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
[ 81, 89, 6, 83 ]
81
[ "81+89=170", "6+83=89", "170-89=81" ]
Current State: 81:[81, 89, 6, 83], Operations: [] Exploring Operation: 81+89=170, Resulting Numbers: [6, 83, 170] Generated Node #2: [6, 83, 170] from Operation: 81+89=170 Current State: 81:[6, 83, 170], Operations: ['81+89=170'] Exploring Operation: 6+83=89, Resulting Numbers: [170, 89] Generated Node #3: [170, 89] from Operation: 6+83=89 Current State: 81:[170, 89], Operations: ['81+89=170', '6+83=89'] Exploring Operation: 170-89=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[81, 89, 6, 83], Operations: [] Exploring Operation: 89-6=83, Resulting Numbers: [81, 83, 83] Generated Node #0,0: 81:[81, 83, 83] Operation: 89-6=83 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[81, 83, 83], Operations: ['89-6=83'] Exploring Operation: 83/83=1, Resulting Numbers: [81, 1] Generated Node #0,0,0: 81:[81, 1] Operation: 83/83=1 Moving to Node #0,0,0 Current State: 81:[81, 1], Operations: ['89-6=83', '83/83=1'] Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[81, 89, 6, 83], Operations: [] Exploring Operation: 89-6=83, Resulting Numbers: [81, 83, 83] Generated Node #0,0: 81:[81, 83, 83] Operation: 89-6=83 Moving to Node #0,0 Current State: 81:[81, 83, 83], Operations: ['89-6=83'] Exploring Operation: 83/83=1, Resulting Numbers: [81, 1] Generated Node #0,0,0: 81:[81, 1] Operation: 83/83=1 Moving to Node #0,0,0 Current State: 81:[81, 1], Operations: ['89-6=83', '83/83=1'] Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 64, 25, 8, 21 ]
18
[ "64+8=72", "25-21=4", "72/4=18" ]
Current State: 18:[64, 25, 8, 21], Operations: [] Exploring Operation: 64+8=72, Resulting Numbers: [25, 21, 72] Generated Node #2: [25, 21, 72] from Operation: 64+8=72 Current State: 18:[25, 21, 72], Operations: ['64+8=72'] Exploring Operation: 25-21=4, Resulting Numbers: [72, 4] Generated Node #3: [72, 4] from Operation: 25-21=4 Current State: 18:[72, 4], Operations: ['64+8=72', '25-21=4'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[64, 25, 8, 21], Operations: [] Exploring Operation: 64/8=8, Resulting Numbers: [25, 21, 8] Generated Node #0,0: 18:[25, 21, 8] Operation: 64/8=8 Exploring Operation: 64-25=39, Resulting Numbers: [8, 21, 39] Generated Node #0,1: 18:[8, 21, 39] Operation: 64-25=39 Exploring Operation: 64-8=56, Resulting Numbers: [25, 21, 56] Generated Node #0,2: 18:[25, 21, 56] Operation: 64-8=56 Exploring Operation: 64-21=43, Resulting Numbers: [25, 8, 43] Generated Node #0,3: 18:[25, 8, 43] Operation: 64-21=43 Moving to Node #0,0 Current State: 18:[25, 21, 8], Operations: ['64/8=8'] Exploring Operation: 25+8=33, Resulting Numbers: [21, 33] Generated Node #0,0,0: 18:[21, 33] Operation: 25+8=33 Exploring Operation: 25-21=4, Resulting Numbers: [8, 4] Generated Node #0,0,1: 18:[8, 4] Operation: 25-21=4 Exploring Operation: 25-8=17, Resulting Numbers: [21, 17] Generated Node #0,0,2: 18:[21, 17] Operation: 25-8=17 Exploring Operation: 21-8=13, Resulting Numbers: [25, 13] Generated Node #0,0,3: 18:[25, 13] Operation: 21-8=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[8, 4], Operations: ['64/8=8', '25-21=4'] Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,18 unequal: No Solution Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[21, 17], Operations: ['64/8=8', '25-8=17'] Exploring Operation: 21*17=357, Resulting Numbers: [357] 357,18 unequal: No Solution Exploring Operation: 21+17=38, Resulting Numbers: [38] 38,18 unequal: No Solution Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 18:[25, 13], Operations: ['64/8=8', '21-8=13'] Exploring Operation: 25+13=38, Resulting Numbers: [38] 38,18 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 25*13=325, Resulting Numbers: [325] 325,18 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 #0,0,0 Current State: 18:[21, 33], Operations: ['64/8=8', '25+8=33'] Exploring Operation: 21+33=54, Resulting Numbers: [54] 54,18 unequal: No Solution Exploring Operation: 21*33=693, Resulting Numbers: [693] 693,18 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,18 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: 18:[8, 21, 39], Operations: ['64-25=39'] Exploring Operation: 8+21=29, Resulting Numbers: [39, 29] Generated Node #0,1,0: 18:[39, 29] Operation: 8+21=29 Exploring Operation: 21-8=13, Resulting Numbers: [39, 13] Generated Node #0,1,1: 18:[39, 13] Operation: 21-8=13 Exploring Operation: 39-8=31, Resulting Numbers: [21, 31] Generated Node #0,1,2: 18:[21, 31] Operation: 39-8=31 Exploring Operation: 39-21=18, Resulting Numbers: [8, 18] Generated Node #0,1,3: 18:[8, 18] Operation: 39-21=18 Moving to Node #0,3 Current State: 18:[25, 8, 43], Operations: ['64-21=43'] Exploring Operation: 25-8=17, Resulting Numbers: [43, 17] Generated Node #0,3,0: 18:[43, 17] Operation: 25-8=17 Exploring Operation: 25+8=33, Resulting Numbers: [43, 33] Generated Node #0,3,1: 18:[43, 33] Operation: 25+8=33 Exploring Operation: 43-25=18, Resulting Numbers: [8, 18] Generated Node #0,3,2: 18:[8, 18] Operation: 43-25=18 Exploring Operation: 43-8=35, Resulting Numbers: [25, 35] Generated Node #0,3,3: 18:[25, 35] Operation: 43-8=35 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 18:[8, 18], Operations: ['64-21=43', '43-25=18'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,18 unequal: No Solution Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 18:[25, 35], Operations: ['64-21=43', '43-8=35'] Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 25*35=875, Resulting Numbers: [875] 875,18 unequal: No Solution Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 18:[43, 17], Operations: ['64-21=43', '25-8=17'] Exploring Operation: 43-17=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 43*17=731, Resulting Numbers: [731] 731,18 unequal: No Solution Exploring Operation: 43+17=60, Resulting Numbers: [60] 60,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 18:[43, 33], Operations: ['64-21=43', '25+8=33'] Exploring Operation: 43*33=1419, Resulting Numbers: [1419] 1419,18 unequal: No Solution Exploring Operation: 43+33=76, Resulting Numbers: [76] 76,18 unequal: No Solution Exploring Operation: 43-33=10, Resulting Numbers: [10] 10,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 18:[25, 21, 56], Operations: ['64-8=56'] Exploring Operation: 25+21=46, Resulting Numbers: [56, 46] Generated Node #0,2,0: 18:[56, 46] Operation: 25+21=46 Exploring Operation: 56-21=35, Resulting Numbers: [25, 35] Generated Node #0,2,1: 18:[25, 35] Operation: 56-21=35 Exploring Operation: 25-21=4, Resulting Numbers: [56, 4] Generated Node #0,2,2: 18:[56, 4] Operation: 25-21=4 Exploring Operation: 56-25=31, Resulting Numbers: [21, 31] Generated Node #0,2,3: 18:[21, 31] Operation: 56-25=31 Moving to Node #0,1,3 Current State: 18:[8, 18], Operations: ['64-25=39', '39-21=18'] Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,18 unequal: No Solution Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[21, 31], Operations: ['64-25=39', '39-8=31'] Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,18 unequal: No Solution Moving to Node #0,2,3 Current State: 18:[21, 31], Operations: ['64-8=56', '56-25=31'] Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,18 unequal: No Solution Moving to Node #0,2,1 Current State: 18:[25, 35], Operations: ['64-8=56', '56-21=35'] Exploring Operation: 25*35=875, Resulting Numbers: [875] 875,18 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[39, 13], Operations: ['64-25=39', '21-8=13'] Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 39*13=507, Resulting Numbers: [507] 507,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[39, 29], Operations: ['64-25=39', '8+21=29'] Exploring Operation: 39*29=1131, Resulting Numbers: [1131] 1131,18 unequal: No Solution Exploring Operation: 39-29=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 39+29=68, Resulting Numbers: [68] 68,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[56, 4], Operations: ['64-8=56', '25-21=4'] Exploring Operation: 56*4=224, Resulting Numbers: [224] 224,18 unequal: No Solution Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 56+4=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[56, 46], Operations: ['64-8=56', '25+21=46'] Exploring Operation: 56-46=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 56+46=102, Resulting Numbers: [102] 102,18 unequal: No Solution Exploring Operation: 56*46=2576, Resulting Numbers: [2576] 2576,18 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 76, 82, 14, 38 ]
75
[ "76/38=2", "14/2=7", "82-7=75" ]
Current State: 75:[76, 82, 14, 38], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [82, 14, 2] Generated Node #2: [82, 14, 2] from Operation: 76/38=2 Current State: 75:[82, 14, 2], Operations: ['76/38=2'] Exploring Operation: 14/2=7, Resulting Numbers: [82, 7] Generated Node #3: [82, 7] from Operation: 14/2=7 Current State: 75:[82, 7], Operations: ['76/38=2', '14/2=7'] Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[76, 82, 14, 38], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [82, 14, 2] Generated Node #0,0: 75:[82, 14, 2] Operation: 76/38=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[82, 14, 2], Operations: ['76/38=2'] Exploring Operation: 82-2=80, Resulting Numbers: [14, 80] Generated Node #0,0,0: 75:[14, 80] Operation: 82-2=80 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[14, 80], Operations: ['76/38=2', '82-2=80'] Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 25, 45, 32, 70 ]
55
[ "32-25=7", "70/7=10", "45+10=55" ]
Current State: 55:[25, 45, 32, 70], Operations: [] Exploring Operation: 32-25=7, Resulting Numbers: [45, 70, 7] Generated Node #2: [45, 70, 7] from Operation: 32-25=7 Current State: 55:[45, 70, 7], Operations: ['32-25=7'] Exploring Operation: 70/7=10, Resulting Numbers: [45, 10] Generated Node #3: [45, 10] from Operation: 70/7=10 Current State: 55:[45, 10], Operations: ['32-25=7', '70/7=10'] Exploring Operation: 45+10=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[25, 45, 32, 70], Operations: [] Exploring Operation: 32-25=7, Resulting Numbers: [45, 70, 7] Generated Node #0,0: 55:[45, 70, 7] Operation: 32-25=7 Exploring Operation: 25+32=57, Resulting Numbers: [45, 70, 57] Generated Node #0,1: 55:[45, 70, 57] Operation: 25+32=57 Exploring Operation: 45-32=13, Resulting Numbers: [25, 70, 13] Generated Node #0,2: 55:[25, 70, 13] Operation: 45-32=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[45, 70, 7], Operations: ['32-25=7'] Exploring Operation: 70/7=10, Resulting Numbers: [45, 10] Generated Node #0,0,0: 55:[45, 10] Operation: 70/7=10 Exploring Operation: 70-45=25, Resulting Numbers: [7, 25] Generated Node #0,0,1: 55:[7, 25] Operation: 70-45=25 Exploring Operation: 45+7=52, Resulting Numbers: [70, 52] Generated Node #0,0,2: 55:[70, 52] Operation: 45+7=52 Moving to Node #0,0,0 Current State: 55:[45, 10], Operations: ['32-25=7', '70/7=10'] Exploring Operation: 45+10=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[25, 45, 32, 70], Operations: [] Exploring Operation: 32-25=7, Resulting Numbers: [45, 70, 7] Generated Node #0,0: 55:[45, 70, 7] Operation: 32-25=7 Moving to Node #0,0 Current State: 55:[45, 70, 7], Operations: ['32-25=7'] Exploring Operation: 70/7=10, Resulting Numbers: [45, 10] Generated Node #0,0,0: 55:[45, 10] Operation: 70/7=10 Moving to Node #0,0,0 Current State: 55:[45, 10], Operations: ['32-25=7', '70/7=10'] Exploring Operation: 45+10=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 3, 4, 79, 1 ]
18
[ "79-3=76", "76/4=19", "19-1=18" ]
Current State: 18:[3, 4, 79, 1], Operations: [] Exploring Operation: 79-3=76, Resulting Numbers: [4, 1, 76] Generated Node #2: [4, 1, 76] from Operation: 79-3=76 Current State: 18:[4, 1, 76], Operations: ['79-3=76'] Exploring Operation: 76/4=19, Resulting Numbers: [1, 19] Generated Node #3: [1, 19] from Operation: 76/4=19 Current State: 18:[1, 19], Operations: ['79-3=76', '76/4=19'] Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[3, 4, 79, 1], Operations: [] Exploring Operation: 79-1=78, Resulting Numbers: [3, 4, 78] Generated Node #0,0: 18:[3, 4, 78] Operation: 79-1=78 Exploring Operation: 79-3=76, Resulting Numbers: [4, 1, 76] Generated Node #0,1: 18:[4, 1, 76] Operation: 79-3=76 Exploring Operation: 4-1=3, Resulting Numbers: [3, 79, 3] Generated Node #0,2: 18:[3, 79, 3] Operation: 4-1=3 Exploring Operation: 79-4=75, Resulting Numbers: [3, 1, 75] Generated Node #0,3: 18:[3, 1, 75] Operation: 79-4=75 Start Sub Search at level 1: Moving to Node #0,3 Current State: 18:[3, 1, 75], Operations: ['79-4=75'] Exploring Operation: 75-3=72, Resulting Numbers: [1, 72] Generated Node #0,3,0: 18:[1, 72] Operation: 75-3=72 Exploring Operation: 3*1=3, Resulting Numbers: [75, 3] Generated Node #0,3,1: 18:[75, 3] Operation: 3*1=3 Exploring Operation: 75-1=74, Resulting Numbers: [3, 74] Generated Node #0,3,2: 18:[3, 74] Operation: 75-1=74 Exploring Operation: 75/3=25, Resulting Numbers: [1, 25] Generated Node #0,3,3: 18:[1, 25] Operation: 75/3=25 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 18:[1, 25], Operations: ['79-4=75', '75/3=25'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 1*25=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 1+25=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 18:[1, 72], Operations: ['79-4=75', '75-3=72'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,18 unequal: No Solution Exploring Operation: 1+72=73, Resulting Numbers: [73] 73,18 unequal: No Solution Exploring Operation: 1*72=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 18:[3, 74], Operations: ['79-4=75', '75-1=74'] Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,18 unequal: No Solution Exploring Operation: 3+74=77, Resulting Numbers: [77] 77,18 unequal: No Solution Exploring Operation: 3*74=222, Resulting Numbers: [222] 222,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 18:[75, 3], Operations: ['79-4=75', '3*1=3'] Exploring Operation: 75-3=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 75+3=78, Resulting Numbers: [78] 78,18 unequal: No Solution Exploring Operation: 75/3=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 75*3=225, Resulting Numbers: [225] 225,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[4, 1, 76], Operations: ['79-3=76'] Exploring Operation: 4-1=3, Resulting Numbers: [76, 3] Generated Node #0,1,0: 18:[76, 3] Operation: 4-1=3 Exploring Operation: 76-1=75, Resulting Numbers: [4, 75] Generated Node #0,1,1: 18:[4, 75] Operation: 76-1=75 Exploring Operation: 76-4=72, Resulting Numbers: [1, 72] Generated Node #0,1,2: 18:[1, 72] Operation: 76-4=72 Exploring Operation: 76/4=19, Resulting Numbers: [1, 19] Generated Node #0,1,3: 18:[1, 19] Operation: 76/4=19 Moving to Node #0,1,3 Current State: 18:[1, 19], Operations: ['79-3=76', '76/4=19'] Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 1+19=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[3, 4, 79, 1], Operations: [] Exploring Operation: 79-3=76, Resulting Numbers: [4, 1, 76] Generated Node #0,1: 18:[4, 1, 76] Operation: 79-3=76 Moving to Node #0,1 Current State: 18:[4, 1, 76], Operations: ['79-3=76'] Exploring Operation: 76/4=19, Resulting Numbers: [1, 19] Generated Node #0,1,3: 18:[1, 19] Operation: 76/4=19 Moving to Node #0,1,3 Current State: 18:[1, 19], Operations: ['79-3=76', '76/4=19'] Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
mult_heuristic
[ 65, 75, 16, 88 ]
94
[ "75-65=10", "16+88=104", "104-10=94" ]
Current State: 94:[65, 75, 16, 88], Operations: [] Exploring Operation: 75-65=10, Resulting Numbers: [16, 88, 10] Generated Node #2: [16, 88, 10] from Operation: 75-65=10 Current State: 94:[16, 88, 10], Operations: ['75-65=10'] Exploring Operation: 16+88=104, Resulting Numbers: [10, 104] Generated Node #3: [10, 104] from Operation: 16+88=104 Current State: 94:[10, 104], Operations: ['75-65=10', '16+88=104'] Exploring Operation: 104-10=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[65, 75, 16, 88], Operations: [] Exploring Operation: 65+16=81, Resulting Numbers: [75, 88, 81] Generated Node #0,0: 94:[75, 88, 81] Operation: 65+16=81 Exploring Operation: 75+16=91, Resulting Numbers: [65, 88, 91] Generated Node #0,1: 94:[65, 88, 91] Operation: 75+16=91 Exploring Operation: 75-65=10, Resulting Numbers: [16, 88, 10] Generated Node #0,2: 94:[16, 88, 10] Operation: 75-65=10 Exploring Operation: 65-16=49, Resulting Numbers: [75, 88, 49] Generated Node #0,3: 94:[75, 88, 49] Operation: 65-16=49 Exploring Operation: 75-16=59, Resulting Numbers: [65, 88, 59] Generated Node #0,4: 94:[65, 88, 59] Operation: 75-16=59 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[65, 88, 91], Operations: ['75+16=91'] Exploring Operation: 65+88=153, Resulting Numbers: [91, 153] Generated Node #0,1,0: 94:[91, 153] Operation: 65+88=153 Exploring Operation: 65+91=156, Resulting Numbers: [88, 156] Generated Node #0,1,1: 94:[88, 156] Operation: 65+91=156 Exploring Operation: 88-65=23, Resulting Numbers: [91, 23] Generated Node #0,1,2: 94:[91, 23] Operation: 88-65=23 Exploring Operation: 91-88=3, Resulting Numbers: [65, 3] Generated Node #0,1,3: 94:[65, 3] Operation: 91-88=3 Exploring Operation: 91-65=26, Resulting Numbers: [88, 26] Generated Node #0,1,4: 94:[88, 26] Operation: 91-65=26 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 94:[65, 3], Operations: ['75+16=91', '91-88=3'] Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,94 unequal: No Solution Exploring Operation: 65*3=195, Resulting Numbers: [195] 195,94 unequal: No Solution Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 94:[91, 23], Operations: ['75+16=91', '88-65=23'] Exploring Operation: 91-23=68, Resulting Numbers: [68] 68,94 unequal: No Solution Exploring Operation: 91*23=2093, Resulting Numbers: [2093] 2093,94 unequal: No Solution Exploring Operation: 91+23=114, Resulting Numbers: [114] 114,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 94:[88, 26], Operations: ['75+16=91', '91-65=26'] Exploring Operation: 88+26=114, Resulting Numbers: [114] 114,94 unequal: No Solution Exploring Operation: 88-26=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 88*26=2288, Resulting Numbers: [2288] 2288,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[91, 153], Operations: ['75+16=91', '65+88=153'] Exploring Operation: 91*153=13923, Resulting Numbers: [13923] 13923,94 unequal: No Solution Exploring Operation: 153-91=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 91+153=244, Resulting Numbers: [244] 244,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[88, 156], Operations: ['75+16=91', '65+91=156'] Exploring Operation: 156-88=68, Resulting Numbers: [68] 68,94 unequal: No Solution Exploring Operation: 88*156=13728, Resulting Numbers: [13728] 13728,94 unequal: No Solution Exploring Operation: 88+156=244, Resulting Numbers: [244] 244,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[75, 88, 49], Operations: ['65-16=49'] Exploring Operation: 88+49=137, Resulting Numbers: [75, 137] Generated Node #0,3,0: 94:[75, 137] Operation: 88+49=137 Exploring Operation: 75-49=26, Resulting Numbers: [88, 26] Generated Node #0,3,1: 94:[88, 26] Operation: 75-49=26 Exploring Operation: 75+49=124, Resulting Numbers: [88, 124] Generated Node #0,3,2: 94:[88, 124] Operation: 75+49=124 Exploring Operation: 88-75=13, Resulting Numbers: [49, 13] Generated Node #0,3,3: 94:[49, 13] Operation: 88-75=13 Exploring Operation: 88-49=39, Resulting Numbers: [75, 39] Generated Node #0,3,4: 94:[75, 39] Operation: 88-49=39 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 94:[49, 13], Operations: ['65-16=49', '88-75=13'] Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,94 unequal: No Solution Exploring Operation: 49*13=637, Resulting Numbers: [637] 637,94 unequal: No Solution Exploring Operation: 49+13=62, Resulting Numbers: [62] 62,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 94:[88, 26], Operations: ['65-16=49', '75-49=26'] Exploring Operation: 88-26=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 88*26=2288, Resulting Numbers: [2288] 2288,94 unequal: No Solution Exploring Operation: 88+26=114, Resulting Numbers: [114] 114,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 94:[75, 39], Operations: ['65-16=49', '88-49=39'] Exploring Operation: 75-39=36, Resulting Numbers: [36] 36,94 unequal: No Solution Exploring Operation: 75*39=2925, Resulting Numbers: [2925] 2925,94 unequal: No Solution Exploring Operation: 75+39=114, Resulting Numbers: [114] 114,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 94:[88, 124], Operations: ['65-16=49', '75+49=124'] Exploring Operation: 88+124=212, Resulting Numbers: [212] 212,94 unequal: No Solution Exploring Operation: 88*124=10912, Resulting Numbers: [10912] 10912,94 unequal: No Solution Exploring Operation: 124-88=36, Resulting Numbers: [36] 36,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 94:[75, 137], Operations: ['65-16=49', '88+49=137'] Exploring Operation: 137-75=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 75*137=10275, Resulting Numbers: [10275] 10275,94 unequal: No Solution Exploring Operation: 75+137=212, Resulting Numbers: [212] 212,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[16, 88, 10], Operations: ['75-65=10'] Exploring Operation: 16+88=104, Resulting Numbers: [10, 104] Generated Node #0,2,0: 94:[10, 104] Operation: 16+88=104 Exploring Operation: 16+10=26, Resulting Numbers: [88, 26] Generated Node #0,2,1: 94:[88, 26] Operation: 16+10=26 Exploring Operation: 16-10=6, Resulting Numbers: [88, 6] Generated Node #0,2,2: 94:[88, 6] Operation: 16-10=6 Exploring Operation: 88-16=72, Resulting Numbers: [10, 72] Generated Node #0,2,3: 94:[10, 72] Operation: 88-16=72 Exploring Operation: 88+10=98, Resulting Numbers: [16, 98] Generated Node #0,2,4: 94:[16, 98] Operation: 88+10=98 Moving to Node #0,2,2 Current State: 94:[88, 6], Operations: ['75-65=10', '16-10=6'] Exploring Operation: 88-6=82, Resulting Numbers: [82] 82,94 unequal: No Solution Exploring Operation: 88*6=528, Resulting Numbers: [528] 528,94 unequal: No Solution Exploring Operation: 88+6=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[65, 75, 16, 88], Operations: [] Exploring Operation: 75-65=10, Resulting Numbers: [16, 88, 10] Generated Node #0,2: 94:[16, 88, 10] Operation: 75-65=10 Moving to Node #0,2 Current State: 94:[16, 88, 10], Operations: ['75-65=10'] Exploring Operation: 16-10=6, Resulting Numbers: [88, 6] Generated Node #0,2,2: 94:[88, 6] Operation: 16-10=6 Moving to Node #0,2,2 Current State: 94:[88, 6], Operations: ['75-65=10', '16-10=6'] Exploring Operation: 88+6=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.950521
hs_5
sum_heuristic
[ 2, 51, 76, 65 ]
45
[ "76-51=25", "65+25=90", "90/2=45" ]
Current State: 45:[2, 51, 76, 65], Operations: [] Exploring Operation: 76-51=25, Resulting Numbers: [2, 65, 25] Generated Node #2: [2, 65, 25] from Operation: 76-51=25 Current State: 45:[2, 65, 25], Operations: ['76-51=25'] Exploring Operation: 65+25=90, Resulting Numbers: [2, 90] Generated Node #3: [2, 90] from Operation: 65+25=90 Current State: 45:[2, 90], Operations: ['76-51=25', '65+25=90'] Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[2, 51, 76, 65], Operations: [] Exploring Operation: 65-51=14, Resulting Numbers: [2, 76, 14] Generated Node #0,0: 45:[2, 76, 14] Operation: 65-51=14 Exploring Operation: 76-65=11, Resulting Numbers: [2, 51, 11] Generated Node #0,1: 45:[2, 51, 11] Operation: 76-65=11 Exploring Operation: 76-51=25, Resulting Numbers: [2, 65, 25] Generated Node #0,2: 45:[2, 65, 25] Operation: 76-51=25 Exploring Operation: 76/2=38, Resulting Numbers: [51, 65, 38] Generated Node #0,3: 45:[51, 65, 38] Operation: 76/2=38 Moving to Node #0,1 Current State: 45:[2, 51, 11], Operations: ['76-65=11'] Exploring Operation: 51-2=49, Resulting Numbers: [11, 49] Generated Node #0,1,0: 45:[11, 49] Operation: 51-2=49 Exploring Operation: 11-2=9, Resulting Numbers: [51, 9] Generated Node #0,1,1: 45:[51, 9] Operation: 11-2=9 Exploring Operation: 2+11=13, Resulting Numbers: [51, 13] Generated Node #0,1,2: 45:[51, 13] Operation: 2+11=13 Exploring Operation: 51-11=40, Resulting Numbers: [2, 40] Generated Node #0,1,3: 45:[2, 40] Operation: 51-11=40 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[11, 49], Operations: ['76-65=11', '51-2=49'] Exploring Operation: 11*49=539, Resulting Numbers: [539] 539,45 unequal: No Solution Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 11+49=60, Resulting Numbers: [60] 60,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[51, 9], Operations: ['76-65=11', '11-2=9'] Exploring Operation: 51+9=60, Resulting Numbers: [60] 60,45 unequal: No Solution Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,45 unequal: No Solution Exploring Operation: 51*9=459, Resulting Numbers: [459] 459,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 45:[2, 40], Operations: ['76-65=11', '51-11=40'] Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,45 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,45 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[51, 13], Operations: ['76-65=11', '2+11=13'] Exploring Operation: 51*13=663, Resulting Numbers: [663] 663,45 unequal: No Solution Exploring Operation: 51-13=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 51+13=64, Resulting Numbers: [64] 64,45 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: 45:[2, 65, 25], Operations: ['76-51=25'] Exploring Operation: 65-2=63, Resulting Numbers: [25, 63] Generated Node #0,2,0: 45:[25, 63] Operation: 65-2=63 Exploring Operation: 65-25=40, Resulting Numbers: [2, 40] Generated Node #0,2,1: 45:[2, 40] Operation: 65-25=40 Exploring Operation: 25-2=23, Resulting Numbers: [65, 23] Generated Node #0,2,2: 45:[65, 23] Operation: 25-2=23 Exploring Operation: 2*25=50, Resulting Numbers: [65, 50] Generated Node #0,2,3: 45:[65, 50] Operation: 2*25=50 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 45:[2, 40], Operations: ['76-51=25', '65-25=40'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,45 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 45:[65, 50], Operations: ['76-51=25', '2*25=50'] Exploring Operation: 65-50=15, Resulting Numbers: [15] 15,45 unequal: No Solution Exploring Operation: 65*50=3250, Resulting Numbers: [3250] 3250,45 unequal: No Solution Exploring Operation: 65+50=115, Resulting Numbers: [115] 115,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 45:[25, 63], Operations: ['76-51=25', '65-2=63'] Exploring Operation: 63-25=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 25+63=88, Resulting Numbers: [88] 88,45 unequal: No Solution Exploring Operation: 25*63=1575, Resulting Numbers: [1575] 1575,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 45:[65, 23], Operations: ['76-51=25', '25-2=23'] Exploring Operation: 65+23=88, Resulting Numbers: [88] 88,45 unequal: No Solution Exploring Operation: 65*23=1495, Resulting Numbers: [1495] 1495,45 unequal: No Solution Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,45 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: 45:[51, 65, 38], Operations: ['76/2=38'] Exploring Operation: 65-38=27, Resulting Numbers: [51, 27] Generated Node #0,3,0: 45:[51, 27] Operation: 65-38=27 Exploring Operation: 51+38=89, Resulting Numbers: [65, 89] Generated Node #0,3,1: 45:[65, 89] Operation: 51+38=89 Exploring Operation: 65-51=14, Resulting Numbers: [38, 14] Generated Node #0,3,2: 45:[38, 14] Operation: 65-51=14 Exploring Operation: 51-38=13, Resulting Numbers: [65, 13] Generated Node #0,3,3: 45:[65, 13] Operation: 51-38=13 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 45:[38, 14], Operations: ['76/2=38', '65-51=14'] Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,45 unequal: No Solution Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,45 unequal: No Solution Exploring Operation: 38*14=532, Resulting Numbers: [532] 532,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 45:[51, 27], Operations: ['76/2=38', '65-38=27'] Exploring Operation: 51+27=78, Resulting Numbers: [78] 78,45 unequal: No Solution Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,45 unequal: No Solution Exploring Operation: 51*27=1377, Resulting Numbers: [1377] 1377,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 45:[65, 13], Operations: ['76/2=38', '51-38=13'] Exploring Operation: 65+13=78, Resulting Numbers: [78] 78,45 unequal: No Solution Exploring Operation: 65*13=845, Resulting Numbers: [845] 845,45 unequal: No Solution Exploring Operation: 65-13=52, Resulting Numbers: [52] 52,45 unequal: No Solution Exploring Operation: 65/13=5, Resulting Numbers: [5] 5,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 45:[65, 89], Operations: ['76/2=38', '51+38=89'] Exploring Operation: 65*89=5785, Resulting Numbers: [5785] 5785,45 unequal: No Solution Exploring Operation: 65+89=154, Resulting Numbers: [154] 154,45 unequal: No Solution Exploring Operation: 89-65=24, Resulting Numbers: [24] 24,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 45:[2, 76, 14], Operations: ['65-51=14'] Exploring Operation: 2+14=16, Resulting Numbers: [76, 16] Generated Node #0,0,0: 45:[76, 16] Operation: 2+14=16 Exploring Operation: 76/2=38, Resulting Numbers: [14, 38] Generated Node #0,0,1: 45:[14, 38] Operation: 76/2=38 Exploring Operation: 76-14=62, Resulting Numbers: [2, 62] Generated Node #0,0,2: 45:[2, 62] Operation: 76-14=62 Exploring Operation: 76-2=74, Resulting Numbers: [14, 74] Generated Node #0,0,3: 45:[14, 74] Operation: 76-2=74 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[14, 38], Operations: ['65-51=14', '76/2=38'] Exploring Operation: 14*38=532, Resulting Numbers: [532] 532,45 unequal: No Solution Exploring Operation: 14+38=52, Resulting Numbers: [52] 52,45 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,45 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 #0,0,2 Current State: 45:[2, 62], Operations: ['65-51=14', '76-14=62'] Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,45 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,45 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 2*62=124, Resulting Numbers: [124] 124,45 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 #0,0,3 Current State: 45:[14, 74], Operations: ['65-51=14', '76-2=74'] Exploring Operation: 74-14=60, Resulting Numbers: [60] 60,45 unequal: No Solution Exploring Operation: 14+74=88, Resulting Numbers: [88] 88,45 unequal: No Solution Exploring Operation: 14*74=1036, Resulting Numbers: [1036] 1036,45 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 #0,0,0 Current State: 45:[76, 16], Operations: ['65-51=14', '2+14=16'] Exploring Operation: 76*16=1216, Resulting Numbers: [1216] 1216,45 unequal: No Solution Exploring Operation: 76+16=92, Resulting Numbers: [92] 92,45 unequal: No Solution Exploring Operation: 76-16=60, Resulting Numbers: [60] 60,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 22, 10, 47, 21 ]
80
[ "22-10=12", "47+21=68", "12+68=80" ]
Current State: 80:[22, 10, 47, 21], Operations: [] Exploring Operation: 22-10=12, Resulting Numbers: [47, 21, 12] Generated Node #2: [47, 21, 12] from Operation: 22-10=12 Current State: 80:[47, 21, 12], Operations: ['22-10=12'] Exploring Operation: 47+21=68, Resulting Numbers: [12, 68] Generated Node #3: [12, 68] from Operation: 47+21=68 Current State: 80:[12, 68], Operations: ['22-10=12', '47+21=68'] Exploring Operation: 12+68=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[22, 10, 47, 21], Operations: [] Exploring Operation: 47-10=37, Resulting Numbers: [22, 21, 37] Generated Node #0,0: 80:[22, 21, 37] Operation: 47-10=37 Exploring Operation: 22-21=1, Resulting Numbers: [10, 47, 1] Generated Node #0,1: 80:[10, 47, 1] Operation: 22-21=1 Exploring Operation: 47-21=26, Resulting Numbers: [22, 10, 26] Generated Node #0,2: 80:[22, 10, 26] Operation: 47-21=26 Exploring Operation: 47-22=25, Resulting Numbers: [10, 21, 25] Generated Node #0,3: 80:[10, 21, 25] Operation: 47-22=25 Moving to Node #0,0 Current State: 80:[22, 21, 37], Operations: ['47-10=37'] Exploring Operation: 37-22=15, Resulting Numbers: [21, 15] Generated Node #0,0,0: 80:[21, 15] Operation: 37-22=15 Exploring Operation: 22-21=1, Resulting Numbers: [37, 1] Generated Node #0,0,1: 80:[37, 1] Operation: 22-21=1 Exploring Operation: 37-21=16, Resulting Numbers: [22, 16] Generated Node #0,0,2: 80:[22, 16] Operation: 37-21=16 Exploring Operation: 22+21=43, Resulting Numbers: [37, 43] Generated Node #0,0,3: 80:[37, 43] Operation: 22+21=43 Moving to Node #0,3 Current State: 80:[10, 21, 25], Operations: ['47-22=25'] Exploring Operation: 25-10=15, Resulting Numbers: [21, 15] Generated Node #0,3,0: 80:[21, 15] Operation: 25-10=15 Exploring Operation: 10+25=35, Resulting Numbers: [21, 35] Generated Node #0,3,1: 80:[21, 35] Operation: 10+25=35 Exploring Operation: 21-10=11, Resulting Numbers: [25, 11] Generated Node #0,3,2: 80:[25, 11] Operation: 21-10=11 Exploring Operation: 25-21=4, Resulting Numbers: [10, 4] Generated Node #0,3,3: 80:[10, 4] Operation: 25-21=4 Moving to Node #0,2 Current State: 80:[22, 10, 26], Operations: ['47-21=26'] Exploring Operation: 10+26=36, Resulting Numbers: [22, 36] Generated Node #0,2,0: 80:[22, 36] Operation: 10+26=36 Exploring Operation: 26-22=4, Resulting Numbers: [10, 4] Generated Node #0,2,1: 80:[10, 4] Operation: 26-22=4 Exploring Operation: 26-10=16, Resulting Numbers: [22, 16] Generated Node #0,2,2: 80:[22, 16] Operation: 26-10=16 Exploring Operation: 22-10=12, Resulting Numbers: [26, 12] Generated Node #0,2,3: 80:[26, 12] Operation: 22-10=12 Moving to Node #0,1 Current State: 80:[10, 47, 1], Operations: ['22-21=1'] Exploring Operation: 10/1=10, Resulting Numbers: [47, 10] Generated Node #0,1,0: 80:[47, 10] Operation: 10/1=10 Exploring Operation: 47-1=46, Resulting Numbers: [10, 46] Generated Node #0,1,1: 80:[10, 46] Operation: 47-1=46 Exploring Operation: 47-10=37, Resulting Numbers: [1, 37] Generated Node #0,1,2: 80:[1, 37] Operation: 47-10=37 Exploring Operation: 10*1=10, Resulting Numbers: [47, 10] Generated Node #0,1,3: 80:[47, 10] Operation: 10*1=10 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 80:[1, 37], Operations: ['22-21=1', '47-10=37'] Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,80 unequal: No Solution Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,80 unequal: No Solution Exploring Operation: 1*37=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:[10, 46], Operations: ['22-21=1', '47-1=46'] Exploring Operation: 10+46=56, Resulting Numbers: [56] 56,80 unequal: No Solution Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,80 unequal: No Solution Exploring Operation: 10*46=460, Resulting Numbers: [460] 460,80 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:[47, 10], Operations: ['22-21=1', '10/1=10'] Exploring Operation: 47+10=57, Resulting Numbers: [57] 57,80 unequal: No Solution Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 47*10=470, Resulting Numbers: [470] 470,80 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 #0,1,3 Current State: 80:[47, 10], Operations: ['22-21=1', '10*1=10'] Exploring Operation: 47*10=470, Resulting Numbers: [470] 470,80 unequal: No Solution Exploring Operation: 47+10=57, Resulting Numbers: [57] 57,80 unequal: No Solution Exploring Operation: 47-10=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 #0,3,3 Current State: 80:[10, 4], Operations: ['47-22=25', '25-21=4'] Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,80 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,80 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[10, 4], Operations: ['47-21=26', '26-22=4'] Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,80 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,80 unequal: No Solution Moving to Node #0,3,0 Current State: 80:[21, 15], Operations: ['47-22=25', '25-10=15'] Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,80 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,80 unequal: No Solution Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[22, 16], Operations: ['47-10=37', '37-21=16'] Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,80 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,80 unequal: No Solution Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[22, 16], Operations: ['47-21=26', '26-10=16'] Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,80 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,80 unequal: No Solution Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[21, 15], Operations: ['47-10=37', '37-22=15'] Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,80 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,80 unequal: No Solution Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[37, 1], Operations: ['47-10=37', '22-21=1'] Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,80 unequal: No Solution Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 37*1=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 37+1=38, Resulting Numbers: [38] 38,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[22, 36], Operations: ['47-21=26', '10+26=36'] Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,80 unequal: No Solution Exploring Operation: 22+36=58, Resulting Numbers: [58] 58,80 unequal: No Solution Exploring Operation: 22*36=792, Resulting Numbers: [792] 792,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[21, 35], Operations: ['47-22=25', '10+25=35'] Exploring Operation: 21+35=56, Resulting Numbers: [56] 56,80 unequal: No Solution Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,80 unequal: No Solution Exploring Operation: 21*35=735, Resulting Numbers: [735] 735,80 unequal: No Solution Moving to Node #0,3,2 Current State: 80:[25, 11], Operations: ['47-22=25', '21-10=11'] Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,80 unequal: No Solution Exploring Operation: 25*11=275, Resulting Numbers: [275] 275,80 unequal: No Solution Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[37, 43], Operations: ['47-10=37', '22+21=43'] Exploring Operation: 37+43=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[22, 10, 47, 21], Operations: [] Exploring Operation: 47-10=37, Resulting Numbers: [22, 21, 37] Generated Node #0,0: 80:[22, 21, 37] Operation: 47-10=37 Moving to Node #0,0 Current State: 80:[22, 21, 37], Operations: ['47-10=37'] Exploring Operation: 22+21=43, Resulting Numbers: [37, 43] Generated Node #0,0,3: 80:[37, 43] Operation: 22+21=43 Moving to Node #0,0,3 Current State: 80:[37, 43], Operations: ['47-10=37', '22+21=43'] Exploring Operation: 37+43=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
0.940104
hs_4
sum_heuristic
[ 49, 50, 40, 5 ]
51
[ "50-40=10", "10/5=2", "49+2=51" ]
Current State: 51:[49, 50, 40, 5], Operations: [] Exploring Operation: 50-40=10, Resulting Numbers: [49, 5, 10] Generated Node #2: [49, 5, 10] from Operation: 50-40=10 Current State: 51:[49, 5, 10], Operations: ['50-40=10'] Exploring Operation: 10/5=2, Resulting Numbers: [49, 2] Generated Node #3: [49, 2] from Operation: 10/5=2 Current State: 51:[49, 2], Operations: ['50-40=10', '10/5=2'] Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[49, 50, 40, 5], Operations: [] Exploring Operation: 40/5=8, Resulting Numbers: [49, 50, 8] Generated Node #0,0: 51:[49, 50, 8] Operation: 40/5=8 Exploring Operation: 50-49=1, Resulting Numbers: [40, 5, 1] Generated Node #0,1: 51:[40, 5, 1] Operation: 50-49=1 Exploring Operation: 50-40=10, Resulting Numbers: [49, 5, 10] Generated Node #0,2: 51:[49, 5, 10] Operation: 50-40=10 Exploring Operation: 49-40=9, Resulting Numbers: [50, 5, 9] Generated Node #0,3: 51:[50, 5, 9] Operation: 49-40=9 Exploring Operation: 40+5=45, Resulting Numbers: [49, 50, 45] Generated Node #0,4: 51:[49, 50, 45] Operation: 40+5=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[49, 50, 8], Operations: ['40/5=8'] Exploring Operation: 49+8=57, Resulting Numbers: [50, 57] Generated Node #0,0,0: 51:[50, 57] Operation: 49+8=57 Exploring Operation: 50-8=42, Resulting Numbers: [49, 42] Generated Node #0,0,1: 51:[49, 42] Operation: 50-8=42 Exploring Operation: 50+8=58, Resulting Numbers: [49, 58] Generated Node #0,0,2: 51:[49, 58] Operation: 50+8=58 Exploring Operation: 49-8=41, Resulting Numbers: [50, 41] Generated Node #0,0,3: 51:[50, 41] Operation: 49-8=41 Exploring Operation: 50-49=1, Resulting Numbers: [8, 1] Generated Node #0,0,4: 51:[8, 1] Operation: 50-49=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[50, 57], Operations: ['40/5=8', '49+8=57'] Exploring Operation: 50+57=107, Resulting Numbers: [107] 107,51 unequal: No Solution Exploring Operation: 57-50=7, Resulting Numbers: [7] 7,51 unequal: No Solution Exploring Operation: 50*57=2850, Resulting Numbers: [2850] 2850,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 51:[8, 1], Operations: ['40/5=8', '50-49=1'] Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,51 unequal: No Solution Exploring Operation: 8+1=9, Resulting Numbers: [9] 9,51 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,51 unequal: No Solution Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 51:[49, 58], Operations: ['40/5=8', '50+8=58'] Exploring Operation: 58-49=9, Resulting Numbers: [9] 9,51 unequal: No Solution Exploring Operation: 49*58=2842, Resulting Numbers: [2842] 2842,51 unequal: No Solution Exploring Operation: 49+58=107, Resulting Numbers: [107] 107,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 51:[49, 42], Operations: ['40/5=8', '50-8=42'] Exploring Operation: 49+42=91, Resulting Numbers: [91] 91,51 unequal: No Solution Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,51 unequal: No Solution Exploring Operation: 49*42=2058, Resulting Numbers: [2058] 2058,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 51:[50, 41], Operations: ['40/5=8', '49-8=41'] Exploring Operation: 50+41=91, Resulting Numbers: [91] 91,51 unequal: No Solution Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,51 unequal: No Solution Exploring Operation: 50*41=2050, Resulting Numbers: [2050] 2050,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[50, 5, 9], Operations: ['49-40=9'] Exploring Operation: 9-5=4, Resulting Numbers: [50, 4] Generated Node #0,3,0: 51:[50, 4] Operation: 9-5=4 Exploring Operation: 50+9=59, Resulting Numbers: [5, 59] Generated Node #0,3,1: 51:[5, 59] Operation: 50+9=59 Exploring Operation: 5+9=14, Resulting Numbers: [50, 14] Generated Node #0,3,2: 51:[50, 14] Operation: 5+9=14 Exploring Operation: 50+5=55, Resulting Numbers: [9, 55] Generated Node #0,3,3: 51:[9, 55] Operation: 50+5=55 Exploring Operation: 5*9=45, Resulting Numbers: [50, 45] Generated Node #0,3,4: 51:[50, 45] Operation: 5*9=45 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 51:[50, 4], Operations: ['49-40=9', '9-5=4'] Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,51 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,51 unequal: No Solution Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 51:[50, 14], Operations: ['49-40=9', '5+9=14'] Exploring Operation: 50+14=64, Resulting Numbers: [64] 64,51 unequal: No Solution Exploring Operation: 50-14=36, Resulting Numbers: [36] 36,51 unequal: No Solution Exploring Operation: 50*14=700, Resulting Numbers: [700] 700,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 51:[50, 45], Operations: ['49-40=9', '5*9=45'] Exploring Operation: 50-45=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 50*45=2250, Resulting Numbers: [2250] 2250,51 unequal: No Solution Exploring Operation: 50+45=95, Resulting Numbers: [95] 95,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 51:[5, 59], Operations: ['49-40=9', '50+9=59'] Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,51 unequal: No Solution Exploring Operation: 5+59=64, Resulting Numbers: [64] 64,51 unequal: No Solution Exploring Operation: 5*59=295, Resulting Numbers: [295] 295,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 51:[9, 55], Operations: ['49-40=9', '50+5=55'] Exploring Operation: 55-9=46, Resulting Numbers: [46] 46,51 unequal: No Solution Exploring Operation: 9*55=495, Resulting Numbers: [495] 495,51 unequal: No Solution Exploring Operation: 9+55=64, Resulting Numbers: [64] 64,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 51:[49, 50, 45], Operations: ['40+5=45'] Exploring Operation: 50+45=95, Resulting Numbers: [49, 95] Generated Node #0,4,0: 51:[49, 95] Operation: 50+45=95 Exploring Operation: 49+45=94, Resulting Numbers: [50, 94] Generated Node #0,4,1: 51:[50, 94] Operation: 49+45=94 Exploring Operation: 50-49=1, Resulting Numbers: [45, 1] Generated Node #0,4,2: 51:[45, 1] Operation: 50-49=1 Exploring Operation: 50-45=5, Resulting Numbers: [49, 5] Generated Node #0,4,3: 51:[49, 5] Operation: 50-45=5 Exploring Operation: 49-45=4, Resulting Numbers: [50, 4] Generated Node #0,4,4: 51:[50, 4] Operation: 49-45=4 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 51:[50, 4], Operations: ['40+5=45', '49-45=4'] Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,51 unequal: No Solution Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,51 unequal: No Solution Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 51:[49, 5], Operations: ['40+5=45', '50-45=5'] Exploring Operation: 49*5=245, Resulting Numbers: [245] 245,51 unequal: No Solution Exploring Operation: 49+5=54, Resulting Numbers: [54] 54,51 unequal: No Solution Exploring Operation: 49-5=44, Resulting Numbers: [44] 44,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 51:[45, 1], Operations: ['40+5=45', '50-49=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,51 unequal: No Solution Exploring Operation: 45+1=46, Resulting Numbers: [46] 46,51 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,51 unequal: No Solution Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 51:[50, 94], Operations: ['40+5=45', '49+45=94'] Exploring Operation: 50*94=4700, Resulting Numbers: [4700] 4700,51 unequal: No Solution Exploring Operation: 94-50=44, Resulting Numbers: [44] 44,51 unequal: No Solution Exploring Operation: 50+94=144, Resulting Numbers: [144] 144,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 51:[49, 95], Operations: ['40+5=45', '50+45=95'] Exploring Operation: 49+95=144, Resulting Numbers: [144] 144,51 unequal: No Solution Exploring Operation: 95-49=46, Resulting Numbers: [46] 46,51 unequal: No Solution Exploring Operation: 49*95=4655, Resulting Numbers: [4655] 4655,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[49, 5, 10], Operations: ['50-40=10'] Exploring Operation: 5*10=50, Resulting Numbers: [49, 50] Generated Node #0,2,0: 51:[49, 50] Operation: 5*10=50 Exploring Operation: 10/5=2, Resulting Numbers: [49, 2] Generated Node #0,2,1: 51:[49, 2] Operation: 10/5=2 Exploring Operation: 10-5=5, Resulting Numbers: [49, 5] Generated Node #0,2,2: 51:[49, 5] Operation: 10-5=5 Exploring Operation: 5+10=15, Resulting Numbers: [49, 15] Generated Node #0,2,3: 51:[49, 15] Operation: 5+10=15 Exploring Operation: 49+5=54, Resulting Numbers: [10, 54] Generated Node #0,2,4: 51:[10, 54] Operation: 49+5=54 Moving to Node #0,2,0 Current State: 51:[49, 50], Operations: ['50-40=10', '5*10=50'] Exploring Operation: 50-49=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 49+50=99, Resulting Numbers: [99] 99,51 unequal: No Solution Exploring Operation: 49*50=2450, Resulting Numbers: [2450] 2450,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[49, 2], Operations: ['50-40=10', '10/5=2'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,51 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[49, 50, 40, 5], Operations: [] Exploring Operation: 50-40=10, Resulting Numbers: [49, 5, 10] Generated Node #0,2: 51:[49, 5, 10] Operation: 50-40=10 Moving to Node #0,2 Current State: 51:[49, 5, 10], Operations: ['50-40=10'] Exploring Operation: 10/5=2, Resulting Numbers: [49, 2] Generated Node #0,2,1: 51:[49, 2] Operation: 10/5=2 Moving to Node #0,2,1 Current State: 51:[49, 2], Operations: ['50-40=10', '10/5=2'] Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.929688
hs_5
sum_heuristic
[ 44, 39, 13, 7 ]
26
[ "44-39=5", "7-5=2", "13*2=26" ]
Current State: 26:[44, 39, 13, 7], Operations: [] Exploring Operation: 44-39=5, Resulting Numbers: [13, 7, 5] Generated Node #2: [13, 7, 5] from Operation: 44-39=5 Current State: 26:[13, 7, 5], Operations: ['44-39=5'] Exploring Operation: 7-5=2, Resulting Numbers: [13, 2] Generated Node #3: [13, 2] from Operation: 7-5=2 Current State: 26:[13, 2], Operations: ['44-39=5', '7-5=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[44, 39, 13, 7], Operations: [] Exploring Operation: 44-13=31, Resulting Numbers: [39, 7, 31] Generated Node #0,0: 26:[39, 7, 31] Operation: 44-13=31 Exploring Operation: 39-13=26, Resulting Numbers: [44, 7, 26] Generated Node #0,1: 26:[44, 7, 26] Operation: 39-13=26 Exploring Operation: 44-39=5, Resulting Numbers: [13, 7, 5] Generated Node #0,2: 26:[13, 7, 5] Operation: 44-39=5 Moving to Node #0,2 Current State: 26:[13, 7, 5], Operations: ['44-39=5'] Exploring Operation: 7+5=12, Resulting Numbers: [13, 12] Generated Node #0,2,0: 26:[13, 12] Operation: 7+5=12 Exploring Operation: 7-5=2, Resulting Numbers: [13, 2] Generated Node #0,2,1: 26:[13, 2] Operation: 7-5=2 Exploring Operation: 13-7=6, Resulting Numbers: [5, 6] Generated Node #0,2,2: 26:[5, 6] Operation: 13-7=6 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 26:[13, 2], Operations: ['44-39=5', '7-5=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,26 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,26 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[44, 39, 13, 7], Operations: [] Exploring Operation: 44-39=5, Resulting Numbers: [13, 7, 5] Generated Node #0,2: 26:[13, 7, 5] Operation: 44-39=5 Moving to Node #0,2 Current State: 26:[13, 7, 5], Operations: ['44-39=5'] Exploring Operation: 7-5=2, Resulting Numbers: [13, 2] Generated Node #0,2,1: 26:[13, 2] Operation: 7-5=2 Moving to Node #0,2,1 Current State: 26:[13, 2], Operations: ['44-39=5', '7-5=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 31, 19, 22, 22 ]
49
[ "31+19=50", "22/22=1", "50-1=49" ]
Current State: 49:[31, 19, 22, 22], Operations: [] Exploring Operation: 31+19=50, Resulting Numbers: [22, 22, 50] Generated Node #2: [22, 22, 50] from Operation: 31+19=50 Current State: 49:[22, 22, 50], Operations: ['31+19=50'] Exploring Operation: 22/22=1, Resulting Numbers: [50, 1] Generated Node #3: [50, 1] from Operation: 22/22=1 Current State: 49:[50, 1], Operations: ['31+19=50', '22/22=1'] Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[31, 19, 22, 22], Operations: [] Exploring Operation: 31-22=9, Resulting Numbers: [19, 22, 9] Generated Node #0,0: 49:[19, 22, 9] Operation: 31-22=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[19, 22, 9], Operations: ['31-22=9'] Exploring Operation: 22-19=3, Resulting Numbers: [9, 3] Generated Node #0,0,0: 49:[9, 3] Operation: 22-19=3 Moving to Node #0,0,0 Current State: 49:[9, 3], Operations: ['31-22=9', '22-19=3'] Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 44, 84, 74, 67 ]
32
[ "74-67=7", "84/7=12", "44-12=32" ]
