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
[ 4, 75, 67, 19 ]
13
[ "75-67=8", "4*8=32", "32-19=13" ]
Current State: 13:[4, 75, 67, 19], Operations: [] Exploring Operation: 75-67=8, Resulting Numbers: [4, 19, 8] Generated Node #2: [4, 19, 8] from Operation: 75-67=8 Current State: 13:[4, 19, 8], Operations: ['75-67=8'] Exploring Operation: 4*8=32, Resulting Numbers: [19, 32] Generated Node #3: [19, 32] from Operation: 4*8=32 Current State: 13:[19, 32], Operations: ['75-67=8', '4*8=32'] Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[4, 75, 67, 19], Operations: [] Exploring Operation: 67-4=63, Resulting Numbers: [75, 19, 63] Generated Node #0,0: 13:[75, 19, 63] Operation: 67-4=63 Exploring Operation: 67-19=48, Resulting Numbers: [4, 75, 48] Generated Node #0,1: 13:[4, 75, 48] Operation: 67-19=48 Exploring Operation: 75-67=8, Resulting Numbers: [4, 19, 8] Generated Node #0,2: 13:[4, 19, 8] Operation: 75-67=8 Exploring Operation: 75-19=56, Resulting Numbers: [4, 67, 56] Generated Node #0,3: 13:[4, 67, 56] Operation: 75-19=56 Exploring Operation: 75-4=71, Resulting Numbers: [67, 19, 71] Generated Node #0,4: 13:[67, 19, 71] Operation: 75-4=71 Moving to Node #0,2 Current State: 13:[4, 19, 8], Operations: ['75-67=8'] Exploring Operation: 4+8=12, Resulting Numbers: [19, 12] Generated Node #0,2,0: 13:[19, 12] Operation: 4+8=12 Exploring Operation: 19-8=11, Resulting Numbers: [4, 11] Generated Node #0,2,1: 13:[4, 11] Operation: 19-8=11 Exploring Operation: 8-4=4, Resulting Numbers: [19, 4] Generated Node #0,2,2: 13:[19, 4] Operation: 8-4=4 Exploring Operation: 19-4=15, Resulting Numbers: [8, 15] Generated Node #0,2,3: 13:[8, 15] Operation: 19-4=15 Exploring Operation: 4+19=23, Resulting Numbers: [8, 23] Generated Node #0,2,4: 13:[8, 23] Operation: 4+19=23 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 13:[19, 12], Operations: ['75-67=8', '4+8=12'] Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,13 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,13 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 13:[8, 15], Operations: ['75-67=8', '19-4=15'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,13 unequal: No Solution Exploring Operation: 8*15=120, Resulting Numbers: [120] 120,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 13:[4, 11], Operations: ['75-67=8', '19-8=11'] Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,13 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 13:[19, 4], Operations: ['75-67=8', '8-4=4'] Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,13 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 13:[8, 23], Operations: ['75-67=8', '4+19=23'] Exploring Operation: 8*23=184, Resulting Numbers: [184] 184,13 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 8+23=31, Resulting Numbers: [31] 31,13 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: 13:[4, 67, 56], Operations: ['75-19=56'] Exploring Operation: 4+67=71, Resulting Numbers: [56, 71] Generated Node #0,3,0: 13:[56, 71] Operation: 4+67=71 Exploring Operation: 56-4=52, Resulting Numbers: [67, 52] Generated Node #0,3,1: 13:[67, 52] Operation: 56-4=52 Exploring Operation: 56/4=14, Resulting Numbers: [67, 14] Generated Node #0,3,2: 13:[67, 14] Operation: 56/4=14 Exploring Operation: 67-4=63, Resulting Numbers: [56, 63] Generated Node #0,3,3: 13:[56, 63] Operation: 67-4=63 Exploring Operation: 67-56=11, Resulting Numbers: [4, 11] Generated Node #0,3,4: 13:[4, 11] Operation: 67-56=11 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 13:[4, 11], Operations: ['75-19=56', '67-56=11'] Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,13 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 13:[67, 14], Operations: ['75-19=56', '56/4=14'] Exploring Operation: 67*14=938, Resulting Numbers: [938] 938,13 unequal: No Solution Exploring Operation: 67-14=53, Resulting Numbers: [53] 53,13 unequal: No Solution Exploring Operation: 67+14=81, Resulting Numbers: [81] 81,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 13:[67, 52], Operations: ['75-19=56', '56-4=52'] Exploring Operation: 67*52=3484, Resulting Numbers: [3484] 3484,13 unequal: No Solution Exploring Operation: 67-52=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 67+52=119, Resulting Numbers: [119] 119,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 13:[56, 63], Operations: ['75-19=56', '67-4=63'] Exploring Operation: 56+63=119, Resulting Numbers: [119] 119,13 unequal: No Solution Exploring Operation: 56*63=3528, Resulting Numbers: [3528] 3528,13 unequal: No Solution Exploring Operation: 63-56=7, Resulting Numbers: [7] 7,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 13:[56, 71], Operations: ['75-19=56', '4+67=71'] Exploring Operation: 56*71=3976, Resulting Numbers: [3976] 3976,13 unequal: No Solution Exploring Operation: 56+71=127, Resulting Numbers: [127] 127,13 unequal: No Solution Exploring Operation: 71-56=15, Resulting Numbers: [15] 15,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 13:[4, 75, 48], Operations: ['67-19=48'] Exploring Operation: 48-4=44, Resulting Numbers: [75, 44] Generated Node #0,1,0: 13:[75, 44] Operation: 48-4=44 Exploring Operation: 48/4=12, Resulting Numbers: [75, 12] Generated Node #0,1,1: 13:[75, 12] Operation: 48/4=12 Exploring Operation: 4+75=79, Resulting Numbers: [48, 79] Generated Node #0,1,2: 13:[48, 79] Operation: 4+75=79 Exploring Operation: 75-4=71, Resulting Numbers: [48, 71] Generated Node #0,1,3: 13:[48, 71] Operation: 75-4=71 Exploring Operation: 75-48=27, Resulting Numbers: [4, 27] Generated Node #0,1,4: 13:[4, 27] Operation: 75-48=27 Moving to Node #0,0 Current State: 13:[75, 19, 63], Operations: ['67-4=63'] Exploring Operation: 63-19=44, Resulting Numbers: [75, 44] Generated Node #0,0,0: 13:[75, 44] Operation: 63-19=44 Exploring Operation: 75-63=12, Resulting Numbers: [19, 12] Generated Node #0,0,1: 13:[19, 12] Operation: 75-63=12 Exploring Operation: 75+63=138, Resulting Numbers: [19, 138] Generated Node #0,0,2: 13:[19, 138] Operation: 75+63=138 Exploring Operation: 75+19=94, Resulting Numbers: [63, 94] Generated Node #0,0,3: 13:[63, 94] Operation: 75+19=94 Exploring Operation: 75-19=56, Resulting Numbers: [63, 56] Generated Node #0,0,4: 13:[63, 56] Operation: 75-19=56 Moving to Node #0,4 Current State: 13:[67, 19, 71], Operations: ['75-4=71'] Exploring Operation: 67-19=48, Resulting Numbers: [71, 48] Generated Node #0,4,0: 13:[71, 48] Operation: 67-19=48 Exploring Operation: 71-67=4, Resulting Numbers: [19, 4] Generated Node #0,4,1: 13:[19, 4] Operation: 71-67=4 Exploring Operation: 71-19=52, Resulting Numbers: [67, 52] Generated Node #0,4,2: 13:[67, 52] Operation: 71-19=52 Exploring Operation: 67+19=86, Resulting Numbers: [71, 86] Generated Node #0,4,3: 13:[71, 86] Operation: 67+19=86 Exploring Operation: 67+71=138, Resulting Numbers: [19, 138] Generated Node #0,4,4: 13:[19, 138] Operation: 67+71=138 Moving to Node #0,0,1 Current State: 13:[19, 12], Operations: ['67-4=63', '75-63=12'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,13 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,13 unequal: No Solution Moving to Node #0,4,1 Current State: 13:[19, 4], Operations: ['75-4=71', '71-67=4'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,13 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,13 unequal: No Solution Moving to Node #0,1,4 Current State: 13:[4, 27], Operations: ['67-19=48', '75-48=27'] Exploring Operation: 4*27=108, Resulting Numbers: [108] 108,13 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,13 unequal: No Solution Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[75, 12], Operations: ['67-19=48', '48/4=12'] Exploring Operation: 75+12=87, Resulting Numbers: [87] 87,13 unequal: No Solution Exploring Operation: 75*12=900, Resulting Numbers: [900] 900,13 unequal: No Solution Exploring Operation: 75-12=63, Resulting Numbers: [63] 63,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[75, 44], Operations: ['67-4=63', '63-19=44'] Exploring Operation: 75*44=3300, Resulting Numbers: [3300] 3300,13 unequal: No Solution Exploring Operation: 75+44=119, Resulting Numbers: [119] 119,13 unequal: No Solution Exploring Operation: 75-44=31, Resulting Numbers: [31] 31,13 unequal: No Solution Moving to Node #0,1,0 Current State: 13:[75, 44], Operations: ['67-19=48', '48-4=44'] Exploring Operation: 75*44=3300, Resulting Numbers: [3300] 3300,13 unequal: No Solution Exploring Operation: 75-44=31, Resulting Numbers: [31] 31,13 unequal: No Solution Exploring Operation: 75+44=119, Resulting Numbers: [119] 119,13 unequal: No Solution Moving to Node #0,4,0 Current State: 13:[71, 48], Operations: ['75-4=71', '67-19=48'] Exploring Operation: 71*48=3408, Resulting Numbers: [3408] 3408,13 unequal: No Solution Exploring Operation: 71+48=119, Resulting Numbers: [119] 119,13 unequal: No Solution Exploring Operation: 71-48=23, Resulting Numbers: [23] 23,13 unequal: No Solution Moving to Node #0,1,3 Current State: 13:[48, 71], Operations: ['67-19=48', '75-4=71'] Exploring Operation: 48*71=3408, Resulting Numbers: [3408] 3408,13 unequal: No Solution Exploring Operation: 71-48=23, Resulting Numbers: [23] 23,13 unequal: No Solution Exploring Operation: 48+71=119, Resulting Numbers: [119] 119,13 unequal: No Solution Moving to Node #0,0,4 Current State: 13:[63, 56], Operations: ['67-4=63', '75-19=56'] Exploring Operation: 63-56=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 63+56=119, Resulting Numbers: [119] 119,13 unequal: No Solution Exploring Operation: 63*56=3528, Resulting Numbers: [3528] 3528,13 unequal: No Solution Moving to Node #0,4,2 Current State: 13:[67, 52], Operations: ['75-4=71', '71-19=52'] Exploring Operation: 67-52=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 67+52=119, Resulting Numbers: [119] 119,13 unequal: No Solution Exploring Operation: 67*52=3484, Resulting Numbers: [3484] 3484,13 unequal: No Solution Moving to Node #0,1,2 Current State: 13:[48, 79], Operations: ['67-19=48', '4+75=79'] Exploring Operation: 48+79=127, Resulting Numbers: [127] 127,13 unequal: No Solution Exploring Operation: 79-48=31, Resulting Numbers: [31] 31,13 unequal: No Solution Exploring Operation: 48*79=3792, Resulting Numbers: [3792] 3792,13 unequal: No Solution Moving to Node #0,4,3 Current State: 13:[71, 86], Operations: ['75-4=71', '67+19=86'] Exploring Operation: 71*86=6106, Resulting Numbers: [6106] 6106,13 unequal: No Solution Exploring Operation: 71+86=157, Resulting Numbers: [157] 157,13 unequal: No Solution Exploring Operation: 86-71=15, Resulting Numbers: [15] 15,13 unequal: No Solution Moving to Node #0,4,4 Current State: 13:[19, 138], Operations: ['75-4=71', '67+71=138'] Exploring Operation: 19*138=2622, Resulting Numbers: [2622] 2622,13 unequal: No Solution Exploring Operation: 19+138=157, Resulting Numbers: [157] 157,13 unequal: No Solution Exploring Operation: 138-19=119, Resulting Numbers: [119] 119,13 unequal: No Solution Moving to Node #0,0,3 Current State: 13:[63, 94], Operations: ['67-4=63', '75+19=94'] Exploring Operation: 94-63=31, Resulting Numbers: [31] 31,13 unequal: No Solution Exploring Operation: 63*94=5922, Resulting Numbers: [5922] 5922,13 unequal: No Solution Exploring Operation: 63+94=157, Resulting Numbers: [157] 157,13 unequal: No Solution Moving to Node #0,0,2 Current State: 13:[19, 138], Operations: ['67-4=63', '75+63=138'] Exploring Operation: 19*138=2622, Resulting Numbers: [2622] 2622,13 unequal: No Solution Exploring Operation: 19+138=157, Resulting Numbers: [157] 157,13 unequal: No Solution Exploring Operation: 138-19=119, Resulting Numbers: [119] 119,13 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 18, 71, 31, 14 ]
10
[ "18-14=4", "71-31=40", "40/4=10" ]
Current State: 10:[18, 71, 31, 14], Operations: [] Exploring Operation: 18-14=4, Resulting Numbers: [71, 31, 4] Generated Node #2: [71, 31, 4] from Operation: 18-14=4 Current State: 10:[71, 31, 4], Operations: ['18-14=4'] Exploring Operation: 71-31=40, Resulting Numbers: [4, 40] Generated Node #3: [4, 40] from Operation: 71-31=40 Current State: 10:[4, 40], Operations: ['18-14=4', '71-31=40'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[18, 71, 31, 14], Operations: [] Exploring Operation: 71-14=57, Resulting Numbers: [18, 31, 57] Generated Node #0,0: 10:[18, 31, 57] Operation: 71-14=57 Exploring Operation: 71-31=40, Resulting Numbers: [18, 14, 40] Generated Node #0,1: 10:[18, 14, 40] Operation: 71-31=40 Exploring Operation: 31-18=13, Resulting Numbers: [71, 14, 13] Generated Node #0,2: 10:[71, 14, 13] Operation: 31-18=13 Exploring Operation: 71-18=53, Resulting Numbers: [31, 14, 53] Generated Node #0,3: 10:[31, 14, 53] Operation: 71-18=53 Moving to Node #0,1 Current State: 10:[18, 14, 40], Operations: ['71-31=40'] Exploring Operation: 18+14=32, Resulting Numbers: [40, 32] Generated Node #0,1,0: 10:[40, 32] Operation: 18+14=32 Exploring Operation: 40-14=26, Resulting Numbers: [18, 26] Generated Node #0,1,1: 10:[18, 26] Operation: 40-14=26 Exploring Operation: 18-14=4, Resulting Numbers: [40, 4] Generated Node #0,1,2: 10:[40, 4] Operation: 18-14=4 Exploring Operation: 40-18=22, Resulting Numbers: [14, 22] Generated Node #0,1,3: 10:[14, 22] Operation: 40-18=22 Moving to Node #0,3 Current State: 10:[31, 14, 53], Operations: ['71-18=53'] Exploring Operation: 53-14=39, Resulting Numbers: [31, 39] Generated Node #0,3,0: 10:[31, 39] Operation: 53-14=39 Exploring Operation: 31+14=45, Resulting Numbers: [53, 45] Generated Node #0,3,1: 10:[53, 45] Operation: 31+14=45 Exploring Operation: 31-14=17, Resulting Numbers: [53, 17] Generated Node #0,3,2: 10:[53, 17] Operation: 31-14=17 Exploring Operation: 53-31=22, Resulting Numbers: [14, 22] Generated Node #0,3,3: 10:[14, 22] Operation: 53-31=22 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 10:[14, 22], Operations: ['71-18=53', '53-31=22'] Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,10 unequal: No Solution Exploring Operation: 14+22=36, Resulting Numbers: [36] 36,10 unequal: No Solution Exploring Operation: 14*22=308, Resulting Numbers: [308] 308,10 unequal: No Solution No 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: 10:[31, 39], Operations: ['71-18=53', '53-14=39'] Exploring Operation: 31*39=1209, Resulting Numbers: [1209] 1209,10 unequal: No Solution Exploring Operation: 31+39=70, Resulting Numbers: [70] 70,10 unequal: No Solution Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,10 unequal: No Solution No 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: 10:[53, 17], Operations: ['71-18=53', '31-14=17'] Exploring Operation: 53+17=70, Resulting Numbers: [70] 70,10 unequal: No Solution Exploring Operation: 53-17=36, Resulting Numbers: [36] 36,10 unequal: No Solution Exploring Operation: 53*17=901, Resulting Numbers: [901] 901,10 unequal: No Solution No 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: 10:[53, 45], Operations: ['71-18=53', '31+14=45'] Exploring Operation: 53+45=98, Resulting Numbers: [98] 98,10 unequal: No Solution Exploring Operation: 53-45=8, Resulting Numbers: [8] 8,10 unequal: No Solution Exploring Operation: 53*45=2385, Resulting Numbers: [2385] 2385,10 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: 10:[71, 14, 13], Operations: ['31-18=13'] Exploring Operation: 14-13=1, Resulting Numbers: [71, 1] Generated Node #0,2,0: 10:[71, 1] Operation: 14-13=1 Exploring Operation: 71-14=57, Resulting Numbers: [13, 57] Generated Node #0,2,1: 10:[13, 57] Operation: 71-14=57 Exploring Operation: 71+14=85, Resulting Numbers: [13, 85] Generated Node #0,2,2: 10:[13, 85] Operation: 71+14=85 Exploring Operation: 71-13=58, Resulting Numbers: [14, 58] Generated Node #0,2,3: 10:[14, 58] Operation: 71-13=58 Moving to Node #0,0 Current State: 10:[18, 31, 57], Operations: ['71-14=57'] Exploring Operation: 31-18=13, Resulting Numbers: [57, 13] Generated Node #0,0,0: 10:[57, 13] Operation: 31-18=13 Exploring Operation: 18+31=49, Resulting Numbers: [57, 49] Generated Node #0,0,1: 10:[57, 49] Operation: 18+31=49 Exploring Operation: 57-31=26, Resulting Numbers: [18, 26] Generated Node #0,0,2: 10:[18, 26] Operation: 57-31=26 Exploring Operation: 57-18=39, Resulting Numbers: [31, 39] Generated Node #0,0,3: 10:[31, 39] Operation: 57-18=39 Moving to Node #0,1,3 Current State: 10:[14, 22], Operations: ['71-31=40', '40-18=22'] Exploring Operation: 14*22=308, Resulting Numbers: [308] 308,10 unequal: No Solution Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,10 unequal: No Solution Exploring Operation: 14+22=36, Resulting Numbers: [36] 36,10 unequal: No Solution Moving to Node #0,1,1 Current State: 10:[18, 26], Operations: ['71-31=40', '40-14=26'] Exploring Operation: 26-18=8, Resulting Numbers: [8] 8,10 unequal: No Solution Exploring Operation: 18+26=44, Resulting Numbers: [44] 44,10 unequal: No Solution Exploring Operation: 18*26=468, Resulting Numbers: [468] 468,10 unequal: No Solution Moving to Node #0,0,2 Current State: 10:[18, 26], Operations: ['71-14=57', '57-31=26'] Exploring Operation: 26-18=8, Resulting Numbers: [8] 8,10 unequal: No Solution Exploring Operation: 18*26=468, Resulting Numbers: [468] 468,10 unequal: No Solution Exploring Operation: 18+26=44, Resulting Numbers: [44] 44,10 unequal: No Solution Moving to Node #0,1,2 Current State: 10:[40, 4], Operations: ['71-31=40', '18-14=4'] Exploring Operation: 40+4=44, Resulting Numbers: [44] 44,10 unequal: No Solution Exploring Operation: 40*4=160, Resulting Numbers: [160] 160,10 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,10 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[18, 71, 31, 14], Operations: [] Exploring Operation: 71-31=40, Resulting Numbers: [18, 14, 40] Generated Node #0,1: 10:[18, 14, 40] Operation: 71-31=40 Moving to Node #0,1 Current State: 10:[18, 14, 40], Operations: ['71-31=40'] Exploring Operation: 18-14=4, Resulting Numbers: [40, 4] Generated Node #0,1,2: 10:[40, 4] Operation: 18-14=4 Moving to Node #0,1,2 Current State: 10:[40, 4], Operations: ['71-31=40', '18-14=4'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.957465
hs_4
sum_heuristic
[ 93, 3, 9, 41 ]
24
[ "3*41=123", "93+123=216", "216/9=24" ]
Current State: 24:[93, 3, 9, 41], Operations: [] Exploring Operation: 3*41=123, Resulting Numbers: [93, 9, 123] Generated Node #2: [93, 9, 123] from Operation: 3*41=123 Current State: 24:[93, 9, 123], Operations: ['3*41=123'] Exploring Operation: 93+123=216, Resulting Numbers: [9, 216] Generated Node #3: [9, 216] from Operation: 93+123=216 Current State: 24:[9, 216], Operations: ['3*41=123', '93+123=216'] Exploring Operation: 216/9=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[93, 3, 9, 41], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [9, 41, 31] Generated Node #0,0: 24:[9, 41, 31] Operation: 93/3=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[9, 41, 31], Operations: ['93/3=31'] Exploring Operation: 41-31=10, Resulting Numbers: [9, 10] Generated Node #0,0,0: 24:[9, 10] Operation: 41-31=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[9, 10], Operations: ['93/3=31', '41-31=10'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,24 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 No solution found.
0
hs_1
mult_heuristic
[ 10, 62, 25, 5 ]
89
[ "10/5=2", "62+25=87", "2+87=89" ]
Current State: 89:[10, 62, 25, 5], Operations: [] Exploring Operation: 10/5=2, Resulting Numbers: [62, 25, 2] Generated Node #2: [62, 25, 2] from Operation: 10/5=2 Current State: 89:[62, 25, 2], Operations: ['10/5=2'] Exploring Operation: 62+25=87, Resulting Numbers: [2, 87] Generated Node #3: [2, 87] from Operation: 62+25=87 Current State: 89:[2, 87], Operations: ['10/5=2', '62+25=87'] Exploring Operation: 2+87=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[10, 62, 25, 5], Operations: [] Exploring Operation: 10+62=72, Resulting Numbers: [25, 5, 72] Generated Node #0,0: 89:[25, 5, 72] Operation: 10+62=72 Exploring Operation: 10*5=50, Resulting Numbers: [62, 25, 50] Generated Node #0,1: 89:[62, 25, 50] Operation: 10*5=50 Exploring Operation: 25*5=125, Resulting Numbers: [10, 62, 125] Generated Node #0,2: 89:[10, 62, 125] Operation: 25*5=125 Exploring Operation: 10+25=35, Resulting Numbers: [62, 5, 35] Generated Node #0,3: 89:[62, 5, 35] Operation: 10+25=35 Moving to Node #0,1 Current State: 89:[62, 25, 50], Operations: ['10*5=50'] Exploring Operation: 62+50=112, Resulting Numbers: [25, 112] Generated Node #0,1,0: 89:[25, 112] Operation: 62+50=112 Exploring Operation: 25+50=75, Resulting Numbers: [62, 75] Generated Node #0,1,1: 89:[62, 75] Operation: 25+50=75 Exploring Operation: 62+25=87, Resulting Numbers: [50, 87] Generated Node #0,1,2: 89:[50, 87] Operation: 62+25=87 Exploring Operation: 62-25=37, Resulting Numbers: [50, 37] Generated Node #0,1,3: 89:[50, 37] Operation: 62-25=37 Moving to Node #0,2 Current State: 89:[10, 62, 125], Operations: ['25*5=125'] Exploring Operation: 10+62=72, Resulting Numbers: [125, 72] Generated Node #0,2,0: 89:[125, 72] Operation: 10+62=72 Exploring Operation: 125-10=115, Resulting Numbers: [62, 115] Generated Node #0,2,1: 89:[62, 115] Operation: 125-10=115 Exploring Operation: 10+125=135, Resulting Numbers: [62, 135] Generated Node #0,2,2: 89:[62, 135] Operation: 10+125=135 Exploring Operation: 62-10=52, Resulting Numbers: [125, 52] Generated Node #0,2,3: 89:[125, 52] Operation: 62-10=52 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 89:[125, 72], Operations: ['25*5=125', '10+62=72'] Exploring Operation: 125+72=197, Resulting Numbers: [197] 197,89 unequal: No Solution Exploring Operation: 125*72=9000, Resulting Numbers: [9000] 9000,89 unequal: No Solution Exploring Operation: 125-72=53, Resulting Numbers: [53] 53,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 89:[62, 115], Operations: ['25*5=125', '125-10=115'] Exploring Operation: 62*115=7130, Resulting Numbers: [7130] 7130,89 unequal: No Solution Exploring Operation: 62+115=177, Resulting Numbers: [177] 177,89 unequal: No Solution Exploring Operation: 115-62=53, Resulting Numbers: [53] 53,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[62, 135], Operations: ['25*5=125', '10+125=135'] Exploring Operation: 62*135=8370, Resulting Numbers: [8370] 8370,89 unequal: No Solution Exploring Operation: 62+135=197, Resulting Numbers: [197] 197,89 unequal: No Solution Exploring Operation: 135-62=73, Resulting Numbers: [73] 73,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 89:[125, 52], Operations: ['25*5=125', '62-10=52'] Exploring Operation: 125*52=6500, Resulting Numbers: [6500] 6500,89 unequal: No Solution Exploring Operation: 125+52=177, Resulting Numbers: [177] 177,89 unequal: No Solution Exploring Operation: 125-52=73, Resulting Numbers: [73] 73,89 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: 89:[62, 5, 35], Operations: ['10+25=35'] Exploring Operation: 62+5=67, Resulting Numbers: [35, 67] Generated Node #0,3,0: 89:[35, 67] Operation: 62+5=67 Exploring Operation: 35-5=30, Resulting Numbers: [62, 30] Generated Node #0,3,1: 89:[62, 30] Operation: 35-5=30 Exploring Operation: 62-5=57, Resulting Numbers: [35, 57] Generated Node #0,3,2: 89:[35, 57] Operation: 62-5=57 Exploring Operation: 5+35=40, Resulting Numbers: [62, 40] Generated Node #0,3,3: 89:[62, 40] Operation: 5+35=40 Moving to Node #0,0 Current State: 89:[25, 5, 72], Operations: ['10+62=72'] Exploring Operation: 25+5=30, Resulting Numbers: [72, 30] Generated Node #0,0,0: 89:[72, 30] Operation: 25+5=30 Exploring Operation: 25-5=20, Resulting Numbers: [72, 20] Generated Node #0,0,1: 89:[72, 20] Operation: 25-5=20 Exploring Operation: 25*5=125, Resulting Numbers: [72, 125] Generated Node #0,0,2: 89:[72, 125] Operation: 25*5=125 Exploring Operation: 5+72=77, Resulting Numbers: [25, 77] Generated Node #0,0,3: 89:[25, 77] Operation: 5+72=77 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 89:[72, 125], Operations: ['10+62=72', '25*5=125'] Exploring Operation: 125-72=53, Resulting Numbers: [53] 53,89 unequal: No Solution Exploring Operation: 72*125=9000, Resulting Numbers: [9000] 9000,89 unequal: No Solution Exploring Operation: 72+125=197, Resulting Numbers: [197] 197,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[72, 30], Operations: ['10+62=72', '25+5=30'] Exploring Operation: 72+30=102, Resulting Numbers: [102] 102,89 unequal: No Solution Exploring Operation: 72*30=2160, Resulting Numbers: [2160] 2160,89 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 89:[25, 77], Operations: ['10+62=72', '5+72=77'] Exploring Operation: 77-25=52, Resulting Numbers: [52] 52,89 unequal: No Solution Exploring Operation: 25+77=102, Resulting Numbers: [102] 102,89 unequal: No Solution Exploring Operation: 25*77=1925, Resulting Numbers: [1925] 1925,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[72, 20], Operations: ['10+62=72', '25-5=20'] Exploring Operation: 72+20=92, Resulting Numbers: [92] 92,89 unequal: No Solution Exploring Operation: 72*20=1440, Resulting Numbers: [1440] 1440,89 unequal: No Solution Exploring Operation: 72-20=52, Resulting Numbers: [52] 52,89 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: 89:[62, 75], Operations: ['10*5=50', '25+50=75'] Exploring Operation: 62+75=137, Resulting Numbers: [137] 137,89 unequal: No Solution Exploring Operation: 75-62=13, Resulting Numbers: [13] 13,89 unequal: No Solution Exploring Operation: 62*75=4650, Resulting Numbers: [4650] 4650,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[50, 87], Operations: ['10*5=50', '62+25=87'] Exploring Operation: 50+87=137, Resulting Numbers: [137] 137,89 unequal: No Solution Exploring Operation: 87-50=37, Resulting Numbers: [37] 37,89 unequal: No Solution Exploring Operation: 50*87=4350, Resulting Numbers: [4350] 4350,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[62, 40], Operations: ['10+25=35', '5+35=40'] Exploring Operation: 62*40=2480, Resulting Numbers: [2480] 2480,89 unequal: No Solution Exploring Operation: 62+40=102, Resulting Numbers: [102] 102,89 unequal: No Solution Exploring Operation: 62-40=22, Resulting Numbers: [22] 22,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[35, 67], Operations: ['10+25=35', '62+5=67'] Exploring Operation: 35*67=2345, Resulting Numbers: [2345] 2345,89 unequal: No Solution Exploring Operation: 35+67=102, Resulting Numbers: [102] 102,89 unequal: No Solution Exploring Operation: 67-35=32, Resulting Numbers: [32] 32,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[62, 30], Operations: ['10+25=35', '35-5=30'] Exploring Operation: 62+30=92, Resulting Numbers: [92] 92,89 unequal: No Solution Exploring Operation: 62-30=32, Resulting Numbers: [32] 32,89 unequal: No Solution Exploring Operation: 62*30=1860, Resulting Numbers: [1860] 1860,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[35, 57], Operations: ['10+25=35', '62-5=57'] Exploring Operation: 35+57=92, Resulting Numbers: [92] 92,89 unequal: No Solution Exploring Operation: 35*57=1995, Resulting Numbers: [1995] 1995,89 unequal: No Solution Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[25, 112], Operations: ['10*5=50', '62+50=112'] Exploring Operation: 25*112=2800, Resulting Numbers: [2800] 2800,89 unequal: No Solution Exploring Operation: 25+112=137, Resulting Numbers: [137] 137,89 unequal: No Solution Exploring Operation: 112-25=87, Resulting Numbers: [87] 87,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[50, 37], Operations: ['10*5=50', '62-25=37'] Exploring Operation: 50*37=1850, Resulting Numbers: [1850] 1850,89 unequal: No Solution Exploring Operation: 50+37=87, Resulting Numbers: [87] 87,89 unequal: No Solution Exploring Operation: 50-37=13, Resulting Numbers: [13] 13,89 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 5, 60, 15, 43 ]
44
[ "5+43=48", "60/15=4", "48-4=44" ]
Current State: 44:[5, 60, 15, 43], Operations: [] Exploring Operation: 5+43=48, Resulting Numbers: [60, 15, 48] Generated Node #2: [60, 15, 48] from Operation: 5+43=48 Current State: 44:[60, 15, 48], Operations: ['5+43=48'] Exploring Operation: 60/15=4, Resulting Numbers: [48, 4] Generated Node #3: [48, 4] from Operation: 60/15=4 Current State: 44:[48, 4], Operations: ['5+43=48', '60/15=4'] Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[5, 60, 15, 43], Operations: [] Exploring Operation: 60-43=17, Resulting Numbers: [5, 15, 17] Generated Node #0,0: 44:[5, 15, 17] Operation: 60-43=17 Exploring Operation: 60/5=12, Resulting Numbers: [15, 43, 12] Generated Node #0,1: 44:[15, 43, 12] Operation: 60/5=12 Exploring Operation: 60/15=4, Resulting Numbers: [5, 43, 4] Generated Node #0,2: 44:[5, 43, 4] Operation: 60/15=4 Exploring Operation: 60-15=45, Resulting Numbers: [5, 43, 45] Generated Node #0,3: 44:[5, 43, 45] Operation: 60-15=45 Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[5, 43, 4], Operations: ['60/15=4'] Exploring Operation: 5+43=48, Resulting Numbers: [4, 48] Generated Node #0,2,0: 44:[4, 48] Operation: 5+43=48 Exploring Operation: 5-4=1, Resulting Numbers: [43, 1] Generated Node #0,2,1: 44:[43, 1] Operation: 5-4=1 Exploring Operation: 5*4=20, Resulting Numbers: [43, 20] Generated Node #0,2,2: 44:[43, 20] Operation: 5*4=20 Exploring Operation: 5+4=9, Resulting Numbers: [43, 9] Generated Node #0,2,3: 44:[43, 9] Operation: 5+4=9 Moving to Node #0,2,1 Current State: 44:[43, 1], Operations: ['60/15=4', '5-4=1'] Exploring Operation: 43+1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[5, 60, 15, 43], Operations: [] Exploring Operation: 60/15=4, Resulting Numbers: [5, 43, 4] Generated Node #0,2: 44:[5, 43, 4] Operation: 60/15=4 Moving to Node #0,2 Current State: 44:[5, 43, 4], Operations: ['60/15=4'] Exploring Operation: 5-4=1, Resulting Numbers: [43, 1] Generated Node #0,2,1: 44:[43, 1] Operation: 5-4=1 Moving to Node #0,2,1 Current State: 44:[43, 1], Operations: ['60/15=4', '5-4=1'] Exploring Operation: 43+1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 91, 66, 97, 66 ]
91
[ "66-66=0", "97*0=0", "91+0=91" ]
Current State: 91:[91, 66, 97, 66], Operations: [] Exploring Operation: 66-66=0, Resulting Numbers: [91, 97, 0] Generated Node #2: [91, 97, 0] from Operation: 66-66=0 Current State: 91:[91, 97, 0], Operations: ['66-66=0'] Exploring Operation: 97*0=0, Resulting Numbers: [91, 0] Generated Node #3: [91, 0] from Operation: 97*0=0 Current State: 91:[91, 0], Operations: ['66-66=0', '97*0=0'] Exploring Operation: 91+0=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[91, 66, 97, 66], Operations: [] Exploring Operation: 66/66=1, Resulting Numbers: [91, 97, 1] Generated Node #0,0: 91:[91, 97, 1] Operation: 66/66=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[91, 97, 1], Operations: ['66/66=1'] Exploring Operation: 97-1=96, Resulting Numbers: [91, 96] Generated Node #0,0,0: 91:[91, 96] Operation: 97-1=96 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[91, 96], Operations: ['66/66=1', '97-1=96'] Exploring Operation: 96-91=5, Resulting Numbers: [5] 5,91 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_1
sum_heuristic
[ 68, 38, 76, 75 ]
31
[ "68-38=30", "76-75=1", "30+1=31" ]
Current State: 31:[68, 38, 76, 75], Operations: [] Exploring Operation: 68-38=30, Resulting Numbers: [76, 75, 30] Generated Node #2: [76, 75, 30] from Operation: 68-38=30 Current State: 31:[76, 75, 30], Operations: ['68-38=30'] Exploring Operation: 76-75=1, Resulting Numbers: [30, 1] Generated Node #3: [30, 1] from Operation: 76-75=1 Current State: 31:[30, 1], Operations: ['68-38=30', '76-75=1'] Exploring Operation: 30+1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[68, 38, 76, 75], Operations: [] Exploring Operation: 76-68=8, Resulting Numbers: [38, 75, 8] Generated Node #0,0: 31:[38, 75, 8] Operation: 76-68=8 Exploring Operation: 76-75=1, Resulting Numbers: [68, 38, 1] Generated Node #0,1: 31:[68, 38, 1] Operation: 76-75=1 Moving to Node #0,0 Current State: 31:[38, 75, 8], Operations: ['76-68=8'] Exploring Operation: 75-8=67, Resulting Numbers: [38, 67] Generated Node #0,0,0: 31:[38, 67] Operation: 75-8=67 Exploring Operation: 75-38=37, Resulting Numbers: [8, 37] Generated Node #0,0,1: 31:[8, 37] Operation: 75-38=37 Moving to Node #0,1 Current State: 31:[68, 38, 1], Operations: ['76-75=1'] Exploring Operation: 68-1=67, Resulting Numbers: [38, 67] Generated Node #0,1,0: 31:[38, 67] Operation: 68-1=67 Exploring Operation: 68-38=30, Resulting Numbers: [1, 30] Generated Node #0,1,1: 31:[1, 30] Operation: 68-38=30 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[1, 30], Operations: ['76-75=1', '68-38=30'] Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,31 unequal: No Solution Exploring Operation: 1+30=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[68, 38, 76, 75], Operations: [] Exploring Operation: 76-75=1, Resulting Numbers: [68, 38, 1] Generated Node #0,1: 31:[68, 38, 1] Operation: 76-75=1 Moving to Node #0,1 Current State: 31:[68, 38, 1], Operations: ['76-75=1'] Exploring Operation: 68-38=30, Resulting Numbers: [1, 30] Generated Node #0,1,1: 31:[1, 30] Operation: 68-38=30 Moving to Node #0,1,1 Current State: 31:[1, 30], Operations: ['76-75=1', '68-38=30'] Exploring Operation: 1+30=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 18, 22, 58, 5 ]
58
[ "22-18=4", "5-4=1", "58*1=58" ]
Current State: 58:[18, 22, 58, 5], Operations: [] Exploring Operation: 22-18=4, Resulting Numbers: [58, 5, 4] Generated Node #2: [58, 5, 4] from Operation: 22-18=4 Current State: 58:[58, 5, 4], Operations: ['22-18=4'] Exploring Operation: 5-4=1, Resulting Numbers: [58, 1] Generated Node #3: [58, 1] from Operation: 5-4=1 Current State: 58:[58, 1], Operations: ['22-18=4', '5-4=1'] Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[18, 22, 58, 5], Operations: [] Exploring Operation: 22-18=4, Resulting Numbers: [58, 5, 4] Generated Node #0,0: 58:[58, 5, 4] Operation: 22-18=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[58, 5, 4], Operations: ['22-18=4'] Exploring Operation: 5-4=1, Resulting Numbers: [58, 1] Generated Node #0,0,0: 58:[58, 1] Operation: 5-4=1 Moving to Node #0,0,0 Current State: 58:[58, 1], Operations: ['22-18=4', '5-4=1'] Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[18, 22, 58, 5], Operations: [] Exploring Operation: 22-18=4, Resulting Numbers: [58, 5, 4] Generated Node #0,0: 58:[58, 5, 4] Operation: 22-18=4 Moving to Node #0,0 Current State: 58:[58, 5, 4], Operations: ['22-18=4'] Exploring Operation: 5-4=1, Resulting Numbers: [58, 1] Generated Node #0,0,0: 58:[58, 1] Operation: 5-4=1 Moving to Node #0,0,0 Current State: 58:[58, 1], Operations: ['22-18=4', '5-4=1'] Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 73, 78, 4, 62 ]
63
[ "78-73=5", "62-4=58", "5+58=63" ]
Current State: 63:[73, 78, 4, 62], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [4, 62, 5] Generated Node #2: [4, 62, 5] from Operation: 78-73=5 Current State: 63:[4, 62, 5], Operations: ['78-73=5'] Exploring Operation: 62-4=58, Resulting Numbers: [5, 58] Generated Node #3: [5, 58] from Operation: 62-4=58 Current State: 63:[5, 58], Operations: ['78-73=5', '62-4=58'] Exploring Operation: 5+58=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[73, 78, 4, 62], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [4, 62, 5] Generated Node #0,0: 63:[4, 62, 5] Operation: 78-73=5 Exploring Operation: 73-4=69, Resulting Numbers: [78, 62, 69] Generated Node #0,1: 63:[78, 62, 69] Operation: 73-4=69 Exploring Operation: 73-62=11, Resulting Numbers: [78, 4, 11] Generated Node #0,2: 63:[78, 4, 11] Operation: 73-62=11 Exploring Operation: 78-62=16, Resulting Numbers: [73, 4, 16] Generated Node #0,3: 63:[73, 4, 16] Operation: 78-62=16 Moving to Node #0,0 Current State: 63:[4, 62, 5], Operations: ['78-73=5'] Exploring Operation: 4+62=66, Resulting Numbers: [5, 66] Generated Node #0,0,0: 63:[5, 66] Operation: 4+62=66 Exploring Operation: 5-4=1, Resulting Numbers: [62, 1] Generated Node #0,0,1: 63:[62, 1] Operation: 5-4=1 Exploring Operation: 4*5=20, Resulting Numbers: [62, 20] Generated Node #0,0,2: 63:[62, 20] Operation: 4*5=20 Exploring Operation: 4+5=9, Resulting Numbers: [62, 9] Generated Node #0,0,3: 63:[62, 9] Operation: 4+5=9 Moving to Node #0,3 Current State: 63:[73, 4, 16], Operations: ['78-62=16'] Exploring Operation: 73-4=69, Resulting Numbers: [16, 69] Generated Node #0,3,0: 63:[16, 69] Operation: 73-4=69 Exploring Operation: 4*16=64, Resulting Numbers: [73, 64] Generated Node #0,3,1: 63:[73, 64] Operation: 4*16=64 Exploring Operation: 4+16=20, Resulting Numbers: [73, 20] Generated Node #0,3,2: 63:[73, 20] Operation: 4+16=20 Exploring Operation: 73-16=57, Resulting Numbers: [4, 57] Generated Node #0,3,3: 63:[4, 57] Operation: 73-16=57 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 63:[4, 57], Operations: ['78-62=16', '73-16=57'] Exploring Operation: 4*57=228, Resulting Numbers: [228] 228,63 unequal: No Solution Exploring Operation: 4+57=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 63:[16, 69], Operations: ['78-62=16', '73-4=69'] Exploring Operation: 16+69=85, Resulting Numbers: [85] 85,63 unequal: No Solution Exploring Operation: 16*69=1104, Resulting Numbers: [1104] 1104,63 unequal: No Solution Exploring Operation: 69-16=53, Resulting Numbers: [53] 53,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 63:[73, 64], Operations: ['78-62=16', '4*16=64'] Exploring Operation: 73*64=4672, Resulting Numbers: [4672] 4672,63 unequal: No Solution Exploring Operation: 73+64=137, Resulting Numbers: [137] 137,63 unequal: No Solution Exploring Operation: 73-64=9, Resulting Numbers: [9] 9,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 63:[73, 20], Operations: ['78-62=16', '4+16=20'] Exploring Operation: 73+20=93, Resulting Numbers: [93] 93,63 unequal: No Solution Exploring Operation: 73*20=1460, Resulting Numbers: [1460] 1460,63 unequal: No Solution Exploring Operation: 73-20=53, Resulting Numbers: [53] 53,63 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: 63:[78, 4, 11], Operations: ['73-62=11'] Exploring Operation: 78-11=67, Resulting Numbers: [4, 67] Generated Node #0,2,0: 63:[4, 67] Operation: 78-11=67 Exploring Operation: 78-4=74, Resulting Numbers: [11, 74] Generated Node #0,2,1: 63:[11, 74] Operation: 78-4=74 Exploring Operation: 78+4=82, Resulting Numbers: [11, 82] Generated Node #0,2,2: 63:[11, 82] Operation: 78+4=82 Exploring Operation: 11-4=7, Resulting Numbers: [78, 7] Generated Node #0,2,3: 63:[78, 7] Operation: 11-4=7 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 63:[4, 67], Operations: ['73-62=11', '78-11=67'] Exploring Operation: 4+67=71, Resulting Numbers: [71] 71,63 unequal: No Solution Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[73, 78, 4, 62], Operations: [] Exploring Operation: 73-62=11, Resulting Numbers: [78, 4, 11] Generated Node #0,2: 63:[78, 4, 11] Operation: 73-62=11 Moving to Node #0,2 Current State: 63:[78, 4, 11], Operations: ['73-62=11'] Exploring Operation: 78-11=67, Resulting Numbers: [4, 67] Generated Node #0,2,0: 63:[4, 67] Operation: 78-11=67 Moving to Node #0,2,0 Current State: 63:[4, 67], Operations: ['73-62=11', '78-11=67'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
sum_heuristic
[ 4, 48, 76, 51 ]
80
[ "76/4=19", "48+51=99", "99-19=80" ]
Current State: 80:[4, 48, 76, 51], Operations: [] Exploring Operation: 76/4=19, Resulting Numbers: [48, 51, 19] Generated Node #2: [48, 51, 19] from Operation: 76/4=19 Current State: 80:[48, 51, 19], Operations: ['76/4=19'] Exploring Operation: 48+51=99, Resulting Numbers: [19, 99] Generated Node #3: [19, 99] from Operation: 48+51=99 Current State: 80:[19, 99], Operations: ['76/4=19', '48+51=99'] Exploring Operation: 99-19=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[4, 48, 76, 51], Operations: [] Exploring Operation: 51-48=3, Resulting Numbers: [4, 76, 3] Generated Node #0,0: 80:[4, 76, 3] Operation: 51-48=3 Exploring Operation: 48/4=12, Resulting Numbers: [76, 51, 12] Generated Node #0,1: 80:[76, 51, 12] Operation: 48/4=12 Exploring Operation: 76-51=25, Resulting Numbers: [4, 48, 25] Generated Node #0,2: 80:[4, 48, 25] Operation: 76-51=25 Moving to Node #0,0 Current State: 80:[4, 76, 3], Operations: ['51-48=3'] Exploring Operation: 4+76=80, Resulting Numbers: [3, 80] Generated Node #0,0,0: 80:[3, 80] Operation: 4+76=80 Exploring Operation: 76+3=79, Resulting Numbers: [4, 79] Generated Node #0,0,1: 80:[4, 79] Operation: 76+3=79 Exploring Operation: 76/4=19, Resulting Numbers: [3, 19] Generated Node #0,0,2: 80:[3, 19] Operation: 76/4=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[3, 80], Operations: ['51-48=3', '4+76=80'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 3+80=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 3*80=240, Resulting Numbers: [240] 240,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[4, 79], Operations: ['51-48=3', '76+3=79'] Exploring Operation: 4+79=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,80 unequal: No Solution Exploring Operation: 4*79=316, Resulting Numbers: [316] 316,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 80:[3, 19], Operations: ['51-48=3', '76/4=19'] Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,80 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,80 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: 80:[4, 48, 25], Operations: ['76-51=25'] Exploring Operation: 48/4=12, Resulting Numbers: [25, 12] Generated Node #0,2,0: 80:[25, 12] Operation: 48/4=12 Exploring Operation: 48-25=23, Resulting Numbers: [4, 23] Generated Node #0,2,1: 80:[4, 23] Operation: 48-25=23 Exploring Operation: 48+25=73, Resulting Numbers: [4, 73] Generated Node #0,2,2: 80:[4, 73] Operation: 48+25=73 Moving to Node #0,1 Current State: 80:[76, 51, 12], Operations: ['48/4=12'] Exploring Operation: 76+12=88, Resulting Numbers: [51, 88] Generated Node #0,1,0: 80:[51, 88] Operation: 76+12=88 Exploring Operation: 76-51=25, Resulting Numbers: [12, 25] Generated Node #0,1,1: 80:[12, 25] Operation: 76-51=25 Exploring Operation: 51-12=39, Resulting Numbers: [76, 39] Generated Node #0,1,2: 80:[76, 39] Operation: 51-12=39 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 80:[76, 39], Operations: ['48/4=12', '51-12=39'] Exploring Operation: 76+39=115, Resulting Numbers: [115] 115,80 unequal: No Solution Exploring Operation: 76*39=2964, Resulting Numbers: [2964] 2964,80 unequal: No Solution Exploring Operation: 76-39=37, Resulting Numbers: [37] 37,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 80:[12, 25], Operations: ['48/4=12', '76-51=25'] Exploring Operation: 12*25=300, Resulting Numbers: [300] 300,80 unequal: No Solution Exploring Operation: 12+25=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 80:[51, 88], Operations: ['48/4=12', '76+12=88'] Exploring Operation: 51*88=4488, Resulting Numbers: [4488] 4488,80 unequal: No Solution Exploring Operation: 51+88=139, Resulting Numbers: [139] 139,80 unequal: No Solution Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 80:[4, 23], Operations: ['76-51=25', '48-25=23'] Exploring Operation: 4+23=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 4*23=92, Resulting Numbers: [92] 92,80 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[25, 12], Operations: ['76-51=25', '48/4=12'] Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,80 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,80 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[4, 73], Operations: ['76-51=25', '48+25=73'] Exploring Operation: 4*73=292, Resulting Numbers: [292] 292,80 unequal: No Solution Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,80 unequal: No Solution Exploring Operation: 4+73=77, Resulting Numbers: [77] 77,80 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 40, 24, 12, 56 ]
60
[ "40-24=16", "56-12=44", "16+44=60" ]
Current State: 60:[40, 24, 12, 56], Operations: [] Exploring Operation: 40-24=16, Resulting Numbers: [12, 56, 16] Generated Node #2: [12, 56, 16] from Operation: 40-24=16 Current State: 60:[12, 56, 16], Operations: ['40-24=16'] Exploring Operation: 56-12=44, Resulting Numbers: [16, 44] Generated Node #3: [16, 44] from Operation: 56-12=44 Current State: 60:[16, 44], Operations: ['40-24=16', '56-12=44'] Exploring Operation: 16+44=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[40, 24, 12, 56], Operations: [] Exploring Operation: 56-40=16, Resulting Numbers: [24, 12, 16] Generated Node #0,0: 60:[24, 12, 16] Operation: 56-40=16 Exploring Operation: 40-24=16, Resulting Numbers: [12, 56, 16] Generated Node #0,1: 60:[12, 56, 16] Operation: 40-24=16 Exploring Operation: 40-12=28, Resulting Numbers: [24, 56, 28] Generated Node #0,2: 60:[24, 56, 28] Operation: 40-12=28 Exploring Operation: 40+24=64, Resulting Numbers: [12, 56, 64] Generated Node #0,3: 60:[12, 56, 64] Operation: 40+24=64 Moving to Node #0,0 Current State: 60:[24, 12, 16], Operations: ['56-40=16'] Exploring Operation: 24-16=8, Resulting Numbers: [12, 8] Generated Node #0,0,0: 60:[12, 8] Operation: 24-16=8 Exploring Operation: 16-12=4, Resulting Numbers: [24, 4] Generated Node #0,0,1: 60:[24, 4] Operation: 16-12=4 Exploring Operation: 24-12=12, Resulting Numbers: [16, 12] Generated Node #0,0,2: 60:[16, 12] Operation: 24-12=12 Exploring Operation: 24/12=2, Resulting Numbers: [16, 2] Generated Node #0,0,3: 60:[16, 2] Operation: 24/12=2 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[16, 12], Operations: ['56-40=16', '24-12=12'] Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,60 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 60:[16, 2], Operations: ['56-40=16', '24/12=2'] Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,60 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,60 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[12, 8], Operations: ['56-40=16', '24-16=8'] Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,60 unequal: No Solution Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[24, 4], Operations: ['56-40=16', '16-12=4'] Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,60 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,60 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 60:[12, 56, 16], Operations: ['40-24=16'] Exploring Operation: 16-12=4, Resulting Numbers: [56, 4] Generated Node #0,1,0: 60:[56, 4] Operation: 16-12=4 Exploring Operation: 56-16=40, Resulting Numbers: [12, 40] Generated Node #0,1,1: 60:[12, 40] Operation: 56-16=40 Exploring Operation: 12+16=28, Resulting Numbers: [56, 28] Generated Node #0,1,2: 60:[56, 28] Operation: 12+16=28 Exploring Operation: 12+56=68, Resulting Numbers: [16, 68] Generated Node #0,1,3: 60:[16, 68] Operation: 12+56=68 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[56, 4], Operations: ['40-24=16', '16-12=4'] Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,60 unequal: No Solution Exploring Operation: 56+4=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[40, 24, 12, 56], Operations: [] Exploring Operation: 40-24=16, Resulting Numbers: [12, 56, 16] Generated Node #0,1: 60:[12, 56, 16] Operation: 40-24=16 Moving to Node #0,1 Current State: 60:[12, 56, 16], Operations: ['40-24=16'] Exploring Operation: 16-12=4, Resulting Numbers: [56, 4] Generated Node #0,1,0: 60:[56, 4] Operation: 16-12=4 Moving to Node #0,1,0 Current State: 60:[56, 4], Operations: ['40-24=16', '16-12=4'] Exploring Operation: 56+4=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 54, 1, 50, 76 ]
36
[ "54*50=2700", "76-1=75", "2700/75=36" ]
Current State: 36:[54, 1, 50, 76], Operations: [] Exploring Operation: 54*50=2700, Resulting Numbers: [1, 76, 2700] Generated Node #2: [1, 76, 2700] from Operation: 54*50=2700 Current State: 36:[1, 76, 2700], Operations: ['54*50=2700'] Exploring Operation: 76-1=75, Resulting Numbers: [2700, 75] Generated Node #3: [2700, 75] from Operation: 76-1=75 Current State: 36:[2700, 75], Operations: ['54*50=2700', '76-1=75'] Exploring Operation: 2700/75=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[54, 1, 50, 76], Operations: [] Exploring Operation: 76-50=26, Resulting Numbers: [54, 1, 26] Generated Node #0,0: 36:[54, 1, 26] Operation: 76-50=26 Exploring Operation: 76-54=22, Resulting Numbers: [1, 50, 22] Generated Node #0,1: 36:[1, 50, 22] Operation: 76-54=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[1, 50, 22], Operations: ['76-54=22'] Exploring Operation: 50-1=49, Resulting Numbers: [22, 49] Generated Node #0,1,0: 36:[22, 49] Operation: 50-1=49 Exploring Operation: 50-22=28, Resulting Numbers: [1, 28] Generated Node #0,1,1: 36:[1, 28] Operation: 50-22=28 Moving to Node #0,1,1 Current State: 36:[1, 28], Operations: ['76-54=22', '50-22=28'] Exploring Operation: 1+28=29, Resulting Numbers: [29] 29,36 unequal: No Solution Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,36 unequal: No Solution Moving to Node #0,1,0 Current State: 36:[22, 49], Operations: ['76-54=22', '50-1=49'] Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,36 unequal: No Solution Exploring Operation: 22+49=71, Resulting Numbers: [71] 71,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[54, 1, 26], Operations: ['76-50=26'] Exploring Operation: 54-26=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 36:[1, 28] Operation: 54-26=28 Exploring Operation: 54-1=53, Resulting Numbers: [26, 53] Generated Node #0,0,1: 36:[26, 53] Operation: 54-1=53 Moving to Node #0,0,0 Current State: 36:[1, 28], Operations: ['76-50=26', '54-26=28'] Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,36 unequal: No Solution Exploring Operation: 1+28=29, Resulting Numbers: [29] 29,36 unequal: No Solution Moving to Node #0,0,1 Current State: 36:[26, 53], Operations: ['76-50=26', '54-1=53'] Exploring Operation: 53-26=27, Resulting Numbers: [27] 27,36 unequal: No Solution Exploring Operation: 26+53=79, Resulting Numbers: [79] 79,36 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
[ 66, 10, 19, 68 ]
58
[ "68-66=2", "10+19=29", "2*29=58" ]
Current State: 58:[66, 10, 19, 68], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [10, 19, 2] Generated Node #2: [10, 19, 2] from Operation: 68-66=2 Current State: 58:[10, 19, 2], Operations: ['68-66=2'] Exploring Operation: 10+19=29, Resulting Numbers: [2, 29] Generated Node #3: [2, 29] from Operation: 10+19=29 Current State: 58:[2, 29], Operations: ['68-66=2', '10+19=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[66, 10, 19, 68], Operations: [] Exploring Operation: 10+19=29, Resulting Numbers: [66, 68, 29] Generated Node #0,0: 58:[66, 68, 29] Operation: 10+19=29 Exploring Operation: 68-66=2, Resulting Numbers: [10, 19, 2] Generated Node #0,1: 58:[10, 19, 2] Operation: 68-66=2 Moving to Node #0,0 Current State: 58:[66, 68, 29], Operations: ['10+19=29'] Exploring Operation: 68-66=2, Resulting Numbers: [29, 2] Generated Node #0,0,0: 58:[29, 2] Operation: 68-66=2 Exploring Operation: 66-29=37, Resulting Numbers: [68, 37] Generated Node #0,0,1: 58:[68, 37] Operation: 66-29=37 Moving to Node #0,1 Current State: 58:[10, 19, 2], Operations: ['68-66=2'] Exploring Operation: 10+19=29, Resulting Numbers: [2, 29] Generated Node #0,1,0: 58:[2, 29] Operation: 10+19=29 Exploring Operation: 19-10=9, Resulting Numbers: [2, 9] Generated Node #0,1,1: 58:[2, 9] Operation: 19-10=9 Moving to Node #0,0,0 Current State: 58:[29, 2], Operations: ['10+19=29', '68-66=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[66, 10, 19, 68], Operations: [] Exploring Operation: 10+19=29, Resulting Numbers: [66, 68, 29] Generated Node #0,0: 58:[66, 68, 29] Operation: 10+19=29 Moving to Node #0,0 Current State: 58:[66, 68, 29], Operations: ['10+19=29'] Exploring Operation: 68-66=2, Resulting Numbers: [29, 2] Generated Node #0,0,0: 58:[29, 2] Operation: 68-66=2 Moving to Node #0,0,0 Current State: 58:[29, 2], Operations: ['10+19=29', '68-66=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
0.989583
hs_2
mult_heuristic
[ 3, 54, 16, 24 ]
74
[ "24/3=8", "16*8=128", "128-54=74" ]
Current State: 74:[3, 54, 16, 24], Operations: [] Exploring Operation: 24/3=8, Resulting Numbers: [54, 16, 8] Generated Node #2: [54, 16, 8] from Operation: 24/3=8 Current State: 74:[54, 16, 8], Operations: ['24/3=8'] Exploring Operation: 16*8=128, Resulting Numbers: [54, 128] Generated Node #3: [54, 128] from Operation: 16*8=128 Current State: 74:[54, 128], Operations: ['24/3=8', '16*8=128'] Exploring Operation: 128-54=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[3, 54, 16, 24], Operations: [] Exploring Operation: 54+24=78, Resulting Numbers: [3, 16, 78] Generated Node #0,0: 74:[3, 16, 78] Operation: 54+24=78 Exploring Operation: 54-16=38, Resulting Numbers: [3, 24, 38] Generated Node #0,1: 74:[3, 24, 38] Operation: 54-16=38 Exploring Operation: 16+24=40, Resulting Numbers: [3, 54, 40] Generated Node #0,2: 74:[3, 54, 40] Operation: 16+24=40 Exploring Operation: 54+16=70, Resulting Numbers: [3, 24, 70] Generated Node #0,3: 74:[3, 24, 70] Operation: 54+16=70 Moving to Node #0,1 Current State: 74:[3, 24, 38], Operations: ['54-16=38'] Exploring Operation: 24/3=8, Resulting Numbers: [38, 8] Generated Node #0,1,0: 74:[38, 8] Operation: 24/3=8 Exploring Operation: 3+24=27, Resulting Numbers: [38, 27] Generated Node #0,1,1: 74:[38, 27] Operation: 3+24=27 Exploring Operation: 24+38=62, Resulting Numbers: [3, 62] Generated Node #0,1,2: 74:[3, 62] Operation: 24+38=62 Exploring Operation: 3*24=72, Resulting Numbers: [38, 72] Generated Node #0,1,3: 74:[38, 72] Operation: 3*24=72 Moving to Node #0,3 Current State: 74:[3, 24, 70], Operations: ['54+16=70'] Exploring Operation: 3+24=27, Resulting Numbers: [70, 27] Generated Node #0,3,0: 74:[70, 27] Operation: 3+24=27 Exploring Operation: 70-24=46, Resulting Numbers: [3, 46] Generated Node #0,3,1: 74:[3, 46] Operation: 70-24=46 Exploring Operation: 3*24=72, Resulting Numbers: [70, 72] Generated Node #0,3,2: 74:[70, 72] Operation: 3*24=72 Exploring Operation: 24/3=8, Resulting Numbers: [70, 8] Generated Node #0,3,3: 74:[70, 8] Operation: 24/3=8 Moving to Node #0,0 Current State: 74:[3, 16, 78], Operations: ['54+24=78'] Exploring Operation: 16-3=13, Resulting Numbers: [78, 13] Generated Node #0,0,0: 74:[78, 13] Operation: 16-3=13 Exploring Operation: 78-3=75, Resulting Numbers: [16, 75] Generated Node #0,0,1: 74:[16, 75] Operation: 78-3=75 Exploring Operation: 78-16=62, Resulting Numbers: [3, 62] Generated Node #0,0,2: 74:[3, 62] Operation: 78-16=62 Exploring Operation: 3*16=48, Resulting Numbers: [78, 48] Generated Node #0,0,3: 74:[78, 48] Operation: 3*16=48 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 74:[3, 62], Operations: ['54+24=78', '78-16=62'] Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,74 unequal: No Solution Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,74 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[78, 13], Operations: ['54+24=78', '16-3=13'] Exploring Operation: 78+13=91, Resulting Numbers: [91] 91,74 unequal: No Solution Exploring Operation: 78*13=1014, Resulting Numbers: [1014] 1014,74 unequal: No Solution Exploring Operation: 78/13=6, Resulting Numbers: [6] 6,74 unequal: No Solution Exploring Operation: 78-13=65, Resulting Numbers: [65] 65,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 74:[16, 75], Operations: ['54+24=78', '78-3=75'] Exploring Operation: 75-16=59, Resulting Numbers: [59] 59,74 unequal: No Solution Exploring Operation: 16+75=91, Resulting Numbers: [91] 91,74 unequal: No Solution Exploring Operation: 16*75=1200, Resulting Numbers: [1200] 1200,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 74:[78, 48], Operations: ['54+24=78', '3*16=48'] Exploring Operation: 78-48=30, Resulting Numbers: [30] 30,74 unequal: No Solution Exploring Operation: 78+48=126, Resulting Numbers: [126] 126,74 unequal: No Solution Exploring Operation: 78*48=3744, Resulting Numbers: [3744] 3744,74 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: 74:[3, 54, 40], Operations: ['16+24=40'] Exploring Operation: 40-3=37, Resulting Numbers: [54, 37] Generated Node #0,2,0: 74:[54, 37] Operation: 40-3=37 Exploring Operation: 54/3=18, Resulting Numbers: [40, 18] Generated Node #0,2,1: 74:[40, 18] Operation: 54/3=18 Exploring Operation: 54-3=51, Resulting Numbers: [40, 51] Generated Node #0,2,2: 74:[40, 51] Operation: 54-3=51 Exploring Operation: 54-40=14, Resulting Numbers: [3, 14] Generated Node #0,2,3: 74:[3, 14] Operation: 54-40=14 Moving to Node #0,1,3 Current State: 74:[38, 72], Operations: ['54-16=38', '3*24=72'] Exploring Operation: 38+72=110, Resulting Numbers: [110] 110,74 unequal: No Solution Exploring Operation: 38*72=2736, Resulting Numbers: [2736] 2736,74 unequal: No Solution Exploring Operation: 72-38=34, Resulting Numbers: [34] 34,74 unequal: No Solution Moving to Node #0,3,2 Current State: 74:[70, 72], Operations: ['54+16=70', '3*24=72'] Exploring Operation: 72-70=2, Resulting Numbers: [2] 2,74 unequal: No Solution Exploring Operation: 70+72=142, Resulting Numbers: [142] 142,74 unequal: No Solution Exploring Operation: 70*72=5040, Resulting Numbers: [5040] 5040,74 unequal: No Solution Moving to Node #0,1,0 Current State: 74:[38, 8], Operations: ['54-16=38', '24/3=8'] Exploring Operation: 38*8=304, Resulting Numbers: [304] 304,74 unequal: No Solution Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,74 unequal: No Solution Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,74 unequal: No Solution Moving to Node #0,3,1 Current State: 74:[3, 46], Operations: ['54+16=70', '70-24=46'] Exploring Operation: 3+46=49, Resulting Numbers: [49] 49,74 unequal: No Solution Exploring Operation: 3*46=138, Resulting Numbers: [138] 138,74 unequal: No Solution Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,74 unequal: No Solution Moving to Node #0,3,3 Current State: 74:[70, 8], Operations: ['54+16=70', '24/3=8'] Exploring Operation: 70*8=560, Resulting Numbers: [560] 560,74 unequal: No Solution Exploring Operation: 70-8=62, Resulting Numbers: [62] 62,74 unequal: No Solution Exploring Operation: 70+8=78, Resulting Numbers: [78] 78,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[38, 27], Operations: ['54-16=38', '3+24=27'] Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,74 unequal: No Solution Exploring Operation: 38+27=65, Resulting Numbers: [65] 65,74 unequal: No Solution Exploring Operation: 38*27=1026, Resulting Numbers: [1026] 1026,74 unequal: No Solution Moving to Node #0,1,2 Current State: 74:[3, 62], Operations: ['54-16=38', '24+38=62'] Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,74 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,74 unequal: No Solution Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,74 unequal: No Solution Moving to Node #0,2,3 Current State: 74:[3, 14], Operations: ['16+24=40', '54-40=14'] Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,74 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,74 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,74 unequal: No Solution Moving to Node #0,3,0 Current State: 74:[70, 27], Operations: ['54+16=70', '3+24=27'] Exploring Operation: 70+27=97, Resulting Numbers: [97] 97,74 unequal: No Solution Exploring Operation: 70*27=1890, Resulting Numbers: [1890] 1890,74 unequal: No Solution Exploring Operation: 70-27=43, Resulting Numbers: [43] 43,74 unequal: No Solution Moving to Node #0,2,2 Current State: 74:[40, 51], Operations: ['16+24=40', '54-3=51'] Exploring Operation: 40*51=2040, Resulting Numbers: [2040] 2040,74 unequal: No Solution Exploring Operation: 40+51=91, Resulting Numbers: [91] 91,74 unequal: No Solution Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,74 unequal: No Solution Moving to Node #0,2,0 Current State: 74:[54, 37], Operations: ['16+24=40', '40-3=37'] Exploring Operation: 54+37=91, Resulting Numbers: [91] 91,74 unequal: No Solution Exploring Operation: 54-37=17, Resulting Numbers: [17] 17,74 unequal: No Solution Exploring Operation: 54*37=1998, Resulting Numbers: [1998] 1998,74 unequal: No Solution Moving to Node #0,2,1 Current State: 74:[40, 18], Operations: ['16+24=40', '54/3=18'] Exploring Operation: 40*18=720, Resulting Numbers: [720] 720,74 unequal: No Solution Exploring Operation: 40+18=58, Resulting Numbers: [58] 58,74 unequal: No Solution Exploring Operation: 40-18=22, Resulting Numbers: [22] 22,74 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 53, 3, 60, 46 ]
79
[ "53+46=99", "60/3=20", "99-20=79" ]
Current State: 79:[53, 3, 60, 46], Operations: [] Exploring Operation: 53+46=99, Resulting Numbers: [3, 60, 99] Generated Node #2: [3, 60, 99] from Operation: 53+46=99 Current State: 79:[3, 60, 99], Operations: ['53+46=99'] Exploring Operation: 60/3=20, Resulting Numbers: [99, 20] Generated Node #3: [99, 20] from Operation: 60/3=20 Current State: 79:[99, 20], Operations: ['53+46=99', '60/3=20'] Exploring Operation: 99-20=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[53, 3, 60, 46], Operations: [] Exploring Operation: 53+3=56, Resulting Numbers: [60, 46, 56] Generated Node #0,0: 79:[60, 46, 56] Operation: 53+3=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[60, 46, 56], Operations: ['53+3=56'] Exploring Operation: 46+56=102, Resulting Numbers: [60, 102] Generated Node #0,0,0: 79:[60, 102] Operation: 46+56=102 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[60, 102], Operations: ['53+3=56', '46+56=102'] Exploring Operation: 102-60=42, Resulting Numbers: [42] 42,79 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_1
mult_heuristic
[ 3, 69, 5, 77 ]
85
[ "5-3=2", "77*2=154", "154-69=85" ]
Current State: 85:[3, 69, 5, 77], Operations: [] Exploring Operation: 5-3=2, Resulting Numbers: [69, 77, 2] Generated Node #2: [69, 77, 2] from Operation: 5-3=2 Current State: 85:[69, 77, 2], Operations: ['5-3=2'] Exploring Operation: 77*2=154, Resulting Numbers: [69, 154] Generated Node #3: [69, 154] from Operation: 77*2=154 Current State: 85:[69, 154], Operations: ['5-3=2', '77*2=154'] Exploring Operation: 154-69=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[3, 69, 5, 77], Operations: [] Exploring Operation: 77-69=8, Resulting Numbers: [3, 5, 8] Generated Node #0,0: 85:[3, 5, 8] Operation: 77-69=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[3, 5, 8], Operations: ['77-69=8'] Exploring Operation: 8-3=5, Resulting Numbers: [5, 5] Generated Node #0,0,0: 85:[5, 5] Operation: 8-3=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[5, 5], Operations: ['77-69=8', '8-3=5'] Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 20, 31, 99, 6 ]
60
[ "99-6=93", "20*93=1860", "1860/31=60" ]
Current State: 60:[20, 31, 99, 6], Operations: [] Exploring Operation: 99-6=93, Resulting Numbers: [20, 31, 93] Generated Node #2: [20, 31, 93] from Operation: 99-6=93 Current State: 60:[20, 31, 93], Operations: ['99-6=93'] Exploring Operation: 20*93=1860, Resulting Numbers: [31, 1860] Generated Node #3: [31, 1860] from Operation: 20*93=1860 Current State: 60:[31, 1860], Operations: ['99-6=93', '20*93=1860'] Exploring Operation: 1860/31=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[20, 31, 99, 6], Operations: [] Exploring Operation: 99-20=79, Resulting Numbers: [31, 6, 79] Generated Node #0,0: 60:[31, 6, 79] Operation: 99-20=79 Exploring Operation: 99-31=68, Resulting Numbers: [20, 6, 68] Generated Node #0,1: 60:[20, 6, 68] Operation: 99-31=68 Moving to Node #0,1 Current State: 60:[20, 6, 68], Operations: ['99-31=68'] Exploring Operation: 20-6=14, Resulting Numbers: [68, 14] Generated Node #0,1,0: 60:[68, 14] Operation: 20-6=14 Exploring Operation: 68-6=62, Resulting Numbers: [20, 62] Generated Node #0,1,1: 60:[20, 62] Operation: 68-6=62 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[20, 62], Operations: ['99-31=68', '68-6=62'] Exploring Operation: 20+62=82, Resulting Numbers: [82] 82,60 unequal: No Solution Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[68, 14], Operations: ['99-31=68', '20-6=14'] Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,60 unequal: No Solution Exploring Operation: 68+14=82, Resulting Numbers: [82] 82,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 60:[31, 6, 79], Operations: ['99-20=79'] Exploring Operation: 79-6=73, Resulting Numbers: [31, 73] Generated Node #0,0,0: 60:[31, 73] Operation: 79-6=73 Exploring Operation: 79-31=48, Resulting Numbers: [6, 48] Generated Node #0,0,1: 60:[6, 48] Operation: 79-31=48 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[6, 48], Operations: ['99-20=79', '79-31=48'] Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,60 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[31, 73], Operations: ['99-20=79', '79-6=73'] Exploring Operation: 31+73=104, Resulting Numbers: [104] 104,60 unequal: No Solution Exploring Operation: 73-31=42, Resulting Numbers: [42] 42,60 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
[ 80, 91, 55, 16 ]
21
[ "91-80=11", "55/11=5", "16+5=21" ]
Current State: 21:[80, 91, 55, 16], Operations: [] Exploring Operation: 91-80=11, Resulting Numbers: [55, 16, 11] Generated Node #2: [55, 16, 11] from Operation: 91-80=11 Current State: 21:[55, 16, 11], Operations: ['91-80=11'] Exploring Operation: 55/11=5, Resulting Numbers: [16, 5] Generated Node #3: [16, 5] from Operation: 55/11=5 Current State: 21:[16, 5], Operations: ['91-80=11', '55/11=5'] Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[80, 91, 55, 16], Operations: [] Exploring Operation: 91-55=36, Resulting Numbers: [80, 16, 36] Generated Node #0,0: 21:[80, 16, 36] Operation: 91-55=36 Exploring Operation: 80-55=25, Resulting Numbers: [91, 16, 25] Generated Node #0,1: 21:[91, 16, 25] Operation: 80-55=25 Exploring Operation: 91-80=11, Resulting Numbers: [55, 16, 11] Generated Node #0,2: 21:[55, 16, 11] Operation: 91-80=11 Exploring Operation: 80-16=64, Resulting Numbers: [91, 55, 64] Generated Node #0,3: 21:[91, 55, 64] Operation: 80-16=64 Exploring Operation: 80/16=5, Resulting Numbers: [91, 55, 5] Generated Node #0,4: 21:[91, 55, 5] Operation: 80/16=5 Moving to Node #0,2 Current State: 21:[55, 16, 11], Operations: ['91-80=11'] Exploring Operation: 55-16=39, Resulting Numbers: [11, 39] Generated Node #0,2,0: 21:[11, 39] Operation: 55-16=39 Exploring Operation: 55-11=44, Resulting Numbers: [16, 44] Generated Node #0,2,1: 21:[16, 44] Operation: 55-11=44 Exploring Operation: 16+11=27, Resulting Numbers: [55, 27] Generated Node #0,2,2: 21:[55, 27] Operation: 16+11=27 Exploring Operation: 55/11=5, Resulting Numbers: [16, 5] Generated Node #0,2,3: 21:[16, 5] Operation: 55/11=5 Exploring Operation: 16-11=5, Resulting Numbers: [55, 5] Generated Node #0,2,4: 21:[55, 5] Operation: 16-11=5 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 21:[16, 5], Operations: ['91-80=11', '55/11=5'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[80, 91, 55, 16], Operations: [] Exploring Operation: 91-80=11, Resulting Numbers: [55, 16, 11] Generated Node #0,2: 21:[55, 16, 11] Operation: 91-80=11 Moving to Node #0,2 Current State: 21:[55, 16, 11], Operations: ['91-80=11'] Exploring Operation: 55/11=5, Resulting Numbers: [16, 5] Generated Node #0,2,3: 21:[16, 5] Operation: 55/11=5 Moving to Node #0,2,3 Current State: 21:[16, 5], Operations: ['91-80=11', '55/11=5'] Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 92, 84, 9, 37 ]
86
[ "9+37=46", "92/46=2", "84+2=86" ]
Current State: 86:[92, 84, 9, 37], Operations: [] Exploring Operation: 9+37=46, Resulting Numbers: [92, 84, 46] Generated Node #2: [92, 84, 46] from Operation: 9+37=46 Current State: 86:[92, 84, 46], Operations: ['9+37=46'] Exploring Operation: 92/46=2, Resulting Numbers: [84, 2] Generated Node #3: [84, 2] from Operation: 92/46=2 Current State: 86:[84, 2], Operations: ['9+37=46', '92/46=2'] Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[92, 84, 9, 37], Operations: [] Exploring Operation: 92-9=83, Resulting Numbers: [84, 37, 83] Generated Node #0,0: 86:[84, 37, 83] Operation: 92-9=83 Exploring Operation: 84-37=47, Resulting Numbers: [92, 9, 47] Generated Node #0,1: 86:[92, 9, 47] Operation: 84-37=47 Exploring Operation: 9+37=46, Resulting Numbers: [92, 84, 46] Generated Node #0,2: 86:[92, 84, 46] Operation: 9+37=46 Moving to Node #0,0 Current State: 86:[84, 37, 83], Operations: ['92-9=83'] Exploring Operation: 83-37=46, Resulting Numbers: [84, 46] Generated Node #0,0,0: 86:[84, 46] Operation: 83-37=46 Exploring Operation: 84-37=47, Resulting Numbers: [83, 47] Generated Node #0,0,1: 86:[83, 47] Operation: 84-37=47 Exploring Operation: 84-83=1, Resulting Numbers: [37, 1] Generated Node #0,0,2: 86:[37, 1] Operation: 84-83=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[84, 46], Operations: ['92-9=83', '83-37=46'] Exploring Operation: 84+46=130, Resulting Numbers: [130] 130,86 unequal: No Solution Exploring Operation: 84*46=3864, Resulting Numbers: [3864] 3864,86 unequal: No Solution Exploring Operation: 84-46=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 #0,0,1 Current State: 86:[83, 47], Operations: ['92-9=83', '84-37=47'] Exploring Operation: 83-47=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 83+47=130, Resulting Numbers: [130] 130,86 unequal: No Solution Exploring Operation: 83*47=3901, Resulting Numbers: [3901] 3901,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 86:[37, 1], Operations: ['92-9=83', '84-83=1'] Exploring Operation: 37*1=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 37+1=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,86 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: 86:[92, 84, 46], Operations: ['9+37=46'] Exploring Operation: 92-84=8, Resulting Numbers: [46, 8] Generated Node #0,2,0: 86:[46, 8] Operation: 92-84=8 Exploring Operation: 92-46=46, Resulting Numbers: [84, 46] Generated Node #0,2,1: 86:[84, 46] Operation: 92-46=46 Exploring Operation: 92/46=2, Resulting Numbers: [84, 2] Generated Node #0,2,2: 86:[84, 2] Operation: 92/46=2 Moving to Node #0,1 Current State: 86:[92, 9, 47], Operations: ['84-37=47'] Exploring Operation: 92-9=83, Resulting Numbers: [47, 83] Generated Node #0,1,0: 86:[47, 83] Operation: 92-9=83 Exploring Operation: 92-47=45, Resulting Numbers: [9, 45] Generated Node #0,1,1: 86:[9, 45] Operation: 92-47=45 Exploring Operation: 47-9=38, Resulting Numbers: [92, 38] Generated Node #0,1,2: 86:[92, 38] Operation: 47-9=38 Moving to Node #0,2,2 Current State: 86:[84, 2], Operations: ['9+37=46', '92/46=2'] Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[92, 84, 9, 37], Operations: [] Exploring Operation: 9+37=46, Resulting Numbers: [92, 84, 46] Generated Node #0,2: 86:[92, 84, 46] Operation: 9+37=46 Moving to Node #0,2 Current State: 86:[92, 84, 46], Operations: ['9+37=46'] Exploring Operation: 92/46=2, Resulting Numbers: [84, 2] Generated Node #0,2,2: 86:[84, 2] Operation: 92/46=2 Moving to Node #0,2,2 Current State: 86:[84, 2], Operations: ['9+37=46', '92/46=2'] Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
0.977431
hs_3
mult_heuristic
[ 1, 59, 87, 77 ]
68
[ "59-1=58", "87-77=10", "58+10=68" ]
Current State: 68:[1, 59, 87, 77], Operations: [] Exploring Operation: 59-1=58, Resulting Numbers: [87, 77, 58] Generated Node #2: [87, 77, 58] from Operation: 59-1=58 Current State: 68:[87, 77, 58], Operations: ['59-1=58'] Exploring Operation: 87-77=10, Resulting Numbers: [58, 10] Generated Node #3: [58, 10] from Operation: 87-77=10 Current State: 68:[58, 10], Operations: ['59-1=58', '87-77=10'] Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[1, 59, 87, 77], Operations: [] Exploring Operation: 1+59=60, Resulting Numbers: [87, 77, 60] Generated Node #0,0: 68:[87, 77, 60] Operation: 1+59=60 Exploring Operation: 77-59=18, Resulting Numbers: [1, 87, 18] Generated Node #0,1: 68:[1, 87, 18] Operation: 77-59=18 Exploring Operation: 87-59=28, Resulting Numbers: [1, 77, 28] Generated Node #0,2: 68:[1, 77, 28] Operation: 87-59=28 Exploring Operation: 87-77=10, Resulting Numbers: [1, 59, 10] Generated Node #0,3: 68:[1, 59, 10] Operation: 87-77=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[1, 77, 28], Operations: ['87-59=28'] Exploring Operation: 77-1=76, Resulting Numbers: [28, 76] Generated Node #0,2,0: 68:[28, 76] Operation: 77-1=76 Exploring Operation: 1*77=77, Resulting Numbers: [28, 77] Generated Node #0,2,1: 68:[28, 77] Operation: 1*77=77 Exploring Operation: 77/1=77, Resulting Numbers: [28, 77] Generated Node #0,2,2: 68:[28, 77] Operation: 77/1=77 Exploring Operation: 1+28=29, Resulting Numbers: [77, 29] Generated Node #0,2,3: 68:[77, 29] Operation: 1+28=29 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 68:[28, 76], Operations: ['87-59=28', '77-1=76'] Exploring Operation: 28*76=2128, Resulting Numbers: [2128] 2128,68 unequal: No Solution Exploring Operation: 76-28=48, Resulting Numbers: [48] 48,68 unequal: No Solution Exploring Operation: 28+76=104, Resulting Numbers: [104] 104,68 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:[77, 29], Operations: ['87-59=28', '1+28=29'] Exploring Operation: 77+29=106, Resulting Numbers: [106] 106,68 unequal: No Solution Exploring Operation: 77*29=2233, Resulting Numbers: [2233] 2233,68 unequal: No Solution Exploring Operation: 77-29=48, Resulting Numbers: [48] 48,68 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 #0,2,1 Current State: 68:[28, 77], Operations: ['87-59=28', '1*77=77'] Exploring Operation: 28*77=2156, Resulting Numbers: [2156] 2156,68 unequal: No Solution Exploring Operation: 28+77=105, Resulting Numbers: [105] 105,68 unequal: No Solution Exploring Operation: 77-28=49, Resulting Numbers: [49] 49,68 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:[28, 77], Operations: ['87-59=28', '77/1=77'] Exploring Operation: 28*77=2156, Resulting Numbers: [2156] 2156,68 unequal: No Solution Exploring Operation: 77-28=49, Resulting Numbers: [49] 49,68 unequal: No Solution Exploring Operation: 28+77=105, Resulting Numbers: [105] 105,68 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:[1, 59, 10], Operations: ['87-77=10'] Exploring Operation: 1+59=60, Resulting Numbers: [10, 60] Generated Node #0,3,0: 68:[10, 60] Operation: 1+59=60 Exploring Operation: 1*59=59, Resulting Numbers: [10, 59] Generated Node #0,3,1: 68:[10, 59] Operation: 1*59=59 Exploring Operation: 10-1=9, Resulting Numbers: [59, 9] Generated Node #0,3,2: 68:[59, 9] Operation: 10-1=9 Exploring Operation: 59+10=69, Resulting Numbers: [1, 69] Generated Node #0,3,3: 68:[1, 69] Operation: 59+10=69 Moving to Node #0,3,3 Current State: 68:[1, 69], Operations: ['87-77=10', '59+10=69'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[1, 59, 87, 77], Operations: [] Exploring Operation: 87-77=10, Resulting Numbers: [1, 59, 10] Generated Node #0,3: 68:[1, 59, 10] Operation: 87-77=10 Moving to Node #0,3 Current State: 68:[1, 59, 10], Operations: ['87-77=10'] Exploring Operation: 59+10=69, Resulting Numbers: [1, 69] Generated Node #0,3,3: 68:[1, 69] Operation: 59+10=69 Moving to Node #0,3,3 Current State: 68:[1, 69], Operations: ['87-77=10', '59+10=69'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 60, 56, 90, 7 ]
42
[ "56+7=63", "60*63=3780", "3780/90=42" ]
Current State: 42:[60, 56, 90, 7], Operations: [] Exploring Operation: 56+7=63, Resulting Numbers: [60, 90, 63] Generated Node #2: [60, 90, 63] from Operation: 56+7=63 Current State: 42:[60, 90, 63], Operations: ['56+7=63'] Exploring Operation: 60*63=3780, Resulting Numbers: [90, 3780] Generated Node #3: [90, 3780] from Operation: 60*63=3780 Current State: 42:[90, 3780], Operations: ['56+7=63', '60*63=3780'] Exploring Operation: 3780/90=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[60, 56, 90, 7], Operations: [] Exploring Operation: 90-56=34, Resulting Numbers: [60, 7, 34] Generated Node #0,0: 42:[60, 7, 34] Operation: 90-56=34 Exploring Operation: 90-60=30, Resulting Numbers: [56, 7, 30] Generated Node #0,1: 42:[56, 7, 30] Operation: 90-60=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[56, 7, 30], Operations: ['90-60=30'] Exploring Operation: 56-30=26, Resulting Numbers: [7, 26] Generated Node #0,1,0: 42:[7, 26] Operation: 56-30=26 Exploring Operation: 56/7=8, Resulting Numbers: [30, 8] Generated Node #0,1,1: 42:[30, 8] Operation: 56/7=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 42:[7, 26], Operations: ['90-60=30', '56-30=26'] Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 42:[30, 8], Operations: ['90-60=30', '56/7=8'] Exploring Operation: 30+8=38, Resulting Numbers: [38] 38,42 unequal: No Solution Exploring Operation: 30-8=22, Resulting Numbers: [22] 22,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[60, 7, 34], Operations: ['90-56=34'] Exploring Operation: 60-34=26, Resulting Numbers: [7, 26] Generated Node #0,0,0: 42:[7, 26] Operation: 60-34=26 Exploring Operation: 60-7=53, Resulting Numbers: [34, 53] Generated Node #0,0,1: 42:[34, 53] Operation: 60-7=53 Moving to Node #0,0,0 Current State: 42:[7, 26], Operations: ['90-56=34', '60-34=26'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[34, 53], Operations: ['90-56=34', '60-7=53'] Exploring Operation: 53-34=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 34+53=87, Resulting Numbers: [87] 87,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 80, 18, 70, 5 ]
72
[ "80/5=16", "18+70=88", "88-16=72" ]
Current State: 72:[80, 18, 70, 5], Operations: [] Exploring Operation: 80/5=16, Resulting Numbers: [18, 70, 16] Generated Node #2: [18, 70, 16] from Operation: 80/5=16 Current State: 72:[18, 70, 16], Operations: ['80/5=16'] Exploring Operation: 18+70=88, Resulting Numbers: [16, 88] Generated Node #3: [16, 88] from Operation: 18+70=88 Current State: 72:[16, 88], Operations: ['80/5=16', '18+70=88'] Exploring Operation: 88-16=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[80, 18, 70, 5], Operations: [] Exploring Operation: 80-70=10, Resulting Numbers: [18, 5, 10] Generated Node #0,0: 72:[18, 5, 10] Operation: 80-70=10 Exploring Operation: 80/5=16, Resulting Numbers: [18, 70, 16] Generated Node #0,1: 72:[18, 70, 16] Operation: 80/5=16 Exploring Operation: 70/5=14, Resulting Numbers: [80, 18, 14] Generated Node #0,2: 72:[80, 18, 14] Operation: 70/5=14 Exploring Operation: 80-5=75, Resulting Numbers: [18, 70, 75] Generated Node #0,3: 72:[18, 70, 75] Operation: 80-5=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[18, 5, 10], Operations: ['80-70=10'] Exploring Operation: 18-10=8, Resulting Numbers: [5, 8] Generated Node #0,0,0: 72:[5, 8] Operation: 18-10=8 Exploring Operation: 18+5=23, Resulting Numbers: [10, 23] Generated Node #0,0,1: 72:[10, 23] Operation: 18+5=23 Exploring Operation: 10/5=2, Resulting Numbers: [18, 2] Generated Node #0,0,2: 72:[18, 2] Operation: 10/5=2 Exploring Operation: 10-5=5, Resulting Numbers: [18, 5] Generated Node #0,0,3: 72:[18, 5] Operation: 10-5=5 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 72:[18, 2], Operations: ['80-70=10', '10/5=2'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,72 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,72 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,72 unequal: No Solution No 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: 72:[5, 8], Operations: ['80-70=10', '18-10=8'] Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,72 unequal: No Solution Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,72 unequal: No Solution No 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: 72:[18, 5], Operations: ['80-70=10', '10-5=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,72 unequal: No Solution No 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: 72:[10, 23], Operations: ['80-70=10', '18+5=23'] Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,72 unequal: No Solution Exploring Operation: 10*23=230, Resulting Numbers: [230] 230,72 unequal: No Solution Exploring Operation: 10+23=33, Resulting Numbers: [33] 33,72 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: 72:[18, 70, 16], Operations: ['80/5=16'] Exploring Operation: 70+16=86, Resulting Numbers: [18, 86] Generated Node #0,1,0: 72:[18, 86] Operation: 70+16=86 Exploring Operation: 18+16=34, Resulting Numbers: [70, 34] Generated Node #0,1,1: 72:[70, 34] Operation: 18+16=34 Exploring Operation: 18+70=88, Resulting Numbers: [16, 88] Generated Node #0,1,2: 72:[16, 88] Operation: 18+70=88 Exploring Operation: 18-16=2, Resulting Numbers: [70, 2] Generated Node #0,1,3: 72:[70, 2] Operation: 18-16=2 Moving to Node #0,1,3 Current State: 72:[70, 2], Operations: ['80/5=16', '18-16=2'] Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[80, 18, 70, 5], Operations: [] Exploring Operation: 80/5=16, Resulting Numbers: [18, 70, 16] Generated Node #0,1: 72:[18, 70, 16] Operation: 80/5=16 Moving to Node #0,1 Current State: 72:[18, 70, 16], Operations: ['80/5=16'] Exploring Operation: 18-16=2, Resulting Numbers: [70, 2] Generated Node #0,1,3: 72:[70, 2] Operation: 18-16=2 Moving to Node #0,1,3 Current State: 72:[70, 2], Operations: ['80/5=16', '18-16=2'] Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 61, 33, 34, 2 ]
73
[ "33+34=67", "2*67=134", "134-61=73" ]
Current State: 73:[61, 33, 34, 2], Operations: [] Exploring Operation: 33+34=67, Resulting Numbers: [61, 2, 67] Generated Node #2: [61, 2, 67] from Operation: 33+34=67 Current State: 73:[61, 2, 67], Operations: ['33+34=67'] Exploring Operation: 2*67=134, Resulting Numbers: [61, 134] Generated Node #3: [61, 134] from Operation: 2*67=134 Current State: 73:[61, 134], Operations: ['33+34=67', '2*67=134'] Exploring Operation: 134-61=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[61, 33, 34, 2], Operations: [] Exploring Operation: 34*2=68, Resulting Numbers: [61, 33, 68] Generated Node #0,0: 73:[61, 33, 68] Operation: 34*2=68 Exploring Operation: 33*2=66, Resulting Numbers: [61, 34, 66] Generated Node #0,1: 73:[61, 34, 66] Operation: 33*2=66 Moving to Node #0,0 Current State: 73:[61, 33, 68], Operations: ['34*2=68'] Exploring Operation: 33+68=101, Resulting Numbers: [61, 101] Generated Node #0,0,0: 73:[61, 101] Operation: 33+68=101 Exploring Operation: 61+33=94, Resulting Numbers: [68, 94] Generated Node #0,0,1: 73:[68, 94] Operation: 61+33=94 Moving to Node #0,1 Current State: 73:[61, 34, 66], Operations: ['33*2=66'] Exploring Operation: 61+34=95, Resulting Numbers: [66, 95] Generated Node #0,1,0: 73:[66, 95] Operation: 61+34=95 Exploring Operation: 34+66=100, Resulting Numbers: [61, 100] Generated Node #0,1,1: 73:[61, 100] Operation: 34+66=100 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[66, 95], Operations: ['33*2=66', '61+34=95'] Exploring Operation: 66+95=161, Resulting Numbers: [161] 161,73 unequal: No Solution Exploring Operation: 95-66=29, Resulting Numbers: [29] 29,73 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 #0,1,1 Current State: 73:[61, 100], Operations: ['33*2=66', '34+66=100'] Exploring Operation: 100-61=39, Resulting Numbers: [39] 39,73 unequal: No Solution Exploring Operation: 61+100=161, Resulting Numbers: [161] 161,73 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: 73:[68, 94], Operations: ['34*2=68', '61+33=94'] Exploring Operation: 68+94=162, Resulting Numbers: [162] 162,73 unequal: No Solution Exploring Operation: 94-68=26, Resulting Numbers: [26] 26,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[61, 101], Operations: ['34*2=68', '33+68=101'] Exploring Operation: 101-61=40, Resulting Numbers: [40] 40,73 unequal: No Solution Exploring Operation: 61+101=162, Resulting Numbers: [162] 162,73 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 20, 34, 40, 94 ]
68
[ "34-20=14", "94-40=54", "14+54=68" ]
Current State: 68:[20, 34, 40, 94], Operations: [] Exploring Operation: 34-20=14, Resulting Numbers: [40, 94, 14] Generated Node #2: [40, 94, 14] from Operation: 34-20=14 Current State: 68:[40, 94, 14], Operations: ['34-20=14'] Exploring Operation: 94-40=54, Resulting Numbers: [14, 54] Generated Node #3: [14, 54] from Operation: 94-40=54 Current State: 68:[14, 54], Operations: ['34-20=14', '94-40=54'] Exploring Operation: 14+54=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[20, 34, 40, 94], Operations: [] Exploring Operation: 94-34=60, Resulting Numbers: [20, 40, 60] Generated Node #0,0: 68:[20, 40, 60] Operation: 94-34=60 Exploring Operation: 94-40=54, Resulting Numbers: [20, 34, 54] Generated Node #0,1: 68:[20, 34, 54] Operation: 94-40=54 Exploring Operation: 94-20=74, Resulting Numbers: [34, 40, 74] Generated Node #0,2: 68:[34, 40, 74] Operation: 94-20=74 Moving to Node #0,2 Current State: 68:[34, 40, 74], Operations: ['94-20=74'] Exploring Operation: 40-34=6, Resulting Numbers: [74, 6] Generated Node #0,2,0: 68:[74, 6] Operation: 40-34=6 Exploring Operation: 74-40=34, Resulting Numbers: [34, 34] Generated Node #0,2,1: 68:[34, 34] Operation: 74-40=34 Exploring Operation: 34+40=74, Resulting Numbers: [74, 74] Generated Node #0,2,2: 68:[74, 74] Operation: 34+40=74 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 68:[34, 34], Operations: ['94-20=74', '74-40=34'] Exploring Operation: 34-34=0, Resulting Numbers: [0] 0,68 unequal: No Solution Exploring Operation: 34+34=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[20, 34, 40, 94], Operations: [] Exploring Operation: 94-20=74, Resulting Numbers: [34, 40, 74] Generated Node #0,2: 68:[34, 40, 74] Operation: 94-20=74 Moving to Node #0,2 Current State: 68:[34, 40, 74], Operations: ['94-20=74'] Exploring Operation: 74-40=34, Resulting Numbers: [34, 34] Generated Node #0,2,1: 68:[34, 34] Operation: 74-40=34 Moving to Node #0,2,1 Current State: 68:[34, 34], Operations: ['94-20=74', '74-40=34'] Exploring Operation: 34+34=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 40, 55, 51, 32 ]
32
[ "40-32=8", "55-51=4", "8*4=32" ]
Current State: 32:[40, 55, 51, 32], Operations: [] Exploring Operation: 40-32=8, Resulting Numbers: [55, 51, 8] Generated Node #2: [55, 51, 8] from Operation: 40-32=8 Current State: 32:[55, 51, 8], Operations: ['40-32=8'] Exploring Operation: 55-51=4, Resulting Numbers: [8, 4] Generated Node #3: [8, 4] from Operation: 55-51=4 Current State: 32:[8, 4], Operations: ['40-32=8', '55-51=4'] Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[40, 55, 51, 32], Operations: [] Exploring Operation: 55-40=15, Resulting Numbers: [51, 32, 15] Generated Node #0,0: 32:[51, 32, 15] Operation: 55-40=15 Exploring Operation: 55-51=4, Resulting Numbers: [40, 32, 4] Generated Node #0,1: 32:[40, 32, 4] Operation: 55-51=4 Exploring Operation: 51-40=11, Resulting Numbers: [55, 32, 11] Generated Node #0,2: 32:[55, 32, 11] Operation: 51-40=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[40, 32, 4], Operations: ['55-51=4'] Exploring Operation: 40/4=10, Resulting Numbers: [32, 10] Generated Node #0,1,0: 32:[32, 10] Operation: 40/4=10 Exploring Operation: 40-4=36, Resulting Numbers: [32, 36] Generated Node #0,1,1: 32:[32, 36] Operation: 40-4=36 Exploring Operation: 40-32=8, Resulting Numbers: [4, 8] Generated Node #0,1,2: 32:[4, 8] Operation: 40-32=8 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 32:[4, 8], Operations: ['55-51=4', '40-32=8'] Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[40, 55, 51, 32], Operations: [] Exploring Operation: 55-51=4, Resulting Numbers: [40, 32, 4] Generated Node #0,1: 32:[40, 32, 4] Operation: 55-51=4 Moving to Node #0,1 Current State: 32:[40, 32, 4], Operations: ['55-51=4'] Exploring Operation: 40-32=8, Resulting Numbers: [4, 8] Generated Node #0,1,2: 32:[4, 8] Operation: 40-32=8 Moving to Node #0,1,2 Current State: 32:[4, 8], Operations: ['55-51=4', '40-32=8'] Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 62, 66, 74, 31 ]
50
[ "66-62=4", "31*4=124", "124-74=50" ]
Current State: 50:[62, 66, 74, 31], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [74, 31, 4] Generated Node #2: [74, 31, 4] from Operation: 66-62=4 Current State: 50:[74, 31, 4], Operations: ['66-62=4'] Exploring Operation: 31*4=124, Resulting Numbers: [74, 124] Generated Node #3: [74, 124] from Operation: 31*4=124 Current State: 50:[74, 124], Operations: ['66-62=4', '31*4=124'] Exploring Operation: 124-74=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[62, 66, 74, 31], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [74, 31, 4] Generated Node #0,0: 50:[74, 31, 4] Operation: 66-62=4 Exploring Operation: 74-62=12, Resulting Numbers: [66, 31, 12] Generated Node #0,1: 50:[66, 31, 12] Operation: 74-62=12 Exploring Operation: 74-66=8, Resulting Numbers: [62, 31, 8] Generated Node #0,2: 50:[62, 31, 8] Operation: 74-66=8 Moving to Node #0,2 Current State: 50:[62, 31, 8], Operations: ['74-66=8'] Exploring Operation: 62-8=54, Resulting Numbers: [31, 54] Generated Node #0,2,0: 50:[31, 54] Operation: 62-8=54 Exploring Operation: 62-31=31, Resulting Numbers: [8, 31] Generated Node #0,2,1: 50:[8, 31] Operation: 62-31=31 Exploring Operation: 62/31=2, Resulting Numbers: [8, 2] Generated Node #0,2,2: 50:[8, 2] Operation: 62/31=2 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 50:[8, 2], Operations: ['74-66=8', '62/31=2'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,50 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,50 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:[8, 31], Operations: ['74-66=8', '62-31=31'] Exploring Operation: 8*31=248, Resulting Numbers: [248] 248,50 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 8+31=39, Resulting Numbers: [39] 39,50 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:[31, 54], Operations: ['74-66=8', '62-8=54'] Exploring Operation: 31+54=85, Resulting Numbers: [85] 85,50 unequal: No Solution Exploring Operation: 54-31=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 31*54=1674, Resulting Numbers: [1674] 1674,50 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: 50:[66, 31, 12], Operations: ['74-62=12'] Exploring Operation: 66-12=54, Resulting Numbers: [31, 54] Generated Node #0,1,0: 50:[31, 54] Operation: 66-12=54 Exploring Operation: 66-31=35, Resulting Numbers: [12, 35] Generated Node #0,1,1: 50:[12, 35] Operation: 66-31=35 Exploring Operation: 31-12=19, Resulting Numbers: [66, 19] Generated Node #0,1,2: 50:[66, 19] Operation: 31-12=19 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[31, 54], Operations: ['74-62=12', '66-12=54'] Exploring Operation: 31*54=1674, Resulting Numbers: [1674] 1674,50 unequal: No Solution Exploring Operation: 31+54=85, Resulting Numbers: [85] 85,50 unequal: No Solution Exploring Operation: 54-31=23, Resulting Numbers: [23] 23,50 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:[12, 35], Operations: ['74-62=12', '66-31=35'] Exploring Operation: 12+35=47, Resulting Numbers: [47] 47,50 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 12*35=420, Resulting Numbers: [420] 420,50 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:[66, 19], Operations: ['74-62=12', '31-12=19'] Exploring Operation: 66+19=85, Resulting Numbers: [85] 85,50 unequal: No Solution Exploring Operation: 66-19=47, Resulting Numbers: [47] 47,50 unequal: No Solution Exploring Operation: 66*19=1254, Resulting Numbers: [1254] 1254,50 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: 50:[74, 31, 4], Operations: ['66-62=4'] Exploring Operation: 74-4=70, Resulting Numbers: [31, 70] Generated Node #0,0,0: 50:[31, 70] Operation: 74-4=70 Exploring Operation: 74-31=43, Resulting Numbers: [4, 43] Generated Node #0,0,1: 50:[4, 43] Operation: 74-31=43 Exploring Operation: 31-4=27, Resulting Numbers: [74, 27] Generated Node #0,0,2: 50:[74, 27] Operation: 31-4=27 Moving to Node #0,0,1 Current State: 50:[4, 43], Operations: ['66-62=4', '74-31=43'] Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,50 unequal: No Solution Exploring Operation: 4+43=47, Resulting Numbers: [47] 47,50 unequal: No Solution Exploring Operation: 4*43=172, Resulting Numbers: [172] 172,50 unequal: No Solution Moving to Node #0,0,0 Current State: 50:[31, 70], Operations: ['66-62=4', '74-4=70'] Exploring Operation: 31+70=101, Resulting Numbers: [101] 101,50 unequal: No Solution Exploring Operation: 70-31=39, Resulting Numbers: [39] 39,50 unequal: No Solution Exploring Operation: 31*70=2170, Resulting Numbers: [2170] 2170,50 unequal: No Solution Moving to Node #0,0,2 Current State: 50:[74, 27], Operations: ['66-62=4', '31-4=27'] Exploring Operation: 74-27=47, Resulting Numbers: [47] 47,50 unequal: No Solution Exploring Operation: 74*27=1998, Resulting Numbers: [1998] 1998,50 unequal: No Solution Exploring Operation: 74+27=101, Resulting Numbers: [101] 101,50 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 47, 14, 50, 5 ]
47
[ "50-47=3", "14*3=42", "5+42=47" ]
Current State: 47:[47, 14, 50, 5], Operations: [] Exploring Operation: 50-47=3, Resulting Numbers: [14, 5, 3] Generated Node #2: [14, 5, 3] from Operation: 50-47=3 Current State: 47:[14, 5, 3], Operations: ['50-47=3'] Exploring Operation: 14*3=42, Resulting Numbers: [5, 42] Generated Node #3: [5, 42] from Operation: 14*3=42 Current State: 47:[5, 42], Operations: ['50-47=3', '14*3=42'] Exploring Operation: 5+42=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[47, 14, 50, 5], Operations: [] Exploring Operation: 47+5=52, Resulting Numbers: [14, 50, 52] Generated Node #0,0: 47:[14, 50, 52] Operation: 47+5=52 Exploring Operation: 50-5=45, Resulting Numbers: [47, 14, 45] Generated Node #0,1: 47:[47, 14, 45] Operation: 50-5=45 Exploring Operation: 47-5=42, Resulting Numbers: [14, 50, 42] Generated Node #0,2: 47:[14, 50, 42] Operation: 47-5=42 Exploring Operation: 14*5=70, Resulting Numbers: [47, 50, 70] Generated Node #0,3: 47:[47, 50, 70] Operation: 14*5=70 Exploring Operation: 14+5=19, Resulting Numbers: [47, 50, 19] Generated Node #0,4: 47:[47, 50, 19] Operation: 14+5=19 Moving to Node #0,3 Current State: 47:[47, 50, 70], Operations: ['14*5=70'] Exploring Operation: 47+50=97, Resulting Numbers: [70, 97] Generated Node #0,3,0: 47:[70, 97] Operation: 47+50=97 Exploring Operation: 70-47=23, Resulting Numbers: [50, 23] Generated Node #0,3,1: 47:[50, 23] Operation: 70-47=23 Exploring Operation: 70-50=20, Resulting Numbers: [47, 20] Generated Node #0,3,2: 47:[47, 20] Operation: 70-50=20 Exploring Operation: 47+70=117, Resulting Numbers: [50, 117] Generated Node #0,3,3: 47:[50, 117] Operation: 47+70=117 Exploring Operation: 50-47=3, Resulting Numbers: [70, 3] Generated Node #0,3,4: 47:[70, 3] Operation: 50-47=3 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 47:[50, 23], Operations: ['14*5=70', '70-47=23'] Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,47 unequal: No Solution Exploring Operation: 50*23=1150, Resulting Numbers: [1150] 1150,47 unequal: No Solution Exploring Operation: 50+23=73, Resulting Numbers: [73] 73,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 47:[47, 20], Operations: ['14*5=70', '70-50=20'] Exploring Operation: 47*20=940, Resulting Numbers: [940] 940,47 unequal: No Solution Exploring Operation: 47+20=67, Resulting Numbers: [67] 67,47 unequal: No Solution Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 47:[70, 3], Operations: ['14*5=70', '50-47=3'] Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,47 unequal: No Solution Exploring Operation: 70+3=73, Resulting Numbers: [73] 73,47 unequal: No Solution Exploring Operation: 70*3=210, Resulting Numbers: [210] 210,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 47:[70, 97], Operations: ['14*5=70', '47+50=97'] Exploring Operation: 70+97=167, Resulting Numbers: [167] 167,47 unequal: No Solution Exploring Operation: 97-70=27, Resulting Numbers: [27] 27,47 unequal: No Solution Exploring Operation: 70*97=6790, Resulting Numbers: [6790] 6790,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 47:[50, 117], Operations: ['14*5=70', '47+70=117'] Exploring Operation: 117-50=67, Resulting Numbers: [67] 67,47 unequal: No Solution Exploring Operation: 50+117=167, Resulting Numbers: [167] 167,47 unequal: No Solution Exploring Operation: 50*117=5850, Resulting Numbers: [5850] 5850,47 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: 47:[47, 50, 19], Operations: ['14+5=19'] Exploring Operation: 50+19=69, Resulting Numbers: [47, 69] Generated Node #0,4,0: 47:[47, 69] Operation: 50+19=69 Exploring Operation: 50-19=31, Resulting Numbers: [47, 31] Generated Node #0,4,1: 47:[47, 31] Operation: 50-19=31 Exploring Operation: 47+19=66, Resulting Numbers: [50, 66] Generated Node #0,4,2: 47:[50, 66] Operation: 47+19=66 Exploring Operation: 50-47=3, Resulting Numbers: [19, 3] Generated Node #0,4,3: 47:[19, 3] Operation: 50-47=3 Exploring Operation: 47-19=28, Resulting Numbers: [50, 28] Generated Node #0,4,4: 47:[50, 28] Operation: 47-19=28 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 47:[47, 31], Operations: ['14+5=19', '50-19=31'] Exploring Operation: 47+31=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 47-31=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 47*31=1457, Resulting Numbers: [1457] 1457,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 47:[47, 69], Operations: ['14+5=19', '50+19=69'] Exploring Operation: 47*69=3243, Resulting Numbers: [3243] 3243,47 unequal: No Solution Exploring Operation: 47+69=116, Resulting Numbers: [116] 116,47 unequal: No Solution Exploring Operation: 69-47=22, Resulting Numbers: [22] 22,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 47:[50, 66], Operations: ['14+5=19', '47+19=66'] Exploring Operation: 66-50=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 50*66=3300, Resulting Numbers: [3300] 3300,47 unequal: No Solution Exploring Operation: 50+66=116, Resulting Numbers: [116] 116,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 47:[50, 28], Operations: ['14+5=19', '47-19=28'] Exploring Operation: 50*28=1400, Resulting Numbers: [1400] 1400,47 unequal: No Solution Exploring Operation: 50+28=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 47:[19, 3], Operations: ['14+5=19', '50-47=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,47 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,47 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: 47:[47, 14, 45], Operations: ['50-5=45'] Exploring Operation: 47-14=33, Resulting Numbers: [45, 33] Generated Node #0,1,0: 47:[45, 33] Operation: 47-14=33 Exploring Operation: 47+14=61, Resulting Numbers: [45, 61] Generated Node #0,1,1: 47:[45, 61] Operation: 47+14=61 Exploring Operation: 47+45=92, Resulting Numbers: [14, 92] Generated Node #0,1,2: 47:[14, 92] Operation: 47+45=92 Exploring Operation: 45-14=31, Resulting Numbers: [47, 31] Generated Node #0,1,3: 47:[47, 31] Operation: 45-14=31 Exploring Operation: 14+45=59, Resulting Numbers: [47, 59] Generated Node #0,1,4: 47:[47, 59] Operation: 14+45=59 Moving to Node #0,0 Current State: 47:[14, 50, 52], Operations: ['47+5=52'] Exploring Operation: 14+52=66, Resulting Numbers: [50, 66] Generated Node #0,0,0: 47:[50, 66] Operation: 14+52=66 Exploring Operation: 50-14=36, Resulting Numbers: [52, 36] Generated Node #0,0,1: 47:[52, 36] Operation: 50-14=36 Exploring Operation: 52-14=38, Resulting Numbers: [50, 38] Generated Node #0,0,2: 47:[50, 38] Operation: 52-14=38 Exploring Operation: 52-50=2, Resulting Numbers: [14, 2] Generated Node #0,0,3: 47:[14, 2] Operation: 52-50=2 Exploring Operation: 14+50=64, Resulting Numbers: [52, 64] Generated Node #0,0,4: 47:[52, 64] Operation: 14+50=64 Moving to Node #0,2 Current State: 47:[14, 50, 42], Operations: ['47-5=42'] Exploring Operation: 42/14=3, Resulting Numbers: [50, 3] Generated Node #0,2,0: 47:[50, 3] Operation: 42/14=3 Exploring Operation: 14+42=56, Resulting Numbers: [50, 56] Generated Node #0,2,1: 47:[50, 56] Operation: 14+42=56 Exploring Operation: 14+50=64, Resulting Numbers: [42, 64] Generated Node #0,2,2: 47:[42, 64] Operation: 14+50=64 Exploring Operation: 50-14=36, Resulting Numbers: [42, 36] Generated Node #0,2,3: 47:[42, 36] Operation: 50-14=36 Exploring Operation: 42-14=28, Resulting Numbers: [50, 28] Generated Node #0,2,4: 47:[50, 28] Operation: 42-14=28 Moving to Node #0,1,4 Current State: 47:[47, 59], Operations: ['50-5=45', '14+45=59'] Exploring Operation: 59-47=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 47+59=106, Resulting Numbers: [106] 106,47 unequal: No Solution Exploring Operation: 47*59=2773, Resulting Numbers: [2773] 2773,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[50, 38], Operations: ['47+5=52', '52-14=38'] Exploring Operation: 50*38=1900, Resulting Numbers: [1900] 1900,47 unequal: No Solution Exploring Operation: 50+38=88, Resulting Numbers: [88] 88,47 unequal: No Solution Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[50, 56], Operations: ['47-5=42', '14+42=56'] Exploring Operation: 50+56=106, Resulting Numbers: [106] 106,47 unequal: No Solution Exploring Operation: 50*56=2800, Resulting Numbers: [2800] 2800,47 unequal: No Solution Exploring Operation: 56-50=6, Resulting Numbers: [6] 6,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[52, 36], Operations: ['47+5=52', '50-14=36'] Exploring Operation: 52-36=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 52*36=1872, Resulting Numbers: [1872] 1872,47 unequal: No Solution Exploring Operation: 52+36=88, Resulting Numbers: [88] 88,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[45, 61], Operations: ['50-5=45', '47+14=61'] Exploring Operation: 45*61=2745, Resulting Numbers: [2745] 2745,47 unequal: No Solution Exploring Operation: 61-45=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 45+61=106, Resulting Numbers: [106] 106,47 unequal: No Solution Moving to Node #0,2,3 Current State: 47:[42, 36], Operations: ['47-5=42', '50-14=36'] Exploring Operation: 42-36=6, Resulting Numbers: [6] 6,47 unequal: No Solution Exploring Operation: 42*36=1512, Resulting Numbers: [1512] 1512,47 unequal: No Solution Exploring Operation: 42+36=78, Resulting Numbers: [78] 78,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[45, 33], Operations: ['50-5=45', '47-14=33'] Exploring Operation: 45*33=1485, Resulting Numbers: [1485] 1485,47 unequal: No Solution Exploring Operation: 45+33=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,47 unequal: No Solution Moving to Node #0,1,3 Current State: 47:[47, 31], Operations: ['50-5=45', '45-14=31'] Exploring Operation: 47-31=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 47*31=1457, Resulting Numbers: [1457] 1457,47 unequal: No Solution Exploring Operation: 47+31=78, Resulting Numbers: [78] 78,47 unequal: No Solution Moving to Node #0,2,4 Current State: 47:[50, 28], Operations: ['47-5=42', '42-14=28'] Exploring Operation: 50+28=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,47 unequal: No Solution Exploring Operation: 50*28=1400, Resulting Numbers: [1400] 1400,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[42, 64], Operations: ['47-5=42', '14+50=64'] Exploring Operation: 42+64=106, Resulting Numbers: [106] 106,47 unequal: No Solution Exploring Operation: 64-42=22, Resulting Numbers: [22] 22,47 unequal: No Solution Exploring Operation: 42*64=2688, Resulting Numbers: [2688] 2688,47 unequal: No Solution Moving to Node #0,0,4 Current State: 47:[52, 64], Operations: ['47+5=52', '14+50=64'] Exploring Operation: 64-52=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 52*64=3328, Resulting Numbers: [3328] 3328,47 unequal: No Solution Exploring Operation: 52+64=116, Resulting Numbers: [116] 116,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[50, 66], Operations: ['47+5=52', '14+52=66'] Exploring Operation: 50+66=116, Resulting Numbers: [116] 116,47 unequal: No Solution Exploring Operation: 66-50=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 50*66=3300, Resulting Numbers: [3300] 3300,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[50, 3], Operations: ['47-5=42', '42/14=3'] Exploring Operation: 50*3=150, Resulting Numbers: [150] 150,47 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[47, 14, 50, 5], Operations: [] Exploring Operation: 47-5=42, Resulting Numbers: [14, 50, 42] Generated Node #0,2: 47:[14, 50, 42] Operation: 47-5=42 Moving to Node #0,2 Current State: 47:[14, 50, 42], Operations: ['47-5=42'] Exploring Operation: 42/14=3, Resulting Numbers: [50, 3] Generated Node #0,2,0: 47:[50, 3] Operation: 42/14=3 Moving to Node #0,2,0 Current State: 47:[50, 3], Operations: ['47-5=42', '42/14=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
0.911458
hs_5
sum_heuristic
[ 46, 1, 2, 49 ]
98
[ "46+1=47", "2+49=51", "47+51=98" ]
Current State: 98:[46, 1, 2, 49], Operations: [] Exploring Operation: 46+1=47, Resulting Numbers: [2, 49, 47] Generated Node #2: [2, 49, 47] from Operation: 46+1=47 Current State: 98:[2, 49, 47], Operations: ['46+1=47'] Exploring Operation: 2+49=51, Resulting Numbers: [47, 51] Generated Node #3: [47, 51] from Operation: 2+49=51 Current State: 98:[47, 51], Operations: ['46+1=47', '2+49=51'] Exploring Operation: 47+51=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[46, 1, 2, 49], Operations: [] Exploring Operation: 46+1=47, Resulting Numbers: [2, 49, 47] Generated Node #0,0: 98:[2, 49, 47] Operation: 46+1=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[2, 49, 47], Operations: ['46+1=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49, 49] Generated Node #0,0,0: 98:[49, 49] Operation: 2+47=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[49, 49], Operations: ['46+1=47', '2+47=49'] Exploring Operation: 49+49=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[46, 1, 2, 49], Operations: [] Exploring Operation: 46+1=47, Resulting Numbers: [2, 49, 47] Generated Node #0,0: 98:[2, 49, 47] Operation: 46+1=47 Moving to Node #0,0 Current State: 98:[2, 49, 47], Operations: ['46+1=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49, 49] Generated Node #0,0,0: 98:[49, 49] Operation: 2+47=49 Moving to Node #0,0,0 Current State: 98:[49, 49], Operations: ['46+1=47', '2+47=49'] Exploring Operation: 49+49=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 70, 51, 87, 27 ]
95
[ "70-51=19", "87+27=114", "114-19=95" ]
Current State: 95:[70, 51, 87, 27], Operations: [] Exploring Operation: 70-51=19, Resulting Numbers: [87, 27, 19] Generated Node #2: [87, 27, 19] from Operation: 70-51=19 Current State: 95:[87, 27, 19], Operations: ['70-51=19'] Exploring Operation: 87+27=114, Resulting Numbers: [19, 114] Generated Node #3: [19, 114] from Operation: 87+27=114 Current State: 95:[19, 114], Operations: ['70-51=19', '87+27=114'] Exploring Operation: 114-19=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[70, 51, 87, 27], Operations: [] Exploring Operation: 51-27=24, Resulting Numbers: [70, 87, 24] Generated Node #0,0: 95:[70, 87, 24] Operation: 51-27=24 Exploring Operation: 70-51=19, Resulting Numbers: [87, 27, 19] Generated Node #0,1: 95:[87, 27, 19] Operation: 70-51=19 Exploring Operation: 70+51=121, Resulting Numbers: [87, 27, 121] Generated Node #0,2: 95:[87, 27, 121] Operation: 70+51=121 Moving to Node #0,1 Current State: 95:[87, 27, 19], Operations: ['70-51=19'] Exploring Operation: 87+19=106, Resulting Numbers: [27, 106] Generated Node #0,1,0: 95:[27, 106] Operation: 87+19=106 Exploring Operation: 87+27=114, Resulting Numbers: [19, 114] Generated Node #0,1,1: 95:[19, 114] Operation: 87+27=114 Exploring Operation: 27-19=8, Resulting Numbers: [87, 8] Generated Node #0,1,2: 95:[87, 8] Operation: 27-19=8 Moving to Node #0,0 Current State: 95:[70, 87, 24], Operations: ['51-27=24'] Exploring Operation: 70+24=94, Resulting Numbers: [87, 94] Generated Node #0,0,0: 95:[87, 94] Operation: 70+24=94 Exploring Operation: 70-24=46, Resulting Numbers: [87, 46] Generated Node #0,0,1: 95:[87, 46] Operation: 70-24=46 Exploring Operation: 87-70=17, Resulting Numbers: [24, 17] Generated Node #0,0,2: 95:[24, 17] Operation: 87-70=17 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 95:[24, 17], Operations: ['51-27=24', '87-70=17'] Exploring Operation: 24-17=7, Resulting Numbers: [7] 7,95 unequal: No Solution Exploring Operation: 24+17=41, Resulting Numbers: [41] 41,95 unequal: No Solution Exploring Operation: 24*17=408, Resulting Numbers: [408] 408,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[87, 94], Operations: ['51-27=24', '70+24=94'] Exploring Operation: 87+94=181, Resulting Numbers: [181] 181,95 unequal: No Solution Exploring Operation: 87*94=8178, Resulting Numbers: [8178] 8178,95 unequal: No Solution Exploring Operation: 94-87=7, Resulting Numbers: [7] 7,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 95:[87, 46], Operations: ['51-27=24', '70-24=46'] Exploring Operation: 87-46=41, Resulting Numbers: [41] 41,95 unequal: No Solution Exploring Operation: 87*46=4002, Resulting Numbers: [4002] 4002,95 unequal: No Solution Exploring Operation: 87+46=133, Resulting Numbers: [133] 133,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 95:[87, 27, 121], Operations: ['70+51=121'] Exploring Operation: 121-87=34, Resulting Numbers: [27, 34] Generated Node #0,2,0: 95:[27, 34] Operation: 121-87=34 Exploring Operation: 87+27=114, Resulting Numbers: [121, 114] Generated Node #0,2,1: 95:[121, 114] Operation: 87+27=114 Exploring Operation: 121-27=94, Resulting Numbers: [87, 94] Generated Node #0,2,2: 95:[87, 94] Operation: 121-27=94 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 95:[87, 94], Operations: ['70+51=121', '121-27=94'] Exploring Operation: 94-87=7, Resulting Numbers: [7] 7,95 unequal: No Solution Exploring Operation: 87*94=8178, Resulting Numbers: [8178] 8178,95 unequal: No Solution Exploring Operation: 87+94=181, Resulting Numbers: [181] 181,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 95:[27, 34], Operations: ['70+51=121', '121-87=34'] Exploring Operation: 27*34=918, Resulting Numbers: [918] 918,95 unequal: No Solution Exploring Operation: 34-27=7, Resulting Numbers: [7] 7,95 unequal: No Solution Exploring Operation: 27+34=61, Resulting Numbers: [61] 61,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 95:[121, 114], Operations: ['70+51=121', '87+27=114'] Exploring Operation: 121-114=7, Resulting Numbers: [7] 7,95 unequal: No Solution Exploring Operation: 121*114=13794, Resulting Numbers: [13794] 13794,95 unequal: No Solution Exploring Operation: 121+114=235, Resulting Numbers: [235] 235,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 95:[87, 8], Operations: ['70-51=19', '27-19=8'] Exploring Operation: 87+8=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[70, 51, 87, 27], Operations: [] Exploring Operation: 70-51=19, Resulting Numbers: [87, 27, 19] Generated Node #0,1: 95:[87, 27, 19] Operation: 70-51=19 Moving to Node #0,1 Current State: 95:[87, 27, 19], Operations: ['70-51=19'] Exploring Operation: 27-19=8, Resulting Numbers: [87, 8] Generated Node #0,1,2: 95:[87, 8] Operation: 27-19=8 Moving to Node #0,1,2 Current State: 95:[87, 8], Operations: ['70-51=19', '27-19=8'] Exploring Operation: 87+8=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
0.969618
hs_3
mult_heuristic
[ 40, 95, 8, 66 ]
85
[ "40/8=5", "95/5=19", "66+19=85" ]
Current State: 85:[40, 95, 8, 66], Operations: [] Exploring Operation: 40/8=5, Resulting Numbers: [95, 66, 5] Generated Node #2: [95, 66, 5] from Operation: 40/8=5 Current State: 85:[95, 66, 5], Operations: ['40/8=5'] Exploring Operation: 95/5=19, Resulting Numbers: [66, 19] Generated Node #3: [66, 19] from Operation: 95/5=19 Current State: 85:[66, 19], Operations: ['40/8=5', '95/5=19'] Exploring Operation: 66+19=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[40, 95, 8, 66], Operations: [] Exploring Operation: 66-40=26, Resulting Numbers: [95, 8, 26] Generated Node #0,0: 85:[95, 8, 26] Operation: 66-40=26 Exploring Operation: 40/8=5, Resulting Numbers: [95, 66, 5] Generated Node #0,1: 85:[95, 66, 5] Operation: 40/8=5 Moving to Node #0,0 Current State: 85:[95, 8, 26], Operations: ['66-40=26'] Exploring Operation: 95-8=87, Resulting Numbers: [26, 87] Generated Node #0,0,0: 85:[26, 87] Operation: 95-8=87 Exploring Operation: 26-8=18, Resulting Numbers: [95, 18] Generated Node #0,0,1: 85:[95, 18] Operation: 26-8=18 Moving to Node #0,1 Current State: 85:[95, 66, 5], Operations: ['40/8=5'] Exploring Operation: 95/5=19, Resulting Numbers: [66, 19] Generated Node #0,1,0: 85:[66, 19] Operation: 95/5=19 Exploring Operation: 95-66=29, Resulting Numbers: [5, 29] Generated Node #0,1,1: 85:[5, 29] Operation: 95-66=29 Moving to Node #0,0,0 Current State: 85:[26, 87], Operations: ['66-40=26', '95-8=87'] Exploring Operation: 87-26=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 26+87=113, Resulting Numbers: [113] 113,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[95, 18], Operations: ['66-40=26', '26-8=18'] Exploring Operation: 95-18=77, Resulting Numbers: [77] 77,85 unequal: No Solution Exploring Operation: 95+18=113, Resulting Numbers: [113] 113,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[5, 29], Operations: ['40/8=5', '95-66=29'] Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[66, 19], Operations: ['40/8=5', '95/5=19'] Exploring Operation: 66+19=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[40, 95, 8, 66], Operations: [] Exploring Operation: 40/8=5, Resulting Numbers: [95, 66, 5] Generated Node #0,1: 85:[95, 66, 5] Operation: 40/8=5 Moving to Node #0,1 Current State: 85:[95, 66, 5], Operations: ['40/8=5'] Exploring Operation: 95/5=19, Resulting Numbers: [66, 19] Generated Node #0,1,0: 85:[66, 19] Operation: 95/5=19 Moving to Node #0,1,0 Current State: 85:[66, 19], Operations: ['40/8=5', '95/5=19'] Exploring Operation: 66+19=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
0.985243
hs_2
mult_heuristic
[ 54, 10, 18, 87 ]
61
[ "54-10=44", "18+87=105", "105-44=61" ]
Current State: 61:[54, 10, 18, 87], Operations: [] Exploring Operation: 54-10=44, Resulting Numbers: [18, 87, 44] Generated Node #2: [18, 87, 44] from Operation: 54-10=44 Current State: 61:[18, 87, 44], Operations: ['54-10=44'] Exploring Operation: 18+87=105, Resulting Numbers: [44, 105] Generated Node #3: [44, 105] from Operation: 18+87=105 Current State: 61:[44, 105], Operations: ['54-10=44', '18+87=105'] Exploring Operation: 105-44=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[54, 10, 18, 87], Operations: [] Exploring Operation: 87-10=77, Resulting Numbers: [54, 18, 77] Generated Node #0,0: 61:[54, 18, 77] Operation: 87-10=77 Exploring Operation: 87-18=69, Resulting Numbers: [54, 10, 69] Generated Node #0,1: 61:[54, 10, 69] Operation: 87-18=69 Exploring Operation: 10+18=28, Resulting Numbers: [54, 87, 28] Generated Node #0,2: 61:[54, 87, 28] Operation: 10+18=28 Moving to Node #0,0 Current State: 61:[54, 18, 77], Operations: ['87-10=77'] Exploring Operation: 54-18=36, Resulting Numbers: [77, 36] Generated Node #0,0,0: 61:[77, 36] Operation: 54-18=36 Exploring Operation: 77-18=59, Resulting Numbers: [54, 59] Generated Node #0,0,1: 61:[54, 59] Operation: 77-18=59 Exploring Operation: 54+18=72, Resulting Numbers: [77, 72] Generated Node #0,0,2: 61:[77, 72] Operation: 54+18=72 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[54, 59], Operations: ['87-10=77', '77-18=59'] Exploring Operation: 54+59=113, Resulting Numbers: [113] 113,61 unequal: No Solution Exploring Operation: 54*59=3186, Resulting Numbers: [3186] 3186,61 unequal: No Solution Exploring Operation: 59-54=5, Resulting Numbers: [5] 5,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 61:[77, 72], Operations: ['87-10=77', '54+18=72'] Exploring Operation: 77+72=149, Resulting Numbers: [149] 149,61 unequal: No Solution Exploring Operation: 77-72=5, Resulting Numbers: [5] 5,61 unequal: No Solution Exploring Operation: 77*72=5544, Resulting Numbers: [5544] 5544,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[77, 36], Operations: ['87-10=77', '54-18=36'] Exploring Operation: 77*36=2772, Resulting Numbers: [2772] 2772,61 unequal: No Solution Exploring Operation: 77-36=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 77+36=113, Resulting Numbers: [113] 113,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 61:[54, 10, 69], Operations: ['87-18=69'] Exploring Operation: 54-10=44, Resulting Numbers: [69, 44] Generated Node #0,1,0: 61:[69, 44] Operation: 54-10=44 Exploring Operation: 54+10=64, Resulting Numbers: [69, 64] Generated Node #0,1,1: 61:[69, 64] Operation: 54+10=64 Exploring Operation: 69-10=59, Resulting Numbers: [54, 59] Generated Node #0,1,2: 61:[54, 59] Operation: 69-10=59 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 61:[54, 59], Operations: ['87-18=69', '69-10=59'] Exploring Operation: 54*59=3186, Resulting Numbers: [3186] 3186,61 unequal: No Solution Exploring Operation: 54+59=113, Resulting Numbers: [113] 113,61 unequal: No Solution Exploring Operation: 59-54=5, Resulting Numbers: [5] 5,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[69, 64], Operations: ['87-18=69', '54+10=64'] Exploring Operation: 69-64=5, Resulting Numbers: [5] 5,61 unequal: No Solution Exploring Operation: 69+64=133, Resulting Numbers: [133] 133,61 unequal: No Solution Exploring Operation: 69*64=4416, Resulting Numbers: [4416] 4416,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 61:[69, 44], Operations: ['87-18=69', '54-10=44'] Exploring Operation: 69-44=25, Resulting Numbers: [25] 25,61 unequal: No Solution Exploring Operation: 69+44=113, Resulting Numbers: [113] 113,61 unequal: No Solution Exploring Operation: 69*44=3036, Resulting Numbers: [3036] 3036,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 61:[54, 87, 28], Operations: ['10+18=28'] Exploring Operation: 87-28=59, Resulting Numbers: [54, 59] Generated Node #0,2,0: 61:[54, 59] Operation: 87-28=59 Exploring Operation: 54+28=82, Resulting Numbers: [87, 82] Generated Node #0,2,1: 61:[87, 82] Operation: 54+28=82 Exploring Operation: 87-54=33, Resulting Numbers: [28, 33] Generated Node #0,2,2: 61:[28, 33] Operation: 87-54=33 Moving to Node #0,2,0 Current State: 61:[54, 59], Operations: ['10+18=28', '87-28=59'] Exploring Operation: 59-54=5, Resulting Numbers: [5] 5,61 unequal: No Solution Exploring Operation: 54*59=3186, Resulting Numbers: [3186] 3186,61 unequal: No Solution Exploring Operation: 54+59=113, Resulting Numbers: [113] 113,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[87, 82], Operations: ['10+18=28', '54+28=82'] Exploring Operation: 87+82=169, Resulting Numbers: [169] 169,61 unequal: No Solution Exploring Operation: 87*82=7134, Resulting Numbers: [7134] 7134,61 unequal: No Solution Exploring Operation: 87-82=5, Resulting Numbers: [5] 5,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[28, 33], Operations: ['10+18=28', '87-54=33'] Exploring Operation: 33-28=5, Resulting Numbers: [5] 5,61 unequal: No Solution Exploring Operation: 28*33=924, Resulting Numbers: [924] 924,61 unequal: No Solution Exploring Operation: 28+33=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[54, 10, 18, 87], Operations: [] Exploring Operation: 10+18=28, Resulting Numbers: [54, 87, 28] Generated Node #0,2: 61:[54, 87, 28] Operation: 10+18=28 Moving to Node #0,2 Current State: 61:[54, 87, 28], Operations: ['10+18=28'] Exploring Operation: 87-54=33, Resulting Numbers: [28, 33] Generated Node #0,2,2: 61:[28, 33] Operation: 87-54=33 Moving to Node #0,2,2 Current State: 61:[28, 33], Operations: ['10+18=28', '87-54=33'] Exploring Operation: 28+33=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
0.962674
hs_3
sum_heuristic
[ 54, 19, 28, 57 ]
27
[ "57-54=3", "28-19=9", "3*9=27" ]
Current State: 27:[54, 19, 28, 57], Operations: [] Exploring Operation: 57-54=3, Resulting Numbers: [19, 28, 3] Generated Node #2: [19, 28, 3] from Operation: 57-54=3 Current State: 27:[19, 28, 3], Operations: ['57-54=3'] Exploring Operation: 28-19=9, Resulting Numbers: [3, 9] Generated Node #3: [3, 9] from Operation: 28-19=9 Current State: 27:[3, 9], Operations: ['57-54=3', '28-19=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[54, 19, 28, 57], Operations: [] Exploring Operation: 57-54=3, Resulting Numbers: [19, 28, 3] Generated Node #0,0: 27:[19, 28, 3] Operation: 57-54=3 Exploring Operation: 57/19=3, Resulting Numbers: [54, 28, 3] Generated Node #0,1: 27:[54, 28, 3] Operation: 57/19=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[19, 28, 3], Operations: ['57-54=3'] Exploring Operation: 28-19=9, Resulting Numbers: [3, 9] Generated Node #0,0,0: 27:[3, 9] Operation: 28-19=9 Exploring Operation: 19+3=22, Resulting Numbers: [28, 22] Generated Node #0,0,1: 27:[28, 22] Operation: 19+3=22 Moving to Node #0,0,0 Current State: 27:[3, 9], Operations: ['57-54=3', '28-19=9'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[54, 19, 28, 57], Operations: [] Exploring Operation: 57-54=3, Resulting Numbers: [19, 28, 3] Generated Node #0,0: 27:[19, 28, 3] Operation: 57-54=3 Moving to Node #0,0 Current State: 27:[19, 28, 3], Operations: ['57-54=3'] Exploring Operation: 28-19=9, Resulting Numbers: [3, 9] Generated Node #0,0,0: 27:[3, 9] Operation: 28-19=9 Moving to Node #0,0,0 Current State: 27:[3, 9], Operations: ['57-54=3', '28-19=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 33, 2, 72, 44 ]
85
[ "33-2=31", "72+44=116", "116-31=85" ]
Current State: 85:[33, 2, 72, 44], Operations: [] Exploring Operation: 33-2=31, Resulting Numbers: [72, 44, 31] Generated Node #2: [72, 44, 31] from Operation: 33-2=31 Current State: 85:[72, 44, 31], Operations: ['33-2=31'] Exploring Operation: 72+44=116, Resulting Numbers: [31, 116] Generated Node #3: [31, 116] from Operation: 72+44=116 Current State: 85:[31, 116], Operations: ['33-2=31', '72+44=116'] Exploring Operation: 116-31=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[33, 2, 72, 44], Operations: [] Exploring Operation: 44-33=11, Resulting Numbers: [2, 72, 11] Generated Node #0,0: 85:[2, 72, 11] Operation: 44-33=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[2, 72, 11], Operations: ['44-33=11'] Exploring Operation: 72+11=83, Resulting Numbers: [2, 83] Generated Node #0,0,0: 85:[2, 83] Operation: 72+11=83 Moving to Node #0,0,0 Current State: 85:[2, 83], Operations: ['44-33=11', '72+11=83'] Exploring Operation: 2+83=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[33, 2, 72, 44], Operations: [] Exploring Operation: 44-33=11, Resulting Numbers: [2, 72, 11] Generated Node #0,0: 85:[2, 72, 11] Operation: 44-33=11 Moving to Node #0,0 Current State: 85:[2, 72, 11], Operations: ['44-33=11'] Exploring Operation: 72+11=83, Resulting Numbers: [2, 83] Generated Node #0,0,0: 85:[2, 83] Operation: 72+11=83 Moving to Node #0,0,0 Current State: 85:[2, 83], Operations: ['44-33=11', '72+11=83'] Exploring Operation: 2+83=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 20, 5, 85, 22 ]
34
[ "22-20=2", "85/5=17", "2*17=34" ]
Current State: 34:[20, 5, 85, 22], Operations: [] Exploring Operation: 22-20=2, Resulting Numbers: [5, 85, 2] Generated Node #2: [5, 85, 2] from Operation: 22-20=2 Current State: 34:[5, 85, 2], Operations: ['22-20=2'] Exploring Operation: 85/5=17, Resulting Numbers: [2, 17] Generated Node #3: [2, 17] from Operation: 85/5=17 Current State: 34:[2, 17], Operations: ['22-20=2', '85/5=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[20, 5, 85, 22], Operations: [] Exploring Operation: 85/5=17, Resulting Numbers: [20, 22, 17] Generated Node #0,0: 34:[20, 22, 17] Operation: 85/5=17 Exploring Operation: 85-22=63, Resulting Numbers: [20, 5, 63] Generated Node #0,1: 34:[20, 5, 63] Operation: 85-22=63 Exploring Operation: 85-20=65, Resulting Numbers: [5, 22, 65] Generated Node #0,2: 34:[5, 22, 65] Operation: 85-20=65 Exploring Operation: 22-20=2, Resulting Numbers: [5, 85, 2] Generated Node #0,3: 34:[5, 85, 2] Operation: 22-20=2 Moving to Node #0,0 Current State: 34:[20, 22, 17], Operations: ['85/5=17'] Exploring Operation: 20-17=3, Resulting Numbers: [22, 3] Generated Node #0,0,0: 34:[22, 3] Operation: 20-17=3 Exploring Operation: 20+22=42, Resulting Numbers: [17, 42] Generated Node #0,0,1: 34:[17, 42] Operation: 20+22=42 Exploring Operation: 22-20=2, Resulting Numbers: [17, 2] Generated Node #0,0,2: 34:[17, 2] Operation: 22-20=2 Exploring Operation: 22-17=5, Resulting Numbers: [20, 5] Generated Node #0,0,3: 34:[20, 5] Operation: 22-17=5 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 34:[17, 2], Operations: ['85/5=17', '22-20=2'] Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,34 unequal: No Solution Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[20, 5, 85, 22], Operations: [] Exploring Operation: 85/5=17, Resulting Numbers: [20, 22, 17] Generated Node #0,0: 34:[20, 22, 17] Operation: 85/5=17 Moving to Node #0,0 Current State: 34:[20, 22, 17], Operations: ['85/5=17'] Exploring Operation: 22-20=2, Resulting Numbers: [17, 2] Generated Node #0,0,2: 34:[17, 2] Operation: 22-20=2 Moving to Node #0,0,2 Current State: 34:[17, 2], Operations: ['85/5=17', '22-20=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 7, 41, 2, 38 ]
20
[ "7+41=48", "48-38=10", "2*10=20" ]
Current State: 20:[7, 41, 2, 38], Operations: [] Exploring Operation: 7+41=48, Resulting Numbers: [2, 38, 48] Generated Node #2: [2, 38, 48] from Operation: 7+41=48 Current State: 20:[2, 38, 48], Operations: ['7+41=48'] Exploring Operation: 48-38=10, Resulting Numbers: [2, 10] Generated Node #3: [2, 10] from Operation: 48-38=10 Current State: 20:[2, 10], Operations: ['7+41=48', '48-38=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[7, 41, 2, 38], Operations: [] Exploring Operation: 38/2=19, Resulting Numbers: [7, 41, 19] Generated Node #0,0: 20:[7, 41, 19] Operation: 38/2=19 Exploring Operation: 41-38=3, Resulting Numbers: [7, 2, 3] Generated Node #0,1: 20:[7, 2, 3] Operation: 41-38=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[7, 2, 3], Operations: ['41-38=3'] Exploring Operation: 7+3=10, Resulting Numbers: [2, 10] Generated Node #0,1,0: 20:[2, 10] Operation: 7+3=10 Exploring Operation: 7-3=4, Resulting Numbers: [2, 4] Generated Node #0,1,1: 20:[2, 4] Operation: 7-3=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 20:[2, 10], Operations: ['41-38=3', '7+3=10'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[7, 41, 2, 38], Operations: [] Exploring Operation: 41-38=3, Resulting Numbers: [7, 2, 3] Generated Node #0,1: 20:[7, 2, 3] Operation: 41-38=3 Moving to Node #0,1 Current State: 20:[7, 2, 3], Operations: ['41-38=3'] Exploring Operation: 7+3=10, Resulting Numbers: [2, 10] Generated Node #0,1,0: 20:[2, 10] Operation: 7+3=10 Moving to Node #0,1,0 Current State: 20:[2, 10], Operations: ['41-38=3', '7+3=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 50, 46, 47, 61 ]
18
[ "50-46=4", "61-47=14", "4+14=18" ]
Current State: 18:[50, 46, 47, 61], Operations: [] Exploring Operation: 50-46=4, Resulting Numbers: [47, 61, 4] Generated Node #2: [47, 61, 4] from Operation: 50-46=4 Current State: 18:[47, 61, 4], Operations: ['50-46=4'] Exploring Operation: 61-47=14, Resulting Numbers: [4, 14] Generated Node #3: [4, 14] from Operation: 61-47=14 Current State: 18:[4, 14], Operations: ['50-46=4', '61-47=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[50, 46, 47, 61], Operations: [] Exploring Operation: 61-46=15, Resulting Numbers: [50, 47, 15] Generated Node #0,0: 18:[50, 47, 15] Operation: 61-46=15 Exploring Operation: 61-50=11, Resulting Numbers: [46, 47, 11] Generated Node #0,1: 18:[46, 47, 11] Operation: 61-50=11 Exploring Operation: 61-47=14, Resulting Numbers: [50, 46, 14] Generated Node #0,2: 18:[50, 46, 14] Operation: 61-47=14 Exploring Operation: 50-47=3, Resulting Numbers: [46, 61, 3] Generated Node #0,3: 18:[46, 61, 3] Operation: 50-47=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[46, 47, 11], Operations: ['61-50=11'] Exploring Operation: 46-11=35, Resulting Numbers: [47, 35] Generated Node #0,1,0: 18:[47, 35] Operation: 46-11=35 Exploring Operation: 47-11=36, Resulting Numbers: [46, 36] Generated Node #0,1,1: 18:[46, 36] Operation: 47-11=36 Exploring Operation: 46+11=57, Resulting Numbers: [47, 57] Generated Node #0,1,2: 18:[47, 57] Operation: 46+11=57 Exploring Operation: 47-46=1, Resulting Numbers: [11, 1] Generated Node #0,1,3: 18:[11, 1] Operation: 47-46=1 Moving to Node #0,1,3 Current State: 18:[11, 1], Operations: ['61-50=11', '47-46=1'] Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[46, 36], Operations: ['61-50=11', '47-11=36'] Exploring Operation: 46*36=1656, Resulting Numbers: [1656] 1656,18 unequal: No Solution Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 46+36=82, Resulting Numbers: [82] 82,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[47, 35], Operations: ['61-50=11', '46-11=35'] Exploring Operation: 47+35=82, Resulting Numbers: [82] 82,18 unequal: No Solution Exploring Operation: 47*35=1645, Resulting Numbers: [1645] 1645,18 unequal: No Solution Exploring Operation: 47-35=12, Resulting Numbers: [12] 12,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[47, 57], Operations: ['61-50=11', '46+11=57'] Exploring Operation: 57-47=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 47*57=2679, Resulting Numbers: [2679] 2679,18 unequal: No Solution Exploring Operation: 47+57=104, Resulting Numbers: [104] 104,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[50, 47, 15], Operations: ['61-46=15'] Exploring Operation: 50-47=3, Resulting Numbers: [15, 3] Generated Node #0,0,0: 18:[15, 3] Operation: 50-47=3 Exploring Operation: 50-15=35, Resulting Numbers: [47, 35] Generated Node #0,0,1: 18:[47, 35] Operation: 50-15=35 Exploring Operation: 47-15=32, Resulting Numbers: [50, 32] Generated Node #0,0,2: 18:[50, 32] Operation: 47-15=32 Exploring Operation: 50+15=65, Resulting Numbers: [47, 65] Generated Node #0,0,3: 18:[47, 65] Operation: 50+15=65 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[15, 3], Operations: ['61-46=15', '50-47=3'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,18 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[50, 46, 47, 61], Operations: [] Exploring Operation: 61-46=15, Resulting Numbers: [50, 47, 15] Generated Node #0,0: 18:[50, 47, 15] Operation: 61-46=15 Moving to Node #0,0 Current State: 18:[50, 47, 15], Operations: ['61-46=15'] Exploring Operation: 50-47=3, Resulting Numbers: [15, 3] Generated Node #0,0,0: 18:[15, 3] Operation: 50-47=3 Moving to Node #0,0,0 Current State: 18:[15, 3], Operations: ['61-46=15', '50-47=3'] Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 80, 83, 79, 56 ]
34
[ "80+56=136", "83-79=4", "136/4=34" ]
Current State: 34:[80, 83, 79, 56], Operations: [] Exploring Operation: 80+56=136, Resulting Numbers: [83, 79, 136] Generated Node #2: [83, 79, 136] from Operation: 80+56=136 Current State: 34:[83, 79, 136], Operations: ['80+56=136'] Exploring Operation: 83-79=4, Resulting Numbers: [136, 4] Generated Node #3: [136, 4] from Operation: 83-79=4 Current State: 34:[136, 4], Operations: ['80+56=136', '83-79=4'] Exploring Operation: 136/4=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[80, 83, 79, 56], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [83, 79, 24] Generated Node #0,0: 34:[83, 79, 24] Operation: 80-56=24 Exploring Operation: 83-56=27, Resulting Numbers: [80, 79, 27] Generated Node #0,1: 34:[80, 79, 27] Operation: 83-56=27 Exploring Operation: 83-80=3, Resulting Numbers: [79, 56, 3] Generated Node #0,2: 34:[79, 56, 3] Operation: 83-80=3 Exploring Operation: 83-79=4, Resulting Numbers: [80, 56, 4] Generated Node #0,3: 34:[80, 56, 4] Operation: 83-79=4 Exploring Operation: 80-79=1, Resulting Numbers: [83, 56, 1] Generated Node #0,4: 34:[83, 56, 1] Operation: 80-79=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[79, 56, 3], Operations: ['83-80=3'] Exploring Operation: 79-56=23, Resulting Numbers: [3, 23] Generated Node #0,2,0: 34:[3, 23] Operation: 79-56=23 Exploring Operation: 79+3=82, Resulting Numbers: [56, 82] Generated Node #0,2,1: 34:[56, 82] Operation: 79+3=82 Exploring Operation: 79-3=76, Resulting Numbers: [56, 76] Generated Node #0,2,2: 34:[56, 76] Operation: 79-3=76 Exploring Operation: 56+3=59, Resulting Numbers: [79, 59] Generated Node #0,2,3: 34:[79, 59] Operation: 56+3=59 Exploring Operation: 56-3=53, Resulting Numbers: [79, 53] Generated Node #0,2,4: 34:[79, 53] Operation: 56-3=53 Moving to Node #0,2,0 Current State: 34:[3, 23], Operations: ['83-80=3', '79-56=23'] Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,34 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,34 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,34 unequal: No Solution Moving to Node #0,2,4 Current State: 34:[79, 53], Operations: ['83-80=3', '56-3=53'] Exploring Operation: 79*53=4187, Resulting Numbers: [4187] 4187,34 unequal: No Solution Exploring Operation: 79+53=132, Resulting Numbers: [132] 132,34 unequal: No Solution Exploring Operation: 79-53=26, Resulting Numbers: [26] 26,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[56, 76], Operations: ['83-80=3', '79-3=76'] Exploring Operation: 76-56=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 56+76=132, Resulting Numbers: [132] 132,34 unequal: No Solution Exploring Operation: 56*76=4256, Resulting Numbers: [4256] 4256,34 unequal: No Solution Moving to Node #0,2,1 Current State: 34:[56, 82], Operations: ['83-80=3', '79+3=82'] Exploring Operation: 56*82=4592, Resulting Numbers: [4592] 4592,34 unequal: No Solution Exploring Operation: 56+82=138, Resulting Numbers: [138] 138,34 unequal: No Solution Exploring Operation: 82-56=26, Resulting Numbers: [26] 26,34 unequal: No Solution Moving to Node #0,2,3 Current State: 34:[79, 59], Operations: ['83-80=3', '56+3=59'] Exploring Operation: 79-59=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 79*59=4661, Resulting Numbers: [4661] 4661,34 unequal: No Solution Exploring Operation: 79+59=138, Resulting Numbers: [138] 138,34 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 #0,3 Current State: 34:[80, 56, 4], Operations: ['83-79=4'] Exploring Operation: 56-4=52, Resulting Numbers: [80, 52] Generated Node #0,3,0: 34:[80, 52] Operation: 56-4=52 Exploring Operation: 56/4=14, Resulting Numbers: [80, 14] Generated Node #0,3,1: 34:[80, 14] Operation: 56/4=14 Exploring Operation: 80-4=76, Resulting Numbers: [56, 76] Generated Node #0,3,2: 34:[56, 76] Operation: 80-4=76 Exploring Operation: 80/4=20, Resulting Numbers: [56, 20] Generated Node #0,3,3: 34:[56, 20] Operation: 80/4=20 Exploring Operation: 80-56=24, Resulting Numbers: [4, 24] Generated Node #0,3,4: 34:[4, 24] Operation: 80-56=24 Moving to Node #0,3,4 Current State: 34:[4, 24], Operations: ['83-79=4', '80-56=24'] Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,34 unequal: No Solution Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,34 unequal: No Solution Moving to Node #0,3,3 Current State: 34:[56, 20], Operations: ['83-79=4', '80/4=20'] Exploring Operation: 56+20=76, Resulting Numbers: [76] 76,34 unequal: No Solution Exploring Operation: 56*20=1120, Resulting Numbers: [1120] 1120,34 unequal: No Solution Exploring Operation: 56-20=36, Resulting Numbers: [36] 36,34 unequal: No Solution Moving to Node #0,3,1 Current State: 34:[80, 14], Operations: ['83-79=4', '56/4=14'] Exploring Operation: 80*14=1120, Resulting Numbers: [1120] 1120,34 unequal: No Solution Exploring Operation: 80+14=94, Resulting Numbers: [94] 94,34 unequal: No Solution Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,34 unequal: No Solution Moving to Node #0,3,0 Current State: 34:[80, 52], Operations: ['83-79=4', '56-4=52'] Exploring Operation: 80-52=28, Resulting Numbers: [28] 28,34 unequal: No Solution Exploring Operation: 80*52=4160, Resulting Numbers: [4160] 4160,34 unequal: No Solution Exploring Operation: 80+52=132, Resulting Numbers: [132] 132,34 unequal: No Solution Moving to Node #0,3,2 Current State: 34:[56, 76], Operations: ['83-79=4', '80-4=76'] Exploring Operation: 56+76=132, Resulting Numbers: [132] 132,34 unequal: No Solution Exploring Operation: 76-56=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 56*76=4256, Resulting Numbers: [4256] 4256,34 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 #0,4 Current State: 34:[83, 56, 1], Operations: ['80-79=1'] Exploring Operation: 83-56=27, Resulting Numbers: [1, 27] Generated Node #0,4,0: 34:[1, 27] Operation: 83-56=27 Exploring Operation: 83-1=82, Resulting Numbers: [56, 82] Generated Node #0,4,1: 34:[56, 82] Operation: 83-1=82 Exploring Operation: 83/1=83, Resulting Numbers: [56, 83] Generated Node #0,4,2: 34:[56, 83] Operation: 83/1=83 Exploring Operation: 83*1=83, Resulting Numbers: [56, 83] Generated Node #0,4,3: 34:[56, 83] Operation: 83*1=83 Exploring Operation: 56-1=55, Resulting Numbers: [83, 55] Generated Node #0,4,4: 34:[83, 55] Operation: 56-1=55 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 34:[1, 27], Operations: ['80-79=1', '83-56=27'] Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,34 unequal: No Solution Exploring Operation: 1*27=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 1+27=28, Resulting Numbers: [28] 28,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 34:[56, 82], Operations: ['80-79=1', '83-1=82'] Exploring Operation: 82-56=26, Resulting Numbers: [26] 26,34 unequal: No Solution Exploring Operation: 56+82=138, Resulting Numbers: [138] 138,34 unequal: No Solution Exploring Operation: 56*82=4592, Resulting Numbers: [4592] 4592,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 34:[83, 55], Operations: ['80-79=1', '56-1=55'] Exploring Operation: 83+55=138, Resulting Numbers: [138] 138,34 unequal: No Solution Exploring Operation: 83-55=28, Resulting Numbers: [28] 28,34 unequal: No Solution Exploring Operation: 83*55=4565, Resulting Numbers: [4565] 4565,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 34:[56, 83], Operations: ['80-79=1', '83/1=83'] Exploring Operation: 56+83=139, Resulting Numbers: [139] 139,34 unequal: No Solution Exploring Operation: 56*83=4648, Resulting Numbers: [4648] 4648,34 unequal: No Solution Exploring Operation: 83-56=27, Resulting Numbers: [27] 27,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 34:[56, 83], Operations: ['80-79=1', '83*1=83'] Exploring Operation: 56+83=139, Resulting Numbers: [139] 139,34 unequal: No Solution Exploring Operation: 83-56=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 56*83=4648, Resulting Numbers: [4648] 4648,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[80, 79, 27], Operations: ['83-56=27'] Exploring Operation: 79-27=52, Resulting Numbers: [80, 52] Generated Node #0,1,0: 34:[80, 52] Operation: 79-27=52 Exploring Operation: 80+27=107, Resulting Numbers: [79, 107] Generated Node #0,1,1: 34:[79, 107] Operation: 80+27=107 Exploring Operation: 80-79=1, Resulting Numbers: [27, 1] Generated Node #0,1,2: 34:[27, 1] Operation: 80-79=1 Exploring Operation: 79+27=106, Resulting Numbers: [80, 106] Generated Node #0,1,3: 34:[80, 106] Operation: 79+27=106 Exploring Operation: 80-27=53, Resulting Numbers: [79, 53] Generated Node #0,1,4: 34:[79, 53] Operation: 80-27=53 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 34:[27, 1], Operations: ['83-56=27', '80-79=1'] Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 27+1=28, Resulting Numbers: [28] 28,34 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,34 unequal: No Solution Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 34:[80, 52], Operations: ['83-56=27', '79-27=52'] Exploring Operation: 80-52=28, Resulting Numbers: [28] 28,34 unequal: No Solution Exploring Operation: 80*52=4160, Resulting Numbers: [4160] 4160,34 unequal: No Solution Exploring Operation: 80+52=132, Resulting Numbers: [132] 132,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 34:[79, 53], Operations: ['83-56=27', '80-27=53'] Exploring Operation: 79-53=26, Resulting Numbers: [26] 26,34 unequal: No Solution Exploring Operation: 79*53=4187, Resulting Numbers: [4187] 4187,34 unequal: No Solution Exploring Operation: 79+53=132, Resulting Numbers: [132] 132,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 34:[79, 107], Operations: ['83-56=27', '80+27=107'] Exploring Operation: 107-79=28, Resulting Numbers: [28] 28,34 unequal: No Solution Exploring Operation: 79+107=186, Resulting Numbers: [186] 186,34 unequal: No Solution Exploring Operation: 79*107=8453, Resulting Numbers: [8453] 8453,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 34:[80, 106], Operations: ['83-56=27', '79+27=106'] Exploring Operation: 106-80=26, Resulting Numbers: [26] 26,34 unequal: No Solution Exploring Operation: 80*106=8480, Resulting Numbers: [8480] 8480,34 unequal: No Solution Exploring Operation: 80+106=186, Resulting Numbers: [186] 186,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[83, 79, 24], Operations: ['80-56=24'] Exploring Operation: 79-24=55, Resulting Numbers: [83, 55] Generated Node #0,0,0: 34:[83, 55] Operation: 79-24=55 Exploring Operation: 83+24=107, Resulting Numbers: [79, 107] Generated Node #0,0,1: 34:[79, 107] Operation: 83+24=107 Exploring Operation: 83-24=59, Resulting Numbers: [79, 59] Generated Node #0,0,2: 34:[79, 59] Operation: 83-24=59 Exploring Operation: 79+24=103, Resulting Numbers: [83, 103] Generated Node #0,0,3: 34:[83, 103] Operation: 79+24=103 Exploring Operation: 83-79=4, Resulting Numbers: [24, 4] Generated Node #0,0,4: 34:[24, 4] Operation: 83-79=4 Moving to Node #0,0,4 Current State: 34:[24, 4], Operations: ['80-56=24', '83-79=4'] Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,34 unequal: No Solution Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,34 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,34 unequal: No Solution Moving to Node #0,0,2 Current State: 34:[79, 59], Operations: ['80-56=24', '83-24=59'] Exploring Operation: 79+59=138, Resulting Numbers: [138] 138,34 unequal: No Solution Exploring Operation: 79-59=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 79*59=4661, Resulting Numbers: [4661] 4661,34 unequal: No Solution Moving to Node #0,0,0 Current State: 34:[83, 55], Operations: ['80-56=24', '79-24=55'] Exploring Operation: 83*55=4565, Resulting Numbers: [4565] 4565,34 unequal: No Solution Exploring Operation: 83-55=28, Resulting Numbers: [28] 28,34 unequal: No Solution Exploring Operation: 83+55=138, Resulting Numbers: [138] 138,34 unequal: No Solution Moving to Node #0,0,1 Current State: 34:[79, 107], Operations: ['80-56=24', '83+24=107'] Exploring Operation: 107-79=28, Resulting Numbers: [28] 28,34 unequal: No Solution Exploring Operation: 79+107=186, Resulting Numbers: [186] 186,34 unequal: No Solution Exploring Operation: 79*107=8453, Resulting Numbers: [8453] 8453,34 unequal: No Solution Moving to Node #0,0,3 Current State: 34:[83, 103], Operations: ['80-56=24', '79+24=103'] Exploring Operation: 83*103=8549, Resulting Numbers: [8549] 8549,34 unequal: No Solution Exploring Operation: 83+103=186, Resulting Numbers: [186] 186,34 unequal: No Solution Exploring Operation: 103-83=20, Resulting Numbers: [20] 20,34 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
[ 82, 51, 27, 38 ]
20
[ "82-51=31", "38-27=11", "31-11=20" ]
Current State: 20:[82, 51, 27, 38], Operations: [] Exploring Operation: 82-51=31, Resulting Numbers: [27, 38, 31] Generated Node #2: [27, 38, 31] from Operation: 82-51=31 Current State: 20:[27, 38, 31], Operations: ['82-51=31'] Exploring Operation: 38-27=11, Resulting Numbers: [31, 11] Generated Node #3: [31, 11] from Operation: 38-27=11 Current State: 20:[31, 11], Operations: ['82-51=31', '38-27=11'] Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[82, 51, 27, 38], Operations: [] Exploring Operation: 82-27=55, Resulting Numbers: [51, 38, 55] Generated Node #0,0: 20:[51, 38, 55] Operation: 82-27=55 Exploring Operation: 82-51=31, Resulting Numbers: [27, 38, 31] Generated Node #0,1: 20:[27, 38, 31] Operation: 82-51=31 Exploring Operation: 51-38=13, Resulting Numbers: [82, 27, 13] Generated Node #0,2: 20:[82, 27, 13] Operation: 51-38=13 Exploring Operation: 82-38=44, Resulting Numbers: [51, 27, 44] Generated Node #0,3: 20:[51, 27, 44] Operation: 82-38=44 Moving to Node #0,1 Current State: 20:[27, 38, 31], Operations: ['82-51=31'] Exploring Operation: 27+38=65, Resulting Numbers: [31, 65] Generated Node #0,1,0: 20:[31, 65] Operation: 27+38=65 Exploring Operation: 38-27=11, Resulting Numbers: [31, 11] Generated Node #0,1,1: 20:[31, 11] Operation: 38-27=11 Exploring Operation: 31-27=4, Resulting Numbers: [38, 4] Generated Node #0,1,2: 20:[38, 4] Operation: 31-27=4 Exploring Operation: 38-31=7, Resulting Numbers: [27, 7] Generated Node #0,1,3: 20:[27, 7] Operation: 38-31=7 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 20:[27, 7], Operations: ['82-51=31', '38-31=7'] Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,20 unequal: No Solution Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[82, 51, 27, 38], Operations: [] Exploring Operation: 82-51=31, Resulting Numbers: [27, 38, 31] Generated Node #0,1: 20:[27, 38, 31] Operation: 82-51=31 Moving to Node #0,1 Current State: 20:[27, 38, 31], Operations: ['82-51=31'] Exploring Operation: 38-31=7, Resulting Numbers: [27, 7] Generated Node #0,1,3: 20:[27, 7] Operation: 38-31=7 Moving to Node #0,1,3 Current State: 20:[27, 7], Operations: ['82-51=31', '38-31=7'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 49, 14, 84, 1 ]
49
[ "49-14=35", "84*1=84", "84-35=49" ]
Current State: 49:[49, 14, 84, 1], Operations: [] Exploring Operation: 49-14=35, Resulting Numbers: [84, 1, 35] Generated Node #2: [84, 1, 35] from Operation: 49-14=35 Current State: 49:[84, 1, 35], Operations: ['49-14=35'] Exploring Operation: 84*1=84, Resulting Numbers: [35, 84] Generated Node #3: [35, 84] from Operation: 84*1=84 Current State: 49:[35, 84], Operations: ['49-14=35', '84*1=84'] Exploring Operation: 84-35=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[49, 14, 84, 1], Operations: [] Exploring Operation: 14-1=13, Resulting Numbers: [49, 84, 13] Generated Node #0,0: 49:[49, 84, 13] Operation: 14-1=13 Exploring Operation: 84-14=70, Resulting Numbers: [49, 1, 70] Generated Node #0,1: 49:[49, 1, 70] Operation: 84-14=70 Exploring Operation: 84/14=6, Resulting Numbers: [49, 1, 6] Generated Node #0,2: 49:[49, 1, 6] Operation: 84/14=6 Exploring Operation: 84-49=35, Resulting Numbers: [14, 1, 35] Generated Node #0,3: 49:[14, 1, 35] Operation: 84-49=35 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[49, 1, 6], Operations: ['84/14=6'] Exploring Operation: 49*1=49, Resulting Numbers: [6, 49] Generated Node #0,2,0: 49:[6, 49] Operation: 49*1=49 Exploring Operation: 49/1=49, Resulting Numbers: [6, 49] Generated Node #0,2,1: 49:[6, 49] Operation: 49/1=49 Exploring Operation: 1*6=6, Resulting Numbers: [49, 6] Generated Node #0,2,2: 49:[49, 6] Operation: 1*6=6 Exploring Operation: 1+6=7, Resulting Numbers: [49, 7] Generated Node #0,2,3: 49:[49, 7] Operation: 1+6=7 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 49:[49, 7], Operations: ['84/14=6', '1+6=7'] Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,49 unequal: No Solution Exploring Operation: 49*7=343, Resulting Numbers: [343] 343,49 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,49 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 49:[6, 49], Operations: ['84/14=6', '49*1=49'] Exploring Operation: 6*49=294, Resulting Numbers: [294] 294,49 unequal: No Solution Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,49 unequal: No Solution Exploring Operation: 6+49=55, Resulting Numbers: [55] 55,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 49:[6, 49], Operations: ['84/14=6', '49/1=49'] Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,49 unequal: No Solution Exploring Operation: 6+49=55, Resulting Numbers: [55] 55,49 unequal: No Solution Exploring Operation: 6*49=294, Resulting Numbers: [294] 294,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 49:[49, 6], Operations: ['84/14=6', '1*6=6'] Exploring Operation: 49*6=294, Resulting Numbers: [294] 294,49 unequal: No Solution Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,49 unequal: No Solution Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,49 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: 49:[49, 1, 70], Operations: ['84-14=70'] Exploring Operation: 49*1=49, Resulting Numbers: [70, 49] Generated Node #0,1,0: 49:[70, 49] Operation: 49*1=49 Exploring Operation: 70-49=21, Resulting Numbers: [1, 21] Generated Node #0,1,1: 49:[1, 21] Operation: 70-49=21 Exploring Operation: 70-1=69, Resulting Numbers: [49, 69] Generated Node #0,1,2: 49:[49, 69] Operation: 70-1=69 Exploring Operation: 49/1=49, Resulting Numbers: [70, 49] Generated Node #0,1,3: 49:[70, 49] Operation: 49/1=49 Moving to Node #0,1,1 Current State: 49:[1, 21], Operations: ['84-14=70', '70-49=21'] Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,49 unequal: No Solution Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 1*21=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,49 unequal: No Solution Moving to Node #0,1,2 Current State: 49:[49, 69], Operations: ['84-14=70', '70-1=69'] Exploring Operation: 49+69=118, Resulting Numbers: [118] 118,49 unequal: No Solution Exploring Operation: 69-49=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 49*69=3381, Resulting Numbers: [3381] 3381,49 unequal: No Solution Moving to Node #0,1,3 Current State: 49:[70, 49], Operations: ['84-14=70', '49/1=49'] Exploring Operation: 70-49=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 70*49=3430, Resulting Numbers: [3430] 3430,49 unequal: No Solution Exploring Operation: 70+49=119, Resulting Numbers: [119] 119,49 unequal: No Solution Moving to Node #0,1,0 Current State: 49:[70, 49], Operations: ['84-14=70', '49*1=49'] Exploring Operation: 70-49=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 70*49=3430, Resulting Numbers: [3430] 3430,49 unequal: No Solution Exploring Operation: 70+49=119, Resulting Numbers: [119] 119,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 49:[14, 1, 35], Operations: ['84-49=35'] Exploring Operation: 35-14=21, Resulting Numbers: [1, 21] Generated Node #0,3,0: 49:[1, 21] Operation: 35-14=21 Exploring Operation: 14-1=13, Resulting Numbers: [35, 13] Generated Node #0,3,1: 49:[35, 13] Operation: 14-1=13 Exploring Operation: 14+35=49, Resulting Numbers: [1, 49] Generated Node #0,3,2: 49:[1, 49] Operation: 14+35=49 Exploring Operation: 1+35=36, Resulting Numbers: [14, 36] Generated Node #0,3,3: 49:[14, 36] Operation: 1+35=36 Moving to Node #0,3,2 Current State: 49:[1, 49], Operations: ['84-49=35', '14+35=49'] Exploring Operation: 1+49=50, Resulting Numbers: [50] 50,49 unequal: No Solution Exploring Operation: 1*49=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[49, 14, 84, 1], Operations: [] Exploring Operation: 84-49=35, Resulting Numbers: [14, 1, 35] Generated Node #0,3: 49:[14, 1, 35] Operation: 84-49=35 Moving to Node #0,3 Current State: 49:[14, 1, 35], Operations: ['84-49=35'] Exploring Operation: 14+35=49, Resulting Numbers: [1, 49] Generated Node #0,3,2: 49:[1, 49] Operation: 14+35=49 Moving to Node #0,3,2 Current State: 49:[1, 49], Operations: ['84-49=35', '14+35=49'] Exploring Operation: 1*49=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.958333
hs_4
mult_heuristic
[ 4, 3, 9, 56 ]
58
[ "4+3=7", "9+56=65", "65-7=58" ]
Current State: 58:[4, 3, 9, 56], Operations: [] Exploring Operation: 4+3=7, Resulting Numbers: [9, 56, 7] Generated Node #2: [9, 56, 7] from Operation: 4+3=7 Current State: 58:[9, 56, 7], Operations: ['4+3=7'] Exploring Operation: 9+56=65, Resulting Numbers: [7, 65] Generated Node #3: [7, 65] from Operation: 9+56=65 Current State: 58:[7, 65], Operations: ['4+3=7', '9+56=65'] Exploring Operation: 65-7=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[4, 3, 9, 56], Operations: [] Exploring Operation: 9-4=5, Resulting Numbers: [3, 56, 5] Generated Node #0,0: 58:[3, 56, 5] Operation: 9-4=5 Exploring Operation: 9/3=3, Resulting Numbers: [4, 56, 3] Generated Node #0,1: 58:[4, 56, 3] Operation: 9/3=3 Exploring Operation: 9-3=6, Resulting Numbers: [4, 56, 6] Generated Node #0,2: 58:[4, 56, 6] Operation: 9-3=6 Exploring Operation: 3*9=27, Resulting Numbers: [4, 56, 27] Generated Node #0,3: 58:[4, 56, 27] Operation: 3*9=27 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[4, 56, 3], Operations: ['9/3=3'] Exploring Operation: 4+56=60, Resulting Numbers: [3, 60] Generated Node #0,1,0: 58:[3, 60] Operation: 4+56=60 Exploring Operation: 4-3=1, Resulting Numbers: [56, 1] Generated Node #0,1,1: 58:[56, 1] Operation: 4-3=1 Exploring Operation: 56-4=52, Resulting Numbers: [3, 52] Generated Node #0,1,2: 58:[3, 52] Operation: 56-4=52 Exploring Operation: 56+3=59, Resulting Numbers: [4, 59] Generated Node #0,1,3: 58:[4, 59] Operation: 56+3=59 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 58:[3, 60], Operations: ['9/3=3', '4+56=60'] Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 3*60=180, Resulting Numbers: [180] 180,58 unequal: No Solution Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,58 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 58:[56, 1], Operations: ['9/3=3', '4-3=1'] Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 58:[4, 59], Operations: ['9/3=3', '56+3=59'] Exploring Operation: 4+59=63, Resulting Numbers: [63] 63,58 unequal: No Solution Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,58 unequal: No Solution Exploring Operation: 4*59=236, Resulting Numbers: [236] 236,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 58:[3, 52], Operations: ['9/3=3', '56-4=52'] Exploring Operation: 3*52=156, Resulting Numbers: [156] 156,58 unequal: No Solution Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,58 unequal: No Solution Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[3, 56, 5], Operations: ['9-4=5'] Exploring Operation: 5-3=2, Resulting Numbers: [56, 2] Generated Node #0,0,0: 58:[56, 2] Operation: 5-3=2 Exploring Operation: 56-3=53, Resulting Numbers: [5, 53] Generated Node #0,0,1: 58:[5, 53] Operation: 56-3=53 Exploring Operation: 3+56=59, Resulting Numbers: [5, 59] Generated Node #0,0,2: 58:[5, 59] Operation: 3+56=59 Exploring Operation: 56+5=61, Resulting Numbers: [3, 61] Generated Node #0,0,3: 58:[3, 61] Operation: 56+5=61 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[56, 2], Operations: ['9-4=5', '5-3=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,58 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,58 unequal: No Solution Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[4, 3, 9, 56], Operations: [] Exploring Operation: 9-4=5, Resulting Numbers: [3, 56, 5] Generated Node #0,0: 58:[3, 56, 5] Operation: 9-4=5 Moving to Node #0,0 Current State: 58:[3, 56, 5], Operations: ['9-4=5'] Exploring Operation: 5-3=2, Resulting Numbers: [56, 2] Generated Node #0,0,0: 58:[56, 2] Operation: 5-3=2 Moving to Node #0,0,0 Current State: 58:[56, 2], Operations: ['9-4=5', '5-3=2'] Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.971354
hs_4
mult_heuristic
[ 56, 63, 62, 64 ]
10
[ "63*64=4032", "4032/56=72", "72-62=10" ]
Current State: 10:[56, 63, 62, 64], Operations: [] Exploring Operation: 63*64=4032, Resulting Numbers: [56, 62, 4032] Generated Node #2: [56, 62, 4032] from Operation: 63*64=4032 Current State: 10:[56, 62, 4032], Operations: ['63*64=4032'] Exploring Operation: 4032/56=72, Resulting Numbers: [62, 72] Generated Node #3: [62, 72] from Operation: 4032/56=72 Current State: 10:[62, 72], Operations: ['63*64=4032', '4032/56=72'] Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[56, 63, 62, 64], Operations: [] Exploring Operation: 64-63=1, Resulting Numbers: [56, 62, 1] Generated Node #0,0: 10:[56, 62, 1] Operation: 64-63=1 Moving to Node #0,0 Current State: 10:[56, 62, 1], Operations: ['64-63=1'] Exploring Operation: 62-56=6, Resulting Numbers: [1, 6] Generated Node #0,0,0: 10:[1, 6] Operation: 62-56=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[1, 6], Operations: ['64-63=1', '62-56=6'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 28, 13, 25, 52 ]
87
[ "28*52=1456", "1456/13=112", "112-25=87" ]
Current State: 87:[28, 13, 25, 52], Operations: [] Exploring Operation: 28*52=1456, Resulting Numbers: [13, 25, 1456] Generated Node #2: [13, 25, 1456] from Operation: 28*52=1456 Current State: 87:[13, 25, 1456], Operations: ['28*52=1456'] Exploring Operation: 1456/13=112, Resulting Numbers: [25, 112] Generated Node #3: [25, 112] from Operation: 1456/13=112 Current State: 87:[25, 112], Operations: ['28*52=1456', '1456/13=112'] Exploring Operation: 112-25=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[28, 13, 25, 52], Operations: [] Exploring Operation: 52/13=4, Resulting Numbers: [28, 25, 4] Generated Node #0,0: 87:[28, 25, 4] Operation: 52/13=4 Exploring Operation: 52-13=39, Resulting Numbers: [28, 25, 39] Generated Node #0,1: 87:[28, 25, 39] Operation: 52-13=39 Exploring Operation: 52-25=27, Resulting Numbers: [28, 13, 27] Generated Node #0,2: 87:[28, 13, 27] Operation: 52-25=27 Moving to Node #0,0 Current State: 87:[28, 25, 4], Operations: ['52/13=4'] Exploring Operation: 28+4=32, Resulting Numbers: [25, 32] Generated Node #0,0,0: 87:[25, 32] Operation: 28+4=32 Exploring Operation: 28-25=3, Resulting Numbers: [4, 3] Generated Node #0,0,1: 87:[4, 3] Operation: 28-25=3 Exploring Operation: 25+4=29, Resulting Numbers: [28, 29] Generated Node #0,0,2: 87:[28, 29] Operation: 25+4=29 Moving to Node #0,2 Current State: 87:[28, 13, 27], Operations: ['52-25=27'] Exploring Operation: 27-13=14, Resulting Numbers: [28, 14] Generated Node #0,2,0: 87:[28, 14] Operation: 27-13=14 Exploring Operation: 13+27=40, Resulting Numbers: [28, 40] Generated Node #0,2,1: 87:[28, 40] Operation: 13+27=40 Exploring Operation: 28-27=1, Resulting Numbers: [13, 1] Generated Node #0,2,2: 87:[13, 1] Operation: 28-27=1 Moving to Node #0,1 Current State: 87:[28, 25, 39], Operations: ['52-13=39'] Exploring Operation: 39-25=14, Resulting Numbers: [28, 14] Generated Node #0,1,0: 87:[28, 14] Operation: 39-25=14 Exploring Operation: 28-25=3, Resulting Numbers: [39, 3] Generated Node #0,1,1: 87:[39, 3] Operation: 28-25=3 Exploring Operation: 39-28=11, Resulting Numbers: [25, 11] Generated Node #0,1,2: 87:[25, 11] Operation: 39-28=11 Moving to Node #0,0,1 Current State: 87:[4, 3], Operations: ['52/13=4', '28-25=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,87 unequal: No Solution Moving to Node #0,0,2 Current State: 87:[28, 29], Operations: ['52/13=4', '25+4=29'] Exploring Operation: 28*29=812, Resulting Numbers: [812] 812,87 unequal: No Solution Exploring Operation: 28+29=57, Resulting Numbers: [57] 57,87 unequal: No Solution Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[25, 32], Operations: ['52/13=4', '28+4=32'] Exploring Operation: 25*32=800, Resulting Numbers: [800] 800,87 unequal: No Solution Exploring Operation: 25+32=57, Resulting Numbers: [57] 57,87 unequal: No Solution Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[39, 3], Operations: ['52-13=39', '28-25=3'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,87 unequal: No Solution Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,87 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,87 unequal: No Solution Moving to Node #0,2,2 Current State: 87:[13, 1], Operations: ['52-25=27', '28-27=1'] Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,87 unequal: No Solution Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,87 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[28, 14], Operations: ['52-13=39', '39-25=14'] Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,87 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,87 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[25, 11], Operations: ['52-13=39', '39-28=11'] Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 25*11=275, Resulting Numbers: [275] 275,87 unequal: No Solution Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,87 unequal: No Solution Moving to Node #0,2,1 Current State: 87:[28, 40], Operations: ['52-25=27', '13+27=40'] Exploring Operation: 28+40=68, Resulting Numbers: [68] 68,87 unequal: No Solution Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 28*40=1120, Resulting Numbers: [1120] 1120,87 unequal: No Solution Moving to Node #0,2,0 Current State: 87:[28, 14], Operations: ['52-25=27', '27-13=14'] Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,87 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,87 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,87 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 38, 26, 5, 29 ]
53
[ "29-26=3", "5*3=15", "38+15=53" ]
Current State: 53:[38, 26, 5, 29], Operations: [] Exploring Operation: 29-26=3, Resulting Numbers: [38, 5, 3] Generated Node #2: [38, 5, 3] from Operation: 29-26=3 Current State: 53:[38, 5, 3], Operations: ['29-26=3'] Exploring Operation: 5*3=15, Resulting Numbers: [38, 15] Generated Node #3: [38, 15] from Operation: 5*3=15 Current State: 53:[38, 15], Operations: ['29-26=3', '5*3=15'] Exploring Operation: 38+15=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[38, 26, 5, 29], Operations: [] Exploring Operation: 26+29=55, Resulting Numbers: [38, 5, 55] Generated Node #0,0: 53:[38, 5, 55] Operation: 26+29=55 Exploring Operation: 26+5=31, Resulting Numbers: [38, 29, 31] Generated Node #0,1: 53:[38, 29, 31] Operation: 26+5=31 Exploring Operation: 5+29=34, Resulting Numbers: [38, 26, 34] Generated Node #0,2: 53:[38, 26, 34] Operation: 5+29=34 Exploring Operation: 38+5=43, Resulting Numbers: [26, 29, 43] Generated Node #0,3: 53:[26, 29, 43] Operation: 38+5=43 Exploring Operation: 38-5=33, Resulting Numbers: [26, 29, 33] Generated Node #0,4: 53:[26, 29, 33] Operation: 38-5=33 Moving to Node #0,1 Current State: 53:[38, 29, 31], Operations: ['26+5=31'] Exploring Operation: 38+29=67, Resulting Numbers: [31, 67] Generated Node #0,1,0: 53:[31, 67] Operation: 38+29=67 Exploring Operation: 29+31=60, Resulting Numbers: [38, 60] Generated Node #0,1,1: 53:[38, 60] Operation: 29+31=60 Exploring Operation: 38+31=69, Resulting Numbers: [29, 69] Generated Node #0,1,2: 53:[29, 69] Operation: 38+31=69 Exploring Operation: 31-29=2, Resulting Numbers: [38, 2] Generated Node #0,1,3: 53:[38, 2] Operation: 31-29=2 Exploring Operation: 38-29=9, Resulting Numbers: [31, 9] Generated Node #0,1,4: 53:[31, 9] Operation: 38-29=9 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 53:[38, 60], Operations: ['26+5=31', '29+31=60'] Exploring Operation: 38+60=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 60-38=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 38*60=2280, Resulting Numbers: [2280] 2280,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[31, 67], Operations: ['26+5=31', '38+29=67'] Exploring Operation: 31*67=2077, Resulting Numbers: [2077] 2077,53 unequal: No Solution Exploring Operation: 31+67=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 67-31=36, Resulting Numbers: [36] 36,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 53:[29, 69], Operations: ['26+5=31', '38+31=69'] Exploring Operation: 29*69=2001, Resulting Numbers: [2001] 2001,53 unequal: No Solution Exploring Operation: 29+69=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 69-29=40, Resulting Numbers: [40] 40,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 53:[38, 2], Operations: ['26+5=31', '31-29=2'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,53 unequal: No Solution Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,53 unequal: No Solution Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 53:[31, 9], Operations: ['26+5=31', '38-29=9'] Exploring Operation: 31+9=40, Resulting Numbers: [40] 40,53 unequal: No Solution Exploring Operation: 31*9=279, Resulting Numbers: [279] 279,53 unequal: No Solution Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,53 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: 53:[26, 29, 43], Operations: ['38+5=43'] Exploring Operation: 26+43=69, Resulting Numbers: [29, 69] Generated Node #0,3,0: 53:[29, 69] Operation: 26+43=69 Exploring Operation: 29-26=3, Resulting Numbers: [43, 3] Generated Node #0,3,1: 53:[43, 3] Operation: 29-26=3 Exploring Operation: 29+43=72, Resulting Numbers: [26, 72] Generated Node #0,3,2: 53:[26, 72] Operation: 29+43=72 Exploring Operation: 43-26=17, Resulting Numbers: [29, 17] Generated Node #0,3,3: 53:[29, 17] Operation: 43-26=17 Exploring Operation: 26+29=55, Resulting Numbers: [43, 55] Generated Node #0,3,4: 53:[43, 55] Operation: 26+29=55 Moving to Node #0,2 Current State: 53:[38, 26, 34], Operations: ['5+29=34'] Exploring Operation: 26+34=60, Resulting Numbers: [38, 60] Generated Node #0,2,0: 53:[38, 60] Operation: 26+34=60 Exploring Operation: 38+26=64, Resulting Numbers: [34, 64] Generated Node #0,2,1: 53:[34, 64] Operation: 38+26=64 Exploring Operation: 38+34=72, Resulting Numbers: [26, 72] Generated Node #0,2,2: 53:[26, 72] Operation: 38+34=72 Exploring Operation: 34-26=8, Resulting Numbers: [38, 8] Generated Node #0,2,3: 53:[38, 8] Operation: 34-26=8 Exploring Operation: 38-26=12, Resulting Numbers: [34, 12] Generated Node #0,2,4: 53:[34, 12] Operation: 38-26=12 Moving to Node #0,0 Current State: 53:[38, 5, 55], Operations: ['26+29=55'] Exploring Operation: 38-5=33, Resulting Numbers: [55, 33] Generated Node #0,0,0: 53:[55, 33] Operation: 38-5=33 Exploring Operation: 55-5=50, Resulting Numbers: [38, 50] Generated Node #0,0,1: 53:[38, 50] Operation: 55-5=50 Exploring Operation: 55/5=11, Resulting Numbers: [38, 11] Generated Node #0,0,2: 53:[38, 11] Operation: 55/5=11 Exploring Operation: 5+55=60, Resulting Numbers: [38, 60] Generated Node #0,0,3: 53:[38, 60] Operation: 5+55=60 Exploring Operation: 38+5=43, Resulting Numbers: [55, 43] Generated Node #0,0,4: 53:[55, 43] Operation: 38+5=43 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 53:[55, 43], Operations: ['26+29=55', '38+5=43'] Exploring Operation: 55*43=2365, Resulting Numbers: [2365] 2365,53 unequal: No Solution Exploring Operation: 55+43=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[38, 50], Operations: ['26+29=55', '55-5=50'] Exploring Operation: 38+50=88, Resulting Numbers: [88] 88,53 unequal: No Solution Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,53 unequal: No Solution Exploring Operation: 38*50=1900, Resulting Numbers: [1900] 1900,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[55, 33], Operations: ['26+29=55', '38-5=33'] Exploring Operation: 55-33=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 55*33=1815, Resulting Numbers: [1815] 1815,53 unequal: No Solution Exploring Operation: 55+33=88, Resulting Numbers: [88] 88,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 53:[38, 60], Operations: ['26+29=55', '5+55=60'] Exploring Operation: 38*60=2280, Resulting Numbers: [2280] 2280,53 unequal: No Solution Exploring Operation: 60-38=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 38+60=98, Resulting Numbers: [98] 98,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 53:[38, 11], Operations: ['26+29=55', '55/5=11'] Exploring Operation: 38-11=27, Resulting Numbers: [27] 27,53 unequal: No Solution Exploring Operation: 38+11=49, Resulting Numbers: [49] 49,53 unequal: No Solution Exploring Operation: 38*11=418, Resulting Numbers: [418] 418,53 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: 53:[26, 29, 33], Operations: ['38-5=33'] Exploring Operation: 29-26=3, Resulting Numbers: [33, 3] Generated Node #0,4,0: 53:[33, 3] Operation: 29-26=3 Exploring Operation: 26+33=59, Resulting Numbers: [29, 59] Generated Node #0,4,1: 53:[29, 59] Operation: 26+33=59 Exploring Operation: 33-26=7, Resulting Numbers: [29, 7] Generated Node #0,4,2: 53:[29, 7] Operation: 33-26=7 Exploring Operation: 26+29=55, Resulting Numbers: [33, 55] Generated Node #0,4,3: 53:[33, 55] Operation: 26+29=55 Exploring Operation: 29+33=62, Resulting Numbers: [26, 62] Generated Node #0,4,4: 53:[26, 62] Operation: 29+33=62 Moving to Node #0,3,4 Current State: 53:[43, 55], Operations: ['38+5=43', '26+29=55'] Exploring Operation: 43+55=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 43*55=2365, Resulting Numbers: [2365] 2365,53 unequal: No Solution Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,53 unequal: No Solution Moving to Node #0,2,0 Current State: 53:[38, 60], Operations: ['5+29=34', '26+34=60'] Exploring Operation: 38+60=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 60-38=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 38*60=2280, Resulting Numbers: [2280] 2280,53 unequal: No Solution Moving to Node #0,4,3 Current State: 53:[33, 55], Operations: ['38-5=33', '26+29=55'] Exploring Operation: 55-33=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 33*55=1815, Resulting Numbers: [1815] 1815,53 unequal: No Solution Exploring Operation: 33+55=88, Resulting Numbers: [88] 88,53 unequal: No Solution Moving to Node #0,2,1 Current State: 53:[34, 64], Operations: ['5+29=34', '38+26=64'] Exploring Operation: 34+64=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 64-34=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 34*64=2176, Resulting Numbers: [2176] 2176,53 unequal: No Solution Moving to Node #0,4,1 Current State: 53:[29, 59], Operations: ['38-5=33', '26+33=59'] Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 29*59=1711, Resulting Numbers: [1711] 1711,53 unequal: No Solution Exploring Operation: 29+59=88, Resulting Numbers: [88] 88,53 unequal: No Solution Moving to Node #0,4,4 Current State: 53:[26, 62], Operations: ['38-5=33', '29+33=62'] Exploring Operation: 62-26=36, Resulting Numbers: [36] 36,53 unequal: No Solution Exploring Operation: 26+62=88, Resulting Numbers: [88] 88,53 unequal: No Solution Exploring Operation: 26*62=1612, Resulting Numbers: [1612] 1612,53 unequal: No Solution Moving to Node #0,3,0 Current State: 53:[29, 69], Operations: ['38+5=43', '26+43=69'] Exploring Operation: 29+69=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 69-29=40, Resulting Numbers: [40] 40,53 unequal: No Solution Exploring Operation: 29*69=2001, Resulting Numbers: [2001] 2001,53 unequal: No Solution Moving to Node #0,3,2 Current State: 53:[26, 72], Operations: ['38+5=43', '29+43=72'] Exploring Operation: 26*72=1872, Resulting Numbers: [1872] 1872,53 unequal: No Solution Exploring Operation: 26+72=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 72-26=46, Resulting Numbers: [46] 46,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[26, 72], Operations: ['5+29=34', '38+34=72'] Exploring Operation: 26*72=1872, Resulting Numbers: [1872] 1872,53 unequal: No Solution Exploring Operation: 26+72=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 72-26=46, Resulting Numbers: [46] 46,53 unequal: No Solution Moving to Node #0,2,4 Current State: 53:[34, 12], Operations: ['5+29=34', '38-26=12'] Exploring Operation: 34+12=46, Resulting Numbers: [46] 46,53 unequal: No Solution Exploring Operation: 34*12=408, Resulting Numbers: [408] 408,53 unequal: No Solution Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,53 unequal: No Solution Moving to Node #0,3,3 Current State: 53:[29, 17], Operations: ['38+5=43', '43-26=17'] Exploring Operation: 29+17=46, Resulting Numbers: [46] 46,53 unequal: No Solution Exploring Operation: 29*17=493, Resulting Numbers: [493] 493,53 unequal: No Solution Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,53 unequal: No Solution Moving to Node #0,3,1 Current State: 53:[43, 3], Operations: ['38+5=43', '29-26=3'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,53 unequal: No Solution Exploring Operation: 43*3=129, Resulting Numbers: [129] 129,53 unequal: No Solution Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,53 unequal: No Solution Moving to Node #0,2,3 Current State: 53:[38, 8], Operations: ['5+29=34', '34-26=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 38*8=304, Resulting Numbers: [304] 304,53 unequal: No Solution Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,53 unequal: No Solution Moving to Node #0,4,0 Current State: 53:[33, 3], Operations: ['38-5=33', '29-26=3'] Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,53 unequal: No Solution Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,53 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,53 unequal: No Solution Moving to Node #0,4,2 Current State: 53:[29, 7], Operations: ['38-5=33', '33-26=7'] Exploring Operation: 29*7=203, Resulting Numbers: [203] 203,53 unequal: No Solution Exploring Operation: 29+7=36, Resulting Numbers: [36] 36,53 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,53 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 25, 15, 19, 49 ]
40
[ "25-15=10", "49-19=30", "10+30=40" ]
Current State: 40:[25, 15, 19, 49], Operations: [] Exploring Operation: 25-15=10, Resulting Numbers: [19, 49, 10] Generated Node #2: [19, 49, 10] from Operation: 25-15=10 Current State: 40:[19, 49, 10], Operations: ['25-15=10'] Exploring Operation: 49-19=30, Resulting Numbers: [10, 30] Generated Node #3: [10, 30] from Operation: 49-19=30 Current State: 40:[10, 30], Operations: ['25-15=10', '49-19=30'] Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[25, 15, 19, 49], Operations: [] Exploring Operation: 49-15=34, Resulting Numbers: [25, 19, 34] Generated Node #0,0: 40:[25, 19, 34] Operation: 49-15=34 Exploring Operation: 25+15=40, Resulting Numbers: [19, 49, 40] Generated Node #0,1: 40:[19, 49, 40] Operation: 25+15=40 Exploring Operation: 19-15=4, Resulting Numbers: [25, 49, 4] Generated Node #0,2: 40:[25, 49, 4] Operation: 19-15=4 Exploring Operation: 49-25=24, Resulting Numbers: [15, 19, 24] Generated Node #0,3: 40:[15, 19, 24] Operation: 49-25=24 Exploring Operation: 25-15=10, Resulting Numbers: [19, 49, 10] Generated Node #0,4: 40:[19, 49, 10] Operation: 25-15=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[19, 49, 40], Operations: ['25+15=40'] Exploring Operation: 49-19=30, Resulting Numbers: [40, 30] Generated Node #0,1,0: 40:[40, 30] Operation: 49-19=30 Exploring Operation: 49-40=9, Resulting Numbers: [19, 9] Generated Node #0,1,1: 40:[19, 9] Operation: 49-40=9 Exploring Operation: 19+40=59, Resulting Numbers: [49, 59] Generated Node #0,1,2: 40:[49, 59] Operation: 19+40=59 Exploring Operation: 19+49=68, Resulting Numbers: [40, 68] Generated Node #0,1,3: 40:[40, 68] Operation: 19+49=68 Exploring Operation: 40-19=21, Resulting Numbers: [49, 21] Generated Node #0,1,4: 40:[49, 21] Operation: 40-19=21 Moving to Node #0,1,1 Current State: 40:[19, 9], Operations: ['25+15=40', '49-40=9'] Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,40 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,40 unequal: No Solution Moving to Node #0,1,4 Current State: 40:[49, 21], Operations: ['25+15=40', '40-19=21'] Exploring Operation: 49+21=70, Resulting Numbers: [70] 70,40 unequal: No Solution Exploring Operation: 49*21=1029, Resulting Numbers: [1029] 1029,40 unequal: No Solution Exploring Operation: 49-21=28, Resulting Numbers: [28] 28,40 unequal: No Solution Moving to Node #0,1,0 Current State: 40:[40, 30], Operations: ['25+15=40', '49-19=30'] Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,40 unequal: No Solution Exploring Operation: 40*30=1200, Resulting Numbers: [1200] 1200,40 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,40 unequal: No Solution Moving to Node #0,1,2 Current State: 40:[49, 59], Operations: ['25+15=40', '19+40=59'] Exploring Operation: 49+59=108, Resulting Numbers: [108] 108,40 unequal: No Solution Exploring Operation: 59-49=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 49*59=2891, Resulting Numbers: [2891] 2891,40 unequal: No Solution Moving to Node #0,1,3 Current State: 40:[40, 68], Operations: ['25+15=40', '19+49=68'] Exploring Operation: 40*68=2720, Resulting Numbers: [2720] 2720,40 unequal: No Solution Exploring Operation: 40+68=108, Resulting Numbers: [108] 108,40 unequal: No Solution Exploring Operation: 68-40=28, Resulting Numbers: [28] 28,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 40:[15, 19, 24], Operations: ['49-25=24'] Exploring Operation: 19+24=43, Resulting Numbers: [15, 43] Generated Node #0,3,0: 40:[15, 43] Operation: 19+24=43 Exploring Operation: 24-19=5, Resulting Numbers: [15, 5] Generated Node #0,3,1: 40:[15, 5] Operation: 24-19=5 Exploring Operation: 15+24=39, Resulting Numbers: [19, 39] Generated Node #0,3,2: 40:[19, 39] Operation: 15+24=39 Exploring Operation: 19-15=4, Resulting Numbers: [24, 4] Generated Node #0,3,3: 40:[24, 4] Operation: 19-15=4 Exploring Operation: 24-15=9, Resulting Numbers: [19, 9] Generated Node #0,3,4: 40:[19, 9] Operation: 24-15=9 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 40:[19, 39], Operations: ['49-25=24', '15+24=39'] Exploring Operation: 19+39=58, Resulting Numbers: [58] 58,40 unequal: No Solution Exploring Operation: 19*39=741, Resulting Numbers: [741] 741,40 unequal: No Solution Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 40:[19, 9], Operations: ['49-25=24', '24-15=9'] Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,40 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 40:[24, 4], Operations: ['49-25=24', '19-15=4'] Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,40 unequal: No Solution Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,40 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 40:[15, 5], Operations: ['49-25=24', '24-19=5'] Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,40 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,40 unequal: No Solution Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 40:[15, 43], Operations: ['49-25=24', '19+24=43'] Exploring Operation: 43-15=28, Resulting Numbers: [28] 28,40 unequal: No Solution Exploring Operation: 15*43=645, Resulting Numbers: [645] 645,40 unequal: No Solution Exploring Operation: 15+43=58, Resulting Numbers: [58] 58,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 40:[19, 49, 10], Operations: ['25-15=10'] Exploring Operation: 49+10=59, Resulting Numbers: [19, 59] Generated Node #0,4,0: 40:[19, 59] Operation: 49+10=59 Exploring Operation: 19-10=9, Resulting Numbers: [49, 9] Generated Node #0,4,1: 40:[49, 9] Operation: 19-10=9 Exploring Operation: 49-19=30, Resulting Numbers: [10, 30] Generated Node #0,4,2: 40:[10, 30] Operation: 49-19=30 Exploring Operation: 19+10=29, Resulting Numbers: [49, 29] Generated Node #0,4,3: 40:[49, 29] Operation: 19+10=29 Exploring Operation: 49-10=39, Resulting Numbers: [19, 39] Generated Node #0,4,4: 40:[19, 39] Operation: 49-10=39 Moving to Node #0,4,4 Current State: 40:[19, 39], Operations: ['25-15=10', '49-10=39'] Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,40 unequal: No Solution Exploring Operation: 19*39=741, Resulting Numbers: [741] 741,40 unequal: No Solution Exploring Operation: 19+39=58, Resulting Numbers: [58] 58,40 unequal: No Solution Moving to Node #0,4,2 Current State: 40:[10, 30], Operations: ['25-15=10', '49-19=30'] Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,40 unequal: No Solution Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[25, 15, 19, 49], Operations: [] Exploring Operation: 25-15=10, Resulting Numbers: [19, 49, 10] Generated Node #0,4: 40:[19, 49, 10] Operation: 25-15=10 Moving to Node #0,4 Current State: 40:[19, 49, 10], Operations: ['25-15=10'] Exploring Operation: 49-19=30, Resulting Numbers: [10, 30] Generated Node #0,4,2: 40:[10, 30] Operation: 49-19=30 Moving to Node #0,4,2 Current State: 40:[10, 30], Operations: ['25-15=10', '49-19=30'] Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.947049
hs_5
mult_heuristic
[ 44, 23, 78, 92 ]
98
[ "44*92=4048", "4048/23=176", "176-78=98" ]
Current State: 98:[44, 23, 78, 92], Operations: [] Exploring Operation: 44*92=4048, Resulting Numbers: [23, 78, 4048] Generated Node #2: [23, 78, 4048] from Operation: 44*92=4048 Current State: 98:[23, 78, 4048], Operations: ['44*92=4048'] Exploring Operation: 4048/23=176, Resulting Numbers: [78, 176] Generated Node #3: [78, 176] from Operation: 4048/23=176 Current State: 98:[78, 176], Operations: ['44*92=4048', '4048/23=176'] Exploring Operation: 176-78=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[44, 23, 78, 92], Operations: [] Exploring Operation: 92-78=14, Resulting Numbers: [44, 23, 14] Generated Node #0,0: 98:[44, 23, 14] Operation: 92-78=14 Exploring Operation: 23+78=101, Resulting Numbers: [44, 92, 101] Generated Node #0,1: 98:[44, 92, 101] Operation: 23+78=101 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[44, 23, 14], Operations: ['92-78=14'] Exploring Operation: 44-23=21, Resulting Numbers: [14, 21] Generated Node #0,0,0: 98:[14, 21] Operation: 44-23=21 Exploring Operation: 23-14=9, Resulting Numbers: [44, 9] Generated Node #0,0,1: 98:[44, 9] Operation: 23-14=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[14, 21], Operations: ['92-78=14', '44-23=21'] Exploring Operation: 14+21=35, Resulting Numbers: [35] 35,98 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,98 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 #0,0,1 Current State: 98:[44, 9], Operations: ['92-78=14', '23-14=9'] Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,98 unequal: No Solution Exploring Operation: 44+9=53, Resulting Numbers: [53] 53,98 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 #0,1 Current State: 98:[44, 92, 101], Operations: ['23+78=101'] Exploring Operation: 92-44=48, Resulting Numbers: [101, 48] Generated Node #0,1,0: 98:[101, 48] Operation: 92-44=48 Exploring Operation: 101-92=9, Resulting Numbers: [44, 9] Generated Node #0,1,1: 98:[44, 9] Operation: 101-92=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 98:[101, 48], Operations: ['23+78=101', '92-44=48'] Exploring Operation: 101+48=149, Resulting Numbers: [149] 149,98 unequal: No Solution Exploring Operation: 101-48=53, Resulting Numbers: [53] 53,98 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:[44, 9], Operations: ['23+78=101', '101-92=9'] Exploring Operation: 44+9=53, Resulting Numbers: [53] 53,98 unequal: No Solution Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,98 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_2
mult_heuristic
[ 2, 67, 90, 89 ]
46
[ "89-67=22", "2*22=44", "90-44=46" ]
Current State: 46:[2, 67, 90, 89], Operations: [] Exploring Operation: 89-67=22, Resulting Numbers: [2, 90, 22] Generated Node #2: [2, 90, 22] from Operation: 89-67=22 Current State: 46:[2, 90, 22], Operations: ['89-67=22'] Exploring Operation: 2*22=44, Resulting Numbers: [90, 44] Generated Node #3: [90, 44] from Operation: 2*22=44 Current State: 46:[90, 44], Operations: ['89-67=22', '2*22=44'] Exploring Operation: 90-44=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[2, 67, 90, 89], Operations: [] Exploring Operation: 90-67=23, Resulting Numbers: [2, 89, 23] Generated Node #0,0: 46:[2, 89, 23] Operation: 90-67=23 Exploring Operation: 90-89=1, Resulting Numbers: [2, 67, 1] Generated Node #0,1: 46:[2, 67, 1] Operation: 90-89=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[2, 67, 1], Operations: ['90-89=1'] Exploring Operation: 67-1=66, Resulting Numbers: [2, 66] Generated Node #0,1,0: 46:[2, 66] Operation: 67-1=66 Exploring Operation: 67-2=65, Resulting Numbers: [1, 65] Generated Node #0,1,1: 46:[1, 65] Operation: 67-2=65 Moving to Node #0,1,0 Current State: 46:[2, 66], Operations: ['90-89=1', '67-1=66'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,46 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,46 unequal: No Solution Moving to Node #0,1,1 Current State: 46:[1, 65], Operations: ['90-89=1', '67-2=65'] Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,46 unequal: No Solution Exploring Operation: 1*65=65, Resulting Numbers: [65] 65,46 unequal: No Solution No 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: 46:[2, 89, 23], Operations: ['90-67=23'] Exploring Operation: 89-23=66, Resulting Numbers: [2, 66] Generated Node #0,0,0: 46:[2, 66] Operation: 89-23=66 Exploring Operation: 89-2=87, Resulting Numbers: [23, 87] Generated Node #0,0,1: 46:[23, 87] Operation: 89-2=87 Moving to Node #0,0,0 Current State: 46:[2, 66], Operations: ['90-67=23', '89-23=66'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[23, 87], Operations: ['90-67=23', '89-2=87'] Exploring Operation: 87-23=64, Resulting Numbers: [64] 64,46 unequal: No Solution Exploring Operation: 23+87=110, Resulting Numbers: [110] 110,46 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
[ 13, 4, 4, 44 ]
20
[ "13-4=9", "44/4=11", "9+11=20" ]
Current State: 20:[13, 4, 4, 44], Operations: [] Exploring Operation: 13-4=9, Resulting Numbers: [44, 9] Generated Node #2: [44, 9] from Operation: 13-4=9 Current State: 20:[44, 9], Operations: ['13-4=9'] Exploring Operation: 44/4=11, Resulting Numbers: [9, 11] Generated Node #3: [9, 11] from Operation: 44/4=11 Current State: 20:[9, 11], Operations: ['13-4=9', '44/4=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[13, 4, 4, 44], Operations: [] Exploring Operation: 44/4=11, Resulting Numbers: [13, 4, 11] Generated Node #0,0: 20:[13, 4, 11] Operation: 44/4=11 Moving to Node #0,0 Current State: 20:[13, 4, 11], Operations: ['44/4=11'] Exploring Operation: 13-11=2, Resulting Numbers: [4, 2] Generated Node #0,0,0: 20:[4, 2] Operation: 13-11=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[4, 2], Operations: ['44/4=11', '13-11=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,20 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
[ 17, 32, 97, 53 ]
47
[ "17*97=1649", "32*53=1696", "1696-1649=47" ]
Current State: 47:[17, 32, 97, 53], Operations: [] Exploring Operation: 17*97=1649, Resulting Numbers: [32, 53, 1649] Generated Node #2: [32, 53, 1649] from Operation: 17*97=1649 Current State: 47:[32, 53, 1649], Operations: ['17*97=1649'] Exploring Operation: 32*53=1696, Resulting Numbers: [1649, 1696] Generated Node #3: [1649, 1696] from Operation: 32*53=1696 Current State: 47:[1649, 1696], Operations: ['17*97=1649', '32*53=1696'] Exploring Operation: 1696-1649=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[17, 32, 97, 53], Operations: [] Exploring Operation: 97-17=80, Resulting Numbers: [32, 53, 80] Generated Node #0,0: 47:[32, 53, 80] Operation: 97-17=80 Exploring Operation: 17+32=49, Resulting Numbers: [97, 53, 49] Generated Node #0,1: 47:[97, 53, 49] Operation: 17+32=49 Exploring Operation: 97-32=65, Resulting Numbers: [17, 53, 65] Generated Node #0,2: 47:[17, 53, 65] Operation: 97-32=65 Exploring Operation: 97-53=44, Resulting Numbers: [17, 32, 44] Generated Node #0,3: 47:[17, 32, 44] Operation: 97-53=44 Moving to Node #0,3 Current State: 47:[17, 32, 44], Operations: ['97-53=44'] Exploring Operation: 44-17=27, Resulting Numbers: [32, 27] Generated Node #0,3,0: 47:[32, 27] Operation: 44-17=27 Exploring Operation: 17+32=49, Resulting Numbers: [44, 49] Generated Node #0,3,1: 47:[44, 49] Operation: 17+32=49 Exploring Operation: 17+44=61, Resulting Numbers: [32, 61] Generated Node #0,3,2: 47:[32, 61] Operation: 17+44=61 Exploring Operation: 32-17=15, Resulting Numbers: [44, 15] Generated Node #0,3,3: 47:[44, 15] Operation: 32-17=15 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 47:[44, 49], Operations: ['97-53=44', '17+32=49'] Exploring Operation: 44+49=93, Resulting Numbers: [93] 93,47 unequal: No Solution Exploring Operation: 44*49=2156, Resulting Numbers: [2156] 2156,47 unequal: No Solution Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 47:[32, 61], Operations: ['97-53=44', '17+44=61'] Exploring Operation: 32+61=93, Resulting Numbers: [93] 93,47 unequal: No Solution Exploring Operation: 61-32=29, Resulting Numbers: [29] 29,47 unequal: No Solution Exploring Operation: 32*61=1952, Resulting Numbers: [1952] 1952,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 47:[32, 27], Operations: ['97-53=44', '44-17=27'] Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,47 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 47:[44, 15], Operations: ['97-53=44', '32-17=15'] Exploring Operation: 44-15=29, Resulting Numbers: [29] 29,47 unequal: No Solution Exploring Operation: 44+15=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 44*15=660, Resulting Numbers: [660] 660,47 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: 47:[17, 53, 65], Operations: ['97-32=65'] Exploring Operation: 53-17=36, Resulting Numbers: [65, 36] Generated Node #0,2,0: 47:[65, 36] Operation: 53-17=36 Exploring Operation: 17+65=82, Resulting Numbers: [53, 82] Generated Node #0,2,1: 47:[53, 82] Operation: 17+65=82 Exploring Operation: 65-17=48, Resulting Numbers: [53, 48] Generated Node #0,2,2: 47:[53, 48] Operation: 65-17=48 Exploring Operation: 17+53=70, Resulting Numbers: [65, 70] Generated Node #0,2,3: 47:[65, 70] Operation: 17+53=70 Moving to Node #0,0 Current State: 47:[32, 53, 80], Operations: ['97-17=80'] Exploring Operation: 80-53=27, Resulting Numbers: [32, 27] Generated Node #0,0,0: 47:[32, 27] Operation: 80-53=27 Exploring Operation: 80-32=48, Resulting Numbers: [53, 48] Generated Node #0,0,1: 47:[53, 48] Operation: 80-32=48 Exploring Operation: 53-32=21, Resulting Numbers: [80, 21] Generated Node #0,0,2: 47:[80, 21] Operation: 53-32=21 Exploring Operation: 32+53=85, Resulting Numbers: [80, 85] Generated Node #0,0,3: 47:[80, 85] Operation: 32+53=85 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[53, 48], Operations: ['97-17=80', '80-32=48'] Exploring Operation: 53+48=101, Resulting Numbers: [101] 101,47 unequal: No Solution Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 53*48=2544, Resulting Numbers: [2544] 2544,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[32, 27], Operations: ['97-17=80', '80-53=27'] Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[80, 21], Operations: ['97-17=80', '53-32=21'] Exploring Operation: 80+21=101, Resulting Numbers: [101] 101,47 unequal: No Solution Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 80*21=1680, Resulting Numbers: [1680] 1680,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 47:[80, 85], Operations: ['97-17=80', '32+53=85'] Exploring Operation: 85-80=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 80+85=165, Resulting Numbers: [165] 165,47 unequal: No Solution Exploring Operation: 80*85=6800, Resulting Numbers: [6800] 6800,47 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: 47:[97, 53, 49], Operations: ['17+32=49'] Exploring Operation: 97-53=44, Resulting Numbers: [49, 44] Generated Node #0,1,0: 47:[49, 44] Operation: 97-53=44 Exploring Operation: 53-49=4, Resulting Numbers: [97, 4] Generated Node #0,1,1: 47:[97, 4] Operation: 53-49=4 Exploring Operation: 97+53=150, Resulting Numbers: [49, 150] Generated Node #0,1,2: 47:[49, 150] Operation: 97+53=150 Exploring Operation: 97-49=48, Resulting Numbers: [53, 48] Generated Node #0,1,3: 47:[53, 48] Operation: 97-49=48 Moving to Node #0,1,0 Current State: 47:[49, 44], Operations: ['17+32=49', '97-53=44'] Exploring Operation: 49+44=93, Resulting Numbers: [93] 93,47 unequal: No Solution Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 49*44=2156, Resulting Numbers: [2156] 2156,47 unequal: No Solution Moving to Node #0,1,3 Current State: 47:[53, 48], Operations: ['17+32=49', '97-49=48'] Exploring Operation: 53*48=2544, Resulting Numbers: [2544] 2544,47 unequal: No Solution Exploring Operation: 53+48=101, Resulting Numbers: [101] 101,47 unequal: No Solution Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[53, 48], Operations: ['97-32=65', '65-17=48'] Exploring Operation: 53+48=101, Resulting Numbers: [101] 101,47 unequal: No Solution Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 53*48=2544, Resulting Numbers: [2544] 2544,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[65, 36], Operations: ['97-32=65', '53-17=36'] Exploring Operation: 65*36=2340, Resulting Numbers: [2340] 2340,47 unequal: No Solution Exploring Operation: 65+36=101, Resulting Numbers: [101] 101,47 unequal: No Solution Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[53, 82], Operations: ['97-32=65', '17+65=82'] Exploring Operation: 53+82=135, Resulting Numbers: [135] 135,47 unequal: No Solution Exploring Operation: 82-53=29, Resulting Numbers: [29] 29,47 unequal: No Solution Exploring Operation: 53*82=4346, Resulting Numbers: [4346] 4346,47 unequal: No Solution Moving to Node #0,2,3 Current State: 47:[65, 70], Operations: ['97-32=65', '17+53=70'] Exploring Operation: 65*70=4550, Resulting Numbers: [4550] 4550,47 unequal: No Solution Exploring Operation: 70-65=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 65+70=135, Resulting Numbers: [135] 135,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[97, 4], Operations: ['17+32=49', '53-49=4'] Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,47 unequal: No Solution Exploring Operation: 97+4=101, Resulting Numbers: [101] 101,47 unequal: No Solution Exploring Operation: 97*4=388, Resulting Numbers: [388] 388,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[49, 150], Operations: ['17+32=49', '97+53=150'] Exploring Operation: 49+150=199, Resulting Numbers: [199] 199,47 unequal: No Solution Exploring Operation: 49*150=7350, Resulting Numbers: [7350] 7350,47 unequal: No Solution Exploring Operation: 150-49=101, Resulting Numbers: [101] 101,47 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 15, 18, 27, 4 ]
21
[ "27-15=12", "12/4=3", "18+3=21" ]
Current State: 21:[15, 18, 27, 4], Operations: [] Exploring Operation: 27-15=12, Resulting Numbers: [18, 4, 12] Generated Node #2: [18, 4, 12] from Operation: 27-15=12 Current State: 21:[18, 4, 12], Operations: ['27-15=12'] Exploring Operation: 12/4=3, Resulting Numbers: [18, 3] Generated Node #3: [18, 3] from Operation: 12/4=3 Current State: 21:[18, 3], Operations: ['27-15=12', '12/4=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[15, 18, 27, 4], Operations: [] Exploring Operation: 15+4=19, Resulting Numbers: [18, 27, 19] Generated Node #0,0: 21:[18, 27, 19] Operation: 15+4=19 Exploring Operation: 27-15=12, Resulting Numbers: [18, 4, 12] Generated Node #0,1: 21:[18, 4, 12] Operation: 27-15=12 Exploring Operation: 27-4=23, Resulting Numbers: [15, 18, 23] Generated Node #0,2: 21:[15, 18, 23] Operation: 27-4=23 Exploring Operation: 27-18=9, Resulting Numbers: [15, 4, 9] Generated Node #0,3: 21:[15, 4, 9] Operation: 27-18=9 Exploring Operation: 18-15=3, Resulting Numbers: [27, 4, 3] Generated Node #0,4: 21:[27, 4, 3] Operation: 18-15=3 Start Sub Search at level 1: Moving to Node #0,4 Current State: 21:[27, 4, 3], Operations: ['18-15=3'] Exploring Operation: 4-3=1, Resulting Numbers: [27, 1] Generated Node #0,4,0: 21:[27, 1] Operation: 4-3=1 Exploring Operation: 27/3=9, Resulting Numbers: [4, 9] Generated Node #0,4,1: 21:[4, 9] Operation: 27/3=9 Exploring Operation: 27-3=24, Resulting Numbers: [4, 24] Generated Node #0,4,2: 21:[4, 24] Operation: 27-3=24 Exploring Operation: 4+3=7, Resulting Numbers: [27, 7] Generated Node #0,4,3: 21:[27, 7] Operation: 4+3=7 Exploring Operation: 27-4=23, Resulting Numbers: [3, 23] Generated Node #0,4,4: 21:[3, 23] Operation: 27-4=23 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 21:[3, 23], Operations: ['18-15=3', '27-4=23'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,21 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,21 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 21:[4, 9], Operations: ['18-15=3', '27/3=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,21 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 21:[4, 24], Operations: ['18-15=3', '27-3=24'] Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,21 unequal: No Solution Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,21 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 21:[27, 7], Operations: ['18-15=3', '4+3=7'] Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,21 unequal: No Solution Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,21 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 21:[27, 1], Operations: ['18-15=3', '4-3=1'] Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,21 unequal: No Solution Exploring Operation: 27+1=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[18, 4, 12], Operations: ['27-15=12'] Exploring Operation: 18+4=22, Resulting Numbers: [12, 22] Generated Node #0,1,0: 21:[12, 22] Operation: 18+4=22 Exploring Operation: 18-12=6, Resulting Numbers: [4, 6] Generated Node #0,1,1: 21:[4, 6] Operation: 18-12=6 Exploring Operation: 4+12=16, Resulting Numbers: [18, 16] Generated Node #0,1,2: 21:[18, 16] Operation: 4+12=16 Exploring Operation: 12-4=8, Resulting Numbers: [18, 8] Generated Node #0,1,3: 21:[18, 8] Operation: 12-4=8 Exploring Operation: 12/4=3, Resulting Numbers: [18, 3] Generated Node #0,1,4: 21:[18, 3] Operation: 12/4=3 Moving to Node #0,1,1 Current State: 21:[4, 6], Operations: ['27-15=12', '18-12=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,21 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,21 unequal: No Solution Moving to Node #0,1,4 Current State: 21:[18, 3], Operations: ['27-15=12', '12/4=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[15, 18, 27, 4], Operations: [] Exploring Operation: 27-15=12, Resulting Numbers: [18, 4, 12] Generated Node #0,1: 21:[18, 4, 12] Operation: 27-15=12 Moving to Node #0,1 Current State: 21:[18, 4, 12], Operations: ['27-15=12'] Exploring Operation: 12/4=3, Resulting Numbers: [18, 3] Generated Node #0,1,4: 21:[18, 3] Operation: 12/4=3 Moving to Node #0,1,4 Current State: 21:[18, 3], Operations: ['27-15=12', '12/4=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_5
sum_heuristic
[ 51, 33, 51, 68 ]
24
[ "51*33=1683", "1683-51=1632", "1632/68=24" ]
Current State: 24:[51, 33, 51, 68], Operations: [] Exploring Operation: 51*33=1683, Resulting Numbers: [68, 1683] Generated Node #2: [68, 1683] from Operation: 51*33=1683 Current State: 24:[68, 1683], Operations: ['51*33=1683'] Exploring Operation: 1683-51=1632, Resulting Numbers: [68, 1632] Generated Node #3: [68, 1632] from Operation: 1683-51=1632 Current State: 24:[68, 1632], Operations: ['51*33=1683', '1683-51=1632'] Exploring Operation: 1632/68=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[51, 33, 51, 68], Operations: [] Exploring Operation: 68-51=17, Resulting Numbers: [33, 51, 17] Generated Node #0,0: 24:[33, 51, 17] Operation: 68-51=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[33, 51, 17], Operations: ['68-51=17'] Exploring Operation: 51/17=3, Resulting Numbers: [33, 3] Generated Node #0,0,0: 24:[33, 3] Operation: 51/17=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[33, 3], Operations: ['68-51=17', '51/17=3'] Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,24 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 No solution found.
0
hs_1
mult_heuristic
[ 83, 36, 2, 62 ]
78
[ "83-36=47", "62/2=31", "47+31=78" ]
Current State: 78:[83, 36, 2, 62], Operations: [] Exploring Operation: 83-36=47, Resulting Numbers: [2, 62, 47] Generated Node #2: [2, 62, 47] from Operation: 83-36=47 Current State: 78:[2, 62, 47], Operations: ['83-36=47'] Exploring Operation: 62/2=31, Resulting Numbers: [47, 31] Generated Node #3: [47, 31] from Operation: 62/2=31 Current State: 78:[47, 31], Operations: ['83-36=47', '62/2=31'] Exploring Operation: 47+31=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[83, 36, 2, 62], Operations: [] Exploring Operation: 62-36=26, Resulting Numbers: [83, 2, 26] Generated Node #0,0: 78:[83, 2, 26] Operation: 62-36=26 Exploring Operation: 83-62=21, Resulting Numbers: [36, 2, 21] Generated Node #0,1: 78:[36, 2, 21] Operation: 83-62=21 Exploring Operation: 62/2=31, Resulting Numbers: [83, 36, 31] Generated Node #0,2: 78:[83, 36, 31] Operation: 62/2=31 Moving to Node #0,0 Current State: 78:[83, 2, 26], Operations: ['62-36=26'] Exploring Operation: 83+2=85, Resulting Numbers: [26, 85] Generated Node #0,0,0: 78:[26, 85] Operation: 83+2=85 Exploring Operation: 26/2=13, Resulting Numbers: [83, 13] Generated Node #0,0,1: 78:[83, 13] Operation: 26/2=13 Exploring Operation: 83-2=81, Resulting Numbers: [26, 81] Generated Node #0,0,2: 78:[26, 81] Operation: 83-2=81 Moving to Node #0,1 Current State: 78:[36, 2, 21], Operations: ['83-62=21'] Exploring Operation: 36+2=38, Resulting Numbers: [21, 38] Generated Node #0,1,0: 78:[21, 38] Operation: 36+2=38 Exploring Operation: 2+21=23, Resulting Numbers: [36, 23] Generated Node #0,1,1: 78:[36, 23] Operation: 2+21=23 Exploring Operation: 36-21=15, Resulting Numbers: [2, 15] Generated Node #0,1,2: 78:[2, 15] Operation: 36-21=15 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 78:[2, 15], Operations: ['83-62=21', '36-21=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[21, 38], Operations: ['83-62=21', '36+2=38'] Exploring Operation: 21+38=59, Resulting Numbers: [59] 59,78 unequal: No Solution Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 21*38=798, Resulting Numbers: [798] 798,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[36, 23], Operations: ['83-62=21', '2+21=23'] Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 36+23=59, Resulting Numbers: [59] 59,78 unequal: No Solution Exploring Operation: 36*23=828, Resulting Numbers: [828] 828,78 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: 78:[83, 36, 31], Operations: ['62/2=31'] Exploring Operation: 83-31=52, Resulting Numbers: [36, 52] Generated Node #0,2,0: 78:[36, 52] Operation: 83-31=52 Exploring Operation: 83-36=47, Resulting Numbers: [31, 47] Generated Node #0,2,1: 78:[31, 47] Operation: 83-36=47 Exploring Operation: 36-31=5, Resulting Numbers: [83, 5] Generated Node #0,2,2: 78:[83, 5] Operation: 36-31=5 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 78:[83, 5], Operations: ['62/2=31', '36-31=5'] Exploring Operation: 83*5=415, Resulting Numbers: [415] 415,78 unequal: No Solution Exploring Operation: 83+5=88, Resulting Numbers: [88] 88,78 unequal: No Solution Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[83, 36, 2, 62], Operations: [] Exploring Operation: 62/2=31, Resulting Numbers: [83, 36, 31] Generated Node #0,2: 78:[83, 36, 31] Operation: 62/2=31 Moving to Node #0,2 Current State: 78:[83, 36, 31], Operations: ['62/2=31'] Exploring Operation: 36-31=5, Resulting Numbers: [83, 5] Generated Node #0,2,2: 78:[83, 5] Operation: 36-31=5 Moving to Node #0,2,2 Current State: 78:[83, 5], Operations: ['62/2=31', '36-31=5'] Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_3
mult_heuristic
[ 2, 76, 7, 14 ]
71
[ "2+76=78", "14-7=7", "78-7=71" ]
Current State: 71:[2, 76, 7, 14], Operations: [] Exploring Operation: 2+76=78, Resulting Numbers: [7, 14, 78] Generated Node #2: [7, 14, 78] from Operation: 2+76=78 Current State: 71:[7, 14, 78], Operations: ['2+76=78'] Exploring Operation: 14-7=7, Resulting Numbers: [78, 7] Generated Node #3: [78, 7] from Operation: 14-7=7 Current State: 71:[78, 7], Operations: ['2+76=78', '14-7=7'] Exploring Operation: 78-7=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[2, 76, 7, 14], Operations: [] Exploring Operation: 2*14=28, Resulting Numbers: [76, 7, 28] Generated Node #0,0: 71:[76, 7, 28] Operation: 2*14=28 Exploring Operation: 7*14=98, Resulting Numbers: [2, 76, 98] Generated Node #0,1: 71:[2, 76, 98] Operation: 7*14=98 Moving to Node #0,1 Current State: 71:[2, 76, 98], Operations: ['7*14=98'] Exploring Operation: 98/2=49, Resulting Numbers: [76, 49] Generated Node #0,1,0: 71:[76, 49] Operation: 98/2=49 Exploring Operation: 76-2=74, Resulting Numbers: [98, 74] Generated Node #0,1,1: 71:[98, 74] Operation: 76-2=74 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 71:[76, 49], Operations: ['7*14=98', '98/2=49'] Exploring Operation: 76+49=125, Resulting Numbers: [125] 125,71 unequal: No Solution Exploring Operation: 76-49=27, Resulting Numbers: [27] 27,71 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 #0,1,1 Current State: 71:[98, 74], Operations: ['7*14=98', '76-2=74'] Exploring Operation: 98+74=172, Resulting Numbers: [172] 172,71 unequal: No Solution Exploring Operation: 98-74=24, Resulting Numbers: [24] 24,71 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: 71:[76, 7, 28], Operations: ['2*14=28'] Exploring Operation: 7+28=35, Resulting Numbers: [76, 35] Generated Node #0,0,0: 71:[76, 35] Operation: 7+28=35 Exploring Operation: 76-7=69, Resulting Numbers: [28, 69] Generated Node #0,0,1: 71:[28, 69] Operation: 76-7=69 Moving to Node #0,0,0 Current State: 71:[76, 35], Operations: ['2*14=28', '7+28=35'] Exploring Operation: 76+35=111, Resulting Numbers: [111] 111,71 unequal: No Solution Exploring Operation: 76-35=41, Resulting Numbers: [41] 41,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[28, 69], Operations: ['2*14=28', '76-7=69'] Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 28+69=97, Resulting Numbers: [97] 97,71 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 38, 18, 33, 58 ]
45
[ "38-18=20", "58-33=25", "20+25=45" ]
Current State: 45:[38, 18, 33, 58], Operations: [] Exploring Operation: 38-18=20, Resulting Numbers: [33, 58, 20] Generated Node #2: [33, 58, 20] from Operation: 38-18=20 Current State: 45:[33, 58, 20], Operations: ['38-18=20'] Exploring Operation: 58-33=25, Resulting Numbers: [20, 25] Generated Node #3: [20, 25] from Operation: 58-33=25 Current State: 45:[20, 25], Operations: ['38-18=20', '58-33=25'] Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[38, 18, 33, 58], Operations: [] Exploring Operation: 38-33=5, Resulting Numbers: [18, 58, 5] Generated Node #0,0: 45:[18, 58, 5] Operation: 38-33=5 Exploring Operation: 33-18=15, Resulting Numbers: [38, 58, 15] Generated Node #0,1: 45:[38, 58, 15] Operation: 33-18=15 Exploring Operation: 58-38=20, Resulting Numbers: [18, 33, 20] Generated Node #0,2: 45:[18, 33, 20] Operation: 58-38=20 Moving to Node #0,0 Current State: 45:[18, 58, 5], Operations: ['38-33=5'] Exploring Operation: 58-5=53, Resulting Numbers: [18, 53] Generated Node #0,0,0: 45:[18, 53] Operation: 58-5=53 Exploring Operation: 58-18=40, Resulting Numbers: [5, 40] Generated Node #0,0,1: 45:[5, 40] Operation: 58-18=40 Exploring Operation: 18-5=13, Resulting Numbers: [58, 13] Generated Node #0,0,2: 45:[58, 13] Operation: 18-5=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[5, 40], Operations: ['38-33=5', '58-18=40'] Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[38, 18, 33, 58], Operations: [] Exploring Operation: 38-33=5, Resulting Numbers: [18, 58, 5] Generated Node #0,0: 45:[18, 58, 5] Operation: 38-33=5 Moving to Node #0,0 Current State: 45:[18, 58, 5], Operations: ['38-33=5'] Exploring Operation: 58-18=40, Resulting Numbers: [5, 40] Generated Node #0,0,1: 45:[5, 40] Operation: 58-18=40 Moving to Node #0,0,1 Current State: 45:[5, 40], Operations: ['38-33=5', '58-18=40'] Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 75, 73, 77, 86 ]
95
[ "75-73=2", "86*2=172", "172-77=95" ]
Current State: 95:[75, 73, 77, 86], Operations: [] Exploring Operation: 75-73=2, Resulting Numbers: [77, 86, 2] Generated Node #2: [77, 86, 2] from Operation: 75-73=2 Current State: 95:[77, 86, 2], Operations: ['75-73=2'] Exploring Operation: 86*2=172, Resulting Numbers: [77, 172] Generated Node #3: [77, 172] from Operation: 86*2=172 Current State: 95:[77, 172], Operations: ['75-73=2', '86*2=172'] Exploring Operation: 172-77=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[75, 73, 77, 86], Operations: [] Exploring Operation: 75-73=2, Resulting Numbers: [77, 86, 2] Generated Node #0,0: 95:[77, 86, 2] Operation: 75-73=2 Exploring Operation: 77-73=4, Resulting Numbers: [75, 86, 4] Generated Node #0,1: 95:[75, 86, 4] Operation: 77-73=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[77, 86, 2], Operations: ['75-73=2'] Exploring Operation: 77+2=79, Resulting Numbers: [86, 79] Generated Node #0,0,0: 95:[86, 79] Operation: 77+2=79 Exploring Operation: 86-77=9, Resulting Numbers: [2, 9] Generated Node #0,0,1: 95:[2, 9] Operation: 86-77=9 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 95:[2, 9], Operations: ['75-73=2', '86-77=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,95 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,95 unequal: No Solution No 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: 95:[86, 79], Operations: ['75-73=2', '77+2=79'] Exploring Operation: 86+79=165, Resulting Numbers: [165] 165,95 unequal: No Solution Exploring Operation: 86-79=7, Resulting Numbers: [7] 7,95 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: 95:[75, 86, 4], Operations: ['77-73=4'] Exploring Operation: 75+4=79, Resulting Numbers: [86, 79] Generated Node #0,1,0: 95:[86, 79] Operation: 75+4=79 Exploring Operation: 86-75=11, Resulting Numbers: [4, 11] Generated Node #0,1,1: 95:[4, 11] Operation: 86-75=11 Moving to Node #0,1,1 Current State: 95:[4, 11], Operations: ['77-73=4', '86-75=11'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,95 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,95 unequal: No Solution Moving to Node #0,1,0 Current State: 95:[86, 79], Operations: ['77-73=4', '75+4=79'] Exploring Operation: 86+79=165, Resulting Numbers: [165] 165,95 unequal: No Solution Exploring Operation: 86-79=7, Resulting Numbers: [7] 7,95 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
[ 74, 21, 91, 77 ]
45
[ "74+91=165", "21*165=3465", "3465/77=45" ]
Current State: 45:[74, 21, 91, 77], Operations: [] Exploring Operation: 74+91=165, Resulting Numbers: [21, 77, 165] Generated Node #2: [21, 77, 165] from Operation: 74+91=165 Current State: 45:[21, 77, 165], Operations: ['74+91=165'] Exploring Operation: 21*165=3465, Resulting Numbers: [77, 3465] Generated Node #3: [77, 3465] from Operation: 21*165=3465 Current State: 45:[77, 3465], Operations: ['74+91=165', '21*165=3465'] Exploring Operation: 3465/77=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[74, 21, 91, 77], Operations: [] Exploring Operation: 91-74=17, Resulting Numbers: [21, 77, 17] Generated Node #0,0: 45:[21, 77, 17] Operation: 91-74=17 Exploring Operation: 77-74=3, Resulting Numbers: [21, 91, 3] Generated Node #0,1: 45:[21, 91, 3] Operation: 77-74=3 Exploring Operation: 91-77=14, Resulting Numbers: [74, 21, 14] Generated Node #0,2: 45:[74, 21, 14] Operation: 91-77=14 Exploring Operation: 74-21=53, Resulting Numbers: [91, 77, 53] Generated Node #0,3: 45:[91, 77, 53] Operation: 74-21=53 Start Sub Search at level 1: Moving to Node #0,2 Current State: 45:[74, 21, 14], Operations: ['91-77=14'] Exploring Operation: 21+14=35, Resulting Numbers: [74, 35] Generated Node #0,2,0: 45:[74, 35] Operation: 21+14=35 Exploring Operation: 74-21=53, Resulting Numbers: [14, 53] Generated Node #0,2,1: 45:[14, 53] Operation: 74-21=53 Exploring Operation: 74-14=60, Resulting Numbers: [21, 60] Generated Node #0,2,2: 45:[21, 60] Operation: 74-14=60 Exploring Operation: 21-14=7, Resulting Numbers: [74, 7] Generated Node #0,2,3: 45:[74, 7] Operation: 21-14=7 Moving to Node #0,2,1 Current State: 45:[14, 53], Operations: ['91-77=14', '74-21=53'] Exploring Operation: 14*53=742, Resulting Numbers: [742] 742,45 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,45 unequal: No Solution Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,45 unequal: No Solution Moving to Node #0,2,2 Current State: 45:[21, 60], Operations: ['91-77=14', '74-14=60'] Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,45 unequal: No Solution Exploring Operation: 21*60=1260, Resulting Numbers: [1260] 1260,45 unequal: No Solution Exploring Operation: 21+60=81, Resulting Numbers: [81] 81,45 unequal: No Solution Moving to Node #0,2,3 Current State: 45:[74, 7], Operations: ['91-77=14', '21-14=7'] Exploring Operation: 74*7=518, Resulting Numbers: [518] 518,45 unequal: No Solution Exploring Operation: 74-7=67, Resulting Numbers: [67] 67,45 unequal: No Solution Exploring Operation: 74+7=81, Resulting Numbers: [81] 81,45 unequal: No Solution Moving to Node #0,2,0 Current State: 45:[74, 35], Operations: ['91-77=14', '21+14=35'] Exploring Operation: 74-35=39, Resulting Numbers: [39] 39,45 unequal: No Solution Exploring Operation: 74+35=109, Resulting Numbers: [109] 109,45 unequal: No Solution Exploring Operation: 74*35=2590, Resulting Numbers: [2590] 2590,45 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 #0,0 Current State: 45:[21, 77, 17], Operations: ['91-74=17'] Exploring Operation: 21+17=38, Resulting Numbers: [77, 38] Generated Node #0,0,0: 45:[77, 38] Operation: 21+17=38 Exploring Operation: 77-17=60, Resulting Numbers: [21, 60] Generated Node #0,0,1: 45:[21, 60] Operation: 77-17=60 Exploring Operation: 77-21=56, Resulting Numbers: [17, 56] Generated Node #0,0,2: 45:[17, 56] Operation: 77-21=56 Exploring Operation: 21-17=4, Resulting Numbers: [77, 4] Generated Node #0,0,3: 45:[77, 4] Operation: 21-17=4 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 45:[17, 56], Operations: ['91-74=17', '77-21=56'] Exploring Operation: 17+56=73, Resulting Numbers: [73] 73,45 unequal: No Solution Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,45 unequal: No Solution Exploring Operation: 17*56=952, Resulting Numbers: [952] 952,45 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 #0,0,1 Current State: 45:[21, 60], Operations: ['91-74=17', '77-17=60'] Exploring Operation: 21+60=81, Resulting Numbers: [81] 81,45 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,45 unequal: No Solution Exploring Operation: 21*60=1260, Resulting Numbers: [1260] 1260,45 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:[77, 4], Operations: ['91-74=17', '21-17=4'] Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,45 unequal: No Solution Exploring Operation: 77*4=308, Resulting Numbers: [308] 308,45 unequal: No Solution Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,45 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:[77, 38], Operations: ['91-74=17', '21+17=38'] Exploring Operation: 77*38=2926, Resulting Numbers: [2926] 2926,45 unequal: No Solution Exploring Operation: 77-38=39, Resulting Numbers: [39] 39,45 unequal: No Solution Exploring Operation: 77+38=115, Resulting Numbers: [115] 115,45 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 #0,1 Current State: 45:[21, 91, 3], Operations: ['77-74=3'] Exploring Operation: 91-3=88, Resulting Numbers: [21, 88] Generated Node #0,1,0: 45:[21, 88] Operation: 91-3=88 Exploring Operation: 91-21=70, Resulting Numbers: [3, 70] Generated Node #0,1,1: 45:[3, 70] Operation: 91-21=70 Exploring Operation: 21/3=7, Resulting Numbers: [91, 7] Generated Node #0,1,2: 45:[91, 7] Operation: 21/3=7 Exploring Operation: 21-3=18, Resulting Numbers: [91, 18] Generated Node #0,1,3: 45:[91, 18] Operation: 21-3=18 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[3, 70], Operations: ['77-74=3', '91-21=70'] Exploring Operation: 3*70=210, Resulting Numbers: [210] 210,45 unequal: No Solution Exploring Operation: 3+70=73, Resulting Numbers: [73] 73,45 unequal: No Solution Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,45 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 #0,1,2 Current State: 45:[91, 7], Operations: ['77-74=3', '21/3=7'] Exploring Operation: 91-7=84, Resulting Numbers: [84] 84,45 unequal: No Solution Exploring Operation: 91/7=13, Resulting Numbers: [13] 13,45 unequal: No Solution Exploring Operation: 91+7=98, Resulting Numbers: [98] 98,45 unequal: No Solution Exploring Operation: 91*7=637, Resulting Numbers: [637] 637,45 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 #0,1,0 Current State: 45:[21, 88], Operations: ['77-74=3', '91-3=88'] Exploring Operation: 21+88=109, Resulting Numbers: [109] 109,45 unequal: No Solution Exploring Operation: 21*88=1848, Resulting Numbers: [1848] 1848,45 unequal: No Solution Exploring Operation: 88-21=67, Resulting Numbers: [67] 67,45 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 #0,1,3 Current State: 45:[91, 18], Operations: ['77-74=3', '21-3=18'] Exploring Operation: 91-18=73, Resulting Numbers: [73] 73,45 unequal: No Solution Exploring Operation: 91*18=1638, Resulting Numbers: [1638] 1638,45 unequal: No Solution Exploring Operation: 91+18=109, Resulting Numbers: [109] 109,45 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 #0,3 Current State: 45:[91, 77, 53], Operations: ['74-21=53'] Exploring Operation: 91-77=14, Resulting Numbers: [53, 14] Generated Node #0,3,0: 45:[53, 14] Operation: 91-77=14 Exploring Operation: 91+77=168, Resulting Numbers: [53, 168] Generated Node #0,3,1: 45:[53, 168] Operation: 91+77=168 Exploring Operation: 91-53=38, Resulting Numbers: [77, 38] Generated Node #0,3,2: 45:[77, 38] Operation: 91-53=38 Exploring Operation: 77-53=24, Resulting Numbers: [91, 24] Generated Node #0,3,3: 45:[91, 24] Operation: 77-53=24 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 45:[53, 14], Operations: ['74-21=53', '91-77=14'] Exploring Operation: 53*14=742, Resulting Numbers: [742] 742,45 unequal: No Solution Exploring Operation: 53+14=67, Resulting Numbers: [67] 67,45 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,45 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 #0,3,2 Current State: 45:[77, 38], Operations: ['74-21=53', '91-53=38'] Exploring Operation: 77*38=2926, Resulting Numbers: [2926] 2926,45 unequal: No Solution Exploring Operation: 77+38=115, Resulting Numbers: [115] 115,45 unequal: No Solution Exploring Operation: 77-38=39, Resulting Numbers: [39] 39,45 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 #0,3,3 Current State: 45:[91, 24], Operations: ['74-21=53', '77-53=24'] Exploring Operation: 91*24=2184, Resulting Numbers: [2184] 2184,45 unequal: No Solution Exploring Operation: 91-24=67, Resulting Numbers: [67] 67,45 unequal: No Solution Exploring Operation: 91+24=115, Resulting Numbers: [115] 115,45 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 #0,3,1 Current State: 45:[53, 168], Operations: ['74-21=53', '91+77=168'] Exploring Operation: 53+168=221, Resulting Numbers: [221] 221,45 unequal: No Solution Exploring Operation: 168-53=115, Resulting Numbers: [115] 115,45 unequal: No Solution Exploring Operation: 53*168=8904, Resulting Numbers: [8904] 8904,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 3, 63, 60, 61 ]
52
[ "63-60=3", "3*3=9", "61-9=52" ]
Current State: 52:[3, 63, 60, 61], Operations: [] Exploring Operation: 63-60=3, Resulting Numbers: [3, 61, 3] Generated Node #2: [3, 61, 3] from Operation: 63-60=3 Current State: 52:[3, 61, 3], Operations: ['63-60=3'] Exploring Operation: 3*3=9, Resulting Numbers: [61, 9] Generated Node #3: [61, 9] from Operation: 3*3=9 Current State: 52:[61, 9], Operations: ['63-60=3', '3*3=9'] Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[3, 63, 60, 61], Operations: [] Exploring Operation: 63-3=60, Resulting Numbers: [60, 61, 60] Generated Node #0,0: 52:[60, 61, 60] Operation: 63-3=60 Exploring Operation: 63/3=21, Resulting Numbers: [60, 61, 21] Generated Node #0,1: 52:[60, 61, 21] Operation: 63/3=21 Exploring Operation: 63-61=2, Resulting Numbers: [3, 60, 2] Generated Node #0,2: 52:[3, 60, 2] Operation: 63-61=2 Exploring Operation: 63-60=3, Resulting Numbers: [3, 61, 3] Generated Node #0,3: 52:[3, 61, 3] Operation: 63-60=3 Exploring Operation: 61-60=1, Resulting Numbers: [3, 63, 1] Generated Node #0,4: 52:[3, 63, 1] Operation: 61-60=1 Moving to Node #0,2 Current State: 52:[3, 60, 2], Operations: ['63-61=2'] Exploring Operation: 60/2=30, Resulting Numbers: [3, 30] Generated Node #0,2,0: 52:[3, 30] Operation: 60/2=30 Exploring Operation: 60-2=58, Resulting Numbers: [3, 58] Generated Node #0,2,1: 52:[3, 58] Operation: 60-2=58 Exploring Operation: 3+2=5, Resulting Numbers: [60, 5] Generated Node #0,2,2: 52:[60, 5] Operation: 3+2=5 Exploring Operation: 60-3=57, Resulting Numbers: [2, 57] Generated Node #0,2,3: 52:[2, 57] Operation: 60-3=57 Exploring Operation: 60/3=20, Resulting Numbers: [2, 20] Generated Node #0,2,4: 52:[2, 20] Operation: 60/3=20 Moving to Node #0,3 Current State: 52:[3, 61, 3], Operations: ['63-60=3'] Exploring Operation: 3-3=0, Resulting Numbers: [61, 0] Generated Node #0,3,0: 52:[61, 0] Operation: 3-3=0 Exploring Operation: 61-3=58, Resulting Numbers: [3, 58] Generated Node #0,3,1: 52:[3, 58] Operation: 61-3=58 Exploring Operation: 3+3=6, Resulting Numbers: [61, 6] Generated Node #0,3,2: 52:[61, 6] Operation: 3+3=6 Exploring Operation: 61-3=58, Resulting Numbers: [3, 58] Generated Node #0,3,3: 52:[3, 58] Operation: 61-3=58 Exploring Operation: 3/3=1, Resulting Numbers: [61, 1] Generated Node #0,3,4: 52:[61, 1] Operation: 3/3=1 Moving to Node #0,4 Current State: 52:[3, 63, 1], Operations: ['61-60=1'] Exploring Operation: 3-1=2, Resulting Numbers: [63, 2] Generated Node #0,4,0: 52:[63, 2] Operation: 3-1=2 Exploring Operation: 63-1=62, Resulting Numbers: [3, 62] Generated Node #0,4,1: 52:[3, 62] Operation: 63-1=62 Exploring Operation: 3+1=4, Resulting Numbers: [63, 4] Generated Node #0,4,2: 52:[63, 4] Operation: 3+1=4 Exploring Operation: 63-3=60, Resulting Numbers: [1, 60] Generated Node #0,4,3: 52:[1, 60] Operation: 63-3=60 Exploring Operation: 63/3=21, Resulting Numbers: [1, 21] Generated Node #0,4,4: 52:[1, 21] Operation: 63/3=21 Moving to Node #0,1 Current State: 52:[60, 61, 21], Operations: ['63/3=21'] Exploring Operation: 60+21=81, Resulting Numbers: [61, 81] Generated Node #0,1,0: 52:[61, 81] Operation: 60+21=81 Exploring Operation: 61-21=40, Resulting Numbers: [60, 40] Generated Node #0,1,1: 52:[60, 40] Operation: 61-21=40 Exploring Operation: 60-21=39, Resulting Numbers: [61, 39] Generated Node #0,1,2: 52:[61, 39] Operation: 60-21=39 Exploring Operation: 61+21=82, Resulting Numbers: [60, 82] Generated Node #0,1,3: 52:[60, 82] Operation: 61+21=82 Exploring Operation: 61-60=1, Resulting Numbers: [21, 1] Generated Node #0,1,4: 52:[21, 1] Operation: 61-60=1 Moving to Node #0,0 Current State: 52:[60, 61, 60], Operations: ['63-3=60'] Exploring Operation: 60-60=0, Resulting Numbers: [61, 0] Generated Node #0,0,0: 52:[61, 0] Operation: 60-60=0 Exploring Operation: 60/60=1, Resulting Numbers: [61, 1] Generated Node #0,0,1: 52:[61, 1] Operation: 60/60=1 Exploring Operation: 61-60=1, Resulting Numbers: [60, 1] Generated Node #0,0,2: 52:[60, 1] Operation: 61-60=1 Exploring Operation: 61-60=1, Resulting Numbers: [60, 1] Generated Node #0,0,3: 52:[60, 1] Operation: 61-60=1 Exploring Operation: 60+61=121, Resulting Numbers: [60, 121] Generated Node #0,0,4: 52:[60, 121] Operation: 60+61=121 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 52:[60, 1], Operations: ['63-3=60', '61-60=1'] Exploring Operation: 60*1=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 60/1=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 60+1=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 60-1=59, Resulting Numbers: [59] 59,52 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 #0,0,3 Current State: 52:[60, 1], Operations: ['63-3=60', '61-60=1'] Exploring Operation: 60/1=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 60+1=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 60*1=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 60-1=59, Resulting Numbers: [59] 59,52 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 #0,0,1 Current State: 52:[61, 1], Operations: ['63-3=60', '60/60=1'] Exploring Operation: 61*1=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,52 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 #0,0,0 Current State: 52:[61, 0], Operations: ['63-3=60', '60-60=0'] Exploring Operation: 61+0=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 61*0=0, Resulting Numbers: [0] 0,52 unequal: No Solution Exploring Operation: 61-0=61, Resulting Numbers: [61] 61,52 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 #0,0,4 Current State: 52:[60, 121], Operations: ['63-3=60', '60+61=121'] Exploring Operation: 121-60=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 60*121=7260, Resulting Numbers: [7260] 7260,52 unequal: No Solution Exploring Operation: 60+121=181, Resulting Numbers: [181] 181,52 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: 52:[3, 30], Operations: ['63-61=2', '60/2=30'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,52 unequal: No Solution Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,52 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,52 unequal: No Solution Moving to Node #0,2,3 Current State: 52:[2, 57], Operations: ['63-61=2', '60-3=57'] Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,52 unequal: No Solution Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,52 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,52 unequal: No Solution Moving to Node #0,2,4 Current State: 52:[2, 20], Operations: ['63-61=2', '60/3=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,52 unequal: No Solution Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,52 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,52 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,52 unequal: No Solution Moving to Node #0,4,4 Current State: 52:[1, 21], Operations: ['61-60=1', '63/3=21'] Exploring Operation: 1*21=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,52 unequal: No Solution Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,52 unequal: No Solution Moving to Node #0,1,4 Current State: 52:[21, 1], Operations: ['63/3=21', '61-60=1'] Exploring Operation: 21*1=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 21+1=22, Resulting Numbers: [22] 22,52 unequal: No Solution Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,52 unequal: No Solution Moving to Node #0,3,3 Current State: 52:[3, 58], Operations: ['63-60=3', '61-3=58'] Exploring Operation: 3*58=174, Resulting Numbers: [174] 174,52 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,52 unequal: No Solution Exploring Operation: 3+58=61, Resulting Numbers: [61] 61,52 unequal: No Solution Moving to Node #0,3,1 Current State: 52:[3, 58], Operations: ['63-60=3', '61-3=58'] Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,52 unequal: No Solution Exploring Operation: 3*58=174, Resulting Numbers: [174] 174,52 unequal: No Solution Exploring Operation: 3+58=61, Resulting Numbers: [61] 61,52 unequal: No Solution Moving to Node #0,2,1 Current State: 52:[3, 58], Operations: ['63-61=2', '60-2=58'] Exploring Operation: 3*58=174, Resulting Numbers: [174] 174,52 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,52 unequal: No Solution Exploring Operation: 3+58=61, Resulting Numbers: [61] 61,52 unequal: No Solution Moving to Node #0,4,3 Current State: 52:[1, 60], Operations: ['61-60=1', '63-3=60'] Exploring Operation: 60/1=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 1*60=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 60-1=59, Resulting Numbers: [59] 59,52 unequal: No Solution Exploring Operation: 1+60=61, Resulting Numbers: [61] 61,52 unequal: No Solution Moving to Node #0,2,2 Current State: 52:[60, 5], Operations: ['63-61=2', '3+2=5'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 60*5=300, Resulting Numbers: [300] 300,52 unequal: No Solution Exploring Operation: 60+5=65, Resulting Numbers: [65] 65,52 unequal: No Solution Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,52 unequal: No Solution Moving to Node #0,3,4 Current State: 52:[61, 1], Operations: ['63-60=3', '3/3=1'] Exploring Operation: 61*1=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,52 unequal: No Solution Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,52 unequal: No Solution Moving to Node #0,4,2 Current State: 52:[63, 4], Operations: ['61-60=1', '3+1=4'] Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,52 unequal: No Solution Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,52 unequal: No Solution Exploring Operation: 63*4=252, Resulting Numbers: [252] 252,52 unequal: No Solution Moving to Node #0,4,0 Current State: 52:[63, 2], Operations: ['61-60=1', '3-1=2'] Exploring Operation: 63*2=126, Resulting Numbers: [126] 126,52 unequal: No Solution Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,52 unequal: No Solution Moving to Node #0,3,2 Current State: 52:[61, 6], Operations: ['63-60=3', '3+3=6'] Exploring Operation: 61+6=67, Resulting Numbers: [67] 67,52 unequal: No Solution Exploring Operation: 61*6=366, Resulting Numbers: [366] 366,52 unequal: No Solution Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,52 unequal: No Solution Moving to Node #0,4,1 Current State: 52:[3, 62], Operations: ['61-60=1', '63-1=62'] Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,52 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,52 unequal: No Solution Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,52 unequal: No Solution Moving to Node #0,3,0 Current State: 52:[61, 0], Operations: ['63-60=3', '3-3=0'] Exploring Operation: 61-0=61, Resulting Numbers: [61] 61,52 unequal: No Solution Exploring Operation: 61*0=0, Resulting Numbers: [0] 0,52 unequal: No Solution Exploring Operation: 61+0=61, Resulting Numbers: [61] 61,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[60, 40], Operations: ['63/3=21', '61-21=40'] Exploring Operation: 60+40=100, Resulting Numbers: [100] 100,52 unequal: No Solution Exploring Operation: 60*40=2400, Resulting Numbers: [2400] 2400,52 unequal: No Solution Exploring Operation: 60-40=20, Resulting Numbers: [20] 20,52 unequal: No Solution Moving to Node #0,1,2 Current State: 52:[61, 39], Operations: ['63/3=21', '60-21=39'] Exploring Operation: 61*39=2379, Resulting Numbers: [2379] 2379,52 unequal: No Solution Exploring Operation: 61-39=22, Resulting Numbers: [22] 22,52 unequal: No Solution Exploring Operation: 61+39=100, Resulting Numbers: [100] 100,52 unequal: No Solution Moving to Node #0,1,0 Current State: 52:[61, 81], Operations: ['63/3=21', '60+21=81'] Exploring Operation: 81-61=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 61+81=142, Resulting Numbers: [142] 142,52 unequal: No Solution Exploring Operation: 61*81=4941, Resulting Numbers: [4941] 4941,52 unequal: No Solution Moving to Node #0,1,3 Current State: 52:[60, 82], Operations: ['63/3=21', '61+21=82'] Exploring Operation: 60+82=142, Resulting Numbers: [142] 142,52 unequal: No Solution Exploring Operation: 82-60=22, Resulting Numbers: [22] 22,52 unequal: No Solution Exploring Operation: 60*82=4920, Resulting Numbers: [4920] 4920,52 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 26, 61, 29, 56 ]
11
[ "26+29=55", "61-56=5", "55/5=11" ]
Current State: 11:[26, 61, 29, 56], Operations: [] Exploring Operation: 26+29=55, Resulting Numbers: [61, 56, 55] Generated Node #2: [61, 56, 55] from Operation: 26+29=55 Current State: 11:[61, 56, 55], Operations: ['26+29=55'] Exploring Operation: 61-56=5, Resulting Numbers: [55, 5] Generated Node #3: [55, 5] from Operation: 61-56=5 Current State: 11:[55, 5], Operations: ['26+29=55', '61-56=5'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[26, 61, 29, 56], Operations: [] Exploring Operation: 61-56=5, Resulting Numbers: [26, 29, 5] Generated Node #0,0: 11:[26, 29, 5] Operation: 61-56=5 Exploring Operation: 56-29=27, Resulting Numbers: [26, 61, 27] Generated Node #0,1: 11:[26, 61, 27] Operation: 56-29=27 Exploring Operation: 61-29=32, Resulting Numbers: [26, 56, 32] Generated Node #0,2: 11:[26, 56, 32] Operation: 61-29=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[26, 29, 5], Operations: ['61-56=5'] Exploring Operation: 29-5=24, Resulting Numbers: [26, 24] Generated Node #0,0,0: 11:[26, 24] Operation: 29-5=24 Exploring Operation: 29-26=3, Resulting Numbers: [5, 3] Generated Node #0,0,1: 11:[5, 3] Operation: 29-26=3 Exploring Operation: 26-5=21, Resulting Numbers: [29, 21] Generated Node #0,0,2: 11:[29, 21] Operation: 26-5=21 Moving to Node #0,0,1 Current State: 11:[5, 3], Operations: ['61-56=5', '29-26=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,11 unequal: No Solution Moving to Node #0,0,0 Current State: 11:[26, 24], Operations: ['61-56=5', '29-5=24'] Exploring Operation: 26*24=624, Resulting Numbers: [624] 624,11 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 26+24=50, Resulting Numbers: [50] 50,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[29, 21], Operations: ['61-56=5', '26-5=21'] Exploring Operation: 29+21=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 29*21=609, Resulting Numbers: [609] 609,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[26, 61, 27], Operations: ['56-29=27'] Exploring Operation: 61-27=34, Resulting Numbers: [26, 34] Generated Node #0,1,0: 11:[26, 34] Operation: 61-27=34 Exploring Operation: 61-26=35, Resulting Numbers: [27, 35] Generated Node #0,1,1: 11:[27, 35] Operation: 61-26=35 Exploring Operation: 27-26=1, Resulting Numbers: [61, 1] Generated Node #0,1,2: 11:[61, 1] Operation: 27-26=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 11:[26, 34], Operations: ['56-29=27', '61-27=34'] Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 26+34=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 26*34=884, Resulting Numbers: [884] 884,11 unequal: No Solution No 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: 11:[27, 35], Operations: ['56-29=27', '61-26=35'] Exploring Operation: 27+35=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 27*35=945, Resulting Numbers: [945] 945,11 unequal: No Solution Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,11 unequal: No Solution No 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: 11:[61, 1], Operations: ['56-29=27', '27-26=1'] Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 61*1=61, Resulting Numbers: [61] 61,11 unequal: No Solution Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,11 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: 11:[26, 56, 32], Operations: ['61-29=32'] Exploring Operation: 56-26=30, Resulting Numbers: [32, 30] Generated Node #0,2,0: 11:[32, 30] Operation: 56-26=30 Exploring Operation: 56-32=24, Resulting Numbers: [26, 24] Generated Node #0,2,1: 11:[26, 24] Operation: 56-32=24 Exploring Operation: 32-26=6, Resulting Numbers: [56, 6] Generated Node #0,2,2: 11:[56, 6] Operation: 32-26=6 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 11:[26, 24], Operations: ['61-29=32', '56-32=24'] Exploring Operation: 26*24=624, Resulting Numbers: [624] 624,11 unequal: No Solution Exploring Operation: 26+24=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,11 unequal: No Solution No 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: 11:[32, 30], Operations: ['61-29=32', '56-26=30'] Exploring Operation: 32+30=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 32*30=960, Resulting Numbers: [960] 960,11 unequal: No Solution No 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: 11:[56, 6], Operations: ['61-29=32', '32-26=6'] Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,11 unequal: No Solution Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,11 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
[ 3, 55, 88, 56 ]
85
[ "88-3=85", "56-55=1", "85*1=85" ]
Current State: 85:[3, 55, 88, 56], Operations: [] Exploring Operation: 88-3=85, Resulting Numbers: [55, 56, 85] Generated Node #2: [55, 56, 85] from Operation: 88-3=85 Current State: 85:[55, 56, 85], Operations: ['88-3=85'] Exploring Operation: 56-55=1, Resulting Numbers: [85, 1] Generated Node #3: [85, 1] from Operation: 56-55=1 Current State: 85:[85, 1], Operations: ['88-3=85', '56-55=1'] Exploring Operation: 85*1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[3, 55, 88, 56], Operations: [] Exploring Operation: 56-55=1, Resulting Numbers: [3, 88, 1] Generated Node #0,0: 85:[3, 88, 1] Operation: 56-55=1 Exploring Operation: 55+56=111, Resulting Numbers: [3, 88, 111] Generated Node #0,1: 85:[3, 88, 111] Operation: 55+56=111 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[3, 88, 1], Operations: ['56-55=1'] Exploring Operation: 88-3=85, Resulting Numbers: [1, 85] Generated Node #0,0,0: 85:[1, 85] Operation: 88-3=85 Exploring Operation: 3+1=4, Resulting Numbers: [88, 4] Generated Node #0,0,1: 85:[88, 4] Operation: 3+1=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[1, 85], Operations: ['56-55=1', '88-3=85'] Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[3, 55, 88, 56], Operations: [] Exploring Operation: 56-55=1, Resulting Numbers: [3, 88, 1] Generated Node #0,0: 85:[3, 88, 1] Operation: 56-55=1 Moving to Node #0,0 Current State: 85:[3, 88, 1], Operations: ['56-55=1'] Exploring Operation: 88-3=85, Resulting Numbers: [1, 85] Generated Node #0,0,0: 85:[1, 85] Operation: 88-3=85 Moving to Node #0,0,0 Current State: 85:[1, 85], Operations: ['56-55=1', '88-3=85'] Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 35, 35, 66, 16 ]
64
[ "35+35=70", "70-66=4", "16*4=64" ]
Current State: 64:[35, 35, 66, 16], Operations: [] Exploring Operation: 35+35=70, Resulting Numbers: [66, 16, 70] Generated Node #2: [66, 16, 70] from Operation: 35+35=70 Current State: 64:[66, 16, 70], Operations: ['35+35=70'] Exploring Operation: 70-66=4, Resulting Numbers: [16, 4] Generated Node #3: [16, 4] from Operation: 70-66=4 Current State: 64:[16, 4], Operations: ['35+35=70', '70-66=4'] Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[35, 35, 66, 16], Operations: [] Exploring Operation: 66-35=31, Resulting Numbers: [35, 16, 31] Generated Node #0,0: 64:[35, 16, 31] Operation: 66-35=31 Exploring Operation: 35-35=0, Resulting Numbers: [66, 16, 0] Generated Node #0,1: 64:[66, 16, 0] Operation: 35-35=0 Exploring Operation: 35/35=1, Resulting Numbers: [66, 16, 1] Generated Node #0,2: 64:[66, 16, 1] Operation: 35/35=1 Exploring Operation: 66-35=31, Resulting Numbers: [35, 16, 31] Generated Node #0,3: 64:[35, 16, 31] Operation: 66-35=31 Exploring Operation: 35+35=70, Resulting Numbers: [66, 16, 70] Generated Node #0,4: 64:[66, 16, 70] Operation: 35+35=70 Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[66, 16, 1], Operations: ['35/35=1'] Exploring Operation: 66*1=66, Resulting Numbers: [16, 66] Generated Node #0,2,0: 64:[16, 66] Operation: 66*1=66 Exploring Operation: 66/1=66, Resulting Numbers: [16, 66] Generated Node #0,2,1: 64:[16, 66] Operation: 66/1=66 Exploring Operation: 66-1=65, Resulting Numbers: [16, 65] Generated Node #0,2,2: 64:[16, 65] Operation: 66-1=65 Exploring Operation: 16/1=16, Resulting Numbers: [66, 16] Generated Node #0,2,3: 64:[66, 16] Operation: 16/1=16 Exploring Operation: 16*1=16, Resulting Numbers: [66, 16] Generated Node #0,2,4: 64:[66, 16] Operation: 16*1=16 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 64:[16, 65], Operations: ['35/35=1', '66-1=65'] Exploring Operation: 16*65=1040, Resulting Numbers: [1040] 1040,64 unequal: No Solution Exploring Operation: 16+65=81, Resulting Numbers: [81] 81,64 unequal: No Solution Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 64:[16, 66], Operations: ['35/35=1', '66*1=66'] Exploring Operation: 16*66=1056, Resulting Numbers: [1056] 1056,64 unequal: No Solution Exploring Operation: 16+66=82, Resulting Numbers: [82] 82,64 unequal: No Solution Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 64:[16, 66], Operations: ['35/35=1', '66/1=66'] Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,64 unequal: No Solution Exploring Operation: 16*66=1056, Resulting Numbers: [1056] 1056,64 unequal: No Solution Exploring Operation: 16+66=82, Resulting Numbers: [82] 82,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 64:[66, 16], Operations: ['35/35=1', '16/1=16'] Exploring Operation: 66*16=1056, Resulting Numbers: [1056] 1056,64 unequal: No Solution Exploring Operation: 66+16=82, Resulting Numbers: [82] 82,64 unequal: No Solution Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 64:[66, 16], Operations: ['35/35=1', '16*1=16'] Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,64 unequal: No Solution Exploring Operation: 66+16=82, Resulting Numbers: [82] 82,64 unequal: No Solution Exploring Operation: 66*16=1056, Resulting Numbers: [1056] 1056,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[35, 16, 31], Operations: ['66-35=31'] Exploring Operation: 35-31=4, Resulting Numbers: [16, 4] Generated Node #0,0,0: 64:[16, 4] Operation: 35-31=4 Exploring Operation: 35-16=19, Resulting Numbers: [31, 19] Generated Node #0,0,1: 64:[31, 19] Operation: 35-16=19 Exploring Operation: 35+31=66, Resulting Numbers: [16, 66] Generated Node #0,0,2: 64:[16, 66] Operation: 35+31=66 Exploring Operation: 31-16=15, Resulting Numbers: [35, 15] Generated Node #0,0,3: 64:[35, 15] Operation: 31-16=15 Exploring Operation: 35+16=51, Resulting Numbers: [31, 51] Generated Node #0,0,4: 64:[31, 51] Operation: 35+16=51 Moving to Node #0,0,0 Current State: 64:[16, 4], Operations: ['66-35=31', '35-31=4'] Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,64 unequal: No Solution Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[35, 35, 66, 16], Operations: [] Exploring Operation: 66-35=31, Resulting Numbers: [35, 16, 31] Generated Node #0,0: 64:[35, 16, 31] Operation: 66-35=31 Moving to Node #0,0 Current State: 64:[35, 16, 31], Operations: ['66-35=31'] Exploring Operation: 35-31=4, Resulting Numbers: [16, 4] Generated Node #0,0,0: 64:[16, 4] Operation: 35-31=4 Moving to Node #0,0,0 Current State: 64:[16, 4], Operations: ['66-35=31', '35-31=4'] Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 74, 46, 72, 2 ]
86
[ "74-46=28", "28/2=14", "72+14=86" ]
Current State: 86:[74, 46, 72, 2], Operations: [] Exploring Operation: 74-46=28, Resulting Numbers: [72, 2, 28] Generated Node #2: [72, 2, 28] from Operation: 74-46=28 Current State: 86:[72, 2, 28], Operations: ['74-46=28'] Exploring Operation: 28/2=14, Resulting Numbers: [72, 14] Generated Node #3: [72, 14] from Operation: 28/2=14 Current State: 86:[72, 14], Operations: ['74-46=28', '28/2=14'] Exploring Operation: 72+14=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[74, 46, 72, 2], Operations: [] Exploring Operation: 74-72=2, Resulting Numbers: [46, 2, 2] Generated Node #0,0: 86:[46, 2, 2] Operation: 74-72=2 Moving to Node #0,0 Current State: 86:[46, 2, 2], Operations: ['74-72=2'] Exploring Operation: 46-2=44, Resulting Numbers: [2, 44] Generated Node #0,0,0: 86:[2, 44] Operation: 46-2=44 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[2, 44], Operations: ['74-72=2', '46-2=44'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 36, 92, 8, 18 ]
23
[ "36*92=3312", "8*18=144", "3312/144=23" ]
Current State: 23:[36, 92, 8, 18], Operations: [] Exploring Operation: 36*92=3312, Resulting Numbers: [8, 18, 3312] Generated Node #2: [8, 18, 3312] from Operation: 36*92=3312 Current State: 23:[8, 18, 3312], Operations: ['36*92=3312'] Exploring Operation: 8*18=144, Resulting Numbers: [3312, 144] Generated Node #3: [3312, 144] from Operation: 8*18=144 Current State: 23:[3312, 144], Operations: ['36*92=3312', '8*18=144'] Exploring Operation: 3312/144=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[36, 92, 8, 18], Operations: [] Exploring Operation: 92-36=56, Resulting Numbers: [8, 18, 56] Generated Node #0,0: 23:[8, 18, 56] Operation: 92-36=56 Exploring Operation: 92-8=84, Resulting Numbers: [36, 18, 84] Generated Node #0,1: 23:[36, 18, 84] Operation: 92-8=84 Exploring Operation: 36-8=28, Resulting Numbers: [92, 18, 28] Generated Node #0,2: 23:[92, 18, 28] Operation: 36-8=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[8, 18, 56], Operations: ['92-36=56'] Exploring Operation: 56/8=7, Resulting Numbers: [18, 7] Generated Node #0,0,0: 23:[18, 7] Operation: 56/8=7 Exploring Operation: 56-8=48, Resulting Numbers: [18, 48] Generated Node #0,0,1: 23:[18, 48] Operation: 56-8=48 Exploring Operation: 56-18=38, Resulting Numbers: [8, 38] Generated Node #0,0,2: 23:[8, 38] Operation: 56-18=38 Moving to Node #0,0,0 Current State: 23:[18, 7], Operations: ['92-36=56', '56/8=7'] Exploring Operation: 18+7=25, Resulting Numbers: [25] 25,23 unequal: No Solution Exploring Operation: 18*7=126, Resulting Numbers: [126] 126,23 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[18, 48], Operations: ['92-36=56', '56-8=48'] Exploring Operation: 18+48=66, Resulting Numbers: [66] 66,23 unequal: No Solution Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,23 unequal: No Solution Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[8, 38], Operations: ['92-36=56', '56-18=38'] Exploring Operation: 8+38=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 8*38=304, Resulting Numbers: [304] 304,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[36, 18, 84], Operations: ['92-8=84'] Exploring Operation: 84-18=66, Resulting Numbers: [36, 66] Generated Node #0,1,0: 23:[36, 66] Operation: 84-18=66 Exploring Operation: 36-18=18, Resulting Numbers: [84, 18] Generated Node #0,1,1: 23:[84, 18] Operation: 36-18=18 Exploring Operation: 84-36=48, Resulting Numbers: [18, 48] Generated Node #0,1,2: 23:[18, 48] Operation: 84-36=48 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 23:[18, 48], Operations: ['92-8=84', '84-36=48'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,23 unequal: No Solution Exploring Operation: 18+48=66, Resulting Numbers: [66] 66,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 23:[36, 66], Operations: ['92-8=84', '84-18=66'] Exploring Operation: 36+66=102, Resulting Numbers: [102] 102,23 unequal: No Solution Exploring Operation: 66-36=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 36*66=2376, Resulting Numbers: [2376] 2376,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 23:[84, 18], Operations: ['92-8=84', '36-18=18'] Exploring Operation: 84*18=1512, Resulting Numbers: [1512] 1512,23 unequal: No Solution Exploring Operation: 84-18=66, Resulting Numbers: [66] 66,23 unequal: No Solution Exploring Operation: 84+18=102, Resulting Numbers: [102] 102,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[92, 18, 28], Operations: ['36-8=28'] Exploring Operation: 28-18=10, Resulting Numbers: [92, 10] Generated Node #0,2,0: 23:[92, 10] Operation: 28-18=10 Exploring Operation: 92-18=74, Resulting Numbers: [28, 74] Generated Node #0,2,1: 23:[28, 74] Operation: 92-18=74 Exploring Operation: 92-28=64, Resulting Numbers: [18, 64] Generated Node #0,2,2: 23:[18, 64] Operation: 92-28=64 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 23:[18, 64], Operations: ['36-8=28', '92-28=64'] Exploring Operation: 18*64=1152, Resulting Numbers: [1152] 1152,23 unequal: No Solution Exploring Operation: 64-18=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 18+64=82, Resulting Numbers: [82] 82,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 23:[28, 74], Operations: ['36-8=28', '92-18=74'] Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 28+74=102, Resulting Numbers: [102] 102,23 unequal: No Solution Exploring Operation: 28*74=2072, Resulting Numbers: [2072] 2072,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 23:[92, 10], Operations: ['36-8=28', '28-18=10'] Exploring Operation: 92+10=102, Resulting Numbers: [102] 102,23 unequal: No Solution Exploring Operation: 92*10=920, Resulting Numbers: [920] 920,23 unequal: No Solution Exploring Operation: 92-10=82, Resulting Numbers: [82] 82,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 14, 27, 63, 92 ]
70
[ "14+27=41", "92-63=29", "41+29=70" ]
Current State: 70:[14, 27, 63, 92], Operations: [] Exploring Operation: 14+27=41, Resulting Numbers: [63, 92, 41] Generated Node #2: [63, 92, 41] from Operation: 14+27=41 Current State: 70:[63, 92, 41], Operations: ['14+27=41'] Exploring Operation: 92-63=29, Resulting Numbers: [41, 29] Generated Node #3: [41, 29] from Operation: 92-63=29 Current State: 70:[41, 29], Operations: ['14+27=41', '92-63=29'] Exploring Operation: 41+29=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[14, 27, 63, 92], Operations: [] Exploring Operation: 92-27=65, Resulting Numbers: [14, 63, 65] Generated Node #0,0: 70:[14, 63, 65] Operation: 92-27=65 Exploring Operation: 27-14=13, Resulting Numbers: [63, 92, 13] Generated Node #0,1: 70:[63, 92, 13] Operation: 27-14=13 Exploring Operation: 63-27=36, Resulting Numbers: [14, 92, 36] Generated Node #0,2: 70:[14, 92, 36] Operation: 63-27=36 Exploring Operation: 92-63=29, Resulting Numbers: [14, 27, 29] Generated Node #0,3: 70:[14, 27, 29] Operation: 92-63=29 Exploring Operation: 92-14=78, Resulting Numbers: [27, 63, 78] Generated Node #0,4: 70:[27, 63, 78] Operation: 92-14=78 Moving to Node #0,0 Current State: 70:[14, 63, 65], Operations: ['92-27=65'] Exploring Operation: 14+63=77, Resulting Numbers: [65, 77] Generated Node #0,0,0: 70:[65, 77] Operation: 14+63=77 Exploring Operation: 14+65=79, Resulting Numbers: [63, 79] Generated Node #0,0,1: 70:[63, 79] Operation: 14+65=79 Exploring Operation: 65-63=2, Resulting Numbers: [14, 2] Generated Node #0,0,2: 70:[14, 2] Operation: 65-63=2 Exploring Operation: 63-14=49, Resulting Numbers: [65, 49] Generated Node #0,0,3: 70:[65, 49] Operation: 63-14=49 Exploring Operation: 65-14=51, Resulting Numbers: [63, 51] Generated Node #0,0,4: 70:[63, 51] Operation: 65-14=51 Moving to Node #0,3 Current State: 70:[14, 27, 29], Operations: ['92-63=29'] Exploring Operation: 29-14=15, Resulting Numbers: [27, 15] Generated Node #0,3,0: 70:[27, 15] Operation: 29-14=15 Exploring Operation: 14+27=41, Resulting Numbers: [29, 41] Generated Node #0,3,1: 70:[29, 41] Operation: 14+27=41 Exploring Operation: 27+29=56, Resulting Numbers: [14, 56] Generated Node #0,3,2: 70:[14, 56] Operation: 27+29=56 Exploring Operation: 27-14=13, Resulting Numbers: [29, 13] Generated Node #0,3,3: 70:[29, 13] Operation: 27-14=13 Exploring Operation: 29-27=2, Resulting Numbers: [14, 2] Generated Node #0,3,4: 70:[14, 2] Operation: 29-27=2 Moving to Node #0,2 Current State: 70:[14, 92, 36], Operations: ['63-27=36'] Exploring Operation: 92-36=56, Resulting Numbers: [14, 56] Generated Node #0,2,0: 70:[14, 56] Operation: 92-36=56 Exploring Operation: 14+36=50, Resulting Numbers: [92, 50] Generated Node #0,2,1: 70:[92, 50] Operation: 14+36=50 Exploring Operation: 36-14=22, Resulting Numbers: [92, 22] Generated Node #0,2,2: 70:[92, 22] Operation: 36-14=22 Exploring Operation: 14+92=106, Resulting Numbers: [36, 106] Generated Node #0,2,3: 70:[36, 106] Operation: 14+92=106 Exploring Operation: 92-14=78, Resulting Numbers: [36, 78] Generated Node #0,2,4: 70:[36, 78] Operation: 92-14=78 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 70:[36, 78], Operations: ['63-27=36', '92-14=78'] Exploring Operation: 36+78=114, Resulting Numbers: [114] 114,70 unequal: No Solution Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,70 unequal: No Solution Exploring Operation: 36*78=2808, Resulting Numbers: [2808] 2808,70 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 #0,2,0 Current State: 70:[14, 56], Operations: ['63-27=36', '92-36=56'] Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,70 unequal: No Solution Exploring Operation: 14*56=784, Resulting Numbers: [784] 784,70 unequal: No Solution Exploring Operation: 14+56=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[14, 27, 63, 92], Operations: [] Exploring Operation: 63-27=36, Resulting Numbers: [14, 92, 36] Generated Node #0,2: 70:[14, 92, 36] Operation: 63-27=36 Moving to Node #0,2 Current State: 70:[14, 92, 36], Operations: ['63-27=36'] Exploring Operation: 92-36=56, Resulting Numbers: [14, 56] Generated Node #0,2,0: 70:[14, 56] Operation: 92-36=56 Moving to Node #0,2,0 Current State: 70:[14, 56], Operations: ['63-27=36', '92-36=56'] Exploring Operation: 14+56=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_5
sum_heuristic
[ 49, 92, 8, 89 ]
54
[ "92-49=43", "8+89=97", "97-43=54" ]
Current State: 54:[49, 92, 8, 89], Operations: [] Exploring Operation: 92-49=43, Resulting Numbers: [8, 89, 43] Generated Node #2: [8, 89, 43] from Operation: 92-49=43 Current State: 54:[8, 89, 43], Operations: ['92-49=43'] Exploring Operation: 8+89=97, Resulting Numbers: [43, 97] Generated Node #3: [43, 97] from Operation: 8+89=97 Current State: 54:[43, 97], Operations: ['92-49=43', '8+89=97'] Exploring Operation: 97-43=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[49, 92, 8, 89], Operations: [] Exploring Operation: 92-89=3, Resulting Numbers: [49, 8, 3] Generated Node #0,0: 54:[49, 8, 3] Operation: 92-89=3 Exploring Operation: 89-49=40, Resulting Numbers: [92, 8, 40] Generated Node #0,1: 54:[92, 8, 40] Operation: 89-49=40 Exploring Operation: 92-49=43, Resulting Numbers: [8, 89, 43] Generated Node #0,2: 54:[8, 89, 43] Operation: 92-49=43 Moving to Node #0,0 Current State: 54:[49, 8, 3], Operations: ['92-89=3'] Exploring Operation: 8-3=5, Resulting Numbers: [49, 5] Generated Node #0,0,0: 54:[49, 5] Operation: 8-3=5 Exploring Operation: 49+8=57, Resulting Numbers: [3, 57] Generated Node #0,0,1: 54:[3, 57] Operation: 49+8=57 Exploring Operation: 49+3=52, Resulting Numbers: [8, 52] Generated Node #0,0,2: 54:[8, 52] Operation: 49+3=52 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[3, 57], Operations: ['92-89=3', '49+8=57'] Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[49, 92, 8, 89], Operations: [] Exploring Operation: 92-89=3, Resulting Numbers: [49, 8, 3] Generated Node #0,0: 54:[49, 8, 3] Operation: 92-89=3 Moving to Node #0,0 Current State: 54:[49, 8, 3], Operations: ['92-89=3'] Exploring Operation: 49+8=57, Resulting Numbers: [3, 57] Generated Node #0,0,1: 54:[3, 57] Operation: 49+8=57 Moving to Node #0,0,1 Current State: 54:[3, 57], Operations: ['92-89=3', '49+8=57'] Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 81, 5, 90, 79 ]
65
[ "81-5=76", "90-79=11", "76-11=65" ]
Current State: 65:[81, 5, 90, 79], Operations: [] Exploring Operation: 81-5=76, Resulting Numbers: [90, 79, 76] Generated Node #2: [90, 79, 76] from Operation: 81-5=76 Current State: 65:[90, 79, 76], Operations: ['81-5=76'] Exploring Operation: 90-79=11, Resulting Numbers: [76, 11] Generated Node #3: [76, 11] from Operation: 90-79=11 Current State: 65:[76, 11], Operations: ['81-5=76', '90-79=11'] Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[81, 5, 90, 79], Operations: [] Exploring Operation: 90-79=11, Resulting Numbers: [81, 5, 11] Generated Node #0,0: 65:[81, 5, 11] Operation: 90-79=11 Exploring Operation: 90/5=18, Resulting Numbers: [81, 79, 18] Generated Node #0,1: 65:[81, 79, 18] Operation: 90/5=18 Exploring Operation: 81-79=2, Resulting Numbers: [5, 90, 2] Generated Node #0,2: 65:[5, 90, 2] Operation: 81-79=2 Exploring Operation: 90-81=9, Resulting Numbers: [5, 79, 9] Generated Node #0,3: 65:[5, 79, 9] Operation: 90-81=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[81, 5, 11], Operations: ['90-79=11'] Exploring Operation: 81-5=76, Resulting Numbers: [11, 76] Generated Node #0,0,0: 65:[11, 76] Operation: 81-5=76 Exploring Operation: 81-11=70, Resulting Numbers: [5, 70] Generated Node #0,0,1: 65:[5, 70] Operation: 81-11=70 Exploring Operation: 11-5=6, Resulting Numbers: [81, 6] Generated Node #0,0,2: 65:[81, 6] Operation: 11-5=6 Exploring Operation: 5+11=16, Resulting Numbers: [81, 16] Generated Node #0,0,3: 65:[81, 16] Operation: 5+11=16 Moving to Node #0,0,1 Current State: 65:[5, 70], Operations: ['90-79=11', '81-11=70'] Exploring Operation: 5*70=350, Resulting Numbers: [350] 350,65 unequal: No Solution Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[81, 5, 90, 79], Operations: [] Exploring Operation: 90-79=11, Resulting Numbers: [81, 5, 11] Generated Node #0,0: 65:[81, 5, 11] Operation: 90-79=11 Moving to Node #0,0 Current State: 65:[81, 5, 11], Operations: ['90-79=11'] Exploring Operation: 81-11=70, Resulting Numbers: [5, 70] Generated Node #0,0,1: 65:[5, 70] Operation: 81-11=70 Moving to Node #0,0,1 Current State: 65:[5, 70], Operations: ['90-79=11', '81-11=70'] Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 96, 17, 9, 72 ]
87
[ "96-17=79", "72/9=8", "79+8=87" ]
Current State: 87:[96, 17, 9, 72], Operations: [] Exploring Operation: 96-17=79, Resulting Numbers: [9, 72, 79] Generated Node #2: [9, 72, 79] from Operation: 96-17=79 Current State: 87:[9, 72, 79], Operations: ['96-17=79'] Exploring Operation: 72/9=8, Resulting Numbers: [79, 8] Generated Node #3: [79, 8] from Operation: 72/9=8 Current State: 87:[79, 8], Operations: ['96-17=79', '72/9=8'] Exploring Operation: 79+8=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[96, 17, 9, 72], Operations: [] Exploring Operation: 17+72=89, Resulting Numbers: [96, 9, 89] Generated Node #0,0: 87:[96, 9, 89] Operation: 17+72=89 Exploring Operation: 96-72=24, Resulting Numbers: [17, 9, 24] Generated Node #0,1: 87:[17, 9, 24] Operation: 96-72=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[96, 9, 89], Operations: ['17+72=89'] Exploring Operation: 96-89=7, Resulting Numbers: [9, 7] Generated Node #0,0,0: 87:[9, 7] Operation: 96-89=7 Exploring Operation: 96-9=87, Resulting Numbers: [89, 87] Generated Node #0,0,1: 87:[89, 87] Operation: 96-9=87 Moving to Node #0,0,1 Current State: 87:[89, 87], Operations: ['17+72=89', '96-9=87'] Exploring Operation: 89+87=176, Resulting Numbers: [176] 176,87 unequal: No Solution Exploring Operation: 89-87=2, Resulting Numbers: [2] 2,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[9, 7], Operations: ['17+72=89', '96-89=7'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,87 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,87 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 Current State: 87:[17, 9, 24], Operations: ['96-72=24'] Exploring Operation: 17+9=26, Resulting Numbers: [24, 26] Generated Node #0,1,0: 87:[24, 26] Operation: 17+9=26 Exploring Operation: 17-9=8, Resulting Numbers: [24, 8] Generated Node #0,1,1: 87:[24, 8] Operation: 17-9=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[24, 26], Operations: ['96-72=24', '17+9=26'] Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,87 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[24, 8], Operations: ['96-72=24', '17-9=8'] Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,87 unequal: No Solution Exploring Operation: 24+8=32, Resulting Numbers: [32] 32,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 95, 86, 36, 99 ]
47
[ "95-86=9", "99/9=11", "36+11=47" ]
Current State: 47:[95, 86, 36, 99], Operations: [] Exploring Operation: 95-86=9, Resulting Numbers: [36, 99, 9] Generated Node #2: [36, 99, 9] from Operation: 95-86=9 Current State: 47:[36, 99, 9], Operations: ['95-86=9'] Exploring Operation: 99/9=11, Resulting Numbers: [36, 11] Generated Node #3: [36, 11] from Operation: 99/9=11 Current State: 47:[36, 11], Operations: ['95-86=9', '99/9=11'] Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[95, 86, 36, 99], Operations: [] Exploring Operation: 95-86=9, Resulting Numbers: [36, 99, 9] Generated Node #0,0: 47:[36, 99, 9] Operation: 95-86=9 Exploring Operation: 99-95=4, Resulting Numbers: [86, 36, 4] Generated Node #0,1: 47:[86, 36, 4] Operation: 99-95=4 Exploring Operation: 99-86=13, Resulting Numbers: [95, 36, 13] Generated Node #0,2: 47:[95, 36, 13] Operation: 99-86=13 Moving to Node #0,1 Current State: 47:[86, 36, 4], Operations: ['99-95=4'] Exploring Operation: 86-4=82, Resulting Numbers: [36, 82] Generated Node #0,1,0: 47:[36, 82] Operation: 86-4=82 Exploring Operation: 86-36=50, Resulting Numbers: [4, 50] Generated Node #0,1,1: 47:[4, 50] Operation: 86-36=50 Exploring Operation: 36+4=40, Resulting Numbers: [86, 40] Generated Node #0,1,2: 47:[86, 40] Operation: 36+4=40 Moving to Node #0,2 Current State: 47:[95, 36, 13], Operations: ['99-86=13'] Exploring Operation: 36+13=49, Resulting Numbers: [95, 49] Generated Node #0,2,0: 47:[95, 49] Operation: 36+13=49 Exploring Operation: 95-36=59, Resulting Numbers: [13, 59] Generated Node #0,2,1: 47:[13, 59] Operation: 95-36=59 Exploring Operation: 95-13=82, Resulting Numbers: [36, 82] Generated Node #0,2,2: 47:[36, 82] Operation: 95-13=82 Moving to Node #0,0 Current State: 47:[36, 99, 9], Operations: ['95-86=9'] Exploring Operation: 99-36=63, Resulting Numbers: [9, 63] Generated Node #0,0,0: 47:[9, 63] Operation: 99-36=63 Exploring Operation: 99/9=11, Resulting Numbers: [36, 11] Generated Node #0,0,1: 47:[36, 11] Operation: 99/9=11 Exploring Operation: 36+9=45, Resulting Numbers: [99, 45] Generated Node #0,0,2: 47:[99, 45] Operation: 36+9=45 Moving to Node #0,1,0 Current State: 47:[36, 82], Operations: ['99-95=4', '86-4=82'] Exploring Operation: 36+82=118, Resulting Numbers: [118] 118,47 unequal: No Solution Exploring Operation: 82-36=46, Resulting Numbers: [46] 46,47 unequal: No Solution Exploring Operation: 36*82=2952, Resulting Numbers: [2952] 2952,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[86, 40], Operations: ['99-95=4', '36+4=40'] Exploring Operation: 86+40=126, Resulting Numbers: [126] 126,47 unequal: No Solution Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,47 unequal: No Solution Exploring Operation: 86*40=3440, Resulting Numbers: [3440] 3440,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[4, 50], Operations: ['99-95=4', '86-36=50'] Exploring Operation: 4+50=54, Resulting Numbers: [54] 54,47 unequal: No Solution Exploring Operation: 4*50=200, Resulting Numbers: [200] 200,47 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[36, 82], Operations: ['99-86=13', '95-13=82'] Exploring Operation: 82-36=46, Resulting Numbers: [46] 46,47 unequal: No Solution Exploring Operation: 36*82=2952, Resulting Numbers: [2952] 2952,47 unequal: No Solution Exploring Operation: 36+82=118, Resulting Numbers: [118] 118,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[13, 59], Operations: ['99-86=13', '95-36=59'] Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,47 unequal: No Solution Exploring Operation: 13+59=72, Resulting Numbers: [72] 72,47 unequal: No Solution Exploring Operation: 13*59=767, Resulting Numbers: [767] 767,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[36, 11], Operations: ['95-86=9', '99/9=11'] Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,47 unequal: No Solution Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[95, 86, 36, 99], Operations: [] Exploring Operation: 95-86=9, Resulting Numbers: [36, 99, 9] Generated Node #0,0: 47:[36, 99, 9] Operation: 95-86=9 Moving to Node #0,0 Current State: 47:[36, 99, 9], Operations: ['95-86=9'] Exploring Operation: 99/9=11, Resulting Numbers: [36, 11] Generated Node #0,0,1: 47:[36, 11] Operation: 99/9=11 Moving to Node #0,0,1 Current State: 47:[36, 11], Operations: ['95-86=9', '99/9=11'] Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
0.971354
hs_3
sum_heuristic
[ 86, 85, 87, 19 ]
48
[ "87-85=2", "19*2=38", "86-38=48" ]
Current State: 48:[86, 85, 87, 19], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [86, 19, 2] Generated Node #2: [86, 19, 2] from Operation: 87-85=2 Current State: 48:[86, 19, 2], Operations: ['87-85=2'] Exploring Operation: 19*2=38, Resulting Numbers: [86, 38] Generated Node #3: [86, 38] from Operation: 19*2=38 Current State: 48:[86, 38], Operations: ['87-85=2', '19*2=38'] Exploring Operation: 86-38=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[86, 85, 87, 19], Operations: [] Exploring Operation: 86-85=1, Resulting Numbers: [87, 19, 1] Generated Node #0,0: 48:[87, 19, 1] Operation: 86-85=1 Exploring Operation: 87-86=1, Resulting Numbers: [85, 19, 1] Generated Node #0,1: 48:[85, 19, 1] Operation: 87-86=1 Exploring Operation: 85-19=66, Resulting Numbers: [86, 87, 66] Generated Node #0,2: 48:[86, 87, 66] Operation: 85-19=66 Exploring Operation: 87-85=2, Resulting Numbers: [86, 19, 2] Generated Node #0,3: 48:[86, 19, 2] Operation: 87-85=2 Exploring Operation: 86-19=67, Resulting Numbers: [85, 87, 67] Generated Node #0,4: 48:[85, 87, 67] Operation: 86-19=67 Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[85, 19, 1], Operations: ['87-86=1'] Exploring Operation: 85-19=66, Resulting Numbers: [1, 66] Generated Node #0,1,0: 48:[1, 66] Operation: 85-19=66 Exploring Operation: 85*1=85, Resulting Numbers: [19, 85] Generated Node #0,1,1: 48:[19, 85] Operation: 85*1=85 Exploring Operation: 85-1=84, Resulting Numbers: [19, 84] Generated Node #0,1,2: 48:[19, 84] Operation: 85-1=84 Exploring Operation: 19-1=18, Resulting Numbers: [85, 18] Generated Node #0,1,3: 48:[85, 18] Operation: 19-1=18 Exploring Operation: 85/1=85, Resulting Numbers: [19, 85] Generated Node #0,1,4: 48:[19, 85] Operation: 85/1=85 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 48:[1, 66], Operations: ['87-86=1', '85-19=66'] Exploring Operation: 1+66=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,48 unequal: No Solution Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,48 unequal: No Solution Exploring Operation: 1*66=66, Resulting Numbers: [66] 66,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 48:[19, 84], Operations: ['87-86=1', '85-1=84'] Exploring Operation: 19+84=103, Resulting Numbers: [103] 103,48 unequal: No Solution Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,48 unequal: No Solution Exploring Operation: 19*84=1596, Resulting Numbers: [1596] 1596,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 48:[85, 18], Operations: ['87-86=1', '19-1=18'] Exploring Operation: 85-18=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 85+18=103, Resulting Numbers: [103] 103,48 unequal: No Solution Exploring Operation: 85*18=1530, Resulting Numbers: [1530] 1530,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 48:[19, 85], Operations: ['87-86=1', '85*1=85'] Exploring Operation: 85-19=66, Resulting Numbers: [66] 66,48 unequal: No Solution Exploring Operation: 19+85=104, Resulting Numbers: [104] 104,48 unequal: No Solution Exploring Operation: 19*85=1615, Resulting Numbers: [1615] 1615,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 48:[19, 85], Operations: ['87-86=1', '85/1=85'] Exploring Operation: 19*85=1615, Resulting Numbers: [1615] 1615,48 unequal: No Solution Exploring Operation: 85-19=66, Resulting Numbers: [66] 66,48 unequal: No Solution Exploring Operation: 19+85=104, Resulting Numbers: [104] 104,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 48:[86, 19, 2], Operations: ['87-85=2'] Exploring Operation: 86-2=84, Resulting Numbers: [19, 84] Generated Node #0,3,0: 48:[19, 84] Operation: 86-2=84 Exploring Operation: 86-19=67, Resulting Numbers: [2, 67] Generated Node #0,3,1: 48:[2, 67] Operation: 86-19=67 Exploring Operation: 86/2=43, Resulting Numbers: [19, 43] Generated Node #0,3,2: 48:[19, 43] Operation: 86/2=43 Exploring Operation: 19-2=17, Resulting Numbers: [86, 17] Generated Node #0,3,3: 48:[86, 17] Operation: 19-2=17 Exploring Operation: 19+2=21, Resulting Numbers: [86, 21] Generated Node #0,3,4: 48:[86, 21] Operation: 19+2=21 Moving to Node #0,3,2 Current State: 48:[19, 43], Operations: ['87-85=2', '86/2=43'] Exploring Operation: 19*43=817, Resulting Numbers: [817] 817,48 unequal: No Solution Exploring Operation: 43-19=24, Resulting Numbers: [24] 24,48 unequal: No Solution Exploring Operation: 19+43=62, Resulting Numbers: [62] 62,48 unequal: No Solution Moving to Node #0,3,1 Current State: 48:[2, 67], Operations: ['87-85=2', '86-19=67'] Exploring Operation: 2+67=69, Resulting Numbers: [69] 69,48 unequal: No Solution Exploring Operation: 2*67=134, Resulting Numbers: [134] 134,48 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,48 unequal: No Solution Moving to Node #0,3,0 Current State: 48:[19, 84], Operations: ['87-85=2', '86-2=84'] Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,48 unequal: No Solution Exploring Operation: 19+84=103, Resulting Numbers: [103] 103,48 unequal: No Solution Exploring Operation: 19*84=1596, Resulting Numbers: [1596] 1596,48 unequal: No Solution Moving to Node #0,3,3 Current State: 48:[86, 17], Operations: ['87-85=2', '19-2=17'] Exploring Operation: 86+17=103, Resulting Numbers: [103] 103,48 unequal: No Solution Exploring Operation: 86-17=69, Resulting Numbers: [69] 69,48 unequal: No Solution Exploring Operation: 86*17=1462, Resulting Numbers: [1462] 1462,48 unequal: No Solution Moving to Node #0,3,4 Current State: 48:[86, 21], Operations: ['87-85=2', '19+2=21'] Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,48 unequal: No Solution Exploring Operation: 86*21=1806, Resulting Numbers: [1806] 1806,48 unequal: No Solution Exploring Operation: 86+21=107, Resulting Numbers: [107] 107,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[87, 19, 1], Operations: ['86-85=1'] Exploring Operation: 87*1=87, Resulting Numbers: [19, 87] Generated Node #0,0,0: 48:[19, 87] Operation: 87*1=87 Exploring Operation: 87-1=86, Resulting Numbers: [19, 86] Generated Node #0,0,1: 48:[19, 86] Operation: 87-1=86 Exploring Operation: 19-1=18, Resulting Numbers: [87, 18] Generated Node #0,0,2: 48:[87, 18] Operation: 19-1=18 Exploring Operation: 87/1=87, Resulting Numbers: [19, 87] Generated Node #0,0,3: 48:[19, 87] Operation: 87/1=87 Exploring Operation: 87-19=68, Resulting Numbers: [1, 68] Generated Node #0,0,4: 48:[1, 68] Operation: 87-19=68 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 48:[1, 68], Operations: ['86-85=1', '87-19=68'] Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 1*68=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 1+68=69, Resulting Numbers: [69] 69,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 48:[19, 86], Operations: ['86-85=1', '87-1=86'] Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 19*86=1634, Resulting Numbers: [1634] 1634,48 unequal: No Solution Exploring Operation: 19+86=105, Resulting Numbers: [105] 105,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 48:[87, 18], Operations: ['86-85=1', '19-1=18'] Exploring Operation: 87+18=105, Resulting Numbers: [105] 105,48 unequal: No Solution Exploring Operation: 87-18=69, Resulting Numbers: [69] 69,48 unequal: No Solution Exploring Operation: 87*18=1566, Resulting Numbers: [1566] 1566,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[19, 87], Operations: ['86-85=1', '87*1=87'] Exploring Operation: 19+87=106, Resulting Numbers: [106] 106,48 unequal: No Solution Exploring Operation: 87-19=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 19*87=1653, Resulting Numbers: [1653] 1653,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 48:[19, 87], Operations: ['86-85=1', '87/1=87'] Exploring Operation: 19*87=1653, Resulting Numbers: [1653] 1653,48 unequal: No Solution Exploring Operation: 87-19=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 19+87=106, Resulting Numbers: [106] 106,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[86, 87, 66], Operations: ['85-19=66'] Exploring Operation: 86+87=173, Resulting Numbers: [66, 173] Generated Node #0,2,0: 48:[66, 173] Operation: 86+87=173 Exploring Operation: 87-66=21, Resulting Numbers: [86, 21] Generated Node #0,2,1: 48:[86, 21] Operation: 87-66=21 Exploring Operation: 86-66=20, Resulting Numbers: [87, 20] Generated Node #0,2,2: 48:[87, 20] Operation: 86-66=20 Exploring Operation: 86+66=152, Resulting Numbers: [87, 152] Generated Node #0,2,3: 48:[87, 152] Operation: 86+66=152 Exploring Operation: 87-86=1, Resulting Numbers: [66, 1] Generated Node #0,2,4: 48:[66, 1] Operation: 87-86=1 Moving to Node #0,2,4 Current State: 48:[66, 1], Operations: ['85-19=66', '87-86=1'] Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,48 unequal: No Solution Exploring Operation: 66*1=66, Resulting Numbers: [66] 66,48 unequal: No Solution Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,48 unequal: No Solution Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,48 unequal: No Solution Moving to Node #0,2,1 Current State: 48:[86, 21], Operations: ['85-19=66', '87-66=21'] Exploring Operation: 86*21=1806, Resulting Numbers: [1806] 1806,48 unequal: No Solution Exploring Operation: 86+21=107, Resulting Numbers: [107] 107,48 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,48 unequal: No Solution Moving to Node #0,2,2 Current State: 48:[87, 20], Operations: ['85-19=66', '86-66=20'] Exploring Operation: 87*20=1740, Resulting Numbers: [1740] 1740,48 unequal: No Solution Exploring Operation: 87+20=107, Resulting Numbers: [107] 107,48 unequal: No Solution Exploring Operation: 87-20=67, Resulting Numbers: [67] 67,48 unequal: No Solution Moving to Node #0,2,0 Current State: 48:[66, 173], Operations: ['85-19=66', '86+87=173'] Exploring Operation: 66+173=239, Resulting Numbers: [239] 239,48 unequal: No Solution Exploring Operation: 66*173=11418, Resulting Numbers: [11418] 11418,48 unequal: No Solution Exploring Operation: 173-66=107, Resulting Numbers: [107] 107,48 unequal: No Solution Moving to Node #0,2,3 Current State: 48:[87, 152], Operations: ['85-19=66', '86+66=152'] Exploring Operation: 87*152=13224, Resulting Numbers: [13224] 13224,48 unequal: No Solution Exploring Operation: 152-87=65, Resulting Numbers: [65] 65,48 unequal: No Solution Exploring Operation: 87+152=239, Resulting Numbers: [239] 239,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 48:[85, 87, 67], Operations: ['86-19=67'] Exploring Operation: 87-85=2, Resulting Numbers: [67, 2] Generated Node #0,4,0: 48:[67, 2] Operation: 87-85=2 Exploring Operation: 85+87=172, Resulting Numbers: [67, 172] Generated Node #0,4,1: 48:[67, 172] Operation: 85+87=172 Exploring Operation: 85-67=18, Resulting Numbers: [87, 18] Generated Node #0,4,2: 48:[87, 18] Operation: 85-67=18 Exploring Operation: 87-67=20, Resulting Numbers: [85, 20] Generated Node #0,4,3: 48:[85, 20] Operation: 87-67=20 Exploring Operation: 85+67=152, Resulting Numbers: [87, 152] Generated Node #0,4,4: 48:[87, 152] Operation: 85+67=152 Moving to Node #0,4,0 Current State: 48:[67, 2], Operations: ['86-19=67', '87-85=2'] Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,48 unequal: No Solution Exploring Operation: 67*2=134, Resulting Numbers: [134] 134,48 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,48 unequal: No Solution Moving to Node #0,4,3 Current State: 48:[85, 20], Operations: ['86-19=67', '87-67=20'] Exploring Operation: 85-20=65, Resulting Numbers: [65] 65,48 unequal: No Solution Exploring Operation: 85+20=105, Resulting Numbers: [105] 105,48 unequal: No Solution Exploring Operation: 85*20=1700, Resulting Numbers: [1700] 1700,48 unequal: No Solution Moving to Node #0,4,2 Current State: 48:[87, 18], Operations: ['86-19=67', '85-67=18'] Exploring Operation: 87*18=1566, Resulting Numbers: [1566] 1566,48 unequal: No Solution Exploring Operation: 87-18=69, Resulting Numbers: [69] 69,48 unequal: No Solution Exploring Operation: 87+18=105, Resulting Numbers: [105] 105,48 unequal: No Solution Moving to Node #0,4,1 Current State: 48:[67, 172], Operations: ['86-19=67', '85+87=172'] Exploring Operation: 172-67=105, Resulting Numbers: [105] 105,48 unequal: No Solution Exploring Operation: 67*172=11524, Resulting Numbers: [11524] 11524,48 unequal: No Solution Exploring Operation: 67+172=239, Resulting Numbers: [239] 239,48 unequal: No Solution Moving to Node #0,4,4 Current State: 48:[87, 152], Operations: ['86-19=67', '85+67=152'] Exploring Operation: 87*152=13224, Resulting Numbers: [13224] 13224,48 unequal: No Solution Exploring Operation: 87+152=239, Resulting Numbers: [239] 239,48 unequal: No Solution Exploring Operation: 152-87=65, Resulting Numbers: [65] 65,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 53, 19, 25, 19 ]
53
[ "19-19=0", "25*0=0", "53+0=53" ]
Current State: 53:[53, 19, 25, 19], Operations: [] Exploring Operation: 19-19=0, Resulting Numbers: [53, 25, 0] Generated Node #2: [53, 25, 0] from Operation: 19-19=0 Current State: 53:[53, 25, 0], Operations: ['19-19=0'] Exploring Operation: 25*0=0, Resulting Numbers: [53, 0] Generated Node #3: [53, 0] from Operation: 25*0=0 Current State: 53:[53, 0], Operations: ['19-19=0', '25*0=0'] Exploring Operation: 53+0=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[53, 19, 25, 19], Operations: [] Exploring Operation: 19+25=44, Resulting Numbers: [53, 19, 44] Generated Node #0,0: 53:[53, 19, 44] Operation: 19+25=44 Exploring Operation: 19+19=38, Resulting Numbers: [53, 25, 38] Generated Node #0,1: 53:[53, 25, 38] Operation: 19+19=38 Exploring Operation: 25+19=44, Resulting Numbers: [53, 19, 44] Generated Node #0,2: 53:[53, 19, 44] Operation: 25+19=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[53, 19, 44], Operations: ['19+25=44'] Exploring Operation: 19+44=63, Resulting Numbers: [53, 63] Generated Node #0,0,0: 53:[53, 63] Operation: 19+44=63 Exploring Operation: 53+19=72, Resulting Numbers: [44, 72] Generated Node #0,0,1: 53:[44, 72] Operation: 53+19=72 Exploring Operation: 53-19=34, Resulting Numbers: [44, 34] Generated Node #0,0,2: 53:[44, 34] Operation: 53-19=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 53:[53, 63], Operations: ['19+25=44', '19+44=63'] Exploring Operation: 63-53=10, Resulting Numbers: [10] 10,53 unequal: No Solution Exploring Operation: 53+63=116, Resulting Numbers: [116] 116,53 unequal: No Solution Exploring Operation: 53*63=3339, Resulting Numbers: [3339] 3339,53 unequal: No Solution No 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: 53:[44, 72], Operations: ['19+25=44', '53+19=72'] Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,53 unequal: No Solution Exploring Operation: 44*72=3168, Resulting Numbers: [3168] 3168,53 unequal: No Solution Exploring Operation: 44+72=116, Resulting Numbers: [116] 116,53 unequal: No Solution No 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: 53:[44, 34], Operations: ['19+25=44', '53-19=34'] Exploring Operation: 44*34=1496, Resulting Numbers: [1496] 1496,53 unequal: No Solution Exploring Operation: 44-34=10, Resulting Numbers: [10] 10,53 unequal: No Solution Exploring Operation: 44+34=78, Resulting Numbers: [78] 78,53 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: 53:[53, 25, 38], Operations: ['19+19=38'] Exploring Operation: 53+25=78, Resulting Numbers: [38, 78] Generated Node #0,1,0: 53:[38, 78] Operation: 53+25=78 Exploring Operation: 53-25=28, Resulting Numbers: [38, 28] Generated Node #0,1,1: 53:[38, 28] Operation: 53-25=28 Exploring Operation: 25+38=63, Resulting Numbers: [53, 63] Generated Node #0,1,2: 53:[53, 63] Operation: 25+38=63 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 53:[53, 63], Operations: ['19+19=38', '25+38=63'] Exploring Operation: 53+63=116, Resulting Numbers: [116] 116,53 unequal: No Solution Exploring Operation: 63-53=10, Resulting Numbers: [10] 10,53 unequal: No Solution Exploring Operation: 53*63=3339, Resulting Numbers: [3339] 3339,53 unequal: No Solution No 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: 53:[38, 78], Operations: ['19+19=38', '53+25=78'] Exploring Operation: 78-38=40, Resulting Numbers: [40] 40,53 unequal: No Solution Exploring Operation: 38+78=116, Resulting Numbers: [116] 116,53 unequal: No Solution Exploring Operation: 38*78=2964, Resulting Numbers: [2964] 2964,53 unequal: No Solution No 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: 53:[38, 28], Operations: ['19+19=38', '53-25=28'] Exploring Operation: 38-28=10, Resulting Numbers: [10] 10,53 unequal: No Solution Exploring Operation: 38*28=1064, Resulting Numbers: [1064] 1064,53 unequal: No Solution Exploring Operation: 38+28=66, Resulting Numbers: [66] 66,53 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: 53:[53, 19, 44], Operations: ['25+19=44'] Exploring Operation: 53-19=34, Resulting Numbers: [44, 34] Generated Node #0,2,0: 53:[44, 34] Operation: 53-19=34 Exploring Operation: 53+19=72, Resulting Numbers: [44, 72] Generated Node #0,2,1: 53:[44, 72] Operation: 53+19=72 Exploring Operation: 19+44=63, Resulting Numbers: [53, 63] Generated Node #0,2,2: 53:[53, 63] Operation: 19+44=63 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 53:[53, 63], Operations: ['25+19=44', '19+44=63'] Exploring Operation: 53+63=116, Resulting Numbers: [116] 116,53 unequal: No Solution Exploring Operation: 53*63=3339, Resulting Numbers: [3339] 3339,53 unequal: No Solution Exploring Operation: 63-53=10, Resulting Numbers: [10] 10,53 unequal: No Solution No 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: 53:[44, 34], Operations: ['25+19=44', '53-19=34'] Exploring Operation: 44+34=78, Resulting Numbers: [78] 78,53 unequal: No Solution Exploring Operation: 44-34=10, Resulting Numbers: [10] 10,53 unequal: No Solution Exploring Operation: 44*34=1496, Resulting Numbers: [1496] 1496,53 unequal: No Solution No 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: 53:[44, 72], Operations: ['25+19=44', '53+19=72'] Exploring Operation: 44+72=116, Resulting Numbers: [116] 116,53 unequal: No Solution Exploring Operation: 44*72=3168, Resulting Numbers: [3168] 3168,53 unequal: No Solution Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,53 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
[ 40, 34, 75, 89 ]
90
[ "40+34=74", "75+89=164", "164-74=90" ]
Current State: 90:[40, 34, 75, 89], Operations: [] Exploring Operation: 40+34=74, Resulting Numbers: [75, 89, 74] Generated Node #2: [75, 89, 74] from Operation: 40+34=74 Current State: 90:[75, 89, 74], Operations: ['40+34=74'] Exploring Operation: 75+89=164, Resulting Numbers: [74, 164] Generated Node #3: [74, 164] from Operation: 75+89=164 Current State: 90:[74, 164], Operations: ['40+34=74', '75+89=164'] Exploring Operation: 164-74=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[40, 34, 75, 89], Operations: [] Exploring Operation: 40-34=6, Resulting Numbers: [75, 89, 6] Generated Node #0,0: 90:[75, 89, 6] Operation: 40-34=6 Exploring Operation: 89-75=14, Resulting Numbers: [40, 34, 14] Generated Node #0,1: 90:[40, 34, 14] Operation: 89-75=14 Exploring Operation: 75-34=41, Resulting Numbers: [40, 89, 41] Generated Node #0,2: 90:[40, 89, 41] Operation: 75-34=41 Exploring Operation: 75-40=35, Resulting Numbers: [34, 89, 35] Generated Node #0,3: 90:[34, 89, 35] Operation: 75-40=35 Moving to Node #0,1 Current State: 90:[40, 34, 14], Operations: ['89-75=14'] Exploring Operation: 40-14=26, Resulting Numbers: [34, 26] Generated Node #0,1,0: 90:[34, 26] Operation: 40-14=26 Exploring Operation: 40-34=6, Resulting Numbers: [14, 6] Generated Node #0,1,1: 90:[14, 6] Operation: 40-34=6 Exploring Operation: 34-14=20, Resulting Numbers: [40, 20] Generated Node #0,1,2: 90:[40, 20] Operation: 34-14=20 Exploring Operation: 34+14=48, Resulting Numbers: [40, 48] Generated Node #0,1,3: 90:[40, 48] Operation: 34+14=48 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[14, 6], Operations: ['89-75=14', '40-34=6'] Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,90 unequal: No Solution Exploring Operation: 14*6=84, Resulting Numbers: [84] 84,90 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 90:[40, 20], Operations: ['89-75=14', '34-14=20'] Exploring Operation: 40+20=60, Resulting Numbers: [60] 60,90 unequal: No Solution Exploring Operation: 40/20=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 40*20=800, Resulting Numbers: [800] 800,90 unequal: No Solution Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[34, 26], Operations: ['89-75=14', '40-14=26'] Exploring Operation: 34*26=884, Resulting Numbers: [884] 884,90 unequal: No Solution Exploring Operation: 34+26=60, Resulting Numbers: [60] 60,90 unequal: No Solution Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 90:[40, 48], Operations: ['89-75=14', '34+14=48'] Exploring Operation: 40+48=88, Resulting Numbers: [88] 88,90 unequal: No Solution Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 40*48=1920, Resulting Numbers: [1920] 1920,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 90:[34, 89, 35], Operations: ['75-40=35'] Exploring Operation: 34+35=69, Resulting Numbers: [89, 69] Generated Node #0,3,0: 90:[89, 69] Operation: 34+35=69 Exploring Operation: 89-34=55, Resulting Numbers: [35, 55] Generated Node #0,3,1: 90:[35, 55] Operation: 89-34=55 Exploring Operation: 89-35=54, Resulting Numbers: [34, 54] Generated Node #0,3,2: 90:[34, 54] Operation: 89-35=54 Exploring Operation: 35-34=1, Resulting Numbers: [89, 1] Generated Node #0,3,3: 90:[89, 1] Operation: 35-34=1 Moving to Node #0,2 Current State: 90:[40, 89, 41], Operations: ['75-34=41'] Exploring Operation: 40+41=81, Resulting Numbers: [89, 81] Generated Node #0,2,0: 90:[89, 81] Operation: 40+41=81 Exploring Operation: 89-41=48, Resulting Numbers: [40, 48] Generated Node #0,2,1: 90:[40, 48] Operation: 89-41=48 Exploring Operation: 89-40=49, Resulting Numbers: [41, 49] Generated Node #0,2,2: 90:[41, 49] Operation: 89-40=49 Exploring Operation: 41-40=1, Resulting Numbers: [89, 1] Generated Node #0,2,3: 90:[89, 1] Operation: 41-40=1 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 90:[89, 1], Operations: ['75-34=41', '41-40=1'] Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,90 unequal: No Solution Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[40, 34, 75, 89], Operations: [] Exploring Operation: 75-34=41, Resulting Numbers: [40, 89, 41] Generated Node #0,2: 90:[40, 89, 41] Operation: 75-34=41 Moving to Node #0,2 Current State: 90:[40, 89, 41], Operations: ['75-34=41'] Exploring Operation: 41-40=1, Resulting Numbers: [89, 1] Generated Node #0,2,3: 90:[89, 1] Operation: 41-40=1 Moving to Node #0,2,3 Current State: 90:[89, 1], Operations: ['75-34=41', '41-40=1'] Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_4
sum_heuristic
[ 67, 5, 33, 27 ]
68
[ "67-5=62", "33-27=6", "62+6=68" ]
Current State: 68:[67, 5, 33, 27], Operations: [] Exploring Operation: 67-5=62, Resulting Numbers: [33, 27, 62] Generated Node #2: [33, 27, 62] from Operation: 67-5=62 Current State: 68:[33, 27, 62], Operations: ['67-5=62'] Exploring Operation: 33-27=6, Resulting Numbers: [62, 6] Generated Node #3: [62, 6] from Operation: 33-27=6 Current State: 68:[62, 6], Operations: ['67-5=62', '33-27=6'] Exploring Operation: 62+6=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[67, 5, 33, 27], Operations: [] Exploring Operation: 5+27=32, Resulting Numbers: [67, 33, 32] Generated Node #0,0: 68:[67, 33, 32] Operation: 5+27=32 Moving to Node #0,0 Current State: 68:[67, 33, 32], Operations: ['5+27=32'] Exploring Operation: 67-33=34, Resulting Numbers: [32, 34] Generated Node #0,0,0: 68:[32, 34] Operation: 67-33=34 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[32, 34], Operations: ['5+27=32', '67-33=34'] Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,68 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
[ 23, 91, 43, 20 ]
90
[ "43-23=20", "20/20=1", "91-1=90" ]
Current State: 90:[23, 91, 43, 20], Operations: [] Exploring Operation: 43-23=20, Resulting Numbers: [91, 20, 20] Generated Node #2: [91, 20, 20] from Operation: 43-23=20 Current State: 90:[91, 20, 20], Operations: ['43-23=20'] Exploring Operation: 20/20=1, Resulting Numbers: [91, 1] Generated Node #3: [91, 1] from Operation: 20/20=1 Current State: 90:[91, 1], Operations: ['43-23=20', '20/20=1'] Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[23, 91, 43, 20], Operations: [] Exploring Operation: 91-43=48, Resulting Numbers: [23, 20, 48] Generated Node #0,0: 90:[23, 20, 48] Operation: 91-43=48 Exploring Operation: 23+20=43, Resulting Numbers: [91, 43, 43] Generated Node #0,1: 90:[91, 43, 43] Operation: 23+20=43 Exploring Operation: 43-23=20, Resulting Numbers: [91, 20, 20] Generated Node #0,2: 90:[91, 20, 20] Operation: 43-23=20 Exploring Operation: 23-20=3, Resulting Numbers: [91, 43, 3] Generated Node #0,3: 90:[91, 43, 3] Operation: 23-20=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[91, 43, 3], Operations: ['23-20=3'] Exploring Operation: 91-43=48, Resulting Numbers: [3, 48] Generated Node #0,3,0: 90:[3, 48] Operation: 91-43=48 Exploring Operation: 43+3=46, Resulting Numbers: [91, 46] Generated Node #0,3,1: 90:[91, 46] Operation: 43+3=46 Exploring Operation: 91+3=94, Resulting Numbers: [43, 94] Generated Node #0,3,2: 90:[43, 94] Operation: 91+3=94 Exploring Operation: 91-3=88, Resulting Numbers: [43, 88] Generated Node #0,3,3: 90:[43, 88] Operation: 91-3=88 Moving to Node #0,3,1 Current State: 90:[91, 46], Operations: ['23-20=3', '43+3=46'] Exploring Operation: 91+46=137, Resulting Numbers: [137] 137,90 unequal: No Solution Exploring Operation: 91-46=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 91*46=4186, Resulting Numbers: [4186] 4186,90 unequal: No Solution Moving to Node #0,3,0 Current State: 90:[3, 48], Operations: ['23-20=3', '91-43=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,90 unequal: No Solution Exploring Operation: 3*48=144, Resulting Numbers: [144] 144,90 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,90 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,90 unequal: No Solution Moving to Node #0,3,3 Current State: 90:[43, 88], Operations: ['23-20=3', '91-3=88'] Exploring Operation: 43+88=131, Resulting Numbers: [131] 131,90 unequal: No Solution Exploring Operation: 88-43=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 43*88=3784, Resulting Numbers: [3784] 3784,90 unequal: No Solution Moving to Node #0,3,2 Current State: 90:[43, 94], Operations: ['23-20=3', '91+3=94'] Exploring Operation: 43*94=4042, Resulting Numbers: [4042] 4042,90 unequal: No Solution Exploring Operation: 94-43=51, Resulting Numbers: [51] 51,90 unequal: No Solution Exploring Operation: 43+94=137, Resulting Numbers: [137] 137,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[91, 43, 43], Operations: ['23+20=43'] Exploring Operation: 91-43=48, Resulting Numbers: [43, 48] Generated Node #0,1,0: 90:[43, 48] Operation: 91-43=48 Exploring Operation: 91-43=48, Resulting Numbers: [43, 48] Generated Node #0,1,1: 90:[43, 48] Operation: 91-43=48 Exploring Operation: 43-43=0, Resulting Numbers: [91, 0] Generated Node #0,1,2: 90:[91, 0] Operation: 43-43=0 Exploring Operation: 43/43=1, Resulting Numbers: [91, 1] Generated Node #0,1,3: 90:[91, 1] Operation: 43/43=1 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 90:[91, 1], Operations: ['23+20=43', '43/43=1'] Exploring Operation: 91+1=92, Resulting Numbers: [92] 92,90 unequal: No Solution Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[23, 91, 43, 20], Operations: [] Exploring Operation: 23+20=43, Resulting Numbers: [91, 43, 43] Generated Node #0,1: 90:[91, 43, 43] Operation: 23+20=43 Moving to Node #0,1 Current State: 90:[91, 43, 43], Operations: ['23+20=43'] Exploring Operation: 43/43=1, Resulting Numbers: [91, 1] Generated Node #0,1,3: 90:[91, 1] Operation: 43/43=1 Moving to Node #0,1,3 Current State: 90:[91, 1], Operations: ['23+20=43', '43/43=1'] Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 31, 2, 28, 56 ]
90
[ "31*2=62", "56-28=28", "62+28=90" ]
Current State: 90:[31, 2, 28, 56], Operations: [] Exploring Operation: 31*2=62, Resulting Numbers: [28, 56, 62] Generated Node #2: [28, 56, 62] from Operation: 31*2=62 Current State: 90:[28, 56, 62], Operations: ['31*2=62'] Exploring Operation: 56-28=28, Resulting Numbers: [62, 28] Generated Node #3: [62, 28] from Operation: 56-28=28 Current State: 90:[62, 28], Operations: ['31*2=62', '56-28=28'] Exploring Operation: 62+28=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[31, 2, 28, 56], Operations: [] Exploring Operation: 56/2=28, Resulting Numbers: [31, 28, 28] Generated Node #0,0: 90:[31, 28, 28] Operation: 56/2=28 Exploring Operation: 56/28=2, Resulting Numbers: [31, 2, 2] Generated Node #0,1: 90:[31, 2, 2] Operation: 56/28=2 Exploring Operation: 31+56=87, Resulting Numbers: [2, 28, 87] Generated Node #0,2: 90:[2, 28, 87] Operation: 31+56=87 Exploring Operation: 56-28=28, Resulting Numbers: [31, 2, 28] Generated Node #0,3: 90:[31, 2, 28] Operation: 56-28=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[31, 2, 2], Operations: ['56/28=2'] Exploring Operation: 2+2=4, Resulting Numbers: [31, 4] Generated Node #0,1,0: 90:[31, 4] Operation: 2+2=4 Exploring Operation: 31-2=29, Resulting Numbers: [2, 29] Generated Node #0,1,1: 90:[2, 29] Operation: 31-2=29 Exploring Operation: 2*2=4, Resulting Numbers: [31, 4] Generated Node #0,1,2: 90:[31, 4] Operation: 2*2=4 Exploring Operation: 31-2=29, Resulting Numbers: [2, 29] Generated Node #0,1,3: 90:[2, 29] Operation: 31-2=29 Moving to Node #0,1,1 Current State: 90:[2, 29], Operations: ['56/28=2', '31-2=29'] Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,90 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,90 unequal: No Solution Moving to Node #0,1,3 Current State: 90:[2, 29], Operations: ['56/28=2', '31-2=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,90 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,90 unequal: No Solution Moving to Node #0,1,2 Current State: 90:[31, 4], Operations: ['56/28=2', '2*2=4'] Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,90 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[31, 4], Operations: ['56/28=2', '2+2=4'] Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,90 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,90 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 #0,3 Current State: 90:[31, 2, 28], Operations: ['56-28=28'] Exploring Operation: 31-28=3, Resulting Numbers: [2, 3] Generated Node #0,3,0: 90:[2, 3] Operation: 31-28=3 Exploring Operation: 2+28=30, Resulting Numbers: [31, 30] Generated Node #0,3,1: 90:[31, 30] Operation: 2+28=30 Exploring Operation: 28/2=14, Resulting Numbers: [31, 14] Generated Node #0,3,2: 90:[31, 14] Operation: 28/2=14 Exploring Operation: 31-2=29, Resulting Numbers: [28, 29] Generated Node #0,3,3: 90:[28, 29] Operation: 31-2=29 Moving to Node #0,3,0 Current State: 90:[2, 3], Operations: ['56-28=28', '31-28=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,90 unequal: No Solution Moving to Node #0,3,1 Current State: 90:[31, 30], Operations: ['56-28=28', '2+28=30'] Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 31*30=930, Resulting Numbers: [930] 930,90 unequal: No Solution Exploring Operation: 31+30=61, Resulting Numbers: [61] 61,90 unequal: No Solution Moving to Node #0,3,2 Current State: 90:[31, 14], Operations: ['56-28=28', '28/2=14'] Exploring Operation: 31*14=434, Resulting Numbers: [434] 434,90 unequal: No Solution Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,90 unequal: No Solution Exploring Operation: 31+14=45, Resulting Numbers: [45] 45,90 unequal: No Solution Moving to Node #0,3,3 Current State: 90:[28, 29], Operations: ['56-28=28', '31-2=29'] Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 28*29=812, Resulting Numbers: [812] 812,90 unequal: No Solution Exploring Operation: 28+29=57, Resulting Numbers: [57] 57,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[31, 28, 28], Operations: ['56/2=28'] Exploring Operation: 31-28=3, Resulting Numbers: [28, 3] Generated Node #0,0,0: 90:[28, 3] Operation: 31-28=3 Exploring Operation: 28-28=0, Resulting Numbers: [31, 0] Generated Node #0,0,1: 90:[31, 0] Operation: 28-28=0 Exploring Operation: 28/28=1, Resulting Numbers: [31, 1] Generated Node #0,0,2: 90:[31, 1] Operation: 28/28=1 Exploring Operation: 31-28=3, Resulting Numbers: [28, 3] Generated Node #0,0,3: 90:[28, 3] Operation: 31-28=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[28, 3], Operations: ['56/2=28', '31-28=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,90 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,90 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:[31, 1], Operations: ['56/2=28', '28/28=1'] Exploring Operation: 31-1=30, Resulting Numbers: [30] 30,90 unequal: No Solution Exploring Operation: 31+1=32, Resulting Numbers: [32] 32,90 unequal: No Solution Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 31*1=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 #0,0,3 Current State: 90:[28, 3], Operations: ['56/2=28', '31-28=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,90 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,90 unequal: No Solution Exploring Operation: 28+3=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 #0,0,1 Current State: 90:[31, 0], Operations: ['56/2=28', '28-28=0'] Exploring Operation: 31*0=0, Resulting Numbers: [0] 0,90 unequal: No Solution Exploring Operation: 31-0=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 31+0=31, Resulting Numbers: [31] 31,90 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:[2, 28, 87], Operations: ['31+56=87'] Exploring Operation: 28-2=26, Resulting Numbers: [87, 26] Generated Node #0,2,0: 90:[87, 26] Operation: 28-2=26 Exploring Operation: 2+28=30, Resulting Numbers: [87, 30] Generated Node #0,2,1: 90:[87, 30] Operation: 2+28=30 Exploring Operation: 2+87=89, Resulting Numbers: [28, 89] Generated Node #0,2,2: 90:[28, 89] Operation: 2+87=89 Exploring Operation: 28/2=14, Resulting Numbers: [87, 14] Generated Node #0,2,3: 90:[87, 14] Operation: 28/2=14 Moving to Node #0,2,1 Current State: 90:[87, 30], Operations: ['31+56=87', '2+28=30'] Exploring Operation: 87+30=117, Resulting Numbers: [117] 117,90 unequal: No Solution Exploring Operation: 87*30=2610, Resulting Numbers: [2610] 2610,90 unequal: No Solution Exploring Operation: 87-30=57, Resulting Numbers: [57] 57,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[28, 89], Operations: ['31+56=87', '2+87=89'] Exploring Operation: 89-28=61, Resulting Numbers: [61] 61,90 unequal: No Solution Exploring Operation: 28*89=2492, Resulting Numbers: [2492] 2492,90 unequal: No Solution Exploring Operation: 28+89=117, Resulting Numbers: [117] 117,90 unequal: No Solution Moving to Node #0,2,3 Current State: 90:[87, 14], Operations: ['31+56=87', '28/2=14'] Exploring Operation: 87*14=1218, Resulting Numbers: [1218] 1218,90 unequal: No Solution Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,90 unequal: No Solution Exploring Operation: 87+14=101, Resulting Numbers: [101] 101,90 unequal: No Solution Moving to Node #0,2,0 Current State: 90:[87, 26], Operations: ['31+56=87', '28-2=26'] Exploring Operation: 87+26=113, Resulting Numbers: [113] 113,90 unequal: No Solution Exploring Operation: 87-26=61, Resulting Numbers: [61] 61,90 unequal: No Solution Exploring Operation: 87*26=2262, Resulting Numbers: [2262] 2262,90 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
[ 61, 80, 91, 46 ]
26
[ "80-61=19", "91-46=45", "45-19=26" ]
Current State: 26:[61, 80, 91, 46], Operations: [] Exploring Operation: 80-61=19, Resulting Numbers: [91, 46, 19] Generated Node #2: [91, 46, 19] from Operation: 80-61=19 Current State: 26:[91, 46, 19], Operations: ['80-61=19'] Exploring Operation: 91-46=45, Resulting Numbers: [19, 45] Generated Node #3: [19, 45] from Operation: 91-46=45 Current State: 26:[19, 45], Operations: ['80-61=19', '91-46=45'] Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[61, 80, 91, 46], Operations: [] Exploring Operation: 91-46=45, Resulting Numbers: [61, 80, 45] Generated Node #0,0: 26:[61, 80, 45] Operation: 91-46=45 Exploring Operation: 91-80=11, Resulting Numbers: [61, 46, 11] Generated Node #0,1: 26:[61, 46, 11] Operation: 91-80=11 Exploring Operation: 80-46=34, Resulting Numbers: [61, 91, 34] Generated Node #0,2: 26:[61, 91, 34] Operation: 80-46=34 Exploring Operation: 80-61=19, Resulting Numbers: [91, 46, 19] Generated Node #0,3: 26:[91, 46, 19] Operation: 80-61=19 Exploring Operation: 91-61=30, Resulting Numbers: [80, 46, 30] Generated Node #0,4: 26:[80, 46, 30] Operation: 91-61=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[61, 46, 11], Operations: ['91-80=11'] Exploring Operation: 61+11=72, Resulting Numbers: [46, 72] Generated Node #0,1,0: 26:[46, 72] Operation: 61+11=72 Exploring Operation: 46-11=35, Resulting Numbers: [61, 35] Generated Node #0,1,1: 26:[61, 35] Operation: 46-11=35 Exploring Operation: 46+11=57, Resulting Numbers: [61, 57] Generated Node #0,1,2: 26:[61, 57] Operation: 46+11=57 Exploring Operation: 61-46=15, Resulting Numbers: [11, 15] Generated Node #0,1,3: 26:[11, 15] Operation: 61-46=15 Exploring Operation: 61-11=50, Resulting Numbers: [46, 50] Generated Node #0,1,4: 26:[46, 50] Operation: 61-11=50 Moving to Node #0,1,3 Current State: 26:[11, 15], Operations: ['91-80=11', '61-46=15'] Exploring Operation: 11+15=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[61, 80, 91, 46], Operations: [] Exploring Operation: 91-80=11, Resulting Numbers: [61, 46, 11] Generated Node #0,1: 26:[61, 46, 11] Operation: 91-80=11 Moving to Node #0,1 Current State: 26:[61, 46, 11], Operations: ['91-80=11'] Exploring Operation: 61-46=15, Resulting Numbers: [11, 15] Generated Node #0,1,3: 26:[11, 15] Operation: 61-46=15 Moving to Node #0,1,3 Current State: 26:[11, 15], Operations: ['91-80=11', '61-46=15'] Exploring Operation: 11+15=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 5, 14, 4, 6 ]
11
[ "5*14=70", "70-4=66", "66/6=11" ]
Current State: 11:[5, 14, 4, 6], Operations: [] Exploring Operation: 5*14=70, Resulting Numbers: [4, 6, 70] Generated Node #2: [4, 6, 70] from Operation: 5*14=70 Current State: 11:[4, 6, 70], Operations: ['5*14=70'] Exploring Operation: 70-4=66, Resulting Numbers: [6, 66] Generated Node #3: [6, 66] from Operation: 70-4=66 Current State: 11:[6, 66], Operations: ['5*14=70', '70-4=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[5, 14, 4, 6], Operations: [] Exploring Operation: 5+6=11, Resulting Numbers: [14, 4, 11] Generated Node #0,0: 11:[14, 4, 11] Operation: 5+6=11 Exploring Operation: 5+4=9, Resulting Numbers: [14, 6, 9] Generated Node #0,1: 11:[14, 6, 9] Operation: 5+4=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[14, 4, 11], Operations: ['5+6=11'] Exploring Operation: 14-4=10, Resulting Numbers: [11, 10] Generated Node #0,0,0: 11:[11, 10] Operation: 14-4=10 Exploring Operation: 14+4=18, Resulting Numbers: [11, 18] Generated Node #0,0,1: 11:[11, 18] Operation: 14+4=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[11, 10], Operations: ['5+6=11', '14-4=10'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 11+10=21, Resulting Numbers: [21] 21,11 unequal: No Solution No 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: 11:[11, 18], Operations: ['5+6=11', '14+4=18'] Exploring Operation: 11+18=29, Resulting Numbers: [29] 29,11 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,11 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: 11:[14, 6, 9], Operations: ['5+4=9'] Exploring Operation: 14-6=8, Resulting Numbers: [9, 8] Generated Node #0,1,0: 11:[9, 8] Operation: 14-6=8 Exploring Operation: 6+9=15, Resulting Numbers: [14, 15] Generated Node #0,1,1: 11:[14, 15] Operation: 6+9=15 Moving to Node #0,1,0 Current State: 11:[9, 8], Operations: ['5+4=9', '14-6=8'] Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,11 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[14, 15], Operations: ['5+4=9', '6+9=15'] Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,11 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
[ 25, 26, 58, 60 ]
12
[ "60-58=2", "26/2=13", "25-13=12" ]
Current State: 12:[25, 26, 58, 60], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [25, 26, 2] Generated Node #2: [25, 26, 2] from Operation: 60-58=2 Current State: 12:[25, 26, 2], Operations: ['60-58=2'] Exploring Operation: 26/2=13, Resulting Numbers: [25, 13] Generated Node #3: [25, 13] from Operation: 26/2=13 Current State: 12:[25, 13], Operations: ['60-58=2', '26/2=13'] Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[25, 26, 58, 60], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [25, 26, 2] Generated Node #0,0: 12:[25, 26, 2] Operation: 60-58=2 Moving to Node #0,0 Current State: 12:[25, 26, 2], Operations: ['60-58=2'] Exploring Operation: 26-25=1, Resulting Numbers: [2, 1] Generated Node #0,0,0: 12:[2, 1] Operation: 26-25=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[2, 1], Operations: ['60-58=2', '26-25=1'] Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,12 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
[ 92, 28, 57, 65 ]
57
[ "92-28=64", "65-64=1", "57*1=57" ]
Current State: 57:[92, 28, 57, 65], Operations: [] Exploring Operation: 92-28=64, Resulting Numbers: [57, 65, 64] Generated Node #2: [57, 65, 64] from Operation: 92-28=64 Current State: 57:[57, 65, 64], Operations: ['92-28=64'] Exploring Operation: 65-64=1, Resulting Numbers: [57, 1] Generated Node #3: [57, 1] from Operation: 65-64=1 Current State: 57:[57, 1], Operations: ['92-28=64', '65-64=1'] Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[92, 28, 57, 65], Operations: [] Exploring Operation: 92-65=27, Resulting Numbers: [28, 57, 27] Generated Node #0,0: 57:[28, 57, 27] Operation: 92-65=27 Exploring Operation: 92-28=64, Resulting Numbers: [57, 65, 64] Generated Node #0,1: 57:[57, 65, 64] Operation: 92-28=64 Exploring Operation: 92-57=35, Resulting Numbers: [28, 65, 35] Generated Node #0,2: 57:[28, 65, 35] Operation: 92-57=35 Moving to Node #0,1 Current State: 57:[57, 65, 64], Operations: ['92-28=64'] Exploring Operation: 65-57=8, Resulting Numbers: [64, 8] Generated Node #0,1,0: 57:[64, 8] Operation: 65-57=8 Exploring Operation: 65-64=1, Resulting Numbers: [57, 1] Generated Node #0,1,1: 57:[57, 1] Operation: 65-64=1 Exploring Operation: 64-57=7, Resulting Numbers: [65, 7] Generated Node #0,1,2: 57:[65, 7] Operation: 64-57=7 Moving to Node #0,0 Current State: 57:[28, 57, 27], Operations: ['92-65=27'] Exploring Operation: 28+27=55, Resulting Numbers: [57, 55] Generated Node #0,0,0: 57:[57, 55] Operation: 28+27=55 Exploring Operation: 57-28=29, Resulting Numbers: [27, 29] Generated Node #0,0,1: 57:[27, 29] Operation: 57-28=29 Exploring Operation: 28-27=1, Resulting Numbers: [57, 1] Generated Node #0,0,2: 57:[57, 1] Operation: 28-27=1 Moving to Node #0,2 Current State: 57:[28, 65, 35], Operations: ['92-57=35'] Exploring Operation: 65-35=30, Resulting Numbers: [28, 30] Generated Node #0,2,0: 57:[28, 30] Operation: 65-35=30 Exploring Operation: 28+35=63, Resulting Numbers: [65, 63] Generated Node #0,2,1: 57:[65, 63] Operation: 28+35=63 Exploring Operation: 35-28=7, Resulting Numbers: [65, 7] Generated Node #0,2,2: 57:[65, 7] Operation: 35-28=7 Moving to Node #0,1,1 Current State: 57:[57, 1], Operations: ['92-28=64', '65-64=1'] Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,57 unequal: No Solution Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[92, 28, 57, 65], Operations: [] Exploring Operation: 92-28=64, Resulting Numbers: [57, 65, 64] Generated Node #0,1: 57:[57, 65, 64] Operation: 92-28=64 Moving to Node #0,1 Current State: 57:[57, 65, 64], Operations: ['92-28=64'] Exploring Operation: 65-64=1, Resulting Numbers: [57, 1] Generated Node #0,1,1: 57:[57, 1] Operation: 65-64=1 Moving to Node #0,1,1 Current State: 57:[57, 1], Operations: ['92-28=64', '65-64=1'] Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
0.984375
hs_3
mult_heuristic
[ 25, 93, 23, 46 ]
49
[ "25+93=118", "23+46=69", "118-69=49" ]
Current State: 49:[25, 93, 23, 46], Operations: [] Exploring Operation: 25+93=118, Resulting Numbers: [23, 46, 118] Generated Node #2: [23, 46, 118] from Operation: 25+93=118 Current State: 49:[23, 46, 118], Operations: ['25+93=118'] Exploring Operation: 23+46=69, Resulting Numbers: [118, 69] Generated Node #3: [118, 69] from Operation: 23+46=69 Current State: 49:[118, 69], Operations: ['25+93=118', '23+46=69'] Exploring Operation: 118-69=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[25, 93, 23, 46], Operations: [] Exploring Operation: 93-25=68, Resulting Numbers: [23, 46, 68] Generated Node #0,0: 49:[23, 46, 68] Operation: 93-25=68 Exploring Operation: 93-46=47, Resulting Numbers: [25, 23, 47] Generated Node #0,1: 49:[25, 23, 47] Operation: 93-46=47 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[25, 23, 47], Operations: ['93-46=47'] Exploring Operation: 25+23=48, Resulting Numbers: [47, 48] Generated Node #0,1,0: 49:[47, 48] Operation: 25+23=48 Exploring Operation: 25-23=2, Resulting Numbers: [47, 2] Generated Node #0,1,1: 49:[47, 2] Operation: 25-23=2 Moving to Node #0,1,0 Current State: 49:[47, 48], Operations: ['93-46=47', '25+23=48'] Exploring Operation: 48-47=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 47+48=95, Resulting Numbers: [95] 95,49 unequal: No Solution Moving to Node #0,1,1 Current State: 49:[47, 2], Operations: ['93-46=47', '25-23=2'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,49 unequal: No Solution Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[25, 93, 23, 46], Operations: [] Exploring Operation: 93-46=47, Resulting Numbers: [25, 23, 47] Generated Node #0,1: 49:[25, 23, 47] Operation: 93-46=47 Moving to Node #0,1 Current State: 49:[25, 23, 47], Operations: ['93-46=47'] Exploring Operation: 25-23=2, Resulting Numbers: [47, 2] Generated Node #0,1,1: 49:[47, 2] Operation: 25-23=2 Moving to Node #0,1,1 Current State: 49:[47, 2], Operations: ['93-46=47', '25-23=2'] Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 90, 60, 8, 38 ]
69
[ "8+38=46", "90*46=4140", "4140/60=69" ]
Current State: 69:[90, 60, 8, 38], Operations: [] Exploring Operation: 8+38=46, Resulting Numbers: [90, 60, 46] Generated Node #2: [90, 60, 46] from Operation: 8+38=46 Current State: 69:[90, 60, 46], Operations: ['8+38=46'] Exploring Operation: 90*46=4140, Resulting Numbers: [60, 4140] Generated Node #3: [60, 4140] from Operation: 90*46=4140 Current State: 69:[60, 4140], Operations: ['8+38=46', '90*46=4140'] Exploring Operation: 4140/60=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[90, 60, 8, 38], Operations: [] Exploring Operation: 90-60=30, Resulting Numbers: [8, 38, 30] Generated Node #0,0: 69:[8, 38, 30] Operation: 90-60=30 Moving to Node #0,0 Current State: 69:[8, 38, 30], Operations: ['90-60=30'] Exploring Operation: 38+30=68, Resulting Numbers: [8, 68] Generated Node #0,0,0: 69:[8, 68] Operation: 38+30=68 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[8, 68], Operations: ['90-60=30', '38+30=68'] Exploring Operation: 8+68=76, Resulting Numbers: [76] 76,69 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
[ 91, 10, 20, 8 ]
97
[ "91+8=99", "20/10=2", "99-2=97" ]
Current State: 97:[91, 10, 20, 8], Operations: [] Exploring Operation: 91+8=99, Resulting Numbers: [10, 20, 99] Generated Node #2: [10, 20, 99] from Operation: 91+8=99 Current State: 97:[10, 20, 99], Operations: ['91+8=99'] Exploring Operation: 20/10=2, Resulting Numbers: [99, 2] Generated Node #3: [99, 2] from Operation: 20/10=2 Current State: 97:[99, 2], Operations: ['91+8=99', '20/10=2'] Exploring Operation: 99-2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[91, 10, 20, 8], Operations: [] Exploring Operation: 20*8=160, Resulting Numbers: [91, 10, 160] Generated Node #0,0: 97:[91, 10, 160] Operation: 20*8=160 Exploring Operation: 10+8=18, Resulting Numbers: [91, 20, 18] Generated Node #0,1: 97:[91, 20, 18] Operation: 10+8=18 Exploring Operation: 10*8=80, Resulting Numbers: [91, 20, 80] Generated Node #0,2: 97:[91, 20, 80] Operation: 10*8=80 Exploring Operation: 10+20=30, Resulting Numbers: [91, 8, 30] Generated Node #0,3: 97:[91, 8, 30] Operation: 10+20=30 Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[91, 20, 80], Operations: ['10*8=80'] Exploring Operation: 91-20=71, Resulting Numbers: [80, 71] Generated Node #0,2,0: 97:[80, 71] Operation: 91-20=71 Exploring Operation: 80-20=60, Resulting Numbers: [91, 60] Generated Node #0,2,1: 97:[91, 60] Operation: 80-20=60 Exploring Operation: 91+20=111, Resulting Numbers: [80, 111] Generated Node #0,2,2: 97:[80, 111] Operation: 91+20=111 Exploring Operation: 20+80=100, Resulting Numbers: [91, 100] Generated Node #0,2,3: 97:[91, 100] Operation: 20+80=100 Moving to Node #0,2,3 Current State: 97:[91, 100], Operations: ['10*8=80', '20+80=100'] Exploring Operation: 100-91=9, Resulting Numbers: [9] 9,97 unequal: No Solution Exploring Operation: 91*100=9100, Resulting Numbers: [9100] 9100,97 unequal: No Solution Exploring Operation: 91+100=191, Resulting Numbers: [191] 191,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[80, 111], Operations: ['10*8=80', '91+20=111'] Exploring Operation: 111-80=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 80+111=191, Resulting Numbers: [191] 191,97 unequal: No Solution Exploring Operation: 80*111=8880, Resulting Numbers: [8880] 8880,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[91, 60], Operations: ['10*8=80', '80-20=60'] Exploring Operation: 91+60=151, Resulting Numbers: [151] 151,97 unequal: No Solution Exploring Operation: 91*60=5460, Resulting Numbers: [5460] 5460,97 unequal: No Solution Exploring Operation: 91-60=31, Resulting Numbers: [31] 31,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[80, 71], Operations: ['10*8=80', '91-20=71'] Exploring Operation: 80+71=151, Resulting Numbers: [151] 151,97 unequal: No Solution Exploring Operation: 80-71=9, Resulting Numbers: [9] 9,97 unequal: No Solution Exploring Operation: 80*71=5680, Resulting Numbers: [5680] 5680,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[91, 10, 160], Operations: ['20*8=160'] Exploring Operation: 160-10=150, Resulting Numbers: [91, 150] Generated Node #0,0,0: 97:[91, 150] Operation: 160-10=150 Exploring Operation: 10+160=170, Resulting Numbers: [91, 170] Generated Node #0,0,1: 97:[91, 170] Operation: 10+160=170 Exploring Operation: 91-10=81, Resulting Numbers: [160, 81] Generated Node #0,0,2: 97:[160, 81] Operation: 91-10=81 Exploring Operation: 91+10=101, Resulting Numbers: [160, 101] Generated Node #0,0,3: 97:[160, 101] Operation: 91+10=101 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[91, 150], Operations: ['20*8=160', '160-10=150'] Exploring Operation: 91+150=241, Resulting Numbers: [241] 241,97 unequal: No Solution Exploring Operation: 150-91=59, Resulting Numbers: [59] 59,97 unequal: No Solution Exploring Operation: 91*150=13650, Resulting Numbers: [13650] 13650,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 97:[160, 101], Operations: ['20*8=160', '91+10=101'] Exploring Operation: 160-101=59, Resulting Numbers: [59] 59,97 unequal: No Solution Exploring Operation: 160*101=16160, Resulting Numbers: [16160] 16160,97 unequal: No Solution Exploring Operation: 160+101=261, Resulting Numbers: [261] 261,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 97:[91, 170], Operations: ['20*8=160', '10+160=170'] Exploring Operation: 170-91=79, Resulting Numbers: [79] 79,97 unequal: No Solution Exploring Operation: 91+170=261, Resulting Numbers: [261] 261,97 unequal: No Solution Exploring Operation: 91*170=15470, Resulting Numbers: [15470] 15470,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 97:[160, 81], Operations: ['20*8=160', '91-10=81'] Exploring Operation: 160-81=79, Resulting Numbers: [79] 79,97 unequal: No Solution Exploring Operation: 160+81=241, Resulting Numbers: [241] 241,97 unequal: No Solution Exploring Operation: 160*81=12960, Resulting Numbers: [12960] 12960,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[91, 20, 18], Operations: ['10+8=18'] Exploring Operation: 91+20=111, Resulting Numbers: [18, 111] Generated Node #0,1,0: 97:[18, 111] Operation: 91+20=111 Exploring Operation: 91-18=73, Resulting Numbers: [20, 73] Generated Node #0,1,1: 97:[20, 73] Operation: 91-18=73 Exploring Operation: 20+18=38, Resulting Numbers: [91, 38] Generated Node #0,1,2: 97:[91, 38] Operation: 20+18=38 Exploring Operation: 91+18=109, Resulting Numbers: [20, 109] Generated Node #0,1,3: 97:[20, 109] Operation: 91+18=109 Moving to Node #0,1,2 Current State: 97:[91, 38], Operations: ['10+8=18', '20+18=38'] Exploring Operation: 91*38=3458, Resulting Numbers: [3458] 3458,97 unequal: No Solution Exploring Operation: 91+38=129, Resulting Numbers: [129] 129,97 unequal: No Solution Exploring Operation: 91-38=53, Resulting Numbers: [53] 53,97 unequal: No Solution Moving to Node #0,1,3 Current State: 97:[20, 109], Operations: ['10+8=18', '91+18=109'] Exploring Operation: 20+109=129, Resulting Numbers: [129] 129,97 unequal: No Solution Exploring Operation: 109-20=89, Resulting Numbers: [89] 89,97 unequal: No Solution Exploring Operation: 20*109=2180, Resulting Numbers: [2180] 2180,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[18, 111], Operations: ['10+8=18', '91+20=111'] Exploring Operation: 111-18=93, Resulting Numbers: [93] 93,97 unequal: No Solution Exploring Operation: 18*111=1998, Resulting Numbers: [1998] 1998,97 unequal: No Solution Exploring Operation: 18+111=129, Resulting Numbers: [129] 129,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[20, 73], Operations: ['10+8=18', '91-18=73'] Exploring Operation: 73-20=53, Resulting Numbers: [53] 53,97 unequal: No Solution Exploring Operation: 20*73=1460, Resulting Numbers: [1460] 1460,97 unequal: No Solution Exploring Operation: 20+73=93, Resulting Numbers: [93] 93,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 97:[91, 8, 30], Operations: ['10+20=30'] Exploring Operation: 91+8=99, Resulting Numbers: [30, 99] Generated Node #0,3,0: 97:[30, 99] Operation: 91+8=99 Exploring Operation: 30-8=22, Resulting Numbers: [91, 22] Generated Node #0,3,1: 97:[91, 22] Operation: 30-8=22 Exploring Operation: 91-8=83, Resulting Numbers: [30, 83] Generated Node #0,3,2: 97:[30, 83] Operation: 91-8=83 Exploring Operation: 8+30=38, Resulting Numbers: [91, 38] Generated Node #0,3,3: 97:[91, 38] Operation: 8+30=38 Moving to Node #0,3,3 Current State: 97:[91, 38], Operations: ['10+20=30', '8+30=38'] Exploring Operation: 91*38=3458, Resulting Numbers: [3458] 3458,97 unequal: No Solution Exploring Operation: 91+38=129, Resulting Numbers: [129] 129,97 unequal: No Solution Exploring Operation: 91-38=53, Resulting Numbers: [53] 53,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[30, 99], Operations: ['10+20=30', '91+8=99'] Exploring Operation: 30+99=129, Resulting Numbers: [129] 129,97 unequal: No Solution Exploring Operation: 99-30=69, Resulting Numbers: [69] 69,97 unequal: No Solution Exploring Operation: 30*99=2970, Resulting Numbers: [2970] 2970,97 unequal: No Solution Moving to Node #0,3,2 Current State: 97:[30, 83], Operations: ['10+20=30', '91-8=83'] Exploring Operation: 83-30=53, Resulting Numbers: [53] 53,97 unequal: No Solution Exploring Operation: 30*83=2490, Resulting Numbers: [2490] 2490,97 unequal: No Solution Exploring Operation: 30+83=113, Resulting Numbers: [113] 113,97 unequal: No Solution Moving to Node #0,3,1 Current State: 97:[91, 22], Operations: ['10+20=30', '30-8=22'] Exploring Operation: 91+22=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 91*22=2002, Resulting Numbers: [2002] 2002,97 unequal: No Solution Exploring Operation: 91-22=69, Resulting Numbers: [69] 69,97 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
[ 84, 2, 5, 43 ]
72
[ "84-5=79", "79-43=36", "2*36=72" ]
Current State: 72:[84, 2, 5, 43], Operations: [] Exploring Operation: 84-5=79, Resulting Numbers: [2, 43, 79] Generated Node #2: [2, 43, 79] from Operation: 84-5=79 Current State: 72:[2, 43, 79], Operations: ['84-5=79'] Exploring Operation: 79-43=36, Resulting Numbers: [2, 36] Generated Node #3: [2, 36] from Operation: 79-43=36 Current State: 72:[2, 36], Operations: ['84-5=79', '79-43=36'] Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[84, 2, 5, 43], Operations: [] Exploring Operation: 84-43=41, Resulting Numbers: [2, 5, 41] Generated Node #0,0: 72:[2, 5, 41] Operation: 84-43=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[2, 5, 41], Operations: ['84-43=41'] Exploring Operation: 41-5=36, Resulting Numbers: [2, 36] Generated Node #0,0,0: 72:[2, 36] Operation: 41-5=36 Moving to Node #0,0,0 Current State: 72:[2, 36], Operations: ['84-43=41', '41-5=36'] Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[84, 2, 5, 43], Operations: [] Exploring Operation: 84-43=41, Resulting Numbers: [2, 5, 41] Generated Node #0,0: 72:[2, 5, 41] Operation: 84-43=41 Moving to Node #0,0 Current State: 72:[2, 5, 41], Operations: ['84-43=41'] Exploring Operation: 41-5=36, Resulting Numbers: [2, 36] Generated Node #0,0,0: 72:[2, 36] Operation: 41-5=36 Moving to Node #0,0,0 Current State: 72:[2, 36], Operations: ['84-43=41', '41-5=36'] Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 4, 37, 25, 2 ]
27
[ "37+25=62", "62/2=31", "31-4=27" ]
Current State: 27:[4, 37, 25, 2], Operations: [] Exploring Operation: 37+25=62, Resulting Numbers: [4, 2, 62] Generated Node #2: [4, 2, 62] from Operation: 37+25=62 Current State: 27:[4, 2, 62], Operations: ['37+25=62'] Exploring Operation: 62/2=31, Resulting Numbers: [4, 31] Generated Node #3: [4, 31] from Operation: 62/2=31 Current State: 27:[4, 31], Operations: ['37+25=62', '62/2=31'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[4, 37, 25, 2], Operations: [] Exploring Operation: 37-25=12, Resulting Numbers: [4, 2, 12] Generated Node #0,0: 27:[4, 2, 12] Operation: 37-25=12 Exploring Operation: 37-4=33, Resulting Numbers: [25, 2, 33] Generated Node #0,1: 27:[25, 2, 33] Operation: 37-4=33 Exploring Operation: 37-2=35, Resulting Numbers: [4, 25, 35] Generated Node #0,2: 27:[4, 25, 35] Operation: 37-2=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[4, 2, 12], Operations: ['37-25=12'] Exploring Operation: 12-2=10, Resulting Numbers: [4, 10] Generated Node #0,0,0: 27:[4, 10] Operation: 12-2=10 Exploring Operation: 12-4=8, Resulting Numbers: [2, 8] Generated Node #0,0,1: 27:[2, 8] Operation: 12-4=8 Exploring Operation: 12/4=3, Resulting Numbers: [2, 3] Generated Node #0,0,2: 27:[2, 3] Operation: 12/4=3 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 27:[2, 3], Operations: ['37-25=12', '12/4=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,27 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,27 unequal: No Solution No 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: 27:[4, 10], Operations: ['37-25=12', '12-2=10'] Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,27 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,27 unequal: No Solution No 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: 27:[2, 8], Operations: ['37-25=12', '12-4=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,27 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,27 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: 27:[25, 2, 33], Operations: ['37-4=33'] Exploring Operation: 25+2=27, Resulting Numbers: [33, 27] Generated Node #0,1,0: 27:[33, 27] Operation: 25+2=27 Exploring Operation: 33-2=31, Resulting Numbers: [25, 31] Generated Node #0,1,1: 27:[25, 31] Operation: 33-2=31 Exploring Operation: 33-25=8, Resulting Numbers: [2, 8] Generated Node #0,1,2: 27:[2, 8] Operation: 33-25=8 Moving to Node #0,1,2 Current State: 27:[2, 8], Operations: ['37-4=33', '33-25=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,27 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,27 unequal: No Solution Moving to Node #0,1,0 Current State: 27:[33, 27], Operations: ['37-4=33', '25+2=27'] Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,27 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,27 unequal: No Solution Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[25, 31], Operations: ['37-4=33', '33-2=31'] Exploring Operation: 25+31=56, Resulting Numbers: [56] 56,27 unequal: No Solution Exploring Operation: 25*31=775, Resulting Numbers: [775] 775,27 unequal: No Solution Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[4, 25, 35], Operations: ['37-2=35'] Exploring Operation: 35-4=31, Resulting Numbers: [25, 31] Generated Node #0,2,0: 27:[25, 31] Operation: 35-4=31 Exploring Operation: 35-25=10, Resulting Numbers: [4, 10] Generated Node #0,2,1: 27:[4, 10] Operation: 35-25=10 Exploring Operation: 4+25=29, Resulting Numbers: [35, 29] Generated Node #0,2,2: 27:[35, 29] Operation: 4+25=29 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 27:[4, 10], Operations: ['37-2=35', '35-25=10'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,27 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,27 unequal: No Solution Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,27 unequal: No Solution No 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: 27:[25, 31], Operations: ['37-2=35', '35-4=31'] Exploring Operation: 25*31=775, Resulting Numbers: [775] 775,27 unequal: No Solution Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,27 unequal: No Solution Exploring Operation: 25+31=56, Resulting Numbers: [56] 56,27 unequal: No Solution No 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: 27:[35, 29], Operations: ['37-2=35', '4+25=29'] Exploring Operation: 35*29=1015, Resulting Numbers: [1015] 1015,27 unequal: No Solution Exploring Operation: 35+29=64, Resulting Numbers: [64] 64,27 unequal: No Solution Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,27 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
[ 59, 89, 80, 10 ]
59
[ "89-80=9", "10-9=1", "59*1=59" ]
Current State: 59:[59, 89, 80, 10], Operations: [] Exploring Operation: 89-80=9, Resulting Numbers: [59, 10, 9] Generated Node #2: [59, 10, 9] from Operation: 89-80=9 Current State: 59:[59, 10, 9], Operations: ['89-80=9'] Exploring Operation: 10-9=1, Resulting Numbers: [59, 1] Generated Node #3: [59, 1] from Operation: 10-9=1 Current State: 59:[59, 1], Operations: ['89-80=9', '10-9=1'] Exploring Operation: 59*1=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[59, 89, 80, 10], Operations: [] Exploring Operation: 89-10=79, Resulting Numbers: [59, 80, 79] Generated Node #0,0: 59:[59, 80, 79] Operation: 89-10=79 Moving to Node #0,0 Current State: 59:[59, 80, 79], Operations: ['89-10=79'] Exploring Operation: 80-59=21, Resulting Numbers: [79, 21] Generated Node #0,0,0: 59:[79, 21] Operation: 80-59=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[79, 21], Operations: ['89-10=79', '80-59=21'] Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,59 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
[ 52, 47, 26, 37 ]
42
[ "52/26=2", "47+37=84", "84/2=42" ]
Current State: 42:[52, 47, 26, 37], Operations: [] Exploring Operation: 52/26=2, Resulting Numbers: [47, 37, 2] Generated Node #2: [47, 37, 2] from Operation: 52/26=2 Current State: 42:[47, 37, 2], Operations: ['52/26=2'] Exploring Operation: 47+37=84, Resulting Numbers: [2, 84] Generated Node #3: [2, 84] from Operation: 47+37=84 Current State: 42:[2, 84], Operations: ['52/26=2', '47+37=84'] Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[52, 47, 26, 37], Operations: [] Exploring Operation: 52-37=15, Resulting Numbers: [47, 26, 15] Generated Node #0,0: 42:[47, 26, 15] Operation: 52-37=15 Exploring Operation: 52-47=5, Resulting Numbers: [26, 37, 5] Generated Node #0,1: 42:[26, 37, 5] Operation: 52-47=5 Exploring Operation: 52/26=2, Resulting Numbers: [47, 37, 2] Generated Node #0,2: 42:[47, 37, 2] Operation: 52/26=2 Moving to Node #0,2 Current State: 42:[47, 37, 2], Operations: ['52/26=2'] Exploring Operation: 37+2=39, Resulting Numbers: [47, 39] Generated Node #0,2,0: 42:[47, 39] Operation: 37+2=39 Exploring Operation: 47-2=45, Resulting Numbers: [37, 45] Generated Node #0,2,1: 42:[37, 45] Operation: 47-2=45 Exploring Operation: 47-37=10, Resulting Numbers: [2, 10] Generated Node #0,2,2: 42:[2, 10] Operation: 47-37=10 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 42:[2, 10], Operations: ['52/26=2', '47-37=10'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,42 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 42:[47, 39], Operations: ['52/26=2', '37+2=39'] Exploring Operation: 47+39=86, Resulting Numbers: [86] 86,42 unequal: No Solution Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 47*39=1833, Resulting Numbers: [1833] 1833,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 42:[37, 45], Operations: ['52/26=2', '47-2=45'] Exploring Operation: 37*45=1665, Resulting Numbers: [1665] 1665,42 unequal: No Solution Exploring Operation: 37+45=82, Resulting Numbers: [82] 82,42 unequal: No Solution Exploring Operation: 45-37=8, Resulting Numbers: [8] 8,42 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: 42:[47, 26, 15], Operations: ['52-37=15'] Exploring Operation: 26-15=11, Resulting Numbers: [47, 11] Generated Node #0,0,0: 42:[47, 11] Operation: 26-15=11 Exploring Operation: 26+15=41, Resulting Numbers: [47, 41] Generated Node #0,0,1: 42:[47, 41] Operation: 26+15=41 Exploring Operation: 47-26=21, Resulting Numbers: [15, 21] Generated Node #0,0,2: 42:[15, 21] Operation: 47-26=21 Moving to Node #0,1 Current State: 42:[26, 37, 5], Operations: ['52-47=5'] Exploring Operation: 37-26=11, Resulting Numbers: [5, 11] Generated Node #0,1,0: 42:[5, 11] Operation: 37-26=11 Exploring Operation: 26-5=21, Resulting Numbers: [37, 21] Generated Node #0,1,1: 42:[37, 21] Operation: 26-5=21 Exploring Operation: 37+5=42, Resulting Numbers: [26, 42] Generated Node #0,1,2: 42:[26, 42] Operation: 37+5=42 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 42:[5, 11], Operations: ['52-47=5', '37-26=11'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,42 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,42 unequal: No Solution Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 42:[37, 21], Operations: ['52-47=5', '26-5=21'] Exploring Operation: 37*21=777, Resulting Numbers: [777] 777,42 unequal: No Solution Exploring Operation: 37+21=58, Resulting Numbers: [58] 58,42 unequal: No Solution Exploring Operation: 37-21=16, Resulting Numbers: [16] 16,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 42:[26, 42], Operations: ['52-47=5', '37+5=42'] Exploring Operation: 26+42=68, Resulting Numbers: [68] 68,42 unequal: No Solution Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 26*42=1092, Resulting Numbers: [1092] 1092,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 42:[15, 21], Operations: ['52-37=15', '47-26=21'] Exploring Operation: 15+21=36, Resulting Numbers: [36] 36,42 unequal: No Solution Exploring Operation: 15*21=315, Resulting Numbers: [315] 315,42 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[47, 41], Operations: ['52-37=15', '26+15=41'] Exploring Operation: 47*41=1927, Resulting Numbers: [1927] 1927,42 unequal: No Solution Exploring Operation: 47+41=88, Resulting Numbers: [88] 88,42 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,42 unequal: No Solution Moving to Node #0,0,0 Current State: 42:[47, 11], Operations: ['52-37=15', '26-15=11'] Exploring Operation: 47-11=36, Resulting Numbers: [36] 36,42 unequal: No Solution Exploring Operation: 47+11=58, Resulting Numbers: [58] 58,42 unequal: No Solution Exploring Operation: 47*11=517, Resulting Numbers: [517] 517,42 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 38, 44, 38, 25 ]
57
[ "44-38=6", "38+25=63", "63-6=57" ]
Current State: 57:[38, 44, 38, 25], Operations: [] Exploring Operation: 44-38=6, Resulting Numbers: [25, 6] Generated Node #2: [25, 6] from Operation: 44-38=6 Current State: 57:[25, 6], Operations: ['44-38=6'] Exploring Operation: 38+25=63, Resulting Numbers: [6, 63] Generated Node #3: [6, 63] from Operation: 38+25=63 Current State: 57:[6, 63], Operations: ['44-38=6', '38+25=63'] Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[38, 44, 38, 25], Operations: [] Exploring Operation: 38-38=0, Resulting Numbers: [44, 25, 0] Generated Node #0,0: 57:[44, 25, 0] Operation: 38-38=0 Exploring Operation: 38/38=1, Resulting Numbers: [44, 25, 1] Generated Node #0,1: 57:[44, 25, 1] Operation: 38/38=1 Moving to Node #0,1 Current State: 57:[44, 25, 1], Operations: ['38/38=1'] Exploring Operation: 44+25=69, Resulting Numbers: [1, 69] Generated Node #0,1,0: 57:[1, 69] Operation: 44+25=69 Exploring Operation: 44-25=19, Resulting Numbers: [1, 19] Generated Node #0,1,1: 57:[1, 19] Operation: 44-25=19 Moving to Node #0,0 Current State: 57:[44, 25, 0], Operations: ['38-38=0'] Exploring Operation: 44*0=0, Resulting Numbers: [25, 0] Generated Node #0,0,0: 57:[25, 0] Operation: 44*0=0 Exploring Operation: 44-25=19, Resulting Numbers: [0, 19] Generated Node #0,0,1: 57:[0, 19] Operation: 44-25=19 Moving to Node #0,1,1 Current State: 57:[1, 19], Operations: ['38/38=1', '44-25=19'] Exploring Operation: 1*19=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[0, 19], Operations: ['38-38=0', '44-25=19'] Exploring Operation: 0+19=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 19-0=19, Resulting Numbers: [19] 19,57 unequal: No Solution Moving to Node #0,0,0 Current State: 57:[25, 0], Operations: ['38-38=0', '44*0=0'] Exploring Operation: 25+0=25, Resulting Numbers: [25] 25,57 unequal: No Solution Exploring Operation: 25*0=0, Resulting Numbers: [0] 0,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[1, 69], Operations: ['38/38=1', '44+25=69'] Exploring Operation: 1*69=69, Resulting Numbers: [69] 69,57 unequal: No Solution Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,57 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 66, 32, 85, 95 ]
37
[ "85-66=19", "95/19=5", "32+5=37" ]
Current State: 37:[66, 32, 85, 95], Operations: [] Exploring Operation: 85-66=19, Resulting Numbers: [32, 95, 19] Generated Node #2: [32, 95, 19] from Operation: 85-66=19 Current State: 37:[32, 95, 19], Operations: ['85-66=19'] Exploring Operation: 95/19=5, Resulting Numbers: [32, 5] Generated Node #3: [32, 5] from Operation: 95/19=5 Current State: 37:[32, 5], Operations: ['85-66=19', '95/19=5'] Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[66, 32, 85, 95], Operations: [] Exploring Operation: 95-66=29, Resulting Numbers: [32, 85, 29] Generated Node #0,0: 37:[32, 85, 29] Operation: 95-66=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[32, 85, 29], Operations: ['95-66=29'] Exploring Operation: 85-32=53, Resulting Numbers: [29, 53] Generated Node #0,0,0: 37:[29, 53] Operation: 85-32=53 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[29, 53], Operations: ['95-66=29', '85-32=53'] Exploring Operation: 53-29=24, Resulting Numbers: [24] 24,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 30, 25, 80, 2 ]
50
[ "30+25=55", "80-55=25", "2*25=50" ]
Current State: 50:[30, 25, 80, 2], Operations: [] Exploring Operation: 30+25=55, Resulting Numbers: [80, 2, 55] Generated Node #2: [80, 2, 55] from Operation: 30+25=55 Current State: 50:[80, 2, 55], Operations: ['30+25=55'] Exploring Operation: 80-55=25, Resulting Numbers: [2, 25] Generated Node #3: [2, 25] from Operation: 80-55=25 Current State: 50:[2, 25], Operations: ['30+25=55', '80-55=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[30, 25, 80, 2], Operations: [] Exploring Operation: 80-30=50, Resulting Numbers: [25, 2, 50] Generated Node #0,0: 50:[25, 2, 50] Operation: 80-30=50 Moving to Node #0,0 Current State: 50:[25, 2, 50], Operations: ['80-30=50'] Exploring Operation: 25*2=50, Resulting Numbers: [50, 50] Generated Node #0,0,0: 50:[50, 50] Operation: 25*2=50 Moving to Node #0,0,0 Current State: 50:[50, 50], Operations: ['80-30=50', '25*2=50'] Exploring Operation: 50/50=1, Resulting Numbers: [1] 1,50 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 7, 4, 60, 81 ]
87
[ "7-4=3", "81/3=27", "60+27=87" ]
Current State: 87:[7, 4, 60, 81], Operations: [] Exploring Operation: 7-4=3, Resulting Numbers: [60, 81, 3] Generated Node #2: [60, 81, 3] from Operation: 7-4=3 Current State: 87:[60, 81, 3], Operations: ['7-4=3'] Exploring Operation: 81/3=27, Resulting Numbers: [60, 27] Generated Node #3: [60, 27] from Operation: 81/3=27 Current State: 87:[60, 27], Operations: ['7-4=3', '81/3=27'] Exploring Operation: 60+27=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[7, 4, 60, 81], Operations: [] Exploring Operation: 60/4=15, Resulting Numbers: [7, 81, 15] Generated Node #0,0: 87:[7, 81, 15] Operation: 60/4=15 Exploring Operation: 81-60=21, Resulting Numbers: [7, 4, 21] Generated Node #0,1: 87:[7, 4, 21] Operation: 81-60=21 Moving to Node #0,1 Current State: 87:[7, 4, 21], Operations: ['81-60=21'] Exploring Operation: 7+21=28, Resulting Numbers: [4, 28] Generated Node #0,1,0: 87:[4, 28] Operation: 7+21=28 Exploring Operation: 21/7=3, Resulting Numbers: [4, 3] Generated Node #0,1,1: 87:[4, 3] Operation: 21/7=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 87:[4, 3], Operations: ['81-60=21', '21/7=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,87 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,87 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:[4, 28], Operations: ['81-60=21', '7+21=28'] Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 4+28=32, Resulting Numbers: [32] 32,87 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: 87:[7, 81, 15], Operations: ['60/4=15'] Exploring Operation: 7+81=88, Resulting Numbers: [15, 88] Generated Node #0,0,0: 87:[15, 88] Operation: 7+81=88 Exploring Operation: 15-7=8, Resulting Numbers: [81, 8] Generated Node #0,0,1: 87:[81, 8] Operation: 15-7=8 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 87:[81, 8], Operations: ['60/4=15', '15-7=8'] Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,87 unequal: No Solution Exploring Operation: 81+8=89, Resulting Numbers: [89] 89,87 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 #0,0,0 Current State: 87:[15, 88], Operations: ['60/4=15', '7+81=88'] Exploring Operation: 88-15=73, Resulting Numbers: [73] 73,87 unequal: No Solution Exploring Operation: 15+88=103, Resulting Numbers: [103] 103,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 93, 82, 36, 62 ]
69
[ "82-36=46", "93*46=4278", "4278/62=69" ]
Current State: 69:[93, 82, 36, 62], Operations: [] Exploring Operation: 82-36=46, Resulting Numbers: [93, 62, 46] Generated Node #2: [93, 62, 46] from Operation: 82-36=46 Current State: 69:[93, 62, 46], Operations: ['82-36=46'] Exploring Operation: 93*46=4278, Resulting Numbers: [62, 4278] Generated Node #3: [62, 4278] from Operation: 93*46=4278 Current State: 69:[62, 4278], Operations: ['82-36=46', '93*46=4278'] Exploring Operation: 4278/62=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[93, 82, 36, 62], Operations: [] Exploring Operation: 82-62=20, Resulting Numbers: [93, 36, 20] Generated Node #0,0: 69:[93, 36, 20] Operation: 82-62=20 Exploring Operation: 93-82=11, Resulting Numbers: [36, 62, 11] Generated Node #0,1: 69:[36, 62, 11] Operation: 93-82=11 Exploring Operation: 93-62=31, Resulting Numbers: [82, 36, 31] Generated Node #0,2: 69:[82, 36, 31] Operation: 93-62=31 Exploring Operation: 93-36=57, Resulting Numbers: [82, 62, 57] Generated Node #0,3: 69:[82, 62, 57] Operation: 93-36=57 Moving to Node #0,1 Current State: 69:[36, 62, 11], Operations: ['93-82=11'] Exploring Operation: 36-11=25, Resulting Numbers: [62, 25] Generated Node #0,1,0: 69:[62, 25] Operation: 36-11=25 Exploring Operation: 62+11=73, Resulting Numbers: [36, 73] Generated Node #0,1,1: 69:[36, 73] Operation: 62+11=73 Exploring Operation: 62-36=26, Resulting Numbers: [11, 26] Generated Node #0,1,2: 69:[11, 26] Operation: 62-36=26 Exploring Operation: 36+11=47, Resulting Numbers: [62, 47] Generated Node #0,1,3: 69:[62, 47] Operation: 36+11=47 Moving to Node #0,3 Current State: 69:[82, 62, 57], Operations: ['93-36=57'] Exploring Operation: 82-57=25, Resulting Numbers: [62, 25] Generated Node #0,3,0: 69:[62, 25] Operation: 82-57=25 Exploring Operation: 62+57=119, Resulting Numbers: [82, 119] Generated Node #0,3,1: 69:[82, 119] Operation: 62+57=119 Exploring Operation: 62-57=5, Resulting Numbers: [82, 5] Generated Node #0,3,2: 69:[82, 5] Operation: 62-57=5 Exploring Operation: 82-62=20, Resulting Numbers: [57, 20] Generated Node #0,3,3: 69:[57, 20] Operation: 82-62=20 Moving to Node #0,2 Current State: 69:[82, 36, 31], Operations: ['93-62=31'] Exploring Operation: 82-31=51, Resulting Numbers: [36, 51] Generated Node #0,2,0: 69:[36, 51] Operation: 82-31=51 Exploring Operation: 36+31=67, Resulting Numbers: [82, 67] Generated Node #0,2,1: 69:[82, 67] Operation: 36+31=67 Exploring Operation: 82-36=46, Resulting Numbers: [31, 46] Generated Node #0,2,2: 69:[31, 46] Operation: 82-36=46 Exploring Operation: 36-31=5, Resulting Numbers: [82, 5] Generated Node #0,2,3: 69:[82, 5] Operation: 36-31=5 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 69:[82, 67], Operations: ['93-62=31', '36+31=67'] Exploring Operation: 82*67=5494, Resulting Numbers: [5494] 5494,69 unequal: No Solution Exploring Operation: 82+67=149, Resulting Numbers: [149] 149,69 unequal: No Solution Exploring Operation: 82-67=15, Resulting Numbers: [15] 15,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 69:[82, 5], Operations: ['93-62=31', '36-31=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 82*5=410, Resulting Numbers: [410] 410,69 unequal: No Solution Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 69:[36, 51], Operations: ['93-62=31', '82-31=51'] Exploring Operation: 51-36=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 36+51=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 36*51=1836, Resulting Numbers: [1836] 1836,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 69:[31, 46], Operations: ['93-62=31', '82-36=46'] Exploring Operation: 31+46=77, Resulting Numbers: [77] 77,69 unequal: No Solution Exploring Operation: 46-31=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 31*46=1426, Resulting Numbers: [1426] 1426,69 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: 69:[93, 36, 20], Operations: ['82-62=20'] Exploring Operation: 93-20=73, Resulting Numbers: [36, 73] Generated Node #0,0,0: 69:[36, 73] Operation: 93-20=73 Exploring Operation: 36-20=16, Resulting Numbers: [93, 16] Generated Node #0,0,1: 69:[93, 16] Operation: 36-20=16 Exploring Operation: 93-36=57, Resulting Numbers: [20, 57] Generated Node #0,0,2: 69:[20, 57] Operation: 93-36=57 Exploring Operation: 36+20=56, Resulting Numbers: [93, 56] Generated Node #0,0,3: 69:[93, 56] Operation: 36+20=56 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[20, 57], Operations: ['82-62=20', '93-36=57'] Exploring Operation: 20*57=1140, Resulting Numbers: [1140] 1140,69 unequal: No Solution Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 20+57=77, Resulting Numbers: [77] 77,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[36, 73], Operations: ['82-62=20', '93-20=73'] Exploring Operation: 36*73=2628, Resulting Numbers: [2628] 2628,69 unequal: No Solution Exploring Operation: 36+73=109, Resulting Numbers: [109] 109,69 unequal: No Solution Exploring Operation: 73-36=37, Resulting Numbers: [37] 37,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[93, 16], Operations: ['82-62=20', '36-20=16'] Exploring Operation: 93*16=1488, Resulting Numbers: [1488] 1488,69 unequal: No Solution Exploring Operation: 93+16=109, Resulting Numbers: [109] 109,69 unequal: No Solution Exploring Operation: 93-16=77, Resulting Numbers: [77] 77,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 69:[93, 56], Operations: ['82-62=20', '36+20=56'] Exploring Operation: 93-56=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 93*56=5208, Resulting Numbers: [5208] 5208,69 unequal: No Solution Exploring Operation: 93+56=149, Resulting Numbers: [149] 149,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 69:[62, 25], Operations: ['93-82=11', '36-11=25'] Exploring Operation: 62-25=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 62+25=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 62*25=1550, Resulting Numbers: [1550] 1550,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[62, 25], Operations: ['93-36=57', '82-57=25'] Exploring Operation: 62+25=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 62-25=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 62*25=1550, Resulting Numbers: [1550] 1550,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[11, 26], Operations: ['93-82=11', '62-36=26'] Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 11*26=286, Resulting Numbers: [286] 286,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[82, 5], Operations: ['93-36=57', '62-57=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 82*5=410, Resulting Numbers: [410] 410,69 unequal: No Solution Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[57, 20], Operations: ['93-36=57', '82-62=20'] Exploring Operation: 57+20=77, Resulting Numbers: [77] 77,69 unequal: No Solution Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 57*20=1140, Resulting Numbers: [1140] 1140,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[36, 73], Operations: ['93-82=11', '62+11=73'] Exploring Operation: 36+73=109, Resulting Numbers: [109] 109,69 unequal: No Solution Exploring Operation: 73-36=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 36*73=2628, Resulting Numbers: [2628] 2628,69 unequal: No Solution Moving to Node #0,1,3 Current State: 69:[62, 47], Operations: ['93-82=11', '36+11=47'] Exploring Operation: 62*47=2914, Resulting Numbers: [2914] 2914,69 unequal: No Solution Exploring Operation: 62-47=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 62+47=109, Resulting Numbers: [109] 109,69 unequal: No Solution Moving to Node #0,3,1 Current State: 69:[82, 119], Operations: ['93-36=57', '62+57=119'] Exploring Operation: 82*119=9758, Resulting Numbers: [9758] 9758,69 unequal: No Solution Exploring Operation: 119-82=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 82+119=201, Resulting Numbers: [201] 201,69 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 1, 1, 70, 44 ]
70
[ "1-1=0", "44*0=0", "70+0=70" ]
Current State: 70:[1, 1, 70, 44], Operations: [] Exploring Operation: 1-1=0, Resulting Numbers: [70, 44, 0] Generated Node #2: [70, 44, 0] from Operation: 1-1=0 Current State: 70:[70, 44, 0], Operations: ['1-1=0'] Exploring Operation: 44*0=0, Resulting Numbers: [70, 0] Generated Node #3: [70, 0] from Operation: 44*0=0 Current State: 70:[70, 0], Operations: ['1-1=0', '44*0=0'] Exploring Operation: 70+0=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[1, 1, 70, 44], Operations: [] Exploring Operation: 44-1=43, Resulting Numbers: [1, 70, 43] Generated Node #0,0: 70:[1, 70, 43] Operation: 44-1=43 Exploring Operation: 1+1=2, Resulting Numbers: [70, 44, 2] Generated Node #0,1: 70:[70, 44, 2] Operation: 1+1=2 Exploring Operation: 44-1=43, Resulting Numbers: [1, 70, 43] Generated Node #0,2: 70:[1, 70, 43] Operation: 44-1=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[1, 70, 43], Operations: ['44-1=43'] Exploring Operation: 1*70=70, Resulting Numbers: [43, 70] Generated Node #0,0,0: 70:[43, 70] Operation: 1*70=70 Exploring Operation: 70/1=70, Resulting Numbers: [43, 70] Generated Node #0,0,1: 70:[43, 70] Operation: 70/1=70 Exploring Operation: 43-1=42, Resulting Numbers: [70, 42] Generated Node #0,0,2: 70:[70, 42] Operation: 43-1=42 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 70:[70, 42], Operations: ['44-1=43', '43-1=42'] Exploring Operation: 70*42=2940, Resulting Numbers: [2940] 2940,70 unequal: No Solution Exploring Operation: 70+42=112, Resulting Numbers: [112] 112,70 unequal: No Solution Exploring Operation: 70-42=28, Resulting Numbers: [28] 28,70 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 #0,0,0 Current State: 70:[43, 70], Operations: ['44-1=43', '1*70=70'] Exploring Operation: 43*70=3010, Resulting Numbers: [3010] 3010,70 unequal: No Solution Exploring Operation: 70-43=27, Resulting Numbers: [27] 27,70 unequal: No Solution Exploring Operation: 43+70=113, Resulting Numbers: [113] 113,70 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:[43, 70], Operations: ['44-1=43', '70/1=70'] Exploring Operation: 70-43=27, Resulting Numbers: [27] 27,70 unequal: No Solution Exploring Operation: 43+70=113, Resulting Numbers: [113] 113,70 unequal: No Solution Exploring Operation: 43*70=3010, Resulting Numbers: [3010] 3010,70 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:[70, 44, 2], Operations: ['1+1=2'] Exploring Operation: 44-2=42, Resulting Numbers: [70, 42] Generated Node #0,1,0: 70:[70, 42] Operation: 44-2=42 Exploring Operation: 44/2=22, Resulting Numbers: [70, 22] Generated Node #0,1,1: 70:[70, 22] Operation: 44/2=22 Exploring Operation: 70-44=26, Resulting Numbers: [2, 26] Generated Node #0,1,2: 70:[2, 26] Operation: 70-44=26 Moving to Node #0,1,0 Current State: 70:[70, 42], Operations: ['1+1=2', '44-2=42'] Exploring Operation: 70+42=112, Resulting Numbers: [112] 112,70 unequal: No Solution Exploring Operation: 70-42=28, Resulting Numbers: [28] 28,70 unequal: No Solution Exploring Operation: 70*42=2940, Resulting Numbers: [2940] 2940,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[70, 22], Operations: ['1+1=2', '44/2=22'] Exploring Operation: 70-22=48, Resulting Numbers: [48] 48,70 unequal: No Solution Exploring Operation: 70*22=1540, Resulting Numbers: [1540] 1540,70 unequal: No Solution Exploring Operation: 70+22=92, Resulting Numbers: [92] 92,70 unequal: No Solution Moving to Node #0,1,2 Current State: 70:[2, 26], Operations: ['1+1=2', '70-44=26'] Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,70 unequal: No Solution Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,70 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 #0,2 Current State: 70:[1, 70, 43], Operations: ['44-1=43'] Exploring Operation: 70/1=70, Resulting Numbers: [43, 70] Generated Node #0,2,0: 70:[43, 70] Operation: 70/1=70 Exploring Operation: 1*70=70, Resulting Numbers: [43, 70] Generated Node #0,2,1: 70:[43, 70] Operation: 1*70=70 Exploring Operation: 43-1=42, Resulting Numbers: [70, 42] Generated Node #0,2,2: 70:[70, 42] Operation: 43-1=42 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 70:[70, 42], Operations: ['44-1=43', '43-1=42'] Exploring Operation: 70*42=2940, Resulting Numbers: [2940] 2940,70 unequal: No Solution Exploring Operation: 70+42=112, Resulting Numbers: [112] 112,70 unequal: No Solution Exploring Operation: 70-42=28, Resulting Numbers: [28] 28,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 70:[43, 70], Operations: ['44-1=43', '70/1=70'] Exploring Operation: 43+70=113, Resulting Numbers: [113] 113,70 unequal: No Solution Exploring Operation: 70-43=27, Resulting Numbers: [27] 27,70 unequal: No Solution Exploring Operation: 43*70=3010, Resulting Numbers: [3010] 3010,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 70:[43, 70], Operations: ['44-1=43', '1*70=70'] Exploring Operation: 43*70=3010, Resulting Numbers: [3010] 3010,70 unequal: No Solution Exploring Operation: 43+70=113, Resulting Numbers: [113] 113,70 unequal: No Solution Exploring Operation: 70-43=27, Resulting Numbers: [27] 27,70 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_3
mult_heuristic
[ 5, 2, 25, 12 ]
43
[ "12-5=7", "2*25=50", "50-7=43" ]
Current State: 43:[5, 2, 25, 12], Operations: [] Exploring Operation: 12-5=7, Resulting Numbers: [2, 25, 7] Generated Node #2: [2, 25, 7] from Operation: 12-5=7 Current State: 43:[2, 25, 7], Operations: ['12-5=7'] Exploring Operation: 2*25=50, Resulting Numbers: [7, 50] Generated Node #3: [7, 50] from Operation: 2*25=50 Current State: 43:[7, 50], Operations: ['12-5=7', '2*25=50'] Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[5, 2, 25, 12], Operations: [] Exploring Operation: 2*12=24, Resulting Numbers: [5, 25, 24] Generated Node #0,0: 43:[5, 25, 24] Operation: 2*12=24 Exploring Operation: 2*25=50, Resulting Numbers: [5, 12, 50] Generated Node #0,1: 43:[5, 12, 50] Operation: 2*25=50 Exploring Operation: 5*12=60, Resulting Numbers: [2, 25, 60] Generated Node #0,2: 43:[2, 25, 60] Operation: 5*12=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[5, 25, 24], Operations: ['2*12=24'] Exploring Operation: 5+25=30, Resulting Numbers: [24, 30] Generated Node #0,0,0: 43:[24, 30] Operation: 5+25=30 Exploring Operation: 5+24=29, Resulting Numbers: [25, 29] Generated Node #0,0,1: 43:[25, 29] Operation: 5+24=29 Exploring Operation: 25-5=20, Resulting Numbers: [24, 20] Generated Node #0,0,2: 43:[24, 20] Operation: 25-5=20 Moving to Node #0,0,0 Current State: 43:[24, 30], Operations: ['2*12=24', '5+25=30'] Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,43 unequal: No Solution Exploring Operation: 24*30=720, Resulting Numbers: [720] 720,43 unequal: No Solution Exploring Operation: 24+30=54, Resulting Numbers: [54] 54,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[25, 29], Operations: ['2*12=24', '5+24=29'] Exploring Operation: 25*29=725, Resulting Numbers: [725] 725,43 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,43 unequal: No Solution Exploring Operation: 25+29=54, Resulting Numbers: [54] 54,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[24, 20], Operations: ['2*12=24', '25-5=20'] Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,43 unequal: No Solution Exploring Operation: 24+20=44, Resulting Numbers: [44] 44,43 unequal: No Solution Exploring Operation: 24*20=480, Resulting Numbers: [480] 480,43 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 Current State: 43:[5, 12, 50], Operations: ['2*25=50'] Exploring Operation: 5+12=17, Resulting Numbers: [50, 17] Generated Node #0,1,0: 43:[50, 17] Operation: 5+12=17 Exploring Operation: 50-5=45, Resulting Numbers: [12, 45] Generated Node #0,1,1: 43:[12, 45] Operation: 50-5=45 Exploring Operation: 5*12=60, Resulting Numbers: [50, 60] Generated Node #0,1,2: 43:[50, 60] Operation: 5*12=60 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 43:[50, 60], Operations: ['2*25=50', '5*12=60'] Exploring Operation: 50+60=110, Resulting Numbers: [110] 110,43 unequal: No Solution Exploring Operation: 50*60=3000, Resulting Numbers: [3000] 3000,43 unequal: No Solution Exploring Operation: 60-50=10, Resulting Numbers: [10] 10,43 unequal: No Solution No 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: 43:[50, 17], Operations: ['2*25=50', '5+12=17'] Exploring Operation: 50*17=850, Resulting Numbers: [850] 850,43 unequal: No Solution Exploring Operation: 50+17=67, Resulting Numbers: [67] 67,43 unequal: No Solution Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,43 unequal: No Solution No 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: 43:[12, 45], Operations: ['2*25=50', '50-5=45'] Exploring Operation: 12+45=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 12*45=540, Resulting Numbers: [540] 540,43 unequal: No Solution Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 43:[2, 25, 60], Operations: ['5*12=60'] Exploring Operation: 60/2=30, Resulting Numbers: [25, 30] Generated Node #0,2,0: 43:[25, 30] Operation: 60/2=30 Exploring Operation: 2*25=50, Resulting Numbers: [60, 50] Generated Node #0,2,1: 43:[60, 50] Operation: 2*25=50 Exploring Operation: 2+25=27, Resulting Numbers: [60, 27] Generated Node #0,2,2: 43:[60, 27] Operation: 2+25=27 Moving to Node #0,2,1 Current State: 43:[60, 50], Operations: ['5*12=60', '2*25=50'] Exploring Operation: 60+50=110, Resulting Numbers: [110] 110,43 unequal: No Solution Exploring Operation: 60-50=10, Resulting Numbers: [10] 10,43 unequal: No Solution Exploring Operation: 60*50=3000, Resulting Numbers: [3000] 3000,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[25, 30], Operations: ['5*12=60', '60/2=30'] Exploring Operation: 30-25=5, Resulting Numbers: [5] 5,43 unequal: No Solution Exploring Operation: 25+30=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 25*30=750, Resulting Numbers: [750] 750,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[60, 27], Operations: ['5*12=60', '2+25=27'] Exploring Operation: 60-27=33, Resulting Numbers: [33] 33,43 unequal: No Solution Exploring Operation: 60+27=87, Resulting Numbers: [87] 87,43 unequal: No Solution Exploring Operation: 60*27=1620, Resulting Numbers: [1620] 1620,43 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
[ 34, 86, 53, 82 ]
20
[ "34*53=1802", "1802-82=1720", "1720/86=20" ]
Current State: 20:[34, 86, 53, 82], Operations: [] Exploring Operation: 34*53=1802, Resulting Numbers: [86, 82, 1802] Generated Node #2: [86, 82, 1802] from Operation: 34*53=1802 Current State: 20:[86, 82, 1802], Operations: ['34*53=1802'] Exploring Operation: 1802-82=1720, Resulting Numbers: [86, 1720] Generated Node #3: [86, 1720] from Operation: 1802-82=1720 Current State: 20:[86, 1720], Operations: ['34*53=1802', '1802-82=1720'] Exploring Operation: 1720/86=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[34, 86, 53, 82], Operations: [] Exploring Operation: 86-82=4, Resulting Numbers: [34, 53, 4] Generated Node #0,0: 20:[34, 53, 4] Operation: 86-82=4 Exploring Operation: 86-53=33, Resulting Numbers: [34, 82, 33] Generated Node #0,1: 20:[34, 82, 33] Operation: 86-53=33 Exploring Operation: 82-53=29, Resulting Numbers: [34, 86, 29] Generated Node #0,2: 20:[34, 86, 29] Operation: 82-53=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[34, 53, 4], Operations: ['86-82=4'] Exploring Operation: 53-4=49, Resulting Numbers: [34, 49] Generated Node #0,0,0: 20:[34, 49] Operation: 53-4=49 Exploring Operation: 53-34=19, Resulting Numbers: [4, 19] Generated Node #0,0,1: 20:[4, 19] Operation: 53-34=19 Exploring Operation: 34-4=30, Resulting Numbers: [53, 30] Generated Node #0,0,2: 20:[53, 30] Operation: 34-4=30 Moving to Node #0,0,1 Current State: 20:[4, 19], Operations: ['86-82=4', '53-34=19'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,20 unequal: No Solution Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,20 unequal: No Solution Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,20 unequal: No Solution Moving to Node #0,0,0 Current State: 20:[34, 49], Operations: ['86-82=4', '53-4=49'] Exploring Operation: 34*49=1666, Resulting Numbers: [1666] 1666,20 unequal: No Solution Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,20 unequal: No Solution Exploring Operation: 34+49=83, Resulting Numbers: [83] 83,20 unequal: No Solution Moving to Node #0,0,2 Current State: 20:[53, 30], Operations: ['86-82=4', '34-4=30'] Exploring Operation: 53*30=1590, Resulting Numbers: [1590] 1590,20 unequal: No Solution Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,20 unequal: No Solution Exploring Operation: 53+30=83, Resulting Numbers: [83] 83,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[34, 82, 33], Operations: ['86-53=33'] Exploring Operation: 34-33=1, Resulting Numbers: [82, 1] Generated Node #0,1,0: 20:[82, 1] Operation: 34-33=1 Exploring Operation: 82-34=48, Resulting Numbers: [33, 48] Generated Node #0,1,1: 20:[33, 48] Operation: 82-34=48 Exploring Operation: 82-33=49, Resulting Numbers: [34, 49] Generated Node #0,1,2: 20:[34, 49] Operation: 82-33=49 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 20:[33, 48], Operations: ['86-53=33', '82-34=48'] Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,20 unequal: No Solution Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,20 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 20:[34, 49], Operations: ['86-53=33', '82-33=49'] Exploring Operation: 34*49=1666, Resulting Numbers: [1666] 1666,20 unequal: No Solution Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,20 unequal: No Solution Exploring Operation: 34+49=83, Resulting Numbers: [83] 83,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 20:[82, 1], Operations: ['86-53=33', '34-33=1'] Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,20 unequal: No Solution Exploring Operation: 82*1=82, Resulting Numbers: [82] 82,20 unequal: No Solution Exploring Operation: 82/1=82, Resulting Numbers: [82] 82,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 20:[34, 86, 29], Operations: ['82-53=29'] Exploring Operation: 34-29=5, Resulting Numbers: [86, 5] Generated Node #0,2,0: 20:[86, 5] Operation: 34-29=5 Exploring Operation: 86-29=57, Resulting Numbers: [34, 57] Generated Node #0,2,1: 20:[34, 57] Operation: 86-29=57 Exploring Operation: 86-34=52, Resulting Numbers: [29, 52] Generated Node #0,2,2: 20:[29, 52] Operation: 86-34=52 Moving to Node #0,2,2 Current State: 20:[29, 52], Operations: ['82-53=29', '86-34=52'] Exploring Operation: 29+52=81, Resulting Numbers: [81] 81,20 unequal: No Solution Exploring Operation: 52-29=23, Resulting Numbers: [23] 23,20 unequal: No Solution Exploring Operation: 29*52=1508, Resulting Numbers: [1508] 1508,20 unequal: No Solution Moving to Node #0,2,1 Current State: 20:[34, 57], Operations: ['82-53=29', '86-29=57'] Exploring Operation: 34+57=91, Resulting Numbers: [91] 91,20 unequal: No Solution Exploring Operation: 34*57=1938, Resulting Numbers: [1938] 1938,20 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,20 unequal: No Solution Moving to Node #0,2,0 Current State: 20:[86, 5], Operations: ['82-53=29', '34-29=5'] Exploring Operation: 86*5=430, Resulting Numbers: [430] 430,20 unequal: No Solution Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,20 unequal: No Solution Exploring Operation: 86+5=91, Resulting Numbers: [91] 91,20 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
[ 65, 22, 68, 26 ]
16
[ "68-65=3", "22+26=48", "48/3=16" ]
Current State: 16:[65, 22, 68, 26], Operations: [] Exploring Operation: 68-65=3, Resulting Numbers: [22, 26, 3] Generated Node #2: [22, 26, 3] from Operation: 68-65=3 Current State: 16:[22, 26, 3], Operations: ['68-65=3'] Exploring Operation: 22+26=48, Resulting Numbers: [3, 48] Generated Node #3: [3, 48] from Operation: 22+26=48 Current State: 16:[3, 48], Operations: ['68-65=3', '22+26=48'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[65, 22, 68, 26], Operations: [] Exploring Operation: 68-65=3, Resulting Numbers: [22, 26, 3] Generated Node #0,0: 16:[22, 26, 3] Operation: 68-65=3 Moving to Node #0,0 Current State: 16:[22, 26, 3], Operations: ['68-65=3'] Exploring Operation: 26-22=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 16:[3, 4] Operation: 26-22=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[3, 4], Operations: ['68-65=3', '26-22=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,16 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
[ 76, 13, 6, 18 ]
72
[ "76*18=1368", "13+6=19", "1368/19=72" ]
Current State: 72:[76, 13, 6, 18], Operations: [] Exploring Operation: 76*18=1368, Resulting Numbers: [13, 6, 1368] Generated Node #2: [13, 6, 1368] from Operation: 76*18=1368 Current State: 72:[13, 6, 1368], Operations: ['76*18=1368'] Exploring Operation: 13+6=19, Resulting Numbers: [1368, 19] Generated Node #3: [1368, 19] from Operation: 13+6=19 Current State: 72:[1368, 19], Operations: ['76*18=1368', '13+6=19'] Exploring Operation: 1368/19=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[76, 13, 6, 18], Operations: [] Exploring Operation: 76-6=70, Resulting Numbers: [13, 18, 70] Generated Node #0,0: 72:[13, 18, 70] Operation: 76-6=70 Exploring Operation: 13+6=19, Resulting Numbers: [76, 18, 19] Generated Node #0,1: 72:[76, 18, 19] Operation: 13+6=19 Moving to Node #0,0 Current State: 72:[13, 18, 70], Operations: ['76-6=70'] Exploring Operation: 18-13=5, Resulting Numbers: [70, 5] Generated Node #0,0,0: 72:[70, 5] Operation: 18-13=5 Exploring Operation: 13+18=31, Resulting Numbers: [70, 31] Generated Node #0,0,1: 72:[70, 31] Operation: 13+18=31 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[70, 5], Operations: ['76-6=70', '18-13=5'] Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 70+5=75, Resulting Numbers: [75] 75,72 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 #0,0,1 Current State: 72:[70, 31], Operations: ['76-6=70', '13+18=31'] Exploring Operation: 70-31=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 70+31=101, Resulting Numbers: [101] 101,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 72:[76, 18, 19], Operations: ['13+6=19'] Exploring Operation: 18+19=37, Resulting Numbers: [76, 37] Generated Node #0,1,0: 72:[76, 37] Operation: 18+19=37 Exploring Operation: 76/19=4, Resulting Numbers: [18, 4] Generated Node #0,1,1: 72:[18, 4] Operation: 76/19=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 72:[18, 4], Operations: ['13+6=19', '76/19=4'] Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[76, 13, 6, 18], Operations: [] Exploring Operation: 13+6=19, Resulting Numbers: [76, 18, 19] Generated Node #0,1: 72:[76, 18, 19] Operation: 13+6=19 Moving to Node #0,1 Current State: 72:[76, 18, 19], Operations: ['13+6=19'] Exploring Operation: 76/19=4, Resulting Numbers: [18, 4] Generated Node #0,1,1: 72:[18, 4] Operation: 76/19=4 Moving to Node #0,1,1 Current State: 72:[18, 4], Operations: ['13+6=19', '76/19=4'] Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 76, 18, 15, 41 ]
42
[ "76-41=35", "18*35=630", "630/15=42" ]
Current State: 42:[76, 18, 15, 41], Operations: [] Exploring Operation: 76-41=35, Resulting Numbers: [18, 15, 35] Generated Node #2: [18, 15, 35] from Operation: 76-41=35 Current State: 42:[18, 15, 35], Operations: ['76-41=35'] Exploring Operation: 18*35=630, Resulting Numbers: [15, 630] Generated Node #3: [15, 630] from Operation: 18*35=630 Current State: 42:[15, 630], Operations: ['76-41=35', '18*35=630'] Exploring Operation: 630/15=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[76, 18, 15, 41], Operations: [] Exploring Operation: 76-41=35, Resulting Numbers: [18, 15, 35] Generated Node #0,0: 42:[18, 15, 35] Operation: 76-41=35 Moving to Node #0,0 Current State: 42:[18, 15, 35], Operations: ['76-41=35'] Exploring Operation: 35-18=17, Resulting Numbers: [15, 17] Generated Node #0,0,0: 42:[15, 17] Operation: 35-18=17 Moving to Node #0,0,0 Current State: 42:[15, 17], Operations: ['76-41=35', '35-18=17'] Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,42 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 22, 35, 58, 46 ]
25
[ "35-22=13", "58-46=12", "13+12=25" ]
Current State: 25:[22, 35, 58, 46], Operations: [] Exploring Operation: 35-22=13, Resulting Numbers: [58, 46, 13] Generated Node #2: [58, 46, 13] from Operation: 35-22=13 Current State: 25:[58, 46, 13], Operations: ['35-22=13'] Exploring Operation: 58-46=12, Resulting Numbers: [13, 12] Generated Node #3: [13, 12] from Operation: 58-46=12 Current State: 25:[13, 12], Operations: ['35-22=13', '58-46=12'] Exploring Operation: 13+12=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[22, 35, 58, 46], Operations: [] Exploring Operation: 58-46=12, Resulting Numbers: [22, 35, 12] Generated Node #0,0: 25:[22, 35, 12] Operation: 58-46=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[22, 35, 12], Operations: ['58-46=12'] Exploring Operation: 35-12=23, Resulting Numbers: [22, 23] Generated Node #0,0,0: 25:[22, 23] Operation: 35-12=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[22, 23], Operations: ['58-46=12', '35-12=23'] Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 25, 59, 60, 75 ]
50
[ "75-25=50", "60-59=1", "50*1=50" ]
Current State: 50:[25, 59, 60, 75], Operations: [] Exploring Operation: 75-25=50, Resulting Numbers: [59, 60, 50] Generated Node #2: [59, 60, 50] from Operation: 75-25=50 Current State: 50:[59, 60, 50], Operations: ['75-25=50'] Exploring Operation: 60-59=1, Resulting Numbers: [50, 1] Generated Node #3: [50, 1] from Operation: 60-59=1 Current State: 50:[50, 1], Operations: ['75-25=50', '60-59=1'] Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[25, 59, 60, 75], Operations: [] Exploring Operation: 75-60=15, Resulting Numbers: [25, 59, 15] Generated Node #0,0: 50:[25, 59, 15] Operation: 75-60=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[25, 59, 15], Operations: ['75-60=15'] Exploring Operation: 59-15=44, Resulting Numbers: [25, 44] Generated Node #0,0,0: 50:[25, 44] Operation: 59-15=44 Moving to Node #0,0,0 Current State: 50:[25, 44], Operations: ['75-60=15', '59-15=44'] Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,50 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
[ 11, 12, 98, 20 ]
95
[ "11+12=23", "98+20=118", "118-23=95" ]
Current State: 95:[11, 12, 98, 20], Operations: [] Exploring Operation: 11+12=23, Resulting Numbers: [98, 20, 23] Generated Node #2: [98, 20, 23] from Operation: 11+12=23 Current State: 95:[98, 20, 23], Operations: ['11+12=23'] Exploring Operation: 98+20=118, Resulting Numbers: [23, 118] Generated Node #3: [23, 118] from Operation: 98+20=118 Current State: 95:[23, 118], Operations: ['11+12=23', '98+20=118'] Exploring Operation: 118-23=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[11, 12, 98, 20], Operations: [] Exploring Operation: 12-11=1, Resulting Numbers: [98, 20, 1] Generated Node #0,0: 95:[98, 20, 1] Operation: 12-11=1 Exploring Operation: 11+12=23, Resulting Numbers: [98, 20, 23] Generated Node #0,1: 95:[98, 20, 23] Operation: 11+12=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[98, 20, 1], Operations: ['12-11=1'] Exploring Operation: 98-1=97, Resulting Numbers: [20, 97] Generated Node #0,0,0: 95:[20, 97] Operation: 98-1=97 Exploring Operation: 20-1=19, Resulting Numbers: [98, 19] Generated Node #0,0,1: 95:[98, 19] Operation: 20-1=19 Moving to Node #0,0,0 Current State: 95:[20, 97], Operations: ['12-11=1', '98-1=97'] Exploring Operation: 20+97=117, Resulting Numbers: [117] 117,95 unequal: No Solution Exploring Operation: 97-20=77, Resulting Numbers: [77] 77,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[98, 19], Operations: ['12-11=1', '20-1=19'] Exploring Operation: 98-19=79, Resulting Numbers: [79] 79,95 unequal: No Solution Exploring Operation: 98+19=117, Resulting Numbers: [117] 117,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[98, 20, 23], Operations: ['11+12=23'] Exploring Operation: 23-20=3, Resulting Numbers: [98, 3] Generated Node #0,1,0: 95:[98, 3] Operation: 23-20=3 Exploring Operation: 98-20=78, Resulting Numbers: [23, 78] Generated Node #0,1,1: 95:[23, 78] Operation: 98-20=78 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 95:[98, 3], Operations: ['11+12=23', '23-20=3'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[11, 12, 98, 20], Operations: [] Exploring Operation: 11+12=23, Resulting Numbers: [98, 20, 23] Generated Node #0,1: 95:[98, 20, 23] Operation: 11+12=23 Moving to Node #0,1 Current State: 95:[98, 20, 23], Operations: ['11+12=23'] Exploring Operation: 23-20=3, Resulting Numbers: [98, 3] Generated Node #0,1,0: 95:[98, 3] Operation: 23-20=3 Moving to Node #0,1,0 Current State: 95:[98, 3], Operations: ['11+12=23', '23-20=3'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 58, 98, 97, 88 ]
31
[ "98-58=40", "97-88=9", "40-9=31" ]
Current State: 31:[58, 98, 97, 88], Operations: [] Exploring Operation: 98-58=40, Resulting Numbers: [97, 88, 40] Generated Node #2: [97, 88, 40] from Operation: 98-58=40 Current State: 31:[97, 88, 40], Operations: ['98-58=40'] Exploring Operation: 97-88=9, Resulting Numbers: [40, 9] Generated Node #3: [40, 9] from Operation: 97-88=9 Current State: 31:[40, 9], Operations: ['98-58=40', '97-88=9'] Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[58, 98, 97, 88], Operations: [] Exploring Operation: 97-88=9, Resulting Numbers: [58, 98, 9] Generated Node #0,0: 31:[58, 98, 9] Operation: 97-88=9 Exploring Operation: 98-88=10, Resulting Numbers: [58, 97, 10] Generated Node #0,1: 31:[58, 97, 10] Operation: 98-88=10 Exploring Operation: 98-97=1, Resulting Numbers: [58, 88, 1] Generated Node #0,2: 31:[58, 88, 1] Operation: 98-97=1 Moving to Node #0,1 Current State: 31:[58, 97, 10], Operations: ['98-88=10'] Exploring Operation: 97-10=87, Resulting Numbers: [58, 87] Generated Node #0,1,0: 31:[58, 87] Operation: 97-10=87 Exploring Operation: 58-10=48, Resulting Numbers: [97, 48] Generated Node #0,1,1: 31:[97, 48] Operation: 58-10=48 Exploring Operation: 97-58=39, Resulting Numbers: [10, 39] Generated Node #0,1,2: 31:[10, 39] Operation: 97-58=39 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[10, 39], Operations: ['98-88=10', '97-58=39'] Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,31 unequal: No Solution Exploring Operation: 10*39=390, Resulting Numbers: [390] 390,31 unequal: No Solution Exploring Operation: 10+39=49, Resulting Numbers: [49] 49,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[58, 87], Operations: ['98-88=10', '97-10=87'] Exploring Operation: 58*87=5046, Resulting Numbers: [5046] 5046,31 unequal: No Solution Exploring Operation: 87-58=29, Resulting Numbers: [29] 29,31 unequal: No Solution Exploring Operation: 58+87=145, Resulting Numbers: [145] 145,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[97, 48], Operations: ['98-88=10', '58-10=48'] Exploring Operation: 97+48=145, Resulting Numbers: [145] 145,31 unequal: No Solution Exploring Operation: 97-48=49, Resulting Numbers: [49] 49,31 unequal: No Solution Exploring Operation: 97*48=4656, Resulting Numbers: [4656] 4656,31 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: 31:[58, 88, 1], Operations: ['98-97=1'] Exploring Operation: 88-1=87, Resulting Numbers: [58, 87] Generated Node #0,2,0: 31:[58, 87] Operation: 88-1=87 Exploring Operation: 88-58=30, Resulting Numbers: [1, 30] Generated Node #0,2,1: 31:[1, 30] Operation: 88-58=30 Exploring Operation: 58-1=57, Resulting Numbers: [88, 57] Generated Node #0,2,2: 31:[88, 57] Operation: 58-1=57 Moving to Node #0,0 Current State: 31:[58, 98, 9], Operations: ['97-88=9'] Exploring Operation: 98-9=89, Resulting Numbers: [58, 89] Generated Node #0,0,0: 31:[58, 89] Operation: 98-9=89 Exploring Operation: 98-58=40, Resulting Numbers: [9, 40] Generated Node #0,0,1: 31:[9, 40] Operation: 98-58=40 Exploring Operation: 58-9=49, Resulting Numbers: [98, 49] Generated Node #0,0,2: 31:[98, 49] Operation: 58-9=49 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[9, 40], Operations: ['97-88=9', '98-58=40'] Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[58, 98, 97, 88], Operations: [] Exploring Operation: 97-88=9, Resulting Numbers: [58, 98, 9] Generated Node #0,0: 31:[58, 98, 9] Operation: 97-88=9 Moving to Node #0,0 Current State: 31:[58, 98, 9], Operations: ['97-88=9'] Exploring Operation: 98-58=40, Resulting Numbers: [9, 40] Generated Node #0,0,1: 31:[9, 40] Operation: 98-58=40 Moving to Node #0,0,1 Current State: 31:[9, 40], Operations: ['97-88=9', '98-58=40'] Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_3
mult_heuristic
[ 78, 81, 83, 52 ]
28
[ "81-78=3", "83-52=31", "31-3=28" ]
Current State: 28:[78, 81, 83, 52], Operations: [] Exploring Operation: 81-78=3, Resulting Numbers: [83, 52, 3] Generated Node #2: [83, 52, 3] from Operation: 81-78=3 Current State: 28:[83, 52, 3], Operations: ['81-78=3'] Exploring Operation: 83-52=31, Resulting Numbers: [3, 31] Generated Node #3: [3, 31] from Operation: 83-52=31 Current State: 28:[3, 31], Operations: ['81-78=3', '83-52=31'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[78, 81, 83, 52], Operations: [] Exploring Operation: 83-78=5, Resulting Numbers: [81, 52, 5] Generated Node #0,0: 28:[81, 52, 5] Operation: 83-78=5 Exploring Operation: 83-81=2, Resulting Numbers: [78, 52, 2] Generated Node #0,1: 28:[78, 52, 2] Operation: 83-81=2 Exploring Operation: 81-78=3, Resulting Numbers: [83, 52, 3] Generated Node #0,2: 28:[83, 52, 3] Operation: 81-78=3 Moving to Node #0,1 Current State: 28:[78, 52, 2], Operations: ['83-81=2'] Exploring Operation: 52/2=26, Resulting Numbers: [78, 26] Generated Node #0,1,0: 28:[78, 26] Operation: 52/2=26 Exploring Operation: 78-52=26, Resulting Numbers: [2, 26] Generated Node #0,1,1: 28:[2, 26] Operation: 78-52=26 Exploring Operation: 78/2=39, Resulting Numbers: [52, 39] Generated Node #0,1,2: 28:[52, 39] Operation: 78/2=39 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 28:[2, 26], Operations: ['83-81=2', '78-52=26'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,28 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,28 unequal: No Solution Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[78, 81, 83, 52], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [78, 52, 2] Generated Node #0,1: 28:[78, 52, 2] Operation: 83-81=2 Moving to Node #0,1 Current State: 28:[78, 52, 2], Operations: ['83-81=2'] Exploring Operation: 78-52=26, Resulting Numbers: [2, 26] Generated Node #0,1,1: 28:[2, 26] Operation: 78-52=26 Moving to Node #0,1,1 Current State: 28:[2, 26], Operations: ['83-81=2', '78-52=26'] Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 28, 25, 66, 21 ]
63
[ "28*66=1848", "1848/21=88", "88-25=63" ]
Current State: 63:[28, 25, 66, 21], Operations: [] Exploring Operation: 28*66=1848, Resulting Numbers: [25, 21, 1848] Generated Node #2: [25, 21, 1848] from Operation: 28*66=1848 Current State: 63:[25, 21, 1848], Operations: ['28*66=1848'] Exploring Operation: 1848/21=88, Resulting Numbers: [25, 88] Generated Node #3: [25, 88] from Operation: 1848/21=88 Current State: 63:[25, 88], Operations: ['28*66=1848', '1848/21=88'] Exploring Operation: 88-25=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[28, 25, 66, 21], Operations: [] Exploring Operation: 28-25=3, Resulting Numbers: [66, 21, 3] Generated Node #0,0: 63:[66, 21, 3] Operation: 28-25=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[66, 21, 3], Operations: ['28-25=3'] Exploring Operation: 66-3=63, Resulting Numbers: [21, 63] Generated Node #0,0,0: 63:[21, 63] Operation: 66-3=63 Moving to Node #0,0,0 Current State: 63:[21, 63], Operations: ['28-25=3', '66-3=63'] Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,63 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