38, 24] Operation: 34-10=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[10, 10, 4], Operations: ['38-34=4'] Exploring Operation: 10/10=1, Resulting Numbers: [4, 1] Generated Node #0,1,0: 92:[4, 1] Operation: 10/10=1 Exploring Operation: 10-10=0, Resulting Numbers: [4, 0] Generated Node #0,1,1: 92:[4, 0] Operation: 10-10=0 Exploring Operation: 10+10=20, Resulting Numbers: [4, 20] Generated Node #0,1,2: 92:[4, 20] Operation: 10+10=20 Exploring Operation: 10*10=100, Resulting Numbers: [4, 100] Generated Node #0,1,3: 92:[4, 100] Operation: 10*10=100 Moving to Node #0,1,0 Current State: 92:[4, 1], Operations: ['38-34=4', '10/10=1'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,92 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[4, 0], Operations: ['38-34=4', '10-10=0'] Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 4*0=0, Resulting Numbers: [0] 0,92 unequal: No Solution Exploring Operation: 4+0=4, Resulting Numbers: [4] 4,92 unequal: No Solution Moving to Node #0,1,2 Current State: 92:[4, 20], Operations: ['38-34=4', '10+10=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,92 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,92 unequal: No Solution Moving to Node #0,1,3 Current State: 92:[4, 100], Operations: ['38-34=4', '10*10=100'] Exploring Operation: 100-4=96, Resulting Numbers: [96] 96,92 unequal: No Solution Exploring Operation: 100/4=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 4+100=104, Resulting Numbers: [104] 104,92 unequal: No Solution Exploring Operation: 4*100=400, Resulting Numbers: [400] 400,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[10, 38, 24], Operations: ['34-10=24'] Exploring Operation: 38-24=14, Resulting Numbers: [10, 14] Generated Node #0,0,0: 92:[10, 14] Operation: 38-24=14 Exploring Operation: 10+38=48, Resulting Numbers: [24, 48] Generated Node #0,0,1: 92:[24, 48] Operation: 10+38=48 Exploring Operation: 38-10=28, Resulting Numbers: [24, 28] Generated Node #0,0,2: 92:[24, 28] Operation: 38-10=28 Exploring Operation: 24-10=14, Resulting Numbers: [38, 14] Generated Node #0,0,3: 92:[38, 14] Operation: 24-10=14 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 92:[24, 48], Operations: ['34-10=24', '10+38=48'] Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 24+48=72, Resulting Numbers: [72] 72,92 unequal: No Solution Exploring Operation: 24*48=1152, Resulting Numbers: [1152] 1152,92 unequal: No Solution Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,92 unequal: No Solution No 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: 92:[24, 28], Operations: ['34-10=24', '38-10=28'] Exploring Operation: 24*28=672, Resulting Numbers: [672] 672,92 unequal: No Solution Exploring Operation: 24+28=52, Resulting Numbers: [52] 52,92 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,92 unequal: No Solution No 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: 92:[10, 14], Operations: ['34-10=24', '38-24=14'] Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 10*14=140, Resulting Numbers: [140] 140,92 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,92 unequal: No Solution No 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: 92:[38, 14], Operations: ['34-10=24', '24-10=14'] Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,92 unequal: No Solution Exploring Operation: 38*14=532, Resulting Numbers: [532] 532,92 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,92 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: 92:[10, 38, 24], Operations: ['34-10=24'] Exploring Operation: 38-24=14, Resulting Numbers: [10, 14] Generated Node #0,3,0: 92:[10, 14] Operation: 38-24=14 Exploring Operation: 24-10=14, Resulting Numbers: [38, 14] Generated Node #0,3,1: 92:[38, 14] Operation: 24-10=14 Exploring Operation: 38-10=28, Resulting Numbers: [24, 28] Generated Node #0,3,2: 92:[24, 28] Operation: 38-10=28 Exploring Operation: 10+38=48, Resulting Numbers: [24, 48] Generated Node #0,3,3: 92:[24, 48] Operation: 10+38=48 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 92:[24, 48], Operations: ['34-10=24', '10+38=48'] Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 24+48=72, Resulting Numbers: [72] 72,92 unequal: No Solution Exploring Operation: 24*48=1152, Resulting Numbers: [1152] 1152,92 unequal: No Solution Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,92 unequal: No Solution No 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: 92:[24, 28], Operations: ['34-10=24', '38-10=28'] Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 24*28=672, Resulting Numbers: [672] 672,92 unequal: No Solution Exploring Operation: 24+28=52, Resulting Numbers: [52] 52,92 unequal: No Solution No 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: 92:[10, 14], Operations: ['34-10=24', '38-24=14'] Exploring Operation: 10*14=140, Resulting Numbers: [140] 140,92 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,92 unequal: No Solution No 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: 92:[38, 14], Operations: ['34-10=24', '24-10=14'] Exploring Operation: 38*14=532, Resulting Numbers: [532] 532,92 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,92 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: 92:[10, 38, 44], Operations: ['10+34=44'] Exploring Operation: 10+44=54, Resulting Numbers: [38, 54] Generated Node #0,2,0: 92:[38, 54] Operation: 10+44=54 Exploring Operation: 38-10=28, Resulting Numbers: [44, 28] Generated Node #0,2,1: 92:[44, 28] Operation: 38-10=28 Exploring Operation: 10+38=48, Resulting Numbers: [44, 48] Generated Node #0,2,2: 92:[44, 48] Operation: 10+38=48 Exploring Operation: 44-38=6, Resulting Numbers: [10, 6] Generated Node #0,2,3: 92:[10, 6] Operation: 44-38=6 Moving to Node #0,2,2 Current State: 92:[44, 48], Operations: ['10+34=44', '10+38=48'] Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[10, 10, 38, 34], Operations: [] Exploring Operation: 10+34=44, Resulting Numbers: [10, 38, 44] Generated Node #0,2: 92:[10, 38, 44] Operation: 10+34=44 Moving to Node #0,2 Current State: 92:[10, 38, 44], Operations: ['10+34=44'] Exploring Operation: 10+38=48, Resulting Numbers: [44, 48] Generated Node #0,2,2: 92:[44, 48] Operation: 10+38=48 Moving to Node #0,2,2 Current State: 92:[44, 48], Operations: ['10+34=44', '10+38=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.94184
hs_4
mult_heuristic
[ 96, 53, 32, 42 ]
75
[ "96+53=149", "32+42=74", "149-74=75" ]
Current State: 75:[96, 53, 32, 42], Operations: [] Exploring Operation: 96+53=149, Resulting Numbers: [32, 42, 149] Generated Node #2: [32, 42, 149] from Operation: 96+53=149 Current State: 75:[32, 42, 149], Operations: ['96+53=149'] Exploring Operation: 32+42=74, Resulting Numbers: [149, 74] Generated Node #3: [149, 74] from Operation: 32+42=74 Current State: 75:[149, 74], Operations: ['96+53=149', '32+42=74'] Exploring Operation: 149-74=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[96, 53, 32, 42], Operations: [] Exploring Operation: 53-42=11, Resulting Numbers: [96, 32, 11] Generated Node #0,0: 75:[96, 32, 11] Operation: 53-42=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[96, 32, 11], Operations: ['53-42=11'] Exploring Operation: 96/32=3, Resulting Numbers: [11, 3] Generated Node #0,0,0: 75:[11, 3] Operation: 96/32=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[11, 3], Operations: ['53-42=11', '96/32=3'] Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,75 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
[ 17, 41, 22, 28 ]
52
[ "17+41=58", "28-22=6", "58-6=52" ]
Current State: 52:[17, 41, 22, 28], Operations: [] Exploring Operation: 17+41=58, Resulting Numbers: [22, 28, 58] Generated Node #2: [22, 28, 58] from Operation: 17+41=58 Current State: 52:[22, 28, 58], Operations: ['17+41=58'] Exploring Operation: 28-22=6, Resulting Numbers: [58, 6] Generated Node #3: [58, 6] from Operation: 28-22=6 Current State: 52:[58, 6], Operations: ['17+41=58', '28-22=6'] Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[17, 41, 22, 28], Operations: [] Exploring Operation: 41-17=24, Resulting Numbers: [22, 28, 24] Generated Node #0,0: 52:[22, 28, 24] Operation: 41-17=24 Exploring Operation: 41-28=13, Resulting Numbers: [17, 22, 13] Generated Node #0,1: 52:[17, 22, 13] Operation: 41-28=13 Exploring Operation: 17+41=58, Resulting Numbers: [22, 28, 58] Generated Node #0,2: 52:[22, 28, 58] Operation: 17+41=58 Moving to Node #0,0 Current State: 52:[22, 28, 24], Operations: ['41-17=24'] Exploring Operation: 24-22=2, Resulting Numbers: [28, 2] Generated Node #0,0,0: 52:[28, 2] Operation: 24-22=2 Exploring Operation: 22+28=50, Resulting Numbers: [24, 50] Generated Node #0,0,1: 52:[24, 50] Operation: 22+28=50 Exploring Operation: 28-22=6, Resulting Numbers: [24, 6] Generated Node #0,0,2: 52:[24, 6] Operation: 28-22=6 Moving to Node #0,1 Current State: 52:[17, 22, 13], Operations: ['41-28=13'] Exploring Operation: 17+13=30, Resulting Numbers: [22, 30] Generated Node #0,1,0: 52:[22, 30] Operation: 17+13=30 Exploring Operation: 22-17=5, Resulting Numbers: [13, 5] Generated Node #0,1,1: 52:[13, 5] Operation: 22-17=5 Exploring Operation: 17-13=4, Resulting Numbers: [22, 4] Generated Node #0,1,2: 52:[22, 4] Operation: 17-13=4 Moving to Node #0,2 Current State: 52:[22, 28, 58], Operations: ['17+41=58'] Exploring Operation: 58-28=30, Resulting Numbers: [22, 30] Generated Node #0,2,0: 52:[22, 30] Operation: 58-28=30 Exploring Operation: 28-22=6, Resulting Numbers: [58, 6] Generated Node #0,2,1: 52:[58, 6] Operation: 28-22=6 Exploring Operation: 22+28=50, Resulting Numbers: [58, 50] Generated Node #0,2,2: 52:[58, 50] Operation: 22+28=50 Moving to Node #0,1,1 Current State: 52:[13, 5], Operations: ['41-28=13', '22-17=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,52 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,52 unequal: No Solution Moving to Node #0,0,0 Current State: 52:[28, 2], Operations: ['41-17=24', '24-22=2'] Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,52 unequal: No Solution Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[24, 6], Operations: ['41-17=24', '28-22=6'] Exploring Operation: 24+6=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,52 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,52 unequal: No Solution Moving to Node #0,1,2 Current State: 52:[22, 4], Operations: ['41-28=13', '17-13=4'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,52 unequal: No Solution Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,52 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[24, 50], Operations: ['41-17=24', '22+28=50'] Exploring Operation: 24+50=74, Resulting Numbers: [74] 74,52 unequal: No Solution Exploring Operation: 24*50=1200, Resulting Numbers: [1200] 1200,52 unequal: No Solution Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,52 unequal: No Solution Moving to Node #0,2,0 Current State: 52:[22, 30], Operations: ['17+41=58', '58-28=30'] Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 22*30=660, Resulting Numbers: [660] 660,52 unequal: No Solution Exploring Operation: 22+30=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[17, 41, 22, 28], Operations: [] Exploring Operation: 17+41=58, Resulting Numbers: [22, 28, 58] Generated Node #0,2: 52:[22, 28, 58] Operation: 17+41=58 Moving to Node #0,2 Current State: 52:[22, 28, 58], Operations: ['17+41=58'] Exploring Operation: 58-28=30, Resulting Numbers: [22, 30] Generated Node #0,2,0: 52:[22, 30] Operation: 58-28=30 Moving to Node #0,2,0 Current State: 52:[22, 30], Operations: ['17+41=58', '58-28=30'] Exploring Operation: 22+30=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
0.970486
hs_3
sum_heuristic
[ 36, 89, 26, 2 ]
43
[ "36*2=72", "89+26=115", "115-72=43" ]
Current State: 43:[36, 89, 26, 2], Operations: [] Exploring Operation: 36*2=72, Resulting Numbers: [89, 26, 72] Generated Node #2: [89, 26, 72] from Operation: 36*2=72 Current State: 43:[89, 26, 72], Operations: ['36*2=72'] Exploring Operation: 89+26=115, Resulting Numbers: [72, 115] Generated Node #3: [72, 115] from Operation: 89+26=115 Current State: 43:[72, 115], Operations: ['36*2=72', '89+26=115'] Exploring Operation: 115-72=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[36, 89, 26, 2], Operations: [] Exploring Operation: 26*2=52, Resulting Numbers: [36, 89, 52] Generated Node #0,0: 43:[36, 89, 52] Operation: 26*2=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[36, 89, 52], Operations: ['26*2=52'] Exploring Operation: 89-52=37, Resulting Numbers: [36, 37] Generated Node #0,0,0: 43:[36, 37] Operation: 89-52=37 Moving to Node #0,0,0 Current State: 43:[36, 37], Operations: ['26*2=52', '89-52=37'] Exploring Operation: 36+37=73, Resulting Numbers: [73] 73,43 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
[ 47, 70, 89, 20 ]
12
[ "89-47=42", "20*42=840", "840/70=12" ]
Current State: 12:[47, 70, 89, 20], Operations: [] Exploring Operation: 89-47=42, Resulting Numbers: [70, 20, 42] Generated Node #2: [70, 20, 42] from Operation: 89-47=42 Current State: 12:[70, 20, 42], Operations: ['89-47=42'] Exploring Operation: 20*42=840, Resulting Numbers: [70, 840] Generated Node #3: [70, 840] from Operation: 20*42=840 Current State: 12:[70, 840], Operations: ['89-47=42', '20*42=840'] Exploring Operation: 840/70=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[47, 70, 89, 20], Operations: [] Exploring Operation: 70-47=23, Resulting Numbers: [89, 20, 23] Generated Node #0,0: 12:[89, 20, 23] Operation: 70-47=23 Exploring Operation: 47-20=27, Resulting Numbers: [70, 89, 27] Generated Node #0,1: 12:[70, 89, 27] Operation: 47-20=27 Exploring Operation: 89-47=42, Resulting Numbers: [70, 20, 42] Generated Node #0,2: 12:[70, 20, 42] Operation: 89-47=42 Exploring Operation: 89-70=19, Resulting Numbers: [47, 20, 19] Generated Node #0,3: 12:[47, 20, 19] Operation: 89-70=19 Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[47, 20, 19], Operations: ['89-70=19'] Exploring Operation: 47+20=67, Resulting Numbers: [19, 67] Generated Node #0,3,0: 12:[19, 67] Operation: 47+20=67 Exploring Operation: 47-19=28, Resulting Numbers: [20, 28] Generated Node #0,3,1: 12:[20, 28] Operation: 47-19=28 Exploring Operation: 47-20=27, Resulting Numbers: [19, 27] Generated Node #0,3,2: 12:[19, 27] Operation: 47-20=27 Exploring Operation: 20-19=1, Resulting Numbers: [47, 1] Generated Node #0,3,3: 12:[47, 1] Operation: 20-19=1 Moving to Node #0,3,2 Current State: 12:[19, 27], Operations: ['89-70=19', '47-20=27'] Exploring Operation: 19*27=513, Resulting Numbers: [513] 513,12 unequal: No Solution Exploring Operation: 19+27=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 27-19=8, Resulting Numbers: [8] 8,12 unequal: No Solution Moving to Node #0,3,1 Current State: 12:[20, 28], Operations: ['89-70=19', '47-19=28'] Exploring Operation: 20*28=560, Resulting Numbers: [560] 560,12 unequal: No Solution Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 20+28=48, Resulting Numbers: [48] 48,12 unequal: No Solution Moving to Node #0,3,3 Current State: 12:[47, 1], Operations: ['89-70=19', '20-19=1'] Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,12 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,12 unequal: No Solution Moving to Node #0,3,0 Current State: 12:[19, 67], Operations: ['89-70=19', '47+20=67'] Exploring Operation: 19*67=1273, Resulting Numbers: [1273] 1273,12 unequal: No Solution Exploring Operation: 19+67=86, Resulting Numbers: [86] 86,12 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,12 unequal: No Solution No 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: 12:[89, 20, 23], Operations: ['70-47=23'] Exploring Operation: 89+20=109, Resulting Numbers: [23, 109] Generated Node #0,0,0: 12:[23, 109] Operation: 89+20=109 Exploring Operation: 23-20=3, Resulting Numbers: [89, 3] Generated Node #0,0,1: 12:[89, 3] Operation: 23-20=3 Exploring Operation: 89-23=66, Resulting Numbers: [20, 66] Generated Node #0,0,2: 12:[20, 66] Operation: 89-23=66 Exploring Operation: 89-20=69, Resulting Numbers: [23, 69] Generated Node #0,0,3: 12:[23, 69] Operation: 89-20=69 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 12:[20, 66], Operations: ['70-47=23', '89-23=66'] Exploring Operation: 20+66=86, Resulting Numbers: [86] 86,12 unequal: No Solution Exploring Operation: 20*66=1320, Resulting Numbers: [1320] 1320,12 unequal: No Solution Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,12 unequal: No Solution No 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: 12:[23, 69], Operations: ['70-47=23', '89-20=69'] Exploring Operation: 69-23=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 69/23=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 23+69=92, Resulting Numbers: [92] 92,12 unequal: No Solution Exploring Operation: 23*69=1587, Resulting Numbers: [1587] 1587,12 unequal: No Solution No 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: 12:[89, 3], Operations: ['70-47=23', '23-20=3'] Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,12 unequal: No Solution Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,12 unequal: No Solution Exploring Operation: 89*3=267, Resulting Numbers: [267] 267,12 unequal: No Solution No 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: 12:[23, 109], Operations: ['70-47=23', '89+20=109'] Exploring Operation: 23+109=132, Resulting Numbers: [132] 132,12 unequal: No Solution Exploring Operation: 23*109=2507, Resulting Numbers: [2507] 2507,12 unequal: No Solution Exploring Operation: 109-23=86, Resulting Numbers: [86] 86,12 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: 12:[70, 20, 42], Operations: ['89-47=42'] Exploring Operation: 70-42=28, Resulting Numbers: [20, 28] Generated Node #0,2,0: 12:[20, 28] Operation: 70-42=28 Exploring Operation: 70+20=90, Resulting Numbers: [42, 90] Generated Node #0,2,1: 12:[42, 90] Operation: 70+20=90 Exploring Operation: 70-20=50, Resulting Numbers: [42, 50] Generated Node #0,2,2: 12:[42, 50] Operation: 70-20=50 Exploring Operation: 42-20=22, Resulting Numbers: [70, 22] Generated Node #0,2,3: 12:[70, 22] Operation: 42-20=22 Moving to Node #0,2,0 Current State: 12:[20, 28], Operations: ['89-47=42', '70-42=28'] Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 20+28=48, Resulting Numbers: [48] 48,12 unequal: No Solution Exploring Operation: 20*28=560, Resulting Numbers: [560] 560,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[70, 22], Operations: ['89-47=42', '42-20=22'] Exploring Operation: 70-22=48, Resulting Numbers: [48] 48,12 unequal: No Solution Exploring Operation: 70+22=92, Resulting Numbers: [92] 92,12 unequal: No Solution Exploring Operation: 70*22=1540, Resulting Numbers: [1540] 1540,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[42, 50], Operations: ['89-47=42', '70-20=50'] Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 42+50=92, Resulting Numbers: [92] 92,12 unequal: No Solution Exploring Operation: 42*50=2100, Resulting Numbers: [2100] 2100,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[42, 90], Operations: ['89-47=42', '70+20=90'] Exploring Operation: 42+90=132, Resulting Numbers: [132] 132,12 unequal: No Solution Exploring Operation: 90-42=48, Resulting Numbers: [48] 48,12 unequal: No Solution Exploring Operation: 42*90=3780, Resulting Numbers: [3780] 3780,12 unequal: No Solution No 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: 12:[70, 89, 27], Operations: ['47-20=27'] Exploring Operation: 89-27=62, Resulting Numbers: [70, 62] Generated Node #0,1,0: 12:[70, 62] Operation: 89-27=62 Exploring Operation: 70+89=159, Resulting Numbers: [27, 159] Generated Node #0,1,1: 12:[27, 159] Operation: 70+89=159 Exploring Operation: 89-70=19, Resulting Numbers: [27, 19] Generated Node #0,1,2: 12:[27, 19] Operation: 89-70=19 Exploring Operation: 70-27=43, Resulting Numbers: [89, 43] Generated Node #0,1,3: 12:[89, 43] Operation: 70-27=43 Moving to Node #0,1,2 Current State: 12:[27, 19], Operations: ['47-20=27', '89-70=19'] Exploring Operation: 27+19=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 27*19=513, Resulting Numbers: [513] 513,12 unequal: No Solution Exploring Operation: 27-19=8, Resulting Numbers: [8] 8,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[89, 43], Operations: ['47-20=27', '70-27=43'] Exploring Operation: 89-43=46, Resulting Numbers: [46] 46,12 unequal: No Solution Exploring Operation: 89+43=132, Resulting Numbers: [132] 132,12 unequal: No Solution Exploring Operation: 89*43=3827, Resulting Numbers: [3827] 3827,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[70, 62], Operations: ['47-20=27', '89-27=62'] Exploring Operation: 70*62=4340, Resulting Numbers: [4340] 4340,12 unequal: No Solution Exploring Operation: 70-62=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 70+62=132, Resulting Numbers: [132] 132,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[27, 159], Operations: ['47-20=27', '70+89=159'] Exploring Operation: 27+159=186, Resulting Numbers: [186] 186,12 unequal: No Solution Exploring Operation: 159-27=132, Resulting Numbers: [132] 132,12 unequal: No Solution Exploring Operation: 27*159=4293, Resulting Numbers: [4293] 4293,12 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
[ 52, 65, 54, 47 ]
49
[ "65-47=18", "54/18=3", "52-3=49" ]
Current State: 49:[52, 65, 54, 47], Operations: [] Exploring Operation: 65-47=18, Resulting Numbers: [52, 54, 18] Generated Node #2: [52, 54, 18] from Operation: 65-47=18 Current State: 49:[52, 54, 18], Operations: ['65-47=18'] Exploring Operation: 54/18=3, Resulting Numbers: [52, 3] Generated Node #3: [52, 3] from Operation: 54/18=3 Current State: 49:[52, 3], Operations: ['65-47=18', '54/18=3'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[52, 65, 54, 47], Operations: [] Exploring Operation: 65-52=13, Resulting Numbers: [54, 47, 13] Generated Node #0,0: 49:[54, 47, 13] Operation: 65-52=13 Exploring Operation: 65-47=18, Resulting Numbers: [52, 54, 18] Generated Node #0,1: 49:[52, 54, 18] Operation: 65-47=18 Exploring Operation: 65-54=11, Resulting Numbers: [52, 47, 11] Generated Node #0,2: 49:[52, 47, 11] Operation: 65-54=11 Moving to Node #0,2 Current State: 49:[52, 47, 11], Operations: ['65-54=11'] Exploring Operation: 52-47=5, Resulting Numbers: [11, 5] Generated Node #0,2,0: 49:[11, 5] Operation: 52-47=5 Exploring Operation: 52-11=41, Resulting Numbers: [47, 41] Generated Node #0,2,1: 49:[47, 41] Operation: 52-11=41 Exploring Operation: 47+11=58, Resulting Numbers: [52, 58] Generated Node #0,2,2: 49:[52, 58] Operation: 47+11=58 Moving to Node #0,0 Current State: 49:[54, 47, 13], Operations: ['65-52=13'] Exploring Operation: 54-13=41, Resulting Numbers: [47, 41] Generated Node #0,0,0: 49:[47, 41] Operation: 54-13=41 Exploring Operation: 47+13=60, Resulting Numbers: [54, 60] Generated Node #0,0,1: 49:[54, 60] Operation: 47+13=60 Exploring Operation: 54-47=7, Resulting Numbers: [13, 7] Generated Node #0,0,2: 49:[13, 7] Operation: 54-47=7 Moving to Node #0,1 Current State: 49:[52, 54, 18], Operations: ['65-47=18'] Exploring Operation: 54-52=2, Resulting Numbers: [18, 2] Generated Node #0,1,0: 49:[18, 2] Operation: 54-52=2 Exploring Operation: 54/18=3, Resulting Numbers: [52, 3] Generated Node #0,1,1: 49:[52, 3] Operation: 54/18=3 Exploring Operation: 54-18=36, Resulting Numbers: [52, 36] Generated Node #0,1,2: 49:[52, 36] Operation: 54-18=36 Moving to Node #0,2,0 Current State: 49:[11, 5], Operations: ['65-54=11', '52-47=5'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,49 unequal: No Solution Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,49 unequal: No Solution Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,49 unequal: No Solution Moving to Node #0,0,2 Current State: 49:[13, 7], Operations: ['65-52=13', '54-47=7'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,49 unequal: No Solution Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,49 unequal: No Solution Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,49 unequal: No Solution Moving to Node #0,1,1 Current State: 49:[52, 3], Operations: ['65-47=18', '54/18=3'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[52, 65, 54, 47], Operations: [] Exploring Operation: 65-47=18, Resulting Numbers: [52, 54, 18] Generated Node #0,1: 49:[52, 54, 18] Operation: 65-47=18 Moving to Node #0,1 Current State: 49:[52, 54, 18], Operations: ['65-47=18'] Exploring Operation: 54/18=3, Resulting Numbers: [52, 3] Generated Node #0,1,1: 49:[52, 3] Operation: 54/18=3 Moving to Node #0,1,1 Current State: 49:[52, 3], Operations: ['65-47=18', '54/18=3'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
0.980035
hs_3
sum_heuristic
[ 77, 96, 24, 23 ]
50
[ "77-23=54", "96/24=4", "54-4=50" ]
Current State: 50:[77, 96, 24, 23], Operations: [] Exploring Operation: 77-23=54, Resulting Numbers: [96, 24, 54] Generated Node #2: [96, 24, 54] from Operation: 77-23=54 Current State: 50:[96, 24, 54], Operations: ['77-23=54'] Exploring Operation: 96/24=4, Resulting Numbers: [54, 4] Generated Node #3: [54, 4] from Operation: 96/24=4 Current State: 50:[54, 4], Operations: ['77-23=54', '96/24=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[77, 96, 24, 23], Operations: [] Exploring Operation: 96-77=19, Resulting Numbers: [24, 23, 19] Generated Node #0,0: 50:[24, 23, 19] Operation: 96-77=19 Exploring Operation: 96-24=72, Resulting Numbers: [77, 23, 72] Generated Node #0,1: 50:[77, 23, 72] Operation: 96-24=72 Exploring Operation: 77-24=53, Resulting Numbers: [96, 23, 53] Generated Node #0,2: 50:[96, 23, 53] Operation: 77-24=53 Exploring Operation: 96/24=4, Resulting Numbers: [77, 23, 4] Generated Node #0,3: 50:[77, 23, 4] Operation: 96/24=4 Exploring Operation: 77-23=54, Resulting Numbers: [96, 24, 54] Generated Node #0,4: 50:[96, 24, 54] Operation: 77-23=54 Moving to Node #0,0 Current State: 50:[24, 23, 19], Operations: ['96-77=19'] Exploring Operation: 23-19=4, Resulting Numbers: [24, 4] Generated Node #0,0,0: 50:[24, 4] Operation: 23-19=4 Exploring Operation: 24-19=5, Resulting Numbers: [23, 5] Generated Node #0,0,1: 50:[23, 5] Operation: 24-19=5 Exploring Operation: 24-23=1, Resulting Numbers: [19, 1] Generated Node #0,0,2: 50:[19, 1] Operation: 24-23=1 Exploring Operation: 24+19=43, Resulting Numbers: [23, 43] Generated Node #0,0,3: 50:[23, 43] Operation: 24+19=43 Exploring Operation: 24+23=47, Resulting Numbers: [19, 47] Generated Node #0,0,4: 50:[19, 47] Operation: 24+23=47 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[24, 4], Operations: ['96-77=19', '23-19=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,50 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,50 unequal: No Solution Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,50 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,50 unequal: No Solution No 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: 50:[23, 5], Operations: ['96-77=19', '24-19=5'] Exploring Operation: 23*5=115, Resulting Numbers: [115] 115,50 unequal: No Solution Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,50 unequal: No Solution Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,50 unequal: No Solution No 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: 50:[19, 1], Operations: ['96-77=19', '24-23=1'] Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,50 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,50 unequal: No Solution Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,50 unequal: No Solution Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,50 unequal: No Solution No 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: 50:[23, 43], Operations: ['96-77=19', '24+19=43'] Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,50 unequal: No Solution Exploring Operation: 23*43=989, Resulting Numbers: [989] 989,50 unequal: No Solution Exploring Operation: 23+43=66, Resulting Numbers: [66] 66,50 unequal: No Solution No 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: 50:[19, 47], Operations: ['96-77=19', '24+23=47'] Exploring Operation: 19*47=893, Resulting Numbers: [893] 893,50 unequal: No Solution Exploring Operation: 47-19=28, Resulting Numbers: [28] 28,50 unequal: No Solution Exploring Operation: 19+47=66, Resulting Numbers: [66] 66,50 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: 50:[77, 23, 4], Operations: ['96/24=4'] Exploring Operation: 77-23=54, Resulting Numbers: [4, 54] Generated Node #0,3,0: 50:[4, 54] Operation: 77-23=54 Exploring Operation: 77-4=73, Resulting Numbers: [23, 73] Generated Node #0,3,1: 50:[23, 73] Operation: 77-4=73 Exploring Operation: 77+4=81, Resulting Numbers: [23, 81] Generated Node #0,3,2: 50:[23, 81] Operation: 77+4=81 Exploring Operation: 23+4=27, Resulting Numbers: [77, 27] Generated Node #0,3,3: 50:[77, 27] Operation: 23+4=27 Exploring Operation: 23-4=19, Resulting Numbers: [77, 19] Generated Node #0,3,4: 50:[77, 19] Operation: 23-4=19 Moving to Node #0,1 Current State: 50:[77, 23, 72], Operations: ['96-24=72'] Exploring Operation: 77-23=54, Resulting Numbers: [72, 54] Generated Node #0,1,0: 50:[72, 54] Operation: 77-23=54 Exploring Operation: 72-23=49, Resulting Numbers: [77, 49] Generated Node #0,1,1: 50:[77, 49] Operation: 72-23=49 Exploring Operation: 23+72=95, Resulting Numbers: [77, 95] Generated Node #0,1,2: 50:[77, 95] Operation: 23+72=95 Exploring Operation: 77+23=100, Resulting Numbers: [72, 100] Generated Node #0,1,3: 50:[72, 100] Operation: 77+23=100 Exploring Operation: 77-72=5, Resulting Numbers: [23, 5] Generated Node #0,1,4: 50:[23, 5] Operation: 77-72=5 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 50:[23, 5], Operations: ['96-24=72', '77-72=5'] Exploring Operation: 23*5=115, Resulting Numbers: [115] 115,50 unequal: No Solution Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,50 unequal: No Solution Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,50 unequal: No Solution No 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: 50:[72, 54], Operations: ['96-24=72', '77-23=54'] Exploring Operation: 72+54=126, Resulting Numbers: [126] 126,50 unequal: No Solution Exploring Operation: 72*54=3888, Resulting Numbers: [3888] 3888,50 unequal: No Solution Exploring Operation: 72-54=18, Resulting Numbers: [18] 18,50 unequal: No Solution No 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: 50:[77, 49], Operations: ['96-24=72', '72-23=49'] Exploring Operation: 77*49=3773, Resulting Numbers: [3773] 3773,50 unequal: No Solution Exploring Operation: 77+49=126, Resulting Numbers: [126] 126,50 unequal: No Solution Exploring Operation: 77-49=28, Resulting Numbers: [28] 28,50 unequal: No Solution No 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: 50:[77, 95], Operations: ['96-24=72', '23+72=95'] Exploring Operation: 77*95=7315, Resulting Numbers: [7315] 7315,50 unequal: No Solution Exploring Operation: 77+95=172, Resulting Numbers: [172] 172,50 unequal: No Solution Exploring Operation: 95-77=18, Resulting Numbers: [18] 18,50 unequal: No Solution No 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: 50:[72, 100], Operations: ['96-24=72', '77+23=100'] Exploring Operation: 100-72=28, Resulting Numbers: [28] 28,50 unequal: No Solution Exploring Operation: 72*100=7200, Resulting Numbers: [7200] 7200,50 unequal: No Solution Exploring Operation: 72+100=172, Resulting Numbers: [172] 172,50 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: 50:[96, 23, 53], Operations: ['77-24=53'] Exploring Operation: 53-23=30, Resulting Numbers: [96, 30] Generated Node #0,2,0: 50:[96, 30] Operation: 53-23=30 Exploring Operation: 23+53=76, Resulting Numbers: [96, 76] Generated Node #0,2,1: 50:[96, 76] Operation: 23+53=76 Exploring Operation: 96-53=43, Resulting Numbers: [23, 43] Generated Node #0,2,2: 50:[23, 43] Operation: 96-53=43 Exploring Operation: 96+23=119, Resulting Numbers: [53, 119] Generated Node #0,2,3: 50:[53, 119] Operation: 96+23=119 Exploring Operation: 96-23=73, Resulting Numbers: [53, 73] Generated Node #0,2,4: 50:[53, 73] Operation: 96-23=73 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 50:[23, 43], Operations: ['77-24=53', '96-53=43'] Exploring Operation: 23*43=989, Resulting Numbers: [989] 989,50 unequal: No Solution Exploring Operation: 23+43=66, Resulting Numbers: [66] 66,50 unequal: No Solution Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,50 unequal: No Solution No 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: 50:[53, 73], Operations: ['77-24=53', '96-23=73'] Exploring Operation: 53*73=3869, Resulting Numbers: [3869] 3869,50 unequal: No Solution Exploring Operation: 73-53=20, Resulting Numbers: [20] 20,50 unequal: No Solution Exploring Operation: 53+73=126, Resulting Numbers: [126] 126,50 unequal: No Solution No 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: 50:[96, 30], Operations: ['77-24=53', '53-23=30'] Exploring Operation: 96*30=2880, Resulting Numbers: [2880] 2880,50 unequal: No Solution Exploring Operation: 96+30=126, Resulting Numbers: [126] 126,50 unequal: No Solution Exploring Operation: 96-30=66, Resulting Numbers: [66] 66,50 unequal: No Solution No 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: 50:[96, 76], Operations: ['77-24=53', '23+53=76'] Exploring Operation: 96*76=7296, Resulting Numbers: [7296] 7296,50 unequal: No Solution Exploring Operation: 96+76=172, Resulting Numbers: [172] 172,50 unequal: No Solution Exploring Operation: 96-76=20, Resulting Numbers: [20] 20,50 unequal: No Solution No 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: 50:[53, 119], Operations: ['77-24=53', '96+23=119'] Exploring Operation: 53*119=6307, Resulting Numbers: [6307] 6307,50 unequal: No Solution Exploring Operation: 119-53=66, Resulting Numbers: [66] 66,50 unequal: No Solution Exploring Operation: 53+119=172, Resulting Numbers: [172] 172,50 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: 50:[96, 24, 54], Operations: ['77-23=54'] Exploring Operation: 96-24=72, Resulting Numbers: [54, 72] Generated Node #0,4,0: 50:[54, 72] Operation: 96-24=72 Exploring Operation: 96/24=4, Resulting Numbers: [54, 4] Generated Node #0,4,1: 50:[54, 4] Operation: 96/24=4 Exploring Operation: 96+24=120, Resulting Numbers: [54, 120] Generated Node #0,4,2: 50:[54, 120] Operation: 96+24=120 Exploring Operation: 96-54=42, Resulting Numbers: [24, 42] Generated Node #0,4,3: 50:[24, 42] Operation: 96-54=42 Exploring Operation: 54-24=30, Resulting Numbers: [96, 30] Generated Node #0,4,4: 50:[96, 30] Operation: 54-24=30 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 50:[54, 4], Operations: ['77-23=54', '96/24=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[77, 96, 24, 23], Operations: [] Exploring Operation: 77-23=54, Resulting Numbers: [96, 24, 54] Generated Node #0,4: 50:[96, 24, 54] Operation: 77-23=54 Moving to Node #0,4 Current State: 50:[96, 24, 54], Operations: ['77-23=54'] Exploring Operation: 96/24=4, Resulting Numbers: [54, 4] Generated Node #0,4,1: 50:[54, 4] Operation: 96/24=4 Moving to Node #0,4,1 Current State: 50:[54, 4], Operations: ['77-23=54', '96/24=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.928819
hs_5
mult_heuristic
[ 64, 56, 8, 93 ]
22
[ "93-64=29", "56/8=7", "29-7=22" ]
Current State: 22:[64, 56, 8, 93], Operations: [] Exploring Operation: 93-64=29, Resulting Numbers: [56, 8, 29] Generated Node #2: [56, 8, 29] from Operation: 93-64=29 Current State: 22:[56, 8, 29], Operations: ['93-64=29'] Exploring Operation: 56/8=7, Resulting Numbers: [29, 7] Generated Node #3: [29, 7] from Operation: 56/8=7 Current State: 22:[29, 7], Operations: ['93-64=29', '56/8=7'] Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[64, 56, 8, 93], Operations: [] Exploring Operation: 64/8=8, Resulting Numbers: [56, 93, 8] Generated Node #0,0: 22:[56, 93, 8] Operation: 64/8=8 Exploring Operation: 93-64=29, Resulting Numbers: [56, 8, 29] Generated Node #0,1: 22:[56, 8, 29] Operation: 93-64=29 Exploring Operation: 64-56=8, Resulting Numbers: [8, 93, 8] Generated Node #0,2: 22:[8, 93, 8] Operation: 64-56=8 Exploring Operation: 93-56=37, Resulting Numbers: [64, 8, 37] Generated Node #0,3: 22:[64, 8, 37] Operation: 93-56=37 Moving to Node #0,1 Current State: 22:[56, 8, 29], Operations: ['93-64=29'] Exploring Operation: 56/8=7, Resulting Numbers: [29, 7] Generated Node #0,1,0: 22:[29, 7] Operation: 56/8=7 Exploring Operation: 56-8=48, Resulting Numbers: [29, 48] Generated Node #0,1,1: 22:[29, 48] Operation: 56-8=48 Exploring Operation: 56-29=27, Resulting Numbers: [8, 27] Generated Node #0,1,2: 22:[8, 27] Operation: 56-29=27 Exploring Operation: 29-8=21, Resulting Numbers: [56, 21] Generated Node #0,1,3: 22:[56, 21] Operation: 29-8=21 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 22:[8, 27], Operations: ['93-64=29', '56-29=27'] Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,22 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,22 unequal: No Solution Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[29, 7], Operations: ['93-64=29', '56/8=7'] Exploring Operation: 29*7=203, Resulting Numbers: [203] 203,22 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[64, 56, 8, 93], Operations: [] Exploring Operation: 93-64=29, Resulting Numbers: [56, 8, 29] Generated Node #0,1: 22:[56, 8, 29] Operation: 93-64=29 Moving to Node #0,1 Current State: 22:[56, 8, 29], Operations: ['93-64=29'] Exploring Operation: 56/8=7, Resulting Numbers: [29, 7] Generated Node #0,1,0: 22:[29, 7] Operation: 56/8=7 Moving to Node #0,1,0 Current State: 22:[29, 7], Operations: ['93-64=29', '56/8=7'] Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 66, 61, 88, 60 ]
100
[ "66-61=5", "60/5=12", "88+12=100" ]
Current State: 100:[66, 61, 88, 60], Operations: [] Exploring Operation: 66-61=5, Resulting Numbers: [88, 60, 5] Generated Node #2: [88, 60, 5] from Operation: 66-61=5 Current State: 100:[88, 60, 5], Operations: ['66-61=5'] Exploring Operation: 60/5=12, Resulting Numbers: [88, 12] Generated Node #3: [88, 12] from Operation: 60/5=12 Current State: 100:[88, 12], Operations: ['66-61=5', '60/5=12'] Exploring Operation: 88+12=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[66, 61, 88, 60], Operations: [] Exploring Operation: 66-61=5, Resulting Numbers: [88, 60, 5] Generated Node #0,0: 100:[88, 60, 5] Operation: 66-61=5 Moving to Node #0,0 Current State: 100:[88, 60, 5], Operations: ['66-61=5'] Exploring Operation: 88-60=28, Resulting Numbers: [5, 28] Generated Node #0,0,0: 100:[5, 28] Operation: 88-60=28 Moving to Node #0,0,0 Current State: 100:[5, 28], Operations: ['66-61=5', '88-60=28'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,100 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 15, 70, 33, 26 ]
48
[ "70-15=55", "33-26=7", "55-7=48" ]
Current State: 48:[15, 70, 33, 26], Operations: [] Exploring Operation: 70-15=55, Resulting Numbers: [33, 26, 55] Generated Node #2: [33, 26, 55] from Operation: 70-15=55 Current State: 48:[33, 26, 55], Operations: ['70-15=55'] Exploring Operation: 33-26=7, Resulting Numbers: [55, 7] Generated Node #3: [55, 7] from Operation: 33-26=7 Current State: 48:[55, 7], Operations: ['70-15=55', '33-26=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[15, 70, 33, 26], Operations: [] Exploring Operation: 70-33=37, Resulting Numbers: [15, 26, 37] Generated Node #0,0: 48:[15, 26, 37] Operation: 70-33=37 Exploring Operation: 70-26=44, Resulting Numbers: [15, 33, 44] Generated Node #0,1: 48:[15, 33, 44] Operation: 70-26=44 Moving to Node #0,0 Current State: 48:[15, 26, 37], Operations: ['70-33=37'] Exploring Operation: 37-26=11, Resulting Numbers: [15, 11] Generated Node #0,0,0: 48:[15, 11] Operation: 37-26=11 Exploring Operation: 37-15=22, Resulting Numbers: [26, 22] Generated Node #0,0,1: 48:[26, 22] Operation: 37-15=22 Moving to Node #0,1 Current State: 48:[15, 33, 44], Operations: ['70-26=44'] Exploring Operation: 15+33=48, Resulting Numbers: [44, 48] Generated Node #0,1,0: 48:[44, 48] Operation: 15+33=48 Exploring Operation: 44-33=11, Resulting Numbers: [15, 11] Generated Node #0,1,1: 48:[15, 11] Operation: 44-33=11 Moving to Node #0,0,0 Current State: 48:[15, 11], Operations: ['70-33=37', '37-26=11'] Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,48 unequal: No Solution Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[15, 11], Operations: ['70-26=44', '44-33=11'] Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[26, 22], Operations: ['70-33=37', '37-15=22'] Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,48 unequal: No Solution Exploring Operation: 26+22=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[15, 70, 33, 26], Operations: [] Exploring Operation: 70-33=37, Resulting Numbers: [15, 26, 37] Generated Node #0,0: 48:[15, 26, 37] Operation: 70-33=37 Moving to Node #0,0 Current State: 48:[15, 26, 37], Operations: ['70-33=37'] Exploring Operation: 37-15=22, Resulting Numbers: [26, 22] Generated Node #0,0,1: 48:[26, 22] Operation: 37-15=22 Moving to Node #0,0,1 Current State: 48:[26, 22], Operations: ['70-33=37', '37-15=22'] Exploring Operation: 26+22=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 47, 5, 68, 10 ]
21
[ "47+68=115", "115-10=105", "105/5=21" ]
Current State: 21:[47, 5, 68, 10], Operations: [] Exploring Operation: 47+68=115, Resulting Numbers: [5, 10, 115] Generated Node #2: [5, 10, 115] from Operation: 47+68=115 Current State: 21:[5, 10, 115], Operations: ['47+68=115'] Exploring Operation: 115-10=105, Resulting Numbers: [5, 105] Generated Node #3: [5, 105] from Operation: 115-10=105 Current State: 21:[5, 105], Operations: ['47+68=115', '115-10=105'] Exploring Operation: 105/5=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[47, 5, 68, 10], Operations: [] Exploring Operation: 68-47=21, Resulting Numbers: [5, 10, 21] Generated Node #0,0: 21:[5, 10, 21] Operation: 68-47=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[5, 10, 21], Operations: ['68-47=21'] Exploring Operation: 10/5=2, Resulting Numbers: [21, 2] Generated Node #0,0,0: 21:[21, 2] Operation: 10/5=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[21, 2], Operations: ['68-47=21', '10/5=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 60, 25, 50, 17 ]
68
[ "60-25=35", "50-17=33", "35+33=68" ]
Current State: 68:[60, 25, 50, 17], Operations: [] Exploring Operation: 60-25=35, Resulting Numbers: [50, 17, 35] Generated Node #2: [50, 17, 35] from Operation: 60-25=35 Current State: 68:[50, 17, 35], Operations: ['60-25=35'] Exploring Operation: 50-17=33, Resulting Numbers: [35, 33] Generated Node #3: [35, 33] from Operation: 50-17=33 Current State: 68:[35, 33], Operations: ['60-25=35', '50-17=33'] Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[60, 25, 50, 17], Operations: [] Exploring Operation: 50-25=25, Resulting Numbers: [60, 17, 25] Generated Node #0,0: 68:[60, 17, 25] Operation: 50-25=25 Exploring Operation: 25+50=75, Resulting Numbers: [60, 17, 75] Generated Node #0,1: 68:[60, 17, 75] Operation: 25+50=75 Exploring Operation: 50/25=2, Resulting Numbers: [60, 17, 2] Generated Node #0,2: 68:[60, 17, 2] Operation: 50/25=2 Exploring Operation: 60-50=10, Resulting Numbers: [25, 17, 10] Generated Node #0,3: 68:[25, 17, 10] Operation: 60-50=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[60, 17, 2], Operations: ['50/25=2'] Exploring Operation: 17*2=34, Resulting Numbers: [60, 34] Generated Node #0,2,0: 68:[60, 34] Operation: 17*2=34 Exploring Operation: 60/2=30, Resulting Numbers: [17, 30] Generated Node #0,2,1: 68:[17, 30] Operation: 60/2=30 Exploring Operation: 60+2=62, Resulting Numbers: [17, 62] Generated Node #0,2,2: 68:[17, 62] Operation: 60+2=62 Exploring Operation: 60+17=77, Resulting Numbers: [2, 77] Generated Node #0,2,3: 68:[2, 77] Operation: 60+17=77 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 68:[17, 30], Operations: ['50/25=2', '60/2=30'] Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 17*30=510, Resulting Numbers: [510] 510,68 unequal: No Solution Exploring Operation: 17+30=47, Resulting Numbers: [47] 47,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 68:[17, 62], Operations: ['50/25=2', '60+2=62'] Exploring Operation: 62-17=45, Resulting Numbers: [45] 45,68 unequal: No Solution Exploring Operation: 17*62=1054, Resulting Numbers: [1054] 1054,68 unequal: No Solution Exploring Operation: 17+62=79, Resulting Numbers: [79] 79,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 68:[60, 34], Operations: ['50/25=2', '17*2=34'] Exploring Operation: 60+34=94, Resulting Numbers: [94] 94,68 unequal: No Solution Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,68 unequal: No Solution Exploring Operation: 60*34=2040, Resulting Numbers: [2040] 2040,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 68:[2, 77], Operations: ['50/25=2', '60+17=77'] Exploring Operation: 2*77=154, Resulting Numbers: [154] 154,68 unequal: No Solution Exploring Operation: 2+77=79, Resulting Numbers: [79] 79,68 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 68:[25, 17, 10], Operations: ['60-50=10'] Exploring Operation: 25-10=15, Resulting Numbers: [17, 15] Generated Node #0,3,0: 68:[17, 15] Operation: 25-10=15 Exploring Operation: 25+10=35, Resulting Numbers: [17, 35] Generated Node #0,3,1: 68:[17, 35] Operation: 25+10=35 Exploring Operation: 17-10=7, Resulting Numbers: [25, 7] Generated Node #0,3,2: 68:[25, 7] Operation: 17-10=7 Exploring Operation: 25-17=8, Resulting Numbers: [10, 8] Generated Node #0,3,3: 68:[10, 8] Operation: 25-17=8 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 68:[17, 35], Operations: ['60-50=10', '25+10=35'] Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,68 unequal: No Solution Exploring Operation: 17+35=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 17*35=595, Resulting Numbers: [595] 595,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 68:[17, 15], Operations: ['60-50=10', '25-10=15'] Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,68 unequal: No Solution Exploring Operation: 17*15=255, Resulting Numbers: [255] 255,68 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 68:[10, 8], Operations: ['60-50=10', '25-17=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,68 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 68:[25, 7], Operations: ['60-50=10', '17-10=7'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,68 unequal: No Solution Exploring Operation: 25*7=175, Resulting Numbers: [175] 175,68 unequal: No Solution Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[60, 17, 75], Operations: ['25+50=75'] Exploring Operation: 75-17=58, Resulting Numbers: [60, 58] Generated Node #0,1,0: 68:[60, 58] Operation: 75-17=58 Exploring Operation: 60+17=77, Resulting Numbers: [75, 77] Generated Node #0,1,1: 68:[75, 77] Operation: 60+17=77 Exploring Operation: 60-17=43, Resulting Numbers: [75, 43] Generated Node #0,1,2: 68:[75, 43] Operation: 60-17=43 Exploring Operation: 75-60=15, Resulting Numbers: [17, 15] Generated Node #0,1,3: 68:[17, 15] Operation: 75-60=15 Moving to Node #0,1,3 Current State: 68:[17, 15], Operations: ['25+50=75', '75-60=15'] Exploring Operation: 17*15=255, Resulting Numbers: [255] 255,68 unequal: No Solution Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,68 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[75, 43], Operations: ['25+50=75', '60-17=43'] Exploring Operation: 75+43=118, Resulting Numbers: [118] 118,68 unequal: No Solution Exploring Operation: 75*43=3225, Resulting Numbers: [3225] 3225,68 unequal: No Solution Exploring Operation: 75-43=32, Resulting Numbers: [32] 32,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[75, 77], Operations: ['25+50=75', '60+17=77'] Exploring Operation: 75+77=152, Resulting Numbers: [152] 152,68 unequal: No Solution Exploring Operation: 75*77=5775, Resulting Numbers: [5775] 5775,68 unequal: No Solution Exploring Operation: 77-75=2, Resulting Numbers: [2] 2,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[60, 58], Operations: ['25+50=75', '75-17=58'] Exploring Operation: 60-58=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 60*58=3480, Resulting Numbers: [3480] 3480,68 unequal: No Solution Exploring Operation: 60+58=118, Resulting Numbers: [118] 118,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[60, 17, 25], Operations: ['50-25=25'] Exploring Operation: 60-25=35, Resulting Numbers: [17, 35] Generated Node #0,0,0: 68:[17, 35] Operation: 60-25=35 Exploring Operation: 60+17=77, Resulting Numbers: [25, 77] Generated Node #0,0,1: 68:[25, 77] Operation: 60+17=77 Exploring Operation: 17+25=42, Resulting Numbers: [60, 42] Generated Node #0,0,2: 68:[60, 42] Operation: 17+25=42 Exploring Operation: 25-17=8, Resulting Numbers: [60, 8] Generated Node #0,0,3: 68:[60, 8] Operation: 25-17=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[17, 35], Operations: ['50-25=25', '60-25=35'] Exploring Operation: 17+35=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,68 unequal: No Solution Exploring Operation: 17*35=595, Resulting Numbers: [595] 595,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 68:[60, 8], Operations: ['50-25=25', '25-17=8'] Exploring Operation: 60-8=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 60+8=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[60, 25, 50, 17], Operations: [] Exploring Operation: 50-25=25, Resulting Numbers: [60, 17, 25] Generated Node #0,0: 68:[60, 17, 25] Operation: 50-25=25 Moving to Node #0,0 Current State: 68:[60, 17, 25], Operations: ['50-25=25'] Exploring Operation: 25-17=8, Resulting Numbers: [60, 8] Generated Node #0,0,3: 68:[60, 8] Operation: 25-17=8 Moving to Node #0,0,3 Current State: 68:[60, 8], Operations: ['50-25=25', '25-17=8'] Exploring Operation: 60+8=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.943576
hs_4
sum_heuristic
[ 34, 29, 87, 80 ]
35
[ "34-29=5", "87-80=7", "5*7=35" ]
Current State: 35:[34, 29, 87, 80], Operations: [] Exploring Operation: 34-29=5, Resulting Numbers: [87, 80, 5] Generated Node #2: [87, 80, 5] from Operation: 34-29=5 Current State: 35:[87, 80, 5], Operations: ['34-29=5'] Exploring Operation: 87-80=7, Resulting Numbers: [5, 7] Generated Node #3: [5, 7] from Operation: 87-80=7 Current State: 35:[5, 7], Operations: ['34-29=5', '87-80=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[34, 29, 87, 80], Operations: [] Exploring Operation: 87-80=7, Resulting Numbers: [34, 29, 7] Generated Node #0,0: 35:[34, 29, 7] Operation: 87-80=7 Moving to Node #0,0 Current State: 35:[34, 29, 7], Operations: ['87-80=7'] Exploring Operation: 34-29=5, Resulting Numbers: [7, 5] Generated Node #0,0,0: 35:[7, 5] Operation: 34-29=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[7, 5], Operations: ['87-80=7', '34-29=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[34, 29, 87, 80], Operations: [] Exploring Operation: 87-80=7, Resulting Numbers: [34, 29, 7] Generated Node #0,0: 35:[34, 29, 7] Operation: 87-80=7 Moving to Node #0,0 Current State: 35:[34, 29, 7], Operations: ['87-80=7'] Exploring Operation: 34-29=5, Resulting Numbers: [7, 5] Generated Node #0,0,0: 35:[7, 5] Operation: 34-29=5 Moving to Node #0,0,0 Current State: 35:[7, 5], Operations: ['87-80=7', '34-29=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 59, 55, 88, 42 ]
50
[ "59-55=4", "88-42=46", "4+46=50" ]
Current State: 50:[59, 55, 88, 42], Operations: [] Exploring Operation: 59-55=4, Resulting Numbers: [88, 42, 4] Generated Node #2: [88, 42, 4] from Operation: 59-55=4 Current State: 50:[88, 42, 4], Operations: ['59-55=4'] Exploring Operation: 88-42=46, Resulting Numbers: [4, 46] Generated Node #3: [4, 46] from Operation: 88-42=46 Current State: 50:[4, 46], Operations: ['59-55=4', '88-42=46'] Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[59, 55, 88, 42], Operations: [] Exploring Operation: 88-59=29, Resulting Numbers: [55, 42, 29] Generated Node #0,0: 50:[55, 42, 29] Operation: 88-59=29 Exploring Operation: 88-55=33, Resulting Numbers: [59, 42, 33] Generated Node #0,1: 50:[59, 42, 33] Operation: 88-55=33 Exploring Operation: 88-42=46, Resulting Numbers: [59, 55, 46] Generated Node #0,2: 50:[59, 55, 46] Operation: 88-42=46 Exploring Operation: 59-55=4, Resulting Numbers: [88, 42, 4] Generated Node #0,3: 50:[88, 42, 4] Operation: 59-55=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[55, 42, 29], Operations: ['88-59=29'] Exploring Operation: 55-42=13, Resulting Numbers: [29, 13] Generated Node #0,0,0: 50:[29, 13] Operation: 55-42=13 Exploring Operation: 55-29=26, Resulting Numbers: [42, 26] Generated Node #0,0,1: 50:[42, 26] Operation: 55-29=26 Exploring Operation: 42+29=71, Resulting Numbers: [55, 71] Generated Node #0,0,2: 50:[55, 71] Operation: 42+29=71 Exploring Operation: 42-29=13, Resulting Numbers: [55, 13] Generated Node #0,0,3: 50:[55, 13] Operation: 42-29=13 Moving to Node #0,0,0 Current State: 50:[29, 13], Operations: ['88-59=29', '55-42=13'] Exploring Operation: 29+13=42, Resulting Numbers: [42] 42,50 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 29*13=377, Resulting Numbers: [377] 377,50 unequal: No Solution Moving to Node #0,0,3 Current State: 50:[55, 13], Operations: ['88-59=29', '42-29=13'] Exploring Operation: 55*13=715, Resulting Numbers: [715] 715,50 unequal: No Solution Exploring Operation: 55+13=68, Resulting Numbers: [68] 68,50 unequal: No Solution Exploring Operation: 55-13=42, Resulting Numbers: [42] 42,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[42, 26], Operations: ['88-59=29', '55-29=26'] Exploring Operation: 42*26=1092, Resulting Numbers: [1092] 1092,50 unequal: No Solution Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 42+26=68, Resulting Numbers: [68] 68,50 unequal: No Solution Moving to Node #0,0,2 Current State: 50:[55, 71], Operations: ['88-59=29', '42+29=71'] Exploring Operation: 71-55=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 55+71=126, Resulting Numbers: [126] 126,50 unequal: No Solution Exploring Operation: 55*71=3905, Resulting Numbers: [3905] 3905,50 unequal: No Solution No 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: 50:[59, 55, 46], Operations: ['88-42=46'] Exploring Operation: 59-46=13, Resulting Numbers: [55, 13] Generated Node #0,2,0: 50:[55, 13] Operation: 59-46=13 Exploring Operation: 59-55=4, Resulting Numbers: [46, 4] Generated Node #0,2,1: 50:[46, 4] Operation: 59-55=4 Exploring Operation: 55-46=9, Resulting Numbers: [59, 9] Generated Node #0,2,2: 50:[59, 9] Operation: 55-46=9 Exploring Operation: 59+46=105, Resulting Numbers: [55, 105] Generated Node #0,2,3: 50:[55, 105] Operation: 59+46=105 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 50:[46, 4], Operations: ['88-42=46', '59-55=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[59, 55, 88, 42], Operations: [] Exploring Operation: 88-42=46, Resulting Numbers: [59, 55, 46] Generated Node #0,2: 50:[59, 55, 46] Operation: 88-42=46 Moving to Node #0,2 Current State: 50:[59, 55, 46], Operations: ['88-42=46'] Exploring Operation: 59-55=4, Resulting Numbers: [46, 4] Generated Node #0,2,1: 50:[46, 4] Operation: 59-55=4 Moving to Node #0,2,1 Current State: 50:[46, 4], Operations: ['88-42=46', '59-55=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic
[ 31, 26, 57, 59 ]
55
[ "31+26=57", "59-57=2", "57-2=55" ]
Current State: 55:[31, 26, 57, 59], Operations: [] Exploring Operation: 31+26=57, Resulting Numbers: [57, 59, 57] Generated Node #2: [57, 59, 57] from Operation: 31+26=57 Current State: 55:[57, 59, 57], Operations: ['31+26=57'] Exploring Operation: 59-57=2, Resulting Numbers: [2] 2,55 equal: Goal Reached Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[31, 26, 57, 59], Operations: [] Exploring Operation: 31+26=57, Resulting Numbers: [57, 59, 57] Generated Node #0,0: 55:[57, 59, 57] Operation: 31+26=57 Exploring Operation: 31-26=5, Resulting Numbers: [57, 59, 5] Generated Node #0,1: 55:[57, 59, 5] Operation: 31-26=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[57, 59, 5], Operations: ['31-26=5'] Exploring Operation: 59-57=2, Resulting Numbers: [5, 2] Generated Node #0,1,0: 55:[5, 2] Operation: 59-57=2 Exploring Operation: 59-5=54, Resulting Numbers: [57, 54] Generated Node #0,1,1: 55:[57, 54] Operation: 59-5=54 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[5, 2], Operations: ['31-26=5', '59-57=2'] Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,55 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:[57, 54], Operations: ['31-26=5', '59-5=54'] Exploring Operation: 57+54=111, Resulting Numbers: [111] 111,55 unequal: No Solution Exploring Operation: 57-54=3, Resulting Numbers: [3] 3,55 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:[57, 59, 57], Operations: ['31+26=57'] Exploring Operation: 59-57=2, Resulting Numbers: [57, 2] Generated Node #0,0,0: 55:[57, 2] Operation: 59-57=2 Exploring Operation: 59-57=2, Resulting Numbers: [57, 2] Generated Node #0,0,1: 55:[57, 2] Operation: 59-57=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[57, 2], Operations: ['31+26=57', '59-57=2'] Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,55 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[31, 26, 57, 59], Operations: [] Exploring Operation: 31+26=57, Resulting Numbers: [57, 59, 57] Generated Node #0,0: 55:[57, 59, 57] Operation: 31+26=57 Moving to Node #0,0 Current State: 55:[57, 59, 57], Operations: ['31+26=57'] Exploring Operation: 59-57=2, Resulting Numbers: [57, 2] Generated Node #0,0,0: 55:[57, 2] Operation: 59-57=2 Moving to Node #0,0,0 Current State: 55:[57, 2], Operations: ['31+26=57', '59-57=2'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 51, 1, 12, 16 ]
79
[ "51*1=51", "12+16=28", "51+28=79" ]
Current State: 79:[51, 1, 12, 16], Operations: [] Exploring Operation: 51*1=51, Resulting Numbers: [12, 16, 51] Generated Node #2: [12, 16, 51] from Operation: 51*1=51 Current State: 79:[12, 16, 51], Operations: ['51*1=51'] Exploring Operation: 12+16=28, Resulting Numbers: [51, 28] Generated Node #3: [51, 28] from Operation: 12+16=28 Current State: 79:[51, 28], Operations: ['51*1=51', '12+16=28'] Exploring Operation: 51+28=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[51, 1, 12, 16], Operations: [] Exploring Operation: 51+1=52, Resulting Numbers: [12, 16, 52] Generated Node #0,0: 79:[12, 16, 52] Operation: 51+1=52 Moving to Node #0,0 Current State: 79:[12, 16, 52], Operations: ['51+1=52'] Exploring Operation: 12+16=28, Resulting Numbers: [52, 28] Generated Node #0,0,0: 79:[52, 28] Operation: 12+16=28 Moving to Node #0,0,0 Current State: 79:[52, 28], Operations: ['51+1=52', '12+16=28'] Exploring Operation: 52+28=80, Resulting Numbers: [80] 80,79 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 64, 2, 16, 47 ]
86
[ "64/16=4", "47-4=43", "2*43=86" ]
Current State: 86:[64, 2, 16, 47], Operations: [] Exploring Operation: 64/16=4, Resulting Numbers: [2, 47, 4] Generated Node #2: [2, 47, 4] from Operation: 64/16=4 Current State: 86:[2, 47, 4], Operations: ['64/16=4'] Exploring Operation: 47-4=43, Resulting Numbers: [2, 43] Generated Node #3: [2, 43] from Operation: 47-4=43 Current State: 86:[2, 43], Operations: ['64/16=4', '47-4=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[64, 2, 16, 47], Operations: [] Exploring Operation: 64-47=17, Resulting Numbers: [2, 16, 17] Generated Node #0,0: 86:[2, 16, 17] Operation: 64-47=17 Exploring Operation: 64+16=80, Resulting Numbers: [2, 47, 80] Generated Node #0,1: 86:[2, 47, 80] Operation: 64+16=80 Exploring Operation: 64-16=48, Resulting Numbers: [2, 47, 48] Generated Node #0,2: 86:[2, 47, 48] Operation: 64-16=48 Exploring Operation: 64/2=32, Resulting Numbers: [16, 47, 32] Generated Node #0,3: 86:[16, 47, 32] Operation: 64/2=32 Exploring Operation: 64/16=4, Resulting Numbers: [2, 47, 4] Generated Node #0,4: 86:[2, 47, 4] Operation: 64/16=4 Start Sub Search at level 1: Moving to Node #0,4 Current State: 86:[2, 47, 4], Operations: ['64/16=4'] Exploring Operation: 2+47=49, Resulting Numbers: [4, 49] Generated Node #0,4,0: 86:[4, 49] Operation: 2+47=49 Exploring Operation: 4/2=2, Resulting Numbers: [47, 2] Generated Node #0,4,1: 86:[47, 2] Operation: 4/2=2 Exploring Operation: 4-2=2, Resulting Numbers: [47, 2] Generated Node #0,4,2: 86:[47, 2] Operation: 4-2=2 Exploring Operation: 47-4=43, Resulting Numbers: [2, 43] Generated Node #0,4,3: 86:[2, 43] Operation: 47-4=43 Exploring Operation: 47-2=45, Resulting Numbers: [4, 45] Generated Node #0,4,4: 86:[4, 45] Operation: 47-2=45 Moving to Node #0,4,3 Current State: 86:[2, 43], Operations: ['64/16=4', '47-4=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[64, 2, 16, 47], Operations: [] Exploring Operation: 64/16=4, Resulting Numbers: [2, 47, 4] Generated Node #0,4: 86:[2, 47, 4] Operation: 64/16=4 Moving to Node #0,4 Current State: 86:[2, 47, 4], Operations: ['64/16=4'] Exploring Operation: 47-4=43, Resulting Numbers: [2, 43] Generated Node #0,4,3: 86:[2, 43] Operation: 47-4=43 Moving to Node #0,4,3 Current State: 86:[2, 43], Operations: ['64/16=4', '47-4=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 33, 18, 7, 98 ]
76
[ "33-18=15", "98-7=91", "91-15=76" ]
Current State: 76:[33, 18, 7, 98], Operations: [] Exploring Operation: 33-18=15, Resulting Numbers: [7, 98, 15] Generated Node #2: [7, 98, 15] from Operation: 33-18=15 Current State: 76:[7, 98, 15], Operations: ['33-18=15'] Exploring Operation: 98-7=91, Resulting Numbers: [15, 91] Generated Node #3: [15, 91] from Operation: 98-7=91 Current State: 76:[15, 91], Operations: ['33-18=15', '98-7=91'] Exploring Operation: 91-15=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[33, 18, 7, 98], Operations: [] Exploring Operation: 98-18=80, Resulting Numbers: [33, 7, 80] Generated Node #0,0: 76:[33, 7, 80] Operation: 98-18=80 Exploring Operation: 33+7=40, Resulting Numbers: [18, 98, 40] Generated Node #0,1: 76:[18, 98, 40] Operation: 33+7=40 Exploring Operation: 98-33=65, Resulting Numbers: [18, 7, 65] Generated Node #0,2: 76:[18, 7, 65] Operation: 98-33=65 Exploring Operation: 98/7=14, Resulting Numbers: [33, 18, 14] Generated Node #0,3: 76:[33, 18, 14] Operation: 98/7=14 Exploring Operation: 98-7=91, Resulting Numbers: [33, 18, 91] Generated Node #0,4: 76:[33, 18, 91] Operation: 98-7=91 Start Sub Search at level 1: Moving to Node #0,3 Current State: 76:[33, 18, 14], Operations: ['98/7=14'] Exploring Operation: 33+14=47, Resulting Numbers: [18, 47] Generated Node #0,3,0: 76:[18, 47] Operation: 33+14=47 Exploring Operation: 33-14=19, Resulting Numbers: [18, 19] Generated Node #0,3,1: 76:[18, 19] Operation: 33-14=19 Exploring Operation: 18-14=4, Resulting Numbers: [33, 4] Generated Node #0,3,2: 76:[33, 4] Operation: 18-14=4 Exploring Operation: 18+14=32, Resulting Numbers: [33, 32] Generated Node #0,3,3: 76:[33, 32] Operation: 18+14=32 Exploring Operation: 33-18=15, Resulting Numbers: [14, 15] Generated Node #0,3,4: 76:[14, 15] Operation: 33-18=15 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 76:[18, 19], Operations: ['98/7=14', '33-14=19'] Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 18*19=342, Resulting Numbers: [342] 342,76 unequal: No Solution Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,76 unequal: No Solution No 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: 76:[33, 4], Operations: ['98/7=14', '18-14=4'] Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,76 unequal: No Solution Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,76 unequal: No Solution Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 76:[14, 15], Operations: ['98/7=14', '33-18=15'] Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,76 unequal: No Solution Exploring Operation: 14*15=210, Resulting Numbers: [210] 210,76 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,76 unequal: No Solution No 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: 76:[18, 47], Operations: ['98/7=14', '33+14=47'] Exploring Operation: 18+47=65, Resulting Numbers: [65] 65,76 unequal: No Solution Exploring Operation: 18*47=846, Resulting Numbers: [846] 846,76 unequal: No Solution Exploring Operation: 47-18=29, Resulting Numbers: [29] 29,76 unequal: No Solution No 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: 76:[33, 32], Operations: ['98/7=14', '18+14=32'] Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,76 unequal: No Solution Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 33*32=1056, Resulting Numbers: [1056] 1056,76 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: 76:[33, 7, 80], Operations: ['98-18=80'] Exploring Operation: 7+80=87, Resulting Numbers: [33, 87] Generated Node #0,0,0: 76:[33, 87] Operation: 7+80=87 Exploring Operation: 33+7=40, Resulting Numbers: [80, 40] Generated Node #0,0,1: 76:[80, 40] Operation: 33+7=40 Exploring Operation: 33-7=26, Resulting Numbers: [80, 26] Generated Node #0,0,2: 76:[80, 26] Operation: 33-7=26 Exploring Operation: 80-33=47, Resulting Numbers: [7, 47] Generated Node #0,0,3: 76:[7, 47] Operation: 80-33=47 Exploring Operation: 80-7=73, Resulting Numbers: [33, 73] Generated Node #0,0,4: 76:[33, 73] Operation: 80-7=73 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 76:[80, 40], Operations: ['98-18=80', '33+7=40'] Exploring Operation: 80/40=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 80-40=40, Resulting Numbers: [40] 40,76 unequal: No Solution Exploring Operation: 80*40=3200, Resulting Numbers: [3200] 3200,76 unequal: No Solution Exploring Operation: 80+40=120, Resulting Numbers: [120] 120,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 76:[33, 73], Operations: ['98-18=80', '80-7=73'] Exploring Operation: 33+73=106, Resulting Numbers: [106] 106,76 unequal: No Solution Exploring Operation: 33*73=2409, Resulting Numbers: [2409] 2409,76 unequal: No Solution Exploring Operation: 73-33=40, Resulting Numbers: [40] 40,76 unequal: No Solution No 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: 76:[80, 26], Operations: ['98-18=80', '33-7=26'] Exploring Operation: 80+26=106, Resulting Numbers: [106] 106,76 unequal: No Solution Exploring Operation: 80*26=2080, Resulting Numbers: [2080] 2080,76 unequal: No Solution Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,76 unequal: No Solution No 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: 76:[7, 47], Operations: ['98-18=80', '80-33=47'] Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,76 unequal: No Solution Exploring Operation: 7*47=329, Resulting Numbers: [329] 329,76 unequal: No Solution Exploring Operation: 7+47=54, Resulting Numbers: [54] 54,76 unequal: No Solution No 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: 76:[33, 87], Operations: ['98-18=80', '7+80=87'] Exploring Operation: 33+87=120, Resulting Numbers: [120] 120,76 unequal: No Solution Exploring Operation: 87-33=54, Resulting Numbers: [54] 54,76 unequal: No Solution Exploring Operation: 33*87=2871, Resulting Numbers: [2871] 2871,76 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: 76:[18, 7, 65], Operations: ['98-33=65'] Exploring Operation: 65-18=47, Resulting Numbers: [7, 47] Generated Node #0,2,0: 76:[7, 47] Operation: 65-18=47 Exploring Operation: 18+65=83, Resulting Numbers: [7, 83] Generated Node #0,2,1: 76:[7, 83] Operation: 18+65=83 Exploring Operation: 7+65=72, Resulting Numbers: [18, 72] Generated Node #0,2,2: 76:[18, 72] Operation: 7+65=72 Exploring Operation: 18-7=11, Resulting Numbers: [65, 11] Generated Node #0,2,3: 76:[65, 11] Operation: 18-7=11 Exploring Operation: 18+7=25, Resulting Numbers: [65, 25] Generated Node #0,2,4: 76:[65, 25] Operation: 18+7=25 Moving to Node #0,2,2 Current State: 76:[18, 72], Operations: ['98-33=65', '7+65=72'] Exploring Operation: 72/18=4, Resulting Numbers: [4] 4,76 unequal: No Solution Exploring Operation: 18+72=90, Resulting Numbers: [90] 90,76 unequal: No Solution Exploring Operation: 72-18=54, Resulting Numbers: [54] 54,76 unequal: No Solution Exploring Operation: 18*72=1296, Resulting Numbers: [1296] 1296,76 unequal: No Solution Moving to Node #0,2,1 Current State: 76:[7, 83], Operations: ['98-33=65', '18+65=83'] Exploring Operation: 7+83=90, Resulting Numbers: [90] 90,76 unequal: No Solution Exploring Operation: 7*83=581, Resulting Numbers: [581] 581,76 unequal: No Solution Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[33, 18, 7, 98], Operations: [] Exploring Operation: 98-33=65, Resulting Numbers: [18, 7, 65] Generated Node #0,2: 76:[18, 7, 65] Operation: 98-33=65 Moving to Node #0,2 Current State: 76:[18, 7, 65], Operations: ['98-33=65'] Exploring Operation: 18+65=83, Resulting Numbers: [7, 83] Generated Node #0,2,1: 76:[7, 83] Operation: 18+65=83 Moving to Node #0,2,1 Current State: 76:[7, 83], Operations: ['98-33=65', '18+65=83'] Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.946181
hs_5
sum_heuristic
[ 29, 35, 55, 42 ]
37
[ "29+55=84", "84/42=2", "35+2=37" ]
Current State: 37:[29, 35, 55, 42], Operations: [] Exploring Operation: 29+55=84, Resulting Numbers: [35, 42, 84] Generated Node #2: [35, 42, 84] from Operation: 29+55=84 Current State: 37:[35, 42, 84], Operations: ['29+55=84'] Exploring Operation: 84/42=2, Resulting Numbers: [35, 2] Generated Node #3: [35, 2] from Operation: 84/42=2 Current State: 37:[35, 2], Operations: ['29+55=84', '84/42=2'] Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[29, 35, 55, 42], Operations: [] Exploring Operation: 55-29=26, Resulting Numbers: [35, 42, 26] Generated Node #0,0: 37:[35, 42, 26] Operation: 55-29=26 Exploring Operation: 55-35=20, Resulting Numbers: [29, 42, 20] Generated Node #0,1: 37:[29, 42, 20] Operation: 55-35=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[35, 42, 26], Operations: ['55-29=26'] Exploring Operation: 35+26=61, Resulting Numbers: [42, 61] Generated Node #0,0,0: 37:[42, 61] Operation: 35+26=61 Exploring Operation: 42-26=16, Resulting Numbers: [35, 16] Generated Node #0,0,1: 37:[35, 16] Operation: 42-26=16 Moving to Node #0,0,1 Current State: 37:[35, 16], Operations: ['55-29=26', '42-26=16'] Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,37 unequal: No Solution Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[42, 61], Operations: ['55-29=26', '35+26=61'] Exploring Operation: 42+61=103, Resulting Numbers: [103] 103,37 unequal: No Solution Exploring Operation: 61-42=19, Resulting Numbers: [19] 19,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[29, 42, 20], Operations: ['55-35=20'] Exploring Operation: 42-20=22, Resulting Numbers: [29, 22] Generated Node #0,1,0: 37:[29, 22] Operation: 42-20=22 Exploring Operation: 29+20=49, Resulting Numbers: [42, 49] Generated Node #0,1,1: 37:[42, 49] Operation: 29+20=49 Moving to Node #0,1,1 Current State: 37:[42, 49], Operations: ['55-35=20', '29+20=49'] Exploring Operation: 42+49=91, Resulting Numbers: [91] 91,37 unequal: No Solution Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[29, 22], Operations: ['55-35=20', '42-20=22'] Exploring Operation: 29+22=51, Resulting Numbers: [51] 51,37 unequal: No Solution Exploring Operation: 29-22=7, Resulting Numbers: [7] 7,37 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, 21, 39, 32 ]
34
[ "21+39=60", "60/30=2", "32+2=34" ]
Current State: 34:[30, 21, 39, 32], Operations: [] Exploring Operation: 21+39=60, Resulting Numbers: [30, 32, 60] Generated Node #2: [30, 32, 60] from Operation: 21+39=60 Current State: 34:[30, 32, 60], Operations: ['21+39=60'] Exploring Operation: 60/30=2, Resulting Numbers: [32, 2] Generated Node #3: [32, 2] from Operation: 60/30=2 Current State: 34:[32, 2], Operations: ['21+39=60', '60/30=2'] Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[30, 21, 39, 32], Operations: [] Exploring Operation: 32-30=2, Resulting Numbers: [21, 39, 2] Generated Node #0,0: 34:[21, 39, 2] Operation: 32-30=2 Exploring Operation: 39-21=18, Resulting Numbers: [30, 32, 18] Generated Node #0,1: 34:[30, 32, 18] Operation: 39-21=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[30, 32, 18], Operations: ['39-21=18'] Exploring Operation: 32-30=2, Resulting Numbers: [18, 2] Generated Node #0,1,0: 34:[18, 2] Operation: 32-30=2 Exploring Operation: 30-18=12, Resulting Numbers: [32, 12] Generated Node #0,1,1: 34:[32, 12] Operation: 30-18=12 Moving to Node #0,1,0 Current State: 34:[18, 2], Operations: ['39-21=18', '32-30=2'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[32, 12], Operations: ['39-21=18', '30-18=12'] Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 32+12=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 Current State: 34:[21, 39, 2], Operations: ['32-30=2'] Exploring Operation: 39-21=18, Resulting Numbers: [2, 18] Generated Node #0,0,0: 34:[2, 18] Operation: 39-21=18 Exploring Operation: 21-2=19, Resulting Numbers: [39, 19] Generated Node #0,0,1: 34:[39, 19] Operation: 21-2=19 Moving to Node #0,0,0 Current State: 34:[2, 18], Operations: ['32-30=2', '39-21=18'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,34 unequal: No Solution Moving to Node #0,0,1 Current State: 34:[39, 19], Operations: ['32-30=2', '21-2=19'] Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 39+19=58, Resulting Numbers: [58] 58,34 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
[ 91, 38, 16, 24 ]
89
[ "91+38=129", "16+24=40", "129-40=89" ]
Current State: 89:[91, 38, 16, 24], Operations: [] Exploring Operation: 91+38=129, Resulting Numbers: [16, 24, 129] Generated Node #2: [16, 24, 129] from Operation: 91+38=129 Current State: 89:[16, 24, 129], Operations: ['91+38=129'] Exploring Operation: 16+24=40, Resulting Numbers: [129, 40] Generated Node #3: [129, 40] from Operation: 16+24=40 Current State: 89:[129, 40], Operations: ['91+38=129', '16+24=40'] Exploring Operation: 129-40=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[91, 38, 16, 24], Operations: [] Exploring Operation: 38+16=54, Resulting Numbers: [91, 24, 54] Generated Node #0,0: 89:[91, 24, 54] Operation: 38+16=54 Exploring Operation: 16+24=40, Resulting Numbers: [91, 38, 40] Generated Node #0,1: 89:[91, 38, 40] Operation: 16+24=40 Exploring Operation: 38+24=62, Resulting Numbers: [91, 16, 62] Generated Node #0,2: 89:[91, 16, 62] Operation: 38+24=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[91, 24, 54], Operations: ['38+16=54'] Exploring Operation: 91+24=115, Resulting Numbers: [54, 115] Generated Node #0,0,0: 89:[54, 115] Operation: 91+24=115 Exploring Operation: 24+54=78, Resulting Numbers: [91, 78] Generated Node #0,0,1: 89:[91, 78] Operation: 24+54=78 Exploring Operation: 91-24=67, Resulting Numbers: [54, 67] Generated Node #0,0,2: 89:[54, 67] Operation: 91-24=67 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[91, 78], Operations: ['38+16=54', '24+54=78'] Exploring Operation: 91+78=169, Resulting Numbers: [169] 169,89 unequal: No Solution Exploring Operation: 91-78=13, Resulting Numbers: [13] 13,89 unequal: No Solution Exploring Operation: 91*78=7098, Resulting Numbers: [7098] 7098,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[54, 67], Operations: ['38+16=54', '91-24=67'] Exploring Operation: 54+67=121, Resulting Numbers: [121] 121,89 unequal: No Solution Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,89 unequal: No Solution Exploring Operation: 54*67=3618, Resulting Numbers: [3618] 3618,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[54, 115], Operations: ['38+16=54', '91+24=115'] Exploring Operation: 115-54=61, Resulting Numbers: [61] 61,89 unequal: No Solution Exploring Operation: 54*115=6210, Resulting Numbers: [6210] 6210,89 unequal: No Solution Exploring Operation: 54+115=169, Resulting Numbers: [169] 169,89 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: 89:[91, 38, 40], Operations: ['16+24=40'] Exploring Operation: 38+40=78, Resulting Numbers: [91, 78] Generated Node #0,1,0: 89:[91, 78] Operation: 38+40=78 Exploring Operation: 91+38=129, Resulting Numbers: [40, 129] Generated Node #0,1,1: 89:[40, 129] Operation: 91+38=129 Exploring Operation: 91-38=53, Resulting Numbers: [40, 53] Generated Node #0,1,2: 89:[40, 53] Operation: 91-38=53 Moving to Node #0,1,0 Current State: 89:[91, 78], Operations: ['16+24=40', '38+40=78'] Exploring Operation: 91+78=169, Resulting Numbers: [169] 169,89 unequal: No Solution Exploring Operation: 91-78=13, Resulting Numbers: [13] 13,89 unequal: No Solution Exploring Operation: 91*78=7098, Resulting Numbers: [7098] 7098,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[40, 53], Operations: ['16+24=40', '91-38=53'] Exploring Operation: 40+53=93, Resulting Numbers: [93] 93,89 unequal: No Solution Exploring Operation: 53-40=13, Resulting Numbers: [13] 13,89 unequal: No Solution Exploring Operation: 40*53=2120, Resulting Numbers: [2120] 2120,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[40, 129], Operations: ['16+24=40', '91+38=129'] Exploring Operation: 40*129=5160, Resulting Numbers: [5160] 5160,89 unequal: No Solution Exploring Operation: 129-40=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[91, 38, 16, 24], Operations: [] Exploring Operation: 16+24=40, Resulting Numbers: [91, 38, 40] Generated Node #0,1: 89:[91, 38, 40] Operation: 16+24=40 Moving to Node #0,1 Current State: 89:[91, 38, 40], Operations: ['16+24=40'] Exploring Operation: 91+38=129, Resulting Numbers: [40, 129] Generated Node #0,1,1: 89:[40, 129] Operation: 91+38=129 Moving to Node #0,1,1 Current State: 89:[40, 129], Operations: ['16+24=40', '91+38=129'] Exploring Operation: 129-40=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_3
sum_heuristic
[ 40, 17, 7, 39 ]
23
[ "40-17=23", "7+39=46", "46-23=23" ]
Current State: 23:[40, 17, 7, 39], Operations: [] Exploring Operation: 40-17=23, Resulting Numbers: [7, 39, 23] Generated Node #2: [7, 39, 23] from Operation: 40-17=23 Current State: 23:[7, 39, 23], Operations: ['40-17=23'] Exploring Operation: 7+39=46, Resulting Numbers: [23, 46] Generated Node #3: [23, 46] from Operation: 7+39=46 Current State: 23:[23, 46], Operations: ['40-17=23', '7+39=46'] Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[40, 17, 7, 39], Operations: [] Exploring Operation: 40-17=23, Resulting Numbers: [7, 39, 23] Generated Node #0,0: 23:[7, 39, 23] Operation: 40-17=23 Exploring Operation: 40-7=33, Resulting Numbers: [17, 39, 33] Generated Node #0,1: 23:[17, 39, 33] Operation: 40-7=33 Moving to Node #0,0 Current State: 23:[7, 39, 23], Operations: ['40-17=23'] Exploring Operation: 39-7=32, Resulting Numbers: [23, 32] Generated Node #0,0,0: 23:[23, 32] Operation: 39-7=32 Exploring Operation: 7+39=46, Resulting Numbers: [23, 46] Generated Node #0,0,1: 23:[23, 46] Operation: 7+39=46 Moving to Node #0,1 Current State: 23:[17, 39, 33], Operations: ['40-7=33'] Exploring Operation: 33-17=16, Resulting Numbers: [39, 16] Generated Node #0,1,0: 23:[39, 16] Operation: 33-17=16 Exploring Operation: 39-17=22, Resulting Numbers: [33, 22] Generated Node #0,1,1: 23:[33, 22] Operation: 39-17=22 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[33, 22], Operations: ['40-7=33', '39-17=22'] Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 33+22=55, Resulting Numbers: [55] 55,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[39, 16], Operations: ['40-7=33', '33-17=16'] Exploring Operation: 39-16=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[40, 17, 7, 39], Operations: [] Exploring Operation: 40-7=33, Resulting Numbers: [17, 39, 33] Generated Node #0,1: 23:[17, 39, 33] Operation: 40-7=33 Moving to Node #0,1 Current State: 23:[17, 39, 33], Operations: ['40-7=33'] Exploring Operation: 33-17=16, Resulting Numbers: [39, 16] Generated Node #0,1,0: 23:[39, 16] Operation: 33-17=16 Moving to Node #0,1,0 Current State: 23:[39, 16], Operations: ['40-7=33', '33-17=16'] Exploring Operation: 39-16=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_2
sum_heuristic
[ 67, 77, 14, 35 ]
59
[ "77-67=10", "14+35=49", "10+49=59" ]
Current State: 59:[67, 77, 14, 35], Operations: [] Exploring Operation: 77-67=10, Resulting Numbers: [14, 35, 10] Generated Node #2: [14, 35, 10] from Operation: 77-67=10 Current State: 59:[14, 35, 10], Operations: ['77-67=10'] Exploring Operation: 14+35=49, Resulting Numbers: [10, 49] Generated Node #3: [10, 49] from Operation: 14+35=49 Current State: 59:[10, 49], Operations: ['77-67=10', '14+35=49'] Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[67, 77, 14, 35], Operations: [] Exploring Operation: 67-14=53, Resulting Numbers: [77, 35, 53] Generated Node #0,0: 59:[77, 35, 53] Operation: 67-14=53 Exploring Operation: 77-14=63, Resulting Numbers: [67, 35, 63] Generated Node #0,1: 59:[67, 35, 63] Operation: 77-14=63 Exploring Operation: 14+35=49, Resulting Numbers: [67, 77, 49] Generated Node #0,2: 59:[67, 77, 49] Operation: 14+35=49 Moving to Node #0,1 Current State: 59:[67, 35, 63], Operations: ['77-14=63'] Exploring Operation: 67-35=32, Resulting Numbers: [63, 32] Generated Node #0,1,0: 59:[63, 32] Operation: 67-35=32 Exploring Operation: 63-35=28, Resulting Numbers: [67, 28] Generated Node #0,1,1: 59:[67, 28] Operation: 63-35=28 Exploring Operation: 67+35=102, Resulting Numbers: [63, 102] Generated Node #0,1,2: 59:[63, 102] Operation: 67+35=102 Moving to Node #0,2 Current State: 59:[67, 77, 49], Operations: ['14+35=49'] Exploring Operation: 77-67=10, Resulting Numbers: [49, 10] Generated Node #0,2,0: 59:[49, 10] Operation: 77-67=10 Exploring Operation: 77-49=28, Resulting Numbers: [67, 28] Generated Node #0,2,1: 59:[67, 28] Operation: 77-49=28 Exploring Operation: 67-49=18, Resulting Numbers: [77, 18] Generated Node #0,2,2: 59:[77, 18] Operation: 67-49=18 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[67, 28], Operations: ['14+35=49', '77-49=28'] Exploring Operation: 67*28=1876, Resulting Numbers: [1876] 1876,59 unequal: No Solution Exploring Operation: 67-28=39, Resulting Numbers: [39] 39,59 unequal: No Solution Exploring Operation: 67+28=95, Resulting Numbers: [95] 95,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[49, 10], Operations: ['14+35=49', '77-67=10'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,59 unequal: No Solution Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[67, 77, 14, 35], Operations: [] Exploring Operation: 14+35=49, Resulting Numbers: [67, 77, 49] Generated Node #0,2: 59:[67, 77, 49] Operation: 14+35=49 Moving to Node #0,2 Current State: 59:[67, 77, 49], Operations: ['14+35=49'] Exploring Operation: 77-67=10, Resulting Numbers: [49, 10] Generated Node #0,2,0: 59:[49, 10] Operation: 77-67=10 Moving to Node #0,2,0 Current State: 59:[49, 10], Operations: ['14+35=49', '77-67=10'] Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 31, 3, 58, 56 ]
65
[ "58-31=27", "27/3=9", "56+9=65" ]
Current State: 65:[31, 3, 58, 56], Operations: [] Exploring Operation: 58-31=27, Resulting Numbers: [3, 56, 27] Generated Node #2: [3, 56, 27] from Operation: 58-31=27 Current State: 65:[3, 56, 27], Operations: ['58-31=27'] Exploring Operation: 27/3=9, Resulting Numbers: [56, 9] Generated Node #3: [56, 9] from Operation: 27/3=9 Current State: 65:[56, 9], Operations: ['58-31=27', '27/3=9'] Exploring Operation: 56+9=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[31, 3, 58, 56], Operations: [] Exploring Operation: 56-31=25, Resulting Numbers: [3, 58, 25] Generated Node #0,0: 65:[3, 58, 25] Operation: 56-31=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[3, 58, 25], Operations: ['56-31=25'] Exploring Operation: 3+58=61, Resulting Numbers: [25, 61] Generated Node #0,0,0: 65:[25, 61] Operation: 3+58=61 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 65:[25, 61], Operations: ['56-31=25', '3+58=61'] Exploring Operation: 25+61=86, Resulting Numbers: [86] 86,65 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
[ 14, 94, 6, 15 ]
18
[ "14+94=108", "6*15=90", "108-90=18" ]
Current State: 18:[14, 94, 6, 15], Operations: [] Exploring Operation: 14+94=108, Resulting Numbers: [6, 15, 108] Generated Node #2: [6, 15, 108] from Operation: 14+94=108 Current State: 18:[6, 15, 108], Operations: ['14+94=108'] Exploring Operation: 6*15=90, Resulting Numbers: [108, 90] Generated Node #3: [108, 90] from Operation: 6*15=90 Current State: 18:[108, 90], Operations: ['14+94=108', '6*15=90'] Exploring Operation: 108-90=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[14, 94, 6, 15], Operations: [] Exploring Operation: 15-14=1, Resulting Numbers: [94, 6, 1] Generated Node #0,0: 18:[94, 6, 1] Operation: 15-14=1 Exploring Operation: 94-14=80, Resulting Numbers: [6, 15, 80] Generated Node #0,1: 18:[6, 15, 80] Operation: 94-14=80 Exploring Operation: 94-15=79, Resulting Numbers: [14, 6, 79] Generated Node #0,2: 18:[14, 6, 79] Operation: 94-15=79 Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[6, 15, 80], Operations: ['94-14=80'] Exploring Operation: 80-15=65, Resulting Numbers: [6, 65] Generated Node #0,1,0: 18:[6, 65] Operation: 80-15=65 Exploring Operation: 15-6=9, Resulting Numbers: [80, 9] Generated Node #0,1,1: 18:[80, 9] Operation: 15-6=9 Exploring Operation: 80-6=74, Resulting Numbers: [15, 74] Generated Node #0,1,2: 18:[15, 74] Operation: 80-6=74 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 18:[6, 65], Operations: ['94-14=80', '80-15=65'] Exploring Operation: 6+65=71, Resulting Numbers: [71] 71,18 unequal: No Solution Exploring Operation: 6*65=390, Resulting Numbers: [390] 390,18 unequal: No Solution Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 18:[15, 74], Operations: ['94-14=80', '80-6=74'] Exploring Operation: 15+74=89, Resulting Numbers: [89] 89,18 unequal: No Solution Exploring Operation: 15*74=1110, Resulting Numbers: [1110] 1110,18 unequal: No Solution Exploring Operation: 74-15=59, Resulting Numbers: [59] 59,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 18:[80, 9], Operations: ['94-14=80', '15-6=9'] Exploring Operation: 80+9=89, Resulting Numbers: [89] 89,18 unequal: No Solution Exploring Operation: 80*9=720, Resulting Numbers: [720] 720,18 unequal: No Solution Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[14, 6, 79], Operations: ['94-15=79'] Exploring Operation: 79-14=65, Resulting Numbers: [6, 65] Generated Node #0,2,0: 18:[6, 65] Operation: 79-14=65 Exploring Operation: 14-6=8, Resulting Numbers: [79, 8] Generated Node #0,2,1: 18:[79, 8] Operation: 14-6=8 Exploring Operation: 79-6=73, Resulting Numbers: [14, 73] Generated Node #0,2,2: 18:[14, 73] Operation: 79-6=73 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 18:[6, 65], Operations: ['94-15=79', '79-14=65'] Exploring Operation: 6*65=390, Resulting Numbers: [390] 390,18 unequal: No Solution Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 6+65=71, Resulting Numbers: [71] 71,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 18:[14, 73], Operations: ['94-15=79', '79-6=73'] Exploring Operation: 73-14=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 14*73=1022, Resulting Numbers: [1022] 1022,18 unequal: No Solution Exploring Operation: 14+73=87, Resulting Numbers: [87] 87,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 18:[79, 8], Operations: ['94-15=79', '14-6=8'] Exploring Operation: 79*8=632, Resulting Numbers: [632] 632,18 unequal: No Solution Exploring Operation: 79+8=87, Resulting Numbers: [87] 87,18 unequal: No Solution Exploring Operation: 79-8=71, Resulting Numbers: [71] 71,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[94, 6, 1], Operations: ['15-14=1'] Exploring Operation: 94-1=93, Resulting Numbers: [6, 93] Generated Node #0,0,0: 18:[6, 93] Operation: 94-1=93 Exploring Operation: 94-6=88, Resulting Numbers: [1, 88] Generated Node #0,0,1: 18:[1, 88] Operation: 94-6=88 Exploring Operation: 94*1=94, Resulting Numbers: [6, 94] Generated Node #0,0,2: 18:[6, 94] Operation: 94*1=94 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 18:[1, 88], Operations: ['15-14=1', '94-6=88'] Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,18 unequal: No Solution Exploring Operation: 88/1=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 1*88=88, Resulting Numbers: [88] 88,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[6, 93], Operations: ['15-14=1', '94-1=93'] Exploring Operation: 6+93=99, Resulting Numbers: [99] 99,18 unequal: No Solution Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,18 unequal: No Solution Exploring Operation: 6*93=558, Resulting Numbers: [558] 558,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 18:[6, 94], Operations: ['15-14=1', '94*1=94'] Exploring Operation: 6+94=100, Resulting Numbers: [100] 100,18 unequal: No Solution Exploring Operation: 94-6=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 6*94=564, Resulting Numbers: [564] 564,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 84, 44, 52, 88 ]
76
[ "84-44=40", "88-52=36", "40+36=76" ]
Current State: 76:[84, 44, 52, 88], Operations: [] Exploring Operation: 84-44=40, Resulting Numbers: [52, 88, 40] Generated Node #2: [52, 88, 40] from Operation: 84-44=40 Current State: 76:[52, 88, 40], Operations: ['84-44=40'] Exploring Operation: 88-52=36, Resulting Numbers: [40, 36] Generated Node #3: [40, 36] from Operation: 88-52=36 Current State: 76:[40, 36], Operations: ['84-44=40', '88-52=36'] Exploring Operation: 40+36=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[84, 44, 52, 88], Operations: [] Exploring Operation: 88-84=4, Resulting Numbers: [44, 52, 4] Generated Node #0,0: 76:[44, 52, 4] Operation: 88-84=4 Exploring Operation: 84-52=32, Resulting Numbers: [44, 88, 32] Generated Node #0,1: 76:[44, 88, 32] Operation: 84-52=32 Exploring Operation: 88-52=36, Resulting Numbers: [84, 44, 36] Generated Node #0,2: 76:[84, 44, 36] Operation: 88-52=36 Exploring Operation: 88/44=2, Resulting Numbers: [84, 52, 2] Generated Node #0,3: 76:[84, 52, 2] Operation: 88/44=2 Moving to Node #0,2 Current State: 76:[84, 44, 36], Operations: ['88-52=36'] Exploring Operation: 44+36=80, Resulting Numbers: [84, 80] Generated Node #0,2,0: 76:[84, 80] Operation: 44+36=80 Exploring Operation: 84-36=48, Resulting Numbers: [44, 48] Generated Node #0,2,1: 76:[44, 48] Operation: 84-36=48 Exploring Operation: 44-36=8, Resulting Numbers: [84, 8] Generated Node #0,2,2: 76:[84, 8] Operation: 44-36=8 Exploring Operation: 84-44=40, Resulting Numbers: [36, 40] Generated Node #0,2,3: 76:[36, 40] Operation: 84-44=40 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 76:[36, 40], Operations: ['88-52=36', '84-44=40'] Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,76 unequal: No Solution Exploring Operation: 36*40=1440, Resulting Numbers: [1440] 1440,76 unequal: No Solution Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[84, 44, 52, 88], Operations: [] Exploring Operation: 88-52=36, Resulting Numbers: [84, 44, 36] Generated Node #0,2: 76:[84, 44, 36] Operation: 88-52=36 Moving to Node #0,2 Current State: 76:[84, 44, 36], Operations: ['88-52=36'] Exploring Operation: 84-44=40, Resulting Numbers: [36, 40] Generated Node #0,2,3: 76:[36, 40] Operation: 84-44=40 Moving to Node #0,2,3 Current State: 76:[36, 40], Operations: ['88-52=36', '84-44=40'] Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 76, 4, 80, 84 ]
77
[ "4+80=84", "84/84=1", "76+1=77" ]
Current State: 77:[76, 4, 80, 84], Operations: [] Exploring Operation: 4+80=84, Resulting Numbers: [76, 84, 84] Generated Node #2: [76, 84, 84] from Operation: 4+80=84 Current State: 77:[76, 84, 84], Operations: ['4+80=84'] Exploring Operation: 84/84=1, Resulting Numbers: [76, 1] Generated Node #3: [76, 1] from Operation: 84/84=1 Current State: 77:[76, 1], Operations: ['4+80=84', '84/84=1'] Exploring Operation: 76+1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[76, 4, 80, 84], Operations: [] Exploring Operation: 84-76=8, Resulting Numbers: [4, 80, 8] Generated Node #0,0: 77:[4, 80, 8] Operation: 84-76=8 Exploring Operation: 84-4=80, Resulting Numbers: [76, 80, 80] Generated Node #0,1: 77:[76, 80, 80] Operation: 84-4=80 Moving to Node #0,0 Current State: 77:[4, 80, 8], Operations: ['84-76=8'] Exploring Operation: 80-4=76, Resulting Numbers: [8, 76] Generated Node #0,0,0: 77:[8, 76] Operation: 80-4=76 Exploring Operation: 4+8=12, Resulting Numbers: [80, 12] Generated Node #0,0,1: 77:[80, 12] Operation: 4+8=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[8, 76], Operations: ['84-76=8', '80-4=76'] Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,77 unequal: No Solution Exploring Operation: 8+76=84, Resulting Numbers: [84] 84,77 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:[80, 12], Operations: ['84-76=8', '4+8=12'] Exploring Operation: 80+12=92, Resulting Numbers: [92] 92,77 unequal: No Solution Exploring Operation: 80-12=68, Resulting Numbers: [68] 68,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 77:[76, 80, 80], Operations: ['84-4=80'] Exploring Operation: 80-76=4, Resulting Numbers: [80, 4] Generated Node #0,1,0: 77:[80, 4] Operation: 80-76=4 Exploring Operation: 80-76=4, Resulting Numbers: [80, 4] Generated Node #0,1,1: 77:[80, 4] Operation: 80-76=4 Moving to Node #0,1,0 Current State: 77:[80, 4], Operations: ['84-4=80', '80-76=4'] Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,77 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[80, 4], Operations: ['84-4=80', '80-76=4'] Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,77 unequal: No Solution Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,77 unequal: No Solution No solution found.
0
hs_2
mult_heuristic