Current State: 32:[44, 84, 74, 67], Operations: [] Exploring Operation: 74-67=7, Resulting Numbers: [44, 84, 7] Generated Node #2: [44, 84, 7] from Operation: 74-67=7 Current State: 32:[44, 84, 7], Operations: ['74-67=7'] Exploring Operation: 84/7=12, Resulting Numbers: [44, 12] Generated Node #3: [44, 12] from Operation: 84/7=12 Current State: 32:[44, 12], Operations: ['74-67=7', '84/7=12'] Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[44, 84, 74, 67], Operations: [] Exploring Operation: 74-67=7, Resulting Numbers: [44, 84, 7] Generated Node #0,0: 32:[44, 84, 7] Operation: 74-67=7 Exploring Operation: 84-67=17, Resulting Numbers: [44, 74, 17] Generated Node #0,1: 32:[44, 74, 17] Operation: 84-67=17 Exploring Operation: 84-74=10, Resulting Numbers: [44, 67, 10] Generated Node #0,2: 32:[44, 67, 10] Operation: 84-74=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[44, 67, 10], Operations: ['84-74=10'] Exploring Operation: 67-44=23, Resulting Numbers: [10, 23] Generated Node #0,2,0: 32:[10, 23] Operation: 67-44=23 Exploring Operation: 44-10=34, Resulting Numbers: [67, 34] Generated Node #0,2,1: 32:[67, 34] Operation: 44-10=34 Exploring Operation: 67-10=57, Resulting Numbers: [44, 57] Generated Node #0,2,2: 32:[44, 57] Operation: 67-10=57 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 32:[10, 23], Operations: ['84-74=10', '67-44=23'] Exploring Operation: 10+23=33, Resulting Numbers: [33] 33,32 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 10*23=230, Resulting Numbers: [230] 230,32 unequal: No Solution No 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: 32:[67, 34], Operations: ['84-74=10', '44-10=34'] Exploring Operation: 67+34=101, Resulting Numbers: [101] 101,32 unequal: No Solution Exploring Operation: 67-34=33, Resulting Numbers: [33] 33,32 unequal: No Solution Exploring Operation: 67*34=2278, Resulting Numbers: [2278] 2278,32 unequal: No Solution No 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: 32:[44, 57], Operations: ['84-74=10', '67-10=57'] Exploring Operation: 57-44=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 44+57=101, Resulting Numbers: [101] 101,32 unequal: No Solution Exploring Operation: 44*57=2508, Resulting Numbers: [2508] 2508,32 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: 32:[44, 74, 17], Operations: ['84-67=17'] Exploring Operation: 74-44=30, Resulting Numbers: [17, 30] Generated Node #0,1,0: 32:[17, 30] Operation: 74-44=30 Exploring Operation: 44-17=27, Resulting Numbers: [74, 27] Generated Node #0,1,1: 32:[74, 27] Operation: 44-17=27 Exploring Operation: 74-17=57, Resulting Numbers: [44, 57] Generated Node #0,1,2: 32:[44, 57] Operation: 74-17=57 Moving to Node #0,1,0 Current State: 32:[17, 30], Operations: ['84-67=17', '74-44=30'] Exploring Operation: 17+30=47, Resulting Numbers: [47] 47,32 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 17*30=510, Resulting Numbers: [510] 510,32 unequal: No Solution Moving to Node #0,1,2 Current State: 32:[44, 57], Operations: ['84-67=17', '74-17=57'] Exploring Operation: 57-44=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 44*57=2508, Resulting Numbers: [2508] 2508,32 unequal: No Solution Exploring Operation: 44+57=101, Resulting Numbers: [101] 101,32 unequal: No Solution Moving to Node #0,1,1 Current State: 32:[74, 27], Operations: ['84-67=17', '44-17=27'] Exploring Operation: 74-27=47, Resulting Numbers: [47] 47,32 unequal: No Solution Exploring Operation: 74*27=1998, Resulting Numbers: [1998] 1998,32 unequal: No Solution Exploring Operation: 74+27=101, Resulting Numbers: [101] 101,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[44, 84, 7], Operations: ['74-67=7'] Exploring Operation: 44-7=37, Resulting Numbers: [84, 37] Generated Node #0,0,0: 32:[84, 37] Operation: 44-7=37 Exploring Operation: 84/7=12, Resulting Numbers: [44, 12] Generated Node #0,0,1: 32:[44, 12] Operation: 84/7=12 Exploring Operation: 84-44=40, Resulting Numbers: [7, 40] Generated Node #0,0,2: 32:[7, 40] Operation: 84-44=40 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 32:[7, 40], Operations: ['74-67=7', '84-44=40'] Exploring Operation: 7+40=47, Resulting Numbers: [47] 47,32 unequal: No Solution Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,32 unequal: No Solution Exploring Operation: 7*40=280, Resulting Numbers: [280] 280,32 unequal: No Solution No 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: 32:[44, 12], Operations: ['74-67=7', '84/7=12'] Exploring Operation: 44*12=528, Resulting Numbers: [528] 528,32 unequal: No Solution Exploring Operation: 44+12=56, Resulting Numbers: [56] 56,32 unequal: No Solution Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[44, 84, 74, 67], Operations: [] Exploring Operation: 74-67=7, Resulting Numbers: [44, 84, 7] Generated Node #0,0: 32:[44, 84, 7] Operation: 74-67=7 Moving to Node #0,0 Current State: 32:[44, 84, 7], Operations: ['74-67=7'] Exploring Operation: 84/7=12, Resulting Numbers: [44, 12] Generated Node #0,0,1: 32:[44, 12] Operation: 84/7=12 Moving to Node #0,0,1 Current State: 32:[44, 12], Operations: ['74-67=7', '84/7=12'] Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_3
sum_heuristic
[ 62, 66, 4, 2 ]
99
[ "62+4=66", "66/2=33", "66+33=99" ]
Current State: 99:[62, 66, 4, 2], Operations: [] Exploring Operation: 62+4=66, Resulting Numbers: [66, 2, 66] Generated Node #2: [66, 2, 66] from Operation: 62+4=66 Current State: 99:[66, 2, 66], Operations: ['62+4=66'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,99 equal: Goal Reached Exploring Operation: 66+33=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[62, 66, 4, 2], Operations: [] Exploring Operation: 66/2=33, Resulting Numbers: [62, 4, 33] Generated Node #0,0: 99:[62, 4, 33] Operation: 66/2=33 Exploring Operation: 66-62=4, Resulting Numbers: [4, 2, 4] Generated Node #0,1: 99:[4, 2, 4] Operation: 66-62=4 Moving to Node #0,1 Current State: 99:[4, 2, 4], Operations: ['66-62=4'] Exploring Operation: 4-2=2, Resulting Numbers: [4, 2] Generated Node #0,1,0: 99:[4, 2] Operation: 4-2=2 Exploring Operation: 4*2=8, Resulting Numbers: [4, 8] Generated Node #0,1,1: 99:[4, 8] Operation: 4*2=8 Moving to Node #0,0 Current State: 99:[62, 4, 33], Operations: ['66/2=33'] Exploring Operation: 62-33=29, Resulting Numbers: [4, 29] Generated Node #0,0,0: 99:[4, 29] Operation: 62-33=29 Exploring Operation: 62+33=95, Resulting Numbers: [4, 95] Generated Node #0,0,1: 99:[4, 95] Operation: 62+33=95 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[4, 29], Operations: ['66/2=33', '62-33=29'] Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[4, 95], Operations: ['66/2=33', '62+33=95'] Exploring Operation: 4+95=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[62, 66, 4, 2], Operations: [] Exploring Operation: 66/2=33, Resulting Numbers: [62, 4, 33] Generated Node #0,0: 99:[62, 4, 33] Operation: 66/2=33 Moving to Node #0,0 Current State: 99:[62, 4, 33], Operations: ['66/2=33'] Exploring Operation: 62+33=95, Resulting Numbers: [4, 95] Generated Node #0,0,1: 99:[4, 95] Operation: 62+33=95 Moving to Node #0,0,1 Current State: 99:[4, 95], Operations: ['66/2=33', '62+33=95'] Exploring Operation: 4+95=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_2
sum_heuristic
[ 34, 63, 6, 21 ]
84
[ "34-6=28", "63/21=3", "28*3=84" ]
Current State: 84:[34, 63, 6, 21], Operations: [] Exploring Operation: 34-6=28, Resulting Numbers: [63, 21, 28] Generated Node #2: [63, 21, 28] from Operation: 34-6=28 Current State: 84:[63, 21, 28], Operations: ['34-6=28'] Exploring Operation: 63/21=3, Resulting Numbers: [28, 3] Generated Node #3: [28, 3] from Operation: 63/21=3 Current State: 84:[28, 3], Operations: ['34-6=28', '63/21=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[34, 63, 6, 21], Operations: [] Exploring Operation: 63-34=29, Resulting Numbers: [6, 21, 29] Generated Node #0,0: 84:[6, 21, 29] Operation: 63-34=29 Moving to Node #0,0 Current State: 84:[6, 21, 29], Operations: ['63-34=29'] Exploring Operation: 29-21=8, Resulting Numbers: [6, 8] Generated Node #0,0,0: 84:[6, 8] Operation: 29-21=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[6, 8], Operations: ['63-34=29', '29-21=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 35, 78, 17, 25 ]
71
[ "35+78=113", "17+25=42", "113-42=71" ]
Current State: 71:[35, 78, 17, 25], Operations: [] Exploring Operation: 35+78=113, Resulting Numbers: [17, 25, 113] Generated Node #2: [17, 25, 113] from Operation: 35+78=113 Current State: 71:[17, 25, 113], Operations: ['35+78=113'] Exploring Operation: 17+25=42, Resulting Numbers: [113, 42] Generated Node #3: [113, 42] from Operation: 17+25=42 Current State: 71:[113, 42], Operations: ['35+78=113', '17+25=42'] Exploring Operation: 113-42=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[35, 78, 17, 25], Operations: [] Exploring Operation: 35+17=52, Resulting Numbers: [78, 25, 52] Generated Node #0,0: 71:[78, 25, 52] Operation: 35+17=52 Exploring Operation: 35+25=60, Resulting Numbers: [78, 17, 60] Generated Node #0,1: 71:[78, 17, 60] Operation: 35+25=60 Exploring Operation: 17+25=42, Resulting Numbers: [35, 78, 42] Generated Node #0,2: 71:[35, 78, 42] Operation: 17+25=42 Moving to Node #0,0 Current State: 71:[78, 25, 52], Operations: ['35+17=52'] Exploring Operation: 25+52=77, Resulting Numbers: [78, 77] Generated Node #0,0,0: 71:[78, 77] Operation: 25+52=77 Exploring Operation: 78-25=53, Resulting Numbers: [52, 53] Generated Node #0,0,1: 71:[52, 53] Operation: 78-25=53 Exploring Operation: 78+25=103, Resulting Numbers: [52, 103] Generated Node #0,0,2: 71:[52, 103] Operation: 78+25=103 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[78, 77], Operations: ['35+17=52', '25+52=77'] Exploring Operation: 78+77=155, Resulting Numbers: [155] 155,71 unequal: No Solution Exploring Operation: 78-77=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 78*77=6006, Resulting Numbers: [6006] 6006,71 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 #0,0,1 Current State: 71:[52, 53], Operations: ['35+17=52', '78-25=53'] Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 52*53=2756, Resulting Numbers: [2756] 2756,71 unequal: No Solution Exploring Operation: 52+53=105, Resulting Numbers: [105] 105,71 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 #0,0,2 Current State: 71:[52, 103], Operations: ['35+17=52', '78+25=103'] Exploring Operation: 103-52=51, Resulting Numbers: [51] 51,71 unequal: No Solution Exploring Operation: 52+103=155, Resulting Numbers: [155] 155,71 unequal: No Solution Exploring Operation: 52*103=5356, Resulting Numbers: [5356] 5356,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 71:[78, 17, 60], Operations: ['35+25=60'] Exploring Operation: 78-17=61, Resulting Numbers: [60, 61] Generated Node #0,1,0: 71:[60, 61] Operation: 78-17=61 Exploring Operation: 78+17=95, Resulting Numbers: [60, 95] Generated Node #0,1,1: 71:[60, 95] Operation: 78+17=95 Exploring Operation: 17+60=77, Resulting Numbers: [78, 77] Generated Node #0,1,2: 71:[78, 77] Operation: 17+60=77 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 71:[78, 77], Operations: ['35+25=60', '17+60=77'] Exploring Operation: 78-77=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 78*77=6006, Resulting Numbers: [6006] 6006,71 unequal: No Solution Exploring Operation: 78+77=155, Resulting Numbers: [155] 155,71 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 #0,1,0 Current State: 71:[60, 61], Operations: ['35+25=60', '78-17=61'] Exploring Operation: 61-60=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 60+61=121, Resulting Numbers: [121] 121,71 unequal: No Solution Exploring Operation: 60*61=3660, Resulting Numbers: [3660] 3660,71 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:[60, 95], Operations: ['35+25=60', '78+17=95'] Exploring Operation: 60+95=155, Resulting Numbers: [155] 155,71 unequal: No Solution Exploring Operation: 95-60=35, Resulting Numbers: [35] 35,71 unequal: No Solution Exploring Operation: 60*95=5700, Resulting Numbers: [5700] 5700,71 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: 71:[35, 78, 42], Operations: ['17+25=42'] Exploring Operation: 35+78=113, Resulting Numbers: [42, 113] Generated Node #0,2,0: 71:[42, 113] Operation: 35+78=113 Exploring Operation: 78-35=43, Resulting Numbers: [42, 43] Generated Node #0,2,1: 71:[42, 43] Operation: 78-35=43 Exploring Operation: 35+42=77, Resulting Numbers: [78, 77] Generated Node #0,2,2: 71:[78, 77] Operation: 35+42=77 Moving to Node #0,2,2 Current State: 71:[78, 77], Operations: ['17+25=42', '35+42=77'] Exploring Operation: 78-77=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 78+77=155, Resulting Numbers: [155] 155,71 unequal: No Solution Exploring Operation: 78*77=6006, Resulting Numbers: [6006] 6006,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[42, 43], Operations: ['17+25=42', '78-35=43'] Exploring Operation: 42+43=85, Resulting Numbers: [85] 85,71 unequal: No Solution Exploring Operation: 42*43=1806, Resulting Numbers: [1806] 1806,71 unequal: No Solution Exploring Operation: 43-42=1, Resulting Numbers: [1] 1,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[42, 113], Operations: ['17+25=42', '35+78=113'] Exploring Operation: 113-42=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[35, 78, 17, 25], Operations: [] Exploring Operation: 17+25=42, Resulting Numbers: [35, 78, 42] Generated Node #0,2: 71:[35, 78, 42] Operation: 17+25=42 Moving to Node #0,2 Current State: 71:[35, 78, 42], Operations: ['17+25=42'] Exploring Operation: 35+78=113, Resulting Numbers: [42, 113] Generated Node #0,2,0: 71:[42, 113] Operation: 35+78=113 Moving to Node #0,2,0 Current State: 71:[42, 113], Operations: ['17+25=42', '35+78=113'] Exploring Operation: 113-42=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
0.96441
hs_3
mult_heuristic
[ 21, 16, 43, 36 ]
12
[ "21-16=5", "43-36=7", "5+7=12" ]
Current State: 12:[21, 16, 43, 36], Operations: [] Exploring Operation: 21-16=5, Resulting Numbers: [43, 36, 5] Generated Node #2: [43, 36, 5] from Operation: 21-16=5 Current State: 12:[43, 36, 5], Operations: ['21-16=5'] Exploring Operation: 43-36=7, Resulting Numbers: [5, 7] Generated Node #3: [5, 7] from Operation: 43-36=7 Current State: 12:[5, 7], Operations: ['21-16=5', '43-36=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[21, 16, 43, 36], Operations: [] Exploring Operation: 43-21=22, Resulting Numbers: [16, 36, 22] Generated Node #0,0: 12:[16, 36, 22] Operation: 43-21=22 Exploring Operation: 43-36=7, Resulting Numbers: [21, 16, 7] Generated Node #0,1: 12:[21, 16, 7] Operation: 43-36=7 Moving to Node #0,1 Current State: 12:[21, 16, 7], Operations: ['43-36=7'] Exploring Operation: 21-16=5, Resulting Numbers: [7, 5] Generated Node #0,1,0: 12:[7, 5] Operation: 21-16=5 Exploring Operation: 21/7=3, Resulting Numbers: [16, 3] Generated Node #0,1,1: 12:[16, 3] Operation: 21/7=3 Moving to Node #0,0 Current State: 12:[16, 36, 22], Operations: ['43-21=22'] Exploring Operation: 36-22=14, Resulting Numbers: [16, 14] Generated Node #0,0,0: 12:[16, 14] Operation: 36-22=14 Exploring Operation: 36-16=20, Resulting Numbers: [22, 20] Generated Node #0,0,1: 12:[22, 20] Operation: 36-16=20 Moving to Node #0,1,0 Current State: 12:[7, 5], Operations: ['43-36=7', '21-16=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[21, 16, 43, 36], Operations: [] Exploring Operation: 43-36=7, Resulting Numbers: [21, 16, 7] Generated Node #0,1: 12:[21, 16, 7] Operation: 43-36=7 Moving to Node #0,1 Current State: 12:[21, 16, 7], Operations: ['43-36=7'] Exploring Operation: 21-16=5, Resulting Numbers: [7, 5] Generated Node #0,1,0: 12:[7, 5] Operation: 21-16=5 Moving to Node #0,1,0 Current State: 12:[7, 5], Operations: ['43-36=7', '21-16=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.990451
hs_2
mult_heuristic
[ 60, 30, 97, 92 ]
90
[ "97-92=5", "30*5=150", "150-60=90" ]
Current State: 90:[60, 30, 97, 92], Operations: [] Exploring Operation: 97-92=5, Resulting Numbers: [60, 30, 5] Generated Node #2: [60, 30, 5] from Operation: 97-92=5 Current State: 90:[60, 30, 5], Operations: ['97-92=5'] Exploring Operation: 30*5=150, Resulting Numbers: [60, 150] Generated Node #3: [60, 150] from Operation: 30*5=150 Current State: 90:[60, 150], Operations: ['97-92=5', '30*5=150'] Exploring Operation: 150-60=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[60, 30, 97, 92], Operations: [] Exploring Operation: 60+30=90, Resulting Numbers: [97, 92, 90] Generated Node #0,0: 90:[97, 92, 90] Operation: 60+30=90 Exploring Operation: 60-30=30, Resulting Numbers: [97, 92, 30] Generated Node #0,1: 90:[97, 92, 30] Operation: 60-30=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[97, 92, 90], Operations: ['60+30=90'] Exploring Operation: 97-90=7, Resulting Numbers: [92, 7] Generated Node #0,0,0: 90:[92, 7] Operation: 97-90=7 Exploring Operation: 97-92=5, Resulting Numbers: [90, 5] Generated Node #0,0,1: 90:[90, 5] Operation: 97-92=5 Moving to Node #0,0,1 Current State: 90:[90, 5], Operations: ['60+30=90', '97-92=5'] Exploring Operation: 90+5=95, Resulting Numbers: [95] 95,90 unequal: No Solution Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[92, 7], Operations: ['60+30=90', '97-90=7'] Exploring Operation: 92-7=85, Resulting Numbers: [85] 85,90 unequal: No Solution Exploring Operation: 92+7=99, Resulting Numbers: [99] 99,90 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:[97, 92, 30], Operations: ['60-30=30'] Exploring Operation: 97-92=5, Resulting Numbers: [30, 5] Generated Node #0,1,0: 90:[30, 5] Operation: 97-92=5 Exploring Operation: 97-30=67, Resulting Numbers: [92, 67] Generated Node #0,1,1: 90:[92, 67] Operation: 97-30=67 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[30, 5], Operations: ['60-30=30', '97-92=5'] Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[92, 67], Operations: ['60-30=30', '97-30=67'] Exploring Operation: 92-67=25, Resulting Numbers: [25] 25,90 unequal: No Solution Exploring Operation: 92+67=159, Resulting Numbers: [159] 159,90 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 No solution found.
0
hs_2
mult_heuristic
[ 5, 15, 36, 35 ]
32
[ "35-15=20", "20/5=4", "36-4=32" ]
Current State: 32:[5, 15, 36, 35], Operations: [] Exploring Operation: 35-15=20, Resulting Numbers: [5, 36, 20] Generated Node #2: [5, 36, 20] from Operation: 35-15=20 Current State: 32:[5, 36, 20], Operations: ['35-15=20'] Exploring Operation: 20/5=4, Resulting Numbers: [36, 4] Generated Node #3: [36, 4] from Operation: 20/5=4 Current State: 32:[36, 4], Operations: ['35-15=20', '20/5=4'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[5, 15, 36, 35], Operations: [] Exploring Operation: 36-35=1, Resulting Numbers: [5, 15, 1] Generated Node #0,0: 32:[5, 15, 1] Operation: 36-35=1 Moving to Node #0,0 Current State: 32:[5, 15, 1], Operations: ['36-35=1'] Exploring Operation: 5-1=4, Resulting Numbers: [15, 4] Generated Node #0,0,0: 32:[15, 4] Operation: 5-1=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[15, 4], Operations: ['36-35=1', '5-1=4'] Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,32 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
[ 56, 19, 78, 63 ]
55
[ "63-56=7", "19*7=133", "133-78=55" ]
Current State: 55:[56, 19, 78, 63], Operations: [] Exploring Operation: 63-56=7, Resulting Numbers: [19, 78, 7] Generated Node #2: [19, 78, 7] from Operation: 63-56=7 Current State: 55:[19, 78, 7], Operations: ['63-56=7'] Exploring Operation: 19*7=133, Resulting Numbers: [78, 133] Generated Node #3: [78, 133] from Operation: 19*7=133 Current State: 55:[78, 133], Operations: ['63-56=7', '19*7=133'] Exploring Operation: 133-78=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[56, 19, 78, 63], Operations: [] Exploring Operation: 78-19=59, Resulting Numbers: [56, 63, 59] Generated Node #0,0: 55:[56, 63, 59] Operation: 78-19=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[56, 63, 59], Operations: ['78-19=59'] Exploring Operation: 63-59=4, Resulting Numbers: [56, 4] Generated Node #0,0,0: 55:[56, 4] Operation: 63-59=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[56, 4], Operations: ['78-19=59', '63-59=4'] Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 92, 5, 27, 37 ]
66
[ "92+27=119", "5*37=185", "185-119=66" ]
Current State: 66:[92, 5, 27, 37], Operations: [] Exploring Operation: 92+27=119, Resulting Numbers: [5, 37, 119] Generated Node #2: [5, 37, 119] from Operation: 92+27=119 Current State: 66:[5, 37, 119], Operations: ['92+27=119'] Exploring Operation: 5*37=185, Resulting Numbers: [119, 185] Generated Node #3: [119, 185] from Operation: 5*37=185 Current State: 66:[119, 185], Operations: ['92+27=119', '5*37=185'] Exploring Operation: 185-119=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[92, 5, 27, 37], Operations: [] Exploring Operation: 92-37=55, Resulting Numbers: [5, 27, 55] Generated Node #0,0: 66:[5, 27, 55] Operation: 92-37=55 Exploring Operation: 37-27=10, Resulting Numbers: [92, 5, 10] Generated Node #0,1: 66:[92, 5, 10] Operation: 37-27=10 Exploring Operation: 92-27=65, Resulting Numbers: [5, 37, 65] Generated Node #0,2: 66:[5, 37, 65] Operation: 92-27=65 Start Sub Search at level 1: Moving to Node #0,2 Current State: 66:[5, 37, 65], Operations: ['92-27=65'] Exploring Operation: 65/5=13, Resulting Numbers: [37, 13] Generated Node #0,2,0: 66:[37, 13] Operation: 65/5=13 Exploring Operation: 37-5=32, Resulting Numbers: [65, 32] Generated Node #0,2,1: 66:[65, 32] Operation: 37-5=32 Exploring Operation: 65-37=28, Resulting Numbers: [5, 28] Generated Node #0,2,2: 66:[5, 28] Operation: 65-37=28 Moving to Node #0,2,1 Current State: 66:[65, 32], Operations: ['92-27=65', '37-5=32'] Exploring Operation: 65*32=2080, Resulting Numbers: [2080] 2080,66 unequal: No Solution Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,66 unequal: No Solution Exploring Operation: 65+32=97, Resulting Numbers: [97] 97,66 unequal: No Solution Moving to Node #0,2,0 Current State: 66:[37, 13], Operations: ['92-27=65', '65/5=13'] Exploring Operation: 37*13=481, Resulting Numbers: [481] 481,66 unequal: No Solution Exploring Operation: 37+13=50, Resulting Numbers: [50] 50,66 unequal: No Solution Exploring Operation: 37-13=24, Resulting Numbers: [24] 24,66 unequal: No Solution Moving to Node #0,2,2 Current State: 66:[5, 28], Operations: ['92-27=65', '65-37=28'] Exploring Operation: 5*28=140, Resulting Numbers: [140] 140,66 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,66 unequal: No Solution Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[5, 27, 55], Operations: ['92-37=55'] Exploring Operation: 27-5=22, Resulting Numbers: [55, 22] Generated Node #0,0,0: 66:[55, 22] Operation: 27-5=22 Exploring Operation: 55/5=11, Resulting Numbers: [27, 11] Generated Node #0,0,1: 66:[27, 11] Operation: 55/5=11 Exploring Operation: 55-27=28, Resulting Numbers: [5, 28] Generated Node #0,0,2: 66:[5, 28] Operation: 55-27=28 Moving to Node #0,0,1 Current State: 66:[27, 11], Operations: ['92-37=55', '55/5=11'] Exploring Operation: 27*11=297, Resulting Numbers: [297] 297,66 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,66 unequal: No Solution Exploring Operation: 27+11=38, Resulting Numbers: [38] 38,66 unequal: No Solution Moving to Node #0,0,2 Current State: 66:[5, 28], Operations: ['92-37=55', '55-27=28'] Exploring Operation: 5*28=140, Resulting Numbers: [140] 140,66 unequal: No Solution Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,66 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,66 unequal: No Solution Moving to Node #0,0,0 Current State: 66:[55, 22], Operations: ['92-37=55', '27-5=22'] Exploring Operation: 55+22=77, Resulting Numbers: [77] 77,66 unequal: No Solution Exploring Operation: 55*22=1210, Resulting Numbers: [1210] 1210,66 unequal: No Solution Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[92, 5, 10], Operations: ['37-27=10'] Exploring Operation: 10/5=2, Resulting Numbers: [92, 2] Generated Node #0,1,0: 66:[92, 2] Operation: 10/5=2 Exploring Operation: 92-10=82, Resulting Numbers: [5, 82] Generated Node #0,1,1: 66:[5, 82] Operation: 92-10=82 Exploring Operation: 92-5=87, Resulting Numbers: [10, 87] Generated Node #0,1,2: 66:[10, 87] Operation: 92-5=87 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 66:[5, 82], Operations: ['37-27=10', '92-10=82'] Exploring Operation: 5+82=87, Resulting Numbers: [87] 87,66 unequal: No Solution Exploring Operation: 5*82=410, Resulting Numbers: [410] 410,66 unequal: No Solution Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,66 unequal: No Solution No 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: 66:[10, 87], Operations: ['37-27=10', '92-5=87'] Exploring Operation: 87-10=77, Resulting Numbers: [77] 77,66 unequal: No Solution Exploring Operation: 10+87=97, Resulting Numbers: [97] 97,66 unequal: No Solution Exploring Operation: 10*87=870, Resulting Numbers: [870] 870,66 unequal: No Solution No 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: 66:[92, 2], Operations: ['37-27=10', '10/5=2'] Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,66 unequal: No Solution Exploring Operation: 92+2=94, Resulting Numbers: [94] 94,66 unequal: No Solution Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 56, 89, 97, 5 ]
68
[ "56+89=145", "145/5=29", "97-29=68" ]
Current State: 68:[56, 89, 97, 5], Operations: [] Exploring Operation: 56+89=145, Resulting Numbers: [97, 5, 145] Generated Node #2: [97, 5, 145] from Operation: 56+89=145 Current State: 68:[97, 5, 145], Operations: ['56+89=145'] Exploring Operation: 145/5=29, Resulting Numbers: [97, 29] Generated Node #3: [97, 29] from Operation: 145/5=29 Current State: 68:[97, 29], Operations: ['56+89=145', '145/5=29'] Exploring Operation: 97-29=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[56, 89, 97, 5], Operations: [] Exploring Operation: 56+5=61, Resulting Numbers: [89, 97, 61] Generated Node #0,0: 68:[89, 97, 61] Operation: 56+5=61 Exploring Operation: 97-56=41, Resulting Numbers: [89, 5, 41] Generated Node #0,1: 68:[89, 5, 41] Operation: 97-56=41 Exploring Operation: 97-89=8, Resulting Numbers: [56, 5, 8] Generated Node #0,2: 68:[56, 5, 8] Operation: 97-89=8 Exploring Operation: 89-56=33, Resulting Numbers: [97, 5, 33] Generated Node #0,3: 68:[97, 5, 33] Operation: 89-56=33 Moving to Node #0,2 Current State: 68:[56, 5, 8], Operations: ['97-89=8'] Exploring Operation: 56/8=7, Resulting Numbers: [5, 7] Generated Node #0,2,0: 68:[5, 7] Operation: 56/8=7 Exploring Operation: 56+5=61, Resulting Numbers: [8, 61] Generated Node #0,2,1: 68:[8, 61] Operation: 56+5=61 Exploring Operation: 56+8=64, Resulting Numbers: [5, 64] Generated Node #0,2,2: 68:[5, 64] Operation: 56+8=64 Exploring Operation: 8-5=3, Resulting Numbers: [56, 3] Generated Node #0,2,3: 68:[56, 3] Operation: 8-5=3 Moving to Node #0,1 Current State: 68:[89, 5, 41], Operations: ['97-56=41'] Exploring Operation: 89-41=48, Resulting Numbers: [5, 48] Generated Node #0,1,0: 68:[5, 48] Operation: 89-41=48 Exploring Operation: 89-5=84, Resulting Numbers: [41, 84] Generated Node #0,1,1: 68:[41, 84] Operation: 89-5=84 Exploring Operation: 41-5=36, Resulting Numbers: [89, 36] Generated Node #0,1,2: 68:[89, 36] Operation: 41-5=36 Exploring Operation: 89+5=94, Resulting Numbers: [41, 94] Generated Node #0,1,3: 68:[41, 94] Operation: 89+5=94 Moving to Node #0,3 Current State: 68:[97, 5, 33], Operations: ['89-56=33'] Exploring Operation: 97+5=102, Resulting Numbers: [33, 102] Generated Node #0,3,0: 68:[33, 102] Operation: 97+5=102 Exploring Operation: 97-5=92, Resulting Numbers: [33, 92] Generated Node #0,3,1: 68:[33, 92] Operation: 97-5=92 Exploring Operation: 5+33=38, Resulting Numbers: [97, 38] Generated Node #0,3,2: 68:[97, 38] Operation: 5+33=38 Exploring Operation: 97-33=64, Resulting Numbers: [5, 64] Generated Node #0,3,3: 68:[5, 64] Operation: 97-33=64 Moving to Node #0,0 Current State: 68:[89, 97, 61], Operations: ['56+5=61'] Exploring Operation: 97-89=8, Resulting Numbers: [61, 8] Generated Node #0,0,0: 68:[61, 8] Operation: 97-89=8 Exploring Operation: 89-61=28, Resulting Numbers: [97, 28] Generated Node #0,0,1: 68:[97, 28] Operation: 89-61=28 Exploring Operation: 89+61=150, Resulting Numbers: [97, 150] Generated Node #0,0,2: 68:[97, 150] Operation: 89+61=150 Exploring Operation: 97-61=36, Resulting Numbers: [89, 36] Generated Node #0,0,3: 68:[89, 36] Operation: 97-61=36 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[61, 8], Operations: ['56+5=61', '97-89=8'] Exploring Operation: 61*8=488, Resulting Numbers: [488] 488,68 unequal: No Solution Exploring Operation: 61-8=53, Resulting Numbers: [53] 53,68 unequal: No Solution Exploring Operation: 61+8=69, Resulting Numbers: [69] 69,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 68:[89, 36], Operations: ['56+5=61', '97-61=36'] Exploring Operation: 89*36=3204, Resulting Numbers: [3204] 3204,68 unequal: No Solution Exploring Operation: 89+36=125, Resulting Numbers: [125] 125,68 unequal: No Solution Exploring Operation: 89-36=53, Resulting Numbers: [53] 53,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 68:[97, 28], Operations: ['56+5=61', '89-61=28'] Exploring Operation: 97*28=2716, Resulting Numbers: [2716] 2716,68 unequal: No Solution Exploring Operation: 97+28=125, Resulting Numbers: [125] 125,68 unequal: No Solution Exploring Operation: 97-28=69, Resulting Numbers: [69] 69,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 68:[97, 150], Operations: ['56+5=61', '89+61=150'] Exploring Operation: 150-97=53, Resulting Numbers: [53] 53,68 unequal: No Solution Exploring Operation: 97*150=14550, Resulting Numbers: [14550] 14550,68 unequal: No Solution Exploring Operation: 97+150=247, Resulting Numbers: [247] 247,68 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: 68:[5, 7], Operations: ['97-89=8', '56/8=7'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,68 unequal: No Solution Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,68 unequal: No Solution Moving to Node #0,2,2 Current State: 68:[5, 64], Operations: ['97-89=8', '56+8=64'] Exploring Operation: 5*64=320, Resulting Numbers: [320] 320,68 unequal: No Solution Exploring Operation: 64-5=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 5+64=69, Resulting Numbers: [69] 69,68 unequal: No Solution Moving to Node #0,3,3 Current State: 68:[5, 64], Operations: ['89-56=33', '97-33=64'] Exploring Operation: 5*64=320, Resulting Numbers: [320] 320,68 unequal: No Solution Exploring Operation: 5+64=69, Resulting Numbers: [69] 69,68 unequal: No Solution Exploring Operation: 64-5=59, Resulting Numbers: [59] 59,68 unequal: No Solution Moving to Node #0,2,1 Current State: 68:[8, 61], Operations: ['97-89=8', '56+5=61'] Exploring Operation: 8*61=488, Resulting Numbers: [488] 488,68 unequal: No Solution Exploring Operation: 61-8=53, Resulting Numbers: [53] 53,68 unequal: No Solution Exploring Operation: 8+61=69, Resulting Numbers: [69] 69,68 unequal: No Solution Moving to Node #0,2,3 Current State: 68:[56, 3], Operations: ['97-89=8', '8-5=3'] Exploring Operation: 56*3=168, Resulting Numbers: [168] 168,68 unequal: No Solution Exploring Operation: 56+3=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[5, 48], Operations: ['97-56=41', '89-41=48'] Exploring Operation: 5*48=240, Resulting Numbers: [240] 240,68 unequal: No Solution Exploring Operation: 5+48=53, Resulting Numbers: [53] 53,68 unequal: No Solution Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[89, 36], Operations: ['97-56=41', '41-5=36'] Exploring Operation: 89-36=53, Resulting Numbers: [53] 53,68 unequal: No Solution Exploring Operation: 89*36=3204, Resulting Numbers: [3204] 3204,68 unequal: No Solution Exploring Operation: 89+36=125, Resulting Numbers: [125] 125,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[41, 84], Operations: ['97-56=41', '89-5=84'] Exploring Operation: 41+84=125, Resulting Numbers: [125] 125,68 unequal: No Solution Exploring Operation: 41*84=3444, Resulting Numbers: [3444] 3444,68 unequal: No Solution Exploring Operation: 84-41=43, Resulting Numbers: [43] 43,68 unequal: No Solution Moving to Node #0,3,1 Current State: 68:[33, 92], Operations: ['89-56=33', '97-5=92'] Exploring Operation: 33+92=125, Resulting Numbers: [125] 125,68 unequal: No Solution Exploring Operation: 33*92=3036, Resulting Numbers: [3036] 3036,68 unequal: No Solution Exploring Operation: 92-33=59, Resulting Numbers: [59] 59,68 unequal: No Solution Moving to Node #0,1,3 Current State: 68:[41, 94], Operations: ['97-56=41', '89+5=94'] Exploring Operation: 41+94=135, Resulting Numbers: [135] 135,68 unequal: No Solution Exploring Operation: 94-41=53, Resulting Numbers: [53] 53,68 unequal: No Solution Exploring Operation: 41*94=3854, Resulting Numbers: [3854] 3854,68 unequal: No Solution Moving to Node #0,3,2 Current State: 68:[97, 38], Operations: ['89-56=33', '5+33=38'] Exploring Operation: 97-38=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 97*38=3686, Resulting Numbers: [3686] 3686,68 unequal: No Solution Exploring Operation: 97+38=135, Resulting Numbers: [135] 135,68 unequal: No Solution Moving to Node #0,3,0 Current State: 68:[33, 102], Operations: ['89-56=33', '97+5=102'] Exploring Operation: 33*102=3366, Resulting Numbers: [3366] 3366,68 unequal: No Solution Exploring Operation: 102-33=69, Resulting Numbers: [69] 69,68 unequal: No Solution Exploring Operation: 33+102=135, Resulting Numbers: [135] 135,68 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 28, 9, 11, 21 ]
13
[ "28-9=19", "11+21=32", "32-19=13" ]
Current State: 13:[28, 9, 11, 21], Operations: [] Exploring Operation: 28-9=19, Resulting Numbers: [11, 21, 19] Generated Node #2: [11, 21, 19] from Operation: 28-9=19 Current State: 13:[11, 21, 19], Operations: ['28-9=19'] Exploring Operation: 11+21=32, Resulting Numbers: [19, 32] Generated Node #3: [19, 32] from Operation: 11+21=32 Current State: 13:[19, 32], Operations: ['28-9=19', '11+21=32'] Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[28, 9, 11, 21], Operations: [] Exploring Operation: 28-21=7, Resulting Numbers: [9, 11, 7] Generated Node #0,0: 13:[9, 11, 7] Operation: 28-21=7 Exploring Operation: 28-9=19, Resulting Numbers: [11, 21, 19] Generated Node #0,1: 13:[11, 21, 19] Operation: 28-9=19 Exploring Operation: 21-11=10, Resulting Numbers: [28, 9, 10] Generated Node #0,2: 13:[28, 9, 10] Operation: 21-11=10 Exploring Operation: 28-11=17, Resulting Numbers: [9, 21, 17] Generated Node #0,3: 13:[9, 21, 17] Operation: 28-11=17 Exploring Operation: 21-9=12, Resulting Numbers: [28, 11, 12] Generated Node #0,4: 13:[28, 11, 12] Operation: 21-9=12 Moving to Node #0,0 Current State: 13:[9, 11, 7], Operations: ['28-21=7'] Exploring Operation: 11-7=4, Resulting Numbers: [9, 4] Generated Node #0,0,0: 13:[9, 4] Operation: 11-7=4 Exploring Operation: 9+7=16, Resulting Numbers: [11, 16] Generated Node #0,0,1: 13:[11, 16] Operation: 9+7=16 Exploring Operation: 9+11=20, Resulting Numbers: [7, 20] Generated Node #0,0,2: 13:[7, 20] Operation: 9+11=20 Exploring Operation: 9-7=2, Resulting Numbers: [11, 2] Generated Node #0,0,3: 13:[11, 2] Operation: 9-7=2 Exploring Operation: 11+7=18, Resulting Numbers: [9, 18] Generated Node #0,0,4: 13:[9, 18] Operation: 11+7=18 Moving to Node #0,3 Current State: 13:[9, 21, 17], Operations: ['28-11=17'] Exploring Operation: 21-9=12, Resulting Numbers: [17, 12] Generated Node #0,3,0: 13:[17, 12] Operation: 21-9=12 Exploring Operation: 17-9=8, Resulting Numbers: [21, 8] Generated Node #0,3,1: 13:[21, 8] Operation: 17-9=8 Exploring Operation: 21-17=4, Resulting Numbers: [9, 4] Generated Node #0,3,2: 13:[9, 4] Operation: 21-17=4 Exploring Operation: 9+17=26, Resulting Numbers: [21, 26] Generated Node #0,3,3: 13:[21, 26] Operation: 9+17=26 Exploring Operation: 9+21=30, Resulting Numbers: [17, 30] Generated Node #0,3,4: 13:[17, 30] Operation: 9+21=30 Moving to Node #0,1 Current State: 13:[11, 21, 19], Operations: ['28-9=19'] Exploring Operation: 21-11=10, Resulting Numbers: [19, 10] Generated Node #0,1,0: 13:[19, 10] Operation: 21-11=10 Exploring Operation: 11+21=32, Resulting Numbers: [19, 32] Generated Node #0,1,1: 13:[19, 32] Operation: 11+21=32 Exploring Operation: 11+19=30, Resulting Numbers: [21, 30] Generated Node #0,1,2: 13:[21, 30] Operation: 11+19=30 Exploring Operation: 19-11=8, Resulting Numbers: [21, 8] Generated Node #0,1,3: 13:[21, 8] Operation: 19-11=8 Exploring Operation: 21-19=2, Resulting Numbers: [11, 2] Generated Node #0,1,4: 13:[11, 2] Operation: 21-19=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 13:[19, 10], Operations: ['28-9=19', '21-11=10'] Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,13 unequal: No Solution Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,13 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 13:[21, 8], Operations: ['28-9=19', '19-11=8'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[28, 9, 11, 21], Operations: [] Exploring Operation: 28-9=19, Resulting Numbers: [11, 21, 19] Generated Node #0,1: 13:[11, 21, 19] Operation: 28-9=19 Moving to Node #0,1 Current State: 13:[11, 21, 19], Operations: ['28-9=19'] Exploring Operation: 19-11=8, Resulting Numbers: [21, 8] Generated Node #0,1,3: 13:[21, 8] Operation: 19-11=8 Moving to Node #0,1,3 Current State: 13:[21, 8], Operations: ['28-9=19', '19-11=8'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_5
mult_heuristic
[ 45, 46, 23, 58 ]
71
[ "46/23=2", "58*2=116", "116-45=71" ]
Current State: 71:[45, 46, 23, 58], Operations: [] Exploring Operation: 46/23=2, Resulting Numbers: [45, 58, 2] Generated Node #2: [45, 58, 2] from Operation: 46/23=2 Current State: 71:[45, 58, 2], Operations: ['46/23=2'] Exploring Operation: 58*2=116, Resulting Numbers: [45, 116] Generated Node #3: [45, 116] from Operation: 58*2=116 Current State: 71:[45, 116], Operations: ['46/23=2', '58*2=116'] Exploring Operation: 116-45=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[45, 46, 23, 58], Operations: [] Exploring Operation: 23+58=81, Resulting Numbers: [45, 46, 81] Generated Node #0,0: 71:[45, 46, 81] Operation: 23+58=81 Exploring Operation: 45+23=68, Resulting Numbers: [46, 58, 68] Generated Node #0,1: 71:[46, 58, 68] Operation: 45+23=68 Exploring Operation: 46+23=69, Resulting Numbers: [45, 58, 69] Generated Node #0,2: 71:[45, 58, 69] Operation: 46+23=69 Exploring Operation: 45+46=91, Resulting Numbers: [23, 58, 91] Generated Node #0,3: 71:[23, 58, 91] Operation: 45+46=91 Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[46, 58, 68], Operations: ['45+23=68'] Exploring Operation: 58-46=12, Resulting Numbers: [68, 12] Generated Node #0,1,0: 71:[68, 12] Operation: 58-46=12 Exploring Operation: 46+58=104, Resulting Numbers: [68, 104] Generated Node #0,1,1: 71:[68, 104] Operation: 46+58=104 Exploring Operation: 46+68=114, Resulting Numbers: [58, 114] Generated Node #0,1,2: 71:[58, 114] Operation: 46+68=114 Exploring Operation: 68-46=22, Resulting Numbers: [58, 22] Generated Node #0,1,3: 71:[58, 22] Operation: 68-46=22 Moving to Node #0,1,1 Current State: 71:[68, 104], Operations: ['45+23=68', '46+58=104'] Exploring Operation: 68*104=7072, Resulting Numbers: [7072] 7072,71 unequal: No Solution Exploring Operation: 68+104=172, Resulting Numbers: [172] 172,71 unequal: No Solution Exploring Operation: 104-68=36, Resulting Numbers: [36] 36,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[58, 114], Operations: ['45+23=68', '46+68=114'] Exploring Operation: 58*114=6612, Resulting Numbers: [6612] 6612,71 unequal: No Solution Exploring Operation: 58+114=172, Resulting Numbers: [172] 172,71 unequal: No Solution Exploring Operation: 114-58=56, Resulting Numbers: [56] 56,71 unequal: No Solution Moving to Node #0,1,3 Current State: 71:[58, 22], Operations: ['45+23=68', '68-46=22'] Exploring Operation: 58-22=36, Resulting Numbers: [36] 36,71 unequal: No Solution Exploring Operation: 58*22=1276, Resulting Numbers: [1276] 1276,71 unequal: No Solution Exploring Operation: 58+22=80, Resulting Numbers: [80] 80,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[68, 12], Operations: ['45+23=68', '58-46=12'] Exploring Operation: 68*12=816, Resulting Numbers: [816] 816,71 unequal: No Solution Exploring Operation: 68+12=80, Resulting Numbers: [80] 80,71 unequal: No Solution Exploring Operation: 68-12=56, Resulting Numbers: [56] 56,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[45, 58, 69], Operations: ['46+23=69'] Exploring Operation: 58-45=13, Resulting Numbers: [69, 13] Generated Node #0,2,0: 71:[69, 13] Operation: 58-45=13 Exploring Operation: 45+58=103, Resulting Numbers: [69, 103] Generated Node #0,2,1: 71:[69, 103] Operation: 45+58=103 Exploring Operation: 69-45=24, Resulting Numbers: [58, 24] Generated Node #0,2,2: 71:[58, 24] Operation: 69-45=24 Exploring Operation: 45+69=114, Resulting Numbers: [58, 114] Generated Node #0,2,3: 71:[58, 114] Operation: 45+69=114 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 71:[69, 103], Operations: ['46+23=69', '45+58=103'] Exploring Operation: 69*103=7107, Resulting Numbers: [7107] 7107,71 unequal: No Solution Exploring Operation: 103-69=34, Resulting Numbers: [34] 34,71 unequal: No Solution Exploring Operation: 69+103=172, Resulting Numbers: [172] 172,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 71:[58, 114], Operations: ['46+23=69', '45+69=114'] Exploring Operation: 58*114=6612, Resulting Numbers: [6612] 6612,71 unequal: No Solution Exploring Operation: 58+114=172, Resulting Numbers: [172] 172,71 unequal: No Solution Exploring Operation: 114-58=56, Resulting Numbers: [56] 56,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 71:[69, 13], Operations: ['46+23=69', '58-45=13'] Exploring Operation: 69+13=82, Resulting Numbers: [82] 82,71 unequal: No Solution Exploring Operation: 69*13=897, Resulting Numbers: [897] 897,71 unequal: No Solution Exploring Operation: 69-13=56, Resulting Numbers: [56] 56,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 71:[58, 24], Operations: ['46+23=69', '69-45=24'] Exploring Operation: 58*24=1392, Resulting Numbers: [1392] 1392,71 unequal: No Solution Exploring Operation: 58-24=34, Resulting Numbers: [34] 34,71 unequal: No Solution Exploring Operation: 58+24=82, Resulting Numbers: [82] 82,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[45, 46, 81], Operations: ['23+58=81'] Exploring Operation: 81-45=36, Resulting Numbers: [46, 36] Generated Node #0,0,0: 71:[46, 36] Operation: 81-45=36 Exploring Operation: 81-46=35, Resulting Numbers: [45, 35] Generated Node #0,0,1: 71:[45, 35] Operation: 81-46=35 Exploring Operation: 45+46=91, Resulting Numbers: [81, 91] Generated Node #0,0,2: 71:[81, 91] Operation: 45+46=91 Exploring Operation: 46-45=1, Resulting Numbers: [81, 1] Generated Node #0,0,3: 71:[81, 1] Operation: 46-45=1 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 71:[81, 91], Operations: ['23+58=81', '45+46=91'] Exploring Operation: 81*91=7371, Resulting Numbers: [7371] 7371,71 unequal: No Solution Exploring Operation: 91-81=10, Resulting Numbers: [10] 10,71 unequal: No Solution Exploring Operation: 81+91=172, Resulting Numbers: [172] 172,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[46, 36], Operations: ['23+58=81', '81-45=36'] Exploring Operation: 46*36=1656, Resulting Numbers: [1656] 1656,71 unequal: No Solution Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,71 unequal: No Solution Exploring Operation: 46+36=82, Resulting Numbers: [82] 82,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 71:[45, 35], Operations: ['23+58=81', '81-46=35'] Exploring Operation: 45-35=10, Resulting Numbers: [10] 10,71 unequal: No Solution Exploring Operation: 45+35=80, Resulting Numbers: [80] 80,71 unequal: No Solution Exploring Operation: 45*35=1575, Resulting Numbers: [1575] 1575,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 71:[81, 1], Operations: ['23+58=81', '46-45=1'] Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,71 unequal: No Solution Exploring Operation: 81/1=81, Resulting Numbers: [81] 81,71 unequal: No Solution Exploring Operation: 81+1=82, Resulting Numbers: [82] 82,71 unequal: No Solution Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 71:[23, 58, 91], Operations: ['45+46=91'] Exploring Operation: 23+58=81, Resulting Numbers: [91, 81] Generated Node #0,3,0: 71:[91, 81] Operation: 23+58=81 Exploring Operation: 91-23=68, Resulting Numbers: [58, 68] Generated Node #0,3,1: 71:[58, 68] Operation: 91-23=68 Exploring Operation: 23+91=114, Resulting Numbers: [58, 114] Generated Node #0,3,2: 71:[58, 114] Operation: 23+91=114 Exploring Operation: 58-23=35, Resulting Numbers: [91, 35] Generated Node #0,3,3: 71:[91, 35] Operation: 58-23=35 Moving to Node #0,3,1 Current State: 71:[58, 68], Operations: ['45+46=91', '91-23=68'] Exploring Operation: 58*68=3944, Resulting Numbers: [3944] 3944,71 unequal: No Solution Exploring Operation: 68-58=10, Resulting Numbers: [10] 10,71 unequal: No Solution Exploring Operation: 58+68=126, Resulting Numbers: [126] 126,71 unequal: No Solution Moving to Node #0,3,0 Current State: 71:[91, 81], Operations: ['45+46=91', '23+58=81'] Exploring Operation: 91+81=172, Resulting Numbers: [172] 172,71 unequal: No Solution Exploring Operation: 91*81=7371, Resulting Numbers: [7371] 7371,71 unequal: No Solution Exploring Operation: 91-81=10, Resulting Numbers: [10] 10,71 unequal: No Solution Moving to Node #0,3,3 Current State: 71:[91, 35], Operations: ['45+46=91', '58-23=35'] Exploring Operation: 91*35=3185, Resulting Numbers: [3185] 3185,71 unequal: No Solution Exploring Operation: 91+35=126, Resulting Numbers: [126] 126,71 unequal: No Solution Exploring Operation: 91-35=56, Resulting Numbers: [56] 56,71 unequal: No Solution Moving to Node #0,3,2 Current State: 71:[58, 114], Operations: ['45+46=91', '23+91=114'] Exploring Operation: 58+114=172, Resulting Numbers: [172] 172,71 unequal: No Solution Exploring Operation: 114-58=56, Resulting Numbers: [56] 56,71 unequal: No Solution Exploring Operation: 58*114=6612, Resulting Numbers: [6612] 6612,71 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
[ 76, 83, 11, 6 ]
73
[ "83-76=7", "11*6=66", "7+66=73" ]
Current State: 73:[76, 83, 11, 6], Operations: [] Exploring Operation: 83-76=7, Resulting Numbers: [11, 6, 7] Generated Node #2: [11, 6, 7] from Operation: 83-76=7 Current State: 73:[11, 6, 7], Operations: ['83-76=7'] Exploring Operation: 11*6=66, Resulting Numbers: [7, 66] Generated Node #3: [7, 66] from Operation: 11*6=66 Current State: 73:[7, 66], Operations: ['83-76=7', '11*6=66'] Exploring Operation: 7+66=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[76, 83, 11, 6], Operations: [] Exploring Operation: 11*6=66, Resulting Numbers: [76, 83, 66] Generated Node #0,0: 73:[76, 83, 66] Operation: 11*6=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[76, 83, 66], Operations: ['11*6=66'] Exploring Operation: 83-66=17, Resulting Numbers: [76, 17] Generated Node #0,0,0: 73:[76, 17] Operation: 83-66=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[76, 17], Operations: ['11*6=66', '83-66=17'] Exploring Operation: 76-17=59, Resulting Numbers: [59] 59,73 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
[ 52, 51, 86, 78 ]
95
[ "52+51=103", "86-78=8", "103-8=95" ]
Current State: 95:[52, 51, 86, 78], Operations: [] Exploring Operation: 52+51=103, Resulting Numbers: [86, 78, 103] Generated Node #2: [86, 78, 103] from Operation: 52+51=103 Current State: 95:[86, 78, 103], Operations: ['52+51=103'] Exploring Operation: 86-78=8, Resulting Numbers: [103, 8] Generated Node #3: [103, 8] from Operation: 86-78=8 Current State: 95:[103, 8], Operations: ['52+51=103', '86-78=8'] Exploring Operation: 103-8=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[52, 51, 86, 78], Operations: [] Exploring Operation: 52+51=103, Resulting Numbers: [86, 78, 103] Generated Node #0,0: 95:[86, 78, 103] Operation: 52+51=103 Exploring Operation: 52-51=1, Resulting Numbers: [86, 78, 1] Generated Node #0,1: 95:[86, 78, 1] Operation: 52-51=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[86, 78, 1], Operations: ['52-51=1'] Exploring Operation: 86-78=8, Resulting Numbers: [1, 8] Generated Node #0,1,0: 95:[1, 8] Operation: 86-78=8 Exploring Operation: 86+1=87, Resulting Numbers: [78, 87] Generated Node #0,1,1: 95:[78, 87] Operation: 86+1=87 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 95:[1, 8], Operations: ['52-51=1', '86-78=8'] Exploring Operation: 1*8=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 8-1=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 #0,1,1 Current State: 95:[78, 87], Operations: ['52-51=1', '86+1=87'] Exploring Operation: 78+87=165, Resulting Numbers: [165] 165,95 unequal: No Solution Exploring Operation: 87-78=9, Resulting Numbers: [9] 9,95 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 #0,0 Current State: 95:[86, 78, 103], Operations: ['52+51=103'] Exploring Operation: 103-78=25, Resulting Numbers: [86, 25] Generated Node #0,0,0: 95:[86, 25] Operation: 103-78=25 Exploring Operation: 86-78=8, Resulting Numbers: [103, 8] Generated Node #0,0,1: 95:[103, 8] Operation: 86-78=8 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 95:[103, 8], Operations: ['52+51=103', '86-78=8'] Exploring Operation: 103+8=111, Resulting Numbers: [111] 111,95 unequal: No Solution Exploring Operation: 103-8=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[52, 51, 86, 78], Operations: [] Exploring Operation: 52+51=103, Resulting Numbers: [86, 78, 103] Generated Node #0,0: 95:[86, 78, 103] Operation: 52+51=103 Moving to Node #0,0 Current State: 95:[86, 78, 103], Operations: ['52+51=103'] Exploring Operation: 86-78=8, Resulting Numbers: [103, 8] Generated Node #0,0,1: 95:[103, 8] Operation: 86-78=8 Moving to Node #0,0,1 Current State: 95:[103, 8], Operations: ['52+51=103', '86-78=8'] Exploring Operation: 103-8=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 6, 56, 42, 37 ]
86
[ "42/6=7", "56+37=93", "93-7=86" ]
Current State: 86:[6, 56, 42, 37], Operations: [] Exploring Operation: 42/6=7, Resulting Numbers: [56, 37, 7] Generated Node #2: [56, 37, 7] from Operation: 42/6=7 Current State: 86:[56, 37, 7], Operations: ['42/6=7'] Exploring Operation: 56+37=93, Resulting Numbers: [7, 93] Generated Node #3: [7, 93] from Operation: 56+37=93 Current State: 86:[7, 93], Operations: ['42/6=7', '56+37=93'] Exploring Operation: 93-7=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[6, 56, 42, 37], Operations: [] Exploring Operation: 56+37=93, Resulting Numbers: [6, 42, 93] Generated Node #0,0: 86:[6, 42, 93] Operation: 56+37=93 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[6, 42, 93], Operations: ['56+37=93'] Exploring Operation: 93-6=87, Resulting Numbers: [42, 87] Generated Node #0,0,0: 86:[42, 87] Operation: 93-6=87 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[42, 87], Operations: ['56+37=93', '93-6=87'] Exploring Operation: 87-42=45, Resulting Numbers: [45] 45,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 10, 71, 60, 16 ]
93
[ "60/10=6", "71+16=87", "6+87=93" ]
Current State: 93:[10, 71, 60, 16], Operations: [] Exploring Operation: 60/10=6, Resulting Numbers: [71, 16, 6] Generated Node #2: [71, 16, 6] from Operation: 60/10=6 Current State: 93:[71, 16, 6], Operations: ['60/10=6'] Exploring Operation: 71+16=87, Resulting Numbers: [6, 87] Generated Node #3: [6, 87] from Operation: 71+16=87 Current State: 93:[6, 87], Operations: ['60/10=6', '71+16=87'] Exploring Operation: 6+87=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[10, 71, 60, 16], Operations: [] Exploring Operation: 60-16=44, Resulting Numbers: [10, 71, 44] Generated Node #0,0: 93:[10, 71, 44] Operation: 60-16=44 Exploring Operation: 71+16=87, Resulting Numbers: [10, 60, 87] Generated Node #0,1: 93:[10, 60, 87] Operation: 71+16=87 Exploring Operation: 71-60=11, Resulting Numbers: [10, 16, 11] Generated Node #0,2: 93:[10, 16, 11] Operation: 71-60=11 Exploring Operation: 60/10=6, Resulting Numbers: [71, 16, 6] Generated Node #0,3: 93:[71, 16, 6] Operation: 60/10=6 Moving to Node #0,2 Current State: 93:[10, 16, 11], Operations: ['71-60=11'] Exploring Operation: 16-11=5, Resulting Numbers: [10, 5] Generated Node #0,2,0: 93:[10, 5] Operation: 16-11=5 Exploring Operation: 10+16=26, Resulting Numbers: [11, 26] Generated Node #0,2,1: 93:[11, 26] Operation: 10+16=26 Exploring Operation: 16-10=6, Resulting Numbers: [11, 6] Generated Node #0,2,2: 93:[11, 6] Operation: 16-10=6 Exploring Operation: 16+11=27, Resulting Numbers: [10, 27] Generated Node #0,2,3: 93:[10, 27] Operation: 16+11=27 Moving to Node #0,3 Current State: 93:[71, 16, 6], Operations: ['60/10=6'] Exploring Operation: 71-16=55, Resulting Numbers: [6, 55] Generated Node #0,3,0: 93:[6, 55] Operation: 71-16=55 Exploring Operation: 71+6=77, Resulting Numbers: [16, 77] Generated Node #0,3,1: 93:[16, 77] Operation: 71+6=77 Exploring Operation: 71+16=87, Resulting Numbers: [6, 87] Generated Node #0,3,2: 93:[6, 87] Operation: 71+16=87 Exploring Operation: 16*6=96, Resulting Numbers: [71, 96] Generated Node #0,3,3: 93:[71, 96] Operation: 16*6=96 Moving to Node #0,1 Current State: 93:[10, 60, 87], Operations: ['71+16=87'] Exploring Operation: 60-10=50, Resulting Numbers: [87, 50] Generated Node #0,1,0: 93:[87, 50] Operation: 60-10=50 Exploring Operation: 60/10=6, Resulting Numbers: [87, 6] Generated Node #0,1,1: 93:[87, 6] Operation: 60/10=6 Exploring Operation: 10+60=70, Resulting Numbers: [87, 70] Generated Node #0,1,2: 93:[87, 70] Operation: 10+60=70 Exploring Operation: 87-60=27, Resulting Numbers: [10, 27] Generated Node #0,1,3: 93:[10, 27] Operation: 87-60=27 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 93:[87, 6], Operations: ['71+16=87', '60/10=6'] Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[10, 71, 60, 16], Operations: [] Exploring Operation: 71+16=87, Resulting Numbers: [10, 60, 87] Generated Node #0,1: 93:[10, 60, 87] Operation: 71+16=87 Moving to Node #0,1 Current State: 93:[10, 60, 87], Operations: ['71+16=87'] Exploring Operation: 60/10=6, Resulting Numbers: [87, 6] Generated Node #0,1,1: 93:[87, 6] Operation: 60/10=6 Moving to Node #0,1,1 Current State: 93:[87, 6], Operations: ['71+16=87', '60/10=6'] Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 77, 2, 52, 1 ]
26
[ "77+2=79", "52+1=53", "79-53=26" ]
Current State: 26:[77, 2, 52, 1], Operations: [] Exploring Operation: 77+2=79, Resulting Numbers: [52, 1, 79] Generated Node #2: [52, 1, 79] from Operation: 77+2=79 Current State: 26:[52, 1, 79], Operations: ['77+2=79'] Exploring Operation: 52+1=53, Resulting Numbers: [79, 53] Generated Node #3: [79, 53] from Operation: 52+1=53 Current State: 26:[79, 53], Operations: ['77+2=79', '52+1=53'] Exploring Operation: 79-53=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[77, 2, 52, 1], Operations: [] Exploring Operation: 77-52=25, Resulting Numbers: [2, 1, 25] Generated Node #0,0: 26:[2, 1, 25] Operation: 77-52=25 Exploring Operation: 77-1=76, Resulting Numbers: [2, 52, 76] Generated Node #0,1: 26:[2, 52, 76] Operation: 77-1=76 Exploring Operation: 52/2=26, Resulting Numbers: [77, 1, 26] Generated Node #0,2: 26:[77, 1, 26] Operation: 52/2=26 Exploring Operation: 77-2=75, Resulting Numbers: [52, 1, 75] Generated Node #0,3: 26:[52, 1, 75] Operation: 77-2=75 Moving to Node #0,0 Current State: 26:[2, 1, 25], Operations: ['77-52=25'] Exploring Operation: 1+25=26, Resulting Numbers: [2, 26] Generated Node #0,0,0: 26:[2, 26] Operation: 1+25=26 Exploring Operation: 2*1=2, Resulting Numbers: [25, 2] Generated Node #0,0,1: 26:[25, 2] Operation: 2*1=2 Exploring Operation: 1*25=25, Resulting Numbers: [2, 25] Generated Node #0,0,2: 26:[2, 25] Operation: 1*25=25 Exploring Operation: 2/1=2, Resulting Numbers: [25, 2] Generated Node #0,0,3: 26:[25, 2] Operation: 2/1=2 Moving to Node #0,2 Current State: 26:[77, 1, 26], Operations: ['52/2=26'] Exploring Operation: 77/1=77, Resulting Numbers: [26, 77] Generated Node #0,2,0: 26:[26, 77] Operation: 77/1=77 Exploring Operation: 77-26=51, Resulting Numbers: [1, 51] Generated Node #0,2,1: 26:[1, 51] Operation: 77-26=51 Exploring Operation: 77*1=77, Resulting Numbers: [26, 77] Generated Node #0,2,2: 26:[26, 77] Operation: 77*1=77 Exploring Operation: 77-1=76, Resulting Numbers: [26, 76] Generated Node #0,2,3: 26:[26, 76] Operation: 77-1=76 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 26:[1, 51], Operations: ['52/2=26', '77-26=51'] Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,26 unequal: No Solution Exploring Operation: 1+51=52, Resulting Numbers: [52] 52,26 unequal: No Solution Exploring Operation: 1*51=51, Resulting Numbers: [51] 51,26 unequal: No Solution Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,26 unequal: No Solution No 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: 26:[26, 76], Operations: ['52/2=26', '77-1=76'] Exploring Operation: 26*76=1976, Resulting Numbers: [1976] 1976,26 unequal: No Solution Exploring Operation: 26+76=102, Resulting Numbers: [102] 102,26 unequal: No Solution Exploring Operation: 76-26=50, Resulting Numbers: [50] 50,26 unequal: No Solution No 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: 26:[26, 77], Operations: ['52/2=26', '77/1=77'] Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,26 unequal: No Solution Exploring Operation: 26*77=2002, Resulting Numbers: [2002] 2002,26 unequal: No Solution Exploring Operation: 26+77=103, Resulting Numbers: [103] 103,26 unequal: No Solution No 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: 26:[26, 77], Operations: ['52/2=26', '77*1=77'] Exploring Operation: 26*77=2002, Resulting Numbers: [2002] 2002,26 unequal: No Solution Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,26 unequal: No Solution Exploring Operation: 26+77=103, Resulting Numbers: [103] 103,26 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: 26:[52, 1, 75], Operations: ['77-2=75'] Exploring Operation: 75-52=23, Resulting Numbers: [1, 23] Generated Node #0,3,0: 26:[1, 23] Operation: 75-52=23 Exploring Operation: 75-1=74, Resulting Numbers: [52, 74] Generated Node #0,3,1: 26:[52, 74] Operation: 75-1=74 Exploring Operation: 52*1=52, Resulting Numbers: [75, 52] Generated Node #0,3,2: 26:[75, 52] Operation: 52*1=52 Exploring Operation: 52-1=51, Resulting Numbers: [75, 51] Generated Node #0,3,3: 26:[75, 51] Operation: 52-1=51 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 26:[1, 23], Operations: ['77-2=75', '75-52=23'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,26 unequal: No Solution Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,26 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,26 unequal: No Solution Exploring Operation: 1*23=23, Resulting Numbers: [23] 23,26 unequal: No Solution No 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: 26:[52, 74], Operations: ['77-2=75', '75-1=74'] Exploring Operation: 52*74=3848, Resulting Numbers: [3848] 3848,26 unequal: No Solution Exploring Operation: 52+74=126, Resulting Numbers: [126] 126,26 unequal: No Solution Exploring Operation: 74-52=22, Resulting Numbers: [22] 22,26 unequal: No Solution No 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: 26:[75, 51], Operations: ['77-2=75', '52-1=51'] Exploring Operation: 75-51=24, Resulting Numbers: [24] 24,26 unequal: No Solution Exploring Operation: 75*51=3825, Resulting Numbers: [3825] 3825,26 unequal: No Solution Exploring Operation: 75+51=126, Resulting Numbers: [126] 126,26 unequal: No Solution No 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: 26:[75, 52], Operations: ['77-2=75', '52*1=52'] Exploring Operation: 75+52=127, Resulting Numbers: [127] 127,26 unequal: No Solution Exploring Operation: 75*52=3900, Resulting Numbers: [3900] 3900,26 unequal: No Solution Exploring Operation: 75-52=23, Resulting Numbers: [23] 23,26 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: 26:[2, 52, 76], Operations: ['77-1=76'] Exploring Operation: 76/2=38, Resulting Numbers: [52, 38] Generated Node #0,1,0: 26:[52, 38] Operation: 76/2=38 Exploring Operation: 52-2=50, Resulting Numbers: [76, 50] Generated Node #0,1,1: 26:[76, 50] Operation: 52-2=50 Exploring Operation: 76-52=24, Resulting Numbers: [2, 24] Generated Node #0,1,2: 26:[2, 24] Operation: 76-52=24 Exploring Operation: 52/2=26, Resulting Numbers: [76, 26] Generated Node #0,1,3: 26:[76, 26] Operation: 52/2=26 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[2, 24], Operations: ['77-1=76', '76-52=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,26 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[77, 2, 52, 1], Operations: [] Exploring Operation: 77-1=76, Resulting Numbers: [2, 52, 76] Generated Node #0,1: 26:[2, 52, 76] Operation: 77-1=76 Moving to Node #0,1 Current State: 26:[2, 52, 76], Operations: ['77-1=76'] Exploring Operation: 76-52=24, Resulting Numbers: [2, 24] Generated Node #0,1,2: 26:[2, 24] Operation: 76-52=24 Moving to Node #0,1,2 Current State: 26:[2, 24], Operations: ['77-1=76', '76-52=24'] Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.954861
hs_4
mult_heuristic
[ 91, 18, 2, 17 ]
93
[ "91+2=93", "18-17=1", "93*1=93" ]
Current State: 93:[91, 18, 2, 17], Operations: [] Exploring Operation: 91+2=93, Resulting Numbers: [18, 17, 93] Generated Node #2: [18, 17, 93] from Operation: 91+2=93 Current State: 93:[18, 17, 93], Operations: ['91+2=93'] Exploring Operation: 18-17=1, Resulting Numbers: [93, 1] Generated Node #3: [93, 1] from Operation: 18-17=1 Current State: 93:[93, 1], Operations: ['91+2=93', '18-17=1'] Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[91, 18, 2, 17], Operations: [] Exploring Operation: 18+17=35, Resulting Numbers: [91, 2, 35] Generated Node #0,0: 93:[91, 2, 35] Operation: 18+17=35 Exploring Operation: 18-17=1, Resulting Numbers: [91, 2, 1] Generated Node #0,1: 93:[91, 2, 1] Operation: 18-17=1 Exploring Operation: 2*17=34, Resulting Numbers: [91, 18, 34] Generated Node #0,2: 93:[91, 18, 34] Operation: 2*17=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[91, 2, 1], Operations: ['18-17=1'] Exploring Operation: 2+1=3, Resulting Numbers: [91, 3] Generated Node #0,1,0: 93:[91, 3] Operation: 2+1=3 Exploring Operation: 91+1=92, Resulting Numbers: [2, 92] Generated Node #0,1,1: 93:[2, 92] Operation: 91+1=92 Exploring Operation: 91+2=93, Resulting Numbers: [1, 93] Generated Node #0,1,2: 93:[1, 93] Operation: 91+2=93 Moving to Node #0,1,0 Current State: 93:[91, 3], Operations: ['18-17=1', '2+1=3'] Exploring Operation: 91*3=273, Resulting Numbers: [273] 273,93 unequal: No Solution Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,93 unequal: No Solution Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,93 unequal: No Solution Moving to Node #0,1,1 Current State: 93:[2, 92], Operations: ['18-17=1', '91+1=92'] Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,93 unequal: No Solution Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,93 unequal: No Solution Exploring Operation: 2+92=94, Resulting Numbers: [94] 94,93 unequal: No Solution Moving to Node #0,1,2 Current State: 93:[1, 93], Operations: ['18-17=1', '91+2=93'] Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[91, 18, 2, 17], Operations: [] Exploring Operation: 18-17=1, Resulting Numbers: [91, 2, 1] Generated Node #0,1: 93:[91, 2, 1] Operation: 18-17=1 Moving to Node #0,1 Current State: 93:[91, 2, 1], Operations: ['18-17=1'] Exploring Operation: 91+2=93, Resulting Numbers: [1, 93] Generated Node #0,1,2: 93:[1, 93] Operation: 91+2=93 Moving to Node #0,1,2 Current State: 93:[1, 93], Operations: ['18-17=1', '91+2=93'] Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 57, 77, 16, 75 ]
65
[ "77-75=2", "16/2=8", "57+8=65" ]
Current State: 65:[57, 77, 16, 75], Operations: [] Exploring Operation: 77-75=2, Resulting Numbers: [57, 16, 2] Generated Node #2: [57, 16, 2] from Operation: 77-75=2 Current State: 65:[57, 16, 2], Operations: ['77-75=2'] Exploring Operation: 16/2=8, Resulting Numbers: [57, 8] Generated Node #3: [57, 8] from Operation: 16/2=8 Current State: 65:[57, 8], Operations: ['77-75=2', '16/2=8'] Exploring Operation: 57+8=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[57, 77, 16, 75], Operations: [] Exploring Operation: 77-16=61, Resulting Numbers: [57, 75, 61] Generated Node #0,0: 65:[57, 75, 61] Operation: 77-16=61 Exploring Operation: 75-57=18, Resulting Numbers: [77, 16, 18] Generated Node #0,1: 65:[77, 16, 18] Operation: 75-57=18 Exploring Operation: 77-75=2, Resulting Numbers: [57, 16, 2] Generated Node #0,2: 65:[57, 16, 2] Operation: 77-75=2 Exploring Operation: 77-57=20, Resulting Numbers: [16, 75, 20] Generated Node #0,3: 65:[16, 75, 20] Operation: 77-57=20 Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[57, 16, 2], Operations: ['77-75=2'] Exploring Operation: 57+2=59, Resulting Numbers: [16, 59] Generated Node #0,2,0: 65:[16, 59] Operation: 57+2=59 Exploring Operation: 57+16=73, Resulting Numbers: [2, 73] Generated Node #0,2,1: 65:[2, 73] Operation: 57+16=73 Exploring Operation: 16/2=8, Resulting Numbers: [57, 8] Generated Node #0,2,2: 65:[57, 8] Operation: 16/2=8 Exploring Operation: 16-2=14, Resulting Numbers: [57, 14] Generated Node #0,2,3: 65:[57, 14] Operation: 16-2=14 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 65:[16, 59], Operations: ['77-75=2', '57+2=59'] Exploring Operation: 59-16=43, Resulting Numbers: [43] 43,65 unequal: No Solution Exploring Operation: 16*59=944, Resulting Numbers: [944] 944,65 unequal: No Solution Exploring Operation: 16+59=75, Resulting Numbers: [75] 75,65 unequal: No Solution No 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: 65:[57, 14], Operations: ['77-75=2', '16-2=14'] Exploring Operation: 57+14=71, Resulting Numbers: [71] 71,65 unequal: No Solution Exploring Operation: 57-14=43, Resulting Numbers: [43] 43,65 unequal: No Solution Exploring Operation: 57*14=798, Resulting Numbers: [798] 798,65 unequal: No Solution No 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: 65:[2, 73], Operations: ['77-75=2', '57+16=73'] Exploring Operation: 2*73=146, Resulting Numbers: [146] 146,65 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,65 unequal: No Solution Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,65 unequal: No Solution No 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: 65:[57, 8], Operations: ['77-75=2', '16/2=8'] Exploring Operation: 57-8=49, Resulting Numbers: [49] 49,65 unequal: No Solution Exploring Operation: 57*8=456, Resulting Numbers: [456] 456,65 unequal: No Solution Exploring Operation: 57+8=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[57, 77, 16, 75], Operations: [] Exploring Operation: 77-75=2, Resulting Numbers: [57, 16, 2] Generated Node #0,2: 65:[57, 16, 2] Operation: 77-75=2 Moving to Node #0,2 Current State: 65:[57, 16, 2], Operations: ['77-75=2'] Exploring Operation: 16/2=8, Resulting Numbers: [57, 8] Generated Node #0,2,2: 65:[57, 8] Operation: 16/2=8 Moving to Node #0,2,2 Current State: 65:[57, 8], Operations: ['77-75=2', '16/2=8'] Exploring Operation: 57+8=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_4
sum_heuristic
[ 91, 99, 81, 93 ]
96
[ "91*99=9009", "9009-81=8928", "8928/93=96" ]
Current State: 96:[91, 99, 81, 93], Operations: [] Exploring Operation: 91*99=9009, Resulting Numbers: [81, 93, 9009] Generated Node #2: [81, 93, 9009] from Operation: 91*99=9009 Current State: 96:[81, 93, 9009], Operations: ['91*99=9009'] Exploring Operation: 9009-81=8928, Resulting Numbers: [93, 8928] Generated Node #3: [93, 8928] from Operation: 9009-81=8928 Current State: 96:[93, 8928], Operations: ['91*99=9009', '9009-81=8928'] Exploring Operation: 8928/93=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[91, 99, 81, 93], Operations: [] Exploring Operation: 91-81=10, Resulting Numbers: [99, 93, 10] Generated Node #0,0: 96:[99, 93, 10] Operation: 91-81=10 Exploring Operation: 99-81=18, Resulting Numbers: [91, 93, 18] Generated Node #0,1: 96:[91, 93, 18] Operation: 99-81=18 Exploring Operation: 93-81=12, Resulting Numbers: [91, 99, 12] Generated Node #0,2: 96:[91, 99, 12] Operation: 93-81=12 Exploring Operation: 99-91=8, Resulting Numbers: [81, 93, 8] Generated Node #0,3: 96:[81, 93, 8] Operation: 99-91=8 Exploring Operation: 93-91=2, Resulting Numbers: [99, 81, 2] Generated Node #0,4: 96:[99, 81, 2] Operation: 93-91=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[99, 93, 10], Operations: ['91-81=10'] Exploring Operation: 93-10=83, Resulting Numbers: [99, 83] Generated Node #0,0,0: 96:[99, 83] Operation: 93-10=83 Exploring Operation: 93+10=103, Resulting Numbers: [99, 103] Generated Node #0,0,1: 96:[99, 103] Operation: 93+10=103 Exploring Operation: 99-10=89, Resulting Numbers: [93, 89] Generated Node #0,0,2: 96:[93, 89] Operation: 99-10=89 Exploring Operation: 99-93=6, Resulting Numbers: [10, 6] Generated Node #0,0,3: 96:[10, 6] Operation: 99-93=6 Exploring Operation: 99+10=109, Resulting Numbers: [93, 109] Generated Node #0,0,4: 96:[93, 109] Operation: 99+10=109 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 96:[10, 6], Operations: ['91-81=10', '99-93=6'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 10*6=60, Resulting Numbers: [60] 60,96 unequal: No Solution Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 96:[99, 103], Operations: ['91-81=10', '93+10=103'] Exploring Operation: 103-99=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 99*103=10197, Resulting Numbers: [10197] 10197,96 unequal: No Solution Exploring Operation: 99+103=202, Resulting Numbers: [202] 202,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 96:[93, 89], Operations: ['91-81=10', '99-10=89'] Exploring Operation: 93-89=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 93*89=8277, Resulting Numbers: [8277] 8277,96 unequal: No Solution Exploring Operation: 93+89=182, Resulting Numbers: [182] 182,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[99, 83], Operations: ['91-81=10', '93-10=83'] Exploring Operation: 99+83=182, Resulting Numbers: [182] 182,96 unequal: No Solution Exploring Operation: 99*83=8217, Resulting Numbers: [8217] 8217,96 unequal: No Solution Exploring Operation: 99-83=16, Resulting Numbers: [16] 16,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 96:[93, 109], Operations: ['91-81=10', '99+10=109'] Exploring Operation: 93+109=202, Resulting Numbers: [202] 202,96 unequal: No Solution Exploring Operation: 93*109=10137, Resulting Numbers: [10137] 10137,96 unequal: No Solution Exploring Operation: 109-93=16, Resulting Numbers: [16] 16,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[91, 99, 12], Operations: ['93-81=12'] Exploring Operation: 91-12=79, Resulting Numbers: [99, 79] Generated Node #0,2,0: 96:[99, 79] Operation: 91-12=79 Exploring Operation: 99-12=87, Resulting Numbers: [91, 87] Generated Node #0,2,1: 96:[91, 87] Operation: 99-12=87 Exploring Operation: 99+12=111, Resulting Numbers: [91, 111] Generated Node #0,2,2: 96:[91, 111] Operation: 99+12=111 Exploring Operation: 91+12=103, Resulting Numbers: [99, 103] Generated Node #0,2,3: 96:[99, 103] Operation: 91+12=103 Exploring Operation: 99-91=8, Resulting Numbers: [12, 8] Generated Node #0,2,4: 96:[12, 8] Operation: 99-91=8 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 96:[12, 8], Operations: ['93-81=12', '99-91=8'] Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[91, 99, 81, 93], Operations: [] Exploring Operation: 93-81=12, Resulting Numbers: [91, 99, 12] Generated Node #0,2: 96:[91, 99, 12] Operation: 93-81=12 Moving to Node #0,2 Current State: 96:[91, 99, 12], Operations: ['93-81=12'] Exploring Operation: 99-91=8, Resulting Numbers: [12, 8] Generated Node #0,2,4: 96:[12, 8] Operation: 99-91=8 Moving to Node #0,2,4 Current State: 96:[12, 8], Operations: ['93-81=12', '99-91=8'] Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_5
sum_heuristic
[ 9, 46, 40, 85 ]
82
[ "46-9=37", "85-40=45", "37+45=82" ]
Current State: 82:[9, 46, 40, 85], Operations: [] Exploring Operation: 46-9=37, Resulting Numbers: [40, 85, 37] Generated Node #2: [40, 85, 37] from Operation: 46-9=37 Current State: 82:[40, 85, 37], Operations: ['46-9=37'] Exploring Operation: 85-40=45, Resulting Numbers: [37, 45] Generated Node #3: [37, 45] from Operation: 85-40=45 Current State: 82:[37, 45], Operations: ['46-9=37', '85-40=45'] Exploring Operation: 37+45=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[9, 46, 40, 85], Operations: [] Exploring Operation: 46-9=37, Resulting Numbers: [40, 85, 37] Generated Node #0,0: 82:[40, 85, 37] Operation: 46-9=37 Moving to Node #0,0 Current State: 82:[40, 85, 37], Operations: ['46-9=37'] Exploring Operation: 40-37=3, Resulting Numbers: [85, 3] Generated Node #0,0,0: 82:[85, 3] Operation: 40-37=3 Moving to Node #0,0,0 Current State: 82:[85, 3], Operations: ['46-9=37', '40-37=3'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[9, 46, 40, 85], Operations: [] Exploring Operation: 46-9=37, Resulting Numbers: [40, 85, 37] Generated Node #0,0: 82:[40, 85, 37] Operation: 46-9=37 Moving to Node #0,0 Current State: 82:[40, 85, 37], Operations: ['46-9=37'] Exploring Operation: 40-37=3, Resulting Numbers: [85, 3] Generated Node #0,0,0: 82:[85, 3] Operation: 40-37=3 Moving to Node #0,0,0 Current State: 82:[85, 3], Operations: ['46-9=37', '40-37=3'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 58, 61, 26, 60 ]
70
[ "60-58=2", "61-26=35", "2*35=70" ]
Current State: 70:[58, 61, 26, 60], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [61, 26, 2] Generated Node #2: [61, 26, 2] from Operation: 60-58=2 Current State: 70:[61, 26, 2], Operations: ['60-58=2'] Exploring Operation: 61-26=35, Resulting Numbers: [2, 35] Generated Node #3: [2, 35] from Operation: 61-26=35 Current State: 70:[2, 35], Operations: ['60-58=2', '61-26=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[58, 61, 26, 60], Operations: [] Exploring Operation: 61-26=35, Resulting Numbers: [58, 60, 35] Generated Node #0,0: 70:[58, 60, 35] Operation: 61-26=35 Exploring Operation: 58-26=32, Resulting Numbers: [61, 60, 32] Generated Node #0,1: 70:[61, 60, 32] Operation: 58-26=32 Exploring Operation: 61-60=1, Resulting Numbers: [58, 26, 1] Generated Node #0,2: 70:[58, 26, 1] Operation: 61-60=1 Exploring Operation: 60-58=2, Resulting Numbers: [61, 26, 2] Generated Node #0,3: 70:[61, 26, 2] Operation: 60-58=2 Exploring Operation: 61-58=3, Resulting Numbers: [26, 60, 3] Generated Node #0,4: 70:[26, 60, 3] Operation: 61-58=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 70:[61, 26, 2], Operations: ['60-58=2'] Exploring Operation: 26+2=28, Resulting Numbers: [61, 28] Generated Node #0,3,0: 70:[61, 28] Operation: 26+2=28 Exploring Operation: 26/2=13, Resulting Numbers: [61, 13] Generated Node #0,3,1: 70:[61, 13] Operation: 26/2=13 Exploring Operation: 61+2=63, Resulting Numbers: [26, 63] Generated Node #0,3,2: 70:[26, 63] Operation: 61+2=63 Exploring Operation: 61-26=35, Resulting Numbers: [2, 35] Generated Node #0,3,3: 70:[2, 35] Operation: 61-26=35 Exploring Operation: 61+26=87, Resulting Numbers: [2, 87] Generated Node #0,3,4: 70:[2, 87] Operation: 61+26=87 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 70:[2, 35], Operations: ['60-58=2', '61-26=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,70 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,70 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[58, 61, 26, 60], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [61, 26, 2] Generated Node #0,3: 70:[61, 26, 2] Operation: 60-58=2 Moving to Node #0,3 Current State: 70:[61, 26, 2], Operations: ['60-58=2'] Exploring Operation: 61-26=35, Resulting Numbers: [2, 35] Generated Node #0,3,3: 70:[2, 35] Operation: 61-26=35 Moving to Node #0,3,3 Current State: 70:[2, 35], Operations: ['60-58=2', '61-26=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 5, 17, 53, 65 ]
16
[ "5*65=325", "325-53=272", "272/17=16" ]
Current State: 16:[5, 17, 53, 65], Operations: [] Exploring Operation: 5*65=325, Resulting Numbers: [17, 53, 325] Generated Node #2: [17, 53, 325] from Operation: 5*65=325 Current State: 16:[17, 53, 325], Operations: ['5*65=325'] Exploring Operation: 325-53=272, Resulting Numbers: [17, 272] Generated Node #3: [17, 272] from Operation: 325-53=272 Current State: 16:[17, 272], Operations: ['5*65=325', '325-53=272'] Exploring Operation: 272/17=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[5, 17, 53, 65], Operations: [] Exploring Operation: 65-53=12, Resulting Numbers: [5, 17, 12] Generated Node #0,0: 16:[5, 17, 12] Operation: 65-53=12 Exploring Operation: 65/5=13, Resulting Numbers: [17, 53, 13] Generated Node #0,1: 16:[17, 53, 13] Operation: 65/5=13 Exploring Operation: 53-17=36, Resulting Numbers: [5, 65, 36] Generated Node #0,2: 16:[5, 65, 36] Operation: 53-17=36 Exploring Operation: 53-5=48, Resulting Numbers: [17, 65, 48] Generated Node #0,3: 16:[17, 65, 48] Operation: 53-5=48 Exploring Operation: 65-17=48, Resulting Numbers: [5, 53, 48] Generated Node #0,4: 16:[5, 53, 48] Operation: 65-17=48 Moving to Node #0,0 Current State: 16:[5, 17, 12], Operations: ['65-53=12'] Exploring Operation: 17-12=5, Resulting Numbers: [5, 5] Generated Node #0,0,0: 16:[5, 5] Operation: 17-12=5 Exploring Operation: 17-5=12, Resulting Numbers: [12, 12] Generated Node #0,0,1: 16:[12, 12] Operation: 17-5=12 Exploring Operation: 12-5=7, Resulting Numbers: [17, 7] Generated Node #0,0,2: 16:[17, 7] Operation: 12-5=7 Exploring Operation: 5+17=22, Resulting Numbers: [12, 22] Generated Node #0,0,3: 16:[12, 22] Operation: 5+17=22 Exploring Operation: 5+12=17, Resulting Numbers: [17, 17] Generated Node #0,0,4: 16:[17, 17] Operation: 5+12=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[5, 5], Operations: ['65-53=12', '17-12=5'] Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[17, 7], Operations: ['65-53=12', '12-5=7'] Exploring Operation: 17*7=119, Resulting Numbers: [119] 119,16 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 17+7=24, Resulting Numbers: [24] 24,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 16:[17, 17], Operations: ['65-53=12', '5+12=17'] Exploring Operation: 17-17=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 17/17=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 17*17=289, Resulting Numbers: [289] 289,16 unequal: No Solution Exploring Operation: 17+17=34, Resulting Numbers: [34] 34,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[12, 12], Operations: ['65-53=12', '17-5=12'] Exploring Operation: 12+12=24, Resulting Numbers: [24] 24,16 unequal: No Solution Exploring Operation: 12-12=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 12/12=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 12*12=144, Resulting Numbers: [144] 144,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 16:[12, 22], Operations: ['65-53=12', '5+17=22'] Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,16 unequal: No Solution Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,16 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: 16:[17, 53, 13], Operations: ['65/5=13'] Exploring Operation: 53-17=36, Resulting Numbers: [13, 36] Generated Node #0,1,0: 16:[13, 36] Operation: 53-17=36 Exploring Operation: 17+13=30, Resulting Numbers: [53, 30] Generated Node #0,1,1: 16:[53, 30] Operation: 17+13=30 Exploring Operation: 17-13=4, Resulting Numbers: [53, 4] Generated Node #0,1,2: 16:[53, 4] Operation: 17-13=4 Exploring Operation: 53-13=40, Resulting Numbers: [17, 40] Generated Node #0,1,3: 16:[17, 40] Operation: 53-13=40 Exploring Operation: 53+13=66, Resulting Numbers: [17, 66] Generated Node #0,1,4: 16:[17, 66] Operation: 53+13=66 Moving to Node #0,2 Current State: 16:[5, 65, 36], Operations: ['53-17=36'] Exploring Operation: 36-5=31, Resulting Numbers: [65, 31] Generated Node #0,2,0: 16:[65, 31] Operation: 36-5=31 Exploring Operation: 65-36=29, Resulting Numbers: [5, 29] Generated Node #0,2,1: 16:[5, 29] Operation: 65-36=29 Exploring Operation: 5+65=70, Resulting Numbers: [36, 70] Generated Node #0,2,2: 16:[36, 70] Operation: 5+65=70 Exploring Operation: 65/5=13, Resulting Numbers: [36, 13] Generated Node #0,2,3: 16:[36, 13] Operation: 65/5=13 Exploring Operation: 65-5=60, Resulting Numbers: [36, 60] Generated Node #0,2,4: 16:[36, 60] Operation: 65-5=60 Moving to Node #0,4 Current State: 16:[5, 53, 48], Operations: ['65-17=48'] Exploring Operation: 5+53=58, Resulting Numbers: [48, 58] Generated Node #0,4,0: 16:[48, 58] Operation: 5+53=58 Exploring Operation: 53-48=5, Resulting Numbers: [5, 5] Generated Node #0,4,1: 16:[5, 5] Operation: 53-48=5 Exploring Operation: 48-5=43, Resulting Numbers: [53, 43] Generated Node #0,4,2: 16:[53, 43] Operation: 48-5=43 Exploring Operation: 5+48=53, Resulting Numbers: [53, 53] Generated Node #0,4,3: 16:[53, 53] Operation: 5+48=53 Exploring Operation: 53-5=48, Resulting Numbers: [48, 48] Generated Node #0,4,4: 16:[48, 48] Operation: 53-5=48 Moving to Node #0,3 Current State: 16:[17, 65, 48], Operations: ['53-5=48'] Exploring Operation: 17+48=65, Resulting Numbers: [65, 65] Generated Node #0,3,0: 16:[65, 65] Operation: 17+48=65 Exploring Operation: 65-48=17, Resulting Numbers: [17, 17] Generated Node #0,3,1: 16:[17, 17] Operation: 65-48=17 Exploring Operation: 17+65=82, Resulting Numbers: [48, 82] Generated Node #0,3,2: 16:[48, 82] Operation: 17+65=82 Exploring Operation: 65-17=48, Resulting Numbers: [48, 48] Generated Node #0,3,3: 16:[48, 48] Operation: 65-17=48 Exploring Operation: 48-17=31, Resulting Numbers: [65, 31] Generated Node #0,3,4: 16:[65, 31] Operation: 48-17=31 Moving to Node #0,4,1 Current State: 16:[5, 5], Operations: ['65-17=48', '53-48=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,16 unequal: No Solution Moving to Node #0,3,1 Current State: 16:[17, 17], Operations: ['53-5=48', '65-48=17'] Exploring Operation: 17+17=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 17-17=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 17/17=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 17*17=289, Resulting Numbers: [289] 289,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[5, 29], Operations: ['53-17=36', '65-36=29'] Exploring Operation: 5*29=145, Resulting Numbers: [145] 145,16 unequal: No Solution Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[13, 36], Operations: ['65/5=13', '53-17=36'] Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,16 unequal: No Solution Exploring Operation: 13*36=468, Resulting Numbers: [468] 468,16 unequal: No Solution Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,16 unequal: No Solution Moving to Node #0,2,3 Current State: 16:[36, 13], Operations: ['53-17=36', '65/5=13'] Exploring Operation: 36+13=49, Resulting Numbers: [49] 49,16 unequal: No Solution Exploring Operation: 36*13=468, Resulting Numbers: [468] 468,16 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,16 unequal: No Solution Moving to Node #0,1,3 Current State: 16:[17, 40], Operations: ['65/5=13', '53-13=40'] Exploring Operation: 17+40=57, Resulting Numbers: [57] 57,16 unequal: No Solution Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,16 unequal: No Solution Exploring Operation: 17*40=680, Resulting Numbers: [680] 680,16 unequal: No Solution Moving to Node #0,1,2 Current State: 16:[53, 4], Operations: ['65/5=13', '17-13=4'] Exploring Operation: 53*4=212, Resulting Numbers: [212] 212,16 unequal: No Solution Exploring Operation: 53+4=57, Resulting Numbers: [57] 57,16 unequal: No Solution Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,16 unequal: No Solution Moving to Node #0,1,4 Current State: 16:[17, 66], Operations: ['65/5=13', '53+13=66'] Exploring Operation: 17+66=83, Resulting Numbers: [83] 83,16 unequal: No Solution Exploring Operation: 17*66=1122, Resulting Numbers: [1122] 1122,16 unequal: No Solution Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[53, 30], Operations: ['65/5=13', '17+13=30'] Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,16 unequal: No Solution Exploring Operation: 53*30=1590, Resulting Numbers: [1590] 1590,16 unequal: No Solution Exploring Operation: 53+30=83, Resulting Numbers: [83] 83,16 unequal: No Solution Moving to Node #0,3,4 Current State: 16:[65, 31], Operations: ['53-5=48', '48-17=31'] Exploring Operation: 65+31=96, Resulting Numbers: [96] 96,16 unequal: No Solution Exploring Operation: 65-31=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 65*31=2015, Resulting Numbers: [2015] 2015,16 unequal: No Solution Moving to Node #0,4,4 Current State: 16:[48, 48], Operations: ['65-17=48', '53-5=48'] Exploring Operation: 48/48=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 48+48=96, Resulting Numbers: [96] 96,16 unequal: No Solution Exploring Operation: 48*48=2304, Resulting Numbers: [2304] 2304,16 unequal: No Solution Exploring Operation: 48-48=0, Resulting Numbers: [0] 0,16 unequal: No Solution Moving to Node #0,4,2 Current State: 16:[53, 43], Operations: ['65-17=48', '48-5=43'] Exploring Operation: 53-43=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 53*43=2279, Resulting Numbers: [2279] 2279,16 unequal: No Solution Exploring Operation: 53+43=96, Resulting Numbers: [96] 96,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[65, 31], Operations: ['53-17=36', '36-5=31'] Exploring Operation: 65*31=2015, Resulting Numbers: [2015] 2015,16 unequal: No Solution Exploring Operation: 65+31=96, Resulting Numbers: [96] 96,16 unequal: No Solution Exploring Operation: 65-31=34, Resulting Numbers: [34] 34,16 unequal: No Solution Moving to Node #0,2,4 Current State: 16:[36, 60], Operations: ['53-17=36', '65-5=60'] Exploring Operation: 60-36=24, Resulting Numbers: [24] 24,16 unequal: No Solution Exploring Operation: 36+60=96, Resulting Numbers: [96] 96,16 unequal: No Solution Exploring Operation: 36*60=2160, Resulting Numbers: [2160] 2160,16 unequal: No Solution Moving to Node #0,3,3 Current State: 16:[48, 48], Operations: ['53-5=48', '65-17=48'] Exploring Operation: 48*48=2304, Resulting Numbers: [2304] 2304,16 unequal: No Solution Exploring Operation: 48-48=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 48/48=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 48+48=96, Resulting Numbers: [96] 96,16 unequal: No Solution Moving to Node #0,4,0 Current State: 16:[48, 58], Operations: ['65-17=48', '5+53=58'] Exploring Operation: 58-48=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 48*58=2784, Resulting Numbers: [2784] 2784,16 unequal: No Solution Exploring Operation: 48+58=106, Resulting Numbers: [106] 106,16 unequal: No Solution Moving to Node #0,2,2 Current State: 16:[36, 70], Operations: ['53-17=36', '5+65=70'] Exploring Operation: 36*70=2520, Resulting Numbers: [2520] 2520,16 unequal: No Solution Exploring Operation: 36+70=106, Resulting Numbers: [106] 106,16 unequal: No Solution Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,16 unequal: No Solution Moving to Node #0,4,3 Current State: 16:[53, 53], Operations: ['65-17=48', '5+48=53'] Exploring Operation: 53-53=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 53/53=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 53*53=2809, Resulting Numbers: [2809] 2809,16 unequal: No Solution Exploring Operation: 53+53=106, Resulting Numbers: [106] 106,16 unequal: No Solution Moving to Node #0,3,2 Current State: 16:[48, 82], Operations: ['53-5=48', '17+65=82'] Exploring Operation: 48+82=130, Resulting Numbers: [130] 130,16 unequal: No Solution Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 48*82=3936, Resulting Numbers: [3936] 3936,16 unequal: No Solution Moving to Node #0,3,0 Current State: 16:[65, 65], Operations: ['53-5=48', '17+48=65'] Exploring Operation: 65+65=130, Resulting Numbers: [130] 130,16 unequal: No Solution Exploring Operation: 65-65=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 65/65=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 65*65=4225, Resulting Numbers: [4225] 4225,16 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 10, 75, 5, 23 ]
28
[ "10+5=15", "75/15=5", "23+5=28" ]
Current State: 28:[10, 75, 5, 23], Operations: [] Exploring Operation: 10+5=15, Resulting Numbers: [75, 23, 15] Generated Node #2: [75, 23, 15] from Operation: 10+5=15 Current State: 28:[75, 23, 15], Operations: ['10+5=15'] Exploring Operation: 75/15=5, Resulting Numbers: [23, 5] Generated Node #3: [23, 5] from Operation: 75/15=5 Current State: 28:[23, 5], Operations: ['10+5=15', '75/15=5'] Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[10, 75, 5, 23], Operations: [] Exploring Operation: 75/5=15, Resulting Numbers: [10, 23, 15] Generated Node #0,0: 28:[10, 23, 15] Operation: 75/5=15 Exploring Operation: 75-5=70, Resulting Numbers: [10, 23, 70] Generated Node #0,1: 28:[10, 23, 70] Operation: 75-5=70 Exploring Operation: 75-10=65, Resulting Numbers: [5, 23, 65] Generated Node #0,2: 28:[5, 23, 65] Operation: 75-10=65 Exploring Operation: 23-10=13, Resulting Numbers: [75, 5, 13] Generated Node #0,3: 28:[75, 5, 13] Operation: 23-10=13 Exploring Operation: 75-23=52, Resulting Numbers: [10, 5, 52] Generated Node #0,4: 28:[10, 5, 52] Operation: 75-23=52 Moving to Node #0,0 Current State: 28:[10, 23, 15], Operations: ['75/5=15'] Exploring Operation: 10+23=33, Resulting Numbers: [15, 33] Generated Node #0,0,0: 28:[15, 33] Operation: 10+23=33 Exploring Operation: 10+15=25, Resulting Numbers: [23, 25] Generated Node #0,0,1: 28:[23, 25] Operation: 10+15=25 Exploring Operation: 23-15=8, Resulting Numbers: [10, 8] Generated Node #0,0,2: 28:[10, 8] Operation: 23-15=8 Exploring Operation: 23-10=13, Resulting Numbers: [15, 13] Generated Node #0,0,3: 28:[15, 13] Operation: 23-10=13 Exploring Operation: 15-10=5, Resulting Numbers: [23, 5] Generated Node #0,0,4: 28:[23, 5] Operation: 15-10=5 Moving to Node #0,4 Current State: 28:[10, 5, 52], Operations: ['75-23=52'] Exploring Operation: 10+5=15, Resulting Numbers: [52, 15] Generated Node #0,4,0: 28:[52, 15] Operation: 10+5=15 Exploring Operation: 10/5=2, Resulting Numbers: [52, 2] Generated Node #0,4,1: 28:[52, 2] Operation: 10/5=2 Exploring Operation: 52-10=42, Resulting Numbers: [5, 42] Generated Node #0,4,2: 28:[5, 42] Operation: 52-10=42 Exploring Operation: 10-5=5, Resulting Numbers: [52, 5] Generated Node #0,4,3: 28:[52, 5] Operation: 10-5=5 Exploring Operation: 52-5=47, Resulting Numbers: [10, 47] Generated Node #0,4,4: 28:[10, 47] Operation: 52-5=47 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 28:[5, 42], Operations: ['75-23=52', '52-10=42'] Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,28 unequal: No Solution Exploring Operation: 5*42=210, Resulting Numbers: [210] 210,28 unequal: No Solution Exploring Operation: 5+42=47, Resulting Numbers: [47] 47,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 28:[10, 47], Operations: ['75-23=52', '52-5=47'] Exploring Operation: 10+47=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 10*47=470, Resulting Numbers: [470] 470,28 unequal: No Solution Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 28:[52, 2], Operations: ['75-23=52', '10/5=2'] Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,28 unequal: No Solution Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,28 unequal: No Solution Exploring Operation: 52*2=104, Resulting Numbers: [104] 104,28 unequal: No Solution Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 28:[52, 15], Operations: ['75-23=52', '10+5=15'] Exploring Operation: 52*15=780, Resulting Numbers: [780] 780,28 unequal: No Solution Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,28 unequal: No Solution Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 28:[52, 5], Operations: ['75-23=52', '10-5=5'] Exploring Operation: 52+5=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,28 unequal: No Solution Exploring Operation: 52*5=260, Resulting Numbers: [260] 260,28 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: 28:[5, 23, 65], Operations: ['75-10=65'] Exploring Operation: 65-23=42, Resulting Numbers: [5, 42] Generated Node #0,2,0: 28:[5, 42] Operation: 65-23=42 Exploring Operation: 65/5=13, Resulting Numbers: [23, 13] Generated Node #0,2,1: 28:[23, 13] Operation: 65/5=13 Exploring Operation: 5+23=28, Resulting Numbers: [65, 28] Generated Node #0,2,2: 28:[65, 28] Operation: 5+23=28 Exploring Operation: 65-5=60, Resulting Numbers: [23, 60] Generated Node #0,2,3: 28:[23, 60] Operation: 65-5=60 Exploring Operation: 23-5=18, Resulting Numbers: [65, 18] Generated Node #0,2,4: 28:[65, 18] Operation: 23-5=18 Moving to Node #0,3 Current State: 28:[75, 5, 13], Operations: ['23-10=13'] Exploring Operation: 75-13=62, Resulting Numbers: [5, 62] Generated Node #0,3,0: 28:[5, 62] Operation: 75-13=62 Exploring Operation: 5+13=18, Resulting Numbers: [75, 18] Generated Node #0,3,1: 28:[75, 18] Operation: 5+13=18 Exploring Operation: 13-5=8, Resulting Numbers: [75, 8] Generated Node #0,3,2: 28:[75, 8] Operation: 13-5=8 Exploring Operation: 75-5=70, Resulting Numbers: [13, 70] Generated Node #0,3,3: 28:[13, 70] Operation: 75-5=70 Exploring Operation: 75/5=15, Resulting Numbers: [13, 15] Generated Node #0,3,4: 28:[13, 15] Operation: 75/5=15 Moving to Node #0,1 Current State: 28:[10, 23, 70], Operations: ['75-5=70'] Exploring Operation: 10+23=33, Resulting Numbers: [70, 33] Generated Node #0,1,0: 28:[70, 33] Operation: 10+23=33 Exploring Operation: 23-10=13, Resulting Numbers: [70, 13] Generated Node #0,1,1: 28:[70, 13] Operation: 23-10=13 Exploring Operation: 70/10=7, Resulting Numbers: [23, 7] Generated Node #0,1,2: 28:[23, 7] Operation: 70/10=7 Exploring Operation: 70-23=47, Resulting Numbers: [10, 47] Generated Node #0,1,3: 28:[10, 47] Operation: 70-23=47 Exploring Operation: 70-10=60, Resulting Numbers: [23, 60] Generated Node #0,1,4: 28:[23, 60] Operation: 70-10=60 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 28:[23, 7], Operations: ['75-5=70', '70/10=7'] Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,28 unequal: No Solution Exploring Operation: 23*7=161, Resulting Numbers: [161] 161,28 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 28:[10, 47], Operations: ['75-5=70', '70-23=47'] Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,28 unequal: No Solution Exploring Operation: 10*47=470, Resulting Numbers: [470] 470,28 unequal: No Solution Exploring Operation: 10+47=57, Resulting Numbers: [57] 57,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 28:[23, 60], Operations: ['75-5=70', '70-10=60'] Exploring Operation: 60-23=37, Resulting Numbers: [37] 37,28 unequal: No Solution Exploring Operation: 23*60=1380, Resulting Numbers: [1380] 1380,28 unequal: No Solution Exploring Operation: 23+60=83, Resulting Numbers: [83] 83,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 28:[70, 13], Operations: ['75-5=70', '23-10=13'] Exploring Operation: 70-13=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 70*13=910, Resulting Numbers: [910] 910,28 unequal: No Solution Exploring Operation: 70+13=83, Resulting Numbers: [83] 83,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 28:[70, 33], Operations: ['75-5=70', '10+23=33'] Exploring Operation: 70-33=37, Resulting Numbers: [37] 37,28 unequal: No Solution Exploring Operation: 70+33=103, Resulting Numbers: [103] 103,28 unequal: No Solution Exploring Operation: 70*33=2310, Resulting Numbers: [2310] 2310,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 28:[15, 13], Operations: ['75/5=15', '23-10=13'] Exploring Operation: 15*13=195, Resulting Numbers: [195] 195,28 unequal: No Solution Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[10, 75, 5, 23], Operations: [] Exploring Operation: 75/5=15, Resulting Numbers: [10, 23, 15] Generated Node #0,0: 28:[10, 23, 15] Operation: 75/5=15 Moving to Node #0,0 Current State: 28:[10, 23, 15], Operations: ['75/5=15'] Exploring Operation: 23-10=13, Resulting Numbers: [15, 13] Generated Node #0,0,3: 28:[15, 13] Operation: 23-10=13 Moving to Node #0,0,3 Current State: 28:[15, 13], Operations: ['75/5=15', '23-10=13'] Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
0.94184
hs_5
sum_heuristic
[ 57, 10, 44, 43 ]
87
[ "57-44=13", "10*13=130", "130-43=87" ]
Current State: 87:[57, 10, 44, 43], Operations: [] Exploring Operation: 57-44=13, Resulting Numbers: [10, 43, 13] Generated Node #2: [10, 43, 13] from Operation: 57-44=13 Current State: 87:[10, 43, 13], Operations: ['57-44=13'] Exploring Operation: 10*13=130, Resulting Numbers: [43, 130] Generated Node #3: [43, 130] from Operation: 10*13=130 Current State: 87:[43, 130], Operations: ['57-44=13', '10*13=130'] Exploring Operation: 130-43=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[57, 10, 44, 43], Operations: [] Exploring Operation: 57-44=13, Resulting Numbers: [10, 43, 13] Generated Node #0,0: 87:[10, 43, 13] Operation: 57-44=13 Exploring Operation: 57-43=14, Resulting Numbers: [10, 44, 14] Generated Node #0,1: 87:[10, 44, 14] Operation: 57-43=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[10, 43, 13], Operations: ['57-44=13'] Exploring Operation: 43-13=30, Resulting Numbers: [10, 30] Generated Node #0,0,0: 87:[10, 30] Operation: 43-13=30 Exploring Operation: 43-10=33, Resulting Numbers: [13, 33] Generated Node #0,0,1: 87:[13, 33] Operation: 43-10=33 Moving to Node #0,0,0 Current State: 87:[10, 30], Operations: ['57-44=13', '43-13=30'] Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,87 unequal: No Solution Moving to Node #0,0,1 Current State: 87:[13, 33], Operations: ['57-44=13', '43-10=33'] Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,87 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:[10, 44, 14], Operations: ['57-43=14'] Exploring Operation: 44-10=34, Resulting Numbers: [14, 34] Generated Node #0,1,0: 87:[14, 34] Operation: 44-10=34 Exploring Operation: 44-14=30, Resulting Numbers: [10, 30] Generated Node #0,1,1: 87:[10, 30] Operation: 44-14=30 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[10, 30], Operations: ['57-43=14', '44-14=30'] Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,87 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,87 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 #0,1,0 Current State: 87:[14, 34], Operations: ['57-43=14', '44-10=34'] Exploring Operation: 14+34=48, Resulting Numbers: [48] 48,87 unequal: No Solution Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,87 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
sum_heuristic
[ 19, 5, 34, 28 ]
47
[ "34-19=15", "5*15=75", "75-28=47" ]
Current State: 47:[19, 5, 34, 28], Operations: [] Exploring Operation: 34-19=15, Resulting Numbers: [5, 28, 15] Generated Node #2: [5, 28, 15] from Operation: 34-19=15 Current State: 47:[5, 28, 15], Operations: ['34-19=15'] Exploring Operation: 5*15=75, Resulting Numbers: [28, 75] Generated Node #3: [28, 75] from Operation: 5*15=75 Current State: 47:[28, 75], Operations: ['34-19=15', '5*15=75'] Exploring Operation: 75-28=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[19, 5, 34, 28], Operations: [] Exploring Operation: 19+5=24, Resulting Numbers: [34, 28, 24] Generated Node #0,0: 47:[34, 28, 24] Operation: 19+5=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[34, 28, 24], Operations: ['19+5=24'] Exploring Operation: 28+24=52, Resulting Numbers: [34, 52] Generated Node #0,0,0: 47:[34, 52] Operation: 28+24=52 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[34, 52], Operations: ['19+5=24', '28+24=52'] Exploring Operation: 52-34=18, Resulting Numbers: [18] 18,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 44, 33, 23, 2 ]
66
[ "44+2=46", "33*46=1518", "1518/23=66" ]
Current State: 66:[44, 33, 23, 2], Operations: [] Exploring Operation: 44+2=46, Resulting Numbers: [33, 23, 46] Generated Node #2: [33, 23, 46] from Operation: 44+2=46 Current State: 66:[33, 23, 46], Operations: ['44+2=46'] Exploring Operation: 33*46=1518, Resulting Numbers: [23, 1518] Generated Node #3: [23, 1518] from Operation: 33*46=1518 Current State: 66:[23, 1518], Operations: ['44+2=46', '33*46=1518'] Exploring Operation: 1518/23=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[44, 33, 23, 2], Operations: [] Exploring Operation: 44-33=11, Resulting Numbers: [23, 2, 11] Generated Node #0,0: 66:[23, 2, 11] Operation: 44-33=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[23, 2, 11], Operations: ['44-33=11'] Exploring Operation: 23-2=21, Resulting Numbers: [11, 21] Generated Node #0,0,0: 66:[11, 21] Operation: 23-2=21 Moving to Node #0,0,0 Current State: 66:[11, 21], Operations: ['44-33=11', '23-2=21'] Exploring Operation: 11+21=32, Resulting Numbers: [32] 32,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 9, 21, 72, 60 ]
66
[ "21-9=12", "72/12=6", "60+6=66" ]
Current State: 66:[9, 21, 72, 60], Operations: [] Exploring Operation: 21-9=12, Resulting Numbers: [72, 60, 12] Generated Node #2: [72, 60, 12] from Operation: 21-9=12 Current State: 66:[72, 60, 12], Operations: ['21-9=12'] Exploring Operation: 72/12=6, Resulting Numbers: [60, 6] Generated Node #3: [60, 6] from Operation: 72/12=6 Current State: 66:[60, 6], Operations: ['21-9=12', '72/12=6'] Exploring Operation: 60+6=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[9, 21, 72, 60], Operations: [] Exploring Operation: 72/9=8, Resulting Numbers: [21, 60, 8] Generated Node #0,0: 66:[21, 60, 8] Operation: 72/9=8 Exploring Operation: 72-60=12, Resulting Numbers: [9, 21, 12] Generated Node #0,1: 66:[9, 21, 12] Operation: 72-60=12 Moving to Node #0,1 Current State: 66:[9, 21, 12], Operations: ['72-60=12'] Exploring Operation: 12-9=3, Resulting Numbers: [21, 3] Generated Node #0,1,0: 66:[21, 3] Operation: 12-9=3 Exploring Operation: 21-9=12, Resulting Numbers: [12, 12] Generated Node #0,1,1: 66:[12, 12] Operation: 21-9=12 Moving to Node #0,0 Current State: 66:[21, 60, 8], Operations: ['72/9=8'] Exploring Operation: 60+8=68, Resulting Numbers: [21, 68] Generated Node #0,0,0: 66:[21, 68] Operation: 60+8=68 Exploring Operation: 60-21=39, Resulting Numbers: [8, 39] Generated Node #0,0,1: 66:[8, 39] Operation: 60-21=39 Moving to Node #0,1,0 Current State: 66:[21, 3], Operations: ['72-60=12', '12-9=3'] Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,66 unequal: No Solution Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,66 unequal: No Solution Moving to Node #0,1,1 Current State: 66:[12, 12], Operations: ['72-60=12', '21-9=12'] Exploring Operation: 12+12=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 12/12=1, Resulting Numbers: [1] 1,66 unequal: No Solution Moving to Node #0,0,0 Current State: 66:[21, 68], Operations: ['72/9=8', '60+8=68'] Exploring Operation: 21+68=89, Resulting Numbers: [89] 89,66 unequal: No Solution Exploring Operation: 68-21=47, Resulting Numbers: [47] 47,66 unequal: No Solution Moving to Node #0,0,1 Current State: 66:[8, 39], Operations: ['72/9=8', '60-21=39'] Exploring Operation: 8+39=47, Resulting Numbers: [47] 47,66 unequal: No Solution Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,66 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 84, 34, 3, 37 ]
55
[ "84-37=47", "34*3=102", "102-47=55" ]
Current State: 55:[84, 34, 3, 37], Operations: [] Exploring Operation: 84-37=47, Resulting Numbers: [34, 3, 47] Generated Node #2: [34, 3, 47] from Operation: 84-37=47 Current State: 55:[34, 3, 47], Operations: ['84-37=47'] Exploring Operation: 34*3=102, Resulting Numbers: [47, 102] Generated Node #3: [47, 102] from Operation: 34*3=102 Current State: 55:[47, 102], Operations: ['84-37=47', '34*3=102'] Exploring Operation: 102-47=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[84, 34, 3, 37], Operations: [] Exploring Operation: 84-37=47, Resulting Numbers: [34, 3, 47] Generated Node #0,0: 55:[34, 3, 47] Operation: 84-37=47 Exploring Operation: 37-34=3, Resulting Numbers: [84, 3, 3] Generated Node #0,1: 55:[84, 3, 3] Operation: 37-34=3 Exploring Operation: 34+37=71, Resulting Numbers: [84, 3, 71] Generated Node #0,2: 55:[84, 3, 71] Operation: 34+37=71 Exploring Operation: 84-34=50, Resulting Numbers: [3, 37, 50] Generated Node #0,3: 55:[3, 37, 50] Operation: 84-34=50 Start Sub Search at level 1: Moving to Node #0,3 Current State: 55:[3, 37, 50], Operations: ['84-34=50'] Exploring Operation: 50-37=13, Resulting Numbers: [3, 13] Generated Node #0,3,0: 55:[3, 13] Operation: 50-37=13 Exploring Operation: 3+50=53, Resulting Numbers: [37, 53] Generated Node #0,3,1: 55:[37, 53] Operation: 3+50=53 Exploring Operation: 3+37=40, Resulting Numbers: [50, 40] Generated Node #0,3,2: 55:[50, 40] Operation: 3+37=40 Exploring Operation: 37-3=34, Resulting Numbers: [50, 34] Generated Node #0,3,3: 55:[50, 34] Operation: 37-3=34 Moving to Node #0,3,0 Current State: 55:[3, 13], Operations: ['84-34=50', '50-37=13'] Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,55 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,55 unequal: No Solution Moving to Node #0,3,2 Current State: 55:[50, 40], Operations: ['84-34=50', '3+37=40'] Exploring Operation: 50+40=90, Resulting Numbers: [90] 90,55 unequal: No Solution Exploring Operation: 50-40=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 50*40=2000, Resulting Numbers: [2000] 2000,55 unequal: No Solution Moving to Node #0,3,1 Current State: 55:[37, 53], Operations: ['84-34=50', '3+50=53'] Exploring Operation: 37+53=90, Resulting Numbers: [90] 90,55 unequal: No Solution Exploring Operation: 37*53=1961, Resulting Numbers: [1961] 1961,55 unequal: No Solution Exploring Operation: 53-37=16, Resulting Numbers: [16] 16,55 unequal: No Solution Moving to Node #0,3,3 Current State: 55:[50, 34], Operations: ['84-34=50', '37-3=34'] Exploring Operation: 50*34=1700, Resulting Numbers: [1700] 1700,55 unequal: No Solution Exploring Operation: 50+34=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[34, 3, 47], Operations: ['84-37=47'] Exploring Operation: 47-34=13, Resulting Numbers: [3, 13] Generated Node #0,0,0: 55:[3, 13] Operation: 47-34=13 Exploring Operation: 34-3=31, Resulting Numbers: [47, 31] Generated Node #0,0,1: 55:[47, 31] Operation: 34-3=31 Exploring Operation: 34+3=37, Resulting Numbers: [47, 37] Generated Node #0,0,2: 55:[47, 37] Operation: 34+3=37 Exploring Operation: 3+47=50, Resulting Numbers: [34, 50] Generated Node #0,0,3: 55:[34, 50] Operation: 3+47=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[3, 13], Operations: ['84-37=47', '47-34=13'] Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,55 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 55:[47, 37], Operations: ['84-37=47', '34+3=37'] Exploring Operation: 47+37=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 47*37=1739, Resulting Numbers: [1739] 1739,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 55:[34, 50], Operations: ['84-37=47', '3+47=50'] Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 34+50=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 34*50=1700, Resulting Numbers: [1700] 1700,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 55:[47, 31], Operations: ['84-37=47', '34-3=31'] Exploring Operation: 47-31=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 47+31=78, Resulting Numbers: [78] 78,55 unequal: No Solution Exploring Operation: 47*31=1457, Resulting Numbers: [1457] 1457,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[84, 3, 3], Operations: ['37-34=3'] Exploring Operation: 84/3=28, Resulting Numbers: [3, 28] Generated Node #0,1,0: 55:[3, 28] Operation: 84/3=28 Exploring Operation: 84/3=28, Resulting Numbers: [3, 28] Generated Node #0,1,1: 55:[3, 28] Operation: 84/3=28 Exploring Operation: 84-3=81, Resulting Numbers: [3, 81] Generated Node #0,1,2: 55:[3, 81] Operation: 84-3=81 Exploring Operation: 84-3=81, Resulting Numbers: [3, 81] Generated Node #0,1,3: 55:[3, 81] Operation: 84-3=81 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[3, 28], Operations: ['37-34=3', '84/3=28'] Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,55 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 55:[3, 28], Operations: ['37-34=3', '84/3=28'] Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,55 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 55:[3, 81], Operations: ['37-34=3', '84-3=81'] Exploring Operation: 3*81=243, Resulting Numbers: [243] 243,55 unequal: No Solution Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,55 unequal: No Solution Exploring Operation: 81/3=27, Resulting Numbers: [27] 27,55 unequal: No Solution Exploring Operation: 3+81=84, Resulting Numbers: [84] 84,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 55:[3, 81], Operations: ['37-34=3', '84-3=81'] Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,55 unequal: No Solution Exploring Operation: 3*81=243, Resulting Numbers: [243] 243,55 unequal: No Solution Exploring Operation: 3+81=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 81/3=27, Resulting Numbers: [27] 27,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[84, 3, 71], Operations: ['34+37=71'] Exploring Operation: 71-3=68, Resulting Numbers: [84, 68] Generated Node #0,2,0: 55:[84, 68] Operation: 71-3=68 Exploring Operation: 84/3=28, Resulting Numbers: [71, 28] Generated Node #0,2,1: 55:[71, 28] Operation: 84/3=28 Exploring Operation: 84-3=81, Resulting Numbers: [71, 81] Generated Node #0,2,2: 55:[71, 81] Operation: 84-3=81 Exploring Operation: 84-71=13, Resulting Numbers: [3, 13] Generated Node #0,2,3: 55:[3, 13] Operation: 84-71=13 Moving to Node #0,2,3 Current State: 55:[3, 13], Operations: ['34+37=71', '84-71=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,55 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,55 unequal: No Solution Moving to Node #0,2,1 Current State: 55:[71, 28], Operations: ['34+37=71', '84/3=28'] Exploring Operation: 71-28=43, Resulting Numbers: [43] 43,55 unequal: No Solution Exploring Operation: 71*28=1988, Resulting Numbers: [1988] 1988,55 unequal: No Solution Exploring Operation: 71+28=99, Resulting Numbers: [99] 99,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[71, 81], Operations: ['34+37=71', '84-3=81'] Exploring Operation: 81-71=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 71+81=152, Resulting Numbers: [152] 152,55 unequal: No Solution Exploring Operation: 71*81=5751, Resulting Numbers: [5751] 5751,55 unequal: No Solution Moving to Node #0,2,0 Current State: 55:[84, 68], Operations: ['34+37=71', '71-3=68'] Exploring Operation: 84+68=152, Resulting Numbers: [152] 152,55 unequal: No Solution Exploring Operation: 84*68=5712, Resulting Numbers: [5712] 5712,55 unequal: No Solution Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,55 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
[ 94, 73, 55, 8 ]
68
[ "94-73=21", "55-8=47", "21+47=68" ]
Current State: 68:[94, 73, 55, 8], Operations: [] Exploring Operation: 94-73=21, Resulting Numbers: [55, 8, 21] Generated Node #2: [55, 8, 21] from Operation: 94-73=21 Current State: 68:[55, 8, 21], Operations: ['94-73=21'] Exploring Operation: 55-8=47, Resulting Numbers: [21, 47] Generated Node #3: [21, 47] from Operation: 55-8=47 Current State: 68:[21, 47], Operations: ['94-73=21', '55-8=47'] Exploring Operation: 21+47=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[94, 73, 55, 8], Operations: [] Exploring Operation: 94-73=21, Resulting Numbers: [55, 8, 21] Generated Node #0,0: 68:[55, 8, 21] Operation: 94-73=21 Exploring Operation: 73-55=18, Resulting Numbers: [94, 8, 18] Generated Node #0,1: 68:[94, 8, 18] Operation: 73-55=18 Exploring Operation: 94-55=39, Resulting Numbers: [73, 8, 39] Generated Node #0,2: 68:[73, 8, 39] Operation: 94-55=39 Exploring Operation: 94-8=86, Resulting Numbers: [73, 55, 86] Generated Node #0,3: 68:[73, 55, 86] Operation: 94-8=86 Moving to Node #0,2 Current State: 68:[73, 8, 39], Operations: ['94-55=39'] Exploring Operation: 73-39=34, Resulting Numbers: [8, 34] Generated Node #0,2,0: 68:[8, 34] Operation: 73-39=34 Exploring Operation: 73+8=81, Resulting Numbers: [39, 81] Generated Node #0,2,1: 68:[39, 81] Operation: 73+8=81 Exploring Operation: 73-8=65, Resulting Numbers: [39, 65] Generated Node #0,2,2: 68:[39, 65] Operation: 73-8=65 Exploring Operation: 39-8=31, Resulting Numbers: [73, 31] Generated Node #0,2,3: 68:[73, 31] Operation: 39-8=31 Moving to Node #0,0 Current State: 68:[55, 8, 21], Operations: ['94-73=21'] Exploring Operation: 55+8=63, Resulting Numbers: [21, 63] Generated Node #0,0,0: 68:[21, 63] Operation: 55+8=63 Exploring Operation: 55+21=76, Resulting Numbers: [8, 76] Generated Node #0,0,1: 68:[8, 76] Operation: 55+21=76 Exploring Operation: 55-8=47, Resulting Numbers: [21, 47] Generated Node #0,0,2: 68:[21, 47] Operation: 55-8=47 Exploring Operation: 55-21=34, Resulting Numbers: [8, 34] Generated Node #0,0,3: 68:[8, 34] Operation: 55-21=34 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 68:[8, 34], Operations: ['94-73=21', '55-21=34'] Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,68 unequal: No Solution Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,68 unequal: No Solution Exploring Operation: 8*34=272, Resulting Numbers: [272] 272,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[21, 63], Operations: ['94-73=21', '55+8=63'] Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,68 unequal: No Solution Exploring Operation: 21+63=84, Resulting Numbers: [84] 84,68 unequal: No Solution Exploring Operation: 21*63=1323, Resulting Numbers: [1323] 1323,68 unequal: No Solution Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 68:[8, 76], Operations: ['94-73=21', '55+21=76'] Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[94, 73, 55, 8], Operations: [] Exploring Operation: 94-73=21, Resulting Numbers: [55, 8, 21] Generated Node #0,0: 68:[55, 8, 21] Operation: 94-73=21 Moving to Node #0,0 Current State: 68:[55, 8, 21], Operations: ['94-73=21'] Exploring Operation: 55+21=76, Resulting Numbers: [8, 76] Generated Node #0,0,1: 68:[8, 76] Operation: 55+21=76 Moving to Node #0,0,1 Current State: 68:[8, 76], Operations: ['94-73=21', '55+21=76'] Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_4
mult_heuristic
[ 26, 68, 68, 13 ]
97
[ "68-26=42", "68-13=55", "42+55=97" ]
Current State: 97:[26, 68, 68, 13], Operations: [] Exploring Operation: 68-26=42, Resulting Numbers: [13, 42] Generated Node #2: [13, 42] from Operation: 68-26=42 Current State: 97:[13, 42], Operations: ['68-26=42'] Exploring Operation: 68-13=55, Resulting Numbers: [42, 55] Generated Node #3: [42, 55] from Operation: 68-13=55 Current State: 97:[42, 55], Operations: ['68-26=42', '68-13=55'] Exploring Operation: 42+55=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[26, 68, 68, 13], Operations: [] Exploring Operation: 26+68=94, Resulting Numbers: [68, 13, 94] Generated Node #0,0: 97:[68, 13, 94] Operation: 26+68=94 Exploring Operation: 26+68=94, Resulting Numbers: [68, 13, 94] Generated Node #0,1: 97:[68, 13, 94] Operation: 26+68=94 Exploring Operation: 68+13=81, Resulting Numbers: [26, 68, 81] Generated Node #0,2: 97:[26, 68, 81] Operation: 68+13=81 Exploring Operation: 68+13=81, Resulting Numbers: [26, 68, 81] Generated Node #0,3: 97:[26, 68, 81] Operation: 68+13=81 Exploring Operation: 26+13=39, Resulting Numbers: [68, 68, 39] Generated Node #0,4: 97:[68, 68, 39] Operation: 26+13=39 Moving to Node #0,0 Current State: 97:[68, 13, 94], Operations: ['26+68=94'] Exploring Operation: 68-13=55, Resulting Numbers: [94, 55] Generated Node #0,0,0: 97:[94, 55] Operation: 68-13=55 Exploring Operation: 94-13=81, Resulting Numbers: [68, 81] Generated Node #0,0,1: 97:[68, 81] Operation: 94-13=81 Exploring Operation: 68+94=162, Resulting Numbers: [13, 162] Generated Node #0,0,2: 97:[13, 162] Operation: 68+94=162 Exploring Operation: 68+13=81, Resulting Numbers: [94, 81] Generated Node #0,0,3: 97:[94, 81] Operation: 68+13=81 Exploring Operation: 13+94=107, Resulting Numbers: [68, 107] Generated Node #0,0,4: 97:[68, 107] Operation: 13+94=107 Moving to Node #0,2 Current State: 97:[26, 68, 81], Operations: ['68+13=81'] Exploring Operation: 81-26=55, Resulting Numbers: [68, 55] Generated Node #0,2,0: 97:[68, 55] Operation: 81-26=55 Exploring Operation: 26+81=107, Resulting Numbers: [68, 107] Generated Node #0,2,1: 97:[68, 107] Operation: 26+81=107 Exploring Operation: 68+81=149, Resulting Numbers: [26, 149] Generated Node #0,2,2: 97:[26, 149] Operation: 68+81=149 Exploring Operation: 26+68=94, Resulting Numbers: [81, 94] Generated Node #0,2,3: 97:[81, 94] Operation: 26+68=94 Exploring Operation: 68-26=42, Resulting Numbers: [81, 42] Generated Node #0,2,4: 97:[81, 42] Operation: 68-26=42 Moving to Node #0,4 Current State: 97:[68, 68, 39], Operations: ['26+13=39'] Exploring Operation: 68-39=29, Resulting Numbers: [68, 29] Generated Node #0,4,0: 97:[68, 29] Operation: 68-39=29 Exploring Operation: 68+39=107, Resulting Numbers: [68, 107] Generated Node #0,4,1: 97:[68, 107] Operation: 68+39=107 Exploring Operation: 68+68=136, Resulting Numbers: [39, 136] Generated Node #0,4,2: 97:[39, 136] Operation: 68+68=136 Exploring Operation: 68+39=107, Resulting Numbers: [68, 107] Generated Node #0,4,3: 97:[68, 107] Operation: 68+39=107 Exploring Operation: 68-39=29, Resulting Numbers: [68, 29] Generated Node #0,4,4: 97:[68, 29] Operation: 68-39=29 Moving to Node #0,1 Current State: 97:[68, 13, 94], Operations: ['26+68=94'] Exploring Operation: 68-13=55, Resulting Numbers: [94, 55] Generated Node #0,1,0: 97:[94, 55] Operation: 68-13=55 Exploring Operation: 13+94=107, Resulting Numbers: [68, 107] Generated Node #0,1,1: 97:[68, 107] Operation: 13+94=107 Exploring Operation: 68+13=81, Resulting Numbers: [94, 81] Generated Node #0,1,2: 97:[94, 81] Operation: 68+13=81 Exploring Operation: 68+94=162, Resulting Numbers: [13, 162] Generated Node #0,1,3: 97:[13, 162] Operation: 68+94=162 Exploring Operation: 94-13=81, Resulting Numbers: [68, 81] Generated Node #0,1,4: 97:[68, 81] Operation: 94-13=81 Moving to Node #0,3 Current State: 97:[26, 68, 81], Operations: ['68+13=81'] Exploring Operation: 81-26=55, Resulting Numbers: [68, 55] Generated Node #0,3,0: 97:[68, 55] Operation: 81-26=55 Exploring Operation: 68+81=149, Resulting Numbers: [26, 149] Generated Node #0,3,1: 97:[26, 149] Operation: 68+81=149 Exploring Operation: 26+68=94, Resulting Numbers: [81, 94] Generated Node #0,3,2: 97:[81, 94] Operation: 26+68=94 Exploring Operation: 68-26=42, Resulting Numbers: [81, 42] Generated Node #0,3,3: 97:[81, 42] Operation: 68-26=42 Exploring Operation: 26+81=107, Resulting Numbers: [68, 107] Generated Node #0,3,4: 97:[68, 107] Operation: 26+81=107 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 97:[81, 94], Operations: ['68+13=81', '26+68=94'] Exploring Operation: 81*94=7614, Resulting Numbers: [7614] 7614,97 unequal: No Solution Exploring Operation: 94-81=13, Resulting Numbers: [13] 13,97 unequal: No Solution Exploring Operation: 81+94=175, Resulting Numbers: [175] 175,97 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 #0,3,4 Current State: 97:[68, 107], Operations: ['68+13=81', '26+81=107'] Exploring Operation: 107-68=39, Resulting Numbers: [39] 39,97 unequal: No Solution Exploring Operation: 68+107=175, Resulting Numbers: [175] 175,97 unequal: No Solution Exploring Operation: 68*107=7276, Resulting Numbers: [7276] 7276,97 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 #0,3,0 Current State: 97:[68, 55], Operations: ['68+13=81', '81-26=55'] Exploring Operation: 68*55=3740, Resulting Numbers: [3740] 3740,97 unequal: No Solution Exploring Operation: 68+55=123, Resulting Numbers: [123] 123,97 unequal: No Solution Exploring Operation: 68-55=13, Resulting Numbers: [13] 13,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 97:[81, 42], Operations: ['68+13=81', '68-26=42'] Exploring Operation: 81*42=3402, Resulting Numbers: [3402] 3402,97 unequal: No Solution Exploring Operation: 81+42=123, Resulting Numbers: [123] 123,97 unequal: No Solution Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 97:[26, 149], Operations: ['68+13=81', '68+81=149'] Exploring Operation: 149-26=123, Resulting Numbers: [123] 123,97 unequal: No Solution Exploring Operation: 26*149=3874, Resulting Numbers: [3874] 3874,97 unequal: No Solution Exploring Operation: 26+149=175, Resulting Numbers: [175] 175,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 97:[94, 81], Operations: ['26+68=94', '68+13=81'] Exploring Operation: 94*81=7614, Resulting Numbers: [7614] 7614,97 unequal: No Solution Exploring Operation: 94-81=13, Resulting Numbers: [13] 13,97 unequal: No Solution Exploring Operation: 94+81=175, Resulting Numbers: [175] 175,97 unequal: No Solution Moving to Node #0,2,3 Current State: 97:[81, 94], Operations: ['68+13=81', '26+68=94'] Exploring Operation: 94-81=13, Resulting Numbers: [13] 13,97 unequal: No Solution Exploring Operation: 81*94=7614, Resulting Numbers: [7614] 7614,97 unequal: No Solution Exploring Operation: 81+94=175, Resulting Numbers: [175] 175,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[94, 81], Operations: ['26+68=94', '68+13=81'] Exploring Operation: 94+81=175, Resulting Numbers: [175] 175,97 unequal: No Solution Exploring Operation: 94*81=7614, Resulting Numbers: [7614] 7614,97 unequal: No Solution Exploring Operation: 94-81=13, Resulting Numbers: [13] 13,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[68, 107], Operations: ['68+13=81', '26+81=107'] Exploring Operation: 68*107=7276, Resulting Numbers: [7276] 7276,97 unequal: No Solution Exploring Operation: 68+107=175, Resulting Numbers: [175] 175,97 unequal: No Solution Exploring Operation: 107-68=39, Resulting Numbers: [39] 39,97 unequal: No Solution Moving to Node #0,4,3 Current State: 97:[68, 107], Operations: ['26+13=39', '68+39=107'] Exploring Operation: 68*107=7276, Resulting Numbers: [7276] 7276,97 unequal: No Solution Exploring Operation: 68+107=175, Resulting Numbers: [175] 175,97 unequal: No Solution Exploring Operation: 107-68=39, Resulting Numbers: [39] 39,97 unequal: No Solution Moving to Node #0,4,1 Current State: 97:[68, 107], Operations: ['26+13=39', '68+39=107'] Exploring Operation: 68*107=7276, Resulting Numbers: [7276] 7276,97 unequal: No Solution Exploring Operation: 68+107=175, Resulting Numbers: [175] 175,97 unequal: No Solution Exploring Operation: 107-68=39, Resulting Numbers: [39] 39,97 unequal: No Solution Moving to Node #0,0,4 Current State: 97:[68, 107], Operations: ['26+68=94', '13+94=107'] Exploring Operation: 107-68=39, Resulting Numbers: [39] 39,97 unequal: No Solution Exploring Operation: 68+107=175, Resulting Numbers: [175] 175,97 unequal: No Solution Exploring Operation: 68*107=7276, Resulting Numbers: [7276] 7276,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[68, 107], Operations: ['26+68=94', '13+94=107'] Exploring Operation: 68+107=175, Resulting Numbers: [175] 175,97 unequal: No Solution Exploring Operation: 68*107=7276, Resulting Numbers: [7276] 7276,97 unequal: No Solution Exploring Operation: 107-68=39, Resulting Numbers: [39] 39,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[94, 55], Operations: ['26+68=94', '68-13=55'] Exploring Operation: 94*55=5170, Resulting Numbers: [5170] 5170,97 unequal: No Solution Exploring Operation: 94-55=39, Resulting Numbers: [39] 39,97 unequal: No Solution Exploring Operation: 94+55=149, Resulting Numbers: [149] 149,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[68, 81], Operations: ['26+68=94', '94-13=81'] Exploring Operation: 68+81=149, Resulting Numbers: [149] 149,97 unequal: No Solution Exploring Operation: 68*81=5508, Resulting Numbers: [5508] 5508,97 unequal: No Solution Exploring Operation: 81-68=13, Resulting Numbers: [13] 13,97 unequal: No Solution Moving to Node #0,1,4 Current State: 97:[68, 81], Operations: ['26+68=94', '94-13=81'] Exploring Operation: 68*81=5508, Resulting Numbers: [5508] 5508,97 unequal: No Solution Exploring Operation: 68+81=149, Resulting Numbers: [149] 149,97 unequal: No Solution Exploring Operation: 81-68=13, Resulting Numbers: [13] 13,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[94, 55], Operations: ['26+68=94', '68-13=55'] Exploring Operation: 94+55=149, Resulting Numbers: [149] 149,97 unequal: No Solution Exploring Operation: 94*55=5170, Resulting Numbers: [5170] 5170,97 unequal: No Solution Exploring Operation: 94-55=39, Resulting Numbers: [39] 39,97 unequal: No Solution Moving to Node #0,2,4 Current State: 97:[81, 42], Operations: ['68+13=81', '68-26=42'] Exploring Operation: 81+42=123, Resulting Numbers: [123] 123,97 unequal: No Solution Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,97 unequal: No Solution Exploring Operation: 81*42=3402, Resulting Numbers: [3402] 3402,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[68, 55], Operations: ['68+13=81', '81-26=55'] Exploring Operation: 68+55=123, Resulting Numbers: [123] 123,97 unequal: No Solution Exploring Operation: 68-55=13, Resulting Numbers: [13] 13,97 unequal: No Solution Exploring Operation: 68*55=3740, Resulting Numbers: [3740] 3740,97 unequal: No Solution Moving to Node #0,4,4 Current State: 97:[68, 29], Operations: ['26+13=39', '68-39=29'] Exploring Operation: 68+29=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[26, 68, 68, 13], Operations: [] Exploring Operation: 26+13=39, Resulting Numbers: [68, 68, 39] Generated Node #0,4: 97:[68, 68, 39] Operation: 26+13=39 Moving to Node #0,4 Current State: 97:[68, 68, 39], Operations: ['26+13=39'] Exploring Operation: 68-39=29, Resulting Numbers: [68, 29] Generated Node #0,4,4: 97:[68, 29] Operation: 68-39=29 Moving to Node #0,4,4 Current State: 97:[68, 29], Operations: ['26+13=39', '68-39=29'] Exploring Operation: 68+29=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
0.920139
hs_5
sum_heuristic
[ 79, 92, 11, 77 ]
35
[ "79-77=2", "92/2=46", "46-11=35" ]
Current State: 35:[79, 92, 11, 77], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [92, 11, 2] Generated Node #2: [92, 11, 2] from Operation: 79-77=2 Current State: 35:[92, 11, 2], Operations: ['79-77=2'] Exploring Operation: 92/2=46, Resulting Numbers: [11, 46] Generated Node #3: [11, 46] from Operation: 92/2=46 Current State: 35:[11, 46], Operations: ['79-77=2', '92/2=46'] Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[79, 92, 11, 77], Operations: [] Exploring Operation: 77/11=7, Resulting Numbers: [79, 92, 7] Generated Node #0,0: 35:[79, 92, 7] Operation: 77/11=7 Exploring Operation: 92-77=15, Resulting Numbers: [79, 11, 15] Generated Node #0,1: 35:[79, 11, 15] Operation: 92-77=15 Exploring Operation: 92-79=13, Resulting Numbers: [11, 77, 13] Generated Node #0,2: 35:[11, 77, 13] Operation: 92-79=13 Exploring Operation: 79-77=2, Resulting Numbers: [92, 11, 2] Generated Node #0,3: 35:[92, 11, 2] Operation: 79-77=2 Exploring Operation: 79-11=68, Resulting Numbers: [92, 77, 68] Generated Node #0,4: 35:[92, 77, 68] Operation: 79-11=68 Moving to Node #0,2 Current State: 35:[11, 77, 13], Operations: ['92-79=13'] Exploring Operation: 77-11=66, Resulting Numbers: [13, 66] Generated Node #0,2,0: 35:[13, 66] Operation: 77-11=66 Exploring Operation: 77-13=64, Resulting Numbers: [11, 64] Generated Node #0,2,1: 35:[11, 64] Operation: 77-13=64 Exploring Operation: 13-11=2, Resulting Numbers: [77, 2] Generated Node #0,2,2: 35:[77, 2] Operation: 13-11=2 Exploring Operation: 11+13=24, Resulting Numbers: [77, 24] Generated Node #0,2,3: 35:[77, 24] Operation: 11+13=24 Exploring Operation: 77/11=7, Resulting Numbers: [13, 7] Generated Node #0,2,4: 35:[13, 7] Operation: 77/11=7 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 35:[13, 7], Operations: ['92-79=13', '77/11=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,35 unequal: No Solution Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,35 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 35:[11, 64], Operations: ['92-79=13', '77-13=64'] Exploring Operation: 64-11=53, Resulting Numbers: [53] 53,35 unequal: No Solution Exploring Operation: 11*64=704, Resulting Numbers: [704] 704,35 unequal: No Solution Exploring Operation: 11+64=75, Resulting Numbers: [75] 75,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 35:[13, 66], Operations: ['92-79=13', '77-11=66'] Exploring Operation: 66-13=53, Resulting Numbers: [53] 53,35 unequal: No Solution Exploring Operation: 13*66=858, Resulting Numbers: [858] 858,35 unequal: No Solution Exploring Operation: 13+66=79, Resulting Numbers: [79] 79,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 35:[77, 2], Operations: ['92-79=13', '13-11=2'] Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,35 unequal: No Solution Exploring Operation: 77*2=154, Resulting Numbers: [154] 154,35 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 35:[77, 24], Operations: ['92-79=13', '11+13=24'] Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,35 unequal: No Solution Exploring Operation: 77*24=1848, Resulting Numbers: [1848] 1848,35 unequal: No Solution Exploring Operation: 77+24=101, Resulting Numbers: [101] 101,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 35:[79, 11, 15], Operations: ['92-77=15'] Exploring Operation: 11+15=26, Resulting Numbers: [79, 26] Generated Node #0,1,0: 35:[79, 26] Operation: 11+15=26 Exploring Operation: 15-11=4, Resulting Numbers: [79, 4] Generated Node #0,1,1: 35:[79, 4] Operation: 15-11=4 Exploring Operation: 79+11=90, Resulting Numbers: [15, 90] Generated Node #0,1,2: 35:[15, 90] Operation: 79+11=90 Exploring Operation: 79-15=64, Resulting Numbers: [11, 64] Generated Node #0,1,3: 35:[11, 64] Operation: 79-15=64 Exploring Operation: 79-11=68, Resulting Numbers: [15, 68] Generated Node #0,1,4: 35:[15, 68] Operation: 79-11=68 Moving to Node #0,3 Current State: 35:[92, 11, 2], Operations: ['79-77=2'] Exploring Operation: 92-11=81, Resulting Numbers: [2, 81] Generated Node #0,3,0: 35:[2, 81] Operation: 92-11=81 Exploring Operation: 92-2=90, Resulting Numbers: [11, 90] Generated Node #0,3,1: 35:[11, 90] Operation: 92-2=90 Exploring Operation: 92+2=94, Resulting Numbers: [11, 94] Generated Node #0,3,2: 35:[11, 94] Operation: 92+2=94 Exploring Operation: 92/2=46, Resulting Numbers: [11, 46] Generated Node #0,3,3: 35:[11, 46] Operation: 92/2=46 Exploring Operation: 11-2=9, Resulting Numbers: [92, 9] Generated Node #0,3,4: 35:[92, 9] Operation: 11-2=9 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 35:[11, 46], Operations: ['79-77=2', '92/2=46'] Exploring Operation: 11*46=506, Resulting Numbers: [506] 506,35 unequal: No Solution Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[79, 92, 11, 77], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [92, 11, 2] Generated Node #0,3: 35:[92, 11, 2] Operation: 79-77=2 Moving to Node #0,3 Current State: 35:[92, 11, 2], Operations: ['79-77=2'] Exploring Operation: 92/2=46, Resulting Numbers: [11, 46] Generated Node #0,3,3: 35:[11, 46] Operation: 92/2=46 Moving to Node #0,3,3 Current State: 35:[11, 46], Operations: ['79-77=2', '92/2=46'] Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 42, 36, 11, 84 ]
49
[ "84/42=2", "36+11=47", "2+47=49" ]
Current State: 49:[42, 36, 11, 84], Operations: [] Exploring Operation: 84/42=2, Resulting Numbers: [36, 11, 2] Generated Node #2: [36, 11, 2] from Operation: 84/42=2 Current State: 49:[36, 11, 2], Operations: ['84/42=2'] Exploring Operation: 36+11=47, Resulting Numbers: [2, 47] Generated Node #3: [2, 47] from Operation: 36+11=47 Current State: 49:[2, 47], Operations: ['84/42=2', '36+11=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[42, 36, 11, 84], Operations: [] Exploring Operation: 84/42=2, Resulting Numbers: [36, 11, 2] Generated Node #0,0: 49:[36, 11, 2] Operation: 84/42=2 Exploring Operation: 84-42=42, Resulting Numbers: [36, 11, 42] Generated Node #0,1: 49:[36, 11, 42] Operation: 84-42=42 Exploring Operation: 84-36=48, Resulting Numbers: [42, 11, 48] Generated Node #0,2: 49:[42, 11, 48] Operation: 84-36=48 Moving to Node #0,2 Current State: 49:[42, 11, 48], Operations: ['84-36=48'] Exploring Operation: 11+48=59, Resulting Numbers: [42, 59] Generated Node #0,2,0: 49:[42, 59] Operation: 11+48=59 Exploring Operation: 42+11=53, Resulting Numbers: [48, 53] Generated Node #0,2,1: 49:[48, 53] Operation: 42+11=53 Exploring Operation: 48-42=6, Resulting Numbers: [11, 6] Generated Node #0,2,2: 49:[11, 6] Operation: 48-42=6 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 49:[48, 53], Operations: ['84-36=48', '42+11=53'] Exploring Operation: 48+53=101, Resulting Numbers: [101] 101,49 unequal: No Solution Exploring Operation: 48*53=2544, Resulting Numbers: [2544] 2544,49 unequal: No Solution Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,49 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 #0,2,2 Current State: 49:[11, 6], Operations: ['84-36=48', '48-42=6'] Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,49 unequal: No Solution Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,49 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,49 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 #0,2,0 Current State: 49:[42, 59], Operations: ['84-36=48', '11+48=59'] Exploring Operation: 42*59=2478, Resulting Numbers: [2478] 2478,49 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,49 unequal: No Solution Exploring Operation: 42+59=101, Resulting Numbers: [101] 101,49 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: 49:[36, 11, 2], Operations: ['84/42=2'] Exploring Operation: 36+2=38, Resulting Numbers: [11, 38] Generated Node #0,0,0: 49:[11, 38] Operation: 36+2=38 Exploring Operation: 36/2=18, Resulting Numbers: [11, 18] Generated Node #0,0,1: 49:[11, 18] Operation: 36/2=18 Exploring Operation: 36+11=47, Resulting Numbers: [2, 47] Generated Node #0,0,2: 49:[2, 47] Operation: 36+11=47 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 49:[2, 47], Operations: ['84/42=2', '36+11=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[42, 36, 11, 84], Operations: [] Exploring Operation: 84/42=2, Resulting Numbers: [36, 11, 2] Generated Node #0,0: 49:[36, 11, 2] Operation: 84/42=2 Moving to Node #0,0 Current State: 49:[36, 11, 2], Operations: ['84/42=2'] Exploring Operation: 36+11=47, Resulting Numbers: [2, 47] Generated Node #0,0,2: 49:[2, 47] Operation: 36+11=47 Moving to Node #0,0,2 Current State: 49:[2, 47], Operations: ['84/42=2', '36+11=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 53, 94, 48, 56 ]
50
[ "56-53=3", "48*3=144", "144-94=50" ]
Current State: 50:[53, 94, 48, 56], Operations: [] Exploring Operation: 56-53=3, Resulting Numbers: [94, 48, 3] Generated Node #2: [94, 48, 3] from Operation: 56-53=3 Current State: 50:[94, 48, 3], Operations: ['56-53=3'] Exploring Operation: 48*3=144, Resulting Numbers: [94, 144] Generated Node #3: [94, 144] from Operation: 48*3=144 Current State: 50:[94, 144], Operations: ['56-53=3', '48*3=144'] Exploring Operation: 144-94=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[53, 94, 48, 56], Operations: [] Exploring Operation: 94-48=46, Resulting Numbers: [53, 56, 46] Generated Node #0,0: 50:[53, 56, 46] Operation: 94-48=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[53, 56, 46], Operations: ['94-48=46'] Exploring Operation: 56-46=10, Resulting Numbers: [53, 10] Generated Node #0,0,0: 50:[53, 10] Operation: 56-46=10 Moving to Node #0,0,0 Current State: 50:[53, 10], Operations: ['94-48=46', '56-46=10'] Exploring Operation: 53-10=43, Resulting Numbers: [43] 43,50 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
[ 59, 41, 51, 9 ]
53
[ "59-41=18", "18/9=2", "51+2=53" ]
Current State: 53:[59, 41, 51, 9], Operations: [] Exploring Operation: 59-41=18, Resulting Numbers: [51, 9, 18] Generated Node #2: [51, 9, 18] from Operation: 59-41=18 Current State: 53:[51, 9, 18], Operations: ['59-41=18'] Exploring Operation: 18/9=2, Resulting Numbers: [51, 2] Generated Node #3: [51, 2] from Operation: 18/9=2 Current State: 53:[51, 2], Operations: ['59-41=18', '18/9=2'] Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[59, 41, 51, 9], Operations: [] Exploring Operation: 41+9=50, Resulting Numbers: [59, 51, 50] Generated Node #0,0: 53:[59, 51, 50] Operation: 41+9=50 Moving to Node #0,0 Current State: 53:[59, 51, 50], Operations: ['41+9=50'] Exploring Operation: 59-50=9, Resulting Numbers: [51, 9] Generated Node #0,0,0: 53:[51, 9] Operation: 59-50=9 Moving to Node #0,0,0 Current State: 53:[51, 9], Operations: ['41+9=50', '59-50=9'] Exploring Operation: 51+9=60, Resulting Numbers: [60] 60,53 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 33, 15, 55, 74 ]
99
[ "15*55=825", "825/33=25", "74+25=99" ]
Current State: 99:[33, 15, 55, 74], Operations: [] Exploring Operation: 15*55=825, Resulting Numbers: [33, 74, 825] Generated Node #2: [33, 74, 825] from Operation: 15*55=825 Current State: 99:[33, 74, 825], Operations: ['15*55=825'] Exploring Operation: 825/33=25, Resulting Numbers: [74, 25] Generated Node #3: [74, 25] from Operation: 825/33=25 Current State: 99:[74, 25], Operations: ['15*55=825', '825/33=25'] Exploring Operation: 74+25=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[33, 15, 55, 74], Operations: [] Exploring Operation: 55-15=40, Resulting Numbers: [33, 74, 40] Generated Node #0,0: 99:[33, 74, 40] Operation: 55-15=40 Exploring Operation: 74-55=19, Resulting Numbers: [33, 15, 19] Generated Node #0,1: 99:[33, 15, 19] Operation: 74-55=19 Exploring Operation: 15+74=89, Resulting Numbers: [33, 55, 89] Generated Node #0,2: 99:[33, 55, 89] Operation: 15+74=89 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[33, 15, 19], Operations: ['74-55=19'] Exploring Operation: 19-15=4, Resulting Numbers: [33, 4] Generated Node #0,1,0: 99:[33, 4] Operation: 19-15=4 Exploring Operation: 15+19=34, Resulting Numbers: [33, 34] Generated Node #0,1,1: 99:[33, 34] Operation: 15+19=34 Exploring Operation: 33-19=14, Resulting Numbers: [15, 14] Generated Node #0,1,2: 99:[15, 14] Operation: 33-19=14 Moving to Node #0,1,0 Current State: 99:[33, 4], Operations: ['74-55=19', '19-15=4'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,99 unequal: No Solution Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[33, 34], Operations: ['74-55=19', '15+19=34'] Exploring Operation: 33+34=67, Resulting Numbers: [67] 67,99 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 33*34=1122, Resulting Numbers: [1122] 1122,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[15, 14], Operations: ['74-55=19', '33-19=14'] Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 15*14=210, Resulting Numbers: [210] 210,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[33, 74, 40], Operations: ['55-15=40'] Exploring Operation: 74-40=34, Resulting Numbers: [33, 34] Generated Node #0,0,0: 99:[33, 34] Operation: 74-40=34 Exploring Operation: 74-33=41, Resulting Numbers: [40, 41] Generated Node #0,0,1: 99:[40, 41] Operation: 74-33=41 Exploring Operation: 33+74=107, Resulting Numbers: [40, 107] Generated Node #0,0,2: 99:[40, 107] Operation: 33+74=107 Moving to Node #0,0,0 Current State: 99:[33, 34], Operations: ['55-15=40', '74-40=34'] Exploring Operation: 33*34=1122, Resulting Numbers: [1122] 1122,99 unequal: No Solution Exploring Operation: 33+34=67, Resulting Numbers: [67] 67,99 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[40, 41], Operations: ['55-15=40', '74-33=41'] Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,99 unequal: No Solution Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,99 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[40, 107], Operations: ['55-15=40', '33+74=107'] Exploring Operation: 40*107=4280, Resulting Numbers: [4280] 4280,99 unequal: No Solution Exploring Operation: 107-40=67, Resulting Numbers: [67] 67,99 unequal: No Solution Exploring Operation: 40+107=147, Resulting Numbers: [147] 147,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[33, 55, 89], Operations: ['15+74=89'] Exploring Operation: 33+55=88, Resulting Numbers: [89, 88] Generated Node #0,2,0: 99:[89, 88] Operation: 33+55=88 Exploring Operation: 89-55=34, Resulting Numbers: [33, 34] Generated Node #0,2,1: 99:[33, 34] Operation: 89-55=34 Exploring Operation: 55-33=22, Resulting Numbers: [89, 22] Generated Node #0,2,2: 99:[89, 22] Operation: 55-33=22 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 99:[33, 34], Operations: ['15+74=89', '89-55=34'] Exploring Operation: 33+34=67, Resulting Numbers: [67] 67,99 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 33*34=1122, Resulting Numbers: [1122] 1122,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 99:[89, 88], Operations: ['15+74=89', '33+55=88'] Exploring Operation: 89+88=177, Resulting Numbers: [177] 177,99 unequal: No Solution Exploring Operation: 89-88=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 89*88=7832, Resulting Numbers: [7832] 7832,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 99:[89, 22], Operations: ['15+74=89', '55-33=22'] Exploring Operation: 89*22=1958, Resulting Numbers: [1958] 1958,99 unequal: No Solution Exploring Operation: 89+22=111, Resulting Numbers: [111] 111,99 unequal: No Solution Exploring Operation: 89-22=67, Resulting Numbers: [67] 67,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 62, 38, 35, 19 ]
84
[ "62+38=100", "35-19=16", "100-16=84" ]
Current State: 84:[62, 38, 35, 19], Operations: [] Exploring Operation: 62+38=100, Resulting Numbers: [35, 19, 100] Generated Node #2: [35, 19, 100] from Operation: 62+38=100 Current State: 84:[35, 19, 100], Operations: ['62+38=100'] Exploring Operation: 35-19=16, Resulting Numbers: [100, 16] Generated Node #3: [100, 16] from Operation: 35-19=16 Current State: 84:[100, 16], Operations: ['62+38=100', '35-19=16'] Exploring Operation: 100-16=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[62, 38, 35, 19], Operations: [] Exploring Operation: 62-35=27, Resulting Numbers: [38, 19, 27] Generated Node #0,0: 84:[38, 19, 27] Operation: 62-35=27 Exploring Operation: 62-38=24, Resulting Numbers: [35, 19, 24] Generated Node #0,1: 84:[35, 19, 24] Operation: 62-38=24 Exploring Operation: 62+35=97, Resulting Numbers: [38, 19, 97] Generated Node #0,2: 84:[38, 19, 97] Operation: 62+35=97 Exploring Operation: 62+19=81, Resulting Numbers: [38, 35, 81] Generated Node #0,3: 84:[38, 35, 81] Operation: 62+19=81 Exploring Operation: 62-19=43, Resulting Numbers: [38, 35, 43] Generated Node #0,4: 84:[38, 35, 43] Operation: 62-19=43 Moving to Node #0,0 Current State: 84:[38, 19, 27], Operations: ['62-35=27'] Exploring Operation: 19+27=46, Resulting Numbers: [38, 46] Generated Node #0,0,0: 84:[38, 46] Operation: 19+27=46 Exploring Operation: 38/19=2, Resulting Numbers: [27, 2] Generated Node #0,0,1: 84:[27, 2] Operation: 38/19=2 Exploring Operation: 38-19=19, Resulting Numbers: [27, 19] Generated Node #0,0,2: 84:[27, 19] Operation: 38-19=19 Exploring Operation: 27-19=8, Resulting Numbers: [38, 8] Generated Node #0,0,3: 84:[38, 8] Operation: 27-19=8 Exploring Operation: 38-27=11, Resulting Numbers: [19, 11] Generated Node #0,0,4: 84:[19, 11] Operation: 38-27=11 Moving to Node #0,4 Current State: 84:[38, 35, 43], Operations: ['62-19=43'] Exploring Operation: 35+43=78, Resulting Numbers: [38, 78] Generated Node #0,4,0: 84:[38, 78] Operation: 35+43=78 Exploring Operation: 43-35=8, Resulting Numbers: [38, 8] Generated Node #0,4,1: 84:[38, 8] Operation: 43-35=8 Exploring Operation: 38-35=3, Resulting Numbers: [43, 3] Generated Node #0,4,2: 84:[43, 3] Operation: 38-35=3 Exploring Operation: 43-38=5, Resulting Numbers: [35, 5] Generated Node #0,4,3: 84:[35, 5] Operation: 43-38=5 Exploring Operation: 38+43=81, Resulting Numbers: [35, 81] Generated Node #0,4,4: 84:[35, 81] Operation: 38+43=81 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 84:[43, 3], Operations: ['62-19=43', '38-35=3'] Exploring Operation: 43*3=129, Resulting Numbers: [129] 129,84 unequal: No Solution Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,84 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 84:[38, 8], Operations: ['62-19=43', '43-35=8'] Exploring Operation: 38*8=304, Resulting Numbers: [304] 304,84 unequal: No Solution Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,84 unequal: No Solution Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 84:[35, 5], Operations: ['62-19=43', '43-38=5'] Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,84 unequal: No Solution Exploring Operation: 35*5=175, Resulting Numbers: [175] 175,84 unequal: No Solution Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,84 unequal: No Solution Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 84:[38, 78], Operations: ['62-19=43', '35+43=78'] Exploring Operation: 38+78=116, Resulting Numbers: [116] 116,84 unequal: No Solution Exploring Operation: 38*78=2964, Resulting Numbers: [2964] 2964,84 unequal: No Solution Exploring Operation: 78-38=40, Resulting Numbers: [40] 40,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 84:[35, 81], Operations: ['62-19=43', '38+43=81'] Exploring Operation: 35*81=2835, Resulting Numbers: [2835] 2835,84 unequal: No Solution Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,84 unequal: No Solution Exploring Operation: 35+81=116, Resulting Numbers: [116] 116,84 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: 84:[35, 19, 24], Operations: ['62-38=24'] Exploring Operation: 35-24=11, Resulting Numbers: [19, 11] Generated Node #0,1,0: 84:[19, 11] Operation: 35-24=11 Exploring Operation: 24-19=5, Resulting Numbers: [35, 5] Generated Node #0,1,1: 84:[35, 5] Operation: 24-19=5 Exploring Operation: 35+19=54, Resulting Numbers: [24, 54] Generated Node #0,1,2: 84:[24, 54] Operation: 35+19=54 Exploring Operation: 19+24=43, Resulting Numbers: [35, 43] Generated Node #0,1,3: 84:[35, 43] Operation: 19+24=43 Exploring Operation: 35-19=16, Resulting Numbers: [24, 16] Generated Node #0,1,4: 84:[24, 16] Operation: 35-19=16 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 84:[19, 11], Operations: ['62-38=24', '35-24=11'] Exploring Operation: 19*11=209, Resulting Numbers: [209] 209,84 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,84 unequal: No Solution Exploring Operation: 19+11=30, Resulting Numbers: [30] 30,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 84:[24, 16], Operations: ['62-38=24', '35-19=16'] Exploring Operation: 24-16=8, Resulting Numbers: [8] 8,84 unequal: No Solution Exploring Operation: 24+16=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 24*16=384, Resulting Numbers: [384] 384,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[35, 5], Operations: ['62-38=24', '24-19=5'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,84 unequal: No Solution Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,84 unequal: No Solution Exploring Operation: 35*5=175, Resulting Numbers: [175] 175,84 unequal: No Solution Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 84:[35, 43], Operations: ['62-38=24', '19+24=43'] Exploring Operation: 35+43=78, Resulting Numbers: [78] 78,84 unequal: No Solution Exploring Operation: 35*43=1505, Resulting Numbers: [1505] 1505,84 unequal: No Solution Exploring Operation: 43-35=8, Resulting Numbers: [8] 8,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 84:[24, 54], Operations: ['62-38=24', '35+19=54'] Exploring Operation: 24+54=78, Resulting Numbers: [78] 78,84 unequal: No Solution Exploring Operation: 24*54=1296, Resulting Numbers: [1296] 1296,84 unequal: No Solution Exploring Operation: 54-24=30, Resulting Numbers: [30] 30,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 84:[38, 35, 81], Operations: ['62+19=81'] Exploring Operation: 81-35=46, Resulting Numbers: [38, 46] Generated Node #0,3,0: 84:[38, 46] Operation: 81-35=46 Exploring Operation: 38-35=3, Resulting Numbers: [81, 3] Generated Node #0,3,1: 84:[81, 3] Operation: 38-35=3 Exploring Operation: 38+35=73, Resulting Numbers: [81, 73] Generated Node #0,3,2: 84:[81, 73] Operation: 38+35=73 Exploring Operation: 81-38=43, Resulting Numbers: [35, 43] Generated Node #0,3,3: 84:[35, 43] Operation: 81-38=43 Exploring Operation: 35+81=116, Resulting Numbers: [38, 116] Generated Node #0,3,4: 84:[38, 116] Operation: 35+81=116 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 84:[81, 3], Operations: ['62+19=81', '38-35=3'] Exploring Operation: 81+3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[62, 38, 35, 19], Operations: [] Exploring Operation: 62+19=81, Resulting Numbers: [38, 35, 81] Generated Node #0,3: 84:[38, 35, 81] Operation: 62+19=81 Moving to Node #0,3 Current State: 84:[38, 35, 81], Operations: ['62+19=81'] Exploring Operation: 38-35=3, Resulting Numbers: [81, 3] Generated Node #0,3,1: 84:[81, 3] Operation: 38-35=3 Moving to Node #0,3,1 Current State: 84:[81, 3], Operations: ['62+19=81', '38-35=3'] Exploring Operation: 81+3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.946181
hs_5
sum_heuristic
[ 1, 12, 83, 69 ]
76
[ "1+83=84", "84/12=7", "69+7=76" ]
Current State: 76:[1, 12, 83, 69], Operations: [] Exploring Operation: 1+83=84, Resulting Numbers: [12, 69, 84] Generated Node #2: [12, 69, 84] from Operation: 1+83=84 Current State: 76:[12, 69, 84], Operations: ['1+83=84'] Exploring Operation: 84/12=7, Resulting Numbers: [69, 7] Generated Node #3: [69, 7] from Operation: 84/12=7 Current State: 76:[69, 7], Operations: ['1+83=84', '84/12=7'] Exploring Operation: 69+7=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[1, 12, 83, 69], Operations: [] Exploring Operation: 83-69=14, Resulting Numbers: [1, 12, 14] Generated Node #0,0: 76:[1, 12, 14] Operation: 83-69=14 Exploring Operation: 1+12=13, Resulting Numbers: [83, 69, 13] Generated Node #0,1: 76:[83, 69, 13] Operation: 1+12=13 Exploring Operation: 12+69=81, Resulting Numbers: [1, 83, 81] Generated Node #0,2: 76:[1, 83, 81] Operation: 12+69=81 Exploring Operation: 83-1=82, Resulting Numbers: [12, 69, 82] Generated Node #0,3: 76:[12, 69, 82] Operation: 83-1=82 Exploring Operation: 83-12=71, Resulting Numbers: [1, 69, 71] Generated Node #0,4: 76:[1, 69, 71] Operation: 83-12=71 Moving to Node #0,0 Current State: 76:[1, 12, 14], Operations: ['83-69=14'] Exploring Operation: 1+12=13, Resulting Numbers: [14, 13] Generated Node #0,0,0: 76:[14, 13] Operation: 1+12=13 Exploring Operation: 1*12=12, Resulting Numbers: [14, 12] Generated Node #0,0,1: 76:[14, 12] Operation: 1*12=12 Exploring Operation: 1+14=15, Resulting Numbers: [12, 15] Generated Node #0,0,2: 76:[12, 15] Operation: 1+14=15 Exploring Operation: 14-12=2, Resulting Numbers: [1, 2] Generated Node #0,0,3: 76:[1, 2] Operation: 14-12=2 Exploring Operation: 12+14=26, Resulting Numbers: [1, 26] Generated Node #0,0,4: 76:[1, 26] Operation: 12+14=26 Moving to Node #0,4 Current State: 76:[1, 69, 71], Operations: ['83-12=71'] Exploring Operation: 1+69=70, Resulting Numbers: [71, 70] Generated Node #0,4,0: 76:[71, 70] Operation: 1+69=70 Exploring Operation: 71-69=2, Resulting Numbers: [1, 2] Generated Node #0,4,1: 76:[1, 2] Operation: 71-69=2 Exploring Operation: 1+71=72, Resulting Numbers: [69, 72] Generated Node #0,4,2: 76:[69, 72] Operation: 1+71=72 Exploring Operation: 69/1=69, Resulting Numbers: [71, 69] Generated Node #0,4,3: 76:[71, 69] Operation: 69/1=69 Exploring Operation: 1*69=69, Resulting Numbers: [71, 69] Generated Node #0,4,4: 76:[71, 69] Operation: 1*69=69 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 76:[1, 2], Operations: ['83-12=71', '71-69=2'] Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 76:[71, 70], Operations: ['83-12=71', '1+69=70'] Exploring Operation: 71-70=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 71+70=141, Resulting Numbers: [141] 141,76 unequal: No Solution Exploring Operation: 71*70=4970, Resulting Numbers: [4970] 4970,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 76:[69, 72], Operations: ['83-12=71', '1+71=72'] Exploring Operation: 69*72=4968, Resulting Numbers: [4968] 4968,76 unequal: No Solution Exploring Operation: 69+72=141, Resulting Numbers: [141] 141,76 unequal: No Solution Exploring Operation: 72-69=3, Resulting Numbers: [3] 3,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 76:[71, 69], Operations: ['83-12=71', '69/1=69'] Exploring Operation: 71*69=4899, Resulting Numbers: [4899] 4899,76 unequal: No Solution Exploring Operation: 71-69=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 71+69=140, Resulting Numbers: [140] 140,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 76:[71, 69], Operations: ['83-12=71', '1*69=69'] Exploring Operation: 71-69=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 71*69=4899, Resulting Numbers: [4899] 4899,76 unequal: No Solution Exploring Operation: 71+69=140, Resulting Numbers: [140] 140,76 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: 76:[1, 83, 81], Operations: ['12+69=81'] Exploring Operation: 1*83=83, Resulting Numbers: [81, 83] Generated Node #0,2,0: 76:[81, 83] Operation: 1*83=83 Exploring Operation: 83-1=82, Resulting Numbers: [81, 82] Generated Node #0,2,1: 76:[81, 82] Operation: 83-1=82 Exploring Operation: 81-1=80, Resulting Numbers: [83, 80] Generated Node #0,2,2: 76:[83, 80] Operation: 81-1=80 Exploring Operation: 83-81=2, Resulting Numbers: [1, 2] Generated Node #0,2,3: 76:[1, 2] Operation: 83-81=2 Exploring Operation: 83/1=83, Resulting Numbers: [81, 83] Generated Node #0,2,4: 76:[81, 83] Operation: 83/1=83 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 76:[1, 2], Operations: ['12+69=81', '83-81=2'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 76:[81, 82], Operations: ['12+69=81', '83-1=82'] Exploring Operation: 81+82=163, Resulting Numbers: [163] 163,76 unequal: No Solution Exploring Operation: 82-81=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 81*82=6642, Resulting Numbers: [6642] 6642,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 76:[83, 80], Operations: ['12+69=81', '81-1=80'] Exploring Operation: 83-80=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 83*80=6640, Resulting Numbers: [6640] 6640,76 unequal: No Solution Exploring Operation: 83+80=163, Resulting Numbers: [163] 163,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 76:[81, 83], Operations: ['12+69=81', '1*83=83'] Exploring Operation: 81*83=6723, Resulting Numbers: [6723] 6723,76 unequal: No Solution Exploring Operation: 83-81=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 81+83=164, Resulting Numbers: [164] 164,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 76:[81, 83], Operations: ['12+69=81', '83/1=83'] Exploring Operation: 81*83=6723, Resulting Numbers: [6723] 6723,76 unequal: No Solution Exploring Operation: 81+83=164, Resulting Numbers: [164] 164,76 unequal: No Solution Exploring Operation: 83-81=2, Resulting Numbers: [2] 2,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 76:[83, 69, 13], Operations: ['1+12=13'] Exploring Operation: 83-69=14, Resulting Numbers: [13, 14] Generated Node #0,1,0: 76:[13, 14] Operation: 83-69=14 Exploring Operation: 83-13=70, Resulting Numbers: [69, 70] Generated Node #0,1,1: 76:[69, 70] Operation: 83-13=70 Exploring Operation: 83+13=96, Resulting Numbers: [69, 96] Generated Node #0,1,2: 76:[69, 96] Operation: 83+13=96 Exploring Operation: 69-13=56, Resulting Numbers: [83, 56] Generated Node #0,1,3: 76:[83, 56] Operation: 69-13=56 Exploring Operation: 69+13=82, Resulting Numbers: [83, 82] Generated Node #0,1,4: 76:[83, 82] Operation: 69+13=82 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 76:[13, 14], Operations: ['1+12=13', '83-69=14'] Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,76 unequal: No Solution Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 76:[69, 70], Operations: ['1+12=13', '83-13=70'] Exploring Operation: 70-69=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 69*70=4830, Resulting Numbers: [4830] 4830,76 unequal: No Solution Exploring Operation: 69+70=139, Resulting Numbers: [139] 139,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 76:[83, 82], Operations: ['1+12=13', '69+13=82'] Exploring Operation: 83+82=165, Resulting Numbers: [165] 165,76 unequal: No Solution Exploring Operation: 83-82=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 83*82=6806, Resulting Numbers: [6806] 6806,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 76:[83, 56], Operations: ['1+12=13', '69-13=56'] Exploring Operation: 83+56=139, Resulting Numbers: [139] 139,76 unequal: No Solution Exploring Operation: 83*56=4648, Resulting Numbers: [4648] 4648,76 unequal: No Solution Exploring Operation: 83-56=27, Resulting Numbers: [27] 27,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 76:[69, 96], Operations: ['1+12=13', '83+13=96'] Exploring Operation: 69*96=6624, Resulting Numbers: [6624] 6624,76 unequal: No Solution Exploring Operation: 69+96=165, Resulting Numbers: [165] 165,76 unequal: No Solution Exploring Operation: 96-69=27, Resulting Numbers: [27] 27,76 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: 76:[12, 69, 82], Operations: ['83-1=82'] Exploring Operation: 69-12=57, Resulting Numbers: [82, 57] Generated Node #0,3,0: 76:[82, 57] Operation: 69-12=57 Exploring Operation: 82-12=70, Resulting Numbers: [69, 70] Generated Node #0,3,1: 76:[69, 70] Operation: 82-12=70 Exploring Operation: 12+82=94, Resulting Numbers: [69, 94] Generated Node #0,3,2: 76:[69, 94] Operation: 12+82=94 Exploring Operation: 12+69=81, Resulting Numbers: [82, 81] Generated Node #0,3,3: 76:[82, 81] Operation: 12+69=81 Exploring Operation: 82-69=13, Resulting Numbers: [12, 13] Generated Node #0,3,4: 76:[12, 13] Operation: 82-69=13 Moving to Node #0,0,3 Current State: 76:[1, 2], Operations: ['83-69=14', '14-12=2'] Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,76 unequal: No Solution Moving to Node #0,0,4 Current State: 76:[1, 26], Operations: ['83-69=14', '12+14=26'] Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 1*26=26, Resulting Numbers: [26] 26,76 unequal: No Solution Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,76 unequal: No Solution Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[14, 13], Operations: ['83-69=14', '1+12=13'] Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,76 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[82, 81], Operations: ['83-1=82', '12+69=81'] Exploring Operation: 82-81=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 82*81=6642, Resulting Numbers: [6642] 6642,76 unequal: No Solution Exploring Operation: 82+81=163, Resulting Numbers: [163] 163,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[12, 15], Operations: ['83-69=14', '1+14=15'] Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,76 unequal: No Solution Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[14, 12], Operations: ['83-69=14', '1*12=12'] Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,76 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,76 unequal: No Solution Moving to Node #0,3,1 Current State: 76:[69, 70], Operations: ['83-1=82', '82-12=70'] Exploring Operation: 70-69=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 69+70=139, Resulting Numbers: [139] 139,76 unequal: No Solution Exploring Operation: 69*70=4830, Resulting Numbers: [4830] 4830,76 unequal: No Solution Moving to Node #0,3,4 Current State: 76:[12, 13], Operations: ['83-1=82', '82-69=13'] Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,76 unequal: No Solution Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[82, 57], Operations: ['83-1=82', '69-12=57'] Exploring Operation: 82+57=139, Resulting Numbers: [139] 139,76 unequal: No Solution Exploring Operation: 82-57=25, Resulting Numbers: [25] 25,76 unequal: No Solution Exploring Operation: 82*57=4674, Resulting Numbers: [4674] 4674,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[69, 94], Operations: ['83-1=82', '12+82=94'] Exploring Operation: 69+94=163, Resulting Numbers: [163] 163,76 unequal: No Solution Exploring Operation: 69*94=6486, Resulting Numbers: [6486] 6486,76 unequal: No Solution Exploring Operation: 94-69=25, Resulting Numbers: [25] 25,76 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 71, 62, 67, 11 ]
12
[ "71-11=60", "67-62=5", "60/5=12" ]
Current State: 12:[71, 62, 67, 11], Operations: [] Exploring Operation: 71-11=60, Resulting Numbers: [62, 67, 60] Generated Node #2: [62, 67, 60] from Operation: 71-11=60 Current State: 12:[62, 67, 60], Operations: ['71-11=60'] Exploring Operation: 67-62=5, Resulting Numbers: [60, 5] Generated Node #3: [60, 5] from Operation: 67-62=5 Current State: 12:[60, 5], Operations: ['71-11=60', '67-62=5'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[71, 62, 67, 11], Operations: [] Exploring Operation: 71-67=4, Resulting Numbers: [62, 11, 4] Generated Node #0,0: 12:[62, 11, 4] Operation: 71-67=4 Exploring Operation: 71-62=9, Resulting Numbers: [67, 11, 9] Generated Node #0,1: 12:[67, 11, 9] Operation: 71-62=9 Exploring Operation: 71-11=60, Resulting Numbers: [62, 67, 60] Generated Node #0,2: 12:[62, 67, 60] Operation: 71-11=60 Exploring Operation: 67-62=5, Resulting Numbers: [71, 11, 5] Generated Node #0,3: 12:[71, 11, 5] Operation: 67-62=5 Moving to Node #0,0 Current State: 12:[62, 11, 4], Operations: ['71-67=4'] Exploring Operation: 11-4=7, Resulting Numbers: [62, 7] Generated Node #0,0,0: 12:[62, 7] Operation: 11-4=7 Exploring Operation: 11+4=15, Resulting Numbers: [62, 15] Generated Node #0,0,1: 12:[62, 15] Operation: 11+4=15 Exploring Operation: 62-4=58, Resulting Numbers: [11, 58] Generated Node #0,0,2: 12:[11, 58] Operation: 62-4=58 Exploring Operation: 62-11=51, Resulting Numbers: [4, 51] Generated Node #0,0,3: 12:[4, 51] Operation: 62-11=51 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 12:[4, 51], Operations: ['71-67=4', '62-11=51'] Exploring Operation: 4*51=204, Resulting Numbers: [204] 204,12 unequal: No Solution Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 4+51=55, Resulting Numbers: [55] 55,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 12:[11, 58], Operations: ['71-67=4', '62-4=58'] Exploring Operation: 11+58=69, Resulting Numbers: [69] 69,12 unequal: No Solution Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 11*58=638, Resulting Numbers: [638] 638,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[62, 7], Operations: ['71-67=4', '11-4=7'] Exploring Operation: 62+7=69, Resulting Numbers: [69] 69,12 unequal: No Solution Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 62*7=434, Resulting Numbers: [434] 434,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[62, 15], Operations: ['71-67=4', '11+4=15'] Exploring Operation: 62-15=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 62+15=77, Resulting Numbers: [77] 77,12 unequal: No Solution Exploring Operation: 62*15=930, Resulting Numbers: [930] 930,12 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: 12:[67, 11, 9], Operations: ['71-62=9'] Exploring Operation: 11+9=20, Resulting Numbers: [67, 20] Generated Node #0,1,0: 12:[67, 20] Operation: 11+9=20 Exploring Operation: 11-9=2, Resulting Numbers: [67, 2] Generated Node #0,1,1: 12:[67, 2] Operation: 11-9=2 Exploring Operation: 67-9=58, Resulting Numbers: [11, 58] Generated Node #0,1,2: 12:[11, 58] Operation: 67-9=58 Exploring Operation: 67-11=56, Resulting Numbers: [9, 56] Generated Node #0,1,3: 12:[9, 56] Operation: 67-11=56 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 12:[11, 58], Operations: ['71-62=9', '67-9=58'] Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 11*58=638, Resulting Numbers: [638] 638,12 unequal: No Solution Exploring Operation: 11+58=69, Resulting Numbers: [69] 69,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 12:[9, 56], Operations: ['71-62=9', '67-11=56'] Exploring Operation: 9+56=65, Resulting Numbers: [65] 65,12 unequal: No Solution Exploring Operation: 9*56=504, Resulting Numbers: [504] 504,12 unequal: No Solution Exploring Operation: 56-9=47, Resulting Numbers: [47] 47,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 12:[67, 2], Operations: ['71-62=9', '11-9=2'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,12 unequal: No Solution Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,12 unequal: No Solution Exploring Operation: 67*2=134, Resulting Numbers: [134] 134,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 12:[67, 20], Operations: ['71-62=9', '11+9=20'] Exploring Operation: 67-20=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 67+20=87, Resulting Numbers: [87] 87,12 unequal: No Solution Exploring Operation: 67*20=1340, Resulting Numbers: [1340] 1340,12 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: 12:[71, 11, 5], Operations: ['67-62=5'] Exploring Operation: 71-11=60, Resulting Numbers: [5, 60] Generated Node #0,3,0: 12:[5, 60] Operation: 71-11=60 Exploring Operation: 11-5=6, Resulting Numbers: [71, 6] Generated Node #0,3,1: 12:[71, 6] Operation: 11-5=6 Exploring Operation: 71-5=66, Resulting Numbers: [11, 66] Generated Node #0,3,2: 12:[11, 66] Operation: 71-5=66 Exploring Operation: 11+5=16, Resulting Numbers: [71, 16] Generated Node #0,3,3: 12:[71, 16] Operation: 11+5=16 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 12:[5, 60], Operations: ['67-62=5', '71-11=60'] Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 5*60=300, Resulting Numbers: [300] 300,12 unequal: No Solution Exploring Operation: 5+60=65, Resulting Numbers: [65] 65,12 unequal: No Solution Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[71, 62, 67, 11], Operations: [] Exploring Operation: 67-62=5, Resulting Numbers: [71, 11, 5] Generated Node #0,3: 12:[71, 11, 5] Operation: 67-62=5 Moving to Node #0,3 Current State: 12:[71, 11, 5], Operations: ['67-62=5'] Exploring Operation: 71-11=60, Resulting Numbers: [5, 60] Generated Node #0,3,0: 12:[5, 60] Operation: 71-11=60 Moving to Node #0,3,0 Current State: 12:[5, 60], Operations: ['67-62=5', '71-11=60'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.958333
hs_4
sum_heuristic
[ 86, 16, 43, 52 ]
88
[ "86/43=2", "52*2=104", "104-16=88" ]
Current State: 88:[86, 16, 43, 52], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [16, 52, 2] Generated Node #2: [16, 52, 2] from Operation: 86/43=2 Current State: 88:[16, 52, 2], Operations: ['86/43=2'] Exploring Operation: 52*2=104, Resulting Numbers: [16, 104] Generated Node #3: [16, 104] from Operation: 52*2=104 Current State: 88:[16, 104], Operations: ['86/43=2', '52*2=104'] Exploring Operation: 104-16=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[86, 16, 43, 52], Operations: [] Exploring Operation: 43+52=95, Resulting Numbers: [86, 16, 95] Generated Node #0,0: 88:[86, 16, 95] Operation: 43+52=95 Exploring Operation: 52-16=36, Resulting Numbers: [86, 43, 36] Generated Node #0,1: 88:[86, 43, 36] Operation: 52-16=36 Exploring Operation: 86/43=2, Resulting Numbers: [16, 52, 2] Generated Node #0,2: 88:[16, 52, 2] Operation: 86/43=2 Exploring Operation: 86-43=43, Resulting Numbers: [16, 52, 43] Generated Node #0,3: 88:[16, 52, 43] Operation: 86-43=43 Exploring Operation: 52-43=9, Resulting Numbers: [86, 16, 9] Generated Node #0,4: 88:[86, 16, 9] Operation: 52-43=9 Start Sub Search at level 1: Moving to Node #0,4 Current State: 88:[86, 16, 9], Operations: ['52-43=9'] Exploring Operation: 16+9=25, Resulting Numbers: [86, 25] Generated Node #0,4,0: 88:[86, 25] Operation: 16+9=25 Exploring Operation: 86-9=77, Resulting Numbers: [16, 77] Generated Node #0,4,1: 88:[16, 77] Operation: 86-9=77 Exploring Operation: 86+9=95, Resulting Numbers: [16, 95] Generated Node #0,4,2: 88:[16, 95] Operation: 86+9=95 Exploring Operation: 16-9=7, Resulting Numbers: [86, 7] Generated Node #0,4,3: 88:[86, 7] Operation: 16-9=7 Exploring Operation: 86+16=102, Resulting Numbers: [9, 102] Generated Node #0,4,4: 88:[9, 102] Operation: 86+16=102 Moving to Node #0,4,3 Current State: 88:[86, 7], Operations: ['52-43=9', '16-9=7'] Exploring Operation: 86*7=602, Resulting Numbers: [602] 602,88 unequal: No Solution Exploring Operation: 86+7=93, Resulting Numbers: [93] 93,88 unequal: No Solution Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,88 unequal: No Solution Moving to Node #0,4,0 Current State: 88:[86, 25], Operations: ['52-43=9', '16+9=25'] Exploring Operation: 86+25=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 86-25=61, Resulting Numbers: [61] 61,88 unequal: No Solution Exploring Operation: 86*25=2150, Resulting Numbers: [2150] 2150,88 unequal: No Solution Moving to Node #0,4,2 Current State: 88:[16, 95], Operations: ['52-43=9', '86+9=95'] Exploring Operation: 95-16=79, Resulting Numbers: [79] 79,88 unequal: No Solution Exploring Operation: 16*95=1520, Resulting Numbers: [1520] 1520,88 unequal: No Solution Exploring Operation: 16+95=111, Resulting Numbers: [111] 111,88 unequal: No Solution Moving to Node #0,4,4 Current State: 88:[9, 102], Operations: ['52-43=9', '86+16=102'] Exploring Operation: 9+102=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 9*102=918, Resulting Numbers: [918] 918,88 unequal: No Solution Exploring Operation: 102-9=93, Resulting Numbers: [93] 93,88 unequal: No Solution Moving to Node #0,4,1 Current State: 88:[16, 77], Operations: ['52-43=9', '86-9=77'] Exploring Operation: 16+77=93, Resulting Numbers: [93] 93,88 unequal: No Solution Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,88 unequal: No Solution Exploring Operation: 16*77=1232, Resulting Numbers: [1232] 1232,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[86, 43, 36], Operations: ['52-16=36'] Exploring Operation: 43-36=7, Resulting Numbers: [86, 7] Generated Node #0,1,0: 88:[86, 7] Operation: 43-36=7 Exploring Operation: 86/43=2, Resulting Numbers: [36, 2] Generated Node #0,1,1: 88:[36, 2] Operation: 86/43=2 Exploring Operation: 86-36=50, Resulting Numbers: [43, 50] Generated Node #0,1,2: 88:[43, 50] Operation: 86-36=50 Exploring Operation: 43+36=79, Resulting Numbers: [86, 79] Generated Node #0,1,3: 88:[86, 79] Operation: 43+36=79 Exploring Operation: 86-43=43, Resulting Numbers: [36, 43] Generated Node #0,1,4: 88:[36, 43] Operation: 86-43=43 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 88:[86, 7], Operations: ['52-16=36', '43-36=7'] Exploring Operation: 86+7=93, Resulting Numbers: [93] 93,88 unequal: No Solution Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,88 unequal: No Solution Exploring Operation: 86*7=602, Resulting Numbers: [602] 602,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 88:[43, 50], Operations: ['52-16=36', '86-36=50'] Exploring Operation: 43+50=93, Resulting Numbers: [93] 93,88 unequal: No Solution Exploring Operation: 50-43=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 43*50=2150, Resulting Numbers: [2150] 2150,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 88:[36, 2], Operations: ['52-16=36', '86/43=2'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,88 unequal: No Solution Exploring Operation: 36*2=72, Resulting Numbers: [72] 72,88 unequal: No Solution Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,88 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 88:[36, 43], Operations: ['52-16=36', '86-43=43'] Exploring Operation: 36+43=79, Resulting Numbers: [79] 79,88 unequal: No Solution Exploring Operation: 43-36=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 36*43=1548, Resulting Numbers: [1548] 1548,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 88:[86, 79], Operations: ['52-16=36', '43+36=79'] Exploring Operation: 86-79=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 86*79=6794, Resulting Numbers: [6794] 6794,88 unequal: No Solution Exploring Operation: 86+79=165, Resulting Numbers: [165] 165,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[16, 52, 2], Operations: ['86/43=2'] Exploring Operation: 52-2=50, Resulting Numbers: [16, 50] Generated Node #0,2,0: 88:[16, 50] Operation: 52-2=50 Exploring Operation: 52/2=26, Resulting Numbers: [16, 26] Generated Node #0,2,1: 88:[16, 26] Operation: 52/2=26 Exploring Operation: 16/2=8, Resulting Numbers: [52, 8] Generated Node #0,2,2: 88:[52, 8] Operation: 16/2=8 Exploring Operation: 52-16=36, Resulting Numbers: [2, 36] Generated Node #0,2,3: 88:[2, 36] Operation: 52-16=36 Exploring Operation: 16-2=14, Resulting Numbers: [52, 14] Generated Node #0,2,4: 88:[52, 14] Operation: 16-2=14 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 88:[52, 8], Operations: ['86/43=2', '16/2=8'] Exploring Operation: 52+8=60, Resulting Numbers: [60] 60,88 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,88 unequal: No Solution Exploring Operation: 52*8=416, Resulting Numbers: [416] 416,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 88:[2, 36], Operations: ['86/43=2', '52-16=36'] Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,88 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,88 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,88 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 88:[16, 26], Operations: ['86/43=2', '52/2=26'] Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,88 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 88:[16, 50], Operations: ['86/43=2', '52-2=50'] Exploring Operation: 16+50=66, Resulting Numbers: [66] 66,88 unequal: No Solution Exploring Operation: 16*50=800, Resulting Numbers: [800] 800,88 unequal: No Solution Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 88:[52, 14], Operations: ['86/43=2', '16-2=14'] Exploring Operation: 52+14=66, Resulting Numbers: [66] 66,88 unequal: No Solution Exploring Operation: 52*14=728, Resulting Numbers: [728] 728,88 unequal: No Solution Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[86, 16, 95], Operations: ['43+52=95'] Exploring Operation: 86-16=70, Resulting Numbers: [95, 70] Generated Node #0,0,0: 88:[95, 70] Operation: 86-16=70 Exploring Operation: 95-86=9, Resulting Numbers: [16, 9] Generated Node #0,0,1: 88:[16, 9] Operation: 95-86=9 Exploring Operation: 86+16=102, Resulting Numbers: [95, 102] Generated Node #0,0,2: 88:[95, 102] Operation: 86+16=102 Exploring Operation: 95-16=79, Resulting Numbers: [86, 79] Generated Node #0,0,3: 88:[86, 79] Operation: 95-16=79 Exploring Operation: 16+95=111, Resulting Numbers: [86, 111] Generated Node #0,0,4: 88:[86, 111] Operation: 16+95=111 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[16, 9], Operations: ['43+52=95', '95-86=9'] Exploring Operation: 16*9=144, Resulting Numbers: [144] 144,88 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 88:[86, 79], Operations: ['43+52=95', '95-16=79'] Exploring Operation: 86-79=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 86+79=165, Resulting Numbers: [165] 165,88 unequal: No Solution Exploring Operation: 86*79=6794, Resulting Numbers: [6794] 6794,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 88:[95, 102], Operations: ['43+52=95', '86+16=102'] Exploring Operation: 95+102=197, Resulting Numbers: [197] 197,88 unequal: No Solution Exploring Operation: 102-95=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 95*102=9690, Resulting Numbers: [9690] 9690,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[95, 70], Operations: ['43+52=95', '86-16=70'] Exploring Operation: 95-70=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 95+70=165, Resulting Numbers: [165] 165,88 unequal: No Solution Exploring Operation: 95*70=6650, Resulting Numbers: [6650] 6650,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 88:[86, 111], Operations: ['43+52=95', '16+95=111'] Exploring Operation: 86*111=9546, Resulting Numbers: [9546] 9546,88 unequal: No Solution Exploring Operation: 111-86=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 86+111=197, Resulting Numbers: [197] 197,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 88:[16, 52, 43], Operations: ['86-43=43'] Exploring Operation: 43-16=27, Resulting Numbers: [52, 27] Generated Node #0,3,0: 88:[52, 27] Operation: 43-16=27 Exploring Operation: 52-16=36, Resulting Numbers: [43, 36] Generated Node #0,3,1: 88:[43, 36] Operation: 52-16=36 Exploring Operation: 52-43=9, Resulting Numbers: [16, 9] Generated Node #0,3,2: 88:[16, 9] Operation: 52-43=9 Exploring Operation: 16+52=68, Resulting Numbers: [43, 68] Generated Node #0,3,3: 88:[43, 68] Operation: 16+52=68 Exploring Operation: 52+43=95, Resulting Numbers: [16, 95] Generated Node #0,3,4: 88:[16, 95] Operation: 52+43=95 Moving to Node #0,3,2 Current State: 88:[16, 9], Operations: ['86-43=43', '52-43=9'] Exploring Operation: 16*9=144, Resulting Numbers: [144] 144,88 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,88 unequal: No Solution Moving to Node #0,3,1 Current State: 88:[43, 36], Operations: ['86-43=43', '52-16=36'] Exploring Operation: 43+36=79, Resulting Numbers: [79] 79,88 unequal: No Solution Exploring Operation: 43-36=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 43*36=1548, Resulting Numbers: [1548] 1548,88 unequal: No Solution Moving to Node #0,3,4 Current State: 88:[16, 95], Operations: ['86-43=43', '52+43=95'] Exploring Operation: 16*95=1520, Resulting Numbers: [1520] 1520,88 unequal: No Solution Exploring Operation: 16+95=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 95-16=79, Resulting Numbers: [79] 79,88 unequal: No Solution Moving to Node #0,3,0 Current State: 88:[52, 27], Operations: ['86-43=43', '43-16=27'] Exploring Operation: 52+27=79, Resulting Numbers: [79] 79,88 unequal: No Solution Exploring Operation: 52*27=1404, Resulting Numbers: [1404] 1404,88 unequal: No Solution Exploring Operation: 52-27=25, Resulting Numbers: [25] 25,88 unequal: No Solution Moving to Node #0,3,3 Current State: 88:[43, 68], Operations: ['86-43=43', '16+52=68'] Exploring Operation: 43*68=2924, Resulting Numbers: [2924] 2924,88 unequal: No Solution Exploring Operation: 43+68=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,88 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
[ 83, 95, 67, 48 ]
98
[ "83-67=16", "48/16=3", "95+3=98" ]
Current State: 98:[83, 95, 67, 48], Operations: [] Exploring Operation: 83-67=16, Resulting Numbers: [95, 48, 16] Generated Node #2: [95, 48, 16] from Operation: 83-67=16 Current State: 98:[95, 48, 16], Operations: ['83-67=16'] Exploring Operation: 48/16=3, Resulting Numbers: [95, 3] Generated Node #3: [95, 3] from Operation: 48/16=3 Current State: 98:[95, 3], Operations: ['83-67=16', '48/16=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[83, 95, 67, 48], Operations: [] Exploring Operation: 67-48=19, Resulting Numbers: [83, 95, 19] Generated Node #0,0: 98:[83, 95, 19] Operation: 67-48=19 Exploring Operation: 95-83=12, Resulting Numbers: [67, 48, 12] Generated Node #0,1: 98:[67, 48, 12] Operation: 95-83=12 Exploring Operation: 95-67=28, Resulting Numbers: [83, 48, 28] Generated Node #0,2: 98:[83, 48, 28] Operation: 95-67=28 Exploring Operation: 83-67=16, Resulting Numbers: [95, 48, 16] Generated Node #0,3: 98:[95, 48, 16] Operation: 83-67=16 Start Sub Search at level 1: Moving to Node #0,3 Current State: 98:[95, 48, 16], Operations: ['83-67=16'] Exploring Operation: 95-48=47, Resulting Numbers: [16, 47] Generated Node #0,3,0: 98:[16, 47] Operation: 95-48=47 Exploring Operation: 95+16=111, Resulting Numbers: [48, 111] Generated Node #0,3,1: 98:[48, 111] Operation: 95+16=111 Exploring Operation: 48+16=64, Resulting Numbers: [95, 64] Generated Node #0,3,2: 98:[95, 64] Operation: 48+16=64 Exploring Operation: 48/16=3, Resulting Numbers: [95, 3] Generated Node #0,3,3: 98:[95, 3] Operation: 48/16=3 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 98:[16, 47], Operations: ['83-67=16', '95-48=47'] Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,98 unequal: No Solution Exploring Operation: 16+47=63, Resulting Numbers: [63] 63,98 unequal: No Solution Exploring Operation: 16*47=752, Resulting Numbers: [752] 752,98 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 #0,3,3 Current State: 98:[95, 3], Operations: ['83-67=16', '48/16=3'] Exploring Operation: 95-3=92, Resulting Numbers: [92] 92,98 unequal: No Solution Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[83, 95, 67, 48], Operations: [] Exploring Operation: 83-67=16, Resulting Numbers: [95, 48, 16] Generated Node #0,3: 98:[95, 48, 16] Operation: 83-67=16 Moving to Node #0,3 Current State: 98:[95, 48, 16], Operations: ['83-67=16'] Exploring Operation: 48/16=3, Resulting Numbers: [95, 3] Generated Node #0,3,3: 98:[95, 3] Operation: 48/16=3 Moving to Node #0,3,3 Current State: 98:[95, 3], Operations: ['83-67=16', '48/16=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 93, 53, 51, 55 ]
76
[ "93-55=38", "53-51=2", "38*2=76" ]
Current State: 76:[93, 53, 51, 55], Operations: [] Exploring Operation: 93-55=38, Resulting Numbers: [53, 51, 38] Generated Node #2: [53, 51, 38] from Operation: 93-55=38 Current State: 76:[53, 51, 38], Operations: ['93-55=38'] Exploring Operation: 53-51=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 53-51=2 Current State: 76:[38, 2], Operations: ['93-55=38', '53-51=2'] Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[93, 53, 51, 55], Operations: [] Exploring Operation: 93-55=38, Resulting Numbers: [53, 51, 38] Generated Node #0,0: 76:[53, 51, 38] Operation: 93-55=38 Moving to Node #0,0 Current State: 76:[53, 51, 38], Operations: ['93-55=38'] Exploring Operation: 53-51=2, Resulting Numbers: [38, 2] Generated Node #0,0,0: 76:[38, 2] Operation: 53-51=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[38, 2], Operations: ['93-55=38', '53-51=2'] Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[93, 53, 51, 55], Operations: [] Exploring Operation: 93-55=38, Resulting Numbers: [53, 51, 38] Generated Node #0,0: 76:[53, 51, 38] Operation: 93-55=38 Moving to Node #0,0 Current State: 76:[53, 51, 38], Operations: ['93-55=38'] Exploring Operation: 53-51=2, Resulting Numbers: [38, 2] Generated Node #0,0,0: 76:[38, 2] Operation: 53-51=2 Moving to Node #0,0,0 Current State: 76:[38, 2], Operations: ['93-55=38', '53-51=2'] Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 22, 30, 18, 24 ]
44
[ "22*24=528", "30-18=12", "528/12=44" ]
Current State: 44:[22, 30, 18, 24], Operations: [] Exploring Operation: 22*24=528, Resulting Numbers: [30, 18, 528] Generated Node #2: [30, 18, 528] from Operation: 22*24=528 Current State: 44:[30, 18, 528], Operations: ['22*24=528'] Exploring Operation: 30-18=12, Resulting Numbers: [528, 12] Generated Node #3: [528, 12] from Operation: 30-18=12 Current State: 44:[528, 12], Operations: ['22*24=528', '30-18=12'] Exploring Operation: 528/12=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[22, 30, 18, 24], Operations: [] Exploring Operation: 30-22=8, Resulting Numbers: [18, 24, 8] Generated Node #0,0: 44:[18, 24, 8] Operation: 30-22=8 Exploring Operation: 22-18=4, Resulting Numbers: [30, 24, 4] Generated Node #0,1: 44:[30, 24, 4] Operation: 22-18=4 Exploring Operation: 30-24=6, Resulting Numbers: [22, 18, 6] Generated Node #0,2: 44:[22, 18, 6] Operation: 30-24=6 Exploring Operation: 30+18=48, Resulting Numbers: [22, 24, 48] Generated Node #0,3: 44:[22, 24, 48] Operation: 30+18=48 Exploring Operation: 30-18=12, Resulting Numbers: [22, 24, 12] Generated Node #0,4: 44:[22, 24, 12] Operation: 30-18=12 Moving to Node #0,4 Current State: 44:[22, 24, 12], Operations: ['30-18=12'] Exploring Operation: 22-12=10, Resulting Numbers: [24, 10] Generated Node #0,4,0: 44:[24, 10] Operation: 22-12=10 Exploring Operation: 24-12=12, Resulting Numbers: [22, 12] Generated Node #0,4,1: 44:[22, 12] Operation: 24-12=12 Exploring Operation: 24/12=2, Resulting Numbers: [22, 2] Generated Node #0,4,2: 44:[22, 2] Operation: 24/12=2 Exploring Operation: 24-22=2, Resulting Numbers: [12, 2] Generated Node #0,4,3: 44:[12, 2] Operation: 24-22=2 Exploring Operation: 22+24=46, Resulting Numbers: [12, 46] Generated Node #0,4,4: 44:[12, 46] Operation: 22+24=46 Moving to Node #0,3 Current State: 44:[22, 24, 48], Operations: ['30+18=48'] Exploring Operation: 48-24=24, Resulting Numbers: [22, 24] Generated Node #0,3,0: 44:[22, 24] Operation: 48-24=24 Exploring Operation: 24-22=2, Resulting Numbers: [48, 2] Generated Node #0,3,1: 44:[48, 2] Operation: 24-22=2 Exploring Operation: 48-22=26, Resulting Numbers: [24, 26] Generated Node #0,3,2: 44:[24, 26] Operation: 48-22=26 Exploring Operation: 22+24=46, Resulting Numbers: [48, 46] Generated Node #0,3,3: 44:[48, 46] Operation: 22+24=46 Exploring Operation: 48/24=2, Resulting Numbers: [22, 2] Generated Node #0,3,4: 44:[22, 2] Operation: 48/24=2 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 44:[22, 2], Operations: ['30+18=48', '48/24=2'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,44 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[22, 30, 18, 24], Operations: [] Exploring Operation: 30+18=48, Resulting Numbers: [22, 24, 48] Generated Node #0,3: 44:[22, 24, 48] Operation: 30+18=48 Moving to Node #0,3 Current State: 44:[22, 24, 48], Operations: ['30+18=48'] Exploring Operation: 48/24=2, Resulting Numbers: [22, 2] Generated Node #0,3,4: 44:[22, 2] Operation: 48/24=2 Moving to Node #0,3,4 Current State: 44:[22, 2], Operations: ['30+18=48', '48/24=2'] Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 92, 9, 73, 45 ]
95
[ "92-73=19", "45/9=5", "19*5=95" ]
Current State: 95:[92, 9, 73, 45], Operations: [] Exploring Operation: 92-73=19, Resulting Numbers: [9, 45, 19] Generated Node #2: [9, 45, 19] from Operation: 92-73=19 Current State: 95:[9, 45, 19], Operations: ['92-73=19'] Exploring Operation: 45/9=5, Resulting Numbers: [19, 5] Generated Node #3: [19, 5] from Operation: 45/9=5 Current State: 95:[19, 5], Operations: ['92-73=19', '45/9=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[92, 9, 73, 45], Operations: [] Exploring Operation: 92-73=19, Resulting Numbers: [9, 45, 19] Generated Node #0,0: 95:[9, 45, 19] Operation: 92-73=19 Exploring Operation: 73+45=118, Resulting Numbers: [92, 9, 118] Generated Node #0,1: 95:[92, 9, 118] Operation: 73+45=118 Exploring Operation: 45/9=5, Resulting Numbers: [92, 73, 5] Generated Node #0,2: 95:[92, 73, 5] Operation: 45/9=5 Exploring Operation: 73-45=28, Resulting Numbers: [92, 9, 28] Generated Node #0,3: 95:[92, 9, 28] Operation: 73-45=28 Start Sub Search at level 1: Moving to Node #0,3 Current State: 95:[92, 9, 28], Operations: ['73-45=28'] Exploring Operation: 9+28=37, Resulting Numbers: [92, 37] Generated Node #0,3,0: 95:[92, 37] Operation: 9+28=37 Exploring Operation: 92-9=83, Resulting Numbers: [28, 83] Generated Node #0,3,1: 95:[28, 83] Operation: 92-9=83 Exploring Operation: 92+9=101, Resulting Numbers: [28, 101] Generated Node #0,3,2: 95:[28, 101] Operation: 92+9=101 Exploring Operation: 28-9=19, Resulting Numbers: [92, 19] Generated Node #0,3,3: 95:[92, 19] Operation: 28-9=19 Moving to Node #0,3,3 Current State: 95:[92, 19], Operations: ['73-45=28', '28-9=19'] Exploring Operation: 92*19=1748, Resulting Numbers: [1748] 1748,95 unequal: No Solution Exploring Operation: 92+19=111, Resulting Numbers: [111] 111,95 unequal: No Solution Exploring Operation: 92-19=73, Resulting Numbers: [73] 73,95 unequal: No Solution Moving to Node #0,3,2 Current State: 95:[28, 101], Operations: ['73-45=28', '92+9=101'] Exploring Operation: 28+101=129, Resulting Numbers: [129] 129,95 unequal: No Solution Exploring Operation: 28*101=2828, Resulting Numbers: [2828] 2828,95 unequal: No Solution Exploring Operation: 101-28=73, Resulting Numbers: [73] 73,95 unequal: No Solution Moving to Node #0,3,1 Current State: 95:[28, 83], Operations: ['73-45=28', '92-9=83'] Exploring Operation: 28*83=2324, Resulting Numbers: [2324] 2324,95 unequal: No Solution Exploring Operation: 83-28=55, Resulting Numbers: [55] 55,95 unequal: No Solution Exploring Operation: 28+83=111, Resulting Numbers: [111] 111,95 unequal: No Solution Moving to Node #0,3,0 Current State: 95:[92, 37], Operations: ['73-45=28', '9+28=37'] Exploring Operation: 92+37=129, Resulting Numbers: [129] 129,95 unequal: No Solution Exploring Operation: 92-37=55, Resulting Numbers: [55] 55,95 unequal: No Solution Exploring Operation: 92*37=3404, Resulting Numbers: [3404] 3404,95 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 Current State: 95:[92, 73, 5], Operations: ['45/9=5'] Exploring Operation: 73+5=78, Resulting Numbers: [92, 78] Generated Node #0,2,0: 95:[92, 78] Operation: 73+5=78 Exploring Operation: 92-73=19, Resulting Numbers: [5, 19] Generated Node #0,2,1: 95:[5, 19] Operation: 92-73=19 Exploring Operation: 92-5=87, Resulting Numbers: [73, 87] Generated Node #0,2,2: 95:[73, 87] Operation: 92-5=87 Exploring Operation: 92+5=97, Resulting Numbers: [73, 97] Generated Node #0,2,3: 95:[73, 97] Operation: 92+5=97 Moving to Node #0,2,1 Current State: 95:[5, 19], Operations: ['45/9=5', '92-73=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[92, 9, 73, 45], Operations: [] Exploring Operation: 45/9=5, Resulting Numbers: [92, 73, 5] Generated Node #0,2: 95:[92, 73, 5] Operation: 45/9=5 Moving to Node #0,2 Current State: 95:[92, 73, 5], Operations: ['45/9=5'] Exploring Operation: 92-73=19, Resulting Numbers: [5, 19] Generated Node #0,2,1: 95:[5, 19] Operation: 92-73=19 Moving to Node #0,2,1 Current State: 95:[5, 19], Operations: ['45/9=5', '92-73=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic
[ 15, 4, 5, 76 ]
52
[ "15+4=19", "76-5=71", "71-19=52" ]
Current State: 52:[15, 4, 5, 76], Operations: [] Exploring Operation: 15+4=19, Resulting Numbers: [5, 76, 19] Generated Node #2: [5, 76, 19] from Operation: 15+4=19 Current State: 52:[5, 76, 19], Operations: ['15+4=19'] Exploring Operation: 76-5=71, Resulting Numbers: [19, 71] Generated Node #3: [19, 71] from Operation: 76-5=71 Current State: 52:[19, 71], Operations: ['15+4=19', '76-5=71'] Exploring Operation: 71-19=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[15, 4, 5, 76], Operations: [] Exploring Operation: 76/4=19, Resulting Numbers: [15, 5, 19] Generated Node #0,0: 52:[15, 5, 19] Operation: 76/4=19 Exploring Operation: 76-4=72, Resulting Numbers: [15, 5, 72] Generated Node #0,1: 52:[15, 5, 72] Operation: 76-4=72 Exploring Operation: 76-5=71, Resulting Numbers: [15, 4, 71] Generated Node #0,2: 52:[15, 4, 71] Operation: 76-5=71 Exploring Operation: 76-15=61, Resulting Numbers: [4, 5, 61] Generated Node #0,3: 52:[4, 5, 61] Operation: 76-15=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[15, 5, 19], Operations: ['76/4=19'] Exploring Operation: 19-15=4, Resulting Numbers: [5, 4] Generated Node #0,0,0: 52:[5, 4] Operation: 19-15=4 Exploring Operation: 15/5=3, Resulting Numbers: [19, 3] Generated Node #0,0,1: 52:[19, 3] Operation: 15/5=3 Exploring Operation: 19-5=14, Resulting Numbers: [15, 14] Generated Node #0,0,2: 52:[15, 14] Operation: 19-5=14 Exploring Operation: 5+19=24, Resulting Numbers: [15, 24] Generated Node #0,0,3: 52:[15, 24] Operation: 5+19=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[5, 4], Operations: ['76/4=19', '19-15=4'] Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,52 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,52 unequal: No Solution No 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: 52:[15, 14], Operations: ['76/4=19', '19-5=14'] Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,52 unequal: No Solution Exploring Operation: 15*14=210, Resulting Numbers: [210] 210,52 unequal: No Solution No 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: 52:[15, 24], Operations: ['76/4=19', '5+19=24'] Exploring Operation: 15+24=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 15*24=360, Resulting Numbers: [360] 360,52 unequal: No Solution Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,52 unequal: No Solution No 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: 52:[19, 3], Operations: ['76/4=19', '15/5=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,52 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[4, 5, 61], Operations: ['76-15=61'] Exploring Operation: 4+5=9, Resulting Numbers: [61, 9] Generated Node #0,3,0: 52:[61, 9] Operation: 4+5=9 Exploring Operation: 61-4=57, Resulting Numbers: [5, 57] Generated Node #0,3,1: 52:[5, 57] Operation: 61-4=57 Exploring Operation: 61-5=56, Resulting Numbers: [4, 56] Generated Node #0,3,2: 52:[4, 56] Operation: 61-5=56 Exploring Operation: 5-4=1, Resulting Numbers: [61, 1] Generated Node #0,3,3: 52:[61, 1] Operation: 5-4=1 Moving to Node #0,3,2 Current State: 52:[4, 56], Operations: ['76-15=61', '61-5=56'] Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[15, 4, 5, 76], Operations: [] Exploring Operation: 76-15=61, Resulting Numbers: [4, 5, 61] Generated Node #0,3: 52:[4, 5, 61] Operation: 76-15=61 Moving to Node #0,3 Current State: 52:[4, 5, 61], Operations: ['76-15=61'] Exploring Operation: 61-5=56, Resulting Numbers: [4, 56] Generated Node #0,3,2: 52:[4, 56] Operation: 61-5=56 Moving to Node #0,3,2 Current State: 52:[4, 56], Operations: ['76-15=61', '61-5=56'] Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic
[ 74, 9, 74, 94 ]
94
[ "74-74=0", "9*0=0", "94+0=94" ]
Current State: 94:[74, 9, 74, 94], Operations: [] Exploring Operation: 74-74=0, Resulting Numbers: [9, 94, 0] Generated Node #2: [9, 94, 0] from Operation: 74-74=0 Current State: 94:[9, 94, 0], Operations: ['74-74=0'] Exploring Operation: 9*0=0, Resulting Numbers: [94, 0] Generated Node #3: [94, 0] from Operation: 9*0=0 Current State: 94:[94, 0], Operations: ['74-74=0', '9*0=0'] Exploring Operation: 94+0=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[74, 9, 74, 94], Operations: [] Exploring Operation: 74/74=1, Resulting Numbers: [9, 94, 1] Generated Node #0,0: 94:[9, 94, 1] Operation: 74/74=1 Moving to Node #0,0 Current State: 94:[9, 94, 1], Operations: ['74/74=1'] Exploring Operation: 9-1=8, Resulting Numbers: [94, 8] Generated Node #0,0,0: 94:[94, 8] Operation: 9-1=8 Moving to Node #0,0,0 Current State: 94:[94, 8], Operations: ['74/74=1', '9-1=8'] Exploring Operation: 94+8=102, Resulting Numbers: [102] 102,94 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 1, 96, 87, 25 ]
83
[ "25-1=24", "96/24=4", "87-4=83" ]
Current State: 83:[1, 96, 87, 25], Operations: [] Exploring Operation: 25-1=24, Resulting Numbers: [96, 87, 24] Generated Node #2: [96, 87, 24] from Operation: 25-1=24 Current State: 83:[96, 87, 24], Operations: ['25-1=24'] Exploring Operation: 96/24=4, Resulting Numbers: [87, 4] Generated Node #3: [87, 4] from Operation: 96/24=4 Current State: 83:[87, 4], Operations: ['25-1=24', '96/24=4'] Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[1, 96, 87, 25], Operations: [] Exploring Operation: 87-1=86, Resulting Numbers: [96, 25, 86] Generated Node #0,0: 83:[96, 25, 86] Operation: 87-1=86 Exploring Operation: 96-1=95, Resulting Numbers: [87, 25, 95] Generated Node #0,1: 83:[87, 25, 95] Operation: 96-1=95 Exploring Operation: 96/1=96, Resulting Numbers: [87, 25, 96] Generated Node #0,2: 83:[87, 25, 96] Operation: 96/1=96 Exploring Operation: 1+25=26, Resulting Numbers: [96, 87, 26] Generated Node #0,3: 83:[96, 87, 26] Operation: 1+25=26 Exploring Operation: 1*96=96, Resulting Numbers: [87, 25, 96] Generated Node #0,4: 83:[87, 25, 96] Operation: 1*96=96 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[96, 25, 86], Operations: ['87-1=86'] Exploring Operation: 96-86=10, Resulting Numbers: [25, 10] Generated Node #0,0,0: 83:[25, 10] Operation: 96-86=10 Exploring Operation: 96-25=71, Resulting Numbers: [86, 71] Generated Node #0,0,1: 83:[86, 71] Operation: 96-25=71 Exploring Operation: 96+25=121, Resulting Numbers: [86, 121] Generated Node #0,0,2: 83:[86, 121] Operation: 96+25=121 Exploring Operation: 25+86=111, Resulting Numbers: [96, 111] Generated Node #0,0,3: 83:[96, 111] Operation: 25+86=111 Exploring Operation: 86-25=61, Resulting Numbers: [96, 61] Generated Node #0,0,4: 83:[96, 61] Operation: 86-25=61 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[86, 71], Operations: ['87-1=86', '96-25=71'] Exploring Operation: 86+71=157, Resulting Numbers: [157] 157,83 unequal: No Solution Exploring Operation: 86-71=15, Resulting Numbers: [15] 15,83 unequal: No Solution Exploring Operation: 86*71=6106, Resulting Numbers: [6106] 6106,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 83:[96, 61], Operations: ['87-1=86', '86-25=61'] Exploring Operation: 96-61=35, Resulting Numbers: [35] 35,83 unequal: No Solution Exploring Operation: 96+61=157, Resulting Numbers: [157] 157,83 unequal: No Solution Exploring Operation: 96*61=5856, Resulting Numbers: [5856] 5856,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 83:[86, 121], Operations: ['87-1=86', '96+25=121'] Exploring Operation: 86*121=10406, Resulting Numbers: [10406] 10406,83 unequal: No Solution Exploring Operation: 121-86=35, Resulting Numbers: [35] 35,83 unequal: No Solution Exploring Operation: 86+121=207, Resulting Numbers: [207] 207,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 83:[96, 111], Operations: ['87-1=86', '25+86=111'] Exploring Operation: 111-96=15, Resulting Numbers: [15] 15,83 unequal: No Solution Exploring Operation: 96*111=10656, Resulting Numbers: [10656] 10656,83 unequal: No Solution Exploring Operation: 96+111=207, Resulting Numbers: [207] 207,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[25, 10], Operations: ['87-1=86', '96-86=10'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,83 unequal: No Solution Exploring Operation: 25*10=250, Resulting Numbers: [250] 250,83 unequal: No Solution Exploring Operation: 25+10=35, Resulting Numbers: [35] 35,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[87, 25, 95], Operations: ['96-1=95'] Exploring Operation: 95-25=70, Resulting Numbers: [87, 70] Generated Node #0,1,0: 83:[87, 70] Operation: 95-25=70 Exploring Operation: 25+95=120, Resulting Numbers: [87, 120] Generated Node #0,1,1: 83:[87, 120] Operation: 25+95=120 Exploring Operation: 95-87=8, Resulting Numbers: [25, 8] Generated Node #0,1,2: 83:[25, 8] Operation: 95-87=8 Exploring Operation: 87+25=112, Resulting Numbers: [95, 112] Generated Node #0,1,3: 83:[95, 112] Operation: 87+25=112 Exploring Operation: 87-25=62, Resulting Numbers: [95, 62] Generated Node #0,1,4: 83:[95, 62] Operation: 87-25=62 Moving to Node #0,1,0 Current State: 83:[87, 70], Operations: ['96-1=95', '95-25=70'] Exploring Operation: 87*70=6090, Resulting Numbers: [6090] 6090,83 unequal: No Solution Exploring Operation: 87+70=157, Resulting Numbers: [157] 157,83 unequal: No Solution Exploring Operation: 87-70=17, Resulting Numbers: [17] 17,83 unequal: No Solution Moving to Node #0,1,4 Current State: 83:[95, 62], Operations: ['96-1=95', '87-25=62'] Exploring Operation: 95+62=157, Resulting Numbers: [157] 157,83 unequal: No Solution Exploring Operation: 95*62=5890, Resulting Numbers: [5890] 5890,83 unequal: No Solution Exploring Operation: 95-62=33, Resulting Numbers: [33] 33,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[87, 120], Operations: ['96-1=95', '25+95=120'] Exploring Operation: 120-87=33, Resulting Numbers: [33] 33,83 unequal: No Solution Exploring Operation: 87*120=10440, Resulting Numbers: [10440] 10440,83 unequal: No Solution Exploring Operation: 87+120=207, Resulting Numbers: [207] 207,83 unequal: No Solution Moving to Node #0,1,3 Current State: 83:[95, 112], Operations: ['96-1=95', '87+25=112'] Exploring Operation: 112-95=17, Resulting Numbers: [17] 17,83 unequal: No Solution Exploring Operation: 95+112=207, Resulting Numbers: [207] 207,83 unequal: No Solution Exploring Operation: 95*112=10640, Resulting Numbers: [10640] 10640,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[25, 8], Operations: ['96-1=95', '95-87=8'] Exploring Operation: 25*8=200, Resulting Numbers: [200] 200,83 unequal: No Solution Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,83 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 83:[96, 87, 26], Operations: ['1+25=26'] Exploring Operation: 87+26=113, Resulting Numbers: [96, 113] Generated Node #0,3,0: 83:[96, 113] Operation: 87+26=113 Exploring Operation: 96-87=9, Resulting Numbers: [26, 9] Generated Node #0,3,1: 83:[26, 9] Operation: 96-87=9 Exploring Operation: 96+26=122, Resulting Numbers: [87, 122] Generated Node #0,3,2: 83:[87, 122] Operation: 96+26=122 Exploring Operation: 96-26=70, Resulting Numbers: [87, 70] Generated Node #0,3,3: 83:[87, 70] Operation: 96-26=70 Exploring Operation: 87-26=61, Resulting Numbers: [96, 61] Generated Node #0,3,4: 83:[96, 61] Operation: 87-26=61 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 83:[87, 70], Operations: ['1+25=26', '96-26=70'] Exploring Operation: 87-70=17, Resulting Numbers: [17] 17,83 unequal: No Solution Exploring Operation: 87+70=157, Resulting Numbers: [157] 157,83 unequal: No Solution Exploring Operation: 87*70=6090, Resulting Numbers: [6090] 6090,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 83:[96, 61], Operations: ['1+25=26', '87-26=61'] Exploring Operation: 96-61=35, Resulting Numbers: [35] 35,83 unequal: No Solution Exploring Operation: 96+61=157, Resulting Numbers: [157] 157,83 unequal: No Solution Exploring Operation: 96*61=5856, Resulting Numbers: [5856] 5856,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 83:[96, 113], Operations: ['1+25=26', '87+26=113'] Exploring Operation: 113-96=17, Resulting Numbers: [17] 17,83 unequal: No Solution Exploring Operation: 96*113=10848, Resulting Numbers: [10848] 10848,83 unequal: No Solution Exploring Operation: 96+113=209, Resulting Numbers: [209] 209,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 83:[87, 122], Operations: ['1+25=26', '96+26=122'] Exploring Operation: 87+122=209, Resulting Numbers: [209] 209,83 unequal: No Solution Exploring Operation: 122-87=35, Resulting Numbers: [35] 35,83 unequal: No Solution Exploring Operation: 87*122=10614, Resulting Numbers: [10614] 10614,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 83:[26, 9], Operations: ['1+25=26', '96-87=9'] Exploring Operation: 26+9=35, Resulting Numbers: [35] 35,83 unequal: No Solution Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,83 unequal: No Solution Exploring Operation: 26*9=234, Resulting Numbers: [234] 234,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[87, 25, 96], Operations: ['96/1=96'] Exploring Operation: 87-25=62, Resulting Numbers: [96, 62] Generated Node #0,2,0: 83:[96, 62] Operation: 87-25=62 Exploring Operation: 25+96=121, Resulting Numbers: [87, 121] Generated Node #0,2,1: 83:[87, 121] Operation: 25+96=121 Exploring Operation: 96-25=71, Resulting Numbers: [87, 71] Generated Node #0,2,2: 83:[87, 71] Operation: 96-25=71 Exploring Operation: 96-87=9, Resulting Numbers: [25, 9] Generated Node #0,2,3: 83:[25, 9] Operation: 96-87=9 Exploring Operation: 87+25=112, Resulting Numbers: [96, 112] Generated Node #0,2,4: 83:[96, 112] Operation: 87+25=112 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 83:[87, 71], Operations: ['96/1=96', '96-25=71'] Exploring Operation: 87-71=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 87*71=6177, Resulting Numbers: [6177] 6177,83 unequal: No Solution Exploring Operation: 87+71=158, Resulting Numbers: [158] 158,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[96, 62], Operations: ['96/1=96', '87-25=62'] Exploring Operation: 96+62=158, Resulting Numbers: [158] 158,83 unequal: No Solution Exploring Operation: 96-62=34, Resulting Numbers: [34] 34,83 unequal: No Solution Exploring Operation: 96*62=5952, Resulting Numbers: [5952] 5952,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[87, 121], Operations: ['96/1=96', '25+96=121'] Exploring Operation: 87*121=10527, Resulting Numbers: [10527] 10527,83 unequal: No Solution Exploring Operation: 87+121=208, Resulting Numbers: [208] 208,83 unequal: No Solution Exploring Operation: 121-87=34, Resulting Numbers: [34] 34,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 83:[96, 112], Operations: ['96/1=96', '87+25=112'] Exploring Operation: 112-96=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 96+112=208, Resulting Numbers: [208] 208,83 unequal: No Solution Exploring Operation: 96*112=10752, Resulting Numbers: [10752] 10752,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 83:[25, 9], Operations: ['96/1=96', '96-87=9'] Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,83 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 83:[87, 25, 96], Operations: ['1*96=96'] Exploring Operation: 96-87=9, Resulting Numbers: [25, 9] Generated Node #0,4,0: 83:[25, 9] Operation: 96-87=9 Exploring Operation: 87+25=112, Resulting Numbers: [96, 112] Generated Node #0,4,1: 83:[96, 112] Operation: 87+25=112 Exploring Operation: 96-25=71, Resulting Numbers: [87, 71] Generated Node #0,4,2: 83:[87, 71] Operation: 96-25=71 Exploring Operation: 25+96=121, Resulting Numbers: [87, 121] Generated Node #0,4,3: 83:[87, 121] Operation: 25+96=121 Exploring Operation: 87-25=62, Resulting Numbers: [96, 62] Generated Node #0,4,4: 83:[96, 62] Operation: 87-25=62 Moving to Node #0,4,2 Current State: 83:[87, 71], Operations: ['1*96=96', '96-25=71'] Exploring Operation: 87+71=158, Resulting Numbers: [158] 158,83 unequal: No Solution Exploring Operation: 87-71=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 87*71=6177, Resulting Numbers: [6177] 6177,83 unequal: No Solution Moving to Node #0,4,4 Current State: 83:[96, 62], Operations: ['1*96=96', '87-25=62'] Exploring Operation: 96*62=5952, Resulting Numbers: [5952] 5952,83 unequal: No Solution Exploring Operation: 96-62=34, Resulting Numbers: [34] 34,83 unequal: No Solution Exploring Operation: 96+62=158, Resulting Numbers: [158] 158,83 unequal: No Solution Moving to Node #0,4,1 Current State: 83:[96, 112], Operations: ['1*96=96', '87+25=112'] Exploring Operation: 96+112=208, Resulting Numbers: [208] 208,83 unequal: No Solution Exploring Operation: 112-96=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 96*112=10752, Resulting Numbers: [10752] 10752,83 unequal: No Solution Moving to Node #0,4,3 Current State: 83:[87, 121], Operations: ['1*96=96', '25+96=121'] Exploring Operation: 87+121=208, Resulting Numbers: [208] 208,83 unequal: No Solution Exploring Operation: 87*121=10527, Resulting Numbers: [10527] 10527,83 unequal: No Solution Exploring Operation: 121-87=34, Resulting Numbers: [34] 34,83 unequal: No Solution Moving to Node #0,4,0 Current State: 83:[25, 9], Operations: ['1*96=96', '96-87=9'] Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,83 unequal: No Solution Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,83 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,83 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
[ 87, 61, 7, 13 ]
57
[ "87+61=148", "7*13=91", "148-91=57" ]
Current State: 57:[87, 61, 7, 13], Operations: [] Exploring Operation: 87+61=148, Resulting Numbers: [7, 13, 148] Generated Node #2: [7, 13, 148] from Operation: 87+61=148 Current State: 57:[7, 13, 148], Operations: ['87+61=148'] Exploring Operation: 7*13=91, Resulting Numbers: [148, 91] Generated Node #3: [148, 91] from Operation: 7*13=91 Current State: 57:[148, 91], Operations: ['87+61=148', '7*13=91'] Exploring Operation: 148-91=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[87, 61, 7, 13], Operations: [] Exploring Operation: 87-61=26, Resulting Numbers: [7, 13, 26] Generated Node #0,0: 57:[7, 13, 26] Operation: 87-61=26 Exploring Operation: 87-7=80, Resulting Numbers: [61, 13, 80] Generated Node #0,1: 57:[61, 13, 80] Operation: 87-7=80 Exploring Operation: 7+13=20, Resulting Numbers: [87, 61, 20] Generated Node #0,2: 57:[87, 61, 20] Operation: 7+13=20 Exploring Operation: 13-7=6, Resulting Numbers: [87, 61, 6] Generated Node #0,3: 57:[87, 61, 6] Operation: 13-7=6 Exploring Operation: 87-13=74, Resulting Numbers: [61, 7, 74] Generated Node #0,4: 57:[61, 7, 74] Operation: 87-13=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[7, 13, 26], Operations: ['87-61=26'] Exploring Operation: 13-7=6, Resulting Numbers: [26, 6] Generated Node #0,0,0: 57:[26, 6] Operation: 13-7=6 Exploring Operation: 26-7=19, Resulting Numbers: [13, 19] Generated Node #0,0,1: 57:[13, 19] Operation: 26-7=19 Exploring Operation: 26-13=13, Resulting Numbers: [7, 13] Generated Node #0,0,2: 57:[7, 13] Operation: 26-13=13 Exploring Operation: 7+13=20, Resulting Numbers: [26, 20] Generated Node #0,0,3: 57:[26, 20] Operation: 7+13=20 Exploring Operation: 26/13=2, Resulting Numbers: [7, 2] Generated Node #0,0,4: 57:[7, 2] Operation: 26/13=2 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 57:[7, 2], Operations: ['87-61=26', '26/13=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,57 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 57:[13, 19], Operations: ['87-61=26', '26-7=19'] Exploring Operation: 13*19=247, Resulting Numbers: [247] 247,57 unequal: No Solution Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 13+19=32, Resulting Numbers: [32] 32,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 57:[26, 20], Operations: ['87-61=26', '7+13=20'] Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 26+20=46, Resulting Numbers: [46] 46,57 unequal: No Solution Exploring Operation: 26*20=520, Resulting Numbers: [520] 520,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[26, 6], Operations: ['87-61=26', '13-7=6'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 26*6=156, Resulting Numbers: [156] 156,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 57:[7, 13], Operations: ['87-61=26', '26-13=13'] Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 7*13=91, Resulting Numbers: [91] 91,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 57:[61, 7, 74], Operations: ['87-13=74'] Exploring Operation: 7+74=81, Resulting Numbers: [61, 81] Generated Node #0,4,0: 57:[61, 81] Operation: 7+74=81 Exploring Operation: 61+7=68, Resulting Numbers: [74, 68] Generated Node #0,4,1: 57:[74, 68] Operation: 61+7=68 Exploring Operation: 74-7=67, Resulting Numbers: [61, 67] Generated Node #0,4,2: 57:[61, 67] Operation: 74-7=67 Exploring Operation: 74-61=13, Resulting Numbers: [7, 13] Generated Node #0,4,3: 57:[7, 13] Operation: 74-61=13 Exploring Operation: 61-7=54, Resulting Numbers: [74, 54] Generated Node #0,4,4: 57:[74, 54] Operation: 61-7=54 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 57:[7, 13], Operations: ['87-13=74', '74-61=13'] Exploring Operation: 7*13=91, Resulting Numbers: [91] 91,57 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 57:[61, 67], Operations: ['87-13=74', '74-7=67'] Exploring Operation: 61+67=128, Resulting Numbers: [128] 128,57 unequal: No Solution Exploring Operation: 67-61=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 61*67=4087, Resulting Numbers: [4087] 4087,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 57:[74, 54], Operations: ['87-13=74', '61-7=54'] Exploring Operation: 74+54=128, Resulting Numbers: [128] 128,57 unequal: No Solution Exploring Operation: 74-54=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 74*54=3996, Resulting Numbers: [3996] 3996,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 57:[61, 81], Operations: ['87-13=74', '7+74=81'] Exploring Operation: 61+81=142, Resulting Numbers: [142] 142,57 unequal: No Solution Exploring Operation: 61*81=4941, Resulting Numbers: [4941] 4941,57 unequal: No Solution Exploring Operation: 81-61=20, Resulting Numbers: [20] 20,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 57:[74, 68], Operations: ['87-13=74', '61+7=68'] Exploring Operation: 74*68=5032, Resulting Numbers: [5032] 5032,57 unequal: No Solution Exploring Operation: 74+68=142, Resulting Numbers: [142] 142,57 unequal: No Solution Exploring Operation: 74-68=6, Resulting Numbers: [6] 6,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[61, 13, 80], Operations: ['87-7=80'] Exploring Operation: 61+13=74, Resulting Numbers: [80, 74] Generated Node #0,1,0: 57:[80, 74] Operation: 61+13=74 Exploring Operation: 80-13=67, Resulting Numbers: [61, 67] Generated Node #0,1,1: 57:[61, 67] Operation: 80-13=67 Exploring Operation: 80-61=19, Resulting Numbers: [13, 19] Generated Node #0,1,2: 57:[13, 19] Operation: 80-61=19 Exploring Operation: 13+80=93, Resulting Numbers: [61, 93] Generated Node #0,1,3: 57:[61, 93] Operation: 13+80=93 Exploring Operation: 61-13=48, Resulting Numbers: [80, 48] Generated Node #0,1,4: 57:[80, 48] Operation: 61-13=48 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 57:[13, 19], Operations: ['87-7=80', '80-61=19'] Exploring Operation: 13*19=247, Resulting Numbers: [247] 247,57 unequal: No Solution Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 13+19=32, Resulting Numbers: [32] 32,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 57:[61, 67], Operations: ['87-7=80', '80-13=67'] Exploring Operation: 61*67=4087, Resulting Numbers: [4087] 4087,57 unequal: No Solution Exploring Operation: 61+67=128, Resulting Numbers: [128] 128,57 unequal: No Solution Exploring Operation: 67-61=6, Resulting Numbers: [6] 6,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 57:[80, 48], Operations: ['87-7=80', '61-13=48'] Exploring Operation: 80+48=128, Resulting Numbers: [128] 128,57 unequal: No Solution Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 80*48=3840, Resulting Numbers: [3840] 3840,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 57:[80, 74], Operations: ['87-7=80', '61+13=74'] Exploring Operation: 80*74=5920, Resulting Numbers: [5920] 5920,57 unequal: No Solution Exploring Operation: 80+74=154, Resulting Numbers: [154] 154,57 unequal: No Solution Exploring Operation: 80-74=6, Resulting Numbers: [6] 6,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 57:[61, 93], Operations: ['87-7=80', '13+80=93'] Exploring Operation: 93-61=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 61*93=5673, Resulting Numbers: [5673] 5673,57 unequal: No Solution Exploring Operation: 61+93=154, Resulting Numbers: [154] 154,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[87, 61, 20], Operations: ['7+13=20'] Exploring Operation: 61+20=81, Resulting Numbers: [87, 81] Generated Node #0,2,0: 57:[87, 81] Operation: 61+20=81 Exploring Operation: 87-20=67, Resulting Numbers: [61, 67] Generated Node #0,2,1: 57:[61, 67] Operation: 87-20=67 Exploring Operation: 87-61=26, Resulting Numbers: [20, 26] Generated Node #0,2,2: 57:[20, 26] Operation: 87-61=26 Exploring Operation: 61-20=41, Resulting Numbers: [87, 41] Generated Node #0,2,3: 57:[87, 41] Operation: 61-20=41 Exploring Operation: 87+20=107, Resulting Numbers: [61, 107] Generated Node #0,2,4: 57:[61, 107] Operation: 87+20=107 Moving to Node #0,2,2 Current State: 57:[20, 26], Operations: ['7+13=20', '87-61=26'] Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,57 unequal: No Solution Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,57 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[61, 67], Operations: ['7+13=20', '87-20=67'] Exploring Operation: 67-61=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 61+67=128, Resulting Numbers: [128] 128,57 unequal: No Solution Exploring Operation: 61*67=4087, Resulting Numbers: [4087] 4087,57 unequal: No Solution Moving to Node #0,2,3 Current State: 57:[87, 41], Operations: ['7+13=20', '61-20=41'] Exploring Operation: 87+41=128, Resulting Numbers: [128] 128,57 unequal: No Solution Exploring Operation: 87*41=3567, Resulting Numbers: [3567] 3567,57 unequal: No Solution Exploring Operation: 87-41=46, Resulting Numbers: [46] 46,57 unequal: No Solution Moving to Node #0,2,0 Current State: 57:[87, 81], Operations: ['7+13=20', '61+20=81'] Exploring Operation: 87-81=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 87*81=7047, Resulting Numbers: [7047] 7047,57 unequal: No Solution Exploring Operation: 87+81=168, Resulting Numbers: [168] 168,57 unequal: No Solution Moving to Node #0,2,4 Current State: 57:[61, 107], Operations: ['7+13=20', '87+20=107'] Exploring Operation: 61+107=168, Resulting Numbers: [168] 168,57 unequal: No Solution Exploring Operation: 107-61=46, Resulting Numbers: [46] 46,57 unequal: No Solution Exploring Operation: 61*107=6527, Resulting Numbers: [6527] 6527,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 57:[87, 61, 6], Operations: ['13-7=6'] Exploring Operation: 87+6=93, Resulting Numbers: [61, 93] Generated Node #0,3,0: 57:[61, 93] Operation: 87+6=93 Exploring Operation: 87-6=81, Resulting Numbers: [61, 81] Generated Node #0,3,1: 57:[61, 81] Operation: 87-6=81 Exploring Operation: 61-6=55, Resulting Numbers: [87, 55] Generated Node #0,3,2: 57:[87, 55] Operation: 61-6=55 Exploring Operation: 61+6=67, Resulting Numbers: [87, 67] Generated Node #0,3,3: 57:[87, 67] Operation: 61+6=67 Exploring Operation: 87-61=26, Resulting Numbers: [6, 26] Generated Node #0,3,4: 57:[6, 26] Operation: 87-61=26 Moving to Node #0,3,4 Current State: 57:[6, 26], Operations: ['13-7=6', '87-61=26'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 6*26=156, Resulting Numbers: [156] 156,57 unequal: No Solution Moving to Node #0,3,1 Current State: 57:[61, 81], Operations: ['13-7=6', '87-6=81'] Exploring Operation: 81-61=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 61+81=142, Resulting Numbers: [142] 142,57 unequal: No Solution Exploring Operation: 61*81=4941, Resulting Numbers: [4941] 4941,57 unequal: No Solution Moving to Node #0,3,2 Current State: 57:[87, 55], Operations: ['13-7=6', '61-6=55'] Exploring Operation: 87*55=4785, Resulting Numbers: [4785] 4785,57 unequal: No Solution Exploring Operation: 87-55=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 87+55=142, Resulting Numbers: [142] 142,57 unequal: No Solution Moving to Node #0,3,0 Current State: 57:[61, 93], Operations: ['13-7=6', '87+6=93'] Exploring Operation: 61*93=5673, Resulting Numbers: [5673] 5673,57 unequal: No Solution Exploring Operation: 93-61=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 61+93=154, Resulting Numbers: [154] 154,57 unequal: No Solution Moving to Node #0,3,3 Current State: 57:[87, 67], Operations: ['13-7=6', '61+6=67'] Exploring Operation: 87-67=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 87*67=5829, Resulting Numbers: [5829] 5829,57 unequal: No Solution Exploring Operation: 87+67=154, Resulting Numbers: [154] 154,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 64, 14, 80, 56 ]
21
[ "64+56=120", "14*120=1680", "1680/80=21" ]
Current State: 21:[64, 14, 80, 56], Operations: [] Exploring Operation: 64+56=120, Resulting Numbers: [14, 80, 120] Generated Node #2: [14, 80, 120] from Operation: 64+56=120 Current State: 21:[14, 80, 120], Operations: ['64+56=120'] Exploring Operation: 14*120=1680, Resulting Numbers: [80, 1680] Generated Node #3: [80, 1680] from Operation: 14*120=1680 Current State: 21:[80, 1680], Operations: ['64+56=120', '14*120=1680'] Exploring Operation: 1680/80=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[64, 14, 80, 56], Operations: [] Exploring Operation: 80-64=16, Resulting Numbers: [14, 56, 16] Generated Node #0,0: 21:[14, 56, 16] Operation: 80-64=16 Exploring Operation: 80-56=24, Resulting Numbers: [64, 14, 24] Generated Node #0,1: 21:[64, 14, 24] Operation: 80-56=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[14, 56, 16], Operations: ['80-64=16'] Exploring Operation: 56-14=42, Resulting Numbers: [16, 42] Generated Node #0,0,0: 21:[16, 42] Operation: 56-14=42 Exploring Operation: 56/14=4, Resulting Numbers: [16, 4] Generated Node #0,0,1: 21:[16, 4] Operation: 56/14=4 Moving to Node #0,0,1 Current State: 21:[16, 4], Operations: ['80-64=16', '56/14=4'] Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[16, 42], Operations: ['80-64=16', '56-14=42'] Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 16+42=58, Resulting Numbers: [58] 58,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[64, 14, 24], Operations: ['80-56=24'] Exploring Operation: 64-14=50, Resulting Numbers: [24, 50] Generated Node #0,1,0: 21:[24, 50] Operation: 64-14=50 Exploring Operation: 64-24=40, Resulting Numbers: [14, 40] Generated Node #0,1,1: 21:[14, 40] Operation: 64-24=40 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 21:[14, 40], Operations: ['80-56=24', '64-24=40'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 14+40=54, Resulting Numbers: [54] 54,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 21:[24, 50], Operations: ['80-56=24', '64-14=50'] Exploring Operation: 24+50=74, Resulting Numbers: [74] 74,21 unequal: No Solution Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 14, 84, 83, 78 ]
93
[ "14+84=98", "83-78=5", "98-5=93" ]
Current State: 93:[14, 84, 83, 78], Operations: [] Exploring Operation: 14+84=98, Resulting Numbers: [83, 78, 98] Generated Node #2: [83, 78, 98] from Operation: 14+84=98 Current State: 93:[83, 78, 98], Operations: ['14+84=98'] Exploring Operation: 83-78=5, Resulting Numbers: [98, 5] Generated Node #3: [98, 5] from Operation: 83-78=5 Current State: 93:[98, 5], Operations: ['14+84=98', '83-78=5'] Exploring Operation: 98-5=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[14, 84, 83, 78], Operations: [] Exploring Operation: 84-78=6, Resulting Numbers: [14, 83, 6] Generated Node #0,0: 93:[14, 83, 6] Operation: 84-78=6 Exploring Operation: 84/14=6, Resulting Numbers: [83, 78, 6] Generated Node #0,1: 93:[83, 78, 6] Operation: 84/14=6 Exploring Operation: 83-78=5, Resulting Numbers: [14, 84, 5] Generated Node #0,2: 93:[14, 84, 5] Operation: 83-78=5 Exploring Operation: 14+78=92, Resulting Numbers: [84, 83, 92] Generated Node #0,3: 93:[84, 83, 92] Operation: 14+78=92 Moving to Node #0,3 Current State: 93:[84, 83, 92], Operations: ['14+78=92'] Exploring Operation: 84-83=1, Resulting Numbers: [92, 1] Generated Node #0,3,0: 93:[92, 1] Operation: 84-83=1 Exploring Operation: 92-84=8, Resulting Numbers: [83, 8] Generated Node #0,3,1: 93:[83, 8] Operation: 92-84=8 Exploring Operation: 92-83=9, Resulting Numbers: [84, 9] Generated Node #0,3,2: 93:[84, 9] Operation: 92-83=9 Exploring Operation: 84+83=167, Resulting Numbers: [92, 167] Generated Node #0,3,3: 93:[92, 167] Operation: 84+83=167 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 93:[92, 1], Operations: ['14+78=92', '84-83=1'] Exploring Operation: 92*1=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[14, 84, 83, 78], Operations: [] Exploring Operation: 14+78=92, Resulting Numbers: [84, 83, 92] Generated Node #0,3: 93:[84, 83, 92] Operation: 14+78=92 Moving to Node #0,3 Current State: 93:[84, 83, 92], Operations: ['14+78=92'] Exploring Operation: 84-83=1, Resulting Numbers: [92, 1] Generated Node #0,3,0: 93:[92, 1] Operation: 84-83=1 Moving to Node #0,3,0 Current State: 93:[92, 1], Operations: ['14+78=92', '84-83=1'] Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 76, 34, 49, 84 ]
23
[ "76+34=110", "49+84=133", "133-110=23" ]
Current State: 23:[76, 34, 49, 84], Operations: [] Exploring Operation: 76+34=110, Resulting Numbers: [49, 84, 110] Generated Node #2: [49, 84, 110] from Operation: 76+34=110 Current State: 23:[49, 84, 110], Operations: ['76+34=110'] Exploring Operation: 49+84=133, Resulting Numbers: [110, 133] Generated Node #3: [110, 133] from Operation: 49+84=133 Current State: 23:[110, 133], Operations: ['76+34=110', '49+84=133'] Exploring Operation: 133-110=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[76, 34, 49, 84], Operations: [] Exploring Operation: 84-76=8, Resulting Numbers: [34, 49, 8] Generated Node #0,0: 23:[34, 49, 8] Operation: 84-76=8 Moving to Node #0,0 Current State: 23:[34, 49, 8], Operations: ['84-76=8'] Exploring Operation: 49-34=15, Resulting Numbers: [8, 15] Generated Node #0,0,0: 23:[8, 15] Operation: 49-34=15 Moving to Node #0,0,0 Current State: 23:[8, 15], Operations: ['84-76=8', '49-34=15'] Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[76, 34, 49, 84], Operations: [] Exploring Operation: 84-76=8, Resulting Numbers: [34, 49, 8] Generated Node #0,0: 23:[34, 49, 8] Operation: 84-76=8 Moving to Node #0,0 Current State: 23:[34, 49, 8], Operations: ['84-76=8'] Exploring Operation: 49-34=15, Resulting Numbers: [8, 15] Generated Node #0,0,0: 23:[8, 15] Operation: 49-34=15 Moving to Node #0,0,0 Current State: 23:[8, 15], Operations: ['84-76=8', '49-34=15'] Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 66, 52, 94, 68 ]
21
[ "68-66=2", "94-52=42", "42/2=21" ]
Current State: 21:[66, 52, 94, 68], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [52, 94, 2] Generated Node #2: [52, 94, 2] from Operation: 68-66=2 Current State: 21:[52, 94, 2], Operations: ['68-66=2'] Exploring Operation: 94-52=42, Resulting Numbers: [2, 42] Generated Node #3: [2, 42] from Operation: 94-52=42 Current State: 21:[2, 42], Operations: ['68-66=2', '94-52=42'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[66, 52, 94, 68], Operations: [] Exploring Operation: 94-68=26, Resulting Numbers: [66, 52, 26] Generated Node #0,0: 21:[66, 52, 26] Operation: 94-68=26 Exploring Operation: 94-52=42, Resulting Numbers: [66, 68, 42] Generated Node #0,1: 21:[66, 68, 42] Operation: 94-52=42 Exploring Operation: 68-66=2, Resulting Numbers: [52, 94, 2] Generated Node #0,2: 21:[52, 94, 2] Operation: 68-66=2 Exploring Operation: 94-66=28, Resulting Numbers: [52, 68, 28] Generated Node #0,3: 21:[52, 68, 28] Operation: 94-66=28 Exploring Operation: 68-52=16, Resulting Numbers: [66, 94, 16] Generated Node #0,4: 21:[66, 94, 16] Operation: 68-52=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[66, 52, 26], Operations: ['94-68=26'] Exploring Operation: 66-26=40, Resulting Numbers: [52, 40] Generated Node #0,0,0: 21:[52, 40] Operation: 66-26=40 Exploring Operation: 52/26=2, Resulting Numbers: [66, 2] Generated Node #0,0,1: 21:[66, 2] Operation: 52/26=2 Exploring Operation: 66-52=14, Resulting Numbers: [26, 14] Generated Node #0,0,2: 21:[26, 14] Operation: 66-52=14 Exploring Operation: 66+52=118, Resulting Numbers: [26, 118] Generated Node #0,0,3: 21:[26, 118] Operation: 66+52=118 Exploring Operation: 52-26=26, Resulting Numbers: [66, 26] Generated Node #0,0,4: 21:[66, 26] Operation: 52-26=26 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 21:[26, 14], Operations: ['94-68=26', '66-52=14'] Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,21 unequal: No Solution Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,21 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 #0,0,1 Current State: 21:[66, 2], Operations: ['94-68=26', '52/26=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,21 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 66*2=132, Resulting Numbers: [132] 132,21 unequal: No Solution Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,21 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 #0,0,0 Current State: 21:[52, 40], Operations: ['94-68=26', '66-26=40'] Exploring Operation: 52*40=2080, Resulting Numbers: [2080] 2080,21 unequal: No Solution Exploring Operation: 52+40=92, Resulting Numbers: [92] 92,21 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,21 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 #0,0,4 Current State: 21:[66, 26], Operations: ['94-68=26', '52-26=26'] Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,21 unequal: No Solution Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,21 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 #0,0,3 Current State: 21:[26, 118], Operations: ['94-68=26', '66+52=118'] Exploring Operation: 26*118=3068, Resulting Numbers: [3068] 3068,21 unequal: No Solution Exploring Operation: 26+118=144, Resulting Numbers: [144] 144,21 unequal: No Solution Exploring Operation: 118-26=92, Resulting Numbers: [92] 92,21 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 #0,3 Current State: 21:[52, 68, 28], Operations: ['94-66=28'] Exploring Operation: 52-28=24, Resulting Numbers: [68, 24] Generated Node #0,3,0: 21:[68, 24] Operation: 52-28=24 Exploring Operation: 52+28=80, Resulting Numbers: [68, 80] Generated Node #0,3,1: 21:[68, 80] Operation: 52+28=80 Exploring Operation: 52+68=120, Resulting Numbers: [28, 120] Generated Node #0,3,2: 21:[28, 120] Operation: 52+68=120 Exploring Operation: 68-52=16, Resulting Numbers: [28, 16] Generated Node #0,3,3: 21:[28, 16] Operation: 68-52=16 Exploring Operation: 68-28=40, Resulting Numbers: [52, 40] Generated Node #0,3,4: 21:[52, 40] Operation: 68-28=40 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 21:[28, 16], Operations: ['94-66=28', '68-52=16'] Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,21 unequal: No Solution Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,21 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,21 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 #0,3,0 Current State: 21:[68, 24], Operations: ['94-66=28', '52-28=24'] Exploring Operation: 68*24=1632, Resulting Numbers: [1632] 1632,21 unequal: No Solution Exploring Operation: 68+24=92, Resulting Numbers: [92] 92,21 unequal: No Solution Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,21 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 #0,3,4 Current State: 21:[52, 40], Operations: ['94-66=28', '68-28=40'] Exploring Operation: 52*40=2080, Resulting Numbers: [2080] 2080,21 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,21 unequal: No Solution Exploring Operation: 52+40=92, Resulting Numbers: [92] 92,21 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 #0,3,1 Current State: 21:[68, 80], Operations: ['94-66=28', '52+28=80'] Exploring Operation: 68*80=5440, Resulting Numbers: [5440] 5440,21 unequal: No Solution Exploring Operation: 68+80=148, Resulting Numbers: [148] 148,21 unequal: No Solution Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,21 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 #0,3,2 Current State: 21:[28, 120], Operations: ['94-66=28', '52+68=120'] Exploring Operation: 28*120=3360, Resulting Numbers: [3360] 3360,21 unequal: No Solution Exploring Operation: 120-28=92, Resulting Numbers: [92] 92,21 unequal: No Solution Exploring Operation: 28+120=148, Resulting Numbers: [148] 148,21 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 #0,2 Current State: 21:[52, 94, 2], Operations: ['68-66=2'] Exploring Operation: 52/2=26, Resulting Numbers: [94, 26] Generated Node #0,2,0: 21:[94, 26] Operation: 52/2=26 Exploring Operation: 94-52=42, Resulting Numbers: [2, 42] Generated Node #0,2,1: 21:[2, 42] Operation: 94-52=42 Exploring Operation: 94-2=92, Resulting Numbers: [52, 92] Generated Node #0,2,2: 21:[52, 92] Operation: 94-2=92 Exploring Operation: 52-2=50, Resulting Numbers: [94, 50] Generated Node #0,2,3: 21:[94, 50] Operation: 52-2=50 Exploring Operation: 94/2=47, Resulting Numbers: [52, 47] Generated Node #0,2,4: 21:[52, 47] Operation: 94/2=47 Moving to Node #0,2,1 Current State: 21:[2, 42], Operations: ['68-66=2', '94-52=42'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[66, 52, 94, 68], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [52, 94, 2] Generated Node #0,2: 21:[52, 94, 2] Operation: 68-66=2 Moving to Node #0,2 Current State: 21:[52, 94, 2], Operations: ['68-66=2'] Exploring Operation: 94-52=42, Resulting Numbers: [2, 42] Generated Node #0,2,1: 21:[2, 42] Operation: 94-52=42 Moving to Node #0,2,1 Current State: 21:[2, 42], Operations: ['68-66=2', '94-52=42'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.951389
hs_5
mult_heuristic
[ 45, 47, 83, 98 ]
68
[ "47-45=2", "83*2=166", "166-98=68" ]
Current State: 68:[45, 47, 83, 98], Operations: [] Exploring Operation: 47-45=2, Resulting Numbers: [83, 98, 2] Generated Node #2: [83, 98, 2] from Operation: 47-45=2 Current State: 68:[83, 98, 2], Operations: ['47-45=2'] Exploring Operation: 83*2=166, Resulting Numbers: [98, 166] Generated Node #3: [98, 166] from Operation: 83*2=166 Current State: 68:[98, 166], Operations: ['47-45=2', '83*2=166'] Exploring Operation: 166-98=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[45, 47, 83, 98], Operations: [] Exploring Operation: 47-45=2, Resulting Numbers: [83, 98, 2] Generated Node #0,0: 68:[83, 98, 2] Operation: 47-45=2 Exploring Operation: 98-83=15, Resulting Numbers: [45, 47, 15] Generated Node #0,1: 68:[45, 47, 15] Operation: 98-83=15 Exploring Operation: 98-45=53, Resulting Numbers: [47, 83, 53] Generated Node #0,2: 68:[47, 83, 53] Operation: 98-45=53 Exploring Operation: 83-47=36, Resulting Numbers: [45, 98, 36] Generated Node #0,3: 68:[45, 98, 36] Operation: 83-47=36 Exploring Operation: 98-47=51, Resulting Numbers: [45, 83, 51] Generated Node #0,4: 68:[45, 83, 51] Operation: 98-47=51 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[45, 47, 15], Operations: ['98-83=15'] Exploring Operation: 47-45=2, Resulting Numbers: [15, 2] Generated Node #0,1,0: 68:[15, 2] Operation: 47-45=2 Exploring Operation: 45/15=3, Resulting Numbers: [47, 3] Generated Node #0,1,1: 68:[47, 3] Operation: 45/15=3 Exploring Operation: 47-15=32, Resulting Numbers: [45, 32] Generated Node #0,1,2: 68:[45, 32] Operation: 47-15=32 Exploring Operation: 45-15=30, Resulting Numbers: [47, 30] Generated Node #0,1,3: 68:[47, 30] Operation: 45-15=30 Exploring Operation: 47+15=62, Resulting Numbers: [45, 62] Generated Node #0,1,4: 68:[45, 62] Operation: 47+15=62 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 68:[15, 2], Operations: ['98-83=15', '47-45=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,68 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 68:[45, 32], Operations: ['98-83=15', '47-15=32'] Exploring Operation: 45-32=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 45*32=1440, Resulting Numbers: [1440] 1440,68 unequal: No Solution Exploring Operation: 45+32=77, Resulting Numbers: [77] 77,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 68:[47, 3], Operations: ['98-83=15', '45/15=3'] Exploring Operation: 47*3=141, Resulting Numbers: [141] 141,68 unequal: No Solution Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,68 unequal: No Solution Exploring Operation: 47+3=50, Resulting Numbers: [50] 50,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 68:[47, 30], Operations: ['98-83=15', '45-15=30'] Exploring Operation: 47+30=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 47*30=1410, Resulting Numbers: [1410] 1410,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 68:[45, 62], Operations: ['98-83=15', '47+15=62'] Exploring Operation: 45*62=2790, Resulting Numbers: [2790] 2790,68 unequal: No Solution Exploring Operation: 62-45=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 45+62=107, Resulting Numbers: [107] 107,68 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 #0,2 Current State: 68:[47, 83, 53], Operations: ['98-45=53'] Exploring Operation: 83-53=30, Resulting Numbers: [47, 30] Generated Node #0,2,0: 68:[47, 30] Operation: 83-53=30 Exploring Operation: 53-47=6, Resulting Numbers: [83, 6] Generated Node #0,2,1: 68:[83, 6] Operation: 53-47=6 Exploring Operation: 83-47=36, Resulting Numbers: [53, 36] Generated Node #0,2,2: 68:[53, 36] Operation: 83-47=36 Exploring Operation: 47+53=100, Resulting Numbers: [83, 100] Generated Node #0,2,3: 68:[83, 100] Operation: 47+53=100 Exploring Operation: 47+83=130, Resulting Numbers: [53, 130] Generated Node #0,2,4: 68:[53, 130] Operation: 47+83=130 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 68:[47, 30], Operations: ['98-45=53', '83-53=30'] Exploring Operation: 47+30=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 47*30=1410, Resulting Numbers: [1410] 1410,68 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,68 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:[83, 6], Operations: ['98-45=53', '53-47=6'] Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,68 unequal: No Solution Exploring Operation: 83*6=498, Resulting Numbers: [498] 498,68 unequal: No Solution Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,68 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:[53, 36], Operations: ['98-45=53', '83-47=36'] Exploring Operation: 53*36=1908, Resulting Numbers: [1908] 1908,68 unequal: No Solution Exploring Operation: 53-36=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 53+36=89, Resulting Numbers: [89] 89,68 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:[83, 100], Operations: ['98-45=53', '47+53=100'] Exploring Operation: 100-83=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 83*100=8300, Resulting Numbers: [8300] 8300,68 unequal: No Solution Exploring Operation: 83+100=183, Resulting Numbers: [183] 183,68 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 #0,2,4 Current State: 68:[53, 130], Operations: ['98-45=53', '47+83=130'] Exploring Operation: 53+130=183, Resulting Numbers: [183] 183,68 unequal: No Solution Exploring Operation: 130-53=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 53*130=6890, Resulting Numbers: [6890] 6890,68 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:[45, 98, 36], Operations: ['83-47=36'] Exploring Operation: 98-36=62, Resulting Numbers: [45, 62] Generated Node #0,3,0: 68:[45, 62] Operation: 98-36=62 Exploring Operation: 45+98=143, Resulting Numbers: [36, 143] Generated Node #0,3,1: 68:[36, 143] Operation: 45+98=143 Exploring Operation: 45+36=81, Resulting Numbers: [98, 81] Generated Node #0,3,2: 68:[98, 81] Operation: 45+36=81 Exploring Operation: 45-36=9, Resulting Numbers: [98, 9] Generated Node #0,3,3: 68:[98, 9] Operation: 45-36=9 Exploring Operation: 98-45=53, Resulting Numbers: [36, 53] Generated Node #0,3,4: 68:[36, 53] Operation: 98-45=53 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 68:[45, 62], Operations: ['83-47=36', '98-36=62'] Exploring Operation: 45*62=2790, Resulting Numbers: [2790] 2790,68 unequal: No Solution Exploring Operation: 62-45=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 45+62=107, Resulting Numbers: [107] 107,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 68:[36, 53], Operations: ['83-47=36', '98-45=53'] Exploring Operation: 36*53=1908, Resulting Numbers: [1908] 1908,68 unequal: No Solution Exploring Operation: 36+53=89, Resulting Numbers: [89] 89,68 unequal: No Solution Exploring Operation: 53-36=17, Resulting Numbers: [17] 17,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 68:[98, 9], Operations: ['83-47=36', '45-36=9'] Exploring Operation: 98+9=107, Resulting Numbers: [107] 107,68 unequal: No Solution Exploring Operation: 98-9=89, Resulting Numbers: [89] 89,68 unequal: No Solution Exploring Operation: 98*9=882, Resulting Numbers: [882] 882,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 68:[98, 81], Operations: ['83-47=36', '45+36=81'] Exploring Operation: 98-81=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 98+81=179, Resulting Numbers: [179] 179,68 unequal: No Solution Exploring Operation: 98*81=7938, Resulting Numbers: [7938] 7938,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 68:[36, 143], Operations: ['83-47=36', '45+98=143'] Exploring Operation: 143-36=107, Resulting Numbers: [107] 107,68 unequal: No Solution Exploring Operation: 36+143=179, Resulting Numbers: [179] 179,68 unequal: No Solution Exploring Operation: 36*143=5148, Resulting Numbers: [5148] 5148,68 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 #0,4 Current State: 68:[45, 83, 51], Operations: ['98-47=51'] Exploring Operation: 45+83=128, Resulting Numbers: [51, 128] Generated Node #0,4,0: 68:[51, 128] Operation: 45+83=128 Exploring Operation: 51-45=6, Resulting Numbers: [83, 6] Generated Node #0,4,1: 68:[83, 6] Operation: 51-45=6 Exploring Operation: 83-51=32, Resulting Numbers: [45, 32] Generated Node #0,4,2: 68:[45, 32] Operation: 83-51=32 Exploring Operation: 45+51=96, Resulting Numbers: [83, 96] Generated Node #0,4,3: 68:[83, 96] Operation: 45+51=96 Exploring Operation: 83-45=38, Resulting Numbers: [51, 38] Generated Node #0,4,4: 68:[51, 38] Operation: 83-45=38 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 68:[45, 32], Operations: ['98-47=51', '83-51=32'] Exploring Operation: 45+32=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 45-32=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 45*32=1440, Resulting Numbers: [1440] 1440,68 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 #0,4,1 Current State: 68:[83, 6], Operations: ['98-47=51', '51-45=6'] Exploring Operation: 83*6=498, Resulting Numbers: [498] 498,68 unequal: No Solution Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,68 unequal: No Solution Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,68 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 #0,4,4 Current State: 68:[51, 38], Operations: ['98-47=51', '83-45=38'] Exploring Operation: 51-38=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 51*38=1938, Resulting Numbers: [1938] 1938,68 unequal: No Solution Exploring Operation: 51+38=89, Resulting Numbers: [89] 89,68 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 #0,4,3 Current State: 68:[83, 96], Operations: ['98-47=51', '45+51=96'] Exploring Operation: 83*96=7968, Resulting Numbers: [7968] 7968,68 unequal: No Solution Exploring Operation: 96-83=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 83+96=179, Resulting Numbers: [179] 179,68 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 #0,4,0 Current State: 68:[51, 128], Operations: ['98-47=51', '45+83=128'] Exploring Operation: 51+128=179, Resulting Numbers: [179] 179,68 unequal: No Solution Exploring Operation: 128-51=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 51*128=6528, Resulting Numbers: [6528] 6528,68 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 #0,0 Current State: 68:[83, 98, 2], Operations: ['47-45=2'] Exploring Operation: 98/2=49, Resulting Numbers: [83, 49] Generated Node #0,0,0: 68:[83, 49] Operation: 98/2=49 Exploring Operation: 83-2=81, Resulting Numbers: [98, 81] Generated Node #0,0,1: 68:[98, 81] Operation: 83-2=81 Exploring Operation: 98-83=15, Resulting Numbers: [2, 15] Generated Node #0,0,2: 68:[2, 15] Operation: 98-83=15 Exploring Operation: 98-2=96, Resulting Numbers: [83, 96] Generated Node #0,0,3: 68:[83, 96] Operation: 98-2=96 Exploring Operation: 83+2=85, Resulting Numbers: [98, 85] Generated Node #0,0,4: 68:[98, 85] Operation: 83+2=85 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 68:[2, 15], Operations: ['47-45=2', '98-83=15'] Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,68 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[83, 49], Operations: ['47-45=2', '98/2=49'] Exploring Operation: 83-49=34, Resulting Numbers: [34] 34,68 unequal: No Solution Exploring Operation: 83*49=4067, Resulting Numbers: [4067] 4067,68 unequal: No Solution Exploring Operation: 83+49=132, Resulting Numbers: [132] 132,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 68:[98, 81], Operations: ['47-45=2', '83-2=81'] Exploring Operation: 98-81=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 98*81=7938, Resulting Numbers: [7938] 7938,68 unequal: No Solution Exploring Operation: 98+81=179, Resulting Numbers: [179] 179,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 68:[83, 96], Operations: ['47-45=2', '98-2=96'] Exploring Operation: 83*96=7968, Resulting Numbers: [7968] 7968,68 unequal: No Solution Exploring Operation: 83+96=179, Resulting Numbers: [179] 179,68 unequal: No Solution Exploring Operation: 96-83=13, Resulting Numbers: [13] 13,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 68:[98, 85], Operations: ['47-45=2', '83+2=85'] Exploring Operation: 98+85=183, Resulting Numbers: [183] 183,68 unequal: No Solution Exploring Operation: 98*85=8330, Resulting Numbers: [8330] 8330,68 unequal: No Solution Exploring Operation: 98-85=13, Resulting Numbers: [13] 13,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 1, 88, 22, 49 ]
52
[ "49-1=48", "88/22=4", "48+4=52" ]
Current State: 52:[1, 88, 22, 49], Operations: [] Exploring Operation: 49-1=48, Resulting Numbers: [88, 22, 48] Generated Node #2: [88, 22, 48] from Operation: 49-1=48 Current State: 52:[88, 22, 48], Operations: ['49-1=48'] Exploring Operation: 88/22=4, Resulting Numbers: [48, 4] Generated Node #3: [48, 4] from Operation: 88/22=4 Current State: 52:[48, 4], Operations: ['49-1=48', '88/22=4'] Exploring Operation: 48+4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[1, 88, 22, 49], Operations: [] Exploring Operation: 88/22=4, Resulting Numbers: [1, 49, 4] Generated Node #0,0: 52:[1, 49, 4] Operation: 88/22=4 Exploring Operation: 49-22=27, Resulting Numbers: [1, 88, 27] Generated Node #0,1: 52:[1, 88, 27] Operation: 49-22=27 Exploring Operation: 88-22=66, Resulting Numbers: [1, 49, 66] Generated Node #0,2: 52:[1, 49, 66] Operation: 88-22=66 Exploring Operation: 88-49=39, Resulting Numbers: [1, 22, 39] Generated Node #0,3: 52:[1, 22, 39] Operation: 88-49=39 Moving to Node #0,0 Current State: 52:[1, 49, 4], Operations: ['88/22=4'] Exploring Operation: 49+4=53, Resulting Numbers: [1, 53] Generated Node #0,0,0: 52:[1, 53] Operation: 49+4=53 Exploring Operation: 49/1=49, Resulting Numbers: [4, 49] Generated Node #0,0,1: 52:[4, 49] Operation: 49/1=49 Exploring Operation: 1*49=49, Resulting Numbers: [4, 49] Generated Node #0,0,2: 52:[4, 49] Operation: 1*49=49 Exploring Operation: 1+49=50, Resulting Numbers: [4, 50] Generated Node #0,0,3: 52:[4, 50] Operation: 1+49=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[1, 53], Operations: ['88/22=4', '49+4=53'] Exploring Operation: 1+53=54, Resulting Numbers: [54] 54,52 unequal: No Solution Exploring Operation: 53-1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[1, 88, 22, 49], Operations: [] Exploring Operation: 88/22=4, Resulting Numbers: [1, 49, 4] Generated Node #0,0: 52:[1, 49, 4] Operation: 88/22=4 Moving to Node #0,0 Current State: 52:[1, 49, 4], Operations: ['88/22=4'] Exploring Operation: 49+4=53, Resulting Numbers: [1, 53] Generated Node #0,0,0: 52:[1, 53] Operation: 49+4=53 Moving to Node #0,0,0 Current State: 52:[1, 53], Operations: ['88/22=4', '49+4=53'] Exploring Operation: 53-1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 43, 63, 18, 43 ]
81
[ "43+63=106", "43-18=25", "106-25=81" ]
Current State: 81:[43, 63, 18, 43], Operations: [] Exploring Operation: 43+63=106, Resulting Numbers: [18, 106] Generated Node #2: [18, 106] from Operation: 43+63=106 Current State: 81:[18, 106], Operations: ['43+63=106'] Exploring Operation: 43-18=25, Resulting Numbers: [106, 25] Generated Node #3: [106, 25] from Operation: 43-18=25 Current State: 81:[106, 25], Operations: ['43+63=106', '43-18=25'] Exploring Operation: 106-25=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[43, 63, 18, 43], Operations: [] Exploring Operation: 43-43=0, Resulting Numbers: [63, 18, 0] Generated Node #0,0: 81:[63, 18, 0] Operation: 43-43=0 Exploring Operation: 63-43=20, Resulting Numbers: [18, 43, 20] Generated Node #0,1: 81:[18, 43, 20] Operation: 63-43=20 Exploring Operation: 43+43=86, Resulting Numbers: [63, 18, 86] Generated Node #0,2: 81:[63, 18, 86] Operation: 43+43=86 Exploring Operation: 63+18=81, Resulting Numbers: [43, 43, 81] Generated Node #0,3: 81:[43, 43, 81] Operation: 63+18=81 Exploring Operation: 43/43=1, Resulting Numbers: [63, 18, 1] Generated Node #0,4: 81:[63, 18, 1] Operation: 43/43=1 Start Sub Search at level 1: Moving to Node #0,4 Current State: 81:[63, 18, 1], Operations: ['43/43=1'] Exploring Operation: 63+18=81, Resulting Numbers: [1, 81] Generated Node #0,4,0: 81:[1, 81] Operation: 63+18=81 Exploring Operation: 18-1=17, Resulting Numbers: [63, 17] Generated Node #0,4,1: 81:[63, 17] Operation: 18-1=17 Exploring Operation: 63-18=45, Resulting Numbers: [1, 45] Generated Node #0,4,2: 81:[1, 45] Operation: 63-18=45 Exploring Operation: 63+1=64, Resulting Numbers: [18, 64] Generated Node #0,4,3: 81:[18, 64] Operation: 63+1=64 Exploring Operation: 18+1=19, Resulting Numbers: [63, 19] Generated Node #0,4,4: 81:[63, 19] Operation: 18+1=19 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 81:[1, 81], Operations: ['43/43=1', '63+18=81'] Exploring Operation: 1*81=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[43, 63, 18, 43], Operations: [] Exploring Operation: 43/43=1, Resulting Numbers: [63, 18, 1] Generated Node #0,4: 81:[63, 18, 1] Operation: 43/43=1 Moving to Node #0,4 Current State: 81:[63, 18, 1], Operations: ['43/43=1'] Exploring Operation: 63+18=81, Resulting Numbers: [1, 81] Generated Node #0,4,0: 81:[1, 81] Operation: 63+18=81 Moving to Node #0,4,0 Current State: 81:[1, 81], Operations: ['43/43=1', '63+18=81'] Exploring Operation: 1*81=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 6, 18, 9, 55 ]
43
[ "6*18=108", "108/9=12", "55-12=43" ]
Current State: 43:[6, 18, 9, 55], Operations: [] Exploring Operation: 6*18=108, Resulting Numbers: [9, 55, 108] Generated Node #2: [9, 55, 108] from Operation: 6*18=108 Current State: 43:[9, 55, 108], Operations: ['6*18=108'] Exploring Operation: 108/9=12, Resulting Numbers: [55, 12] Generated Node #3: [55, 12] from Operation: 108/9=12 Current State: 43:[55, 12], Operations: ['6*18=108', '108/9=12'] Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[6, 18, 9, 55], Operations: [] Exploring Operation: 6*9=54, Resulting Numbers: [18, 55, 54] Generated Node #0,0: 43:[18, 55, 54] Operation: 6*9=54 Moving to Node #0,0 Current State: 43:[18, 55, 54], Operations: ['6*9=54'] Exploring Operation: 55-18=37, Resulting Numbers: [54, 37] Generated Node #0,0,0: 43:[54, 37] Operation: 55-18=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[54, 37], Operations: ['6*9=54', '55-18=37'] Exploring Operation: 54-37=17, Resulting Numbers: [17] 17,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 96, 61, 24, 81 ]
92
[ "96-61=35", "81-24=57", "35+57=92" ]
Current State: 92:[96, 61, 24, 81], Operations: [] Exploring Operation: 96-61=35, Resulting Numbers: [24, 81, 35] Generated Node #2: [24, 81, 35] from Operation: 96-61=35 Current State: 92:[24, 81, 35], Operations: ['96-61=35'] Exploring Operation: 81-24=57, Resulting Numbers: [35, 57] Generated Node #3: [35, 57] from Operation: 81-24=57 Current State: 92:[35, 57], Operations: ['96-61=35', '81-24=57'] Exploring Operation: 35+57=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[96, 61, 24, 81], Operations: [] Exploring Operation: 96-61=35, Resulting Numbers: [24, 81, 35] Generated Node #0,0: 92:[24, 81, 35] Operation: 96-61=35 Exploring Operation: 61+24=85, Resulting Numbers: [96, 81, 85] Generated Node #0,1: 92:[96, 81, 85] Operation: 61+24=85 Exploring Operation: 81-61=20, Resulting Numbers: [96, 24, 20] Generated Node #0,2: 92:[96, 24, 20] Operation: 81-61=20 Exploring Operation: 96-81=15, Resulting Numbers: [61, 24, 15] Generated Node #0,3: 92:[61, 24, 15] Operation: 96-81=15 Exploring Operation: 61-24=37, Resulting Numbers: [96, 81, 37] Generated Node #0,4: 92:[96, 81, 37] Operation: 61-24=37 Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[96, 24, 20], Operations: ['81-61=20'] Exploring Operation: 96/24=4, Resulting Numbers: [20, 4] Generated Node #0,2,0: 92:[20, 4] Operation: 96/24=4 Exploring Operation: 24+20=44, Resulting Numbers: [96, 44] Generated Node #0,2,1: 92:[96, 44] Operation: 24+20=44 Exploring Operation: 24-20=4, Resulting Numbers: [96, 4] Generated Node #0,2,2: 92:[96, 4] Operation: 24-20=4 Exploring Operation: 96-24=72, Resulting Numbers: [20, 72] Generated Node #0,2,3: 92:[20, 72] Operation: 96-24=72 Exploring Operation: 96-20=76, Resulting Numbers: [24, 76] Generated Node #0,2,4: 92:[24, 76] Operation: 96-20=76 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 92:[20, 4], Operations: ['81-61=20', '96/24=4'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,92 unequal: No Solution Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 92:[96, 4], Operations: ['81-61=20', '24-20=4'] Exploring Operation: 96/4=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 96*4=384, Resulting Numbers: [384] 384,92 unequal: No Solution Exploring Operation: 96-4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[96, 61, 24, 81], Operations: [] Exploring Operation: 81-61=20, Resulting Numbers: [96, 24, 20] Generated Node #0,2: 92:[96, 24, 20] Operation: 81-61=20 Moving to Node #0,2 Current State: 92:[96, 24, 20], Operations: ['81-61=20'] Exploring Operation: 24-20=4, Resulting Numbers: [96, 4] Generated Node #0,2,2: 92:[96, 4] Operation: 24-20=4 Moving to Node #0,2,2 Current State: 92:[96, 4], Operations: ['81-61=20', '24-20=4'] Exploring Operation: 96-4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 38, 49, 15, 60 ]
34
[ "49-38=11", "60-15=45", "45-11=34" ]
Current State: 34:[38, 49, 15, 60], Operations: [] Exploring Operation: 49-38=11, Resulting Numbers: [15, 60, 11] Generated Node #2: [15, 60, 11] from Operation: 49-38=11 Current State: 34:[15, 60, 11], Operations: ['49-38=11'] Exploring Operation: 60-15=45, Resulting Numbers: [11, 45] Generated Node #3: [11, 45] from Operation: 60-15=45 Current State: 34:[11, 45], Operations: ['49-38=11', '60-15=45'] Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[38, 49, 15, 60], Operations: [] Exploring Operation: 60-49=11, Resulting Numbers: [38, 15, 11] Generated Node #0,0: 34:[38, 15, 11] Operation: 60-49=11 Exploring Operation: 60/15=4, Resulting Numbers: [38, 49, 4] Generated Node #0,1: 34:[38, 49, 4] Operation: 60/15=4 Moving to Node #0,0 Current State: 34:[38, 15, 11], Operations: ['60-49=11'] Exploring Operation: 15-11=4, Resulting Numbers: [38, 4] Generated Node #0,0,0: 34:[38, 4] Operation: 15-11=4 Exploring Operation: 38-11=27, Resulting Numbers: [15, 27] Generated Node #0,0,1: 34:[15, 27] Operation: 38-11=27 Moving to Node #0,1 Current State: 34:[38, 49, 4], Operations: ['60/15=4'] Exploring Operation: 49-38=11, Resulting Numbers: [4, 11] Generated Node #0,1,0: 34:[4, 11] Operation: 49-38=11 Exploring Operation: 38-4=34, Resulting Numbers: [49, 34] Generated Node #0,1,1: 34:[49, 34] Operation: 38-4=34 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 34:[4, 11], Operations: ['60/15=4', '49-38=11'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,34 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 #0,1,1 Current State: 34:[49, 34], Operations: ['60/15=4', '38-4=34'] Exploring Operation: 49+34=83, Resulting Numbers: [83] 83,34 unequal: No Solution Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 34:[38, 4], Operations: ['60-49=11', '15-11=4'] Exploring Operation: 38+4=42, Resulting Numbers: [42] 42,34 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[38, 49, 15, 60], Operations: [] Exploring Operation: 60-49=11, Resulting Numbers: [38, 15, 11] Generated Node #0,0: 34:[38, 15, 11] Operation: 60-49=11 Moving to Node #0,0 Current State: 34:[38, 15, 11], Operations: ['60-49=11'] Exploring Operation: 15-11=4, Resulting Numbers: [38, 4] Generated Node #0,0,0: 34:[38, 4] Operation: 15-11=4 Moving to Node #0,0,0 Current State: 34:[38, 4], Operations: ['60-49=11', '15-11=4'] Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 45, 9, 65, 84 ]
35
[ "45+9=54", "84-65=19", "54-19=35" ]
Current State: 35:[45, 9, 65, 84], Operations: [] Exploring Operation: 45+9=54, Resulting Numbers: [65, 84, 54] Generated Node #2: [65, 84, 54] from Operation: 45+9=54 Current State: 35:[65, 84, 54], Operations: ['45+9=54'] Exploring Operation: 84-65=19, Resulting Numbers: [54, 19] Generated Node #3: [54, 19] from Operation: 84-65=19 Current State: 35:[54, 19], Operations: ['45+9=54', '84-65=19'] Exploring Operation: 54-19=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[45, 9, 65, 84], Operations: [] Exploring Operation: 45-9=36, Resulting Numbers: [65, 84, 36] Generated Node #0,0: 35:[65, 84, 36] Operation: 45-9=36 Exploring Operation: 84-45=39, Resulting Numbers: [9, 65, 39] Generated Node #0,1: 35:[9, 65, 39] Operation: 84-45=39 Exploring Operation: 84-65=19, Resulting Numbers: [45, 9, 19] Generated Node #0,2: 35:[45, 9, 19] Operation: 84-65=19 Exploring Operation: 45/9=5, Resulting Numbers: [65, 84, 5] Generated Node #0,3: 35:[65, 84, 5] Operation: 45/9=5 Exploring Operation: 65-45=20, Resulting Numbers: [9, 84, 20] Generated Node #0,4: 35:[9, 84, 20] Operation: 65-45=20 Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[45, 9, 19], Operations: ['84-65=19'] Exploring Operation: 45-19=26, Resulting Numbers: [9, 26] Generated Node #0,2,0: 35:[9, 26] Operation: 45-19=26 Exploring Operation: 19-9=10, Resulting Numbers: [45, 10] Generated Node #0,2,1: 35:[45, 10] Operation: 19-9=10 Exploring Operation: 9+19=28, Resulting Numbers: [45, 28] Generated Node #0,2,2: 35:[45, 28] Operation: 9+19=28 Exploring Operation: 45-9=36, Resulting Numbers: [19, 36] Generated Node #0,2,3: 35:[19, 36] Operation: 45-9=36 Exploring Operation: 45/9=5, Resulting Numbers: [19, 5] Generated Node #0,2,4: 35:[19, 5] Operation: 45/9=5 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 35:[9, 26], Operations: ['84-65=19', '45-19=26'] Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[45, 9, 65, 84], Operations: [] Exploring Operation: 84-65=19, Resulting Numbers: [45, 9, 19] Generated Node #0,2: 35:[45, 9, 19] Operation: 84-65=19 Moving to Node #0,2 Current State: 35:[45, 9, 19], Operations: ['84-65=19'] Exploring Operation: 45-19=26, Resulting Numbers: [9, 26] Generated Node #0,2,0: 35:[9, 26] Operation: 45-19=26 Moving to Node #0,2,0 Current State: 35:[9, 26], Operations: ['84-65=19', '45-19=26'] Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 28, 30, 4, 33 ]
62
[ "30-28=2", "33*2=66", "66-4=62" ]
Current State: 62:[28, 30, 4, 33], Operations: [] Exploring Operation: 30-28=2, Resulting Numbers: [4, 33, 2] Generated Node #2: [4, 33, 2] from Operation: 30-28=2 Current State: 62:[4, 33, 2], Operations: ['30-28=2'] Exploring Operation: 33*2=66, Resulting Numbers: [4, 66] Generated Node #3: [4, 66] from Operation: 33*2=66 Current State: 62:[4, 66], Operations: ['30-28=2', '33*2=66'] Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[28, 30, 4, 33], Operations: [] Exploring Operation: 28+4=32, Resulting Numbers: [30, 33, 32] Generated Node #0,0: 62:[30, 33, 32] Operation: 28+4=32 Exploring Operation: 30-28=2, Resulting Numbers: [4, 33, 2] Generated Node #0,1: 62:[4, 33, 2] Operation: 30-28=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[30, 33, 32], Operations: ['28+4=32'] Exploring Operation: 33-30=3, Resulting Numbers: [32, 3] Generated Node #0,0,0: 62:[32, 3] Operation: 33-30=3 Exploring Operation: 30+33=63, Resulting Numbers: [32, 63] Generated Node #0,0,1: 62:[32, 63] Operation: 30+33=63 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[32, 3], Operations: ['28+4=32', '33-30=3'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,62 unequal: No Solution No 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: 62:[32, 63], Operations: ['28+4=32', '30+33=63'] Exploring Operation: 32+63=95, Resulting Numbers: [95] 95,62 unequal: No Solution Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,62 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: 62:[4, 33, 2], Operations: ['30-28=2'] Exploring Operation: 33-4=29, Resulting Numbers: [2, 29] Generated Node #0,1,0: 62:[2, 29] Operation: 33-4=29 Exploring Operation: 4-2=2, Resulting Numbers: [33, 2] Generated Node #0,1,1: 62:[33, 2] Operation: 4-2=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 62:[2, 29], Operations: ['30-28=2', '33-4=29'] Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,62 unequal: No Solution No 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: 62:[33, 2], Operations: ['30-28=2', '4-2=2'] Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,62 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
[ 42, 80, 91, 41 ]
18
[ "80-41=39", "42*39=1638", "1638/91=18" ]
Current State: 18:[42, 80, 91, 41], Operations: [] Exploring Operation: 80-41=39, Resulting Numbers: [42, 91, 39] Generated Node #2: [42, 91, 39] from Operation: 80-41=39 Current State: 18:[42, 91, 39], Operations: ['80-41=39'] Exploring Operation: 42*39=1638, Resulting Numbers: [91, 1638] Generated Node #3: [91, 1638] from Operation: 42*39=1638 Current State: 18:[91, 1638], Operations: ['80-41=39', '42*39=1638'] Exploring Operation: 1638/91=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[42, 80, 91, 41], Operations: [] Exploring Operation: 91-80=11, Resulting Numbers: [42, 41, 11] Generated Node #0,0: 18:[42, 41, 11] Operation: 91-80=11 Exploring Operation: 80-42=38, Resulting Numbers: [91, 41, 38] Generated Node #0,1: 18:[91, 41, 38] Operation: 80-42=38 Exploring Operation: 91-42=49, Resulting Numbers: [80, 41, 49] Generated Node #0,2: 18:[80, 41, 49] Operation: 91-42=49 Moving to Node #0,0 Current State: 18:[42, 41, 11], Operations: ['91-80=11'] Exploring Operation: 42-41=1, Resulting Numbers: [11, 1] Generated Node #0,0,0: 18:[11, 1] Operation: 42-41=1 Exploring Operation: 41-11=30, Resulting Numbers: [42, 30] Generated Node #0,0,1: 18:[42, 30] Operation: 41-11=30 Exploring Operation: 42-11=31, Resulting Numbers: [41, 31] Generated Node #0,0,2: 18:[41, 31] Operation: 42-11=31 Moving to Node #0,1 Current State: 18:[91, 41, 38], Operations: ['80-42=38'] Exploring Operation: 91-41=50, Resulting Numbers: [38, 50] Generated Node #0,1,0: 18:[38, 50] Operation: 91-41=50 Exploring Operation: 41-38=3, Resulting Numbers: [91, 3] Generated Node #0,1,1: 18:[91, 3] Operation: 41-38=3 Exploring Operation: 91-38=53, Resulting Numbers: [41, 53] Generated Node #0,1,2: 18:[41, 53] Operation: 91-38=53 Moving to Node #0,2 Current State: 18:[80, 41, 49], Operations: ['91-42=49'] Exploring Operation: 80-41=39, Resulting Numbers: [49, 39] Generated Node #0,2,0: 18:[49, 39] Operation: 80-41=39 Exploring Operation: 80-49=31, Resulting Numbers: [41, 31] Generated Node #0,2,1: 18:[41, 31] Operation: 80-49=31 Exploring Operation: 49-41=8, Resulting Numbers: [80, 8] Generated Node #0,2,2: 18:[80, 8] Operation: 49-41=8 Moving to Node #0,0,0 Current State: 18:[11, 1], Operations: ['91-80=11', '42-41=1'] 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 Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[41, 31], Operations: ['91-80=11', '42-11=31'] Exploring Operation: 41+31=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 41*31=1271, Resulting Numbers: [1271] 1271,18 unequal: No Solution Exploring Operation: 41-31=10, Resulting Numbers: [10] 10,18 unequal: No Solution Moving to Node #0,2,1 Current State: 18:[41, 31], Operations: ['91-42=49', '80-49=31'] Exploring Operation: 41-31=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 41+31=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 41*31=1271, Resulting Numbers: [1271] 1271,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[42, 30], Operations: ['91-80=11', '41-11=30'] Exploring Operation: 42*30=1260, Resulting Numbers: [1260] 1260,18 unequal: No Solution Exploring Operation: 42+30=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[49, 39], Operations: ['91-42=49', '80-41=39'] Exploring Operation: 49*39=1911, Resulting Numbers: [1911] 1911,18 unequal: No Solution Exploring Operation: 49-39=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 49+39=88, Resulting Numbers: [88] 88,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[38, 50], Operations: ['80-42=38', '91-41=50'] Exploring Operation: 38*50=1900, Resulting Numbers: [1900] 1900,18 unequal: No Solution Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 38+50=88, Resulting Numbers: [88] 88,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[41, 53], Operations: ['80-42=38', '91-38=53'] Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 41*53=2173, Resulting Numbers: [2173] 2173,18 unequal: No Solution Exploring Operation: 41+53=94, Resulting Numbers: [94] 94,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[80, 8], Operations: ['91-42=49', '49-41=8'] Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 80+8=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[91, 3], Operations: ['80-42=38', '41-38=3'] Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 91*3=273, Resulting Numbers: [273] 273,18 unequal: No Solution Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,18 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 97, 73, 20, 10 ]
30
[ "97+73=170", "20*10=200", "200-170=30" ]
Current State: 30:[97, 73, 20, 10], Operations: [] Exploring Operation: 97+73=170, Resulting Numbers: [20, 10, 170] Generated Node #2: [20, 10, 170] from Operation: 97+73=170 Current State: 30:[20, 10, 170], Operations: ['97+73=170'] Exploring Operation: 20*10=200, Resulting Numbers: [170, 200] Generated Node #3: [170, 200] from Operation: 20*10=200 Current State: 30:[170, 200], Operations: ['97+73=170', '20*10=200'] Exploring Operation: 200-170=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[97, 73, 20, 10], Operations: [] Exploring Operation: 97-73=24, Resulting Numbers: [20, 10, 24] Generated Node #0,0: 30:[20, 10, 24] Operation: 97-73=24 Exploring Operation: 97-10=87, Resulting Numbers: [73, 20, 87] Generated Node #0,1: 30:[73, 20, 87] Operation: 97-10=87 Exploring Operation: 97-20=77, Resulting Numbers: [73, 10, 77] Generated Node #0,2: 30:[73, 10, 77] Operation: 97-20=77 Exploring Operation: 73-20=53, Resulting Numbers: [97, 10, 53] Generated Node #0,3: 30:[97, 10, 53] Operation: 73-20=53 Exploring Operation: 73-10=63, Resulting Numbers: [97, 20, 63] Generated Node #0,4: 30:[97, 20, 63] Operation: 73-10=63 Moving to Node #0,0 Current State: 30:[20, 10, 24], Operations: ['97-73=24'] Exploring Operation: 24-10=14, Resulting Numbers: [20, 14] Generated Node #0,0,0: 30:[20, 14] Operation: 24-10=14 Exploring Operation: 24-20=4, Resulting Numbers: [10, 4] Generated Node #0,0,1: 30:[10, 4] Operation: 24-20=4 Exploring Operation: 20/10=2, Resulting Numbers: [24, 2] Generated Node #0,0,2: 30:[24, 2] Operation: 20/10=2 Exploring Operation: 20+10=30, Resulting Numbers: [24, 30] Generated Node #0,0,3: 30:[24, 30] Operation: 20+10=30 Exploring Operation: 20-10=10, Resulting Numbers: [24, 10] Generated Node #0,0,4: 30:[24, 10] Operation: 20-10=10 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[10, 4], Operations: ['97-73=24', '24-20=4'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[20, 14], Operations: ['97-73=24', '24-10=14'] Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,30 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 30:[24, 2], Operations: ['97-73=24', '20/10=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,30 unequal: No Solution Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,30 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 30:[24, 30], Operations: ['97-73=24', '20+10=30'] Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 24*30=720, Resulting Numbers: [720] 720,30 unequal: No Solution Exploring Operation: 24+30=54, Resulting Numbers: [54] 54,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 30:[24, 10], Operations: ['97-73=24', '20-10=10'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 24*10=240, Resulting Numbers: [240] 240,30 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: 30:[97, 10, 53], Operations: ['73-20=53'] Exploring Operation: 53-10=43, Resulting Numbers: [97, 43] Generated Node #0,3,0: 30:[97, 43] Operation: 53-10=43 Exploring Operation: 97+10=107, Resulting Numbers: [53, 107] Generated Node #0,3,1: 30:[53, 107] Operation: 97+10=107 Exploring Operation: 10+53=63, Resulting Numbers: [97, 63] Generated Node #0,3,2: 30:[97, 63] Operation: 10+53=63 Exploring Operation: 97-53=44, Resulting Numbers: [10, 44] Generated Node #0,3,3: 30:[10, 44] Operation: 97-53=44 Exploring Operation: 97-10=87, Resulting Numbers: [53, 87] Generated Node #0,3,4: 30:[53, 87] Operation: 97-10=87 Moving to Node #0,2 Current State: 30:[73, 10, 77], Operations: ['97-20=77'] Exploring Operation: 10+77=87, Resulting Numbers: [73, 87] Generated Node #0,2,0: 30:[73, 87] Operation: 10+77=87 Exploring Operation: 77-10=67, Resulting Numbers: [73, 67] Generated Node #0,2,1: 30:[73, 67] Operation: 77-10=67 Exploring Operation: 77-73=4, Resulting Numbers: [10, 4] Generated Node #0,2,2: 30:[10, 4] Operation: 77-73=4 Exploring Operation: 73-10=63, Resulting Numbers: [77, 63] Generated Node #0,2,3: 30:[77, 63] Operation: 73-10=63 Exploring Operation: 73+10=83, Resulting Numbers: [77, 83] Generated Node #0,2,4: 30:[77, 83] Operation: 73+10=83 Moving to Node #0,1 Current State: 30:[73, 20, 87], Operations: ['97-10=87'] Exploring Operation: 20+87=107, Resulting Numbers: [73, 107] Generated Node #0,1,0: 30:[73, 107] Operation: 20+87=107 Exploring Operation: 87-20=67, Resulting Numbers: [73, 67] Generated Node #0,1,1: 30:[73, 67] Operation: 87-20=67 Exploring Operation: 73-20=53, Resulting Numbers: [87, 53] Generated Node #0,1,2: 30:[87, 53] Operation: 73-20=53 Exploring Operation: 73+20=93, Resulting Numbers: [87, 93] Generated Node #0,1,3: 30:[87, 93] Operation: 73+20=93 Exploring Operation: 87-73=14, Resulting Numbers: [20, 14] Generated Node #0,1,4: 30:[20, 14] Operation: 87-73=14 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 30:[20, 14], Operations: ['97-10=87', '87-73=14'] Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 30:[73, 67], Operations: ['97-10=87', '87-20=67'] Exploring Operation: 73-67=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 73*67=4891, Resulting Numbers: [4891] 4891,30 unequal: No Solution Exploring Operation: 73+67=140, Resulting Numbers: [140] 140,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 30:[87, 53], Operations: ['97-10=87', '73-20=53'] Exploring Operation: 87+53=140, Resulting Numbers: [140] 140,30 unequal: No Solution Exploring Operation: 87-53=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 87*53=4611, Resulting Numbers: [4611] 4611,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 30:[73, 107], Operations: ['97-10=87', '20+87=107'] Exploring Operation: 73*107=7811, Resulting Numbers: [7811] 7811,30 unequal: No Solution Exploring Operation: 107-73=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 73+107=180, Resulting Numbers: [180] 180,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 30:[87, 93], Operations: ['97-10=87', '73+20=93'] Exploring Operation: 87*93=8091, Resulting Numbers: [8091] 8091,30 unequal: No Solution Exploring Operation: 93-87=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 87+93=180, Resulting Numbers: [180] 180,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 30:[97, 20, 63], Operations: ['73-10=63'] Exploring Operation: 97-20=77, Resulting Numbers: [63, 77] Generated Node #0,4,0: 30:[63, 77] Operation: 97-20=77 Exploring Operation: 20+63=83, Resulting Numbers: [97, 83] Generated Node #0,4,1: 30:[97, 83] Operation: 20+63=83 Exploring Operation: 97-63=34, Resulting Numbers: [20, 34] Generated Node #0,4,2: 30:[20, 34] Operation: 97-63=34 Exploring Operation: 97+20=117, Resulting Numbers: [63, 117] Generated Node #0,4,3: 30:[63, 117] Operation: 97+20=117 Exploring Operation: 63-20=43, Resulting Numbers: [97, 43] Generated Node #0,4,4: 30:[97, 43] Operation: 63-20=43 Moving to Node #0,2,2 Current State: 30:[10, 4], Operations: ['97-20=77', '77-73=4'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,30 unequal: No Solution Moving to Node #0,4,2 Current State: 30:[20, 34], Operations: ['73-10=63', '97-63=34'] Exploring Operation: 20+34=54, Resulting Numbers: [54] 54,30 unequal: No Solution Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 20*34=680, Resulting Numbers: [680] 680,30 unequal: No Solution Moving to Node #0,3,3 Current State: 30:[10, 44], Operations: ['73-20=53', '97-53=44'] Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 10+44=54, Resulting Numbers: [54] 54,30 unequal: No Solution Exploring Operation: 10*44=440, Resulting Numbers: [440] 440,30 unequal: No Solution Moving to Node #0,2,1 Current State: 30:[73, 67], Operations: ['97-20=77', '77-10=67'] Exploring Operation: 73*67=4891, Resulting Numbers: [4891] 4891,30 unequal: No Solution Exploring Operation: 73+67=140, Resulting Numbers: [140] 140,30 unequal: No Solution Exploring Operation: 73-67=6, Resulting Numbers: [6] 6,30 unequal: No Solution Moving to Node #0,3,4 Current State: 30:[53, 87], Operations: ['73-20=53', '97-10=87'] Exploring Operation: 53+87=140, Resulting Numbers: [140] 140,30 unequal: No Solution Exploring Operation: 53*87=4611, Resulting Numbers: [4611] 4611,30 unequal: No Solution Exploring Operation: 87-53=34, Resulting Numbers: [34] 34,30 unequal: No Solution Moving to Node #0,4,0 Current State: 30:[63, 77], Operations: ['73-10=63', '97-20=77'] Exploring Operation: 77-63=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 63+77=140, Resulting Numbers: [140] 140,30 unequal: No Solution Exploring Operation: 63*77=4851, Resulting Numbers: [4851] 4851,30 unequal: No Solution Moving to Node #0,4,4 Current State: 30:[97, 43], Operations: ['73-10=63', '63-20=43'] Exploring Operation: 97-43=54, Resulting Numbers: [54] 54,30 unequal: No Solution Exploring Operation: 97+43=140, Resulting Numbers: [140] 140,30 unequal: No Solution Exploring Operation: 97*43=4171, Resulting Numbers: [4171] 4171,30 unequal: No Solution Moving to Node #0,3,0 Current State: 30:[97, 43], Operations: ['73-20=53', '53-10=43'] Exploring Operation: 97*43=4171, Resulting Numbers: [4171] 4171,30 unequal: No Solution Exploring Operation: 97-43=54, Resulting Numbers: [54] 54,30 unequal: No Solution Exploring Operation: 97+43=140, Resulting Numbers: [140] 140,30 unequal: No Solution Moving to Node #0,2,3 Current State: 30:[77, 63], Operations: ['97-20=77', '73-10=63'] Exploring Operation: 77-63=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 77*63=4851, Resulting Numbers: [4851] 4851,30 unequal: No Solution Exploring Operation: 77+63=140, Resulting Numbers: [140] 140,30 unequal: No Solution Moving to Node #0,2,4 Current State: 30:[77, 83], Operations: ['97-20=77', '73+10=83'] Exploring Operation: 77+83=160, Resulting Numbers: [160] 160,30 unequal: No Solution Exploring Operation: 83-77=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 77*83=6391, Resulting Numbers: [6391] 6391,30 unequal: No Solution Moving to Node #0,3,2 Current State: 30:[97, 63], Operations: ['73-20=53', '10+53=63'] Exploring Operation: 97-63=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 97*63=6111, Resulting Numbers: [6111] 6111,30 unequal: No Solution Exploring Operation: 97+63=160, Resulting Numbers: [160] 160,30 unequal: No Solution Moving to Node #0,2,0 Current State: 30:[73, 87], Operations: ['97-20=77', '10+77=87'] Exploring Operation: 73+87=160, Resulting Numbers: [160] 160,30 unequal: No Solution Exploring Operation: 73*87=6351, Resulting Numbers: [6351] 6351,30 unequal: No Solution Exploring Operation: 87-73=14, Resulting Numbers: [14] 14,30 unequal: No Solution Moving to Node #0,3,1 Current State: 30:[53, 107], Operations: ['73-20=53', '97+10=107'] Exploring Operation: 53+107=160, Resulting Numbers: [160] 160,30 unequal: No Solution Exploring Operation: 107-53=54, Resulting Numbers: [54] 54,30 unequal: No Solution Exploring Operation: 53*107=5671, Resulting Numbers: [5671] 5671,30 unequal: No Solution Moving to Node #0,4,1 Current State: 30:[97, 83], Operations: ['73-10=63', '20+63=83'] Exploring Operation: 97-83=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 97+83=180, Resulting Numbers: [180] 180,30 unequal: No Solution Exploring Operation: 97*83=8051, Resulting Numbers: [8051] 8051,30 unequal: No Solution Moving to Node #0,4,3 Current State: 30:[63, 117], Operations: ['73-10=63', '97+20=117'] Exploring Operation: 117-63=54, Resulting Numbers: [54] 54,30 unequal: No Solution Exploring Operation: 63*117=7371, Resulting Numbers: [7371] 7371,30 unequal: No Solution Exploring Operation: 63+117=180, Resulting Numbers: [180] 180,30 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 54, 22, 72, 2 ]
31
[ "72-54=18", "18/2=9", "22+9=31" ]
Current State: 31:[54, 22, 72, 2], Operations: [] Exploring Operation: 72-54=18, Resulting Numbers: [22, 2, 18] Generated Node #2: [22, 2, 18] from Operation: 72-54=18 Current State: 31:[22, 2, 18], Operations: ['72-54=18'] Exploring Operation: 18/2=9, Resulting Numbers: [22, 9] Generated Node #3: [22, 9] from Operation: 18/2=9 Current State: 31:[22, 9], Operations: ['72-54=18', '18/2=9'] Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[54, 22, 72, 2], Operations: [] Exploring Operation: 72/2=36, Resulting Numbers: [54, 22, 36] Generated Node #0,0: 31:[54, 22, 36] Operation: 72/2=36 Exploring Operation: 72-54=18, Resulting Numbers: [22, 2, 18] Generated Node #0,1: 31:[22, 2, 18] Operation: 72-54=18 Exploring Operation: 54/2=27, Resulting Numbers: [22, 72, 27] Generated Node #0,2: 31:[22, 72, 27] Operation: 54/2=27 Exploring Operation: 54-22=32, Resulting Numbers: [72, 2, 32] Generated Node #0,3: 31:[72, 2, 32] Operation: 54-22=32 Exploring Operation: 54-2=52, Resulting Numbers: [22, 72, 52] Generated Node #0,4: 31:[22, 72, 52] Operation: 54-2=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[54, 22, 36], Operations: ['72/2=36'] Exploring Operation: 54-22=32, Resulting Numbers: [36, 32] Generated Node #0,0,0: 31:[36, 32] Operation: 54-22=32 Exploring Operation: 22+36=58, Resulting Numbers: [54, 58] Generated Node #0,0,1: 31:[54, 58] Operation: 22+36=58 Exploring Operation: 54-36=18, Resulting Numbers: [22, 18] Generated Node #0,0,2: 31:[22, 18] Operation: 54-36=18 Exploring Operation: 54+22=76, Resulting Numbers: [36, 76] Generated Node #0,0,3: 31:[36, 76] Operation: 54+22=76 Exploring Operation: 36-22=14, Resulting Numbers: [54, 14] Generated Node #0,0,4: 31:[54, 14] Operation: 36-22=14 Moving to Node #0,0,0 Current State: 31:[36, 32], Operations: ['72/2=36', '54-22=32'] Exploring Operation: 36*32=1152, Resulting Numbers: [1152] 1152,31 unequal: No Solution Exploring Operation: 36+32=68, Resulting Numbers: [68] 68,31 unequal: No Solution Exploring Operation: 36-32=4, Resulting Numbers: [4] 4,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[22, 18], Operations: ['72/2=36', '54-36=18'] Exploring Operation: 22*18=396, Resulting Numbers: [396] 396,31 unequal: No Solution Exploring Operation: 22+18=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,31 unequal: No Solution Moving to Node #0,0,4 Current State: 31:[54, 14], Operations: ['72/2=36', '36-22=14'] Exploring Operation: 54*14=756, Resulting Numbers: [756] 756,31 unequal: No Solution Exploring Operation: 54-14=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 54+14=68, Resulting Numbers: [68] 68,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[54, 58], Operations: ['72/2=36', '22+36=58'] Exploring Operation: 54+58=112, Resulting Numbers: [112] 112,31 unequal: No Solution Exploring Operation: 58-54=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 54*58=3132, Resulting Numbers: [3132] 3132,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[36, 76], Operations: ['72/2=36', '54+22=76'] Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 36+76=112, Resulting Numbers: [112] 112,31 unequal: No Solution Exploring Operation: 36*76=2736, Resulting Numbers: [2736] 2736,31 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 Current State: 31:[22, 2, 18], Operations: ['72-54=18'] Exploring Operation: 22+2=24, Resulting Numbers: [18, 24] Generated Node #0,1,0: 31:[18, 24] Operation: 22+2=24 Exploring Operation: 2+18=20, Resulting Numbers: [22, 20] Generated Node #0,1,1: 31:[22, 20] Operation: 2+18=20 Exploring Operation: 18-2=16, Resulting Numbers: [22, 16] Generated Node #0,1,2: 31:[22, 16] Operation: 18-2=16 Exploring Operation: 2*18=36, Resulting Numbers: [22, 36] Generated Node #0,1,3: 31:[22, 36] Operation: 2*18=36 Exploring Operation: 22-2=20, Resulting Numbers: [18, 20] Generated Node #0,1,4: 31:[18, 20] Operation: 22-2=20 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 31:[22, 36], Operations: ['72-54=18', '2*18=36'] Exploring Operation: 22+36=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 22*36=792, Resulting Numbers: [792] 792,31 unequal: No Solution No 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: 31:[18, 24], Operations: ['72-54=18', '22+2=24'] Exploring Operation: 18*24=432, Resulting Numbers: [432] 432,31 unequal: No Solution Exploring Operation: 18+24=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,31 unequal: No Solution No 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: 31:[22, 20], Operations: ['72-54=18', '2+18=20'] Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,31 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,31 unequal: No Solution No 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: 31:[22, 16], Operations: ['72-54=18', '18-2=16'] Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,31 unequal: No Solution Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,31 unequal: No Solution No 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: 31:[18, 20], Operations: ['72-54=18', '22-2=20'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 18*20=360, Resulting Numbers: [360] 360,31 unequal: No Solution Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,31 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: 31:[22, 72, 27], Operations: ['54/2=27'] Exploring Operation: 22+27=49, Resulting Numbers: [72, 49] Generated Node #0,2,0: 31:[72, 49] Operation: 22+27=49 Exploring Operation: 72-22=50, Resulting Numbers: [27, 50] Generated Node #0,2,1: 31:[27, 50] Operation: 72-22=50 Exploring Operation: 72-27=45, Resulting Numbers: [22, 45] Generated Node #0,2,2: 31:[22, 45] Operation: 72-27=45 Exploring Operation: 27-22=5, Resulting Numbers: [72, 5] Generated Node #0,2,3: 31:[72, 5] Operation: 27-22=5 Exploring Operation: 22+72=94, Resulting Numbers: [27, 94] Generated Node #0,2,4: 31:[27, 94] Operation: 22+72=94 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 31:[27, 50], Operations: ['54/2=27', '72-22=50'] Exploring Operation: 50-27=23, Resulting Numbers: [23] 23,31 unequal: No Solution Exploring Operation: 27+50=77, Resulting Numbers: [77] 77,31 unequal: No Solution Exploring Operation: 27*50=1350, Resulting Numbers: [1350] 1350,31 unequal: No Solution No 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: 31:[22, 45], Operations: ['54/2=27', '72-27=45'] Exploring Operation: 22*45=990, Resulting Numbers: [990] 990,31 unequal: No Solution Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,31 unequal: No Solution Exploring Operation: 22+45=67, Resulting Numbers: [67] 67,31 unequal: No Solution No 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: 31:[72, 49], Operations: ['54/2=27', '22+27=49'] Exploring Operation: 72-49=23, Resulting Numbers: [23] 23,31 unequal: No Solution Exploring Operation: 72*49=3528, Resulting Numbers: [3528] 3528,31 unequal: No Solution Exploring Operation: 72+49=121, Resulting Numbers: [121] 121,31 unequal: No Solution No 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: 31:[72, 5], Operations: ['54/2=27', '27-22=5'] Exploring Operation: 72*5=360, Resulting Numbers: [360] 360,31 unequal: No Solution Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,31 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,31 unequal: No Solution No 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: 31:[27, 94], Operations: ['54/2=27', '22+72=94'] Exploring Operation: 27*94=2538, Resulting Numbers: [2538] 2538,31 unequal: No Solution Exploring Operation: 94-27=67, Resulting Numbers: [67] 67,31 unequal: No Solution Exploring Operation: 27+94=121, Resulting Numbers: [121] 121,31 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: 31:[72, 2, 32], Operations: ['54-22=32'] Exploring Operation: 32-2=30, Resulting Numbers: [72, 30] Generated Node #0,3,0: 31:[72, 30] Operation: 32-2=30 Exploring Operation: 72/2=36, Resulting Numbers: [32, 36] Generated Node #0,3,1: 31:[32, 36] Operation: 72/2=36 Exploring Operation: 72-2=70, Resulting Numbers: [32, 70] Generated Node #0,3,2: 31:[32, 70] Operation: 72-2=70 Exploring Operation: 72-32=40, Resulting Numbers: [2, 40] Generated Node #0,3,3: 31:[2, 40] Operation: 72-32=40 Exploring Operation: 72+2=74, Resulting Numbers: [32, 74] Generated Node #0,3,4: 31:[32, 74] Operation: 72+2=74 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 31:[32, 36], Operations: ['54-22=32', '72/2=36'] Exploring Operation: 36-32=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 32*36=1152, Resulting Numbers: [1152] 1152,31 unequal: No Solution Exploring Operation: 32+36=68, Resulting Numbers: [68] 68,31 unequal: No Solution No 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: 31:[2, 40], Operations: ['54-22=32', '72-32=40'] Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,31 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,31 unequal: No Solution No 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: 31:[32, 70], Operations: ['54-22=32', '72-2=70'] Exploring Operation: 32+70=102, Resulting Numbers: [102] 102,31 unequal: No Solution Exploring Operation: 70-32=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 32*70=2240, Resulting Numbers: [2240] 2240,31 unequal: No Solution No 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: 31:[72, 30], Operations: ['54-22=32', '32-2=30'] Exploring Operation: 72*30=2160, Resulting Numbers: [2160] 2160,31 unequal: No Solution Exploring Operation: 72+30=102, Resulting Numbers: [102] 102,31 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,31 unequal: No Solution No 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: 31:[32, 74], Operations: ['54-22=32', '72+2=74'] Exploring Operation: 32*74=2368, Resulting Numbers: [2368] 2368,31 unequal: No Solution Exploring Operation: 74-32=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 32+74=106, Resulting Numbers: [106] 106,31 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: 31:[22, 72, 52], Operations: ['54-2=52'] Exploring Operation: 72-22=50, Resulting Numbers: [52, 50] Generated Node #0,4,0: 31:[52, 50] Operation: 72-22=50 Exploring Operation: 22+72=94, Resulting Numbers: [52, 94] Generated Node #0,4,1: 31:[52, 94] Operation: 22+72=94 Exploring Operation: 72-52=20, Resulting Numbers: [22, 20] Generated Node #0,4,2: 31:[22, 20] Operation: 72-52=20 Exploring Operation: 52-22=30, Resulting Numbers: [72, 30] Generated Node #0,4,3: 31:[72, 30] Operation: 52-22=30 Exploring Operation: 22+52=74, Resulting Numbers: [72, 74] Generated Node #0,4,4: 31:[72, 74] Operation: 22+52=74 Moving to Node #0,4,2 Current State: 31:[22, 20], Operations: ['54-2=52', '72-52=20'] Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,31 unequal: No Solution Moving to Node #0,4,0 Current State: 31:[52, 50], Operations: ['54-2=52', '72-22=50'] Exploring Operation: 52+50=102, Resulting Numbers: [102] 102,31 unequal: No Solution Exploring Operation: 52*50=2600, Resulting Numbers: [2600] 2600,31 unequal: No Solution Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,4,3 Current State: 31:[72, 30], Operations: ['54-2=52', '52-22=30'] Exploring Operation: 72+30=102, Resulting Numbers: [102] 102,31 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 72*30=2160, Resulting Numbers: [2160] 2160,31 unequal: No Solution Moving to Node #0,4,1 Current State: 31:[52, 94], Operations: ['54-2=52', '22+72=94'] Exploring Operation: 94-52=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 52+94=146, Resulting Numbers: [146] 146,31 unequal: No Solution Exploring Operation: 52*94=4888, Resulting Numbers: [4888] 4888,31 unequal: No Solution Moving to Node #0,4,4 Current State: 31:[72, 74], Operations: ['54-2=52', '22+52=74'] Exploring Operation: 72+74=146, Resulting Numbers: [146] 146,31 unequal: No Solution Exploring Operation: 74-72=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 72*74=5328, Resulting Numbers: [5328] 5328,31 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
[ 41, 21, 82, 86 ]
66
[ "41+21=62", "86-82=4", "62+4=66" ]
Current State: 66:[41, 21, 82, 86], Operations: [] Exploring Operation: 41+21=62, Resulting Numbers: [82, 86, 62] Generated Node #2: [82, 86, 62] from Operation: 41+21=62 Current State: 66:[82, 86, 62], Operations: ['41+21=62'] Exploring Operation: 86-82=4, Resulting Numbers: [62, 4] Generated Node #3: [62, 4] from Operation: 86-82=4 Current State: 66:[62, 4], Operations: ['41+21=62', '86-82=4'] Exploring Operation: 62+4=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[41, 21, 82, 86], Operations: [] Exploring Operation: 82/41=2, Resulting Numbers: [21, 86, 2] Generated Node #0,0: 66:[21, 86, 2] Operation: 82/41=2 Exploring Operation: 86-82=4, Resulting Numbers: [41, 21, 4] Generated Node #0,1: 66:[41, 21, 4] Operation: 86-82=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[41, 21, 4], Operations: ['86-82=4'] Exploring Operation: 41+21=62, Resulting Numbers: [4, 62] Generated Node #0,1,0: 66:[4, 62] Operation: 41+21=62 Exploring Operation: 41-21=20, Resulting Numbers: [4, 20] Generated Node #0,1,1: 66:[4, 20] Operation: 41-21=20 Moving to Node #0,1,1 Current State: 66:[4, 20], Operations: ['86-82=4', '41-21=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,66 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,66 unequal: No Solution Moving to Node #0,1,0 Current State: 66:[4, 62], Operations: ['86-82=4', '41+21=62'] Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,66 unequal: No Solution Exploring Operation: 4+62=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[41, 21, 82, 86], Operations: [] Exploring Operation: 86-82=4, Resulting Numbers: [41, 21, 4] Generated Node #0,1: 66:[41, 21, 4] Operation: 86-82=4 Moving to Node #0,1 Current State: 66:[41, 21, 4], Operations: ['86-82=4'] Exploring Operation: 41+21=62, Resulting Numbers: [4, 62] Generated Node #0,1,0: 66:[4, 62] Operation: 41+21=62 Moving to Node #0,1,0 Current State: 66:[4, 62], Operations: ['86-82=4', '41+21=62'] Exploring Operation: 4+62=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 98, 67, 18, 90 ]
33
[ "98+67=165", "90/18=5", "165/5=33" ]
Current State: 33:[98, 67, 18, 90], Operations: [] Exploring Operation: 98+67=165, Resulting Numbers: [18, 90, 165] Generated Node #2: [18, 90, 165] from Operation: 98+67=165 Current State: 33:[18, 90, 165], Operations: ['98+67=165'] Exploring Operation: 90/18=5, Resulting Numbers: [165, 5] Generated Node #3: [165, 5] from Operation: 90/18=5 Current State: 33:[165, 5], Operations: ['98+67=165', '90/18=5'] Exploring Operation: 165/5=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[98, 67, 18, 90], Operations: [] Exploring Operation: 98-90=8, Resulting Numbers: [67, 18, 8] Generated Node #0,0: 33:[67, 18, 8] Operation: 98-90=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[67, 18, 8], Operations: ['98-90=8'] Exploring Operation: 67-18=49, Resulting Numbers: [8, 49] Generated Node #0,0,0: 33:[8, 49] Operation: 67-18=49 Moving to Node #0,0,0 Current State: 33:[8, 49], Operations: ['98-90=8', '67-18=49'] Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 71, 59, 69, 98 ]
41
[ "71-59=12", "98-69=29", "12+29=41" ]
Current State: 41:[71, 59, 69, 98], Operations: [] Exploring Operation: 71-59=12, Resulting Numbers: [69, 98, 12] Generated Node #2: [69, 98, 12] from Operation: 71-59=12 Current State: 41:[69, 98, 12], Operations: ['71-59=12'] Exploring Operation: 98-69=29, Resulting Numbers: [12, 29] Generated Node #3: [12, 29] from Operation: 98-69=29 Current State: 41:[12, 29], Operations: ['71-59=12', '98-69=29'] Exploring Operation: 12+29=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[71, 59, 69, 98], Operations: [] Exploring Operation: 71-69=2, Resulting Numbers: [59, 98, 2] Generated Node #0,0: 41:[59, 98, 2] Operation: 71-69=2 Exploring Operation: 98-71=27, Resulting Numbers: [59, 69, 27] Generated Node #0,1: 41:[59, 69, 27] Operation: 98-71=27 Exploring Operation: 98-59=39, Resulting Numbers: [71, 69, 39] Generated Node #0,2: 41:[71, 69, 39] Operation: 98-59=39 Exploring Operation: 98-69=29, Resulting Numbers: [71, 59, 29] Generated Node #0,3: 41:[71, 59, 29] Operation: 98-69=29 Exploring Operation: 71-59=12, Resulting Numbers: [69, 98, 12] Generated Node #0,4: 41:[69, 98, 12] Operation: 71-59=12 Moving to Node #0,1 Current State: 41:[59, 69, 27], Operations: ['98-71=27'] Exploring Operation: 69+27=96, Resulting Numbers: [59, 96] Generated Node #0,1,0: 41:[59, 96] Operation: 69+27=96 Exploring Operation: 59+27=86, Resulting Numbers: [69, 86] Generated Node #0,1,1: 41:[69, 86] Operation: 59+27=86 Exploring Operation: 69-27=42, Resulting Numbers: [59, 42] Generated Node #0,1,2: 41:[59, 42] Operation: 69-27=42 Exploring Operation: 59-27=32, Resulting Numbers: [69, 32] Generated Node #0,1,3: 41:[69, 32] Operation: 59-27=32 Exploring Operation: 69-59=10, Resulting Numbers: [27, 10] Generated Node #0,1,4: 41:[27, 10] Operation: 69-59=10 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 41:[59, 42], Operations: ['98-71=27', '69-27=42'] Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,41 unequal: No Solution Exploring Operation: 59*42=2478, Resulting Numbers: [2478] 2478,41 unequal: No Solution Exploring Operation: 59+42=101, Resulting Numbers: [101] 101,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 41:[69, 32], Operations: ['98-71=27', '59-27=32'] Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,41 unequal: No Solution Exploring Operation: 69+32=101, Resulting Numbers: [101] 101,41 unequal: No Solution Exploring Operation: 69*32=2208, Resulting Numbers: [2208] 2208,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 41:[27, 10], Operations: ['98-71=27', '69-59=10'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,41 unequal: No Solution Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,41 unequal: No Solution Exploring Operation: 27*10=270, Resulting Numbers: [270] 270,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[59, 96], Operations: ['98-71=27', '69+27=96'] Exploring Operation: 59+96=155, Resulting Numbers: [155] 155,41 unequal: No Solution Exploring Operation: 96-59=37, Resulting Numbers: [37] 37,41 unequal: No Solution Exploring Operation: 59*96=5664, Resulting Numbers: [5664] 5664,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[69, 86], Operations: ['98-71=27', '59+27=86'] Exploring Operation: 69*86=5934, Resulting Numbers: [5934] 5934,41 unequal: No Solution Exploring Operation: 86-69=17, Resulting Numbers: [17] 17,41 unequal: No Solution Exploring Operation: 69+86=155, Resulting Numbers: [155] 155,41 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: 41:[71, 59, 29], Operations: ['98-69=29'] Exploring Operation: 71-29=42, Resulting Numbers: [59, 42] Generated Node #0,3,0: 41:[59, 42] Operation: 71-29=42 Exploring Operation: 59+29=88, Resulting Numbers: [71, 88] Generated Node #0,3,1: 41:[71, 88] Operation: 59+29=88 Exploring Operation: 59-29=30, Resulting Numbers: [71, 30] Generated Node #0,3,2: 41:[71, 30] Operation: 59-29=30 Exploring Operation: 71+29=100, Resulting Numbers: [59, 100] Generated Node #0,3,3: 41:[59, 100] Operation: 71+29=100 Exploring Operation: 71-59=12, Resulting Numbers: [29, 12] Generated Node #0,3,4: 41:[29, 12] Operation: 71-59=12 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 41:[59, 42], Operations: ['98-69=29', '71-29=42'] Exploring Operation: 59+42=101, Resulting Numbers: [101] 101,41 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,41 unequal: No Solution Exploring Operation: 59*42=2478, Resulting Numbers: [2478] 2478,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 41:[71, 30], Operations: ['98-69=29', '59-29=30'] Exploring Operation: 71+30=101, Resulting Numbers: [101] 101,41 unequal: No Solution Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[71, 59, 69, 98], Operations: [] Exploring Operation: 98-69=29, Resulting Numbers: [71, 59, 29] Generated Node #0,3: 41:[71, 59, 29] Operation: 98-69=29 Moving to Node #0,3 Current State: 41:[71, 59, 29], Operations: ['98-69=29'] Exploring Operation: 59-29=30, Resulting Numbers: [71, 30] Generated Node #0,3,2: 41:[71, 30] Operation: 59-29=30 Moving to Node #0,3,2 Current State: 41:[71, 30], Operations: ['98-69=29', '59-29=30'] Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_5
mult_heuristic
[ 12, 36, 51, 41 ]
84
[ "51-41=10", "12*10=120", "120-36=84" ]
Current State: 84:[12, 36, 51, 41], Operations: [] Exploring Operation: 51-41=10, Resulting Numbers: [12, 36, 10] Generated Node #2: [12, 36, 10] from Operation: 51-41=10 Current State: 84:[12, 36, 10], Operations: ['51-41=10'] Exploring Operation: 12*10=120, Resulting Numbers: [36, 120] Generated Node #3: [36, 120] from Operation: 12*10=120 Current State: 84:[36, 120], Operations: ['51-41=10', '12*10=120'] Exploring Operation: 120-36=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[12, 36, 51, 41], Operations: [] Exploring Operation: 51-36=15, Resulting Numbers: [12, 41, 15] Generated Node #0,0: 84:[12, 41, 15] Operation: 51-36=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[12, 41, 15], Operations: ['51-36=15'] Exploring Operation: 15-12=3, Resulting Numbers: [41, 3] Generated Node #0,0,0: 84:[41, 3] Operation: 15-12=3 Moving to Node #0,0,0 Current State: 84:[41, 3], Operations: ['51-36=15', '15-12=3'] Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,84 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
[ 25, 19, 38, 54 ]
58
[ "54-25=29", "38/19=2", "29*2=58" ]
Current State: 58:[25, 19, 38, 54], Operations: [] Exploring Operation: 54-25=29, Resulting Numbers: [19, 38, 29] Generated Node #2: [19, 38, 29] from Operation: 54-25=29 Current State: 58:[19, 38, 29], Operations: ['54-25=29'] Exploring Operation: 38/19=2, Resulting Numbers: [29, 2] Generated Node #3: [29, 2] from Operation: 38/19=2 Current State: 58:[29, 2], Operations: ['54-25=29', '38/19=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[25, 19, 38, 54], Operations: [] Exploring Operation: 38/19=2, Resulting Numbers: [25, 54, 2] Generated Node #0,0: 58:[25, 54, 2] Operation: 38/19=2 Exploring Operation: 19+38=57, Resulting Numbers: [25, 54, 57] Generated Node #0,1: 58:[25, 54, 57] Operation: 19+38=57 Exploring Operation: 25+38=63, Resulting Numbers: [19, 54, 63] Generated Node #0,2: 58:[19, 54, 63] Operation: 25+38=63 Exploring Operation: 25-19=6, Resulting Numbers: [38, 54, 6] Generated Node #0,3: 58:[38, 54, 6] Operation: 25-19=6 Exploring Operation: 38-19=19, Resulting Numbers: [25, 54, 19] Generated Node #0,4: 58:[25, 54, 19] Operation: 38-19=19 Moving to Node #0,0 Current State: 58:[25, 54, 2], Operations: ['38/19=2'] Exploring Operation: 54/2=27, Resulting Numbers: [25, 27] Generated Node #0,0,0: 58:[25, 27] Operation: 54/2=27 Exploring Operation: 54+2=56, Resulting Numbers: [25, 56] Generated Node #0,0,1: 58:[25, 56] Operation: 54+2=56 Exploring Operation: 25+2=27, Resulting Numbers: [54, 27] Generated Node #0,0,2: 58:[54, 27] Operation: 25+2=27 Exploring Operation: 54-25=29, Resulting Numbers: [2, 29] Generated Node #0,0,3: 58:[2, 29] Operation: 54-25=29 Exploring Operation: 25-2=23, Resulting Numbers: [54, 23] Generated Node #0,0,4: 58:[54, 23] Operation: 25-2=23 Moving to Node #0,1 Current State: 58:[25, 54, 57], Operations: ['19+38=57'] Exploring Operation: 25+57=82, Resulting Numbers: [54, 82] Generated Node #0,1,0: 58:[54, 82] Operation: 25+57=82 Exploring Operation: 57-25=32, Resulting Numbers: [54, 32] Generated Node #0,1,1: 58:[54, 32] Operation: 57-25=32 Exploring Operation: 25+54=79, Resulting Numbers: [57, 79] Generated Node #0,1,2: 58:[57, 79] Operation: 25+54=79 Exploring Operation: 54-25=29, Resulting Numbers: [57, 29] Generated Node #0,1,3: 58:[57, 29] Operation: 54-25=29 Exploring Operation: 57-54=3, Resulting Numbers: [25, 3] Generated Node #0,1,4: 58:[25, 3] Operation: 57-54=3 Moving to Node #0,3 Current State: 58:[38, 54, 6], Operations: ['25-19=6'] Exploring Operation: 54+6=60, Resulting Numbers: [38, 60] Generated Node #0,3,0: 58:[38, 60] Operation: 54+6=60 Exploring Operation: 54/6=9, Resulting Numbers: [38, 9] Generated Node #0,3,1: 58:[38, 9] Operation: 54/6=9 Exploring Operation: 38+6=44, Resulting Numbers: [54, 44] Generated Node #0,3,2: 58:[54, 44] Operation: 38+6=44 Exploring Operation: 54-38=16, Resulting Numbers: [6, 16] Generated Node #0,3,3: 58:[6, 16] Operation: 54-38=16 Exploring Operation: 38-6=32, Resulting Numbers: [54, 32] Generated Node #0,3,4: 58:[54, 32] Operation: 38-6=32 Moving to Node #0,4 Current State: 58:[25, 54, 19], Operations: ['38-19=19'] Exploring Operation: 54-19=35, Resulting Numbers: [25, 35] Generated Node #0,4,0: 58:[25, 35] Operation: 54-19=35 Exploring Operation: 25+19=44, Resulting Numbers: [54, 44] Generated Node #0,4,1: 58:[54, 44] Operation: 25+19=44 Exploring Operation: 54+19=73, Resulting Numbers: [25, 73] Generated Node #0,4,2: 58:[25, 73] Operation: 54+19=73 Exploring Operation: 25-19=6, Resulting Numbers: [54, 6] Generated Node #0,4,3: 58:[54, 6] Operation: 25-19=6 Exploring Operation: 54-25=29, Resulting Numbers: [19, 29] Generated Node #0,4,4: 58:[19, 29] Operation: 54-25=29 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 58:[54, 6], Operations: ['38-19=19', '25-19=6'] Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,58 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,58 unequal: No Solution Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,58 unequal: No Solution Exploring Operation: 54*6=324, Resulting Numbers: [324] 324,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 58:[25, 35], Operations: ['38-19=19', '54-19=35'] Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,58 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,58 unequal: No Solution Exploring Operation: 25*35=875, Resulting Numbers: [875] 875,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 58:[19, 29], Operations: ['38-19=19', '54-25=29'] Exploring Operation: 19*29=551, Resulting Numbers: [551] 551,58 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,58 unequal: No Solution Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 58:[54, 44], Operations: ['38-19=19', '25+19=44'] Exploring Operation: 54*44=2376, Resulting Numbers: [2376] 2376,58 unequal: No Solution Exploring Operation: 54+44=98, Resulting Numbers: [98] 98,58 unequal: No Solution Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 58:[25, 73], Operations: ['38-19=19', '54+19=73'] Exploring Operation: 25*73=1825, Resulting Numbers: [1825] 1825,58 unequal: No Solution Exploring Operation: 73-25=48, Resulting Numbers: [48] 48,58 unequal: No Solution Exploring Operation: 25+73=98, Resulting Numbers: [98] 98,58 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: 58:[19, 54, 63], Operations: ['25+38=63'] Exploring Operation: 19+54=73, Resulting Numbers: [63, 73] Generated Node #0,2,0: 58:[63, 73] Operation: 19+54=73 Exploring Operation: 54-19=35, Resulting Numbers: [63, 35] Generated Node #0,2,1: 58:[63, 35] Operation: 54-19=35 Exploring Operation: 63-54=9, Resulting Numbers: [19, 9] Generated Node #0,2,2: 58:[19, 9] Operation: 63-54=9 Exploring Operation: 19+63=82, Resulting Numbers: [54, 82] Generated Node #0,2,3: 58:[54, 82] Operation: 19+63=82 Exploring Operation: 63-19=44, Resulting Numbers: [54, 44] Generated Node #0,2,4: 58:[54, 44] Operation: 63-19=44 Moving to Node #0,0,3 Current State: 58:[2, 29], Operations: ['38/19=2', '54-25=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[25, 19, 38, 54], Operations: [] Exploring Operation: 38/19=2, Resulting Numbers: [25, 54, 2] Generated Node #0,0: 58:[25, 54, 2] Operation: 38/19=2 Moving to Node #0,0 Current State: 58:[25, 54, 2], Operations: ['38/19=2'] Exploring Operation: 54-25=29, Resulting Numbers: [2, 29] Generated Node #0,0,3: 58:[2, 29] Operation: 54-25=29 Moving to Node #0,0,3 Current State: 58:[2, 29], Operations: ['38/19=2', '54-25=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
0.955729
hs_5
mult_heuristic
[ 46, 38, 69, 15 ]
92
[ "46-38=8", "69+15=84", "8+84=92" ]
Current State: 92:[46, 38, 69, 15], Operations: [] Exploring Operation: 46-38=8, Resulting Numbers: [69, 15, 8] Generated Node #2: [69, 15, 8] from Operation: 46-38=8 Current State: 92:[69, 15, 8], Operations: ['46-38=8'] Exploring Operation: 69+15=84, Resulting Numbers: [8, 84] Generated Node #3: [8, 84] from Operation: 69+15=84 Current State: 92:[8, 84], Operations: ['46-38=8', '69+15=84'] Exploring Operation: 8+84=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[46, 38, 69, 15], Operations: [] Exploring Operation: 69-38=31, Resulting Numbers: [46, 15, 31] Generated Node #0,0: 92:[46, 15, 31] Operation: 69-38=31 Exploring Operation: 69+15=84, Resulting Numbers: [46, 38, 84] Generated Node #0,1: 92:[46, 38, 84] Operation: 69+15=84 Exploring Operation: 69-15=54, Resulting Numbers: [46, 38, 54] Generated Node #0,2: 92:[46, 38, 54] Operation: 69-15=54 Exploring Operation: 69-46=23, Resulting Numbers: [38, 15, 23] Generated Node #0,3: 92:[38, 15, 23] Operation: 69-46=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[46, 15, 31], Operations: ['69-38=31'] Exploring Operation: 15+31=46, Resulting Numbers: [46, 46] Generated Node #0,0,0: 92:[46, 46] Operation: 15+31=46 Exploring Operation: 31-15=16, Resulting Numbers: [46, 16] Generated Node #0,0,1: 92:[46, 16] Operation: 31-15=16 Exploring Operation: 46-31=15, Resulting Numbers: [15, 15] Generated Node #0,0,2: 92:[15, 15] Operation: 46-31=15 Exploring Operation: 46-15=31, Resulting Numbers: [31, 31] Generated Node #0,0,3: 92:[31, 31] Operation: 46-15=31 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[46, 46], Operations: ['69-38=31', '15+31=46'] Exploring Operation: 46/46=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 46-46=0, Resulting Numbers: [0] 0,92 unequal: No Solution Exploring Operation: 46+46=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[46, 38, 69, 15], Operations: [] Exploring Operation: 69-38=31, Resulting Numbers: [46, 15, 31] Generated Node #0,0: 92:[46, 15, 31] Operation: 69-38=31 Moving to Node #0,0 Current State: 92:[46, 15, 31], Operations: ['69-38=31'] Exploring Operation: 15+31=46, Resulting Numbers: [46, 46] Generated Node #0,0,0: 92:[46, 46] Operation: 15+31=46 Moving to Node #0,0,0 Current State: 92:[46, 46], Operations: ['69-38=31', '15+31=46'] Exploring Operation: 46+46=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 6, 25, 49, 56 ]
88
[ "49-25=24", "6*24=144", "144-56=88" ]
Current State: 88:[6, 25, 49, 56], Operations: [] Exploring Operation: 49-25=24, Resulting Numbers: [6, 56, 24] Generated Node #2: [6, 56, 24] from Operation: 49-25=24 Current State: 88:[6, 56, 24], Operations: ['49-25=24'] Exploring Operation: 6*24=144, Resulting Numbers: [56, 144] Generated Node #3: [56, 144] from Operation: 6*24=144 Current State: 88:[56, 144], Operations: ['49-25=24', '6*24=144'] Exploring Operation: 144-56=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[6, 25, 49, 56], Operations: [] Exploring Operation: 56-49=7, Resulting Numbers: [6, 25, 7] Generated Node #0,0: 88:[6, 25, 7] Operation: 56-49=7 Exploring Operation: 25+56=81, Resulting Numbers: [6, 49, 81] Generated Node #0,1: 88:[6, 49, 81] Operation: 25+56=81 Exploring Operation: 56-6=50, Resulting Numbers: [25, 49, 50] Generated Node #0,2: 88:[25, 49, 50] Operation: 56-6=50 Moving to Node #0,0 Current State: 88:[6, 25, 7], Operations: ['56-49=7'] Exploring Operation: 7-6=1, Resulting Numbers: [25, 1] Generated Node #0,0,0: 88:[25, 1] Operation: 7-6=1 Exploring Operation: 25-6=19, Resulting Numbers: [7, 19] Generated Node #0,0,1: 88:[7, 19] Operation: 25-6=19 Exploring Operation: 6+7=13, Resulting Numbers: [25, 13] Generated Node #0,0,2: 88:[25, 13] Operation: 6+7=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[25, 1], Operations: ['56-49=7', '7-6=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,88 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 88:[7, 19], Operations: ['56-49=7', '25-6=19'] Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 7*19=133, Resulting Numbers: [133] 133,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 88:[25, 13], Operations: ['56-49=7', '6+7=13'] Exploring Operation: 25*13=325, Resulting Numbers: [325] 325,88 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 25+13=38, Resulting Numbers: [38] 38,88 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: 88:[6, 49, 81], Operations: ['25+56=81'] Exploring Operation: 49-6=43, Resulting Numbers: [81, 43] Generated Node #0,1,0: 88:[81, 43] Operation: 49-6=43 Exploring Operation: 6+81=87, Resulting Numbers: [49, 87] Generated Node #0,1,1: 88:[49, 87] Operation: 6+81=87 Exploring Operation: 81-49=32, Resulting Numbers: [6, 32] Generated Node #0,1,2: 88:[6, 32] Operation: 81-49=32 Moving to Node #0,2 Current State: 88:[25, 49, 50], Operations: ['56-6=50'] Exploring Operation: 50-49=1, Resulting Numbers: [25, 1] Generated Node #0,2,0: 88:[25, 1] Operation: 50-49=1 Exploring Operation: 49-25=24, Resulting Numbers: [50, 24] Generated Node #0,2,1: 88:[50, 24] Operation: 49-25=24 Exploring Operation: 50/25=2, Resulting Numbers: [49, 2] Generated Node #0,2,2: 88:[49, 2] Operation: 50/25=2 Moving to Node #0,2,0 Current State: 88:[25, 1], Operations: ['56-6=50', '50-49=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,88 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[49, 2], Operations: ['56-6=50', '50/25=2'] Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,88 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,88 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[49, 87], Operations: ['25+56=81', '6+81=87'] Exploring Operation: 87-49=38, Resulting Numbers: [38] 38,88 unequal: No Solution Exploring Operation: 49+87=136, Resulting Numbers: [136] 136,88 unequal: No Solution Exploring Operation: 49*87=4263, Resulting Numbers: [4263] 4263,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[50, 24], Operations: ['56-6=50', '49-25=24'] Exploring Operation: 50*24=1200, Resulting Numbers: [1200] 1200,88 unequal: No Solution Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 50+24=74, Resulting Numbers: [74] 74,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[81, 43], Operations: ['25+56=81', '49-6=43'] Exploring Operation: 81*43=3483, Resulting Numbers: [3483] 3483,88 unequal: No Solution Exploring Operation: 81+43=124, Resulting Numbers: [124] 124,88 unequal: No Solution Exploring Operation: 81-43=38, Resulting Numbers: [38] 38,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[6, 32], Operations: ['25+56=81', '81-49=32'] Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 6+32=38, Resulting Numbers: [38] 38,88 unequal: No Solution Exploring Operation: 6*32=192, Resulting Numbers: [192] 192,88 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 54, 7, 4, 37 ]
96
[ "54+7=61", "61-37=24", "4*24=96" ]
Current State: 96:[54, 7, 4, 37], Operations: [] Exploring Operation: 54+7=61, Resulting Numbers: [4, 37, 61] Generated Node #2: [4, 37, 61] from Operation: 54+7=61 Current State: 96:[4, 37, 61], Operations: ['54+7=61'] Exploring Operation: 61-37=24, Resulting Numbers: [4, 24] Generated Node #3: [4, 24] from Operation: 61-37=24 Current State: 96:[4, 24], Operations: ['54+7=61', '61-37=24'] Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[54, 7, 4, 37], Operations: [] Exploring Operation: 54-37=17, Resulting Numbers: [7, 4, 17] Generated Node #0,0: 96:[7, 4, 17] Operation: 54-37=17 Exploring Operation: 54-7=47, Resulting Numbers: [4, 37, 47] Generated Node #0,1: 96:[4, 37, 47] Operation: 54-7=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[7, 4, 17], Operations: ['54-37=17'] Exploring Operation: 7-4=3, Resulting Numbers: [17, 3] Generated Node #0,0,0: 96:[17, 3] Operation: 7-4=3 Exploring Operation: 7+17=24, Resulting Numbers: [4, 24] Generated Node #0,0,1: 96:[4, 24] Operation: 7+17=24 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 96:[4, 24], Operations: ['54-37=17', '7+17=24'] Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[54, 7, 4, 37], Operations: [] Exploring Operation: 54-37=17, Resulting Numbers: [7, 4, 17] Generated Node #0,0: 96:[7, 4, 17] Operation: 54-37=17 Moving to Node #0,0 Current State: 96:[7, 4, 17], Operations: ['54-37=17'] Exploring Operation: 7+17=24, Resulting Numbers: [4, 24] Generated Node #0,0,1: 96:[4, 24] Operation: 7+17=24 Moving to Node #0,0,1 Current State: 96:[4, 24], Operations: ['54-37=17', '7+17=24'] Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 26, 67, 81, 92 ]
82
[ "26+67=93", "92-81=11", "93-11=82" ]
Current State: 82:[26, 67, 81, 92], Operations: [] Exploring Operation: 26+67=93, Resulting Numbers: [81, 92, 93] Generated Node #2: [81, 92, 93] from Operation: 26+67=93 Current State: 82:[81, 92, 93], Operations: ['26+67=93'] Exploring Operation: 92-81=11, Resulting Numbers: [93, 11] Generated Node #3: [93, 11] from Operation: 92-81=11 Current State: 82:[93, 11], Operations: ['26+67=93', '92-81=11'] Exploring Operation: 93-11=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[26, 67, 81, 92], Operations: [] Exploring Operation: 67-26=41, Resulting Numbers: [81, 92, 41] Generated Node #0,0: 82:[81, 92, 41] Operation: 67-26=41 Exploring Operation: 26+67=93, Resulting Numbers: [81, 92, 93] Generated Node #0,1: 82:[81, 92, 93] Operation: 26+67=93 Exploring Operation: 92-67=25, Resulting Numbers: [26, 81, 25] Generated Node #0,2: 82:[26, 81, 25] Operation: 92-67=25 Exploring Operation: 81-67=14, Resulting Numbers: [26, 92, 14] Generated Node #0,3: 82:[26, 92, 14] Operation: 81-67=14 Exploring Operation: 92-26=66, Resulting Numbers: [67, 81, 66] Generated Node #0,4: 82:[67, 81, 66] Operation: 92-26=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[81, 92, 41], Operations: ['67-26=41'] Exploring Operation: 92+41=133, Resulting Numbers: [81, 133] Generated Node #0,0,0: 82:[81, 133] Operation: 92+41=133 Exploring Operation: 92-81=11, Resulting Numbers: [41, 11] Generated Node #0,0,1: 82:[41, 11] Operation: 92-81=11 Exploring Operation: 81+41=122, Resulting Numbers: [92, 122] Generated Node #0,0,2: 82:[92, 122] Operation: 81+41=122 Exploring Operation: 92-41=51, Resulting Numbers: [81, 51] Generated Node #0,0,3: 82:[81, 51] Operation: 92-41=51 Exploring Operation: 81-41=40, Resulting Numbers: [92, 40] Generated Node #0,0,4: 82:[92, 40] Operation: 81-41=40 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[41, 11], Operations: ['67-26=41', '92-81=11'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 41+11=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 41*11=451, Resulting Numbers: [451] 451,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 82:[81, 51], Operations: ['67-26=41', '92-41=51'] Exploring Operation: 81*51=4131, Resulting Numbers: [4131] 4131,82 unequal: No Solution Exploring Operation: 81+51=132, Resulting Numbers: [132] 132,82 unequal: No Solution Exploring Operation: 81-51=30, Resulting Numbers: [30] 30,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 82:[92, 40], Operations: ['67-26=41', '81-41=40'] Exploring Operation: 92+40=132, Resulting Numbers: [132] 132,82 unequal: No Solution Exploring Operation: 92-40=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 92*40=3680, Resulting Numbers: [3680] 3680,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[92, 122], Operations: ['67-26=41', '81+41=122'] Exploring Operation: 92*122=11224, Resulting Numbers: [11224] 11224,82 unequal: No Solution Exploring Operation: 92+122=214, Resulting Numbers: [214] 214,82 unequal: No Solution Exploring Operation: 122-92=30, Resulting Numbers: [30] 30,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[81, 133], Operations: ['67-26=41', '92+41=133'] Exploring Operation: 81*133=10773, Resulting Numbers: [10773] 10773,82 unequal: No Solution Exploring Operation: 133-81=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 81+133=214, Resulting Numbers: [214] 214,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[81, 92, 93], Operations: ['26+67=93'] Exploring Operation: 81+92=173, Resulting Numbers: [93, 173] Generated Node #0,1,0: 82:[93, 173] Operation: 81+92=173 Exploring Operation: 93-92=1, Resulting Numbers: [81, 1] Generated Node #0,1,1: 82:[81, 1] Operation: 93-92=1 Exploring Operation: 92-81=11, Resulting Numbers: [93, 11] Generated Node #0,1,2: 82:[93, 11] Operation: 92-81=11 Exploring Operation: 93-81=12, Resulting Numbers: [92, 12] Generated Node #0,1,3: 82:[92, 12] Operation: 93-81=12 Exploring Operation: 81+93=174, Resulting Numbers: [92, 174] Generated Node #0,1,4: 82:[92, 174] Operation: 81+93=174 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[81, 1], Operations: ['26+67=93', '93-92=1'] Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,82 unequal: No Solution Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,82 unequal: No Solution Exploring Operation: 81+1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[26, 67, 81, 92], Operations: [] Exploring Operation: 26+67=93, Resulting Numbers: [81, 92, 93] Generated Node #0,1: 82:[81, 92, 93] Operation: 26+67=93 Moving to Node #0,1 Current State: 82:[81, 92, 93], Operations: ['26+67=93'] Exploring Operation: 93-92=1, Resulting Numbers: [81, 1] Generated Node #0,1,1: 82:[81, 1] Operation: 93-92=1 Moving to Node #0,1,1 Current State: 82:[81, 1], Operations: ['26+67=93', '93-92=1'] Exploring Operation: 81+1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_5
mult_heuristic
[ 42, 3, 84, 62 ]
68
[ "42/3=14", "84/14=6", "62+6=68" ]
Current State: 68:[42, 3, 84, 62], Operations: [] Exploring Operation: 42/3=14, Resulting Numbers: [84, 62, 14] Generated Node #2: [84, 62, 14] from Operation: 42/3=14 Current State: 68:[84, 62, 14], Operations: ['42/3=14'] Exploring Operation: 84/14=6, Resulting Numbers: [62, 6] Generated Node #3: [62, 6] from Operation: 84/14=6 Current State: 68:[62, 6], Operations: ['42/3=14', '84/14=6'] Exploring Operation: 62+6=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[42, 3, 84, 62], Operations: [] Exploring Operation: 84/42=2, Resulting Numbers: [3, 62, 2] Generated Node #0,0: 68:[3, 62, 2] Operation: 84/42=2 Exploring Operation: 84-62=22, Resulting Numbers: [42, 3, 22] Generated Node #0,1: 68:[42, 3, 22] Operation: 84-62=22 Moving to Node #0,0 Current State: 68:[3, 62, 2], Operations: ['84/42=2'] Exploring Operation: 3+62=65, Resulting Numbers: [2, 65] Generated Node #0,0,0: 68:[2, 65] Operation: 3+62=65 Exploring Operation: 62/2=31, Resulting Numbers: [3, 31] Generated Node #0,0,1: 68:[3, 31] Operation: 62/2=31 Moving to Node #0,1 Current State: 68:[42, 3, 22], Operations: ['84-62=22'] Exploring Operation: 42+22=64, Resulting Numbers: [3, 64] Generated Node #0,1,0: 68:[3, 64] Operation: 42+22=64 Exploring Operation: 42-22=20, Resulting Numbers: [3, 20] Generated Node #0,1,1: 68:[3, 20] Operation: 42-22=20 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 68:[3, 20], Operations: ['84-62=22', '42-22=20'] Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,68 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 68:[3, 64], Operations: ['84-62=22', '42+22=64'] Exploring Operation: 3+64=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 64-3=61, Resulting Numbers: [61] 61,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 68:[2, 65], Operations: ['84/42=2', '3+62=65'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,68 unequal: No Solution Exploring Operation: 2+65=67, Resulting Numbers: [67] 67,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[3, 31], Operations: ['84/42=2', '62/2=31'] Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,68 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,68 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 11, 23, 51, 23 ]
55
[ "51-23=28", "28-23=5", "11*5=55" ]
Current State: 55:[11, 23, 51, 23], Operations: [] Exploring Operation: 51-23=28, Resulting Numbers: [11, 28] Generated Node #2: [11, 28] from Operation: 51-23=28 Current State: 55:[11, 28], Operations: ['51-23=28'] Exploring Operation: 28-23=5, Resulting Numbers: [11, 5] Generated Node #3: [11, 5] from Operation: 28-23=5 Current State: 55:[11, 5], Operations: ['51-23=28', '28-23=5'] Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[11, 23, 51, 23], Operations: [] Exploring Operation: 23+23=46, Resulting Numbers: [11, 51, 46] Generated Node #0,0: 55:[11, 51, 46] Operation: 23+23=46 Exploring Operation: 23-11=12, Resulting Numbers: [23, 51, 12] Generated Node #0,1: 55:[23, 51, 12] Operation: 23-11=12 Exploring Operation: 23-11=12, Resulting Numbers: [51, 23, 12] Generated Node #0,2: 55:[51, 23, 12] Operation: 23-11=12 Exploring Operation: 23-23=0, Resulting Numbers: [11, 51, 0] Generated Node #0,3: 55:[11, 51, 0] Operation: 23-23=0 Exploring Operation: 23/23=1, Resulting Numbers: [11, 51, 1] Generated Node #0,4: 55:[11, 51, 1] Operation: 23/23=1 Start Sub Search at level 1: Moving to Node #0,4 Current State: 55:[11, 51, 1], Operations: ['23/23=1'] Exploring Operation: 11*1=11, Resulting Numbers: [51, 11] Generated Node #0,4,0: 55:[51, 11] Operation: 11*1=11 Exploring Operation: 51+1=52, Resulting Numbers: [11, 52] Generated Node #0,4,1: 55:[11, 52] Operation: 51+1=52 Exploring Operation: 11/1=11, Resulting Numbers: [51, 11] Generated Node #0,4,2: 55:[51, 11] Operation: 11/1=11 Exploring Operation: 51*1=51, Resulting Numbers: [11, 51] Generated Node #0,4,3: 55:[11, 51] Operation: 51*1=51 Exploring Operation: 51/1=51, Resulting Numbers: [11, 51] Generated Node #0,4,4: 55:[11, 51] Operation: 51/1=51 Moving to Node #0,4,1 Current State: 55:[11, 52], Operations: ['23/23=1', '51+1=52'] Exploring Operation: 11+52=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 11*52=572, Resulting Numbers: [572] 572,55 unequal: No Solution Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,55 unequal: No Solution Moving to Node #0,4,2 Current State: 55:[51, 11], Operations: ['23/23=1', '11/1=11'] Exploring Operation: 51+11=62, Resulting Numbers: [62] 62,55 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,55 unequal: No Solution Exploring Operation: 51*11=561, Resulting Numbers: [561] 561,55 unequal: No Solution Moving to Node #0,4,4 Current State: 55:[11, 51], Operations: ['23/23=1', '51/1=51'] Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,55 unequal: No Solution Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,55 unequal: No Solution Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,55 unequal: No Solution Moving to Node #0,4,0 Current State: 55:[51, 11], Operations: ['23/23=1', '11*1=11'] Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,55 unequal: No Solution Exploring Operation: 51*11=561, Resulting Numbers: [561] 561,55 unequal: No Solution Exploring Operation: 51+11=62, Resulting Numbers: [62] 62,55 unequal: No Solution Moving to Node #0,4,3 Current State: 55:[11, 51], Operations: ['23/23=1', '51*1=51'] Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,55 unequal: No Solution Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,55 unequal: No Solution Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 55:[11, 51, 0], Operations: ['23-23=0'] Exploring Operation: 11-0=11, Resulting Numbers: [51, 11] Generated Node #0,3,0: 55:[51, 11] Operation: 11-0=11 Exploring Operation: 51+0=51, Resulting Numbers: [11, 51] Generated Node #0,3,1: 55:[11, 51] Operation: 51+0=51 Exploring Operation: 51*0=0, Resulting Numbers: [11, 0] Generated Node #0,3,2: 55:[11, 0] Operation: 51*0=0 Exploring Operation: 11+0=11, Resulting Numbers: [51, 11] Generated Node #0,3,3: 55:[51, 11] Operation: 11+0=11 Exploring Operation: 51-0=51, Resulting Numbers: [11, 51] Generated Node #0,3,4: 55:[11, 51] Operation: 51-0=51 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 55:[51, 11], Operations: ['23-23=0', '11-0=11'] Exploring Operation: 51*11=561, Resulting Numbers: [561] 561,55 unequal: No Solution Exploring Operation: 51+11=62, Resulting Numbers: [62] 62,55 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 55:[11, 51], Operations: ['23-23=0', '51+0=51'] Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,55 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,55 unequal: No Solution Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 55:[51, 11], Operations: ['23-23=0', '11+0=11'] Exploring Operation: 51*11=561, Resulting Numbers: [561] 561,55 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,55 unequal: No Solution Exploring Operation: 51+11=62, Resulting Numbers: [62] 62,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 55:[11, 51], Operations: ['23-23=0', '51-0=51'] Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,55 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,55 unequal: No Solution Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 55:[11, 0], Operations: ['23-23=0', '51*0=0'] Exploring Operation: 11*0=0, Resulting Numbers: [0] 0,55 unequal: No Solution Exploring Operation: 11-0=11, Resulting Numbers: [11] 11,55 unequal: No Solution Exploring Operation: 11+0=11, Resulting Numbers: [11] 11,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[11, 51, 46], Operations: ['23+23=46'] Exploring Operation: 11+46=57, Resulting Numbers: [51, 57] Generated Node #0,0,0: 55:[51, 57] Operation: 11+46=57 Exploring Operation: 51-11=40, Resulting Numbers: [46, 40] Generated Node #0,0,1: 55:[46, 40] Operation: 51-11=40 Exploring Operation: 46-11=35, Resulting Numbers: [51, 35] Generated Node #0,0,2: 55:[51, 35] Operation: 46-11=35 Exploring Operation: 11+51=62, Resulting Numbers: [46, 62] Generated Node #0,0,3: 55:[46, 62] Operation: 11+51=62 Exploring Operation: 51-46=5, Resulting Numbers: [11, 5] Generated Node #0,0,4: 55:[11, 5] Operation: 51-46=5 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 55:[11, 5], Operations: ['23+23=46', '51-46=5'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,55 unequal: No Solution Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[11, 23, 51, 23], Operations: [] Exploring Operation: 23+23=46, Resulting Numbers: [11, 51, 46] Generated Node #0,0: 55:[11, 51, 46] Operation: 23+23=46 Moving to Node #0,0 Current State: 55:[11, 51, 46], Operations: ['23+23=46'] Exploring Operation: 51-46=5, Resulting Numbers: [11, 5] Generated Node #0,0,4: 55:[11, 5] Operation: 51-46=5 Moving to Node #0,0,4 Current State: 55:[11, 5], Operations: ['23+23=46', '51-46=5'] Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.950521
hs_5
sum_heuristic
[ 22, 62, 15, 48 ]
22
[ "62-15=47", "48-47=1", "22*1=22" ]
Current State: 22:[22, 62, 15, 48], Operations: [] Exploring Operation: 62-15=47, Resulting Numbers: [22, 48, 47] Generated Node #2: [22, 48, 47] from Operation: 62-15=47 Current State: 22:[22, 48, 47], Operations: ['62-15=47'] Exploring Operation: 48-47=1, Resulting Numbers: [22, 1] Generated Node #3: [22, 1] from Operation: 48-47=1 Current State: 22:[22, 1], Operations: ['62-15=47', '48-47=1'] Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[22, 62, 15, 48], Operations: [] Exploring Operation: 62-48=14, Resulting Numbers: [22, 15, 14] Generated Node #0,0: 22:[22, 15, 14] Operation: 62-48=14 Moving to Node #0,0 Current State: 22:[22, 15, 14], Operations: ['62-48=14'] Exploring Operation: 15-14=1, Resulting Numbers: [22, 1] Generated Node #0,0,0: 22:[22, 1] Operation: 15-14=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[22, 1], Operations: ['62-48=14', '15-14=1'] Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[22, 62, 15, 48], Operations: [] Exploring Operation: 62-48=14, Resulting Numbers: [22, 15, 14] Generated Node #0,0: 22:[22, 15, 14] Operation: 62-48=14 Moving to Node #0,0 Current State: 22:[22, 15, 14], Operations: ['62-48=14'] Exploring Operation: 15-14=1, Resulting Numbers: [22, 1] Generated Node #0,0,0: 22:[22, 1] Operation: 15-14=1 Moving to Node #0,0,0 Current State: 22:[22, 1], Operations: ['62-48=14', '15-14=1'] Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 9, 3, 12, 52 ]
43
[ "9/3=3", "52-12=40", "3+40=43" ]
Current State: 43:[9, 3, 12, 52], Operations: [] Exploring Operation: 9/3=3, Resulting Numbers: [12, 52, 3] Generated Node #2: [12, 52, 3] from Operation: 9/3=3 Current State: 43:[12, 52, 3], Operations: ['9/3=3'] Exploring Operation: 52-12=40, Resulting Numbers: [3, 40] Generated Node #3: [3, 40] from Operation: 52-12=40 Current State: 43:[3, 40], Operations: ['9/3=3', '52-12=40'] Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[9, 3, 12, 52], Operations: [] Exploring Operation: 9*3=27, Resulting Numbers: [12, 52, 27] Generated Node #0,0: 43:[12, 52, 27] Operation: 9*3=27 Exploring Operation: 3*12=36, Resulting Numbers: [9, 52, 36] Generated Node #0,1: 43:[9, 52, 36] Operation: 3*12=36 Exploring Operation: 9+3=12, Resulting Numbers: [12, 52, 12] Generated Node #0,2: 43:[12, 52, 12] Operation: 9+3=12 Moving to Node #0,1 Current State: 43:[9, 52, 36], Operations: ['3*12=36'] Exploring Operation: 52-9=43, Resulting Numbers: [36, 43] Generated Node #0,1,0: 43:[36, 43] Operation: 52-9=43 Exploring Operation: 9+36=45, Resulting Numbers: [52, 45] Generated Node #0,1,1: 43:[52, 45] Operation: 9+36=45 Exploring Operation: 9+52=61, Resulting Numbers: [36, 61] Generated Node #0,1,2: 43:[36, 61] Operation: 9+52=61 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[36, 43], Operations: ['3*12=36', '52-9=43'] Exploring Operation: 36*43=1548, Resulting Numbers: [1548] 1548,43 unequal: No Solution Exploring Operation: 43-36=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 36+43=79, Resulting Numbers: [79] 79,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 43:[52, 45], Operations: ['3*12=36', '9+36=45'] Exploring Operation: 52+45=97, Resulting Numbers: [97] 97,43 unequal: No Solution Exploring Operation: 52*45=2340, Resulting Numbers: [2340] 2340,43 unequal: No Solution Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,43 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 #0,1,2 Current State: 43:[36, 61], Operations: ['3*12=36', '9+52=61'] Exploring Operation: 36+61=97, Resulting Numbers: [97] 97,43 unequal: No Solution Exploring Operation: 61-36=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 36*61=2196, Resulting Numbers: [2196] 2196,43 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: 43:[12, 52, 27], Operations: ['9*3=27'] Exploring Operation: 52-12=40, Resulting Numbers: [27, 40] Generated Node #0,0,0: 43:[27, 40] Operation: 52-12=40 Exploring Operation: 12+27=39, Resulting Numbers: [52, 39] Generated Node #0,0,1: 43:[52, 39] Operation: 12+27=39 Exploring Operation: 12+52=64, Resulting Numbers: [27, 64] Generated Node #0,0,2: 43:[27, 64] Operation: 12+52=64 Moving to Node #0,2 Current State: 43:[12, 52, 12], Operations: ['9+3=12'] Exploring Operation: 52-12=40, Resulting Numbers: [12, 40] Generated Node #0,2,0: 43:[12, 40] Operation: 52-12=40 Exploring Operation: 12+12=24, Resulting Numbers: [52, 24] Generated Node #0,2,1: 43:[52, 24] Operation: 12+12=24 Exploring Operation: 52-12=40, Resulting Numbers: [12, 40] Generated Node #0,2,2: 43:[12, 40] Operation: 52-12=40 Moving to Node #0,0,1 Current State: 43:[52, 39], Operations: ['9*3=27', '12+27=39'] Exploring Operation: 52+39=91, Resulting Numbers: [91] 91,43 unequal: No Solution Exploring Operation: 52*39=2028, Resulting Numbers: [2028] 2028,43 unequal: No Solution Exploring Operation: 52-39=13, Resulting Numbers: [13] 13,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[27, 40], Operations: ['9*3=27', '52-12=40'] Exploring Operation: 27+40=67, Resulting Numbers: [67] 67,43 unequal: No Solution Exploring Operation: 27*40=1080, Resulting Numbers: [1080] 1080,43 unequal: No Solution Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[52, 24], Operations: ['9+3=12', '12+12=24'] Exploring Operation: 52+24=76, Resulting Numbers: [76] 76,43 unequal: No Solution Exploring Operation: 52*24=1248, Resulting Numbers: [1248] 1248,43 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[12, 40], Operations: ['9+3=12', '52-12=40'] Exploring Operation: 12+40=52, Resulting Numbers: [52] 52,43 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,43 unequal: No Solution Exploring Operation: 12*40=480, Resulting Numbers: [480] 480,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[12, 40], Operations: ['9+3=12', '52-12=40'] Exploring Operation: 12*40=480, Resulting Numbers: [480] 480,43 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,43 unequal: No Solution Exploring Operation: 12+40=52, Resulting Numbers: [52] 52,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[27, 64], Operations: ['9*3=27', '12+52=64'] Exploring Operation: 64-27=37, Resulting Numbers: [37] 37,43 unequal: No Solution Exploring Operation: 27*64=1728, Resulting Numbers: [1728] 1728,43 unequal: No Solution Exploring Operation: 27+64=91, Resulting Numbers: [91] 91,43 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 45, 57, 61, 26 ]
58
[ "45-26=19", "57/19=3", "61-3=58" ]
Current State: 58:[45, 57, 61, 26], Operations: [] Exploring Operation: 45-26=19, Resulting Numbers: [57, 61, 19] Generated Node #2: [57, 61, 19] from Operation: 45-26=19 Current State: 58:[57, 61, 19], Operations: ['45-26=19'] Exploring Operation: 57/19=3, Resulting Numbers: [61, 3] Generated Node #3: [61, 3] from Operation: 57/19=3 Current State: 58:[61, 3], Operations: ['45-26=19', '57/19=3'] Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[45, 57, 61, 26], Operations: [] Exploring Operation: 45-26=19, Resulting Numbers: [57, 61, 19] Generated Node #0,0: 58:[57, 61, 19] Operation: 45-26=19 Exploring Operation: 61-45=16, Resulting Numbers: [57, 26, 16] Generated Node #0,1: 58:[57, 26, 16] Operation: 61-45=16 Exploring Operation: 57-45=12, Resulting Numbers: [61, 26, 12] Generated Node #0,2: 58:[61, 26, 12] Operation: 57-45=12 Exploring Operation: 45+26=71, Resulting Numbers: [57, 61, 71] Generated Node #0,3: 58:[57, 61, 71] Operation: 45+26=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[57, 61, 19], Operations: ['45-26=19'] Exploring Operation: 57-19=38, Resulting Numbers: [61, 38] Generated Node #0,0,0: 58:[61, 38] Operation: 57-19=38 Exploring Operation: 57/19=3, Resulting Numbers: [61, 3] Generated Node #0,0,1: 58:[61, 3] Operation: 57/19=3 Exploring Operation: 61-57=4, Resulting Numbers: [19, 4] Generated Node #0,0,2: 58:[19, 4] Operation: 61-57=4 Exploring Operation: 61-19=42, Resulting Numbers: [57, 42] Generated Node #0,0,3: 58:[57, 42] Operation: 61-19=42 Moving to Node #0,0,1 Current State: 58:[61, 3], Operations: ['45-26=19', '57/19=3'] Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[45, 57, 61, 26], Operations: [] Exploring Operation: 45-26=19, Resulting Numbers: [57, 61, 19] Generated Node #0,0: 58:[57, 61, 19] Operation: 45-26=19 Moving to Node #0,0 Current State: 58:[57, 61, 19], Operations: ['45-26=19'] Exploring Operation: 57/19=3, Resulting Numbers: [61, 3] Generated Node #0,0,1: 58:[61, 3] Operation: 57/19=3 Moving to Node #0,0,1 Current State: 58:[61, 3], Operations: ['45-26=19', '57/19=3'] Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 41, 91, 59, 6 ]
79
[ "41+91=132", "59-6=53", "132-53=79" ]
Current State: 79:[41, 91, 59, 6], Operations: [] Exploring Operation: 41+91=132, Resulting Numbers: [59, 6, 132] Generated Node #2: [59, 6, 132] from Operation: 41+91=132 Current State: 79:[59, 6, 132], Operations: ['41+91=132'] Exploring Operation: 59-6=53, Resulting Numbers: [132, 53] Generated Node #3: [132, 53] from Operation: 59-6=53 Current State: 79:[132, 53], Operations: ['41+91=132', '59-6=53'] Exploring Operation: 132-53=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[41, 91, 59, 6], Operations: [] Exploring Operation: 41+6=47, Resulting Numbers: [91, 59, 47] Generated Node #0,0: 79:[91, 59, 47] Operation: 41+6=47 Moving to Node #0,0 Current State: 79:[91, 59, 47], Operations: ['41+6=47'] Exploring Operation: 59+47=106, Resulting Numbers: [91, 106] Generated Node #0,0,0: 79:[91, 106] Operation: 59+47=106 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[91, 106], Operations: ['41+6=47', '59+47=106'] Exploring Operation: 106-91=15, Resulting Numbers: [15] 15,79 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
[ 99, 25, 97, 98 ]
48
[ "99-97=2", "25*2=50", "98-50=48" ]
Current State: 48:[99, 25, 97, 98], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [25, 98, 2] Generated Node #2: [25, 98, 2] from Operation: 99-97=2 Current State: 48:[25, 98, 2], Operations: ['99-97=2'] Exploring Operation: 25*2=50, Resulting Numbers: [98, 50] Generated Node #3: [98, 50] from Operation: 25*2=50 Current State: 48:[98, 50], Operations: ['99-97=2', '25*2=50'] Exploring Operation: 98-50=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[99, 25, 97, 98], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [25, 98, 2] Generated Node #0,0: 48:[25, 98, 2] Operation: 99-97=2 Exploring Operation: 99-98=1, Resulting Numbers: [25, 97, 1] Generated Node #0,1: 48:[25, 97, 1] Operation: 99-98=1 Moving to Node #0,0 Current State: 48:[25, 98, 2], Operations: ['99-97=2'] Exploring Operation: 98/2=49, Resulting Numbers: [25, 49] Generated Node #0,0,0: 48:[25, 49] Operation: 98/2=49 Exploring Operation: 98-25=73, Resulting Numbers: [2, 73] Generated Node #0,0,1: 48:[2, 73] Operation: 98-25=73 Moving to Node #0,1 Current State: 48:[25, 97, 1], Operations: ['99-98=1'] Exploring Operation: 97-25=72, Resulting Numbers: [1, 72] Generated Node #0,1,0: 48:[1, 72] Operation: 97-25=72 Exploring Operation: 25-1=24, Resulting Numbers: [97, 24] Generated Node #0,1,1: 48:[97, 24] Operation: 25-1=24 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[1, 72], Operations: ['99-98=1', '97-25=72'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,48 unequal: No Solution Exploring Operation: 1*72=72, Resulting Numbers: [72] 72,48 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 #0,1,1 Current State: 48:[97, 24], Operations: ['99-98=1', '25-1=24'] Exploring Operation: 97+24=121, Resulting Numbers: [121] 121,48 unequal: No Solution Exploring Operation: 97-24=73, Resulting Numbers: [73] 73,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 48:[25, 49], Operations: ['99-97=2', '98/2=49'] Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,48 unequal: No Solution Exploring Operation: 25+49=74, Resulting Numbers: [74] 74,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[2, 73], Operations: ['99-97=2', '98-25=73'] Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,48 unequal: No Solution Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,48 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 69, 54, 6, 81 ]
11
[ "69-54=15", "81-15=66", "66/6=11" ]
Current State: 11:[69, 54, 6, 81], Operations: [] Exploring Operation: 69-54=15, Resulting Numbers: [6, 81, 15] Generated Node #2: [6, 81, 15] from Operation: 69-54=15 Current State: 11:[6, 81, 15], Operations: ['69-54=15'] Exploring Operation: 81-15=66, Resulting Numbers: [6, 66] Generated Node #3: [6, 66] from Operation: 81-15=66 Current State: 11:[6, 66], Operations: ['69-54=15', '81-15=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[69, 54, 6, 81], Operations: [] Exploring Operation: 54/6=9, Resulting Numbers: [69, 81, 9] Generated Node #0,0: 11:[69, 81, 9] Operation: 54/6=9 Exploring Operation: 81-54=27, Resulting Numbers: [69, 6, 27] Generated Node #0,1: 11:[69, 6, 27] Operation: 81-54=27 Exploring Operation: 81-69=12, Resulting Numbers: [54, 6, 12] Generated Node #0,2: 11:[54, 6, 12] Operation: 81-69=12 Exploring Operation: 69-54=15, Resulting Numbers: [6, 81, 15] Generated Node #0,3: 11:[6, 81, 15] Operation: 69-54=15 Exploring Operation: 69-6=63, Resulting Numbers: [54, 81, 63] Generated Node #0,4: 11:[54, 81, 63] Operation: 69-6=63 Moving to Node #0,2 Current State: 11:[54, 6, 12], Operations: ['81-69=12'] Exploring Operation: 54/6=9, Resulting Numbers: [12, 9] Generated Node #0,2,0: 11:[12, 9] Operation: 54/6=9 Exploring Operation: 12-6=6, Resulting Numbers: [54, 6] Generated Node #0,2,1: 11:[54, 6] Operation: 12-6=6 Exploring Operation: 54-12=42, Resulting Numbers: [6, 42] Generated Node #0,2,2: 11:[6, 42] Operation: 54-12=42 Exploring Operation: 54+6=60, Resulting Numbers: [12, 60] Generated Node #0,2,3: 11:[12, 60] Operation: 54+6=60 Exploring Operation: 54-6=48, Resulting Numbers: [12, 48] Generated Node #0,2,4: 11:[12, 48] Operation: 54-6=48 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[12, 9], Operations: ['81-69=12', '54/6=9'] Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 12*9=108, Resulting Numbers: [108] 108,11 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 11:[6, 42], Operations: ['81-69=12', '54-12=42'] Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,11 unequal: No Solution Exploring Operation: 6+42=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 6*42=252, Resulting Numbers: [252] 252,11 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 11:[12, 48], Operations: ['81-69=12', '54-6=48'] Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 48-12=36, Resulting Numbers: [36] 36,11 unequal: No Solution Exploring Operation: 12*48=576, Resulting Numbers: [576] 576,11 unequal: No Solution Exploring Operation: 12+48=60, Resulting Numbers: [60] 60,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 11:[54, 6], Operations: ['81-69=12', '12-6=6'] Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 54*6=324, Resulting Numbers: [324] 324,11 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 11:[12, 60], Operations: ['81-69=12', '54+6=60'] Exploring Operation: 12+60=72, Resulting Numbers: [72] 72,11 unequal: No Solution Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,11 unequal: No Solution Exploring Operation: 12*60=720, Resulting Numbers: [720] 720,11 unequal: No Solution Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,11 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: 11:[6, 81, 15], Operations: ['69-54=15'] Exploring Operation: 6+81=87, Resulting Numbers: [15, 87] Generated Node #0,3,0: 11:[15, 87] Operation: 6+81=87 Exploring Operation: 81-6=75, Resulting Numbers: [15, 75] Generated Node #0,3,1: 11:[15, 75] Operation: 81-6=75 Exploring Operation: 6+15=21, Resulting Numbers: [81, 21] Generated Node #0,3,2: 11:[81, 21] Operation: 6+15=21 Exploring Operation: 81-15=66, Resulting Numbers: [6, 66] Generated Node #0,3,3: 11:[6, 66] Operation: 81-15=66 Exploring Operation: 15-6=9, Resulting Numbers: [81, 9] Generated Node #0,3,4: 11:[81, 9] Operation: 15-6=9 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 11:[6, 66], Operations: ['69-54=15', '81-15=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[69, 54, 6, 81], Operations: [] Exploring Operation: 69-54=15, Resulting Numbers: [6, 81, 15] Generated Node #0,3: 11:[6, 81, 15] Operation: 69-54=15 Moving to Node #0,3 Current State: 11:[6, 81, 15], Operations: ['69-54=15'] Exploring Operation: 81-15=66, Resulting Numbers: [6, 66] Generated Node #0,3,3: 11:[6, 66] Operation: 81-15=66 Moving to Node #0,3,3 Current State: 11:[6, 66], Operations: ['69-54=15', '81-15=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_5
sum_heuristic
[ 62, 59, 33, 4 ]
34
[ "62-59=3", "33+4=37", "37-3=34" ]
Current State: 34:[62, 59, 33, 4], Operations: [] Exploring Operation: 62-59=3, Resulting Numbers: [33, 4, 3] Generated Node #2: [33, 4, 3] from Operation: 62-59=3 Current State: 34:[33, 4, 3], Operations: ['62-59=3'] Exploring Operation: 33+4=37, Resulting Numbers: [3, 37] Generated Node #3: [3, 37] from Operation: 33+4=37 Current State: 34:[3, 37], Operations: ['62-59=3', '33+4=37'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[62, 59, 33, 4], Operations: [] Exploring Operation: 59-33=26, Resulting Numbers: [62, 4, 26] Generated Node #0,0: 34:[62, 4, 26] Operation: 59-33=26 Exploring Operation: 62-33=29, Resulting Numbers: [59, 4, 29] Generated Node #0,1: 34:[59, 4, 29] Operation: 62-33=29 Exploring Operation: 62-59=3, Resulting Numbers: [33, 4, 3] Generated Node #0,2: 34:[33, 4, 3] Operation: 62-59=3 Exploring Operation: 59-4=55, Resulting Numbers: [62, 33, 55] Generated Node #0,3: 34:[62, 33, 55] Operation: 59-4=55 Exploring Operation: 62-4=58, Resulting Numbers: [59, 33, 58] Generated Node #0,4: 34:[59, 33, 58] Operation: 62-4=58 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[33, 4, 3], Operations: ['62-59=3'] Exploring Operation: 33-3=30, Resulting Numbers: [4, 30] Generated Node #0,2,0: 34:[4, 30] Operation: 33-3=30 Exploring Operation: 33+3=36, Resulting Numbers: [4, 36] Generated Node #0,2,1: 34:[4, 36] Operation: 33+3=36 Exploring Operation: 33-4=29, Resulting Numbers: [3, 29] Generated Node #0,2,2: 34:[3, 29] Operation: 33-4=29 Exploring Operation: 4-3=1, Resulting Numbers: [33, 1] Generated Node #0,2,3: 34:[33, 1] Operation: 4-3=1 Exploring Operation: 33+4=37, Resulting Numbers: [3, 37] Generated Node #0,2,4: 34:[3, 37] Operation: 33+4=37 Moving to Node #0,2,3 Current State: 34:[33, 1], Operations: ['62-59=3', '4-3=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[62, 59, 33, 4], Operations: [] Exploring Operation: 62-59=3, Resulting Numbers: [33, 4, 3] Generated Node #0,2: 34:[33, 4, 3] Operation: 62-59=3 Moving to Node #0,2 Current State: 34:[33, 4, 3], Operations: ['62-59=3'] Exploring Operation: 4-3=1, Resulting Numbers: [33, 1] Generated Node #0,2,3: 34:[33, 1] Operation: 4-3=1 Moving to Node #0,2,3 Current State: 34:[33, 1], Operations: ['62-59=3', '4-3=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 23, 3, 83, 1 ]
30
[ "83-23=60", "3-1=2", "60/2=30" ]
Current State: 30:[23, 3, 83, 1], Operations: [] Exploring Operation: 83-23=60, Resulting Numbers: [3, 1, 60] Generated Node #2: [3, 1, 60] from Operation: 83-23=60 Current State: 30:[3, 1, 60], Operations: ['83-23=60'] Exploring Operation: 3-1=2, Resulting Numbers: [60, 2] Generated Node #3: [60, 2] from Operation: 3-1=2 Current State: 30:[60, 2], Operations: ['83-23=60', '3-1=2'] Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[23, 3, 83, 1], Operations: [] Exploring Operation: 23+3=26, Resulting Numbers: [83, 1, 26] Generated Node #0,0: 30:[83, 1, 26] Operation: 23+3=26 Exploring Operation: 23-3=20, Resulting Numbers: [83, 1, 20] Generated Node #0,1: 30:[83, 1, 20] Operation: 23-3=20 Exploring Operation: 83-3=80, Resulting Numbers: [23, 1, 80] Generated Node #0,2: 30:[23, 1, 80] Operation: 83-3=80 Exploring Operation: 83-23=60, Resulting Numbers: [3, 1, 60] Generated Node #0,3: 30:[3, 1, 60] Operation: 83-23=60 Moving to Node #0,3 Current State: 30:[3, 1, 60], Operations: ['83-23=60'] Exploring Operation: 60-1=59, Resulting Numbers: [3, 59] Generated Node #0,3,0: 30:[3, 59] Operation: 60-1=59 Exploring Operation: 60/3=20, Resulting Numbers: [1, 20] Generated Node #0,3,1: 30:[1, 20] Operation: 60/3=20 Exploring Operation: 60-3=57, Resulting Numbers: [1, 57] Generated Node #0,3,2: 30:[1, 57] Operation: 60-3=57 Exploring Operation: 3*1=3, Resulting Numbers: [60, 3] Generated Node #0,3,3: 30:[60, 3] Operation: 3*1=3 Moving to Node #0,2 Current State: 30:[23, 1, 80], Operations: ['83-3=80'] Exploring Operation: 23*1=23, Resulting Numbers: [80, 23] Generated Node #0,2,0: 30:[80, 23] Operation: 23*1=23 Exploring Operation: 80-23=57, Resulting Numbers: [1, 57] Generated Node #0,2,1: 30:[1, 57] Operation: 80-23=57 Exploring Operation: 23+1=24, Resulting Numbers: [80, 24] Generated Node #0,2,2: 30:[80, 24] Operation: 23+1=24 Exploring Operation: 80-1=79, Resulting Numbers: [23, 79] Generated Node #0,2,3: 30:[23, 79] Operation: 80-1=79 Moving to Node #0,0 Current State: 30:[83, 1, 26], Operations: ['23+3=26'] Exploring Operation: 83-26=57, Resulting Numbers: [1, 57] Generated Node #0,0,0: 30:[1, 57] Operation: 83-26=57 Exploring Operation: 83*1=83, Resulting Numbers: [26, 83] Generated Node #0,0,1: 30:[26, 83] Operation: 83*1=83 Exploring Operation: 83-1=82, Resulting Numbers: [26, 82] Generated Node #0,0,2: 30:[26, 82] Operation: 83-1=82 Exploring Operation: 1+26=27, Resulting Numbers: [83, 27] Generated Node #0,0,3: 30:[83, 27] Operation: 1+26=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[1, 57], Operations: ['23+3=26', '83-26=57'] Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,30 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,30 unequal: No Solution Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,30 unequal: No Solution Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 30:[26, 82], Operations: ['23+3=26', '83-1=82'] Exploring Operation: 26+82=108, Resulting Numbers: [108] 108,30 unequal: No Solution Exploring Operation: 26*82=2132, Resulting Numbers: [2132] 2132,30 unequal: No Solution Exploring Operation: 82-26=56, Resulting Numbers: [56] 56,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 30:[83, 27], Operations: ['23+3=26', '1+26=27'] Exploring Operation: 83*27=2241, Resulting Numbers: [2241] 2241,30 unequal: No Solution Exploring Operation: 83+27=110, Resulting Numbers: [110] 110,30 unequal: No Solution Exploring Operation: 83-27=56, Resulting Numbers: [56] 56,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[26, 83], Operations: ['23+3=26', '83*1=83'] Exploring Operation: 26*83=2158, Resulting Numbers: [2158] 2158,30 unequal: No Solution Exploring Operation: 83-26=57, Resulting Numbers: [57] 57,30 unequal: No Solution Exploring Operation: 26+83=109, Resulting Numbers: [109] 109,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 30:[83, 1, 20], Operations: ['23-3=20'] Exploring Operation: 83-20=63, Resulting Numbers: [1, 63] Generated Node #0,1,0: 30:[1, 63] Operation: 83-20=63 Exploring Operation: 83*1=83, Resulting Numbers: [20, 83] Generated Node #0,1,1: 30:[20, 83] Operation: 83*1=83 Exploring Operation: 20-1=19, Resulting Numbers: [83, 19] Generated Node #0,1,2: 30:[83, 19] Operation: 20-1=19 Exploring Operation: 83-1=82, Resulting Numbers: [20, 82] Generated Node #0,1,3: 30:[20, 82] Operation: 83-1=82 Moving to Node #0,3,1 Current State: 30:[1, 20], Operations: ['83-23=60', '60/3=20'] Exploring Operation: 1+20=21, Resulting Numbers: [21] 21,30 unequal: No Solution Exploring Operation: 1*20=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,30 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,30 unequal: No Solution Moving to Node #0,3,2 Current State: 30:[1, 57], Operations: ['83-23=60', '60-3=57'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,30 unequal: No Solution Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,30 unequal: No Solution Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,30 unequal: No Solution Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,30 unequal: No Solution Moving to Node #0,2,1 Current State: 30:[1, 57], Operations: ['83-3=80', '80-23=57'] Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,30 unequal: No Solution Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,30 unequal: No Solution Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,30 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,30 unequal: No Solution Moving to Node #0,3,0 Current State: 30:[3, 59], Operations: ['83-23=60', '60-1=59'] Exploring Operation: 3+59=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 3*59=177, Resulting Numbers: [177] 177,30 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,30 unequal: No Solution Moving to Node #0,3,3 Current State: 30:[60, 3], Operations: ['83-23=60', '3*1=3'] Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,30 unequal: No Solution Exploring Operation: 60*3=180, Resulting Numbers: [180] 180,30 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[1, 63], Operations: ['23-3=20', '83-20=63'] Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 1*63=63, Resulting Numbers: [63] 63,30 unequal: No Solution Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,30 unequal: No Solution Exploring Operation: 1+63=64, Resulting Numbers: [64] 64,30 unequal: No Solution Moving to Node #0,2,3 Current State: 30:[23, 79], Operations: ['83-3=80', '80-1=79'] Exploring Operation: 23+79=102, Resulting Numbers: [102] 102,30 unequal: No Solution Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,30 unequal: No Solution Exploring Operation: 23*79=1817, Resulting Numbers: [1817] 1817,30 unequal: No Solution Moving to Node #0,2,2 Current State: 30:[80, 24], Operations: ['83-3=80', '23+1=24'] Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,30 unequal: No Solution Exploring Operation: 80*24=1920, Resulting Numbers: [1920] 1920,30 unequal: No Solution Exploring Operation: 80+24=104, Resulting Numbers: [104] 104,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[83, 19], Operations: ['23-3=20', '20-1=19'] Exploring Operation: 83+19=102, Resulting Numbers: [102] 102,30 unequal: No Solution Exploring Operation: 83-19=64, Resulting Numbers: [64] 64,30 unequal: No Solution Exploring Operation: 83*19=1577, Resulting Numbers: [1577] 1577,30 unequal: No Solution Moving to Node #0,1,3 Current State: 30:[20, 82], Operations: ['23-3=20', '83-1=82'] Exploring Operation: 20*82=1640, Resulting Numbers: [1640] 1640,30 unequal: No Solution Exploring Operation: 82-20=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 20+82=102, Resulting Numbers: [102] 102,30 unequal: No Solution Moving to Node #0,2,0 Current State: 30:[80, 23], Operations: ['83-3=80', '23*1=23'] Exploring Operation: 80+23=103, Resulting Numbers: [103] 103,30 unequal: No Solution Exploring Operation: 80-23=57, Resulting Numbers: [57] 57,30 unequal: No Solution Exploring Operation: 80*23=1840, Resulting Numbers: [1840] 1840,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[20, 83], Operations: ['23-3=20', '83*1=83'] Exploring Operation: 20+83=103, Resulting Numbers: [103] 103,30 unequal: No Solution Exploring Operation: 83-20=63, Resulting Numbers: [63] 63,30 unequal: No Solution Exploring Operation: 20*83=1660, Resulting Numbers: [1660] 1660,30 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 2, 79, 7, 87 ]
78
[ "2*79=158", "87-7=80", "158-80=78" ]
Current State: 78:[2, 79, 7, 87], Operations: [] Exploring Operation: 2*79=158, Resulting Numbers: [7, 87, 158] Generated Node #2: [7, 87, 158] from Operation: 2*79=158 Current State: 78:[7, 87, 158], Operations: ['2*79=158'] Exploring Operation: 87-7=80, Resulting Numbers: [158, 80] Generated Node #3: [158, 80] from Operation: 87-7=80 Current State: 78:[158, 80], Operations: ['2*79=158', '87-7=80'] Exploring Operation: 158-80=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[2, 79, 7, 87], Operations: [] Exploring Operation: 87-79=8, Resulting Numbers: [2, 7, 8] Generated Node #0,0: 78:[2, 7, 8] Operation: 87-79=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[2, 7, 8], Operations: ['87-79=8'] Exploring Operation: 8-2=6, Resulting Numbers: [7, 6] Generated Node #0,0,0: 78:[7, 6] Operation: 8-2=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 78:[7, 6], Operations: ['87-79=8', '8-2=6'] Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,78 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
[ 41, 81, 79, 35 ]
29
[ "81-79=2", "35*2=70", "70-41=29" ]
Current State: 29:[41, 81, 79, 35], Operations: [] Exploring Operation: 81-79=2, Resulting Numbers: [41, 35, 2] Generated Node #2: [41, 35, 2] from Operation: 81-79=2 Current State: 29:[41, 35, 2], Operations: ['81-79=2'] Exploring Operation: 35*2=70, Resulting Numbers: [41, 70] Generated Node #3: [41, 70] from Operation: 35*2=70 Current State: 29:[41, 70], Operations: ['81-79=2', '35*2=70'] Exploring Operation: 70-41=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[41, 81, 79, 35], Operations: [] Exploring Operation: 81-79=2, Resulting Numbers: [41, 35, 2] Generated Node #0,0: 29:[41, 35, 2] Operation: 81-79=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[41, 35, 2], Operations: ['81-79=2'] Exploring Operation: 41-2=39, Resulting Numbers: [35, 39] Generated Node #0,0,0: 29:[35, 39] Operation: 41-2=39 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[35, 39], Operations: ['81-79=2', '41-2=39'] Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 49, 64, 48, 13 ]
96
[ "64-49=15", "15-13=2", "48*2=96" ]
Current State: 96:[49, 64, 48, 13], Operations: [] Exploring Operation: 64-49=15, Resulting Numbers: [48, 13, 15] Generated Node #2: [48, 13, 15] from Operation: 64-49=15 Current State: 96:[48, 13, 15], Operations: ['64-49=15'] Exploring Operation: 15-13=2, Resulting Numbers: [48, 2] Generated Node #3: [48, 2] from Operation: 15-13=2 Current State: 96:[48, 2], Operations: ['64-49=15', '15-13=2'] Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[49, 64, 48, 13], Operations: [] Exploring Operation: 49+64=113, Resulting Numbers: [48, 13, 113] Generated Node #0,0: 96:[48, 13, 113] Operation: 49+64=113 Exploring Operation: 64-48=16, Resulting Numbers: [49, 13, 16] Generated Node #0,1: 96:[49, 13, 16] Operation: 64-48=16 Exploring Operation: 49+48=97, Resulting Numbers: [64, 13, 97] Generated Node #0,2: 96:[64, 13, 97] Operation: 49+48=97 Exploring Operation: 64-49=15, Resulting Numbers: [48, 13, 15] Generated Node #0,3: 96:[48, 13, 15] Operation: 64-49=15 Exploring Operation: 64-13=51, Resulting Numbers: [49, 48, 51] Generated Node #0,4: 96:[49, 48, 51] Operation: 64-13=51 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[49, 13, 16], Operations: ['64-48=16'] Exploring Operation: 49-13=36, Resulting Numbers: [16, 36] Generated Node #0,1,0: 96:[16, 36] Operation: 49-13=36 Exploring Operation: 16-13=3, Resulting Numbers: [49, 3] Generated Node #0,1,1: 96:[49, 3] Operation: 16-13=3 Exploring Operation: 49+13=62, Resulting Numbers: [16, 62] Generated Node #0,1,2: 96:[16, 62] Operation: 49+13=62 Exploring Operation: 49-16=33, Resulting Numbers: [13, 33] Generated Node #0,1,3: 96:[13, 33] Operation: 49-16=33 Exploring Operation: 13+16=29, Resulting Numbers: [49, 29] Generated Node #0,1,4: 96:[49, 29] Operation: 13+16=29 Moving to Node #0,1,1 Current State: 96:[49, 3], Operations: ['64-48=16', '16-13=3'] Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,96 unequal: No Solution Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,96 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,96 unequal: No Solution Moving to Node #0,1,3 Current State: 96:[13, 33], Operations: ['64-48=16', '49-16=33'] Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,96 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[16, 36], Operations: ['64-48=16', '49-13=36'] Exploring Operation: 16*36=576, Resulting Numbers: [576] 576,96 unequal: No Solution Exploring Operation: 16+36=52, Resulting Numbers: [52] 52,96 unequal: No Solution Exploring Operation: 36-16=20, Resulting Numbers: [20] 20,96 unequal: No Solution Moving to Node #0,1,4 Current State: 96:[49, 29], Operations: ['64-48=16', '13+16=29'] Exploring Operation: 49+29=78, Resulting Numbers: [78] 78,96 unequal: No Solution Exploring Operation: 49*29=1421, Resulting Numbers: [1421] 1421,96 unequal: No Solution Exploring Operation: 49-29=20, Resulting Numbers: [20] 20,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[16, 62], Operations: ['64-48=16', '49+13=62'] Exploring Operation: 16+62=78, Resulting Numbers: [78] 78,96 unequal: No Solution Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 16*62=992, Resulting Numbers: [992] 992,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 96:[48, 13, 15], Operations: ['64-49=15'] Exploring Operation: 15-13=2, Resulting Numbers: [48, 2] Generated Node #0,3,0: 96:[48, 2] Operation: 15-13=2 Exploring Operation: 13+15=28, Resulting Numbers: [48, 28] Generated Node #0,3,1: 96:[48, 28] Operation: 13+15=28 Exploring Operation: 48+13=61, Resulting Numbers: [15, 61] Generated Node #0,3,2: 96:[15, 61] Operation: 48+13=61 Exploring Operation: 48-15=33, Resulting Numbers: [13, 33] Generated Node #0,3,3: 96:[13, 33] Operation: 48-15=33 Exploring Operation: 48-13=35, Resulting Numbers: [15, 35] Generated Node #0,3,4: 96:[15, 35] Operation: 48-13=35 Moving to Node #0,3,0 Current State: 96:[48, 2], Operations: ['64-49=15', '15-13=2'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[49, 64, 48, 13], Operations: [] Exploring Operation: 64-49=15, Resulting Numbers: [48, 13, 15] Generated Node #0,3: 96:[48, 13, 15] Operation: 64-49=15 Moving to Node #0,3 Current State: 96:[48, 13, 15], Operations: ['64-49=15'] Exploring Operation: 15-13=2, Resulting Numbers: [48, 2] Generated Node #0,3,0: 96:[48, 2] Operation: 15-13=2 Moving to Node #0,3,0 Current State: 96:[48, 2], Operations: ['64-49=15', '15-13=2'] Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
sum_heuristic
[ 34, 46, 60, 19 ]
39
[ "34+46=80", "60-19=41", "80-41=39" ]
Current State: 39:[34, 46, 60, 19], Operations: [] Exploring Operation: 34+46=80, Resulting Numbers: [60, 19, 80] Generated Node #2: [60, 19, 80] from Operation: 34+46=80 Current State: 39:[60, 19, 80], Operations: ['34+46=80'] Exploring Operation: 60-19=41, Resulting Numbers: [80, 41] Generated Node #3: [80, 41] from Operation: 60-19=41 Current State: 39:[80, 41], Operations: ['34+46=80', '60-19=41'] Exploring Operation: 80-41=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[34, 46, 60, 19], Operations: [] Exploring Operation: 60-46=14, Resulting Numbers: [34, 19, 14] Generated Node #0,0: 39:[34, 19, 14] Operation: 60-46=14 Moving to Node #0,0 Current State: 39:[34, 19, 14], Operations: ['60-46=14'] Exploring Operation: 34-19=15, Resulting Numbers: [14, 15] Generated Node #0,0,0: 39:[14, 15] Operation: 34-19=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[14, 15], Operations: ['60-46=14', '34-19=15'] Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 54, 72, 58, 93 ]
91
[ "54+72=126", "93-58=35", "126-35=91" ]
Current State: 91:[54, 72, 58, 93], Operations: [] Exploring Operation: 54+72=126, Resulting Numbers: [58, 93, 126] Generated Node #2: [58, 93, 126] from Operation: 54+72=126 Current State: 91:[58, 93, 126], Operations: ['54+72=126'] Exploring Operation: 93-58=35, Resulting Numbers: [126, 35] Generated Node #3: [126, 35] from Operation: 93-58=35 Current State: 91:[126, 35], Operations: ['54+72=126', '93-58=35'] Exploring Operation: 126-35=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[54, 72, 58, 93], Operations: [] Exploring Operation: 58-54=4, Resulting Numbers: [72, 93, 4] Generated Node #0,0: 91:[72, 93, 4] Operation: 58-54=4 Exploring Operation: 72-54=18, Resulting Numbers: [58, 93, 18] Generated Node #0,1: 91:[58, 93, 18] Operation: 72-54=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[72, 93, 4], Operations: ['58-54=4'] Exploring Operation: 72/4=18, Resulting Numbers: [93, 18] Generated Node #0,0,0: 91:[93, 18] Operation: 72/4=18 Exploring Operation: 93-72=21, Resulting Numbers: [4, 21] Generated Node #0,0,1: 91:[4, 21] Operation: 93-72=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[93, 18], Operations: ['58-54=4', '72/4=18'] Exploring Operation: 93-18=75, Resulting Numbers: [75] 75,91 unequal: No Solution Exploring Operation: 93+18=111, Resulting Numbers: [111] 111,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[4, 21], Operations: ['58-54=4', '93-72=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,91 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,91 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[58, 93, 18], Operations: ['72-54=18'] Exploring Operation: 58+18=76, Resulting Numbers: [93, 76] Generated Node #0,1,0: 91:[93, 76] Operation: 58+18=76 Exploring Operation: 93-58=35, Resulting Numbers: [18, 35] Generated Node #0,1,1: 91:[18, 35] Operation: 93-58=35 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[93, 76], Operations: ['72-54=18', '58+18=76'] Exploring Operation: 93+76=169, Resulting Numbers: [169] 169,91 unequal: No Solution Exploring Operation: 93-76=17, Resulting Numbers: [17] 17,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[18, 35], Operations: ['72-54=18', '93-58=35'] Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,91 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,91 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_2
sum_heuristic
[ 85, 13, 19, 27 ]
19
[ "85+19=104", "104/13=8", "27-8=19" ]
Current State: 19:[85, 13, 19, 27], Operations: [] Exploring Operation: 85+19=104, Resulting Numbers: [13, 27, 104] Generated Node #2: [13, 27, 104] from Operation: 85+19=104 Current State: 19:[13, 27, 104], Operations: ['85+19=104'] Exploring Operation: 104/13=8, Resulting Numbers: [27, 8] Generated Node #3: [27, 8] from Operation: 104/13=8 Current State: 19:[27, 8], Operations: ['85+19=104', '104/13=8'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[85, 13, 19, 27], Operations: [] Exploring Operation: 85-13=72, Resulting Numbers: [19, 27, 72] Generated Node #0,0: 19:[19, 27, 72] Operation: 85-13=72 Exploring Operation: 85-27=58, Resulting Numbers: [13, 19, 58] Generated Node #0,1: 19:[13, 19, 58] Operation: 85-27=58 Moving to Node #0,1 Current State: 19:[13, 19, 58], Operations: ['85-27=58'] Exploring Operation: 58-19=39, Resulting Numbers: [13, 39] Generated Node #0,1,0: 19:[13, 39] Operation: 58-19=39 Exploring Operation: 58-13=45, Resulting Numbers: [19, 45] Generated Node #0,1,1: 19:[19, 45] Operation: 58-13=45 Moving to Node #0,0 Current State: 19:[19, 27, 72], Operations: ['85-13=72'] Exploring Operation: 72-27=45, Resulting Numbers: [19, 45] Generated Node #0,0,0: 19:[19, 45] Operation: 72-27=45 Exploring Operation: 72-19=53, Resulting Numbers: [27, 53] Generated Node #0,0,1: 19:[27, 53] Operation: 72-19=53 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[19, 45], Operations: ['85-13=72', '72-27=45'] Exploring Operation: 19+45=64, Resulting Numbers: [64] 64,19 unequal: No Solution Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,19 unequal: No Solution No 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: 19:[27, 53], Operations: ['85-13=72', '72-19=53'] Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,19 unequal: No Solution Exploring Operation: 27+53=80, Resulting Numbers: [80] 80,19 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: 19:[13, 39], Operations: ['85-27=58', '58-19=39'] Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,19 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,19 unequal: No Solution Moving to Node #0,1,1 Current State: 19:[19, 45], Operations: ['85-27=58', '58-13=45'] Exploring Operation: 19+45=64, Resulting Numbers: [64] 64,19 unequal: No Solution Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,19 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 12, 51, 32, 36 ]
96
[ "51-12=39", "39-36=3", "32*3=96" ]
Current State: 96:[12, 51, 32, 36], Operations: [] Exploring Operation: 51-12=39, Resulting Numbers: [32, 36, 39] Generated Node #2: [32, 36, 39] from Operation: 51-12=39 Current State: 96:[32, 36, 39], Operations: ['51-12=39'] Exploring Operation: 39-36=3, Resulting Numbers: [32, 3] Generated Node #3: [32, 3] from Operation: 39-36=3 Current State: 96:[32, 3], Operations: ['51-12=39', '39-36=3'] Exploring Operation: 32*3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[12, 51, 32, 36], Operations: [] Exploring Operation: 51-36=15, Resulting Numbers: [12, 32, 15] Generated Node #0,0: 96:[12, 32, 15] Operation: 51-36=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[12, 32, 15], Operations: ['51-36=15'] Exploring Operation: 15-12=3, Resulting Numbers: [32, 3] Generated Node #0,0,0: 96:[32, 3] Operation: 15-12=3 Moving to Node #0,0,0 Current State: 96:[32, 3], Operations: ['51-36=15', '15-12=3'] Exploring Operation: 32*3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[12, 51, 32, 36], Operations: [] Exploring Operation: 51-36=15, Resulting Numbers: [12, 32, 15] Generated Node #0,0: 96:[12, 32, 15] Operation: 51-36=15 Moving to Node #0,0 Current State: 96:[12, 32, 15], Operations: ['51-36=15'] Exploring Operation: 15-12=3, Resulting Numbers: [32, 3] Generated Node #0,0,0: 96:[32, 3] Operation: 15-12=3 Moving to Node #0,0,0 Current State: 96:[32, 3], Operations: ['51-36=15', '15-12=3'] Exploring Operation: 32*3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic