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
[ 22, 63, 37, 60 ]
45
[ "37-22=15", "63-60=3", "15*3=45" ]
Current State: 45:[22, 63, 37, 60], Operations: [] Exploring Operation: 37-22=15, Resulting Numbers: [63, 60, 15] Generated Node #2: [63, 60, 15] from Operation: 37-22=15 Current State: 45:[63, 60, 15], Operations: ['37-22=15'] Exploring Operation: 63-60=3, Resulting Numbers: [15, 3] Generated Node #3: [15, 3] from Operation: 63-60=3 Current State: 45:[15, 3], Operations: ['37-22=15', '63-60=3'] Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[22, 63, 37, 60], Operations: [] Exploring Operation: 63-22=41, Resulting Numbers: [37, 60, 41] Generated Node #0,0: 45:[37, 60, 41] Operation: 63-22=41 Exploring Operation: 63-60=3, Resulting Numbers: [22, 37, 3] Generated Node #0,1: 45:[22, 37, 3] Operation: 63-60=3 Moving to Node #0,1 Current State: 45:[22, 37, 3], Operations: ['63-60=3'] Exploring Operation: 37-22=15, Resulting Numbers: [3, 15] Generated Node #0,1,0: 45:[3, 15] Operation: 37-22=15 Exploring Operation: 22-3=19, Resulting Numbers: [37, 19] Generated Node #0,1,1: 45:[37, 19] Operation: 22-3=19 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[3, 15], Operations: ['63-60=3', '37-22=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[22, 63, 37, 60], Operations: [] Exploring Operation: 63-60=3, Resulting Numbers: [22, 37, 3] Generated Node #0,1: 45:[22, 37, 3] Operation: 63-60=3 Moving to Node #0,1 Current State: 45:[22, 37, 3], Operations: ['63-60=3'] Exploring Operation: 37-22=15, Resulting Numbers: [3, 15] Generated Node #0,1,0: 45:[3, 15] Operation: 37-22=15 Moving to Node #0,1,0 Current State: 45:[3, 15], Operations: ['63-60=3', '37-22=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 37, 14, 41, 18 ]
38
[ "41-37=4", "14*4=56", "56-18=38" ]
Current State: 38:[37, 14, 41, 18], Operations: [] Exploring Operation: 41-37=4, Resulting Numbers: [14, 18, 4] Generated Node #2: [14, 18, 4] from Operation: 41-37=4 Current State: 38:[14, 18, 4], Operations: ['41-37=4'] Exploring Operation: 14*4=56, Resulting Numbers: [18, 56] Generated Node #3: [18, 56] from Operation: 14*4=56 Current State: 38:[18, 56], Operations: ['41-37=4', '14*4=56'] Exploring Operation: 56-18=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[37, 14, 41, 18], Operations: [] Exploring Operation: 18-14=4, Resulting Numbers: [37, 41, 4] Generated Node #0,0: 38:[37, 41, 4] Operation: 18-14=4 Exploring Operation: 37-14=23, Resulting Numbers: [41, 18, 23] Generated Node #0,1: 38:[41, 18, 23] Operation: 37-14=23 Exploring Operation: 41-37=4, Resulting Numbers: [14, 18, 4] Generated Node #0,2: 38:[14, 18, 4] Operation: 41-37=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[37, 41, 4], Operations: ['18-14=4'] Exploring Operation: 41-4=37, Resulting Numbers: [37, 37] Generated Node #0,0,0: 38:[37, 37] Operation: 41-4=37 Exploring Operation: 37+4=41, Resulting Numbers: [41, 41] Generated Node #0,0,1: 38:[41, 41] Operation: 37+4=41 Exploring Operation: 41-37=4, Resulting Numbers: [4, 4] Generated Node #0,0,2: 38:[4, 4] Operation: 41-37=4 Moving to Node #0,0,0 Current State: 38:[37, 37], Operations: ['18-14=4', '41-4=37'] Exploring Operation: 37-37=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 37+37=74, Resulting Numbers: [74] 74,38 unequal: No Solution Exploring Operation: 37/37=1, Resulting Numbers: [1] 1,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[4, 4], Operations: ['18-14=4', '41-37=4'] Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[41, 41], Operations: ['18-14=4', '37+4=41'] Exploring Operation: 41/41=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,38 unequal: No Solution Exploring Operation: 41-41=0, Resulting Numbers: [0] 0,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[41, 18, 23], Operations: ['37-14=23'] Exploring Operation: 23-18=5, Resulting Numbers: [41, 5] Generated Node #0,1,0: 38:[41, 5] Operation: 23-18=5 Exploring Operation: 41-23=18, Resulting Numbers: [18, 18] Generated Node #0,1,1: 38:[18, 18] Operation: 41-23=18 Exploring Operation: 18+23=41, Resulting Numbers: [41, 41] Generated Node #0,1,2: 38:[41, 41] Operation: 18+23=41 Moving to Node #0,1,1 Current State: 38:[18, 18], Operations: ['37-14=23', '41-23=18'] Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 18-18=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[41, 5], Operations: ['37-14=23', '23-18=5'] Exploring Operation: 41*5=205, Resulting Numbers: [205] 205,38 unequal: No Solution Exploring Operation: 41+5=46, Resulting Numbers: [46] 46,38 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,38 unequal: No Solution Moving to Node #0,1,2 Current State: 38:[41, 41], Operations: ['37-14=23', '18+23=41'] Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,38 unequal: No Solution Exploring Operation: 41-41=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 41/41=1, Resulting Numbers: [1] 1,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[14, 18, 4], Operations: ['41-37=4'] Exploring Operation: 14+4=18, Resulting Numbers: [18, 18] Generated Node #0,2,0: 38:[18, 18] Operation: 14+4=18 Exploring Operation: 14+18=32, Resulting Numbers: [4, 32] Generated Node #0,2,1: 38:[4, 32] Operation: 14+18=32 Exploring Operation: 18-14=4, Resulting Numbers: [4, 4] Generated Node #0,2,2: 38:[4, 4] Operation: 18-14=4 Moving to Node #0,2,0 Current State: 38:[18, 18], Operations: ['41-37=4', '14+4=18'] Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 18-18=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[4, 4], Operations: ['41-37=4', '18-14=4'] Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,38 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,38 unequal: No Solution Moving to Node #0,2,1 Current State: 38:[4, 32], Operations: ['41-37=4', '14+18=32'] Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,38 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 36, 80, 59, 84 ]
68
[ "84-80=4", "36/4=9", "59+9=68" ]
Current State: 68:[36, 80, 59, 84], Operations: [] Exploring Operation: 84-80=4, Resulting Numbers: [36, 59, 4] Generated Node #2: [36, 59, 4] from Operation: 84-80=4 Current State: 68:[36, 59, 4], Operations: ['84-80=4'] Exploring Operation: 36/4=9, Resulting Numbers: [59, 9] Generated Node #3: [59, 9] from Operation: 36/4=9 Current State: 68:[59, 9], Operations: ['84-80=4', '36/4=9'] Exploring Operation: 59+9=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[36, 80, 59, 84], Operations: [] Exploring Operation: 80-59=21, Resulting Numbers: [36, 84, 21] Generated Node #0,0: 68:[36, 84, 21] Operation: 80-59=21 Exploring Operation: 84-80=4, Resulting Numbers: [36, 59, 4] Generated Node #0,1: 68:[36, 59, 4] Operation: 84-80=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[36, 59, 4], Operations: ['84-80=4'] Exploring Operation: 59-36=23, Resulting Numbers: [4, 23] Generated Node #0,1,0: 68:[4, 23] Operation: 59-36=23 Exploring Operation: 59+4=63, Resulting Numbers: [36, 63] Generated Node #0,1,1: 68:[36, 63] Operation: 59+4=63 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 68:[4, 23], Operations: ['84-80=4', '59-36=23'] Exploring Operation: 4+23=27, Resulting Numbers: [27] 27,68 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,68 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:[36, 63], Operations: ['84-80=4', '59+4=63'] Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,68 unequal: No Solution Exploring Operation: 36+63=99, Resulting Numbers: [99] 99,68 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:[36, 84, 21], Operations: ['80-59=21'] Exploring Operation: 84/21=4, Resulting Numbers: [36, 4] Generated Node #0,0,0: 68:[36, 4] Operation: 84/21=4 Exploring Operation: 84-21=63, Resulting Numbers: [36, 63] Generated Node #0,0,1: 68:[36, 63] Operation: 84-21=63 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[36, 4], Operations: ['80-59=21', '84/21=4'] Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,68 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,68 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:[36, 63], Operations: ['80-59=21', '84-21=63'] Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,68 unequal: No Solution Exploring Operation: 36+63=99, Resulting Numbers: [99] 99,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 31, 40, 23, 78 ]
46
[ "40-31=9", "78-23=55", "55-9=46" ]
Current State: 46:[31, 40, 23, 78], Operations: [] Exploring Operation: 40-31=9, Resulting Numbers: [23, 78, 9] Generated Node #2: [23, 78, 9] from Operation: 40-31=9 Current State: 46:[23, 78, 9], Operations: ['40-31=9'] Exploring Operation: 78-23=55, Resulting Numbers: [9, 55] Generated Node #3: [9, 55] from Operation: 78-23=55 Current State: 46:[9, 55], Operations: ['40-31=9', '78-23=55'] Exploring Operation: 55-9=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[31, 40, 23, 78], Operations: [] Exploring Operation: 78-40=38, Resulting Numbers: [31, 23, 38] Generated Node #0,0: 46:[31, 23, 38] Operation: 78-40=38 Exploring Operation: 78-31=47, Resulting Numbers: [40, 23, 47] Generated Node #0,1: 46:[40, 23, 47] Operation: 78-31=47 Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[40, 23, 47], Operations: ['78-31=47'] Exploring Operation: 40-23=17, Resulting Numbers: [47, 17] Generated Node #0,1,0: 46:[47, 17] Operation: 40-23=17 Exploring Operation: 47-40=7, Resulting Numbers: [23, 7] Generated Node #0,1,1: 46:[23, 7] Operation: 47-40=7 Moving to Node #0,1,1 Current State: 46:[23, 7], Operations: ['78-31=47', '47-40=7'] Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,46 unequal: No Solution Moving to Node #0,1,0 Current State: 46:[47, 17], Operations: ['78-31=47', '40-23=17'] Exploring Operation: 47+17=64, Resulting Numbers: [64] 64,46 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[31, 23, 38], Operations: ['78-40=38'] Exploring Operation: 31-23=8, Resulting Numbers: [38, 8] Generated Node #0,0,0: 46:[38, 8] Operation: 31-23=8 Exploring Operation: 38-31=7, Resulting Numbers: [23, 7] Generated Node #0,0,1: 46:[23, 7] Operation: 38-31=7 Moving to Node #0,0,1 Current State: 46:[23, 7], Operations: ['78-40=38', '38-31=7'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,46 unequal: No Solution Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[38, 8], Operations: ['78-40=38', '31-23=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[31, 40, 23, 78], Operations: [] Exploring Operation: 78-40=38, Resulting Numbers: [31, 23, 38] Generated Node #0,0: 46:[31, 23, 38] Operation: 78-40=38 Moving to Node #0,0 Current State: 46:[31, 23, 38], Operations: ['78-40=38'] Exploring Operation: 31-23=8, Resulting Numbers: [38, 8] Generated Node #0,0,0: 46:[38, 8] Operation: 31-23=8 Moving to Node #0,0,0 Current State: 46:[38, 8], Operations: ['78-40=38', '31-23=8'] Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 13, 3, 31, 49 ]
55
[ "31-13=18", "18/3=6", "49+6=55" ]
Current State: 55:[13, 3, 31, 49], Operations: [] Exploring Operation: 31-13=18, Resulting Numbers: [3, 49, 18] Generated Node #2: [3, 49, 18] from Operation: 31-13=18 Current State: 55:[3, 49, 18], Operations: ['31-13=18'] Exploring Operation: 18/3=6, Resulting Numbers: [49, 6] Generated Node #3: [49, 6] from Operation: 18/3=6 Current State: 55:[49, 6], Operations: ['31-13=18', '18/3=6'] Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[13, 3, 31, 49], Operations: [] Exploring Operation: 31-13=18, Resulting Numbers: [3, 49, 18] Generated Node #0,0: 55:[3, 49, 18] Operation: 31-13=18 Exploring Operation: 49-31=18, Resulting Numbers: [13, 3, 18] Generated Node #0,1: 55:[13, 3, 18] Operation: 49-31=18 Exploring Operation: 13+31=44, Resulting Numbers: [3, 49, 44] Generated Node #0,2: 55:[3, 49, 44] Operation: 13+31=44 Exploring Operation: 31-3=28, Resulting Numbers: [13, 49, 28] Generated Node #0,3: 55:[13, 49, 28] Operation: 31-3=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[13, 3, 18], Operations: ['49-31=18'] Exploring Operation: 18-13=5, Resulting Numbers: [3, 5] Generated Node #0,1,0: 55:[3, 5] Operation: 18-13=5 Exploring Operation: 3*18=54, Resulting Numbers: [13, 54] Generated Node #0,1,1: 55:[13, 54] Operation: 3*18=54 Exploring Operation: 18/3=6, Resulting Numbers: [13, 6] Generated Node #0,1,2: 55:[13, 6] Operation: 18/3=6 Exploring Operation: 18-3=15, Resulting Numbers: [13, 15] Generated Node #0,1,3: 55:[13, 15] Operation: 18-3=15 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[3, 5], Operations: ['49-31=18', '18-13=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,55 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:[13, 54], Operations: ['49-31=18', '3*18=54'] Exploring Operation: 13+54=67, Resulting Numbers: [67] 67,55 unequal: No Solution Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,55 unequal: No Solution Exploring Operation: 13*54=702, Resulting Numbers: [702] 702,55 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:[13, 6], Operations: ['49-31=18', '18/3=6'] Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,55 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,55 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:[13, 15], Operations: ['49-31=18', '18-3=15'] Exploring Operation: 13+15=28, Resulting Numbers: [28] 28,55 unequal: No Solution Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 13*15=195, Resulting Numbers: [195] 195,55 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:[3, 49, 18], Operations: ['31-13=18'] Exploring Operation: 3+49=52, Resulting Numbers: [18, 52] Generated Node #0,0,0: 55:[18, 52] Operation: 3+49=52 Exploring Operation: 3*18=54, Resulting Numbers: [49, 54] Generated Node #0,0,1: 55:[49, 54] Operation: 3*18=54 Exploring Operation: 18/3=6, Resulting Numbers: [49, 6] Generated Node #0,0,2: 55:[49, 6] Operation: 18/3=6 Exploring Operation: 18-3=15, Resulting Numbers: [49, 15] Generated Node #0,0,3: 55:[49, 15] Operation: 18-3=15 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 55:[49, 54], Operations: ['31-13=18', '3*18=54'] Exploring Operation: 49*54=2646, Resulting Numbers: [2646] 2646,55 unequal: No Solution Exploring Operation: 49+54=103, Resulting Numbers: [103] 103,55 unequal: No Solution Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,55 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:[49, 6], Operations: ['31-13=18', '18/3=6'] Exploring Operation: 49*6=294, Resulting Numbers: [294] 294,55 unequal: No Solution Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[13, 3, 31, 49], Operations: [] Exploring Operation: 31-13=18, Resulting Numbers: [3, 49, 18] Generated Node #0,0: 55:[3, 49, 18] Operation: 31-13=18 Moving to Node #0,0 Current State: 55:[3, 49, 18], Operations: ['31-13=18'] Exploring Operation: 18/3=6, Resulting Numbers: [49, 6] Generated Node #0,0,2: 55:[49, 6] Operation: 18/3=6 Moving to Node #0,0,2 Current State: 55:[49, 6], Operations: ['31-13=18', '18/3=6'] Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.971354
hs_4
sum_heuristic
[ 85, 87, 47, 11 ]
83
[ "87-85=2", "47*2=94", "94-11=83" ]
Current State: 83:[85, 87, 47, 11], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [47, 11, 2] Generated Node #2: [47, 11, 2] from Operation: 87-85=2 Current State: 83:[47, 11, 2], Operations: ['87-85=2'] Exploring Operation: 47*2=94, Resulting Numbers: [11, 94] Generated Node #3: [11, 94] from Operation: 47*2=94 Current State: 83:[11, 94], Operations: ['87-85=2', '47*2=94'] Exploring Operation: 94-11=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[85, 87, 47, 11], Operations: [] Exploring Operation: 87-11=76, Resulting Numbers: [85, 47, 76] Generated Node #0,0: 83:[85, 47, 76] Operation: 87-11=76 Exploring Operation: 85-11=74, Resulting Numbers: [87, 47, 74] Generated Node #0,1: 83:[87, 47, 74] Operation: 85-11=74 Exploring Operation: 47+11=58, Resulting Numbers: [85, 87, 58] Generated Node #0,2: 83:[85, 87, 58] Operation: 47+11=58 Exploring Operation: 85+11=96, Resulting Numbers: [87, 47, 96] Generated Node #0,3: 83:[87, 47, 96] Operation: 85+11=96 Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[85, 87, 58], Operations: ['47+11=58'] Exploring Operation: 87-58=29, Resulting Numbers: [85, 29] Generated Node #0,2,0: 83:[85, 29] Operation: 87-58=29 Exploring Operation: 87+58=145, Resulting Numbers: [85, 145] Generated Node #0,2,1: 83:[85, 145] Operation: 87+58=145 Exploring Operation: 85-58=27, Resulting Numbers: [87, 27] Generated Node #0,2,2: 83:[87, 27] Operation: 85-58=27 Exploring Operation: 85+58=143, Resulting Numbers: [87, 143] Generated Node #0,2,3: 83:[87, 143] Operation: 85+58=143 Moving to Node #0,2,0 Current State: 83:[85, 29], Operations: ['47+11=58', '87-58=29'] Exploring Operation: 85*29=2465, Resulting Numbers: [2465] 2465,83 unequal: No Solution Exploring Operation: 85+29=114, Resulting Numbers: [114] 114,83 unequal: No Solution Exploring Operation: 85-29=56, Resulting Numbers: [56] 56,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[87, 27], Operations: ['47+11=58', '85-58=27'] Exploring Operation: 87-27=60, Resulting Numbers: [60] 60,83 unequal: No Solution Exploring Operation: 87+27=114, Resulting Numbers: [114] 114,83 unequal: No Solution Exploring Operation: 87*27=2349, Resulting Numbers: [2349] 2349,83 unequal: No Solution Moving to Node #0,2,3 Current State: 83:[87, 143], Operations: ['47+11=58', '85+58=143'] Exploring Operation: 87+143=230, Resulting Numbers: [230] 230,83 unequal: No Solution Exploring Operation: 87*143=12441, Resulting Numbers: [12441] 12441,83 unequal: No Solution Exploring Operation: 143-87=56, Resulting Numbers: [56] 56,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[85, 145], Operations: ['47+11=58', '87+58=145'] Exploring Operation: 85+145=230, Resulting Numbers: [230] 230,83 unequal: No Solution Exploring Operation: 85*145=12325, Resulting Numbers: [12325] 12325,83 unequal: No Solution Exploring Operation: 145-85=60, Resulting Numbers: [60] 60,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[85, 47, 76], Operations: ['87-11=76'] Exploring Operation: 47+76=123, Resulting Numbers: [85, 123] Generated Node #0,0,0: 83:[85, 123] Operation: 47+76=123 Exploring Operation: 85+47=132, Resulting Numbers: [76, 132] Generated Node #0,0,1: 83:[76, 132] Operation: 85+47=132 Exploring Operation: 76-47=29, Resulting Numbers: [85, 29] Generated Node #0,0,2: 83:[85, 29] Operation: 76-47=29 Exploring Operation: 85-47=38, Resulting Numbers: [76, 38] Generated Node #0,0,3: 83:[76, 38] Operation: 85-47=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[85, 123], Operations: ['87-11=76', '47+76=123'] Exploring Operation: 85+123=208, Resulting Numbers: [208] 208,83 unequal: No Solution Exploring Operation: 85*123=10455, Resulting Numbers: [10455] 10455,83 unequal: No Solution Exploring Operation: 123-85=38, Resulting Numbers: [38] 38,83 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:[76, 38], Operations: ['87-11=76', '85-47=38'] Exploring Operation: 76*38=2888, Resulting Numbers: [2888] 2888,83 unequal: No Solution Exploring Operation: 76-38=38, Resulting Numbers: [38] 38,83 unequal: No Solution Exploring Operation: 76+38=114, Resulting Numbers: [114] 114,83 unequal: No Solution Exploring Operation: 76/38=2, Resulting Numbers: [2] 2,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[76, 132], Operations: ['87-11=76', '85+47=132'] Exploring Operation: 76+132=208, Resulting Numbers: [208] 208,83 unequal: No Solution Exploring Operation: 76*132=10032, Resulting Numbers: [10032] 10032,83 unequal: No Solution Exploring Operation: 132-76=56, Resulting Numbers: [56] 56,83 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:[85, 29], Operations: ['87-11=76', '76-47=29'] Exploring Operation: 85*29=2465, Resulting Numbers: [2465] 2465,83 unequal: No Solution Exploring Operation: 85-29=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 85+29=114, Resulting Numbers: [114] 114,83 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, 47, 74], Operations: ['85-11=74'] Exploring Operation: 74-47=27, Resulting Numbers: [87, 27] Generated Node #0,1,0: 83:[87, 27] Operation: 74-47=27 Exploring Operation: 87-47=40, Resulting Numbers: [74, 40] Generated Node #0,1,1: 83:[74, 40] Operation: 87-47=40 Exploring Operation: 87+47=134, Resulting Numbers: [74, 134] Generated Node #0,1,2: 83:[74, 134] Operation: 87+47=134 Exploring Operation: 47+74=121, Resulting Numbers: [87, 121] Generated Node #0,1,3: 83:[87, 121] Operation: 47+74=121 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 83:[87, 121], Operations: ['85-11=74', '47+74=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 No 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: 83:[74, 40], Operations: ['85-11=74', '87-47=40'] Exploring Operation: 74+40=114, Resulting Numbers: [114] 114,83 unequal: No Solution Exploring Operation: 74*40=2960, Resulting Numbers: [2960] 2960,83 unequal: No Solution Exploring Operation: 74-40=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 #0,1,0 Current State: 83:[87, 27], Operations: ['85-11=74', '74-47=27'] Exploring Operation: 87+27=114, Resulting Numbers: [114] 114,83 unequal: No Solution Exploring Operation: 87-27=60, Resulting Numbers: [60] 60,83 unequal: No Solution Exploring Operation: 87*27=2349, Resulting Numbers: [2349] 2349,83 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 #0,1,2 Current State: 83:[74, 134], Operations: ['85-11=74', '87+47=134'] Exploring Operation: 74+134=208, Resulting Numbers: [208] 208,83 unequal: No Solution Exploring Operation: 74*134=9916, Resulting Numbers: [9916] 9916,83 unequal: No Solution Exploring Operation: 134-74=60, Resulting Numbers: [60] 60,83 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 #0,3 Current State: 83:[87, 47, 96], Operations: ['85+11=96'] Exploring Operation: 87+47=134, Resulting Numbers: [96, 134] Generated Node #0,3,0: 83:[96, 134] Operation: 87+47=134 Exploring Operation: 47+96=143, Resulting Numbers: [87, 143] Generated Node #0,3,1: 83:[87, 143] Operation: 47+96=143 Exploring Operation: 96-47=49, Resulting Numbers: [87, 49] Generated Node #0,3,2: 83:[87, 49] Operation: 96-47=49 Exploring Operation: 87-47=40, Resulting Numbers: [96, 40] Generated Node #0,3,3: 83:[96, 40] Operation: 87-47=40 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 83:[87, 49], Operations: ['85+11=96', '96-47=49'] Exploring Operation: 87+49=136, Resulting Numbers: [136] 136,83 unequal: No Solution Exploring Operation: 87-49=38, Resulting Numbers: [38] 38,83 unequal: No Solution Exploring Operation: 87*49=4263, Resulting Numbers: [4263] 4263,83 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 #0,3,3 Current State: 83:[96, 40], Operations: ['85+11=96', '87-47=40'] Exploring Operation: 96-40=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 96*40=3840, Resulting Numbers: [3840] 3840,83 unequal: No Solution Exploring Operation: 96+40=136, Resulting Numbers: [136] 136,83 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, 134], Operations: ['85+11=96', '87+47=134'] Exploring Operation: 134-96=38, Resulting Numbers: [38] 38,83 unequal: No Solution Exploring Operation: 96*134=12864, Resulting Numbers: [12864] 12864,83 unequal: No Solution Exploring Operation: 96+134=230, Resulting Numbers: [230] 230,83 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:[87, 143], Operations: ['85+11=96', '47+96=143'] Exploring Operation: 143-87=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 87*143=12441, Resulting Numbers: [12441] 12441,83 unequal: No Solution Exploring Operation: 87+143=230, Resulting Numbers: [230] 230,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 20, 9, 3, 43 ]
21
[ "20+43=63", "9/3=3", "63/3=21" ]
Current State: 21:[20, 9, 3, 43], Operations: [] Exploring Operation: 20+43=63, Resulting Numbers: [9, 3, 63] Generated Node #2: [9, 3, 63] from Operation: 20+43=63 Current State: 21:[9, 3, 63], Operations: ['20+43=63'] Exploring Operation: 9/3=3, Resulting Numbers: [63, 3] Generated Node #3: [63, 3] from Operation: 9/3=3 Current State: 21:[63, 3], Operations: ['20+43=63', '9/3=3'] Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[20, 9, 3, 43], Operations: [] Exploring Operation: 43-9=34, Resulting Numbers: [20, 3, 34] Generated Node #0,0: 21:[20, 3, 34] Operation: 43-9=34 Exploring Operation: 43-20=23, Resulting Numbers: [9, 3, 23] Generated Node #0,1: 21:[9, 3, 23] Operation: 43-20=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[9, 3, 23], Operations: ['43-20=23'] Exploring Operation: 9/3=3, Resulting Numbers: [23, 3] Generated Node #0,1,0: 21:[23, 3] Operation: 9/3=3 Exploring Operation: 9-3=6, Resulting Numbers: [23, 6] Generated Node #0,1,1: 21:[23, 6] Operation: 9-3=6 Moving to Node #0,1,0 Current State: 21:[23, 3], Operations: ['43-20=23', '9/3=3'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,21 unequal: No Solution Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[23, 6], Operations: ['43-20=23', '9-3=6'] Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,21 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[20, 3, 34], Operations: ['43-9=34'] Exploring Operation: 34-20=14, Resulting Numbers: [3, 14] Generated Node #0,0,0: 21:[3, 14] Operation: 34-20=14 Exploring Operation: 34-3=31, Resulting Numbers: [20, 31] Generated Node #0,0,1: 21:[20, 31] Operation: 34-3=31 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[3, 14], Operations: ['43-9=34', '34-20=14'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,21 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:[20, 31], Operations: ['43-9=34', '34-3=31'] Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,21 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
sum_heuristic
[ 19, 10, 54, 4 ]
96
[ "19-4=15", "10*15=150", "150-54=96" ]
Current State: 96:[19, 10, 54, 4], Operations: [] Exploring Operation: 19-4=15, Resulting Numbers: [10, 54, 15] Generated Node #2: [10, 54, 15] from Operation: 19-4=15 Current State: 96:[10, 54, 15], Operations: ['19-4=15'] Exploring Operation: 10*15=150, Resulting Numbers: [54, 150] Generated Node #3: [54, 150] from Operation: 10*15=150 Current State: 96:[54, 150], Operations: ['19-4=15', '10*15=150'] Exploring Operation: 150-54=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[19, 10, 54, 4], Operations: [] Exploring Operation: 54-19=35, Resulting Numbers: [10, 4, 35] Generated Node #0,0: 96:[10, 4, 35] Operation: 54-19=35 Exploring Operation: 19-10=9, Resulting Numbers: [54, 4, 9] Generated Node #0,1: 96:[54, 4, 9] Operation: 19-10=9 Exploring Operation: 54-10=44, Resulting Numbers: [19, 4, 44] Generated Node #0,2: 96:[19, 4, 44] Operation: 54-10=44 Exploring Operation: 54-4=50, Resulting Numbers: [19, 10, 50] Generated Node #0,3: 96:[19, 10, 50] Operation: 54-4=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[10, 4, 35], Operations: ['54-19=35'] Exploring Operation: 35-10=25, Resulting Numbers: [4, 25] Generated Node #0,0,0: 96:[4, 25] Operation: 35-10=25 Exploring Operation: 10-4=6, Resulting Numbers: [35, 6] Generated Node #0,0,1: 96:[35, 6] Operation: 10-4=6 Exploring Operation: 10+35=45, Resulting Numbers: [4, 45] Generated Node #0,0,2: 96:[4, 45] Operation: 10+35=45 Exploring Operation: 35-4=31, Resulting Numbers: [10, 31] Generated Node #0,0,3: 96:[10, 31] Operation: 35-4=31 Moving to Node #0,0,0 Current State: 96:[4, 25], Operations: ['54-19=35', '35-10=25'] Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,96 unequal: No Solution Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,96 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[4, 45], Operations: ['54-19=35', '10+35=45'] Exploring Operation: 4*45=180, Resulting Numbers: [180] 180,96 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,96 unequal: No Solution Exploring Operation: 4+45=49, Resulting Numbers: [49] 49,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[35, 6], Operations: ['54-19=35', '10-4=6'] Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,96 unequal: No Solution Exploring Operation: 35*6=210, Resulting Numbers: [210] 210,96 unequal: No Solution Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[10, 31], Operations: ['54-19=35', '35-4=31'] Exploring Operation: 10*31=310, Resulting Numbers: [310] 310,96 unequal: No Solution Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 10+31=41, Resulting Numbers: [41] 41,96 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 #0,1 Current State: 96:[54, 4, 9], Operations: ['19-10=9'] Exploring Operation: 54-4=50, Resulting Numbers: [9, 50] Generated Node #0,1,0: 96:[9, 50] Operation: 54-4=50 Exploring Operation: 54-9=45, Resulting Numbers: [4, 45] Generated Node #0,1,1: 96:[4, 45] Operation: 54-9=45 Exploring Operation: 4+9=13, Resulting Numbers: [54, 13] Generated Node #0,1,2: 96:[54, 13] Operation: 4+9=13 Exploring Operation: 54/9=6, Resulting Numbers: [4, 6] Generated Node #0,1,3: 96:[4, 6] Operation: 54/9=6 Moving to Node #0,1,3 Current State: 96:[4, 6], Operations: ['19-10=9', '54/9=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[4, 45], Operations: ['19-10=9', '54-9=45'] Exploring Operation: 4+45=49, Resulting Numbers: [49] 49,96 unequal: No Solution Exploring Operation: 4*45=180, Resulting Numbers: [180] 180,96 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[9, 50], Operations: ['19-10=9', '54-4=50'] Exploring Operation: 50-9=41, Resulting Numbers: [41] 41,96 unequal: No Solution Exploring Operation: 9+50=59, Resulting Numbers: [59] 59,96 unequal: No Solution Exploring Operation: 9*50=450, Resulting Numbers: [450] 450,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[54, 13], Operations: ['19-10=9', '4+9=13'] Exploring Operation: 54+13=67, Resulting Numbers: [67] 67,96 unequal: No Solution Exploring Operation: 54*13=702, Resulting Numbers: [702] 702,96 unequal: No Solution Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,96 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 #0,2 Current State: 96:[19, 4, 44], Operations: ['54-10=44'] Exploring Operation: 44/4=11, Resulting Numbers: [19, 11] Generated Node #0,2,0: 96:[19, 11] Operation: 44/4=11 Exploring Operation: 19+4=23, Resulting Numbers: [44, 23] Generated Node #0,2,1: 96:[44, 23] Operation: 19+4=23 Exploring Operation: 44-19=25, Resulting Numbers: [4, 25] Generated Node #0,2,2: 96:[4, 25] Operation: 44-19=25 Exploring Operation: 4+44=48, Resulting Numbers: [19, 48] Generated Node #0,2,3: 96:[19, 48] Operation: 4+44=48 Moving to Node #0,2,2 Current State: 96:[4, 25], Operations: ['54-10=44', '44-19=25'] Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,96 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,96 unequal: No Solution Moving to Node #0,2,3 Current State: 96:[19, 48], Operations: ['54-10=44', '4+44=48'] Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,96 unequal: No Solution Exploring Operation: 19*48=912, Resulting Numbers: [912] 912,96 unequal: No Solution Exploring Operation: 19+48=67, Resulting Numbers: [67] 67,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[19, 11], Operations: ['54-10=44', '44/4=11'] Exploring Operation: 19*11=209, Resulting Numbers: [209] 209,96 unequal: No Solution Exploring Operation: 19+11=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[44, 23], Operations: ['54-10=44', '19+4=23'] Exploring Operation: 44*23=1012, Resulting Numbers: [1012] 1012,96 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 44+23=67, Resulting Numbers: [67] 67,96 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:[19, 10, 50], Operations: ['54-4=50'] Exploring Operation: 50/10=5, Resulting Numbers: [19, 5] Generated Node #0,3,0: 96:[19, 5] Operation: 50/10=5 Exploring Operation: 19-10=9, Resulting Numbers: [50, 9] Generated Node #0,3,1: 96:[50, 9] Operation: 19-10=9 Exploring Operation: 50-19=31, Resulting Numbers: [10, 31] Generated Node #0,3,2: 96:[10, 31] Operation: 50-19=31 Exploring Operation: 19+10=29, Resulting Numbers: [50, 29] Generated Node #0,3,3: 96:[50, 29] Operation: 19+10=29 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 96:[50, 9], Operations: ['54-4=50', '19-10=9'] Exploring Operation: 50*9=450, Resulting Numbers: [450] 450,96 unequal: No Solution Exploring Operation: 50+9=59, Resulting Numbers: [59] 59,96 unequal: No Solution Exploring Operation: 50-9=41, Resulting Numbers: [41] 41,96 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 #0,3,2 Current State: 96:[10, 31], Operations: ['54-4=50', '50-19=31'] Exploring Operation: 10*31=310, Resulting Numbers: [310] 310,96 unequal: No Solution Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 10+31=41, Resulting Numbers: [41] 41,96 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 #0,3,0 Current State: 96:[19, 5], Operations: ['54-4=50', '50/10=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,96 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,96 unequal: No Solution Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 96:[50, 29], Operations: ['54-4=50', '19+10=29'] Exploring Operation: 50*29=1450, Resulting Numbers: [1450] 1450,96 unequal: No Solution Exploring Operation: 50+29=79, Resulting Numbers: [79] 79,96 unequal: No Solution Exploring Operation: 50-29=21, Resulting Numbers: [21] 21,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 27, 42, 64, 7 ]
31
[ "64-27=37", "42/7=6", "37-6=31" ]
Current State: 31:[27, 42, 64, 7], Operations: [] Exploring Operation: 64-27=37, Resulting Numbers: [42, 7, 37] Generated Node #2: [42, 7, 37] from Operation: 64-27=37 Current State: 31:[42, 7, 37], Operations: ['64-27=37'] Exploring Operation: 42/7=6, Resulting Numbers: [37, 6] Generated Node #3: [37, 6] from Operation: 42/7=6 Current State: 31:[37, 6], Operations: ['64-27=37', '42/7=6'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[27, 42, 64, 7], Operations: [] Exploring Operation: 64-42=22, Resulting Numbers: [27, 7, 22] Generated Node #0,0: 31:[27, 7, 22] Operation: 64-42=22 Exploring Operation: 64-27=37, Resulting Numbers: [42, 7, 37] Generated Node #0,1: 31:[42, 7, 37] Operation: 64-27=37 Exploring Operation: 42-7=35, Resulting Numbers: [27, 64, 35] Generated Node #0,2: 31:[27, 64, 35] Operation: 42-7=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[27, 7, 22], Operations: ['64-42=22'] Exploring Operation: 27+7=34, Resulting Numbers: [22, 34] Generated Node #0,0,0: 31:[22, 34] Operation: 27+7=34 Exploring Operation: 27-7=20, Resulting Numbers: [22, 20] Generated Node #0,0,1: 31:[22, 20] Operation: 27-7=20 Exploring Operation: 7+22=29, Resulting Numbers: [27, 29] Generated Node #0,0,2: 31:[27, 29] Operation: 7+22=29 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 31:[27, 29], Operations: ['64-42=22', '7+22=29'] Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,31 unequal: No Solution Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,31 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 #0,0,0 Current State: 31:[22, 34], Operations: ['64-42=22', '27+7=34'] Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,31 unequal: No Solution Exploring Operation: 22+34=56, Resulting Numbers: [56] 56,31 unequal: No Solution Exploring Operation: 22*34=748, Resulting Numbers: [748] 748,31 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 #0,0,1 Current State: 31:[22, 20], Operations: ['64-42=22', '27-7=20'] 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 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 No 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:[42, 7, 37], Operations: ['64-27=37'] Exploring Operation: 42-7=35, Resulting Numbers: [37, 35] Generated Node #0,1,0: 31:[37, 35] Operation: 42-7=35 Exploring Operation: 42+7=49, Resulting Numbers: [37, 49] Generated Node #0,1,1: 31:[37, 49] Operation: 42+7=49 Exploring Operation: 37-7=30, Resulting Numbers: [42, 30] Generated Node #0,1,2: 31:[42, 30] Operation: 37-7=30 Moving to Node #0,1,0 Current State: 31:[37, 35], Operations: ['64-27=37', '42-7=35'] Exploring Operation: 37+35=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 37*35=1295, Resulting Numbers: [1295] 1295,31 unequal: No Solution Exploring Operation: 37-35=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,1,2 Current State: 31:[42, 30], Operations: ['64-27=37', '37-7=30'] Exploring Operation: 42+30=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 42*30=1260, Resulting Numbers: [1260] 1260,31 unequal: No Solution Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[37, 49], Operations: ['64-27=37', '42+7=49'] Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,31 unequal: No Solution Exploring Operation: 37*49=1813, Resulting Numbers: [1813] 1813,31 unequal: No Solution Exploring Operation: 37+49=86, Resulting Numbers: [86] 86,31 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 #0,2 Current State: 31:[27, 64, 35], Operations: ['42-7=35'] Exploring Operation: 35-27=8, Resulting Numbers: [64, 8] Generated Node #0,2,0: 31:[64, 8] Operation: 35-27=8 Exploring Operation: 64-27=37, Resulting Numbers: [35, 37] Generated Node #0,2,1: 31:[35, 37] Operation: 64-27=37 Exploring Operation: 64-35=29, Resulting Numbers: [27, 29] Generated Node #0,2,2: 31:[27, 29] Operation: 64-35=29 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 31:[27, 29], Operations: ['42-7=35', '64-35=29'] Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,31 unequal: No Solution Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,31 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,31 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 #0,2,1 Current State: 31:[35, 37], Operations: ['42-7=35', '64-27=37'] Exploring Operation: 35*37=1295, Resulting Numbers: [1295] 1295,31 unequal: No Solution Exploring Operation: 37-35=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 35+37=72, Resulting Numbers: [72] 72,31 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:[64, 8], Operations: ['42-7=35', '35-27=8'] Exploring Operation: 64/8=8, Resulting Numbers: [8] 8,31 unequal: No Solution Exploring Operation: 64-8=56, Resulting Numbers: [56] 56,31 unequal: No Solution Exploring Operation: 64+8=72, Resulting Numbers: [72] 72,31 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 No solution found.
0
hs_3
mult_heuristic
[ 21, 53, 87, 35 ]
29
[ "53-21=32", "35-32=3", "87/3=29" ]
Current State: 29:[21, 53, 87, 35], Operations: [] Exploring Operation: 53-21=32, Resulting Numbers: [87, 35, 32] Generated Node #2: [87, 35, 32] from Operation: 53-21=32 Current State: 29:[87, 35, 32], Operations: ['53-21=32'] Exploring Operation: 35-32=3, Resulting Numbers: [87, 3] Generated Node #3: [87, 3] from Operation: 35-32=3 Current State: 29:[87, 3], Operations: ['53-21=32', '35-32=3'] Exploring Operation: 87/3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[21, 53, 87, 35], Operations: [] Exploring Operation: 53-21=32, Resulting Numbers: [87, 35, 32] Generated Node #0,0: 29:[87, 35, 32] Operation: 53-21=32 Exploring Operation: 87-35=52, Resulting Numbers: [21, 53, 52] Generated Node #0,1: 29:[21, 53, 52] Operation: 87-35=52 Exploring Operation: 87-53=34, Resulting Numbers: [21, 35, 34] Generated Node #0,2: 29:[21, 35, 34] Operation: 87-53=34 Start Sub Search at level 1: Moving to Node #0,2 Current State: 29:[21, 35, 34], Operations: ['87-53=34'] Exploring Operation: 35-21=14, Resulting Numbers: [34, 14] Generated Node #0,2,0: 29:[34, 14] Operation: 35-21=14 Exploring Operation: 34-21=13, Resulting Numbers: [35, 13] Generated Node #0,2,1: 29:[35, 13] Operation: 34-21=13 Exploring Operation: 21+35=56, Resulting Numbers: [34, 56] Generated Node #0,2,2: 29:[34, 56] Operation: 21+35=56 Moving to Node #0,2,0 Current State: 29:[34, 14], Operations: ['87-53=34', '35-21=14'] Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,29 unequal: No Solution Exploring Operation: 34+14=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 34*14=476, Resulting Numbers: [476] 476,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[35, 13], Operations: ['87-53=34', '34-21=13'] Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 35*13=455, Resulting Numbers: [455] 455,29 unequal: No Solution Moving to Node #0,2,2 Current State: 29:[34, 56], Operations: ['87-53=34', '21+35=56'] Exploring Operation: 34*56=1904, Resulting Numbers: [1904] 1904,29 unequal: No Solution Exploring Operation: 34+56=90, Resulting Numbers: [90] 90,29 unequal: No Solution Exploring Operation: 56-34=22, Resulting Numbers: [22] 22,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[21, 53, 52], Operations: ['87-35=52'] Exploring Operation: 53-21=32, Resulting Numbers: [52, 32] Generated Node #0,1,0: 29:[52, 32] Operation: 53-21=32 Exploring Operation: 53-52=1, Resulting Numbers: [21, 1] Generated Node #0,1,1: 29:[21, 1] Operation: 53-52=1 Exploring Operation: 52-21=31, Resulting Numbers: [53, 31] Generated Node #0,1,2: 29:[53, 31] Operation: 52-21=31 Moving to Node #0,1,0 Current State: 29:[52, 32], Operations: ['87-35=52', '53-21=32'] Exploring Operation: 52*32=1664, Resulting Numbers: [1664] 1664,29 unequal: No Solution Exploring Operation: 52+32=84, Resulting Numbers: [84] 84,29 unequal: No Solution Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,29 unequal: No Solution Moving to Node #0,1,2 Current State: 29:[53, 31], Operations: ['87-35=52', '52-21=31'] Exploring Operation: 53+31=84, Resulting Numbers: [84] 84,29 unequal: No Solution Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 53*31=1643, Resulting Numbers: [1643] 1643,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[21, 1], Operations: ['87-35=52', '53-52=1'] Exploring Operation: 21*1=21, Resulting Numbers: [21] 21,29 unequal: No Solution Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,29 unequal: No Solution Exploring Operation: 21+1=22, Resulting Numbers: [22] 22,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[87, 35, 32], Operations: ['53-21=32'] Exploring Operation: 35-32=3, Resulting Numbers: [87, 3] Generated Node #0,0,0: 29:[87, 3] Operation: 35-32=3 Exploring Operation: 87-32=55, Resulting Numbers: [35, 55] Generated Node #0,0,1: 29:[35, 55] Operation: 87-32=55 Exploring Operation: 87-35=52, Resulting Numbers: [32, 52] Generated Node #0,0,2: 29:[32, 52] Operation: 87-35=52 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 29:[32, 52], Operations: ['53-21=32', '87-35=52'] Exploring Operation: 32*52=1664, Resulting Numbers: [1664] 1664,29 unequal: No Solution Exploring Operation: 32+52=84, Resulting Numbers: [84] 84,29 unequal: No Solution Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 29:[35, 55], Operations: ['53-21=32', '87-32=55'] Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,29 unequal: No Solution Exploring Operation: 35*55=1925, Resulting Numbers: [1925] 1925,29 unequal: No Solution Exploring Operation: 35+55=90, Resulting Numbers: [90] 90,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[87, 3], Operations: ['53-21=32', '35-32=3'] Exploring Operation: 87/3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[21, 53, 87, 35], Operations: [] Exploring Operation: 53-21=32, Resulting Numbers: [87, 35, 32] Generated Node #0,0: 29:[87, 35, 32] Operation: 53-21=32 Moving to Node #0,0 Current State: 29:[87, 35, 32], Operations: ['53-21=32'] Exploring Operation: 35-32=3, Resulting Numbers: [87, 3] Generated Node #0,0,0: 29:[87, 3] Operation: 35-32=3 Moving to Node #0,0,0 Current State: 29:[87, 3], Operations: ['53-21=32', '35-32=3'] Exploring Operation: 87/3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_3
sum_heuristic
[ 1, 7, 4, 3 ]
38
[ "1+4=5", "7*5=35", "3+35=38" ]
Current State: 38:[1, 7, 4, 3], Operations: [] Exploring Operation: 1+4=5, Resulting Numbers: [7, 3, 5] Generated Node #2: [7, 3, 5] from Operation: 1+4=5 Current State: 38:[7, 3, 5], Operations: ['1+4=5'] Exploring Operation: 7*5=35, Resulting Numbers: [3, 35] Generated Node #3: [3, 35] from Operation: 7*5=35 Current State: 38:[3, 35], Operations: ['1+4=5', '7*5=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[1, 7, 4, 3], Operations: [] Exploring Operation: 7-4=3, Resulting Numbers: [1, 3, 3] Generated Node #0,0: 38:[1, 3, 3] Operation: 7-4=3 Exploring Operation: 7*3=21, Resulting Numbers: [1, 4, 21] Generated Node #0,1: 38:[1, 4, 21] Operation: 7*3=21 Moving to Node #0,0 Current State: 38:[1, 3, 3], Operations: ['7-4=3'] Exploring Operation: 3-1=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 38:[3, 2] Operation: 3-1=2 Exploring Operation: 3-1=2, Resulting Numbers: [3, 2] Generated Node #0,0,1: 38:[3, 2] Operation: 3-1=2 Moving to Node #0,1 Current State: 38:[1, 4, 21], Operations: ['7*3=21'] Exploring Operation: 4-1=3, Resulting Numbers: [21, 3] Generated Node #0,1,0: 38:[21, 3] Operation: 4-1=3 Exploring Operation: 21-1=20, Resulting Numbers: [4, 20] Generated Node #0,1,1: 38:[4, 20] Operation: 21-1=20 Moving to Node #0,0,0 Current State: 38:[3, 2], Operations: ['7-4=3', '3-1=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[3, 2], Operations: ['7-4=3', '3-1=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,38 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[4, 20], Operations: ['7*3=21', '21-1=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,38 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[21, 3], Operations: ['7*3=21', '4-1=3'] Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,38 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 27, 63, 91, 72 ]
71
[ "27+63=90", "91-72=19", "90-19=71" ]
Current State: 71:[27, 63, 91, 72], Operations: [] Exploring Operation: 27+63=90, Resulting Numbers: [91, 72, 90] Generated Node #2: [91, 72, 90] from Operation: 27+63=90 Current State: 71:[91, 72, 90], Operations: ['27+63=90'] Exploring Operation: 91-72=19, Resulting Numbers: [90, 19] Generated Node #3: [90, 19] from Operation: 91-72=19 Current State: 71:[90, 19], Operations: ['27+63=90', '91-72=19'] Exploring Operation: 90-19=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[27, 63, 91, 72], Operations: [] Exploring Operation: 91-27=64, Resulting Numbers: [63, 72, 64] Generated Node #0,0: 71:[63, 72, 64] Operation: 91-27=64 Exploring Operation: 72-27=45, Resulting Numbers: [63, 91, 45] Generated Node #0,1: 71:[63, 91, 45] Operation: 72-27=45 Exploring Operation: 27+63=90, Resulting Numbers: [91, 72, 90] Generated Node #0,2: 71:[91, 72, 90] Operation: 27+63=90 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[63, 72, 64], Operations: ['91-27=64'] Exploring Operation: 72-63=9, Resulting Numbers: [64, 9] Generated Node #0,0,0: 71:[64, 9] Operation: 72-63=9 Exploring Operation: 63+64=127, Resulting Numbers: [72, 127] Generated Node #0,0,1: 71:[72, 127] Operation: 63+64=127 Exploring Operation: 63+72=135, Resulting Numbers: [64, 135] Generated Node #0,0,2: 71:[64, 135] Operation: 63+72=135 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 71:[72, 127], Operations: ['91-27=64', '63+64=127'] Exploring Operation: 127-72=55, Resulting Numbers: [55] 55,71 unequal: No Solution Exploring Operation: 72*127=9144, Resulting Numbers: [9144] 9144,71 unequal: No Solution Exploring Operation: 72+127=199, Resulting Numbers: [199] 199,71 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:[64, 9], Operations: ['91-27=64', '72-63=9'] Exploring Operation: 64+9=73, Resulting Numbers: [73] 73,71 unequal: No Solution Exploring Operation: 64-9=55, Resulting Numbers: [55] 55,71 unequal: No Solution Exploring Operation: 64*9=576, Resulting Numbers: [576] 576,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 71:[64, 135], Operations: ['91-27=64', '63+72=135'] Exploring Operation: 135-64=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[27, 63, 91, 72], Operations: [] Exploring Operation: 91-27=64, Resulting Numbers: [63, 72, 64] Generated Node #0,0: 71:[63, 72, 64] Operation: 91-27=64 Moving to Node #0,0 Current State: 71:[63, 72, 64], Operations: ['91-27=64'] Exploring Operation: 63+72=135, Resulting Numbers: [64, 135] Generated Node #0,0,2: 71:[64, 135] Operation: 63+72=135 Moving to Node #0,0,2 Current State: 71:[64, 135], Operations: ['91-27=64', '63+72=135'] Exploring Operation: 135-64=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 89, 91, 8, 83 ]
43
[ "89-83=6", "8*6=48", "91-48=43" ]
Current State: 43:[89, 91, 8, 83], Operations: [] Exploring Operation: 89-83=6, Resulting Numbers: [91, 8, 6] Generated Node #2: [91, 8, 6] from Operation: 89-83=6 Current State: 43:[91, 8, 6], Operations: ['89-83=6'] Exploring Operation: 8*6=48, Resulting Numbers: [91, 48] Generated Node #3: [91, 48] from Operation: 8*6=48 Current State: 43:[91, 48], Operations: ['89-83=6', '8*6=48'] Exploring Operation: 91-48=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[89, 91, 8, 83], Operations: [] Exploring Operation: 89-83=6, Resulting Numbers: [91, 8, 6] Generated Node #0,0: 43:[91, 8, 6] Operation: 89-83=6 Exploring Operation: 91-83=8, Resulting Numbers: [89, 8, 8] Generated Node #0,1: 43:[89, 8, 8] Operation: 91-83=8 Exploring Operation: 91-89=2, Resulting Numbers: [8, 83, 2] Generated Node #0,2: 43:[8, 83, 2] Operation: 91-89=2 Moving to Node #0,1 Current State: 43:[89, 8, 8], Operations: ['91-83=8'] Exploring Operation: 8*8=64, Resulting Numbers: [89, 64] Generated Node #0,1,0: 43:[89, 64] Operation: 8*8=64 Exploring Operation: 89-8=81, Resulting Numbers: [8, 81] Generated Node #0,1,1: 43:[8, 81] Operation: 89-8=81 Exploring Operation: 89-8=81, Resulting Numbers: [8, 81] Generated Node #0,1,2: 43:[8, 81] Operation: 89-8=81 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[89, 64], Operations: ['91-83=8', '8*8=64'] Exploring Operation: 89*64=5696, Resulting Numbers: [5696] 5696,43 unequal: No Solution Exploring Operation: 89-64=25, Resulting Numbers: [25] 25,43 unequal: No Solution Exploring Operation: 89+64=153, Resulting Numbers: [153] 153,43 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:[8, 81], Operations: ['91-83=8', '89-8=81'] Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,43 unequal: No Solution Exploring Operation: 8+81=89, Resulting Numbers: [89] 89,43 unequal: No Solution Exploring Operation: 8*81=648, Resulting Numbers: [648] 648,43 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:[8, 81], Operations: ['91-83=8', '89-8=81'] Exploring Operation: 8*81=648, Resulting Numbers: [648] 648,43 unequal: No Solution Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,43 unequal: No Solution Exploring Operation: 8+81=89, Resulting Numbers: [89] 89,43 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: 43:[8, 83, 2], Operations: ['91-89=2'] Exploring Operation: 83-8=75, Resulting Numbers: [2, 75] Generated Node #0,2,0: 43:[2, 75] Operation: 83-8=75 Exploring Operation: 8*2=16, Resulting Numbers: [83, 16] Generated Node #0,2,1: 43:[83, 16] Operation: 8*2=16 Exploring Operation: 8+2=10, Resulting Numbers: [83, 10] Generated Node #0,2,2: 43:[83, 10] Operation: 8+2=10 Moving to Node #0,0 Current State: 43:[91, 8, 6], Operations: ['89-83=6'] Exploring Operation: 8*6=48, Resulting Numbers: [91, 48] Generated Node #0,0,0: 43:[91, 48] Operation: 8*6=48 Exploring Operation: 91-6=85, Resulting Numbers: [8, 85] Generated Node #0,0,1: 43:[8, 85] Operation: 91-6=85 Exploring Operation: 91-8=83, Resulting Numbers: [6, 83] Generated Node #0,0,2: 43:[6, 83] Operation: 91-8=83 Moving to Node #0,0,0 Current State: 43:[91, 48], Operations: ['89-83=6', '8*6=48'] Exploring Operation: 91+48=139, Resulting Numbers: [139] 139,43 unequal: No Solution Exploring Operation: 91-48=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[89, 91, 8, 83], Operations: [] Exploring Operation: 89-83=6, Resulting Numbers: [91, 8, 6] Generated Node #0,0: 43:[91, 8, 6] Operation: 89-83=6 Moving to Node #0,0 Current State: 43:[91, 8, 6], Operations: ['89-83=6'] Exploring Operation: 8*6=48, Resulting Numbers: [91, 48] Generated Node #0,0,0: 43:[91, 48] Operation: 8*6=48 Moving to Node #0,0,0 Current State: 43:[91, 48], Operations: ['89-83=6', '8*6=48'] Exploring Operation: 91-48=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
0.976563
hs_3
sum_heuristic
[ 6, 81, 84, 65 ]
30
[ "84/6=14", "81-65=16", "14+16=30" ]
Current State: 30:[6, 81, 84, 65], Operations: [] Exploring Operation: 84/6=14, Resulting Numbers: [81, 65, 14] Generated Node #2: [81, 65, 14] from Operation: 84/6=14 Current State: 30:[81, 65, 14], Operations: ['84/6=14'] Exploring Operation: 81-65=16, Resulting Numbers: [14, 16] Generated Node #3: [14, 16] from Operation: 81-65=16 Current State: 30:[14, 16], Operations: ['84/6=14', '81-65=16'] Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[6, 81, 84, 65], Operations: [] Exploring Operation: 81-65=16, Resulting Numbers: [6, 84, 16] Generated Node #0,0: 30:[6, 84, 16] Operation: 81-65=16 Exploring Operation: 84-65=19, Resulting Numbers: [6, 81, 19] Generated Node #0,1: 30:[6, 81, 19] Operation: 84-65=19 Exploring Operation: 84-81=3, Resulting Numbers: [6, 65, 3] Generated Node #0,2: 30:[6, 65, 3] Operation: 84-81=3 Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[6, 65, 3], Operations: ['84-81=3'] Exploring Operation: 65-6=59, Resulting Numbers: [3, 59] Generated Node #0,2,0: 30:[3, 59] Operation: 65-6=59 Exploring Operation: 6-3=3, Resulting Numbers: [65, 3] Generated Node #0,2,1: 30:[65, 3] Operation: 6-3=3 Exploring Operation: 65-3=62, Resulting Numbers: [6, 62] Generated Node #0,2,2: 30:[6, 62] Operation: 65-3=62 Moving to Node #0,2,0 Current State: 30:[3, 59], Operations: ['84-81=3', '65-6=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 #0,2,2 Current State: 30:[6, 62], Operations: ['84-81=3', '65-3=62'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,30 unequal: No Solution Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,30 unequal: No Solution Exploring Operation: 6*62=372, Resulting Numbers: [372] 372,30 unequal: No Solution Moving to Node #0,2,1 Current State: 30:[65, 3], Operations: ['84-81=3', '6-3=3'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 65*3=195, Resulting Numbers: [195] 195,30 unequal: No Solution Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,30 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 Current State: 30:[6, 84, 16], Operations: ['81-65=16'] Exploring Operation: 84-16=68, Resulting Numbers: [6, 68] Generated Node #0,0,0: 30:[6, 68] Operation: 84-16=68 Exploring Operation: 84-6=78, Resulting Numbers: [16, 78] Generated Node #0,0,1: 30:[16, 78] Operation: 84-6=78 Exploring Operation: 84/6=14, Resulting Numbers: [16, 14] Generated Node #0,0,2: 30:[16, 14] Operation: 84/6=14 Moving to Node #0,0,2 Current State: 30:[16, 14], Operations: ['81-65=16', '84/6=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[6, 81, 84, 65], Operations: [] Exploring Operation: 81-65=16, Resulting Numbers: [6, 84, 16] Generated Node #0,0: 30:[6, 84, 16] Operation: 81-65=16 Moving to Node #0,0 Current State: 30:[6, 84, 16], Operations: ['81-65=16'] Exploring Operation: 84/6=14, Resulting Numbers: [16, 14] Generated Node #0,0,2: 30:[16, 14] Operation: 84/6=14 Moving to Node #0,0,2 Current State: 30:[16, 14], Operations: ['81-65=16', '84/6=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 59, 29, 97, 97 ]
87
[ "59+29=88", "97/97=1", "88-1=87" ]
Current State: 87:[59, 29, 97, 97], Operations: [] Exploring Operation: 59+29=88, Resulting Numbers: [97, 97, 88] Generated Node #2: [97, 97, 88] from Operation: 59+29=88 Current State: 87:[97, 97, 88], Operations: ['59+29=88'] Exploring Operation: 97/97=1, Resulting Numbers: [88, 1] Generated Node #3: [88, 1] from Operation: 97/97=1 Current State: 87:[88, 1], Operations: ['59+29=88', '97/97=1'] Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[59, 29, 97, 97], Operations: [] Exploring Operation: 59+29=88, Resulting Numbers: [97, 97, 88] Generated Node #0,0: 87:[97, 97, 88] Operation: 59+29=88 Exploring Operation: 97-59=38, Resulting Numbers: [29, 97, 38] Generated Node #0,1: 87:[29, 97, 38] Operation: 97-59=38 Exploring Operation: 97/97=1, Resulting Numbers: [59, 29, 1] Generated Node #0,2: 87:[59, 29, 1] Operation: 97/97=1 Exploring Operation: 59-29=30, Resulting Numbers: [97, 97, 30] Generated Node #0,3: 87:[97, 97, 30] Operation: 59-29=30 Exploring Operation: 97-59=38, Resulting Numbers: [29, 97, 38] Generated Node #0,4: 87:[29, 97, 38] Operation: 97-59=38 Moving to Node #0,1 Current State: 87:[29, 97, 38], Operations: ['97-59=38'] Exploring Operation: 29+38=67, Resulting Numbers: [97, 67] Generated Node #0,1,0: 87:[97, 67] Operation: 29+38=67 Exploring Operation: 29+97=126, Resulting Numbers: [38, 126] Generated Node #0,1,1: 87:[38, 126] Operation: 29+97=126 Exploring Operation: 97-29=68, Resulting Numbers: [38, 68] Generated Node #0,1,2: 87:[38, 68] Operation: 97-29=68 Exploring Operation: 38-29=9, Resulting Numbers: [97, 9] Generated Node #0,1,3: 87:[97, 9] Operation: 38-29=9 Exploring Operation: 97-38=59, Resulting Numbers: [29, 59] Generated Node #0,1,4: 87:[29, 59] Operation: 97-38=59 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 87:[97, 9], Operations: ['97-59=38', '38-29=9'] Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,87 unequal: No Solution Exploring Operation: 97+9=106, Resulting Numbers: [106] 106,87 unequal: No Solution Exploring Operation: 97*9=873, Resulting Numbers: [873] 873,87 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 #0,1,2 Current State: 87:[38, 68], Operations: ['97-59=38', '97-29=68'] Exploring Operation: 38+68=106, Resulting Numbers: [106] 106,87 unequal: No Solution Exploring Operation: 68-38=30, Resulting Numbers: [30] 30,87 unequal: No Solution Exploring Operation: 38*68=2584, Resulting Numbers: [2584] 2584,87 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 #0,1,4 Current State: 87:[29, 59], Operations: ['97-59=38', '97-38=59'] Exploring Operation: 29+59=88, Resulting Numbers: [88] 88,87 unequal: No Solution Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,87 unequal: No Solution Exploring Operation: 29*59=1711, Resulting Numbers: [1711] 1711,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 87:[97, 67], Operations: ['97-59=38', '29+38=67'] Exploring Operation: 97-67=30, Resulting Numbers: [30] 30,87 unequal: No Solution Exploring Operation: 97+67=164, Resulting Numbers: [164] 164,87 unequal: No Solution Exploring Operation: 97*67=6499, Resulting Numbers: [6499] 6499,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 87:[38, 126], Operations: ['97-59=38', '29+97=126'] Exploring Operation: 38*126=4788, Resulting Numbers: [4788] 4788,87 unequal: No Solution Exploring Operation: 38+126=164, Resulting Numbers: [164] 164,87 unequal: No Solution Exploring Operation: 126-38=88, Resulting Numbers: [88] 88,87 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: 87:[29, 97, 38], Operations: ['97-59=38'] Exploring Operation: 38-29=9, Resulting Numbers: [97, 9] Generated Node #0,4,0: 87:[97, 9] Operation: 38-29=9 Exploring Operation: 29+97=126, Resulting Numbers: [38, 126] Generated Node #0,4,1: 87:[38, 126] Operation: 29+97=126 Exploring Operation: 97-29=68, Resulting Numbers: [38, 68] Generated Node #0,4,2: 87:[38, 68] Operation: 97-29=68 Exploring Operation: 97-38=59, Resulting Numbers: [29, 59] Generated Node #0,4,3: 87:[29, 59] Operation: 97-38=59 Exploring Operation: 29+38=67, Resulting Numbers: [97, 67] Generated Node #0,4,4: 87:[97, 67] Operation: 29+38=67 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 87:[97, 9], Operations: ['97-59=38', '38-29=9'] Exploring Operation: 97*9=873, Resulting Numbers: [873] 873,87 unequal: No Solution Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,87 unequal: No Solution Exploring Operation: 97+9=106, Resulting Numbers: [106] 106,87 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 #0,4,2 Current State: 87:[38, 68], Operations: ['97-59=38', '97-29=68'] Exploring Operation: 68-38=30, Resulting Numbers: [30] 30,87 unequal: No Solution Exploring Operation: 38*68=2584, Resulting Numbers: [2584] 2584,87 unequal: No Solution Exploring Operation: 38+68=106, Resulting Numbers: [106] 106,87 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 #0,4,3 Current State: 87:[29, 59], Operations: ['97-59=38', '97-38=59'] Exploring Operation: 29*59=1711, Resulting Numbers: [1711] 1711,87 unequal: No Solution Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,87 unequal: No Solution Exploring Operation: 29+59=88, Resulting Numbers: [88] 88,87 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 #0,4,4 Current State: 87:[97, 67], Operations: ['97-59=38', '29+38=67'] Exploring Operation: 97*67=6499, Resulting Numbers: [6499] 6499,87 unequal: No Solution Exploring Operation: 97+67=164, Resulting Numbers: [164] 164,87 unequal: No Solution Exploring Operation: 97-67=30, Resulting Numbers: [30] 30,87 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 #0,4,1 Current State: 87:[38, 126], Operations: ['97-59=38', '29+97=126'] Exploring Operation: 38*126=4788, Resulting Numbers: [4788] 4788,87 unequal: No Solution Exploring Operation: 126-38=88, Resulting Numbers: [88] 88,87 unequal: No Solution Exploring Operation: 38+126=164, Resulting Numbers: [164] 164,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 87:[97, 97, 88], Operations: ['59+29=88'] Exploring Operation: 97-88=9, Resulting Numbers: [97, 9] Generated Node #0,0,0: 87:[97, 9] Operation: 97-88=9 Exploring Operation: 97/97=1, Resulting Numbers: [88, 1] Generated Node #0,0,1: 87:[88, 1] Operation: 97/97=1 Exploring Operation: 97-97=0, Resulting Numbers: [88, 0] Generated Node #0,0,2: 87:[88, 0] Operation: 97-97=0 Exploring Operation: 97+97=194, Resulting Numbers: [88, 194] Generated Node #0,0,3: 87:[88, 194] Operation: 97+97=194 Exploring Operation: 97-88=9, Resulting Numbers: [97, 9] Generated Node #0,0,4: 87:[97, 9] Operation: 97-88=9 Moving to Node #0,3 Current State: 87:[97, 97, 30], Operations: ['59-29=30'] Exploring Operation: 97-30=67, Resulting Numbers: [97, 67] Generated Node #0,3,0: 87:[97, 67] Operation: 97-30=67 Exploring Operation: 97-97=0, Resulting Numbers: [30, 0] Generated Node #0,3,1: 87:[30, 0] Operation: 97-97=0 Exploring Operation: 97+30=127, Resulting Numbers: [97, 127] Generated Node #0,3,2: 87:[97, 127] Operation: 97+30=127 Exploring Operation: 97/97=1, Resulting Numbers: [30, 1] Generated Node #0,3,3: 87:[30, 1] Operation: 97/97=1 Exploring Operation: 97-30=67, Resulting Numbers: [97, 67] Generated Node #0,3,4: 87:[97, 67] Operation: 97-30=67 Moving to Node #0,2 Current State: 87:[59, 29, 1], Operations: ['97/97=1'] Exploring Operation: 59+1=60, Resulting Numbers: [29, 60] Generated Node #0,2,0: 87:[29, 60] Operation: 59+1=60 Exploring Operation: 59/1=59, Resulting Numbers: [29, 59] Generated Node #0,2,1: 87:[29, 59] Operation: 59/1=59 Exploring Operation: 59-29=30, Resulting Numbers: [1, 30] Generated Node #0,2,2: 87:[1, 30] Operation: 59-29=30 Exploring Operation: 59+29=88, Resulting Numbers: [1, 88] Generated Node #0,2,3: 87:[1, 88] Operation: 59+29=88 Exploring Operation: 59*1=59, Resulting Numbers: [29, 59] Generated Node #0,2,4: 87:[29, 59] Operation: 59*1=59 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 87:[1, 30], Operations: ['97/97=1', '59-29=30'] Exploring Operation: 1+30=31, Resulting Numbers: [31] 31,87 unequal: No Solution Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,87 unequal: No Solution Exploring Operation: 30/1=30, Resulting Numbers: [30] 30,87 unequal: No Solution Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,87 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 #0,2,3 Current State: 87:[1, 88], Operations: ['97/97=1', '59+29=88'] Exploring Operation: 1+88=89, Resulting Numbers: [89] 89,87 unequal: No Solution Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[59, 29, 97, 97], Operations: [] Exploring Operation: 97/97=1, Resulting Numbers: [59, 29, 1] Generated Node #0,2: 87:[59, 29, 1] Operation: 97/97=1 Moving to Node #0,2 Current State: 87:[59, 29, 1], Operations: ['97/97=1'] Exploring Operation: 59+29=88, Resulting Numbers: [1, 88] Generated Node #0,2,3: 87:[1, 88] Operation: 59+29=88 Moving to Node #0,2,3 Current State: 87:[1, 88], Operations: ['97/97=1', '59+29=88'] Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.939236
hs_5
mult_heuristic
[ 90, 81, 31, 87 ]
46
[ "87-81=6", "90/6=15", "31+15=46" ]
Current State: 46:[90, 81, 31, 87], Operations: [] Exploring Operation: 87-81=6, Resulting Numbers: [90, 31, 6] Generated Node #2: [90, 31, 6] from Operation: 87-81=6 Current State: 46:[90, 31, 6], Operations: ['87-81=6'] Exploring Operation: 90/6=15, Resulting Numbers: [31, 15] Generated Node #3: [31, 15] from Operation: 90/6=15 Current State: 46:[31, 15], Operations: ['87-81=6', '90/6=15'] Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[90, 81, 31, 87], Operations: [] Exploring Operation: 90-87=3, Resulting Numbers: [81, 31, 3] Generated Node #0,0: 46:[81, 31, 3] Operation: 90-87=3 Moving to Node #0,0 Current State: 46:[81, 31, 3], Operations: ['90-87=3'] Exploring Operation: 81-31=50, Resulting Numbers: [3, 50] Generated Node #0,0,0: 46:[3, 50] Operation: 81-31=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 46:[3, 50], Operations: ['90-87=3', '81-31=50'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,46 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, 32, 26, 90 ]
22
[ "9*90=810", "32*26=832", "832-810=22" ]
Current State: 22:[9, 32, 26, 90], Operations: [] Exploring Operation: 9*90=810, Resulting Numbers: [32, 26, 810] Generated Node #2: [32, 26, 810] from Operation: 9*90=810 Current State: 22:[32, 26, 810], Operations: ['9*90=810'] Exploring Operation: 32*26=832, Resulting Numbers: [810, 832] Generated Node #3: [810, 832] from Operation: 32*26=832 Current State: 22:[810, 832], Operations: ['9*90=810', '32*26=832'] Exploring Operation: 832-810=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[9, 32, 26, 90], Operations: [] Exploring Operation: 90/9=10, Resulting Numbers: [32, 26, 10] Generated Node #0,0: 22:[32, 26, 10] Operation: 90/9=10 Exploring Operation: 90-32=58, Resulting Numbers: [9, 26, 58] Generated Node #0,1: 22:[9, 26, 58] Operation: 90-32=58 Moving to Node #0,0 Current State: 22:[32, 26, 10], Operations: ['90/9=10'] Exploring Operation: 32-10=22, Resulting Numbers: [26, 22] Generated Node #0,0,0: 22:[26, 22] Operation: 32-10=22 Exploring Operation: 32-26=6, Resulting Numbers: [10, 6] Generated Node #0,0,1: 22:[10, 6] Operation: 32-26=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[26, 22], Operations: ['90/9=10', '32-10=22'] Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 26+22=48, Resulting Numbers: [48] 48,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 22:[10, 6], Operations: ['90/9=10', '32-26=6'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,22 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: 22:[9, 26, 58], Operations: ['90-32=58'] Exploring Operation: 58-9=49, Resulting Numbers: [26, 49] Generated Node #0,1,0: 22:[26, 49] Operation: 58-9=49 Exploring Operation: 58-26=32, Resulting Numbers: [9, 32] Generated Node #0,1,1: 22:[9, 32] Operation: 58-26=32 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[9, 32], Operations: ['90-32=58', '58-26=32'] Exploring Operation: 9+32=41, Resulting Numbers: [41] 41,22 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[26, 49], Operations: ['90-32=58', '58-9=49'] Exploring Operation: 26+49=75, Resulting Numbers: [75] 75,22 unequal: No Solution Exploring Operation: 49-26=23, Resulting Numbers: [23] 23,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 90, 21, 68, 42 ]
24
[ "90-68=22", "42/21=2", "22+2=24" ]
Current State: 24:[90, 21, 68, 42], Operations: [] Exploring Operation: 90-68=22, Resulting Numbers: [21, 42, 22] Generated Node #2: [21, 42, 22] from Operation: 90-68=22 Current State: 24:[21, 42, 22], Operations: ['90-68=22'] Exploring Operation: 42/21=2, Resulting Numbers: [22, 2] Generated Node #3: [22, 2] from Operation: 42/21=2 Current State: 24:[22, 2], Operations: ['90-68=22', '42/21=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[90, 21, 68, 42], Operations: [] Exploring Operation: 90-42=48, Resulting Numbers: [21, 68, 48] Generated Node #0,0: 24:[21, 68, 48] Operation: 90-42=48 Exploring Operation: 90-68=22, Resulting Numbers: [21, 42, 22] Generated Node #0,1: 24:[21, 42, 22] Operation: 90-68=22 Exploring Operation: 68-42=26, Resulting Numbers: [90, 21, 26] Generated Node #0,2: 24:[90, 21, 26] Operation: 68-42=26 Exploring Operation: 90-21=69, Resulting Numbers: [68, 42, 69] Generated Node #0,3: 24:[68, 42, 69] Operation: 90-21=69 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[21, 42, 22], Operations: ['90-68=22'] Exploring Operation: 42-22=20, Resulting Numbers: [21, 20] Generated Node #0,1,0: 24:[21, 20] Operation: 42-22=20 Exploring Operation: 22-21=1, Resulting Numbers: [42, 1] Generated Node #0,1,1: 24:[42, 1] Operation: 22-21=1 Exploring Operation: 42-21=21, Resulting Numbers: [22, 21] Generated Node #0,1,2: 24:[22, 21] Operation: 42-21=21 Exploring Operation: 42/21=2, Resulting Numbers: [22, 2] Generated Node #0,1,3: 24:[22, 2] Operation: 42/21=2 Moving to Node #0,1,3 Current State: 24:[22, 2], Operations: ['90-68=22', '42/21=2'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,24 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[90, 21, 68, 42], Operations: [] Exploring Operation: 90-68=22, Resulting Numbers: [21, 42, 22] Generated Node #0,1: 24:[21, 42, 22] Operation: 90-68=22 Moving to Node #0,1 Current State: 24:[21, 42, 22], Operations: ['90-68=22'] Exploring Operation: 42/21=2, Resulting Numbers: [22, 2] Generated Node #0,1,3: 24:[22, 2] Operation: 42/21=2 Moving to Node #0,1,3 Current State: 24:[22, 2], Operations: ['90-68=22', '42/21=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 88, 55, 5, 79 ]
41
[ "88-55=33", "79-5=74", "74-33=41" ]
Current State: 41:[88, 55, 5, 79], Operations: [] Exploring Operation: 88-55=33, Resulting Numbers: [5, 79, 33] Generated Node #2: [5, 79, 33] from Operation: 88-55=33 Current State: 41:[5, 79, 33], Operations: ['88-55=33'] Exploring Operation: 79-5=74, Resulting Numbers: [33, 74] Generated Node #3: [33, 74] from Operation: 79-5=74 Current State: 41:[33, 74], Operations: ['88-55=33', '79-5=74'] Exploring Operation: 74-33=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[88, 55, 5, 79], Operations: [] Exploring Operation: 88-5=83, Resulting Numbers: [55, 79, 83] Generated Node #0,0: 41:[55, 79, 83] Operation: 88-5=83 Exploring Operation: 88-79=9, Resulting Numbers: [55, 5, 9] Generated Node #0,1: 41:[55, 5, 9] Operation: 88-79=9 Exploring Operation: 55-5=50, Resulting Numbers: [88, 79, 50] Generated Node #0,2: 41:[88, 79, 50] Operation: 55-5=50 Exploring Operation: 88-55=33, Resulting Numbers: [5, 79, 33] Generated Node #0,3: 41:[5, 79, 33] Operation: 88-55=33 Moving to Node #0,1 Current State: 41:[55, 5, 9], Operations: ['88-79=9'] Exploring Operation: 55-9=46, Resulting Numbers: [5, 46] Generated Node #0,1,0: 41:[5, 46] Operation: 55-9=46 Exploring Operation: 5+9=14, Resulting Numbers: [55, 14] Generated Node #0,1,1: 41:[55, 14] Operation: 5+9=14 Exploring Operation: 5*9=45, Resulting Numbers: [55, 45] Generated Node #0,1,2: 41:[55, 45] Operation: 5*9=45 Exploring Operation: 55-5=50, Resulting Numbers: [9, 50] Generated Node #0,1,3: 41:[9, 50] Operation: 55-5=50 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 41:[55, 45], Operations: ['88-79=9', '5*9=45'] Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,41 unequal: No Solution Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,41 unequal: No Solution Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,41 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:[5, 46], Operations: ['88-79=9', '55-9=46'] Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,41 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[88, 55, 5, 79], Operations: [] Exploring Operation: 88-79=9, Resulting Numbers: [55, 5, 9] Generated Node #0,1: 41:[55, 5, 9] Operation: 88-79=9 Moving to Node #0,1 Current State: 41:[55, 5, 9], Operations: ['88-79=9'] Exploring Operation: 55-9=46, Resulting Numbers: [5, 46] Generated Node #0,1,0: 41:[5, 46] Operation: 55-9=46 Moving to Node #0,1,0 Current State: 41:[5, 46], Operations: ['88-79=9', '55-9=46'] Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 83, 11, 9, 2 ]
48
[ "83-9=74", "74/2=37", "11+37=48" ]
Current State: 48:[83, 11, 9, 2], Operations: [] Exploring Operation: 83-9=74, Resulting Numbers: [11, 2, 74] Generated Node #2: [11, 2, 74] from Operation: 83-9=74 Current State: 48:[11, 2, 74], Operations: ['83-9=74'] Exploring Operation: 74/2=37, Resulting Numbers: [11, 37] Generated Node #3: [11, 37] from Operation: 74/2=37 Current State: 48:[11, 37], Operations: ['83-9=74', '74/2=37'] Exploring Operation: 11+37=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[83, 11, 9, 2], Operations: [] Exploring Operation: 83-9=74, Resulting Numbers: [11, 2, 74] Generated Node #0,0: 48:[11, 2, 74] Operation: 83-9=74 Exploring Operation: 83-11=72, Resulting Numbers: [9, 2, 72] Generated Node #0,1: 48:[9, 2, 72] Operation: 83-11=72 Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[9, 2, 72], Operations: ['83-11=72'] Exploring Operation: 72/9=8, Resulting Numbers: [2, 8] Generated Node #0,1,0: 48:[2, 8] Operation: 72/9=8 Exploring Operation: 72/2=36, Resulting Numbers: [9, 36] Generated Node #0,1,1: 48:[9, 36] Operation: 72/2=36 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 48:[2, 8], Operations: ['83-11=72', '72/9=8'] Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 48:[9, 36], Operations: ['83-11=72', '72/2=36'] Exploring Operation: 9+36=45, Resulting Numbers: [45] 45,48 unequal: No Solution Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[11, 2, 74], Operations: ['83-9=74'] Exploring Operation: 74-11=63, Resulting Numbers: [2, 63] Generated Node #0,0,0: 48:[2, 63] Operation: 74-11=63 Exploring Operation: 74/2=37, Resulting Numbers: [11, 37] Generated Node #0,0,1: 48:[11, 37] Operation: 74/2=37 Moving to Node #0,0,1 Current State: 48:[11, 37], Operations: ['83-9=74', '74/2=37'] Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 11+37=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[83, 11, 9, 2], Operations: [] Exploring Operation: 83-9=74, Resulting Numbers: [11, 2, 74] Generated Node #0,0: 48:[11, 2, 74] Operation: 83-9=74 Moving to Node #0,0 Current State: 48:[11, 2, 74], Operations: ['83-9=74'] Exploring Operation: 74/2=37, Resulting Numbers: [11, 37] Generated Node #0,0,1: 48:[11, 37] Operation: 74/2=37 Moving to Node #0,0,1 Current State: 48:[11, 37], Operations: ['83-9=74', '74/2=37'] Exploring Operation: 11+37=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 49, 87, 87, 32 ]
49
[ "87-87=0", "32*0=0", "49+0=49" ]
Current State: 49:[49, 87, 87, 32], Operations: [] Exploring Operation: 87-87=0, Resulting Numbers: [49, 32, 0] Generated Node #2: [49, 32, 0] from Operation: 87-87=0 Current State: 49:[49, 32, 0], Operations: ['87-87=0'] Exploring Operation: 32*0=0, Resulting Numbers: [49, 0] Generated Node #3: [49, 0] from Operation: 32*0=0 Current State: 49:[49, 0], Operations: ['87-87=0', '32*0=0'] Exploring Operation: 49+0=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[49, 87, 87, 32], Operations: [] Exploring Operation: 87-87=0, Resulting Numbers: [49, 32, 0] Generated Node #0,0: 49:[49, 32, 0] Operation: 87-87=0 Exploring Operation: 87/87=1, Resulting Numbers: [49, 32, 1] Generated Node #0,1: 49:[49, 32, 1] Operation: 87/87=1 Moving to Node #0,1 Current State: 49:[49, 32, 1], Operations: ['87/87=1'] Exploring Operation: 49-32=17, Resulting Numbers: [1, 17] Generated Node #0,1,0: 49:[1, 17] Operation: 49-32=17 Exploring Operation: 32+1=33, Resulting Numbers: [49, 33] Generated Node #0,1,1: 49:[49, 33] Operation: 32+1=33 Moving to Node #0,0 Current State: 49:[49, 32, 0], Operations: ['87-87=0'] Exploring Operation: 49-32=17, Resulting Numbers: [0, 17] Generated Node #0,0,0: 49:[0, 17] Operation: 49-32=17 Exploring Operation: 32*0=0, Resulting Numbers: [49, 0] Generated Node #0,0,1: 49:[49, 0] Operation: 32*0=0 Moving to Node #0,0,1 Current State: 49:[49, 0], Operations: ['87-87=0', '32*0=0'] Exploring Operation: 49+0=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[49, 87, 87, 32], Operations: [] Exploring Operation: 87-87=0, Resulting Numbers: [49, 32, 0] Generated Node #0,0: 49:[49, 32, 0] Operation: 87-87=0 Moving to Node #0,0 Current State: 49:[49, 32, 0], Operations: ['87-87=0'] Exploring Operation: 32*0=0, Resulting Numbers: [49, 0] Generated Node #0,0,1: 49:[49, 0] Operation: 32*0=0 Moving to Node #0,0,1 Current State: 49:[49, 0], Operations: ['87-87=0', '32*0=0'] Exploring Operation: 49+0=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 73, 9, 20, 2 ]
64
[ "73+9=82", "20-2=18", "82-18=64" ]
Current State: 64:[73, 9, 20, 2], Operations: [] Exploring Operation: 73+9=82, Resulting Numbers: [20, 2, 82] Generated Node #2: [20, 2, 82] from Operation: 73+9=82 Current State: 64:[20, 2, 82], Operations: ['73+9=82'] Exploring Operation: 20-2=18, Resulting Numbers: [82, 18] Generated Node #3: [82, 18] from Operation: 20-2=18 Current State: 64:[82, 18], Operations: ['73+9=82', '20-2=18'] Exploring Operation: 82-18=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[73, 9, 20, 2], Operations: [] Exploring Operation: 73-2=71, Resulting Numbers: [9, 20, 71] Generated Node #0,0: 64:[9, 20, 71] Operation: 73-2=71 Exploring Operation: 73-9=64, Resulting Numbers: [20, 2, 64] Generated Node #0,1: 64:[20, 2, 64] Operation: 73-9=64 Exploring Operation: 73-20=53, Resulting Numbers: [9, 2, 53] Generated Node #0,2: 64:[9, 2, 53] Operation: 73-20=53 Exploring Operation: 9+20=29, Resulting Numbers: [73, 2, 29] Generated Node #0,3: 64:[73, 2, 29] Operation: 9+20=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[20, 2, 64], Operations: ['73-9=64'] Exploring Operation: 20/2=10, Resulting Numbers: [64, 10] Generated Node #0,1,0: 64:[64, 10] Operation: 20/2=10 Exploring Operation: 64/2=32, Resulting Numbers: [20, 32] Generated Node #0,1,1: 64:[20, 32] Operation: 64/2=32 Exploring Operation: 20-2=18, Resulting Numbers: [64, 18] Generated Node #0,1,2: 64:[64, 18] Operation: 20-2=18 Exploring Operation: 20+2=22, Resulting Numbers: [64, 22] Generated Node #0,1,3: 64:[64, 22] Operation: 20+2=22 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 64:[64, 10], Operations: ['73-9=64', '20/2=10'] Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,64 unequal: No Solution Exploring Operation: 64*10=640, Resulting Numbers: [640] 640,64 unequal: No Solution Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 64:[64, 18], Operations: ['73-9=64', '20-2=18'] Exploring Operation: 64*18=1152, Resulting Numbers: [1152] 1152,64 unequal: No Solution Exploring Operation: 64+18=82, Resulting Numbers: [82] 82,64 unequal: No Solution Exploring Operation: 64-18=46, Resulting Numbers: [46] 46,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 64:[20, 32], Operations: ['73-9=64', '64/2=32'] Exploring Operation: 20*32=640, Resulting Numbers: [640] 640,64 unequal: No Solution Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,64 unequal: No Solution Exploring Operation: 20+32=52, Resulting Numbers: [52] 52,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 64:[64, 22], Operations: ['73-9=64', '20+2=22'] Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,64 unequal: No Solution Exploring Operation: 64+22=86, Resulting Numbers: [86] 86,64 unequal: No Solution Exploring Operation: 64*22=1408, Resulting Numbers: [1408] 1408,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[9, 20, 71], Operations: ['73-2=71'] Exploring Operation: 9+20=29, Resulting Numbers: [71, 29] Generated Node #0,0,0: 64:[71, 29] Operation: 9+20=29 Exploring Operation: 20-9=11, Resulting Numbers: [71, 11] Generated Node #0,0,1: 64:[71, 11] Operation: 20-9=11 Exploring Operation: 71-9=62, Resulting Numbers: [20, 62] Generated Node #0,0,2: 64:[20, 62] Operation: 71-9=62 Exploring Operation: 71-20=51, Resulting Numbers: [9, 51] Generated Node #0,0,3: 64:[9, 51] Operation: 71-20=51 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 64:[20, 62], Operations: ['73-2=71', '71-9=62'] Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,64 unequal: No Solution Exploring Operation: 20+62=82, Resulting Numbers: [82] 82,64 unequal: No Solution Exploring Operation: 20*62=1240, Resulting Numbers: [1240] 1240,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 64:[71, 29], Operations: ['73-2=71', '9+20=29'] Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,64 unequal: No Solution Exploring Operation: 71*29=2059, Resulting Numbers: [2059] 2059,64 unequal: No Solution Exploring Operation: 71+29=100, Resulting Numbers: [100] 100,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 64:[71, 11], Operations: ['73-2=71', '20-9=11'] Exploring Operation: 71-11=60, Resulting Numbers: [60] 60,64 unequal: No Solution Exploring Operation: 71*11=781, Resulting Numbers: [781] 781,64 unequal: No Solution Exploring Operation: 71+11=82, Resulting Numbers: [82] 82,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 64:[9, 51], Operations: ['73-2=71', '71-20=51'] Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,64 unequal: No Solution Exploring Operation: 9*51=459, Resulting Numbers: [459] 459,64 unequal: No Solution Exploring Operation: 9+51=60, Resulting Numbers: [60] 60,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[9, 2, 53], Operations: ['73-20=53'] Exploring Operation: 2+53=55, Resulting Numbers: [9, 55] Generated Node #0,2,0: 64:[9, 55] Operation: 2+53=55 Exploring Operation: 9-2=7, Resulting Numbers: [53, 7] Generated Node #0,2,1: 64:[53, 7] Operation: 9-2=7 Exploring Operation: 9+53=62, Resulting Numbers: [2, 62] Generated Node #0,2,2: 64:[2, 62] Operation: 9+53=62 Exploring Operation: 53-9=44, Resulting Numbers: [2, 44] Generated Node #0,2,3: 64:[2, 44] Operation: 53-9=44 Moving to Node #0,2,2 Current State: 64:[2, 62], Operations: ['73-20=53', '9+53=62'] Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[73, 9, 20, 2], Operations: [] Exploring Operation: 73-20=53, Resulting Numbers: [9, 2, 53] Generated Node #0,2: 64:[9, 2, 53] Operation: 73-20=53 Moving to Node #0,2 Current State: 64:[9, 2, 53], Operations: ['73-20=53'] Exploring Operation: 9+53=62, Resulting Numbers: [2, 62] Generated Node #0,2,2: 64:[2, 62] Operation: 9+53=62 Moving to Node #0,2,2 Current State: 64:[2, 62], Operations: ['73-20=53', '9+53=62'] Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.960938
hs_4
mult_heuristic
[ 24, 23, 72, 36 ]
56
[ "72/24=3", "23+36=59", "59-3=56" ]
Current State: 56:[24, 23, 72, 36], Operations: [] Exploring Operation: 72/24=3, Resulting Numbers: [23, 36, 3] Generated Node #2: [23, 36, 3] from Operation: 72/24=3 Current State: 56:[23, 36, 3], Operations: ['72/24=3'] Exploring Operation: 23+36=59, Resulting Numbers: [3, 59] Generated Node #3: [3, 59] from Operation: 23+36=59 Current State: 56:[3, 59], Operations: ['72/24=3', '23+36=59'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[24, 23, 72, 36], Operations: [] Exploring Operation: 72/36=2, Resulting Numbers: [24, 23, 2] Generated Node #0,0: 56:[24, 23, 2] Operation: 72/36=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[24, 23, 2], Operations: ['72/36=2'] Exploring Operation: 24-23=1, Resulting Numbers: [2, 1] Generated Node #0,0,0: 56:[2, 1] Operation: 24-23=1 Moving to Node #0,0,0 Current State: 56:[2, 1], Operations: ['72/36=2', '24-23=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,56 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, 6, 67, 63 ]
89
[ "99-6=93", "67-63=4", "93-4=89" ]
Current State: 89:[99, 6, 67, 63], Operations: [] Exploring Operation: 99-6=93, Resulting Numbers: [67, 63, 93] Generated Node #2: [67, 63, 93] from Operation: 99-6=93 Current State: 89:[67, 63, 93], Operations: ['99-6=93'] Exploring Operation: 67-63=4, Resulting Numbers: [93, 4] Generated Node #3: [93, 4] from Operation: 67-63=4 Current State: 89:[93, 4], Operations: ['99-6=93', '67-63=4'] Exploring Operation: 93-4=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[99, 6, 67, 63], Operations: [] Exploring Operation: 6+67=73, Resulting Numbers: [99, 63, 73] Generated Node #0,0: 89:[99, 63, 73] Operation: 6+67=73 Exploring Operation: 99-6=93, Resulting Numbers: [67, 63, 93] Generated Node #0,1: 89:[67, 63, 93] Operation: 99-6=93 Moving to Node #0,0 Current State: 89:[99, 63, 73], Operations: ['6+67=73'] Exploring Operation: 63+73=136, Resulting Numbers: [99, 136] Generated Node #0,0,0: 89:[99, 136] Operation: 63+73=136 Exploring Operation: 99-63=36, Resulting Numbers: [73, 36] Generated Node #0,0,1: 89:[73, 36] Operation: 99-63=36 Moving to Node #0,1 Current State: 89:[67, 63, 93], Operations: ['99-6=93'] Exploring Operation: 93-63=30, Resulting Numbers: [67, 30] Generated Node #0,1,0: 89:[67, 30] Operation: 93-63=30 Exploring Operation: 67+63=130, Resulting Numbers: [93, 130] Generated Node #0,1,1: 89:[93, 130] Operation: 67+63=130 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[93, 130], Operations: ['99-6=93', '67+63=130'] Exploring Operation: 93+130=223, Resulting Numbers: [223] 223,89 unequal: No Solution Exploring Operation: 130-93=37, Resulting Numbers: [37] 37,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[67, 30], Operations: ['99-6=93', '93-63=30'] Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,89 unequal: No Solution Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,89 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: 89:[99, 136], Operations: ['6+67=73', '63+73=136'] Exploring Operation: 136-99=37, Resulting Numbers: [37] 37,89 unequal: No Solution Exploring Operation: 99+136=235, Resulting Numbers: [235] 235,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[73, 36], Operations: ['6+67=73', '99-63=36'] Exploring Operation: 73-36=37, Resulting Numbers: [37] 37,89 unequal: No Solution Exploring Operation: 73+36=109, Resulting Numbers: [109] 109,89 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 17, 90, 6, 8 ]
75
[ "90-17=73", "8-6=2", "73+2=75" ]
Current State: 75:[17, 90, 6, 8], Operations: [] Exploring Operation: 90-17=73, Resulting Numbers: [6, 8, 73] Generated Node #2: [6, 8, 73] from Operation: 90-17=73 Current State: 75:[6, 8, 73], Operations: ['90-17=73'] Exploring Operation: 8-6=2, Resulting Numbers: [73, 2] Generated Node #3: [73, 2] from Operation: 8-6=2 Current State: 75:[73, 2], Operations: ['90-17=73', '8-6=2'] Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[17, 90, 6, 8], Operations: [] Exploring Operation: 90/6=15, Resulting Numbers: [17, 8, 15] Generated Node #0,0: 75:[17, 8, 15] Operation: 90/6=15 Exploring Operation: 90-17=73, Resulting Numbers: [6, 8, 73] Generated Node #0,1: 75:[6, 8, 73] Operation: 90-17=73 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[17, 8, 15], Operations: ['90/6=15'] Exploring Operation: 17-8=9, Resulting Numbers: [15, 9] Generated Node #0,0,0: 75:[15, 9] Operation: 17-8=9 Exploring Operation: 17+8=25, Resulting Numbers: [15, 25] Generated Node #0,0,1: 75:[15, 25] Operation: 17+8=25 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 75:[15, 25], Operations: ['90/6=15', '17+8=25'] Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,75 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,75 unequal: No Solution No 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: 75:[15, 9], Operations: ['90/6=15', '17-8=9'] Exploring Operation: 15+9=24, Resulting Numbers: [24] 24,75 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,75 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[6, 8, 73], Operations: ['90-17=73'] Exploring Operation: 6+8=14, Resulting Numbers: [73, 14] Generated Node #0,1,0: 75:[73, 14] Operation: 6+8=14 Exploring Operation: 8-6=2, Resulting Numbers: [73, 2] Generated Node #0,1,1: 75:[73, 2] Operation: 8-6=2 Moving to Node #0,1,0 Current State: 75:[73, 14], Operations: ['90-17=73', '6+8=14'] Exploring Operation: 73+14=87, Resulting Numbers: [87] 87,75 unequal: No Solution Exploring Operation: 73-14=59, Resulting Numbers: [59] 59,75 unequal: No Solution Moving to Node #0,1,1 Current State: 75:[73, 2], Operations: ['90-17=73', '8-6=2'] Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[17, 90, 6, 8], Operations: [] Exploring Operation: 90-17=73, Resulting Numbers: [6, 8, 73] Generated Node #0,1: 75:[6, 8, 73] Operation: 90-17=73 Moving to Node #0,1 Current State: 75:[6, 8, 73], Operations: ['90-17=73'] Exploring Operation: 8-6=2, Resulting Numbers: [73, 2] Generated Node #0,1,1: 75:[73, 2] Operation: 8-6=2 Moving to Node #0,1,1 Current State: 75:[73, 2], Operations: ['90-17=73', '8-6=2'] Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_2
mult_heuristic
[ 6, 3, 7, 62 ]
46
[ "6+3=9", "62-7=55", "55-9=46" ]
Current State: 46:[6, 3, 7, 62], Operations: [] Exploring Operation: 6+3=9, Resulting Numbers: [7, 62, 9] Generated Node #2: [7, 62, 9] from Operation: 6+3=9 Current State: 46:[7, 62, 9], Operations: ['6+3=9'] Exploring Operation: 62-7=55, Resulting Numbers: [9, 55] Generated Node #3: [9, 55] from Operation: 62-7=55 Current State: 46:[9, 55], Operations: ['6+3=9', '62-7=55'] Exploring Operation: 55-9=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[6, 3, 7, 62], Operations: [] Exploring Operation: 62-6=56, Resulting Numbers: [3, 7, 56] Generated Node #0,0: 46:[3, 7, 56] Operation: 62-6=56 Exploring Operation: 62-7=55, Resulting Numbers: [6, 3, 55] Generated Node #0,1: 46:[6, 3, 55] Operation: 62-7=55 Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[6, 3, 55], Operations: ['62-7=55'] Exploring Operation: 6/3=2, Resulting Numbers: [55, 2] Generated Node #0,1,0: 46:[55, 2] Operation: 6/3=2 Exploring Operation: 55-6=49, Resulting Numbers: [3, 49] Generated Node #0,1,1: 46:[3, 49] Operation: 55-6=49 Moving to Node #0,1,1 Current State: 46:[3, 49], Operations: ['62-7=55', '55-6=49'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[6, 3, 7, 62], Operations: [] Exploring Operation: 62-7=55, Resulting Numbers: [6, 3, 55] Generated Node #0,1: 46:[6, 3, 55] Operation: 62-7=55 Moving to Node #0,1 Current State: 46:[6, 3, 55], Operations: ['62-7=55'] Exploring Operation: 55-6=49, Resulting Numbers: [3, 49] Generated Node #0,1,1: 46:[3, 49] Operation: 55-6=49 Moving to Node #0,1,1 Current State: 46:[3, 49], Operations: ['62-7=55', '55-6=49'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 99, 78, 43, 52 ]
23
[ "99*52=5148", "5148/78=66", "66-43=23" ]
Current State: 23:[99, 78, 43, 52], Operations: [] Exploring Operation: 99*52=5148, Resulting Numbers: [78, 43, 5148] Generated Node #2: [78, 43, 5148] from Operation: 99*52=5148 Current State: 23:[78, 43, 5148], Operations: ['99*52=5148'] Exploring Operation: 5148/78=66, Resulting Numbers: [43, 66] Generated Node #3: [43, 66] from Operation: 5148/78=66 Current State: 23:[43, 66], Operations: ['99*52=5148', '5148/78=66'] Exploring Operation: 66-43=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[99, 78, 43, 52], Operations: [] Exploring Operation: 99-78=21, Resulting Numbers: [43, 52, 21] Generated Node #0,0: 23:[43, 52, 21] Operation: 99-78=21 Exploring Operation: 99-52=47, Resulting Numbers: [78, 43, 47] Generated Node #0,1: 23:[78, 43, 47] Operation: 99-52=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[43, 52, 21], Operations: ['99-78=21'] Exploring Operation: 52-43=9, Resulting Numbers: [21, 9] Generated Node #0,0,0: 23:[21, 9] Operation: 52-43=9 Exploring Operation: 52-21=31, Resulting Numbers: [43, 31] Generated Node #0,0,1: 23:[43, 31] Operation: 52-21=31 Moving to Node #0,0,0 Current State: 23:[21, 9], Operations: ['99-78=21', '52-43=9'] Exploring Operation: 21+9=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[43, 31], Operations: ['99-78=21', '52-21=31'] Exploring Operation: 43+31=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 43-31=12, Resulting Numbers: [12] 12,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[78, 43, 47], Operations: ['99-52=47'] Exploring Operation: 78-47=31, Resulting Numbers: [43, 31] Generated Node #0,1,0: 23:[43, 31] Operation: 78-47=31 Exploring Operation: 78-43=35, Resulting Numbers: [47, 35] Generated Node #0,1,1: 23:[47, 35] Operation: 78-43=35 Moving to Node #0,1,0 Current State: 23:[43, 31], Operations: ['99-52=47', '78-47=31'] Exploring Operation: 43-31=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 43+31=74, Resulting Numbers: [74] 74,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[47, 35], Operations: ['99-52=47', '78-43=35'] Exploring Operation: 47-35=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 47+35=82, Resulting Numbers: [82] 82,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 76, 8, 77, 60 ]
60
[ "76+60=136", "136/8=17", "77-17=60" ]
Current State: 60:[76, 8, 77, 60], Operations: [] Exploring Operation: 76+60=136, Resulting Numbers: [8, 77, 136] Generated Node #2: [8, 77, 136] from Operation: 76+60=136 Current State: 60:[8, 77, 136], Operations: ['76+60=136'] Exploring Operation: 136/8=17, Resulting Numbers: [77, 17] Generated Node #3: [77, 17] from Operation: 136/8=17 Current State: 60:[77, 17], Operations: ['76+60=136', '136/8=17'] Exploring Operation: 77-17=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[76, 8, 77, 60], Operations: [] Exploring Operation: 77-76=1, Resulting Numbers: [8, 60, 1] Generated Node #0,0: 60:[8, 60, 1] Operation: 77-76=1 Moving to Node #0,0 Current State: 60:[8, 60, 1], Operations: ['77-76=1'] Exploring Operation: 8+1=9, Resulting Numbers: [60, 9] Generated Node #0,0,0: 60:[60, 9] Operation: 8+1=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[60, 9], Operations: ['77-76=1', '8+1=9'] Exploring Operation: 60+9=69, Resulting Numbers: [69] 69,60 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
[ 71, 48, 88, 20 ]
45
[ "71-48=23", "88-20=68", "68-23=45" ]
Current State: 45:[71, 48, 88, 20], Operations: [] Exploring Operation: 71-48=23, Resulting Numbers: [88, 20, 23] Generated Node #2: [88, 20, 23] from Operation: 71-48=23 Current State: 45:[88, 20, 23], Operations: ['71-48=23'] Exploring Operation: 88-20=68, Resulting Numbers: [23, 68] Generated Node #3: [23, 68] from Operation: 88-20=68 Current State: 45:[23, 68], Operations: ['71-48=23', '88-20=68'] Exploring Operation: 68-23=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[71, 48, 88, 20], Operations: [] Exploring Operation: 88-71=17, Resulting Numbers: [48, 20, 17] Generated Node #0,0: 45:[48, 20, 17] Operation: 88-71=17 Exploring Operation: 88-48=40, Resulting Numbers: [71, 20, 40] Generated Node #0,1: 45:[71, 20, 40] Operation: 88-48=40 Moving to Node #0,0 Current State: 45:[48, 20, 17], Operations: ['88-71=17'] Exploring Operation: 20-17=3, Resulting Numbers: [48, 3] Generated Node #0,0,0: 45:[48, 3] Operation: 20-17=3 Exploring Operation: 20+17=37, Resulting Numbers: [48, 37] Generated Node #0,0,1: 45:[48, 37] Operation: 20+17=37 Moving to Node #0,1 Current State: 45:[71, 20, 40], Operations: ['88-48=40'] Exploring Operation: 71-40=31, Resulting Numbers: [20, 31] Generated Node #0,1,0: 45:[20, 31] Operation: 71-40=31 Exploring Operation: 71-20=51, Resulting Numbers: [40, 51] Generated Node #0,1,1: 45:[40, 51] Operation: 71-20=51 Moving to Node #0,0,0 Current State: 45:[48, 3], Operations: ['88-71=17', '20-17=3'] Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[71, 48, 88, 20], Operations: [] Exploring Operation: 88-71=17, Resulting Numbers: [48, 20, 17] Generated Node #0,0: 45:[48, 20, 17] Operation: 88-71=17 Moving to Node #0,0 Current State: 45:[48, 20, 17], Operations: ['88-71=17'] Exploring Operation: 20-17=3, Resulting Numbers: [48, 3] Generated Node #0,0,0: 45:[48, 3] Operation: 20-17=3 Moving to Node #0,0,0 Current State: 45:[48, 3], Operations: ['88-71=17', '20-17=3'] Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 38, 99, 8, 97 ]
54
[ "99-97=2", "8*2=16", "38+16=54" ]
Current State: 54:[38, 99, 8, 97], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [38, 8, 2] Generated Node #2: [38, 8, 2] from Operation: 99-97=2 Current State: 54:[38, 8, 2], Operations: ['99-97=2'] Exploring Operation: 8*2=16, Resulting Numbers: [38, 16] Generated Node #3: [38, 16] from Operation: 8*2=16 Current State: 54:[38, 16], Operations: ['99-97=2', '8*2=16'] Exploring Operation: 38+16=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[38, 99, 8, 97], Operations: [] Exploring Operation: 99-8=91, Resulting Numbers: [38, 97, 91] Generated Node #0,0: 54:[38, 97, 91] Operation: 99-8=91 Exploring Operation: 38-8=30, Resulting Numbers: [99, 97, 30] Generated Node #0,1: 54:[99, 97, 30] Operation: 38-8=30 Exploring Operation: 99-97=2, Resulting Numbers: [38, 8, 2] Generated Node #0,2: 54:[38, 8, 2] Operation: 99-97=2 Exploring Operation: 99-38=61, Resulting Numbers: [8, 97, 61] Generated Node #0,3: 54:[8, 97, 61] Operation: 99-38=61 Exploring Operation: 97-38=59, Resulting Numbers: [99, 8, 59] Generated Node #0,4: 54:[99, 8, 59] Operation: 97-38=59 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[38, 8, 2], Operations: ['99-97=2'] Exploring Operation: 38-8=30, Resulting Numbers: [2, 30] Generated Node #0,2,0: 54:[2, 30] Operation: 38-8=30 Exploring Operation: 38/2=19, Resulting Numbers: [8, 19] Generated Node #0,2,1: 54:[8, 19] Operation: 38/2=19 Exploring Operation: 38-2=36, Resulting Numbers: [8, 36] Generated Node #0,2,2: 54:[8, 36] Operation: 38-2=36 Exploring Operation: 8-2=6, Resulting Numbers: [38, 6] Generated Node #0,2,3: 54:[38, 6] Operation: 8-2=6 Exploring Operation: 38+8=46, Resulting Numbers: [2, 46] Generated Node #0,2,4: 54:[2, 46] Operation: 38+8=46 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 54:[8, 19], Operations: ['99-97=2', '38/2=19'] Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,54 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,54 unequal: No Solution Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,54 unequal: No Solution No 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: 54:[2, 30], Operations: ['99-97=2', '38-8=30'] Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,54 unequal: No Solution Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,54 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,54 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,54 unequal: No Solution No 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: 54:[2, 46], Operations: ['99-97=2', '38+8=46'] Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,54 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,54 unequal: No Solution Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,54 unequal: No Solution No 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: 54:[8, 36], Operations: ['99-97=2', '38-2=36'] Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 8+36=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 8*36=288, Resulting Numbers: [288] 288,54 unequal: No Solution No 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: 54:[38, 6], Operations: ['99-97=2', '8-2=6'] Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,54 unequal: No Solution Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,54 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: 54:[8, 97, 61], Operations: ['99-38=61'] Exploring Operation: 97-8=89, Resulting Numbers: [61, 89] Generated Node #0,3,0: 54:[61, 89] Operation: 97-8=89 Exploring Operation: 61-8=53, Resulting Numbers: [97, 53] Generated Node #0,3,1: 54:[97, 53] Operation: 61-8=53 Exploring Operation: 97-61=36, Resulting Numbers: [8, 36] Generated Node #0,3,2: 54:[8, 36] Operation: 97-61=36 Exploring Operation: 8+97=105, Resulting Numbers: [61, 105] Generated Node #0,3,3: 54:[61, 105] Operation: 8+97=105 Exploring Operation: 8+61=69, Resulting Numbers: [97, 69] Generated Node #0,3,4: 54:[97, 69] Operation: 8+61=69 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 54:[8, 36], Operations: ['99-38=61', '97-61=36'] Exploring Operation: 8+36=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 8*36=288, Resulting Numbers: [288] 288,54 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,54 unequal: No Solution No 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: 54:[61, 89], Operations: ['99-38=61', '97-8=89'] Exploring Operation: 61+89=150, Resulting Numbers: [150] 150,54 unequal: No Solution Exploring Operation: 89-61=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 61*89=5429, Resulting Numbers: [5429] 5429,54 unequal: No Solution No 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: 54:[97, 53], Operations: ['99-38=61', '61-8=53'] Exploring Operation: 97-53=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 97+53=150, Resulting Numbers: [150] 150,54 unequal: No Solution Exploring Operation: 97*53=5141, Resulting Numbers: [5141] 5141,54 unequal: No Solution No 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: 54:[61, 105], Operations: ['99-38=61', '8+97=105'] Exploring Operation: 105-61=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 61+105=166, Resulting Numbers: [166] 166,54 unequal: No Solution Exploring Operation: 61*105=6405, Resulting Numbers: [6405] 6405,54 unequal: No Solution No 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: 54:[97, 69], Operations: ['99-38=61', '8+61=69'] Exploring Operation: 97-69=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 97+69=166, Resulting Numbers: [166] 166,54 unequal: No Solution Exploring Operation: 97*69=6693, Resulting Numbers: [6693] 6693,54 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: 54:[99, 8, 59], Operations: ['97-38=59'] Exploring Operation: 99-8=91, Resulting Numbers: [59, 91] Generated Node #0,4,0: 54:[59, 91] Operation: 99-8=91 Exploring Operation: 8+59=67, Resulting Numbers: [99, 67] Generated Node #0,4,1: 54:[99, 67] Operation: 8+59=67 Exploring Operation: 99+8=107, Resulting Numbers: [59, 107] Generated Node #0,4,2: 54:[59, 107] Operation: 99+8=107 Exploring Operation: 99-59=40, Resulting Numbers: [8, 40] Generated Node #0,4,3: 54:[8, 40] Operation: 99-59=40 Exploring Operation: 59-8=51, Resulting Numbers: [99, 51] Generated Node #0,4,4: 54:[99, 51] Operation: 59-8=51 Moving to Node #0,4,3 Current State: 54:[8, 40], Operations: ['97-38=59', '99-59=40'] Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,54 unequal: No Solution Exploring Operation: 8+40=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 8*40=320, Resulting Numbers: [320] 320,54 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,54 unequal: No Solution Moving to Node #0,4,0 Current State: 54:[59, 91], Operations: ['97-38=59', '99-8=91'] Exploring Operation: 59*91=5369, Resulting Numbers: [5369] 5369,54 unequal: No Solution Exploring Operation: 91-59=32, Resulting Numbers: [32] 32,54 unequal: No Solution Exploring Operation: 59+91=150, Resulting Numbers: [150] 150,54 unequal: No Solution Moving to Node #0,4,4 Current State: 54:[99, 51], Operations: ['97-38=59', '59-8=51'] Exploring Operation: 99*51=5049, Resulting Numbers: [5049] 5049,54 unequal: No Solution Exploring Operation: 99+51=150, Resulting Numbers: [150] 150,54 unequal: No Solution Exploring Operation: 99-51=48, Resulting Numbers: [48] 48,54 unequal: No Solution Moving to Node #0,4,1 Current State: 54:[99, 67], Operations: ['97-38=59', '8+59=67'] Exploring Operation: 99*67=6633, Resulting Numbers: [6633] 6633,54 unequal: No Solution Exploring Operation: 99-67=32, Resulting Numbers: [32] 32,54 unequal: No Solution Exploring Operation: 99+67=166, Resulting Numbers: [166] 166,54 unequal: No Solution Moving to Node #0,4,2 Current State: 54:[59, 107], Operations: ['97-38=59', '99+8=107'] Exploring Operation: 59+107=166, Resulting Numbers: [166] 166,54 unequal: No Solution Exploring Operation: 59*107=6313, Resulting Numbers: [6313] 6313,54 unequal: No Solution Exploring Operation: 107-59=48, Resulting Numbers: [48] 48,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[38, 97, 91], Operations: ['99-8=91'] Exploring Operation: 38+91=129, Resulting Numbers: [97, 129] Generated Node #0,0,0: 54:[97, 129] Operation: 38+91=129 Exploring Operation: 97-38=59, Resulting Numbers: [91, 59] Generated Node #0,0,1: 54:[91, 59] Operation: 97-38=59 Exploring Operation: 38+97=135, Resulting Numbers: [91, 135] Generated Node #0,0,2: 54:[91, 135] Operation: 38+97=135 Exploring Operation: 97-91=6, Resulting Numbers: [38, 6] Generated Node #0,0,3: 54:[38, 6] Operation: 97-91=6 Exploring Operation: 91-38=53, Resulting Numbers: [97, 53] Generated Node #0,0,4: 54:[97, 53] Operation: 91-38=53 Moving to Node #0,0,3 Current State: 54:[38, 6], Operations: ['99-8=91', '97-91=6'] Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,54 unequal: No Solution Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[91, 59], Operations: ['99-8=91', '97-38=59'] Exploring Operation: 91*59=5369, Resulting Numbers: [5369] 5369,54 unequal: No Solution Exploring Operation: 91+59=150, Resulting Numbers: [150] 150,54 unequal: No Solution Exploring Operation: 91-59=32, Resulting Numbers: [32] 32,54 unequal: No Solution Moving to Node #0,0,4 Current State: 54:[97, 53], Operations: ['99-8=91', '91-38=53'] Exploring Operation: 97*53=5141, Resulting Numbers: [5141] 5141,54 unequal: No Solution Exploring Operation: 97+53=150, Resulting Numbers: [150] 150,54 unequal: No Solution Exploring Operation: 97-53=44, Resulting Numbers: [44] 44,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[97, 129], Operations: ['99-8=91', '38+91=129'] Exploring Operation: 97*129=12513, Resulting Numbers: [12513] 12513,54 unequal: No Solution Exploring Operation: 129-97=32, Resulting Numbers: [32] 32,54 unequal: No Solution Exploring Operation: 97+129=226, Resulting Numbers: [226] 226,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[91, 135], Operations: ['99-8=91', '38+97=135'] Exploring Operation: 135-91=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 91*135=12285, Resulting Numbers: [12285] 12285,54 unequal: No Solution Exploring Operation: 91+135=226, Resulting Numbers: [226] 226,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[99, 97, 30], Operations: ['38-8=30'] Exploring Operation: 99-97=2, Resulting Numbers: [30, 2] Generated Node #0,1,0: 54:[30, 2] Operation: 99-97=2 Exploring Operation: 99+30=129, Resulting Numbers: [97, 129] Generated Node #0,1,1: 54:[97, 129] Operation: 99+30=129 Exploring Operation: 97+30=127, Resulting Numbers: [99, 127] Generated Node #0,1,2: 54:[99, 127] Operation: 97+30=127 Exploring Operation: 97-30=67, Resulting Numbers: [99, 67] Generated Node #0,1,3: 54:[99, 67] Operation: 97-30=67 Exploring Operation: 99-30=69, Resulting Numbers: [97, 69] Generated Node #0,1,4: 54:[97, 69] Operation: 99-30=69 Moving to Node #0,1,0 Current State: 54:[30, 2], Operations: ['38-8=30', '99-97=2'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,54 unequal: No Solution Exploring Operation: 30*2=60, Resulting Numbers: [60] 60,54 unequal: No Solution Exploring Operation: 30+2=32, Resulting Numbers: [32] 32,54 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,54 unequal: No Solution Moving to Node #0,1,4 Current State: 54:[97, 69], Operations: ['38-8=30', '99-30=69'] Exploring Operation: 97*69=6693, Resulting Numbers: [6693] 6693,54 unequal: No Solution Exploring Operation: 97+69=166, Resulting Numbers: [166] 166,54 unequal: No Solution Exploring Operation: 97-69=28, Resulting Numbers: [28] 28,54 unequal: No Solution Moving to Node #0,1,3 Current State: 54:[99, 67], Operations: ['38-8=30', '97-30=67'] Exploring Operation: 99+67=166, Resulting Numbers: [166] 166,54 unequal: No Solution Exploring Operation: 99*67=6633, Resulting Numbers: [6633] 6633,54 unequal: No Solution Exploring Operation: 99-67=32, Resulting Numbers: [32] 32,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[97, 129], Operations: ['38-8=30', '99+30=129'] Exploring Operation: 129-97=32, Resulting Numbers: [32] 32,54 unequal: No Solution Exploring Operation: 97+129=226, Resulting Numbers: [226] 226,54 unequal: No Solution Exploring Operation: 97*129=12513, Resulting Numbers: [12513] 12513,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[99, 127], Operations: ['38-8=30', '97+30=127'] Exploring Operation: 127-99=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 99*127=12573, Resulting Numbers: [12573] 12573,54 unequal: No Solution Exploring Operation: 99+127=226, Resulting Numbers: [226] 226,54 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
[ 45, 52, 61, 15 ]
44
[ "52-45=7", "15*7=105", "105-61=44" ]
Current State: 44:[45, 52, 61, 15], Operations: [] Exploring Operation: 52-45=7, Resulting Numbers: [61, 15, 7] Generated Node #2: [61, 15, 7] from Operation: 52-45=7 Current State: 44:[61, 15, 7], Operations: ['52-45=7'] Exploring Operation: 15*7=105, Resulting Numbers: [61, 105] Generated Node #3: [61, 105] from Operation: 15*7=105 Current State: 44:[61, 105], Operations: ['52-45=7', '15*7=105'] Exploring Operation: 105-61=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[45, 52, 61, 15], Operations: [] Exploring Operation: 61-52=9, Resulting Numbers: [45, 15, 9] Generated Node #0,0: 44:[45, 15, 9] Operation: 61-52=9 Exploring Operation: 61-15=46, Resulting Numbers: [45, 52, 46] Generated Node #0,1: 44:[45, 52, 46] Operation: 61-15=46 Moving to Node #0,0 Current State: 44:[45, 15, 9], Operations: ['61-52=9'] Exploring Operation: 45/15=3, Resulting Numbers: [9, 3] Generated Node #0,0,0: 44:[9, 3] Operation: 45/15=3 Exploring Operation: 15+9=24, Resulting Numbers: [45, 24] Generated Node #0,0,1: 44:[45, 24] Operation: 15+9=24 Moving to Node #0,1 Current State: 44:[45, 52, 46], Operations: ['61-15=46'] Exploring Operation: 52-45=7, Resulting Numbers: [46, 7] Generated Node #0,1,0: 44:[46, 7] Operation: 52-45=7 Exploring Operation: 52-46=6, Resulting Numbers: [45, 6] Generated Node #0,1,1: 44:[45, 6] Operation: 52-46=6 Moving to Node #0,0,0 Current State: 44:[9, 3], Operations: ['61-52=9', '45/15=3'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,44 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[45, 6], Operations: ['61-15=46', '52-46=6'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,44 unequal: No Solution Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,44 unequal: No Solution Moving to Node #0,0,1 Current State: 44:[45, 24], Operations: ['61-52=9', '15+9=24'] Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,44 unequal: No Solution Exploring Operation: 45+24=69, Resulting Numbers: [69] 69,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[46, 7], Operations: ['61-15=46', '52-45=7'] Exploring Operation: 46+7=53, Resulting Numbers: [53] 53,44 unequal: No Solution Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,44 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 45, 57, 86, 62 ]
78
[ "45+57=102", "86-62=24", "102-24=78" ]
Current State: 78:[45, 57, 86, 62], Operations: [] Exploring Operation: 45+57=102, Resulting Numbers: [86, 62, 102] Generated Node #2: [86, 62, 102] from Operation: 45+57=102 Current State: 78:[86, 62, 102], Operations: ['45+57=102'] Exploring Operation: 86-62=24, Resulting Numbers: [102, 24] Generated Node #3: [102, 24] from Operation: 86-62=24 Current State: 78:[102, 24], Operations: ['45+57=102', '86-62=24'] Exploring Operation: 102-24=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[45, 57, 86, 62], Operations: [] Exploring Operation: 86-57=29, Resulting Numbers: [45, 62, 29] Generated Node #0,0: 78:[45, 62, 29] Operation: 86-57=29 Exploring Operation: 86-62=24, Resulting Numbers: [45, 57, 24] Generated Node #0,1: 78:[45, 57, 24] Operation: 86-62=24 Exploring Operation: 57-45=12, Resulting Numbers: [86, 62, 12] Generated Node #0,2: 78:[86, 62, 12] Operation: 57-45=12 Exploring Operation: 62-57=5, Resulting Numbers: [45, 86, 5] Generated Node #0,3: 78:[45, 86, 5] Operation: 62-57=5 Start Sub Search at level 1: Moving to Node #0,3 Current State: 78:[45, 86, 5], Operations: ['62-57=5'] Exploring Operation: 86-45=41, Resulting Numbers: [5, 41] Generated Node #0,3,0: 78:[5, 41] Operation: 86-45=41 Exploring Operation: 86-5=81, Resulting Numbers: [45, 81] Generated Node #0,3,1: 78:[45, 81] Operation: 86-5=81 Exploring Operation: 45/5=9, Resulting Numbers: [86, 9] Generated Node #0,3,2: 78:[86, 9] Operation: 45/5=9 Exploring Operation: 45-5=40, Resulting Numbers: [86, 40] Generated Node #0,3,3: 78:[86, 40] Operation: 45-5=40 Moving to Node #0,3,0 Current State: 78:[5, 41], Operations: ['62-57=5', '86-45=41'] Exploring Operation: 5*41=205, Resulting Numbers: [205] 205,78 unequal: No Solution Exploring Operation: 5+41=46, Resulting Numbers: [46] 46,78 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,78 unequal: No Solution Moving to Node #0,3,3 Current State: 78:[86, 40], Operations: ['62-57=5', '45-5=40'] Exploring Operation: 86+40=126, Resulting Numbers: [126] 126,78 unequal: No Solution Exploring Operation: 86*40=3440, Resulting Numbers: [3440] 3440,78 unequal: No Solution Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,78 unequal: No Solution Moving to Node #0,3,1 Current State: 78:[45, 81], Operations: ['62-57=5', '86-5=81'] Exploring Operation: 45+81=126, Resulting Numbers: [126] 126,78 unequal: No Solution Exploring Operation: 81-45=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 45*81=3645, Resulting Numbers: [3645] 3645,78 unequal: No Solution Moving to Node #0,3,2 Current State: 78:[86, 9], Operations: ['62-57=5', '45/5=9'] Exploring Operation: 86+9=95, Resulting Numbers: [95] 95,78 unequal: No Solution Exploring Operation: 86*9=774, Resulting Numbers: [774] 774,78 unequal: No Solution Exploring Operation: 86-9=77, Resulting Numbers: [77] 77,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[45, 62, 29], Operations: ['86-57=29'] Exploring Operation: 45-29=16, Resulting Numbers: [62, 16] Generated Node #0,0,0: 78:[62, 16] Operation: 45-29=16 Exploring Operation: 62-45=17, Resulting Numbers: [29, 17] Generated Node #0,0,1: 78:[29, 17] Operation: 62-45=17 Exploring Operation: 62-29=33, Resulting Numbers: [45, 33] Generated Node #0,0,2: 78:[45, 33] Operation: 62-29=33 Exploring Operation: 62+29=91, Resulting Numbers: [45, 91] Generated Node #0,0,3: 78:[45, 91] Operation: 62+29=91 Moving to Node #0,0,1 Current State: 78:[29, 17], Operations: ['86-57=29', '62-45=17'] Exploring Operation: 29+17=46, Resulting Numbers: [46] 46,78 unequal: No Solution Exploring Operation: 29*17=493, Resulting Numbers: [493] 493,78 unequal: No Solution Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,78 unequal: No Solution Moving to Node #0,0,2 Current State: 78:[45, 33], Operations: ['86-57=29', '62-29=33'] Exploring Operation: 45*33=1485, Resulting Numbers: [1485] 1485,78 unequal: No Solution Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,78 unequal: No Solution Exploring Operation: 45+33=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[45, 57, 86, 62], Operations: [] Exploring Operation: 86-57=29, Resulting Numbers: [45, 62, 29] Generated Node #0,0: 78:[45, 62, 29] Operation: 86-57=29 Moving to Node #0,0 Current State: 78:[45, 62, 29], Operations: ['86-57=29'] Exploring Operation: 62-29=33, Resulting Numbers: [45, 33] Generated Node #0,0,2: 78:[45, 33] Operation: 62-29=33 Moving to Node #0,0,2 Current State: 78:[45, 33], Operations: ['86-57=29', '62-29=33'] Exploring Operation: 45+33=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
mult_heuristic
[ 67, 37, 50, 6 ]
11
[ "50-37=13", "6*13=78", "78-67=11" ]
Current State: 11:[67, 37, 50, 6], Operations: [] Exploring Operation: 50-37=13, Resulting Numbers: [67, 6, 13] Generated Node #2: [67, 6, 13] from Operation: 50-37=13 Current State: 11:[67, 6, 13], Operations: ['50-37=13'] Exploring Operation: 6*13=78, Resulting Numbers: [67, 78] Generated Node #3: [67, 78] from Operation: 6*13=78 Current State: 11:[67, 78], Operations: ['50-37=13', '6*13=78'] Exploring Operation: 78-67=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[67, 37, 50, 6], Operations: [] Exploring Operation: 67-50=17, Resulting Numbers: [37, 6, 17] Generated Node #0,0: 11:[37, 6, 17] Operation: 67-50=17 Exploring Operation: 67-37=30, Resulting Numbers: [50, 6, 30] Generated Node #0,1: 11:[50, 6, 30] Operation: 67-37=30 Exploring Operation: 50-37=13, Resulting Numbers: [67, 6, 13] Generated Node #0,2: 11:[67, 6, 13] Operation: 50-37=13 Moving to Node #0,0 Current State: 11:[37, 6, 17], Operations: ['67-50=17'] Exploring Operation: 17-6=11, Resulting Numbers: [37, 11] Generated Node #0,0,0: 11:[37, 11] Operation: 17-6=11 Exploring Operation: 37-6=31, Resulting Numbers: [17, 31] Generated Node #0,0,1: 11:[17, 31] Operation: 37-6=31 Exploring Operation: 37-17=20, Resulting Numbers: [6, 20] Generated Node #0,0,2: 11:[6, 20] Operation: 37-17=20 Moving to Node #0,1 Current State: 11:[50, 6, 30], Operations: ['67-37=30'] Exploring Operation: 30/6=5, Resulting Numbers: [50, 5] Generated Node #0,1,0: 11:[50, 5] Operation: 30/6=5 Exploring Operation: 50-6=44, Resulting Numbers: [30, 44] Generated Node #0,1,1: 11:[30, 44] Operation: 50-6=44 Exploring Operation: 50-30=20, Resulting Numbers: [6, 20] Generated Node #0,1,2: 11:[6, 20] Operation: 50-30=20 Moving to Node #0,2 Current State: 11:[67, 6, 13], Operations: ['50-37=13'] Exploring Operation: 67-13=54, Resulting Numbers: [6, 54] Generated Node #0,2,0: 11:[6, 54] Operation: 67-13=54 Exploring Operation: 67-6=61, Resulting Numbers: [13, 61] Generated Node #0,2,1: 11:[13, 61] Operation: 67-6=61 Exploring Operation: 13-6=7, Resulting Numbers: [67, 7] Generated Node #0,2,2: 11:[67, 7] Operation: 13-6=7 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[6, 54], Operations: ['50-37=13', '67-13=54'] 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 Exploring Operation: 6+54=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:[13, 61], Operations: ['50-37=13', '67-6=61'] Exploring Operation: 13*61=793, Resulting Numbers: [793] 793,11 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 13+61=74, Resulting Numbers: [74] 74,11 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:[67, 7], Operations: ['50-37=13', '13-6=7'] Exploring Operation: 67+7=74, Resulting Numbers: [74] 74,11 unequal: No Solution Exploring Operation: 67*7=469, Resulting Numbers: [469] 469,11 unequal: No Solution Exploring Operation: 67-7=60, Resulting Numbers: [60] 60,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 11:[6, 20], Operations: ['67-50=17', '37-17=20'] Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[6, 20], Operations: ['67-37=30', '50-30=20'] Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[17, 31], Operations: ['67-50=17', '37-6=31'] Exploring Operation: 17*31=527, Resulting Numbers: [527] 527,11 unequal: No Solution Exploring Operation: 17+31=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 31-17=14, Resulting Numbers: [14] 14,11 unequal: No Solution Moving to Node #0,0,0 Current State: 11:[37, 11], Operations: ['67-50=17', '17-6=11'] Exploring Operation: 37*11=407, Resulting Numbers: [407] 407,11 unequal: No Solution Exploring Operation: 37+11=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[50, 5], Operations: ['67-37=30', '30/6=5'] Exploring Operation: 50+5=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,11 unequal: No Solution Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[30, 44], Operations: ['67-37=30', '50-6=44'] Exploring Operation: 30*44=1320, Resulting Numbers: [1320] 1320,11 unequal: No Solution Exploring Operation: 30+44=74, Resulting Numbers: [74] 74,11 unequal: No Solution Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,11 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 92, 10, 7, 83 ]
11
[ "92*10=920", "920-7=913", "913/83=11" ]
Current State: 11:[92, 10, 7, 83], Operations: [] Exploring Operation: 92*10=920, Resulting Numbers: [7, 83, 920] Generated Node #2: [7, 83, 920] from Operation: 92*10=920 Current State: 11:[7, 83, 920], Operations: ['92*10=920'] Exploring Operation: 920-7=913, Resulting Numbers: [83, 913] Generated Node #3: [83, 913] from Operation: 920-7=913 Current State: 11:[83, 913], Operations: ['92*10=920', '920-7=913'] Exploring Operation: 913/83=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[92, 10, 7, 83], Operations: [] Exploring Operation: 92-83=9, Resulting Numbers: [10, 7, 9] Generated Node #0,0: 11:[10, 7, 9] Operation: 92-83=9 Exploring Operation: 92-7=85, Resulting Numbers: [10, 83, 85] Generated Node #0,1: 11:[10, 83, 85] Operation: 92-7=85 Exploring Operation: 83-7=76, Resulting Numbers: [92, 10, 76] Generated Node #0,2: 11:[92, 10, 76] Operation: 83-7=76 Exploring Operation: 83-10=73, Resulting Numbers: [92, 7, 73] Generated Node #0,3: 11:[92, 7, 73] Operation: 83-10=73 Exploring Operation: 92-10=82, Resulting Numbers: [7, 83, 82] Generated Node #0,4: 11:[7, 83, 82] Operation: 92-10=82 Moving to Node #0,0 Current State: 11:[10, 7, 9], Operations: ['92-83=9'] Exploring Operation: 10+9=19, Resulting Numbers: [7, 19] Generated Node #0,0,0: 11:[7, 19] Operation: 10+9=19 Exploring Operation: 10+7=17, Resulting Numbers: [9, 17] Generated Node #0,0,1: 11:[9, 17] Operation: 10+7=17 Exploring Operation: 9-7=2, Resulting Numbers: [10, 2] Generated Node #0,0,2: 11:[10, 2] Operation: 9-7=2 Exploring Operation: 10-7=3, Resulting Numbers: [9, 3] Generated Node #0,0,3: 11:[9, 3] Operation: 10-7=3 Exploring Operation: 7+9=16, Resulting Numbers: [10, 16] Generated Node #0,0,4: 11:[10, 16] Operation: 7+9=16 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 11:[10, 16], Operations: ['92-83=9', '7+9=16'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,11 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 #0,0,1 Current State: 11:[9, 17], Operations: ['92-83=9', '10+7=17'] Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 9*17=153, Resulting Numbers: [153] 153,11 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 #0,0,2 Current State: 11:[10, 2], Operations: ['92-83=9', '9-7=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,11 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,11 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 #0,0,3 Current State: 11:[9, 3], Operations: ['92-83=9', '10-7=3'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,11 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 #0,0,0 Current State: 11:[7, 19], Operations: ['92-83=9', '10+9=19'] Exploring Operation: 7*19=133, Resulting Numbers: [133] 133,11 unequal: No Solution Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 11:[92, 10, 76], Operations: ['83-7=76'] Exploring Operation: 92-76=16, Resulting Numbers: [10, 16] Generated Node #0,2,0: 11:[10, 16] Operation: 92-76=16 Exploring Operation: 10+76=86, Resulting Numbers: [92, 86] Generated Node #0,2,1: 11:[92, 86] Operation: 10+76=86 Exploring Operation: 76-10=66, Resulting Numbers: [92, 66] Generated Node #0,2,2: 11:[92, 66] Operation: 76-10=66 Exploring Operation: 92-10=82, Resulting Numbers: [76, 82] Generated Node #0,2,3: 11:[76, 82] Operation: 92-10=82 Exploring Operation: 92+10=102, Resulting Numbers: [76, 102] Generated Node #0,2,4: 11:[76, 102] Operation: 92+10=102 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[10, 16], Operations: ['83-7=76', '92-76=16'] Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,11 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:[92, 66], Operations: ['83-7=76', '76-10=66'] Exploring Operation: 92*66=6072, Resulting Numbers: [6072] 6072,11 unequal: No Solution Exploring Operation: 92+66=158, Resulting Numbers: [158] 158,11 unequal: No Solution Exploring Operation: 92-66=26, Resulting Numbers: [26] 26,11 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:[76, 82], Operations: ['83-7=76', '92-10=82'] Exploring Operation: 82-76=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 76*82=6232, Resulting Numbers: [6232] 6232,11 unequal: No Solution Exploring Operation: 76+82=158, Resulting Numbers: [158] 158,11 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:[92, 86], Operations: ['83-7=76', '10+76=86'] Exploring Operation: 92+86=178, Resulting Numbers: [178] 178,11 unequal: No Solution Exploring Operation: 92-86=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 92*86=7912, Resulting Numbers: [7912] 7912,11 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:[76, 102], Operations: ['83-7=76', '92+10=102'] Exploring Operation: 76*102=7752, Resulting Numbers: [7752] 7752,11 unequal: No Solution Exploring Operation: 102-76=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 76+102=178, Resulting Numbers: [178] 178,11 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: 11:[7, 83, 82], Operations: ['92-10=82'] Exploring Operation: 83-7=76, Resulting Numbers: [82, 76] Generated Node #0,4,0: 11:[82, 76] Operation: 83-7=76 Exploring Operation: 7+83=90, Resulting Numbers: [82, 90] Generated Node #0,4,1: 11:[82, 90] Operation: 7+83=90 Exploring Operation: 83-82=1, Resulting Numbers: [7, 1] Generated Node #0,4,2: 11:[7, 1] Operation: 83-82=1 Exploring Operation: 82-7=75, Resulting Numbers: [83, 75] Generated Node #0,4,3: 11:[83, 75] Operation: 82-7=75 Exploring Operation: 7+82=89, Resulting Numbers: [83, 89] Generated Node #0,4,4: 11:[83, 89] Operation: 7+82=89 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 11:[7, 1], Operations: ['92-10=82', '83-82=1'] Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,11 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 #0,4,0 Current State: 11:[82, 76], Operations: ['92-10=82', '83-7=76'] Exploring Operation: 82*76=6232, Resulting Numbers: [6232] 6232,11 unequal: No Solution Exploring Operation: 82+76=158, Resulting Numbers: [158] 158,11 unequal: No Solution Exploring Operation: 82-76=6, Resulting Numbers: [6] 6,11 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 #0,4,3 Current State: 11:[83, 75], Operations: ['92-10=82', '82-7=75'] Exploring Operation: 83+75=158, Resulting Numbers: [158] 158,11 unequal: No Solution Exploring Operation: 83*75=6225, Resulting Numbers: [6225] 6225,11 unequal: No Solution Exploring Operation: 83-75=8, Resulting Numbers: [8] 8,11 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 #0,4,1 Current State: 11:[82, 90], Operations: ['92-10=82', '7+83=90'] Exploring Operation: 90-82=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 82*90=7380, Resulting Numbers: [7380] 7380,11 unequal: No Solution Exploring Operation: 82+90=172, Resulting Numbers: [172] 172,11 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 #0,4,4 Current State: 11:[83, 89], Operations: ['92-10=82', '7+82=89'] Exploring Operation: 83+89=172, Resulting Numbers: [172] 172,11 unequal: No Solution Exploring Operation: 89-83=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 83*89=7387, Resulting Numbers: [7387] 7387,11 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: 11:[10, 83, 85], Operations: ['92-7=85'] Exploring Operation: 10+83=93, Resulting Numbers: [85, 93] Generated Node #0,1,0: 11:[85, 93] Operation: 10+83=93 Exploring Operation: 83-10=73, Resulting Numbers: [85, 73] Generated Node #0,1,1: 11:[85, 73] Operation: 83-10=73 Exploring Operation: 85-10=75, Resulting Numbers: [83, 75] Generated Node #0,1,2: 11:[83, 75] Operation: 85-10=75 Exploring Operation: 85-83=2, Resulting Numbers: [10, 2] Generated Node #0,1,3: 11:[10, 2] Operation: 85-83=2 Exploring Operation: 10+85=95, Resulting Numbers: [83, 95] Generated Node #0,1,4: 11:[83, 95] Operation: 10+85=95 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 11:[10, 2], Operations: ['92-7=85', '85-83=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,11 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,11 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 11:[85, 73], Operations: ['92-7=85', '83-10=73'] Exploring Operation: 85*73=6205, Resulting Numbers: [6205] 6205,11 unequal: No Solution Exploring Operation: 85+73=158, Resulting Numbers: [158] 158,11 unequal: No Solution Exploring Operation: 85-73=12, Resulting Numbers: [12] 12,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 11:[83, 75], Operations: ['92-7=85', '85-10=75'] Exploring Operation: 83*75=6225, Resulting Numbers: [6225] 6225,11 unequal: No Solution Exploring Operation: 83+75=158, Resulting Numbers: [158] 158,11 unequal: No Solution Exploring Operation: 83-75=8, Resulting Numbers: [8] 8,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 11:[85, 93], Operations: ['92-7=85', '10+83=93'] Exploring Operation: 85*93=7905, Resulting Numbers: [7905] 7905,11 unequal: No Solution Exploring Operation: 85+93=178, Resulting Numbers: [178] 178,11 unequal: No Solution Exploring Operation: 93-85=8, Resulting Numbers: [8] 8,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 11:[83, 95], Operations: ['92-7=85', '10+85=95'] Exploring Operation: 83*95=7885, Resulting Numbers: [7885] 7885,11 unequal: No Solution Exploring Operation: 95-83=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 83+95=178, Resulting Numbers: [178] 178,11 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:[92, 7, 73], Operations: ['83-10=73'] Exploring Operation: 73-7=66, Resulting Numbers: [92, 66] Generated Node #0,3,0: 11:[92, 66] Operation: 73-7=66 Exploring Operation: 92-7=85, Resulting Numbers: [73, 85] Generated Node #0,3,1: 11:[73, 85] Operation: 92-7=85 Exploring Operation: 92-73=19, Resulting Numbers: [7, 19] Generated Node #0,3,2: 11:[7, 19] Operation: 92-73=19 Exploring Operation: 92+7=99, Resulting Numbers: [73, 99] Generated Node #0,3,3: 11:[73, 99] Operation: 92+7=99 Exploring Operation: 7+73=80, Resulting Numbers: [92, 80] Generated Node #0,3,4: 11:[92, 80] Operation: 7+73=80 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 11:[7, 19], Operations: ['83-10=73', '92-73=19'] Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 7*19=133, Resulting Numbers: [133] 133,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 11:[92, 66], Operations: ['83-10=73', '73-7=66'] Exploring Operation: 92-66=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 92*66=6072, Resulting Numbers: [6072] 6072,11 unequal: No Solution Exploring Operation: 92+66=158, Resulting Numbers: [158] 158,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 11:[73, 85], Operations: ['83-10=73', '92-7=85'] Exploring Operation: 73+85=158, Resulting Numbers: [158] 158,11 unequal: No Solution Exploring Operation: 85-73=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 73*85=6205, Resulting Numbers: [6205] 6205,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 11:[73, 99], Operations: ['83-10=73', '92+7=99'] Exploring Operation: 73+99=172, Resulting Numbers: [172] 172,11 unequal: No Solution Exploring Operation: 73*99=7227, Resulting Numbers: [7227] 7227,11 unequal: No Solution Exploring Operation: 99-73=26, Resulting Numbers: [26] 26,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 11:[92, 80], Operations: ['83-10=73', '7+73=80'] Exploring Operation: 92+80=172, Resulting Numbers: [172] 172,11 unequal: No Solution Exploring Operation: 92*80=7360, Resulting Numbers: [7360] 7360,11 unequal: No Solution Exploring Operation: 92-80=12, Resulting Numbers: [12] 12,11 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
[ 77, 24, 10, 7 ]
69
[ "10-7=3", "24/3=8", "77-8=69" ]
Current State: 69:[77, 24, 10, 7], Operations: [] Exploring Operation: 10-7=3, Resulting Numbers: [77, 24, 3] Generated Node #2: [77, 24, 3] from Operation: 10-7=3 Current State: 69:[77, 24, 3], Operations: ['10-7=3'] Exploring Operation: 24/3=8, Resulting Numbers: [77, 8] Generated Node #3: [77, 8] from Operation: 24/3=8 Current State: 69:[77, 8], Operations: ['10-7=3', '24/3=8'] Exploring Operation: 77-8=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[77, 24, 10, 7], Operations: [] Exploring Operation: 77-10=67, Resulting Numbers: [24, 7, 67] Generated Node #0,0: 69:[24, 7, 67] Operation: 77-10=67 Exploring Operation: 10-7=3, Resulting Numbers: [77, 24, 3] Generated Node #0,1: 69:[77, 24, 3] Operation: 10-7=3 Exploring Operation: 10*7=70, Resulting Numbers: [77, 24, 70] Generated Node #0,2: 69:[77, 24, 70] Operation: 10*7=70 Exploring Operation: 77-7=70, Resulting Numbers: [24, 10, 70] Generated Node #0,3: 69:[24, 10, 70] Operation: 77-7=70 Moving to Node #0,0 Current State: 69:[24, 7, 67], Operations: ['77-10=67'] Exploring Operation: 24-7=17, Resulting Numbers: [67, 17] Generated Node #0,0,0: 69:[67, 17] Operation: 24-7=17 Exploring Operation: 24+7=31, Resulting Numbers: [67, 31] Generated Node #0,0,1: 69:[67, 31] Operation: 24+7=31 Exploring Operation: 7+67=74, Resulting Numbers: [24, 74] Generated Node #0,0,2: 69:[24, 74] Operation: 7+67=74 Exploring Operation: 67-7=60, Resulting Numbers: [24, 60] Generated Node #0,0,3: 69:[24, 60] Operation: 67-7=60 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[24, 74], Operations: ['77-10=67', '7+67=74'] Exploring Operation: 24+74=98, Resulting Numbers: [98] 98,69 unequal: No Solution Exploring Operation: 24*74=1776, Resulting Numbers: [1776] 1776,69 unequal: No Solution Exploring Operation: 74-24=50, Resulting Numbers: [50] 50,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[67, 17], Operations: ['77-10=67', '24-7=17'] Exploring Operation: 67*17=1139, Resulting Numbers: [1139] 1139,69 unequal: No Solution Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 67+17=84, Resulting Numbers: [84] 84,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[67, 31], Operations: ['77-10=67', '24+7=31'] Exploring Operation: 67+31=98, Resulting Numbers: [98] 98,69 unequal: No Solution Exploring Operation: 67*31=2077, Resulting Numbers: [2077] 2077,69 unequal: No Solution Exploring Operation: 67-31=36, Resulting Numbers: [36] 36,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 69:[24, 60], Operations: ['77-10=67', '67-7=60'] Exploring Operation: 24*60=1440, Resulting Numbers: [1440] 1440,69 unequal: No Solution Exploring Operation: 60-24=36, Resulting Numbers: [36] 36,69 unequal: No Solution Exploring Operation: 24+60=84, Resulting Numbers: [84] 84,69 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: 69:[24, 10, 70], Operations: ['77-7=70'] Exploring Operation: 24-10=14, Resulting Numbers: [70, 14] Generated Node #0,3,0: 69:[70, 14] Operation: 24-10=14 Exploring Operation: 70-10=60, Resulting Numbers: [24, 60] Generated Node #0,3,1: 69:[24, 60] Operation: 70-10=60 Exploring Operation: 24+10=34, Resulting Numbers: [70, 34] Generated Node #0,3,2: 69:[70, 34] Operation: 24+10=34 Exploring Operation: 70/10=7, Resulting Numbers: [24, 7] Generated Node #0,3,3: 69:[24, 7] Operation: 70/10=7 Moving to Node #0,1 Current State: 69:[77, 24, 3], Operations: ['10-7=3'] Exploring Operation: 24*3=72, Resulting Numbers: [77, 72] Generated Node #0,1,0: 69:[77, 72] Operation: 24*3=72 Exploring Operation: 77-3=74, Resulting Numbers: [24, 74] Generated Node #0,1,1: 69:[24, 74] Operation: 77-3=74 Exploring Operation: 24-3=21, Resulting Numbers: [77, 21] Generated Node #0,1,2: 69:[77, 21] Operation: 24-3=21 Exploring Operation: 77+3=80, Resulting Numbers: [24, 80] Generated Node #0,1,3: 69:[24, 80] Operation: 77+3=80 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[24, 74], Operations: ['10-7=3', '77-3=74'] Exploring Operation: 74-24=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 24+74=98, Resulting Numbers: [98] 98,69 unequal: No Solution Exploring Operation: 24*74=1776, Resulting Numbers: [1776] 1776,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[77, 21], Operations: ['10-7=3', '24-3=21'] Exploring Operation: 77-21=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 77*21=1617, Resulting Numbers: [1617] 1617,69 unequal: No Solution Exploring Operation: 77+21=98, Resulting Numbers: [98] 98,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[77, 72], Operations: ['10-7=3', '24*3=72'] Exploring Operation: 77-72=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 77*72=5544, Resulting Numbers: [5544] 5544,69 unequal: No Solution Exploring Operation: 77+72=149, Resulting Numbers: [149] 149,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 69:[24, 80], Operations: ['10-7=3', '77+3=80'] Exploring Operation: 24*80=1920, Resulting Numbers: [1920] 1920,69 unequal: No Solution Exploring Operation: 24+80=104, Resulting Numbers: [104] 104,69 unequal: No Solution Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,69 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: 69:[77, 24, 70], Operations: ['10*7=70'] Exploring Operation: 77+24=101, Resulting Numbers: [70, 101] Generated Node #0,2,0: 69:[70, 101] Operation: 77+24=101 Exploring Operation: 77-70=7, Resulting Numbers: [24, 7] Generated Node #0,2,1: 69:[24, 7] Operation: 77-70=7 Exploring Operation: 70-24=46, Resulting Numbers: [77, 46] Generated Node #0,2,2: 69:[77, 46] Operation: 70-24=46 Exploring Operation: 77-24=53, Resulting Numbers: [70, 53] Generated Node #0,2,3: 69:[70, 53] Operation: 77-24=53 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 69:[24, 7], Operations: ['10*7=70', '77-70=7'] Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,69 unequal: No Solution Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 24*7=168, Resulting Numbers: [168] 168,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 69:[70, 53], Operations: ['10*7=70', '77-24=53'] Exploring Operation: 70*53=3710, Resulting Numbers: [3710] 3710,69 unequal: No Solution Exploring Operation: 70-53=17, Resulting Numbers: [17] 17,69 unequal: No Solution Exploring Operation: 70+53=123, Resulting Numbers: [123] 123,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 69:[77, 46], Operations: ['10*7=70', '70-24=46'] Exploring Operation: 77-46=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 77+46=123, Resulting Numbers: [123] 123,69 unequal: No Solution Exploring Operation: 77*46=3542, Resulting Numbers: [3542] 3542,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 69:[70, 101], Operations: ['10*7=70', '77+24=101'] Exploring Operation: 101-70=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 70+101=171, Resulting Numbers: [171] 171,69 unequal: No Solution Exploring Operation: 70*101=7070, Resulting Numbers: [7070] 7070,69 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: 69:[24, 7], Operations: ['77-7=70', '70/10=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,69 unequal: No Solution Exploring Operation: 24*7=168, Resulting Numbers: [168] 168,69 unequal: No Solution Moving to Node #0,3,1 Current State: 69:[24, 60], Operations: ['77-7=70', '70-10=60'] Exploring Operation: 24+60=84, Resulting Numbers: [84] 84,69 unequal: No Solution Exploring Operation: 60-24=36, Resulting Numbers: [36] 36,69 unequal: No Solution Exploring Operation: 24*60=1440, Resulting Numbers: [1440] 1440,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[70, 14], Operations: ['77-7=70', '24-10=14'] Exploring Operation: 70-14=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 70/14=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 70*14=980, Resulting Numbers: [980] 980,69 unequal: No Solution Exploring Operation: 70+14=84, Resulting Numbers: [84] 84,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[70, 34], Operations: ['77-7=70', '24+10=34'] Exploring Operation: 70*34=2380, Resulting Numbers: [2380] 2380,69 unequal: No Solution Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,69 unequal: No Solution Exploring Operation: 70+34=104, Resulting Numbers: [104] 104,69 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 4, 18, 81, 85 ]
76
[ "4*18=72", "85-81=4", "72+4=76" ]
Current State: 76:[4, 18, 81, 85], Operations: [] Exploring Operation: 4*18=72, Resulting Numbers: [81, 85, 72] Generated Node #2: [81, 85, 72] from Operation: 4*18=72 Current State: 76:[81, 85, 72], Operations: ['4*18=72'] Exploring Operation: 85-81=4, Resulting Numbers: [72, 4] Generated Node #3: [72, 4] from Operation: 85-81=4 Current State: 76:[72, 4], Operations: ['4*18=72', '85-81=4'] Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[4, 18, 81, 85], Operations: [] Exploring Operation: 85-81=4, Resulting Numbers: [4, 18, 4] Generated Node #0,0: 76:[4, 18, 4] Operation: 85-81=4 Moving to Node #0,0 Current State: 76:[4, 18, 4], Operations: ['85-81=4'] Exploring Operation: 4/4=1, Resulting Numbers: [18, 1] Generated Node #0,0,0: 76:[18, 1] Operation: 4/4=1 Moving to Node #0,0,0 Current State: 76:[18, 1], Operations: ['85-81=4', '4/4=1'] Exploring Operation: 18+1=19, Resulting Numbers: [19] 19,76 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 33, 18, 31, 97 ]
51
[ "33-18=15", "97-31=66", "66-15=51" ]
Current State: 51:[33, 18, 31, 97], Operations: [] Exploring Operation: 33-18=15, Resulting Numbers: [31, 97, 15] Generated Node #2: [31, 97, 15] from Operation: 33-18=15 Current State: 51:[31, 97, 15], Operations: ['33-18=15'] Exploring Operation: 97-31=66, Resulting Numbers: [15, 66] Generated Node #3: [15, 66] from Operation: 97-31=66 Current State: 51:[15, 66], Operations: ['33-18=15', '97-31=66'] Exploring Operation: 66-15=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[33, 18, 31, 97], Operations: [] Exploring Operation: 97-33=64, Resulting Numbers: [18, 31, 64] Generated Node #0,0: 51:[18, 31, 64] Operation: 97-33=64 Exploring Operation: 97-31=66, Resulting Numbers: [33, 18, 66] Generated Node #0,1: 51:[33, 18, 66] Operation: 97-31=66 Moving to Node #0,0 Current State: 51:[18, 31, 64], Operations: ['97-33=64'] Exploring Operation: 31-18=13, Resulting Numbers: [64, 13] Generated Node #0,0,0: 51:[64, 13] Operation: 31-18=13 Exploring Operation: 18+31=49, Resulting Numbers: [64, 49] Generated Node #0,0,1: 51:[64, 49] Operation: 18+31=49 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 51:[64, 49], Operations: ['97-33=64', '18+31=49'] Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 64+49=113, Resulting Numbers: [113] 113,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[64, 13], Operations: ['97-33=64', '31-18=13'] Exploring Operation: 64+13=77, Resulting Numbers: [77] 77,51 unequal: No Solution Exploring Operation: 64-13=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[33, 18, 31, 97], Operations: [] Exploring Operation: 97-33=64, Resulting Numbers: [18, 31, 64] Generated Node #0,0: 51:[18, 31, 64] Operation: 97-33=64 Moving to Node #0,0 Current State: 51:[18, 31, 64], Operations: ['97-33=64'] Exploring Operation: 31-18=13, Resulting Numbers: [64, 13] Generated Node #0,0,0: 51:[64, 13] Operation: 31-18=13 Moving to Node #0,0,0 Current State: 51:[64, 13], Operations: ['97-33=64', '31-18=13'] Exploring Operation: 64-13=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 14, 50, 75, 9 ]
99
[ "14+50=64", "75-64=11", "9*11=99" ]
Current State: 99:[14, 50, 75, 9], Operations: [] Exploring Operation: 14+50=64, Resulting Numbers: [75, 9, 64] Generated Node #2: [75, 9, 64] from Operation: 14+50=64 Current State: 99:[75, 9, 64], Operations: ['14+50=64'] Exploring Operation: 75-64=11, Resulting Numbers: [9, 11] Generated Node #3: [9, 11] from Operation: 75-64=11 Current State: 99:[9, 11], Operations: ['14+50=64', '75-64=11'] Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[14, 50, 75, 9], Operations: [] Exploring Operation: 50-14=36, Resulting Numbers: [75, 9, 36] Generated Node #0,0: 99:[75, 9, 36] Operation: 50-14=36 Exploring Operation: 75-50=25, Resulting Numbers: [14, 9, 25] Generated Node #0,1: 99:[14, 9, 25] Operation: 75-50=25 Moving to Node #0,1 Current State: 99:[14, 9, 25], Operations: ['75-50=25'] Exploring Operation: 9+25=34, Resulting Numbers: [14, 34] Generated Node #0,1,0: 99:[14, 34] Operation: 9+25=34 Exploring Operation: 25-14=11, Resulting Numbers: [9, 11] Generated Node #0,1,1: 99:[9, 11] Operation: 25-14=11 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[9, 11], Operations: ['75-50=25', '25-14=11'] Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[14, 50, 75, 9], Operations: [] Exploring Operation: 75-50=25, Resulting Numbers: [14, 9, 25] Generated Node #0,1: 99:[14, 9, 25] Operation: 75-50=25 Moving to Node #0,1 Current State: 99:[14, 9, 25], Operations: ['75-50=25'] Exploring Operation: 25-14=11, Resulting Numbers: [9, 11] Generated Node #0,1,1: 99:[9, 11] Operation: 25-14=11 Moving to Node #0,1,1 Current State: 99:[9, 11], Operations: ['75-50=25', '25-14=11'] Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 9, 66, 93, 11 ]
62
[ "9*11=99", "66*93=6138", "6138/99=62" ]
Current State: 62:[9, 66, 93, 11], Operations: [] Exploring Operation: 9*11=99, Resulting Numbers: [66, 93, 99] Generated Node #2: [66, 93, 99] from Operation: 9*11=99 Current State: 62:[66, 93, 99], Operations: ['9*11=99'] Exploring Operation: 66*93=6138, Resulting Numbers: [99, 6138] Generated Node #3: [99, 6138] from Operation: 66*93=6138 Current State: 62:[99, 6138], Operations: ['9*11=99', '66*93=6138'] Exploring Operation: 6138/99=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[9, 66, 93, 11], Operations: [] Exploring Operation: 93-66=27, Resulting Numbers: [9, 11, 27] Generated Node #0,0: 62:[9, 11, 27] Operation: 93-66=27 Exploring Operation: 11-9=2, Resulting Numbers: [66, 93, 2] Generated Node #0,1: 62:[66, 93, 2] Operation: 11-9=2 Exploring Operation: 66/11=6, Resulting Numbers: [9, 93, 6] Generated Node #0,2: 62:[9, 93, 6] Operation: 66/11=6 Exploring Operation: 93-11=82, Resulting Numbers: [9, 66, 82] Generated Node #0,3: 62:[9, 66, 82] Operation: 93-11=82 Exploring Operation: 93-9=84, Resulting Numbers: [66, 11, 84] Generated Node #0,4: 62:[66, 11, 84] Operation: 93-9=84 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[9, 11, 27], Operations: ['93-66=27'] Exploring Operation: 9+27=36, Resulting Numbers: [11, 36] Generated Node #0,0,0: 62:[11, 36] Operation: 9+27=36 Exploring Operation: 11-9=2, Resulting Numbers: [27, 2] Generated Node #0,0,1: 62:[27, 2] Operation: 11-9=2 Exploring Operation: 11+27=38, Resulting Numbers: [9, 38] Generated Node #0,0,2: 62:[9, 38] Operation: 11+27=38 Exploring Operation: 9+11=20, Resulting Numbers: [27, 20] Generated Node #0,0,3: 62:[27, 20] Operation: 9+11=20 Exploring Operation: 27/9=3, Resulting Numbers: [11, 3] Generated Node #0,0,4: 62:[11, 3] Operation: 27/9=3 Moving to Node #0,0,1 Current State: 62:[27, 2], Operations: ['93-66=27', '11-9=2'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 27+2=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,62 unequal: No Solution Moving to Node #0,0,4 Current State: 62:[11, 3], Operations: ['93-66=27', '27/9=3'] Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,62 unequal: No Solution Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,62 unequal: No Solution Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,62 unequal: No Solution Moving to Node #0,0,0 Current State: 62:[11, 36], Operations: ['93-66=27', '9+27=36'] Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 11*36=396, Resulting Numbers: [396] 396,62 unequal: No Solution Exploring Operation: 11+36=47, Resulting Numbers: [47] 47,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[9, 38], Operations: ['93-66=27', '11+27=38'] Exploring Operation: 9+38=47, Resulting Numbers: [47] 47,62 unequal: No Solution Exploring Operation: 9*38=342, Resulting Numbers: [342] 342,62 unequal: No Solution Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,62 unequal: No Solution Moving to Node #0,0,3 Current State: 62:[27, 20], Operations: ['93-66=27', '9+11=20'] Exploring Operation: 27+20=47, Resulting Numbers: [47] 47,62 unequal: No Solution Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,62 unequal: No Solution Exploring Operation: 27*20=540, Resulting Numbers: [540] 540,62 unequal: No Solution No 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: 62:[9, 66, 82], Operations: ['93-11=82'] Exploring Operation: 66-9=57, Resulting Numbers: [82, 57] Generated Node #0,3,0: 62:[82, 57] Operation: 66-9=57 Exploring Operation: 82-9=73, Resulting Numbers: [66, 73] Generated Node #0,3,1: 62:[66, 73] Operation: 82-9=73 Exploring Operation: 9+82=91, Resulting Numbers: [66, 91] Generated Node #0,3,2: 62:[66, 91] Operation: 9+82=91 Exploring Operation: 82-66=16, Resulting Numbers: [9, 16] Generated Node #0,3,3: 62:[9, 16] Operation: 82-66=16 Exploring Operation: 9+66=75, Resulting Numbers: [82, 75] Generated Node #0,3,4: 62:[82, 75] Operation: 9+66=75 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 62:[66, 73], Operations: ['93-11=82', '82-9=73'] Exploring Operation: 73-66=7, Resulting Numbers: [7] 7,62 unequal: No Solution Exploring Operation: 66+73=139, Resulting Numbers: [139] 139,62 unequal: No Solution Exploring Operation: 66*73=4818, Resulting Numbers: [4818] 4818,62 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 #0,3,3 Current State: 62:[9, 16], Operations: ['93-11=82', '82-66=16'] Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,62 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,62 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,62 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 #0,3,0 Current State: 62:[82, 57], Operations: ['93-11=82', '66-9=57'] Exploring Operation: 82*57=4674, Resulting Numbers: [4674] 4674,62 unequal: No Solution Exploring Operation: 82-57=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 82+57=139, Resulting Numbers: [139] 139,62 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 #0,3,2 Current State: 62:[66, 91], Operations: ['93-11=82', '9+82=91'] Exploring Operation: 66+91=157, Resulting Numbers: [157] 157,62 unequal: No Solution Exploring Operation: 66*91=6006, Resulting Numbers: [6006] 6006,62 unequal: No Solution Exploring Operation: 91-66=25, Resulting Numbers: [25] 25,62 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 #0,3,4 Current State: 62:[82, 75], Operations: ['93-11=82', '9+66=75'] Exploring Operation: 82-75=7, Resulting Numbers: [7] 7,62 unequal: No Solution Exploring Operation: 82+75=157, Resulting Numbers: [157] 157,62 unequal: No Solution Exploring Operation: 82*75=6150, Resulting Numbers: [6150] 6150,62 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:[66, 93, 2], Operations: ['11-9=2'] Exploring Operation: 66/2=33, Resulting Numbers: [93, 33] Generated Node #0,1,0: 62:[93, 33] Operation: 66/2=33 Exploring Operation: 93-66=27, Resulting Numbers: [2, 27] Generated Node #0,1,1: 62:[2, 27] Operation: 93-66=27 Exploring Operation: 93-2=91, Resulting Numbers: [66, 91] Generated Node #0,1,2: 62:[66, 91] Operation: 93-2=91 Exploring Operation: 66-2=64, Resulting Numbers: [93, 64] Generated Node #0,1,3: 62:[93, 64] Operation: 66-2=64 Exploring Operation: 66+2=68, Resulting Numbers: [93, 68] Generated Node #0,1,4: 62:[93, 68] Operation: 66+2=68 Moving to Node #0,1,1 Current State: 62:[2, 27], Operations: ['11-9=2', '93-66=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,62 unequal: No Solution Moving to Node #0,1,2 Current State: 62:[66, 91], Operations: ['11-9=2', '93-2=91'] Exploring Operation: 91-66=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 66*91=6006, Resulting Numbers: [6006] 6006,62 unequal: No Solution Exploring Operation: 66+91=157, Resulting Numbers: [157] 157,62 unequal: No Solution Moving to Node #0,1,0 Current State: 62:[93, 33], Operations: ['11-9=2', '66/2=33'] Exploring Operation: 93*33=3069, Resulting Numbers: [3069] 3069,62 unequal: No Solution Exploring Operation: 93-33=60, Resulting Numbers: [60] 60,62 unequal: No Solution Exploring Operation: 93+33=126, Resulting Numbers: [126] 126,62 unequal: No Solution Moving to Node #0,1,3 Current State: 62:[93, 64], Operations: ['11-9=2', '66-2=64'] Exploring Operation: 93-64=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 93*64=5952, Resulting Numbers: [5952] 5952,62 unequal: No Solution Exploring Operation: 93+64=157, Resulting Numbers: [157] 157,62 unequal: No Solution Moving to Node #0,1,4 Current State: 62:[93, 68], Operations: ['11-9=2', '66+2=68'] Exploring Operation: 93-68=25, Resulting Numbers: [25] 25,62 unequal: No Solution Exploring Operation: 93+68=161, Resulting Numbers: [161] 161,62 unequal: No Solution Exploring Operation: 93*68=6324, Resulting Numbers: [6324] 6324,62 unequal: No Solution No 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: 62:[66, 11, 84], Operations: ['93-9=84'] Exploring Operation: 66+11=77, Resulting Numbers: [84, 77] Generated Node #0,4,0: 62:[84, 77] Operation: 66+11=77 Exploring Operation: 84-11=73, Resulting Numbers: [66, 73] Generated Node #0,4,1: 62:[66, 73] Operation: 84-11=73 Exploring Operation: 84-66=18, Resulting Numbers: [11, 18] Generated Node #0,4,2: 62:[11, 18] Operation: 84-66=18 Exploring Operation: 66-11=55, Resulting Numbers: [84, 55] Generated Node #0,4,3: 62:[84, 55] Operation: 66-11=55 Exploring Operation: 66/11=6, Resulting Numbers: [84, 6] Generated Node #0,4,4: 62:[84, 6] Operation: 66/11=6 Moving to Node #0,4,1 Current State: 62:[66, 73], Operations: ['93-9=84', '84-11=73'] Exploring Operation: 66*73=4818, Resulting Numbers: [4818] 4818,62 unequal: No Solution Exploring Operation: 66+73=139, Resulting Numbers: [139] 139,62 unequal: No Solution Exploring Operation: 73-66=7, Resulting Numbers: [7] 7,62 unequal: No Solution Moving to Node #0,4,2 Current State: 62:[11, 18], Operations: ['93-9=84', '84-66=18'] Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,62 unequal: No Solution Exploring Operation: 11+18=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 11*18=198, Resulting Numbers: [198] 198,62 unequal: No Solution Moving to Node #0,4,4 Current State: 62:[84, 6], Operations: ['93-9=84', '66/11=6'] Exploring Operation: 84-6=78, Resulting Numbers: [78] 78,62 unequal: No Solution Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 84+6=90, Resulting Numbers: [90] 90,62 unequal: No Solution Exploring Operation: 84*6=504, Resulting Numbers: [504] 504,62 unequal: No Solution Moving to Node #0,4,3 Current State: 62:[84, 55], Operations: ['93-9=84', '66-11=55'] Exploring Operation: 84-55=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 84*55=4620, Resulting Numbers: [4620] 4620,62 unequal: No Solution Exploring Operation: 84+55=139, Resulting Numbers: [139] 139,62 unequal: No Solution Moving to Node #0,4,0 Current State: 62:[84, 77], Operations: ['93-9=84', '66+11=77'] Exploring Operation: 84*77=6468, Resulting Numbers: [6468] 6468,62 unequal: No Solution Exploring Operation: 84-77=7, Resulting Numbers: [7] 7,62 unequal: No Solution Exploring Operation: 84+77=161, Resulting Numbers: [161] 161,62 unequal: No Solution No 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: 62:[9, 93, 6], Operations: ['66/11=6'] Exploring Operation: 9*6=54, Resulting Numbers: [93, 54] Generated Node #0,2,0: 62:[93, 54] Operation: 9*6=54 Exploring Operation: 93-9=84, Resulting Numbers: [6, 84] Generated Node #0,2,1: 62:[6, 84] Operation: 93-9=84 Exploring Operation: 9+93=102, Resulting Numbers: [6, 102] Generated Node #0,2,2: 62:[6, 102] Operation: 9+93=102 Exploring Operation: 93-6=87, Resulting Numbers: [9, 87] Generated Node #0,2,3: 62:[9, 87] Operation: 93-6=87 Exploring Operation: 9-6=3, Resulting Numbers: [93, 3] Generated Node #0,2,4: 62:[93, 3] Operation: 9-6=3 Moving to Node #0,2,1 Current State: 62:[6, 84], Operations: ['66/11=6', '93-9=84'] Exploring Operation: 84-6=78, Resulting Numbers: [78] 78,62 unequal: No Solution Exploring Operation: 6+84=90, Resulting Numbers: [90] 90,62 unequal: No Solution Exploring Operation: 6*84=504, Resulting Numbers: [504] 504,62 unequal: No Solution Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,62 unequal: No Solution Moving to Node #0,2,4 Current State: 62:[93, 3], Operations: ['66/11=6', '9-6=3'] Exploring Operation: 93*3=279, Resulting Numbers: [279] 279,62 unequal: No Solution Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,62 unequal: No Solution Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,62 unequal: No Solution Moving to Node #0,2,3 Current State: 62:[9, 87], Operations: ['66/11=6', '93-6=87'] Exploring Operation: 87-9=78, Resulting Numbers: [78] 78,62 unequal: No Solution Exploring Operation: 9*87=783, Resulting Numbers: [783] 783,62 unequal: No Solution Exploring Operation: 9+87=96, Resulting Numbers: [96] 96,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[93, 54], Operations: ['66/11=6', '9*6=54'] Exploring Operation: 93*54=5022, Resulting Numbers: [5022] 5022,62 unequal: No Solution Exploring Operation: 93+54=147, Resulting Numbers: [147] 147,62 unequal: No Solution Exploring Operation: 93-54=39, Resulting Numbers: [39] 39,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[6, 102], Operations: ['66/11=6', '9+93=102'] Exploring Operation: 102/6=17, Resulting Numbers: [17] 17,62 unequal: No Solution Exploring Operation: 6+102=108, Resulting Numbers: [108] 108,62 unequal: No Solution Exploring Operation: 102-6=96, Resulting Numbers: [96] 96,62 unequal: No Solution Exploring Operation: 6*102=612, Resulting Numbers: [612] 612,62 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
[ 56, 29, 93, 42 ]
78
[ "56-29=27", "93-42=51", "27+51=78" ]
Current State: 78:[56, 29, 93, 42], Operations: [] Exploring Operation: 56-29=27, Resulting Numbers: [93, 42, 27] Generated Node #2: [93, 42, 27] from Operation: 56-29=27 Current State: 78:[93, 42, 27], Operations: ['56-29=27'] Exploring Operation: 93-42=51, Resulting Numbers: [27, 51] Generated Node #3: [27, 51] from Operation: 93-42=51 Current State: 78:[27, 51], Operations: ['56-29=27', '93-42=51'] Exploring Operation: 27+51=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[56, 29, 93, 42], Operations: [] Exploring Operation: 56-42=14, Resulting Numbers: [29, 93, 14] Generated Node #0,0: 78:[29, 93, 14] Operation: 56-42=14 Exploring Operation: 56-29=27, Resulting Numbers: [93, 42, 27] Generated Node #0,1: 78:[93, 42, 27] Operation: 56-29=27 Exploring Operation: 93-56=37, Resulting Numbers: [29, 42, 37] Generated Node #0,2: 78:[29, 42, 37] Operation: 93-56=37 Moving to Node #0,2 Current State: 78:[29, 42, 37], Operations: ['93-56=37'] Exploring Operation: 42-37=5, Resulting Numbers: [29, 5] Generated Node #0,2,0: 78:[29, 5] Operation: 42-37=5 Exploring Operation: 42-29=13, Resulting Numbers: [37, 13] Generated Node #0,2,1: 78:[37, 13] Operation: 42-29=13 Exploring Operation: 42+37=79, Resulting Numbers: [29, 79] Generated Node #0,2,2: 78:[29, 79] Operation: 42+37=79 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 78:[37, 13], Operations: ['93-56=37', '42-29=13'] Exploring Operation: 37+13=50, Resulting Numbers: [50] 50,78 unequal: No Solution Exploring Operation: 37-13=24, Resulting Numbers: [24] 24,78 unequal: No Solution Exploring Operation: 37*13=481, Resulting Numbers: [481] 481,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 78:[29, 5], Operations: ['93-56=37', '42-37=5'] Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,78 unequal: No Solution Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 78:[29, 79], Operations: ['93-56=37', '42+37=79'] Exploring Operation: 29+79=108, Resulting Numbers: [108] 108,78 unequal: No Solution Exploring Operation: 79-29=50, Resulting Numbers: [50] 50,78 unequal: No Solution Exploring Operation: 29*79=2291, Resulting Numbers: [2291] 2291,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 78:[29, 93, 14], Operations: ['56-42=14'] Exploring Operation: 29-14=15, Resulting Numbers: [93, 15] Generated Node #0,0,0: 78:[93, 15] Operation: 29-14=15 Exploring Operation: 93-14=79, Resulting Numbers: [29, 79] Generated Node #0,0,1: 78:[29, 79] Operation: 93-14=79 Exploring Operation: 93-29=64, Resulting Numbers: [14, 64] Generated Node #0,0,2: 78:[14, 64] Operation: 93-29=64 Moving to Node #0,1 Current State: 78:[93, 42, 27], Operations: ['56-29=27'] Exploring Operation: 93-27=66, Resulting Numbers: [42, 66] Generated Node #0,1,0: 78:[42, 66] Operation: 93-27=66 Exploring Operation: 93-42=51, Resulting Numbers: [27, 51] Generated Node #0,1,1: 78:[27, 51] Operation: 93-42=51 Exploring Operation: 42-27=15, Resulting Numbers: [93, 15] Generated Node #0,1,2: 78:[93, 15] Operation: 42-27=15 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[27, 51], Operations: ['56-29=27', '93-42=51'] Exploring Operation: 27*51=1377, Resulting Numbers: [1377] 1377,78 unequal: No Solution Exploring Operation: 27+51=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[56, 29, 93, 42], Operations: [] Exploring Operation: 56-29=27, Resulting Numbers: [93, 42, 27] Generated Node #0,1: 78:[93, 42, 27] Operation: 56-29=27 Moving to Node #0,1 Current State: 78:[93, 42, 27], Operations: ['56-29=27'] Exploring Operation: 93-42=51, Resulting Numbers: [27, 51] Generated Node #0,1,1: 78:[27, 51] Operation: 93-42=51 Moving to Node #0,1,1 Current State: 78:[27, 51], Operations: ['56-29=27', '93-42=51'] Exploring Operation: 27+51=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_3
mult_heuristic
[ 47, 24, 82, 88 ]
99
[ "47+24=71", "82+88=170", "170-71=99" ]
Current State: 99:[47, 24, 82, 88], Operations: [] Exploring Operation: 47+24=71, Resulting Numbers: [82, 88, 71] Generated Node #2: [82, 88, 71] from Operation: 47+24=71 Current State: 99:[82, 88, 71], Operations: ['47+24=71'] Exploring Operation: 82+88=170, Resulting Numbers: [71, 170] Generated Node #3: [71, 170] from Operation: 82+88=170 Current State: 99:[71, 170], Operations: ['47+24=71', '82+88=170'] Exploring Operation: 170-71=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[47, 24, 82, 88], Operations: [] Exploring Operation: 82-47=35, Resulting Numbers: [24, 88, 35] Generated Node #0,0: 99:[24, 88, 35] Operation: 82-47=35 Exploring Operation: 88-82=6, Resulting Numbers: [47, 24, 6] Generated Node #0,1: 99:[47, 24, 6] Operation: 88-82=6 Moving to Node #0,0 Current State: 99:[24, 88, 35], Operations: ['82-47=35'] Exploring Operation: 35-24=11, Resulting Numbers: [88, 11] Generated Node #0,0,0: 99:[88, 11] Operation: 35-24=11 Exploring Operation: 24+88=112, Resulting Numbers: [35, 112] Generated Node #0,0,1: 99:[35, 112] Operation: 24+88=112 Moving to Node #0,1 Current State: 99:[47, 24, 6], Operations: ['88-82=6'] Exploring Operation: 47-24=23, Resulting Numbers: [6, 23] Generated Node #0,1,0: 99:[6, 23] Operation: 47-24=23 Exploring Operation: 24/6=4, Resulting Numbers: [47, 4] Generated Node #0,1,1: 99:[47, 4] Operation: 24/6=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[6, 23], Operations: ['88-82=6', '47-24=23'] Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,99 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 #0,1,1 Current State: 99:[47, 4], Operations: ['88-82=6', '24/6=4'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,99 unequal: No Solution Exploring Operation: 47+4=51, Resulting Numbers: [51] 51,99 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: 99:[88, 11], Operations: ['82-47=35', '35-24=11'] Exploring Operation: 88+11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[47, 24, 82, 88], Operations: [] Exploring Operation: 82-47=35, Resulting Numbers: [24, 88, 35] Generated Node #0,0: 99:[24, 88, 35] Operation: 82-47=35 Moving to Node #0,0 Current State: 99:[24, 88, 35], Operations: ['82-47=35'] Exploring Operation: 35-24=11, Resulting Numbers: [88, 11] Generated Node #0,0,0: 99:[88, 11] Operation: 35-24=11 Moving to Node #0,0,0 Current State: 99:[88, 11], Operations: ['82-47=35', '35-24=11'] Exploring Operation: 88+11=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 30, 76, 6, 88 ]
15
[ "30*6=180", "88-76=12", "180/12=15" ]
Current State: 15:[30, 76, 6, 88], Operations: [] Exploring Operation: 30*6=180, Resulting Numbers: [76, 88, 180] Generated Node #2: [76, 88, 180] from Operation: 30*6=180 Current State: 15:[76, 88, 180], Operations: ['30*6=180'] Exploring Operation: 88-76=12, Resulting Numbers: [180, 12] Generated Node #3: [180, 12] from Operation: 88-76=12 Current State: 15:[180, 12], Operations: ['30*6=180', '88-76=12'] Exploring Operation: 180/12=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[30, 76, 6, 88], Operations: [] Exploring Operation: 88-76=12, Resulting Numbers: [30, 6, 12] Generated Node #0,0: 15:[30, 6, 12] Operation: 88-76=12 Exploring Operation: 76-30=46, Resulting Numbers: [6, 88, 46] Generated Node #0,1: 15:[6, 88, 46] Operation: 76-30=46 Moving to Node #0,0 Current State: 15:[30, 6, 12], Operations: ['88-76=12'] Exploring Operation: 30/6=5, Resulting Numbers: [12, 5] Generated Node #0,0,0: 15:[12, 5] Operation: 30/6=5 Exploring Operation: 30-12=18, Resulting Numbers: [6, 18] Generated Node #0,0,1: 15:[6, 18] Operation: 30-12=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[12, 5], Operations: ['88-76=12', '30/6=5'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,15 unequal: No Solution No 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: 15:[6, 18], Operations: ['88-76=12', '30-12=18'] Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,15 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,15 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: 15:[6, 88, 46], Operations: ['76-30=46'] Exploring Operation: 88-46=42, Resulting Numbers: [6, 42] Generated Node #0,1,0: 15:[6, 42] Operation: 88-46=42 Exploring Operation: 88-6=82, Resulting Numbers: [46, 82] Generated Node #0,1,1: 15:[46, 82] Operation: 88-6=82 Moving to Node #0,1,0 Current State: 15:[6, 42], Operations: ['76-30=46', '88-46=42'] Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,15 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[46, 82], Operations: ['76-30=46', '88-6=82'] Exploring Operation: 46+82=128, Resulting Numbers: [128] 128,15 unequal: No Solution Exploring Operation: 82-46=36, Resulting Numbers: [36] 36,15 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 65, 15, 39, 81 ]
56
[ "65*15=975", "975/39=25", "81-25=56" ]
Current State: 56:[65, 15, 39, 81], Operations: [] Exploring Operation: 65*15=975, Resulting Numbers: [39, 81, 975] Generated Node #2: [39, 81, 975] from Operation: 65*15=975 Current State: 56:[39, 81, 975], Operations: ['65*15=975'] Exploring Operation: 975/39=25, Resulting Numbers: [81, 25] Generated Node #3: [81, 25] from Operation: 975/39=25 Current State: 56:[81, 25], Operations: ['65*15=975', '975/39=25'] Exploring Operation: 81-25=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[65, 15, 39, 81], Operations: [] Exploring Operation: 81-15=66, Resulting Numbers: [65, 39, 66] Generated Node #0,0: 56:[65, 39, 66] Operation: 81-15=66 Exploring Operation: 65-39=26, Resulting Numbers: [15, 81, 26] Generated Node #0,1: 56:[15, 81, 26] Operation: 65-39=26 Exploring Operation: 81-65=16, Resulting Numbers: [15, 39, 16] Generated Node #0,2: 56:[15, 39, 16] Operation: 81-65=16 Exploring Operation: 81-39=42, Resulting Numbers: [65, 15, 42] Generated Node #0,3: 56:[65, 15, 42] Operation: 81-39=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[15, 39, 16], Operations: ['81-65=16'] Exploring Operation: 15+39=54, Resulting Numbers: [16, 54] Generated Node #0,2,0: 56:[16, 54] Operation: 15+39=54 Exploring Operation: 39-15=24, Resulting Numbers: [16, 24] Generated Node #0,2,1: 56:[16, 24] Operation: 39-15=24 Exploring Operation: 39+16=55, Resulting Numbers: [15, 55] Generated Node #0,2,2: 56:[15, 55] Operation: 39+16=55 Exploring Operation: 39-16=23, Resulting Numbers: [15, 23] Generated Node #0,2,3: 56:[15, 23] Operation: 39-16=23 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 56:[15, 55], Operations: ['81-65=16', '39+16=55'] Exploring Operation: 15*55=825, Resulting Numbers: [825] 825,56 unequal: No Solution Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,56 unequal: No Solution Exploring Operation: 15+55=70, Resulting Numbers: [70] 70,56 unequal: No Solution No 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: 56:[16, 54], Operations: ['81-65=16', '15+39=54'] Exploring Operation: 16*54=864, Resulting Numbers: [864] 864,56 unequal: No Solution Exploring Operation: 16+54=70, Resulting Numbers: [70] 70,56 unequal: No Solution Exploring Operation: 54-16=38, Resulting Numbers: [38] 38,56 unequal: No Solution No 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: 56:[16, 24], Operations: ['81-65=16', '39-15=24'] Exploring Operation: 16+24=40, Resulting Numbers: [40] 40,56 unequal: No Solution Exploring Operation: 24-16=8, Resulting Numbers: [8] 8,56 unequal: No Solution Exploring Operation: 16*24=384, Resulting Numbers: [384] 384,56 unequal: No Solution No 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: 56:[15, 23], Operations: ['81-65=16', '39-16=23'] Exploring Operation: 15+23=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,56 unequal: No Solution Exploring Operation: 15*23=345, Resulting Numbers: [345] 345,56 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: 56:[65, 15, 42], Operations: ['81-39=42'] Exploring Operation: 65-42=23, Resulting Numbers: [15, 23] Generated Node #0,3,0: 56:[15, 23] Operation: 65-42=23 Exploring Operation: 42-15=27, Resulting Numbers: [65, 27] Generated Node #0,3,1: 56:[65, 27] Operation: 42-15=27 Exploring Operation: 65-15=50, Resulting Numbers: [42, 50] Generated Node #0,3,2: 56:[42, 50] Operation: 65-15=50 Exploring Operation: 15+42=57, Resulting Numbers: [65, 57] Generated Node #0,3,3: 56:[65, 57] Operation: 15+42=57 Moving to Node #0,3,0 Current State: 56:[15, 23], Operations: ['81-39=42', '65-42=23'] Exploring Operation: 15+23=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,56 unequal: No Solution Exploring Operation: 15*23=345, Resulting Numbers: [345] 345,56 unequal: No Solution Moving to Node #0,3,3 Current State: 56:[65, 57], Operations: ['81-39=42', '15+42=57'] Exploring Operation: 65-57=8, Resulting Numbers: [8] 8,56 unequal: No Solution Exploring Operation: 65+57=122, Resulting Numbers: [122] 122,56 unequal: No Solution Exploring Operation: 65*57=3705, Resulting Numbers: [3705] 3705,56 unequal: No Solution Moving to Node #0,3,1 Current State: 56:[65, 27], Operations: ['81-39=42', '42-15=27'] Exploring Operation: 65*27=1755, Resulting Numbers: [1755] 1755,56 unequal: No Solution Exploring Operation: 65-27=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 65+27=92, Resulting Numbers: [92] 92,56 unequal: No Solution Moving to Node #0,3,2 Current State: 56:[42, 50], Operations: ['81-39=42', '65-15=50'] Exploring Operation: 42+50=92, Resulting Numbers: [92] 92,56 unequal: No Solution Exploring Operation: 42*50=2100, Resulting Numbers: [2100] 2100,56 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[15, 81, 26], Operations: ['65-39=26'] Exploring Operation: 81-26=55, Resulting Numbers: [15, 55] Generated Node #0,1,0: 56:[15, 55] Operation: 81-26=55 Exploring Operation: 81-15=66, Resulting Numbers: [26, 66] Generated Node #0,1,1: 56:[26, 66] Operation: 81-15=66 Exploring Operation: 15+26=41, Resulting Numbers: [81, 41] Generated Node #0,1,2: 56:[81, 41] Operation: 15+26=41 Exploring Operation: 26-15=11, Resulting Numbers: [81, 11] Generated Node #0,1,3: 56:[81, 11] Operation: 26-15=11 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 56:[15, 55], Operations: ['65-39=26', '81-26=55'] Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,56 unequal: No Solution Exploring Operation: 15+55=70, Resulting Numbers: [70] 70,56 unequal: No Solution Exploring Operation: 15*55=825, Resulting Numbers: [825] 825,56 unequal: No Solution No 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: 56:[26, 66], Operations: ['65-39=26', '81-15=66'] Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,56 unequal: No Solution Exploring Operation: 26*66=1716, Resulting Numbers: [1716] 1716,56 unequal: No Solution Exploring Operation: 26+66=92, Resulting Numbers: [92] 92,56 unequal: No Solution No 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: 56:[81, 11], Operations: ['65-39=26', '26-15=11'] Exploring Operation: 81*11=891, Resulting Numbers: [891] 891,56 unequal: No Solution Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,56 unequal: No Solution Exploring Operation: 81+11=92, Resulting Numbers: [92] 92,56 unequal: No Solution No 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: 56:[81, 41], Operations: ['65-39=26', '15+26=41'] Exploring Operation: 81+41=122, Resulting Numbers: [122] 122,56 unequal: No Solution Exploring Operation: 81*41=3321, Resulting Numbers: [3321] 3321,56 unequal: No Solution Exploring Operation: 81-41=40, Resulting Numbers: [40] 40,56 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: 56:[65, 39, 66], Operations: ['81-15=66'] Exploring Operation: 66-39=27, Resulting Numbers: [65, 27] Generated Node #0,0,0: 56:[65, 27] Operation: 66-39=27 Exploring Operation: 65-39=26, Resulting Numbers: [66, 26] Generated Node #0,0,1: 56:[66, 26] Operation: 65-39=26 Exploring Operation: 66-65=1, Resulting Numbers: [39, 1] Generated Node #0,0,2: 56:[39, 1] Operation: 66-65=1 Exploring Operation: 65+39=104, Resulting Numbers: [66, 104] Generated Node #0,0,3: 56:[66, 104] Operation: 65+39=104 Moving to Node #0,0,0 Current State: 56:[65, 27], Operations: ['81-15=66', '66-39=27'] Exploring Operation: 65-27=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 65+27=92, Resulting Numbers: [92] 92,56 unequal: No Solution Exploring Operation: 65*27=1755, Resulting Numbers: [1755] 1755,56 unequal: No Solution Moving to Node #0,0,2 Current State: 56:[39, 1], Operations: ['81-15=66', '66-65=1'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,56 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,56 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[66, 26], Operations: ['81-15=66', '65-39=26'] Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,56 unequal: No Solution Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,56 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,56 unequal: No Solution Moving to Node #0,0,3 Current State: 56:[66, 104], Operations: ['81-15=66', '65+39=104'] Exploring Operation: 104-66=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 66*104=6864, Resulting Numbers: [6864] 6864,56 unequal: No Solution Exploring Operation: 66+104=170, Resulting Numbers: [170] 170,56 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
[ 44, 64, 29, 76 ]
31
[ "76-44=32", "64/32=2", "29+2=31" ]
Current State: 31:[44, 64, 29, 76], Operations: [] Exploring Operation: 76-44=32, Resulting Numbers: [64, 29, 32] Generated Node #2: [64, 29, 32] from Operation: 76-44=32 Current State: 31:[64, 29, 32], Operations: ['76-44=32'] Exploring Operation: 64/32=2, Resulting Numbers: [29, 2] Generated Node #3: [29, 2] from Operation: 64/32=2 Current State: 31:[29, 2], Operations: ['76-44=32', '64/32=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[44, 64, 29, 76], Operations: [] Exploring Operation: 76-64=12, Resulting Numbers: [44, 29, 12] Generated Node #0,0: 31:[44, 29, 12] Operation: 76-64=12 Exploring Operation: 76-29=47, Resulting Numbers: [44, 64, 47] Generated Node #0,1: 31:[44, 64, 47] Operation: 76-29=47 Exploring Operation: 76-44=32, Resulting Numbers: [64, 29, 32] Generated Node #0,2: 31:[64, 29, 32] Operation: 76-44=32 Exploring Operation: 64-29=35, Resulting Numbers: [44, 76, 35] Generated Node #0,3: 31:[44, 76, 35] Operation: 64-29=35 Exploring Operation: 64-44=20, Resulting Numbers: [29, 76, 20] Generated Node #0,4: 31:[29, 76, 20] Operation: 64-44=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[44, 29, 12], Operations: ['76-64=12'] Exploring Operation: 44-12=32, Resulting Numbers: [29, 32] Generated Node #0,0,0: 31:[29, 32] Operation: 44-12=32 Exploring Operation: 44+12=56, Resulting Numbers: [29, 56] Generated Node #0,0,1: 31:[29, 56] Operation: 44+12=56 Exploring Operation: 29-12=17, Resulting Numbers: [44, 17] Generated Node #0,0,2: 31:[44, 17] Operation: 29-12=17 Exploring Operation: 29+12=41, Resulting Numbers: [44, 41] Generated Node #0,0,3: 31:[44, 41] Operation: 29+12=41 Exploring Operation: 44-29=15, Resulting Numbers: [12, 15] Generated Node #0,0,4: 31:[12, 15] Operation: 44-29=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[29, 32], Operations: ['76-64=12', '44-12=32'] Exploring Operation: 32-29=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 29*32=928, Resulting Numbers: [928] 928,31 unequal: No Solution Exploring Operation: 29+32=61, Resulting Numbers: [61] 61,31 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 #0,0,3 Current State: 31:[44, 41], Operations: ['76-64=12', '29+12=41'] Exploring Operation: 44+41=85, Resulting Numbers: [85] 85,31 unequal: No Solution Exploring Operation: 44*41=1804, Resulting Numbers: [1804] 1804,31 unequal: No Solution Exploring Operation: 44-41=3, Resulting Numbers: [3] 3,31 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 #0,0,1 Current State: 31:[29, 56], Operations: ['76-64=12', '44+12=56'] Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 29*56=1624, Resulting Numbers: [1624] 1624,31 unequal: No Solution Exploring Operation: 29+56=85, Resulting Numbers: [85] 85,31 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 #0,0,2 Current State: 31:[44, 17], Operations: ['76-64=12', '29-12=17'] Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 44*17=748, Resulting Numbers: [748] 748,31 unequal: No Solution Exploring Operation: 44+17=61, Resulting Numbers: [61] 61,31 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 #0,0,4 Current State: 31:[12, 15], Operations: ['76-64=12', '44-29=15'] Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,31 unequal: No Solution Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,31 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:[64, 29, 32], Operations: ['76-44=32'] Exploring Operation: 64/32=2, Resulting Numbers: [29, 2] Generated Node #0,2,0: 31:[29, 2] Operation: 64/32=2 Exploring Operation: 32-29=3, Resulting Numbers: [64, 3] Generated Node #0,2,1: 31:[64, 3] Operation: 32-29=3 Exploring Operation: 64-29=35, Resulting Numbers: [32, 35] Generated Node #0,2,2: 31:[32, 35] Operation: 64-29=35 Exploring Operation: 64-32=32, Resulting Numbers: [29, 32] Generated Node #0,2,3: 31:[29, 32] Operation: 64-32=32 Exploring Operation: 64+29=93, Resulting Numbers: [32, 93] Generated Node #0,2,4: 31:[32, 93] Operation: 64+29=93 Moving to Node #0,2,3 Current State: 31:[29, 32], Operations: ['76-44=32', '64-32=32'] Exploring Operation: 29+32=61, Resulting Numbers: [61] 61,31 unequal: No Solution Exploring Operation: 29*32=928, Resulting Numbers: [928] 928,31 unequal: No Solution Exploring Operation: 32-29=3, Resulting Numbers: [3] 3,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[32, 35], Operations: ['76-44=32', '64-29=35'] Exploring Operation: 32+35=67, Resulting Numbers: [67] 67,31 unequal: No Solution Exploring Operation: 32*35=1120, Resulting Numbers: [1120] 1120,31 unequal: No Solution Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,31 unequal: No Solution Moving to Node #0,2,0 Current State: 31:[29, 2], Operations: ['76-44=32', '64/32=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[44, 64, 29, 76], Operations: [] Exploring Operation: 76-44=32, Resulting Numbers: [64, 29, 32] Generated Node #0,2: 31:[64, 29, 32] Operation: 76-44=32 Moving to Node #0,2 Current State: 31:[64, 29, 32], Operations: ['76-44=32'] Exploring Operation: 64/32=2, Resulting Numbers: [29, 2] Generated Node #0,2,0: 31:[29, 2] Operation: 64/32=2 Moving to Node #0,2,0 Current State: 31:[29, 2], Operations: ['76-44=32', '64/32=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_5
mult_heuristic
[ 63, 47, 16, 49 ]
77
[ "63+47=110", "49-16=33", "110-33=77" ]
Current State: 77:[63, 47, 16, 49], Operations: [] Exploring Operation: 63+47=110, Resulting Numbers: [16, 49, 110] Generated Node #2: [16, 49, 110] from Operation: 63+47=110 Current State: 77:[16, 49, 110], Operations: ['63+47=110'] Exploring Operation: 49-16=33, Resulting Numbers: [110, 33] Generated Node #3: [110, 33] from Operation: 49-16=33 Current State: 77:[110, 33], Operations: ['63+47=110', '49-16=33'] Exploring Operation: 110-33=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[63, 47, 16, 49], Operations: [] Exploring Operation: 47+16=63, Resulting Numbers: [63, 49, 63] Generated Node #0,0: 77:[63, 49, 63] Operation: 47+16=63 Exploring Operation: 47+49=96, Resulting Numbers: [63, 16, 96] Generated Node #0,1: 77:[63, 16, 96] Operation: 47+49=96 Exploring Operation: 63-47=16, Resulting Numbers: [16, 49, 16] Generated Node #0,2: 77:[16, 49, 16] Operation: 63-47=16 Exploring Operation: 49-47=2, Resulting Numbers: [63, 16, 2] Generated Node #0,3: 77:[63, 16, 2] Operation: 49-47=2 Exploring Operation: 63-49=14, Resulting Numbers: [47, 16, 14] Generated Node #0,4: 77:[47, 16, 14] Operation: 63-49=14 Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[63, 16, 2], Operations: ['49-47=2'] Exploring Operation: 63+2=65, Resulting Numbers: [16, 65] Generated Node #0,3,0: 77:[16, 65] Operation: 63+2=65 Exploring Operation: 16/2=8, Resulting Numbers: [63, 8] Generated Node #0,3,1: 77:[63, 8] Operation: 16/2=8 Exploring Operation: 16-2=14, Resulting Numbers: [63, 14] Generated Node #0,3,2: 77:[63, 14] Operation: 16-2=14 Exploring Operation: 63-2=61, Resulting Numbers: [16, 61] Generated Node #0,3,3: 77:[16, 61] Operation: 63-2=61 Exploring Operation: 63+16=79, Resulting Numbers: [2, 79] Generated Node #0,3,4: 77:[2, 79] Operation: 63+16=79 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 77:[2, 79], Operations: ['49-47=2', '63+16=79'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[63, 47, 16, 49], Operations: [] Exploring Operation: 49-47=2, Resulting Numbers: [63, 16, 2] Generated Node #0,3: 77:[63, 16, 2] Operation: 49-47=2 Moving to Node #0,3 Current State: 77:[63, 16, 2], Operations: ['49-47=2'] Exploring Operation: 63+16=79, Resulting Numbers: [2, 79] Generated Node #0,3,4: 77:[2, 79] Operation: 63+16=79 Moving to Node #0,3,4 Current State: 77:[2, 79], Operations: ['49-47=2', '63+16=79'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 93, 82, 96, 8 ]
71
[ "93+82=175", "96+8=104", "175-104=71" ]
Current State: 71:[93, 82, 96, 8], Operations: [] Exploring Operation: 93+82=175, Resulting Numbers: [96, 8, 175] Generated Node #2: [96, 8, 175] from Operation: 93+82=175 Current State: 71:[96, 8, 175], Operations: ['93+82=175'] Exploring Operation: 96+8=104, Resulting Numbers: [175, 104] Generated Node #3: [175, 104] from Operation: 96+8=104 Current State: 71:[175, 104], Operations: ['93+82=175', '96+8=104'] Exploring Operation: 175-104=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[93, 82, 96, 8], Operations: [] Exploring Operation: 93-8=85, Resulting Numbers: [82, 96, 85] Generated Node #0,0: 71:[82, 96, 85] Operation: 93-8=85 Exploring Operation: 96-8=88, Resulting Numbers: [93, 82, 88] Generated Node #0,1: 71:[93, 82, 88] Operation: 96-8=88 Exploring Operation: 82-8=74, Resulting Numbers: [93, 96, 74] Generated Node #0,2: 71:[93, 96, 74] Operation: 82-8=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[82, 96, 85], Operations: ['93-8=85'] Exploring Operation: 96-85=11, Resulting Numbers: [82, 11] Generated Node #0,0,0: 71:[82, 11] Operation: 96-85=11 Exploring Operation: 85-82=3, Resulting Numbers: [96, 3] Generated Node #0,0,1: 71:[96, 3] Operation: 85-82=3 Exploring Operation: 96-82=14, Resulting Numbers: [85, 14] Generated Node #0,0,2: 71:[85, 14] Operation: 96-82=14 Moving to Node #0,0,0 Current State: 71:[82, 11], Operations: ['93-8=85', '96-85=11'] Exploring Operation: 82+11=93, Resulting Numbers: [93] 93,71 unequal: No Solution Exploring Operation: 82*11=902, Resulting Numbers: [902] 902,71 unequal: No Solution Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[93, 82, 96, 8], Operations: [] Exploring Operation: 93-8=85, Resulting Numbers: [82, 96, 85] Generated Node #0,0: 71:[82, 96, 85] Operation: 93-8=85 Moving to Node #0,0 Current State: 71:[82, 96, 85], Operations: ['93-8=85'] Exploring Operation: 96-85=11, Resulting Numbers: [82, 11] Generated Node #0,0,0: 71:[82, 11] Operation: 96-85=11 Moving to Node #0,0,0 Current State: 71:[82, 11], Operations: ['93-8=85', '96-85=11'] Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 56, 2, 46, 32 ]
26
[ "56-46=10", "32/2=16", "10+16=26" ]
Current State: 26:[56, 2, 46, 32], Operations: [] Exploring Operation: 56-46=10, Resulting Numbers: [2, 32, 10] Generated Node #2: [2, 32, 10] from Operation: 56-46=10 Current State: 26:[2, 32, 10], Operations: ['56-46=10'] Exploring Operation: 32/2=16, Resulting Numbers: [10, 16] Generated Node #3: [10, 16] from Operation: 32/2=16 Current State: 26:[10, 16], Operations: ['56-46=10', '32/2=16'] Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[56, 2, 46, 32], Operations: [] Exploring Operation: 56-46=10, Resulting Numbers: [2, 32, 10] Generated Node #0,0: 26:[2, 32, 10] Operation: 56-46=10 Exploring Operation: 56-32=24, Resulting Numbers: [2, 46, 24] Generated Node #0,1: 26:[2, 46, 24] Operation: 56-32=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[2, 32, 10], Operations: ['56-46=10'] Exploring Operation: 32-10=22, Resulting Numbers: [2, 22] Generated Node #0,0,0: 26:[2, 22] Operation: 32-10=22 Exploring Operation: 32/2=16, Resulting Numbers: [10, 16] Generated Node #0,0,1: 26:[10, 16] Operation: 32/2=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 26:[2, 22], Operations: ['56-46=10', '32-10=22'] Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,26 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,26 unequal: No Solution No 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: 26:[10, 16], Operations: ['56-46=10', '32/2=16'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,26 unequal: No Solution Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[56, 2, 46, 32], Operations: [] Exploring Operation: 56-46=10, Resulting Numbers: [2, 32, 10] Generated Node #0,0: 26:[2, 32, 10] Operation: 56-46=10 Moving to Node #0,0 Current State: 26:[2, 32, 10], Operations: ['56-46=10'] Exploring Operation: 32/2=16, Resulting Numbers: [10, 16] Generated Node #0,0,1: 26:[10, 16] Operation: 32/2=16 Moving to Node #0,0,1 Current State: 26:[10, 16], Operations: ['56-46=10', '32/2=16'] Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 37, 96, 79, 4 ]
31
[ "96-79=17", "4*17=68", "68-37=31" ]
Current State: 31:[37, 96, 79, 4], Operations: [] Exploring Operation: 96-79=17, Resulting Numbers: [37, 4, 17] Generated Node #2: [37, 4, 17] from Operation: 96-79=17 Current State: 31:[37, 4, 17], Operations: ['96-79=17'] Exploring Operation: 4*17=68, Resulting Numbers: [37, 68] Generated Node #3: [37, 68] from Operation: 4*17=68 Current State: 31:[37, 68], Operations: ['96-79=17', '4*17=68'] Exploring Operation: 68-37=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[37, 96, 79, 4], Operations: [] Exploring Operation: 96-79=17, Resulting Numbers: [37, 4, 17] Generated Node #0,0: 31:[37, 4, 17] Operation: 96-79=17 Exploring Operation: 96-37=59, Resulting Numbers: [79, 4, 59] Generated Node #0,1: 31:[79, 4, 59] Operation: 96-37=59 Exploring Operation: 79-37=42, Resulting Numbers: [96, 4, 42] Generated Node #0,2: 31:[96, 4, 42] Operation: 79-37=42 Exploring Operation: 96/4=24, Resulting Numbers: [37, 79, 24] Generated Node #0,3: 31:[37, 79, 24] Operation: 96/4=24 Moving to Node #0,0 Current State: 31:[37, 4, 17], Operations: ['96-79=17'] Exploring Operation: 37-4=33, Resulting Numbers: [17, 33] Generated Node #0,0,0: 31:[17, 33] Operation: 37-4=33 Exploring Operation: 17-4=13, Resulting Numbers: [37, 13] Generated Node #0,0,1: 31:[37, 13] Operation: 17-4=13 Exploring Operation: 37+4=41, Resulting Numbers: [17, 41] Generated Node #0,0,2: 31:[17, 41] Operation: 37+4=41 Exploring Operation: 4+17=21, Resulting Numbers: [37, 21] Generated Node #0,0,3: 31:[37, 21] Operation: 4+17=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[17, 33], Operations: ['96-79=17', '37-4=33'] Exploring Operation: 17*33=561, Resulting Numbers: [561] 561,31 unequal: No Solution Exploring Operation: 17+33=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,31 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 #0,0,3 Current State: 31:[37, 21], Operations: ['96-79=17', '4+17=21'] Exploring Operation: 37+21=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 37-21=16, Resulting Numbers: [16] 16,31 unequal: No Solution Exploring Operation: 37*21=777, Resulting Numbers: [777] 777,31 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 #0,0,1 Current State: 31:[37, 13], Operations: ['96-79=17', '17-4=13'] Exploring Operation: 37*13=481, Resulting Numbers: [481] 481,31 unequal: No Solution Exploring Operation: 37-13=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 37+13=50, Resulting Numbers: [50] 50,31 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 #0,0,2 Current State: 31:[17, 41], Operations: ['96-79=17', '37+4=41'] Exploring Operation: 41-17=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 17+41=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 17*41=697, Resulting Numbers: [697] 697,31 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: 31:[37, 79, 24], Operations: ['96/4=24'] Exploring Operation: 79-24=55, Resulting Numbers: [37, 55] Generated Node #0,3,0: 31:[37, 55] Operation: 79-24=55 Exploring Operation: 37-24=13, Resulting Numbers: [79, 13] Generated Node #0,3,1: 31:[79, 13] Operation: 37-24=13 Exploring Operation: 37+24=61, Resulting Numbers: [79, 61] Generated Node #0,3,2: 31:[79, 61] Operation: 37+24=61 Exploring Operation: 79-37=42, Resulting Numbers: [24, 42] Generated Node #0,3,3: 31:[24, 42] Operation: 79-37=42 Moving to Node #0,2 Current State: 31:[96, 4, 42], Operations: ['79-37=42'] Exploring Operation: 42-4=38, Resulting Numbers: [96, 38] Generated Node #0,2,0: 31:[96, 38] Operation: 42-4=38 Exploring Operation: 96-4=92, Resulting Numbers: [42, 92] Generated Node #0,2,1: 31:[42, 92] Operation: 96-4=92 Exploring Operation: 96-42=54, Resulting Numbers: [4, 54] Generated Node #0,2,2: 31:[4, 54] Operation: 96-42=54 Exploring Operation: 96/4=24, Resulting Numbers: [42, 24] Generated Node #0,2,3: 31:[42, 24] Operation: 96/4=24 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 31:[42, 24], Operations: ['79-37=42', '96/4=24'] Exploring Operation: 42+24=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 42*24=1008, Resulting Numbers: [1008] 1008,31 unequal: No Solution Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,31 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 #0,2,2 Current State: 31:[4, 54], Operations: ['79-37=42', '96-42=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 4*54=216, Resulting Numbers: [216] 216,31 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 #0,2,0 Current State: 31:[96, 38], Operations: ['79-37=42', '42-4=38'] Exploring Operation: 96+38=134, Resulting Numbers: [134] 134,31 unequal: No Solution Exploring Operation: 96*38=3648, Resulting Numbers: [3648] 3648,31 unequal: No Solution Exploring Operation: 96-38=58, Resulting Numbers: [58] 58,31 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 #0,2,1 Current State: 31:[42, 92], Operations: ['79-37=42', '96-4=92'] Exploring Operation: 42+92=134, Resulting Numbers: [134] 134,31 unequal: No Solution Exploring Operation: 42*92=3864, Resulting Numbers: [3864] 3864,31 unequal: No Solution Exploring Operation: 92-42=50, Resulting Numbers: [50] 50,31 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: 31:[79, 4, 59], Operations: ['96-37=59'] Exploring Operation: 59-4=55, Resulting Numbers: [79, 55] Generated Node #0,1,0: 31:[79, 55] Operation: 59-4=55 Exploring Operation: 79+4=83, Resulting Numbers: [59, 83] Generated Node #0,1,1: 31:[59, 83] Operation: 79+4=83 Exploring Operation: 79-59=20, Resulting Numbers: [4, 20] Generated Node #0,1,2: 31:[4, 20] Operation: 79-59=20 Exploring Operation: 79-4=75, Resulting Numbers: [59, 75] Generated Node #0,1,3: 31:[59, 75] Operation: 79-4=75 Moving to Node #0,3,3 Current State: 31:[24, 42], Operations: ['96/4=24', '79-37=42'] Exploring Operation: 24*42=1008, Resulting Numbers: [1008] 1008,31 unequal: No Solution Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 24+42=66, Resulting Numbers: [66] 66,31 unequal: No Solution Moving to Node #0,3,0 Current State: 31:[37, 55], Operations: ['96/4=24', '79-24=55'] Exploring Operation: 55-37=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 37*55=2035, Resulting Numbers: [2035] 2035,31 unequal: No Solution Exploring Operation: 37+55=92, Resulting Numbers: [92] 92,31 unequal: No Solution Moving to Node #0,1,2 Current State: 31:[4, 20], Operations: ['96-37=59', '79-59=20'] Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,31 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,31 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,31 unequal: No Solution Moving to Node #0,3,1 Current State: 31:[79, 13], Operations: ['96/4=24', '37-24=13'] Exploring Operation: 79+13=92, Resulting Numbers: [92] 92,31 unequal: No Solution Exploring Operation: 79-13=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 79*13=1027, Resulting Numbers: [1027] 1027,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[79, 55], Operations: ['96-37=59', '59-4=55'] Exploring Operation: 79-55=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 79*55=4345, Resulting Numbers: [4345] 4345,31 unequal: No Solution Exploring Operation: 79+55=134, Resulting Numbers: [134] 134,31 unequal: No Solution Moving to Node #0,1,3 Current State: 31:[59, 75], Operations: ['96-37=59', '79-4=75'] Exploring Operation: 75-59=16, Resulting Numbers: [16] 16,31 unequal: No Solution Exploring Operation: 59*75=4425, Resulting Numbers: [4425] 4425,31 unequal: No Solution Exploring Operation: 59+75=134, Resulting Numbers: [134] 134,31 unequal: No Solution Moving to Node #0,3,2 Current State: 31:[79, 61], Operations: ['96/4=24', '37+24=61'] Exploring Operation: 79+61=140, Resulting Numbers: [140] 140,31 unequal: No Solution Exploring Operation: 79*61=4819, Resulting Numbers: [4819] 4819,31 unequal: No Solution Exploring Operation: 79-61=18, Resulting Numbers: [18] 18,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[59, 83], Operations: ['96-37=59', '79+4=83'] Exploring Operation: 59*83=4897, Resulting Numbers: [4897] 4897,31 unequal: No Solution Exploring Operation: 83-59=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 59+83=142, Resulting Numbers: [142] 142,31 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 26, 27, 54, 5 ]
55
[ "26+54=80", "27*5=135", "135-80=55" ]
Current State: 55:[26, 27, 54, 5], Operations: [] Exploring Operation: 26+54=80, Resulting Numbers: [27, 5, 80] Generated Node #2: [27, 5, 80] from Operation: 26+54=80 Current State: 55:[27, 5, 80], Operations: ['26+54=80'] Exploring Operation: 27*5=135, Resulting Numbers: [80, 135] Generated Node #3: [80, 135] from Operation: 27*5=135 Current State: 55:[80, 135], Operations: ['26+54=80', '27*5=135'] Exploring Operation: 135-80=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[26, 27, 54, 5], Operations: [] Exploring Operation: 26-5=21, Resulting Numbers: [27, 54, 21] Generated Node #0,0: 55:[27, 54, 21] Operation: 26-5=21 Exploring Operation: 26+27=53, Resulting Numbers: [54, 5, 53] Generated Node #0,1: 55:[54, 5, 53] Operation: 26+27=53 Exploring Operation: 54/27=2, Resulting Numbers: [26, 5, 2] Generated Node #0,2: 55:[26, 5, 2] Operation: 54/27=2 Exploring Operation: 27-26=1, Resulting Numbers: [54, 5, 1] Generated Node #0,3: 55:[54, 5, 1] Operation: 27-26=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[54, 5, 53], Operations: ['26+27=53'] Exploring Operation: 54+5=59, Resulting Numbers: [53, 59] Generated Node #0,1,0: 55:[53, 59] Operation: 54+5=59 Exploring Operation: 5+53=58, Resulting Numbers: [54, 58] Generated Node #0,1,1: 55:[54, 58] Operation: 5+53=58 Exploring Operation: 54-5=49, Resulting Numbers: [53, 49] Generated Node #0,1,2: 55:[53, 49] Operation: 54-5=49 Exploring Operation: 54-53=1, Resulting Numbers: [5, 1] Generated Node #0,1,3: 55:[5, 1] Operation: 54-53=1 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 55:[54, 58], Operations: ['26+27=53', '5+53=58'] Exploring Operation: 58-54=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 54*58=3132, Resulting Numbers: [3132] 3132,55 unequal: No Solution Exploring Operation: 54+58=112, Resulting Numbers: [112] 112,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 55:[5, 1], Operations: ['26+27=53', '54-53=1'] Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[53, 59], Operations: ['26+27=53', '54+5=59'] Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,55 unequal: No Solution Exploring Operation: 53*59=3127, Resulting Numbers: [3127] 3127,55 unequal: No Solution Exploring Operation: 53+59=112, Resulting Numbers: [112] 112,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 55:[53, 49], Operations: ['26+27=53', '54-5=49'] Exploring Operation: 53-49=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 53+49=102, Resulting Numbers: [102] 102,55 unequal: No Solution Exploring Operation: 53*49=2597, Resulting Numbers: [2597] 2597,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 55:[54, 5, 1], Operations: ['27-26=1'] Exploring Operation: 5*1=5, Resulting Numbers: [54, 5] Generated Node #0,3,0: 55:[54, 5] Operation: 5*1=5 Exploring Operation: 54+1=55, Resulting Numbers: [5, 55] Generated Node #0,3,1: 55:[5, 55] Operation: 54+1=55 Exploring Operation: 54/1=54, Resulting Numbers: [5, 54] Generated Node #0,3,2: 55:[5, 54] Operation: 54/1=54 Exploring Operation: 54*1=54, Resulting Numbers: [5, 54] Generated Node #0,3,3: 55:[5, 54] Operation: 54*1=54 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 55:[5, 55], Operations: ['27-26=1', '54+1=55'] Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,55 unequal: No Solution Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,55 unequal: No Solution Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 5*55=275, Resulting Numbers: [275] 275,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 55:[54, 5], Operations: ['27-26=1', '5*1=5'] Exploring Operation: 54+5=59, Resulting Numbers: [59] 59,55 unequal: No Solution Exploring Operation: 54*5=270, Resulting Numbers: [270] 270,55 unequal: No Solution Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,55 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:[5, 54], Operations: ['27-26=1', '54/1=54'] Exploring Operation: 5*54=270, Resulting Numbers: [270] 270,55 unequal: No Solution Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,55 unequal: No Solution Exploring Operation: 5+54=59, Resulting Numbers: [59] 59,55 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:[5, 54], Operations: ['27-26=1', '54*1=54'] Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,55 unequal: No Solution Exploring Operation: 5*54=270, Resulting Numbers: [270] 270,55 unequal: No Solution Exploring Operation: 5+54=59, Resulting Numbers: [59] 59,55 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:[26, 5, 2], Operations: ['54/27=2'] Exploring Operation: 26*2=52, Resulting Numbers: [5, 52] Generated Node #0,2,0: 55:[5, 52] Operation: 26*2=52 Exploring Operation: 26-2=24, Resulting Numbers: [5, 24] Generated Node #0,2,1: 55:[5, 24] Operation: 26-2=24 Exploring Operation: 26/2=13, Resulting Numbers: [5, 13] Generated Node #0,2,2: 55:[5, 13] Operation: 26/2=13 Exploring Operation: 26-5=21, Resulting Numbers: [2, 21] Generated Node #0,2,3: 55:[2, 21] Operation: 26-5=21 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 55:[5, 13], Operations: ['54/27=2', '26/2=13'] Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,55 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 55:[5, 52], Operations: ['54/27=2', '26*2=52'] Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,55 unequal: No Solution Exploring Operation: 5+52=57, Resulting Numbers: [57] 57,55 unequal: No Solution Exploring Operation: 5*52=260, Resulting Numbers: [260] 260,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 55:[5, 24], Operations: ['54/27=2', '26-2=24'] Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,55 unequal: No Solution Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,55 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 55:[2, 21], Operations: ['54/27=2', '26-5=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,55 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,55 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:[27, 54, 21], Operations: ['26-5=21'] Exploring Operation: 54/27=2, Resulting Numbers: [21, 2] Generated Node #0,0,0: 55:[21, 2] Operation: 54/27=2 Exploring Operation: 27-21=6, Resulting Numbers: [54, 6] Generated Node #0,0,1: 55:[54, 6] Operation: 27-21=6 Exploring Operation: 27+21=48, Resulting Numbers: [54, 48] Generated Node #0,0,2: 55:[54, 48] Operation: 27+21=48 Exploring Operation: 54-27=27, Resulting Numbers: [21, 27] Generated Node #0,0,3: 55:[21, 27] Operation: 54-27=27 Moving to Node #0,0,1 Current State: 55:[54, 6], Operations: ['26-5=21', '27-21=6'] Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,55 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,55 unequal: No Solution Exploring Operation: 54*6=324, Resulting Numbers: [324] 324,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[54, 48], Operations: ['26-5=21', '27+21=48'] Exploring Operation: 54+48=102, Resulting Numbers: [102] 102,55 unequal: No Solution Exploring Operation: 54*48=2592, Resulting Numbers: [2592] 2592,55 unequal: No Solution Exploring Operation: 54-48=6, Resulting Numbers: [6] 6,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[21, 2], Operations: ['26-5=21', '54/27=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,55 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,55 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,55 unequal: No Solution Moving to Node #0,0,3 Current State: 55:[21, 27], Operations: ['26-5=21', '54-27=27'] Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,55 unequal: No Solution Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,55 unequal: No Solution Exploring Operation: 21*27=567, Resulting Numbers: [567] 567,55 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
[ 83, 8, 55, 84 ]
48
[ "83+8=91", "55+84=139", "139-91=48" ]
Current State: 48:[83, 8, 55, 84], Operations: [] Exploring Operation: 83+8=91, Resulting Numbers: [55, 84, 91] Generated Node #2: [55, 84, 91] from Operation: 83+8=91 Current State: 48:[55, 84, 91], Operations: ['83+8=91'] Exploring Operation: 55+84=139, Resulting Numbers: [91, 139] Generated Node #3: [91, 139] from Operation: 55+84=139 Current State: 48:[91, 139], Operations: ['83+8=91', '55+84=139'] Exploring Operation: 139-91=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[83, 8, 55, 84], Operations: [] Exploring Operation: 84-55=29, Resulting Numbers: [83, 8, 29] Generated Node #0,0: 48:[83, 8, 29] Operation: 84-55=29 Exploring Operation: 84-83=1, Resulting Numbers: [8, 55, 1] Generated Node #0,1: 48:[8, 55, 1] Operation: 84-83=1 Exploring Operation: 83-55=28, Resulting Numbers: [8, 84, 28] Generated Node #0,2: 48:[8, 84, 28] Operation: 83-55=28 Moving to Node #0,1 Current State: 48:[8, 55, 1], Operations: ['84-83=1'] Exploring Operation: 8*1=8, Resulting Numbers: [55, 8] Generated Node #0,1,0: 48:[55, 8] Operation: 8*1=8 Exploring Operation: 55-1=54, Resulting Numbers: [8, 54] Generated Node #0,1,1: 48:[8, 54] Operation: 55-1=54 Exploring Operation: 55-8=47, Resulting Numbers: [1, 47] Generated Node #0,1,2: 48:[1, 47] Operation: 55-8=47 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 48:[1, 47], Operations: ['84-83=1', '55-8=47'] Exploring Operation: 1+47=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[83, 8, 55, 84], Operations: [] Exploring Operation: 84-83=1, Resulting Numbers: [8, 55, 1] Generated Node #0,1: 48:[8, 55, 1] Operation: 84-83=1 Moving to Node #0,1 Current State: 48:[8, 55, 1], Operations: ['84-83=1'] Exploring Operation: 55-8=47, Resulting Numbers: [1, 47] Generated Node #0,1,2: 48:[1, 47] Operation: 55-8=47 Moving to Node #0,1,2 Current State: 48:[1, 47], Operations: ['84-83=1', '55-8=47'] Exploring Operation: 1+47=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 19, 87, 2, 15 ]
98
[ "87-19=68", "2*15=30", "68+30=98" ]
Current State: 98:[19, 87, 2, 15], Operations: [] Exploring Operation: 87-19=68, Resulting Numbers: [2, 15, 68] Generated Node #2: [2, 15, 68] from Operation: 87-19=68 Current State: 98:[2, 15, 68], Operations: ['87-19=68'] Exploring Operation: 2*15=30, Resulting Numbers: [68, 30] Generated Node #3: [68, 30] from Operation: 2*15=30 Current State: 98:[68, 30], Operations: ['87-19=68', '2*15=30'] Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[19, 87, 2, 15], Operations: [] Exploring Operation: 19-2=17, Resulting Numbers: [87, 15, 17] Generated Node #0,0: 98:[87, 15, 17] Operation: 19-2=17 Exploring Operation: 19+87=106, Resulting Numbers: [2, 15, 106] Generated Node #0,1: 98:[2, 15, 106] Operation: 19+87=106 Exploring Operation: 87+15=102, Resulting Numbers: [19, 2, 102] Generated Node #0,2: 98:[19, 2, 102] Operation: 87+15=102 Exploring Operation: 19-15=4, Resulting Numbers: [87, 2, 4] Generated Node #0,3: 98:[87, 2, 4] Operation: 19-15=4 Moving to Node #0,1 Current State: 98:[2, 15, 106], Operations: ['19+87=106'] Exploring Operation: 106-15=91, Resulting Numbers: [2, 91] Generated Node #0,1,0: 98:[2, 91] Operation: 106-15=91 Exploring Operation: 106/2=53, Resulting Numbers: [15, 53] Generated Node #0,1,1: 98:[15, 53] Operation: 106/2=53 Exploring Operation: 15-2=13, Resulting Numbers: [106, 13] Generated Node #0,1,2: 98:[106, 13] Operation: 15-2=13 Exploring Operation: 106-2=104, Resulting Numbers: [15, 104] Generated Node #0,1,3: 98:[15, 104] Operation: 106-2=104 Moving to Node #0,2 Current State: 98:[19, 2, 102], Operations: ['87+15=102'] Exploring Operation: 102/2=51, Resulting Numbers: [19, 51] Generated Node #0,2,0: 98:[19, 51] Operation: 102/2=51 Exploring Operation: 19+2=21, Resulting Numbers: [102, 21] Generated Node #0,2,1: 98:[102, 21] Operation: 19+2=21 Exploring Operation: 102-2=100, Resulting Numbers: [19, 100] Generated Node #0,2,2: 98:[19, 100] Operation: 102-2=100 Exploring Operation: 19-2=17, Resulting Numbers: [102, 17] Generated Node #0,2,3: 98:[102, 17] Operation: 19-2=17 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 98:[19, 51], Operations: ['87+15=102', '102/2=51'] Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,98 unequal: No Solution Exploring Operation: 19+51=70, Resulting Numbers: [70] 70,98 unequal: No Solution Exploring Operation: 19*51=969, Resulting Numbers: [969] 969,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 98:[19, 100], Operations: ['87+15=102', '102-2=100'] Exploring Operation: 19+100=119, Resulting Numbers: [119] 119,98 unequal: No Solution Exploring Operation: 100-19=81, Resulting Numbers: [81] 81,98 unequal: No Solution Exploring Operation: 19*100=1900, Resulting Numbers: [1900] 1900,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 98:[102, 17], Operations: ['87+15=102', '19-2=17'] Exploring Operation: 102+17=119, Resulting Numbers: [119] 119,98 unequal: No Solution Exploring Operation: 102/17=6, Resulting Numbers: [6] 6,98 unequal: No Solution Exploring Operation: 102-17=85, Resulting Numbers: [85] 85,98 unequal: No Solution Exploring Operation: 102*17=1734, Resulting Numbers: [1734] 1734,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 98:[102, 21], Operations: ['87+15=102', '19+2=21'] Exploring Operation: 102*21=2142, Resulting Numbers: [2142] 2142,98 unequal: No Solution Exploring Operation: 102-21=81, Resulting Numbers: [81] 81,98 unequal: No Solution Exploring Operation: 102+21=123, Resulting Numbers: [123] 123,98 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: 98:[87, 2, 4], Operations: ['19-15=4'] Exploring Operation: 87+4=91, Resulting Numbers: [2, 91] Generated Node #0,3,0: 98:[2, 91] Operation: 87+4=91 Exploring Operation: 4/2=2, Resulting Numbers: [87, 2] Generated Node #0,3,1: 98:[87, 2] Operation: 4/2=2 Exploring Operation: 87+2=89, Resulting Numbers: [4, 89] Generated Node #0,3,2: 98:[4, 89] Operation: 87+2=89 Exploring Operation: 4-2=2, Resulting Numbers: [87, 2] Generated Node #0,3,3: 98:[87, 2] Operation: 4-2=2 Moving to Node #0,0 Current State: 98:[87, 15, 17], Operations: ['19-2=17'] Exploring Operation: 87+15=102, Resulting Numbers: [17, 102] Generated Node #0,0,0: 98:[17, 102] Operation: 87+15=102 Exploring Operation: 87+17=104, Resulting Numbers: [15, 104] Generated Node #0,0,1: 98:[15, 104] Operation: 87+17=104 Exploring Operation: 87-17=70, Resulting Numbers: [15, 70] Generated Node #0,0,2: 98:[15, 70] Operation: 87-17=70 Exploring Operation: 17-15=2, Resulting Numbers: [87, 2] Generated Node #0,0,3: 98:[87, 2] Operation: 17-15=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[17, 102], Operations: ['19-2=17', '87+15=102'] Exploring Operation: 102/17=6, Resulting Numbers: [6] 6,98 unequal: No Solution Exploring Operation: 17+102=119, Resulting Numbers: [119] 119,98 unequal: No Solution Exploring Operation: 17*102=1734, Resulting Numbers: [1734] 1734,98 unequal: No Solution Exploring Operation: 102-17=85, Resulting Numbers: [85] 85,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 98:[15, 104], Operations: ['19-2=17', '87+17=104'] Exploring Operation: 15+104=119, Resulting Numbers: [119] 119,98 unequal: No Solution Exploring Operation: 104-15=89, Resulting Numbers: [89] 89,98 unequal: No Solution Exploring Operation: 15*104=1560, Resulting Numbers: [1560] 1560,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 98:[87, 2], Operations: ['19-2=17', '17-15=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,98 unequal: No Solution Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,98 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 98:[15, 70], Operations: ['19-2=17', '87-17=70'] Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,98 unequal: No Solution Exploring Operation: 15*70=1050, Resulting Numbers: [1050] 1050,98 unequal: No Solution Exploring Operation: 15+70=85, Resulting Numbers: [85] 85,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 98:[15, 53], Operations: ['19+87=106', '106/2=53'] Exploring Operation: 53-15=38, Resulting Numbers: [38] 38,98 unequal: No Solution Exploring Operation: 15*53=795, Resulting Numbers: [795] 795,98 unequal: No Solution Exploring Operation: 15+53=68, Resulting Numbers: [68] 68,98 unequal: No Solution Moving to Node #0,1,3 Current State: 98:[15, 104], Operations: ['19+87=106', '106-2=104'] Exploring Operation: 15+104=119, Resulting Numbers: [119] 119,98 unequal: No Solution Exploring Operation: 15*104=1560, Resulting Numbers: [1560] 1560,98 unequal: No Solution Exploring Operation: 104-15=89, Resulting Numbers: [89] 89,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[2, 91], Operations: ['19+87=106', '106-15=91'] Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,98 unequal: No Solution Exploring Operation: 2*91=182, Resulting Numbers: [182] 182,98 unequal: No Solution Exploring Operation: 2+91=93, Resulting Numbers: [93] 93,98 unequal: No Solution Moving to Node #0,3,0 Current State: 98:[2, 91], Operations: ['19-15=4', '87+4=91'] Exploring Operation: 2+91=93, Resulting Numbers: [93] 93,98 unequal: No Solution Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,98 unequal: No Solution Exploring Operation: 2*91=182, Resulting Numbers: [182] 182,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[106, 13], Operations: ['19+87=106', '15-2=13'] Exploring Operation: 106+13=119, Resulting Numbers: [119] 119,98 unequal: No Solution Exploring Operation: 106-13=93, Resulting Numbers: [93] 93,98 unequal: No Solution Exploring Operation: 106*13=1378, Resulting Numbers: [1378] 1378,98 unequal: No Solution Moving to Node #0,3,2 Current State: 98:[4, 89], Operations: ['19-15=4', '87+2=89'] Exploring Operation: 89-4=85, Resulting Numbers: [85] 85,98 unequal: No Solution Exploring Operation: 4*89=356, Resulting Numbers: [356] 356,98 unequal: No Solution Exploring Operation: 4+89=93, Resulting Numbers: [93] 93,98 unequal: No Solution Moving to Node #0,3,1 Current State: 98:[87, 2], Operations: ['19-15=4', '4/2=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,98 unequal: No Solution Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,98 unequal: No Solution Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,98 unequal: No Solution Moving to Node #0,3,3 Current State: 98:[87, 2], Operations: ['19-15=4', '4-2=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,98 unequal: No Solution Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,98 unequal: No Solution Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,98 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 93, 24, 39, 32 ]
62
[ "93-24=69", "39-32=7", "69-7=62" ]
Current State: 62:[93, 24, 39, 32], Operations: [] Exploring Operation: 93-24=69, Resulting Numbers: [39, 32, 69] Generated Node #2: [39, 32, 69] from Operation: 93-24=69 Current State: 62:[39, 32, 69], Operations: ['93-24=69'] Exploring Operation: 39-32=7, Resulting Numbers: [69, 7] Generated Node #3: [69, 7] from Operation: 39-32=7 Current State: 62:[69, 7], Operations: ['93-24=69', '39-32=7'] Exploring Operation: 69-7=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[93, 24, 39, 32], Operations: [] Exploring Operation: 93-24=69, Resulting Numbers: [39, 32, 69] Generated Node #0,0: 62:[39, 32, 69] Operation: 93-24=69 Moving to Node #0,0 Current State: 62:[39, 32, 69], Operations: ['93-24=69'] Exploring Operation: 69-39=30, Resulting Numbers: [32, 30] Generated Node #0,0,0: 62:[32, 30] Operation: 69-39=30 Moving to Node #0,0,0 Current State: 62:[32, 30], Operations: ['93-24=69', '69-39=30'] Exploring Operation: 32+30=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[93, 24, 39, 32], Operations: [] Exploring Operation: 93-24=69, Resulting Numbers: [39, 32, 69] Generated Node #0,0: 62:[39, 32, 69] Operation: 93-24=69 Moving to Node #0,0 Current State: 62:[39, 32, 69], Operations: ['93-24=69'] Exploring Operation: 69-39=30, Resulting Numbers: [32, 30] Generated Node #0,0,0: 62:[32, 30] Operation: 69-39=30 Moving to Node #0,0,0 Current State: 62:[32, 30], Operations: ['93-24=69', '69-39=30'] Exploring Operation: 32+30=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 22, 37, 3, 89 ]
33
[ "22+37=59", "3+89=92", "92-59=33" ]
Current State: 33:[22, 37, 3, 89], Operations: [] Exploring Operation: 22+37=59, Resulting Numbers: [3, 89, 59] Generated Node #2: [3, 89, 59] from Operation: 22+37=59 Current State: 33:[3, 89, 59], Operations: ['22+37=59'] Exploring Operation: 3+89=92, Resulting Numbers: [59, 92] Generated Node #3: [59, 92] from Operation: 3+89=92 Current State: 33:[59, 92], Operations: ['22+37=59', '3+89=92'] Exploring Operation: 92-59=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[22, 37, 3, 89], Operations: [] Exploring Operation: 89-37=52, Resulting Numbers: [22, 3, 52] Generated Node #0,0: 33:[22, 3, 52] Operation: 89-37=52 Moving to Node #0,0 Current State: 33:[22, 3, 52], Operations: ['89-37=52'] Exploring Operation: 52-22=30, Resulting Numbers: [3, 30] Generated Node #0,0,0: 33:[3, 30] Operation: 52-22=30 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[3, 30], Operations: ['89-37=52', '52-22=30'] Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[22, 37, 3, 89], Operations: [] Exploring Operation: 89-37=52, Resulting Numbers: [22, 3, 52] Generated Node #0,0: 33:[22, 3, 52] Operation: 89-37=52 Moving to Node #0,0 Current State: 33:[22, 3, 52], Operations: ['89-37=52'] Exploring Operation: 52-22=30, Resulting Numbers: [3, 30] Generated Node #0,0,0: 33:[3, 30] Operation: 52-22=30 Moving to Node #0,0,0 Current State: 33:[3, 30], Operations: ['89-37=52', '52-22=30'] Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 14, 7, 63, 23 ]
55
[ "14*23=322", "63+322=385", "385/7=55" ]
Current State: 55:[14, 7, 63, 23], Operations: [] Exploring Operation: 14*23=322, Resulting Numbers: [7, 63, 322] Generated Node #2: [7, 63, 322] from Operation: 14*23=322 Current State: 55:[7, 63, 322], Operations: ['14*23=322'] Exploring Operation: 63+322=385, Resulting Numbers: [7, 385] Generated Node #3: [7, 385] from Operation: 63+322=385 Current State: 55:[7, 385], Operations: ['14*23=322', '63+322=385'] Exploring Operation: 385/7=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[14, 7, 63, 23], Operations: [] Exploring Operation: 23-14=9, Resulting Numbers: [7, 63, 9] Generated Node #0,0: 55:[7, 63, 9] Operation: 23-14=9 Exploring Operation: 23-7=16, Resulting Numbers: [14, 63, 16] Generated Node #0,1: 55:[14, 63, 16] Operation: 23-7=16 Exploring Operation: 63-7=56, Resulting Numbers: [14, 23, 56] Generated Node #0,2: 55:[14, 23, 56] Operation: 63-7=56 Moving to Node #0,0 Current State: 55:[7, 63, 9], Operations: ['23-14=9'] Exploring Operation: 63/7=9, Resulting Numbers: [9, 9] Generated Node #0,0,0: 55:[9, 9] Operation: 63/7=9 Exploring Operation: 63-9=54, Resulting Numbers: [7, 54] Generated Node #0,0,1: 55:[7, 54] Operation: 63-9=54 Exploring Operation: 63-7=56, Resulting Numbers: [9, 56] Generated Node #0,0,2: 55:[9, 56] Operation: 63-7=56 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 55:[7, 54], Operations: ['23-14=9', '63-9=54'] Exploring Operation: 54-7=47, Resulting Numbers: [47] 47,55 unequal: No Solution Exploring Operation: 7+54=61, Resulting Numbers: [61] 61,55 unequal: No Solution Exploring Operation: 7*54=378, Resulting Numbers: [378] 378,55 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 #0,0,2 Current State: 55:[9, 56], Operations: ['23-14=9', '63-7=56'] Exploring Operation: 9*56=504, Resulting Numbers: [504] 504,55 unequal: No Solution Exploring Operation: 9+56=65, Resulting Numbers: [65] 65,55 unequal: No Solution Exploring Operation: 56-9=47, Resulting Numbers: [47] 47,55 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 #0,0,0 Current State: 55:[9, 9], Operations: ['23-14=9', '63/7=9'] Exploring Operation: 9/9=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 9-9=0, Resulting Numbers: [0] 0,55 unequal: No Solution Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,55 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: 55:[14, 63, 16], Operations: ['23-7=16'] Exploring Operation: 63-16=47, Resulting Numbers: [14, 47] Generated Node #0,1,0: 55:[14, 47] Operation: 63-16=47 Exploring Operation: 16-14=2, Resulting Numbers: [63, 2] Generated Node #0,1,1: 55:[63, 2] Operation: 16-14=2 Exploring Operation: 63-14=49, Resulting Numbers: [16, 49] Generated Node #0,1,2: 55:[16, 49] Operation: 63-14=49 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[14, 47], Operations: ['23-7=16', '63-16=47'] Exploring Operation: 14+47=61, Resulting Numbers: [61] 61,55 unequal: No Solution Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,55 unequal: No Solution Exploring Operation: 14*47=658, Resulting Numbers: [658] 658,55 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 #0,1,1 Current State: 55:[63, 2], Operations: ['23-7=16', '16-14=2'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,55 unequal: No Solution Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,55 unequal: No Solution Exploring Operation: 63*2=126, Resulting Numbers: [126] 126,55 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 #0,1,2 Current State: 55:[16, 49], Operations: ['23-7=16', '63-14=49'] Exploring Operation: 49-16=33, Resulting Numbers: [33] 33,55 unequal: No Solution Exploring Operation: 16+49=65, Resulting Numbers: [65] 65,55 unequal: No Solution Exploring Operation: 16*49=784, Resulting Numbers: [784] 784,55 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: 55:[14, 23, 56], Operations: ['63-7=56'] Exploring Operation: 56/14=4, Resulting Numbers: [23, 4] Generated Node #0,2,0: 55:[23, 4] Operation: 56/14=4 Exploring Operation: 14+23=37, Resulting Numbers: [56, 37] Generated Node #0,2,1: 55:[56, 37] Operation: 14+23=37 Exploring Operation: 23-14=9, Resulting Numbers: [56, 9] Generated Node #0,2,2: 55:[56, 9] Operation: 23-14=9 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 55:[56, 9], Operations: ['63-7=56', '23-14=9'] Exploring Operation: 56+9=65, Resulting Numbers: [65] 65,55 unequal: No Solution Exploring Operation: 56*9=504, Resulting Numbers: [504] 504,55 unequal: No Solution Exploring Operation: 56-9=47, Resulting Numbers: [47] 47,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 55:[23, 4], Operations: ['63-7=56', '56/14=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,55 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,55 unequal: No Solution Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 55:[56, 37], Operations: ['63-7=56', '14+23=37'] Exploring Operation: 56*37=2072, Resulting Numbers: [2072] 2072,55 unequal: No Solution Exploring Operation: 56-37=19, Resulting Numbers: [19] 19,55 unequal: No Solution Exploring Operation: 56+37=93, Resulting Numbers: [93] 93,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 80, 53, 35, 2 ]
61
[ "80-35=45", "53*2=106", "106-45=61" ]
Current State: 61:[80, 53, 35, 2], Operations: [] Exploring Operation: 80-35=45, Resulting Numbers: [53, 2, 45] Generated Node #2: [53, 2, 45] from Operation: 80-35=45 Current State: 61:[53, 2, 45], Operations: ['80-35=45'] Exploring Operation: 53*2=106, Resulting Numbers: [45, 106] Generated Node #3: [45, 106] from Operation: 53*2=106 Current State: 61:[45, 106], Operations: ['80-35=45', '53*2=106'] Exploring Operation: 106-45=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[80, 53, 35, 2], Operations: [] Exploring Operation: 53+2=55, Resulting Numbers: [80, 35, 55] Generated Node #0,0: 61:[80, 35, 55] Operation: 53+2=55 Exploring Operation: 35+2=37, Resulting Numbers: [80, 53, 37] Generated Node #0,1: 61:[80, 53, 37] Operation: 35+2=37 Exploring Operation: 80-2=78, Resulting Numbers: [53, 35, 78] Generated Node #0,2: 61:[53, 35, 78] Operation: 80-2=78 Exploring Operation: 35*2=70, Resulting Numbers: [80, 53, 70] Generated Node #0,3: 61:[80, 53, 70] Operation: 35*2=70 Exploring Operation: 80+2=82, Resulting Numbers: [53, 35, 82] Generated Node #0,4: 61:[53, 35, 82] Operation: 80+2=82 Start Sub Search at level 1: Moving to Node #0,3 Current State: 61:[80, 53, 70], Operations: ['35*2=70'] Exploring Operation: 80-53=27, Resulting Numbers: [70, 27] Generated Node #0,3,0: 61:[70, 27] Operation: 80-53=27 Exploring Operation: 80-70=10, Resulting Numbers: [53, 10] Generated Node #0,3,1: 61:[53, 10] Operation: 80-70=10 Exploring Operation: 70-53=17, Resulting Numbers: [80, 17] Generated Node #0,3,2: 61:[80, 17] Operation: 70-53=17 Exploring Operation: 53+70=123, Resulting Numbers: [80, 123] Generated Node #0,3,3: 61:[80, 123] Operation: 53+70=123 Exploring Operation: 80+53=133, Resulting Numbers: [70, 133] Generated Node #0,3,4: 61:[70, 133] Operation: 80+53=133 Moving to Node #0,3,0 Current State: 61:[70, 27], Operations: ['35*2=70', '80-53=27'] Exploring Operation: 70+27=97, Resulting Numbers: [97] 97,61 unequal: No Solution Exploring Operation: 70-27=43, Resulting Numbers: [43] 43,61 unequal: No Solution Exploring Operation: 70*27=1890, Resulting Numbers: [1890] 1890,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[53, 10], Operations: ['35*2=70', '80-70=10'] Exploring Operation: 53-10=43, Resulting Numbers: [43] 43,61 unequal: No Solution Exploring Operation: 53+10=63, Resulting Numbers: [63] 63,61 unequal: No Solution Exploring Operation: 53*10=530, Resulting Numbers: [530] 530,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[80, 17], Operations: ['35*2=70', '70-53=17'] Exploring Operation: 80+17=97, Resulting Numbers: [97] 97,61 unequal: No Solution Exploring Operation: 80-17=63, Resulting Numbers: [63] 63,61 unequal: No Solution Exploring Operation: 80*17=1360, Resulting Numbers: [1360] 1360,61 unequal: No Solution Moving to Node #0,3,3 Current State: 61:[80, 123], Operations: ['35*2=70', '53+70=123'] Exploring Operation: 80*123=9840, Resulting Numbers: [9840] 9840,61 unequal: No Solution Exploring Operation: 80+123=203, Resulting Numbers: [203] 203,61 unequal: No Solution Exploring Operation: 123-80=43, Resulting Numbers: [43] 43,61 unequal: No Solution Moving to Node #0,3,4 Current State: 61:[70, 133], Operations: ['35*2=70', '80+53=133'] Exploring Operation: 133-70=63, Resulting Numbers: [63] 63,61 unequal: No Solution Exploring Operation: 70*133=9310, Resulting Numbers: [9310] 9310,61 unequal: No Solution Exploring Operation: 70+133=203, Resulting Numbers: [203] 203,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[80, 35, 55], Operations: ['53+2=55'] Exploring Operation: 80-55=25, Resulting Numbers: [35, 25] Generated Node #0,0,0: 61:[35, 25] Operation: 80-55=25 Exploring Operation: 35+55=90, Resulting Numbers: [80, 90] Generated Node #0,0,1: 61:[80, 90] Operation: 35+55=90 Exploring Operation: 80-35=45, Resulting Numbers: [55, 45] Generated Node #0,0,2: 61:[55, 45] Operation: 80-35=45 Exploring Operation: 80+35=115, Resulting Numbers: [55, 115] Generated Node #0,0,3: 61:[55, 115] Operation: 80+35=115 Exploring Operation: 55-35=20, Resulting Numbers: [80, 20] Generated Node #0,0,4: 61:[80, 20] Operation: 55-35=20 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 61:[55, 45], Operations: ['53+2=55', '80-35=45'] Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,61 unequal: No Solution Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 61:[80, 90], Operations: ['53+2=55', '35+55=90'] Exploring Operation: 80*90=7200, Resulting Numbers: [7200] 7200,61 unequal: No Solution Exploring Operation: 90-80=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 80+90=170, Resulting Numbers: [170] 170,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 61:[55, 115], Operations: ['53+2=55', '80+35=115'] Exploring Operation: 115-55=60, Resulting Numbers: [60] 60,61 unequal: No Solution Exploring Operation: 55*115=6325, Resulting Numbers: [6325] 6325,61 unequal: No Solution Exploring Operation: 55+115=170, Resulting Numbers: [170] 170,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 61:[80, 20], Operations: ['53+2=55', '55-35=20'] Exploring Operation: 80-20=60, Resulting Numbers: [60] 60,61 unequal: No Solution Exploring Operation: 80*20=1600, Resulting Numbers: [1600] 1600,61 unequal: No Solution Exploring Operation: 80/20=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 80+20=100, Resulting Numbers: [100] 100,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[35, 25], Operations: ['53+2=55', '80-55=25'] Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,61 unequal: No Solution Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,61 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[80, 53, 37], Operations: ['35+2=37'] Exploring Operation: 80-37=43, Resulting Numbers: [53, 43] Generated Node #0,1,0: 61:[53, 43] Operation: 80-37=43 Exploring Operation: 53+37=90, Resulting Numbers: [80, 90] Generated Node #0,1,1: 61:[80, 90] Operation: 53+37=90 Exploring Operation: 80-53=27, Resulting Numbers: [37, 27] Generated Node #0,1,2: 61:[37, 27] Operation: 80-53=27 Exploring Operation: 53-37=16, Resulting Numbers: [80, 16] Generated Node #0,1,3: 61:[80, 16] Operation: 53-37=16 Exploring Operation: 80+37=117, Resulting Numbers: [53, 117] Generated Node #0,1,4: 61:[53, 117] Operation: 80+37=117 Moving to Node #0,1,0 Current State: 61:[53, 43], Operations: ['35+2=37', '80-37=43'] Exploring Operation: 53+43=96, Resulting Numbers: [96] 96,61 unequal: No Solution Exploring Operation: 53*43=2279, Resulting Numbers: [2279] 2279,61 unequal: No Solution Exploring Operation: 53-43=10, Resulting Numbers: [10] 10,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[80, 90], Operations: ['35+2=37', '53+37=90'] Exploring Operation: 80*90=7200, Resulting Numbers: [7200] 7200,61 unequal: No Solution Exploring Operation: 80+90=170, Resulting Numbers: [170] 170,61 unequal: No Solution Exploring Operation: 90-80=10, Resulting Numbers: [10] 10,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[37, 27], Operations: ['35+2=37', '80-53=27'] Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 37*27=999, Resulting Numbers: [999] 999,61 unequal: No Solution Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[80, 16], Operations: ['35+2=37', '53-37=16'] Exploring Operation: 80/16=5, Resulting Numbers: [5] 5,61 unequal: No Solution Exploring Operation: 80+16=96, Resulting Numbers: [96] 96,61 unequal: No Solution Exploring Operation: 80-16=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 80*16=1280, Resulting Numbers: [1280] 1280,61 unequal: No Solution Moving to Node #0,1,4 Current State: 61:[53, 117], Operations: ['35+2=37', '80+37=117'] Exploring Operation: 53+117=170, Resulting Numbers: [170] 170,61 unequal: No Solution Exploring Operation: 53*117=6201, Resulting Numbers: [6201] 6201,61 unequal: No Solution Exploring Operation: 117-53=64, Resulting Numbers: [64] 64,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[53, 35, 78], Operations: ['80-2=78'] Exploring Operation: 78-35=43, Resulting Numbers: [53, 43] Generated Node #0,2,0: 61:[53, 43] Operation: 78-35=43 Exploring Operation: 53-35=18, Resulting Numbers: [78, 18] Generated Node #0,2,1: 61:[78, 18] Operation: 53-35=18 Exploring Operation: 78-53=25, Resulting Numbers: [35, 25] Generated Node #0,2,2: 61:[35, 25] Operation: 78-53=25 Exploring Operation: 53+35=88, Resulting Numbers: [78, 88] Generated Node #0,2,3: 61:[78, 88] Operation: 53+35=88 Exploring Operation: 35+78=113, Resulting Numbers: [53, 113] Generated Node #0,2,4: 61:[53, 113] Operation: 35+78=113 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 61:[53, 43], Operations: ['80-2=78', '78-35=43'] Exploring Operation: 53-43=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 53+43=96, Resulting Numbers: [96] 96,61 unequal: No Solution Exploring Operation: 53*43=2279, Resulting Numbers: [2279] 2279,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 61:[78, 88], Operations: ['80-2=78', '53+35=88'] Exploring Operation: 88-78=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 78*88=6864, Resulting Numbers: [6864] 6864,61 unequal: No Solution Exploring Operation: 78+88=166, Resulting Numbers: [166] 166,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 61:[78, 18], Operations: ['80-2=78', '53-35=18'] Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,61 unequal: No Solution Exploring Operation: 78+18=96, Resulting Numbers: [96] 96,61 unequal: No Solution Exploring Operation: 78*18=1404, Resulting Numbers: [1404] 1404,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 61:[53, 113], Operations: ['80-2=78', '35+78=113'] Exploring Operation: 53+113=166, Resulting Numbers: [166] 166,61 unequal: No Solution Exploring Operation: 53*113=5989, Resulting Numbers: [5989] 5989,61 unequal: No Solution Exploring Operation: 113-53=60, Resulting Numbers: [60] 60,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 61:[35, 25], Operations: ['80-2=78', '78-53=25'] Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,61 unequal: No Solution Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,61 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 61:[53, 35, 82], Operations: ['80+2=82'] Exploring Operation: 35+82=117, Resulting Numbers: [53, 117] Generated Node #0,4,0: 61:[53, 117] Operation: 35+82=117 Exploring Operation: 82-53=29, Resulting Numbers: [35, 29] Generated Node #0,4,1: 61:[35, 29] Operation: 82-53=29 Exploring Operation: 53-35=18, Resulting Numbers: [82, 18] Generated Node #0,4,2: 61:[82, 18] Operation: 53-35=18 Exploring Operation: 53+35=88, Resulting Numbers: [82, 88] Generated Node #0,4,3: 61:[82, 88] Operation: 53+35=88 Exploring Operation: 82-35=47, Resulting Numbers: [53, 47] Generated Node #0,4,4: 61:[53, 47] Operation: 82-35=47 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 61:[53, 47], Operations: ['80+2=82', '82-35=47'] Exploring Operation: 53*47=2491, Resulting Numbers: [2491] 2491,61 unequal: No Solution Exploring Operation: 53+47=100, Resulting Numbers: [100] 100,61 unequal: No Solution Exploring Operation: 53-47=6, Resulting Numbers: [6] 6,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 61:[82, 88], Operations: ['80+2=82', '53+35=88'] Exploring Operation: 82*88=7216, Resulting Numbers: [7216] 7216,61 unequal: No Solution Exploring Operation: 88-82=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 82+88=170, Resulting Numbers: [170] 170,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 61:[35, 29], Operations: ['80+2=82', '82-53=29'] Exploring Operation: 35*29=1015, Resulting Numbers: [1015] 1015,61 unequal: No Solution Exploring Operation: 35+29=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 61:[53, 117], Operations: ['80+2=82', '35+82=117'] Exploring Operation: 117-53=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 53*117=6201, Resulting Numbers: [6201] 6201,61 unequal: No Solution Exploring Operation: 53+117=170, Resulting Numbers: [170] 170,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 61:[82, 18], Operations: ['80+2=82', '53-35=18'] Exploring Operation: 82-18=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 82+18=100, Resulting Numbers: [100] 100,61 unequal: No Solution Exploring Operation: 82*18=1476, Resulting Numbers: [1476] 1476,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 16, 76, 44, 66 ]
18
[ "16+76=92", "44+66=110", "110-92=18" ]
Current State: 18:[16, 76, 44, 66], Operations: [] Exploring Operation: 16+76=92, Resulting Numbers: [44, 66, 92] Generated Node #2: [44, 66, 92] from Operation: 16+76=92 Current State: 18:[44, 66, 92], Operations: ['16+76=92'] Exploring Operation: 44+66=110, Resulting Numbers: [92, 110] Generated Node #3: [92, 110] from Operation: 44+66=110 Current State: 18:[92, 110], Operations: ['16+76=92', '44+66=110'] Exploring Operation: 110-92=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[16, 76, 44, 66], Operations: [] Exploring Operation: 76-66=10, Resulting Numbers: [16, 44, 10] Generated Node #0,0: 18:[16, 44, 10] Operation: 76-66=10 Exploring Operation: 76-44=32, Resulting Numbers: [16, 66, 32] Generated Node #0,1: 18:[16, 66, 32] Operation: 76-44=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[16, 44, 10], Operations: ['76-66=10'] Exploring Operation: 44-10=34, Resulting Numbers: [16, 34] Generated Node #0,0,0: 18:[16, 34] Operation: 44-10=34 Exploring Operation: 44-16=28, Resulting Numbers: [10, 28] Generated Node #0,0,1: 18:[10, 28] Operation: 44-16=28 Moving to Node #0,0,1 Current State: 18:[10, 28], Operations: ['76-66=10', '44-16=28'] Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[16, 76, 44, 66], Operations: [] Exploring Operation: 76-66=10, Resulting Numbers: [16, 44, 10] Generated Node #0,0: 18:[16, 44, 10] Operation: 76-66=10 Moving to Node #0,0 Current State: 18:[16, 44, 10], Operations: ['76-66=10'] Exploring Operation: 44-16=28, Resulting Numbers: [10, 28] Generated Node #0,0,1: 18:[10, 28] Operation: 44-16=28 Moving to Node #0,0,1 Current State: 18:[10, 28], Operations: ['76-66=10', '44-16=28'] Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 38, 3, 7, 5 ]
98
[ "38-7=31", "3*31=93", "5+93=98" ]
Current State: 98:[38, 3, 7, 5], Operations: [] Exploring Operation: 38-7=31, Resulting Numbers: [3, 5, 31] Generated Node #2: [3, 5, 31] from Operation: 38-7=31 Current State: 98:[3, 5, 31], Operations: ['38-7=31'] Exploring Operation: 3*31=93, Resulting Numbers: [5, 93] Generated Node #3: [5, 93] from Operation: 3*31=93 Current State: 98:[5, 93], Operations: ['38-7=31', '3*31=93'] Exploring Operation: 5+93=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[38, 3, 7, 5], Operations: [] Exploring Operation: 38+7=45, Resulting Numbers: [3, 5, 45] Generated Node #0,0: 98:[3, 5, 45] Operation: 38+7=45 Moving to Node #0,0 Current State: 98:[3, 5, 45], Operations: ['38+7=45'] Exploring Operation: 5+45=50, Resulting Numbers: [3, 50] Generated Node #0,0,0: 98:[3, 50] Operation: 5+45=50 Moving to Node #0,0,0 Current State: 98:[3, 50], Operations: ['38+7=45', '5+45=50'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,98 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 62, 68, 7, 34 ]
67
[ "62+7=69", "68/34=2", "69-2=67" ]
Current State: 67:[62, 68, 7, 34], Operations: [] Exploring Operation: 62+7=69, Resulting Numbers: [68, 34, 69] Generated Node #2: [68, 34, 69] from Operation: 62+7=69 Current State: 67:[68, 34, 69], Operations: ['62+7=69'] Exploring Operation: 68/34=2, Resulting Numbers: [69, 2] Generated Node #3: [69, 2] from Operation: 68/34=2 Current State: 67:[69, 2], Operations: ['62+7=69', '68/34=2'] Exploring Operation: 69-2=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[62, 68, 7, 34], Operations: [] Exploring Operation: 7+34=41, Resulting Numbers: [62, 68, 41] Generated Node #0,0: 67:[62, 68, 41] Operation: 7+34=41 Exploring Operation: 62+7=69, Resulting Numbers: [68, 34, 69] Generated Node #0,1: 67:[68, 34, 69] Operation: 62+7=69 Exploring Operation: 68-7=61, Resulting Numbers: [62, 34, 61] Generated Node #0,2: 67:[62, 34, 61] Operation: 68-7=61 Moving to Node #0,0 Current State: 67:[62, 68, 41], Operations: ['7+34=41'] Exploring Operation: 68-41=27, Resulting Numbers: [62, 27] Generated Node #0,0,0: 67:[62, 27] Operation: 68-41=27 Exploring Operation: 62+41=103, Resulting Numbers: [68, 103] Generated Node #0,0,1: 67:[68, 103] Operation: 62+41=103 Exploring Operation: 62-41=21, Resulting Numbers: [68, 21] Generated Node #0,0,2: 67:[68, 21] Operation: 62-41=21 Moving to Node #0,1 Current State: 67:[68, 34, 69], Operations: ['62+7=69'] Exploring Operation: 69-34=35, Resulting Numbers: [68, 35] Generated Node #0,1,0: 67:[68, 35] Operation: 69-34=35 Exploring Operation: 68-34=34, Resulting Numbers: [69, 34] Generated Node #0,1,1: 67:[69, 34] Operation: 68-34=34 Exploring Operation: 68+34=102, Resulting Numbers: [69, 102] Generated Node #0,1,2: 67:[69, 102] Operation: 68+34=102 Moving to Node #0,2 Current State: 67:[62, 34, 61], Operations: ['68-7=61'] Exploring Operation: 62-34=28, Resulting Numbers: [61, 28] Generated Node #0,2,0: 67:[61, 28] Operation: 62-34=28 Exploring Operation: 34+61=95, Resulting Numbers: [62, 95] Generated Node #0,2,1: 67:[62, 95] Operation: 34+61=95 Exploring Operation: 62+34=96, Resulting Numbers: [61, 96] Generated Node #0,2,2: 67:[61, 96] Operation: 62+34=96 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[62, 95], Operations: ['68-7=61', '34+61=95'] Exploring Operation: 62+95=157, Resulting Numbers: [157] 157,67 unequal: No Solution Exploring Operation: 62*95=5890, Resulting Numbers: [5890] 5890,67 unequal: No Solution Exploring Operation: 95-62=33, Resulting Numbers: [33] 33,67 unequal: No Solution No 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: 67:[61, 96], Operations: ['68-7=61', '62+34=96'] Exploring Operation: 61+96=157, Resulting Numbers: [157] 157,67 unequal: No Solution Exploring Operation: 96-61=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 61*96=5856, Resulting Numbers: [5856] 5856,67 unequal: No Solution No 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: 67:[61, 28], Operations: ['68-7=61', '62-34=28'] Exploring Operation: 61-28=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 61*28=1708, Resulting Numbers: [1708] 1708,67 unequal: No Solution Exploring Operation: 61+28=89, Resulting Numbers: [89] 89,67 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: 67:[68, 35], Operations: ['62+7=69', '69-34=35'] Exploring Operation: 68*35=2380, Resulting Numbers: [2380] 2380,67 unequal: No Solution Exploring Operation: 68-35=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 68+35=103, Resulting Numbers: [103] 103,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[69, 34], Operations: ['62+7=69', '68-34=34'] Exploring Operation: 69-34=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 69+34=103, Resulting Numbers: [103] 103,67 unequal: No Solution Exploring Operation: 69*34=2346, Resulting Numbers: [2346] 2346,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[69, 102], Operations: ['62+7=69', '68+34=102'] Exploring Operation: 102-69=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 69+102=171, Resulting Numbers: [171] 171,67 unequal: No Solution Exploring Operation: 69*102=7038, Resulting Numbers: [7038] 7038,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[68, 103], Operations: ['7+34=41', '62+41=103'] Exploring Operation: 68+103=171, Resulting Numbers: [171] 171,67 unequal: No Solution Exploring Operation: 103-68=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 68*103=7004, Resulting Numbers: [7004] 7004,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[62, 27], Operations: ['7+34=41', '68-41=27'] Exploring Operation: 62-27=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 62*27=1674, Resulting Numbers: [1674] 1674,67 unequal: No Solution Exploring Operation: 62+27=89, Resulting Numbers: [89] 89,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[68, 21], Operations: ['7+34=41', '62-41=21'] Exploring Operation: 68-21=47, Resulting Numbers: [47] 47,67 unequal: No Solution Exploring Operation: 68+21=89, Resulting Numbers: [89] 89,67 unequal: No Solution Exploring Operation: 68*21=1428, Resulting Numbers: [1428] 1428,67 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 14, 15, 51, 43 ]
93
[ "15-14=1", "51+43=94", "94-1=93" ]
Current State: 93:[14, 15, 51, 43], Operations: [] Exploring Operation: 15-14=1, Resulting Numbers: [51, 43, 1] Generated Node #2: [51, 43, 1] from Operation: 15-14=1 Current State: 93:[51, 43, 1], Operations: ['15-14=1'] Exploring Operation: 51+43=94, Resulting Numbers: [1, 94] Generated Node #3: [1, 94] from Operation: 51+43=94 Current State: 93:[1, 94], Operations: ['15-14=1', '51+43=94'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[14, 15, 51, 43], Operations: [] Exploring Operation: 51+43=94, Resulting Numbers: [14, 15, 94] Generated Node #0,0: 93:[14, 15, 94] Operation: 51+43=94 Exploring Operation: 51-15=36, Resulting Numbers: [14, 43, 36] Generated Node #0,1: 93:[14, 43, 36] Operation: 51-15=36 Moving to Node #0,0 Current State: 93:[14, 15, 94], Operations: ['51+43=94'] Exploring Operation: 14+15=29, Resulting Numbers: [94, 29] Generated Node #0,0,0: 93:[94, 29] Operation: 14+15=29 Exploring Operation: 15-14=1, Resulting Numbers: [94, 1] Generated Node #0,0,1: 93:[94, 1] Operation: 15-14=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[94, 29], Operations: ['51+43=94', '14+15=29'] Exploring Operation: 94+29=123, Resulting Numbers: [123] 123,93 unequal: No Solution Exploring Operation: 94-29=65, Resulting Numbers: [65] 65,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 93:[94, 1], Operations: ['51+43=94', '15-14=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[14, 15, 51, 43], Operations: [] Exploring Operation: 51+43=94, Resulting Numbers: [14, 15, 94] Generated Node #0,0: 93:[14, 15, 94] Operation: 51+43=94 Moving to Node #0,0 Current State: 93:[14, 15, 94], Operations: ['51+43=94'] Exploring Operation: 15-14=1, Resulting Numbers: [94, 1] Generated Node #0,0,1: 93:[94, 1] Operation: 15-14=1 Moving to Node #0,0,1 Current State: 93:[94, 1], Operations: ['51+43=94', '15-14=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 90, 95, 97, 50 ]
42
[ "95-90=5", "97-50=47", "47-5=42" ]
Current State: 42:[90, 95, 97, 50], Operations: [] Exploring Operation: 95-90=5, Resulting Numbers: [97, 50, 5] Generated Node #2: [97, 50, 5] from Operation: 95-90=5 Current State: 42:[97, 50, 5], Operations: ['95-90=5'] Exploring Operation: 97-50=47, Resulting Numbers: [5, 47] Generated Node #3: [5, 47] from Operation: 97-50=47 Current State: 42:[5, 47], Operations: ['95-90=5', '97-50=47'] Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[90, 95, 97, 50], Operations: [] Exploring Operation: 95-90=5, Resulting Numbers: [97, 50, 5] Generated Node #0,0: 42:[97, 50, 5] Operation: 95-90=5 Exploring Operation: 97-95=2, Resulting Numbers: [90, 50, 2] Generated Node #0,1: 42:[90, 50, 2] Operation: 97-95=2 Exploring Operation: 95-50=45, Resulting Numbers: [90, 97, 45] Generated Node #0,2: 42:[90, 97, 45] Operation: 95-50=45 Exploring Operation: 97-90=7, Resulting Numbers: [95, 50, 7] Generated Node #0,3: 42:[95, 50, 7] Operation: 97-90=7 Exploring Operation: 97-50=47, Resulting Numbers: [90, 95, 47] Generated Node #0,4: 42:[90, 95, 47] Operation: 97-50=47 Moving to Node #0,1 Current State: 42:[90, 50, 2], Operations: ['97-95=2'] Exploring Operation: 90-2=88, Resulting Numbers: [50, 88] Generated Node #0,1,0: 42:[50, 88] Operation: 90-2=88 Exploring Operation: 50/2=25, Resulting Numbers: [90, 25] Generated Node #0,1,1: 42:[90, 25] Operation: 50/2=25 Exploring Operation: 90/2=45, Resulting Numbers: [50, 45] Generated Node #0,1,2: 42:[50, 45] Operation: 90/2=45 Exploring Operation: 90-50=40, Resulting Numbers: [2, 40] Generated Node #0,1,3: 42:[2, 40] Operation: 90-50=40 Exploring Operation: 50-2=48, Resulting Numbers: [90, 48] Generated Node #0,1,4: 42:[90, 48] Operation: 50-2=48 Moving to Node #0,3 Current State: 42:[95, 50, 7], Operations: ['97-90=7'] Exploring Operation: 50+7=57, Resulting Numbers: [95, 57] Generated Node #0,3,0: 42:[95, 57] Operation: 50+7=57 Exploring Operation: 95-50=45, Resulting Numbers: [7, 45] Generated Node #0,3,1: 42:[7, 45] Operation: 95-50=45 Exploring Operation: 95-7=88, Resulting Numbers: [50, 88] Generated Node #0,3,2: 42:[50, 88] Operation: 95-7=88 Exploring Operation: 95+7=102, Resulting Numbers: [50, 102] Generated Node #0,3,3: 42:[50, 102] Operation: 95+7=102 Exploring Operation: 50-7=43, Resulting Numbers: [95, 43] Generated Node #0,3,4: 42:[95, 43] Operation: 50-7=43 Moving to Node #0,0 Current State: 42:[97, 50, 5], Operations: ['95-90=5'] Exploring Operation: 97-50=47, Resulting Numbers: [5, 47] Generated Node #0,0,0: 42:[5, 47] Operation: 97-50=47 Exploring Operation: 50-5=45, Resulting Numbers: [97, 45] Generated Node #0,0,1: 42:[97, 45] Operation: 50-5=45 Exploring Operation: 97-5=92, Resulting Numbers: [50, 92] Generated Node #0,0,2: 42:[50, 92] Operation: 97-5=92 Exploring Operation: 50/5=10, Resulting Numbers: [97, 10] Generated Node #0,0,3: 42:[97, 10] Operation: 50/5=10 Exploring Operation: 97+5=102, Resulting Numbers: [50, 102] Generated Node #0,0,4: 42:[50, 102] Operation: 97+5=102 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[5, 47], Operations: ['95-90=5', '97-50=47'] Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[90, 95, 97, 50], Operations: [] Exploring Operation: 95-90=5, Resulting Numbers: [97, 50, 5] Generated Node #0,0: 42:[97, 50, 5] Operation: 95-90=5 Moving to Node #0,0 Current State: 42:[97, 50, 5], Operations: ['95-90=5'] Exploring Operation: 97-50=47, Resulting Numbers: [5, 47] Generated Node #0,0,0: 42:[5, 47] Operation: 97-50=47 Moving to Node #0,0,0 Current State: 42:[5, 47], Operations: ['95-90=5', '97-50=47'] Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_5
mult_heuristic
[ 24, 42, 30, 8 ]
10
[ "42-30=12", "24/12=2", "8+2=10" ]
Current State: 10:[24, 42, 30, 8], Operations: [] Exploring Operation: 42-30=12, Resulting Numbers: [24, 8, 12] Generated Node #2: [24, 8, 12] from Operation: 42-30=12 Current State: 10:[24, 8, 12], Operations: ['42-30=12'] Exploring Operation: 24/12=2, Resulting Numbers: [8, 2] Generated Node #3: [8, 2] from Operation: 24/12=2 Current State: 10:[8, 2], Operations: ['42-30=12', '24/12=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[24, 42, 30, 8], Operations: [] Exploring Operation: 42-24=18, Resulting Numbers: [30, 8, 18] Generated Node #0,0: 10:[30, 8, 18] Operation: 42-24=18 Exploring Operation: 30-24=6, Resulting Numbers: [42, 8, 6] Generated Node #0,1: 10:[42, 8, 6] Operation: 30-24=6 Exploring Operation: 42-30=12, Resulting Numbers: [24, 8, 12] Generated Node #0,2: 10:[24, 8, 12] Operation: 42-30=12 Exploring Operation: 24/8=3, Resulting Numbers: [42, 30, 3] Generated Node #0,3: 10:[42, 30, 3] Operation: 24/8=3 Moving to Node #0,2 Current State: 10:[24, 8, 12], Operations: ['42-30=12'] Exploring Operation: 24/12=2, Resulting Numbers: [8, 2] Generated Node #0,2,0: 10:[8, 2] Operation: 24/12=2 Exploring Operation: 24-8=16, Resulting Numbers: [12, 16] Generated Node #0,2,1: 10:[12, 16] Operation: 24-8=16 Exploring Operation: 24-12=12, Resulting Numbers: [8, 12] Generated Node #0,2,2: 10:[8, 12] Operation: 24-12=12 Exploring Operation: 24/8=3, Resulting Numbers: [12, 3] Generated Node #0,2,3: 10:[12, 3] Operation: 24/8=3 Moving to Node #0,0 Current State: 10:[30, 8, 18], Operations: ['42-24=18'] Exploring Operation: 18-8=10, Resulting Numbers: [30, 10] Generated Node #0,0,0: 10:[30, 10] Operation: 18-8=10 Exploring Operation: 30-8=22, Resulting Numbers: [18, 22] Generated Node #0,0,1: 10:[18, 22] Operation: 30-8=22 Exploring Operation: 30+8=38, Resulting Numbers: [18, 38] Generated Node #0,0,2: 10:[18, 38] Operation: 30+8=38 Exploring Operation: 30-18=12, Resulting Numbers: [8, 12] Generated Node #0,0,3: 10:[8, 12] Operation: 30-18=12 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 10:[8, 12], Operations: ['42-24=18', '30-18=12'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 8+12=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 8*12=96, Resulting Numbers: [96] 96,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[30, 10], Operations: ['42-24=18', '18-8=10'] Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 30*10=300, Resulting Numbers: [300] 300,10 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,10 unequal: No Solution Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 10:[18, 22], Operations: ['42-24=18', '30-8=22'] Exploring Operation: 18*22=396, Resulting Numbers: [396] 396,10 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 10:[18, 38], Operations: ['42-24=18', '30+8=38'] Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,10 unequal: No Solution Exploring Operation: 18*38=684, Resulting Numbers: [684] 684,10 unequal: No Solution Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,10 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: 10:[42, 8, 6], Operations: ['30-24=6'] Exploring Operation: 42-8=34, Resulting Numbers: [6, 34] Generated Node #0,1,0: 10:[6, 34] Operation: 42-8=34 Exploring Operation: 8-6=2, Resulting Numbers: [42, 2] Generated Node #0,1,1: 10:[42, 2] Operation: 8-6=2 Exploring Operation: 42/6=7, Resulting Numbers: [8, 7] Generated Node #0,1,2: 10:[8, 7] Operation: 42/6=7 Exploring Operation: 42-6=36, Resulting Numbers: [8, 36] Generated Node #0,1,3: 10:[8, 36] Operation: 42-6=36 Moving to Node #0,3 Current State: 10:[42, 30, 3], Operations: ['24/8=3'] Exploring Operation: 42/3=14, Resulting Numbers: [30, 14] Generated Node #0,3,0: 10:[30, 14] Operation: 42/3=14 Exploring Operation: 30/3=10, Resulting Numbers: [42, 10] Generated Node #0,3,1: 10:[42, 10] Operation: 30/3=10 Exploring Operation: 42-3=39, Resulting Numbers: [30, 39] Generated Node #0,3,2: 10:[30, 39] Operation: 42-3=39 Exploring Operation: 42-30=12, Resulting Numbers: [3, 12] Generated Node #0,3,3: 10:[3, 12] Operation: 42-30=12 Moving to Node #0,2,0 Current State: 10:[8, 2], Operations: ['42-30=12', '24/12=2'] Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,10 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[24, 42, 30, 8], Operations: [] Exploring Operation: 42-30=12, Resulting Numbers: [24, 8, 12] Generated Node #0,2: 10:[24, 8, 12] Operation: 42-30=12 Moving to Node #0,2 Current State: 10:[24, 8, 12], Operations: ['42-30=12'] Exploring Operation: 24/12=2, Resulting Numbers: [8, 2] Generated Node #0,2,0: 10:[8, 2] Operation: 24/12=2 Moving to Node #0,2,0 Current State: 10:[8, 2], Operations: ['42-30=12', '24/12=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.965278
hs_4
mult_heuristic
[ 68, 11, 15, 70 ]
28
[ "68-11=57", "15+70=85", "85-57=28" ]
Current State: 28:[68, 11, 15, 70], Operations: [] Exploring Operation: 68-11=57, Resulting Numbers: [15, 70, 57] Generated Node #2: [15, 70, 57] from Operation: 68-11=57 Current State: 28:[15, 70, 57], Operations: ['68-11=57'] Exploring Operation: 15+70=85, Resulting Numbers: [57, 85] Generated Node #3: [57, 85] from Operation: 15+70=85 Current State: 28:[57, 85], Operations: ['68-11=57', '15+70=85'] Exploring Operation: 85-57=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[68, 11, 15, 70], Operations: [] Exploring Operation: 70-68=2, Resulting Numbers: [11, 15, 2] Generated Node #0,0: 28:[11, 15, 2] Operation: 70-68=2 Exploring Operation: 68-15=53, Resulting Numbers: [11, 70, 53] Generated Node #0,1: 28:[11, 70, 53] Operation: 68-15=53 Moving to Node #0,0 Current State: 28:[11, 15, 2], Operations: ['70-68=2'] Exploring Operation: 11+15=26, Resulting Numbers: [2, 26] Generated Node #0,0,0: 28:[2, 26] Operation: 11+15=26 Exploring Operation: 15-11=4, Resulting Numbers: [2, 4] Generated Node #0,0,1: 28:[2, 4] Operation: 15-11=4 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 28:[2, 4], Operations: ['70-68=2', '15-11=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,28 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 #0,0,0 Current State: 28:[2, 26], Operations: ['70-68=2', '11+15=26'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,28 unequal: No Solution Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[68, 11, 15, 70], Operations: [] Exploring Operation: 70-68=2, Resulting Numbers: [11, 15, 2] Generated Node #0,0: 28:[11, 15, 2] Operation: 70-68=2 Moving to Node #0,0 Current State: 28:[11, 15, 2], Operations: ['70-68=2'] Exploring Operation: 11+15=26, Resulting Numbers: [2, 26] Generated Node #0,0,0: 28:[2, 26] Operation: 11+15=26 Moving to Node #0,0,0 Current State: 28:[2, 26], Operations: ['70-68=2', '11+15=26'] Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 99, 2, 1, 99 ]
98
[ "99*2=198", "1+99=100", "198-100=98" ]
Current State: 98:[99, 2, 1, 99], Operations: [] Exploring Operation: 99*2=198, Resulting Numbers: [1, 198] Generated Node #2: [1, 198] from Operation: 99*2=198 Current State: 98:[1, 198], Operations: ['99*2=198'] Exploring Operation: 1+99=100, Resulting Numbers: [198, 100] Generated Node #3: [198, 100] from Operation: 1+99=100 Current State: 98:[198, 100], Operations: ['99*2=198', '1+99=100'] Exploring Operation: 198-100=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[99, 2, 1, 99], Operations: [] Exploring Operation: 99-1=98, Resulting Numbers: [99, 2, 98] Generated Node #0,0: 98:[99, 2, 98] Operation: 99-1=98 Exploring Operation: 99*1=99, Resulting Numbers: [2, 99, 99] Generated Node #0,1: 98:[2, 99, 99] Operation: 99*1=99 Exploring Operation: 99-1=98, Resulting Numbers: [2, 99, 98] Generated Node #0,2: 98:[2, 99, 98] Operation: 99-1=98 Exploring Operation: 99/1=99, Resulting Numbers: [2, 99, 99] Generated Node #0,3: 98:[2, 99, 99] Operation: 99/1=99 Moving to Node #0,0 Current State: 98:[99, 2, 98], Operations: ['99-1=98'] Exploring Operation: 98/2=49, Resulting Numbers: [99, 49] Generated Node #0,0,0: 98:[99, 49] Operation: 98/2=49 Exploring Operation: 99-98=1, Resulting Numbers: [2, 1] Generated Node #0,0,1: 98:[2, 1] Operation: 99-98=1 Exploring Operation: 99-2=97, Resulting Numbers: [98, 97] Generated Node #0,0,2: 98:[98, 97] Operation: 99-2=97 Exploring Operation: 99+2=101, Resulting Numbers: [98, 101] Generated Node #0,0,3: 98:[98, 101] Operation: 99+2=101 Moving to Node #0,2 Current State: 98:[2, 99, 98], Operations: ['99-1=98'] Exploring Operation: 99-2=97, Resulting Numbers: [98, 97] Generated Node #0,2,0: 98:[98, 97] Operation: 99-2=97 Exploring Operation: 99-98=1, Resulting Numbers: [2, 1] Generated Node #0,2,1: 98:[2, 1] Operation: 99-98=1 Exploring Operation: 98/2=49, Resulting Numbers: [99, 49] Generated Node #0,2,2: 98:[99, 49] Operation: 98/2=49 Exploring Operation: 2+99=101, Resulting Numbers: [98, 101] Generated Node #0,2,3: 98:[98, 101] Operation: 2+99=101 Moving to Node #0,3 Current State: 98:[2, 99, 99], Operations: ['99/1=99'] Exploring Operation: 99-2=97, Resulting Numbers: [99, 97] Generated Node #0,3,0: 98:[99, 97] Operation: 99-2=97 Exploring Operation: 99-99=0, Resulting Numbers: [2, 0] Generated Node #0,3,1: 98:[2, 0] Operation: 99-99=0 Exploring Operation: 99/99=1, Resulting Numbers: [2, 1] Generated Node #0,3,2: 98:[2, 1] Operation: 99/99=1 Exploring Operation: 99-2=97, Resulting Numbers: [99, 97] Generated Node #0,3,3: 98:[99, 97] Operation: 99-2=97 Moving to Node #0,1 Current State: 98:[2, 99, 99], Operations: ['99*1=99'] Exploring Operation: 99-2=97, Resulting Numbers: [99, 97] Generated Node #0,1,0: 98:[99, 97] Operation: 99-2=97 Exploring Operation: 99-99=0, Resulting Numbers: [2, 0] Generated Node #0,1,1: 98:[2, 0] Operation: 99-99=0 Exploring Operation: 99-2=97, Resulting Numbers: [99, 97] Generated Node #0,1,2: 98:[99, 97] Operation: 99-2=97 Exploring Operation: 99/99=1, Resulting Numbers: [2, 1] Generated Node #0,1,3: 98:[2, 1] Operation: 99/99=1 Moving to Node #0,0,0 Current State: 98:[99, 49], Operations: ['99-1=98', '98/2=49'] Exploring Operation: 99+49=148, Resulting Numbers: [148] 148,98 unequal: No Solution Exploring Operation: 99*49=4851, Resulting Numbers: [4851] 4851,98 unequal: No Solution Exploring Operation: 99-49=50, Resulting Numbers: [50] 50,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[98, 97], Operations: ['99-1=98', '99-2=97'] Exploring Operation: 98-97=1, Resulting Numbers: [1] 1,98 unequal: No Solution Exploring Operation: 98*97=9506, Resulting Numbers: [9506] 9506,98 unequal: No Solution Exploring Operation: 98+97=195, Resulting Numbers: [195] 195,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[99, 49], Operations: ['99-1=98', '98/2=49'] Exploring Operation: 99-49=50, Resulting Numbers: [50] 50,98 unequal: No Solution Exploring Operation: 99*49=4851, Resulting Numbers: [4851] 4851,98 unequal: No Solution Exploring Operation: 99+49=148, Resulting Numbers: [148] 148,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[2, 1], Operations: ['99-1=98', '99-98=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,98 unequal: No Solution Moving to Node #0,1,3 Current State: 98:[2, 1], Operations: ['99*1=99', '99/99=1'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,98 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[2, 1], Operations: ['99-1=98', '99-98=1'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,98 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,98 unequal: No Solution Moving to Node #0,2,0 Current State: 98:[98, 97], Operations: ['99-1=98', '99-2=97'] Exploring Operation: 98-97=1, Resulting Numbers: [1] 1,98 unequal: No Solution Exploring Operation: 98*97=9506, Resulting Numbers: [9506] 9506,98 unequal: No Solution Exploring Operation: 98+97=195, Resulting Numbers: [195] 195,98 unequal: No Solution Moving to Node #0,3,2 Current State: 98:[2, 1], Operations: ['99/1=99', '99/99=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[2, 0], Operations: ['99*1=99', '99-99=0'] Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,98 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,98 unequal: No Solution Moving to Node #0,3,3 Current State: 98:[99, 97], Operations: ['99/1=99', '99-2=97'] Exploring Operation: 99-97=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 99*97=9603, Resulting Numbers: [9603] 9603,98 unequal: No Solution Exploring Operation: 99+97=196, Resulting Numbers: [196] 196,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[99, 97], Operations: ['99*1=99', '99-2=97'] Exploring Operation: 99+97=196, Resulting Numbers: [196] 196,98 unequal: No Solution Exploring Operation: 99-97=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 99*97=9603, Resulting Numbers: [9603] 9603,98 unequal: No Solution Moving to Node #0,3,1 Current State: 98:[2, 0], Operations: ['99/1=99', '99-99=0'] Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,98 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,98 unequal: No Solution Moving to Node #0,3,0 Current State: 98:[99, 97], Operations: ['99/1=99', '99-2=97'] Exploring Operation: 99+97=196, Resulting Numbers: [196] 196,98 unequal: No Solution Exploring Operation: 99-97=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 99*97=9603, Resulting Numbers: [9603] 9603,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[99, 97], Operations: ['99*1=99', '99-2=97'] Exploring Operation: 99+97=196, Resulting Numbers: [196] 196,98 unequal: No Solution Exploring Operation: 99*97=9603, Resulting Numbers: [9603] 9603,98 unequal: No Solution Exploring Operation: 99-97=2, Resulting Numbers: [2] 2,98 unequal: No Solution Moving to Node #0,2,3 Current State: 98:[98, 101], Operations: ['99-1=98', '2+99=101'] Exploring Operation: 101-98=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 98*101=9898, Resulting Numbers: [9898] 9898,98 unequal: No Solution Exploring Operation: 98+101=199, Resulting Numbers: [199] 199,98 unequal: No Solution Moving to Node #0,0,3 Current State: 98:[98, 101], Operations: ['99-1=98', '99+2=101'] Exploring Operation: 101-98=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 98*101=9898, Resulting Numbers: [9898] 9898,98 unequal: No Solution Exploring Operation: 98+101=199, Resulting Numbers: [199] 199,98 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 17, 92, 47, 23 ]
21
[ "17*92=1564", "1564/23=68", "68-47=21" ]
Current State: 21:[17, 92, 47, 23], Operations: [] Exploring Operation: 17*92=1564, Resulting Numbers: [47, 23, 1564] Generated Node #2: [47, 23, 1564] from Operation: 17*92=1564 Current State: 21:[47, 23, 1564], Operations: ['17*92=1564'] Exploring Operation: 1564/23=68, Resulting Numbers: [47, 68] Generated Node #3: [47, 68] from Operation: 1564/23=68 Current State: 21:[47, 68], Operations: ['17*92=1564', '1564/23=68'] Exploring Operation: 68-47=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[17, 92, 47, 23], Operations: [] Exploring Operation: 92-47=45, Resulting Numbers: [17, 23, 45] Generated Node #0,0: 21:[17, 23, 45] Operation: 92-47=45 Exploring Operation: 92-17=75, Resulting Numbers: [47, 23, 75] Generated Node #0,1: 21:[47, 23, 75] Operation: 92-17=75 Exploring Operation: 92-23=69, Resulting Numbers: [17, 47, 69] Generated Node #0,2: 21:[17, 47, 69] Operation: 92-23=69 Exploring Operation: 47-23=24, Resulting Numbers: [17, 92, 24] Generated Node #0,3: 21:[17, 92, 24] Operation: 47-23=24 Exploring Operation: 92/23=4, Resulting Numbers: [17, 47, 4] Generated Node #0,4: 21:[17, 47, 4] Operation: 92/23=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[17, 23, 45], Operations: ['92-47=45'] Exploring Operation: 45-17=28, Resulting Numbers: [23, 28] Generated Node #0,0,0: 21:[23, 28] Operation: 45-17=28 Exploring Operation: 23-17=6, Resulting Numbers: [45, 6] Generated Node #0,0,1: 21:[45, 6] Operation: 23-17=6 Exploring Operation: 45-23=22, Resulting Numbers: [17, 22] Generated Node #0,0,2: 21:[17, 22] Operation: 45-23=22 Exploring Operation: 17+45=62, Resulting Numbers: [23, 62] Generated Node #0,0,3: 21:[23, 62] Operation: 17+45=62 Exploring Operation: 17+23=40, Resulting Numbers: [45, 40] Generated Node #0,0,4: 21:[45, 40] Operation: 17+23=40 Moving to Node #0,0,2 Current State: 21:[17, 22], Operations: ['92-47=45', '45-23=22'] Exploring Operation: 17*22=374, Resulting Numbers: [374] 374,21 unequal: No Solution Exploring Operation: 17+22=39, Resulting Numbers: [39] 39,21 unequal: No Solution Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[23, 28], Operations: ['92-47=45', '45-17=28'] Exploring Operation: 23+28=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 23*28=644, Resulting Numbers: [644] 644,21 unequal: No Solution Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[45, 6], Operations: ['92-47=45', '23-17=6'] Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,21 unequal: No Solution Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,21 unequal: No Solution Moving to Node #0,0,3 Current State: 21:[23, 62], Operations: ['92-47=45', '17+45=62'] Exploring Operation: 23*62=1426, Resulting Numbers: [1426] 1426,21 unequal: No Solution Exploring Operation: 23+62=85, Resulting Numbers: [85] 85,21 unequal: No Solution Exploring Operation: 62-23=39, Resulting Numbers: [39] 39,21 unequal: No Solution Moving to Node #0,0,4 Current State: 21:[45, 40], Operations: ['92-47=45', '17+23=40'] Exploring Operation: 45-40=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 45*40=1800, Resulting Numbers: [1800] 1800,21 unequal: No Solution Exploring Operation: 45+40=85, Resulting Numbers: [85] 85,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 21:[17, 47, 4], Operations: ['92/23=4'] Exploring Operation: 47+4=51, Resulting Numbers: [17, 51] Generated Node #0,4,0: 21:[17, 51] Operation: 47+4=51 Exploring Operation: 17-4=13, Resulting Numbers: [47, 13] Generated Node #0,4,1: 21:[47, 13] Operation: 17-4=13 Exploring Operation: 47-4=43, Resulting Numbers: [17, 43] Generated Node #0,4,2: 21:[17, 43] Operation: 47-4=43 Exploring Operation: 47-17=30, Resulting Numbers: [4, 30] Generated Node #0,4,3: 21:[4, 30] Operation: 47-17=30 Exploring Operation: 17+4=21, Resulting Numbers: [47, 21] Generated Node #0,4,4: 21:[47, 21] Operation: 17+4=21 Moving to Node #0,4,3 Current State: 21:[4, 30], Operations: ['92/23=4', '47-17=30'] Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,21 unequal: No Solution Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,21 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,21 unequal: No Solution Moving to Node #0,4,4 Current State: 21:[47, 21], Operations: ['92/23=4', '17+4=21'] Exploring Operation: 47-21=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 47+21=68, Resulting Numbers: [68] 68,21 unequal: No Solution Exploring Operation: 47*21=987, Resulting Numbers: [987] 987,21 unequal: No Solution Moving to Node #0,4,2 Current State: 21:[17, 43], Operations: ['92/23=4', '47-4=43'] Exploring Operation: 43-17=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 17+43=60, Resulting Numbers: [60] 60,21 unequal: No Solution Exploring Operation: 17*43=731, Resulting Numbers: [731] 731,21 unequal: No Solution Moving to Node #0,4,1 Current State: 21:[47, 13], Operations: ['92/23=4', '17-4=13'] Exploring Operation: 47*13=611, Resulting Numbers: [611] 611,21 unequal: No Solution Exploring Operation: 47+13=60, Resulting Numbers: [60] 60,21 unequal: No Solution Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,21 unequal: No Solution Moving to Node #0,4,0 Current State: 21:[17, 51], Operations: ['92/23=4', '47+4=51'] Exploring Operation: 51/17=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 17+51=68, Resulting Numbers: [68] 68,21 unequal: No Solution Exploring Operation: 17*51=867, Resulting Numbers: [867] 867,21 unequal: No Solution Exploring Operation: 51-17=34, Resulting Numbers: [34] 34,21 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 #0,2 Current State: 21:[17, 47, 69], Operations: ['92-23=69'] Exploring Operation: 17+47=64, Resulting Numbers: [69, 64] Generated Node #0,2,0: 21:[69, 64] Operation: 17+47=64 Exploring Operation: 17+69=86, Resulting Numbers: [47, 86] Generated Node #0,2,1: 21:[47, 86] Operation: 17+69=86 Exploring Operation: 47-17=30, Resulting Numbers: [69, 30] Generated Node #0,2,2: 21:[69, 30] Operation: 47-17=30 Exploring Operation: 69-47=22, Resulting Numbers: [17, 22] Generated Node #0,2,3: 21:[17, 22] Operation: 69-47=22 Exploring Operation: 69-17=52, Resulting Numbers: [47, 52] Generated Node #0,2,4: 21:[47, 52] Operation: 69-17=52 Moving to Node #0,2,3 Current State: 21:[17, 22], Operations: ['92-23=69', '69-47=22'] Exploring Operation: 17*22=374, Resulting Numbers: [374] 374,21 unequal: No Solution Exploring Operation: 17+22=39, Resulting Numbers: [39] 39,21 unequal: No Solution Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,21 unequal: No Solution Moving to Node #0,2,4 Current State: 21:[47, 52], Operations: ['92-23=69', '69-17=52'] Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 47*52=2444, Resulting Numbers: [2444] 2444,21 unequal: No Solution Exploring Operation: 47+52=99, Resulting Numbers: [99] 99,21 unequal: No Solution Moving to Node #0,2,2 Current State: 21:[69, 30], Operations: ['92-23=69', '47-17=30'] Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,21 unequal: No Solution Exploring Operation: 69+30=99, Resulting Numbers: [99] 99,21 unequal: No Solution Exploring Operation: 69*30=2070, Resulting Numbers: [2070] 2070,21 unequal: No Solution Moving to Node #0,2,0 Current State: 21:[69, 64], Operations: ['92-23=69', '17+47=64'] Exploring Operation: 69-64=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 69+64=133, Resulting Numbers: [133] 133,21 unequal: No Solution Exploring Operation: 69*64=4416, Resulting Numbers: [4416] 4416,21 unequal: No Solution Moving to Node #0,2,1 Current State: 21:[47, 86], Operations: ['92-23=69', '17+69=86'] Exploring Operation: 47+86=133, Resulting Numbers: [133] 133,21 unequal: No Solution Exploring Operation: 86-47=39, Resulting Numbers: [39] 39,21 unequal: No Solution Exploring Operation: 47*86=4042, Resulting Numbers: [4042] 4042,21 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 #0,3 Current State: 21:[17, 92, 24], Operations: ['47-23=24'] Exploring Operation: 17+92=109, Resulting Numbers: [24, 109] Generated Node #0,3,0: 21:[24, 109] Operation: 17+92=109 Exploring Operation: 24-17=7, Resulting Numbers: [92, 7] Generated Node #0,3,1: 21:[92, 7] Operation: 24-17=7 Exploring Operation: 92-24=68, Resulting Numbers: [17, 68] Generated Node #0,3,2: 21:[17, 68] Operation: 92-24=68 Exploring Operation: 17+24=41, Resulting Numbers: [92, 41] Generated Node #0,3,3: 21:[92, 41] Operation: 17+24=41 Exploring Operation: 92-17=75, Resulting Numbers: [24, 75] Generated Node #0,3,4: 21:[24, 75] Operation: 92-17=75 Moving to Node #0,3,2 Current State: 21:[17, 68], Operations: ['47-23=24', '92-24=68'] Exploring Operation: 68-17=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 17*68=1156, Resulting Numbers: [1156] 1156,21 unequal: No Solution Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 17+68=85, Resulting Numbers: [85] 85,21 unequal: No Solution Moving to Node #0,3,4 Current State: 21:[24, 75], Operations: ['47-23=24', '92-17=75'] Exploring Operation: 24*75=1800, Resulting Numbers: [1800] 1800,21 unequal: No Solution Exploring Operation: 24+75=99, Resulting Numbers: [99] 99,21 unequal: No Solution Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,21 unequal: No Solution Moving to Node #0,3,1 Current State: 21:[92, 7], Operations: ['47-23=24', '24-17=7'] Exploring Operation: 92*7=644, Resulting Numbers: [644] 644,21 unequal: No Solution Exploring Operation: 92-7=85, Resulting Numbers: [85] 85,21 unequal: No Solution Exploring Operation: 92+7=99, Resulting Numbers: [99] 99,21 unequal: No Solution Moving to Node #0,3,0 Current State: 21:[24, 109], Operations: ['47-23=24', '17+92=109'] Exploring Operation: 24+109=133, Resulting Numbers: [133] 133,21 unequal: No Solution Exploring Operation: 109-24=85, Resulting Numbers: [85] 85,21 unequal: No Solution Exploring Operation: 24*109=2616, Resulting Numbers: [2616] 2616,21 unequal: No Solution Moving to Node #0,3,3 Current State: 21:[92, 41], Operations: ['47-23=24', '17+24=41'] Exploring Operation: 92*41=3772, Resulting Numbers: [3772] 3772,21 unequal: No Solution Exploring Operation: 92+41=133, Resulting Numbers: [133] 133,21 unequal: No Solution Exploring Operation: 92-41=51, Resulting Numbers: [51] 51,21 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:[47, 23, 75], Operations: ['92-17=75'] Exploring Operation: 75-23=52, Resulting Numbers: [47, 52] Generated Node #0,1,0: 21:[47, 52] Operation: 75-23=52 Exploring Operation: 75-47=28, Resulting Numbers: [23, 28] Generated Node #0,1,1: 21:[23, 28] Operation: 75-47=28 Exploring Operation: 47-23=24, Resulting Numbers: [75, 24] Generated Node #0,1,2: 21:[75, 24] Operation: 47-23=24 Exploring Operation: 47+23=70, Resulting Numbers: [75, 70] Generated Node #0,1,3: 21:[75, 70] Operation: 47+23=70 Exploring Operation: 47+75=122, Resulting Numbers: [23, 122] Generated Node #0,1,4: 21:[23, 122] Operation: 47+75=122 Moving to Node #0,1,1 Current State: 21:[23, 28], Operations: ['92-17=75', '75-47=28'] Exploring Operation: 23+28=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 23*28=644, Resulting Numbers: [644] 644,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[75, 24], Operations: ['92-17=75', '47-23=24'] Exploring Operation: 75+24=99, Resulting Numbers: [99] 99,21 unequal: No Solution Exploring Operation: 75*24=1800, Resulting Numbers: [1800] 1800,21 unequal: No Solution Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,21 unequal: No Solution Moving to Node #0,1,0 Current State: 21:[47, 52], Operations: ['92-17=75', '75-23=52'] Exploring Operation: 47*52=2444, Resulting Numbers: [2444] 2444,21 unequal: No Solution Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 47+52=99, Resulting Numbers: [99] 99,21 unequal: No Solution Moving to Node #0,1,3 Current State: 21:[75, 70], Operations: ['92-17=75', '47+23=70'] Exploring Operation: 75+70=145, Resulting Numbers: [145] 145,21 unequal: No Solution Exploring Operation: 75*70=5250, Resulting Numbers: [5250] 5250,21 unequal: No Solution Exploring Operation: 75-70=5, Resulting Numbers: [5] 5,21 unequal: No Solution Moving to Node #0,1,4 Current State: 21:[23, 122], Operations: ['92-17=75', '47+75=122'] Exploring Operation: 23*122=2806, Resulting Numbers: [2806] 2806,21 unequal: No Solution Exploring Operation: 23+122=145, Resulting Numbers: [145] 145,21 unequal: No Solution Exploring Operation: 122-23=99, Resulting Numbers: [99] 99,21 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
[ 54, 9, 87, 89 ]
65
[ "54+9=63", "89-87=2", "63+2=65" ]
Current State: 65:[54, 9, 87, 89], Operations: [] Exploring Operation: 54+9=63, Resulting Numbers: [87, 89, 63] Generated Node #2: [87, 89, 63] from Operation: 54+9=63 Current State: 65:[87, 89, 63], Operations: ['54+9=63'] Exploring Operation: 89-87=2, Resulting Numbers: [63, 2] Generated Node #3: [63, 2] from Operation: 89-87=2 Current State: 65:[63, 2], Operations: ['54+9=63', '89-87=2'] Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[54, 9, 87, 89], Operations: [] Exploring Operation: 89-87=2, Resulting Numbers: [54, 9, 2] Generated Node #0,0: 65:[54, 9, 2] Operation: 89-87=2 Moving to Node #0,0 Current State: 65:[54, 9, 2], Operations: ['89-87=2'] Exploring Operation: 54/9=6, Resulting Numbers: [2, 6] Generated Node #0,0,0: 65:[2, 6] Operation: 54/9=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[2, 6], Operations: ['89-87=2', '54/9=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,65 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
[ 18, 90, 47, 41 ]
83
[ "90/18=5", "47+41=88", "88-5=83" ]
Current State: 83:[18, 90, 47, 41], Operations: [] Exploring Operation: 90/18=5, Resulting Numbers: [47, 41, 5] Generated Node #2: [47, 41, 5] from Operation: 90/18=5 Current State: 83:[47, 41, 5], Operations: ['90/18=5'] Exploring Operation: 47+41=88, Resulting Numbers: [5, 88] Generated Node #3: [5, 88] from Operation: 47+41=88 Current State: 83:[5, 88], Operations: ['90/18=5', '47+41=88'] Exploring Operation: 88-5=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[18, 90, 47, 41], Operations: [] Exploring Operation: 18+41=59, Resulting Numbers: [90, 47, 59] Generated Node #0,0: 83:[90, 47, 59] Operation: 18+41=59 Exploring Operation: 18+47=65, Resulting Numbers: [90, 41, 65] Generated Node #0,1: 83:[90, 41, 65] Operation: 18+47=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[90, 47, 59], Operations: ['18+41=59'] Exploring Operation: 47+59=106, Resulting Numbers: [90, 106] Generated Node #0,0,0: 83:[90, 106] Operation: 47+59=106 Exploring Operation: 90-47=43, Resulting Numbers: [59, 43] Generated Node #0,0,1: 83:[59, 43] Operation: 90-47=43 Moving to Node #0,0,0 Current State: 83:[90, 106], Operations: ['18+41=59', '47+59=106'] Exploring Operation: 106-90=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 90+106=196, Resulting Numbers: [196] 196,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[59, 43], Operations: ['18+41=59', '90-47=43'] Exploring Operation: 59-43=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 59+43=102, Resulting Numbers: [102] 102,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[90, 41, 65], Operations: ['18+47=65'] Exploring Operation: 90-41=49, Resulting Numbers: [65, 49] Generated Node #0,1,0: 83:[65, 49] Operation: 90-41=49 Exploring Operation: 41+65=106, Resulting Numbers: [90, 106] Generated Node #0,1,1: 83:[90, 106] Operation: 41+65=106 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[90, 106], Operations: ['18+47=65', '41+65=106'] Exploring Operation: 106-90=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 90+106=196, Resulting Numbers: [196] 196,83 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 #0,1,0 Current State: 83:[65, 49], Operations: ['18+47=65', '90-41=49'] Exploring Operation: 65+49=114, Resulting Numbers: [114] 114,83 unequal: No Solution Exploring Operation: 65-49=16, Resulting Numbers: [16] 16,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 88, 23, 87, 13 ]
53
[ "87*13=1131", "88+1131=1219", "1219/23=53" ]
Current State: 53:[88, 23, 87, 13], Operations: [] Exploring Operation: 87*13=1131, Resulting Numbers: [88, 23, 1131] Generated Node #2: [88, 23, 1131] from Operation: 87*13=1131 Current State: 53:[88, 23, 1131], Operations: ['87*13=1131'] Exploring Operation: 88+1131=1219, Resulting Numbers: [23, 1219] Generated Node #3: [23, 1219] from Operation: 88+1131=1219 Current State: 53:[23, 1219], Operations: ['87*13=1131', '88+1131=1219'] Exploring Operation: 1219/23=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[88, 23, 87, 13], Operations: [] Exploring Operation: 23+13=36, Resulting Numbers: [88, 87, 36] Generated Node #0,0: 53:[88, 87, 36] Operation: 23+13=36 Exploring Operation: 87-23=64, Resulting Numbers: [88, 13, 64] Generated Node #0,1: 53:[88, 13, 64] Operation: 87-23=64 Exploring Operation: 88-13=75, Resulting Numbers: [23, 87, 75] Generated Node #0,2: 53:[23, 87, 75] Operation: 88-13=75 Exploring Operation: 87-13=74, Resulting Numbers: [88, 23, 74] Generated Node #0,3: 53:[88, 23, 74] Operation: 87-13=74 Exploring Operation: 88-23=65, Resulting Numbers: [87, 13, 65] Generated Node #0,4: 53:[87, 13, 65] Operation: 88-23=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[88, 87, 36], Operations: ['23+13=36'] Exploring Operation: 88-36=52, Resulting Numbers: [87, 52] Generated Node #0,0,0: 53:[87, 52] Operation: 88-36=52 Exploring Operation: 88-87=1, Resulting Numbers: [36, 1] Generated Node #0,0,1: 53:[36, 1] Operation: 88-87=1 Exploring Operation: 87+36=123, Resulting Numbers: [88, 123] Generated Node #0,0,2: 53:[88, 123] Operation: 87+36=123 Exploring Operation: 87-36=51, Resulting Numbers: [88, 51] Generated Node #0,0,3: 53:[88, 51] Operation: 87-36=51 Exploring Operation: 88+36=124, Resulting Numbers: [87, 124] Generated Node #0,0,4: 53:[87, 124] Operation: 88+36=124 Moving to Node #0,0,0 Current State: 53:[87, 52], Operations: ['23+13=36', '88-36=52'] Exploring Operation: 87-52=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 87*52=4524, Resulting Numbers: [4524] 4524,53 unequal: No Solution Exploring Operation: 87+52=139, Resulting Numbers: [139] 139,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[88, 51], Operations: ['23+13=36', '87-36=51'] Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,53 unequal: No Solution Exploring Operation: 88+51=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 88*51=4488, Resulting Numbers: [4488] 4488,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[36, 1], Operations: ['23+13=36', '88-87=1'] Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 36+1=37, Resulting Numbers: [37] 37,53 unequal: No Solution Exploring Operation: 36*1=36, Resulting Numbers: [36] 36,53 unequal: No Solution Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[88, 123], Operations: ['23+13=36', '87+36=123'] Exploring Operation: 88+123=211, Resulting Numbers: [211] 211,53 unequal: No Solution Exploring Operation: 88*123=10824, Resulting Numbers: [10824] 10824,53 unequal: No Solution Exploring Operation: 123-88=35, Resulting Numbers: [35] 35,53 unequal: No Solution Moving to Node #0,0,4 Current State: 53:[87, 124], Operations: ['23+13=36', '88+36=124'] Exploring Operation: 87+124=211, Resulting Numbers: [211] 211,53 unequal: No Solution Exploring Operation: 124-87=37, Resulting Numbers: [37] 37,53 unequal: No Solution Exploring Operation: 87*124=10788, Resulting Numbers: [10788] 10788,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[88, 13, 64], Operations: ['87-23=64'] Exploring Operation: 88-13=75, Resulting Numbers: [64, 75] Generated Node #0,1,0: 53:[64, 75] Operation: 88-13=75 Exploring Operation: 64-13=51, Resulting Numbers: [88, 51] Generated Node #0,1,1: 53:[88, 51] Operation: 64-13=51 Exploring Operation: 88-64=24, Resulting Numbers: [13, 24] Generated Node #0,1,2: 53:[13, 24] Operation: 88-64=24 Exploring Operation: 88+13=101, Resulting Numbers: [64, 101] Generated Node #0,1,3: 53:[64, 101] Operation: 88+13=101 Exploring Operation: 13+64=77, Resulting Numbers: [88, 77] Generated Node #0,1,4: 53:[88, 77] Operation: 13+64=77 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[64, 75], Operations: ['87-23=64', '88-13=75'] Exploring Operation: 64*75=4800, Resulting Numbers: [4800] 4800,53 unequal: No Solution Exploring Operation: 64+75=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[88, 51], Operations: ['87-23=64', '64-13=51'] Exploring Operation: 88+51=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 88*51=4488, Resulting Numbers: [4488] 4488,53 unequal: No Solution Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 53:[64, 101], Operations: ['87-23=64', '88+13=101'] Exploring Operation: 64*101=6464, Resulting Numbers: [6464] 6464,53 unequal: No Solution Exploring Operation: 64+101=165, Resulting Numbers: [165] 165,53 unequal: No Solution Exploring Operation: 101-64=37, Resulting Numbers: [37] 37,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 53:[88, 77], Operations: ['87-23=64', '13+64=77'] Exploring Operation: 88-77=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 88*77=6776, Resulting Numbers: [6776] 6776,53 unequal: No Solution Exploring Operation: 88+77=165, Resulting Numbers: [165] 165,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 53:[13, 24], Operations: ['87-23=64', '88-64=24'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 13*24=312, Resulting Numbers: [312] 312,53 unequal: No Solution Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 53:[23, 87, 75], Operations: ['88-13=75'] Exploring Operation: 87-23=64, Resulting Numbers: [75, 64] Generated Node #0,2,0: 53:[75, 64] Operation: 87-23=64 Exploring Operation: 75-23=52, Resulting Numbers: [87, 52] Generated Node #0,2,1: 53:[87, 52] Operation: 75-23=52 Exploring Operation: 23+75=98, Resulting Numbers: [87, 98] Generated Node #0,2,2: 53:[87, 98] Operation: 23+75=98 Exploring Operation: 87-75=12, Resulting Numbers: [23, 12] Generated Node #0,2,3: 53:[23, 12] Operation: 87-75=12 Exploring Operation: 23+87=110, Resulting Numbers: [75, 110] Generated Node #0,2,4: 53:[75, 110] Operation: 23+87=110 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 53:[75, 64], Operations: ['88-13=75', '87-23=64'] Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 75+64=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 75*64=4800, Resulting Numbers: [4800] 4800,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 53:[87, 52], Operations: ['88-13=75', '75-23=52'] Exploring Operation: 87+52=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 87*52=4524, Resulting Numbers: [4524] 4524,53 unequal: No Solution Exploring Operation: 87-52=35, Resulting Numbers: [35] 35,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 53:[23, 12], Operations: ['88-13=75', '87-75=12'] Exploring Operation: 23+12=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 23*12=276, Resulting Numbers: [276] 276,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 53:[87, 98], Operations: ['88-13=75', '23+75=98'] Exploring Operation: 87+98=185, Resulting Numbers: [185] 185,53 unequal: No Solution Exploring Operation: 87*98=8526, Resulting Numbers: [8526] 8526,53 unequal: No Solution Exploring Operation: 98-87=11, Resulting Numbers: [11] 11,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 53:[75, 110], Operations: ['88-13=75', '23+87=110'] Exploring Operation: 110-75=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 75+110=185, Resulting Numbers: [185] 185,53 unequal: No Solution Exploring Operation: 75*110=8250, Resulting Numbers: [8250] 8250,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 53:[88, 23, 74], Operations: ['87-13=74'] Exploring Operation: 88+23=111, Resulting Numbers: [74, 111] Generated Node #0,3,0: 53:[74, 111] Operation: 88+23=111 Exploring Operation: 88-23=65, Resulting Numbers: [74, 65] Generated Node #0,3,1: 53:[74, 65] Operation: 88-23=65 Exploring Operation: 74-23=51, Resulting Numbers: [88, 51] Generated Node #0,3,2: 53:[88, 51] Operation: 74-23=51 Exploring Operation: 23+74=97, Resulting Numbers: [88, 97] Generated Node #0,3,3: 53:[88, 97] Operation: 23+74=97 Exploring Operation: 88-74=14, Resulting Numbers: [23, 14] Generated Node #0,3,4: 53:[23, 14] Operation: 88-74=14 Moving to Node #0,3,1 Current State: 53:[74, 65], Operations: ['87-13=74', '88-23=65'] Exploring Operation: 74*65=4810, Resulting Numbers: [4810] 4810,53 unequal: No Solution Exploring Operation: 74+65=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 74-65=9, Resulting Numbers: [9] 9,53 unequal: No Solution Moving to Node #0,3,2 Current State: 53:[88, 51], Operations: ['87-13=74', '74-23=51'] Exploring Operation: 88*51=4488, Resulting Numbers: [4488] 4488,53 unequal: No Solution Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,53 unequal: No Solution Exploring Operation: 88+51=139, Resulting Numbers: [139] 139,53 unequal: No Solution Moving to Node #0,3,4 Current State: 53:[23, 14], Operations: ['87-13=74', '88-74=14'] Exploring Operation: 23-14=9, Resulting Numbers: [9] 9,53 unequal: No Solution Exploring Operation: 23+14=37, Resulting Numbers: [37] 37,53 unequal: No Solution Exploring Operation: 23*14=322, Resulting Numbers: [322] 322,53 unequal: No Solution Moving to Node #0,3,0 Current State: 53:[74, 111], Operations: ['87-13=74', '88+23=111'] Exploring Operation: 74*111=8214, Resulting Numbers: [8214] 8214,53 unequal: No Solution Exploring Operation: 74+111=185, Resulting Numbers: [185] 185,53 unequal: No Solution Exploring Operation: 111-74=37, Resulting Numbers: [37] 37,53 unequal: No Solution Moving to Node #0,3,3 Current State: 53:[88, 97], Operations: ['87-13=74', '23+74=97'] Exploring Operation: 97-88=9, Resulting Numbers: [9] 9,53 unequal: No Solution Exploring Operation: 88*97=8536, Resulting Numbers: [8536] 8536,53 unequal: No Solution Exploring Operation: 88+97=185, Resulting Numbers: [185] 185,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 53:[87, 13, 65], Operations: ['88-23=65'] Exploring Operation: 87+13=100, Resulting Numbers: [65, 100] Generated Node #0,4,0: 53:[65, 100] Operation: 87+13=100 Exploring Operation: 13+65=78, Resulting Numbers: [87, 78] Generated Node #0,4,1: 53:[87, 78] Operation: 13+65=78 Exploring Operation: 87-13=74, Resulting Numbers: [65, 74] Generated Node #0,4,2: 53:[65, 74] Operation: 87-13=74 Exploring Operation: 65-13=52, Resulting Numbers: [87, 52] Generated Node #0,4,3: 53:[87, 52] Operation: 65-13=52 Exploring Operation: 87-65=22, Resulting Numbers: [13, 22] Generated Node #0,4,4: 53:[13, 22] Operation: 87-65=22 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 53:[65, 74], Operations: ['88-23=65', '87-13=74'] Exploring Operation: 65+74=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 65*74=4810, Resulting Numbers: [4810] 4810,53 unequal: No Solution Exploring Operation: 74-65=9, Resulting Numbers: [9] 9,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 53:[87, 52], Operations: ['88-23=65', '65-13=52'] Exploring Operation: 87+52=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 87-52=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 87*52=4524, Resulting Numbers: [4524] 4524,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 53:[65, 100], Operations: ['88-23=65', '87+13=100'] Exploring Operation: 65*100=6500, Resulting Numbers: [6500] 6500,53 unequal: No Solution Exploring Operation: 65+100=165, Resulting Numbers: [165] 165,53 unequal: No Solution Exploring Operation: 100-65=35, Resulting Numbers: [35] 35,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 53:[87, 78], Operations: ['88-23=65', '13+65=78'] Exploring Operation: 87*78=6786, Resulting Numbers: [6786] 6786,53 unequal: No Solution Exploring Operation: 87+78=165, Resulting Numbers: [165] 165,53 unequal: No Solution Exploring Operation: 87-78=9, Resulting Numbers: [9] 9,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 53:[13, 22], Operations: ['88-23=65', '87-65=22'] Exploring Operation: 13+22=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 13*22=286, Resulting Numbers: [286] 286,53 unequal: No Solution Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 22, 50, 63, 32 ]
41
[ "22+50=72", "63-32=31", "72-31=41" ]
Current State: 41:[22, 50, 63, 32], Operations: [] Exploring Operation: 22+50=72, Resulting Numbers: [63, 32, 72] Generated Node #2: [63, 32, 72] from Operation: 22+50=72 Current State: 41:[63, 32, 72], Operations: ['22+50=72'] Exploring Operation: 63-32=31, Resulting Numbers: [72, 31] Generated Node #3: [72, 31] from Operation: 63-32=31 Current State: 41:[72, 31], Operations: ['22+50=72', '63-32=31'] Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[22, 50, 63, 32], Operations: [] Exploring Operation: 63-50=13, Resulting Numbers: [22, 32, 13] Generated Node #0,0: 41:[22, 32, 13] Operation: 63-50=13 Exploring Operation: 22+32=54, Resulting Numbers: [50, 63, 54] Generated Node #0,1: 41:[50, 63, 54] Operation: 22+32=54 Exploring Operation: 63-32=31, Resulting Numbers: [22, 50, 31] Generated Node #0,2: 41:[22, 50, 31] Operation: 63-32=31 Exploring Operation: 63-22=41, Resulting Numbers: [50, 32, 41] Generated Node #0,3: 41:[50, 32, 41] Operation: 63-22=41 Exploring Operation: 50-22=28, Resulting Numbers: [63, 32, 28] Generated Node #0,4: 41:[63, 32, 28] Operation: 50-22=28 Moving to Node #0,3 Current State: 41:[50, 32, 41], Operations: ['63-22=41'] Exploring Operation: 50-32=18, Resulting Numbers: [41, 18] Generated Node #0,3,0: 41:[41, 18] Operation: 50-32=18 Exploring Operation: 32+41=73, Resulting Numbers: [50, 73] Generated Node #0,3,1: 41:[50, 73] Operation: 32+41=73 Exploring Operation: 41-32=9, Resulting Numbers: [50, 9] Generated Node #0,3,2: 41:[50, 9] Operation: 41-32=9 Exploring Operation: 50-41=9, Resulting Numbers: [32, 9] Generated Node #0,3,3: 41:[32, 9] Operation: 50-41=9 Exploring Operation: 50+32=82, Resulting Numbers: [41, 82] Generated Node #0,3,4: 41:[41, 82] Operation: 50+32=82 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 41:[41, 18], Operations: ['63-22=41', '50-32=18'] Exploring Operation: 41-18=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 41*18=738, Resulting Numbers: [738] 738,41 unequal: No Solution Exploring Operation: 41+18=59, Resulting Numbers: [59] 59,41 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 #0,3,1 Current State: 41:[50, 73], Operations: ['63-22=41', '32+41=73'] Exploring Operation: 50+73=123, Resulting Numbers: [123] 123,41 unequal: No Solution Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 50*73=3650, Resulting Numbers: [3650] 3650,41 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:[50, 9], Operations: ['63-22=41', '41-32=9'] Exploring Operation: 50+9=59, Resulting Numbers: [59] 59,41 unequal: No Solution Exploring Operation: 50*9=450, Resulting Numbers: [450] 450,41 unequal: No Solution Exploring Operation: 50-9=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[22, 50, 63, 32], Operations: [] Exploring Operation: 63-22=41, Resulting Numbers: [50, 32, 41] Generated Node #0,3: 41:[50, 32, 41] Operation: 63-22=41 Moving to Node #0,3 Current State: 41:[50, 32, 41], Operations: ['63-22=41'] Exploring Operation: 41-32=9, Resulting Numbers: [50, 9] Generated Node #0,3,2: 41:[50, 9] Operation: 41-32=9 Moving to Node #0,3,2 Current State: 41:[50, 9], Operations: ['63-22=41', '41-32=9'] Exploring Operation: 50-9=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 14, 38, 80, 38 ]
93
[ "14+80=94", "38/38=1", "94-1=93" ]
Current State: 93:[14, 38, 80, 38], Operations: [] Exploring Operation: 14+80=94, Resulting Numbers: [38, 38, 94] Generated Node #2: [38, 38, 94] from Operation: 14+80=94 Current State: 93:[38, 38, 94], Operations: ['14+80=94'] Exploring Operation: 38/38=1, Resulting Numbers: [94, 1] Generated Node #3: [94, 1] from Operation: 38/38=1 Current State: 93:[94, 1], Operations: ['14+80=94', '38/38=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[14, 38, 80, 38], Operations: [] Exploring Operation: 14+80=94, Resulting Numbers: [38, 38, 94] Generated Node #0,0: 93:[38, 38, 94] Operation: 14+80=94 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[38, 38, 94], Operations: ['14+80=94'] Exploring Operation: 38/38=1, Resulting Numbers: [94, 1] Generated Node #0,0,0: 93:[94, 1] Operation: 38/38=1 Moving to Node #0,0,0 Current State: 93:[94, 1], Operations: ['14+80=94', '38/38=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[14, 38, 80, 38], Operations: [] Exploring Operation: 14+80=94, Resulting Numbers: [38, 38, 94] Generated Node #0,0: 93:[38, 38, 94] Operation: 14+80=94 Moving to Node #0,0 Current State: 93:[38, 38, 94], Operations: ['14+80=94'] Exploring Operation: 38/38=1, Resulting Numbers: [94, 1] Generated Node #0,0,0: 93:[94, 1] Operation: 38/38=1 Moving to Node #0,0,0 Current State: 93:[94, 1], Operations: ['14+80=94', '38/38=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 33, 12, 2, 40 ]
26
[ "40-33=7", "2*7=14", "12+14=26" ]
Current State: 26:[33, 12, 2, 40], Operations: [] Exploring Operation: 40-33=7, Resulting Numbers: [12, 2, 7] Generated Node #2: [12, 2, 7] from Operation: 40-33=7 Current State: 26:[12, 2, 7], Operations: ['40-33=7'] Exploring Operation: 2*7=14, Resulting Numbers: [12, 14] Generated Node #3: [12, 14] from Operation: 2*7=14 Current State: 26:[12, 14], Operations: ['40-33=7', '2*7=14'] Exploring Operation: 12+14=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[33, 12, 2, 40], Operations: [] Exploring Operation: 40/2=20, Resulting Numbers: [33, 12, 20] Generated Node #0,0: 26:[33, 12, 20] Operation: 40/2=20 Exploring Operation: 40-12=28, Resulting Numbers: [33, 2, 28] Generated Node #0,1: 26:[33, 2, 28] Operation: 40-12=28 Exploring Operation: 40-33=7, Resulting Numbers: [12, 2, 7] Generated Node #0,2: 26:[12, 2, 7] Operation: 40-33=7 Moving to Node #0,2 Current State: 26:[12, 2, 7], Operations: ['40-33=7'] Exploring Operation: 7-2=5, Resulting Numbers: [12, 5] Generated Node #0,2,0: 26:[12, 5] Operation: 7-2=5 Exploring Operation: 12-7=5, Resulting Numbers: [2, 5] Generated Node #0,2,1: 26:[2, 5] Operation: 12-7=5 Exploring Operation: 2*7=14, Resulting Numbers: [12, 14] Generated Node #0,2,2: 26:[12, 14] Operation: 2*7=14 Moving to Node #0,1 Current State: 26:[33, 2, 28], Operations: ['40-12=28'] Exploring Operation: 28-2=26, Resulting Numbers: [33, 26] Generated Node #0,1,0: 26:[33, 26] Operation: 28-2=26 Exploring Operation: 33-28=5, Resulting Numbers: [2, 5] Generated Node #0,1,1: 26:[2, 5] Operation: 33-28=5 Exploring Operation: 33-2=31, Resulting Numbers: [28, 31] Generated Node #0,1,2: 26:[28, 31] Operation: 33-2=31 Moving to Node #0,0 Current State: 26:[33, 12, 20], Operations: ['40/2=20'] Exploring Operation: 33-20=13, Resulting Numbers: [12, 13] Generated Node #0,0,0: 26:[12, 13] Operation: 33-20=13 Exploring Operation: 20-12=8, Resulting Numbers: [33, 8] Generated Node #0,0,1: 26:[33, 8] Operation: 20-12=8 Exploring Operation: 33-12=21, Resulting Numbers: [20, 21] Generated Node #0,0,2: 26:[20, 21] Operation: 33-12=21 Moving to Node #0,0,0 Current State: 26:[12, 13], Operations: ['40/2=20', '33-20=13'] Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,26 unequal: No Solution Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,26 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[12, 14], Operations: ['40-33=7', '2*7=14'] Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 12+14=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[33, 12, 2, 40], Operations: [] Exploring Operation: 40-33=7, Resulting Numbers: [12, 2, 7] Generated Node #0,2: 26:[12, 2, 7] Operation: 40-33=7 Moving to Node #0,2 Current State: 26:[12, 2, 7], Operations: ['40-33=7'] Exploring Operation: 2*7=14, Resulting Numbers: [12, 14] Generated Node #0,2,2: 26:[12, 14] Operation: 2*7=14 Moving to Node #0,2,2 Current State: 26:[12, 14], Operations: ['40-33=7', '2*7=14'] Exploring Operation: 12+14=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
0.981771
hs_3
mult_heuristic
[ 40, 91, 91, 26 ]
65
[ "40+26=66", "91/91=1", "66-1=65" ]
Current State: 65:[40, 91, 91, 26], Operations: [] Exploring Operation: 40+26=66, Resulting Numbers: [91, 91, 66] Generated Node #2: [91, 91, 66] from Operation: 40+26=66 Current State: 65:[91, 91, 66], Operations: ['40+26=66'] Exploring Operation: 91/91=1, Resulting Numbers: [66, 1] Generated Node #3: [66, 1] from Operation: 91/91=1 Current State: 65:[66, 1], Operations: ['40+26=66', '91/91=1'] Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[40, 91, 91, 26], Operations: [] Exploring Operation: 91/91=1, Resulting Numbers: [40, 26, 1] Generated Node #0,0: 65:[40, 26, 1] Operation: 91/91=1 Exploring Operation: 91-26=65, Resulting Numbers: [40, 91, 65] Generated Node #0,1: 65:[40, 91, 65] Operation: 91-26=65 Exploring Operation: 91-91=0, Resulting Numbers: [40, 26, 0] Generated Node #0,2: 65:[40, 26, 0] Operation: 91-91=0 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[40, 26, 1], Operations: ['91/91=1'] Exploring Operation: 40-26=14, Resulting Numbers: [1, 14] Generated Node #0,0,0: 65:[1, 14] Operation: 40-26=14 Exploring Operation: 40+26=66, Resulting Numbers: [1, 66] Generated Node #0,0,1: 65:[1, 66] Operation: 40+26=66 Exploring Operation: 40+1=41, Resulting Numbers: [26, 41] Generated Node #0,0,2: 65:[26, 41] Operation: 40+1=41 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 65:[1, 14], Operations: ['91/91=1', '40-26=14'] Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,65 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 #0,0,1 Current State: 65:[1, 66], Operations: ['91/91=1', '40+26=66'] Exploring Operation: 1*66=66, Resulting Numbers: [66] 66,65 unequal: No Solution Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[40, 91, 91, 26], Operations: [] Exploring Operation: 91/91=1, Resulting Numbers: [40, 26, 1] Generated Node #0,0: 65:[40, 26, 1] Operation: 91/91=1 Moving to Node #0,0 Current State: 65:[40, 26, 1], Operations: ['91/91=1'] Exploring Operation: 40+26=66, Resulting Numbers: [1, 66] Generated Node #0,0,1: 65:[1, 66] Operation: 40+26=66 Moving to Node #0,0,1 Current State: 65:[1, 66], Operations: ['91/91=1', '40+26=66'] Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 36, 65, 59, 38 ]
44
[ "65-59=6", "36/6=6", "38+6=44" ]
Current State: 44:[36, 65, 59, 38], Operations: [] Exploring Operation: 65-59=6, Resulting Numbers: [36, 38, 6] Generated Node #2: [36, 38, 6] from Operation: 65-59=6 Current State: 44:[36, 38, 6], Operations: ['65-59=6'] Exploring Operation: 36/6=6, Resulting Numbers: [38, 6] Generated Node #3: [38, 6] from Operation: 36/6=6 Current State: 44:[38, 6], Operations: ['65-59=6', '36/6=6'] Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[36, 65, 59, 38], Operations: [] Exploring Operation: 59-38=21, Resulting Numbers: [36, 65, 21] Generated Node #0,0: 44:[36, 65, 21] Operation: 59-38=21 Exploring Operation: 59-36=23, Resulting Numbers: [65, 38, 23] Generated Node #0,1: 44:[65, 38, 23] Operation: 59-36=23 Exploring Operation: 65-36=29, Resulting Numbers: [59, 38, 29] Generated Node #0,2: 44:[59, 38, 29] Operation: 65-36=29 Exploring Operation: 65-38=27, Resulting Numbers: [36, 59, 27] Generated Node #0,3: 44:[36, 59, 27] Operation: 65-38=27 Exploring Operation: 65-59=6, Resulting Numbers: [36, 38, 6] Generated Node #0,4: 44:[36, 38, 6] Operation: 65-59=6 Moving to Node #0,4 Current State: 44:[36, 38, 6], Operations: ['65-59=6'] Exploring Operation: 38+6=44, Resulting Numbers: [36, 44] Generated Node #0,4,0: 44:[36, 44] Operation: 38+6=44 Exploring Operation: 36+6=42, Resulting Numbers: [38, 42] Generated Node #0,4,1: 44:[38, 42] Operation: 36+6=42 Exploring Operation: 36-6=30, Resulting Numbers: [38, 30] Generated Node #0,4,2: 44:[38, 30] Operation: 36-6=30 Exploring Operation: 38-36=2, Resulting Numbers: [6, 2] Generated Node #0,4,3: 44:[6, 2] Operation: 38-36=2 Exploring Operation: 36/6=6, Resulting Numbers: [38, 6] Generated Node #0,4,4: 44:[38, 6] Operation: 36/6=6 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 44:[6, 2], Operations: ['65-59=6', '38-36=2'] Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,44 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 44:[36, 44], Operations: ['65-59=6', '38+6=44'] Exploring Operation: 36+44=80, Resulting Numbers: [80] 80,44 unequal: No Solution Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 36*44=1584, Resulting Numbers: [1584] 1584,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 44:[38, 42], Operations: ['65-59=6', '36+6=42'] Exploring Operation: 38+42=80, Resulting Numbers: [80] 80,44 unequal: No Solution Exploring Operation: 42-38=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 38*42=1596, Resulting Numbers: [1596] 1596,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 44:[38, 6], Operations: ['65-59=6', '36/6=6'] Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,44 unequal: No Solution Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,44 unequal: No Solution Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[36, 65, 59, 38], Operations: [] Exploring Operation: 65-59=6, Resulting Numbers: [36, 38, 6] Generated Node #0,4: 44:[36, 38, 6] Operation: 65-59=6 Moving to Node #0,4 Current State: 44:[36, 38, 6], Operations: ['65-59=6'] Exploring Operation: 36/6=6, Resulting Numbers: [38, 6] Generated Node #0,4,4: 44:[38, 6] Operation: 36/6=6 Moving to Node #0,4,4 Current State: 44:[38, 6], Operations: ['65-59=6', '36/6=6'] Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_5
sum_heuristic
[ 48, 28, 8, 26 ]
13
[ "48+8=56", "28*26=728", "728/56=13" ]
Current State: 13:[48, 28, 8, 26], Operations: [] Exploring Operation: 48+8=56, Resulting Numbers: [28, 26, 56] Generated Node #2: [28, 26, 56] from Operation: 48+8=56 Current State: 13:[28, 26, 56], Operations: ['48+8=56'] Exploring Operation: 28*26=728, Resulting Numbers: [56, 728] Generated Node #3: [56, 728] from Operation: 28*26=728 Current State: 13:[56, 728], Operations: ['48+8=56', '28*26=728'] Exploring Operation: 728/56=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[48, 28, 8, 26], Operations: [] Exploring Operation: 48/8=6, Resulting Numbers: [28, 26, 6] Generated Node #0,0: 13:[28, 26, 6] Operation: 48/8=6 Exploring Operation: 48-26=22, Resulting Numbers: [28, 8, 22] Generated Node #0,1: 13:[28, 8, 22] Operation: 48-26=22 Exploring Operation: 28-26=2, Resulting Numbers: [48, 8, 2] Generated Node #0,2: 13:[48, 8, 2] Operation: 28-26=2 Exploring Operation: 48-28=20, Resulting Numbers: [8, 26, 20] Generated Node #0,3: 13:[8, 26, 20] Operation: 48-28=20 Start Sub Search at level 1: Moving to Node #0,3 Current State: 13:[8, 26, 20], Operations: ['48-28=20'] Exploring Operation: 26-8=18, Resulting Numbers: [20, 18] Generated Node #0,3,0: 13:[20, 18] Operation: 26-8=18 Exploring Operation: 26-20=6, Resulting Numbers: [8, 6] Generated Node #0,3,1: 13:[8, 6] Operation: 26-20=6 Exploring Operation: 20-8=12, Resulting Numbers: [26, 12] Generated Node #0,3,2: 13:[26, 12] Operation: 20-8=12 Exploring Operation: 8+26=34, Resulting Numbers: [20, 34] Generated Node #0,3,3: 13:[20, 34] Operation: 8+26=34 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 13:[20, 18], Operations: ['48-28=20', '26-8=18'] Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,13 unequal: No Solution Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,13 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,13 unequal: No Solution No 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: 13:[8, 6], Operations: ['48-28=20', '26-20=6'] Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,13 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,13 unequal: No Solution No 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: 13:[26, 12], Operations: ['48-28=20', '20-8=12'] Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 26+12=38, Resulting Numbers: [38] 38,13 unequal: No Solution Exploring Operation: 26*12=312, Resulting Numbers: [312] 312,13 unequal: No Solution No 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: 13:[20, 34], Operations: ['48-28=20', '8+26=34'] Exploring Operation: 20+34=54, Resulting Numbers: [54] 54,13 unequal: No Solution Exploring Operation: 20*34=680, Resulting Numbers: [680] 680,13 unequal: No Solution Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,13 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: 13:[28, 8, 22], Operations: ['48-26=22'] Exploring Operation: 22-8=14, Resulting Numbers: [28, 14] Generated Node #0,1,0: 13:[28, 14] Operation: 22-8=14 Exploring Operation: 28+8=36, Resulting Numbers: [22, 36] Generated Node #0,1,1: 13:[22, 36] Operation: 28+8=36 Exploring Operation: 28-22=6, Resulting Numbers: [8, 6] Generated Node #0,1,2: 13:[8, 6] Operation: 28-22=6 Exploring Operation: 28-8=20, Resulting Numbers: [22, 20] Generated Node #0,1,3: 13:[22, 20] Operation: 28-8=20 Moving to Node #0,1,2 Current State: 13:[8, 6], Operations: ['48-26=22', '28-22=6'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,13 unequal: No Solution Moving to Node #0,1,3 Current State: 13:[22, 20], Operations: ['48-26=22', '28-8=20'] Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,13 unequal: No Solution Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,13 unequal: No Solution Moving to Node #0,1,0 Current State: 13:[28, 14], Operations: ['48-26=22', '22-8=14'] Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,13 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 28*14=392, Resulting Numbers: [392] 392,13 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[22, 36], Operations: ['48-26=22', '28+8=36'] Exploring Operation: 22+36=58, Resulting Numbers: [58] 58,13 unequal: No Solution Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 22*36=792, Resulting Numbers: [792] 792,13 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 #0,0 Current State: 13:[28, 26, 6], Operations: ['48/8=6'] Exploring Operation: 28+6=34, Resulting Numbers: [26, 34] Generated Node #0,0,0: 13:[26, 34] Operation: 28+6=34 Exploring Operation: 28-26=2, Resulting Numbers: [6, 2] Generated Node #0,0,1: 13:[6, 2] Operation: 28-26=2 Exploring Operation: 28-6=22, Resulting Numbers: [26, 22] Generated Node #0,0,2: 13:[26, 22] Operation: 28-6=22 Exploring Operation: 26-6=20, Resulting Numbers: [28, 20] Generated Node #0,0,3: 13:[28, 20] Operation: 26-6=20 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 13:[6, 2], Operations: ['48/8=6', '28-26=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,13 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,13 unequal: No Solution No 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: 13:[26, 22], Operations: ['48/8=6', '28-6=22'] Exploring Operation: 26+22=48, Resulting Numbers: [48] 48,13 unequal: No Solution Exploring Operation: 26*22=572, Resulting Numbers: [572] 572,13 unequal: No Solution Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,13 unequal: No Solution No 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: 13:[28, 20], Operations: ['48/8=6', '26-6=20'] Exploring Operation: 28+20=48, Resulting Numbers: [48] 48,13 unequal: No Solution Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 28*20=560, Resulting Numbers: [560] 560,13 unequal: No Solution No 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: 13:[26, 34], Operations: ['48/8=6', '28+6=34'] Exploring Operation: 26+34=60, Resulting Numbers: [60] 60,13 unequal: No Solution Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 26*34=884, Resulting Numbers: [884] 884,13 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: 13:[48, 8, 2], Operations: ['28-26=2'] Exploring Operation: 48/2=24, Resulting Numbers: [8, 24] Generated Node #0,2,0: 13:[8, 24] Operation: 48/2=24 Exploring Operation: 48-8=40, Resulting Numbers: [2, 40] Generated Node #0,2,1: 13:[2, 40] Operation: 48-8=40 Exploring Operation: 48/8=6, Resulting Numbers: [2, 6] Generated Node #0,2,2: 13:[2, 6] Operation: 48/8=6 Exploring Operation: 48-2=46, Resulting Numbers: [8, 46] Generated Node #0,2,3: 13:[8, 46] Operation: 48-2=46 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 13:[8, 24], Operations: ['28-26=2', '48/2=24'] Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 8*24=192, Resulting Numbers: [192] 192,13 unequal: No Solution Exploring Operation: 8+24=32, Resulting Numbers: [32] 32,13 unequal: No Solution Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,13 unequal: No Solution No 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: 13:[2, 6], Operations: ['28-26=2', '48/8=6'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,13 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,13 unequal: No Solution No 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: 13:[2, 40], Operations: ['28-26=2', '48-8=40'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,13 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,13 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,13 unequal: No Solution No 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: 13:[8, 46], Operations: ['28-26=2', '48-2=46'] Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,13 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,13 unequal: No Solution Exploring Operation: 8*46=368, Resulting Numbers: [368] 368,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 62, 58, 90, 64 ]
64
[ "64-62=2", "90-58=32", "2*32=64" ]
Current State: 64:[62, 58, 90, 64], Operations: [] Exploring Operation: 64-62=2, Resulting Numbers: [58, 90, 2] Generated Node #2: [58, 90, 2] from Operation: 64-62=2 Current State: 64:[58, 90, 2], Operations: ['64-62=2'] Exploring Operation: 90-58=32, Resulting Numbers: [2, 32] Generated Node #3: [2, 32] from Operation: 90-58=32 Current State: 64:[2, 32], Operations: ['64-62=2', '90-58=32'] Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[62, 58, 90, 64], Operations: [] Exploring Operation: 90-58=32, Resulting Numbers: [62, 64, 32] Generated Node #0,0: 64:[62, 64, 32] Operation: 90-58=32 Exploring Operation: 90-62=28, Resulting Numbers: [58, 64, 28] Generated Node #0,1: 64:[58, 64, 28] Operation: 90-62=28 Moving to Node #0,0 Current State: 64:[62, 64, 32], Operations: ['90-58=32'] Exploring Operation: 62-32=30, Resulting Numbers: [64, 30] Generated Node #0,0,0: 64:[64, 30] Operation: 62-32=30 Exploring Operation: 64-62=2, Resulting Numbers: [32, 2] Generated Node #0,0,1: 64:[32, 2] Operation: 64-62=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 64:[32, 2], Operations: ['90-58=32', '64-62=2'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,64 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[62, 58, 90, 64], Operations: [] Exploring Operation: 90-58=32, Resulting Numbers: [62, 64, 32] Generated Node #0,0: 64:[62, 64, 32] Operation: 90-58=32 Moving to Node #0,0 Current State: 64:[62, 64, 32], Operations: ['90-58=32'] Exploring Operation: 64-62=2, Resulting Numbers: [32, 2] Generated Node #0,0,1: 64:[32, 2] Operation: 64-62=2 Moving to Node #0,0,1 Current State: 64:[32, 2], Operations: ['90-58=32', '64-62=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 44, 40, 36, 74 ]
85
[ "40-36=4", "44/4=11", "74+11=85" ]
Current State: 85:[44, 40, 36, 74], Operations: [] Exploring Operation: 40-36=4, Resulting Numbers: [44, 74, 4] Generated Node #2: [44, 74, 4] from Operation: 40-36=4 Current State: 85:[44, 74, 4], Operations: ['40-36=4'] Exploring Operation: 44/4=11, Resulting Numbers: [74, 11] Generated Node #3: [74, 11] from Operation: 44/4=11 Current State: 85:[74, 11], Operations: ['40-36=4', '44/4=11'] Exploring Operation: 74+11=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[44, 40, 36, 74], Operations: [] Exploring Operation: 44+40=84, Resulting Numbers: [36, 74, 84] Generated Node #0,0: 85:[36, 74, 84] Operation: 44+40=84 Exploring Operation: 44-40=4, Resulting Numbers: [36, 74, 4] Generated Node #0,1: 85:[36, 74, 4] Operation: 44-40=4 Moving to Node #0,0 Current State: 85:[36, 74, 84], Operations: ['44+40=84'] Exploring Operation: 84-74=10, Resulting Numbers: [36, 10] Generated Node #0,0,0: 85:[36, 10] Operation: 84-74=10 Exploring Operation: 74-36=38, Resulting Numbers: [84, 38] Generated Node #0,0,1: 85:[84, 38] Operation: 74-36=38 Moving to Node #0,1 Current State: 85:[36, 74, 4], Operations: ['44-40=4'] Exploring Operation: 74-36=38, Resulting Numbers: [4, 38] Generated Node #0,1,0: 85:[4, 38] Operation: 74-36=38 Exploring Operation: 36/4=9, Resulting Numbers: [74, 9] Generated Node #0,1,1: 85:[74, 9] Operation: 36/4=9 Moving to Node #0,1,1 Current State: 85:[74, 9], Operations: ['44-40=4', '36/4=9'] Exploring Operation: 74-9=65, Resulting Numbers: [65] 65,85 unequal: No Solution Exploring Operation: 74+9=83, Resulting Numbers: [83] 83,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[84, 38], Operations: ['44+40=84', '74-36=38'] Exploring Operation: 84+38=122, Resulting Numbers: [122] 122,85 unequal: No Solution Exploring Operation: 84-38=46, Resulting Numbers: [46] 46,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[4, 38], Operations: ['44-40=4', '74-36=38'] Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,85 unequal: No Solution Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[36, 10], Operations: ['44+40=84', '84-74=10'] Exploring Operation: 36+10=46, Resulting Numbers: [46] 46,85 unequal: No Solution Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,85 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 11, 60, 38, 37 ]
74
[ "60-38=22", "22/11=2", "37*2=74" ]
Current State: 74:[11, 60, 38, 37], Operations: [] Exploring Operation: 60-38=22, Resulting Numbers: [11, 37, 22] Generated Node #2: [11, 37, 22] from Operation: 60-38=22 Current State: 74:[11, 37, 22], Operations: ['60-38=22'] Exploring Operation: 22/11=2, Resulting Numbers: [37, 2] Generated Node #3: [37, 2] from Operation: 22/11=2 Current State: 74:[37, 2], Operations: ['60-38=22', '22/11=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[11, 60, 38, 37], Operations: [] Exploring Operation: 38-11=27, Resulting Numbers: [60, 37, 27] Generated Node #0,0: 74:[60, 37, 27] Operation: 38-11=27 Exploring Operation: 60-37=23, Resulting Numbers: [11, 38, 23] Generated Node #0,1: 74:[11, 38, 23] Operation: 60-37=23 Exploring Operation: 60-11=49, Resulting Numbers: [38, 37, 49] Generated Node #0,2: 74:[38, 37, 49] Operation: 60-11=49 Exploring Operation: 11+60=71, Resulting Numbers: [38, 37, 71] Generated Node #0,3: 74:[38, 37, 71] Operation: 11+60=71 Exploring Operation: 60-38=22, Resulting Numbers: [11, 37, 22] Generated Node #0,4: 74:[11, 37, 22] Operation: 60-38=22 Moving to Node #0,3 Current State: 74:[38, 37, 71], Operations: ['11+60=71'] Exploring Operation: 38+71=109, Resulting Numbers: [37, 109] Generated Node #0,3,0: 74:[37, 109] Operation: 38+71=109 Exploring Operation: 38+37=75, Resulting Numbers: [71, 75] Generated Node #0,3,1: 74:[71, 75] Operation: 38+37=75 Exploring Operation: 71-38=33, Resulting Numbers: [37, 33] Generated Node #0,3,2: 74:[37, 33] Operation: 71-38=33 Exploring Operation: 38-37=1, Resulting Numbers: [71, 1] Generated Node #0,3,3: 74:[71, 1] Operation: 38-37=1 Exploring Operation: 71-37=34, Resulting Numbers: [38, 34] Generated Node #0,3,4: 74:[38, 34] Operation: 71-37=34 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 74:[71, 75], Operations: ['11+60=71', '38+37=75'] Exploring Operation: 75-71=4, Resulting Numbers: [4] 4,74 unequal: No Solution Exploring Operation: 71+75=146, Resulting Numbers: [146] 146,74 unequal: No Solution Exploring Operation: 71*75=5325, Resulting Numbers: [5325] 5325,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 74:[37, 33], Operations: ['11+60=71', '71-38=33'] Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,74 unequal: No Solution Exploring Operation: 37*33=1221, Resulting Numbers: [1221] 1221,74 unequal: No Solution Exploring Operation: 37+33=70, Resulting Numbers: [70] 70,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 74:[71, 1], Operations: ['11+60=71', '38-37=1'] Exploring Operation: 71/1=71, Resulting Numbers: [71] 71,74 unequal: No Solution Exploring Operation: 71-1=70, Resulting Numbers: [70] 70,74 unequal: No Solution Exploring Operation: 71+1=72, Resulting Numbers: [72] 72,74 unequal: No Solution Exploring Operation: 71*1=71, Resulting Numbers: [71] 71,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 74:[38, 34], Operations: ['11+60=71', '71-37=34'] Exploring Operation: 38+34=72, Resulting Numbers: [72] 72,74 unequal: No Solution Exploring Operation: 38*34=1292, Resulting Numbers: [1292] 1292,74 unequal: No Solution Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 74:[37, 109], Operations: ['11+60=71', '38+71=109'] Exploring Operation: 37*109=4033, Resulting Numbers: [4033] 4033,74 unequal: No Solution Exploring Operation: 109-37=72, Resulting Numbers: [72] 72,74 unequal: No Solution Exploring Operation: 37+109=146, Resulting Numbers: [146] 146,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 74:[38, 37, 49], Operations: ['60-11=49'] Exploring Operation: 49-38=11, Resulting Numbers: [37, 11] Generated Node #0,2,0: 74:[37, 11] Operation: 49-38=11 Exploring Operation: 38+49=87, Resulting Numbers: [37, 87] Generated Node #0,2,1: 74:[37, 87] Operation: 38+49=87 Exploring Operation: 38+37=75, Resulting Numbers: [49, 75] Generated Node #0,2,2: 74:[49, 75] Operation: 38+37=75 Exploring Operation: 49-37=12, Resulting Numbers: [38, 12] Generated Node #0,2,3: 74:[38, 12] Operation: 49-37=12 Exploring Operation: 38-37=1, Resulting Numbers: [49, 1] Generated Node #0,2,4: 74:[49, 1] Operation: 38-37=1 Moving to Node #0,0 Current State: 74:[60, 37, 27], Operations: ['38-11=27'] Exploring Operation: 60-37=23, Resulting Numbers: [27, 23] Generated Node #0,0,0: 74:[27, 23] Operation: 60-37=23 Exploring Operation: 60+27=87, Resulting Numbers: [37, 87] Generated Node #0,0,1: 74:[37, 87] Operation: 60+27=87 Exploring Operation: 60-27=33, Resulting Numbers: [37, 33] Generated Node #0,0,2: 74:[37, 33] Operation: 60-27=33 Exploring Operation: 37-27=10, Resulting Numbers: [60, 10] Generated Node #0,0,3: 74:[60, 10] Operation: 37-27=10 Exploring Operation: 37+27=64, Resulting Numbers: [60, 64] Generated Node #0,0,4: 74:[60, 64] Operation: 37+27=64 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 74:[37, 33], Operations: ['38-11=27', '60-27=33'] Exploring Operation: 37*33=1221, Resulting Numbers: [1221] 1221,74 unequal: No Solution Exploring Operation: 37+33=70, Resulting Numbers: [70] 70,74 unequal: No Solution Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 74:[37, 87], Operations: ['38-11=27', '60+27=87'] Exploring Operation: 87-37=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 37+87=124, Resulting Numbers: [124] 124,74 unequal: No Solution Exploring Operation: 37*87=3219, Resulting Numbers: [3219] 3219,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 74:[60, 10], Operations: ['38-11=27', '37-27=10'] Exploring Operation: 60+10=70, Resulting Numbers: [70] 70,74 unequal: No Solution Exploring Operation: 60-10=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 60*10=600, Resulting Numbers: [600] 600,74 unequal: No Solution Exploring Operation: 60/10=6, Resulting Numbers: [6] 6,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[27, 23], Operations: ['38-11=27', '60-37=23'] Exploring Operation: 27*23=621, Resulting Numbers: [621] 621,74 unequal: No Solution Exploring Operation: 27+23=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 74:[60, 64], Operations: ['38-11=27', '37+27=64'] Exploring Operation: 60+64=124, Resulting Numbers: [124] 124,74 unequal: No Solution Exploring Operation: 60*64=3840, Resulting Numbers: [3840] 3840,74 unequal: No Solution Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 74:[11, 38, 23], Operations: ['60-37=23'] Exploring Operation: 11+23=34, Resulting Numbers: [38, 34] Generated Node #0,1,0: 74:[38, 34] Operation: 11+23=34 Exploring Operation: 38+23=61, Resulting Numbers: [11, 61] Generated Node #0,1,1: 74:[11, 61] Operation: 38+23=61 Exploring Operation: 38-11=27, Resulting Numbers: [23, 27] Generated Node #0,1,2: 74:[23, 27] Operation: 38-11=27 Exploring Operation: 23-11=12, Resulting Numbers: [38, 12] Generated Node #0,1,3: 74:[38, 12] Operation: 23-11=12 Exploring Operation: 38-23=15, Resulting Numbers: [11, 15] Generated Node #0,1,4: 74:[11, 15] Operation: 38-23=15 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 74:[38, 34], Operations: ['60-37=23', '11+23=34'] Exploring Operation: 38*34=1292, Resulting Numbers: [1292] 1292,74 unequal: No Solution Exploring Operation: 38+34=72, Resulting Numbers: [72] 72,74 unequal: No Solution Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 74:[38, 12], Operations: ['60-37=23', '23-11=12'] Exploring Operation: 38-12=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 38+12=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 38*12=456, Resulting Numbers: [456] 456,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 74:[11, 61], Operations: ['60-37=23', '38+23=61'] Exploring Operation: 61-11=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 11+61=72, Resulting Numbers: [72] 72,74 unequal: No Solution Exploring Operation: 11*61=671, Resulting Numbers: [671] 671,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 74:[11, 15], Operations: ['60-37=23', '38-23=15'] Exploring Operation: 11+15=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,74 unequal: No Solution Exploring Operation: 11*15=165, Resulting Numbers: [165] 165,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 74:[23, 27], Operations: ['60-37=23', '38-11=27'] Exploring Operation: 23+27=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 23*27=621, Resulting Numbers: [621] 621,74 unequal: No Solution Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,74 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: 74:[11, 37, 22], Operations: ['60-38=22'] Exploring Operation: 11+22=33, Resulting Numbers: [37, 33] Generated Node #0,4,0: 74:[37, 33] Operation: 11+22=33 Exploring Operation: 37-22=15, Resulting Numbers: [11, 15] Generated Node #0,4,1: 74:[11, 15] Operation: 37-22=15 Exploring Operation: 22/11=2, Resulting Numbers: [37, 2] Generated Node #0,4,2: 74:[37, 2] Operation: 22/11=2 Exploring Operation: 22-11=11, Resulting Numbers: [37, 11] Generated Node #0,4,3: 74:[37, 11] Operation: 22-11=11 Exploring Operation: 37+22=59, Resulting Numbers: [11, 59] Generated Node #0,4,4: 74:[11, 59] Operation: 37+22=59 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 74:[37, 2], Operations: ['60-38=22', '22/11=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[11, 60, 38, 37], Operations: [] Exploring Operation: 60-38=22, Resulting Numbers: [11, 37, 22] Generated Node #0,4: 74:[11, 37, 22] Operation: 60-38=22 Moving to Node #0,4 Current State: 74:[11, 37, 22], Operations: ['60-38=22'] Exploring Operation: 22/11=2, Resulting Numbers: [37, 2] Generated Node #0,4,2: 74:[37, 2] Operation: 22/11=2 Moving to Node #0,4,2 Current State: 74:[37, 2], Operations: ['60-38=22', '22/11=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.928819
hs_5
sum_heuristic
[ 38, 34, 50, 41 ]
57
[ "34+41=75", "38*75=2850", "2850/50=57" ]
Current State: 57:[38, 34, 50, 41], Operations: [] Exploring Operation: 34+41=75, Resulting Numbers: [38, 50, 75] Generated Node #2: [38, 50, 75] from Operation: 34+41=75 Current State: 57:[38, 50, 75], Operations: ['34+41=75'] Exploring Operation: 38*75=2850, Resulting Numbers: [50, 2850] Generated Node #3: [50, 2850] from Operation: 38*75=2850 Current State: 57:[50, 2850], Operations: ['34+41=75', '38*75=2850'] Exploring Operation: 2850/50=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[38, 34, 50, 41], Operations: [] Exploring Operation: 38+34=72, Resulting Numbers: [50, 41, 72] Generated Node #0,0: 57:[50, 41, 72] Operation: 38+34=72 Exploring Operation: 41-34=7, Resulting Numbers: [38, 50, 7] Generated Node #0,1: 57:[38, 50, 7] Operation: 41-34=7 Exploring Operation: 41-38=3, Resulting Numbers: [34, 50, 3] Generated Node #0,2: 57:[34, 50, 3] Operation: 41-38=3 Exploring Operation: 38-34=4, Resulting Numbers: [50, 41, 4] Generated Node #0,3: 57:[50, 41, 4] Operation: 38-34=4 Moving to Node #0,2 Current State: 57:[34, 50, 3], Operations: ['41-38=3'] Exploring Operation: 50-34=16, Resulting Numbers: [3, 16] Generated Node #0,2,0: 57:[3, 16] Operation: 50-34=16 Exploring Operation: 34-3=31, Resulting Numbers: [50, 31] Generated Node #0,2,1: 57:[50, 31] Operation: 34-3=31 Exploring Operation: 50+3=53, Resulting Numbers: [34, 53] Generated Node #0,2,2: 57:[34, 53] Operation: 50+3=53 Exploring Operation: 34+3=37, Resulting Numbers: [50, 37] Generated Node #0,2,3: 57:[50, 37] Operation: 34+3=37 Moving to Node #0,3 Current State: 57:[50, 41, 4], Operations: ['38-34=4'] Exploring Operation: 50+4=54, Resulting Numbers: [41, 54] Generated Node #0,3,0: 57:[41, 54] Operation: 50+4=54 Exploring Operation: 41-4=37, Resulting Numbers: [50, 37] Generated Node #0,3,1: 57:[50, 37] Operation: 41-4=37 Exploring Operation: 41+4=45, Resulting Numbers: [50, 45] Generated Node #0,3,2: 57:[50, 45] Operation: 41+4=45 Exploring Operation: 50-41=9, Resulting Numbers: [4, 9] Generated Node #0,3,3: 57:[4, 9] Operation: 50-41=9 Moving to Node #0,1 Current State: 57:[38, 50, 7], Operations: ['41-34=7'] Exploring Operation: 50+7=57, Resulting Numbers: [38, 57] Generated Node #0,1,0: 57:[38, 57] Operation: 50+7=57 Exploring Operation: 38+7=45, Resulting Numbers: [50, 45] Generated Node #0,1,1: 57:[50, 45] Operation: 38+7=45 Exploring Operation: 50-38=12, Resulting Numbers: [7, 12] Generated Node #0,1,2: 57:[7, 12] Operation: 50-38=12 Exploring Operation: 38-7=31, Resulting Numbers: [50, 31] Generated Node #0,1,3: 57:[50, 31] Operation: 38-7=31 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 57:[7, 12], Operations: ['41-34=7', '50-38=12'] Exploring Operation: 7+12=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,57 unequal: No Solution Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[38, 57], Operations: ['41-34=7', '50+7=57'] Exploring Operation: 57-38=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 38*57=2166, Resulting Numbers: [2166] 2166,57 unequal: No Solution Exploring Operation: 38+57=95, Resulting Numbers: [95] 95,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 57:[50, 45], Operations: ['41-34=7', '38+7=45'] Exploring Operation: 50-45=5, Resulting Numbers: [5] 5,57 unequal: No Solution Exploring Operation: 50*45=2250, Resulting Numbers: [2250] 2250,57 unequal: No Solution Exploring Operation: 50+45=95, Resulting Numbers: [95] 95,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 57:[50, 31], Operations: ['41-34=7', '38-7=31'] Exploring Operation: 50-31=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 50+31=81, Resulting Numbers: [81] 81,57 unequal: No Solution Exploring Operation: 50*31=1550, Resulting Numbers: [1550] 1550,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 57:[50, 41, 72], Operations: ['38+34=72'] Exploring Operation: 72-41=31, Resulting Numbers: [50, 31] Generated Node #0,0,0: 57:[50, 31] Operation: 72-41=31 Exploring Operation: 50+41=91, Resulting Numbers: [72, 91] Generated Node #0,0,1: 57:[72, 91] Operation: 50+41=91 Exploring Operation: 72-50=22, Resulting Numbers: [41, 22] Generated Node #0,0,2: 57:[41, 22] Operation: 72-50=22 Exploring Operation: 50-41=9, Resulting Numbers: [72, 9] Generated Node #0,0,3: 57:[72, 9] Operation: 50-41=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[50, 31], Operations: ['38+34=72', '72-41=31'] Exploring Operation: 50*31=1550, Resulting Numbers: [1550] 1550,57 unequal: No Solution Exploring Operation: 50+31=81, Resulting Numbers: [81] 81,57 unequal: No Solution Exploring Operation: 50-31=19, Resulting Numbers: [19] 19,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 57:[41, 22], Operations: ['38+34=72', '72-50=22'] Exploring Operation: 41*22=902, Resulting Numbers: [902] 902,57 unequal: No Solution Exploring Operation: 41+22=63, Resulting Numbers: [63] 63,57 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 57:[72, 9], Operations: ['38+34=72', '50-41=9'] Exploring Operation: 72+9=81, Resulting Numbers: [81] 81,57 unequal: No Solution Exploring Operation: 72/9=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 72*9=648, Resulting Numbers: [648] 648,57 unequal: No Solution Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 57:[72, 91], Operations: ['38+34=72', '50+41=91'] Exploring Operation: 72+91=163, Resulting Numbers: [163] 163,57 unequal: No Solution Exploring Operation: 72*91=6552, Resulting Numbers: [6552] 6552,57 unequal: No Solution Exploring Operation: 91-72=19, Resulting Numbers: [19] 19,57 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: 57:[3, 16], Operations: ['41-38=3', '50-34=16'] Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,57 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,57 unequal: No Solution Moving to Node #0,3,3 Current State: 57:[4, 9], Operations: ['38-34=4', '50-41=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,57 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,57 unequal: No Solution Moving to Node #0,2,2 Current State: 57:[34, 53], Operations: ['41-38=3', '50+3=53'] Exploring Operation: 34+53=87, Resulting Numbers: [87] 87,57 unequal: No Solution Exploring Operation: 34*53=1802, Resulting Numbers: [1802] 1802,57 unequal: No Solution Exploring Operation: 53-34=19, Resulting Numbers: [19] 19,57 unequal: No Solution Moving to Node #0,3,0 Current State: 57:[41, 54], Operations: ['38-34=4', '50+4=54'] Exploring Operation: 41*54=2214, Resulting Numbers: [2214] 2214,57 unequal: No Solution Exploring Operation: 54-41=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 41+54=95, Resulting Numbers: [95] 95,57 unequal: No Solution Moving to Node #0,3,2 Current State: 57:[50, 45], Operations: ['38-34=4', '41+4=45'] Exploring Operation: 50-45=5, Resulting Numbers: [5] 5,57 unequal: No Solution Exploring Operation: 50+45=95, Resulting Numbers: [95] 95,57 unequal: No Solution Exploring Operation: 50*45=2250, Resulting Numbers: [2250] 2250,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[50, 31], Operations: ['41-38=3', '34-3=31'] Exploring Operation: 50-31=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 50+31=81, Resulting Numbers: [81] 81,57 unequal: No Solution Exploring Operation: 50*31=1550, Resulting Numbers: [1550] 1550,57 unequal: No Solution Moving to Node #0,2,3 Current State: 57:[50, 37], Operations: ['41-38=3', '34+3=37'] Exploring Operation: 50*37=1850, Resulting Numbers: [1850] 1850,57 unequal: No Solution Exploring Operation: 50-37=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 50+37=87, Resulting Numbers: [87] 87,57 unequal: No Solution Moving to Node #0,3,1 Current State: 57:[50, 37], Operations: ['38-34=4', '41-4=37'] Exploring Operation: 50-37=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 50*37=1850, Resulting Numbers: [1850] 1850,57 unequal: No Solution Exploring Operation: 50+37=87, Resulting Numbers: [87] 87,57 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 70, 35, 28, 59 ]
90
[ "70/35=2", "59*2=118", "118-28=90" ]
Current State: 90:[70, 35, 28, 59], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [28, 59, 2] Generated Node #2: [28, 59, 2] from Operation: 70/35=2 Current State: 90:[28, 59, 2], Operations: ['70/35=2'] Exploring Operation: 59*2=118, Resulting Numbers: [28, 118] Generated Node #3: [28, 118] from Operation: 59*2=118 Current State: 90:[28, 118], Operations: ['70/35=2', '59*2=118'] Exploring Operation: 118-28=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[70, 35, 28, 59], Operations: [] Exploring Operation: 70-28=42, Resulting Numbers: [35, 59, 42] Generated Node #0,0: 90:[35, 59, 42] Operation: 70-28=42 Exploring Operation: 70-59=11, Resulting Numbers: [35, 28, 11] Generated Node #0,1: 90:[35, 28, 11] Operation: 70-59=11 Exploring Operation: 70/35=2, Resulting Numbers: [28, 59, 2] Generated Node #0,2: 90:[28, 59, 2] Operation: 70/35=2 Exploring Operation: 70-35=35, Resulting Numbers: [28, 59, 35] Generated Node #0,3: 90:[28, 59, 35] Operation: 70-35=35 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[35, 28, 11], Operations: ['70-59=11'] Exploring Operation: 35-28=7, Resulting Numbers: [11, 7] Generated Node #0,1,0: 90:[11, 7] Operation: 35-28=7 Exploring Operation: 28-11=17, Resulting Numbers: [35, 17] Generated Node #0,1,1: 90:[35, 17] Operation: 28-11=17 Exploring Operation: 35-11=24, Resulting Numbers: [28, 24] Generated Node #0,1,2: 90:[28, 24] Operation: 35-11=24 Exploring Operation: 35+11=46, Resulting Numbers: [28, 46] Generated Node #0,1,3: 90:[28, 46] Operation: 35+11=46 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[11, 7], Operations: ['70-59=11', '35-28=7'] Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 11+7=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 11*7=77, Resulting Numbers: [77] 77,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 90:[28, 46], Operations: ['70-59=11', '35+11=46'] Exploring Operation: 46-28=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 28+46=74, Resulting Numbers: [74] 74,90 unequal: No Solution Exploring Operation: 28*46=1288, Resulting Numbers: [1288] 1288,90 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:[35, 17], Operations: ['70-59=11', '28-11=17'] Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 35+17=52, Resulting Numbers: [52] 52,90 unequal: No Solution Exploring Operation: 35*17=595, Resulting Numbers: [595] 595,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 90:[28, 24], Operations: ['70-59=11', '35-11=24'] Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,90 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[28, 59, 2], Operations: ['70/35=2'] Exploring Operation: 28+2=30, Resulting Numbers: [59, 30] Generated Node #0,2,0: 90:[59, 30] Operation: 28+2=30 Exploring Operation: 28+59=87, Resulting Numbers: [2, 87] Generated Node #0,2,1: 90:[2, 87] Operation: 28+59=87 Exploring Operation: 59-28=31, Resulting Numbers: [2, 31] Generated Node #0,2,2: 90:[2, 31] Operation: 59-28=31 Exploring Operation: 59-2=57, Resulting Numbers: [28, 57] Generated Node #0,2,3: 90:[28, 57] Operation: 59-2=57 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 90:[2, 31], Operations: ['70/35=2', '59-28=31'] Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,90 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,90 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 #0,2,1 Current State: 90:[2, 87], Operations: ['70/35=2', '28+59=87'] Exploring Operation: 2+87=89, Resulting Numbers: [89] 89,90 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,90 unequal: No Solution Exploring Operation: 2*87=174, Resulting Numbers: [174] 174,90 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 #0,2,0 Current State: 90:[59, 30], Operations: ['70/35=2', '28+2=30'] Exploring Operation: 59*30=1770, Resulting Numbers: [1770] 1770,90 unequal: No Solution Exploring Operation: 59+30=89, Resulting Numbers: [89] 89,90 unequal: No Solution Exploring Operation: 59-30=29, Resulting Numbers: [29] 29,90 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 #0,2,3 Current State: 90:[28, 57], Operations: ['70/35=2', '59-2=57'] Exploring Operation: 28*57=1596, Resulting Numbers: [1596] 1596,90 unequal: No Solution Exploring Operation: 57-28=29, Resulting Numbers: [29] 29,90 unequal: No Solution Exploring Operation: 28+57=85, Resulting Numbers: [85] 85,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[28, 59, 35], Operations: ['70-35=35'] Exploring Operation: 59-35=24, Resulting Numbers: [28, 24] Generated Node #0,3,0: 90:[28, 24] Operation: 59-35=24 Exploring Operation: 59-28=31, Resulting Numbers: [35, 31] Generated Node #0,3,1: 90:[35, 31] Operation: 59-28=31 Exploring Operation: 59+35=94, Resulting Numbers: [28, 94] Generated Node #0,3,2: 90:[28, 94] Operation: 59+35=94 Exploring Operation: 28+59=87, Resulting Numbers: [35, 87] Generated Node #0,3,3: 90:[35, 87] Operation: 28+59=87 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 90:[35, 31], Operations: ['70-35=35', '59-28=31'] Exploring Operation: 35*31=1085, Resulting Numbers: [1085] 1085,90 unequal: No Solution Exploring Operation: 35+31=66, Resulting Numbers: [66] 66,90 unequal: No Solution Exploring Operation: 35-31=4, Resulting Numbers: [4] 4,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 90:[28, 94], Operations: ['70-35=35', '59+35=94'] Exploring Operation: 28+94=122, Resulting Numbers: [122] 122,90 unequal: No Solution Exploring Operation: 28*94=2632, Resulting Numbers: [2632] 2632,90 unequal: No Solution Exploring Operation: 94-28=66, Resulting Numbers: [66] 66,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 90:[28, 24], Operations: ['70-35=35', '59-35=24'] Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,90 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,90 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 90:[35, 87], Operations: ['70-35=35', '28+59=87'] Exploring Operation: 35+87=122, Resulting Numbers: [122] 122,90 unequal: No Solution Exploring Operation: 35*87=3045, Resulting Numbers: [3045] 3045,90 unequal: No Solution Exploring Operation: 87-35=52, Resulting Numbers: [52] 52,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[35, 59, 42], Operations: ['70-28=42'] Exploring Operation: 59-42=17, Resulting Numbers: [35, 17] Generated Node #0,0,0: 90:[35, 17] Operation: 59-42=17 Exploring Operation: 59-35=24, Resulting Numbers: [42, 24] Generated Node #0,0,1: 90:[42, 24] Operation: 59-35=24 Exploring Operation: 35+59=94, Resulting Numbers: [42, 94] Generated Node #0,0,2: 90:[42, 94] Operation: 35+59=94 Exploring Operation: 42-35=7, Resulting Numbers: [59, 7] Generated Node #0,0,3: 90:[59, 7] Operation: 42-35=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[35, 17], Operations: ['70-28=42', '59-42=17'] Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 35*17=595, Resulting Numbers: [595] 595,90 unequal: No Solution Exploring Operation: 35+17=52, Resulting Numbers: [52] 52,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 90:[42, 94], Operations: ['70-28=42', '35+59=94'] Exploring Operation: 42*94=3948, Resulting Numbers: [3948] 3948,90 unequal: No Solution Exploring Operation: 94-42=52, Resulting Numbers: [52] 52,90 unequal: No Solution Exploring Operation: 42+94=136, Resulting Numbers: [136] 136,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 90:[42, 24], Operations: ['70-28=42', '59-35=24'] Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 42+24=66, Resulting Numbers: [66] 66,90 unequal: No Solution Exploring Operation: 42*24=1008, Resulting Numbers: [1008] 1008,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 90:[59, 7], Operations: ['70-28=42', '42-35=7'] Exploring Operation: 59+7=66, Resulting Numbers: [66] 66,90 unequal: No Solution Exploring Operation: 59*7=413, Resulting Numbers: [413] 413,90 unequal: No Solution Exploring Operation: 59-7=52, Resulting Numbers: [52] 52,90 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_4
sum_heuristic
[ 12, 63, 43, 40 ]
48
[ "63-12=51", "43-40=3", "51-3=48" ]
Current State: 48:[12, 63, 43, 40], Operations: [] Exploring Operation: 63-12=51, Resulting Numbers: [43, 40, 51] Generated Node #2: [43, 40, 51] from Operation: 63-12=51 Current State: 48:[43, 40, 51], Operations: ['63-12=51'] Exploring Operation: 43-40=3, Resulting Numbers: [51, 3] Generated Node #3: [51, 3] from Operation: 43-40=3 Current State: 48:[51, 3], Operations: ['63-12=51', '43-40=3'] Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[12, 63, 43, 40], Operations: [] Exploring Operation: 63-40=23, Resulting Numbers: [12, 43, 23] Generated Node #0,0: 48:[12, 43, 23] Operation: 63-40=23 Exploring Operation: 63-43=20, Resulting Numbers: [12, 40, 20] Generated Node #0,1: 48:[12, 40, 20] Operation: 63-43=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[12, 43, 23], Operations: ['63-40=23'] Exploring Operation: 43-23=20, Resulting Numbers: [12, 20] Generated Node #0,0,0: 48:[12, 20] Operation: 43-23=20 Exploring Operation: 23-12=11, Resulting Numbers: [43, 11] Generated Node #0,0,1: 48:[43, 11] Operation: 23-12=11 Moving to Node #0,0,0 Current State: 48:[12, 20], Operations: ['63-40=23', '43-23=20'] Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 12+20=32, Resulting Numbers: [32] 32,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[43, 11], Operations: ['63-40=23', '23-12=11'] Exploring Operation: 43+11=54, Resulting Numbers: [54] 54,48 unequal: No Solution Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,48 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 Current State: 48:[12, 40, 20], Operations: ['63-43=20'] Exploring Operation: 40/20=2, Resulting Numbers: [12, 2] Generated Node #0,1,0: 48:[12, 2] Operation: 40/20=2 Exploring Operation: 40-20=20, Resulting Numbers: [12, 20] Generated Node #0,1,1: 48:[12, 20] Operation: 40-20=20 Moving to Node #0,1,0 Current State: 48:[12, 2], Operations: ['63-43=20', '40/20=2'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,48 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[12, 20], Operations: ['63-43=20', '40-20=20'] Exploring Operation: 12+20=32, Resulting Numbers: [32] 32,48 unequal: No Solution Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 3, 93, 22, 37 ]
64
[ "3*22=66", "93+37=130", "130-66=64" ]
Current State: 64:[3, 93, 22, 37], Operations: [] Exploring Operation: 3*22=66, Resulting Numbers: [93, 37, 66] Generated Node #2: [93, 37, 66] from Operation: 3*22=66 Current State: 64:[93, 37, 66], Operations: ['3*22=66'] Exploring Operation: 93+37=130, Resulting Numbers: [66, 130] Generated Node #3: [66, 130] from Operation: 93+37=130 Current State: 64:[66, 130], Operations: ['3*22=66', '93+37=130'] Exploring Operation: 130-66=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[3, 93, 22, 37], Operations: [] Exploring Operation: 93-22=71, Resulting Numbers: [3, 37, 71] Generated Node #0,0: 64:[3, 37, 71] Operation: 93-22=71 Exploring Operation: 93-37=56, Resulting Numbers: [3, 22, 56] Generated Node #0,1: 64:[3, 22, 56] Operation: 93-37=56 Exploring Operation: 37-22=15, Resulting Numbers: [3, 93, 15] Generated Node #0,2: 64:[3, 93, 15] Operation: 37-22=15 Exploring Operation: 93/3=31, Resulting Numbers: [22, 37, 31] Generated Node #0,3: 64:[22, 37, 31] Operation: 93/3=31 Start Sub Search at level 1: Moving to Node #0,3 Current State: 64:[22, 37, 31], Operations: ['93/3=31'] Exploring Operation: 37-31=6, Resulting Numbers: [22, 6] Generated Node #0,3,0: 64:[22, 6] Operation: 37-31=6 Exploring Operation: 31-22=9, Resulting Numbers: [37, 9] Generated Node #0,3,1: 64:[37, 9] Operation: 31-22=9 Exploring Operation: 37-22=15, Resulting Numbers: [31, 15] Generated Node #0,3,2: 64:[31, 15] Operation: 37-22=15 Exploring Operation: 22+37=59, Resulting Numbers: [31, 59] Generated Node #0,3,3: 64:[31, 59] Operation: 22+37=59 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 64:[31, 15], Operations: ['93/3=31', '37-22=15'] Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,64 unequal: No Solution Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,64 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 64:[37, 9], Operations: ['93/3=31', '31-22=9'] Exploring Operation: 37+9=46, Resulting Numbers: [46] 46,64 unequal: No Solution Exploring Operation: 37*9=333, Resulting Numbers: [333] 333,64 unequal: No Solution Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 64:[31, 59], Operations: ['93/3=31', '22+37=59'] Exploring Operation: 31*59=1829, Resulting Numbers: [1829] 1829,64 unequal: No Solution Exploring Operation: 31+59=90, Resulting Numbers: [90] 90,64 unequal: No Solution Exploring Operation: 59-31=28, Resulting Numbers: [28] 28,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 64:[22, 6], Operations: ['93/3=31', '37-31=6'] Exploring Operation: 22*6=132, Resulting Numbers: [132] 132,64 unequal: No Solution Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,64 unequal: No Solution Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[3, 37, 71], Operations: ['93-22=71'] Exploring Operation: 37-3=34, Resulting Numbers: [71, 34] Generated Node #0,0,0: 64:[71, 34] Operation: 37-3=34 Exploring Operation: 3+37=40, Resulting Numbers: [71, 40] Generated Node #0,0,1: 64:[71, 40] Operation: 3+37=40 Exploring Operation: 71-3=68, Resulting Numbers: [37, 68] Generated Node #0,0,2: 64:[37, 68] Operation: 71-3=68 Exploring Operation: 71-37=34, Resulting Numbers: [3, 34] Generated Node #0,0,3: 64:[3, 34] Operation: 71-37=34 Moving to Node #0,0,3 Current State: 64:[3, 34], Operations: ['93-22=71', '71-37=34'] Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,64 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,64 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,64 unequal: No Solution Moving to Node #0,0,2 Current State: 64:[37, 68], Operations: ['93-22=71', '71-3=68'] Exploring Operation: 37*68=2516, Resulting Numbers: [2516] 2516,64 unequal: No Solution Exploring Operation: 68-37=31, Resulting Numbers: [31] 31,64 unequal: No Solution Exploring Operation: 37+68=105, Resulting Numbers: [105] 105,64 unequal: No Solution Moving to Node #0,0,0 Current State: 64:[71, 34], Operations: ['93-22=71', '37-3=34'] Exploring Operation: 71*34=2414, Resulting Numbers: [2414] 2414,64 unequal: No Solution Exploring Operation: 71+34=105, Resulting Numbers: [105] 105,64 unequal: No Solution Exploring Operation: 71-34=37, Resulting Numbers: [37] 37,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[71, 40], Operations: ['93-22=71', '3+37=40'] Exploring Operation: 71-40=31, Resulting Numbers: [31] 31,64 unequal: No Solution Exploring Operation: 71*40=2840, Resulting Numbers: [2840] 2840,64 unequal: No Solution Exploring Operation: 71+40=111, Resulting Numbers: [111] 111,64 unequal: No Solution No 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: 64:[3, 22, 56], Operations: ['93-37=56'] Exploring Operation: 56-22=34, Resulting Numbers: [3, 34] Generated Node #0,1,0: 64:[3, 34] Operation: 56-22=34 Exploring Operation: 3+56=59, Resulting Numbers: [22, 59] Generated Node #0,1,1: 64:[22, 59] Operation: 3+56=59 Exploring Operation: 22-3=19, Resulting Numbers: [56, 19] Generated Node #0,1,2: 64:[56, 19] Operation: 22-3=19 Exploring Operation: 3*22=66, Resulting Numbers: [56, 66] Generated Node #0,1,3: 64:[56, 66] Operation: 3*22=66 Moving to Node #0,1,0 Current State: 64:[3, 34], Operations: ['93-37=56', '56-22=34'] Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,64 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,64 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,64 unequal: No Solution Moving to Node #0,1,3 Current State: 64:[56, 66], Operations: ['93-37=56', '3*22=66'] Exploring Operation: 56*66=3696, Resulting Numbers: [3696] 3696,64 unequal: No Solution Exploring Operation: 56+66=122, Resulting Numbers: [122] 122,64 unequal: No Solution Exploring Operation: 66-56=10, Resulting Numbers: [10] 10,64 unequal: No Solution Moving to Node #0,1,2 Current State: 64:[56, 19], Operations: ['93-37=56', '22-3=19'] Exploring Operation: 56*19=1064, Resulting Numbers: [1064] 1064,64 unequal: No Solution Exploring Operation: 56+19=75, Resulting Numbers: [75] 75,64 unequal: No Solution Exploring Operation: 56-19=37, Resulting Numbers: [37] 37,64 unequal: No Solution Moving to Node #0,1,1 Current State: 64:[22, 59], Operations: ['93-37=56', '3+56=59'] Exploring Operation: 22+59=81, Resulting Numbers: [81] 81,64 unequal: No Solution Exploring Operation: 22*59=1298, Resulting Numbers: [1298] 1298,64 unequal: No Solution Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,64 unequal: No Solution No 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: 64:[3, 93, 15], Operations: ['37-22=15'] Exploring Operation: 93-15=78, Resulting Numbers: [3, 78] Generated Node #0,2,0: 64:[3, 78] Operation: 93-15=78 Exploring Operation: 93/3=31, Resulting Numbers: [15, 31] Generated Node #0,2,1: 64:[15, 31] Operation: 93/3=31 Exploring Operation: 15/3=5, Resulting Numbers: [93, 5] Generated Node #0,2,2: 64:[93, 5] Operation: 15/3=5 Exploring Operation: 93-3=90, Resulting Numbers: [15, 90] Generated Node #0,2,3: 64:[15, 90] Operation: 93-3=90 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 64:[15, 31], Operations: ['37-22=15', '93/3=31'] Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,64 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,64 unequal: No Solution Exploring Operation: 15*31=465, Resulting Numbers: [465] 465,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 64:[3, 78], Operations: ['37-22=15', '93-15=78'] Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,64 unequal: No Solution Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,64 unequal: No Solution Exploring Operation: 3*78=234, Resulting Numbers: [234] 234,64 unequal: No Solution Exploring Operation: 3+78=81, Resulting Numbers: [81] 81,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 64:[15, 90], Operations: ['37-22=15', '93-3=90'] Exploring Operation: 15+90=105, Resulting Numbers: [105] 105,64 unequal: No Solution Exploring Operation: 90-15=75, Resulting Numbers: [75] 75,64 unequal: No Solution Exploring Operation: 90/15=6, Resulting Numbers: [6] 6,64 unequal: No Solution Exploring Operation: 15*90=1350, Resulting Numbers: [1350] 1350,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 64:[93, 5], Operations: ['37-22=15', '15/3=5'] Exploring Operation: 93*5=465, Resulting Numbers: [465] 465,64 unequal: No Solution Exploring Operation: 93+5=98, Resulting Numbers: [98] 98,64 unequal: No Solution Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 84, 52, 39, 55 ]
67
[ "55-52=3", "84/3=28", "39+28=67" ]
Current State: 67:[84, 52, 39, 55], Operations: [] Exploring Operation: 55-52=3, Resulting Numbers: [84, 39, 3] Generated Node #2: [84, 39, 3] from Operation: 55-52=3 Current State: 67:[84, 39, 3], Operations: ['55-52=3'] Exploring Operation: 84/3=28, Resulting Numbers: [39, 28] Generated Node #3: [39, 28] from Operation: 84/3=28 Current State: 67:[39, 28], Operations: ['55-52=3', '84/3=28'] Exploring Operation: 39+28=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[84, 52, 39, 55], Operations: [] Exploring Operation: 84-39=45, Resulting Numbers: [52, 55, 45] Generated Node #0,0: 67:[52, 55, 45] Operation: 84-39=45 Exploring Operation: 52+39=91, Resulting Numbers: [84, 55, 91] Generated Node #0,1: 67:[84, 55, 91] Operation: 52+39=91 Exploring Operation: 39+55=94, Resulting Numbers: [84, 52, 94] Generated Node #0,2: 67:[84, 52, 94] Operation: 39+55=94 Exploring Operation: 84-52=32, Resulting Numbers: [39, 55, 32] Generated Node #0,3: 67:[39, 55, 32] Operation: 84-52=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[52, 55, 45], Operations: ['84-39=45'] Exploring Operation: 52+55=107, Resulting Numbers: [45, 107] Generated Node #0,0,0: 67:[45, 107] Operation: 52+55=107 Exploring Operation: 52+45=97, Resulting Numbers: [55, 97] Generated Node #0,0,1: 67:[55, 97] Operation: 52+45=97 Exploring Operation: 55+45=100, Resulting Numbers: [52, 100] Generated Node #0,0,2: 67:[52, 100] Operation: 55+45=100 Exploring Operation: 52-45=7, Resulting Numbers: [55, 7] Generated Node #0,0,3: 67:[55, 7] Operation: 52-45=7 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 67:[55, 97], Operations: ['84-39=45', '52+45=97'] Exploring Operation: 55+97=152, Resulting Numbers: [152] 152,67 unequal: No Solution Exploring Operation: 97-55=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 55*97=5335, Resulting Numbers: [5335] 5335,67 unequal: No Solution No 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: 67:[52, 100], Operations: ['84-39=45', '55+45=100'] Exploring Operation: 52+100=152, Resulting Numbers: [152] 152,67 unequal: No Solution Exploring Operation: 52*100=5200, Resulting Numbers: [5200] 5200,67 unequal: No Solution Exploring Operation: 100-52=48, Resulting Numbers: [48] 48,67 unequal: No Solution No 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: 67:[45, 107], Operations: ['84-39=45', '52+55=107'] Exploring Operation: 45*107=4815, Resulting Numbers: [4815] 4815,67 unequal: No Solution Exploring Operation: 107-45=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 45+107=152, Resulting Numbers: [152] 152,67 unequal: No Solution No 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: 67:[55, 7], Operations: ['84-39=45', '52-45=7'] Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,67 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,67 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: 67:[84, 55, 91], Operations: ['52+39=91'] Exploring Operation: 91-55=36, Resulting Numbers: [84, 36] Generated Node #0,1,0: 67:[84, 36] Operation: 91-55=36 Exploring Operation: 91-84=7, Resulting Numbers: [55, 7] Generated Node #0,1,1: 67:[55, 7] Operation: 91-84=7 Exploring Operation: 84+55=139, Resulting Numbers: [91, 139] Generated Node #0,1,2: 67:[91, 139] Operation: 84+55=139 Exploring Operation: 84-55=29, Resulting Numbers: [91, 29] Generated Node #0,1,3: 67:[91, 29] Operation: 84-55=29 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 67:[84, 36], Operations: ['52+39=91', '91-55=36'] Exploring Operation: 84+36=120, Resulting Numbers: [120] 120,67 unequal: No Solution Exploring Operation: 84*36=3024, Resulting Numbers: [3024] 3024,67 unequal: No Solution Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,67 unequal: No Solution No 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: 67:[91, 29], Operations: ['52+39=91', '84-55=29'] Exploring Operation: 91-29=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 91*29=2639, Resulting Numbers: [2639] 2639,67 unequal: No Solution Exploring Operation: 91+29=120, Resulting Numbers: [120] 120,67 unequal: No Solution No 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: 67:[55, 7], Operations: ['52+39=91', '91-84=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,67 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,67 unequal: No Solution No 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: 67:[91, 139], Operations: ['52+39=91', '84+55=139'] Exploring Operation: 139-91=48, Resulting Numbers: [48] 48,67 unequal: No Solution Exploring Operation: 91*139=12649, Resulting Numbers: [12649] 12649,67 unequal: No Solution Exploring Operation: 91+139=230, Resulting Numbers: [230] 230,67 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: 67:[84, 52, 94], Operations: ['39+55=94'] Exploring Operation: 94-84=10, Resulting Numbers: [52, 10] Generated Node #0,2,0: 67:[52, 10] Operation: 94-84=10 Exploring Operation: 84+52=136, Resulting Numbers: [94, 136] Generated Node #0,2,1: 67:[94, 136] Operation: 84+52=136 Exploring Operation: 94-52=42, Resulting Numbers: [84, 42] Generated Node #0,2,2: 67:[84, 42] Operation: 94-52=42 Exploring Operation: 84-52=32, Resulting Numbers: [94, 32] Generated Node #0,2,3: 67:[94, 32] Operation: 84-52=32 Moving to Node #0,2,2 Current State: 67:[84, 42], Operations: ['39+55=94', '94-52=42'] Exploring Operation: 84*42=3528, Resulting Numbers: [3528] 3528,67 unequal: No Solution Exploring Operation: 84/42=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 84+42=126, Resulting Numbers: [126] 126,67 unequal: No Solution Exploring Operation: 84-42=42, Resulting Numbers: [42] 42,67 unequal: No Solution Moving to Node #0,2,3 Current State: 67:[94, 32], Operations: ['39+55=94', '84-52=32'] Exploring Operation: 94-32=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 94*32=3008, Resulting Numbers: [3008] 3008,67 unequal: No Solution Exploring Operation: 94+32=126, Resulting Numbers: [126] 126,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[52, 10], Operations: ['39+55=94', '94-84=10'] Exploring Operation: 52*10=520, Resulting Numbers: [520] 520,67 unequal: No Solution Exploring Operation: 52+10=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[94, 136], Operations: ['39+55=94', '84+52=136'] Exploring Operation: 94+136=230, Resulting Numbers: [230] 230,67 unequal: No Solution Exploring Operation: 136-94=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 94*136=12784, Resulting Numbers: [12784] 12784,67 unequal: No Solution No 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: 67:[39, 55, 32], Operations: ['84-52=32'] Exploring Operation: 55+32=87, Resulting Numbers: [39, 87] Generated Node #0,3,0: 67:[39, 87] Operation: 55+32=87 Exploring Operation: 39-32=7, Resulting Numbers: [55, 7] Generated Node #0,3,1: 67:[55, 7] Operation: 39-32=7 Exploring Operation: 39+32=71, Resulting Numbers: [55, 71] Generated Node #0,3,2: 67:[55, 71] Operation: 39+32=71 Exploring Operation: 39+55=94, Resulting Numbers: [32, 94] Generated Node #0,3,3: 67:[32, 94] Operation: 39+55=94 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 67:[55, 71], Operations: ['84-52=32', '39+32=71'] Exploring Operation: 55*71=3905, Resulting Numbers: [3905] 3905,67 unequal: No Solution Exploring Operation: 71-55=16, Resulting Numbers: [16] 16,67 unequal: No Solution Exploring Operation: 55+71=126, Resulting Numbers: [126] 126,67 unequal: No Solution No 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: 67:[39, 87], Operations: ['84-52=32', '55+32=87'] Exploring Operation: 39+87=126, Resulting Numbers: [126] 126,67 unequal: No Solution Exploring Operation: 87-39=48, Resulting Numbers: [48] 48,67 unequal: No Solution Exploring Operation: 39*87=3393, Resulting Numbers: [3393] 3393,67 unequal: No Solution No 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: 67:[32, 94], Operations: ['84-52=32', '39+55=94'] Exploring Operation: 94-32=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 32*94=3008, Resulting Numbers: [3008] 3008,67 unequal: No Solution Exploring Operation: 32+94=126, Resulting Numbers: [126] 126,67 unequal: No Solution No 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: 67:[55, 7], Operations: ['84-52=32', '39-32=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,67 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,67 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 7, 45, 73, 97 ]
28
[ "7+45=52", "97-73=24", "52-24=28" ]
Current State: 28:[7, 45, 73, 97], Operations: [] Exploring Operation: 7+45=52, Resulting Numbers: [73, 97, 52] Generated Node #2: [73, 97, 52] from Operation: 7+45=52 Current State: 28:[73, 97, 52], Operations: ['7+45=52'] Exploring Operation: 97-73=24, Resulting Numbers: [52, 24] Generated Node #3: [52, 24] from Operation: 97-73=24 Current State: 28:[52, 24], Operations: ['7+45=52', '97-73=24'] Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[7, 45, 73, 97], Operations: [] Exploring Operation: 97-73=24, Resulting Numbers: [7, 45, 24] Generated Node #0,0: 28:[7, 45, 24] Operation: 97-73=24 Moving to Node #0,0 Current State: 28:[7, 45, 24], Operations: ['97-73=24'] Exploring Operation: 45-24=21, Resulting Numbers: [7, 21] Generated Node #0,0,0: 28:[7, 21] Operation: 45-24=21 Moving to Node #0,0,0 Current State: 28:[7, 21], Operations: ['97-73=24', '45-24=21'] Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[7, 45, 73, 97], Operations: [] Exploring Operation: 97-73=24, Resulting Numbers: [7, 45, 24] Generated Node #0,0: 28:[7, 45, 24] Operation: 97-73=24 Moving to Node #0,0 Current State: 28:[7, 45, 24], Operations: ['97-73=24'] Exploring Operation: 45-24=21, Resulting Numbers: [7, 21] Generated Node #0,0,0: 28:[7, 21] Operation: 45-24=21 Moving to Node #0,0,0 Current State: 28:[7, 21], Operations: ['97-73=24', '45-24=21'] Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 66, 65, 4, 18 ]
53
[ "66-18=48", "48/4=12", "65-12=53" ]
Current State: 53:[66, 65, 4, 18], Operations: [] Exploring Operation: 66-18=48, Resulting Numbers: [65, 4, 48] Generated Node #2: [65, 4, 48] from Operation: 66-18=48 Current State: 53:[65, 4, 48], Operations: ['66-18=48'] Exploring Operation: 48/4=12, Resulting Numbers: [65, 12] Generated Node #3: [65, 12] from Operation: 48/4=12 Current State: 53:[65, 12], Operations: ['66-18=48', '48/4=12'] Exploring Operation: 65-12=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[66, 65, 4, 18], Operations: [] Exploring Operation: 4*18=72, Resulting Numbers: [66, 65, 72] Generated Node #0,0: 53:[66, 65, 72] Operation: 4*18=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[66, 65, 72], Operations: ['4*18=72'] Exploring Operation: 72-66=6, Resulting Numbers: [65, 6] Generated Node #0,0,0: 53:[65, 6] Operation: 72-66=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 53:[65, 6], Operations: ['4*18=72', '72-66=6'] Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 74, 39, 16, 19 ]
78
[ "74+39=113", "16+19=35", "113-35=78" ]
Current State: 78:[74, 39, 16, 19], Operations: [] Exploring Operation: 74+39=113, Resulting Numbers: [16, 19, 113] Generated Node #2: [16, 19, 113] from Operation: 74+39=113 Current State: 78:[16, 19, 113], Operations: ['74+39=113'] Exploring Operation: 16+19=35, Resulting Numbers: [113, 35] Generated Node #3: [113, 35] from Operation: 16+19=35 Current State: 78:[113, 35], Operations: ['74+39=113', '16+19=35'] Exploring Operation: 113-35=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[74, 39, 16, 19], Operations: [] Exploring Operation: 16+19=35, Resulting Numbers: [74, 39, 35] Generated Node #0,0: 78:[74, 39, 35] Operation: 16+19=35 Exploring Operation: 19-16=3, Resulting Numbers: [74, 39, 3] Generated Node #0,1: 78:[74, 39, 3] Operation: 19-16=3 Exploring Operation: 74-39=35, Resulting Numbers: [16, 19, 35] Generated Node #0,2: 78:[16, 19, 35] Operation: 74-39=35 Moving to Node #0,1 Current State: 78:[74, 39, 3], Operations: ['19-16=3'] Exploring Operation: 74-39=35, Resulting Numbers: [3, 35] Generated Node #0,1,0: 78:[3, 35] Operation: 74-39=35 Exploring Operation: 39/3=13, Resulting Numbers: [74, 13] Generated Node #0,1,1: 78:[74, 13] Operation: 39/3=13 Exploring Operation: 74+3=77, Resulting Numbers: [39, 77] Generated Node #0,1,2: 78:[39, 77] Operation: 74+3=77 Moving to Node #0,0 Current State: 78:[74, 39, 35], Operations: ['16+19=35'] Exploring Operation: 74-35=39, Resulting Numbers: [39, 39] Generated Node #0,0,0: 78:[39, 39] Operation: 74-35=39 Exploring Operation: 74-39=35, Resulting Numbers: [35, 35] Generated Node #0,0,1: 78:[35, 35] Operation: 74-39=35 Exploring Operation: 39-35=4, Resulting Numbers: [74, 4] Generated Node #0,0,2: 78:[74, 4] Operation: 39-35=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[39, 39], Operations: ['16+19=35', '74-35=39'] Exploring Operation: 39+39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[74, 39, 16, 19], Operations: [] Exploring Operation: 16+19=35, Resulting Numbers: [74, 39, 35] Generated Node #0,0: 78:[74, 39, 35] Operation: 16+19=35 Moving to Node #0,0 Current State: 78:[74, 39, 35], Operations: ['16+19=35'] Exploring Operation: 74-35=39, Resulting Numbers: [39, 39] Generated Node #0,0,0: 78:[39, 39] Operation: 74-35=39 Moving to Node #0,0,0 Current State: 78:[39, 39], Operations: ['16+19=35', '74-35=39'] Exploring Operation: 39+39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 2, 11, 7, 91 ]
89
[ "11-2=9", "7+91=98", "98-9=89" ]
Current State: 89:[2, 11, 7, 91], Operations: [] Exploring Operation: 11-2=9, Resulting Numbers: [7, 91, 9] Generated Node #2: [7, 91, 9] from Operation: 11-2=9 Current State: 89:[7, 91, 9], Operations: ['11-2=9'] Exploring Operation: 7+91=98, Resulting Numbers: [9, 98] Generated Node #3: [9, 98] from Operation: 7+91=98 Current State: 89:[9, 98], Operations: ['11-2=9', '7+91=98'] Exploring Operation: 98-9=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[2, 11, 7, 91], Operations: [] Exploring Operation: 2+7=9, Resulting Numbers: [11, 91, 9] Generated Node #0,0: 89:[11, 91, 9] Operation: 2+7=9 Exploring Operation: 2+11=13, Resulting Numbers: [7, 91, 13] Generated Node #0,1: 89:[7, 91, 13] Operation: 2+11=13 Exploring Operation: 2*11=22, Resulting Numbers: [7, 91, 22] Generated Node #0,2: 89:[7, 91, 22] Operation: 2*11=22 Exploring Operation: 11*7=77, Resulting Numbers: [2, 91, 77] Generated Node #0,3: 89:[2, 91, 77] Operation: 11*7=77 Exploring Operation: 2*7=14, Resulting Numbers: [11, 91, 14] Generated Node #0,4: 89:[11, 91, 14] Operation: 2*7=14 Start Sub Search at level 1: Moving to Node #0,3 Current State: 89:[2, 91, 77], Operations: ['11*7=77'] Exploring Operation: 2*77=154, Resulting Numbers: [91, 154] Generated Node #0,3,0: 89:[91, 154] Operation: 2*77=154 Exploring Operation: 77-2=75, Resulting Numbers: [91, 75] Generated Node #0,3,1: 89:[91, 75] Operation: 77-2=75 Exploring Operation: 2+77=79, Resulting Numbers: [91, 79] Generated Node #0,3,2: 89:[91, 79] Operation: 2+77=79 Exploring Operation: 91-2=89, Resulting Numbers: [77, 89] Generated Node #0,3,3: 89:[77, 89] Operation: 91-2=89 Exploring Operation: 2+91=93, Resulting Numbers: [77, 93] Generated Node #0,3,4: 89:[77, 93] Operation: 2+91=93 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 89:[91, 79], Operations: ['11*7=77', '2+77=79'] Exploring Operation: 91+79=170, Resulting Numbers: [170] 170,89 unequal: No Solution Exploring Operation: 91*79=7189, Resulting Numbers: [7189] 7189,89 unequal: No Solution Exploring Operation: 91-79=12, Resulting Numbers: [12] 12,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 89:[77, 89], Operations: ['11*7=77', '91-2=89'] Exploring Operation: 77*89=6853, Resulting Numbers: [6853] 6853,89 unequal: No Solution Exploring Operation: 77+89=166, Resulting Numbers: [166] 166,89 unequal: No Solution Exploring Operation: 89-77=12, Resulting Numbers: [12] 12,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 89:[91, 75], Operations: ['11*7=77', '77-2=75'] Exploring Operation: 91+75=166, Resulting Numbers: [166] 166,89 unequal: No Solution Exploring Operation: 91*75=6825, Resulting Numbers: [6825] 6825,89 unequal: No Solution Exploring Operation: 91-75=16, Resulting Numbers: [16] 16,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 89:[77, 93], Operations: ['11*7=77', '2+91=93'] Exploring Operation: 93-77=16, Resulting Numbers: [16] 16,89 unequal: No Solution Exploring Operation: 77*93=7161, Resulting Numbers: [7161] 7161,89 unequal: No Solution Exploring Operation: 77+93=170, Resulting Numbers: [170] 170,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 89:[91, 154], Operations: ['11*7=77', '2*77=154'] Exploring Operation: 91+154=245, Resulting Numbers: [245] 245,89 unequal: No Solution Exploring Operation: 154-91=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 91*154=14014, Resulting Numbers: [14014] 14014,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[7, 91, 22], Operations: ['2*11=22'] Exploring Operation: 7+22=29, Resulting Numbers: [91, 29] Generated Node #0,2,0: 89:[91, 29] Operation: 7+22=29 Exploring Operation: 22-7=15, Resulting Numbers: [91, 15] Generated Node #0,2,1: 89:[91, 15] Operation: 22-7=15 Exploring Operation: 91-7=84, Resulting Numbers: [22, 84] Generated Node #0,2,2: 89:[22, 84] Operation: 91-7=84 Exploring Operation: 7*22=154, Resulting Numbers: [91, 154] Generated Node #0,2,3: 89:[91, 154] Operation: 7*22=154 Exploring Operation: 7+91=98, Resulting Numbers: [22, 98] Generated Node #0,2,4: 89:[22, 98] Operation: 7+91=98 Moving to Node #0,2,0 Current State: 89:[91, 29], Operations: ['2*11=22', '7+22=29'] Exploring Operation: 91*29=2639, Resulting Numbers: [2639] 2639,89 unequal: No Solution Exploring Operation: 91-29=62, Resulting Numbers: [62] 62,89 unequal: No Solution Exploring Operation: 91+29=120, Resulting Numbers: [120] 120,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[91, 154], Operations: ['2*11=22', '7*22=154'] Exploring Operation: 91+154=245, Resulting Numbers: [245] 245,89 unequal: No Solution Exploring Operation: 154-91=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 91*154=14014, Resulting Numbers: [14014] 14014,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[22, 84], Operations: ['2*11=22', '91-7=84'] Exploring Operation: 22+84=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 22*84=1848, Resulting Numbers: [1848] 1848,89 unequal: No Solution Exploring Operation: 84-22=62, Resulting Numbers: [62] 62,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[91, 15], Operations: ['2*11=22', '22-7=15'] Exploring Operation: 91*15=1365, Resulting Numbers: [1365] 1365,89 unequal: No Solution Exploring Operation: 91-15=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 91+15=106, Resulting Numbers: [106] 106,89 unequal: No Solution Moving to Node #0,2,4 Current State: 89:[22, 98], Operations: ['2*11=22', '7+91=98'] Exploring Operation: 22*98=2156, Resulting Numbers: [2156] 2156,89 unequal: No Solution Exploring Operation: 22+98=120, Resulting Numbers: [120] 120,89 unequal: No Solution Exploring Operation: 98-22=76, Resulting Numbers: [76] 76,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 89:[11, 91, 14], Operations: ['2*7=14'] Exploring Operation: 11+14=25, Resulting Numbers: [91, 25] Generated Node #0,4,0: 89:[91, 25] Operation: 11+14=25 Exploring Operation: 14-11=3, Resulting Numbers: [91, 3] Generated Node #0,4,1: 89:[91, 3] Operation: 14-11=3 Exploring Operation: 11+91=102, Resulting Numbers: [14, 102] Generated Node #0,4,2: 89:[14, 102] Operation: 11+91=102 Exploring Operation: 11*14=154, Resulting Numbers: [91, 154] Generated Node #0,4,3: 89:[91, 154] Operation: 11*14=154 Exploring Operation: 91-11=80, Resulting Numbers: [14, 80] Generated Node #0,4,4: 89:[14, 80] Operation: 91-11=80 Moving to Node #0,4,0 Current State: 89:[91, 25], Operations: ['2*7=14', '11+14=25'] Exploring Operation: 91-25=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 91*25=2275, Resulting Numbers: [2275] 2275,89 unequal: No Solution Exploring Operation: 91+25=116, Resulting Numbers: [116] 116,89 unequal: No Solution Moving to Node #0,4,3 Current State: 89:[91, 154], Operations: ['2*7=14', '11*14=154'] Exploring Operation: 154-91=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 91+154=245, Resulting Numbers: [245] 245,89 unequal: No Solution Exploring Operation: 91*154=14014, Resulting Numbers: [14014] 14014,89 unequal: No Solution Moving to Node #0,4,4 Current State: 89:[14, 80], Operations: ['2*7=14', '91-11=80'] Exploring Operation: 14*80=1120, Resulting Numbers: [1120] 1120,89 unequal: No Solution Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 14+80=94, Resulting Numbers: [94] 94,89 unequal: No Solution Moving to Node #0,4,1 Current State: 89:[91, 3], Operations: ['2*7=14', '14-11=3'] Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,89 unequal: No Solution Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,89 unequal: No Solution Exploring Operation: 91*3=273, Resulting Numbers: [273] 273,89 unequal: No Solution Moving to Node #0,4,2 Current State: 89:[14, 102], Operations: ['2*7=14', '11+91=102'] Exploring Operation: 14+102=116, Resulting Numbers: [116] 116,89 unequal: No Solution Exploring Operation: 102-14=88, Resulting Numbers: [88] 88,89 unequal: No Solution Exploring Operation: 14*102=1428, Resulting Numbers: [1428] 1428,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[11, 91, 9], Operations: ['2+7=9'] Exploring Operation: 91-9=82, Resulting Numbers: [11, 82] Generated Node #0,0,0: 89:[11, 82] Operation: 91-9=82 Exploring Operation: 11-9=2, Resulting Numbers: [91, 2] Generated Node #0,0,1: 89:[91, 2] Operation: 11-9=2 Exploring Operation: 11+9=20, Resulting Numbers: [91, 20] Generated Node #0,0,2: 89:[91, 20] Operation: 11+9=20 Exploring Operation: 91-11=80, Resulting Numbers: [9, 80] Generated Node #0,0,3: 89:[9, 80] Operation: 91-11=80 Exploring Operation: 11*9=99, Resulting Numbers: [91, 99] Generated Node #0,0,4: 89:[91, 99] Operation: 11*9=99 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 89:[91, 99], Operations: ['2+7=9', '11*9=99'] Exploring Operation: 99-91=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 91*99=9009, Resulting Numbers: [9009] 9009,89 unequal: No Solution Exploring Operation: 91+99=190, Resulting Numbers: [190] 190,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[91, 20], Operations: ['2+7=9', '11+9=20'] Exploring Operation: 91*20=1820, Resulting Numbers: [1820] 1820,89 unequal: No Solution Exploring Operation: 91+20=111, Resulting Numbers: [111] 111,89 unequal: No Solution Exploring Operation: 91-20=71, Resulting Numbers: [71] 71,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[11, 82], Operations: ['2+7=9', '91-9=82'] Exploring Operation: 11*82=902, Resulting Numbers: [902] 902,89 unequal: No Solution Exploring Operation: 11+82=93, Resulting Numbers: [93] 93,89 unequal: No Solution Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[91, 2], Operations: ['2+7=9', '11-9=2'] Exploring Operation: 91*2=182, Resulting Numbers: [182] 182,89 unequal: No Solution Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[2, 11, 7, 91], Operations: [] Exploring Operation: 2+7=9, Resulting Numbers: [11, 91, 9] Generated Node #0,0: 89:[11, 91, 9] Operation: 2+7=9 Moving to Node #0,0 Current State: 89:[11, 91, 9], Operations: ['2+7=9'] Exploring Operation: 11-9=2, Resulting Numbers: [91, 2] Generated Node #0,0,1: 89:[91, 2] Operation: 11-9=2 Moving to Node #0,0,1 Current State: 89:[91, 2], Operations: ['2+7=9', '11-9=2'] Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.926215
hs_5
sum_heuristic
[ 50, 37, 51, 63 ]
27
[ "50+37=87", "51+63=114", "114-87=27" ]
Current State: 27:[50, 37, 51, 63], Operations: [] Exploring Operation: 50+37=87, Resulting Numbers: [51, 63, 87] Generated Node #2: [51, 63, 87] from Operation: 50+37=87 Current State: 27:[51, 63, 87], Operations: ['50+37=87'] Exploring Operation: 51+63=114, Resulting Numbers: [87, 114] Generated Node #3: [87, 114] from Operation: 51+63=114 Current State: 27:[87, 114], Operations: ['50+37=87', '51+63=114'] Exploring Operation: 114-87=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[50, 37, 51, 63], Operations: [] Exploring Operation: 51-50=1, Resulting Numbers: [37, 63, 1] Generated Node #0,0: 27:[37, 63, 1] Operation: 51-50=1 Exploring Operation: 63-51=12, Resulting Numbers: [50, 37, 12] Generated Node #0,1: 27:[50, 37, 12] Operation: 63-51=12 Exploring Operation: 63-50=13, Resulting Numbers: [37, 51, 13] Generated Node #0,2: 27:[37, 51, 13] Operation: 63-50=13 Moving to Node #0,1 Current State: 27:[50, 37, 12], Operations: ['63-51=12'] Exploring Operation: 37-12=25, Resulting Numbers: [50, 25] Generated Node #0,1,0: 27:[50, 25] Operation: 37-12=25 Exploring Operation: 50-12=38, Resulting Numbers: [37, 38] Generated Node #0,1,1: 27:[37, 38] Operation: 50-12=38 Exploring Operation: 50-37=13, Resulting Numbers: [12, 13] Generated Node #0,1,2: 27:[12, 13] Operation: 50-37=13 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 27:[12, 13], Operations: ['63-51=12', '50-37=13'] Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,27 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 27:[37, 38], Operations: ['63-51=12', '50-12=38'] Exploring Operation: 37+38=75, Resulting Numbers: [75] 75,27 unequal: No Solution Exploring Operation: 38-37=1, Resulting Numbers: [1] 1,27 unequal: No Solution Exploring Operation: 37*38=1406, Resulting Numbers: [1406] 1406,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 27:[50, 25], Operations: ['63-51=12', '37-12=25'] Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 50+25=75, Resulting Numbers: [75] 75,27 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: 27:[37, 51, 13], Operations: ['63-50=13'] Exploring Operation: 51-13=38, Resulting Numbers: [37, 38] Generated Node #0,2,0: 27:[37, 38] Operation: 51-13=38 Exploring Operation: 37-13=24, Resulting Numbers: [51, 24] Generated Node #0,2,1: 27:[51, 24] Operation: 37-13=24 Exploring Operation: 51-37=14, Resulting Numbers: [13, 14] Generated Node #0,2,2: 27:[13, 14] Operation: 51-37=14 Moving to Node #0,0 Current State: 27:[37, 63, 1], Operations: ['51-50=1'] Exploring Operation: 37-1=36, Resulting Numbers: [63, 36] Generated Node #0,0,0: 27:[63, 36] Operation: 37-1=36 Exploring Operation: 63-1=62, Resulting Numbers: [37, 62] Generated Node #0,0,1: 27:[37, 62] Operation: 63-1=62 Exploring Operation: 63-37=26, Resulting Numbers: [1, 26] Generated Node #0,0,2: 27:[1, 26] Operation: 63-37=26 Moving to Node #0,0,2 Current State: 27:[1, 26], Operations: ['51-50=1', '63-37=26'] Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,27 unequal: No Solution Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[50, 37, 51, 63], Operations: [] Exploring Operation: 51-50=1, Resulting Numbers: [37, 63, 1] Generated Node #0,0: 27:[37, 63, 1] Operation: 51-50=1 Moving to Node #0,0 Current State: 27:[37, 63, 1], Operations: ['51-50=1'] Exploring Operation: 63-37=26, Resulting Numbers: [1, 26] Generated Node #0,0,2: 27:[1, 26] Operation: 63-37=26 Moving to Node #0,0,2 Current State: 27:[1, 26], Operations: ['51-50=1', '63-37=26'] Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
0.976563
hs_3
mult_heuristic
[ 75, 25, 8, 33 ]
19
[ "75/25=3", "33/3=11", "8+11=19" ]
Current State: 19:[75, 25, 8, 33], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [8, 33, 3] Generated Node #2: [8, 33, 3] from Operation: 75/25=3 Current State: 19:[8, 33, 3], Operations: ['75/25=3'] Exploring Operation: 33/3=11, Resulting Numbers: [8, 11] Generated Node #3: [8, 11] from Operation: 33/3=11 Current State: 19:[8, 11], Operations: ['75/25=3', '33/3=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[75, 25, 8, 33], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [8, 33, 3] Generated Node #0,0: 19:[8, 33, 3] Operation: 75/25=3 Exploring Operation: 75-33=42, Resulting Numbers: [25, 8, 42] Generated Node #0,1: 19:[25, 8, 42] Operation: 75-33=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[25, 8, 42], Operations: ['75-33=42'] Exploring Operation: 42-8=34, Resulting Numbers: [25, 34] Generated Node #0,1,0: 19:[25, 34] Operation: 42-8=34 Exploring Operation: 42-25=17, Resulting Numbers: [8, 17] Generated Node #0,1,1: 19:[8, 17] Operation: 42-25=17 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 19:[8, 17], Operations: ['75-33=42', '42-25=17'] Exploring Operation: 8+17=25, Resulting Numbers: [25] 25,19 unequal: No Solution Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,19 unequal: No Solution No 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: 19:[25, 34], Operations: ['75-33=42', '42-8=34'] Exploring Operation: 25+34=59, Resulting Numbers: [59] 59,19 unequal: No Solution Exploring Operation: 34-25=9, Resulting Numbers: [9] 9,19 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: 19:[8, 33, 3], Operations: ['75/25=3'] Exploring Operation: 8*3=24, Resulting Numbers: [33, 24] Generated Node #0,0,0: 19:[33, 24] Operation: 8*3=24 Exploring Operation: 33/3=11, Resulting Numbers: [8, 11] Generated Node #0,0,1: 19:[8, 11] Operation: 33/3=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[33, 24], Operations: ['75/25=3', '8*3=24'] Exploring Operation: 33+24=57, Resulting Numbers: [57] 57,19 unequal: No Solution Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,19 unequal: No Solution No 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: 19:[8, 11], Operations: ['75/25=3', '33/3=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[75, 25, 8, 33], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [8, 33, 3] Generated Node #0,0: 19:[8, 33, 3] Operation: 75/25=3 Moving to Node #0,0 Current State: 19:[8, 33, 3], Operations: ['75/25=3'] Exploring Operation: 33/3=11, Resulting Numbers: [8, 11] Generated Node #0,0,1: 19:[8, 11] Operation: 33/3=11 Moving to Node #0,0,1 Current State: 19:[8, 11], Operations: ['75/25=3', '33/3=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_2
mult_heuristic
[ 8, 67, 78, 42 ]
61
[ "67-8=59", "78+42=120", "120-59=61" ]
Current State: 61:[8, 67, 78, 42], Operations: [] Exploring Operation: 67-8=59, Resulting Numbers: [78, 42, 59] Generated Node #2: [78, 42, 59] from Operation: 67-8=59 Current State: 61:[78, 42, 59], Operations: ['67-8=59'] Exploring Operation: 78+42=120, Resulting Numbers: [59, 120] Generated Node #3: [59, 120] from Operation: 78+42=120 Current State: 61:[59, 120], Operations: ['67-8=59', '78+42=120'] Exploring Operation: 120-59=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[8, 67, 78, 42], Operations: [] Exploring Operation: 8+42=50, Resulting Numbers: [67, 78, 50] Generated Node #0,0: 61:[67, 78, 50] Operation: 8+42=50 Exploring Operation: 78-8=70, Resulting Numbers: [67, 42, 70] Generated Node #0,1: 61:[67, 42, 70] Operation: 78-8=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[67, 78, 50], Operations: ['8+42=50'] Exploring Operation: 78-67=11, Resulting Numbers: [50, 11] Generated Node #0,0,0: 61:[50, 11] Operation: 78-67=11 Exploring Operation: 78-50=28, Resulting Numbers: [67, 28] Generated Node #0,0,1: 61:[67, 28] Operation: 78-50=28 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 61:[67, 28], Operations: ['8+42=50', '78-50=28'] Exploring Operation: 67+28=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 67-28=39, Resulting Numbers: [39] 39,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[50, 11], Operations: ['8+42=50', '78-67=11'] Exploring Operation: 50-11=39, Resulting Numbers: [39] 39,61 unequal: No Solution Exploring Operation: 50+11=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[8, 67, 78, 42], Operations: [] Exploring Operation: 8+42=50, Resulting Numbers: [67, 78, 50] Generated Node #0,0: 61:[67, 78, 50] Operation: 8+42=50 Moving to Node #0,0 Current State: 61:[67, 78, 50], Operations: ['8+42=50'] Exploring Operation: 78-67=11, Resulting Numbers: [50, 11] Generated Node #0,0,0: 61:[50, 11] Operation: 78-67=11 Moving to Node #0,0,0 Current State: 61:[50, 11], Operations: ['8+42=50', '78-67=11'] Exploring Operation: 50+11=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 34, 33, 53, 57 ]
79
[ "34*53=1802", "33*57=1881", "1881-1802=79" ]
Current State: 79:[34, 33, 53, 57], Operations: [] Exploring Operation: 34*53=1802, Resulting Numbers: [33, 57, 1802] Generated Node #2: [33, 57, 1802] from Operation: 34*53=1802 Current State: 79:[33, 57, 1802], Operations: ['34*53=1802'] Exploring Operation: 33*57=1881, Resulting Numbers: [1802, 1881] Generated Node #3: [1802, 1881] from Operation: 33*57=1881 Current State: 79:[1802, 1881], Operations: ['34*53=1802', '33*57=1881'] Exploring Operation: 1881-1802=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[34, 33, 53, 57], Operations: [] Exploring Operation: 33+53=86, Resulting Numbers: [34, 57, 86] Generated Node #0,0: 79:[34, 57, 86] Operation: 33+53=86 Exploring Operation: 34+53=87, Resulting Numbers: [33, 57, 87] Generated Node #0,1: 79:[33, 57, 87] Operation: 34+53=87 Exploring Operation: 34+33=67, Resulting Numbers: [53, 57, 67] Generated Node #0,2: 79:[53, 57, 67] Operation: 34+33=67 Moving to Node #0,2 Current State: 79:[53, 57, 67], Operations: ['34+33=67'] Exploring Operation: 53+67=120, Resulting Numbers: [57, 120] Generated Node #0,2,0: 79:[57, 120] Operation: 53+67=120 Exploring Operation: 53+57=110, Resulting Numbers: [67, 110] Generated Node #0,2,1: 79:[67, 110] Operation: 53+57=110 Exploring Operation: 57+67=124, Resulting Numbers: [53, 124] Generated Node #0,2,2: 79:[53, 124] Operation: 57+67=124 Moving to Node #0,0 Current State: 79:[34, 57, 86], Operations: ['33+53=86'] Exploring Operation: 34+57=91, Resulting Numbers: [86, 91] Generated Node #0,0,0: 79:[86, 91] Operation: 34+57=91 Exploring Operation: 86-34=52, Resulting Numbers: [57, 52] Generated Node #0,0,1: 79:[57, 52] Operation: 86-34=52 Exploring Operation: 57-34=23, Resulting Numbers: [86, 23] Generated Node #0,0,2: 79:[86, 23] Operation: 57-34=23 Moving to Node #0,1 Current State: 79:[33, 57, 87], Operations: ['34+53=87'] Exploring Operation: 33+57=90, Resulting Numbers: [87, 90] Generated Node #0,1,0: 79:[87, 90] Operation: 33+57=90 Exploring Operation: 57-33=24, Resulting Numbers: [87, 24] Generated Node #0,1,1: 79:[87, 24] Operation: 57-33=24 Exploring Operation: 87-33=54, Resulting Numbers: [57, 54] Generated Node #0,1,2: 79:[57, 54] Operation: 87-33=54 Moving to Node #0,0,0 Current State: 79:[86, 91], Operations: ['33+53=86', '34+57=91'] Exploring Operation: 86*91=7826, Resulting Numbers: [7826] 7826,79 unequal: No Solution Exploring Operation: 86+91=177, Resulting Numbers: [177] 177,79 unequal: No Solution Exploring Operation: 91-86=5, Resulting Numbers: [5] 5,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[87, 90], Operations: ['34+53=87', '33+57=90'] Exploring Operation: 90-87=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 87*90=7830, Resulting Numbers: [7830] 7830,79 unequal: No Solution Exploring Operation: 87+90=177, Resulting Numbers: [177] 177,79 unequal: No Solution Moving to Node #0,2,1 Current State: 79:[67, 110], Operations: ['34+33=67', '53+57=110'] Exploring Operation: 67+110=177, Resulting Numbers: [177] 177,79 unequal: No Solution Exploring Operation: 67*110=7370, Resulting Numbers: [7370] 7370,79 unequal: No Solution Exploring Operation: 110-67=43, Resulting Numbers: [43] 43,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[57, 54], Operations: ['34+53=87', '87-33=54'] Exploring Operation: 57+54=111, Resulting Numbers: [111] 111,79 unequal: No Solution Exploring Operation: 57*54=3078, Resulting Numbers: [3078] 3078,79 unequal: No Solution Exploring Operation: 57-54=3, Resulting Numbers: [3] 3,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[57, 52], Operations: ['33+53=86', '86-34=52'] Exploring Operation: 57*52=2964, Resulting Numbers: [2964] 2964,79 unequal: No Solution Exploring Operation: 57-52=5, Resulting Numbers: [5] 5,79 unequal: No Solution Exploring Operation: 57+52=109, Resulting Numbers: [109] 109,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[86, 23], Operations: ['33+53=86', '57-34=23'] Exploring Operation: 86-23=63, Resulting Numbers: [63] 63,79 unequal: No Solution Exploring Operation: 86*23=1978, Resulting Numbers: [1978] 1978,79 unequal: No Solution Exploring Operation: 86+23=109, Resulting Numbers: [109] 109,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[87, 24], Operations: ['34+53=87', '57-33=24'] Exploring Operation: 87*24=2088, Resulting Numbers: [2088] 2088,79 unequal: No Solution Exploring Operation: 87+24=111, Resulting Numbers: [111] 111,79 unequal: No Solution Exploring Operation: 87-24=63, Resulting Numbers: [63] 63,79 unequal: No Solution Moving to Node #0,2,0 Current State: 79:[57, 120], Operations: ['34+33=67', '53+67=120'] Exploring Operation: 120-57=63, Resulting Numbers: [63] 63,79 unequal: No Solution Exploring Operation: 57*120=6840, Resulting Numbers: [6840] 6840,79 unequal: No Solution Exploring Operation: 57+120=177, Resulting Numbers: [177] 177,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[53, 124], Operations: ['34+33=67', '57+67=124'] Exploring Operation: 124-53=71, Resulting Numbers: [71] 71,79 unequal: No Solution Exploring Operation: 53*124=6572, Resulting Numbers: [6572] 6572,79 unequal: No Solution Exploring Operation: 53+124=177, Resulting Numbers: [177] 177,79 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 31, 9, 1, 37 ]
45
[ "31+1=32", "37-32=5", "9*5=45" ]
Current State: 45:[31, 9, 1, 37], Operations: [] Exploring Operation: 31+1=32, Resulting Numbers: [9, 37, 32] Generated Node #2: [9, 37, 32] from Operation: 31+1=32 Current State: 45:[9, 37, 32], Operations: ['31+1=32'] Exploring Operation: 37-32=5, Resulting Numbers: [9, 5] Generated Node #3: [9, 5] from Operation: 37-32=5 Current State: 45:[9, 5], Operations: ['31+1=32', '37-32=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[31, 9, 1, 37], Operations: [] Exploring Operation: 37-31=6, Resulting Numbers: [9, 1, 6] Generated Node #0,0: 45:[9, 1, 6] Operation: 37-31=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[9, 1, 6], Operations: ['37-31=6'] Exploring Operation: 6-1=5, Resulting Numbers: [9, 5] Generated Node #0,0,0: 45:[9, 5] Operation: 6-1=5 Moving to Node #0,0,0 Current State: 45:[9, 5], Operations: ['37-31=6', '6-1=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[31, 9, 1, 37], Operations: [] Exploring Operation: 37-31=6, Resulting Numbers: [9, 1, 6] Generated Node #0,0: 45:[9, 1, 6] Operation: 37-31=6 Moving to Node #0,0 Current State: 45:[9, 1, 6], Operations: ['37-31=6'] Exploring Operation: 6-1=5, Resulting Numbers: [9, 5] Generated Node #0,0,0: 45:[9, 5] Operation: 6-1=5 Moving to Node #0,0,0 Current State: 45:[9, 5], Operations: ['37-31=6', '6-1=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 86, 89, 50, 91 ]
44
[ "89-86=3", "91-50=41", "3+41=44" ]
Current State: 44:[86, 89, 50, 91], Operations: [] Exploring Operation: 89-86=3, Resulting Numbers: [50, 91, 3] Generated Node #2: [50, 91, 3] from Operation: 89-86=3 Current State: 44:[50, 91, 3], Operations: ['89-86=3'] Exploring Operation: 91-50=41, Resulting Numbers: [3, 41] Generated Node #3: [3, 41] from Operation: 91-50=41 Current State: 44:[3, 41], Operations: ['89-86=3', '91-50=41'] Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[86, 89, 50, 91], Operations: [] Exploring Operation: 91-89=2, Resulting Numbers: [86, 50, 2] Generated Node #0,0: 44:[86, 50, 2] Operation: 91-89=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[86, 50, 2], Operations: ['91-89=2'] Exploring Operation: 86/2=43, Resulting Numbers: [50, 43] Generated Node #0,0,0: 44:[50, 43] Operation: 86/2=43 Moving to Node #0,0,0 Current State: 44:[50, 43], Operations: ['91-89=2', '86/2=43'] Exploring Operation: 50-43=7, Resulting Numbers: [7] 7,44 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
[ 61, 75, 89, 86 ]
92
[ "86-61=25", "75/25=3", "89+3=92" ]
Current State: 92:[61, 75, 89, 86], Operations: [] Exploring Operation: 86-61=25, Resulting Numbers: [75, 89, 25] Generated Node #2: [75, 89, 25] from Operation: 86-61=25 Current State: 92:[75, 89, 25], Operations: ['86-61=25'] Exploring Operation: 75/25=3, Resulting Numbers: [89, 3] Generated Node #3: [89, 3] from Operation: 75/25=3 Current State: 92:[89, 3], Operations: ['86-61=25', '75/25=3'] Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[61, 75, 89, 86], Operations: [] Exploring Operation: 86-75=11, Resulting Numbers: [61, 89, 11] Generated Node #0,0: 92:[61, 89, 11] Operation: 86-75=11 Exploring Operation: 89-61=28, Resulting Numbers: [75, 86, 28] Generated Node #0,1: 92:[75, 86, 28] Operation: 89-61=28 Exploring Operation: 75-61=14, Resulting Numbers: [89, 86, 14] Generated Node #0,2: 92:[89, 86, 14] Operation: 75-61=14 Exploring Operation: 86-61=25, Resulting Numbers: [75, 89, 25] Generated Node #0,3: 92:[75, 89, 25] Operation: 86-61=25 Moving to Node #0,2 Current State: 92:[89, 86, 14], Operations: ['75-61=14'] Exploring Operation: 89-14=75, Resulting Numbers: [86, 75] Generated Node #0,2,0: 92:[86, 75] Operation: 89-14=75 Exploring Operation: 89-86=3, Resulting Numbers: [14, 3] Generated Node #0,2,1: 92:[14, 3] Operation: 89-86=3 Exploring Operation: 89+14=103, Resulting Numbers: [86, 103] Generated Node #0,2,2: 92:[86, 103] Operation: 89+14=103 Exploring Operation: 86+14=100, Resulting Numbers: [89, 100] Generated Node #0,2,3: 92:[89, 100] Operation: 86+14=100 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 92:[14, 3], Operations: ['75-61=14', '89-86=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,92 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 92:[89, 100], Operations: ['75-61=14', '86+14=100'] Exploring Operation: 89*100=8900, Resulting Numbers: [8900] 8900,92 unequal: No Solution Exploring Operation: 89+100=189, Resulting Numbers: [189] 189,92 unequal: No Solution Exploring Operation: 100-89=11, Resulting Numbers: [11] 11,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 92:[86, 103], Operations: ['75-61=14', '89+14=103'] Exploring Operation: 86*103=8858, Resulting Numbers: [8858] 8858,92 unequal: No Solution Exploring Operation: 86+103=189, Resulting Numbers: [189] 189,92 unequal: No Solution Exploring Operation: 103-86=17, Resulting Numbers: [17] 17,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 92:[86, 75], Operations: ['75-61=14', '89-14=75'] Exploring Operation: 86+75=161, Resulting Numbers: [161] 161,92 unequal: No Solution Exploring Operation: 86*75=6450, Resulting Numbers: [6450] 6450,92 unequal: No Solution Exploring Operation: 86-75=11, Resulting Numbers: [11] 11,92 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: 92:[75, 89, 25], Operations: ['86-61=25'] Exploring Operation: 89-75=14, Resulting Numbers: [25, 14] Generated Node #0,3,0: 92:[25, 14] Operation: 89-75=14 Exploring Operation: 75+25=100, Resulting Numbers: [89, 100] Generated Node #0,3,1: 92:[89, 100] Operation: 75+25=100 Exploring Operation: 75-25=50, Resulting Numbers: [89, 50] Generated Node #0,3,2: 92:[89, 50] Operation: 75-25=50 Exploring Operation: 75/25=3, Resulting Numbers: [89, 3] Generated Node #0,3,3: 92:[89, 3] Operation: 75/25=3 Moving to Node #0,0 Current State: 92:[61, 89, 11], Operations: ['86-75=11'] Exploring Operation: 89+11=100, Resulting Numbers: [61, 100] Generated Node #0,0,0: 92:[61, 100] Operation: 89+11=100 Exploring Operation: 61-11=50, Resulting Numbers: [89, 50] Generated Node #0,0,1: 92:[89, 50] Operation: 61-11=50 Exploring Operation: 89-61=28, Resulting Numbers: [11, 28] Generated Node #0,0,2: 92:[11, 28] Operation: 89-61=28 Exploring Operation: 61+11=72, Resulting Numbers: [89, 72] Generated Node #0,0,3: 92:[89, 72] Operation: 61+11=72 Moving to Node #0,1 Current State: 92:[75, 86, 28], Operations: ['89-61=28'] Exploring Operation: 75-28=47, Resulting Numbers: [86, 47] Generated Node #0,1,0: 92:[86, 47] Operation: 75-28=47 Exploring Operation: 86-75=11, Resulting Numbers: [28, 11] Generated Node #0,1,1: 92:[28, 11] Operation: 86-75=11 Exploring Operation: 86-28=58, Resulting Numbers: [75, 58] Generated Node #0,1,2: 92:[75, 58] Operation: 86-28=58 Exploring Operation: 75+28=103, Resulting Numbers: [86, 103] Generated Node #0,1,3: 92:[86, 103] Operation: 75+28=103 Moving to Node #0,3,3 Current State: 92:[89, 3], Operations: ['86-61=25', '75/25=3'] Exploring Operation: 89*3=267, Resulting Numbers: [267] 267,92 unequal: No Solution Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[61, 75, 89, 86], Operations: [] Exploring Operation: 86-61=25, Resulting Numbers: [75, 89, 25] Generated Node #0,3: 92:[75, 89, 25] Operation: 86-61=25 Moving to Node #0,3 Current State: 92:[75, 89, 25], Operations: ['86-61=25'] Exploring Operation: 75/25=3, Resulting Numbers: [89, 3] Generated Node #0,3,3: 92:[89, 3] Operation: 75/25=3 Moving to Node #0,3,3 Current State: 92:[89, 3], Operations: ['86-61=25', '75/25=3'] Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
0.967014
hs_4
mult_heuristic
[ 9, 50, 69, 79 ]
89
[ "9+50=59", "69+79=148", "148-59=89" ]
Current State: 89:[9, 50, 69, 79], Operations: [] Exploring Operation: 9+50=59, Resulting Numbers: [69, 79, 59] Generated Node #2: [69, 79, 59] from Operation: 9+50=59 Current State: 89:[69, 79, 59], Operations: ['9+50=59'] Exploring Operation: 69+79=148, Resulting Numbers: [59, 148] Generated Node #3: [59, 148] from Operation: 69+79=148 Current State: 89:[59, 148], Operations: ['9+50=59', '69+79=148'] Exploring Operation: 148-59=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[9, 50, 69, 79], Operations: [] Exploring Operation: 50-9=41, Resulting Numbers: [69, 79, 41] Generated Node #0,0: 89:[69, 79, 41] Operation: 50-9=41 Exploring Operation: 9+79=88, Resulting Numbers: [50, 69, 88] Generated Node #0,1: 89:[50, 69, 88] Operation: 9+79=88 Exploring Operation: 9+69=78, Resulting Numbers: [50, 79, 78] Generated Node #0,2: 89:[50, 79, 78] Operation: 9+69=78 Exploring Operation: 9+50=59, Resulting Numbers: [69, 79, 59] Generated Node #0,3: 89:[69, 79, 59] Operation: 9+50=59 Moving to Node #0,1 Current State: 89:[50, 69, 88], Operations: ['9+79=88'] Exploring Operation: 88-50=38, Resulting Numbers: [69, 38] Generated Node #0,1,0: 89:[69, 38] Operation: 88-50=38 Exploring Operation: 50+69=119, Resulting Numbers: [88, 119] Generated Node #0,1,1: 89:[88, 119] Operation: 50+69=119 Exploring Operation: 50+88=138, Resulting Numbers: [69, 138] Generated Node #0,1,2: 89:[69, 138] Operation: 50+88=138 Exploring Operation: 69-50=19, Resulting Numbers: [88, 19] Generated Node #0,1,3: 89:[88, 19] Operation: 69-50=19 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[88, 119], Operations: ['9+79=88', '50+69=119'] Exploring Operation: 88*119=10472, Resulting Numbers: [10472] 10472,89 unequal: No Solution Exploring Operation: 88+119=207, Resulting Numbers: [207] 207,89 unequal: No Solution Exploring Operation: 119-88=31, Resulting Numbers: [31] 31,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 89:[69, 138], Operations: ['9+79=88', '50+88=138'] Exploring Operation: 69+138=207, Resulting Numbers: [207] 207,89 unequal: No Solution Exploring Operation: 138/69=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 69*138=9522, Resulting Numbers: [9522] 9522,89 unequal: No Solution Exploring Operation: 138-69=69, Resulting Numbers: [69] 69,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[69, 38], Operations: ['9+79=88', '88-50=38'] Exploring Operation: 69*38=2622, Resulting Numbers: [2622] 2622,89 unequal: No Solution Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,89 unequal: No Solution Exploring Operation: 69+38=107, Resulting Numbers: [107] 107,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 89:[88, 19], Operations: ['9+79=88', '69-50=19'] Exploring Operation: 88*19=1672, Resulting Numbers: [1672] 1672,89 unequal: No Solution Exploring Operation: 88-19=69, Resulting Numbers: [69] 69,89 unequal: No Solution Exploring Operation: 88+19=107, Resulting Numbers: [107] 107,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 89:[69, 79, 59], Operations: ['9+50=59'] Exploring Operation: 79+59=138, Resulting Numbers: [69, 138] Generated Node #0,3,0: 89:[69, 138] Operation: 79+59=138 Exploring Operation: 69-59=10, Resulting Numbers: [79, 10] Generated Node #0,3,1: 89:[79, 10] Operation: 69-59=10 Exploring Operation: 69+79=148, Resulting Numbers: [59, 148] Generated Node #0,3,2: 89:[59, 148] Operation: 69+79=148 Exploring Operation: 69+59=128, Resulting Numbers: [79, 128] Generated Node #0,3,3: 89:[79, 128] Operation: 69+59=128 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 89:[79, 128], Operations: ['9+50=59', '69+59=128'] Exploring Operation: 128-79=49, Resulting Numbers: [49] 49,89 unequal: No Solution Exploring Operation: 79*128=10112, Resulting Numbers: [10112] 10112,89 unequal: No Solution Exploring Operation: 79+128=207, Resulting Numbers: [207] 207,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 89:[69, 138], Operations: ['9+50=59', '79+59=138'] Exploring Operation: 69*138=9522, Resulting Numbers: [9522] 9522,89 unequal: No Solution Exploring Operation: 69+138=207, Resulting Numbers: [207] 207,89 unequal: No Solution Exploring Operation: 138-69=69, Resulting Numbers: [69] 69,89 unequal: No Solution Exploring Operation: 138/69=2, Resulting Numbers: [2] 2,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 89:[79, 10], Operations: ['9+50=59', '69-59=10'] Exploring Operation: 79+10=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[9, 50, 69, 79], Operations: [] Exploring Operation: 9+50=59, Resulting Numbers: [69, 79, 59] Generated Node #0,3: 89:[69, 79, 59] Operation: 9+50=59 Moving to Node #0,3 Current State: 89:[69, 79, 59], Operations: ['9+50=59'] Exploring Operation: 69-59=10, Resulting Numbers: [79, 10] Generated Node #0,3,1: 89:[79, 10] Operation: 69-59=10 Moving to Node #0,3,1 Current State: 89:[79, 10], Operations: ['9+50=59', '69-59=10'] Exploring Operation: 79+10=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_4
sum_heuristic
[ 69, 88, 89, 69 ]
89
[ "69-69=0", "88*0=0", "89+0=89" ]
Current State: 89:[69, 88, 89, 69], Operations: [] Exploring Operation: 69-69=0, Resulting Numbers: [88, 89, 0] Generated Node #2: [88, 89, 0] from Operation: 69-69=0 Current State: 89:[88, 89, 0], Operations: ['69-69=0'] Exploring Operation: 88*0=0, Resulting Numbers: [89, 0] Generated Node #3: [89, 0] from Operation: 88*0=0 Current State: 89:[89, 0], Operations: ['69-69=0', '88*0=0'] Exploring Operation: 89+0=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[69, 88, 89, 69], Operations: [] Exploring Operation: 88+69=157, Resulting Numbers: [69, 89, 157] Generated Node #0,0: 89:[69, 89, 157] Operation: 88+69=157 Exploring Operation: 69+88=157, Resulting Numbers: [89, 69, 157] Generated Node #0,1: 89:[89, 69, 157] Operation: 69+88=157 Exploring Operation: 69/69=1, Resulting Numbers: [88, 89, 1] Generated Node #0,2: 89:[88, 89, 1] Operation: 69/69=1 Exploring Operation: 69+69=138, Resulting Numbers: [88, 89, 138] Generated Node #0,3: 89:[88, 89, 138] Operation: 69+69=138 Moving to Node #0,3 Current State: 89:[88, 89, 138], Operations: ['69+69=138'] Exploring Operation: 138-89=49, Resulting Numbers: [88, 49] Generated Node #0,3,0: 89:[88, 49] Operation: 138-89=49 Exploring Operation: 88+89=177, Resulting Numbers: [138, 177] Generated Node #0,3,1: 89:[138, 177] Operation: 88+89=177 Exploring Operation: 89-88=1, Resulting Numbers: [138, 1] Generated Node #0,3,2: 89:[138, 1] Operation: 89-88=1 Exploring Operation: 138-88=50, Resulting Numbers: [89, 50] Generated Node #0,3,3: 89:[89, 50] Operation: 138-88=50 Moving to Node #0,1 Current State: 89:[89, 69, 157], Operations: ['69+88=157'] Exploring Operation: 157-89=68, Resulting Numbers: [69, 68] Generated Node #0,1,0: 89:[69, 68] Operation: 157-89=68 Exploring Operation: 89-69=20, Resulting Numbers: [157, 20] Generated Node #0,1,1: 89:[157, 20] Operation: 89-69=20 Exploring Operation: 157-69=88, Resulting Numbers: [89, 88] Generated Node #0,1,2: 89:[89, 88] Operation: 157-69=88 Exploring Operation: 89+69=158, Resulting Numbers: [157, 158] Generated Node #0,1,3: 89:[157, 158] Operation: 89+69=158 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 89:[89, 88], Operations: ['69+88=157', '157-69=88'] Exploring Operation: 89+88=177, Resulting Numbers: [177] 177,89 unequal: No Solution Exploring Operation: 89*88=7832, Resulting Numbers: [7832] 7832,89 unequal: No Solution Exploring Operation: 89-88=1, Resulting Numbers: [1] 1,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[69, 68], Operations: ['69+88=157', '157-89=68'] Exploring Operation: 69-68=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 69+68=137, Resulting Numbers: [137] 137,89 unequal: No Solution Exploring Operation: 69*68=4692, Resulting Numbers: [4692] 4692,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[157, 20], Operations: ['69+88=157', '89-69=20'] Exploring Operation: 157+20=177, Resulting Numbers: [177] 177,89 unequal: No Solution Exploring Operation: 157*20=3140, Resulting Numbers: [3140] 3140,89 unequal: No Solution Exploring Operation: 157-20=137, Resulting Numbers: [137] 137,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 89:[157, 158], Operations: ['69+88=157', '89+69=158'] Exploring Operation: 157+158=315, Resulting Numbers: [315] 315,89 unequal: No Solution Exploring Operation: 158-157=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 157*158=24806, Resulting Numbers: [24806] 24806,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 89:[69, 89, 157], Operations: ['88+69=157'] Exploring Operation: 157-69=88, Resulting Numbers: [89, 88] Generated Node #0,0,0: 89:[89, 88] Operation: 157-69=88 Exploring Operation: 157-89=68, Resulting Numbers: [69, 68] Generated Node #0,0,1: 89:[69, 68] Operation: 157-89=68 Exploring Operation: 89-69=20, Resulting Numbers: [157, 20] Generated Node #0,0,2: 89:[157, 20] Operation: 89-69=20 Exploring Operation: 69+89=158, Resulting Numbers: [157, 158] Generated Node #0,0,3: 89:[157, 158] Operation: 69+89=158 Moving to Node #0,2 Current State: 89:[88, 89, 1], Operations: ['69/69=1'] Exploring Operation: 88/1=88, Resulting Numbers: [89, 88] Generated Node #0,2,0: 89:[89, 88] Operation: 88/1=88 Exploring Operation: 88*1=88, Resulting Numbers: [89, 88] Generated Node #0,2,1: 89:[89, 88] Operation: 88*1=88 Exploring Operation: 88+1=89, Resulting Numbers: [89, 89] Generated Node #0,2,2: 89:[89, 89] Operation: 88+1=89 Exploring Operation: 89*1=89, Resulting Numbers: [88, 89] Generated Node #0,2,3: 89:[88, 89] Operation: 89*1=89 Moving to Node #0,2,2 Current State: 89:[89, 89], Operations: ['69/69=1', '88+1=89'] Exploring Operation: 89-89=0, Resulting Numbers: [0] 0,89 unequal: No Solution Exploring Operation: 89/89=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 89+89=178, Resulting Numbers: [178] 178,89 unequal: No Solution Exploring Operation: 89*89=7921, Resulting Numbers: [7921] 7921,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[88, 89], Operations: ['69/69=1', '89*1=89'] Exploring Operation: 89-88=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 88+89=177, Resulting Numbers: [177] 177,89 unequal: No Solution Exploring Operation: 88*89=7832, Resulting Numbers: [7832] 7832,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[89, 88], Operations: ['88+69=157', '157-69=88'] Exploring Operation: 89*88=7832, Resulting Numbers: [7832] 7832,89 unequal: No Solution Exploring Operation: 89-88=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 89+88=177, Resulting Numbers: [177] 177,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[89, 88], Operations: ['69/69=1', '88/1=88'] Exploring Operation: 89-88=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 89*88=7832, Resulting Numbers: [7832] 7832,89 unequal: No Solution Exploring Operation: 89+88=177, Resulting Numbers: [177] 177,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[89, 88], Operations: ['69/69=1', '88*1=88'] Exploring Operation: 89-88=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 89*88=7832, Resulting Numbers: [7832] 7832,89 unequal: No Solution Exploring Operation: 89+88=177, Resulting Numbers: [177] 177,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[89, 50], Operations: ['69+69=138', '138-88=50'] Exploring Operation: 89*50=4450, Resulting Numbers: [4450] 4450,89 unequal: No Solution Exploring Operation: 89-50=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 89+50=139, Resulting Numbers: [139] 139,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[69, 68], Operations: ['88+69=157', '157-89=68'] Exploring Operation: 69+68=137, Resulting Numbers: [137] 137,89 unequal: No Solution Exploring Operation: 69*68=4692, Resulting Numbers: [4692] 4692,89 unequal: No Solution Exploring Operation: 69-68=1, Resulting Numbers: [1] 1,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[88, 49], Operations: ['69+69=138', '138-89=49'] Exploring Operation: 88-49=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 88*49=4312, Resulting Numbers: [4312] 4312,89 unequal: No Solution Exploring Operation: 88+49=137, Resulting Numbers: [137] 137,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[138, 177], Operations: ['69+69=138', '88+89=177'] Exploring Operation: 138+177=315, Resulting Numbers: [315] 315,89 unequal: No Solution Exploring Operation: 177-138=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 138*177=24426, Resulting Numbers: [24426] 24426,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[157, 20], Operations: ['88+69=157', '89-69=20'] Exploring Operation: 157*20=3140, Resulting Numbers: [3140] 3140,89 unequal: No Solution Exploring Operation: 157-20=137, Resulting Numbers: [137] 137,89 unequal: No Solution Exploring Operation: 157+20=177, Resulting Numbers: [177] 177,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[138, 1], Operations: ['69+69=138', '89-88=1'] Exploring Operation: 138/1=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 138*1=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 138+1=139, Resulting Numbers: [139] 139,89 unequal: No Solution Exploring Operation: 138-1=137, Resulting Numbers: [137] 137,89 unequal: No Solution Moving to Node #0,0,3 Current State: 89:[157, 158], Operations: ['88+69=157', '69+89=158'] Exploring Operation: 158-157=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 157*158=24806, Resulting Numbers: [24806] 24806,89 unequal: No Solution Exploring Operation: 157+158=315, Resulting Numbers: [315] 315,89 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 19, 46, 60, 46 ]
42
[ "60-19=41", "46/46=1", "41+1=42" ]
Current State: 42:[19, 46, 60, 46], Operations: [] Exploring Operation: 60-19=41, Resulting Numbers: [46, 46, 41] Generated Node #2: [46, 46, 41] from Operation: 60-19=41 Current State: 42:[46, 46, 41], Operations: ['60-19=41'] Exploring Operation: 46/46=1, Resulting Numbers: [41, 1] Generated Node #3: [41, 1] from Operation: 46/46=1 Current State: 42:[41, 1], Operations: ['60-19=41', '46/46=1'] Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[19, 46, 60, 46], Operations: [] Exploring Operation: 46/46=1, Resulting Numbers: [19, 60, 1] Generated Node #0,0: 42:[19, 60, 1] Operation: 46/46=1 Exploring Operation: 60-46=14, Resulting Numbers: [19, 46, 14] Generated Node #0,1: 42:[19, 46, 14] Operation: 60-46=14 Exploring Operation: 60-19=41, Resulting Numbers: [46, 46, 41] Generated Node #0,2: 42:[46, 46, 41] Operation: 60-19=41 Exploring Operation: 60-46=14, Resulting Numbers: [19, 46, 14] Generated Node #0,3: 42:[19, 46, 14] Operation: 60-46=14 Moving to Node #0,1 Current State: 42:[19, 46, 14], Operations: ['60-46=14'] Exploring Operation: 19-14=5, Resulting Numbers: [46, 5] Generated Node #0,1,0: 42:[46, 5] Operation: 19-14=5 Exploring Operation: 46-19=27, Resulting Numbers: [14, 27] Generated Node #0,1,1: 42:[14, 27] Operation: 46-19=27 Exploring Operation: 19+14=33, Resulting Numbers: [46, 33] Generated Node #0,1,2: 42:[46, 33] Operation: 19+14=33 Exploring Operation: 46-14=32, Resulting Numbers: [19, 32] Generated Node #0,1,3: 42:[19, 32] Operation: 46-14=32 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 42:[46, 5], Operations: ['60-46=14', '19-14=5'] Exploring Operation: 46+5=51, Resulting Numbers: [51] 51,42 unequal: No Solution Exploring Operation: 46*5=230, Resulting Numbers: [230] 230,42 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 42:[14, 27], Operations: ['60-46=14', '46-19=27'] Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 14+27=41, Resulting Numbers: [41] 41,42 unequal: No Solution Exploring Operation: 14*27=378, Resulting Numbers: [378] 378,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 42:[19, 32], Operations: ['60-46=14', '46-14=32'] Exploring Operation: 19*32=608, Resulting Numbers: [608] 608,42 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 19+32=51, Resulting Numbers: [51] 51,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 42:[46, 33], Operations: ['60-46=14', '19+14=33'] Exploring Operation: 46+33=79, Resulting Numbers: [79] 79,42 unequal: No Solution Exploring Operation: 46*33=1518, Resulting Numbers: [1518] 1518,42 unequal: No Solution Exploring Operation: 46-33=13, Resulting Numbers: [13] 13,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 42:[19, 46, 14], Operations: ['60-46=14'] Exploring Operation: 19+14=33, Resulting Numbers: [46, 33] Generated Node #0,3,0: 42:[46, 33] Operation: 19+14=33 Exploring Operation: 46-19=27, Resulting Numbers: [14, 27] Generated Node #0,3,1: 42:[14, 27] Operation: 46-19=27 Exploring Operation: 19-14=5, Resulting Numbers: [46, 5] Generated Node #0,3,2: 42:[46, 5] Operation: 19-14=5 Exploring Operation: 46-14=32, Resulting Numbers: [19, 32] Generated Node #0,3,3: 42:[19, 32] Operation: 46-14=32 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 42:[46, 5], Operations: ['60-46=14', '19-14=5'] Exploring Operation: 46*5=230, Resulting Numbers: [230] 230,42 unequal: No Solution Exploring Operation: 46+5=51, Resulting Numbers: [51] 51,42 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 42:[14, 27], Operations: ['60-46=14', '46-19=27'] Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 14*27=378, Resulting Numbers: [378] 378,42 unequal: No Solution Exploring Operation: 14+27=41, Resulting Numbers: [41] 41,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 42:[19, 32], Operations: ['60-46=14', '46-14=32'] Exploring Operation: 19+32=51, Resulting Numbers: [51] 51,42 unequal: No Solution Exploring Operation: 19*32=608, Resulting Numbers: [608] 608,42 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 42:[46, 33], Operations: ['60-46=14', '19+14=33'] Exploring Operation: 46-33=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 46+33=79, Resulting Numbers: [79] 79,42 unequal: No Solution Exploring Operation: 46*33=1518, Resulting Numbers: [1518] 1518,42 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: 42:[46, 46, 41], Operations: ['60-19=41'] Exploring Operation: 46-46=0, Resulting Numbers: [41, 0] Generated Node #0,2,0: 42:[41, 0] Operation: 46-46=0 Exploring Operation: 46/46=1, Resulting Numbers: [41, 1] Generated Node #0,2,1: 42:[41, 1] Operation: 46/46=1 Exploring Operation: 46-41=5, Resulting Numbers: [46, 5] Generated Node #0,2,2: 42:[46, 5] Operation: 46-41=5 Exploring Operation: 46-41=5, Resulting Numbers: [46, 5] Generated Node #0,2,3: 42:[46, 5] Operation: 46-41=5 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 42:[41, 1], Operations: ['60-19=41', '46/46=1'] Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,42 unequal: No Solution Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,42 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,42 unequal: No Solution Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[19, 46, 60, 46], Operations: [] Exploring Operation: 60-19=41, Resulting Numbers: [46, 46, 41] Generated Node #0,2: 42:[46, 46, 41] Operation: 60-19=41 Moving to Node #0,2 Current State: 42:[46, 46, 41], Operations: ['60-19=41'] Exploring Operation: 46/46=1, Resulting Numbers: [41, 1] Generated Node #0,2,1: 42:[41, 1] Operation: 46/46=1 Moving to Node #0,2,1 Current State: 42:[41, 1], Operations: ['60-19=41', '46/46=1'] Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.958333
hs_4
sum_heuristic
[ 46, 57, 44, 2 ]
57
[ "46+57=103", "44+2=46", "103-46=57" ]
Current State: 57:[46, 57, 44, 2], Operations: [] Exploring Operation: 46+57=103, Resulting Numbers: [44, 2, 103] Generated Node #2: [44, 2, 103] from Operation: 46+57=103 Current State: 57:[44, 2, 103], Operations: ['46+57=103'] Exploring Operation: 44+2=46, Resulting Numbers: [103, 46] Generated Node #3: [103, 46] from Operation: 44+2=46 Current State: 57:[103, 46], Operations: ['46+57=103', '44+2=46'] Exploring Operation: 103-46=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[46, 57, 44, 2], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [57, 2, 2] Generated Node #0,0: 57:[57, 2, 2] Operation: 46-44=2 Exploring Operation: 44/2=22, Resulting Numbers: [46, 57, 22] Generated Node #0,1: 57:[46, 57, 22] Operation: 44/2=22 Moving to Node #0,0 Current State: 57:[57, 2, 2], Operations: ['46-44=2'] Exploring Operation: 2*2=4, Resulting Numbers: [57, 4] Generated Node #0,0,0: 57:[57, 4] Operation: 2*2=4 Exploring Operation: 2+2=4, Resulting Numbers: [57, 4] Generated Node #0,0,1: 57:[57, 4] Operation: 2+2=4 Moving to Node #0,1 Current State: 57:[46, 57, 22], Operations: ['44/2=22'] Exploring Operation: 46-22=24, Resulting Numbers: [57, 24] Generated Node #0,1,0: 57:[57, 24] Operation: 46-22=24 Exploring Operation: 57-46=11, Resulting Numbers: [22, 11] Generated Node #0,1,1: 57:[22, 11] Operation: 57-46=11 Moving to Node #0,0,0 Current State: 57:[57, 4], Operations: ['46-44=2', '2*2=4'] Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,57 unequal: No Solution Exploring Operation: 57+4=61, Resulting Numbers: [61] 61,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[57, 4], Operations: ['46-44=2', '2+2=4'] Exploring Operation: 57+4=61, Resulting Numbers: [61] 61,57 unequal: No Solution Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[57, 24], Operations: ['44/2=22', '46-22=24'] Exploring Operation: 57+24=81, Resulting Numbers: [81] 81,57 unequal: No Solution Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[22, 11], Operations: ['44/2=22', '57-46=11'] Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,57 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,57 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 15, 37, 18, 87 ]
44
[ "18+87=105", "105/15=7", "37+7=44" ]
Current State: 44:[15, 37, 18, 87], Operations: [] Exploring Operation: 18+87=105, Resulting Numbers: [15, 37, 105] Generated Node #2: [15, 37, 105] from Operation: 18+87=105 Current State: 44:[15, 37, 105], Operations: ['18+87=105'] Exploring Operation: 105/15=7, Resulting Numbers: [37, 7] Generated Node #3: [37, 7] from Operation: 105/15=7 Current State: 44:[37, 7], Operations: ['18+87=105', '105/15=7'] Exploring Operation: 37+7=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[15, 37, 18, 87], Operations: [] Exploring Operation: 87-18=69, Resulting Numbers: [15, 37, 69] Generated Node #0,0: 44:[15, 37, 69] Operation: 87-18=69 Exploring Operation: 87-15=72, Resulting Numbers: [37, 18, 72] Generated Node #0,1: 44:[37, 18, 72] Operation: 87-15=72 Exploring Operation: 87-37=50, Resulting Numbers: [15, 18, 50] Generated Node #0,2: 44:[15, 18, 50] Operation: 87-37=50 Moving to Node #0,2 Current State: 44:[15, 18, 50], Operations: ['87-37=50'] Exploring Operation: 50-15=35, Resulting Numbers: [18, 35] Generated Node #0,2,0: 44:[18, 35] Operation: 50-15=35 Exploring Operation: 50-18=32, Resulting Numbers: [15, 32] Generated Node #0,2,1: 44:[15, 32] Operation: 50-18=32 Exploring Operation: 18-15=3, Resulting Numbers: [50, 3] Generated Node #0,2,2: 44:[50, 3] Operation: 18-15=3 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 44:[50, 3], Operations: ['87-37=50', '18-15=3'] Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,44 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,44 unequal: No Solution Exploring Operation: 50*3=150, Resulting Numbers: [150] 150,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 44:[18, 35], Operations: ['87-37=50', '50-15=35'] Exploring Operation: 18*35=630, Resulting Numbers: [630] 630,44 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,44 unequal: No Solution Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 44:[15, 32], Operations: ['87-37=50', '50-18=32'] Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,44 unequal: No Solution Exploring Operation: 15*32=480, Resulting Numbers: [480] 480,44 unequal: No Solution Exploring Operation: 15+32=47, Resulting Numbers: [47] 47,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 44:[15, 37, 69], Operations: ['87-18=69'] Exploring Operation: 69-37=32, Resulting Numbers: [15, 32] Generated Node #0,0,0: 44:[15, 32] Operation: 69-37=32 Exploring Operation: 69-15=54, Resulting Numbers: [37, 54] Generated Node #0,0,1: 44:[37, 54] Operation: 69-15=54 Exploring Operation: 37-15=22, Resulting Numbers: [69, 22] Generated Node #0,0,2: 44:[69, 22] Operation: 37-15=22 Moving to Node #0,1 Current State: 44:[37, 18, 72], Operations: ['87-15=72'] Exploring Operation: 72-37=35, Resulting Numbers: [18, 35] Generated Node #0,1,0: 44:[18, 35] Operation: 72-37=35 Exploring Operation: 72-18=54, Resulting Numbers: [37, 54] Generated Node #0,1,1: 44:[37, 54] Operation: 72-18=54 Exploring Operation: 72/18=4, Resulting Numbers: [37, 4] Generated Node #0,1,2: 44:[37, 4] Operation: 72/18=4 Moving to Node #0,1,2 Current State: 44:[37, 4], Operations: ['87-15=72', '72/18=4'] Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,44 unequal: No Solution Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,44 unequal: No Solution Exploring Operation: 37*4=148, Resulting Numbers: [148] 148,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[18, 35], Operations: ['87-15=72', '72-37=35'] Exploring Operation: 18*35=630, Resulting Numbers: [630] 630,44 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,44 unequal: No Solution Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,44 unequal: No Solution Moving to Node #0,0,0 Current State: 44:[15, 32], Operations: ['87-18=69', '69-37=32'] Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,44 unequal: No Solution Exploring Operation: 15*32=480, Resulting Numbers: [480] 480,44 unequal: No Solution Exploring Operation: 15+32=47, Resulting Numbers: [47] 47,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[37, 54], Operations: ['87-15=72', '72-18=54'] Exploring Operation: 37+54=91, Resulting Numbers: [91] 91,44 unequal: No Solution Exploring Operation: 37*54=1998, Resulting Numbers: [1998] 1998,44 unequal: No Solution Exploring Operation: 54-37=17, Resulting Numbers: [17] 17,44 unequal: No Solution Moving to Node #0,0,1 Current State: 44:[37, 54], Operations: ['87-18=69', '69-15=54'] Exploring Operation: 37+54=91, Resulting Numbers: [91] 91,44 unequal: No Solution Exploring Operation: 37*54=1998, Resulting Numbers: [1998] 1998,44 unequal: No Solution Exploring Operation: 54-37=17, Resulting Numbers: [17] 17,44 unequal: No Solution Moving to Node #0,0,2 Current State: 44:[69, 22], Operations: ['87-18=69', '37-15=22'] Exploring Operation: 69*22=1518, Resulting Numbers: [1518] 1518,44 unequal: No Solution Exploring Operation: 69-22=47, Resulting Numbers: [47] 47,44 unequal: No Solution Exploring Operation: 69+22=91, Resulting Numbers: [91] 91,44 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 1, 62, 30, 7 ]
86
[ "1+62=63", "30-7=23", "63+23=86" ]
Current State: 86:[1, 62, 30, 7], Operations: [] Exploring Operation: 1+62=63, Resulting Numbers: [30, 7, 63] Generated Node #2: [30, 7, 63] from Operation: 1+62=63 Current State: 86:[30, 7, 63], Operations: ['1+62=63'] Exploring Operation: 30-7=23, Resulting Numbers: [63, 23] Generated Node #3: [63, 23] from Operation: 30-7=23 Current State: 86:[63, 23], Operations: ['1+62=63', '30-7=23'] Exploring Operation: 63+23=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[1, 62, 30, 7], Operations: [] Exploring Operation: 62+30=92, Resulting Numbers: [1, 7, 92] Generated Node #0,0: 86:[1, 7, 92] Operation: 62+30=92 Exploring Operation: 62-7=55, Resulting Numbers: [1, 30, 55] Generated Node #0,1: 86:[1, 30, 55] Operation: 62-7=55 Exploring Operation: 62-30=32, Resulting Numbers: [1, 7, 32] Generated Node #0,2: 86:[1, 7, 32] Operation: 62-30=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[1, 7, 92], Operations: ['62+30=92'] Exploring Operation: 92-1=91, Resulting Numbers: [7, 91] Generated Node #0,0,0: 86:[7, 91] Operation: 92-1=91 Exploring Operation: 92-7=85, Resulting Numbers: [1, 85] Generated Node #0,0,1: 86:[1, 85] Operation: 92-7=85 Exploring Operation: 7-1=6, Resulting Numbers: [92, 6] Generated Node #0,0,2: 86:[92, 6] Operation: 7-1=6 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[1, 85], Operations: ['62+30=92', '92-7=85'] Exploring Operation: 1*85=85, Resulting Numbers: [85] 85,86 unequal: No Solution Exploring Operation: 1+85=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[1, 62, 30, 7], Operations: [] Exploring Operation: 62+30=92, Resulting Numbers: [1, 7, 92] Generated Node #0,0: 86:[1, 7, 92] Operation: 62+30=92 Moving to Node #0,0 Current State: 86:[1, 7, 92], Operations: ['62+30=92'] Exploring Operation: 92-7=85, Resulting Numbers: [1, 85] Generated Node #0,0,1: 86:[1, 85] Operation: 92-7=85 Moving to Node #0,0,1 Current State: 86:[1, 85], Operations: ['62+30=92', '92-7=85'] Exploring Operation: 1+85=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 6, 55, 69, 34 ]
50
[ "69-55=14", "6*14=84", "84-34=50" ]
Current State: 50:[6, 55, 69, 34], Operations: [] Exploring Operation: 69-55=14, Resulting Numbers: [6, 34, 14] Generated Node #2: [6, 34, 14] from Operation: 69-55=14 Current State: 50:[6, 34, 14], Operations: ['69-55=14'] Exploring Operation: 6*14=84, Resulting Numbers: [34, 84] Generated Node #3: [34, 84] from Operation: 6*14=84 Current State: 50:[34, 84], Operations: ['69-55=14', '6*14=84'] Exploring Operation: 84-34=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[6, 55, 69, 34], Operations: [] Exploring Operation: 55-34=21, Resulting Numbers: [6, 69, 21] Generated Node #0,0: 50:[6, 69, 21] Operation: 55-34=21 Exploring Operation: 69-34=35, Resulting Numbers: [6, 55, 35] Generated Node #0,1: 50:[6, 55, 35] Operation: 69-34=35 Exploring Operation: 69-55=14, Resulting Numbers: [6, 34, 14] Generated Node #0,2: 50:[6, 34, 14] Operation: 69-55=14 Moving to Node #0,2 Current State: 50:[6, 34, 14], Operations: ['69-55=14'] Exploring Operation: 34-6=28, Resulting Numbers: [14, 28] Generated Node #0,2,0: 50:[14, 28] Operation: 34-6=28 Exploring Operation: 34-14=20, Resulting Numbers: [6, 20] Generated Node #0,2,1: 50:[6, 20] Operation: 34-14=20 Exploring Operation: 34+14=48, Resulting Numbers: [6, 48] Generated Node #0,2,2: 50:[6, 48] Operation: 34+14=48 Moving to Node #0,1 Current State: 50:[6, 55, 35], Operations: ['69-34=35'] Exploring Operation: 55-35=20, Resulting Numbers: [6, 20] Generated Node #0,1,0: 50:[6, 20] Operation: 55-35=20 Exploring Operation: 55-6=49, Resulting Numbers: [35, 49] Generated Node #0,1,1: 50:[35, 49] Operation: 55-6=49 Exploring Operation: 35-6=29, Resulting Numbers: [55, 29] Generated Node #0,1,2: 50:[55, 29] Operation: 35-6=29 Moving to Node #0,0 Current State: 50:[6, 69, 21], Operations: ['55-34=21'] Exploring Operation: 69-6=63, Resulting Numbers: [21, 63] Generated Node #0,0,0: 50:[21, 63] Operation: 69-6=63 Exploring Operation: 6+21=27, Resulting Numbers: [69, 27] Generated Node #0,0,1: 50:[69, 27] Operation: 6+21=27 Exploring Operation: 69-21=48, Resulting Numbers: [6, 48] Generated Node #0,0,2: 50:[6, 48] Operation: 69-21=48 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 50:[6, 48], Operations: ['55-34=21', '69-21=48'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,50 unequal: No Solution Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,50 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[21, 63], Operations: ['55-34=21', '69-6=63'] Exploring Operation: 21+63=84, Resulting Numbers: [84] 84,50 unequal: No Solution Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,50 unequal: No Solution Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 50:[69, 27], Operations: ['55-34=21', '6+21=27'] Exploring Operation: 69+27=96, Resulting Numbers: [96] 96,50 unequal: No Solution Exploring Operation: 69*27=1863, Resulting Numbers: [1863] 1863,50 unequal: No Solution Exploring Operation: 69-27=42, Resulting Numbers: [42] 42,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 50:[6, 48], Operations: ['69-55=14', '34+14=48'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,50 unequal: No Solution Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,50 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,50 unequal: No Solution Moving to Node #0,2,1 Current State: 50:[6, 20], Operations: ['69-55=14', '34-14=20'] Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,50 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,50 unequal: No Solution Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,50 unequal: No Solution Moving to Node #0,1,0 Current State: 50:[6, 20], Operations: ['69-34=35', '55-35=20'] Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,50 unequal: No Solution Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,50 unequal: No Solution Moving to Node #0,2,0 Current State: 50:[14, 28], Operations: ['69-55=14', '34-6=28'] Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,50 unequal: No Solution Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,50 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,50 unequal: No Solution Moving to Node #0,1,2 Current State: 50:[55, 29], Operations: ['69-34=35', '35-6=29'] Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 55+29=84, Resulting Numbers: [84] 84,50 unequal: No Solution Exploring Operation: 55*29=1595, Resulting Numbers: [1595] 1595,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[35, 49], Operations: ['69-34=35', '55-6=49'] Exploring Operation: 35+49=84, Resulting Numbers: [84] 84,50 unequal: No Solution Exploring Operation: 35*49=1715, Resulting Numbers: [1715] 1715,50 unequal: No Solution Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,50 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 30, 31, 61, 27 ]
88
[ "31-30=1", "61+27=88", "1*88=88" ]
Current State: 88:[30, 31, 61, 27], Operations: [] Exploring Operation: 31-30=1, Resulting Numbers: [61, 27, 1] Generated Node #2: [61, 27, 1] from Operation: 31-30=1 Current State: 88:[61, 27, 1], Operations: ['31-30=1'] Exploring Operation: 61+27=88, Resulting Numbers: [1, 88] Generated Node #3: [1, 88] from Operation: 61+27=88 Current State: 88:[1, 88], Operations: ['31-30=1', '61+27=88'] Exploring Operation: 1*88=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[30, 31, 61, 27], Operations: [] Exploring Operation: 61+27=88, Resulting Numbers: [30, 31, 88] Generated Node #0,0: 88:[30, 31, 88] Operation: 61+27=88 Exploring Operation: 30+61=91, Resulting Numbers: [31, 27, 91] Generated Node #0,1: 88:[31, 27, 91] Operation: 30+61=91 Exploring Operation: 31+61=92, Resulting Numbers: [30, 27, 92] Generated Node #0,2: 88:[30, 27, 92] Operation: 31+61=92 Moving to Node #0,0 Current State: 88:[30, 31, 88], Operations: ['61+27=88'] Exploring Operation: 88-31=57, Resulting Numbers: [30, 57] Generated Node #0,0,0: 88:[30, 57] Operation: 88-31=57 Exploring Operation: 31-30=1, Resulting Numbers: [88, 1] Generated Node #0,0,1: 88:[88, 1] Operation: 31-30=1 Exploring Operation: 30+31=61, Resulting Numbers: [88, 61] Generated Node #0,0,2: 88:[88, 61] Operation: 30+31=61 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 88:[88, 1], Operations: ['61+27=88', '31-30=1'] Exploring Operation: 88+1=89, Resulting Numbers: [89] 89,88 unequal: No Solution Exploring Operation: 88*1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[30, 31, 61, 27], Operations: [] Exploring Operation: 61+27=88, Resulting Numbers: [30, 31, 88] Generated Node #0,0: 88:[30, 31, 88] Operation: 61+27=88 Moving to Node #0,0 Current State: 88:[30, 31, 88], Operations: ['61+27=88'] Exploring Operation: 31-30=1, Resulting Numbers: [88, 1] Generated Node #0,0,1: 88:[88, 1] Operation: 31-30=1 Moving to Node #0,0,1 Current State: 88:[88, 1], Operations: ['61+27=88', '31-30=1'] Exploring Operation: 88*1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic